Subgroups — C₃×C₅×#3534 #14276568

Order 1920.

2332 conjugacy classes of subgroups.

The subgroup lattice has 1280 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#562	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#560	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×D₄²	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#540	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#539	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#538	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#538	C₂	1	2	yes	maximal, complemented
14	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#534	C₂	1	2	yes	maximal, complemented
16	C₃×C₅×#534	C₂	1	1	yes	maximal, characteristic, complemented
17	C₃×C₅×#525	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₃×C₅×#123	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#3534	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
23	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
26	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
27	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
28	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₅×#127	C₂²	1	2	yes	complemented
30	C₃×C₅×#126	C₂²	1	2	yes	complemented
31	C₃×C₅×#126	C₂²	1	2	yes	complemented
32	C₃×C₅×#126	C₂²	1	2	yes	complemented
33	C₃×C₅×#126	C₂²	1	2	yes	complemented
34	C₃×C₅×#125	C₂²	1	2	yes	complemented
35	C₃×C₅×#125	C₂²	1	2	yes	complemented
36	C₃×C₅×#124	C₂²	1	2	yes	complemented
37	C₃×C₅×#124	C₂²	1	2	yes	complemented
38	C₃×C₅×#124	C₂²	1	2	yes	complemented
39	C₃×C₅×#123	C₂²	1	2	yes	complemented
40	C₃×C₅×#123	C₂²	1	2	yes	complemented
41	C₃×C₅×#123	C₂²	1	2	yes	complemented
42	C₃×C₅×#123	C₂²	1	2	yes	complemented
43	C₃×C₅×#123	C₂²	1	2	yes	complemented
44	C₃×C₅×#123	C₂²	1	2	yes	complemented
45	C₃×C₅×#123	C₂²	1	2	yes	complemented
46	C₃×C₅×#123	C₂²	1	2	yes	complemented
47	C₃×C₅×#123	C₂²	1	2	yes	complemented
48	C₃×C₅×#123	C₂²	1	2	yes	complemented
49	C₃×C₅×#123	C₂²	1	2	yes	complemented
50	C₃×C₅×#123	C₂²	1	2	yes	complemented
51	C₃×C₅×#123	C₂²	1	2	yes	complemented
52	C₃×C₅×#123	C₂²	1	2	yes	complemented
53	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
54	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
57	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
58	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
59	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
60	C₃×C₅×#121	C₂²	1	1	yes	characteristic
61	C₃×C₅×#121	C₂²	1	2	yes	—
62	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
63	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
64	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
65	C₃×C₅×#121	C₂²	1	2	yes	complemented
66	C₃×C₅×#121	C₂²	1	2	yes	complemented
67	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
68	C₃×C₅×#121	C₂²	1	1	yes	characteristic, complemented
69	C₃×C₅×#121	C₂²	1	2	yes	complemented
70	C₃×C₅×#121	C₂²	1	2	yes	complemented
71	C₃×C₅×#121	C₂²	1	2	yes	complemented
72	C₃×C₅×#121	C₂²	1	2	yes	complemented
73	C₃×C₅×#121	C₂²	1	2	yes	complemented
74	C₃×C₅×#121	C₂²	1	2	yes	complemented
75	C₃×C₅×#121	C₂²	1	2	yes	complemented
76	C₃×C₅×#121	C₂²	1	2	yes	complemented
77	C₃×C₅×#121	C₂²	1	2	yes	complemented
78	C₃×C₅×#121	C₂²	1	2	yes	complemented
79	C₃×C₅×#121	C₂²	1	2	yes	complemented
80	C₃×C₅×#121	C₂²	1	2	yes	complemented
81	C₃×C₅×#120	C₂²	1	2	yes	—
82	C₃×C₅×#120	C₂²	1	2	yes	complemented
83	C₃×C₅×#120	C₂²	1	2	yes	complemented
84	C₃×C₅×#120	C₂²	1	2	yes	complemented
85	C₃×C₅×#120	C₂²	1	2	yes	complemented
86	C₃×C₅×#120	C₂²	1	2	yes	complemented
87	C₃×C₅×#120	C₂²	1	2	yes	complemented
88	C₃×C₅×#120	C₂²	1	2	yes	complemented
89	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
90	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
91	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
92	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
93	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
94	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
95	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
96	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
97	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
98	C₃×C₅×#117	C₂²	1	2	yes	complemented
99	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
100	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
101	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
103	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
104	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
106	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
107	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	complemented
108	C₃×#3534	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
109	C₅×#562	C₂×C₃	1	2	yes	complemented
110	C₅×#560	C₂×C₃	1	2	yes	complemented
111	C₅×#553	C₂×C₃	1	2	yes	complemented
112	C₅×#551	C₂×C₃	1	2	yes	complemented
113	C₅×#546	C₂×C₃	1	2	yes	complemented
114	C₅×#546	C₂×C₃	1	2	yes	complemented
115	C₅×#546	C₂×C₃	1	2	yes	complemented
116	C₅×D₄²	C₂×C₃	1	2	yes	complemented
117	C₅×#540	C₂×C₃	1	2	yes	complemented
118	C₅×#539	C₂×C₃	1	2	yes	complemented
119	C₅×#539	C₂×C₃	1	1	yes	characteristic, complemented
120	C₅×#538	C₂×C₃	1	1	yes	characteristic, complemented
121	C₅×#538	C₂×C₃	1	2	yes	complemented
122	C₅×#537	C₂×C₃	1	1	yes	characteristic, complemented
123	C₅×#534	C₂×C₃	1	2	yes	complemented
124	C₅×#534	C₂×C₃	1	1	yes	characteristic, complemented
125	C₅×#525	C₂×C₃	1	1	yes	characteristic, complemented
126	C₂×C₅×#123	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×C₅×#121	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
129	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
130	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
131	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
132	C₃×C₅×#41	—	4	2	no	—
133	C₃×C₅×#41	—	4	4	no	—
134	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
136	C₂×C₃×C₅×D₄	—	4	2	no	—
137	C₂×C₃×C₅×D₄	—	4	2	no	—
138	C₂×C₃×C₅×D₄	—	4	4	no	—
139	C₂×C₃×C₅×D₄	—	4	4	no	—
140	C₂×C₃×C₅×D₄	—	4	4	no	—
141	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
142	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
143	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
144	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
145	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
146	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
147	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
148	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
149	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
150	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
151	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
152	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
153	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
154	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
155	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
156	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
157	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
158	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
159	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
160	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
161	C₂²×C₃×C₄×C₅	—	4	2	no	—
162	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
163	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
164	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
165	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
166	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
167	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
168	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
169	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
170	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
171	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
172	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
173	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
174	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
175	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
176	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
177	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
178	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
179	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
182	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
183	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
184	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
185	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
187	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
189	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
190	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
