Subgroups — C₇×#36750 #13213966

Order 1792.

1778 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2857	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2807	C₂	1	2	yes	maximal, complemented
4	C₇×#2788	C₂	1	2	yes	maximal, complemented
5	C₇×#2768	C₂	1	2	yes	maximal, complemented
6	C₇×#2763	C₂	1	2	yes	maximal, complemented
7	C₇×#2729	C₂	1	2	yes	maximal, complemented
8	C₇×#2720	C₂	1	2	yes	maximal, complemented
9	C₇×#2704	C₂	1	2	yes	maximal, complemented
10	C₇×#2704	C₂	1	2	yes	maximal, complemented
11	C₇×#2659	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2646	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2549	C₂	1	2	yes	maximal, complemented
14	C₇×#2442	C₂	1	2	yes	maximal, complemented
15	C₇×#2437	C₂	1	2	yes	maximal
16	C₇×#2437	C₂	1	2	yes	maximal
17	C₇×#2315	C₂	1	1	yes	maximal, characteristic
18	C₇×#2312	C₂	1	1	yes	maximal, characteristic
19	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₇×#125	C₂²	1	2	yes	complemented
22	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
30	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂²×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
33	C₇×#400	C₂²	1	2	yes	complemented
34	C₇×#400	C₂²	1	2	yes	complemented
35	C₇×#400	C₂²	1	2	yes	complemented
36	C₇×#400	C₂²	1	2	yes	complemented
37	C₇×#399	C₂²	1	2	yes	—
38	C₇×#399	C₂²	1	2	yes	—
39	C₇×#398	C₂²	1	2	yes	complemented
40	C₇×#398	C₂²	1	2	yes	complemented
41	C₇×#398	C₂²	1	2	yes	complemented
42	C₇×#398	C₂²	1	2	yes	complemented
43	C₇×#398	C₂²	1	2	yes	complemented
44	C₇×#398	C₂²	1	2	yes	complemented
45	C₇×#398	C₂²	1	2	yes	complemented
46	C₇×#398	C₂²	1	2	yes	complemented
47	C₇×#396	C₂²	1	2	yes	—
48	C₇×#396	C₂²	1	2	yes	—
49	C₇×#396	C₂²	1	2	yes	—
50	C₇×#396	C₂²	1	2	yes	—
51	C₇×#395	C₂²	1	2	yes	complemented
52	C₇×#395	C₂²	1	2	yes	complemented
53	C₇×#395	C₂²	1	2	yes	complemented
54	C₇×#395	C₂²	1	2	yes	complemented
55	C₇×#393	C₂²	1	2	yes	—
56	C₇×#393	C₂²	1	2	yes	—
57	C₇×#391	C₂²	1	2	yes	complemented
58	C₇×#391	C₂²	1	2	yes	complemented
59	C₇×#391	C₂²	1	2	yes	complemented
60	C₇×#389	C₂²	1	2	yes	complemented
61	C₇×#389	C₂²	1	2	yes	complemented
62	C₇×#389	C₂²	1	1	yes	characteristic, complemented
63	C₇×#389	C₂²	1	2	yes	complemented
64	C₇×#389	C₂²	1	2	yes	complemented
65	C₇×#389	C₂²	1	1	yes	characteristic, complemented
66	C₇×#389	C₂²	1	2	yes	complemented
67	C₇×#389	C₂²	1	1	yes	characteristic, complemented
68	C₇×#389	C₂²	1	1	yes	characteristic, complemented
69	C₇×#388	C₂²	1	2	yes	—
70	C₇×#388	C₂²	1	2	yes	—
71	C₇×#388	C₂²	1	2	yes	—
72	C₇×#388	C₂²	1	2	yes	—
73	C₇×#388	C₂²	1	2	yes	—
74	C₇×#388	C₂²	1	2	yes	—
75	C₇×#388	C₂²	1	2	yes	—
76	C₇×#388	C₂²	1	2	yes	—
77	C₇×#387	C₂²	1	2	yes	complemented
78	C₇×#387	C₂²	1	2	yes	complemented
79	C₇×#385	C₂²	1	2	yes	—
80	C₇×#385	C₂²	1	2	yes	—
81	C₇×#385	C₂²	1	2	yes	—
82	C₇×#385	C₂²	1	2	yes	—
83	C₇×#385	C₂²	1	2	yes	—
84	C₇×#385	C₂²	1	2	yes	—
85	C₇×#385	C₂²	1	2	yes	—
86	C₇×#385	C₂²	1	2	yes	—
87	C₇×#385	C₂²	1	2	yes	—
88	C₇×#385	C₂²	1	2	yes	—
89	C₇×#385	C₂²	1	2	yes	—
90	C₇×#385	C₂²	1	2	yes	—
91	C₇×#384	C₂²	1	1	yes	characteristic, complemented
92	C₇×#382	C₂²	1	2	yes	complemented
93	C₇×#382	C₂²	1	1	yes	characteristic, complemented
94	C₇×#380	C₂²	1	1	yes	characteristic
95	C₇×#380	C₂²	1	1	yes	characteristic
96	C₇×#380	C₂²	1	2	yes	—
97	C₇×#380	C₂²	1	1	yes	characteristic
98	C₇×#380	C₂²	1	1	yes	characteristic
