Subgroups — C₇×#60892 #13238108

Order 1792.

1736 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3460	C₂	1	1	yes	maximal, characteristic
3	C₇×#3244	C₂	1	4	yes	maximal, complemented
4	C₇×#3241	C₂	1	4	yes	maximal, complemented
5	C₇×#3238	C₂	1	2	yes	maximal, complemented
6	C₇×#3235	C₂	1	2	yes	maximal, complemented
7	C₇×#3233	C₂	1	2	yes	maximal, complemented
8	C₇×#3227	C₂	1	2	yes	maximal, complemented
9	C₇×#3163	C₂	1	2	yes	maximal, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3099	C₂	1	2	yes	maximal, complemented
12	C₇×#3096	C₂	1	2	yes	maximal, complemented
13	C₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×Q₈²	—	2	1	no	—
19	C₇×#557	—	2	1	no	—
20	C₇×#554	—	2	2	no	—
21	C₇×#554	—	2	1	no	—
22	C₇×D₄×Q₈	—	2	2	no	—
23	C₇×D₄×Q₈	—	2	1	no	—
24	C₇×#544	C₂²	1	1	yes	characteristic
25	C₇×#544	C₂²	1	2	yes	—
26	C₇×#544	C₂²	1	4	yes	complemented
27	C₇×#542	—	2	1	no	—
28	C₇×#542	C₂²	1	2	yes	—
29	C₇×#540	—	2	1	no	—
30	C₇×#540	C₂²	1	2	yes	—
31	C₇×#538	—	2	2	no	—
32	C₇×#537	C₂²	1	1	yes	characteristic
33	C₇×#535	C₂²	1	1	yes	characteristic
34	C₇×#535	C₂²	1	1	yes	characteristic
35	C₇×#533	C₂²	1	1	yes	characteristic
36	C₇×#533	C₂²	1	2	yes	complemented
37	C₇×#532	—	2	1	no	—
38	C₇×#532	C₂²	1	2	yes	—
39	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	complemented
41	C₇×#529	—	2	1	no	—
42	C₇×#529	C₂²	1	2	yes	—
43	C₇×#525	—	2	2	no	—
44	C₇×#520	C₂²	1	2	yes	—
45	C₄×C₇×#41	C₂²	1	1	yes	characteristic
46	C₄×C₇×#41	C₂²	1	1	yes	characteristic
47	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
48	C₇×#501	C₂²	1	4	yes	complemented
49	C₇×#501	C₂²	1	4	yes	complemented
50	C₇×#499	C₂²	1	4	yes	complemented
51	C₇×#498	C₂²	1	4	yes	complemented
52	C₇×#490	C₂²	1	4	yes	—
53	C₇×#489	C₂²	1	4	yes	—
54	C₇×#488	C₂²	1	4	yes	—
55	C₇×#486	C₂²	1	4	yes	—
56	C₇×#485	C₂²	1	4	yes	complemented
57	C₇×#483	C₂²	1	4	yes	complemented
58	C₇×#482	C₂²	1	4	yes	—
59	C₇×#482	C₂²	1	4	yes	—
60	C₇×#482	C₂²	1	4	yes	complemented
61	C₇×#481	C₂²	1	4	yes	—
62	C₇×#481	C₂²	1	4	yes	complemented
63	C₇×#480	C₂²	1	4	yes	—
64	C₇×#479	C₂²	1	2	yes	complemented
65	C₇×#478	C₂²	1	4	yes	—
66	C₇×#478	C₂²	1	2	yes	complemented
67	C₇×#477	C₂²	1	2	yes	complemented
68	C₇×#477	C₂²	1	1	yes	characteristic, complemented
69	C₇×#476	C₂²	1	2	yes	—
70	C₇×#476	C₂²	1	2	yes	—
71	C₇×#476	C₂²	1	2	yes	—
72	C₇×#476	C₂²	1	4	yes	—
73	C₇×#476	C₂²	1	1	yes	characteristic, complemented
74	C₇×#476	C₂²	1	2	yes	complemented
75	C₇×#475	C₂²	1	1	yes	characteristic, complemented
76	C₇×#475	C₂²	1	2	yes	complemented
77	C₇×#474	C₂²	1	2	yes	—
78	C₇×#474	C₂²	1	1	yes	characteristic, complemented
79	C₇×#474	C₂²	1	2	yes	complemented
80	C₇×#433	C₂²	1	4	yes	complemented
81	C₇×#432	C₂²	1	2	yes	complemented
82	C₇×#431	C₂²	1	2	yes	complemented
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	2	yes	—
85	C₇×#427	C₂²	1	2	yes	—
86	C₂×C₇×#106	C₂²	1	2	yes	—
87	C₇×#423	C₂²	1	1	yes	characteristic
88	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
89	C₇×#418	C₂²	1	2	yes	—
90	C₇×#417	C₂²	1	2	yes	—
91	C₇×#416	C₂²	1	2	yes	—
92	C₂×C₇×#102	C₂²	1	2	yes	—
93	C₇×#408	C₂²	1	2	yes	—
94	C₇×#405	C₂²	1	2	yes	—
95	#60892	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	—	2	2	no	—
97	C₂×C₇×#41	C₂³	1	1	yes	characteristic
98	C₂×C₇×#41	C₂³	1	1	yes	characteristic
99	C₂²×C₇×Q₈	—	2	1	no	—
100	C₂²×C₇×Q₈	—	2	2	no	—
101	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₇	—	2	1	no	—
103	C₂×C₇×M₁₆	C₂³	1	2	yes	—
104	C₂²×C₇×C₈	C₂³	1	2	yes	—
105	C₇×C₄⋊Q₈	—	2	1	no	—
106	C₇×C₄⋊Q₈	—	2	2	no	—
107	C₇×C₄⋊Q₈	—	2	4	no	—
