Subgroups — C₇×#60727 #13237943

Order 1792.

1902 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×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3181	C₂	1	2	yes	maximal, complemented
4	C₇×#3180	C₂	1	2	yes	maximal, complemented
5	C₇×#3175	C₂	1	4	yes	maximal, complemented
6	C₇×#3173	C₂	1	4	yes	maximal, complemented
7	C₇×#3172	C₂	1	2	yes	maximal, complemented
8	C₇×#3171	C₂	1	2	yes	maximal, complemented
9	C₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3153	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3135	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3063	C₂	1	2	yes	maximal, complemented
14	C₇×#3062	C₂	1	2	yes	maximal, complemented
15	C₇×#2947	C₂	1	2	yes	maximal, complemented
16	C₇×#2946	C₂	1	2	yes	maximal, complemented
17	C₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×#137	C₂²	1	2	yes	—
19	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₇×#131	C₂²	1	2	yes	—
21	C₇×#559	—	2	1	no	—
22	C₇×#559	—	2	1	no	—
23	C₇×#556	—	2	1	no	—
24	C₇×#556	—	2	1	no	—
25	C₇×#556	—	2	1	no	—
26	C₇×#555	—	2	1	no	—
27	C₇×#554	—	2	1	no	—
28	C₇×#553	—	2	2	no	—
29	C₇×#551	—	2	2	no	—
30	C₇×#551	—	2	2	no	—
31	C₇×#548	—	2	2	no	—
32	C₇×#547	—	2	1	no	—
33	C₇×#542	C₂²	1	2	yes	—
34	C₇×#542	C₂²	1	2	yes	—
35	C₇×#542	C₂²	1	4	yes	complemented
36	C₇×#537	C₂²	1	2	yes	—
37	C₇×#536	C₂²	1	1	yes	characteristic
38	C₇×#535	C₂²	1	1	yes	characteristic
39	C₇×#533	C₂²	1	1	yes	characteristic
40	C₇×#533	C₂²	1	2	yes	complemented
41	C₇×#532	C₂²	1	1	yes	characteristic
42	C₇×#532	C₂²	1	2	yes	complemented
43	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
44	C₇×#529	C₂²	1	2	yes	—
45	C₇×#529	C₂²	1	2	yes	—
46	C₂×C₇×#124	C₂²	1	1	yes	characteristic
47	C₇×#520	C₂²	1	2	yes	—
48	C₇×#519	C₂²	1	1	yes	characteristic
49	C₇×#518	C₂²	1	1	yes	characteristic
50	C₄×C₇×#41	C₂²	1	1	yes	characteristic
51	C₇×#501	C₂²	1	2	yes	complemented
52	C₇×#501	C₂²	1	2	yes	complemented
53	C₇×#500	C₂²	1	2	yes	complemented
54	C₇×#498	C₂²	1	2	yes	complemented
55	C₇×#497	C₂²	1	2	yes	—
56	C₇×#496	C₂²	1	2	yes	—
57	C₇×#495	C₂²	1	4	yes	—
58	C₇×#491	C₂²	1	1	yes	characteristic, complemented
59	C₇×#491	C₂²	1	1	yes	characteristic, complemented
60	C₇×#490	C₂²	1	1	yes	characteristic, complemented
61	C₇×#490	C₂²	1	1	yes	characteristic, complemented
62	C₇×#489	C₂²	1	2	yes	—
63	C₇×#489	C₂²	1	4	yes	—
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#489	C₂²	1	2	yes	complemented
66	C₇×#489	C₂²	1	2	yes	complemented
67	C₇×#470	C₂²	1	4	yes	complemented
68	C₇×#469	C₂²	1	4	yes	—
69	C₇×#468	C₂²	1	4	yes	—
70	C₇×#468	C₂²	1	4	yes	complemented
71	C₇×#467	C₂²	1	4	yes	complemented
72	C₇×#466	C₂²	1	4	yes	—
73	C₇×#465	C₂²	1	4	yes	—
74	C₇×#465	C₂²	1	4	yes	complemented
75	C₇×#442	C₂²	1	4	yes	—
76	C₇×#441	C₂²	1	4	yes	complemented
77	C₇×#440	C₂²	1	4	yes	—
78	C₇×#440	C₂²	1	4	yes	complemented
79	C₄×C₇×Q₁₆	C₂²	1	4	yes	complemented
80	C₄×C₇×SD₁₆	C₂²	1	4	yes	—
81	C₄×C₇×SD₁₆	C₂²	1	4	yes	complemented
82	C₄×C₇×D₈	C₂²	1	4	yes	—
83	C₇×#428	C₂²	1	2	yes	—
84	C₇×#428	C₂²	1	2	yes	—
85	C₇×#416	C₂²	1	2	yes	—
86	C₇×#416	C₂²	1	2	yes	—
87	C₂×C₇×#103	C₂²	1	2	yes	—
88	C₂×C₇×#102	C₂²	1	2	yes	—
89	C₇×#405	C₂²	1	2	yes	—
90	C₇×#405	C₂²	1	4	yes	complemented
91	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
92	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
93	C₂×C₇×#97	C₂²	1	1	yes	characteristic
94	C₂×C₇×#97	C₂²	1	2	yes	complemented
95	#60727	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₇×#41	—	2	2	no	—
97	C₂×C₇×#41	C₂³	1	2	yes	—
98	C₂×C₇×#41	C₂³	1	1	yes	characteristic
99	C₂²×C₇×Q₈	—	2	1	no	—
