Subgroups — C₃×C₅×#3551 #14276585

Order 1920.

2100 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#563	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#560	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#555	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#553	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#548	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#540	C₂	1	4	yes	maximal, complemented
10	C₃×C₅×#538	C₂	1	4	yes	maximal, complemented
11	C₃×C₅×#537	C₂	1	2	yes	maximal, complemented
12	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#529	C₂	1	2	yes	maximal, complemented
16	C₅×#3551	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
19	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₃×C₅×#127	C₂²	1	1	yes	characteristic
25	C₃×C₅×#127	C₂²	1	2	yes	—
26	C₃×C₅×#126	C₂²	1	4	yes	—
27	C₃×C₅×#126	C₂²	1	4	yes	complemented
28	C₃×C₅×#126	C₂²	1	4	yes	complemented
29	C₃×C₅×#125	C₂²	1	2	yes	complemented
30	C₃×C₅×#125	C₂²	1	4	yes	complemented
31	C₃×C₅×#124	C₂²	1	2	yes	—
32	C₃×C₅×#124	C₂²	1	1	yes	characteristic
33	C₃×C₅×#124	C₂²	1	2	yes	—
34	C₃×C₅×#124	C₂²	1	2	yes	—
35	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#124	C₂²	1	4	yes	complemented
37	C₃×C₅×#123	C₂²	1	2	yes	—
38	C₃×C₅×#123	C₂²	1	4	yes	—
39	C₃×C₅×#123	C₂²	1	4	yes	—
40	C₃×C₅×#123	C₂²	1	4	yes	complemented
41	C₃×C₅×#123	C₂²	1	2	yes	complemented
42	C₃×C₅×#123	C₂²	1	4	yes	complemented
43	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
44	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
45	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
46	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
47	C₃×C₅×C₂²⋊Q₈	C₂²	1	4	yes	complemented
48	C₃×C₅×#121	C₂²	1	2	yes	—
49	C₃×C₅×#121	C₂²	1	2	yes	—
50	C₃×C₅×#121	C₂²	1	2	yes	—
51	C₃×C₅×#121	C₂²	1	2	yes	—
52	C₃×C₅×#121	C₂²	1	4	yes	—
53	C₃×C₅×#121	C₂²	1	2	yes	complemented
54	C₃×C₅×#121	C₂²	1	4	yes	complemented
55	C₃×C₅×#121	C₂²	1	4	yes	complemented
56	C₃×C₅×#121	C₂²	1	4	yes	complemented
57	C₃×C₅×#121	C₂²	1	4	yes	complemented
58	C₃×C₅×#121	C₂²	1	4	yes	complemented
59	C₃×C₅×#120	C₂²	1	2	yes	—
60	C₃×C₅×#120	C₂²	1	2	yes	—
61	C₃×C₅×#120	C₂²	1	4	yes	—
62	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
63	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
64	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
65	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
66	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
67	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
68	C₃×C₄×C₅×D₄	C₂²	1	4	yes	complemented
69	C₃×C₅×#117	C₂²	1	1	yes	characteristic
70	C₃×C₅×#117	C₂²	1	4	yes	complemented
71	C₃×C₅×#117	C₂²	1	1	yes	characteristic, complemented
72	C₃×C₅×#117	C₂²	1	4	yes	complemented
73	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
74	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
75	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic, complemented
76	C₃×#3551	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
77	C₅×#563	C₂×C₃	1	2	yes	complemented
78	C₅×#560	C₂×C₃	1	2	yes	complemented
79	C₅×#555	C₂×C₃	1	2	yes	complemented
80	C₅×#553	C₂×C₃	1	2	yes	complemented
81	C₅×#552	C₂×C₃	1	2	yes	complemented
82	C₅×#551	C₂×C₃	1	2	yes	complemented
83	C₅×#548	C₂×C₃	1	2	yes	complemented
84	C₅×#546	C₂×C₃	1	2	yes	complemented
85	C₅×#540	C₂×C₃	1	4	yes	complemented
86	C₅×#538	C₂×C₃	1	4	yes	complemented
87	C₅×#537	C₂×C₃	1	2	yes	complemented
88	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
89	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
90	C₅×#532	C₂×C₃	1	1	yes	characteristic, complemented
91	C₅×#529	C₂×C₃	1	2	yes	complemented
92	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
93	C₃×C₅×#41	—	4	2	no	—
94	C₃×C₅×#41	—	4	2	no	—
95	C₃×C₅×#41	—	4	4	no	—
96	C₂×C₃×C₅×Q₈	—	4	2	no	—
97	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
98	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
99	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×D₄	—	4	2	no	—
102	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
103	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
104	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
105	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
106	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
107	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
108	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
110	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
111	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
112	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
113	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
114	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
115	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
116	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
117	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
118	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
119	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
120	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
121	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
122	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
123	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
124	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
125	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