99	C₇×#380	C₂²	1	2	yes	—
100	C₇×#380	C₂²	1	2	yes	—
101	C₇×#380	C₂²	1	2	yes	—
102	C₇×#380	C₂²	1	2	yes	—
103	C₇×#379	C₂²	1	2	yes	—
104	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
105	C₂×C₇×#95	C₂²	1	1	yes	characteristic
106	C₂×C₇×#95	C₂²	1	1	yes	characteristic
107	#36750	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₇	C₂³	1	1	yes	characteristic
109	C₂²×C₇×Q₈	C₂³	1	2	yes	—
110	C₂²×C₇×Q₈	C₂³	1	2	yes	—
111	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
113	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₇	C₂³	1	2	yes	—
116	C₂³×C₄×C₇	C₂³	1	2	yes	—
117	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₇×C₄⋊Q₈	—	4	2	no	—
120	C₇×#125	—	4	2	no	—
121	C₇×#125	—	4	4	no	—
122	C₇×C₂²⋊Q₈	—	4	4	no	—
123	C₇×C₂²⋊Q₈	—	4	4	no	—
124	C₇×C₂²⋊Q₈	—	4	4	no	—
125	C₇×C₂²⋊Q₈	—	4	4	no	—
126	C₂×C₇×C₄⋊C₄	—	4	2	no	—
127	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
129	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
130	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
131	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
132	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
135	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
136	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
138	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
139	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
140	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
142	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
158	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
159	C₂×C₇×C₂²⋊C₄	—	4	4	no	—
160	C₂×C₇×C₂²⋊C₄	Q₈	1	8	yes	complemented
161	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₄²×C₇	—	4	2	no	—
178	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
179	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
180	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
181	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₇	C₂³	1	2	yes	—
183	C₂×C₄²×C₇	C₂³	1	2	yes	—
184	C₇×#95	C₂³	1	2	yes	—
185	C₇×#95	C₂³	1	2	yes	—
186	C₇×#95	C₂³	1	2	yes	—
187	C₇×#95	C₂³	1	2	yes	—
188	C₇×#95	C₂³	1	2	yes	—
189	C₇×#95	C₂³	1	2	yes	—
190	C₇×#95	C₂³	1	2	yes	—
191	C₇×#95	C₂³	1	2	yes	—
192	C₇×#95	C₂³	1	2	yes	—
193	C₇×#95	C₂³	1	2	yes	—
194	C₇×#95	C₂³	1	2	yes	—
195	C₇×#95	C₂³	1	2	yes	—
196	C₇×#95	C₂³	1	2	yes	—
197	C₇×#95	C₂³	1	2	yes	—
198	C₇×#95	C₂³	1	2	yes	—
199	C₇×#95	C₂³	1	2	yes	—
200	C₇×#95	C₂³	1	2	yes	—
201	C₇×#95	C₂³	1	2	yes	—
202	C₇×#95	C₂³	1	2	yes	—
203	C₇×#95	C₂³	1	2	yes	—
204	C₇×#95	C₂³	1	2	yes	—
205	C₇×#95	C₂³	1	2	yes	—
206	C₇×#95	C₂³	1	2	yes	—
207	C₇×#95	C₂³	1	2	yes	—
208	#2857	C₂×C₇	1	1	yes	characteristic, complemented
209	#2851	C₂×C₇	1	1	yes	characteristic, complemented
210	#2807	C₂×C₇	1	2	yes	complemented
211	#2788	C₂×C₇	1	2	yes	complemented
212	#2768	C₂×C₇	1	2	yes	complemented
213	#2763	C₂×C₇	1	2	yes	complemented
214	#2729	C₂×C₇	1	2	yes	complemented
215	#2720	C₂×C₇	1	2	yes	complemented
216	#2704	C₂×C₇	1	2	yes	complemented
217	#2704	C₂×C₇	1	2	yes	complemented
218	#2659	C₂×C₇	1	1	yes	characteristic, complemented
219	#2646	C₂×C₇	1	1	yes	characteristic, complemented
220	#2549	C₂×C₇	1	2	yes	complemented
221	#2442	C₂×C₇	1	2	yes	complemented
222	#2437	C₂×C₇	1	2	yes	—
223	#2437	C₂×C₇	1	2	yes	—
224	#2315	C₂×C₇	1	1	yes	characteristic
225	#2312	C₂×C₇	1	1	yes	characteristic
226	C₂×#388	C₂×C₇	1	1	yes	characteristic
227	C₂⁴×C₇	—	2	2	no	—
