Subgroups — C₇×#62814 #13240030

Order 1792.

7286 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	8	yes	maximal, complemented
2	C₇×#3494	C₂	1	8	yes	maximal, complemented
3	C₇×#3493	C₂	1	4	yes	maximal, complemented
4	C₇×#3492	C₂	1	4	yes	maximal, complemented
5	C₇×#3491	C₂	1	4	yes	maximal, complemented
6	C₇×#3490	C₂	1	4	yes	maximal, complemented
7	C₇×#3475	C₂	1	16	yes	maximal, complemented
8	C₇×#3458	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3455	C₂	1	4	yes	maximal, complemented
10	C₇×#3449	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3444	C₂	1	4	yes	maximal, complemented
12	C₂×C₇×#525	C₂	1	2	yes	maximal, complemented
13	C₇×#3428	C₂	1	2	yes	maximal, complemented
14	C₂²×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₇×#41	C₂²	1	2	yes	—
16	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
17	C₇×#556	C₂²	1	16	yes	complemented
18	C₇×#555	C₂²	1	16	yes	complemented
19	C₇×#554	C₂²	1	16	yes	complemented
20	C₇×#553	C₂²	1	16	yes	complemented
21	C₇×#553	C₂²	1	16	yes	complemented
22	C₇×#552	C₂²	1	32	yes	complemented
23	C₇×#552	C₂²	1	16	yes	complemented
24	C₇×#552	C₂²	1	16	yes	complemented
25	C₇×#551	C₂²	1	32	yes	complemented
26	C₇×#551	C₂²	1	32	yes	complemented
27	C₇×#547	C₂²	1	16	yes	complemented
28	C₇×#546	C₂²	1	32	yes	complemented
29	C₇×#544	C₂²	1	4	yes	complemented
30	C₇×#544	C₂²	1	8	yes	complemented
31	C₇×#543	C₂²	1	4	yes	—
32	C₇×#542	C₂²	1	16	yes	complemented
33	C₇×#541	C₂²	1	8	yes	complemented
34	C₇×#540	C₂²	1	8	yes	complemented
35	C₇×#539	C₂²	1	16	yes	complemented
36	C₇×#538	C₂²	1	16	yes	complemented
37	C₇×#537	C₂²	1	4	yes	complemented
38	C₇×#536	C₂²	1	4	yes	complemented
39	C₇×#535	C₂²	1	4	yes	complemented
40	C₇×#534	C₂²	1	4	yes	—
41	C₇×#533	C₂²	1	4	yes	complemented
42	C₇×#533	C₂²	1	8	yes	complemented
43	C₇×#533	C₂²	1	8	yes	complemented
44	C₇×#532	C₂²	1	4	yes	complemented
45	C₇×#532	C₂²	1	8	yes	complemented
46	C₇×#529	C₂²	1	16	yes	complemented
47	C₇×#529	C₂²	1	16	yes	complemented
48	C₇×#529	C₂²	1	16	yes	complemented
49	C₇×#529	C₂²	1	32	yes	complemented
50	C₇×#525	C₂²	1	8	yes	—
51	C₇×#525	C₂²	1	8	yes	—
52	C₇×#525	C₂²	1	4	yes	complemented
53	C₇×#525	C₂²	1	4	yes	complemented
54	C₇×#525	C₂²	1	4	yes	complemented
55	C₇×#525	C₂²	1	4	yes	complemented
56	C₇×#525	C₂²	1	16	yes	complemented
57	C₇×#525	C₂²	1	8	yes	complemented
58	C₂×C₇×#123	C₂²	1	4	yes	—
59	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₇×#121	C₂²	1	4	yes	complemented
61	C₂×C₇×#120	C₂²	1	4	yes	—
62	C₇×#520	C₂²	1	8	yes	complemented
63	C₇×#520	C₂²	1	8	yes	complemented
64	C₇×#519	C₂²	1	4	yes	complemented
65	C₇×#518	C₂²	1	8	yes	—
66	C₇×#518	C₂²	1	4	yes	complemented
67	C₄×C₇×#41	C₂²	1	8	yes	complemented
68	C₄×C₇×#41	C₂²	1	8	yes	complemented
69	C₄×C₇×#41	C₂²	1	16	yes	complemented
70	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
71	C₂×C₇×#117	C₂²	1	1	yes	characteristic
72	C₂×C₇×#117	C₂²	1	1	yes	characteristic
73	C₂×C₇×#117	C₂²	1	2	yes	—
74	C₂×C₇×#117	C₂²	1	2	yes	—
75	C₂×C₇×#117	C₂²	1	2	yes	complemented
76	C₂×C₇×#117	C₂²	1	8	yes	complemented
77	C₂×C₇×#117	C₂²	1	2	yes	complemented
78	C₂×C₇×#117	C₂²	1	8	yes	complemented
79	C₂×C₇×#117	C₂²	1	8	yes	complemented
80	C₂²×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
81	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
82	C₂²×C₄²×C₇	C₂²	1	2	yes	complemented
83	#62814	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂⁵×C₇	C₂³	1	1	yes	characteristic
85	C₂×C₇×#41	—	2	16	no	—
86	C₂×C₇×#41	C₂³	1	4	yes	—
87	C₂×C₇×#41	C₂³	1	4	yes	—
88	C₂×C₇×#41	C₂³	1	4	yes	—
89	C₂×C₇×#41	C₂³	1	4	yes	—
90	C₂×C₇×#41	C₂³	1	16	yes	—
91	C₂²×C₇×Q₈	C₂³	1	2	yes	—
92	C₂²×C₇×D₄	C₂³	1	4	yes	—
93	C₂²×C₇×D₄	C₂³	1	2	yes	—
94	C₂²×C₇×D₄	C₂³	1	8	yes	—
95	C₂³×C₄×C₇	—	2	8	no	—
96	C₂³×C₄×C₇	C₂³	1	4	yes	—
97	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₇	C₂³	1	4	yes	—
101	C₂³×C₄×C₇	C₂³	1	4	yes	—
102	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
103	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₇	C₂³	1	4	yes	—
105	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
106	C₇×C₄⋊Q₈	C₂³	1	4	yes	complemented
