Subgroups — C₇×#60846 #13238062

Order 1792.

1800 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#533	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3233	C₂	1	4	yes	maximal, complemented
4	C₇×#3232	C₂	1	4	yes	maximal, complemented
5	C₇×#3231	C₂	1	2	yes	maximal, complemented
6	C₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3228	C₂	1	2	yes	maximal, complemented
9	C₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3160	C₂	1	2	yes	maximal, complemented
12	C₇×#3131	C₂	1	2	yes	maximal, complemented
13	C₇×#3091	C₂	1	4	yes	maximal, complemented
14	C₇×#3076	C₂	1	4	yes	maximal, complemented
15	C₂×C₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#533	—	2	1	no	—
17	C₇×#533	—	2	1	no	—
18	C₇×#533	—	2	1	no	—
19	C₇×#533	—	2	1	no	—
20	C₇×#533	C₂²	1	1	yes	characteristic
21	C₇×#533	C₂²	1	1	yes	characteristic
22	C₇×#533	C₂²	1	1	yes	characteristic
23	C₇×#533	C₂²	1	2	yes	—
24	C₇×#533	C₂²	1	2	yes	—
25	C₇×#533	C₂²	1	2	yes	—
26	C₇×#533	C₂²	1	2	yes	—
27	C₇×#532	C₂²	1	1	yes	characteristic
28	C₇×#532	C₂²	1	1	yes	characteristic
29	C₇×#532	C₂²	1	1	yes	characteristic
30	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
32	C₇×#529	—	2	1	no	—
33	C₇×#529	—	2	1	no	—
34	C₇×#529	—	2	1	no	—
35	C₇×#529	—	2	1	no	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₂×C₇×#125	C₂²	1	2	yes	—
39	C₇×#525	—	2	1	no	—
40	C₇×#525	—	2	1	no	—
41	C₇×#525	C₂²	1	2	yes	—
42	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
43	C₂×C₇×C₂²⋊Q₈	—	2	1	no	—
44	C₄×C₇×#41	—	2	1	no	—
45	C₄×C₇×#41	—	2	1	no	—
46	C₄×C₇×#41	C₂²	1	2	yes	—
47	C₂×C₄×C₇×Q₈	—	2	1	no	—
48	C₂×C₄×C₇×Q₈	—	2	1	no	—
49	C₂×C₇×#117	C₂²	1	2	yes	—
50	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
51	C₇×#500	C₂²	1	2	yes	complemented
52	C₇×#500	C₂²	1	2	yes	complemented
53	C₇×#499	C₂²	1	8	yes	complemented
54	C₇×#498	C₂²	1	2	yes	complemented
55	C₇×#498	C₂²	1	2	yes	complemented
56	C₇×#488	C₂²	1	8	yes	complemented
57	C₇×#487	C₂²	1	2	yes	complemented
58	C₇×#487	C₂²	1	2	yes	complemented
59	C₇×#486	C₂²	1	2	yes	complemented
60	C₇×#486	C₂²	1	2	yes	complemented
61	C₇×#485	C₂²	1	8	yes	—
62	C₇×#484	C₂²	1	4	yes	—
63	C₇×#483	C₂²	1	4	yes	—
64	C₇×#482	C₂²	1	8	yes	—
65	C₇×#481	C₂²	1	4	yes	—
66	C₇×#480	C₂²	1	4	yes	—
67	C₇×#479	C₂²	1	8	yes	complemented
68	C₇×#478	C₂²	1	8	yes	complemented
69	C₇×#477	C₂²	1	4	yes	complemented
70	C₇×#476	C₂²	1	4	yes	complemented
71	C₇×#475	C₂²	1	4	yes	complemented
72	C₇×#474	C₂²	1	4	yes	complemented
73	C₇×#431	C₂²	1	1	yes	characteristic
74	C₇×#431	C₂²	1	1	yes	characteristic
75	C₇×#431	C₂²	1	2	yes	—
76	C₇×#431	C₂²	1	2	yes	—
77	C₇×#431	C₂²	1	2	yes	—
78	C₇×#427	C₂²	1	8	yes	—
79	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	—
80	C₇×#416	C₂²	1	8	yes	—
81	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
82	C₂×C₄×C₇×C₈	C₂²	1	2	yes	—
83	#60846	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
84	C₂×C₇×#41	—	2	1	no	—
85	C₂×C₇×#41	—	2	1	no	—
86	C₂×C₇×#41	C₂³	1	2	yes	—
87	C₂²×C₇×Q₈	—	2	1	no	—
88	C₂²×C₇×Q₈	—	2	1	no	—
89	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
90	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
91	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
92	C₂²×C₇×C₈	C₂³	1	4	yes	—
93	C₇×C₄⋊Q₈	—	2	1	no	—
94	C₇×C₄⋊Q₈	—	2	1	no	—
95	C₇×C₄⋊Q₈	—	2	1	no	—
96	C₇×C₄⋊Q₈	—	2	1	no	—
97	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