228	C₂⁴×C₇	—	2	2	no	—
229	C₂⁴×C₇	—	4	1	no	—
230	C₂⁴×C₇	—	4	1	no	—
231	C₂⁴×C₇	—	4	1	no	—
232	C₂⁴×C₇	—	4	1	no	—
233	C₂⁴×C₇	C₂×Q₈	1	4	yes	—
234	C₂⁴×C₇	C₂⁴	1	2	yes	—
235	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₇×Q₈	—	2	4	no	—
237	C₂×C₇×Q₈	—	4	2	no	—
238	C₂×C₇×Q₈	—	4	2	no	—
239	C₂×C₇×Q₈	—	4	2	no	—
240	C₂×C₇×Q₈	—	4	2	no	—
241	C₂×C₇×Q₈	—	4	2	no	—
242	C₂²×C₄×C₇	—	2	2	no	—
243	C₂²×C₄×C₇	—	2	2	no	—
244	C₂²×C₄×C₇	—	2	2	no	—
245	C₂²×C₄×C₇	—	2	2	no	—
246	C₂²×C₄×C₇	—	2	2	no	—
247	C₂²×C₄×C₇	—	2	2	no	—
248	C₂²×C₄×C₇	—	4	1	no	—
249	C₂²×C₄×C₇	—	4	1	no	—
250	C₂²×C₄×C₇	—	4	1	no	—
251	C₂²×C₄×C₇	—	4	1	no	—
252	C₂²×C₄×C₇	—	4	1	no	—
253	C₂²×C₄×C₇	—	4	1	no	—
254	C₂²×C₄×C₇	—	4	1	no	—
255	C₂²×C₄×C₇	—	4	2	no	—
256	C₂²×C₄×C₇	—	4	2	no	—
257	C₂²×C₄×C₇	—	4	1	no	—
258	C₂²×C₄×C₇	—	4	1	no	—
259	C₂²×C₄×C₇	—	4	2	no	—
260	C₂²×C₄×C₇	—	4	2	no	—
261	C₂²×C₄×C₇	—	4	2	no	—
262	C₂²×C₄×C₇	—	4	2	no	—
263	C₂²×C₄×C₇	—	4	1	no	—
264	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
265	C₂²×C₄×C₇	C₂×Q₈	1	4	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
268	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
269	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
270	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
274	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
277	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
281	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
283	C₇×C₄⋊C₄	—	2	4	no	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	2	4	no	—
286	C₇×C₄⋊C₄	—	2	4	no	—
287	C₇×C₄⋊C₄	—	4	2	no	—
288	C₇×C₄⋊C₄	—	4	2	no	—
289	C₇×C₄⋊C₄	—	4	1	no	—
290	C₇×C₄⋊C₄	—	4	1	no	—
291	C₇×C₄⋊C₄	—	4	1	no	—
292	C₇×C₄⋊C₄	—	4	1	no	—
293	C₇×C₄⋊C₄	—	4	2	no	—
294	C₇×C₄⋊C₄	—	4	2	no	—
295	C₇×C₄⋊C₄	—	4	2	no	—
296	C₇×C₄⋊C₄	—	4	2	no	—
297	C₇×C₄⋊C₄	—	4	2	no	—
298	C₇×C₄⋊C₄	—	4	2	no	—
299	C₇×C₄⋊C₄	—	4	2	no	—
300	C₇×C₄⋊C₄	—	4	2	no	—
301	C₇×C₄⋊C₄	—	4	2	no	—
302	C₇×C₄⋊C₄	—	4	2	no	—
303	C₇×C₄⋊C₄	—	4	2	no	—
304	C₇×C₄⋊C₄	—	4	1	no	—
305	C₇×C₄⋊C₄	—	4	1	no	—
306	C₇×C₄⋊C₄	—	4	2	no	—
307	C₇×C₄⋊C₄	—	4	2	no	—
308	C₇×C₄⋊C₄	—	4	2	no	—
309	C₇×C₄⋊C₄	—	4	2	no	—
310	C₇×C₄⋊C₄	—	4	1	no	—
311	C₇×C₄⋊C₄	—	4	2	no	—
312	C₇×C₄⋊C₄	—	4	1	no	—
313	C₇×C₂²⋊C₄	—	2	4	no	—
314	C₇×C₂²⋊C₄	—	2	4	no	—
315	C₇×C₂²⋊C₄	—	2	4	no	—
316	C₇×C₂²⋊C₄	—	2	4	no	—
317	C₇×C₂²⋊C₄	—	2	4	no	—
318	C₇×C₂²⋊C₄	—	2	4	no	—
319	C₇×C₂²⋊C₄	—	4	2	no	—
320	C₇×C₂²⋊C₄	—	4	2	no	—
321	C₇×C₂²⋊C₄	—	4	2	no	—
322	C₇×C₂²⋊C₄	—	4	2	no	—
323	C₇×C₂²⋊C₄	—	4	2	no	—
324	C₇×C₂²⋊C₄	—	4	2	no	—
325	C₇×C₂²⋊C₄	—	4	2	no	—
326	C₇×C₂²⋊C₄	—	4	2	no	—
327	C₇×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
328	C₇×C₂²⋊C₄	C₂×Q₈	1	8	yes	—
329	C₄²×C₇	—	2	2	no	—
330	C₄²×C₇	—	2	2	no	—
331	C₄²×C₇	—	4	1	no	—
332	C₄²×C₇	—	4	1	no	—
333	C₄²×C₇	—	4	2	no	—
334	C₄²×C₇	—	4	2	no	—
335	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
336	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
337	C₂×#125	C₂²×C₇	1	2	yes	complemented
338	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
339	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
340	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
341	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
342	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
343	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
344	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
346	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
