Subgroups — C₃×C₅×#3564 #14276598

Order 1920.

1872 conjugacy classes of subgroups.

The subgroup lattice has 1084 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×#563	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#556	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#554	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#552	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#551	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#544	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#542	C₂	1	2	yes	maximal, complemented
12	C₃×C₅×#541	C₂	1	2	yes	maximal, complemented
13	C₃×C₅×#541	C₂	1	2	yes	maximal, complemented
14	C₃×C₅×#539	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#539	C₂	1	2	yes	maximal, complemented
16	C₃×C₅×#538	C₂	1	1	yes	maximal, characteristic
17	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
18	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₃×C₅×#126	C₂	1	1	yes	maximal, characteristic, complemented
20	C₅×#3564	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
24	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
25	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
26	C₃×C₅×#126	C₂²	1	2	yes	—
27	C₃×C₅×#126	C₂²	1	2	yes	—
28	C₃×C₅×#126	C₂²	1	2	yes	—
29	C₃×C₅×#126	C₂²	1	2	yes	—
30	C₃×C₅×#126	C₂²	1	2	yes	—
31	C₃×C₅×#126	C₂²	1	2	yes	—
32	C₃×C₅×#126	C₂²	1	2	yes	—
33	C₃×C₅×#126	C₂²	1	2	yes	—
34	C₃×C₅×#126	C₂²	1	2	yes	—
35	C₃×C₅×#126	C₂²	1	2	yes	complemented
36	C₃×C₅×#126	C₂²	1	2	yes	complemented
37	C₃×C₅×#126	C₂²	1	2	yes	complemented
38	C₃×C₅×#126	C₂²	1	2	yes	complemented
39	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
40	C₃×C₅×#125	C₂²	1	2	yes	complemented
41	C₃×C₅×#125	C₂²	1	2	yes	complemented
42	C₃×C₅×#125	C₂²	1	2	yes	complemented
43	C₃×C₅×#125	C₂²	1	2	yes	complemented
44	C₃×C₅×#125	C₂²	1	2	yes	complemented
45	C₃×C₅×#125	C₂²	1	2	yes	complemented
46	C₃×C₅×#125	C₂²	1	2	yes	complemented
47	C₃×C₅×#125	C₂²	1	2	yes	complemented
48	C₃×C₅×#125	C₂²	1	2	yes	complemented
49	C₃×C₅×#124	C₂²	1	2	yes	—
50	C₃×C₅×#124	C₂²	1	2	yes	—
51	C₃×C₅×#124	C₂²	1	2	yes	—
52	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
53	C₃×C₅×#123	C₂²	1	2	yes	—
54	C₃×C₅×#123	C₂²	1	2	yes	—
55	C₃×C₅×#123	C₂²	1	2	yes	—
56	C₃×C₅×#123	C₂²	1	2	yes	—
57	C₃×C₅×#123	C₂²	1	2	yes	—
58	C₃×C₅×#123	C₂²	1	2	yes	—
59	C₃×C₅×#123	C₂²	1	2	yes	—
60	C₃×C₅×#123	C₂²	1	2	yes	complemented
61	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
62	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
63	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
64	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
65	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
66	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
67	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
68	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
69	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
70	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
71	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
72	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
73	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
74	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
75	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
76	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
77	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	complemented
78	C₃×C₅×#121	C₂²	1	1	yes	characteristic
79	C₃×C₅×#121	C₂²	1	2	yes	—
80	C₃×C₅×#120	C₂²	1	2	yes	—
81	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
82	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
83	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
84	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
86	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
87	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
88	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
89	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
90	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
91	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
92	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
93	C₃×C₅×#117	C₂²	1	2	yes	—
94	C₃×C₅×#117	C₂²	1	2	yes	—
95	C₃×C₅×#117	C₂²	1	2	yes	—
96	C₃×C₅×#117	C₂²	1	2	yes	—
97	C₃×C₅×#117	C₂²	1	2	yes	complemented
98	C₃×C₅×#117	C₂²	1	2	yes	complemented
99	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
100	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
101	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
102	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
103	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
104	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
105	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
106	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
107	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
108	C₃×#3564	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
109	C₅×#563	C₂×C₃	1	2	yes	complemented
110	C₅×#563	C₂×C₃	1	2	yes	complemented
111	C₅×#556	C₂×C₃	1	2	yes	complemented
112	C₅×#554	C₂×C₃	1	2	yes	complemented
113	C₅×#552	C₂×C₃	1	2	yes	complemented
114	C₅×#552	C₂×C₃	1	2	yes	complemented
115	C₅×#551	C₂×C₃	1	2	yes	complemented
116	C₅×#551	C₂×C₃	1	2	yes	complemented
117	C₅×#544	C₂×C₃	1	1	yes	characteristic, complemented
118	C₅×#543	C₂×C₃	1	1	yes	characteristic, complemented
119	C₅×#542	C₂×C₃	1	2	yes	complemented
120	C₅×#541	C₂×C₃	1	2	yes	complemented
121	C₅×#541	C₂×C₃	1	2	yes	complemented
122	C₅×#539	C₂×C₃	1	1	yes	characteristic, complemented
123	C₅×#539	C₂×C₃	1	2	yes	complemented
124	C₅×#538	C₂×C₃	1	1	yes	characteristic
125	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
126	C₅×#529	C₂×C₃	1	1	yes	characteristic, complemented
127	C₂×C₅×#126	C₂×C₃	1	1	yes	characteristic, complemented
128	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
129	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
130	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
131	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
132	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
133	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
134	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
135	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
136	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
137	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
138	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
139	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
140	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
141	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
142	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
143	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
144	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
145	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
146	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
147	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
148	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
149	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