107	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
108	C₇×C₄⋊Q₈	C₂³	1	16	yes	complemented
109	C₇×#127	C₂³	1	4	yes	complemented
110	C₇×#126	C₂³	1	32	yes	—
111	C₇×#126	C₂³	1	32	yes	complemented
112	C₇×#126	C₂³	1	32	yes	complemented
113	C₇×#125	C₂³	1	8	yes	complemented
114	C₇×#125	C₂³	1	16	yes	complemented
115	C₇×#125	C₂³	1	32	yes	complemented
116	C₇×#125	C₂³	1	16	yes	complemented
117	C₇×#124	C₂³	1	32	yes	—
118	C₇×#124	C₂³	1	8	yes	complemented
119	C₇×#124	C₂³	1	16	yes	complemented
120	C₇×#123	C₂³	1	16	yes	—
121	C₇×#123	C₂³	1	8	yes	—
122	C₇×#123	C₂³	1	8	yes	—
123	C₇×#123	C₂³	1	32	yes	—
124	C₇×#123	C₂³	1	16	yes	—
125	C₇×#123	C₂³	1	32	yes	—
126	C₇×#123	C₂³	1	32	yes	complemented
127	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
128	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
129	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
130	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
131	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
132	C₇×C₂²⋊Q₈	C₂³	1	16	yes	—
133	C₇×C₂²⋊Q₈	C₂³	1	32	yes	—
134	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
135	C₇×C₂²⋊Q₈	C₂³	1	32	yes	complemented
136	C₇×#121	C₂³	1	8	yes	—
137	C₇×#121	C₂³	1	8	yes	—
138	C₇×#121	C₂³	1	8	yes	—
139	C₇×#121	C₂³	1	8	yes	—
140	C₇×#121	C₂³	1	16	yes	—
141	C₇×#121	C₂³	1	16	yes	—
142	C₇×#121	C₂³	1	32	yes	—
143	C₇×#121	C₂³	1	16	yes	complemented
144	C₇×#120	C₂³	1	16	yes	—
145	C₇×#120	C₂³	1	8	yes	—
146	C₇×#120	C₂³	1	8	yes	—
147	C₇×#120	C₂³	1	16	yes	—
148	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
149	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
150	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
151	C₄×C₇×Q₈	C₂³	1	16	yes	complemented
152	C₄×C₇×D₄	C₂³	1	16	yes	—
153	C₄×C₇×D₄	C₂³	1	16	yes	—
154	C₄×C₇×D₄	C₂³	1	16	yes	—
155	C₄×C₇×D₄	C₂³	1	16	yes	—
156	C₄×C₇×D₄	C₂³	1	32	yes	—
157	C₄×C₇×D₄	C₂³	1	32	yes	—
158	C₄×C₇×D₄	C₂³	1	32	yes	—
159	C₄×C₇×D₄	C₂³	1	16	yes	complemented
160	C₄×C₇×D₄	C₂³	1	16	yes	complemented
161	C₄×C₇×D₄	C₂³	1	16	yes	complemented
162	C₄×C₇×D₄	C₂³	1	16	yes	complemented
163	C₇×#117	C₂³	1	4	yes	—
164	C₇×#117	C₂³	1	4	yes	—
165	C₇×#117	C₂³	1	4	yes	—
166	C₇×#117	C₂³	1	4	yes	—
167	C₇×#117	C₂³	1	4	yes	—
168	C₇×#117	C₂³	1	16	yes	—
169	C₇×#117	C₂³	1	4	yes	—
170	C₇×#117	C₂³	1	4	yes	—
171	C₇×#117	C₂³	1	4	yes	—
172	C₇×#117	C₂³	1	8	yes	—
173	C₇×#117	C₂³	1	8	yes	—
174	C₇×#117	C₂³	1	8	yes	—
175	C₇×#117	C₂³	1	8	yes	—
176	C₇×#117	C₂³	1	16	yes	—
177	C₇×#117	C₂³	1	16	yes	—
178	C₇×#117	C₂³	1	16	yes	complemented
179	C₇×#117	C₂³	1	16	yes	complemented
180	C₇×#117	C₂³	1	32	yes	complemented
181	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
184	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
185	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
186	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
187	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	—
188	C₂×C₇×C₄⋊C₄	C₂³	1	16	yes	complemented
189	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
190	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
191	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
192	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
193	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
194	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
195	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
196	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
197	C₂×C₄²×C₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₇	C₂³	1	4	yes	—
199	C₂×C₄²×C₇	C₂³	1	2	yes	—
200	C₂×C₄²×C₇	C₂³	1	8	yes	—
201	C₂×C₄²×C₇	C₂³	1	8	yes	—
202	C₂×C₄²×C₇	C₂³	1	4	yes	—
203	C₂×C₄²×C₇	C₂³	1	16	yes	complemented
204	#3495	C₂×C₇	1	8	yes	complemented
205	#3494	C₂×C₇	1	8	yes	complemented
206	#3493	C₂×C₇	1	4	yes	complemented
207	#3492	C₂×C₇	1	4	yes	complemented
208	#3491	C₂×C₇	1	4	yes	complemented
209	#3490	C₂×C₇	1	4	yes	complemented
210	#3475	C₂×C₇	1	16	yes	complemented
211	#3458	C₂×C₇	1	1	yes	characteristic, complemented
212	#3455	C₂×C₇	1	4	yes	complemented
213	#3449	C₂×C₇	1	1	yes	characteristic, complemented
214	#3444	C₂×C₇	1	4	yes	complemented