98	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
99	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
100	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
101	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
102	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
104	C₇×#127	C₂³	1	1	yes	characteristic
105	C₇×#126	—	2	2	no	—
106	C₇×#126	—	2	2	no	—
107	C₇×#125	—	2	2	no	—
108	C₇×#125	—	2	2	no	—
109	C₇×#125	—	2	1	no	—
110	C₇×#125	—	2	1	no	—
111	C₇×#125	C₂³	1	4	yes	—
112	C₇×#125	C₂³	1	4	yes	—
113	C₇×#125	C₂³	1	2	yes	—
114	C₇×#124	—	2	1	no	—
115	C₇×#124	—	2	1	no	—
116	C₇×#124	C₂³	1	2	yes	—
117	C₇×#123	—	2	2	no	—
118	C₇×#123	—	2	2	no	—
119	C₇×#123	—	2	2	no	—
120	C₇×C₂²⋊Q₈	—	2	2	no	—
121	C₇×C₂²⋊Q₈	—	2	2	no	—
122	C₇×C₂²⋊Q₈	—	2	2	no	—
123	C₇×C₂²⋊Q₈	—	2	2	no	—
124	C₇×C₂²⋊Q₈	—	2	2	no	—
125	C₇×C₂²⋊Q₈	—	2	2	no	—
126	C₇×C₂²⋊Q₈	—	2	2	no	—
127	C₇×C₂²⋊Q₈	—	2	2	no	—
128	C₇×C₂²⋊Q₈	—	2	1	no	—
129	C₇×C₂²⋊Q₈	—	2	1	no	—
130	C₇×C₂²⋊Q₈	—	2	1	no	—
131	C₇×C₂²⋊Q₈	—	2	1	no	—
132	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
133	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
134	C₇×#121	—	2	1	no	—
135	C₇×#121	—	2	1	no	—
136	C₇×#121	—	2	1	no	—
137	C₇×#121	—	2	1	no	—
138	C₇×#121	C₂³	1	2	yes	—
139	C₇×#121	C₂³	1	2	yes	—
140	C₇×#120	—	2	2	no	—
141	C₄×C₇×Q₈	—	2	2	no	—
142	C₄×C₇×Q₈	—	2	2	no	—
143	C₄×C₇×Q₈	—	2	2	no	—
144	C₄×C₇×Q₈	—	2	2	no	—
145	C₄×C₇×Q₈	—	2	2	no	—
146	C₄×C₇×Q₈	—	2	2	no	—
147	C₄×C₇×Q₈	—	2	2	no	—
148	C₄×C₇×Q₈	—	2	2	no	—
149	C₄×C₇×Q₈	—	2	1	no	—
150	C₄×C₇×Q₈	—	2	1	no	—
151	C₄×C₇×Q₈	—	2	1	no	—
152	C₄×C₇×Q₈	—	2	1	no	—
153	C₄×C₇×Q₈	C₂³	1	2	yes	—
154	C₄×C₇×Q₈	C₂³	1	2	yes	—
155	C₄×C₇×D₄	—	2	2	no	—
156	C₄×C₇×D₄	—	2	2	no	—
157	C₄×C₇×D₄	—	2	2	no	—
158	C₄×C₇×D₄	—	2	2	no	—
159	C₄×C₇×D₄	—	2	2	no	—
160	C₄×C₇×D₄	—	2	2	no	—
161	C₄×C₇×D₄	—	2	1	no	—
162	C₄×C₇×D₄	—	2	1	no	—
163	C₄×C₇×D₄	—	2	1	no	—
164	C₄×C₇×D₄	—	2	1	no	—
165	C₄×C₇×D₄	C₂³	1	2	yes	—
166	C₄×C₇×D₄	C₂³	1	2	yes	—
167	C₇×#117	—	2	2	no	—
168	C₇×#117	—	2	2	no	—
169	C₇×#117	—	2	1	no	—
170	C₇×#117	—	2	1	no	—
171	C₇×#117	—	2	2	no	—
172	C₇×#117	—	2	2	no	—
173	C₇×#117	—	2	2	no	—
174	C₇×#117	C₂³	1	4	yes	—
175	C₇×#117	C₂³	1	4	yes	—
176	C₇×#117	C₂³	1	2	yes	—
177	C₂×C₇×C₄⋊C₄	—	2	2	no	—
178	C₂×C₇×C₄⋊C₄	—	2	2	no	—
179	C₂×C₇×C₄⋊C₄	—	2	1	no	—
180	C₂×C₇×C₄⋊C₄	—	2	1	no	—
181	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
184	C₂×C₄²×C₇	—	2	2	no	—
185	C₂×C₄²×C₇	—	2	2	no	—
186	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
187	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₇×#107	C₂³	1	8	yes	—
199	C₇×#107	C₂³	1	8	yes	—
200	C₇×#106	C₂³	1	8	yes	—
201	C₇×#106	C₂³	1	8	yes	—
202	C₇×C₄⋊C₈	C₂³	1	2	yes	—
203	C₇×C₄⋊C₈	C₂³	1	2	yes	—
204	C₇×C₄⋊C₈	C₂³	1	4	yes	—
205	C₇×#103	C₂³	1	8	yes	—
206	C₇×#103	C₂³	1	8	yes	—
207	C₇×#102	C₂³	1	8	yes	—
208	C₇×#102	C₂³	1	8	yes	—
209	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
210	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
211	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₄×C₇×C₈	C₂³	1	2	yes	—
213	C₄×C₇×C₈	C₂³	1	2	yes	—
214	C₄×C₇×C₈	C₂³	1	4	yes	—
215	#3444	C₂×C₇	1	1	yes	characteristic
216	C₂×#533	C₂×C₇	1	1	yes	characteristic, complemented
217	#3233	C₂×C₇	1	4	yes	complemented
218	#3232	C₂×C₇	1	4	yes	complemented
219	#3231	C₂×C₇	1	2	yes	complemented