150	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
151	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
152	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
153	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
154	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
155	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
156	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
157	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
161	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
162	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
163	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
164	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
165	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
166	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
167	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
168	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
169	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
170	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
171	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
172	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
175	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
176	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
177	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
178	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×C₂²⋊C₄	C₂³	1	2	yes	—
184	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
185	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
186	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
187	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
188	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
189	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
192	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
193	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
194	C₃×C₅×C₂²⋊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×C₄²×C₅	C₂³	1	1	yes	characteristic
205	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
206	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
207	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
208	C₃×C₄²×C₅	C₂³	1	2	yes	—
209	C₃×C₄²×C₅	C₂³	1	2	yes	—
210	C₃×C₄²×C₅	C₂³	1	2	yes	—
211	C₃×C₄²×C₅	C₂³	1	2	yes	—
212	C₃×C₄²×C₅	C₂³	1	2	yes	—
213	C₃×C₄²×C₅	C₂³	1	2	yes	—
214	C₃×C₄²×C₅	C₂³	1	2	yes	—
215	C₃×#563	C₂×C₅	1	2	yes	complemented
216	C₃×#563	C₂×C₅	1	2	yes	complemented
217	C₃×#556	C₂×C₅	1	2	yes	complemented
218	C₃×#554	C₂×C₅	1	2	yes	complemented
219	C₃×#552	C₂×C₅	1	2	yes	complemented
220	C₃×#552	C₂×C₅	1	2	yes	complemented
221	C₃×#551	C₂×C₅	1	2	yes	complemented
222	C₃×#551	C₂×C₅	1	2	yes	complemented
223	C₃×#544	C₂×C₅	1	1	yes	characteristic, complemented
224	C₃×#543	C₂×C₅	1	1	yes	characteristic, complemented
225	C₃×#542	C₂×C₅	1	2	yes	complemented
226	C₃×#541	C₂×C₅	1	2	yes	complemented
227	C₃×#541	C₂×C₅	1	2	yes	complemented
228	C₃×#539	C₂×C₅	1	1	yes	characteristic, complemented
229	C₃×#539	C₂×C₅	1	2	yes	complemented
230	C₃×#538	C₂×C₅	1	1	yes	characteristic
231	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
232	C₃×#529	C₂×C₅	1	1	yes	characteristic, complemented
233	C₂×C₃×#126	C₂×C₅	1	1	yes	characteristic, complemented
234	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
235	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
236	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
237	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
238	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
239	C₅×#126	C₂²×C₃	1	2	yes	—
240	C₅×#126	C₂²×C₃	1	2	yes	—
241	C₅×#126	C₂²×C₃	1	2	yes	—
242	C₅×#126	C₂²×C₃	1	2	yes	—
243	C₅×#126	C₂²×C₃	1	2	yes	—
244	C₅×#126	C₂²×C₃	1	2	yes	—
245	C₅×#126	C₂²×C₃	1	2	yes	—
246	C₅×#126	C₂²×C₃	1	2	yes	—
247	C₅×#126	C₂²×C₃	1	2	yes	—
248	C₅×#126	C₂²×C₃	1	2	yes	complemented
249	C₅×#126	C₂²×C₃	1	2	yes	complemented
250	C₅×#126	C₂²×C₃	1	2	yes	complemented
251	C₅×#126	C₂²×C₃	1	2	yes	complemented
252	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
253	C₅×#125	C₂²×C₃	1	2	yes	complemented
254	C₅×#125	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×#125	C₂²×C₃	1	2	yes	complemented
258	C₅×#125	C₂²×C₃	1	2	yes	complemented
259	C₅×#125	C₂²×C₃	1	2	yes	complemented
260	C₅×#125	C₂²×C₃	1	2	yes	complemented
261	C₅×#125	C₂²×C₃	1	2	yes	complemented
262	C₅×#124	C₂²×C₃	1	2	yes	—
263	C₅×#124	C₂²×C₃	1	2	yes	—
264	C₅×#124	C₂²×C₃	1	2	yes	—
265	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
266	C₅×#123	C₂²×C₃	1	2	yes	—
267	C₅×#123	C₂²×C₃	1	2	yes	—
268	C₅×#123	C₂²×C₃	1	2	yes	—
269	C₅×#123	C₂²×C₃	1	2	yes	—
270	C₅×#123	C₂²×C₃	1	2	yes	—
271	C₅×#123	C₂²×C₃	1	2	yes	—
272	C₅×#123	C₂²×C₃	1	2	yes	—
273	C₅×#123	C₂²×C₃	1	2	yes	complemented
274	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
275	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
276	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
277	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
278	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
279	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
280	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
281	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
282	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
283	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
284	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
285	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
286	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
287	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
288	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
289	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
290	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	complemented
291	C₅×#121	C₂²×C₃	1	1	yes	characteristic
292	C₅×#121	C₂²×C₃	1	2	yes	—
293	C₅×#120	C₂²×C₃	1	2	yes	—
294	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
295	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
296	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
297	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
298	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
299	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
300	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
301	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
302	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
303	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
304	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
305	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
306	C₅×#117	C₂²×C₃	1	2	yes	—
307	C₅×#117	C₂²×C₃	1	2	yes	—
308	C₅×#117	C₂²×C₃	1	2	yes	—
309	C₅×#117	C₂²×C₃	1	2	yes	—
310	C₅×#117	C₂²×C₃	1	2	yes	complemented
311	C₅×#117	C₂²×C₃	1	2	yes	complemented
312	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
313	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
314	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
315	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
316	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
317	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