215	C₂×#525	C₂×C₇	1	2	yes	complemented
216	#3428	C₂×C₇	1	2	yes	complemented
217	C₂²×#117	C₂×C₇	1	1	yes	characteristic, complemented
218	C₂⁴×C₇	—	2	4	no	—
219	C₂⁴×C₇	—	4	4	no	—
220	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
221	C₂⁴×C₇	C₂⁴	1	4	yes	—
222	C₂⁴×C₇	C₂⁴	1	4	yes	—
223	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
224	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
225	C₇×#41	—	2	16	no	—
226	C₇×#41	—	2	16	no	—
227	C₇×#41	—	2	16	no	—
228	C₇×#41	—	2	16	no	—
229	C₇×#41	—	4	32	no	—
230	C₂×C₇×Q₈	—	2	8	no	—
231	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
232	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
233	C₂×C₇×Q₈	C₂⁴	1	16	yes	—
234	C₂×C₇×D₄	—	2	16	no	—
235	C₂×C₇×D₄	—	2	8	no	—
236	C₂×C₇×D₄	—	4	16	no	—
237	C₂×C₇×D₄	C₂⁴	1	8	yes	—
238	C₂×C₇×D₄	C₂⁴	1	8	yes	—
239	C₂×C₇×D₄	C₂⁴	1	16	yes	—
240	C₂×C₇×D₄	C₂⁴	1	4	yes	—
241	C₂×C₇×D₄	C₂⁴	1	4	yes	—
242	C₂×C₇×D₄	C₂⁴	1	16	yes	—
243	C₂×C₇×D₄	C₂⁴	1	16	yes	—
244	C₂²×C₄×C₇	—	2	4	no	—
245	C₂²×C₄×C₇	—	2	16	no	—
246	C₂²×C₄×C₇	—	2	16	no	—
247	C₂²×C₄×C₇	—	2	4	no	—
248	C₂²×C₄×C₇	—	2	4	no	—
249	C₂²×C₄×C₇	—	2	4	no	—
250	C₂²×C₄×C₇	—	2	4	no	—
251	C₂²×C₄×C₇	—	2	16	no	—
252	C₂²×C₄×C₇	—	4	8	no	—
253	C₂²×C₄×C₇	#41	1	8	yes	complemented
254	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
257	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
258	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
260	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
262	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
263	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
268	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
269	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
270	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
271	C₂²×C₄×C₇	C₂⁴	1	32	yes	—
272	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
277	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
278	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
279	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
280	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
281	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
282	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
283	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
284	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
285	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
286	C₇×C₄⋊C₄	C₂⁴	1	32	yes	—
287	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
288	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
289	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
290	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
291	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
292	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
293	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
294	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
295	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
296	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
297	C₇×C₂²⋊C₄	C₂⁴	1	32	yes	—
298	C₄²×C₇	C₂⁴	1	8	yes	—
299	C₄²×C₇	C₂⁴	1	4	yes	—
300	C₄²×C₇	C₂⁴	1	8	yes	—
301	C₄²×C₇	C₂⁴	1	4	yes	—
302	C₄²×C₇	C₂⁴	1	8	yes	—
303	C₄²×C₇	C₂⁴	1	32	yes	—
304	C₄²×C₇	C₂⁴	1	4	yes	—
305	C₄²×C₇	C₂⁴	1	4	yes	—
306	C₄²×C₇	C₂⁴	1	8	yes	—
307	C₂²×#41	C₂²×C₇	1	2	yes	—
308	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
309	#556	C₂²×C₇	1	16	yes	complemented
310	#555	C₂²×C₇	1	16	yes	complemented
311	#554	C₂²×C₇	1	16	yes	complemented
312	#553	C₂²×C₇	1	16	yes	complemented
313	#553	C₂²×C₇	1	16	yes	complemented
314	#552	C₂²×C₇	1	32	yes	complemented
315	#552	C₂²×C₇	1	16	yes	complemented
316	#552	C₂²×C₇	1	16	yes	complemented
317	#551	C₂²×C₇	1	32	yes	complemented
318	#551	C₂²×C₇	1	32	yes	complemented
319	#547	C₂²×C₇	1	16	yes	complemented
320	#546	C₂²×C₇	1	32	yes	complemented
321	#544	C₂²×C₇	1	4	yes	complemented
322	#544	C₂²×C₇	1	8	yes	complemented
323	#543	C₂²×C₇	1	4	yes	—
324	#542	C₂²×C₇	1	16	yes	complemented
325	#541	C₂²×C₇	1	8	yes	complemented
326	#540	C₂²×C₇	1	8	yes	complemented
327	#539	C₂²×C₇	1	16	yes	complemented