108	C₇×C₄⋊Q₈	—	2	1	no	—
109	C₇×C₄⋊Q₈	—	2	1	no	—
110	C₇×C₄⋊Q₈	—	2	2	no	—
111	C₇×C₄⋊Q₈	—	2	2	no	—
112	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
114	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
115	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
116	C₇×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₇×#127	—	2	1	no	—
119	C₇×#127	C₂³	1	2	yes	—
120	C₇×#126	—	2	2	no	—
121	C₇×#126	—	2	2	no	—
122	C₇×#125	—	2	1	no	—
123	C₇×#125	—	2	2	no	—
124	C₇×#125	—	2	4	no	—
125	C₇×#125	C₂³	1	2	yes	—
126	C₇×#125	C₂³	1	4	yes	—
127	C₇×#125	C₂³	1	2	yes	—
128	C₇×#124	—	2	1	no	—
129	C₇×#124	—	2	2	no	—
130	C₇×#124	—	2	2	no	—
131	C₇×#124	C₂³	1	2	yes	—
132	C₇×#123	—	2	2	no	—
133	C₇×#123	—	2	2	no	—
134	C₇×#123	—	2	2	no	—
135	C₇×#123	—	2	2	no	—
136	C₇×C₂²⋊Q₈	—	2	1	no	—
137	C₇×C₂²⋊Q₈	—	2	1	no	—
138	C₇×C₂²⋊Q₈	—	2	1	no	—
139	C₇×C₂²⋊Q₈	—	2	2	no	—
140	C₇×C₂²⋊Q₈	—	2	2	no	—
141	C₇×C₂²⋊Q₈	—	2	2	no	—
142	C₇×C₂²⋊Q₈	—	2	2	no	—
143	C₇×C₂²⋊Q₈	—	2	4	no	—
144	C₇×C₂²⋊Q₈	—	2	4	no	—
145	C₇×C₂²⋊Q₈	—	2	4	no	—
146	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
147	C₇×#121	—	2	2	no	—
148	C₇×#121	—	2	1	no	—
149	C₇×#121	—	2	2	no	—
150	C₇×#121	—	2	1	no	—
151	C₇×#121	—	2	1	no	—
152	C₇×#121	—	2	2	no	—
153	C₇×#121	—	2	2	no	—
154	C₇×#121	C₂³	1	2	yes	—
155	C₇×#121	C₂³	1	2	yes	—
156	C₇×#121	C₂³	1	2	yes	—
157	C₇×#120	—	2	2	no	—
158	C₇×#120	—	2	2	no	—
159	C₄×C₇×Q₈	—	2	2	no	—
160	C₄×C₇×Q₈	—	2	1	no	—
161	C₄×C₇×Q₈	—	2	1	no	—
162	C₄×C₇×Q₈	—	2	2	no	—
163	C₄×C₇×Q₈	—	2	2	no	—
164	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
165	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
166	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
167	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
168	C₄×C₇×D₄	—	2	4	no	—
169	C₄×C₇×D₄	—	2	2	no	—
170	C₄×C₇×D₄	—	2	1	no	—
171	C₄×C₇×D₄	—	2	1	no	—
172	C₄×C₇×D₄	—	2	2	no	—
173	C₄×C₇×D₄	—	2	1	no	—
174	C₄×C₇×D₄	—	2	1	no	—
175	C₄×C₇×D₄	—	2	2	no	—
176	C₄×C₇×D₄	D₄	1	2	yes	—
177	C₄×C₇×D₄	D₄	1	1	yes	characteristic
178	C₄×C₇×D₄	D₄	1	2	yes	—
179	C₄×C₇×D₄	D₄	1	1	yes	characteristic
180	C₄×C₇×D₄	C₂³	1	2	yes	—
181	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
182	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
183	C₄×C₇×D₄	C₂³	1	2	yes	—
184	C₇×#117	—	2	1	no	—
185	C₇×#117	—	2	2	no	—
186	C₇×#117	C₂³	1	4	yes	—
187	C₇×#117	C₂³	1	1	yes	characteristic
188	C₇×#117	C₂³	1	2	yes	—
189	C₇×#117	C₂³	1	1	yes	characteristic
190	C₇×#117	C₂³	1	2	yes	—
191	C₂×C₇×C₄⋊C₄	—	2	1	no	—
192	C₂×C₇×C₄⋊C₄	—	2	2	no	—
193	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
194	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
195	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
196	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
197	C₂×C₄²×C₇	—	2	1	no	—
198	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	2	yes	—
200	C₇×#107	C₂³	1	4	yes	—
201	C₇×#107	C₂³	1	4	yes	—
202	C₇×#107	C₂³	1	2	yes	—
203	C₇×#107	C₂³	1	2	yes	—
204	C₇×#106	C₂³	1	4	yes	—
205	C₇×#106	C₂³	1	2	yes	—
206	C₇×#106	C₂³	1	4	yes	—
207	C₇×#106	C₂³	1	4	yes	—
208	C₇×#106	C₂³	1	4	yes	—
209	C₇×#106	C₂³	1	2	yes	—
210	C₇×C₄⋊C₈	C₂³	1	2	yes	—
211	C₇×C₄⋊C₈	C₂³	1	2	yes	—
212	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
213	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
214	C₇×C₄⋊C₈	C₂³	1	2	yes	—
215	C₇×#103	C₂³	1	4	yes	—
216	C₇×#103	C₂³	1	2	yes	—
217	C₇×#103	C₂³	1	2	yes	—
218	C₇×#102	C₂³	1	4	yes	—
219	C₇×#102	C₂³	1	4	yes	—
220	C₇×#102	C₂³	1	2	yes	—
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×#102	C₂³	1	4	yes	—
