Subgroups — C₇×#62893 #13240109

Order 1792.

6998 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3561	C₂	1	6	yes	maximal, complemented
2	C₇×#3552	C₂	1	12	yes	maximal, complemented
3	C₇×#3541	C₂	1	12	yes	maximal, complemented
4	C₇×#3538	C₂	1	6	yes	maximal, complemented
5	C₇×#3523	C₂	1	2	yes	maximal, complemented
6	C₇×#3516	C₂	1	4	yes	maximal, complemented
7	C₇×#3505	C₂	1	6	yes	maximal, complemented
8	C₇×#3501	C₂	1	3	yes	maximal, complemented
9	C₇×#3489	C₂	1	2	yes	maximal, complemented
10	C₇×#3486	C₂	1	4	yes	maximal, complemented
11	C₂×C₇×D₄×Q₈	C₂	1	2	yes	maximal, complemented
12	C₂×C₇×#548	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3459	C₂	1	3	yes	maximal, complemented
14	C₂×C₇×2₋¹⁺⁴	C₂²	1	2	yes	complemented
15	C₂²×C₇×#41	C₂²	1	1	yes	characteristic, complemented
16	C₂³×C₇×Q₈	C₂²	1	1	yes	characteristic
17	C₂³×C₇×Q₈	C₂²	1	2	yes	complemented
18	C₇×#563	C₂²	1	12	yes	complemented
19	C₇×#563	C₂²	1	24	yes	complemented
20	C₇×#562	C₂²	1	12	yes	complemented
21	C₇×#557	C₂²	1	2	yes	complemented
22	C₇×#557	C₂²	1	6	yes	complemented
23	C₇×#556	C₂²	1	12	yes	complemented
24	C₇×#556	C₂²	1	6	yes	complemented
25	C₇×#554	C₂²	1	12	yes	complemented
26	C₇×#554	C₂²	1	24	yes	complemented
27	C₇×#553	C₂²	1	12	yes	complemented
28	C₇×#553	C₂²	1	24	yes	complemented
29	C₇×#552	C₂²	1	12	yes	complemented
30	C₇×#552	C₂²	1	12	yes	complemented
31	C₇×#551	C₂²	1	24	yes	complemented
32	C₇×D₄×Q₈	C₂²	1	12	yes	complemented
33	C₇×D₄×Q₈	C₂²	1	4	yes	complemented
34	C₇×D₄×Q₈	C₂²	1	4	yes	complemented
35	C₇×D₄×Q₈	C₂²	1	12	yes	complemented
36	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
37	C₇×D₄×Q₈	C₂²	1	12	yes	complemented
38	C₇×D₄×Q₈	C₂²	1	12	yes	complemented
39	C₇×#548	C₂²	1	12	yes	complemented
40	C₇×#548	C₂²	1	4	yes	complemented
41	C₇×#548	C₂²	1	12	yes	complemented
42	C₇×#548	C₂²	1	4	yes	complemented
43	C₇×#548	C₂²	1	12	yes	complemented
44	C₇×#547	C₂²	1	12	yes	complemented
45	C₇×#546	C₂²	1	12	yes	complemented
46	C₇×#544	C₂²	1	6	yes	complemented
47	C₇×#544	C₂²	1	12	yes	complemented
48	C₇×#543	C₂²	1	3	yes	—
49	C₇×#543	C₂²	1	6	yes	complemented
50	C₇×#542	C₂²	1	12	yes	complemented
51	C₇×#542	C₂²	1	24	yes	complemented
52	C₇×#541	C₂²	1	12	yes	complemented
53	C₇×#541	C₂²	1	12	yes	complemented
54	C₇×#539	C₂²	1	6	yes	—
55	C₇×#539	C₂²	1	12	yes	complemented
56	C₇×#539	C₂²	1	12	yes	complemented
57	C₇×#539	C₂²	1	12	yes	complemented
58	C₇×#538	C₂²	1	6	yes	—
59	C₇×#538	C₂²	1	12	yes	complemented
60	C₇×#538	C₂²	1	12	yes	complemented
61	C₇×#537	C₂²	1	6	yes	complemented
62	C₇×#536	C₂²	1	12	yes	complemented
63	C₇×#536	C₂²	1	12	yes	complemented
64	C₇×#536	C₂²	1	6	yes	complemented
65	C₇×#534	C₂²	1	1	yes	characteristic
66	C₇×#534	C₂²	1	6	yes	—
67	C₇×#533	C₂²	1	6	yes	complemented
68	C₂×C₇×C₄⋊Q₈	C₂²	1	6	yes	complemented
69	C₇×#529	C₂²	1	6	yes	—
70	C₇×#529	C₂²	1	12	yes	complemented
71	C₇×#529	C₂²	1	12	yes	complemented
72	C₂×C₇×#124	C₂²	1	3	yes	complemented
73	C₇×#525	C₂²	1	6	yes	—
74	C₇×#525	C₂²	1	12	yes	complemented
75	C₇×#525	C₂²	1	12	yes	complemented
76	C₂×C₇×C₂²⋊Q₈	C₂²	1	6	yes	—
77	C₂×C₇×C₂²⋊Q₈	C₂²	1	3	yes	complemented
78	C₂×C₇×C₂²⋊Q₈	C₂²	1	6	yes	complemented
79	C₂×C₇×C₂²⋊Q₈	C₂²	1	6	yes	complemented
80	C₂×C₇×#121	C₂²	1	3	yes	—
81	C₇×#520	C₂²	1	2	yes	complemented
82	C₇×#519	C₂²	1	4	yes	complemented
83	C₇×#518	C₂²	1	6	yes	—
84	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	complemented
86	C₂×C₄×C₇×D₄	C₂²	1	3	yes	—
87	C₂×C₄×C₇×D₄	C₂²	1	6	yes	—
88	#62893	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
89	C₇×2₋¹⁺⁴	—	4	8	no	—
90	C₂×C₇×#41	—	4	4	no	—
91	C₂×C₇×#41	C₂³	1	2	yes	—
92	C₂×C₇×#41	C₂³	1	6	yes	—
93	C₂×C₇×#41	C₂³	1	6	yes	—
94	C₂×C₇×#41	C₂³	1	12	yes	—
95	C₂²×C₇×Q₈	—	4	4	no	—
96	C₂²×C₇×Q₈	—	4	8	no	—
97	C₂²×C₇×Q₈	C₂³	1	2	yes	—
98	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
99	C₂²×C₇×Q₈	C₂³	1	4	yes	—
100	C₂²×C₇×Q₈	C₂³	1	3	yes	—
101	C₂²×C₇×Q₈	C₂³	1	6	yes	—
102	C₂²×C₇×Q₈	C₂³	1	6	yes	—
103	C₂²×C₇×Q₈	C₂³	1	12	yes	—
104	C₂²×C₇×Q₈	C₂³	1	6	yes	—