328	#538	C₂²×C₇	1	16	yes	complemented
329	#537	C₂²×C₇	1	4	yes	complemented
330	#536	C₂²×C₇	1	4	yes	complemented
331	#535	C₂²×C₇	1	4	yes	complemented
332	#534	C₂²×C₇	1	4	yes	—
333	#533	C₂²×C₇	1	4	yes	complemented
334	#533	C₂²×C₇	1	8	yes	complemented
335	#533	C₂²×C₇	1	8	yes	complemented
336	#532	C₂²×C₇	1	4	yes	complemented
337	#532	C₂²×C₇	1	8	yes	complemented
338	#529	C₂²×C₇	1	16	yes	complemented
339	#529	C₂²×C₇	1	16	yes	complemented
340	#529	C₂²×C₇	1	16	yes	complemented
341	#529	C₂²×C₇	1	32	yes	complemented
342	#525	C₂²×C₇	1	8	yes	—
343	#525	C₂²×C₇	1	8	yes	—
344	#525	C₂²×C₇	1	4	yes	complemented
345	#525	C₂²×C₇	1	4	yes	complemented
346	#525	C₂²×C₇	1	4	yes	complemented
347	#525	C₂²×C₇	1	4	yes	complemented
348	#525	C₂²×C₇	1	16	yes	complemented
349	#525	C₂²×C₇	1	8	yes	complemented
350	C₂×#123	C₂²×C₇	1	4	yes	—
351	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
352	C₂×#121	C₂²×C₇	1	4	yes	complemented
353	C₂×#120	C₂²×C₇	1	4	yes	—
354	#520	C₂²×C₇	1	8	yes	complemented
355	#520	C₂²×C₇	1	8	yes	complemented
356	#519	C₂²×C₇	1	4	yes	complemented
357	#518	C₂²×C₇	1	8	yes	—
358	#518	C₂²×C₇	1	4	yes	complemented
359	C₄×#41	C₂²×C₇	1	8	yes	complemented
360	C₄×#41	C₂²×C₇	1	8	yes	complemented
361	C₄×#41	C₂²×C₇	1	16	yes	complemented
362	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
363	C₂×#117	C₂²×C₇	1	1	yes	characteristic
364	C₂×#117	C₂²×C₇	1	1	yes	characteristic
365	C₂×#117	C₂²×C₇	1	2	yes	—
366	C₂×#117	C₂²×C₇	1	2	yes	—
367	C₂×#117	C₂²×C₇	1	2	yes	complemented
368	C₂×#117	C₂²×C₇	1	8	yes	complemented
369	C₂×#117	C₂²×C₇	1	2	yes	complemented
370	C₂×#117	C₂²×C₇	1	8	yes	complemented
371	C₂×#117	C₂²×C₇	1	8	yes	complemented
372	C₂²×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
373	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
374	C₂²×C₄²	C₂²×C₇	1	2	yes	complemented
375	C₂³×C₇	—	2	2	no	—
376	C₂³×C₇	—	2	4	no	—
377	C₂³×C₇	—	2	8	no	—
378	C₂³×C₇	—	2	2	no	—
379	C₂³×C₇	—	2	8	no	—
380	C₂³×C₇	—	2	8	no	—
381	C₂³×C₇	—	4	2	no	—
382	C₂³×C₇	—	4	4	no	—
383	C₂³×C₇	—	4	2	no	—
384	C₂³×C₇	—	4	8	no	—
385	C₂³×C₇	—	4	16	no	—
386	C₂³×C₇	C₂×#41	1	4	yes	—
387	C₂³×C₇	C₂⁵	1	2	yes	—
388	C₂³×C₇	C₂⁵	1	8	yes	—
389	C₂³×C₇	C₂⁵	1	2	yes	—
390	C₂³×C₇	C₂⁵	1	1	yes	characteristic
391	C₂³×C₇	C₂⁵	1	2	yes	—
392	C₇×Q₈	—	2	8	no	—
393	C₇×Q₈	—	2	8	no	—
394	C₇×Q₈	—	4	16	no	—
395	C₇×D₄	—	2	16	no	—
396	C₇×D₄	—	2	16	no	—
397	C₇×D₄	—	2	32	no	—
398	C₇×D₄	—	2	8	no	—
399	C₇×D₄	—	2	8	no	—
400	C₇×D₄	—	4	16	no	—
401	C₇×D₄	—	4	16	no	—
402	C₂×C₄×C₇	—	2	8	no	—
403	C₂×C₄×C₇	—	2	2	no	—
404	C₂×C₄×C₇	—	2	2	no	—
405	C₂×C₄×C₇	—	2	8	no	—
406	C₂×C₄×C₇	—	2	16	no	—
407	C₂×C₄×C₇	—	2	4	no	—
408	C₂×C₄×C₇	—	2	4	no	—
409	C₂×C₄×C₇	—	2	8	no	—
410	C₂×C₄×C₇	—	2	8	no	—
411	C₂×C₄×C₇	—	2	4	no	—
412	C₂×C₄×C₇	—	2	4	no	—
413	C₂×C₄×C₇	—	2	16	no	—
414	C₂×C₄×C₇	—	2	16	no	—
415	C₂×C₄×C₇	—	4	4	no	—
416	C₂×C₄×C₇	—	4	8	no	—
417	C₂×C₄×C₇	—	4	4	no	—
418	C₂×C₄×C₇	—	4	8	no	—
419	C₂×C₄×C₇	—	4	32	no	—
420	C₂×C₄×C₇	C₂×#41	1	8	yes	—
421	C₂×C₄×C₇	C₂×#41	1	8	yes	—
422	C₂×C₄×C₇	C₂×#41	1	4	yes	—
423	C₂×C₄×C₇	C₂×#41	1	4	yes	—
424	C₂×C₄×C₇	C₂⁵	1	2	yes	—
425	C₂×C₄×C₇	C₂⁵	1	8	yes	—
426	C₂×C₄×C₇	C₂⁵	1	8	yes	—
427	C₂×C₄×C₇	C₂⁵	1	8	yes	—
428	C₂×C₄×C₇	C₂⁵	1	16	yes	—
429	C₂×C₄×C₇	C₂⁵	1	2	yes	—
430	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
431	C₂×C₄×C₇	C₂⁵	1	2	yes	—
432	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
433	C₂⁵	C₂³×C₇	1	1	yes	characteristic
434	C₂×#41	—	2	16	no	—
435	C₂×#41	C₂³×C₇	1	4	yes	—
436	C₂×#41	C₂³×C₇	1	4	yes	—
437	C₂×#41	C₂³×C₇	1	4	yes	—
438	C₂×#41	C₂³×C₇	1	4	yes	—
439	C₂×#41	C₂³×C₇	1	16	yes	—
440	C₂²×Q₈	C₂³×C₇	1	2	yes	—
441	C₂²×D₄	C₂³×C₇	1	4	yes	—
442	C₂²×D₄	C₂³×C₇	1	2	yes	—
443	C₂²×D₄	C₂³×C₇	1	8	yes	—
444	C₂³×C₄	—	2	8	no	—
445	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
446	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
447	C₂³×C₄	C₂³×C₇	1	4	yes	—
448	C₂³×C₄	C₂³×C₇	1	4	yes	—
449	C₂³×C₄	C₂³×C₇	1	4	yes	—
450	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
451	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
452	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
453	C₂³×C₄	C₂³×C₇	1	4	yes	—