318	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
319	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
320	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
321	#3564	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
322	C₂³×C₃×C₅	—	2	2	no	—
323	C₂³×C₃×C₅	—	4	1	no	—
324	C₂³×C₃×C₅	—	4	1	no	—
325	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
326	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
327	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
328	C₃×C₅×Q₈	—	4	1	no	—
329	C₃×C₅×Q₈	—	4	2	no	—
330	C₃×C₅×Q₈	—	4	2	no	—
331	C₃×C₅×Q₈	—	4	1	no	—
332	C₃×C₅×Q₈	—	4	2	no	—
333	C₃×C₅×Q₈	—	4	1	no	—
334	C₃×C₅×D₄	—	2	4	no	—
335	C₃×C₅×D₄	—	4	2	no	—
336	C₃×C₅×D₄	—	4	1	no	—
337	C₃×C₅×D₄	—	4	2	no	—
338	C₂×C₃×C₄×C₅	—	2	2	no	—
339	C₂×C₃×C₄×C₅	—	2	2	no	—
340	C₂×C₃×C₄×C₅	—	4	2	no	—
341	C₂×C₃×C₄×C₅	—	4	1	no	—
342	C₂×C₃×C₄×C₅	—	4	1	no	—
343	C₂×C₃×C₄×C₅	—	4	1	no	—
344	C₂×C₃×C₄×C₅	—	4	2	no	—
345	C₂×C₃×C₄×C₅	—	4	2	no	—
346	C₂×C₃×C₄×C₅	—	4	2	no	—
347	C₂×C₃×C₄×C₅	—	4	2	no	—
348	C₂×C₃×C₄×C₅	—	4	1	no	—
349	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
350	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
351	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
352	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
353	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
354	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
355	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
356	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
357	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
358	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
359	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
360	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
361	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
362	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
363	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
364	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
365	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
366	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
367	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
368	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
369	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
370	C₃×#126	C₂²×C₅	1	2	yes	—
371	C₃×#126	C₂²×C₅	1	2	yes	—
372	C₃×#126	C₂²×C₅	1	2	yes	—
373	C₃×#126	C₂²×C₅	1	2	yes	—
374	C₃×#126	C₂²×C₅	1	2	yes	—
375	C₃×#126	C₂²×C₅	1	2	yes	—
376	C₃×#126	C₂²×C₅	1	2	yes	—
377	C₃×#126	C₂²×C₅	1	2	yes	—
378	C₃×#126	C₂²×C₅	1	2	yes	—
379	C₃×#126	C₂²×C₅	1	2	yes	complemented
380	C₃×#126	C₂²×C₅	1	2	yes	complemented
381	C₃×#126	C₂²×C₅	1	2	yes	complemented
382	C₃×#126	C₂²×C₅	1	2	yes	complemented
383	C₃×#125	C₂²×C₅	1	2	yes	complemented
384	C₃×#125	C₂²×C₅	1	2	yes	complemented
385	C₃×#125	C₂²×C₅	1	2	yes	complemented
386	C₃×#125	C₂²×C₅	1	2	yes	complemented
387	C₃×#125	C₂²×C₅	1	1	yes	characteristic, complemented
388	C₃×#125	C₂²×C₅	1	2	yes	complemented
389	C₃×#125	C₂²×C₅	1	2	yes	complemented
390	C₃×#125	C₂²×C₅	1	2	yes	complemented
391	C₃×#125	C₂²×C₅	1	2	yes	complemented
392	C₃×#125	C₂²×C₅	1	2	yes	complemented
393	C₃×#124	C₂²×C₅	1	2	yes	—
394	C₃×#124	C₂²×C₅	1	2	yes	—
395	C₃×#124	C₂²×C₅	1	2	yes	—
396	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
397	C₃×#123	C₂²×C₅	1	2	yes	—
398	C₃×#123	C₂²×C₅	1	2	yes	—
399	C₃×#123	C₂²×C₅	1	2	yes	—
400	C₃×#123	C₂²×C₅	1	2	yes	—
401	C₃×#123	C₂²×C₅	1	2	yes	—
402	C₃×#123	C₂²×C₅	1	2	yes	—
403	C₃×#123	C₂²×C₅	1	2	yes	—
404	C₃×#123	C₂²×C₅	1	2	yes	complemented
405	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
406	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
407	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
408	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
409	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
410	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
411	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
412	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
413	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
414	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
415	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
416	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
417	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
418	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
419	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
420	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
421	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	complemented
422	C₃×#121	C₂²×C₅	1	1	yes	characteristic
423	C₃×#121	C₂²×C₅	1	2	yes	—
424	C₃×#120	C₂²×C₅	1	2	yes	—
425	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
426	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
427	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
428	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
429	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
430	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
431	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
432	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
433	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
434	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
435	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
436	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
437	C₃×#117	C₂²×C₅	1	2	yes	—
438	C₃×#117	C₂²×C₅	1	2	yes	—
439	C₃×#117	C₂²×C₅	1	2	yes	—
440	C₃×#117	C₂²×C₅	1	2	yes	—
441	C₃×#117	C₂²×C₅	1	2	yes	complemented
442	C₃×#117	C₂²×C₅	1	2	yes	complemented
443	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
444	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
445	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
446	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
447	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
448	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
449	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
450	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
451	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
452	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
453	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
454	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
455	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
456	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
457	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
458	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
459	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
460	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
461	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
462	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
463	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
464	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
465	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
466	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
467	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
468	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