220	#3230	C₂×C₇	1	1	yes	characteristic, complemented
221	#3229	C₂×C₇	1	1	yes	characteristic, complemented
222	#3228	C₂×C₇	1	2	yes	complemented
223	#3227	C₂×C₇	1	1	yes	characteristic, complemented
224	#3226	C₂×C₇	1	1	yes	characteristic, complemented
225	#3160	C₂×C₇	1	2	yes	complemented
226	#3131	C₂×C₇	1	2	yes	complemented
227	#3091	C₂×C₇	1	4	yes	complemented
228	#3076	C₂×C₇	1	4	yes	complemented
229	C₂×#431	C₂×C₇	1	1	yes	characteristic, complemented
230	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
231	C₇×#41	—	2	8	no	—
232	C₇×#41	—	4	4	no	—
233	C₇×#41	—	4	4	no	—
234	C₂×C₇×Q₈	—	2	1	no	—
235	C₂×C₇×Q₈	—	2	1	no	—
236	C₂×C₇×Q₈	—	2	2	no	—
237	C₂×C₇×Q₈	—	2	2	no	—
238	C₂×C₇×Q₈	—	2	2	no	—
239	C₂×C₇×Q₈	—	2	2	no	—
240	C₂×C₇×Q₈	—	4	4	no	—
241	C₂×C₇×Q₈	—	4	4	no	—
242	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
243	C₂×C₇×D₄	—	2	2	no	—
244	C₂×C₇×D₄	—	2	2	no	—
245	C₂×C₇×D₄	—	2	2	no	—
246	C₂×C₇×D₄	—	2	1	no	—
247	C₂×C₇×D₄	—	2	1	no	—
248	C₂×C₇×D₄	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₇	—	2	4	no	—
250	C₂²×C₄×C₇	—	2	4	no	—
251	C₂²×C₄×C₇	—	2	2	no	—
252	C₂²×C₄×C₇	—	2	2	no	—
253	C₂²×C₄×C₇	—	2	2	no	—
254	C₂²×C₄×C₇	—	2	2	no	—
255	C₂²×C₄×C₇	—	2	2	no	—
256	C₂²×C₄×C₇	—	4	2	no	—
257	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
259	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
261	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
264	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
265	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
266	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
267	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
268	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
269	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
270	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂×C₇×C₈	—	2	8	no	—
276	C₂×C₇×C₈	C₂⁴	1	4	yes	—
277	C₂×C₇×C₈	C₂⁴	1	4	yes	—
278	C₇×C₄⋊C₄	—	2	4	no	—
279	C₇×C₄⋊C₄	—	2	4	no	—
280	C₇×C₄⋊C₄	—	2	4	no	—
281	C₇×C₄⋊C₄	—	2	4	no	—
282	C₇×C₄⋊C₄	—	2	2	no	—
283	C₇×C₄⋊C₄	—	2	2	no	—
284	C₇×C₄⋊C₄	—	2	2	no	—
285	C₇×C₄⋊C₄	—	2	2	no	—
286	C₇×C₄⋊C₄	—	2	2	no	—
287	C₇×C₄⋊C₄	—	2	2	no	—
288	C₇×C₄⋊C₄	—	2	1	no	—
289	C₇×C₄⋊C₄	—	2	1	no	—
290	C₇×C₄⋊C₄	—	2	1	no	—
291	C₇×C₄⋊C₄	—	2	1	no	—
292	C₇×C₄⋊C₄	—	2	2	no	—
293	C₇×C₄⋊C₄	—	2	2	no	—
294	C₇×C₄⋊C₄	—	2	2	no	—
295	C₇×C₄⋊C₄	—	2	2	no	—
296	C₇×C₄⋊C₄	—	2	2	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
299	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
300	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₇×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	2	no	—
305	C₇×C₂²⋊C₄	—	2	2	no	—
306	C₇×C₂²⋊C₄	—	2	2	no	—
307	C₇×C₂²⋊C₄	—	2	2	no	—
308	C₇×C₂²⋊C₄	—	2	2	no	—
309	C₇×C₂²⋊C₄	—	2	2	no	—
310	C₇×C₂²⋊C₄	—	2	2	no	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	2	no	—
313	C₄²×C₇	—	2	2	no	—
314	C₄²×C₇	—	2	2	no	—
315	C₄²×C₇	—	2	4	no	—
316	C₄²×C₇	—	2	2	no	—
317	C₄²×C₇	—	2	4	no	—
318	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
321	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
322	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
323	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
324	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
327	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₇	C₂⁴	1	1	yes	characteristic
331	C₄²×C₇	C₂⁴	1	1	yes	characteristic