105	C₂²×C₇×D₄	C₂³	1	2	yes	—
106	C₂²×C₇×D₄	C₂³	1	3	yes	—
107	C₂²×C₇×D₄	C₂³	1	3	yes	—
108	C₂³×C₄×C₇	C₂³	1	3	yes	—
109	C₂³×C₄×C₇	C₂³	1	6	yes	—
110	C₂³×C₄×C₇	C₂³	1	3	yes	—
111	C₇×C₄⋊Q₈	C₂³	1	12	yes	—
112	C₇×C₄⋊Q₈	C₂³	1	12	yes	—
113	C₇×C₄⋊Q₈	C₂³	1	24	yes	—
114	C₇×C₄⋊Q₈	C₂³	1	6	yes	—
115	C₇×C₄⋊Q₈	C₂³	1	6	yes	—
116	C₇×C₄⋊Q₈	C₂³	1	24	yes	—
117	C₇×#126	C₂³	1	12	yes	—
118	C₇×#126	C₂³	1	12	yes	—
119	C₇×#126	C₂³	1	12	yes	—
120	C₇×#126	C₂³	1	24	yes	—
121	C₇×#126	C₂³	1	24	yes	—
122	C₇×#126	C₂³	1	24	yes	—
123	C₇×#125	C₂³	1	6	yes	—
124	C₇×#125	C₂³	1	12	yes	—
125	C₇×#125	C₂³	1	12	yes	—
126	C₇×#125	C₂³	1	12	yes	—
127	C₇×#125	C₂³	1	24	yes	—
128	C₇×#125	C₂³	1	24	yes	—
129	C₇×#124	C₂³	1	12	yes	—
130	C₇×#124	C₂³	1	12	yes	—
131	C₇×#124	C₂³	1	6	yes	—
132	C₇×#124	C₂³	1	12	yes	—
133	C₇×#124	C₂³	1	12	yes	—
134	C₇×#124	C₂³	1	24	yes	—
135	C₇×#123	C₂³	1	12	yes	—
136	C₇×#123	C₂³	1	12	yes	—
137	C₇×#123	C₂³	1	12	yes	—
138	C₇×#123	C₂³	1	24	yes	—
139	C₇×#123	C₂³	1	12	yes	—
140	C₇×#123	C₂³	1	4	yes	—
141	C₇×#123	C₂³	1	12	yes	—
142	C₇×#123	C₂³	1	24	yes	—
143	C₇×#123	C₂³	1	24	yes	—
144	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
145	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
146	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
147	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
148	C₇×C₂²⋊Q₈	C₂³	1	6	yes	—
149	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
150	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
151	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
152	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
153	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
154	C₇×C₂²⋊Q₈	C₂³	1	24	yes	—
155	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
156	C₇×C₂²⋊Q₈	C₂³	1	6	yes	—
157	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
158	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
159	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
160	C₇×C₂²⋊Q₈	C₂³	1	6	yes	—
161	C₇×C₂²⋊Q₈	C₂³	1	12	yes	—
162	C₇×C₂²⋊Q₈	C₂³	1	24	yes	—
163	C₇×C₂²⋊Q₈	C₂³	1	24	yes	—
164	C₇×C₂²⋊Q₈	C₂³	1	24	yes	—
165	C₇×#121	C₂³	1	12	yes	—
166	C₇×#121	C₂³	1	12	yes	—
167	C₇×#121	C₂³	1	2	yes	—
168	C₇×#121	C₂³	1	6	yes	—
169	C₇×#121	C₂³	1	12	yes	—
170	C₇×#121	C₂³	1	12	yes	—
171	C₇×#121	C₂³	1	12	yes	—
172	C₇×#121	C₂³	1	2	yes	—
173	C₇×#121	C₂³	1	12	yes	—
174	C₇×#121	C₂³	1	24	yes	—
175	C₇×#120	C₂³	1	12	yes	—
176	C₇×#120	C₂³	1	12	yes	—
177	C₇×#120	C₂³	1	4	yes	—
178	C₄×C₇×Q₈	C₂³	1	2	yes	—
179	C₄×C₇×Q₈	C₂³	1	4	yes	—
180	C₄×C₇×Q₈	C₂³	1	6	yes	—
181	C₄×C₇×Q₈	C₂³	1	12	yes	—
182	C₄×C₇×Q₈	C₂³	1	12	yes	—
183	C₄×C₇×Q₈	C₂³	1	12	yes	—
184	C₄×C₇×Q₈	C₂³	1	6	yes	—
185	C₄×C₇×Q₈	C₂³	1	12	yes	—
186	C₄×C₇×D₄	C₂³	1	12	yes	—
187	C₄×C₇×D₄	C₂³	1	12	yes	—
188	C₄×C₇×D₄	C₂³	1	12	yes	—
189	C₄×C₇×D₄	C₂³	1	12	yes	—
190	C₄×C₇×D₄	C₂³	1	12	yes	—
191	C₄×C₇×D₄	C₂³	1	12	yes	—
192	C₄×C₇×D₄	C₂³	1	24	yes	—
193	C₄×C₇×D₄	C₂³	1	24	yes	—
194	C₄×C₇×D₄	C₂³	1	12	yes	—
195	C₄×C₇×D₄	C₂³	1	12	yes	—
196	C₄×C₇×D₄	C₂³	1	6	yes	—
197	C₄×C₇×D₄	C₂³	1	24	yes	—
198	C₇×#117	C₂³	1	12	yes	—
199	C₇×#117	C₂³	1	12	yes	—
200	C₇×#117	C₂³	1	12	yes	—
201	C₇×#117	C₂³	1	6	yes	—
202	C₇×#117	C₂³	1	24	yes	—
203	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
204	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
205	C₂×C₇×C₄⋊C₄	C₂³	1	3	yes	—
206	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
207	C₂×C₇×C₄⋊C₄	C₂³	1	6	yes	—
208	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	—
209	C₂×C₇×C₄⋊C₄	C₂³	1	12	yes	—
210	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
212	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
213	C₂×C₇×C₂²⋊C₄	C₂³	1	3	yes	—
214	C₂×C₇×C₂²⋊C₄	C₂³	1	12	yes	—
215	C₂×C₇×C₂²⋊C₄	C₂³	1	6	yes	—
216	C₂×C₄²×C₇	C₂³	1	3	yes	—
217	C₂×C₄²×C₇	C₂³	1	6	yes	—
218	#3561	C₂×C₇	1	6	yes	complemented
219	#3552	C₂×C₇	1	12	yes	complemented
220	#3541	C₂×C₇	1	12	yes	complemented
221	#3538	C₂×C₇	1	6	yes	complemented
222	#3523	C₂×C₇	1	2	yes	complemented