191	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
195	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
196	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
197	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
198	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
200	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
201	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
202	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
203	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
204	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
205	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
206	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
216	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
217	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₃×C₄²×C₅	C₂³	1	2	yes	—
221	C₃×C₄²×C₅	C₂³	1	2	yes	—
222	C₃×C₄²×C₅	C₂³	1	2	yes	—
223	C₃×#562	C₂×C₅	1	2	yes	complemented
224	C₃×#560	C₂×C₅	1	2	yes	complemented
225	C₃×#553	C₂×C₅	1	2	yes	complemented
226	C₃×#551	C₂×C₅	1	2	yes	complemented
227	C₃×#546	C₂×C₅	1	2	yes	complemented
228	C₃×#546	C₂×C₅	1	2	yes	complemented
229	C₃×#546	C₂×C₅	1	2	yes	complemented
230	C₃×D₄²	C₂×C₅	1	2	yes	complemented
231	C₃×#540	C₂×C₅	1	2	yes	complemented
232	C₃×#539	C₂×C₅	1	2	yes	complemented
233	C₃×#539	C₂×C₅	1	1	yes	characteristic, complemented
234	C₃×#538	C₂×C₅	1	1	yes	characteristic, complemented
235	C₃×#538	C₂×C₅	1	2	yes	complemented
236	C₃×#537	C₂×C₅	1	1	yes	characteristic, complemented
237	C₃×#534	C₂×C₅	1	2	yes	complemented
238	C₃×#534	C₂×C₅	1	1	yes	characteristic, complemented
239	C₃×#525	C₂×C₅	1	1	yes	characteristic, complemented
240	C₂×C₃×#123	C₂×C₅	1	1	yes	characteristic, complemented
241	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic, complemented
242	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
243	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
244	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
245	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
246	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
247	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
248	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
249	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
250	C₅×#127	C₂²×C₃	1	2	yes	complemented
251	C₅×#126	C₂²×C₃	1	2	yes	complemented
252	C₅×#126	C₂²×C₃	1	2	yes	complemented
253	C₅×#126	C₂²×C₃	1	2	yes	complemented
254	C₅×#126	C₂²×C₃	1	2	yes	complemented
255	C₅×#125	C₂²×C₃	1	2	yes	complemented
256	C₅×#125	C₂²×C₃	1	2	yes	complemented
257	C₅×#124	C₂²×C₃	1	2	yes	complemented
258	C₅×#124	C₂²×C₃	1	2	yes	complemented
259	C₅×#124	C₂²×C₃	1	2	yes	complemented
260	C₅×#123	C₂²×C₃	1	2	yes	complemented
261	C₅×#123	C₂²×C₃	1	2	yes	complemented
262	C₅×#123	C₂²×C₃	1	2	yes	complemented
263	C₅×#123	C₂²×C₃	1	2	yes	complemented
264	C₅×#123	C₂²×C₃	1	2	yes	complemented
265	C₅×#123	C₂²×C₃	1	2	yes	complemented
266	C₅×#123	C₂²×C₃	1	2	yes	complemented
267	C₅×#123	C₂²×C₃	1	2	yes	complemented
268	C₅×#123	C₂²×C₃	1	2	yes	complemented
269	C₅×#123	C₂²×C₃	1	2	yes	complemented
270	C₅×#123	C₂²×C₃	1	2	yes	complemented
271	C₅×#123	C₂²×C₃	1	2	yes	complemented
272	C₅×#123	C₂²×C₃	1	2	yes	complemented
273	C₅×#123	C₂²×C₃	1	2	yes	complemented
274	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
275	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
276	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
277	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
278	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
279	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
280	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
281	C₅×#121	C₂²×C₃	1	1	yes	characteristic
282	C₅×#121	C₂²×C₃	1	2	yes	—
283	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
284	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
285	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
286	C₅×#121	C₂²×C₃	1	2	yes	complemented
287	C₅×#121	C₂²×C₃	1	2	yes	complemented
288	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
289	C₅×#121	C₂²×C₃	1	1	yes	characteristic, complemented
290	C₅×#121	C₂²×C₃	1	2	yes	complemented
291	C₅×#121	C₂²×C₃	1	2	yes	complemented
292	C₅×#121	C₂²×C₃	1	2	yes	complemented
293	C₅×#121	C₂²×C₃	1	2	yes	complemented
294	C₅×#121	C₂²×C₃	1	2	yes	complemented
295	C₅×#121	C₂²×C₃	1	2	yes	complemented
296	C₅×#121	C₂²×C₃	1	2	yes	complemented
297	C₅×#121	C₂²×C₃	1	2	yes	complemented
298	C₅×#121	C₂²×C₃	1	2	yes	complemented
299	C₅×#121	C₂²×C₃	1	2	yes	complemented
300	C₅×#121	C₂²×C₃	1	2	yes	complemented
301	C₅×#121	C₂²×C₃	1	2	yes	complemented
302	C₅×#120	C₂²×C₃	1	2	yes	—
303	C₅×#120	C₂²×C₃	1	2	yes	complemented
304	C₅×#120	C₂²×C₃	1	2	yes	complemented
305	C₅×#120	C₂²×C₃	1	2	yes	complemented
306	C₅×#120	C₂²×C₃	1	2	yes	complemented
307	C₅×#120	C₂²×C₃	1	2	yes	complemented
308	C₅×#120	C₂²×C₃	1	2	yes	complemented
309	C₅×#120	C₂²×C₃	1	2	yes	complemented
310	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
311	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
312	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
313	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
314	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
315	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
316	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
317	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
318	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
319	C₅×#117	C₂²×C₃	1	2	yes	complemented
320	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
321	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
322	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
323	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
324	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
325	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
326	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
327	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
328	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	complemented
329	#3534	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
330	C₂³×C₃×C₅	—	2	2	no	—
331	C₂³×C₃×C₅	—	2	2	no	—
332	C₂³×C₃×C₅	—	2	2	no	—
333	C₂³×C₃×C₅	—	2	4	no	—
334	C₂³×C₃×C₅	—	4	1	no	—
335	C₂³×C₃×C₅	—	4	1	no	—
336	C₂³×C₃×C₅	—	4	2	no	—
337	C₂³×C₃×C₅	—	4	2	no	—
338	C₂³×C₃×C₅	—	4	2	no	—
339	C₂³×C₃×C₅	—	4	1	no	—
340	C₂³×C₃×C₅	—	4	2	no	—
341	C₂³×C₃×C₅	—	4	2	no	—
342	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
343	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
344	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
345	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
346	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
347	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
348	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
349	C₃×C₅×Q₈	—	4	1	no	—
350	C₃×C₅×Q₈	—	4	2	no	—
351	C₃×C₅×D₄	—	2	4	no	—
352	C₃×C₅×D₄	—	2	4	no	—
353	C₃×C₅×D₄	—	2	4	no	—
354	C₃×C₅×D₄	—	2	4	no	—
355	C₃×C₅×D₄	—	2	4	no	—
356	C₃×C₅×D₄	—	4	1	no	—
357	C₃×C₅×D₄	—	4	2	no	—
358	C₃×C₅×D₄	—	4	1	no	—
359	C₃×C₅×D₄	—	4	2	no	—
360	C₃×C₅×D₄	—	4	2	no	—
361	C₃×C₅×D₄	—	4	2	no	—
362	C₃×C₅×D₄	—	4	2	no	—
363	C₃×C₅×D₄	—	4	2	no	—
364	C₃×C₅×D₄	—	4	2	no	—
365	C₃×C₅×D₄	—	4	2	no	—
366	C₃×C₅×D₄	—	4	2	no	—
367	C₃×C₅×D₄	—	4	2	no	—
368	C₃×C₅×D₄	—	4	2	no	—
369	C₃×C₅×D₄	—	4	1	no	—
370	C₃×C₅×D₄	—	4	2	no	—
371	C₂×C₃×C₄×C₅	—	2	2	no	—
372	C₂×C₃×C₄×C₅	—	2	2	no	—
373	C₂×C₃×C₄×C₅	—	2	2	no	—
374	C₂×C₃×C₄×C₅	—	4	1	no	—
375	C₂×C₃×C₄×C₅	—	4	1	no	—
376	C₂×C₃×C₄×C₅	—	4	1	no	—
377	C₂×C₃×C₄×C₅	—	4	1	no	—
378	C₂×C₃×C₄×C₅	—	4	1	no	—
379	C₂×C₃×C₄×C₅	—	4	2	no	—
380	C₂×C₃×C₄×C₅	—	4	1	no	—
381	C₂×C₃×C₄×C₅	—	4	2	no	—
382	C₂×C₃×C₄×C₅	—	4	2	no	—
383	C₂×C₃×C₄×C₅	—	4	2	no	—
384	C₂×C₃×C₄×C₅	—	4	2	no	—
385	C₂×C₃×C₄×C₅	—	4	2	no	—
386	C₂×C₃×C₄×C₅	—	4	2	no	—
387	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
388	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
389	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
390	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
391	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
392	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
393	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
394	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
395	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
396	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
397	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
398	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
399	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
400	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
401	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