332	C₄²×C₇	C₂⁴	1	1	yes	characteristic
333	C₄²×C₇	C₂⁴	1	1	yes	characteristic
334	#533	—	2	1	no	—
335	#533	—	2	1	no	—
336	#533	—	2	1	no	—
337	#533	—	2	1	no	—
338	#533	C₂²×C₇	1	1	yes	characteristic
339	#533	C₂²×C₇	1	1	yes	characteristic
340	#533	C₂²×C₇	1	2	yes	—
341	#533	C₂²×C₇	1	2	yes	—
342	#533	C₂²×C₇	1	1	yes	characteristic
343	#533	C₂²×C₇	1	2	yes	—
344	#533	C₂²×C₇	1	2	yes	—
345	#532	C₂²×C₇	1	1	yes	characteristic
346	#532	C₂²×C₇	1	1	yes	characteristic
347	#532	C₂²×C₇	1	1	yes	characteristic
348	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
349	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
350	#529	—	2	1	no	—
351	#529	—	2	1	no	—
352	#529	—	2	1	no	—
353	#529	—	2	1	no	—
354	#529	C₂²×C₇	1	2	yes	—
355	#529	C₂²×C₇	1	2	yes	—
356	C₂×#125	C₂²×C₇	1	2	yes	—
357	#525	—	2	1	no	—
358	#525	—	2	1	no	—
359	#525	C₂²×C₇	1	2	yes	—
360	C₂×C₂²⋊Q₈	—	2	1	no	—
361	C₂×C₂²⋊Q₈	—	2	1	no	—
362	C₄×#41	—	2	1	no	—
363	C₄×#41	—	2	1	no	—
364	C₄×#41	C₂²×C₇	1	2	yes	—
365	C₂×C₄×Q₈	—	2	1	no	—
366	C₂×C₄×Q₈	—	2	1	no	—
367	C₂×#117	C₂²×C₇	1	2	yes	—
368	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
369	#500	C₂²×C₇	1	2	yes	complemented
370	#500	C₂²×C₇	1	2	yes	complemented
371	#499	C₂²×C₇	1	8	yes	complemented
372	#498	C₂²×C₇	1	2	yes	complemented
373	#498	C₂²×C₇	1	2	yes	complemented
374	#488	C₂²×C₇	1	8	yes	complemented
375	#487	C₂²×C₇	1	2	yes	complemented
376	#487	C₂²×C₇	1	2	yes	complemented
377	#486	C₂²×C₇	1	2	yes	complemented
378	#486	C₂²×C₇	1	2	yes	complemented
379	#485	C₂²×C₇	1	8	yes	—
380	#484	C₂²×C₇	1	4	yes	—
381	#483	C₂²×C₇	1	4	yes	—
382	#482	C₂²×C₇	1	8	yes	—
383	#481	C₂²×C₇	1	4	yes	—
384	#480	C₂²×C₇	1	4	yes	—
385	#479	C₂²×C₇	1	8	yes	complemented
386	#478	C₂²×C₇	1	8	yes	complemented
387	#477	C₂²×C₇	1	4	yes	complemented
388	#476	C₂²×C₇	1	4	yes	complemented
389	#475	C₂²×C₇	1	4	yes	complemented
390	#474	C₂²×C₇	1	4	yes	complemented
391	#431	C₂²×C₇	1	1	yes	characteristic
392	#431	C₂²×C₇	1	1	yes	characteristic
393	#431	C₂²×C₇	1	2	yes	—
394	#431	C₂²×C₇	1	2	yes	—
395	#431	C₂²×C₇	1	2	yes	—
396	#427	C₂²×C₇	1	8	yes	—
397	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	—
398	#416	C₂²×C₇	1	8	yes	—
399	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
400	C₂×C₄×C₈	C₂²×C₇	1	2	yes	—
401	C₂³×C₇	—	2	2	no	—
402	C₂³×C₇	—	2	2	no	—
403	C₂³×C₇	—	2	2	no	—
404	C₂³×C₇	—	4	1	no	—
405	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
406	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
407	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
408	C₇×Q₈	—	2	4	no	—
409	C₇×Q₈	—	4	4	no	—
410	C₇×Q₈	—	4	4	no	—
411	C₇×Q₈	—	4	4	no	—
412	C₇×Q₈	—	4	2	no	—
413	C₇×Q₈	—	4	4	no	—
414	C₇×Q₈	—	4	2	no	—
415	C₇×D₄	—	2	4	no	—
416	C₇×D₄	—	4	4	no	—
417	C₇×D₄	—	4	4	no	—
418	C₇×D₄	—	4	4	no	—
419	C₇×D₄	—	4	2	no	—
420	C₇×D₄	—	4	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	2	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	2	no	—
437	C₂×C₄×C₇	—	2	4	no	—
438	C₂×C₄×C₇	—	2	4	no	—
439	C₂×C₄×C₇	—	4	1	no	—
440	C₂×C₄×C₇	—	4	1	no	—
441	C₂×C₄×C₇	—	4	1	no	—
442	C₂×C₄×C₇	—	4	4	no	—
443	C₂×C₄×C₇	—	4	4	no	—
444	C₂×C₄×C₇	—	4	4	no	—
445	C₂×C₄×C₇	—	4	4	no	—
446	C₂×C₄×C₇	—	4	4	no	—
447	C₂×C₄×C₇	#135	1	4	yes	—
448	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₇	2₋¹⁺⁴	1	4	yes	—
460	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
461	C₇×C₈	—	2	4	no	—