126	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
127	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
128	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
129	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
131	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
134	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
135	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
137	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
138	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
139	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
140	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
141	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
142	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
143	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
144	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
145	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
146	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
148	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
149	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
150	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
151	C₃×C₄²×C₅	C₂³	1	2	yes	—
152	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
153	C₃×C₄²×C₅	C₂³	1	2	yes	—
154	C₃×C₄²×C₅	C₂³	1	4	yes	—
155	C₃×C₄²×C₅	C₂³	1	2	yes	—
156	C₃×#563	C₂×C₅	1	2	yes	complemented
157	C₃×#560	C₂×C₅	1	2	yes	complemented
158	C₃×#555	C₂×C₅	1	2	yes	complemented
159	C₃×#553	C₂×C₅	1	2	yes	complemented
160	C₃×#552	C₂×C₅	1	2	yes	complemented
161	C₃×#551	C₂×C₅	1	2	yes	complemented
162	C₃×#548	C₂×C₅	1	2	yes	complemented
163	C₃×#546	C₂×C₅	1	2	yes	complemented
164	C₃×#540	C₂×C₅	1	4	yes	complemented
165	C₃×#538	C₂×C₅	1	4	yes	complemented
166	C₃×#537	C₂×C₅	1	2	yes	complemented
167	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
168	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
169	C₃×#532	C₂×C₅	1	1	yes	characteristic, complemented
170	C₃×#529	C₂×C₅	1	2	yes	complemented
171	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
172	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
173	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
175	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
176	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
178	C₅×#127	C₂²×C₃	1	1	yes	characteristic
179	C₅×#127	C₂²×C₃	1	2	yes	—
180	C₅×#126	C₂²×C₃	1	4	yes	—
181	C₅×#126	C₂²×C₃	1	4	yes	complemented
182	C₅×#126	C₂²×C₃	1	4	yes	complemented
183	C₅×#125	C₂²×C₃	1	2	yes	complemented
184	C₅×#125	C₂²×C₃	1	4	yes	complemented
185	C₅×#124	C₂²×C₃	1	2	yes	—
186	C₅×#124	C₂²×C₃	1	1	yes	characteristic
187	C₅×#124	C₂²×C₃	1	2	yes	—
188	C₅×#124	C₂²×C₃	1	2	yes	—
189	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
190	C₅×#124	C₂²×C₃	1	4	yes	complemented
191	C₅×#123	C₂²×C₃	1	2	yes	—
192	C₅×#123	C₂²×C₃	1	4	yes	—
193	C₅×#123	C₂²×C₃	1	4	yes	—
194	C₅×#123	C₂²×C₃	1	4	yes	complemented
195	C₅×#123	C₂²×C₃	1	2	yes	complemented
196	C₅×#123	C₂²×C₃	1	4	yes	complemented
197	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
198	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
199	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
200	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
201	C₅×C₂²⋊Q₈	C₂²×C₃	1	4	yes	complemented
202	C₅×#121	C₂²×C₃	1	2	yes	—
203	C₅×#121	C₂²×C₃	1	2	yes	—
204	C₅×#121	C₂²×C₃	1	2	yes	—
205	C₅×#121	C₂²×C₃	1	2	yes	—
206	C₅×#121	C₂²×C₃	1	4	yes	—
207	C₅×#121	C₂²×C₃	1	2	yes	complemented
208	C₅×#121	C₂²×C₃	1	4	yes	complemented
209	C₅×#121	C₂²×C₃	1	4	yes	complemented
210	C₅×#121	C₂²×C₃	1	4	yes	complemented
211	C₅×#121	C₂²×C₃	1	4	yes	complemented
212	C₅×#121	C₂²×C₃	1	4	yes	complemented
213	C₅×#120	C₂²×C₃	1	2	yes	—
214	C₅×#120	C₂²×C₃	1	2	yes	—
215	C₅×#120	C₂²×C₃	1	4	yes	—
216	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
217	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
218	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
219	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
220	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
221	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
222	C₄×C₅×D₄	C₂²×C₃	1	4	yes	complemented
223	C₅×#117	C₂²×C₃	1	1	yes	characteristic
224	C₅×#117	C₂²×C₃	1	4	yes	complemented
225	C₅×#117	C₂²×C₃	1	1	yes	characteristic, complemented
226	C₅×#117	C₂²×C₃	1	4	yes	complemented
227	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
228	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
229	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic, complemented
230	#3551	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
231	C₂³×C₃×C₅	—	4	2	no	—
232	C₂³×C₃×C₅	—	4	4	no	—
233	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
234	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
235	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
236	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
237	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
238	C₃×C₅×Q₈	—	2	4	no	—
239	C₃×C₅×Q₈	—	4	2	no	—
240	C₃×C₅×Q₈	—	4	1	no	—
241	C₃×C₅×Q₈	—	4	1	no	—
242	C₃×C₅×D₄	—	2	4	no	—
243	C₃×C₅×D₄	—	4	2	no	—
244	C₃×C₅×D₄	—	4	4	no	—
245	C₃×C₅×D₄	—	4	2	no	—
246	C₃×C₅×D₄	—	4	4	no	—
247	C₃×C₅×D₄	—	4	4	no	—
248	C₃×C₅×D₄	—	4	2	no	—
249	C₃×C₅×D₄	—	4	2	no	—
250	C₃×C₅×D₄	—	4	1	no	—
251	C₃×C₅×D₄	—	4	1	no	—