100	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
101	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
102	C₇×#137	—	2	8	no	—
103	C₇×AGL(1,ℤ/8)	—	2	8	no	—
104	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
105	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
106	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
107	C₂×C₇×D₈	C₂³	1	4	yes	—
108	C₇×#131	—	2	8	no	—
109	C₂×C₇×M₁₆	C₂³	1	4	yes	—
110	C₂×C₇×M₁₆	C₂³	1	2	yes	—
111	C₂²×C₇×C₈	C₂³	1	4	yes	—
112	C₂²×C₇×C₈	C₂³	1	2	yes	—
113	C₇×C₄⋊Q₈	—	2	1	no	—
114	C₇×C₄⋊Q₈	—	2	1	no	—
115	C₇×C₄⋊Q₈	—	2	1	no	—
116	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
120	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
121	C₇×#127	—	2	1	no	—
122	C₇×#127	C₂³	1	1	yes	characteristic
123	C₇×#126	—	2	2	no	—
124	C₇×#126	—	2	2	no	—
125	C₇×#126	—	2	4	no	—
126	C₇×#126	—	2	2	no	—
127	C₇×#126	—	2	2	no	—
128	C₇×#125	—	2	2	no	—
129	C₇×#125	C₂³	1	1	yes	characteristic
130	C₇×#125	C₂³	1	1	yes	characteristic
131	C₇×#124	—	2	1	no	—
132	C₇×#124	—	2	1	no	—
133	C₇×#124	—	2	2	no	—
134	C₇×#124	—	2	2	no	—
135	C₇×#124	—	2	4	no	—
136	C₇×#124	—	2	1	no	—
137	C₇×#124	—	2	1	no	—
138	C₇×#124	—	2	2	no	—
139	C₇×#124	C₂³	1	2	yes	—
140	C₇×#124	C₂³	1	2	yes	—
141	C₇×#124	C₂³	1	2	yes	—
142	C₇×#123	—	2	2	no	—
143	C₇×#123	—	2	2	no	—
144	C₇×#123	—	2	2	no	—
145	C₇×#123	—	2	2	no	—
146	C₇×#123	—	2	2	no	—
147	C₇×#123	—	2	4	no	—
148	C₇×C₂²⋊Q₈	—	2	2	no	—
149	C₇×C₂²⋊Q₈	—	2	1	no	—
150	C₇×C₂²⋊Q₈	—	2	1	no	—
151	C₇×C₂²⋊Q₈	—	2	2	no	—
152	C₇×C₂²⋊Q₈	—	2	2	no	—
153	C₇×C₂²⋊Q₈	—	2	2	no	—
154	C₇×C₂²⋊Q₈	—	2	4	no	—
155	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
156	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
157	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
158	C₇×#121	—	2	2	no	—
159	C₇×#121	—	2	4	no	—
160	C₇×#121	—	2	1	no	—
161	C₇×#121	—	2	1	no	—
162	C₇×#121	—	2	2	no	—
163	C₇×#121	C₂³	1	2	yes	—
164	C₇×#121	C₂³	1	4	yes	—
165	C₇×#121	C₂³	1	2	yes	—
166	C₇×#120	—	2	2	no	—
167	C₄×C₇×Q₈	—	2	1	no	—
168	C₄×C₇×Q₈	—	2	1	no	—
169	C₄×C₇×Q₈	—	2	1	no	—
170	C₄×C₇×Q₈	—	2	1	no	—
171	C₄×C₇×Q₈	—	2	2	no	—
172	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
173	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
174	C₄×C₇×Q₈	C₂³	1	2	yes	—
175	C₄×C₇×Q₈	C₂³	1	2	yes	—
176	C₄×C₇×Q₈	C₂³	1	4	yes	—
177	C₄×C₇×D₄	—	2	2	no	—
178	C₄×C₇×D₄	—	2	2	no	—
179	C₄×C₇×D₄	—	2	1	no	—
180	C₄×C₇×D₄	—	2	1	no	—
181	C₄×C₇×D₄	—	2	4	no	—
182	C₄×C₇×D₄	—	2	1	no	—
183	C₄×C₇×D₄	—	2	1	no	—
184	C₄×C₇×D₄	—	2	2	no	—
185	C₄×C₇×D₄	D₄	1	1	yes	characteristic
186	C₄×C₇×D₄	D₄	1	2	yes	—
187	C₄×C₇×D₄	D₄	1	2	yes	—
188	C₄×C₇×D₄	D₄	1	1	yes	characteristic
189	C₄×C₇×D₄	C₂³	1	2	yes	—
190	C₄×C₇×D₄	C₂³	1	2	yes	—
191	C₄×C₇×D₄	C₂³	1	4	yes	—
192	C₇×#117	—	2	2	no	—
193	C₇×#117	—	2	2	no	—
194	C₇×#117	—	2	2	no	—
195	C₇×#117	—	2	2	no	—
196	C₇×#117	—	2	2	no	—
197	C₇×#117	C₂³	1	1	yes	characteristic
198	C₇×#117	C₂³	1	1	yes	characteristic
199	C₇×#117	C₂³	1	1	yes	characteristic
200	C₇×#117	C₂³	1	2	yes	—
201	C₂×C₇×C₄⋊C₄	—	2	1	no	—
202	C₂×C₇×C₄⋊C₄	—	2	2	no	—
203	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
204	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
205	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
206	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	2	yes	—
209	C₇×#107	C₂³	1	4	yes	—
210	C₇×#107	C₂³	1	4	yes	—
211	C₇×#106	C₂³	1	4	yes	—
212	C₇×#106	C₂³	1	4	yes	—
213	C₇×#103	C₂³	1	2	yes	—
214	C₇×#103	C₂³	1	4	yes	—
215	C₇×#103	C₂³	1	2	yes	—
216	C₇×#103	C₂³	1	4	yes	—
217	C₇×#103	C₂³	1	2	yes	—
218	C₇×#103	C₂³	1	2	yes	—