347	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
348	#400	C₂²×C₇	1	2	yes	complemented
349	#400	C₂²×C₇	1	2	yes	complemented
350	#400	C₂²×C₇	1	2	yes	complemented
351	#400	C₂²×C₇	1	2	yes	complemented
352	#399	C₂²×C₇	1	2	yes	—
353	#399	C₂²×C₇	1	2	yes	—
354	#398	C₂²×C₇	1	2	yes	complemented
355	#398	C₂²×C₇	1	2	yes	complemented
356	#398	C₂²×C₇	1	2	yes	complemented
357	#398	C₂²×C₇	1	2	yes	complemented
358	#398	C₂²×C₇	1	2	yes	complemented
359	#398	C₂²×C₇	1	2	yes	complemented
360	#398	C₂²×C₇	1	2	yes	complemented
361	#398	C₂²×C₇	1	2	yes	complemented
362	#396	C₂²×C₇	1	2	yes	—
363	#396	C₂²×C₇	1	2	yes	—
364	#396	C₂²×C₇	1	2	yes	—
365	#396	C₂²×C₇	1	2	yes	—
366	#395	C₂²×C₇	1	2	yes	complemented
367	#395	C₂²×C₇	1	2	yes	complemented
368	#395	C₂²×C₇	1	2	yes	complemented
369	#395	C₂²×C₇	1	2	yes	complemented
370	#393	C₂²×C₇	1	2	yes	—
371	#393	C₂²×C₇	1	2	yes	—
372	#391	C₂²×C₇	1	2	yes	complemented
373	#391	C₂²×C₇	1	2	yes	complemented
374	#391	C₂²×C₇	1	2	yes	complemented
375	#389	C₂²×C₇	1	1	yes	characteristic, complemented
376	#389	C₂²×C₇	1	1	yes	characteristic, complemented
377	#389	C₂²×C₇	1	2	yes	complemented
378	#389	C₂²×C₇	1	1	yes	characteristic, complemented
379	#389	C₂²×C₇	1	1	yes	characteristic, complemented
380	#389	C₂²×C₇	1	2	yes	complemented
381	#389	C₂²×C₇	1	2	yes	complemented
382	#389	C₂²×C₇	1	2	yes	complemented
383	#389	C₂²×C₇	1	2	yes	complemented
384	#388	C₂²×C₇	1	2	yes	—
385	#388	C₂²×C₇	1	2	yes	—
386	#388	C₂²×C₇	1	2	yes	—
387	#388	C₂²×C₇	1	2	yes	—
388	#388	C₂²×C₇	1	2	yes	—
389	#388	C₂²×C₇	1	2	yes	—
390	#388	C₂²×C₇	1	2	yes	—
391	#388	C₂²×C₇	1	2	yes	—
392	#387	C₂²×C₇	1	2	yes	complemented
393	#387	C₂²×C₇	1	2	yes	complemented
394	#385	C₂²×C₇	1	2	yes	—
395	#385	C₂²×C₇	1	2	yes	—
396	#385	C₂²×C₇	1	2	yes	—
397	#385	C₂²×C₇	1	2	yes	—
398	#385	C₂²×C₇	1	2	yes	—
399	#385	C₂²×C₇	1	2	yes	—
400	#385	C₂²×C₇	1	2	yes	—
401	#385	C₂²×C₇	1	2	yes	—
402	#385	C₂²×C₇	1	2	yes	—
403	#385	C₂²×C₇	1	2	yes	—
404	#385	C₂²×C₇	1	2	yes	—
405	#385	C₂²×C₇	1	2	yes	—
406	#384	C₂²×C₇	1	1	yes	characteristic, complemented
407	#382	C₂²×C₇	1	1	yes	characteristic, complemented
408	#382	C₂²×C₇	1	2	yes	complemented
409	#380	C₂²×C₇	1	1	yes	characteristic
410	#380	C₂²×C₇	1	1	yes	characteristic
411	#380	C₂²×C₇	1	1	yes	characteristic
412	#380	C₂²×C₇	1	1	yes	characteristic
413	#380	C₂²×C₇	1	2	yes	—
414	#380	C₂²×C₇	1	2	yes	—
415	#380	C₂²×C₇	1	2	yes	—
416	#380	C₂²×C₇	1	2	yes	—
417	#380	C₂²×C₇	1	2	yes	—
418	#379	C₂²×C₇	1	2	yes	—
419	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
420	C₂×#95	C₂²×C₇	1	1	yes	characteristic
421	C₂×#95	C₂²×C₇	1	1	yes	characteristic
422	C₂³×C₇	—	2	1	no	—
423	C₂³×C₇	—	2	1	no	—
424	C₂³×C₇	—	2	1	no	—
425	C₂³×C₇	—	2	1	no	—
426	C₂³×C₇	—	2	2	no	—
427	C₂³×C₇	—	2	2	no	—
428	C₂³×C₇	—	2	2	no	—
429	C₂³×C₇	—	2	2	no	—
430	C₂³×C₇	—	2	2	no	—
431	C₂³×C₇	—	2	2	no	—
432	C₂³×C₇	—	2	8	no	—
433	C₂³×C₇	—	4	4	no	—
434	C₂³×C₇	—	4	4	no	—
435	C₂³×C₇	—	8	2	no	—
436	C₂³×C₇	—	8	2	no	—
437	C₂³×C₇	—	8	2	no	—
438	C₂³×C₇	—	8	2	no	—
439	C₂³×C₇	C₂²×Q₈	1	4	yes	—
440	C₂³×C₇	C₂²×Q₈	1	2	yes	—
441	C₂³×C₇	H(5,𝔽₂)	1	2	yes	—
442	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
443	C₂³×C₇	C₂⁵	1	1	yes	characteristic
444	C₇×Q₈	—	8	4	no	—
445	C₇×Q₈	—	8	4	no	—
446	C₂×C₄×C₇	—	2	1	no	—
447	C₂×C₄×C₇	—	2	1	no	—
448	C₂×C₄×C₇	—	2	1	no	—
449	C₂×C₄×C₇	—	2	2	no	—
450	C₂×C₄×C₇	—	2	1	no	—