223	#3516	C₂×C₇	1	4	yes	complemented
224	#3505	C₂×C₇	1	6	yes	complemented
225	#3501	C₂×C₇	1	3	yes	complemented
226	#3489	C₂×C₇	1	2	yes	complemented
227	#3486	C₂×C₇	1	4	yes	complemented
228	C₂×D₄×Q₈	C₂×C₇	1	2	yes	complemented
229	C₂×#548	C₂×C₇	1	1	yes	characteristic, complemented
230	#3459	C₂×C₇	1	3	yes	complemented
231	C₂⁴×C₇	C₂⁴	1	3	yes	—
232	C₂⁴×C₇	C₂⁴	1	2	yes	—
233	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
234	C₇×#41	—	2	8	no	—
235	C₇×#41	—	4	12	no	—
236	C₇×#41	—	4	12	no	—
237	C₇×#41	—	4	24	no	—
238	C₂×C₇×Q₈	—	2	8	no	—
239	C₂×C₇×Q₈	—	2	4	no	—
240	C₂×C₇×Q₈	—	2	16	no	—
241	C₂×C₇×Q₈	—	4	6	no	—
242	C₂×C₇×Q₈	—	4	12	no	—
243	C₂×C₇×Q₈	—	4	12	no	—
244	C₂×C₇×Q₈	—	4	24	no	—
245	C₂×C₇×Q₈	—	4	12	no	—
246	C₂×C₇×Q₈	C₂⁴	1	6	yes	—
247	C₂×C₇×Q₈	C₂⁴	1	12	yes	—
248	C₂×C₇×Q₈	C₂⁴	1	3	yes	—
249	C₂×C₇×Q₈	C₂⁴	1	6	yes	—
250	C₂×C₇×Q₈	C₂⁴	1	6	yes	—
251	C₂×C₇×Q₈	C₂⁴	1	6	yes	—
252	C₂×C₇×Q₈	C₂⁴	1	12	yes	—
253	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
254	C₂×C₇×D₄	—	2	8	no	—
255	C₂×C₇×D₄	—	2	12	no	—
256	C₂×C₇×D₄	—	4	6	no	—
257	C₂×C₇×D₄	C₂⁴	1	4	yes	—
258	C₂×C₇×D₄	C₂⁴	1	12	yes	—
259	C₂×C₇×D₄	C₂⁴	1	4	yes	—
260	C₂×C₇×D₄	C₂⁴	1	6	yes	—
261	C₂×C₇×D₄	C₂⁴	1	12	yes	—
262	C₂×C₇×D₄	C₂⁴	1	2	yes	—
263	C₂×C₇×D₄	C₂⁴	1	2	yes	—
264	C₂×C₇×D₄	C₂⁴	1	12	yes	—
265	C₂×C₇×D₄	C₂⁴	1	6	yes	—
266	C₂²×C₄×C₇	—	4	6	no	—
267	C₂²×C₄×C₇	—	4	12	no	—
268	C₂²×C₄×C₇	—	4	6	no	—
269	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
271	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
272	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
273	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
274	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
275	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	3	yes	—
278	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
279	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
280	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
283	C₂²×C₄×C₇	C₂⁴	1	6	yes	—
284	C₂²×C₄×C₇	C₂⁴	1	12	yes	—
285	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
286	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
287	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
288	C₇×C₄⋊C₄	C₂⁴	1	24	yes	—
289	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
290	C₇×C₄⋊C₄	C₂⁴	1	24	yes	—
291	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
292	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
293	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
294	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
295	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
296	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
297	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
298	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	12	yes	—
302	C₇×C₄⋊C₄	C₂⁴	1	6	yes	—
303	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
304	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
305	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
306	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
307	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
308	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
309	C₇×C₂²⋊C₄	C₂⁴	1	24	yes	—
310	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
311	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
312	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
313	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
314	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
315	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
316	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
317	C₇×C₂²⋊C₄	C₂⁴	1	12	yes	—
318	C₄²×C₇	C₂⁴	1	12	yes	—
319	C₄²×C₇	C₂⁴	1	6	yes	—
320	C₄²×C₇	C₂⁴	1	12	yes	—
321	C₄²×C₇	C₂⁴	1	6	yes	—
322	C₄²×C₇	C₂⁴	1	24	yes	—
323	C₂×2₋¹⁺⁴	C₂²×C₇	1	2	yes	complemented
324	C₂²×#41	C₂²×C₇	1	1	yes	characteristic, complemented
325	C₂³×Q₈	C₂²×C₇	1	1	yes	characteristic
326	C₂³×Q₈	C₂²×C₇	1	2	yes	complemented
327	#563	C₂²×C₇	1	24	yes	complemented