219	C₇×#102	C₂³	1	2	yes	—
220	C₇×#102	C₂³	1	4	yes	—
221	C₇×#102	C₂³	1	4	yes	—
222	C₇×#102	C₂³	1	2	yes	—
223	C₇×#102	C₂³	1	2	yes	—
224	C₇×#102	C₂³	1	2	yes	—
225	C₇×#97	C₂³	1	2	yes	—
226	C₇×#97	C₂³	1	1	yes	characteristic
227	C₇×#97	C₂³	1	1	yes	characteristic
228	C₇×#97	C₂³	1	2	yes	—
229	C₇×#97	C₂³	1	4	yes	—
230	C₄×C₇×C₈	C₂³	1	2	yes	—
231	C₄×C₇×C₈	C₂³	1	4	yes	—
232	#3511	C₂×C₇	1	1	yes	characteristic, complemented
233	#3510	C₂×C₇	1	1	yes	characteristic, complemented
234	#3181	C₂×C₇	1	2	yes	complemented
235	#3180	C₂×C₇	1	2	yes	complemented
236	#3175	C₂×C₇	1	4	yes	complemented
237	#3173	C₂×C₇	1	4	yes	complemented
238	#3172	C₂×C₇	1	2	yes	complemented
239	#3171	C₂×C₇	1	2	yes	complemented
240	#3165	C₂×C₇	1	1	yes	characteristic, complemented
241	#3153	C₂×C₇	1	1	yes	characteristic, complemented
242	#3135	C₂×C₇	1	1	yes	characteristic, complemented
243	C₂×#489	C₂×C₇	1	1	yes	characteristic, complemented
244	#3063	C₂×C₇	1	2	yes	complemented
245	#3062	C₂×C₇	1	2	yes	complemented
246	#2947	C₂×C₇	1	2	yes	complemented
247	#2946	C₂×C₇	1	2	yes	complemented
248	#2875	C₂×C₇	1	1	yes	characteristic, complemented
249	C₂⁴×C₇	—	2	1	no	—
250	C₇×#41	—	2	4	no	—
251	C₇×#41	—	2	4	no	—
252	C₇×#41	—	2	4	no	—
253	C₇×#41	—	8	4	no	—
254	C₂×C₇×Q₈	—	2	1	no	—
255	C₂×C₇×Q₈	—	2	2	no	—
256	C₂×C₇×Q₈	—	2	1	no	—
257	C₂×C₇×Q₈	—	2	1	no	—
258	C₂×C₇×Q₈	—	2	2	no	—
259	C₂×C₇×Q₈	—	2	4	no	—
260	C₂×C₇×Q₈	—	8	2	no	—
261	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
262	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
263	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	—	2	2	no	—
267	C₂×C₇×D₄	—	2	4	no	—
268	C₂×C₇×D₄	—	2	1	no	—
269	C₂×C₇×D₄	—	2	1	no	—
270	C₂×C₇×D₄	—	2	1	no	—
271	C₂×C₇×D₄	—	2	4	no	—
272	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
273	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
274	C₂×C₇×D₄	C₂⁴	1	2	yes	—
275	C₂×C₇×D₄	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	—	2	1	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	4	no	—
282	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
285	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₇×Q₁₆	—	2	8	no	—
289	C₇×SD₁₆	—	2	8	no	—
290	C₇×SD₁₆	—	2	8	no	—
291	C₇×D₈	—	2	8	no	—
292	C₇×M₁₆	—	2	8	no	—
293	C₇×M₁₆	#41	1	8	yes	complemented
294	C₂×C₇×C₈	—	2	4	no	—
295	C₂×C₇×C₈	—	2	8	no	—
296	C₂×C₇×C₈	C₂⁴	1	2	yes	—
297	C₂×C₇×C₈	C₂⁴	1	2	yes	—
298	C₂×C₇×C₈	C₂⁴	1	4	yes	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	4	no	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	1	no	—
304	C₇×C₄⋊C₄	—	2	1	no	—
305	C₇×C₄⋊C₄	—	2	1	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	2	no	—
308	C₇×C₄⋊C₄	—	2	2	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	1	no	—
311	C₇×C₄⋊C₄	—	2	1	no	—
312	C₇×C₄⋊C₄	—	2	1	no	—
313	C₇×C₄⋊C₄	—	2	4	no	—
314	C₇×C₄⋊C₄	—	2	1	no	—
315	C₇×C₄⋊C₄	—	2	1	no	—
316	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
317	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
318	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
319	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
320	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
321	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
322	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
323	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
324	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
325	C₇×C₂²⋊C₄	—	2	1	no	—
326	C₇×C₂²⋊C₄	—	2	1	no	—
327	C₇×C₂²⋊C₄	—	2	4	no	—
328	C₇×C₂²⋊C₄	—	2	2	no	—
329	C₇×C₂²⋊C₄	—	2	2	no	—
330	C₇×C₂²⋊C₄	—	2	2	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	—	2	4	no	—