462	C₇×C₈	—	2	4	no	—
463	C₂×#41	—	2	1	no	—
464	C₂×#41	—	2	1	no	—
465	C₂×#41	C₂³×C₇	1	2	yes	—
466	C₂²×Q₈	—	2	1	no	—
467	C₂²×Q₈	—	2	1	no	—
468	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
469	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
470	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
471	C₂²×C₈	C₂³×C₇	1	4	yes	—
472	C₄⋊Q₈	—	2	1	no	—
473	C₄⋊Q₈	—	2	1	no	—
474	C₄⋊Q₈	—	2	1	no	—
475	C₄⋊Q₈	—	2	1	no	—
476	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
477	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
478	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
479	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
480	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
481	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
482	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
483	#127	C₂³×C₇	1	1	yes	characteristic
484	#126	—	2	2	no	—
485	#126	—	2	2	no	—
486	#125	—	2	2	no	—
487	#125	—	2	2	no	—
488	#125	—	2	1	no	—
489	#125	—	2	1	no	—
490	#125	C₂³×C₇	1	4	yes	—
491	#125	C₂³×C₇	1	4	yes	—
492	#125	C₂³×C₇	1	2	yes	—
493	#124	—	2	1	no	—
494	#124	—	2	1	no	—
495	#124	C₂³×C₇	1	2	yes	—
496	#123	—	2	2	no	—
497	#123	—	2	2	no	—
498	#123	—	2	2	no	—
499	C₂²⋊Q₈	—	2	2	no	—
500	C₂²⋊Q₈	—	2	2	no	—
501	C₂²⋊Q₈	—	2	2	no	—
502	C₂²⋊Q₈	—	2	2	no	—
503	C₂²⋊Q₈	—	2	2	no	—
504	C₂²⋊Q₈	—	2	2	no	—
505	C₂²⋊Q₈	—	2	2	no	—
506	C₂²⋊Q₈	—	2	2	no	—
507	C₂²⋊Q₈	—	2	1	no	—
508	C₂²⋊Q₈	—	2	1	no	—
509	C₂²⋊Q₈	—	2	1	no	—
510	C₂²⋊Q₈	—	2	1	no	—
511	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
512	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
513	#121	—	2	1	no	—
514	#121	—	2	1	no	—
515	#121	—	2	1	no	—
516	#121	—	2	1	no	—
517	#121	C₂³×C₇	1	2	yes	—
518	#121	C₂³×C₇	1	2	yes	—
519	#120	—	2	2	no	—
520	C₄×Q₈	—	2	2	no	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	—	2	2	no	—
523	C₄×Q₈	—	2	2	no	—
524	C₄×Q₈	—	2	2	no	—
525	C₄×Q₈	—	2	2	no	—
526	C₄×Q₈	—	2	2	no	—
527	C₄×Q₈	—	2	2	no	—
528	C₄×Q₈	—	2	1	no	—
529	C₄×Q₈	—	2	1	no	—
530	C₄×Q₈	—	2	1	no	—
531	C₄×Q₈	—	2	1	no	—
532	C₄×Q₈	C₂³×C₇	1	2	yes	—
533	C₄×Q₈	C₂³×C₇	1	2	yes	—
534	C₄×D₄	—	2	2	no	—
535	C₄×D₄	—	2	2	no	—
536	C₄×D₄	—	2	2	no	—
537	C₄×D₄	—	2	2	no	—
538	C₄×D₄	—	2	2	no	—
539	C₄×D₄	—	2	2	no	—
540	C₄×D₄	—	2	1	no	—
541	C₄×D₄	—	2	1	no	—
542	C₄×D₄	—	2	1	no	—
543	C₄×D₄	—	2	1	no	—
544	C₄×D₄	C₂³×C₇	1	2	yes	—
545	C₄×D₄	C₂³×C₇	1	2	yes	—
546	#117	—	2	2	no	—
547	#117	—	2	2	no	—
548	#117	—	2	1	no	—
549	#117	—	2	1	no	—
550	#117	—	2	2	no	—
551	#117	—	2	2	no	—
552	#117	—	2	2	no	—
553	#117	C₂³×C₇	1	4	yes	—
554	#117	C₂³×C₇	1	4	yes	—
555	#117	C₂³×C₇	1	2	yes	—
556	C₂×C₄⋊C₄	—	2	2	no	—
557	C₂×C₄⋊C₄	—	2	2	no	—
558	C₂×C₄⋊C₄	—	2	1	no	—
559	C₂×C₄⋊C₄	—	2	1	no	—
560	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
561	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
562	C₂×C₂²⋊C₄	—	2	2	no	—
563	C₂×C₄²	—	2	2	no	—
564	C₂×C₄²	—	2	2	no	—
565	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
566	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
567	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
568	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
569	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
570	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
571	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
572	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