328	#563	C₂²×C₇	1	12	yes	complemented
329	#562	C₂²×C₇	1	12	yes	complemented
330	#557	C₂²×C₇	1	2	yes	complemented
331	#557	C₂²×C₇	1	6	yes	complemented
332	#556	C₂²×C₇	1	12	yes	complemented
333	#556	C₂²×C₇	1	6	yes	complemented
334	#554	C₂²×C₇	1	12	yes	complemented
335	#554	C₂²×C₇	1	24	yes	complemented
336	#553	C₂²×C₇	1	12	yes	complemented
337	#553	C₂²×C₇	1	24	yes	complemented
338	#552	C₂²×C₇	1	12	yes	complemented
339	#552	C₂²×C₇	1	12	yes	complemented
340	#551	C₂²×C₇	1	24	yes	complemented
341	D₄×Q₈	C₂²×C₇	1	4	yes	complemented
342	D₄×Q₈	C₂²×C₇	1	4	yes	complemented
343	D₄×Q₈	C₂²×C₇	1	12	yes	complemented
344	D₄×Q₈	C₂²×C₇	1	12	yes	complemented
345	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
346	D₄×Q₈	C₂²×C₇	1	12	yes	complemented
347	D₄×Q₈	C₂²×C₇	1	12	yes	complemented
348	#548	C₂²×C₇	1	4	yes	complemented
349	#548	C₂²×C₇	1	12	yes	complemented
350	#548	C₂²×C₇	1	4	yes	complemented
351	#548	C₂²×C₇	1	12	yes	complemented
352	#548	C₂²×C₇	1	12	yes	complemented
353	#547	C₂²×C₇	1	12	yes	complemented
354	#546	C₂²×C₇	1	12	yes	complemented
355	#544	C₂²×C₇	1	6	yes	complemented
356	#544	C₂²×C₇	1	12	yes	complemented
357	#543	C₂²×C₇	1	3	yes	—
358	#543	C₂²×C₇	1	6	yes	complemented
359	#542	C₂²×C₇	1	12	yes	complemented
360	#542	C₂²×C₇	1	24	yes	complemented
361	#541	C₂²×C₇	1	12	yes	complemented
362	#541	C₂²×C₇	1	12	yes	complemented
363	#539	C₂²×C₇	1	6	yes	—
364	#539	C₂²×C₇	1	12	yes	complemented
365	#539	C₂²×C₇	1	12	yes	complemented
366	#539	C₂²×C₇	1	12	yes	complemented
367	#538	C₂²×C₇	1	6	yes	—
368	#538	C₂²×C₇	1	12	yes	complemented
369	#538	C₂²×C₇	1	12	yes	complemented
370	#537	C₂²×C₇	1	6	yes	complemented
371	#536	C₂²×C₇	1	12	yes	complemented
372	#536	C₂²×C₇	1	12	yes	complemented
373	#536	C₂²×C₇	1	6	yes	complemented
374	#534	C₂²×C₇	1	1	yes	characteristic
375	#534	C₂²×C₇	1	6	yes	—
376	#533	C₂²×C₇	1	6	yes	complemented
377	C₂×C₄⋊Q₈	C₂²×C₇	1	6	yes	complemented
378	#529	C₂²×C₇	1	6	yes	—
379	#529	C₂²×C₇	1	12	yes	complemented
380	#529	C₂²×C₇	1	12	yes	complemented
381	C₂×#124	C₂²×C₇	1	3	yes	complemented
382	#525	C₂²×C₇	1	6	yes	—
383	#525	C₂²×C₇	1	12	yes	complemented
384	#525	C₂²×C₇	1	12	yes	complemented
385	C₂×C₂²⋊Q₈	C₂²×C₇	1	6	yes	—
386	C₂×C₂²⋊Q₈	C₂²×C₇	1	3	yes	complemented
387	C₂×C₂²⋊Q₈	C₂²×C₇	1	6	yes	complemented
388	C₂×C₂²⋊Q₈	C₂²×C₇	1	6	yes	complemented
389	C₂×#121	C₂²×C₇	1	3	yes	—
390	#520	C₂²×C₇	1	2	yes	complemented
391	#519	C₂²×C₇	1	4	yes	complemented
392	#518	C₂²×C₇	1	6	yes	—
393	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
394	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	complemented
395	C₂×C₄×D₄	C₂²×C₇	1	3	yes	—
396	C₂×C₄×D₄	C₂²×C₇	1	6	yes	—
397	C₂³×C₇	—	2	4	no	—
398	C₂³×C₇	—	2	6	no	—
399	C₂³×C₇	—	4	1	no	—
400	C₂³×C₇	—	4	2	no	—
401	C₂³×C₇	—	4	1	no	—
402	C₂³×C₇	—	4	2	no	—
403	C₂³×C₇	—	4	3	no	—
404	C₂³×C₇	—	4	3	no	—
405	C₂³×C₇	2₋¹⁺⁴	1	4	yes	complemented
406	C₂³×C₇	C₂⁵	1	4	yes	—
407	C₂³×C₇	C₂⁵	1	6	yes	—
408	C₂³×C₇	C₂⁵	1	1	yes	characteristic
409	C₂³×C₇	C₂⁵	1	2	yes	—
410	C₇×Q₈	—	2	12	no	—
411	C₇×Q₈	—	2	24	no	—
412	C₇×Q₈	—	2	6	no	—
413	C₇×Q₈	—	4	6	no	—
414	C₇×Q₈	—	4	12	no	—
415	C₇×Q₈	—	4	6	no	—
416	C₇×Q₈	—	4	6	no	—
417	C₇×Q₈	H(5,𝔽₂)	1	4	yes	—
418	C₇×D₄	—	2	8	no	—
419	C₇×D₄	—	2	8	no	—
420	C₇×D₄	—	2	24	no	—
421	C₇×D₄	—	2	12	no	—
422	C₇×D₄	—	4	6	no	—
423	C₇×D₄	—	4	12	no	—
424	C₇×D₄	—	4	2	no	—
425	C₇×D₄	—	4	2	no	—
426	C₇×D₄	—	4	12	no	—
427	C₂×C₄×C₇	—	2	6	no	—
428	C₂×C₄×C₇	—	2	4	no	—
429	C₂×C₄×C₇	—	2	6	no	—
430	C₂×C₄×C₇	—	2	12	no	—
431	C₂×C₄×C₇	—	2	24	no	—
432	C₂×C₄×C₇	—	2	12	no	—
433	C₂×C₄×C₇	—	4	1	no	—
434	C₂×C₄×C₇	—	4	6	no	—
435	C₂×C₄×C₇	—	4	6	no	—
436	C₂×C₄×C₇	—	4	12	no	—
437	C₂×C₄×C₇	—	4	3	no	—
438	C₂×C₄×C₇	—	4	6	no	—
439	C₂×C₄×C₇	—	4	6	no	—
440	C₂×C₄×C₇	—	4	12	no	—
441	C₂×C₄×C₇	—	4	1	no	—
442	C₂×C₄×C₇	—	4	12	no	—
443	C₂×C₄×C₇	C₂⁵	1	2	yes	—
444	C₂×C₄×C₇	C₂⁵	1	4	yes	—
445	C₂×C₄×C₇	C₂⁵	1	6	yes	—
446	C₂×C₄×C₇	C₂⁵	1	12	yes	—
447	C₂×C₄×C₇	C₂⁵	1	6	yes	—
448	C₂×C₄×C₇	C₂⁵	1	12	yes	—
449	C₂×C₄×C₇	C₂⁵	1	3	yes	—
450	C₂×C₄×C₇	C₂⁵	1	2	yes	—