337	C₇×C₂²⋊C₄	—	2	2	no	—
338	C₇×C₂²⋊C₄	—	2	2	no	—
339	C₇×C₂²⋊C₄	—	2	4	no	—
340	C₇×C₂²⋊C₄	—	2	2	no	—
341	C₇×C₂²⋊C₄	—	2	2	no	—
342	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
344	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
345	C₄²×C₇	—	2	2	no	—
346	C₄²×C₇	—	2	2	no	—
347	C₄²×C₇	—	2	4	no	—
348	C₄²×C₇	—	2	1	no	—
349	C₄²×C₇	—	2	1	no	—
350	C₄²×C₇	C₂×D₄	1	2	yes	—
351	C₄²×C₇	C₂×D₄	1	2	yes	—
352	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
353	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₇	C₂⁴	1	2	yes	—
355	C₄²×C₇	C₂⁴	1	1	yes	characteristic
356	C₄²×C₇	C₂⁴	1	1	yes	characteristic
357	C₂×#137	C₂²×C₇	1	2	yes	—
358	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	—
359	C₂×#131	C₂²×C₇	1	2	yes	—
360	#559	—	2	1	no	—
361	#559	—	2	1	no	—
362	#556	—	2	1	no	—
363	#556	—	2	1	no	—
364	#556	—	2	1	no	—
365	#555	—	2	1	no	—
366	#554	—	2	1	no	—
367	#553	—	2	2	no	—
368	#551	—	2	2	no	—
369	#551	—	2	2	no	—
370	#548	—	2	2	no	—
371	#547	—	2	1	no	—
372	#542	C₂²×C₇	1	2	yes	—
373	#542	C₂²×C₇	1	2	yes	—
374	#542	C₂²×C₇	1	4	yes	complemented
375	#537	C₂²×C₇	1	2	yes	—
376	#536	C₂²×C₇	1	1	yes	characteristic
377	#535	C₂²×C₇	1	1	yes	characteristic
378	#533	C₂²×C₇	1	1	yes	characteristic
379	#533	C₂²×C₇	1	2	yes	complemented
380	#532	C₂²×C₇	1	1	yes	characteristic
381	#532	C₂²×C₇	1	2	yes	complemented
382	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
383	#529	C₂²×C₇	1	2	yes	—
384	#529	C₂²×C₇	1	2	yes	—
385	C₂×#124	C₂²×C₇	1	1	yes	characteristic
386	#520	C₂²×C₇	1	2	yes	—
387	#519	C₂²×C₇	1	1	yes	characteristic
388	#518	C₂²×C₇	1	1	yes	characteristic
389	C₄×#41	C₂²×C₇	1	1	yes	characteristic
390	#501	C₂²×C₇	1	2	yes	complemented
391	#501	C₂²×C₇	1	2	yes	complemented
392	#500	C₂²×C₇	1	2	yes	complemented
393	#498	C₂²×C₇	1	2	yes	complemented
394	#497	C₂²×C₇	1	2	yes	—
395	#496	C₂²×C₇	1	2	yes	—
396	#495	C₂²×C₇	1	4	yes	—
397	#491	C₂²×C₇	1	1	yes	characteristic, complemented
398	#491	C₂²×C₇	1	1	yes	characteristic, complemented
399	#490	C₂²×C₇	1	1	yes	characteristic, complemented
400	#490	C₂²×C₇	1	1	yes	characteristic, complemented
401	#489	C₂²×C₇	1	2	yes	—
402	#489	C₂²×C₇	1	4	yes	—
403	#489	C₂²×C₇	1	2	yes	—
404	#489	C₂²×C₇	1	2	yes	complemented
405	#489	C₂²×C₇	1	2	yes	complemented
406	#470	C₂²×C₇	1	4	yes	complemented
407	#469	C₂²×C₇	1	4	yes	—
408	#468	C₂²×C₇	1	4	yes	—
409	#468	C₂²×C₇	1	4	yes	complemented
410	#467	C₂²×C₇	1	4	yes	complemented
411	#466	C₂²×C₇	1	4	yes	—
412	#465	C₂²×C₇	1	4	yes	—
413	#465	C₂²×C₇	1	4	yes	complemented
414	#442	C₂²×C₇	1	4	yes	—
415	#441	C₂²×C₇	1	4	yes	complemented
416	#440	C₂²×C₇	1	4	yes	—
417	#440	C₂²×C₇	1	4	yes	complemented
418	C₄×Q₁₆	C₂²×C₇	1	4	yes	complemented
419	C₄×SD₁₆	C₂²×C₇	1	4	yes	—
420	C₄×SD₁₆	C₂²×C₇	1	4	yes	complemented
421	C₄×D₈	C₂²×C₇	1	4	yes	—
422	#428	C₂²×C₇	1	2	yes	—
423	#428	C₂²×C₇	1	2	yes	—
424	#416	C₂²×C₇	1	2	yes	—
425	#416	C₂²×C₇	1	2	yes	—
426	C₂×#103	C₂²×C₇	1	2	yes	—
427	C₂×#102	C₂²×C₇	1	2	yes	—
428	#405	C₂²×C₇	1	2	yes	—
429	#405	C₂²×C₇	1	4	yes	complemented
430	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
431	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
432	C₂×#97	C₂²×C₇	1	1	yes	characteristic
433	C₂×#97	C₂²×C₇	1	2	yes	complemented
434	C₂³×C₇	—	2	2	no	—
435	C₂³×C₇	—	2	2	no	—
436	C₂³×C₇	—	4	2	no	—
437	C₂³×C₇	—	8	1	no	—
438	C₂³×C₇	—	8	1	no	—
439	C₂³×C₇	C₂²×D₄	1	2	yes	—
440	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
441	C₇×Q₈	—	2	2	no	—
442	C₇×Q₈	—	2	2	no	—
443	C₇×Q₈	—	2	4	no	—
444	C₇×Q₈	—	2	2	no	—
445	C₇×Q₈	—	4	4	no	—
446	C₇×Q₈	—	4	2	no	—