402	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
403	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
404	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
405	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	complemented
406	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic, complemented
407	C₃×#127	C₂²×C₅	1	2	yes	complemented
408	C₃×#126	C₂²×C₅	1	2	yes	complemented
409	C₃×#126	C₂²×C₅	1	2	yes	complemented
410	C₃×#126	C₂²×C₅	1	2	yes	complemented
411	C₃×#126	C₂²×C₅	1	2	yes	complemented
412	C₃×#125	C₂²×C₅	1	2	yes	complemented
413	C₃×#125	C₂²×C₅	1	2	yes	complemented
414	C₃×#124	C₂²×C₅	1	2	yes	complemented
415	C₃×#124	C₂²×C₅	1	2	yes	complemented
416	C₃×#124	C₂²×C₅	1	2	yes	complemented
417	C₃×#123	C₂²×C₅	1	2	yes	complemented
418	C₃×#123	C₂²×C₅	1	2	yes	complemented
419	C₃×#123	C₂²×C₅	1	2	yes	complemented
420	C₃×#123	C₂²×C₅	1	2	yes	complemented
421	C₃×#123	C₂²×C₅	1	2	yes	complemented
422	C₃×#123	C₂²×C₅	1	2	yes	complemented
423	C₃×#123	C₂²×C₅	1	2	yes	complemented
424	C₃×#123	C₂²×C₅	1	2	yes	complemented
425	C₃×#123	C₂²×C₅	1	2	yes	complemented
426	C₃×#123	C₂²×C₅	1	2	yes	complemented
427	C₃×#123	C₂²×C₅	1	2	yes	complemented
428	C₃×#123	C₂²×C₅	1	2	yes	complemented
429	C₃×#123	C₂²×C₅	1	2	yes	complemented
430	C₃×#123	C₂²×C₅	1	2	yes	complemented
431	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
432	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
433	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
434	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
435	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
436	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
437	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
438	C₃×#121	C₂²×C₅	1	1	yes	characteristic
439	C₃×#121	C₂²×C₅	1	2	yes	—
440	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
441	C₃×#121	C₂²×C₅	1	2	yes	complemented
442	C₃×#121	C₂²×C₅	1	2	yes	complemented
443	C₃×#121	C₂²×C₅	1	2	yes	complemented
444	C₃×#121	C₂²×C₅	1	2	yes	complemented
445	C₃×#121	C₂²×C₅	1	2	yes	complemented
446	C₃×#121	C₂²×C₅	1	2	yes	complemented
447	C₃×#121	C₂²×C₅	1	2	yes	complemented
448	C₃×#121	C₂²×C₅	1	2	yes	complemented
449	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
450	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
451	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
452	C₃×#121	C₂²×C₅	1	2	yes	complemented
453	C₃×#121	C₂²×C₅	1	1	yes	characteristic, complemented
454	C₃×#121	C₂²×C₅	1	2	yes	complemented
455	C₃×#121	C₂²×C₅	1	2	yes	complemented
456	C₃×#121	C₂²×C₅	1	2	yes	complemented
457	C₃×#121	C₂²×C₅	1	2	yes	complemented
458	C₃×#121	C₂²×C₅	1	2	yes	complemented
459	C₃×#120	C₂²×C₅	1	2	yes	—
460	C₃×#120	C₂²×C₅	1	2	yes	complemented
461	C₃×#120	C₂²×C₅	1	2	yes	complemented
462	C₃×#120	C₂²×C₅	1	2	yes	complemented
463	C₃×#120	C₂²×C₅	1	2	yes	complemented
464	C₃×#120	C₂²×C₅	1	2	yes	complemented
465	C₃×#120	C₂²×C₅	1	2	yes	complemented
466	C₃×#120	C₂²×C₅	1	2	yes	complemented
467	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
468	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
469	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
470	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
471	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
472	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
473	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
474	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
475	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
476	C₃×#117	C₂²×C₅	1	2	yes	complemented
477	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
478	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
479	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
480	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
481	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
482	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
483	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic, complemented
484	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
485	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	complemented
486	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
487	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
488	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
489	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
490	C₅×#41	—	4	2	no	—
491	C₅×#41	—	4	4	no	—
492	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
493	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
494	C₂×C₅×D₄	—	4	2	no	—
495	C₂×C₅×D₄	—	4	2	no	—
496	C₂×C₅×D₄	—	4	4	no	—
497	C₂×C₅×D₄	—	4	4	no	—
498	C₂×C₅×D₄	—	4	4	no	—
499	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
500	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
501	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
502	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
503	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
504	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
505	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
506	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
507	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
508	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
509	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
510	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
511	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
512	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
513	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
514	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
515	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
516	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
517	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
518	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
519	C₂²×C₄×C₅	—	4	2	no	—
520	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
521	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
522	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
523	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
524	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
525	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
526	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
527	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
528	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
529	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
530	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
531	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
532	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
533	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
534	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
535	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
536	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
537	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
538	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
539	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
540	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
541	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
542	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
543	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
544	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
545	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
546	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
547	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
548	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
549	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
550	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
551	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
552	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
553	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
554	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
555	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
556	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
557	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
558	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
559	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
560	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
561	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
562	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
563	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
564	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
565	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
566	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
567	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