451	C₂×C₄×C₇	C₂⁵	1	3	yes	—
452	2₋¹⁺⁴	—	4	8	no	—
453	C₂×#41	—	4	4	no	—
454	C₂×#41	C₂³×C₇	1	2	yes	—
455	C₂×#41	C₂³×C₇	1	6	yes	—
456	C₂×#41	C₂³×C₇	1	12	yes	—
457	C₂×#41	C₂³×C₇	1	6	yes	—
458	C₂²×Q₈	—	4	4	no	—
459	C₂²×Q₈	—	4	8	no	—
460	C₂²×Q₈	C₂³×C₇	1	2	yes	—
461	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
462	C₂²×Q₈	C₂³×C₇	1	4	yes	—
463	C₂²×Q₈	C₂³×C₇	1	6	yes	—
464	C₂²×Q₈	C₂³×C₇	1	3	yes	—
465	C₂²×Q₈	C₂³×C₇	1	6	yes	—
466	C₂²×Q₈	C₂³×C₇	1	6	yes	—
467	C₂²×Q₈	C₂³×C₇	1	12	yes	—
468	C₂²×D₄	C₂³×C₇	1	2	yes	—
469	C₂²×D₄	C₂³×C₇	1	3	yes	—
470	C₂²×D₄	C₂³×C₇	1	3	yes	—
471	C₂³×C₄	C₂³×C₇	1	3	yes	—
472	C₂³×C₄	C₂³×C₇	1	3	yes	—
473	C₂³×C₄	C₂³×C₇	1	6	yes	—
474	C₄⋊Q₈	C₂³×C₇	1	12	yes	—
475	C₄⋊Q₈	C₂³×C₇	1	12	yes	—
476	C₄⋊Q₈	C₂³×C₇	1	24	yes	—
477	C₄⋊Q₈	C₂³×C₇	1	6	yes	—
478	C₄⋊Q₈	C₂³×C₇	1	6	yes	—
479	C₄⋊Q₈	C₂³×C₇	1	24	yes	—
480	#126	C₂³×C₇	1	12	yes	—
481	#126	C₂³×C₇	1	12	yes	—
482	#126	C₂³×C₇	1	12	yes	—
483	#126	C₂³×C₇	1	24	yes	—
484	#126	C₂³×C₇	1	24	yes	—
485	#126	C₂³×C₇	1	24	yes	—
486	#125	C₂³×C₇	1	6	yes	—
487	#125	C₂³×C₇	1	12	yes	—
488	#125	C₂³×C₇	1	12	yes	—
489	#125	C₂³×C₇	1	12	yes	—
490	#125	C₂³×C₇	1	24	yes	—
491	#125	C₂³×C₇	1	24	yes	—
492	#124	C₂³×C₇	1	12	yes	—
493	#124	C₂³×C₇	1	12	yes	—
494	#124	C₂³×C₇	1	6	yes	—
495	#124	C₂³×C₇	1	12	yes	—
496	#124	C₂³×C₇	1	12	yes	—
497	#124	C₂³×C₇	1	24	yes	—
498	#123	C₂³×C₇	1	12	yes	—
499	#123	C₂³×C₇	1	12	yes	—
500	#123	C₂³×C₇	1	12	yes	—
501	#123	C₂³×C₇	1	24	yes	—
502	#123	C₂³×C₇	1	12	yes	—
503	#123	C₂³×C₇	1	4	yes	—
504	#123	C₂³×C₇	1	12	yes	—
505	#123	C₂³×C₇	1	24	yes	—
506	#123	C₂³×C₇	1	24	yes	—
507	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
508	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
509	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
510	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
511	C₂²⋊Q₈	C₂³×C₇	1	6	yes	—
512	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
513	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
514	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
515	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
516	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
517	C₂²⋊Q₈	C₂³×C₇	1	24	yes	—
518	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
519	C₂²⋊Q₈	C₂³×C₇	1	6	yes	—
520	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
521	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
522	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
523	C₂²⋊Q₈	C₂³×C₇	1	6	yes	—
524	C₂²⋊Q₈	C₂³×C₇	1	12	yes	—
525	C₂²⋊Q₈	C₂³×C₇	1	24	yes	—
526	C₂²⋊Q₈	C₂³×C₇	1	24	yes	—
527	C₂²⋊Q₈	C₂³×C₇	1	24	yes	—
528	#121	C₂³×C₇	1	12	yes	—
529	#121	C₂³×C₇	1	12	yes	—
530	#121	C₂³×C₇	1	2	yes	—
531	#121	C₂³×C₇	1	6	yes	—
532	#121	C₂³×C₇	1	12	yes	—
533	#121	C₂³×C₇	1	12	yes	—
534	#121	C₂³×C₇	1	12	yes	—
535	#121	C₂³×C₇	1	2	yes	—
536	#121	C₂³×C₇	1	12	yes	—
537	#121	C₂³×C₇	1	24	yes	—
538	#120	C₂³×C₇	1	12	yes	—
539	#120	C₂³×C₇	1	12	yes	—
540	#120	C₂³×C₇	1	4	yes	—
541	C₄×Q₈	C₂³×C₇	1	2	yes	—
542	C₄×Q₈	C₂³×C₇	1	4	yes	—
543	C₄×Q₈	C₂³×C₇	1	6	yes	—
544	C₄×Q₈	C₂³×C₇	1	12	yes	—
545	C₄×Q₈	C₂³×C₇	1	12	yes	—
546	C₄×Q₈	C₂³×C₇	1	12	yes	—
547	C₄×Q₈	C₂³×C₇	1	6	yes	—
548	C₄×Q₈	C₂³×C₇	1	12	yes	—
549	C₄×D₄	C₂³×C₇	1	12	yes	—
550	C₄×D₄	C₂³×C₇	1	12	yes	—
551	C₄×D₄	C₂³×C₇	1	12	yes	—
552	C₄×D₄	C₂³×C₇	1	12	yes	—
553	C₄×D₄	C₂³×C₇	1	12	yes	—
554	C₄×D₄	C₂³×C₇	1	12	yes	—
555	C₄×D₄	C₂³×C₇	1	24	yes	—
556	C₄×D₄	C₂³×C₇	1	24	yes	—
557	C₄×D₄	C₂³×C₇	1	12	yes	—
558	C₄×D₄	C₂³×C₇	1	12	yes	—
559	C₄×D₄	C₂³×C₇	1	6	yes	—
560	C₄×D₄	C₂³×C₇	1	24	yes	—
561	#117	C₂³×C₇	1	12	yes	—
562	#117	C₂³×C₇	1	12	yes	—
563	#117	C₂³×C₇	1	12	yes	—
564	#117	C₂³×C₇	1	6	yes	—
565	#117	C₂³×C₇	1	24	yes	—
566	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
567	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
568	C₂×C₄⋊C₄	C₂³×C₇	1	3	yes	—
569	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
570	C₂×C₄⋊C₄	C₂³×C₇	1	6	yes	—
571	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	—