451	C₂×C₄×C₇	—	2	1	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	2	1	no	—
454	C₂×C₄×C₇	—	2	1	no	—
455	C₂×C₄×C₇	—	2	1	no	—
456	C₂×C₄×C₇	—	2	1	no	—
457	C₂×C₄×C₇	—	2	1	no	—
458	C₂×C₄×C₇	—	2	2	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	2	no	—
463	C₂×C₄×C₇	—	2	2	no	—
464	C₂×C₄×C₇	—	2	2	no	—
465	C₂×C₄×C₇	—	2	2	no	—
466	C₂×C₄×C₇	—	2	2	no	—
467	C₂×C₄×C₇	—	2	2	no	—
468	C₂×C₄×C₇	—	2	1	no	—
469	C₂×C₄×C₇	—	2	2	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	2	no	—
472	C₂×C₄×C₇	—	2	2	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	2	no	—
475	C₂×C₄×C₇	—	2	1	no	—
476	C₂×C₄×C₇	—	2	2	no	—
477	C₂×C₄×C₇	—	2	2	no	—
478	C₂×C₄×C₇	—	2	2	no	—
479	C₂×C₄×C₇	—	2	2	no	—
480	C₂×C₄×C₇	—	2	1	no	—
481	C₂×C₄×C₇	—	2	2	no	—
482	C₂×C₄×C₇	—	2	2	no	—
483	C₂×C₄×C₇	—	2	2	no	—
484	C₂×C₄×C₇	—	2	2	no	—
485	C₂×C₄×C₇	—	2	2	no	—
486	C₂×C₄×C₇	—	2	1	no	—
487	C₂×C₄×C₇	—	2	2	no	—
488	C₂×C₄×C₇	—	2	2	no	—
489	C₂×C₄×C₇	—	2	2	no	—
490	C₂×C₄×C₇	—	2	2	no	—
491	C₂×C₄×C₇	—	2	2	no	—
492	C₂×C₄×C₇	—	4	4	no	—
493	C₂×C₄×C₇	—	4	4	no	—
494	C₂×C₄×C₇	—	4	4	no	—
495	C₂×C₄×C₇	—	4	4	no	—
496	C₂×C₄×C₇	—	8	2	no	—
497	C₂×C₄×C₇	—	8	2	no	—
498	C₂×C₄×C₇	—	8	4	no	—
499	C₂×C₄×C₇	—	8	4	no	—
500	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
501	C₂×C₄×C₇	C₂²×Q₈	1	2	yes	—
502	C₂×C₄×C₇	C₂²×Q₈	1	4	yes	—
503	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
504	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
505	C₂⁵	C₂³×C₇	1	1	yes	characteristic
506	C₂²×Q₈	C₂³×C₇	1	2	yes	—
507	C₂²×Q₈	C₂³×C₇	1	2	yes	—
508	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
509	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
510	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
511	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
512	C₂³×C₄	C₂³×C₇	1	2	yes	—
513	C₂³×C₄	C₂³×C₇	1	2	yes	—
514	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
515	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
516	C₄⋊Q₈	—	4	2	no	—
517	#125	—	4	2	no	—
518	#125	—	4	4	no	—
519	C₂²⋊Q₈	—	4	4	no	—
520	C₂²⋊Q₈	—	4	4	no	—
521	C₂²⋊Q₈	—	4	4	no	—
522	C₂²⋊Q₈	—	4	4	no	—
523	C₂×C₄⋊C₄	—	4	2	no	—
524	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
525	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
526	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
527	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
528	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
529	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
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	2	yes	—
533	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
534	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
535	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
536	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
537	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
538	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
541	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
542	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
543	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
544	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
545	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
546	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
547	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
548	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