447	C₇×Q₈	—	8	1	no	—
448	C₇×Q₈	—	8	1	no	—
449	C₇×Q₈	—	8	2	no	—
450	C₇×D₄	—	2	4	no	—
451	C₇×D₄	—	2	2	no	—
452	C₇×D₄	—	2	2	no	—
453	C₇×D₄	—	2	4	no	—
454	C₇×D₄	—	2	2	no	—
455	C₇×D₄	—	4	2	no	—
456	C₇×D₄	—	4	2	no	—
457	C₇×D₄	—	4	4	no	—
458	C₇×D₄	—	4	2	no	—
459	C₇×D₄	—	8	2	no	—
460	C₇×D₄	—	8	2	no	—
461	C₇×D₄	—	8	4	no	—
462	C₂×C₄×C₇	—	2	4	no	—
463	C₂×C₄×C₇	—	2	1	no	—
464	C₂×C₄×C₇	—	2	1	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	2	no	—
467	C₂×C₄×C₇	—	2	1	no	—
468	C₂×C₄×C₇	—	2	1	no	—
469	C₂×C₄×C₇	—	2	4	no	—
470	C₂×C₄×C₇	—	4	2	no	—
471	C₂×C₄×C₇	—	4	1	no	—
472	C₂×C₄×C₇	—	4	1	no	—
473	C₂×C₄×C₇	—	4	2	no	—
474	C₂×C₄×C₇	—	4	2	no	—
475	C₂×C₄×C₇	—	4	4	no	—
476	C₂×C₄×C₇	—	8	2	no	—
477	C₂×C₄×C₇	—	8	2	no	—
478	C₂×C₄×C₇	—	8	4	no	—
479	C₂×C₄×C₇	—	8	2	no	—
480	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
485	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₇	C₂×#41	1	4	yes	—
489	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
490	C₇×C₈	—	2	2	no	—
491	C₇×C₈	—	2	2	no	—
492	C₇×C₈	C₂×#41	1	8	yes	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	C₂³×C₇	1	2	yes	—
495	C₂×#41	C₂³×C₇	1	1	yes	characteristic
496	C₂²×Q₈	—	2	1	no	—
497	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
498	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
499	#137	—	2	8	no	—
500	AGL(1,ℤ/8)	—	2	8	no	—
501	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
502	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
503	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
504	C₂×D₈	C₂³×C₇	1	4	yes	—
505	#131	—	2	8	no	—
506	C₂×M₁₆	C₂³×C₇	1	4	yes	—
507	C₂×M₁₆	C₂³×C₇	1	2	yes	—
508	C₂²×C₈	C₂³×C₇	1	2	yes	—
509	C₂²×C₈	C₂³×C₇	1	4	yes	—
510	C₄⋊Q₈	—	2	1	no	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	—	2	1	no	—
513	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
514	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
516	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
518	#127	—	2	1	no	—
519	#127	C₂³×C₇	1	1	yes	characteristic
520	#126	—	2	2	no	—
521	#126	—	2	2	no	—
522	#126	—	2	4	no	—
523	#126	—	2	2	no	—
524	#126	—	2	2	no	—
525	#125	—	2	2	no	—
526	#125	C₂³×C₇	1	1	yes	characteristic
527	#125	C₂³×C₇	1	1	yes	characteristic
528	#124	—	2	1	no	—
529	#124	—	2	1	no	—
530	#124	—	2	2	no	—
531	#124	—	2	2	no	—
532	#124	—	2	4	no	—
533	#124	—	2	1	no	—
534	#124	—	2	1	no	—
535	#124	—	2	2	no	—
536	#124	C₂³×C₇	1	2	yes	—
537	#124	C₂³×C₇	1	2	yes	—
538	#124	C₂³×C₇	1	2	yes	—
539	#123	—	2	2	no	—
540	#123	—	2	2	no	—
541	#123	—	2	2	no	—
542	#123	—	2	2	no	—
543	#123	—	2	2	no	—
544	#123	—	2	4	no	—
545	C₂²⋊Q₈	—	2	2	no	—
546	C₂²⋊Q₈	—	2	1	no	—
547	C₂²⋊Q₈	—	2	1	no	—
548	C₂²⋊Q₈	—	2	2	no	—
549	C₂²⋊Q₈	—	2	2	no	—
550	C₂²⋊Q₈	—	2	2	no	—
551	C₂²⋊Q₈	—	2	4	no	—
552	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
553	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
554	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
555	#121	—	2	2	no	—
556	#121	—	2	4	no	—
557	#121	—	2	1	no	—
558	#121	—	2	1	no	—
559	#121	—	2	2	no	—
560	#121	C₂³×C₇	1	2	yes	—
561	#121	C₂³×C₇	1	2	yes	—
562	#121	C₂³×C₇	1	4	yes	—
563	#120	—	2	2	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	1	no	—
566	C₄×Q₈	—	2	1	no	—
567	C₄×Q₈	—	2	1	no	—
568	C₄×Q₈	—	2	2	no	—
569	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
570	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
571	C₄×Q₈	C₂³×C₇	1	2	yes	—
572	C₄×Q₈	C₂³×C₇	1	2	yes	—
573	C₄×Q₈	C₂³×C₇	1	4	yes	—
574	C₄×D₄	—	2	2	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	1	no	—
577	C₄×D₄	—	2	1	no	—
578	C₄×D₄	—	2	4	no	—