223	C₇×#102	C₂³	1	4	yes	—
224	C₇×#102	C₂³	1	2	yes	—
225	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
226	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
227	C₇×#97	C₂³	1	4	yes	—
228	C₄×C₇×C₈	C₂³	1	4	yes	—
229	#3503	C₂×C₇	1	1	yes	characteristic, complemented
230	#3460	C₂×C₇	1	1	yes	characteristic
231	#3244	C₂×C₇	1	4	yes	complemented
232	#3241	C₂×C₇	1	4	yes	complemented
233	#3238	C₂×C₇	1	2	yes	complemented
234	#3235	C₂×C₇	1	2	yes	complemented
235	#3233	C₂×C₇	1	2	yes	complemented
236	#3227	C₂×C₇	1	2	yes	complemented
237	#3163	C₂×C₇	1	2	yes	complemented
238	#3136	C₂×C₇	1	2	yes	complemented
239	#3099	C₂×C₇	1	2	yes	complemented
240	#3096	C₂×C₇	1	2	yes	complemented
241	#3079	C₂×C₇	1	1	yes	characteristic, complemented
242	#3077	C₂×C₇	1	1	yes	characteristic, complemented
243	#3076	C₂×C₇	1	1	yes	characteristic, complemented
244	C₂×#476	C₂×C₇	1	1	yes	characteristic, complemented
245	#2925	C₂×C₇	1	1	yes	characteristic, complemented
246	C₂⁴×C₇	—	2	1	no	—
247	C₇×#41	—	2	2	no	—
248	C₇×#41	—	2	2	no	—
249	C₇×#41	—	2	2	no	—
250	C₇×#41	—	2	2	no	—
251	C₇×#41	—	8	4	no	—
252	C₂×C₇×Q₈	—	2	1	no	—
253	C₂×C₇×Q₈	—	2	1	no	—
254	C₂×C₇×Q₈	—	2	2	no	—
255	C₂×C₇×Q₈	—	2	2	no	—
256	C₂×C₇×Q₈	—	2	2	no	—
257	C₂×C₇×Q₈	—	2	4	no	—
258	C₂×C₇×Q₈	—	8	2	no	—
259	C₂×C₇×Q₈	—	8	4	no	—
260	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
261	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
262	C₂×C₇×D₄	—	2	1	no	—
263	C₂×C₇×D₄	—	2	2	no	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	—	2	1	no	—
267	C₂×C₇×D₄	—	2	2	no	—
268	C₂×C₇×D₄	—	2	2	no	—
269	C₂×C₇×D₄	—	2	2	no	—
270	C₂×C₇×D₄	—	2	2	no	—
271	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
272	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
273	C₂×C₇×D₄	C₂⁴	1	2	yes	—
274	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇	—	2	1	no	—
276	C₂²×C₄×C₇	—	2	4	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	1	no	—
279	C₂²×C₄×C₇	—	2	1	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	1	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	8	2	no	—
284	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
288	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
289	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
290	C₇×M₁₆	—	2	4	no	—
291	C₂×C₇×C₈	—	2	4	no	—
292	C₂×C₇×C₈	C₂⁴	1	2	yes	—
293	C₂×C₇×C₈	C₂⁴	1	4	yes	—
294	C₂×C₇×C₈	C₂⁴	1	2	yes	—
295	C₇×C₄⋊C₄	—	2	2	no	—
296	C₇×C₄⋊C₄	—	2	1	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	4	no	—
299	C₇×C₄⋊C₄	—	2	1	no	—
300	C₇×C₄⋊C₄	—	2	4	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	1	no	—
303	C₇×C₄⋊C₄	—	2	1	no	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	1	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	4	no	—
311	C₇×C₄⋊C₄	—	2	2	no	—
312	C₇×C₄⋊C₄	—	2	4	no	—
313	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
314	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
315	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
316	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
318	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
319	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
321	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
322	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
323	C₇×C₂²⋊C₄	—	2	1	no	—
324	C₇×C₂²⋊C₄	—	2	4	no	—
325	C₇×C₂²⋊C₄	—	2	2	no	—
326	C₇×C₂²⋊C₄	—	2	2	no	—
327	C₇×C₂²⋊C₄	—	2	2	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	1	no	—
330	C₇×C₂²⋊C₄	—	2	1	no	—
331	C₇×C₂²⋊C₄	—	2	2	no	—
332	C₇×C₂²⋊C₄	—	2	2	no	—
333	C₇×C₂²⋊C₄	—	2	2	no	—