469	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
470	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
471	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
472	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
473	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
474	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
475	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
476	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
477	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
478	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
479	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
480	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
481	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
482	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
483	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
484	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
485	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
486	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
487	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
488	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
489	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
490	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
491	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
492	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
493	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
494	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
495	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
496	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
497	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
498	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
499	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
500	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
501	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
502	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
503	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
504	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
505	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
506	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
507	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
508	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
509	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
510	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
511	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
512	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
513	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
514	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
515	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
516	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
517	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
518	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
519	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
520	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
521	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
522	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
523	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
524	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
525	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
526	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
527	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
528	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
529	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
530	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
531	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
532	C₄²×C₅	C₂³×C₃	1	2	yes	—
533	C₄²×C₅	C₂³×C₃	1	2	yes	—
534	C₄²×C₅	C₂³×C₃	1	2	yes	—
535	C₄²×C₅	C₂³×C₃	1	2	yes	—
536	C₄²×C₅	C₂³×C₃	1	2	yes	—
537	C₄²×C₅	C₂³×C₃	1	2	yes	—
538	C₄²×C₅	C₂³×C₃	1	2	yes	—
539	#563	C₂×C₃×C₅	1	2	yes	complemented
540	#563	C₂×C₃×C₅	1	2	yes	complemented
541	#556	C₂×C₃×C₅	1	2	yes	complemented
542	#554	C₂×C₃×C₅	1	2	yes	complemented
543	#552	C₂×C₃×C₅	1	2	yes	complemented
544	#552	C₂×C₃×C₅	1	2	yes	complemented
545	#551	C₂×C₃×C₅	1	2	yes	complemented
546	#551	C₂×C₃×C₅	1	2	yes	complemented
547	#544	C₂×C₃×C₅	1	1	yes	characteristic, complemented
548	#543	C₂×C₃×C₅	1	1	yes	characteristic, complemented
549	#542	C₂×C₃×C₅	1	2	yes	complemented
550	#541	C₂×C₃×C₅	1	2	yes	complemented
551	#541	C₂×C₃×C₅	1	2	yes	complemented
552	#539	C₂×C₃×C₅	1	1	yes	characteristic, complemented
553	#539	C₂×C₃×C₅	1	2	yes	complemented
554	#538	C₂×C₃×C₅	1	1	yes	characteristic
555	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
556	#529	C₂×C₃×C₅	1	1	yes	characteristic, complemented
557	C₂×#126	C₂×C₃×C₅	1	1	yes	characteristic, complemented
558	C₂²×C₃×C₅	—	2	1	no	—
559	C₂²×C₃×C₅	—	2	1	no	—
560	C₂²×C₃×C₅	—	2	2	no	—
561	C₂²×C₃×C₅	—	2	2	no	—
562	C₂²×C₃×C₅	—	2	2	no	—
563	C₂²×C₃×C₅	—	2	2	no	—
564	C₂²×C₃×C₅	—	2	2	no	—
565	C₂²×C₃×C₅	—	2	2	no	—
566	C₂²×C₃×C₅	—	8	2	no	—
567	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
568	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
569	C₃×C₄×C₅	—	2	1	no	—
570	C₃×C₄×C₅	—	2	1	no	—
571	C₃×C₄×C₅	—	2	2	no	—
572	C₃×C₄×C₅	—	2	2	no	—
573	C₃×C₄×C₅	—	2	1	no	—
574	C₃×C₄×C₅	—	2	2	no	—
575	C₃×C₄×C₅	—	2	2	no	—
576	C₃×C₄×C₅	—	2	2	no	—
577	C₃×C₄×C₅	—	2	2	no	—
578	C₃×C₄×C₅	—	2	2	no	—
579	C₃×C₄×C₅	—	2	1	no	—
580	C₃×C₄×C₅	—	2	1	no	—
581	C₃×C₄×C₅	—	2	2	no	—
582	C₃×C₄×C₅	—	2	2	no	—
583	C₃×C₄×C₅	—	2	1	no	—
584	C₃×C₄×C₅	—	2	2	no	—
585	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
586	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
587	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
588	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
589	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
590	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
591	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
592	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
593	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
594	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
595	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
596	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
597	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
598	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
599	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
600	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
601	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
602	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
603	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
604	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
605	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
606	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
607	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
608	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
609	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
610	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
611	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