549	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
550	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
551	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
552	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
553	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
554	C₂×C₂²⋊C₄	—	4	2	no	—
555	C₂×C₂²⋊C₄	—	4	2	no	—
556	C₂×C₂²⋊C₄	—	4	4	no	—
557	C₂×C₂²⋊C₄	C₇×Q₈	1	8	yes	complemented
558	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
560	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
561	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
562	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
563	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
564	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
565	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
566	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
567	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
568	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
569	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
574	C₂×C₄²	—	4	2	no	—
575	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
576	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
577	C₂×C₄²	C₂³×C₇	1	2	yes	—
578	C₂×C₄²	C₂³×C₇	1	2	yes	—
579	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
580	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
581	#95	C₂³×C₇	1	2	yes	—
582	#95	C₂³×C₇	1	2	yes	—
583	#95	C₂³×C₇	1	2	yes	—
584	#95	C₂³×C₇	1	2	yes	—
585	#95	C₂³×C₇	1	2	yes	—
586	#95	C₂³×C₇	1	2	yes	—
587	#95	C₂³×C₇	1	2	yes	—
588	#95	C₂³×C₇	1	2	yes	—
589	#95	C₂³×C₇	1	2	yes	—
590	#95	C₂³×C₇	1	2	yes	—
591	#95	C₂³×C₇	1	2	yes	—
592	#95	C₂³×C₇	1	2	yes	—
593	#95	C₂³×C₇	1	2	yes	—
594	#95	C₂³×C₇	1	2	yes	—
595	#95	C₂³×C₇	1	2	yes	—
596	#95	C₂³×C₇	1	2	yes	—
597	#95	C₂³×C₇	1	2	yes	—
598	#95	C₂³×C₇	1	2	yes	—
599	#95	C₂³×C₇	1	2	yes	—
600	#95	C₂³×C₇	1	2	yes	—
601	#95	C₂³×C₇	1	2	yes	—
602	#95	C₂³×C₇	1	2	yes	—
603	#95	C₂³×C₇	1	2	yes	—
604	#95	C₂³×C₇	1	2	yes	—
605	C₂²×C₇	—	2	2	no	—
606	C₂²×C₇	—	2	2	no	—
607	C₂²×C₇	—	2	2	no	—
608	C₂²×C₇	—	2	2	no	—
609	C₂²×C₇	—	2	2	no	—
610	C₂²×C₇	—	2	2	no	—
611	C₂²×C₇	—	2	4	no	—
612	C₂²×C₇	—	2	4	no	—
613	C₂²×C₇	—	2	4	no	—
614	C₂²×C₇	—	4	2	no	—
615	C₂²×C₇	—	4	2	no	—
616	C₂²×C₇	—	4	2	no	—
617	C₂²×C₇	—	4	2	no	—
618	C₂²×C₇	—	8	8	no	—
619	C₂²×C₇	#544	1	4	yes	—
620	C₂²×C₇	C₂³×Q₈	1	1	yes	characteristic
621	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
622	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
623	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
624	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
625	C₂²×C₇	#585	1	1	yes	characteristic
626	C₂²×C₇	#585	1	1	yes	characteristic
627	C₄×C₇	—	2	2	no	—
628	C₄×C₇	—	2	2	no	—
629	C₄×C₇	—	2	4	no	—
630	C₄×C₇	—	2	2	no	—
631	C₄×C₇	—	2	2	no	—
632	C₄×C₇	—	4	1	no	—
633	C₄×C₇	—	4	2	no	—
634	C₄×C₇	—	4	2	no	—
635	C₄×C₇	—	4	2	no	—
636	C₄×C₇	—	4	2	no	—
637	C₄×C₇	—	4	1	no	—
638	C₄×C₇	—	4	2	no	—
639	C₄×C₇	—	4	2	no	—
640	C₄×C₇	—	4	2	no	—
641	C₄×C₇	—	4	2	no	—
642	C₄×C₇	—	4	2	no	—
643	C₄×C₇	—	4	2	no	—
644	C₂⁴	—	2	2	no	—
645	C₂⁴	—	2	2	no	—
646	C₂⁴	—	4	1	no	—
647	C₂⁴	—	4	1	no	—
648	C₂⁴	—	4	1	no	—
649	C₂⁴	—	4	1	no	—
650	C₂⁴	C₂×C₇×Q₈	1	4	yes	—
651	C₂⁴	C₂⁴×C₇	1	2	yes	—
652	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
653	C₂×Q₈	—	2	4	no	—
654	C₂×Q₈	—	4	2	no	—
655	C₂×Q₈	—	4	2	no	—
656	C₂×Q₈	—	4	2	no	—
657	C₂×Q₈	—	4	2	no	—