334	C₇×C₂²⋊C₄	—	2	2	no	—
335	C₇×C₂²⋊C₄	—	2	2	no	—
336	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
337	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
338	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
339	C₄²×C₇	—	2	1	no	—
340	C₄²×C₇	—	2	1	no	—
341	C₄²×C₇	—	2	1	no	—
342	C₄²×C₇	—	2	4	no	—
343	C₄²×C₇	—	2	2	no	—
344	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
345	C₄²×C₇	C₂×D₄	1	2	yes	—
346	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₇	C₂×D₄	1	2	yes	—
348	C₄²×C₇	C₂⁴	1	2	yes	—
349	C₄²×C₇	C₂⁴	1	1	yes	characteristic
350	C₄²×C₇	C₂⁴	1	1	yes	characteristic
351	Q₈²	—	2	1	no	—
352	#557	—	2	1	no	—
353	#554	—	2	2	no	—
354	#554	—	2	1	no	—
355	D₄×Q₈	—	2	2	no	—
356	D₄×Q₈	—	2	1	no	—
357	#544	C₂²×C₇	1	2	yes	—
358	#544	C₂²×C₇	1	1	yes	characteristic
359	#544	C₂²×C₇	1	4	yes	complemented
360	#542	—	2	1	no	—
361	#542	C₂²×C₇	1	2	yes	—
362	#540	—	2	1	no	—
363	#540	C₂²×C₇	1	2	yes	—
364	#538	—	2	2	no	—
365	#537	C₂²×C₇	1	1	yes	characteristic
366	#535	C₂²×C₇	1	1	yes	characteristic
367	#535	C₂²×C₇	1	1	yes	characteristic
368	#533	C₂²×C₇	1	1	yes	characteristic
369	#533	C₂²×C₇	1	2	yes	complemented
370	#532	—	2	1	no	—
371	#532	C₂²×C₇	1	2	yes	—
372	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
373	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	complemented
374	#529	—	2	1	no	—
375	#529	C₂²×C₇	1	2	yes	—
376	#525	—	2	2	no	—
377	#520	C₂²×C₇	1	2	yes	—
378	C₄×#41	C₂²×C₇	1	1	yes	characteristic
379	C₄×#41	C₂²×C₇	1	1	yes	characteristic
380	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
381	#501	C₂²×C₇	1	4	yes	complemented
382	#501	C₂²×C₇	1	4	yes	complemented
383	#499	C₂²×C₇	1	4	yes	complemented
384	#498	C₂²×C₇	1	4	yes	complemented
385	#490	C₂²×C₇	1	4	yes	—
386	#489	C₂²×C₇	1	4	yes	—
387	#488	C₂²×C₇	1	4	yes	—
388	#486	C₂²×C₇	1	4	yes	—
389	#485	C₂²×C₇	1	4	yes	complemented
390	#483	C₂²×C₇	1	4	yes	complemented
391	#482	C₂²×C₇	1	4	yes	—
392	#482	C₂²×C₇	1	4	yes	—
393	#482	C₂²×C₇	1	4	yes	complemented
394	#481	C₂²×C₇	1	4	yes	—
395	#481	C₂²×C₇	1	4	yes	complemented
396	#480	C₂²×C₇	1	4	yes	—
397	#479	C₂²×C₇	1	2	yes	complemented
398	#478	C₂²×C₇	1	4	yes	—
399	#478	C₂²×C₇	1	2	yes	complemented
400	#477	C₂²×C₇	1	1	yes	characteristic, complemented
401	#477	C₂²×C₇	1	2	yes	complemented
402	#476	C₂²×C₇	1	2	yes	—
403	#476	C₂²×C₇	1	2	yes	—
404	#476	C₂²×C₇	1	2	yes	—
405	#476	C₂²×C₇	1	4	yes	—
406	#476	C₂²×C₇	1	1	yes	characteristic, complemented
407	#476	C₂²×C₇	1	2	yes	complemented
408	#475	C₂²×C₇	1	1	yes	characteristic, complemented
409	#475	C₂²×C₇	1	2	yes	complemented
410	#474	C₂²×C₇	1	2	yes	—
411	#474	C₂²×C₇	1	1	yes	characteristic, complemented
412	#474	C₂²×C₇	1	2	yes	complemented
413	#433	C₂²×C₇	1	4	yes	complemented
414	#432	C₂²×C₇	1	2	yes	complemented
415	#431	C₂²×C₇	1	2	yes	complemented
416	#428	C₂²×C₇	1	2	yes	—
417	#428	C₂²×C₇	1	2	yes	—
418	#427	C₂²×C₇	1	2	yes	—
419	C₂×#106	C₂²×C₇	1	2	yes	—
420	#423	C₂²×C₇	1	1	yes	characteristic
421	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
422	#418	C₂²×C₇	1	2	yes	—
423	#417	C₂²×C₇	1	2	yes	—
424	#416	C₂²×C₇	1	2	yes	—
425	C₂×#102	C₂²×C₇	1	2	yes	—
426	#408	C₂²×C₇	1	2	yes	—
427	#405	C₂²×C₇	1	2	yes	—
428	C₂³×C₇	—	2	2	no	—
429	C₂³×C₇	—	2	1	no	—
430	C₂³×C₇	—	4	2	no	—
431	C₂³×C₇	—	8	1	no	—
432	C₂³×C₇	—	8	1	no	—
433	C₂³×C₇	C₂²×D₄	1	2	yes	—
434	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
435	C₇×Q₈	—	2	2	no	—
436	C₇×Q₈	—	2	1	no	—
437	C₇×Q₈	—	2	1	no	—
438	C₇×Q₈	—	4	2	no	—
439	C₇×Q₈	—	4	4	no	—
440	C₇×Q₈	—	4	2	no	—
441	C₇×Q₈	—	8	2	no	—