454	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₇	1	4	yes	complemented
456	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
457	C₄⋊Q₈	C₂³×C₇	1	16	yes	complemented
458	#127	C₂³×C₇	1	4	yes	complemented
459	#126	C₂³×C₇	1	32	yes	—
460	#126	C₂³×C₇	1	32	yes	complemented
461	#126	C₂³×C₇	1	32	yes	complemented
462	#125	C₂³×C₇	1	8	yes	complemented
463	#125	C₂³×C₇	1	16	yes	complemented
464	#125	C₂³×C₇	1	32	yes	complemented
465	#125	C₂³×C₇	1	16	yes	complemented
466	#124	C₂³×C₇	1	32	yes	—
467	#124	C₂³×C₇	1	8	yes	complemented
468	#124	C₂³×C₇	1	16	yes	complemented
469	#123	C₂³×C₇	1	16	yes	—
470	#123	C₂³×C₇	1	8	yes	—
471	#123	C₂³×C₇	1	8	yes	—
472	#123	C₂³×C₇	1	32	yes	—
473	#123	C₂³×C₇	1	16	yes	—
474	#123	C₂³×C₇	1	32	yes	—
475	#123	C₂³×C₇	1	32	yes	complemented
476	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
477	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
478	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
479	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
480	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
481	C₂²⋊Q₈	C₂³×C₇	1	16	yes	—
482	C₂²⋊Q₈	C₂³×C₇	1	32	yes	—
483	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
484	C₂²⋊Q₈	C₂³×C₇	1	32	yes	complemented
485	#121	C₂³×C₇	1	8	yes	—
486	#121	C₂³×C₇	1	8	yes	—
487	#121	C₂³×C₇	1	8	yes	—
488	#121	C₂³×C₇	1	8	yes	—
489	#121	C₂³×C₇	1	16	yes	—
490	#121	C₂³×C₇	1	16	yes	—
491	#121	C₂³×C₇	1	32	yes	—
492	#121	C₂³×C₇	1	16	yes	complemented
493	#120	C₂³×C₇	1	16	yes	—
494	#120	C₂³×C₇	1	8	yes	—
495	#120	C₂³×C₇	1	8	yes	—
496	#120	C₂³×C₇	1	16	yes	—
497	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
498	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
499	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
500	C₄×Q₈	C₂³×C₇	1	16	yes	complemented
501	C₄×D₄	C₂³×C₇	1	16	yes	—
502	C₄×D₄	C₂³×C₇	1	16	yes	—
503	C₄×D₄	C₂³×C₇	1	16	yes	—
504	C₄×D₄	C₂³×C₇	1	16	yes	—
505	C₄×D₄	C₂³×C₇	1	32	yes	—
506	C₄×D₄	C₂³×C₇	1	32	yes	—
507	C₄×D₄	C₂³×C₇	1	32	yes	—
508	C₄×D₄	C₂³×C₇	1	16	yes	complemented
509	C₄×D₄	C₂³×C₇	1	16	yes	complemented
510	C₄×D₄	C₂³×C₇	1	16	yes	complemented
511	C₄×D₄	C₂³×C₇	1	16	yes	complemented
512	#117	C₂³×C₇	1	4	yes	—
513	#117	C₂³×C₇	1	4	yes	—
514	#117	C₂³×C₇	1	4	yes	—
515	#117	C₂³×C₇	1	4	yes	—
516	#117	C₂³×C₇	1	4	yes	—
517	#117	C₂³×C₇	1	16	yes	—
518	#117	C₂³×C₇	1	4	yes	—
519	#117	C₂³×C₇	1	4	yes	—
520	#117	C₂³×C₇	1	4	yes	—
521	#117	C₂³×C₇	1	8	yes	—
522	#117	C₂³×C₇	1	8	yes	—
523	#117	C₂³×C₇	1	8	yes	—
524	#117	C₂³×C₇	1	8	yes	—
525	#117	C₂³×C₇	1	16	yes	—
526	#117	C₂³×C₇	1	16	yes	—
527	#117	C₂³×C₇	1	16	yes	complemented
528	#117	C₂³×C₇	1	16	yes	complemented
529	#117	C₂³×C₇	1	32	yes	complemented
530	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
531	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
532	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
534	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
535	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
536	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	—
537	C₂×C₄⋊C₄	C₂³×C₇	1	16	yes	complemented
538	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
546	C₂×C₄²	C₂³×C₇	1	2	yes	—
547	C₂×C₄²	C₂³×C₇	1	4	yes	—
548	C₂×C₄²	C₂³×C₇	1	2	yes	—
549	C₂×C₄²	C₂³×C₇	1	4	yes	—
550	C₂×C₄²	C₂³×C₇	1	8	yes	—
551	C₂×C₄²	C₂³×C₇	1	8	yes	—
552	C₂×C₄²	C₂³×C₇	1	16	yes	complemented
553	C₂²×C₇	—	2	8	no	—
554	C₂²×C₇	—	2	2	no	—
555	C₂²×C₇	—	2	2	no	—
556	C₂²×C₇	—	2	2	no	—
557	C₂²×C₇	—	2	4	no	—
558	C₂²×C₇	—	2	2	no	—
559	C₂²×C₇	—	2	8	no	—
560	C₂²×C₇	—	2	16	no	—
561	C₂²×C₇	—	2	4	no	—
562	C₂²×C₇	—	4	4	no	—
563	C₂²×C₇	—	4	16	no	—
564	C₂²×C₇	—	4	4	no	—
565	C₂²×C₇	—	8	8	no	—
566	C₂²×C₇	C₂²×#41	1	4	yes	—
567	C₂²×C₇	C₂²×#41	1	2	yes	—
568	C₂²×C₇	#585	1	4	yes	—
569	C₂²×C₇	C₂⁶	1	1	yes	characteristic
570	C₄×C₇	—	2	2	no	—
571	C₄×C₇	—	2	2	no	—
572	C₄×C₇	—	2	8	no	—
573	C₄×C₇	—	2	8	no	—
574	C₄×C₇	—	2	8	no	—
575	C₄×C₇	—	2	16	no	—
576	C₄×C₇	C₂²×#41	1	2	yes	—
577	C₄×C₇	C₂²×#41	1	4	yes	—
578	C₄×C₇	C₂²×#41	1	2	yes	—
579	C₂⁴	—	2	4	no	—
580	C₂⁴	—	4	4	no	—
581	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
582	C₂⁴	C₂⁴×C₇	1	4	yes	—