568	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
569	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
570	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
571	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
572	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
573	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
574	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
575	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
576	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
577	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
578	C₄²×C₅	C₂³×C₃	1	2	yes	—
579	C₄²×C₅	C₂³×C₃	1	2	yes	—
580	C₄²×C₅	C₂³×C₃	1	2	yes	—
581	#562	C₂×C₃×C₅	1	2	yes	complemented
582	#560	C₂×C₃×C₅	1	2	yes	complemented
583	#553	C₂×C₃×C₅	1	2	yes	complemented
584	#551	C₂×C₃×C₅	1	2	yes	complemented
585	#546	C₂×C₃×C₅	1	2	yes	complemented
586	#546	C₂×C₃×C₅	1	2	yes	complemented
587	#546	C₂×C₃×C₅	1	2	yes	complemented
588	D₄²	C₂×C₃×C₅	1	2	yes	complemented
589	#540	C₂×C₃×C₅	1	2	yes	complemented
590	#539	C₂×C₃×C₅	1	2	yes	complemented
591	#539	C₂×C₃×C₅	1	1	yes	characteristic, complemented
592	#538	C₂×C₃×C₅	1	1	yes	characteristic, complemented
593	#538	C₂×C₃×C₅	1	2	yes	complemented
594	#537	C₂×C₃×C₅	1	1	yes	characteristic, complemented
595	#534	C₂×C₃×C₅	1	2	yes	complemented
596	#534	C₂×C₃×C₅	1	1	yes	characteristic, complemented
597	#525	C₂×C₃×C₅	1	1	yes	characteristic, complemented
598	C₂×#123	C₂×C₃×C₅	1	1	yes	characteristic, complemented
599	C₂×#121	C₂×C₃×C₅	1	1	yes	characteristic, complemented
600	C₂²×C₃×C₅	—	2	1	no	—
601	C₂²×C₃×C₅	—	2	1	no	—
602	C₂²×C₃×C₅	—	2	1	no	—
603	C₂²×C₃×C₅	—	2	1	no	—
604	C₂²×C₃×C₅	—	2	1	no	—
605	C₂²×C₃×C₅	—	2	2	no	—
606	C₂²×C₃×C₅	—	2	2	no	—
607	C₂²×C₃×C₅	—	2	2	no	—
608	C₂²×C₃×C₅	—	2	2	no	—
609	C₂²×C₃×C₅	—	2	2	no	—
610	C₂²×C₃×C₅	—	2	2	no	—
611	C₂²×C₃×C₅	—	2	2	no	—
612	C₂²×C₃×C₅	—	2	1	no	—
613	C₂²×C₃×C₅	—	2	2	no	—
614	C₂²×C₃×C₅	—	2	2	no	—
615	C₂²×C₃×C₅	—	2	1	no	—
616	C₂²×C₃×C₅	—	2	2	no	—
617	C₂²×C₃×C₅	—	2	2	no	—
618	C₂²×C₃×C₅	—	2	2	no	—
619	C₂²×C₃×C₅	—	4	4	no	—
620	C₂²×C₃×C₅	—	8	4	no	—
621	C₂²×C₃×C₅	—	8	2	no	—
622	C₂²×C₃×C₅	—	8	4	no	—
623	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
624	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
625	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
626	C₃×C₄×C₅	—	2	1	no	—
627	C₃×C₄×C₅	—	2	1	no	—
628	C₃×C₄×C₅	—	2	1	no	—
629	C₃×C₄×C₅	—	2	1	no	—
630	C₃×C₄×C₅	—	2	2	no	—
631	C₃×C₄×C₅	—	2	2	no	—
632	C₃×C₄×C₅	—	2	2	no	—
633	C₃×C₄×C₅	—	2	2	no	—
634	C₃×C₄×C₅	—	2	2	no	—
635	C₃×C₄×C₅	—	2	2	no	—
636	C₃×C₄×C₅	—	2	2	no	—
637	C₃×C₄×C₅	—	2	2	no	—
638	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
639	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
640	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
641	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
642	C₃×#41	—	4	2	no	—
643	C₃×#41	—	4	4	no	—
644	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
645	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
646	C₂×C₃×D₄	—	4	2	no	—
647	C₂×C₃×D₄	—	4	2	no	—
648	C₂×C₃×D₄	—	4	4	no	—
649	C₂×C₃×D₄	—	4	4	no	—
650	C₂×C₃×D₄	—	4	4	no	—
651	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
652	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
653	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
654	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
655	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
656	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
657	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
658	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
659	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
660	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
661	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
662	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
663	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
664	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
665	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
666	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
667	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
668	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
669	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
670	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
671	C₂²×C₃×C₄	—	4	2	no	—
672	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
673	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
674	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
675	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
676	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
677	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
678	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
679	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
680	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
681	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
682	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
683	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
684	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
685	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
686	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
687	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
688	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
689	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
690	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
691	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
692	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
693	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
694	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
695	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
696	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
697	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
698	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
699	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
700	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
701	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
702	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
703	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
704	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
705	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
706	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
707	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
708	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
709	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
710	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
711	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
712	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
713	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
714	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
715	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
716	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
717	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
718	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
719	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
720	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
721	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
722	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
723	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
724	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
725	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
726	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
727	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
728	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
729	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
730	C₃×C₄²	C₂³×C₅	1	2	yes	—
731	C₃×C₄²	C₂³×C₅	1	2	yes	—
732	C₃×C₄²	C₂³×C₅	1	2	yes	—
733	C₂³×C₅	—	2	2	no	—
734	C₂³×C₅	—	2	2	no	—
735	C₂³×C₅	—	2	2	no	—
736	C₂³×C₅	—	2	4	no	—
737	C₂³×C₅	—	4	1	no	—
738	C₂³×C₅	—	4	1	no	—
739	C₂³×C₅	—	4	2	no	—
740	C₂³×C₅	—	4	2	no	—
741	C₂³×C₅	—	4	2	no	—
742	C₂³×C₅	—	4	1	no	—
743	C₂³×C₅	—	4	2	no	—
744	C₂³×C₅	—	4	2	no	—
745	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
746	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
747	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
748	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
749	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
750	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
751	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
752	C₅×Q₈	—	4	1	no	—
753	C₅×Q₈	—	4	2	no	—
754	C₅×D₄	—	2	4	no	—
755	C₅×D₄	—	2	4	no	—
756	C₅×D₄	—	2	4	no	—
757	C₅×D₄	—	2	4	no	—
758	C₅×D₄	—	2	4	no	—