658	C₂×Q₈	—	4	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	—	4	1	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	1	no	—
675	C₂²×C₄	—	4	1	no	—
676	C₂²×C₄	—	4	2	no	—
677	C₂²×C₄	—	4	2	no	—
678	C₂²×C₄	—	4	2	no	—
679	C₂²×C₄	—	4	2	no	—
680	C₂²×C₄	—	4	1	no	—
681	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
682	C₂²×C₄	C₂×C₇×Q₈	1	4	yes	—
683	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
690	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
693	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
694	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
695	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
696	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
698	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
699	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	4	no	—
704	C₄⋊C₄	—	4	2	no	—
705	C₄⋊C₄	—	4	2	no	—
706	C₄⋊C₄	—	4	2	no	—
707	C₄⋊C₄	—	4	2	no	—
708	C₄⋊C₄	—	4	2	no	—
709	C₄⋊C₄	—	4	2	no	—
710	C₄⋊C₄	—	4	2	no	—
711	C₄⋊C₄	—	4	2	no	—
712	C₄⋊C₄	—	4	2	no	—
713	C₄⋊C₄	—	4	2	no	—
714	C₄⋊C₄	—	4	2	no	—
715	C₄⋊C₄	—	4	1	no	—
716	C₄⋊C₄	—	4	1	no	—
717	C₄⋊C₄	—	4	1	no	—
718	C₄⋊C₄	—	4	1	no	—
719	C₄⋊C₄	—	4	2	no	—
720	C₄⋊C₄	—	4	2	no	—
721	C₄⋊C₄	—	4	1	no	—
722	C₄⋊C₄	—	4	1	no	—
723	C₄⋊C₄	—	4	2	no	—
724	C₄⋊C₄	—	4	2	no	—
725	C₄⋊C₄	—	4	2	no	—
726	C₄⋊C₄	—	4	2	no	—
727	C₄⋊C₄	—	4	1	no	—
728	C₄⋊C₄	—	4	2	no	—
729	C₄⋊C₄	—	4	1	no	—
730	C₂²⋊C₄	—	2	4	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	4	no	—
735	C₂²⋊C₄	—	2	4	no	—
736	C₂²⋊C₄	—	4	2	no	—
737	C₂²⋊C₄	—	4	2	no	—
738	C₂²⋊C₄	—	4	2	no	—
739	C₂²⋊C₄	—	4	2	no	—
740	C₂²⋊C₄	—	4	2	no	—
741	C₂²⋊C₄	—	4	2	no	—
742	C₂²⋊C₄	—	4	2	no	—
743	C₂²⋊C₄	—	4	2	no	—
744	C₂²⋊C₄	C₂×C₇×Q₈	1	8	yes	—
745	C₂²⋊C₄	C₂×C₇×Q₈	1	8	yes	—
746	C₄²	—	2	2	no	—
747	C₄²	—	2	2	no	—
748	C₄²	—	4	1	no	—
749	C₄²	—	4	1	no	—
750	C₄²	—	4	2	no	—
751	C₄²	—	4	2	no	—
752	C₂×C₇	—	2	4	no	—
753	C₂×C₇	—	4	4	no	—
754	C₂×C₇	C₂×#544	1	1	yes	characteristic
755	C₂×C₇	#3501	1	1	yes	characteristic
756	C₂×C₇	#3501	1	1	yes	characteristic
757	C₂×C₇	#3534	1	1	yes	characteristic
758	C₂×C₇	#3536	1	1	yes	characteristic
759	C₂×C₇	#3558	1	1	yes	characteristic
760	C₂×C₇	#3564	1	1	yes	characteristic
761	C₂³	—	2	1	no	—
762	C₂³	—	2	1	no	—
763	C₂³	—	2	1	no	—
764	C₂³	—	2	1	no	—
765	C₂³	—	2	2	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	2	no	—
768	C₂³	—	2	2	no	—
769	C₂³	—	2	2	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	2	8	no	—
772	C₂³	—	4	4	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	8	2	no	—
775	C₂³	—	8	2	no	—
776	C₂³	—	8	2	no	—
777	C₂³	—	8	2	no	—
778	C₂³	C₂²×C₇×Q₈	1	4	yes	—
779	C₂³	C₂²×C₇×Q₈	1	2	yes	—
780	C₂³	C₇×H(5,𝔽₂)	1	2	yes	—
781	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
782	C₂³	C₂⁵×C₇	1	1	yes	characteristic
783	Q₈	—	8	4	no	—
784	Q₈	—	8	4	no	—
785	C₂×C₄	—	2	1	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	1	no	—
790	C₂×C₄	—	2	1	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	1	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	1	no	—
795	C₂×C₄	—	2	1	no	—
796	C₂×C₄	—	2	1	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	1	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	1	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	1	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	—	8	2	no	—
836	C₂×C₄	—	8	2	no	—
837	C₂×C₄	—	8	4	no	—
838	C₂×C₄	—	8	4	no	—