612	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
613	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
614	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
615	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
616	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
617	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
618	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
619	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
620	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
621	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
622	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
623	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
624	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
625	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
626	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
627	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
628	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
629	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
630	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
631	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
632	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
633	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
634	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
635	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
636	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
637	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
638	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
639	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
640	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
641	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
642	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
643	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
644	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
645	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
646	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
647	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
648	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
649	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
650	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
651	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
652	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
653	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
654	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
655	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
656	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
657	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
658	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
659	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
660	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
661	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
662	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
663	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
664	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
665	C₃×C₄²	C₂³×C₅	1	2	yes	—
666	C₃×C₄²	C₂³×C₅	1	2	yes	—
667	C₃×C₄²	C₂³×C₅	1	2	yes	—
668	C₃×C₄²	C₂³×C₅	1	2	yes	—
669	C₃×C₄²	C₂³×C₅	1	2	yes	—
670	C₃×C₄²	C₂³×C₅	1	2	yes	—
671	C₃×C₄²	C₂³×C₅	1	2	yes	—
672	C₂³×C₅	—	2	2	no	—
673	C₂³×C₅	—	4	1	no	—
674	C₂³×C₅	—	4	1	no	—
675	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
676	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
677	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
678	C₅×Q₈	—	4	1	no	—
679	C₅×Q₈	—	4	2	no	—
680	C₅×Q₈	—	4	2	no	—
681	C₅×Q₈	—	4	1	no	—
682	C₅×Q₈	—	4	2	no	—
683	C₅×Q₈	—	4	1	no	—
684	C₅×D₄	—	2	4	no	—
685	C₅×D₄	—	4	2	no	—
686	C₅×D₄	—	4	1	no	—
687	C₅×D₄	—	4	2	no	—
688	C₂×C₄×C₅	—	2	2	no	—
689	C₂×C₄×C₅	—	2	2	no	—
690	C₂×C₄×C₅	—	4	2	no	—
691	C₂×C₄×C₅	—	4	1	no	—
692	C₂×C₄×C₅	—	4	1	no	—
693	C₂×C₄×C₅	—	4	1	no	—
694	C₂×C₄×C₅	—	4	2	no	—
695	C₂×C₄×C₅	—	4	2	no	—
696	C₂×C₄×C₅	—	4	2	no	—
697	C₂×C₄×C₅	—	4	2	no	—
698	C₂×C₄×C₅	—	4	1	no	—
699	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
700	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
701	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
702	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
703	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
704	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
705	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
706	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
707	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
708	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
709	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
710	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
711	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
712	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
713	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
714	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
715	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
716	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
717	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
718	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
719	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
720	#126	C₂²×C₃×C₅	1	2	yes	—
721	#126	C₂²×C₃×C₅	1	2	yes	—
722	#126	C₂²×C₃×C₅	1	2	yes	—
723	#126	C₂²×C₃×C₅	1	2	yes	—
724	#126	C₂²×C₃×C₅	1	2	yes	—
725	#126	C₂²×C₃×C₅	1	2	yes	—
726	#126	C₂²×C₃×C₅	1	2	yes	—
727	#126	C₂²×C₃×C₅	1	2	yes	—
728	#126	C₂²×C₃×C₅	1	2	yes	—
729	#126	C₂²×C₃×C₅	1	2	yes	complemented
730	#126	C₂²×C₃×C₅	1	2	yes	complemented
731	#126	C₂²×C₃×C₅	1	2	yes	complemented
732	#126	C₂²×C₃×C₅	1	2	yes	complemented
733	#125	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
734	#125	C₂²×C₃×C₅	1	2	yes	complemented
735	#125	C₂²×C₃×C₅	1	2	yes	complemented
736	#125	C₂²×C₃×C₅	1	2	yes	complemented
737	#125	C₂²×C₃×C₅	1	2	yes	complemented
738	#125	C₂²×C₃×C₅	1	2	yes	complemented
739	#125	C₂²×C₃×C₅	1	2	yes	complemented
740	#125	C₂²×C₃×C₅	1	2	yes	complemented
741	#125	C₂²×C₃×C₅	1	2	yes	complemented
742	#125	C₂²×C₃×C₅	1	2	yes	complemented
743	#124	C₂²×C₃×C₅	1	2	yes	—
744	#124	C₂²×C₃×C₅	1	2	yes	—
745	#124	C₂²×C₃×C₅	1	2	yes	—
746	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
747	#123	C₂²×C₃×C₅	1	2	yes	—
748	#123	C₂²×C₃×C₅	1	2	yes	—
749	#123	C₂²×C₃×C₅	1	2	yes	—
750	#123	C₂²×C₃×C₅	1	2	yes	—
751	#123	C₂²×C₃×C₅	1	2	yes	—
752	#123	C₂²×C₃×C₅	1	2	yes	—
753	#123	C₂²×C₃×C₅	1	2	yes	—
754	#123	C₂²×C₃×C₅	1	2	yes	complemented
755	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
756	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
759	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
760	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
761	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
762	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
763	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
764	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
765	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