252	C₃×C₅×D₄	—	4	1	no	—
253	C₃×C₅×D₄	—	4	1	no	—
254	C₃×C₅×D₄	—	4	4	no	—
255	C₂×C₃×C₄×C₅	—	2	2	no	—
256	C₂×C₃×C₄×C₅	—	2	2	no	—
257	C₂×C₃×C₄×C₅	—	2	4	no	—
258	C₂×C₃×C₄×C₅	—	2	2	no	—
259	C₂×C₃×C₄×C₅	—	4	4	no	—
260	C₂×C₃×C₄×C₅	—	4	2	no	—
261	C₂×C₃×C₄×C₅	—	4	4	no	—
262	C₂×C₃×C₄×C₅	—	4	2	no	—
263	C₂×C₃×C₄×C₅	—	4	4	no	—
264	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
265	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
266	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
267	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
268	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
272	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
276	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic, complemented
277	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
279	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
280	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
281	C₃×#127	C₂²×C₅	1	1	yes	characteristic
282	C₃×#127	C₂²×C₅	1	2	yes	—
283	C₃×#126	C₂²×C₅	1	4	yes	—
284	C₃×#126	C₂²×C₅	1	4	yes	complemented
285	C₃×#126	C₂²×C₅	1	4	yes	complemented
286	C₃×#125	C₂²×C₅	1	4	yes	complemented
287	C₃×#125	C₂²×C₅	1	2	yes	complemented
288	C₃×#124	C₂²×C₅	1	2	yes	—
289	C₃×#124	C₂²×C₅	1	2	yes	—
290	C₃×#124	C₂²×C₅	1	1	yes	characteristic
291	C₃×#124	C₂²×C₅	1	2	yes	—
292	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
293	C₃×#124	C₂²×C₅	1	4	yes	complemented
294	C₃×#123	C₂²×C₅	1	2	yes	—
295	C₃×#123	C₂²×C₅	1	4	yes	—
296	C₃×#123	C₂²×C₅	1	4	yes	—
297	C₃×#123	C₂²×C₅	1	4	yes	complemented
298	C₃×#123	C₂²×C₅	1	2	yes	complemented
299	C₃×#123	C₂²×C₅	1	4	yes	complemented
300	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
301	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
302	C₃×C₂²⋊Q₈	C₂²×C₅	1	4	yes	complemented
303	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
304	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
305	C₃×#121	C₂²×C₅	1	2	yes	—
306	C₃×#121	C₂²×C₅	1	2	yes	—
307	C₃×#121	C₂²×C₅	1	2	yes	—
308	C₃×#121	C₂²×C₅	1	2	yes	—
309	C₃×#121	C₂²×C₅	1	4	yes	—
310	C₃×#121	C₂²×C₅	1	4	yes	complemented
311	C₃×#121	C₂²×C₅	1	4	yes	complemented
312	C₃×#121	C₂²×C₅	1	4	yes	complemented
313	C₃×#121	C₂²×C₅	1	2	yes	complemented
314	C₃×#121	C₂²×C₅	1	4	yes	complemented
315	C₃×#121	C₂²×C₅	1	4	yes	complemented
316	C₃×#120	C₂²×C₅	1	2	yes	—
317	C₃×#120	C₂²×C₅	1	4	yes	—
318	C₃×#120	C₂²×C₅	1	2	yes	—
319	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
320	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
321	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
322	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
323	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
324	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
325	C₃×C₄×D₄	C₂²×C₅	1	4	yes	complemented
326	C₃×#117	C₂²×C₅	1	1	yes	characteristic
327	C₃×#117	C₂²×C₅	1	4	yes	complemented
328	C₃×#117	C₂²×C₅	1	1	yes	characteristic, complemented
329	C₃×#117	C₂²×C₅	1	4	yes	complemented
330	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
331	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
332	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic, complemented
333	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
334	C₅×#41	—	4	2	no	—
335	C₅×#41	—	4	2	no	—
336	C₅×#41	—	4	4	no	—
337	C₂×C₅×Q₈	—	4	2	no	—
338	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
339	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
340	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
341	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
342	C₂×C₅×D₄	—	4	2	no	—
343	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
344	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
345	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
346	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
347	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
348	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
349	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
350	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
351	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
352	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
353	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
354	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
355	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
356	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
357	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
358	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
359	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
360	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
361	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
362	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
363	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
364	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
365	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
366	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
367	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
368	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
369	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
370	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
371	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