572	C₂×C₄⋊C₄	C₂³×C₇	1	12	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₇	1	3	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₇	1	12	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₇	1	6	yes	—
579	C₂×C₄²	C₂³×C₇	1	3	yes	—
580	C₂×C₄²	C₂³×C₇	1	6	yes	—
581	C₂²×C₇	—	2	2	no	—
582	C₂²×C₇	—	2	1	no	—
583	C₂²×C₇	—	2	2	no	—
584	C₂²×C₇	—	2	1	no	—
585	C₂²×C₇	—	2	4	no	—
586	C₂²×C₇	—	2	6	no	—
587	C₂²×C₇	—	2	4	no	—
588	C₂²×C₇	—	2	6	no	—
589	C₂²×C₇	—	2	6	no	—
590	C₂²×C₇	—	2	4	no	—
591	C₂²×C₇	—	4	4	no	—
592	C₂²×C₇	—	4	8	no	—
593	C₂²×C₇	—	8	6	no	—
594	C₂²×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
595	C₂²×C₇	C₂×2₋¹⁺⁴	1	4	yes	—
596	C₂²×C₇	C₂⁶	1	1	yes	characteristic
597	C₄×C₇	—	2	2	no	—
598	C₄×C₇	—	2	3	no	—
599	C₄×C₇	—	2	12	no	—
600	C₄×C₇	—	2	6	no	—
601	C₄×C₇	—	2	6	no	—
602	C₄×C₇	—	2	4	no	—
603	C₄×C₇	—	2	12	no	—
604	C₄×C₇	—	2	2	no	—
605	C₄×C₇	C₂×H(5,𝔽₂)	1	6	yes	—
606	C₂⁴	C₂⁴×C₇	1	3	yes	—
607	C₂⁴	C₂⁴×C₇	1	2	yes	—
608	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
609	#41	—	2	8	no	—
610	#41	—	4	12	no	—
611	#41	—	4	12	no	—
612	#41	—	4	24	no	—
613	C₂×Q₈	—	2	8	no	—
614	C₂×Q₈	—	2	4	no	—
615	C₂×Q₈	—	2	16	no	—
616	C₂×Q₈	—	4	6	no	—
617	C₂×Q₈	—	4	12	no	—
618	C₂×Q₈	—	4	12	no	—
619	C₂×Q₈	—	4	24	no	—
620	C₂×Q₈	—	4	12	no	—
621	C₂×Q₈	C₂⁴×C₇	1	6	yes	—
622	C₂×Q₈	C₂⁴×C₇	1	12	yes	—
623	C₂×Q₈	C₂⁴×C₇	1	3	yes	—
624	C₂×Q₈	C₂⁴×C₇	1	6	yes	—
625	C₂×Q₈	C₂⁴×C₇	1	6	yes	—
626	C₂×Q₈	C₂⁴×C₇	1	6	yes	—
627	C₂×Q₈	C₂⁴×C₇	1	12	yes	—
628	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
629	C₂×D₄	—	2	8	no	—
630	C₂×D₄	—	2	12	no	—
631	C₂×D₄	—	4	6	no	—
632	C₂×D₄	C₂⁴×C₇	1	4	yes	—
633	C₂×D₄	C₂⁴×C₇	1	12	yes	—
634	C₂×D₄	C₂⁴×C₇	1	4	yes	—
635	C₂×D₄	C₂⁴×C₇	1	6	yes	—
636	C₂×D₄	C₂⁴×C₇	1	12	yes	—
637	C₂×D₄	C₂⁴×C₇	1	2	yes	—
638	C₂×D₄	C₂⁴×C₇	1	2	yes	—
639	C₂×D₄	C₂⁴×C₇	1	12	yes	—
640	C₂×D₄	C₂⁴×C₇	1	6	yes	—
641	C₂²×C₄	—	4	6	no	—
642	C₂²×C₄	—	4	12	no	—
643	C₂²×C₄	—	4	6	no	—
644	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
645	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
646	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
647	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
648	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
649	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
650	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
651	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
652	C₂²×C₄	C₂⁴×C₇	1	3	yes	—
653	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
654	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
655	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
657	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
658	C₂²×C₄	C₂⁴×C₇	1	6	yes	—
659	C₂²×C₄	C₂⁴×C₇	1	12	yes	—
660	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
661	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
662	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
663	C₄⋊C₄	C₂⁴×C₇	1	24	yes	—
664	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
665	C₄⋊C₄	C₂⁴×C₇	1	24	yes	—
666	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
667	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
668	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
669	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
670	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
671	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
672	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
673	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
674	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
675	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
676	C₄⋊C₄	C₂⁴×C₇	1	12	yes	—
677	C₄⋊C₄	C₂⁴×C₇	1	6	yes	—
678	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
679	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
680	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
681	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
682	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