442	C₇×Q₈	—	8	4	no	—
443	C₇×Q₈	—	8	2	no	—
444	C₇×D₄	—	2	4	no	—
445	C₇×D₄	—	2	2	no	—
446	C₇×D₄	—	2	2	no	—
447	C₇×D₄	—	2	2	no	—
448	C₇×D₄	—	2	1	no	—
449	C₇×D₄	—	2	1	no	—
450	C₇×D₄	—	4	2	no	—
451	C₇×D₄	—	4	2	no	—
452	C₇×D₄	—	8	2	no	—
453	C₇×D₄	—	8	2	no	—
454	C₇×D₄	—	8	2	no	—
455	C₇×D₄	—	8	2	no	—
456	C₇×D₄	—	8	2	no	—
457	C₂×C₄×C₇	—	2	2	no	—
458	C₂×C₄×C₇	—	2	4	no	—
459	C₂×C₄×C₇	—	2	2	no	—
460	C₂×C₄×C₇	—	2	2	no	—
461	C₂×C₄×C₇	—	2	2	no	—
462	C₂×C₄×C₇	—	2	1	no	—
463	C₂×C₄×C₇	—	2	1	no	—
464	C₂×C₄×C₇	—	2	1	no	—
465	C₂×C₄×C₇	—	2	4	no	—
466	C₂×C₄×C₇	—	2	2	no	—
467	C₂×C₄×C₇	—	2	2	no	—
468	C₂×C₄×C₇	—	4	1	no	—
469	C₂×C₄×C₇	—	4	2	no	—
470	C₂×C₄×C₇	—	4	2	no	—
471	C₂×C₄×C₇	—	4	4	no	—
472	C₂×C₄×C₇	—	4	2	no	—
473	C₂×C₄×C₇	—	8	1	no	—
474	C₂×C₄×C₇	—	8	2	no	—
475	C₂×C₄×C₇	—	8	1	no	—
476	C₂×C₄×C₇	—	8	2	no	—
477	C₂×C₄×C₇	—	8	4	no	—
478	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
479	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
487	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
488	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
489	C₇×C₈	—	2	2	no	—
490	C₇×C₈	—	2	2	no	—
491	C₇×C₈	—	2	4	no	—
492	C₂×#41	—	2	2	no	—
493	C₂×#41	C₂³×C₇	1	1	yes	characteristic
494	C₂×#41	C₂³×C₇	1	1	yes	characteristic
495	C₂²×Q₈	—	2	1	no	—
496	C₂²×Q₈	—	2	2	no	—
497	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
498	C₂³×C₄	—	2	1	no	—
499	C₂×M₁₆	C₂³×C₇	1	2	yes	—
500	C₂²×C₈	C₂³×C₇	1	2	yes	—
501	C₄⋊Q₈	—	2	1	no	—
502	C₄⋊Q₈	—	2	2	no	—
503	C₄⋊Q₈	—	2	4	no	—
504	C₄⋊Q₈	—	2	1	no	—
505	C₄⋊Q₈	—	2	1	no	—
506	C₄⋊Q₈	—	2	2	no	—
507	C₄⋊Q₈	—	2	2	no	—
508	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
509	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
510	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
511	C₄⋊Q₈	C₂³×C₇	1	4	yes	—
512	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
513	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
514	#127	—	2	1	no	—
515	#127	C₂³×C₇	1	2	yes	—
516	#126	—	2	2	no	—
517	#126	—	2	2	no	—
518	#125	—	2	1	no	—
519	#125	—	2	2	no	—
520	#125	—	2	4	no	—
521	#125	C₂³×C₇	1	2	yes	—
522	#125	C₂³×C₇	1	2	yes	—
523	#125	C₂³×C₇	1	4	yes	—
524	#124	—	2	1	no	—
525	#124	—	2	2	no	—
526	#124	—	2	2	no	—
527	#124	C₂³×C₇	1	2	yes	—
528	#123	—	2	2	no	—
529	#123	—	2	2	no	—
530	#123	—	2	2	no	—
531	#123	—	2	2	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	2	no	—
537	C₂²⋊Q₈	—	2	2	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	4	no	—
540	C₂²⋊Q₈	—	2	4	no	—
541	C₂²⋊Q₈	—	2	4	no	—
542	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
543	#121	—	2	2	no	—
544	#121	—	2	1	no	—
545	#121	—	2	2	no	—
546	#121	—	2	1	no	—
547	#121	—	2	1	no	—
548	#121	—	2	2	no	—
549	#121	—	2	2	no	—
550	#121	C₂³×C₇	1	2	yes	—
551	#121	C₂³×C₇	1	2	yes	—
552	#121	C₂³×C₇	1	2	yes	—
553	#120	—	2	2	no	—
554	#120	—	2	2	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	1	no	—
557	C₄×Q₈	—	2	1	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	2	no	—
560	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
561	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
562	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
563	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
564	C₄×D₄	—	2	4	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	2	no	—
569	C₄×D₄	—	2	1	no	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	2	no	—
572	C₄×D₄	C₇×D₄	1	2	yes	—
573	C₄×D₄	C₇×D₄	1	1	yes	characteristic
574	C₄×D₄	C₇×D₄	1	2	yes	—
575	C₄×D₄	C₇×D₄	1	1	yes	characteristic
576	C₄×D₄	C₂³×C₇	1	2	yes	—
577	C₄×D₄	C₂³×C₇	1	2	yes	—