759	C₅×D₄	—	4	1	no	—
760	C₅×D₄	—	4	2	no	—
761	C₅×D₄	—	4	1	no	—
762	C₅×D₄	—	4	2	no	—
763	C₅×D₄	—	4	2	no	—
764	C₅×D₄	—	4	2	no	—
765	C₅×D₄	—	4	2	no	—
766	C₅×D₄	—	4	2	no	—
767	C₅×D₄	—	4	2	no	—
768	C₅×D₄	—	4	2	no	—
769	C₅×D₄	—	4	2	no	—
770	C₅×D₄	—	4	2	no	—
771	C₅×D₄	—	4	2	no	—
772	C₅×D₄	—	4	1	no	—
773	C₅×D₄	—	4	2	no	—
774	C₂×C₄×C₅	—	2	2	no	—
775	C₂×C₄×C₅	—	2	2	no	—
776	C₂×C₄×C₅	—	2	2	no	—
777	C₂×C₄×C₅	—	4	1	no	—
778	C₂×C₄×C₅	—	4	1	no	—
779	C₂×C₄×C₅	—	4	1	no	—
780	C₂×C₄×C₅	—	4	1	no	—
781	C₂×C₄×C₅	—	4	1	no	—
782	C₂×C₄×C₅	—	4	2	no	—
783	C₂×C₄×C₅	—	4	1	no	—
784	C₂×C₄×C₅	—	4	2	no	—
785	C₂×C₄×C₅	—	4	2	no	—
786	C₂×C₄×C₅	—	4	2	no	—
787	C₂×C₄×C₅	—	4	2	no	—
788	C₂×C₄×C₅	—	4	2	no	—
789	C₂×C₄×C₅	—	4	2	no	—
790	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
791	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
792	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
793	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
794	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
795	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
796	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
797	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
798	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
799	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
800	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
801	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
802	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
803	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
804	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
805	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
806	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
807	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
808	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	complemented
809	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
810	#127	C₂²×C₃×C₅	1	2	yes	complemented
811	#126	C₂²×C₃×C₅	1	2	yes	complemented
812	#126	C₂²×C₃×C₅	1	2	yes	complemented
813	#126	C₂²×C₃×C₅	1	2	yes	complemented
814	#126	C₂²×C₃×C₅	1	2	yes	complemented
815	#125	C₂²×C₃×C₅	1	2	yes	complemented
816	#125	C₂²×C₃×C₅	1	2	yes	complemented
817	#124	C₂²×C₃×C₅	1	2	yes	complemented
818	#124	C₂²×C₃×C₅	1	2	yes	complemented
819	#124	C₂²×C₃×C₅	1	2	yes	complemented
820	#123	C₂²×C₃×C₅	1	2	yes	complemented
821	#123	C₂²×C₃×C₅	1	2	yes	complemented
822	#123	C₂²×C₃×C₅	1	2	yes	complemented
823	#123	C₂²×C₃×C₅	1	2	yes	complemented
824	#123	C₂²×C₃×C₅	1	2	yes	complemented
825	#123	C₂²×C₃×C₅	1	2	yes	complemented
826	#123	C₂²×C₃×C₅	1	2	yes	complemented
827	#123	C₂²×C₃×C₅	1	2	yes	complemented
828	#123	C₂²×C₃×C₅	1	2	yes	complemented
829	#123	C₂²×C₃×C₅	1	2	yes	complemented
830	#123	C₂²×C₃×C₅	1	2	yes	complemented
831	#123	C₂²×C₃×C₅	1	2	yes	complemented
832	#123	C₂²×C₃×C₅	1	2	yes	complemented
833	#123	C₂²×C₃×C₅	1	2	yes	complemented
834	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
835	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
836	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
837	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
838	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
839	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
840	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
841	#121	C₂²×C₃×C₅	1	1	yes	characteristic
842	#121	C₂²×C₃×C₅	1	2	yes	—
843	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
844	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
845	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
846	#121	C₂²×C₃×C₅	1	2	yes	complemented
847	#121	C₂²×C₃×C₅	1	2	yes	complemented
848	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
849	#121	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
850	#121	C₂²×C₃×C₅	1	2	yes	complemented
851	#121	C₂²×C₃×C₅	1	2	yes	complemented
852	#121	C₂²×C₃×C₅	1	2	yes	complemented
853	#121	C₂²×C₃×C₅	1	2	yes	complemented
854	#121	C₂²×C₃×C₅	1	2	yes	complemented
855	#121	C₂²×C₃×C₅	1	2	yes	complemented
856	#121	C₂²×C₃×C₅	1	2	yes	complemented
857	#121	C₂²×C₃×C₅	1	2	yes	complemented
858	#121	C₂²×C₃×C₅	1	2	yes	complemented
859	#121	C₂²×C₃×C₅	1	2	yes	complemented
860	#121	C₂²×C₃×C₅	1	2	yes	complemented
861	#121	C₂²×C₃×C₅	1	2	yes	complemented
862	#120	C₂²×C₃×C₅	1	2	yes	—
863	#120	C₂²×C₃×C₅	1	2	yes	complemented
864	#120	C₂²×C₃×C₅	1	2	yes	complemented
865	#120	C₂²×C₃×C₅	1	2	yes	complemented
866	#120	C₂²×C₃×C₅	1	2	yes	complemented
867	#120	C₂²×C₃×C₅	1	2	yes	complemented
868	#120	C₂²×C₃×C₅	1	2	yes	complemented
869	#120	C₂²×C₃×C₅	1	2	yes	complemented
870	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
871	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
872	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
873	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
874	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
875	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
876	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
877	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
878	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
879	#117	C₂²×C₃×C₅	1	2	yes	complemented
880	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
881	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
882	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
883	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
884	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
885	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
886	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
887	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
888	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
889	C₂×C₃×C₅	—	2	2	no	—
890	C₂×C₃×C₅	—	2	2	no	—
891	C₂×C₃×C₅	—	4	1	no	—
892	C₂×C₃×C₅	—	4	2	no	—
893	C₂×C₃×C₅	—	4	2	no	—
894	C₂×C₃×C₅	—	4	2	no	—
895	C₂×C₃×C₅	—	4	2	no	—
896	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
897	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
898	C₂×C₃×C₅	#585	1	1	yes	characteristic
899	C₂³×C₃	—	2	2	no	—
900	C₂³×C₃	—	2	2	no	—
901	C₂³×C₃	—	2	2	no	—
902	C₂³×C₃	—	2	4	no	—
903	C₂³×C₃	—	4	1	no	—
904	C₂³×C₃	—	4	1	no	—
905	C₂³×C₃	—	4	2	no	—
906	C₂³×C₃	—	4	2	no	—
907	C₂³×C₃	—	4	2	no	—
908	C₂³×C₃	—	4	1	no	—
909	C₂³×C₃	—	4	2	no	—
910	C₂³×C₃	—	4	2	no	—
911	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
912	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
913	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
914	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
915	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
916	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
917	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
918	C₃×Q₈	—	4	1	no	—
919	C₃×Q₈	—	4	2	no	—
920	C₃×D₄	—	2	4	no	—
921	C₃×D₄	—	2	4	no	—
922	C₃×D₄	—	2	4	no	—
923	C₃×D₄	—	2	4	no	—
924	C₃×D₄	—	2	4	no	—
925	C₃×D₄	—	4	1	no	—
926	C₃×D₄	—	4	2	no	—
927	C₃×D₄	—	4	1	no	—
928	C₃×D₄	—	4	2	no	—
929	C₃×D₄	—	4	2	no	—
930	C₃×D₄	—	4	2	no	—
931	C₃×D₄	—	4	2	no	—
932	C₃×D₄	—	4	2	no	—
933	C₃×D₄	—	4	2	no	—
934	C₃×D₄	—	4	2	no	—
935	C₃×D₄	—	4	2	no	—
936	C₃×D₄	—	4	2	no	—
937	C₃×D₄	—	4	2	no	—
938	C₃×D₄	—	4	1	no	—
939	C₃×D₄	—	4	2	no	—
940	C₂×C₃×C₄	—	2	2	no	—
941	C₂×C₃×C₄	—	2	2	no	—
942	C₂×C₃×C₄	—	2	2	no	—
943	C₂×C₃×C₄	—	4	1	no	—
944	C₂×C₃×C₄	—	4	1	no	—
945	C₂×C₃×C₄	—	4	1	no	—
946	C₂×C₃×C₄	—	4	1	no	—
947	C₂×C₃×C₄	—	4	1	no	—
948	C₂×C₃×C₄	—	4	2	no	—
949	C₂×C₃×C₄	—	4	1	no	—
950	C₂×C₃×C₄	—	4	2	no	—
951	C₂×C₃×C₄	—	4	2	no	—
952	C₂×C₃×C₄	—	4	2	no	—
953	C₂×C₃×C₄	—	4	2	no	—
954	C₂×C₃×C₄	—	4	2	no	—
955	C₂×C₃×C₄	—	4	2	no	—
956	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
957	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
958	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
959	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
960	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
961	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
962	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
963	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
964	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
965	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
966	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
967	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
968	C₂²×C₅	—	2	1	no	—
969	C₂²×C₅	—	2	1	no	—
970	C₂²×C₅	—	2	1	no	—
971	C₂²×C₅	—	2	1	no	—
972	C₂²×C₅	—	2	1	no	—
973	C₂²×C₅	—	2	2	no	—
974	C₂²×C₅	—	2	2	no	—
975	C₂²×C₅	—	2	2	no	—
976	C₂²×C₅	—	2	2	no	—
977	C₂²×C₅	—	2	2	no	—
978	C₂²×C₅	—	2	2	no	—
979	C₂²×C₅	—	2	2	no	—
980	C₂²×C₅	—	2	1	no	—
981	C₂²×C₅	—	2	2	no	—
982	C₂²×C₅	—	2	2	no	—
983	C₂²×C₅	—	2	1	no	—
984	C₂²×C₅	—	2	2	no	—
985	C₂²×C₅	—	2	2	no	—
986	C₂²×C₅	—	2	2	no	—