579	C₄×D₄	—	2	1	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	C₇×D₄	1	1	yes	characteristic
583	C₄×D₄	C₇×D₄	1	2	yes	—
584	C₄×D₄	C₇×D₄	1	2	yes	—
585	C₄×D₄	C₇×D₄	1	1	yes	characteristic
586	C₄×D₄	C₂³×C₇	1	2	yes	—
587	C₄×D₄	C₂³×C₇	1	2	yes	—
588	C₄×D₄	C₂³×C₇	1	4	yes	—
589	#117	—	2	2	no	—
590	#117	—	2	2	no	—
591	#117	—	2	2	no	—
592	#117	—	2	2	no	—
593	#117	—	2	2	no	—
594	#117	C₂³×C₇	1	1	yes	characteristic
595	#117	C₂³×C₇	1	1	yes	characteristic
596	#117	C₂³×C₇	1	1	yes	characteristic
597	#117	C₂³×C₇	1	2	yes	—
598	C₂×C₄⋊C₄	—	2	1	no	—
599	C₂×C₄⋊C₄	—	2	2	no	—
600	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
601	C₂×C₂²⋊C₄	—	2	1	no	—
602	C₂×C₂²⋊C₄	—	2	1	no	—
603	C₂×C₂²⋊C₄	—	2	2	no	—
604	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₇	1	2	yes	—
606	#107	C₂³×C₇	1	4	yes	—
607	#107	C₂³×C₇	1	4	yes	—
608	#106	C₂³×C₇	1	4	yes	—
609	#106	C₂³×C₇	1	4	yes	—
610	#103	C₂³×C₇	1	4	yes	—
611	#103	C₂³×C₇	1	4	yes	—
612	#103	C₂³×C₇	1	2	yes	—
613	#103	C₂³×C₇	1	2	yes	—
614	#103	C₂³×C₇	1	2	yes	—
615	#103	C₂³×C₇	1	2	yes	—
616	#102	C₂³×C₇	1	4	yes	—
617	#102	C₂³×C₇	1	4	yes	—
618	#102	C₂³×C₇	1	2	yes	—
619	#102	C₂³×C₇	1	2	yes	—
620	#102	C₂³×C₇	1	2	yes	—
621	#102	C₂³×C₇	1	2	yes	—
622	#97	C₂³×C₇	1	1	yes	characteristic
623	#97	C₂³×C₇	1	1	yes	characteristic
624	#97	C₂³×C₇	1	2	yes	—
625	#97	C₂³×C₇	1	2	yes	—
626	#97	C₂³×C₇	1	4	yes	—
627	C₄×C₈	C₂³×C₇	1	2	yes	—
628	C₄×C₈	C₂³×C₇	1	4	yes	—
629	C₂²×C₇	—	2	1	no	—
630	C₂²×C₇	—	2	1	no	—
631	C₂²×C₇	—	2	2	no	—
632	C₂²×C₇	—	2	2	no	—
633	C₂²×C₇	—	2	2	no	—
634	C₂²×C₇	—	4	2	no	—
635	C₂²×C₇	—	4	2	no	—
636	C₂²×C₇	—	4	2	no	—
637	C₂²×C₇	—	4	2	no	—
638	C₂²×C₇	—	4	2	no	—
639	C₂²×C₇	—	4	2	no	—
640	C₂²×C₇	—	16	2	no	—
641	C₂²×C₇	#532	1	2	yes	—
642	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
643	C₄×C₇	—	2	1	no	—
644	C₄×C₇	—	2	2	no	—
645	C₄×C₇	—	2	1	no	—
646	C₄×C₇	—	2	1	no	—
647	C₄×C₇	—	2	2	no	—
648	C₄×C₇	—	2	1	no	—
649	C₄×C₇	—	2	2	no	—
650	C₄×C₇	—	4	4	no	—
651	C₄×C₇	—	4	1	no	—
652	C₄×C₇	—	4	1	no	—
653	C₄×C₇	—	4	1	no	—
654	C₄×C₇	—	4	1	no	—
655	C₄×C₇	—	4	2	no	—
656	C₄×C₇	—	4	2	no	—
657	C₄×C₇	#532	1	2	yes	—
658	C₄×C₇	C₂²×#41	1	2	yes	—
659	C₂⁴	—	2	1	no	—
660	#41	—	2	4	no	—
661	#41	—	2	4	no	—
662	#41	—	2	4	no	—
663	#41	—	8	4	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	1	no	—
667	C₂×Q₈	—	2	1	no	—
668	C₂×Q₈	—	2	2	no	—
669	C₂×Q₈	—	2	4	no	—
670	C₂×Q₈	—	8	2	no	—
671	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
672	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
674	C₂×D₄	—	2	2	no	—
675	C₂×D₄	—	2	2	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	—	2	1	no	—
680	C₂×D₄	—	2	1	no	—
681	C₂×D₄	—	2	4	no	—
682	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
683	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
684	C₂×D₄	C₂⁴×C₇	1	2	yes	—
685	C₂×D₄	C₂⁴×C₇	1	2	yes	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	2	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	—	2	4	no	—
692	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
693	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
694	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
695	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
697	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
698	Q₁₆	—	2	8	no	—
699	SD₁₆	—	2	8	no	—
700	SD₁₆	—	2	8	no	—
701	D₈	—	2	8	no	—
702	M₁₆	—	2	8	no	—
703	M₁₆	C₇×#41	1	8	yes	complemented
704	C₂×C₈	—	2	4	no	—
705	C₂×C₈	—	2	8	no	—
706	C₂×C₈	C₂⁴×C₇	1	2	yes	—
707	C₂×C₈	C₂⁴×C₇	1	2	yes	—
708	C₂×C₈	C₂⁴×C₇	1	4	yes	—
709	C₄⋊C₄	—	2	2	no	—