372	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
373	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
374	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
375	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
376	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
377	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
378	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
379	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
380	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
381	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
382	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
383	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
384	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
385	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
386	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
387	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
388	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
389	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
390	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
391	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
392	C₄²×C₅	C₂³×C₃	1	2	yes	—
393	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
394	C₄²×C₅	C₂³×C₃	1	2	yes	—
395	C₄²×C₅	C₂³×C₃	1	4	yes	—
396	C₄²×C₅	C₂³×C₃	1	2	yes	—
397	#563	C₂×C₃×C₅	1	2	yes	complemented
398	#560	C₂×C₃×C₅	1	2	yes	complemented
399	#555	C₂×C₃×C₅	1	2	yes	complemented
400	#553	C₂×C₃×C₅	1	2	yes	complemented
401	#552	C₂×C₃×C₅	1	2	yes	complemented
402	#551	C₂×C₃×C₅	1	2	yes	complemented
403	#548	C₂×C₃×C₅	1	2	yes	complemented
404	#546	C₂×C₃×C₅	1	2	yes	complemented
405	#540	C₂×C₃×C₅	1	4	yes	complemented
406	#538	C₂×C₃×C₅	1	4	yes	complemented
407	#537	C₂×C₃×C₅	1	2	yes	complemented
408	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
409	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
410	#532	C₂×C₃×C₅	1	1	yes	characteristic, complemented
411	#529	C₂×C₃×C₅	1	2	yes	complemented
412	C₂²×C₃×C₅	—	2	1	no	—
413	C₂²×C₃×C₅	—	2	2	no	—
414	C₂²×C₃×C₅	—	2	1	no	—
415	C₂²×C₃×C₅	—	2	1	no	—
416	C₂²×C₃×C₅	—	2	4	no	—
417	C₂²×C₃×C₅	—	2	2	no	—
418	C₂²×C₃×C₅	—	2	2	no	—
419	C₂²×C₃×C₅	—	2	4	no	—
420	C₂²×C₃×C₅	—	2	2	no	—
421	C₂²×C₃×C₅	—	2	2	no	—
422	C₂²×C₃×C₅	—	2	4	no	—
423	C₂²×C₃×C₅	—	2	2	no	—
424	C₂²×C₃×C₅	—	8	4	no	—
425	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
426	C₃×C₄×C₅	—	2	2	no	—
427	C₃×C₄×C₅	—	2	1	no	—
428	C₃×C₄×C₅	—	2	1	no	—
429	C₃×C₄×C₅	—	2	1	no	—
430	C₃×C₄×C₅	—	2	4	no	—
431	C₃×C₄×C₅	—	2	2	no	—
432	C₃×C₄×C₅	—	2	4	no	—
433	C₃×C₄×C₅	—	2	2	no	—
434	C₃×C₄×C₅	—	2	4	no	—
435	C₃×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
436	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
437	C₃×#41	—	4	2	no	—
438	C₃×#41	—	4	2	no	—
439	C₃×#41	—	4	4	no	—
440	C₂×C₃×Q₈	—	4	2	no	—
441	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
442	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
443	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
444	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
445	C₂×C₃×D₄	—	4	2	no	—
446	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
447	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
448	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
449	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
450	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
451	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
452	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
453	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
454	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
455	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
456	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
457	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
458	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
459	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
460	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
461	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
462	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
463	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
464	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
465	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
466	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
467	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
468	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
469	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
470	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
471	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
472	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
473	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
474	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
475	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
476	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
477	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
478	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
479	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
480	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
481	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
482	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
483	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