683	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
684	C₂²⋊C₄	C₂⁴×C₇	1	24	yes	—
685	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
686	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
687	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
688	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
689	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
690	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
691	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
692	C₂²⋊C₄	C₂⁴×C₇	1	12	yes	—
693	C₄²	C₂⁴×C₇	1	12	yes	—
694	C₄²	C₂⁴×C₇	1	6	yes	—
695	C₄²	C₂⁴×C₇	1	12	yes	—
696	C₄²	C₂⁴×C₇	1	6	yes	—
697	C₄²	C₂⁴×C₇	1	24	yes	—
698	C₂×C₇	—	2	4	no	—
699	C₂×C₇	—	2	2	no	—
700	C₂×C₇	—	4	4	no	—
701	C₂×C₇	—	4	6	no	—
702	C₂×C₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂×C₇	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
704	C₂×C₇	2₋¹⁺⁶	1	1	yes	characteristic
705	C₂³	—	2	4	no	—
706	C₂³	—	2	6	no	—
707	C₂³	—	4	1	no	—
708	C₂³	—	4	2	no	—
709	C₂³	—	4	1	no	—
710	C₂³	—	4	2	no	—
711	C₂³	—	4	3	no	—
712	C₂³	—	4	3	no	—
713	C₂³	C₇×2₋¹⁺⁴	1	4	yes	complemented
714	C₂³	C₂⁵×C₇	1	4	yes	—
715	C₂³	C₂⁵×C₇	1	6	yes	—
716	C₂³	C₂⁵×C₇	1	1	yes	characteristic
717	C₂³	C₂⁵×C₇	1	2	yes	—
718	Q₈	—	2	12	no	—
719	Q₈	—	2	24	no	—
720	Q₈	—	2	6	no	—
721	Q₈	—	4	6	no	—
722	Q₈	—	4	12	no	—
723	Q₈	—	4	6	no	—
724	Q₈	—	4	6	no	—
725	Q₈	C₇×H(5,𝔽₂)	1	4	yes	—
726	D₄	—	2	8	no	—
727	D₄	—	2	8	no	—
728	D₄	—	2	24	no	—
729	D₄	—	2	12	no	—
730	D₄	—	4	6	no	—
731	D₄	—	4	12	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	2	no	—
734	D₄	—	4	12	no	—
735	C₂×C₄	—	2	6	no	—
736	C₂×C₄	—	2	4	no	—
737	C₂×C₄	—	2	6	no	—
738	C₂×C₄	—	2	12	no	—
739	C₂×C₄	—	2	24	no	—
740	C₂×C₄	—	2	12	no	—
741	C₂×C₄	—	4	1	no	—
742	C₂×C₄	—	4	6	no	—
743	C₂×C₄	—	4	6	no	—
744	C₂×C₄	—	4	12	no	—
745	C₂×C₄	—	4	3	no	—
746	C₂×C₄	—	4	6	no	—
747	C₂×C₄	—	4	6	no	—
748	C₂×C₄	—	4	12	no	—
749	C₂×C₄	—	4	1	no	—
750	C₂×C₄	—	4	12	no	—
751	C₂×C₄	C₂⁵×C₇	1	2	yes	—
752	C₂×C₄	C₂⁵×C₇	1	4	yes	—
753	C₂×C₄	C₂⁵×C₇	1	6	yes	—
754	C₂×C₄	C₂⁵×C₇	1	12	yes	—
755	C₂×C₄	C₂⁵×C₇	1	6	yes	—
756	C₂×C₄	C₂⁵×C₇	1	12	yes	—
757	C₂×C₄	C₂⁵×C₇	1	3	yes	—
758	C₂×C₄	C₂⁵×C₇	1	2	yes	—
759	C₂×C₄	C₂⁵×C₇	1	3	yes	—
760	C₇	#62893	1	1	yes	characteristic, direct product factor, Sylow
761	C₂²	—	2	2	no	—
762	C₂²	—	2	1	no	—
763	C₂²	—	2	2	no	—
764	C₂²	—	2	1	no	—
765	C₂²	—	2	4	no	—
766	C₂²	—	2	6	no	—
767	C₂²	—	2	4	no	—
768	C₂²	—	2	6	no	—
769	C₂²	—	2	6	no	—
770	C₂²	—	2	4	no	—
771	C₂²	—	4	4	no	—
772	C₂²	—	4	8	no	—
773	C₂²	—	8	6	no	—
774	C₂²	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
775	C₂²	C₂×C₇×2₋¹⁺⁴	1	4	yes	—
776	C₂²	C₂⁶×C₇	1	1	yes	characteristic
777	C₄	—	2	2	no	—
778	C₄	—	2	3	no	—
779	C₄	—	2	12	no	—
780	C₄	—	2	6	no	—
781	C₄	—	2	6	no	—
782	C₄	—	2	4	no	—
783	C₄	—	2	12	no	—
784	C₄	—	2	2	no	—
785	C₄	C₂×C₇×H(5,𝔽₂)	1	6	yes	—
786	C₂	—	2	4	no	—
787	C₂	—	2	2	no	—
788	C₂	—	4	4	no	—
789	C₂	—	4	6	no	—
790	C₂	C₂²×C₇×H(5,𝔽₂)	1	1	yes	characteristic
791	C₂	C₂²×C₇×2₋¹⁺⁴	1	1	yes	characteristic
792	C₂	C₇×2₋¹⁺⁶	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3561	C₂	semidirect
2. C₇×#3552	C₂	semidirect
3. C₇×#3541	C₂	semidirect
4. C₇×#3538	C₂	semidirect
5. C₇×#3523	C₂	semidirect
6. C₇×#3516	C₂	semidirect
7. C₇×#3505	C₂	semidirect
8. C₇×#3501	C₂	semidirect
9. C₇×#3489	C₂	semidirect
10. C₇×#3486	C₂	semidirect
11. C₂×C₇×D₄×Q₈	C₂	semidirect
12. C₂×C₇×#548	C₂	semidirect
13. C₇×#3459	C₂	semidirect
14. C₂×C₇×2₋¹⁺⁴	C₂²	semidirect
15. C₂²×C₇×#41	C₂²	semidirect
17. C₂³×C₇×Q₈	C₂²	semidirect
18. C₇×#563	C₂²	semidirect
19. C₇×#563	C₂²	semidirect
20. C₇×#562	C₂²	semidirect
21. C₇×#557	C₂²	semidirect
22. C₇×#557	C₂²	semidirect
23. C₇×#556	C₂²	semidirect
24. C₇×#556	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
27. C₇×#553	C₂²	semidirect
28. C₇×#553	C₂²	semidirect
29. C₇×#552	C₂²	semidirect
30. C₇×#552	C₂²	semidirect
31. C₇×#551	C₂²	semidirect
32. C₇×D₄×Q₈	C₂²	semidirect
33. C₇×D₄×Q₈	C₂²	semidirect
34. C₇×D₄×Q₈	C₂²	semidirect
35. C₇×D₄×Q₈	C₂²	semidirect
36. C₇×D₄×Q₈	C₂²	semidirect