710	C₄⋊C₄	—	2	2	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	2	no	—
713	C₄⋊C₄	—	2	1	no	—
714	C₄⋊C₄	—	2	1	no	—
715	C₄⋊C₄	—	2	1	no	—
716	C₄⋊C₄	—	2	2	no	—
717	C₄⋊C₄	—	2	2	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	1	no	—
721	C₄⋊C₄	—	2	1	no	—
722	C₄⋊C₄	—	2	1	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	—	2	1	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
727	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
728	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
729	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
730	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
731	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
732	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
733	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
734	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
735	C₂²⋊C₄	—	2	1	no	—
736	C₂²⋊C₄	—	2	1	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	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	—	2	4	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	4	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
753	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
754	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
755	C₄²	—	2	2	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	2	1	no	—
759	C₄²	—	2	1	no	—
760	C₄²	C₂×C₇×D₄	1	2	yes	—
761	C₄²	C₂×C₇×D₄	1	2	yes	—
762	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
763	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
764	C₄²	C₂⁴×C₇	1	2	yes	—
765	C₄²	C₂⁴×C₇	1	1	yes	characteristic
766	C₄²	C₂⁴×C₇	1	1	yes	characteristic
767	C₂×C₇	—	2	2	no	—
768	C₂×C₇	—	4	2	no	—
769	C₂×C₇	—	8	2	no	—
770	C₂×C₇	—	8	2	no	—
771	C₂×C₇	C₂×#532	1	1	yes	characteristic
772	C₂×C₇	#3585	1	1	yes	characteristic
773	C₂×C₇	#3586	1	1	yes	characteristic
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	4	2	no	—
777	C₂³	—	8	1	no	—
778	C₂³	—	8	1	no	—
779	C₂³	C₂²×C₇×D₄	1	2	yes	—
780	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
781	Q₈	—	2	2	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	2	4	no	—
784	Q₈	—	2	2	no	—
785	Q₈	—	4	4	no	—
786	Q₈	—	4	2	no	—
787	Q₈	—	8	1	no	—
788	Q₈	—	8	1	no	—
789	Q₈	—	8	2	no	—
790	D₄	—	2	4	no	—
791	D₄	—	2	2	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	2	no	—
794	D₄	—	2	2	no	—
795	D₄	—	4	2	no	—
796	D₄	—	4	2	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	8	2	no	—
800	D₄	—	8	2	no	—
801	D₄	—	8	4	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	1	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	4	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	1	no	—
812	C₂×C₄	—	4	1	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	—	8	2	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	—	8	4	no	—
819	C₂×C₄	—	8	2	no	—
820	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
821	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
822	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
823	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
824	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
825	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
826	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
827	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
828	C₂×C₄	C₂×C₇×#41	1	4	yes	—
829	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
830	C₈	—	2	2	no	—
831	C₈	—	2	2	no	—
832	C₈	C₂×C₇×#41	1	8	yes	—
833	C₇	#60727	1	1	yes	characteristic, direct product factor, Sylow
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	2	no	—