573	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
575	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
577	#107	C₂³×C₇	1	8	yes	—
578	#107	C₂³×C₇	1	8	yes	—
579	#106	C₂³×C₇	1	8	yes	—
580	#106	C₂³×C₇	1	8	yes	—
581	C₄⋊C₈	C₂³×C₇	1	2	yes	—
582	C₄⋊C₈	C₂³×C₇	1	2	yes	—
583	C₄⋊C₈	C₂³×C₇	1	4	yes	—
584	#103	C₂³×C₇	1	8	yes	—
585	#103	C₂³×C₇	1	8	yes	—
586	#102	C₂³×C₇	1	8	yes	—
587	#102	C₂³×C₇	1	8	yes	—
588	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
589	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
590	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
591	C₄×C₈	C₂³×C₇	1	2	yes	—
592	C₄×C₈	C₂³×C₇	1	2	yes	—
593	C₄×C₈	C₂³×C₇	1	4	yes	—
594	C₂²×C₇	—	2	1	no	—
595	C₂²×C₇	—	2	1	no	—
596	C₂²×C₇	—	2	1	no	—
597	C₂²×C₇	—	2	1	no	—
598	C₂²×C₇	—	2	1	no	—
599	C₂²×C₇	—	2	1	no	—
600	C₂²×C₇	—	2	1	no	—
601	C₂²×C₇	—	4	4	no	—
602	C₂²×C₇	—	4	2	no	—
603	C₂²×C₇	—	4	2	no	—
604	C₂²×C₇	—	4	2	no	—
605	C₂²×C₇	#536	1	2	yes	—
606	C₂²×C₇	C₂×#135	1	2	yes	—
607	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
608	C₄×C₇	—	2	1	no	—
609	C₄×C₇	—	2	1	no	—
610	C₄×C₇	—	2	1	no	—
611	C₄×C₇	—	2	1	no	—
612	C₄×C₇	—	2	1	no	—
613	C₄×C₇	—	2	1	no	—
614	C₄×C₇	—	2	1	no	—
615	C₄×C₇	—	4	2	no	—
616	C₄×C₇	—	4	2	no	—
617	C₄×C₇	—	4	4	no	—
618	C₄×C₇	—	4	2	no	—
619	C₄×C₇	—	4	4	no	—
620	C₄×C₇	#536	1	2	yes	—
621	C₄×C₇	C₂×#135	1	2	yes	—
622	C₄×C₇	C₂×#135	1	2	yes	—
623	C₄×C₇	#575	1	2	yes	—
624	C₄×C₇	C₂×2₋¹⁺⁴	1	2	yes	—
625	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
626	#41	—	2	8	no	—
627	#41	—	4	4	no	—
628	#41	—	4	4	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	2	2	no	—
632	C₂×Q₈	—	2	2	no	—
633	C₂×Q₈	—	2	2	no	—
634	C₂×Q₈	—	2	2	no	—
635	C₂×Q₈	—	4	4	no	—
636	C₂×Q₈	—	4	4	no	—
637	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
638	C₂×D₄	—	2	2	no	—
639	C₂×D₄	—	2	2	no	—
640	C₂×D₄	—	2	2	no	—
641	C₂×D₄	—	2	1	no	—
642	C₂×D₄	—	2	1	no	—
643	C₂×D₄	C₂⁴×C₇	1	2	yes	—
644	C₂²×C₄	—	2	4	no	—
645	C₂²×C₄	—	2	4	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	4	2	no	—
652	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
653	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
654	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
655	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
656	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
657	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
658	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
659	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
660	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
661	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
662	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
663	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
664	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
665	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
666	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
667	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
669	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
670	C₂×C₈	—	2	8	no	—
671	C₂×C₈	C₂⁴×C₇	1	4	yes	—
672	C₂×C₈	C₂⁴×C₇	1	4	yes	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	2	no	—
678	C₄⋊C₄	—	2	2	no	—
679	C₄⋊C₄	—	2	2	no	—
680	C₄⋊C₄	—	2	2	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	—	2	1	no	—
684	C₄⋊C₄	—	2	1	no	—