766	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
767	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
768	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
769	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
770	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
771	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
772	#121	C₂²×C₃×C₅	1	1	yes	characteristic
773	#121	C₂²×C₃×C₅	1	2	yes	—
774	#120	C₂²×C₃×C₅	1	2	yes	—
775	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
776	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
777	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
778	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
779	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
780	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	complemented
781	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
782	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
783	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
784	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
785	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
786	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
787	#117	C₂²×C₃×C₅	1	2	yes	—
788	#117	C₂²×C₃×C₅	1	2	yes	—
789	#117	C₂²×C₃×C₅	1	2	yes	—
790	#117	C₂²×C₃×C₅	1	2	yes	—
791	#117	C₂²×C₃×C₅	1	2	yes	complemented
792	#117	C₂²×C₃×C₅	1	2	yes	complemented
793	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
794	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
795	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
796	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
797	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
798	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
799	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
800	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
801	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
802	C₂×C₃×C₅	—	2	2	no	—
803	C₂×C₃×C₅	—	4	2	no	—
804	C₂×C₃×C₅	—	4	2	no	—
805	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
806	C₂×C₃×C₅	#585	1	1	yes	characteristic
807	C₂×C₃×C₅	#585	1	1	yes	characteristic
808	C₂³×C₃	—	2	2	no	—
809	C₂³×C₃	—	4	1	no	—
810	C₂³×C₃	—	4	1	no	—
811	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
812	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
813	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
814	C₃×Q₈	—	4	1	no	—
815	C₃×Q₈	—	4	2	no	—
816	C₃×Q₈	—	4	2	no	—
817	C₃×Q₈	—	4	1	no	—
818	C₃×Q₈	—	4	2	no	—
819	C₃×Q₈	—	4	1	no	—
820	C₃×D₄	—	2	4	no	—
821	C₃×D₄	—	4	2	no	—
822	C₃×D₄	—	4	1	no	—
823	C₃×D₄	—	4	2	no	—
824	C₂×C₃×C₄	—	2	2	no	—
825	C₂×C₃×C₄	—	2	2	no	—
826	C₂×C₃×C₄	—	4	2	no	—
827	C₂×C₃×C₄	—	4	1	no	—
828	C₂×C₃×C₄	—	4	1	no	—
829	C₂×C₃×C₄	—	4	1	no	—
830	C₂×C₃×C₄	—	4	2	no	—
831	C₂×C₃×C₄	—	4	2	no	—
832	C₂×C₃×C₄	—	4	2	no	—
833	C₂×C₃×C₄	—	4	2	no	—
834	C₂×C₃×C₄	—	4	1	no	—
835	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
836	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
837	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
838	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
839	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
840	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
841	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
842	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
843	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
844	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
845	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
846	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
847	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
848	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
849	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
850	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
851	C₂²×C₅	—	2	1	no	—
852	C₂²×C₅	—	2	1	no	—
853	C₂²×C₅	—	2	2	no	—
854	C₂²×C₅	—	2	2	no	—
855	C₂²×C₅	—	2	2	no	—
856	C₂²×C₅	—	2	2	no	—
857	C₂²×C₅	—	2	2	no	—
858	C₂²×C₅	—	2	2	no	—
859	C₂²×C₅	—	8	2	no	—
860	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
861	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
862	C₄×C₅	—	2	1	no	—
863	C₄×C₅	—	2	1	no	—
864	C₄×C₅	—	2	2	no	—
865	C₄×C₅	—	2	2	no	—
866	C₄×C₅	—	2	1	no	—
867	C₄×C₅	—	2	2	no	—
868	C₄×C₅	—	2	2	no	—
869	C₄×C₅	—	2	2	no	—
870	C₄×C₅	—	2	2	no	—
871	C₄×C₅	—	2	2	no	—
872	C₄×C₅	—	2	1	no	—
873	C₄×C₅	—	2	1	no	—
874	C₄×C₅	—	2	2	no	—
875	C₄×C₅	—	2	2	no	—
876	C₄×C₅	—	2	1	no	—
877	C₄×C₅	—	2	2	no	—
878	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
879	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
880	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
881	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
882	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
883	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
884	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
885	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
886	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
887	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
888	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
889	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
890	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
891	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
892	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
893	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
894	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
895	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
896	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
897	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
898	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
899	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
900	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
901	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
902	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
903	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
904	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
905	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
906	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
907	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
908	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
909	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
910	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
911	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
912	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
913	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
914	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
915	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
916	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
917	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
918	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
919	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
920	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
921	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
922	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