578	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
579	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
580	#117	—	2	1	no	—
581	#117	—	2	2	no	—
582	#117	C₂³×C₇	1	1	yes	characteristic
583	#117	C₂³×C₇	1	2	yes	—
584	#117	C₂³×C₇	1	4	yes	—
585	#117	C₂³×C₇	1	1	yes	characteristic
586	#117	C₂³×C₇	1	2	yes	—
587	C₂×C₄⋊C₄	—	2	1	no	—
588	C₂×C₄⋊C₄	—	2	2	no	—
589	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
590	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
592	C₂×C₂²⋊C₄	—	2	1	no	—
593	C₂×C₄²	—	2	1	no	—
594	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄²	C₂³×C₇	1	2	yes	—
596	#107	C₂³×C₇	1	2	yes	—
597	#107	C₂³×C₇	1	2	yes	—
598	#107	C₂³×C₇	1	4	yes	—
599	#107	C₂³×C₇	1	4	yes	—
600	#106	C₂³×C₇	1	4	yes	—
601	#106	C₂³×C₇	1	4	yes	—
602	#106	C₂³×C₇	1	2	yes	—
603	#106	C₂³×C₇	1	2	yes	—
604	#106	C₂³×C₇	1	4	yes	—
605	#106	C₂³×C₇	1	4	yes	—
606	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
607	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
608	C₄⋊C₈	C₂³×C₇	1	2	yes	—
609	C₄⋊C₈	C₂³×C₇	1	2	yes	—
610	C₄⋊C₈	C₂³×C₇	1	2	yes	—
611	#103	C₂³×C₇	1	2	yes	—
612	#103	C₂³×C₇	1	2	yes	—
613	#103	C₂³×C₇	1	4	yes	—
614	#102	C₂³×C₇	1	4	yes	—
615	#102	C₂³×C₇	1	4	yes	—
616	#102	C₂³×C₇	1	2	yes	—
617	#102	C₂³×C₇	1	2	yes	—
618	#102	C₂³×C₇	1	4	yes	—
619	#102	C₂³×C₇	1	4	yes	—
620	#102	C₂³×C₇	1	4	yes	—
621	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
622	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
623	#97	C₂³×C₇	1	4	yes	—
624	C₄×C₈	C₂³×C₇	1	4	yes	—
625	C₂²×C₇	—	2	1	no	—
626	C₂²×C₇	—	2	1	no	—
627	C₂²×C₇	—	2	2	no	—
628	C₂²×C₇	—	2	2	no	—
629	C₂²×C₇	—	2	2	no	—
630	C₂²×C₇	—	4	1	no	—
631	C₂²×C₇	—	4	2	no	—
632	C₂²×C₇	—	4	1	no	—
633	C₂²×C₇	—	4	2	no	—
634	C₂²×C₇	—	4	2	no	—
635	C₂²×C₇	—	4	1	no	—
636	C₂²×C₇	—	8	4	no	—
637	C₂²×C₇	#536	1	2	yes	—
638	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
639	C₄×C₇	—	2	1	no	—
640	C₄×C₇	—	2	1	no	—
641	C₄×C₇	—	2	2	no	—
642	C₄×C₇	—	2	2	no	—
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	2	no	—
645	C₄×C₇	—	4	4	no	—
646	C₄×C₇	—	4	2	no	—
647	C₄×C₇	—	4	1	no	—
648	C₄×C₇	—	4	1	no	—
649	C₄×C₇	—	4	2	no	—
650	C₄×C₇	—	4	1	no	—
651	C₄×C₇	—	4	2	no	—
652	C₄×C₇	#536	1	2	yes	—
653	C₄×C₇	#577	1	2	yes	—
654	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
655	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
656	C₂⁴	—	2	1	no	—
657	#41	—	2	2	no	—
658	#41	—	2	2	no	—
659	#41	—	2	2	no	—
660	#41	—	2	2	no	—
661	#41	—	8	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	1	no	—
664	C₂×Q₈	—	2	2	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	4	no	—
668	C₂×Q₈	—	8	2	no	—
669	C₂×Q₈	—	8	4	no	—
670	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
671	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
672	C₂×D₄	—	2	1	no	—
673	C₂×D₄	—	2	2	no	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	2	no	—
680	C₂×D₄	—	2	2	no	—
681	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
682	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
683	C₂×D₄	C₂⁴×C₇	1	2	yes	—
684	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	4	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	1	no	—
692	C₂²×C₄	—	2	2	no	—
693	C₂²×C₄	—	8	2	no	—
694	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
695	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
696	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
697	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
699	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
700	M₁₆	—	2	4	no	—
701	C₂×C₈	—	2	4	no	—
702	C₂×C₈	C₂⁴×C₇	1	2	yes	—