484	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
485	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
486	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
487	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
488	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
489	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
490	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
491	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
492	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
493	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
494	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
495	C₃×C₄²	C₂³×C₅	1	2	yes	—
496	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
497	C₃×C₄²	C₂³×C₅	1	2	yes	—
498	C₃×C₄²	C₂³×C₅	1	4	yes	—
499	C₃×C₄²	C₂³×C₅	1	2	yes	—
500	C₂³×C₅	—	4	2	no	—
501	C₂³×C₅	—	4	4	no	—
502	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
503	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
504	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
505	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
506	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
507	C₅×Q₈	—	2	4	no	—
508	C₅×Q₈	—	4	2	no	—
509	C₅×Q₈	—	4	1	no	—
510	C₅×Q₈	—	4	1	no	—
511	C₅×D₄	—	2	4	no	—
512	C₅×D₄	—	4	2	no	—
513	C₅×D₄	—	4	4	no	—
514	C₅×D₄	—	4	2	no	—
515	C₅×D₄	—	4	4	no	—
516	C₅×D₄	—	4	4	no	—
517	C₅×D₄	—	4	2	no	—
518	C₅×D₄	—	4	2	no	—
519	C₅×D₄	—	4	1	no	—
520	C₅×D₄	—	4	1	no	—
521	C₅×D₄	—	4	1	no	—
522	C₅×D₄	—	4	1	no	—
523	C₅×D₄	—	4	4	no	—
524	C₂×C₄×C₅	—	2	2	no	—
525	C₂×C₄×C₅	—	2	2	no	—
526	C₂×C₄×C₅	—	2	4	no	—
527	C₂×C₄×C₅	—	2	2	no	—
528	C₂×C₄×C₅	—	4	4	no	—
529	C₂×C₄×C₅	—	4	2	no	—
530	C₂×C₄×C₅	—	4	4	no	—
531	C₂×C₄×C₅	—	4	2	no	—
532	C₂×C₄×C₅	—	4	4	no	—
533	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
534	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
535	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
536	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
537	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
538	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
539	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
540	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
541	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
542	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
543	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
544	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
545	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
546	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
547	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
548	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
549	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
550	#127	C₂²×C₃×C₅	1	1	yes	characteristic
551	#127	C₂²×C₃×C₅	1	2	yes	—
552	#126	C₂²×C₃×C₅	1	4	yes	—
553	#126	C₂²×C₃×C₅	1	4	yes	complemented
554	#126	C₂²×C₃×C₅	1	4	yes	complemented
555	#125	C₂²×C₃×C₅	1	2	yes	complemented
556	#125	C₂²×C₃×C₅	1	4	yes	complemented
557	#124	C₂²×C₃×C₅	1	2	yes	—
558	#124	C₂²×C₃×C₅	1	1	yes	characteristic
559	#124	C₂²×C₃×C₅	1	2	yes	—
560	#124	C₂²×C₃×C₅	1	2	yes	—
561	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
562	#124	C₂²×C₃×C₅	1	4	yes	complemented
563	#123	C₂²×C₃×C₅	1	2	yes	—
564	#123	C₂²×C₃×C₅	1	4	yes	—
565	#123	C₂²×C₃×C₅	1	4	yes	—
566	#123	C₂²×C₃×C₅	1	4	yes	complemented
567	#123	C₂²×C₃×C₅	1	2	yes	complemented
568	#123	C₂²×C₃×C₅	1	4	yes	complemented
569	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
570	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
571	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
572	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
573	C₂²⋊Q₈	C₂²×C₃×C₅	1	4	yes	complemented
574	#121	C₂²×C₃×C₅	1	2	yes	—
575	#121	C₂²×C₃×C₅	1	2	yes	—
576	#121	C₂²×C₃×C₅	1	2	yes	—
577	#121	C₂²×C₃×C₅	1	2	yes	—
578	#121	C₂²×C₃×C₅	1	4	yes	—
579	#121	C₂²×C₃×C₅	1	2	yes	complemented
580	#121	C₂²×C₃×C₅	1	4	yes	complemented
581	#121	C₂²×C₃×C₅	1	4	yes	complemented
582	#121	C₂²×C₃×C₅	1	4	yes	complemented
583	#121	C₂²×C₃×C₅	1	4	yes	complemented
584	#121	C₂²×C₃×C₅	1	4	yes	complemented
585	#120	C₂²×C₃×C₅	1	2	yes	—
586	#120	C₂²×C₃×C₅	1	2	yes	—
587	#120	C₂²×C₃×C₅	1	4	yes	—
588	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
589	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
590	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
591	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
592	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
593	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
594	C₄×D₄	C₂²×C₃×C₅	1	4	yes	complemented
595	#117	C₂²×C₃×C₅	1	1	yes	characteristic
596	#117	C₂²×C₃×C₅	1	4	yes	complemented
597	#117	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
598	#117	C₂²×C₃×C₅	1	4	yes	complemented
599	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
600	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
601	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
602	C₂×C₃×C₅	—	4	1	no	—
603	C₂×C₃×C₅	—	4	2	no	—
604	C₂×C₃×C₅	—	4	1	no	—
605	C₂×C₃×C₅	—	4	4	no	—
606	C₂×C₃×C₅	—	4	1	no	—
607	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
608	C₂×C₃×C₅	#585	1	2	yes	—
609	C₂³×C₃	—	4	2	no	—
610	C₂³×C₃	—	4	4	no	—
611	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