583	C₂⁴	C₂⁴×C₇	1	4	yes	—
584	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
585	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
586	#41	—	2	16	no	—
587	#41	—	2	16	no	—
588	#41	—	2	16	no	—
589	#41	—	2	16	no	—
590	#41	—	4	32	no	—
591	C₂×Q₈	—	2	8	no	—
592	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
593	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
594	C₂×Q₈	C₂⁴×C₇	1	16	yes	—
595	C₂×D₄	—	2	16	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	4	16	no	—
598	C₂×D₄	C₂⁴×C₇	1	8	yes	—
599	C₂×D₄	C₂⁴×C₇	1	8	yes	—
600	C₂×D₄	C₂⁴×C₇	1	16	yes	—
601	C₂×D₄	C₂⁴×C₇	1	4	yes	—
602	C₂×D₄	C₂⁴×C₇	1	4	yes	—
603	C₂×D₄	C₂⁴×C₇	1	16	yes	—
604	C₂×D₄	C₂⁴×C₇	1	16	yes	—
605	C₂²×C₄	—	2	4	no	—
606	C₂²×C₄	—	2	16	no	—
607	C₂²×C₄	—	2	16	no	—
608	C₂²×C₄	—	2	4	no	—
609	C₂²×C₄	—	2	4	no	—
610	C₂²×C₄	—	2	4	no	—
611	C₂²×C₄	—	2	4	no	—
612	C₂²×C₄	—	2	16	no	—
613	C₂²×C₄	—	4	8	no	—
614	C₂²×C₄	C₇×#41	1	8	yes	complemented
615	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
616	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
617	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
619	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
620	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
621	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
622	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
623	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
624	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
625	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
626	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
627	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
628	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
629	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
630	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
631	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
632	C₂²×C₄	C₂⁴×C₇	1	32	yes	—
633	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
634	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
635	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
636	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
638	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
639	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
640	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
641	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
642	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
643	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
644	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
645	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
646	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
647	C₄⋊C₄	C₂⁴×C₇	1	32	yes	—
648	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
649	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
650	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
651	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
652	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
653	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
654	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
655	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
656	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
657	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
658	C₂²⋊C₄	C₂⁴×C₇	1	32	yes	—
659	C₄²	C₂⁴×C₇	1	4	yes	—
660	C₄²	C₂⁴×C₇	1	8	yes	—
661	C₄²	C₂⁴×C₇	1	4	yes	—
662	C₄²	C₂⁴×C₇	1	4	yes	—
663	C₄²	C₂⁴×C₇	1	8	yes	—
664	C₄²	C₂⁴×C₇	1	4	yes	—
665	C₄²	C₂⁴×C₇	1	8	yes	—
666	C₄²	C₂⁴×C₇	1	8	yes	—
667	C₄²	C₂⁴×C₇	1	32	yes	—
668	C₂×C₇	—	2	2	no	—
669	C₂×C₇	—	2	4	no	—
670	C₂×C₇	—	2	4	no	—
671	C₂×C₇	—	4	2	no	—
672	C₂×C₇	—	4	8	no	—
673	C₂×C₇	C₂³×#41	1	1	yes	characteristic
674	C₂×C₇	C₂×#585	1	2	yes	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	4	no	—
677	C₂³	—	2	8	no	—
678	C₂³	—	2	2	no	—
679	C₂³	—	2	8	no	—
680	C₂³	—	2	8	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	4	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	8	no	—
685	C₂³	—	4	16	no	—
686	C₂³	C₂×C₇×#41	1	4	yes	—
687	C₂³	C₂⁵×C₇	1	2	yes	—