703	C₂×C₈	C₂⁴×C₇	1	4	yes	—
704	C₂×C₈	C₂⁴×C₇	1	2	yes	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	4	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	2	no	—
712	C₄⋊C₄	—	2	1	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	1	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	4	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	4	no	—
723	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
724	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
725	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
726	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
728	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
729	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
731	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
732	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
733	C₂²⋊C₄	—	2	1	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	1	no	—
740	C₂²⋊C₄	—	2	1	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	2	no	—
743	C₂²⋊C₄	—	2	2	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
747	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
748	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
749	C₄²	—	2	1	no	—
750	C₄²	—	2	1	no	—
751	C₄²	—	2	1	no	—
752	C₄²	—	2	4	no	—
753	C₄²	—	2	2	no	—
754	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
755	C₄²	C₂×C₇×D₄	1	2	yes	—
756	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
757	C₄²	C₂×C₇×D₄	1	2	yes	—
758	C₄²	C₂⁴×C₇	1	2	yes	—
759	C₄²	C₂⁴×C₇	1	1	yes	characteristic
760	C₄²	C₂⁴×C₇	1	1	yes	characteristic
761	C₂×C₇	—	2	2	no	—
762	C₂×C₇	—	4	2	no	—
763	C₂×C₇	—	8	1	no	—
764	C₂×C₇	—	8	2	no	—
765	C₂×C₇	C₂×#536	1	1	yes	characteristic
766	C₂×C₇	C₂×#577	1	1	yes	characteristic
767	C₂×C₇	#3585	1	1	yes	characteristic
768	C₂³	—	2	2	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	4	2	no	—
771	C₂³	—	8	1	no	—
772	C₂³	—	8	1	no	—
773	C₂³	C₂²×C₇×D₄	1	2	yes	—
774	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
775	Q₈	—	2	2	no	—
776	Q₈	—	2	1	no	—
777	Q₈	—	2	1	no	—
778	Q₈	—	4	2	no	—
779	Q₈	—	4	4	no	—
780	Q₈	—	4	2	no	—
781	Q₈	—	8	2	no	—
782	Q₈	—	8	4	no	—
783	Q₈	—	8	2	no	—
784	D₄	—	2	4	no	—
785	D₄	—	2	2	no	—
786	D₄	—	2	2	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	1	no	—
789	D₄	—	2	2	no	—
790	D₄	—	4	2	no	—
791	D₄	—	4	2	no	—
792	D₄	—	8	2	no	—
793	D₄	—	8	2	no	—
794	D₄	—	8	2	no	—
795	D₄	—	8	2	no	—
796	D₄	—	8	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	4	1	no	—
809	C₂×C₄	—	4	2	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	8	1	no	—
814	C₂×C₄	—	8	2	no	—
815	C₂×C₄	—	8	1	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	4	no	—
818	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
819	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
820	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
821	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
822	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
823	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
824	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
825	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
826	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
827	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
828	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
829	C₈	—	2	2	no	—
830	C₈	—	2	2	no	—
831	C₈	—	2	4	no	—
832	C₇	#60892	1	1	yes	characteristic, direct product factor, Sylow