838	C₂²	—	2	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	2	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	16	2	no	—
846	C₂²	C₇×#532	1	2	yes	—
847	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	1	no	—
851	C₄	—	2	1	no	—
852	C₄	—	2	2	no	—
853	C₄	—	2	1	no	—
854	C₄	—	2	2	no	—
855	C₄	—	4	4	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	1	no	—
858	C₄	—	4	1	no	—
859	C₄	—	4	1	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	C₇×#532	1	2	yes	—
863	C₄	C₂²×C₇×#41	1	2	yes	—
864	C₂	—	2	2	no	—
865	C₂	—	4	2	no	—
866	C₂	—	8	2	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂×C₇×#532	1	1	yes	characteristic
869	C₂	C₇×#3585	1	1	yes	characteristic
870	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
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×#3511	C₂	semidirect
2. C₇×#3510	C₂	semidirect
3. C₇×#3181	C₂	semidirect
4. C₇×#3180	C₂	semidirect
5. C₇×#3175	C₂	semidirect
6. C₇×#3173	C₂	semidirect
7. C₇×#3172	C₂	semidirect
8. C₇×#3171	C₂	semidirect
9. C₇×#3165	C₂	semidirect
10. C₇×#3153	C₂	semidirect
11. C₇×#3135	C₂	semidirect
12. C₂×C₇×#489	C₂	semidirect
13. C₇×#3063	C₂	semidirect
14. C₇×#3062	C₂	semidirect
15. C₇×#2947	C₂	semidirect
16. C₇×#2946	C₂	semidirect
17. C₇×#2875	C₂	semidirect
35. C₇×#542	C₂²	semidirect
40. C₇×#533	C₂²	semidirect
42. C₇×#532	C₂²	semidirect
51. C₇×#501	C₂²	semidirect
52. C₇×#501	C₂²	semidirect
53. C₇×#500	C₂²	semidirect
54. C₇×#498	C₂²	semidirect
58. C₇×#491	C₂²	semidirect
59. C₇×#491	C₂²	semidirect
60. C₇×#490	C₂²	semidirect
61. C₇×#490	C₂²	semidirect
65. C₇×#489	C₂²	semidirect
66. C₇×#489	C₂²	semidirect
67. C₇×#470	C₂²	semidirect
70. C₇×#468	C₂²	semidirect
71. C₇×#467	C₂²	semidirect
74. C₇×#465	C₂²	semidirect
76. C₇×#441	C₂²	semidirect
78. C₇×#440	C₂²	semidirect
79. C₄×C₇×Q₁₆	C₂²	semidirect
81. C₄×C₇×SD₁₆	C₂²	semidirect
90. C₇×#405	C₂²	semidirect
92. C₄×C₇×M₁₆	C₂²	semidirect
94. C₂×C₇×#97	C₂²	semidirect
95. #60727	C₇	direct (N × H)
232. #3511	C₂×C₇	semidirect
233. #3510	C₂×C₇	semidirect
234. #3181	C₂×C₇	semidirect
235. #3180	C₂×C₇	semidirect
236. #3175	C₂×C₇	semidirect
237. #3173	C₂×C₇	semidirect
238. #3172	C₂×C₇	semidirect
239. #3171	C₂×C₇	semidirect
240. #3165	C₂×C₇	semidirect
241. #3153	C₂×C₇	semidirect
242. #3135	C₂×C₇	semidirect
243. C₂×#489	C₂×C₇	semidirect
244. #3063	C₂×C₇	semidirect
245. #3062	C₂×C₇	semidirect
246. #2947	C₂×C₇	semidirect
247. #2946	C₂×C₇	semidirect
248. #2875	C₂×C₇	semidirect
293. C₇×M₁₆	#41	semidirect
374. #542	C₂²×C₇	semidirect
379. #533	C₂²×C₇	semidirect
381. #532	C₂²×C₇	semidirect
390. #501	C₂²×C₇	semidirect
391. #501	C₂²×C₇	semidirect
392. #500	C₂²×C₇	semidirect
393. #498	C₂²×C₇	semidirect
397. #491	C₂²×C₇	semidirect
398. #491	C₂²×C₇	semidirect
399. #490	C₂²×C₇	semidirect
400. #490	C₂²×C₇	semidirect
404. #489	C₂²×C₇	semidirect
405. #489	C₂²×C₇	semidirect
406. #470	C₂²×C₇	semidirect
409. #468	C₂²×C₇	semidirect
410. #467	C₂²×C₇	semidirect
413. #465	C₂²×C₇	semidirect
415. #441	C₂²×C₇	semidirect
417. #440	C₂²×C₇	semidirect
418. C₄×Q₁₆	C₂²×C₇	semidirect
420. C₄×SD₁₆	C₂²×C₇	semidirect
429. #405	C₂²×C₇	semidirect
431. C₄×M₁₆	C₂²×C₇	semidirect
433. C₂×#97	C₂²×C₇	semidirect
703. M₁₆	C₇×#41	semidirect
833. C₇	#60727	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×#3511	2
C₇×#3510	2
C₇×#3181	2
C₇×#3180	2
C₇×#3175	2
C₇×#3173	2
C₇×#3172	2
C₇×#3171	2
C₇×#3165	2
C₇×#3153	2
C₇×#3135	2
C₂×C₇×#489	2
C₇×#3063	2
C₇×#3062	2
C₇×#2947	2
C₇×#2946	2
C₇×#2875	2
#60727	7

Subgroups — C7×#60727 #13237943

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60727 #13237943