688	C₂³	C₂⁵×C₇	1	8	yes	—
689	C₂³	C₂⁵×C₇	1	2	yes	—
690	C₂³	C₂⁵×C₇	1	1	yes	characteristic
691	C₂³	C₂⁵×C₇	1	2	yes	—
692	Q₈	—	2	8	no	—
693	Q₈	—	2	8	no	—
694	Q₈	—	4	16	no	—
695	D₄	—	2	16	no	—
696	D₄	—	2	16	no	—
697	D₄	—	2	32	no	—
698	D₄	—	2	8	no	—
699	D₄	—	2	8	no	—
700	D₄	—	4	16	no	—
701	D₄	—	4	16	no	—
702	C₂×C₄	—	2	8	no	—
703	C₂×C₄	—	2	2	no	—
704	C₂×C₄	—	2	2	no	—
705	C₂×C₄	—	2	8	no	—
706	C₂×C₄	—	2	16	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	4	no	—
709	C₂×C₄	—	2	8	no	—
710	C₂×C₄	—	2	8	no	—
711	C₂×C₄	—	2	4	no	—
712	C₂×C₄	—	2	4	no	—
713	C₂×C₄	—	2	16	no	—
714	C₂×C₄	—	2	16	no	—
715	C₂×C₄	—	4	4	no	—
716	C₂×C₄	—	4	8	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	8	no	—
719	C₂×C₄	—	4	32	no	—
720	C₂×C₄	C₂×C₇×#41	1	8	yes	—
721	C₂×C₄	C₂×C₇×#41	1	8	yes	—
722	C₂×C₄	C₂×C₇×#41	1	4	yes	—
723	C₂×C₄	C₂×C₇×#41	1	4	yes	—
724	C₂×C₄	C₂⁵×C₇	1	2	yes	—
725	C₂×C₄	C₂⁵×C₇	1	8	yes	—
726	C₂×C₄	C₂⁵×C₇	1	8	yes	—
727	C₂×C₄	C₂⁵×C₇	1	8	yes	—
728	C₂×C₄	C₂⁵×C₇	1	16	yes	—
729	C₂×C₄	C₂⁵×C₇	1	2	yes	—
730	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
731	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
732	C₂×C₄	C₂⁵×C₇	1	2	yes	—
733	C₇	#62814	1	1	yes	characteristic, direct product factor, Sylow
734	C₂²	—	2	8	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	4	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	8	no	—
741	C₂²	—	2	16	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	16	no	—
745	C₂²	—	4	4	no	—
746	C₂²	—	8	8	no	—
747	C₂²	C₂²×C₇×#41	1	4	yes	—
748	C₂²	C₂²×C₇×#41	1	2	yes	—
749	C₂²	C₇×#585	1	4	yes	—
750	C₂²	C₂⁶×C₇	1	1	yes	characteristic
751	C₄	—	2	2	no	—
752	C₄	—	2	2	no	—
753	C₄	—	2	8	no	—
754	C₄	—	2	8	no	—
755	C₄	—	2	8	no	—
756	C₄	—	2	16	no	—
757	C₄	C₂²×C₇×#41	1	2	yes	—
758	C₄	C₂²×C₇×#41	1	4	yes	—
759	C₄	C₂²×C₇×#41	1	2	yes	—
760	C₂	—	2	2	no	—
761	C₂	—	2	4	no	—
762	C₂	—	2	4	no	—
763	C₂	—	4	2	no	—
764	C₂	—	4	8	no	—
765	C₂	C₂³×C₇×#41	1	1	yes	characteristic
766	C₂	C₂×C₇×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
socle	C₂²×C₇	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3495	C₂	semidirect
2. C₇×#3494	C₂	semidirect
3. C₇×#3493	C₂	semidirect
4. C₇×#3492	C₂	semidirect
5. C₇×#3491	C₂	semidirect
6. C₇×#3490	C₂	semidirect
7. C₇×#3475	C₂	semidirect
8. C₇×#3458	C₂	semidirect
9. C₇×#3455	C₂	semidirect
10. C₇×#3449	C₂	semidirect
11. C₇×#3444	C₂	semidirect
12. C₂×C₇×#525	C₂	semidirect
13. C₇×#3428	C₂	semidirect
14. C₂²×C₇×#117	C₂	semidirect
17. C₇×#556	C₂²	semidirect
18. C₇×#555	C₂²	semidirect
19. C₇×#554	C₂²	semidirect
20. C₇×#553	C₂²	semidirect
21. C₇×#553	C₂²	semidirect
22. C₇×#552	C₂²	semidirect
23. C₇×#552	C₂²	semidirect
24. C₇×#552	C₂²	semidirect
25. C₇×#551	C₂²	semidirect
26. C₇×#551	C₂²	semidirect
27. C₇×#547	C₂²	semidirect
28. C₇×#546	C₂²	semidirect
29. C₇×#544	C₂²	semidirect
30. C₇×#544	C₂²	semidirect
32. C₇×#542	C₂²	semidirect
33. C₇×#541	C₂²	semidirect
34. C₇×#540	C₂²	semidirect
35. C₇×#539	C₂²	semidirect
36. C₇×#538	C₂²	semidirect
37. C₇×#537	C₂²	semidirect
38. C₇×#536	C₂²	semidirect
39. C₇×#535	C₂²	semidirect
41. C₇×#533	C₂²	semidirect
42. C₇×#533	C₂²	semidirect
43. C₇×#533	C₂²	semidirect
44. C₇×#532	C₂²	semidirect
45. C₇×#532	C₂²	semidirect
46. C₇×#529	C₂²	semidirect
47. C₇×#529	C₂²	semidirect
48. C₇×#529	C₂²	semidirect
49. C₇×#529	C₂²	semidirect
52. C₇×#525	C₂²	semidirect
53. C₇×#525	C₂²	semidirect
54. C₇×#525	C₂²	semidirect
55. C₇×#525	C₂²	semidirect
56. C₇×#525	C₂²	semidirect
57. C₇×#525	C₂²	semidirect
59. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₇×#121	C₂²	semidirect
62. C₇×#520	C₂²	semidirect
63. C₇×#520	C₂²	semidirect
64. C₇×#519	C₂²	semidirect
66. C₇×#518	C₂²	semidirect
67. C₄×C₇×#41	C₂²	semidirect
68. C₄×C₇×#41	C₂²	semidirect
69. C₄×C₇×#41	C₂²	semidirect
70. C₂×C₄×C₇×D₄	C₂²	semidirect
75. C₂×C₇×#117	C₂²	semidirect
76. C₂×C₇×#117	C₂²	semidirect
77. C₂×C₇×#117	C₂²	semidirect
78. C₂×C₇×#117	C₂²	semidirect
79. C₂×C₇×#117	C₂²	semidirect
80. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
82. C₂²×C₄²×C₇	C₂²	semidirect
83. #62814	C₇	direct (N × H)
106. C₇×C₄⋊Q₈	C₂³	semidirect
107. C₇×C₄⋊Q₈	C₂³	semidirect