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	2	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	1	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	1	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	8	4	no	—
845	C₂²	C₇×#536	1	2	yes	—
846	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
847	C₄	—	2	1	no	—
848	C₄	—	2	2	no	—
849	C₄	—	2	1	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	4	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	C₇×#536	1	2	yes	—
861	C₄	C₇×#577	1	2	yes	—
862	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
863	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
864	C₂	—	2	2	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	—	8	1	no	—
868	C₂	C₂×C₇×#536	1	1	yes	characteristic
869	C₂	C₂×C₇×#577	1	1	yes	characteristic
870	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3460	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3503	C₂	semidirect
3. C₇×#3244	C₂	semidirect
4. C₇×#3241	C₂	semidirect
5. C₇×#3238	C₂	semidirect
6. C₇×#3235	C₂	semidirect
7. C₇×#3233	C₂	semidirect
8. C₇×#3227	C₂	semidirect
9. C₇×#3163	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3099	C₂	semidirect
12. C₇×#3096	C₂	semidirect
13. C₇×#3079	C₂	semidirect
14. C₇×#3077	C₂	semidirect
15. C₇×#3076	C₂	semidirect
16. C₂×C₇×#476	C₂	semidirect
17. C₇×#2925	C₂	semidirect
26. C₇×#544	C₂²	semidirect
36. C₇×#533	C₂²	semidirect
40. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
48. C₇×#501	C₂²	semidirect
49. C₇×#501	C₂²	semidirect
50. C₇×#499	C₂²	semidirect
51. C₇×#498	C₂²	semidirect
56. C₇×#485	C₂²	semidirect
57. C₇×#483	C₂²	semidirect
60. C₇×#482	C₂²	semidirect
62. C₇×#481	C₂²	semidirect
64. C₇×#479	C₂²	semidirect
66. C₇×#478	C₂²	semidirect
67. C₇×#477	C₂²	semidirect
68. C₇×#477	C₂²	semidirect
73. C₇×#476	C₂²	semidirect
74. C₇×#476	C₂²	semidirect
75. C₇×#475	C₂²	semidirect
76. C₇×#475	C₂²	semidirect
78. C₇×#474	C₂²	semidirect
79. C₇×#474	C₂²	semidirect
80. C₇×#433	C₂²	semidirect
81. C₇×#432	C₂²	semidirect
82. C₇×#431	C₂²	semidirect
95. #60892	C₇	direct (N × H)
229. #3503	C₂×C₇	semidirect
231. #3244	C₂×C₇	semidirect
232. #3241	C₂×C₇	semidirect
233. #3238	C₂×C₇	semidirect
234. #3235	C₂×C₇	semidirect
235. #3233	C₂×C₇	semidirect
236. #3227	C₂×C₇	semidirect
237. #3163	C₂×C₇	semidirect
238. #3136	C₂×C₇	semidirect
239. #3099	C₂×C₇	semidirect
240. #3096	C₂×C₇	semidirect
241. #3079	C₂×C₇	semidirect
242. #3077	C₂×C₇	semidirect
243. #3076	C₂×C₇	semidirect
244. C₂×#476	C₂×C₇	semidirect
245. #2925	C₂×C₇	semidirect
359. #544	C₂²×C₇	semidirect
369. #533	C₂²×C₇	semidirect
373. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
381. #501	C₂²×C₇	semidirect
382. #501	C₂²×C₇	semidirect
383. #499	C₂²×C₇	semidirect
384. #498	C₂²×C₇	semidirect
389. #485	C₂²×C₇	semidirect
390. #483	C₂²×C₇	semidirect
393. #482	C₂²×C₇	semidirect
395. #481	C₂²×C₇	semidirect
397. #479	C₂²×C₇	semidirect
399. #478	C₂²×C₇	semidirect
400. #477	C₂²×C₇	semidirect
401. #477	C₂²×C₇	semidirect
406. #476	C₂²×C₇	semidirect
407. #476	C₂²×C₇	semidirect
408. #475	C₂²×C₇	semidirect
409. #475	C₂²×C₇	semidirect
411. #474	C₂²×C₇	semidirect
412. #474	C₂²×C₇	semidirect
413. #433	C₂²×C₇	semidirect
414. #432	C₂²×C₇	semidirect
415. #431	C₂²×C₇	semidirect
832. C₇	#60892	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×#3503	2
C₇×#3460	2
C₇×#3244	2
C₇×#3241	2
C₇×#3238	2
C₇×#3235	2
C₇×#3233	2
C₇×#3227	2
C₇×#3163	2
C₇×#3136	2
C₇×#3099	2
C₇×#3096	2
C₇×#3079	2
C₇×#3077	2
C₇×#3076	2
C₂×C₇×#476	2
C₇×#2925	2
#60892	7

Subgroups — C7×#60892 #13238108

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60892 #13238108