612	C₂³×C₃	C₂⁴×C₅	1	4	yes	—
613	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
614	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
615	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
616	C₃×Q₈	—	2	4	no	—
617	C₃×Q₈	—	4	2	no	—
618	C₃×Q₈	—	4	1	no	—
619	C₃×Q₈	—	4	1	no	—
620	C₃×D₄	—	2	4	no	—
621	C₃×D₄	—	4	2	no	—
622	C₃×D₄	—	4	4	no	—
623	C₃×D₄	—	4	2	no	—
624	C₃×D₄	—	4	4	no	—
625	C₃×D₄	—	4	4	no	—
626	C₃×D₄	—	4	2	no	—
627	C₃×D₄	—	4	2	no	—
628	C₃×D₄	—	4	1	no	—
629	C₃×D₄	—	4	1	no	—
630	C₃×D₄	—	4	1	no	—
631	C₃×D₄	—	4	1	no	—
632	C₃×D₄	—	4	4	no	—
633	C₂×C₃×C₄	—	2	2	no	—
634	C₂×C₃×C₄	—	2	2	no	—
635	C₂×C₃×C₄	—	2	4	no	—
636	C₂×C₃×C₄	—	2	2	no	—
637	C₂×C₃×C₄	—	4	4	no	—
638	C₂×C₃×C₄	—	4	2	no	—
639	C₂×C₃×C₄	—	4	4	no	—
640	C₂×C₃×C₄	—	4	2	no	—
641	C₂×C₃×C₄	—	4	4	no	—
642	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
643	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
644	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
645	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
646	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
647	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
648	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
649	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
650	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
651	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
652	C₂²×C₅	—	2	1	no	—
653	C₂²×C₅	—	2	2	no	—
654	C₂²×C₅	—	2	1	no	—
655	C₂²×C₅	—	2	1	no	—
656	C₂²×C₅	—	2	4	no	—
657	C₂²×C₅	—	2	2	no	—
658	C₂²×C₅	—	2	2	no	—
659	C₂²×C₅	—	2	4	no	—
660	C₂²×C₅	—	2	2	no	—
661	C₂²×C₅	—	2	2	no	—
662	C₂²×C₅	—	2	4	no	—
663	C₂²×C₅	—	2	2	no	—
664	C₂²×C₅	—	8	4	no	—
665	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
666	C₄×C₅	—	2	2	no	—
667	C₄×C₅	—	2	1	no	—
668	C₄×C₅	—	2	1	no	—
669	C₄×C₅	—	2	1	no	—
670	C₄×C₅	—	2	4	no	—
671	C₄×C₅	—	2	2	no	—
672	C₄×C₅	—	2	4	no	—
673	C₄×C₅	—	2	2	no	—
674	C₄×C₅	—	2	4	no	—
675	C₄×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
676	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
677	#41	—	4	2	no	—
678	#41	—	4	2	no	—
679	#41	—	4	4	no	—
680	C₂×Q₈	—	4	2	no	—
681	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
682	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
683	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
684	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
685	C₂×D₄	—	4	2	no	—
686	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
687	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
688	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
689	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
690	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
691	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
692	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
693	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
694	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
695	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
696	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
697	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
698	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
699	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
700	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
701	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
702	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
703	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
704	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
705	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
706	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
707	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
708	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
709	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
710	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
711	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
712	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
713	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
714	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
715	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
716	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
717	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
718	C₄⋊C₄	C₂³×C₃×C₅	1	4	yes	—
719	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
720	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
721	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
722	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
723	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
724	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
725	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
726	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
727	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
728	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
729	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
730	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
731	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
732	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
733	C₂²⋊C₄	C₂³×C₃×C₅	1	4	yes	—
734	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
735	C₄²	C₂³×C₃×C₅	1	2	yes	—
736	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