987	C₂²×C₅	—	4	4	no	—
988	C₂²×C₅	—	8	4	no	—
989	C₂²×C₅	—	8	2	no	—
990	C₂²×C₅	—	8	4	no	—
991	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
992	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
993	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
994	C₄×C₅	—	2	1	no	—
995	C₄×C₅	—	2	1	no	—
996	C₄×C₅	—	2	1	no	—
997	C₄×C₅	—	2	1	no	—
998	C₄×C₅	—	2	2	no	—
999	C₄×C₅	—	2	2	no	—
1000	C₄×C₅	—	2	2	no	—
1001	C₄×C₅	—	2	2	no	—
1002	C₄×C₅	—	2	2	no	—
1003	C₄×C₅	—	2	2	no	—
1004	C₄×C₅	—	2	2	no	—
1005	C₄×C₅	—	2	2	no	—
1006	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
1007	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
1008	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
1009	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
1010	#41	—	4	2	no	—
1011	#41	—	4	4	no	—
1012	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
1013	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
1014	C₂×D₄	—	4	2	no	—
1015	C₂×D₄	—	4	2	no	—
1016	C₂×D₄	—	4	4	no	—
1017	C₂×D₄	—	4	4	no	—
1018	C₂×D₄	—	4	4	no	—
1019	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1020	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1021	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1022	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1023	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1024	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1025	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1026	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1027	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1028	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1029	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1030	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1031	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1032	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1033	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1034	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1035	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1036	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
1037	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1038	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
1039	C₂²×C₄	—	4	2	no	—
1040	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1041	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1042	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1043	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1044	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1045	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1046	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1047	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1048	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1049	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1050	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1051	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1052	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1053	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1054	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
1055	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1056	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1057	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1058	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1059	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1060	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1061	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1062	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1063	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1064	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1065	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
1066	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1067	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1068	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1069	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1070	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1071	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1072	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1073	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1074	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1075	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1076	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1077	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1078	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1079	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1080	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1081	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1082	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1083	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1084	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1085	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1086	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1087	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1088	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1089	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1090	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1091	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1092	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1093	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1094	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1095	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1096	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1097	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
1098	C₄²	C₂³×C₃×C₅	1	2	yes	—
1099	C₄²	C₂³×C₃×C₅	1	2	yes	—
1100	C₄²	C₂³×C₃×C₅	1	2	yes	—
1101	C₃×C₅	#3534	1	1	yes	characteristic, direct product factor, Hall
1102	C₂²×C₃	—	2	1	no	—
1103	C₂²×C₃	—	2	1	no	—
1104	C₂²×C₃	—	2	1	no	—
1105	C₂²×C₃	—	2	1	no	—
1106	C₂²×C₃	—	2	1	no	—
1107	C₂²×C₃	—	2	2	no	—
1108	C₂²×C₃	—	2	2	no	—
1109	C₂²×C₃	—	2	2	no	—
1110	C₂²×C₃	—	2	2	no	—
1111	C₂²×C₃	—	2	2	no	—
1112	C₂²×C₃	—	2	2	no	—
1113	C₂²×C₃	—	2	2	no	—
1114	C₂²×C₃	—	2	1	no	—
1115	C₂²×C₃	—	2	2	no	—
1116	C₂²×C₃	—	2	2	no	—
1117	C₂²×C₃	—	2	1	no	—
1118	C₂²×C₃	—	2	2	no	—
1119	C₂²×C₃	—	2	2	no	—
1120	C₂²×C₃	—	2	2	no	—
1121	C₂²×C₃	—	4	4	no	—
1122	C₂²×C₃	—	8	4	no	—
1123	C₂²×C₃	—	8	2	no	—
1124	C₂²×C₃	—	8	4	no	—
1125	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
1126	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
1127	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
1128	C₃×C₄	—	2	1	no	—
1129	C₃×C₄	—	2	1	no	—
1130	C₃×C₄	—	2	1	no	—
1131	C₃×C₄	—	2	1	no	—
1132	C₃×C₄	—	2	2	no	—
1133	C₃×C₄	—	2	2	no	—
1134	C₃×C₄	—	2	2	no	—
1135	C₃×C₄	—	2	2	no	—
1136	C₃×C₄	—	2	2	no	—
1137	C₃×C₄	—	2	2	no	—
1138	C₃×C₄	—	2	2	no	—
1139	C₃×C₄	—	2	2	no	—
1140	C₂×C₅	—	2	2	no	—
1141	C₂×C₅	—	2	2	no	—
1142	C₂×C₅	—	4	1	no	—
1143	C₂×C₅	—	4	2	no	—
1144	C₂×C₅	—	4	2	no	—
1145	C₂×C₅	—	4	2	no	—
1146	C₂×C₅	—	4	2	no	—
1147	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1148	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
1149	C₂×C₅	C₃×#585	1	1	yes	characteristic
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	2	no	—
1152	C₂³	—	2	2	no	—
1153	C₂³	—	2	4	no	—
1154	C₂³	—	4	1	no	—
1155	C₂³	—	4	1	no	—
1156	C₂³	—	4	2	no	—
1157	C₂³	—	4	2	no	—
1158	C₂³	—	4	2	no	—
1159	C₂³	—	4	1	no	—
1160	C₂³	—	4	2	no	—
1161	C₂³	—	4	2	no	—
1162	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1163	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1164	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1165	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1166	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1167	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1168	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1169	Q₈	—	4	1	no	—
1170	Q₈	—	4	2	no	—
1171	D₄	—	2	4	no	—
1172	D₄	—	2	4	no	—
1173	D₄	—	2	4	no	—
1174	D₄	—	2	4	no	—
1175	D₄	—	2	4	no	—
1176	D₄	—	4	1	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	1	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	1	no	—
1187	D₄	—	4	2	no	—
1188	D₄	—	4	2	no	—
1189	D₄	—	4	2	no	—
1190	D₄	—	4	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	4	1	no	—
1195	C₂×C₄	—	4	1	no	—
1196	C₂×C₄	—	4	1	no	—
1197	C₂×C₄	—	4	1	no	—
1198	C₂×C₄	—	4	1	no	—
1199	C₂×C₄	—	4	2	no	—
1200	C₂×C₄	—	4	2	no	—
1201	C₂×C₄	—	4	2	no	—
1202	C₂×C₄	—	4	2	no	—
1203	C₂×C₄	—	4	2	no	—
1204	C₂×C₄	—	4	2	no	—