685	C₄⋊C₄	—	2	1	no	—
686	C₄⋊C₄	—	2	1	no	—
687	C₄⋊C₄	—	2	2	no	—
688	C₄⋊C₄	—	2	2	no	—
689	C₄⋊C₄	—	2	2	no	—
690	C₄⋊C₄	—	2	2	no	—
691	C₄⋊C₄	—	2	2	no	—
692	C₄⋊C₄	—	2	2	no	—
693	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
694	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
695	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
696	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
697	C₂²⋊C₄	—	2	4	no	—
698	C₂²⋊C₄	—	2	4	no	—
699	C₂²⋊C₄	—	2	2	no	—
700	C₂²⋊C₄	—	2	2	no	—
701	C₂²⋊C₄	—	2	2	no	—
702	C₂²⋊C₄	—	2	2	no	—
703	C₂²⋊C₄	—	2	2	no	—
704	C₂²⋊C₄	—	2	2	no	—
705	C₂²⋊C₄	—	2	2	no	—
706	C₂²⋊C₄	—	2	2	no	—
707	C₂²⋊C₄	—	2	2	no	—
708	C₄²	—	2	2	no	—
709	C₄²	—	2	2	no	—
710	C₄²	—	2	2	no	—
711	C₄²	—	2	4	no	—
712	C₄²	—	2	4	no	—
713	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
714	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
715	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
716	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
717	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
718	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
719	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
720	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
721	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
722	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
723	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
724	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
725	C₄²	C₂⁴×C₇	1	1	yes	characteristic
726	C₄²	C₂⁴×C₇	1	1	yes	characteristic
727	C₄²	C₂⁴×C₇	1	1	yes	characteristic
728	C₄²	C₂⁴×C₇	1	1	yes	characteristic
729	C₂×C₇	—	2	2	no	—
730	C₂×C₇	—	2	2	no	—
731	C₂×C₇	—	4	1	no	—
732	C₂×C₇	—	8	2	no	—
733	C₂×C₇	C₂×#536	1	1	yes	characteristic
734	C₂×C₇	C₂²×#135	1	1	yes	characteristic
735	C₂×C₇	C₂×#575	1	1	yes	characteristic
736	C₂³	—	2	2	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	2	2	no	—
739	C₂³	—	4	1	no	—
740	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
741	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
742	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
743	Q₈	—	2	4	no	—
744	Q₈	—	4	4	no	—
745	Q₈	—	4	4	no	—
746	Q₈	—	4	4	no	—
747	Q₈	—	4	2	no	—
748	Q₈	—	4	4	no	—
749	Q₈	—	4	2	no	—
750	D₄	—	2	4	no	—
751	D₄	—	4	4	no	—
752	D₄	—	4	4	no	—
753	D₄	—	4	4	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	2	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	2	no	—
765	C₂×C₄	—	2	2	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	4	no	—
773	C₂×C₄	—	2	4	no	—
774	C₂×C₄	—	4	1	no	—
775	C₂×C₄	—	4	1	no	—
776	C₂×C₄	—	4	1	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	4	4	no	—
779	C₂×C₄	—	4	4	no	—
780	C₂×C₄	—	4	4	no	—
781	C₂×C₄	—	4	4	no	—
782	C₂×C₄	C₇×#135	1	4	yes	—
783	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
784	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
785	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
786	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
787	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
788	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
789	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
790	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
791	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
792	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