737	C₄²	C₂³×C₃×C₅	1	2	yes	—
738	C₄²	C₂³×C₃×C₅	1	4	yes	—
739	C₄²	C₂³×C₃×C₅	1	2	yes	—
740	C₃×C₅	#3551	1	1	yes	characteristic, direct product factor, Hall
741	C₂²×C₃	—	2	1	no	—
742	C₂²×C₃	—	2	2	no	—
743	C₂²×C₃	—	2	1	no	—
744	C₂²×C₃	—	2	1	no	—
745	C₂²×C₃	—	2	4	no	—
746	C₂²×C₃	—	2	2	no	—
747	C₂²×C₃	—	2	2	no	—
748	C₂²×C₃	—	2	4	no	—
749	C₂²×C₃	—	2	2	no	—
750	C₂²×C₃	—	2	2	no	—
751	C₂²×C₃	—	2	4	no	—
752	C₂²×C₃	—	2	2	no	—
753	C₂²×C₃	—	8	4	no	—
754	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
755	C₃×C₄	—	2	2	no	—
756	C₃×C₄	—	2	1	no	—
757	C₃×C₄	—	2	1	no	—
758	C₃×C₄	—	2	1	no	—
759	C₃×C₄	—	2	4	no	—
760	C₃×C₄	—	2	2	no	—
761	C₃×C₄	—	2	4	no	—
762	C₃×C₄	—	2	2	no	—
763	C₃×C₄	—	2	4	no	—
764	C₃×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
765	C₂×C₅	—	4	1	no	—
766	C₂×C₅	—	4	4	no	—
767	C₂×C₅	—	4	1	no	—
768	C₂×C₅	—	4	2	no	—
769	C₂×C₅	—	4	1	no	—
770	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
771	C₂×C₅	C₃×#585	1	2	yes	—
772	C₂³	—	4	2	no	—
773	C₂³	—	4	4	no	—
774	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
775	C₂³	C₂⁴×C₃×C₅	1	4	yes	—
776	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
777	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
778	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
779	Q₈	—	2	4	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	4	1	no	—
782	Q₈	—	4	1	no	—
783	D₄	—	2	4	no	—
784	D₄	—	4	2	no	—
785	D₄	—	4	2	no	—
786	D₄	—	4	1	no	—
787	D₄	—	4	1	no	—
788	D₄	—	4	1	no	—
789	D₄	—	4	1	no	—
790	D₄	—	4	4	no	—
791	D₄	—	4	4	no	—
792	D₄	—	4	2	no	—
793	D₄	—	4	4	no	—
794	D₄	—	4	4	no	—
795	D₄	—	4	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	4	2	no	—
801	C₂×C₄	—	4	4	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	2	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
806	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
807	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
808	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
809	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
810	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
811	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
812	C₂×C₄	C₂⁴×C₃×C₅	1	4	yes	—
813	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
814	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
815	C₂×C₃	—	4	1	no	—
816	C₂×C₃	—	4	4	no	—
817	C₂×C₃	—	4	1	no	—
818	C₂×C₃	—	4	2	no	—
819	C₂×C₃	—	4	1	no	—
820	C₂×C₃	C₂×C₅×H(5,𝔽₂)	1	1	yes	characteristic
821	C₂×C₃	C₅×#585	1	2	yes	—
822	C₅	C₃×#3551	1	1	yes	characteristic, direct product factor, Sylow
823	C₂²	—	2	1	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	1	no	—
826	C₂²	—	2	1	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	4	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	4	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	8	4	no	—
836	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
837	C₄	—	2	2	no	—
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	4	no	—
842	C₄	—	2	2	no	—
843	C₄	—	2	4	no	—
844	C₄	—	2	2	no	—
845	C₄	—	2	4	no	—
846	C₄	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
847	C₃	C₅×#3551	1	1	yes	characteristic, direct product factor, Sylow
848	C₂	—	4	1	no	—
849	C₂	—	4	4	no	—
850	C₂	—	4	1	no	—
851	C₂	—	4	2	no	—
852	C₂	—	4	1	no	—
853	C₂	C₂×C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
854	C₂	C₃×C₅×#585	1	2	yes	—

	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×#563	C₂	semidirect
2. C₃×C₅×#560	C₂	semidirect
3. C₃×C₅×#555	C₂	semidirect
4. C₃×C₅×#553	C₂	semidirect
5. C₃×C₅×#552	C₂	semidirect
6. C₃×C₅×#551	C₂	semidirect
7. C₃×C₅×#548	C₂	semidirect
8. C₃×C₅×#546	C₂	semidirect
9. C₃×C₅×#540	C₂	semidirect
10. C₃×C₅×#538	C₂	semidirect
11. C₃×C₅×#537	C₂	semidirect
12. C₃×C₅×#536	C₂	semidirect
13. C₃×C₅×#535	C₂	semidirect
14. C₃×C₅×#532	C₂	semidirect
15. C₃×C₅×#529	C₂	semidirect
16. C₅×#3551	C₃	direct (N × H)
19. C₂×C₃×C₅×#41	C₂²	semidirect
20. C₂²×C₃×C₅×Q₈	C₂²	semidirect
22. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
27. C₃×C₅×#126	C₂²	semidirect
28. C₃×C₅×#126	C₂²	semidirect
29. C₃×C₅×#125	C₂²	semidirect
30. C₃×C₅×#125	C₂²	semidirect
35. C₃×C₅×#124	C₂²	semidirect
36. C₃×C₅×#124	C₂²	semidirect
40. C₃×C₅×#123	C₂²	semidirect
41. C₃×C₅×#123	C₂²	semidirect
42. C₃×C₅×#123	C₂²	semidirect
44. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
45. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
46. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
47. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
53. C₃×C₅×#121	C₂²	semidirect
54. C₃×C₅×#121	C₂²	semidirect
55. C₃×C₅×#121	C₂²	semidirect
56. C₃×C₅×#121	C₂²	semidirect
57. C₃×C₅×#121	C₂²	semidirect
58. C₃×C₅×#121	C₂²	semidirect
62. C₃×C₄×C₅×Q₈	C₂²	semidirect
65. C₃×C₄×C₅×D₄	C₂²	semidirect
66. C₃×C₄×C₅×D₄	C₂²	semidirect
67. C₃×C₄×C₅×D₄	C₂²	semidirect
68. C₃×C₄×C₅×D₄	C₂²	semidirect
70. C₃×C₅×#117	C₂²	semidirect
71. C₃×C₅×#117	C₂²	semidirect
72. C₃×C₅×#117	C₂²	semidirect
73. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
75. C₂×C₃×C₄²×C₅	C₂²	semidirect
76. C₃×#3551	C₅	direct (N × H)
77. C₅×#563	C₂×C₃	semidirect
78. C₅×#560	C₂×C₃	semidirect
79. C₅×#555	C₂×C₃	semidirect
80. C₅×#553	C₂×C₃	semidirect
81. C₅×#552	C₂×C₃	semidirect
82. C₅×#551	C₂×C₃	semidirect
83. C₅×#548	C₂×C₃	semidirect
84. C₅×#546	C₂×C₃	semidirect
85. C₅×#540	C₂×C₃	semidirect