1205	C₂×C₄	—	4	1	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1208	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1209	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1210	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1211	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1212	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1213	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1214	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1215	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1216	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1217	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1218	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1219	C₂×C₃	—	2	2	no	—
1220	C₂×C₃	—	2	2	no	—
1221	C₂×C₃	—	4	1	no	—
1222	C₂×C₃	—	4	2	no	—
1223	C₂×C₃	—	4	2	no	—
1224	C₂×C₃	—	4	2	no	—
1225	C₂×C₃	—	4	2	no	—
1226	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1227	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1228	C₂×C₃	C₅×#585	1	1	yes	characteristic
1229	C₅	C₃×#3534	1	1	yes	characteristic, direct product factor, Sylow
1230	C₂²	—	2	1	no	—
1231	C₂²	—	2	1	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	1	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	2	no	—
1236	C₂²	—	2	2	no	—
1237	C₂²	—	2	2	no	—
1238	C₂²	—	2	2	no	—
1239	C₂²	—	2	2	no	—
1240	C₂²	—	2	2	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	2	no	—
1244	C₂²	—	2	2	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	2	no	—
1247	C₂²	—	2	2	no	—
1248	C₂²	—	2	2	no	—
1249	C₂²	—	4	4	no	—
1250	C₂²	—	8	4	no	—
1251	C₂²	—	8	2	no	—
1252	C₂²	—	8	4	no	—
1253	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
1254	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
1255	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
1256	C₄	—	2	1	no	—
1257	C₄	—	2	1	no	—
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	2	no	—
1261	C₄	—	2	2	no	—
1262	C₄	—	2	2	no	—
1263	C₄	—	2	2	no	—
1264	C₄	—	2	2	no	—
1265	C₄	—	2	2	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	2	2	no	—
1268	C₃	C₅×#3534	1	1	yes	characteristic, direct product factor, Sylow
1269	C₂	—	2	2	no	—
1270	C₂	—	2	2	no	—
1271	C₂	—	4	1	no	—
1272	C₂	—	4	2	no	—
1273	C₂	—	4	2	no	—
1274	C₂	—	4	2	no	—
1275	C₂	—	4	2	no	—
1276	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1277	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
1278	C₂	C₃×C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₃×C₅×#562	C₂	semidirect
2. C₃×C₅×#560	C₂	semidirect
3. C₃×C₅×#553	C₂	semidirect
4. C₃×C₅×#551	C₂	semidirect
5. C₃×C₅×#546	C₂	semidirect
6. C₃×C₅×#546	C₂	semidirect
7. C₃×C₅×#546	C₂	semidirect
8. C₃×C₅×D₄²	C₂	semidirect
9. C₃×C₅×#540	C₂	semidirect
10. C₃×C₅×#539	C₂	semidirect
11. C₃×C₅×#539	C₂	semidirect
12. C₃×C₅×#538	C₂	semidirect
13. C₃×C₅×#538	C₂	semidirect
14. C₃×C₅×#537	C₂	semidirect
15. C₃×C₅×#534	C₂	semidirect
16. C₃×C₅×#534	C₂	semidirect
17. C₃×C₅×#525	C₂	semidirect
18. C₂×C₃×C₅×#123	C₂	semidirect
19. C₂×C₃×C₅×#121	C₂	semidirect
20. C₅×#3534	C₃	direct (N × H)
21. C₂×C₃×C₅×#41	C₂²	semidirect
22. C₂×C₃×C₅×#41	C₂²	semidirect
24. C₂²×C₃×C₅×D₄	C₂²	semidirect
25. C₂²×C₃×C₅×D₄	C₂²	semidirect
26. C₂²×C₃×C₅×D₄	C₂²	semidirect
27. C₂²×C₃×C₅×D₄	C₂²	semidirect
28. C₂³×C₃×C₄×C₅	C₂²	semidirect
29. C₃×C₅×#127	C₂²	semidirect
30. C₃×C₅×#126	C₂²	semidirect
31. C₃×C₅×#126	C₂²	semidirect
32. C₃×C₅×#126	C₂²	semidirect
33. C₃×C₅×#126	C₂²	semidirect
34. C₃×C₅×#125	C₂²	semidirect
35. C₃×C₅×#125	C₂²	semidirect
36. C₃×C₅×#124	C₂²	semidirect
37. C₃×C₅×#124	C₂²	semidirect
38. C₃×C₅×#124	C₂²	semidirect
39. C₃×C₅×#123	C₂²	semidirect
40. C₃×C₅×#123	C₂²	semidirect
41. C₃×C₅×#123	C₂²	semidirect
42. C₃×C₅×#123	C₂²	semidirect
43. C₃×C₅×#123	C₂²	semidirect
44. C₃×C₅×#123	C₂²	semidirect
45. C₃×C₅×#123	C₂²	semidirect
46. C₃×C₅×#123	C₂²	semidirect
47. C₃×C₅×#123	C₂²	semidirect
48. C₃×C₅×#123	C₂²	semidirect
49. C₃×C₅×#123	C₂²	semidirect
50. C₃×C₅×#123	C₂²	semidirect
51. C₃×C₅×#123	C₂²	semidirect
52. C₃×C₅×#123	C₂²	semidirect
53. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
54. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
55. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
56. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
57. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
58. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
59. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
62. C₃×C₅×#121	C₂²	semidirect
63. C₃×C₅×#121	C₂²	semidirect
64. C₃×C₅×#121	C₂²	semidirect
65. C₃×C₅×#121	C₂²	semidirect
66. C₃×C₅×#121	C₂²	semidirect
67. C₃×C₅×#121	C₂²	semidirect
68. C₃×C₅×#121	C₂²	semidirect
69. C₃×C₅×#121	C₂²	semidirect
70. C₃×C₅×#121	C₂²	semidirect
71. C₃×C₅×#121	C₂²	semidirect
72. C₃×C₅×#121	C₂²	semidirect
73. C₃×C₅×#121	C₂²	semidirect
74. C₃×C₅×#121	C₂²	semidirect
75. C₃×C₅×#121	C₂²	semidirect
76. C₃×C₅×#121	C₂²	semidirect
77. C₃×C₅×#121	C₂²	semidirect
78. C₃×C₅×#121	C₂²	semidirect
79. C₃×C₅×#121	C₂²	semidirect
80. C₃×C₅×#121	C₂²	semidirect
82. C₃×C₅×#120	C₂²	semidirect
83. C₃×C₅×#120	C₂²	semidirect
84. C₃×C₅×#120	C₂²	semidirect
85. C₃×C₅×#120	C₂²	semidirect
86. C₃×C₅×#120	C₂²	semidirect
87. C₃×C₅×#120	C₂²	semidirect
88. C₃×C₅×#120	C₂²	semidirect
89. C₃×C₄×C₅×D₄	C₂²	semidirect
90. C₃×C₄×C₅×D₄	C₂²	semidirect
91. C₃×C₄×C₅×D₄	C₂²	semidirect
92. C₃×C₄×C₅×D₄	C₂²	semidirect
93. C₃×C₄×C₅×D₄	C₂²	semidirect
94. C₃×C₄×C₅×D₄	C₂²	semidirect
95. C₃×C₄×C₅×D₄	C₂²	semidirect
96. C₃×C₄×C₅×D₄	C₂²	semidirect
97. C₃×C₅×#117	C₂²	semidirect
98. C₃×C₅×#117	C₂²	semidirect
99. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
100. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
101. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
102. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
103. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
104. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
105. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
106. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
107. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
108. C₃×#3534	C₅	direct (N × H)
109. C₅×#562	C₂×C₃	semidirect
110. C₅×#560	C₂×C₃	semidirect
111. C₅×#553	C₂×C₃	semidirect
112. C₅×#551	C₂×C₃	semidirect
113. C₅×#546	C₂×C₃	semidirect
114. C₅×#546	C₂×C₃	semidirect
115. C₅×#546	C₂×C₃	semidirect
116. C₅×D₄²	C₂×C₃	semidirect
117. C₅×#540	C₂×C₃	semidirect
118. C₅×#539	C₂×C₃	semidirect
119. C₅×#539	C₂×C₃	semidirect
120. C₅×#538	C₂×C₃	semidirect
121. C₅×#538	C₂×C₃	semidirect
122. C₅×#537	C₂×C₃	semidirect
123. C₅×#534	C₂×C₃	semidirect
124. C₅×#534	C₂×C₃	semidirect
125. C₅×#525	C₂×C₃	semidirect
126. C₂×C₅×#123	C₂×C₃	semidirect
127. C₂×C₅×#121	C₂×C₃	semidirect
223. C₃×#562	C₂×C₅	semidirect
224. C₃×#560	C₂×C₅	semidirect
225. C₃×#553	C₂×C₅	semidirect
226. C₃×#551	C₂×C₅	semidirect
227. C₃×#546	C₂×C₅	semidirect
228. C₃×#546	C₂×C₅	semidirect
229. C₃×#546	C₂×C₅	semidirect
230. C₃×D₄²	C₂×C₅	semidirect
231. C₃×#540	C₂×C₅	semidirect
232. C₃×#539	C₂×C₅	semidirect
233. C₃×#539	C₂×C₅	semidirect
234. C₃×#538	C₂×C₅	semidirect
235. C₃×#538	C₂×C₅	semidirect
236. C₃×#537	C₂×C₅	semidirect
237. C₃×#534	C₂×C₅	semidirect
238. C₃×#534	C₂×C₅	semidirect
239. C₃×#525	C₂×C₅	semidirect
240. C₂×C₃×#123	C₂×C₅	semidirect
241. C₂×C₃×#121	C₂×C₅	semidirect
242. C₂×C₅×#41	C₂²×C₃	semidirect
243. C₂×C₅×#41	C₂²×C₃	semidirect
245. C₂²×C₅×D₄	C₂²×C₃	semidirect
246. C₂²×C₅×D₄	C₂²×C₃	semidirect
247. C₂²×C₅×D₄	C₂²×C₃	semidirect
248. C₂²×C₅×D₄	C₂²×C₃	semidirect
249. C₂³×C₄×C₅	C₂²×C₃	semidirect
250. C₅×#127	C₂²×C₃	semidirect
251. C₅×#126	C₂²×C₃	semidirect
252. C₅×#126	C₂²×C₃	semidirect
253. C₅×#126	C₂²×C₃	semidirect
254. C₅×#126	C₂²×C₃	semidirect
255. C₅×#125	C₂²×C₃	semidirect
256. C₅×#125	C₂²×C₃	semidirect
257. C₅×#124	C₂²×C₃	semidirect
258. C₅×#124	C₂²×C₃	semidirect
259. C₅×#124	C₂²×C₃	semidirect
260. C₅×#123	C₂²×C₃	semidirect
261. C₅×#123	C₂²×C₃	semidirect
262. C₅×#123	C₂²×C₃	semidirect
263. C₅×#123	C₂²×C₃	semidirect
264. C₅×#123	C₂²×C₃	semidirect
265. C₅×#123	C₂²×C₃	semidirect
266. C₅×#123	C₂²×C₃	semidirect
267. C₅×#123	C₂²×C₃	semidirect
268. C₅×#123	C₂²×C₃	semidirect
269. C₅×#123	C₂²×C₃	semidirect
270. C₅×#123	C₂²×C₃	semidirect
271. C₅×#123	C₂²×C₃	semidirect
272. C₅×#123	C₂²×C₃	semidirect
273. C₅×#123	C₂²×C₃	semidirect
274. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
275. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
276. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
277. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
278. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
279. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
280. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
283. C₅×#121	C₂²×C₃	semidirect
284. C₅×#121	C₂²×C₃	semidirect
285. C₅×#121	C₂²×C₃	semidirect
286. C₅×#121	C₂²×C₃	semidirect
287. C₅×#121	C₂²×C₃	semidirect
288. C₅×#121	C₂²×C₃	semidirect
289. C₅×#121	C₂²×C₃	semidirect
290. C₅×#121	C₂²×C₃	semidirect