793	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
794	C₂×C₄	C₇×2₋¹⁺⁴	1	4	yes	—
795	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
796	C₈	—	2	4	no	—
797	C₈	—	2	4	no	—
798	C₇	#60846	1	1	yes	characteristic, direct product factor, Sylow
799	C₂²	—	2	1	no	—
800	C₂²	—	2	1	no	—
801	C₂²	—	2	1	no	—
802	C₂²	—	2	1	no	—
803	C₂²	—	2	1	no	—
804	C₂²	—	2	1	no	—
805	C₂²	—	2	1	no	—
806	C₂²	—	4	4	no	—
807	C₂²	—	4	2	no	—
808	C₂²	—	4	2	no	—
809	C₂²	—	4	2	no	—
810	C₂²	C₇×#536	1	2	yes	—
811	C₂²	C₂×C₇×#135	1	2	yes	—
812	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
813	C₄	—	2	1	no	—
814	C₄	—	2	1	no	—
815	C₄	—	2	1	no	—
816	C₄	—	2	1	no	—
817	C₄	—	2	1	no	—
818	C₄	—	2	1	no	—
819	C₄	—	2	1	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	4	no	—
822	C₄	—	4	2	no	—
823	C₄	—	4	4	no	—
824	C₄	—	4	2	no	—
825	C₄	C₇×#536	1	2	yes	—
826	C₄	C₂×C₇×#135	1	2	yes	—
827	C₄	C₂×C₇×#135	1	2	yes	—
828	C₄	C₇×#575	1	2	yes	—
829	C₄	C₂×C₇×2₋¹⁺⁴	1	2	yes	—
830	C₂	—	2	2	no	—
831	C₂	—	2	2	no	—
832	C₂	—	4	1	no	—
833	C₂	—	8	2	no	—
834	C₂	C₂×C₇×#536	1	1	yes	characteristic
835	C₂	C₂²×C₇×#135	1	1	yes	characteristic
836	C₂	C₂×C₇×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
prime radical	C₇×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#533	C₂	semidirect
3. C₇×#3233	C₂	semidirect
4. C₇×#3232	C₂	semidirect
5. C₇×#3231	C₂	semidirect
6. C₇×#3230	C₂	semidirect
7. C₇×#3229	C₂	semidirect
8. C₇×#3228	C₂	semidirect
9. C₇×#3227	C₂	semidirect
10. C₇×#3226	C₂	semidirect
11. C₇×#3160	C₂	semidirect
12. C₇×#3131	C₂	semidirect
13. C₇×#3091	C₂	semidirect
14. C₇×#3076	C₂	semidirect
15. C₂×C₇×#431	C₂	semidirect
51. C₇×#500	C₂²	semidirect
52. C₇×#500	C₂²	semidirect
53. C₇×#499	C₂²	semidirect
54. C₇×#498	C₂²	semidirect
55. C₇×#498	C₂²	semidirect
56. C₇×#488	C₂²	semidirect
57. C₇×#487	C₂²	semidirect
58. C₇×#487	C₂²	semidirect
59. C₇×#486	C₂²	semidirect
60. C₇×#486	C₂²	semidirect
67. C₇×#479	C₂²	semidirect
68. C₇×#478	C₂²	semidirect
69. C₇×#477	C₂²	semidirect
70. C₇×#476	C₂²	semidirect
71. C₇×#475	C₂²	semidirect
72. C₇×#474	C₂²	semidirect
83. #60846	C₇	direct (N × H)
216. C₂×#533	C₂×C₇	semidirect
217. #3233	C₂×C₇	semidirect
218. #3232	C₂×C₇	semidirect
219. #3231	C₂×C₇	semidirect
220. #3230	C₂×C₇	semidirect
221. #3229	C₂×C₇	semidirect
222. #3228	C₂×C₇	semidirect
223. #3227	C₂×C₇	semidirect
224. #3226	C₂×C₇	semidirect
225. #3160	C₂×C₇	semidirect
226. #3131	C₂×C₇	semidirect
227. #3091	C₂×C₇	semidirect
228. #3076	C₂×C₇	semidirect
229. C₂×#431	C₂×C₇	semidirect
369. #500	C₂²×C₇	semidirect
370. #500	C₂²×C₇	semidirect
371. #499	C₂²×C₇	semidirect
372. #498	C₂²×C₇	semidirect
373. #498	C₂²×C₇	semidirect
374. #488	C₂²×C₇	semidirect
375. #487	C₂²×C₇	semidirect
376. #487	C₂²×C₇	semidirect
377. #486	C₂²×C₇	semidirect
378. #486	C₂²×C₇	semidirect
385. #479	C₂²×C₇	semidirect
386. #478	C₂²×C₇	semidirect
387. #477	C₂²×C₇	semidirect
388. #476	C₂²×C₇	semidirect
389. #475	C₂²×C₇	semidirect
390. #474	C₂²×C₇	semidirect
798. C₇	#60846	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×#3444	2
C₂×C₇×#533	2
C₇×#3233	2
C₇×#3232	2
C₇×#3231	2
C₇×#3230	2
C₇×#3229	2
C₇×#3228	2
C₇×#3227	2
C₇×#3226	2
C₇×#3160	2
C₇×#3131	2
C₇×#3091	2
C₇×#3076	2
C₂×C₇×#431	2
#60846	7

Subgroups — C7×#60846 #13238062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60846 #13238062