86. C₅×#538	C₂×C₃	semidirect
87. C₅×#537	C₂×C₃	semidirect
88. C₅×#536	C₂×C₃	semidirect
89. C₅×#535	C₂×C₃	semidirect
90. C₅×#532	C₂×C₃	semidirect
91. C₅×#529	C₂×C₃	semidirect
156. C₃×#563	C₂×C₅	semidirect
157. C₃×#560	C₂×C₅	semidirect
158. C₃×#555	C₂×C₅	semidirect
159. C₃×#553	C₂×C₅	semidirect
160. C₃×#552	C₂×C₅	semidirect
161. C₃×#551	C₂×C₅	semidirect
162. C₃×#548	C₂×C₅	semidirect
163. C₃×#546	C₂×C₅	semidirect
164. C₃×#540	C₂×C₅	semidirect
165. C₃×#538	C₂×C₅	semidirect
166. C₃×#537	C₂×C₅	semidirect
167. C₃×#536	C₂×C₅	semidirect
168. C₃×#535	C₂×C₅	semidirect
169. C₃×#532	C₂×C₅	semidirect
170. C₃×#529	C₂×C₅	semidirect
173. C₂×C₅×#41	C₂²×C₃	semidirect
174. C₂²×C₅×Q₈	C₂²×C₃	semidirect
176. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
177. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
181. C₅×#126	C₂²×C₃	semidirect
182. C₅×#126	C₂²×C₃	semidirect
183. C₅×#125	C₂²×C₃	semidirect
184. C₅×#125	C₂²×C₃	semidirect
189. C₅×#124	C₂²×C₃	semidirect
190. C₅×#124	C₂²×C₃	semidirect
194. C₅×#123	C₂²×C₃	semidirect
195. C₅×#123	C₂²×C₃	semidirect
196. C₅×#123	C₂²×C₃	semidirect
198. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
199. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
200. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
201. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
207. C₅×#121	C₂²×C₃	semidirect
208. C₅×#121	C₂²×C₃	semidirect
209. C₅×#121	C₂²×C₃	semidirect
210. C₅×#121	C₂²×C₃	semidirect
211. C₅×#121	C₂²×C₃	semidirect
212. C₅×#121	C₂²×C₃	semidirect
216. C₄×C₅×Q₈	C₂²×C₃	semidirect
219. C₄×C₅×D₄	C₂²×C₃	semidirect
220. C₄×C₅×D₄	C₂²×C₃	semidirect
221. C₄×C₅×D₄	C₂²×C₃	semidirect
222. C₄×C₅×D₄	C₂²×C₃	semidirect
224. C₅×#117	C₂²×C₃	semidirect
225. C₅×#117	C₂²×C₃	semidirect
226. C₅×#117	C₂²×C₃	semidirect
227. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
229. C₂×C₄²×C₅	C₂²×C₃	semidirect
230. #3551	C₃×C₅	direct (N × H)
276. C₂×C₃×#41	C₂²×C₅	semidirect
277. C₂²×C₃×Q₈	C₂²×C₅	semidirect
279. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
280. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
284. C₃×#126	C₂²×C₅	semidirect
285. C₃×#126	C₂²×C₅	semidirect
286. C₃×#125	C₂²×C₅	semidirect
287. C₃×#125	C₂²×C₅	semidirect
292. C₃×#124	C₂²×C₅	semidirect
293. C₃×#124	C₂²×C₅	semidirect
297. C₃×#123	C₂²×C₅	semidirect
298. C₃×#123	C₂²×C₅	semidirect
299. C₃×#123	C₂²×C₅	semidirect
301. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
302. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
303. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
304. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
310. C₃×#121	C₂²×C₅	semidirect
311. C₃×#121	C₂²×C₅	semidirect
312. C₃×#121	C₂²×C₅	semidirect
313. C₃×#121	C₂²×C₅	semidirect
314. C₃×#121	C₂²×C₅	semidirect
315. C₃×#121	C₂²×C₅	semidirect
319. C₃×C₄×Q₈	C₂²×C₅	semidirect
322. C₃×C₄×D₄	C₂²×C₅	semidirect
323. C₃×C₄×D₄	C₂²×C₅	semidirect
324. C₃×C₄×D₄	C₂²×C₅	semidirect
325. C₃×C₄×D₄	C₂²×C₅	semidirect
327. C₃×#117	C₂²×C₅	semidirect
328. C₃×#117	C₂²×C₅	semidirect
329. C₃×#117	C₂²×C₅	semidirect
330. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
332. C₂×C₃×C₄²	C₂²×C₅	semidirect
397. #563	C₂×C₃×C₅	semidirect
398. #560	C₂×C₃×C₅	semidirect
399. #555	C₂×C₃×C₅	semidirect
400. #553	C₂×C₃×C₅	semidirect
401. #552	C₂×C₃×C₅	semidirect
402. #551	C₂×C₃×C₅	semidirect
403. #548	C₂×C₃×C₅	semidirect
404. #546	C₂×C₃×C₅	semidirect
405. #540	C₂×C₃×C₅	semidirect
406. #538	C₂×C₃×C₅	semidirect
407. #537	C₂×C₃×C₅	semidirect
408. #536	C₂×C₃×C₅	semidirect
409. #535	C₂×C₃×C₅	semidirect
410. #532	C₂×C₃×C₅	semidirect
411. #529	C₂×C₃×C₅	semidirect
545. C₂×#41	C₂²×C₃×C₅	semidirect
546. C₂²×Q₈	C₂²×C₃×C₅	semidirect
548. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
549. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
553. #126	C₂²×C₃×C₅	semidirect
554. #126	C₂²×C₃×C₅	semidirect
555. #125	C₂²×C₃×C₅	semidirect
556. #125	C₂²×C₃×C₅	semidirect
561. #124	C₂²×C₃×C₅	semidirect
562. #124	C₂²×C₃×C₅	semidirect
566. #123	C₂²×C₃×C₅	semidirect
567. #123	C₂²×C₃×C₅	semidirect
568. #123	C₂²×C₃×C₅	semidirect
570. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
571. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
572. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
573. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
579. #121	C₂²×C₃×C₅	semidirect
580. #121	C₂²×C₃×C₅	semidirect
581. #121	C₂²×C₃×C₅	semidirect
582. #121	C₂²×C₃×C₅	semidirect
583. #121	C₂²×C₃×C₅	semidirect
584. #121	C₂²×C₃×C₅	semidirect
588. C₄×Q₈	C₂²×C₃×C₅	semidirect
591. C₄×D₄	C₂²×C₃×C₅	semidirect
592. C₄×D₄	C₂²×C₃×C₅	semidirect
593. C₄×D₄	C₂²×C₃×C₅	semidirect
594. C₄×D₄	C₂²×C₃×C₅	semidirect
596. #117	C₂²×C₃×C₅	semidirect
597. #117	C₂²×C₃×C₅	semidirect
598. #117	C₂²×C₃×C₅	semidirect
599. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
601. C₂×C₄²	C₂²×C₃×C₅	semidirect
740. C₃×C₅	#3551	direct (N × H)
822. C₅	C₃×#3551	direct (N × H)
847. C₃	C₅×#3551	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×#563	2
C₃×C₅×#560	2
C₃×C₅×#555	2
C₃×C₅×#553	2
C₃×C₅×#552	2
C₃×C₅×#551	2
C₃×C₅×#548	2
C₃×C₅×#546	2
C₃×C₅×#540	2
C₃×C₅×#538	2
C₃×C₅×#537	2
C₃×C₅×#536	2
C₃×C₅×#535	2
C₃×C₅×#532	2
C₃×C₅×#529	2
C₅×#3551	3
C₃×#3551	5

Subgroups — C3×C5×#3551 #14276585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3551 #14276585