923	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
924	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
925	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
926	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
927	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
928	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
929	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
930	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
931	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
932	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
933	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
934	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
935	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
936	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
937	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
938	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
939	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
940	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
941	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
942	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
943	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
944	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
945	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
946	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
947	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
948	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
949	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
950	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
951	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
952	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
953	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
954	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
955	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
956	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
957	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
958	C₄²	C₂³×C₃×C₅	1	2	yes	—
959	C₄²	C₂³×C₃×C₅	1	2	yes	—
960	C₄²	C₂³×C₃×C₅	1	2	yes	—
961	C₄²	C₂³×C₃×C₅	1	2	yes	—
962	C₄²	C₂³×C₃×C₅	1	2	yes	—
963	C₄²	C₂³×C₃×C₅	1	2	yes	—
964	C₄²	C₂³×C₃×C₅	1	2	yes	—
965	C₃×C₅	#3564	1	1	yes	characteristic, direct product factor, Hall
966	C₂²×C₃	—	2	1	no	—
967	C₂²×C₃	—	2	1	no	—
968	C₂²×C₃	—	2	2	no	—
969	C₂²×C₃	—	2	2	no	—
970	C₂²×C₃	—	2	2	no	—
971	C₂²×C₃	—	2	2	no	—
972	C₂²×C₃	—	2	2	no	—
973	C₂²×C₃	—	2	2	no	—
974	C₂²×C₃	—	8	2	no	—
975	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
976	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
977	C₃×C₄	—	2	1	no	—
978	C₃×C₄	—	2	1	no	—
979	C₃×C₄	—	2	2	no	—
980	C₃×C₄	—	2	2	no	—
981	C₃×C₄	—	2	1	no	—
982	C₃×C₄	—	2	2	no	—
983	C₃×C₄	—	2	2	no	—
984	C₃×C₄	—	2	2	no	—
985	C₃×C₄	—	2	2	no	—
986	C₃×C₄	—	2	2	no	—
987	C₃×C₄	—	2	1	no	—
988	C₃×C₄	—	2	1	no	—
989	C₃×C₄	—	2	2	no	—
990	C₃×C₄	—	2	2	no	—
991	C₃×C₄	—	2	1	no	—
992	C₃×C₄	—	2	2	no	—
993	C₂×C₅	—	2	2	no	—
994	C₂×C₅	—	4	2	no	—
995	C₂×C₅	—	4	2	no	—
996	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
997	C₂×C₅	C₃×#585	1	1	yes	characteristic
998	C₂×C₅	C₃×#585	1	1	yes	characteristic
999	C₂³	—	2	2	no	—
1000	C₂³	—	4	1	no	—
1001	C₂³	—	4	1	no	—
1002	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1003	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
1004	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
1005	Q₈	—	4	1	no	—
1006	Q₈	—	4	2	no	—
1007	Q₈	—	4	2	no	—
1008	Q₈	—	4	1	no	—
1009	Q₈	—	4	2	no	—
1010	Q₈	—	4	1	no	—
1011	D₄	—	2	4	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	4	1	no	—
1014	D₄	—	4	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	4	2	no	—
1018	C₂×C₄	—	4	1	no	—
1019	C₂×C₄	—	4	1	no	—
1020	C₂×C₄	—	4	1	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	4	2	no	—
1023	C₂×C₄	—	4	2	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	1	no	—
1026	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1027	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1028	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1029	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1030	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1031	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1032	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1033	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1034	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1035	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1036	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
1037	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1038	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1039	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1040	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1041	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
1042	C₂×C₃	—	2	2	no	—
1043	C₂×C₃	—	4	2	no	—
1044	C₂×C₃	—	4	2	no	—
1045	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1046	C₂×C₃	C₅×#585	1	1	yes	characteristic
1047	C₂×C₃	C₅×#585	1	1	yes	characteristic
1048	C₅	C₃×#3564	1	1	yes	characteristic, direct product factor, Sylow
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	2	no	—
1054	C₂²	—	2	2	no	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	2	2	no	—
1057	C₂²	—	8	2	no	—
1058	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
1059	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	2	no	—
1063	C₄	—	2	2	no	—
1064	C₄	—	2	1	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	2	no	—
1076	C₃	C₅×#3564	1	1	yes	characteristic, direct product factor, Sylow
1077	C₂	—	2	2	no	—
1078	C₂	—	4	2	no	—
1079	C₂	—	4	2	no	—
1080	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
1081	C₂	C₃×C₅×#585	1	1	yes	characteristic
1082	C₂	C₃×C₅×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
prime radical	C₃×C₅×#538	C₂
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×#563	C₂	semidirect
3. C₃×C₅×#556	C₂	semidirect
4. C₃×C₅×#554	C₂	semidirect
5. C₃×C₅×#552	C₂	semidirect
6. C₃×C₅×#552	C₂	semidirect
7. C₃×C₅×#551	C₂	semidirect
8. C₃×C₅×#551	C₂	semidirect
9. C₃×C₅×#544	C₂	semidirect
10. C₃×C₅×#543	C₂	semidirect
11. C₃×C₅×#542	C₂	semidirect
12. C₃×C₅×#541	C₂	semidirect
13. C₃×C₅×#541	C₂	semidirect
14. C₃×C₅×#539	C₂	semidirect
15. C₃×C₅×#539	C₂	semidirect
17. C₃×C₅×#533	C₂	semidirect
18. C₃×C₅×#529	C₂	semidirect
19. C₂×C₃×C₅×#126	C₂	semidirect
20. C₅×#3564	C₃	direct (N × H)
21. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
22. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
23. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
24. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
35. C₃×C₅×#126	C₂²	semidirect
36. C₃×C₅×#126	C₂²	semidirect
37. C₃×C₅×#126	C₂²	semidirect
38. C₃×C₅×#126	C₂²	semidirect
39. C₃×C₅×#125	C₂²	semidirect
40. C₃×C₅×#125	C₂²	semidirect
41. C₃×C₅×#125	C₂²	semidirect
42. C₃×C₅×#125	C₂²	semidirect
43. C₃×C₅×#125	C₂²	semidirect
44. C₃×C₅×#125	C₂²	semidirect
45. C₃×C₅×#125	C₂²	semidirect
46. C₃×C₅×#125	C₂²	semidirect
47. C₃×C₅×#125	C₂²	semidirect
48. C₃×C₅×#125	C₂²	semidirect