291. C₅×#121	C₂²×C₃	semidirect
292. C₅×#121	C₂²×C₃	semidirect
293. C₅×#121	C₂²×C₃	semidirect
294. C₅×#121	C₂²×C₃	semidirect
295. C₅×#121	C₂²×C₃	semidirect
296. C₅×#121	C₂²×C₃	semidirect
297. C₅×#121	C₂²×C₃	semidirect
298. C₅×#121	C₂²×C₃	semidirect
299. C₅×#121	C₂²×C₃	semidirect
300. C₅×#121	C₂²×C₃	semidirect
301. C₅×#121	C₂²×C₃	semidirect
303. C₅×#120	C₂²×C₃	semidirect
304. C₅×#120	C₂²×C₃	semidirect
305. C₅×#120	C₂²×C₃	semidirect
306. C₅×#120	C₂²×C₃	semidirect
307. C₅×#120	C₂²×C₃	semidirect
308. C₅×#120	C₂²×C₃	semidirect
309. C₅×#120	C₂²×C₃	semidirect
310. C₄×C₅×D₄	C₂²×C₃	semidirect
311. C₄×C₅×D₄	C₂²×C₃	semidirect
312. C₄×C₅×D₄	C₂²×C₃	semidirect
313. C₄×C₅×D₄	C₂²×C₃	semidirect
314. C₄×C₅×D₄	C₂²×C₃	semidirect
315. C₄×C₅×D₄	C₂²×C₃	semidirect
316. C₄×C₅×D₄	C₂²×C₃	semidirect
317. C₄×C₅×D₄	C₂²×C₃	semidirect
318. C₅×#117	C₂²×C₃	semidirect
319. C₅×#117	C₂²×C₃	semidirect
320. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
321. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
322. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
323. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
324. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
325. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
326. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
327. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
328. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
329. #3534	C₃×C₅	direct (N × H)
399. C₂×C₃×#41	C₂²×C₅	semidirect
400. C₂×C₃×#41	C₂²×C₅	semidirect
402. C₂²×C₃×D₄	C₂²×C₅	semidirect
403. C₂²×C₃×D₄	C₂²×C₅	semidirect
404. C₂²×C₃×D₄	C₂²×C₅	semidirect
405. C₂²×C₃×D₄	C₂²×C₅	semidirect
406. C₂³×C₃×C₄	C₂²×C₅	semidirect
407. C₃×#127	C₂²×C₅	semidirect
408. C₃×#126	C₂²×C₅	semidirect
409. C₃×#126	C₂²×C₅	semidirect
410. C₃×#126	C₂²×C₅	semidirect
411. C₃×#126	C₂²×C₅	semidirect
412. C₃×#125	C₂²×C₅	semidirect
413. C₃×#125	C₂²×C₅	semidirect
414. C₃×#124	C₂²×C₅	semidirect
415. C₃×#124	C₂²×C₅	semidirect
416. C₃×#124	C₂²×C₅	semidirect
417. C₃×#123	C₂²×C₅	semidirect
418. C₃×#123	C₂²×C₅	semidirect
419. C₃×#123	C₂²×C₅	semidirect
420. C₃×#123	C₂²×C₅	semidirect
421. C₃×#123	C₂²×C₅	semidirect
422. C₃×#123	C₂²×C₅	semidirect
423. C₃×#123	C₂²×C₅	semidirect
424. C₃×#123	C₂²×C₅	semidirect
425. C₃×#123	C₂²×C₅	semidirect
426. C₃×#123	C₂²×C₅	semidirect
427. C₃×#123	C₂²×C₅	semidirect
428. C₃×#123	C₂²×C₅	semidirect
429. C₃×#123	C₂²×C₅	semidirect
430. C₃×#123	C₂²×C₅	semidirect
431. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
432. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
433. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
434. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
435. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
436. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
437. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
440. C₃×#121	C₂²×C₅	semidirect
441. C₃×#121	C₂²×C₅	semidirect
442. C₃×#121	C₂²×C₅	semidirect
443. C₃×#121	C₂²×C₅	semidirect
444. C₃×#121	C₂²×C₅	semidirect
445. C₃×#121	C₂²×C₅	semidirect
446. C₃×#121	C₂²×C₅	semidirect
447. C₃×#121	C₂²×C₅	semidirect
448. C₃×#121	C₂²×C₅	semidirect
449. C₃×#121	C₂²×C₅	semidirect
450. C₃×#121	C₂²×C₅	semidirect
451. C₃×#121	C₂²×C₅	semidirect
452. C₃×#121	C₂²×C₅	semidirect
453. C₃×#121	C₂²×C₅	semidirect
454. C₃×#121	C₂²×C₅	semidirect
455. C₃×#121	C₂²×C₅	semidirect
456. C₃×#121	C₂²×C₅	semidirect
457. C₃×#121	C₂²×C₅	semidirect
458. C₃×#121	C₂²×C₅	semidirect
460. C₃×#120	C₂²×C₅	semidirect
461. C₃×#120	C₂²×C₅	semidirect
462. C₃×#120	C₂²×C₅	semidirect
463. C₃×#120	C₂²×C₅	semidirect
464. C₃×#120	C₂²×C₅	semidirect
465. C₃×#120	C₂²×C₅	semidirect
466. C₃×#120	C₂²×C₅	semidirect
467. C₃×C₄×D₄	C₂²×C₅	semidirect
468. C₃×C₄×D₄	C₂²×C₅	semidirect
469. C₃×C₄×D₄	C₂²×C₅	semidirect
470. C₃×C₄×D₄	C₂²×C₅	semidirect
471. C₃×C₄×D₄	C₂²×C₅	semidirect
472. C₃×C₄×D₄	C₂²×C₅	semidirect
473. C₃×C₄×D₄	C₂²×C₅	semidirect
474. C₃×C₄×D₄	C₂²×C₅	semidirect
475. C₃×#117	C₂²×C₅	semidirect
476. C₃×#117	C₂²×C₅	semidirect
477. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
478. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
479. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
480. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
481. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
482. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
483. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
484. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
485. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
581. #562	C₂×C₃×C₅	semidirect
582. #560	C₂×C₃×C₅	semidirect
583. #553	C₂×C₃×C₅	semidirect
584. #551	C₂×C₃×C₅	semidirect
585. #546	C₂×C₃×C₅	semidirect
586. #546	C₂×C₃×C₅	semidirect
587. #546	C₂×C₃×C₅	semidirect
588. D₄²	C₂×C₃×C₅	semidirect
589. #540	C₂×C₃×C₅	semidirect
590. #539	C₂×C₃×C₅	semidirect
591. #539	C₂×C₃×C₅	semidirect
592. #538	C₂×C₃×C₅	semidirect
593. #538	C₂×C₃×C₅	semidirect
594. #537	C₂×C₃×C₅	semidirect
595. #534	C₂×C₃×C₅	semidirect
596. #534	C₂×C₃×C₅	semidirect
597. #525	C₂×C₃×C₅	semidirect
598. C₂×#123	C₂×C₃×C₅	semidirect
599. C₂×#121	C₂×C₃×C₅	semidirect
802. C₂×#41	C₂²×C₃×C₅	semidirect
803. C₂×#41	C₂²×C₃×C₅	semidirect
805. C₂²×D₄	C₂²×C₃×C₅	semidirect
806. C₂²×D₄	C₂²×C₃×C₅	semidirect
807. C₂²×D₄	C₂²×C₃×C₅	semidirect
808. C₂²×D₄	C₂²×C₃×C₅	semidirect
809. C₂³×C₄	C₂²×C₃×C₅	semidirect
810. #127	C₂²×C₃×C₅	semidirect
811. #126	C₂²×C₃×C₅	semidirect
812. #126	C₂²×C₃×C₅	semidirect
813. #126	C₂²×C₃×C₅	semidirect
814. #126	C₂²×C₃×C₅	semidirect
815. #125	C₂²×C₃×C₅	semidirect
816. #125	C₂²×C₃×C₅	semidirect
817. #124	C₂²×C₃×C₅	semidirect
818. #124	C₂²×C₃×C₅	semidirect
819. #124	C₂²×C₃×C₅	semidirect
820. #123	C₂²×C₃×C₅	semidirect
821. #123	C₂²×C₃×C₅	semidirect
822. #123	C₂²×C₃×C₅	semidirect
823. #123	C₂²×C₃×C₅	semidirect
824. #123	C₂²×C₃×C₅	semidirect
825. #123	C₂²×C₃×C₅	semidirect
826. #123	C₂²×C₃×C₅	semidirect
827. #123	C₂²×C₃×C₅	semidirect
828. #123	C₂²×C₃×C₅	semidirect
829. #123	C₂²×C₃×C₅	semidirect
830. #123	C₂²×C₃×C₅	semidirect
831. #123	C₂²×C₃×C₅	semidirect
832. #123	C₂²×C₃×C₅	semidirect
833. #123	C₂²×C₃×C₅	semidirect
834. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
835. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
836. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
837. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
838. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
839. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
840. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
843. #121	C₂²×C₃×C₅	semidirect
844. #121	C₂²×C₃×C₅	semidirect
845. #121	C₂²×C₃×C₅	semidirect
846. #121	C₂²×C₃×C₅	semidirect
847. #121	C₂²×C₃×C₅	semidirect
848. #121	C₂²×C₃×C₅	semidirect
849. #121	C₂²×C₃×C₅	semidirect
850. #121	C₂²×C₃×C₅	semidirect
851. #121	C₂²×C₃×C₅	semidirect
852. #121	C₂²×C₃×C₅	semidirect
853. #121	C₂²×C₃×C₅	semidirect
854. #121	C₂²×C₃×C₅	semidirect
855. #121	C₂²×C₃×C₅	semidirect
856. #121	C₂²×C₃×C₅	semidirect
857. #121	C₂²×C₃×C₅	semidirect
858. #121	C₂²×C₃×C₅	semidirect
859. #121	C₂²×C₃×C₅	semidirect
860. #121	C₂²×C₃×C₅	semidirect
861. #121	C₂²×C₃×C₅	semidirect
863. #120	C₂²×C₃×C₅	semidirect
864. #120	C₂²×C₃×C₅	semidirect
865. #120	C₂²×C₃×C₅	semidirect
866. #120	C₂²×C₃×C₅	semidirect
867. #120	C₂²×C₃×C₅	semidirect
868. #120	C₂²×C₃×C₅	semidirect
869. #120	C₂²×C₃×C₅	semidirect
870. C₄×D₄	C₂²×C₃×C₅	semidirect
871. C₄×D₄	C₂²×C₃×C₅	semidirect
872. C₄×D₄	C₂²×C₃×C₅	semidirect
873. C₄×D₄	C₂²×C₃×C₅	semidirect
874. C₄×D₄	C₂²×C₃×C₅	semidirect
875. C₄×D₄	C₂²×C₃×C₅	semidirect
876. C₄×D₄	C₂²×C₃×C₅	semidirect
877. C₄×D₄	C₂²×C₃×C₅	semidirect
878. #117	C₂²×C₃×C₅	semidirect
879. #117	C₂²×C₃×C₅	semidirect
880. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
881. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
882. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
883. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
884. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
885. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
886. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
887. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
888. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
1101. C₃×C₅	#3534	direct (N × H)
1229. C₅	C₃×#3534	direct (N × H)
1268. C₃	C₅×#3534	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#562	2
C₃×C₅×#560	2
C₃×C₅×#553	2
C₃×C₅×#551	2
C₃×C₅×#546	2
C₃×C₅×D₄²	2
C₃×C₅×#540	2
C₃×C₅×#539	2
C₃×C₅×#538	2
C₃×C₅×#537	2
C₃×C₅×#534	2
C₃×C₅×#525	2
C₂×C₃×C₅×#123	2
C₂×C₃×C₅×#121	2
C₅×#3534	3
C₃×#3534	5

Subgroups — C3×C5×#3534 #14276568

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3534 #14276568