108. C₇×C₄⋊Q₈	C₂³	semidirect
109. C₇×#127	C₂³	semidirect
111. C₇×#126	C₂³	semidirect
112. C₇×#126	C₂³	semidirect
113. C₇×#125	C₂³	semidirect
114. C₇×#125	C₂³	semidirect
115. C₇×#125	C₂³	semidirect
116. C₇×#125	C₂³	semidirect
118. C₇×#124	C₂³	semidirect
119. C₇×#124	C₂³	semidirect
126. C₇×#123	C₂³	semidirect
134. C₇×C₂²⋊Q₈	C₂³	semidirect
135. C₇×C₂²⋊Q₈	C₂³	semidirect
143. C₇×#121	C₂³	semidirect
148. C₄×C₇×Q₈	C₂³	semidirect
149. C₄×C₇×Q₈	C₂³	semidirect
150. C₄×C₇×Q₈	C₂³	semidirect
151. C₄×C₇×Q₈	C₂³	semidirect
159. C₄×C₇×D₄	C₂³	semidirect
160. C₄×C₇×D₄	C₂³	semidirect
161. C₄×C₇×D₄	C₂³	semidirect
162. C₄×C₇×D₄	C₂³	semidirect
178. C₇×#117	C₂³	semidirect
179. C₇×#117	C₂³	semidirect
180. C₇×#117	C₂³	semidirect
188. C₂×C₇×C₄⋊C₄	C₂³	semidirect
203. C₂×C₄²×C₇	C₂³	semidirect
204. #3495	C₂×C₇	semidirect
205. #3494	C₂×C₇	semidirect
206. #3493	C₂×C₇	semidirect
207. #3492	C₂×C₇	semidirect
208. #3491	C₂×C₇	semidirect
209. #3490	C₂×C₇	semidirect
210. #3475	C₂×C₇	semidirect
211. #3458	C₂×C₇	semidirect
212. #3455	C₂×C₇	semidirect
213. #3449	C₂×C₇	semidirect
214. #3444	C₂×C₇	semidirect
215. C₂×#525	C₂×C₇	semidirect
216. #3428	C₂×C₇	semidirect
217. C₂²×#117	C₂×C₇	semidirect
253. C₂²×C₄×C₇	#41	semidirect
309. #556	C₂²×C₇	semidirect
310. #555	C₂²×C₇	semidirect
311. #554	C₂²×C₇	semidirect
312. #553	C₂²×C₇	semidirect
313. #553	C₂²×C₇	semidirect
314. #552	C₂²×C₇	semidirect
315. #552	C₂²×C₇	semidirect
316. #552	C₂²×C₇	semidirect
317. #551	C₂²×C₇	semidirect
318. #551	C₂²×C₇	semidirect
319. #547	C₂²×C₇	semidirect
320. #546	C₂²×C₇	semidirect
321. #544	C₂²×C₇	semidirect
322. #544	C₂²×C₇	semidirect
324. #542	C₂²×C₇	semidirect
325. #541	C₂²×C₇	semidirect
326. #540	C₂²×C₇	semidirect
327. #539	C₂²×C₇	semidirect
328. #538	C₂²×C₇	semidirect
329. #537	C₂²×C₇	semidirect
330. #536	C₂²×C₇	semidirect
331. #535	C₂²×C₇	semidirect
333. #533	C₂²×C₇	semidirect
334. #533	C₂²×C₇	semidirect
335. #533	C₂²×C₇	semidirect
336. #532	C₂²×C₇	semidirect
337. #532	C₂²×C₇	semidirect
338. #529	C₂²×C₇	semidirect
339. #529	C₂²×C₇	semidirect
340. #529	C₂²×C₇	semidirect
341. #529	C₂²×C₇	semidirect
344. #525	C₂²×C₇	semidirect
345. #525	C₂²×C₇	semidirect
346. #525	C₂²×C₇	semidirect
347. #525	C₂²×C₇	semidirect
348. #525	C₂²×C₇	semidirect
349. #525	C₂²×C₇	semidirect
351. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
352. C₂×#121	C₂²×C₇	semidirect
354. #520	C₂²×C₇	semidirect
355. #520	C₂²×C₇	semidirect
356. #519	C₂²×C₇	semidirect
358. #518	C₂²×C₇	semidirect
359. C₄×#41	C₂²×C₇	semidirect
360. C₄×#41	C₂²×C₇	semidirect
361. C₄×#41	C₂²×C₇	semidirect
362. C₂×C₄×D₄	C₂²×C₇	semidirect
367. C₂×#117	C₂²×C₇	semidirect
368. C₂×#117	C₂²×C₇	semidirect
369. C₂×#117	C₂²×C₇	semidirect
370. C₂×#117	C₂²×C₇	semidirect
371. C₂×#117	C₂²×C₇	semidirect
372. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
374. C₂²×C₄²	C₂²×C₇	semidirect
455. C₄⋊Q₈	C₂³×C₇	semidirect
456. C₄⋊Q₈	C₂³×C₇	semidirect
457. C₄⋊Q₈	C₂³×C₇	semidirect
458. #127	C₂³×C₇	semidirect
460. #126	C₂³×C₇	semidirect
461. #126	C₂³×C₇	semidirect
462. #125	C₂³×C₇	semidirect
463. #125	C₂³×C₇	semidirect
464. #125	C₂³×C₇	semidirect
465. #125	C₂³×C₇	semidirect
467. #124	C₂³×C₇	semidirect
468. #124	C₂³×C₇	semidirect
475. #123	C₂³×C₇	semidirect
483. C₂²⋊Q₈	C₂³×C₇	semidirect
484. C₂²⋊Q₈	C₂³×C₇	semidirect
492. #121	C₂³×C₇	semidirect
497. C₄×Q₈	C₂³×C₇	semidirect
498. C₄×Q₈	C₂³×C₇	semidirect
499. C₄×Q₈	C₂³×C₇	semidirect
500. C₄×Q₈	C₂³×C₇	semidirect
508. C₄×D₄	C₂³×C₇	semidirect
509. C₄×D₄	C₂³×C₇	semidirect
510. C₄×D₄	C₂³×C₇	semidirect
511. C₄×D₄	C₂³×C₇	semidirect
527. #117	C₂³×C₇	semidirect
528. #117	C₂³×C₇	semidirect
529. #117	C₂³×C₇	semidirect
537. C₂×C₄⋊C₄	C₂³×C₇	semidirect
552. C₂×C₄²	C₂³×C₇	semidirect
614. C₂²×C₄	C₇×#41	semidirect
733. C₇	#62814	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×#3495	2
C₇×#3494	2
C₇×#3493	2
C₇×#3492	2
C₇×#3491	2
C₇×#3490	2
C₇×#3475	2
C₇×#3458	2
C₇×#3455	2
C₇×#3449	2
C₇×#3444	2
C₂×C₇×#525	2
C₇×#3428	2
C₂²×C₇×#117	2
#62814	7

Subgroups — C7×#62814 #13240030

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62814 #13240030