52. C₃×C₅×#124	C₂²	semidirect
60. C₃×C₅×#123	C₂²	semidirect
73. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
74. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
75. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
76. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
77. C₃×C₅×C₂²⋊Q₈	C₂²	semidirect
81. C₃×C₄×C₅×Q₈	C₂²	semidirect
82. C₃×C₄×C₅×Q₈	C₂²	semidirect
83. C₃×C₄×C₅×Q₈	C₂²	semidirect
84. C₃×C₄×C₅×Q₈	C₂²	semidirect
85. C₃×C₄×C₅×Q₈	C₂²	semidirect
86. C₃×C₄×C₅×Q₈	C₂²	semidirect
92. C₃×C₄×C₅×D₄	C₂²	semidirect
97. C₃×C₅×#117	C₂²	semidirect
98. C₃×C₅×#117	C₂²	semidirect
102. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
108. C₃×#3564	C₅	direct (N × H)
109. C₅×#563	C₂×C₃	semidirect
110. C₅×#563	C₂×C₃	semidirect
111. C₅×#556	C₂×C₃	semidirect
112. C₅×#554	C₂×C₃	semidirect
113. C₅×#552	C₂×C₃	semidirect
114. C₅×#552	C₂×C₃	semidirect
115. C₅×#551	C₂×C₃	semidirect
116. C₅×#551	C₂×C₃	semidirect
117. C₅×#544	C₂×C₃	semidirect
118. C₅×#543	C₂×C₃	semidirect
119. C₅×#542	C₂×C₃	semidirect
120. C₅×#541	C₂×C₃	semidirect
121. C₅×#541	C₂×C₃	semidirect
122. C₅×#539	C₂×C₃	semidirect
123. C₅×#539	C₂×C₃	semidirect
125. C₅×#533	C₂×C₃	semidirect
126. C₅×#529	C₂×C₃	semidirect
127. C₂×C₅×#126	C₂×C₃	semidirect
215. C₃×#563	C₂×C₅	semidirect
216. C₃×#563	C₂×C₅	semidirect
217. C₃×#556	C₂×C₅	semidirect
218. C₃×#554	C₂×C₅	semidirect
219. C₃×#552	C₂×C₅	semidirect
220. C₃×#552	C₂×C₅	semidirect
221. C₃×#551	C₂×C₅	semidirect
222. C₃×#551	C₂×C₅	semidirect
223. C₃×#544	C₂×C₅	semidirect
224. C₃×#543	C₂×C₅	semidirect
225. C₃×#542	C₂×C₅	semidirect
226. C₃×#541	C₂×C₅	semidirect
227. C₃×#541	C₂×C₅	semidirect
228. C₃×#539	C₂×C₅	semidirect
229. C₃×#539	C₂×C₅	semidirect
231. C₃×#533	C₂×C₅	semidirect
232. C₃×#529	C₂×C₅	semidirect
233. C₂×C₃×#126	C₂×C₅	semidirect
234. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
235. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
236. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
237. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
238. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
248. C₅×#126	C₂²×C₃	semidirect
249. C₅×#126	C₂²×C₃	semidirect
250. C₅×#126	C₂²×C₃	semidirect
251. C₅×#126	C₂²×C₃	semidirect
252. C₅×#125	C₂²×C₃	semidirect
253. C₅×#125	C₂²×C₃	semidirect
254. C₅×#125	C₂²×C₃	semidirect
255. C₅×#125	C₂²×C₃	semidirect
256. C₅×#125	C₂²×C₃	semidirect
257. C₅×#125	C₂²×C₃	semidirect
258. C₅×#125	C₂²×C₃	semidirect
259. C₅×#125	C₂²×C₃	semidirect
260. C₅×#125	C₂²×C₃	semidirect
261. C₅×#125	C₂²×C₃	semidirect
265. C₅×#124	C₂²×C₃	semidirect
273. C₅×#123	C₂²×C₃	semidirect
286. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
287. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
288. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
289. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
290. C₅×C₂²⋊Q₈	C₂²×C₃	semidirect
294. C₄×C₅×Q₈	C₂²×C₃	semidirect
295. C₄×C₅×Q₈	C₂²×C₃	semidirect
296. C₄×C₅×Q₈	C₂²×C₃	semidirect
297. C₄×C₅×Q₈	C₂²×C₃	semidirect
298. C₄×C₅×Q₈	C₂²×C₃	semidirect
299. C₄×C₅×Q₈	C₂²×C₃	semidirect
305. C₄×C₅×D₄	C₂²×C₃	semidirect
310. C₅×#117	C₂²×C₃	semidirect
311. C₅×#117	C₂²×C₃	semidirect
315. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
321. #3564	C₃×C₅	direct (N × H)
365. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
366. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
367. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
368. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
369. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
379. C₃×#126	C₂²×C₅	semidirect
380. C₃×#126	C₂²×C₅	semidirect
381. C₃×#126	C₂²×C₅	semidirect
382. C₃×#126	C₂²×C₅	semidirect
383. C₃×#125	C₂²×C₅	semidirect
384. C₃×#125	C₂²×C₅	semidirect
385. C₃×#125	C₂²×C₅	semidirect
386. C₃×#125	C₂²×C₅	semidirect
387. C₃×#125	C₂²×C₅	semidirect
388. C₃×#125	C₂²×C₅	semidirect
389. C₃×#125	C₂²×C₅	semidirect
390. C₃×#125	C₂²×C₅	semidirect
391. C₃×#125	C₂²×C₅	semidirect
392. C₃×#125	C₂²×C₅	semidirect
396. C₃×#124	C₂²×C₅	semidirect
404. C₃×#123	C₂²×C₅	semidirect
417. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
418. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
419. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
420. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
421. C₃×C₂²⋊Q₈	C₂²×C₅	semidirect
425. C₃×C₄×Q₈	C₂²×C₅	semidirect
426. C₃×C₄×Q₈	C₂²×C₅	semidirect
427. C₃×C₄×Q₈	C₂²×C₅	semidirect
428. C₃×C₄×Q₈	C₂²×C₅	semidirect
429. C₃×C₄×Q₈	C₂²×C₅	semidirect
430. C₃×C₄×Q₈	C₂²×C₅	semidirect
436. C₃×C₄×D₄	C₂²×C₅	semidirect
441. C₃×#117	C₂²×C₅	semidirect
442. C₃×#117	C₂²×C₅	semidirect
446. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
539. #563	C₂×C₃×C₅	semidirect
540. #563	C₂×C₃×C₅	semidirect
541. #556	C₂×C₃×C₅	semidirect
542. #554	C₂×C₃×C₅	semidirect
543. #552	C₂×C₃×C₅	semidirect
544. #552	C₂×C₃×C₅	semidirect
545. #551	C₂×C₃×C₅	semidirect
546. #551	C₂×C₃×C₅	semidirect
547. #544	C₂×C₃×C₅	semidirect
548. #543	C₂×C₃×C₅	semidirect
549. #542	C₂×C₃×C₅	semidirect
550. #541	C₂×C₃×C₅	semidirect
551. #541	C₂×C₃×C₅	semidirect
552. #539	C₂×C₃×C₅	semidirect
553. #539	C₂×C₃×C₅	semidirect
555. #533	C₂×C₃×C₅	semidirect
556. #529	C₂×C₃×C₅	semidirect
557. C₂×#126	C₂×C₃×C₅	semidirect
715. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
716. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
717. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
718. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
719. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
729. #126	C₂²×C₃×C₅	semidirect
730. #126	C₂²×C₃×C₅	semidirect
731. #126	C₂²×C₃×C₅	semidirect
732. #126	C₂²×C₃×C₅	semidirect
733. #125	C₂²×C₃×C₅	semidirect
734. #125	C₂²×C₃×C₅	semidirect
735. #125	C₂²×C₃×C₅	semidirect
736. #125	C₂²×C₃×C₅	semidirect
737. #125	C₂²×C₃×C₅	semidirect
738. #125	C₂²×C₃×C₅	semidirect
739. #125	C₂²×C₃×C₅	semidirect
740. #125	C₂²×C₃×C₅	semidirect
741. #125	C₂²×C₃×C₅	semidirect
742. #125	C₂²×C₃×C₅	semidirect
746. #124	C₂²×C₃×C₅	semidirect
754. #123	C₂²×C₃×C₅	semidirect
767. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
768. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
769. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
770. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
771. C₂²⋊Q₈	C₂²×C₃×C₅	semidirect
775. C₄×Q₈	C₂²×C₃×C₅	semidirect
776. C₄×Q₈	C₂²×C₃×C₅	semidirect
777. C₄×Q₈	C₂²×C₃×C₅	semidirect
778. C₄×Q₈	C₂²×C₃×C₅	semidirect
779. C₄×Q₈	C₂²×C₃×C₅	semidirect
780. C₄×Q₈	C₂²×C₃×C₅	semidirect
786. C₄×D₄	C₂²×C₃×C₅	semidirect
791. #117	C₂²×C₃×C₅	semidirect
792. #117	C₂²×C₃×C₅	semidirect
796. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
965. C₃×C₅	#3564	direct (N × H)
1048. C₅	C₃×#3564	direct (N × H)
1076. C₃	C₅×#3564	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×#556	2
C₃×C₅×#554	2
C₃×C₅×#552	2
C₃×C₅×#551	2
C₃×C₅×#544	2
C₃×C₅×#543	2
C₃×C₅×#542	2
C₃×C₅×#541	2
C₃×C₅×#539	2
C₃×C₅×#538	2
C₃×C₅×#533	2
C₃×C₅×#529	2
C₂×C₃×C₅×#126	2
C₅×#3564	3
C₃×#3564	5

Subgroups — C3×C5×#3564 #14276598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3564 #14276598