37. C₇×D₄×Q₈	C₂²	semidirect
38. C₇×D₄×Q₈	C₂²	semidirect
39. C₇×#548	C₂²	semidirect
40. C₇×#548	C₂²	semidirect
41. C₇×#548	C₂²	semidirect
42. C₇×#548	C₂²	semidirect
43. C₇×#548	C₂²	semidirect
44. C₇×#547	C₂²	semidirect
45. C₇×#546	C₂²	semidirect
46. C₇×#544	C₂²	semidirect
47. C₇×#544	C₂²	semidirect
49. C₇×#543	C₂²	semidirect
50. C₇×#542	C₂²	semidirect
51. C₇×#542	C₂²	semidirect
52. C₇×#541	C₂²	semidirect
53. C₇×#541	C₂²	semidirect
55. C₇×#539	C₂²	semidirect
56. C₇×#539	C₂²	semidirect
57. C₇×#539	C₂²	semidirect
59. C₇×#538	C₂²	semidirect
60. C₇×#538	C₂²	semidirect
61. C₇×#537	C₂²	semidirect
62. C₇×#536	C₂²	semidirect
63. C₇×#536	C₂²	semidirect
64. C₇×#536	C₂²	semidirect
67. C₇×#533	C₂²	semidirect
68. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
70. C₇×#529	C₂²	semidirect
71. C₇×#529	C₂²	semidirect
72. C₂×C₇×#124	C₂²	semidirect
74. C₇×#525	C₂²	semidirect
75. C₇×#525	C₂²	semidirect
77. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
78. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
79. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
81. C₇×#520	C₂²	semidirect
82. C₇×#519	C₂²	semidirect
84. C₂×C₄×C₇×Q₈	C₂²	semidirect
85. C₂×C₄×C₇×Q₈	C₂²	semidirect
88. #62893	C₇	direct (N × H)
218. #3561	C₂×C₇	semidirect
219. #3552	C₂×C₇	semidirect
220. #3541	C₂×C₇	semidirect
221. #3538	C₂×C₇	semidirect
222. #3523	C₂×C₇	semidirect
223. #3516	C₂×C₇	semidirect
224. #3505	C₂×C₇	semidirect
225. #3501	C₂×C₇	semidirect
226. #3489	C₂×C₇	semidirect
227. #3486	C₂×C₇	semidirect
228. C₂×D₄×Q₈	C₂×C₇	semidirect
229. C₂×#548	C₂×C₇	semidirect
230. #3459	C₂×C₇	semidirect
323. C₂×2₋¹⁺⁴	C₂²×C₇	semidirect
324. C₂²×#41	C₂²×C₇	semidirect
326. C₂³×Q₈	C₂²×C₇	semidirect
327. #563	C₂²×C₇	semidirect
328. #563	C₂²×C₇	semidirect
329. #562	C₂²×C₇	semidirect
330. #557	C₂²×C₇	semidirect
331. #557	C₂²×C₇	semidirect
332. #556	C₂²×C₇	semidirect
333. #556	C₂²×C₇	semidirect
334. #554	C₂²×C₇	semidirect
335. #554	C₂²×C₇	semidirect
336. #553	C₂²×C₇	semidirect
337. #553	C₂²×C₇	semidirect
338. #552	C₂²×C₇	semidirect
339. #552	C₂²×C₇	semidirect
340. #551	C₂²×C₇	semidirect
341. D₄×Q₈	C₂²×C₇	semidirect
342. D₄×Q₈	C₂²×C₇	semidirect
343. D₄×Q₈	C₂²×C₇	semidirect
344. D₄×Q₈	C₂²×C₇	semidirect
345. D₄×Q₈	C₂²×C₇	semidirect
346. D₄×Q₈	C₂²×C₇	semidirect
347. D₄×Q₈	C₂²×C₇	semidirect
348. #548	C₂²×C₇	semidirect
349. #548	C₂²×C₇	semidirect
350. #548	C₂²×C₇	semidirect
351. #548	C₂²×C₇	semidirect
352. #548	C₂²×C₇	semidirect
353. #547	C₂²×C₇	semidirect
354. #546	C₂²×C₇	semidirect
355. #544	C₂²×C₇	semidirect
356. #544	C₂²×C₇	semidirect
358. #543	C₂²×C₇	semidirect
359. #542	C₂²×C₇	semidirect
360. #542	C₂²×C₇	semidirect
361. #541	C₂²×C₇	semidirect
362. #541	C₂²×C₇	semidirect
364. #539	C₂²×C₇	semidirect
365. #539	C₂²×C₇	semidirect
366. #539	C₂²×C₇	semidirect
368. #538	C₂²×C₇	semidirect
369. #538	C₂²×C₇	semidirect
370. #537	C₂²×C₇	semidirect
371. #536	C₂²×C₇	semidirect
372. #536	C₂²×C₇	semidirect
373. #536	C₂²×C₇	semidirect
376. #533	C₂²×C₇	semidirect
377. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
379. #529	C₂²×C₇	semidirect
380. #529	C₂²×C₇	semidirect
381. C₂×#124	C₂²×C₇	semidirect
383. #525	C₂²×C₇	semidirect
384. #525	C₂²×C₇	semidirect
386. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
387. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
388. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
390. #520	C₂²×C₇	semidirect
391. #519	C₂²×C₇	semidirect
393. C₂×C₄×Q₈	C₂²×C₇	semidirect
394. C₂×C₄×Q₈	C₂²×C₇	semidirect
405. C₂³×C₇	2₋¹⁺⁴	semidirect
713. C₂³	C₇×2₋¹⁺⁴	semidirect
760. C₇	#62893	direct (N × H)

Maximal subgroups

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

subgroup	index
C₇×#3561	2
C₇×#3552	2
C₇×#3541	2
C₇×#3538	2
C₇×#3523	2
C₇×#3516	2
C₇×#3505	2
C₇×#3501	2
C₇×#3489	2
C₇×#3486	2
C₂×C₇×D₄×Q₈	2
C₂×C₇×#548	2
C₇×#3459	2
#62893	7

Subgroups — C7×#62893 #13240109

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62893 #13240109