839	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
840	C₂×C₄	C₂²×C₇×Q₈	1	2	yes	—
841	C₂×C₄	C₂²×C₇×Q₈	1	4	yes	—
842	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
843	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
844	C₇	#36750	1	1	yes	characteristic, direct product factor, Sylow
845	C₂²	—	2	2	no	—
846	C₂²	—	2	2	no	—
847	C₂²	—	2	2	no	—
848	C₂²	—	2	2	no	—
849	C₂²	—	2	2	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	4	no	—
852	C₂²	—	2	4	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	2	no	—
857	C₂²	—	4	2	no	—
858	C₂²	—	8	8	no	—
859	C₂²	C₇×#544	1	4	yes	—
860	C₂²	C₂³×C₇×Q₈	1	1	yes	characteristic
861	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
862	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
863	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
864	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
865	C₂²	C₇×#585	1	1	yes	characteristic
866	C₂²	C₇×#585	1	1	yes	characteristic
867	C₄	—	2	2	no	—
868	C₄	—	2	2	no	—
869	C₄	—	2	4	no	—
870	C₄	—	2	2	no	—
871	C₄	—	2	2	no	—
872	C₄	—	4	2	no	—
873	C₄	—	4	1	no	—
874	C₄	—	4	2	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	2	no	—
877	C₄	—	4	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	2	no	—
881	C₄	—	4	2	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₂	—	2	4	no	—
885	C₂	—	4	4	no	—
886	C₂	C₂×C₇×#544	1	1	yes	characteristic
887	C₂	C₇×#3501	1	1	yes	characteristic
888	C₂	C₇×#3501	1	1	yes	characteristic
889	C₂	C₇×#3534	1	1	yes	characteristic
890	C₂	C₇×#3536	1	1	yes	characteristic
891	C₂	C₇×#3558	1	1	yes	characteristic
892	C₂	C₇×#3564	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
prime radical	C₂⁵×C₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2857	C₂	semidirect
2. C₇×#2851	C₂	semidirect
3. C₇×#2807	C₂	semidirect
4. C₇×#2788	C₂	semidirect
5. C₇×#2768	C₂	semidirect
6. C₇×#2763	C₂	semidirect
7. C₇×#2729	C₂	semidirect
8. C₇×#2720	C₂	semidirect
9. C₇×#2704	C₂	semidirect
10. C₇×#2704	C₂	semidirect
11. C₇×#2659	C₂	semidirect
12. C₇×#2646	C₂	semidirect
13. C₇×#2549	C₂	semidirect
14. C₇×#2442	C₂	semidirect
20. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₇×#125	C₂²	semidirect
22. C₂×C₇×#125	C₂²	semidirect
33. C₇×#400	C₂²	semidirect
34. C₇×#400	C₂²	semidirect
35. C₇×#400	C₂²	semidirect
36. C₇×#400	C₂²	semidirect
39. C₇×#398	C₂²	semidirect
40. C₇×#398	C₂²	semidirect
41. C₇×#398	C₂²	semidirect
42. C₇×#398	C₂²	semidirect
43. C₇×#398	C₂²	semidirect
44. C₇×#398	C₂²	semidirect
45. C₇×#398	C₂²	semidirect
46. C₇×#398	C₂²	semidirect
51. C₇×#395	C₂²	semidirect
52. C₇×#395	C₂²	semidirect
53. C₇×#395	C₂²	semidirect
54. C₇×#395	C₂²	semidirect
57. C₇×#391	C₂²	semidirect
58. C₇×#391	C₂²	semidirect
59. C₇×#391	C₂²	semidirect
60. C₇×#389	C₂²	semidirect
61. C₇×#389	C₂²	semidirect
62. C₇×#389	C₂²	semidirect
63. C₇×#389	C₂²	semidirect
64. C₇×#389	C₂²	semidirect
65. C₇×#389	C₂²	semidirect
66. C₇×#389	C₂²	semidirect
67. C₇×#389	C₂²	semidirect
68. C₇×#389	C₂²	semidirect
77. C₇×#387	C₂²	semidirect
78. C₇×#387	C₂²	semidirect
91. C₇×#384	C₂²	semidirect
92. C₇×#382	C₂²	semidirect
93. C₇×#382	C₂²	semidirect
107. #36750	C₇	direct (N × H)
160. C₂×C₇×C₂²⋊C₄	Q₈	semidirect
208. #2857	C₂×C₇	semidirect
209. #2851	C₂×C₇	semidirect
210. #2807	C₂×C₇	semidirect
211. #2788	C₂×C₇	semidirect
212. #2768	C₂×C₇	semidirect
213. #2763	C₂×C₇	semidirect
214. #2729	C₂×C₇	semidirect
215. #2720	C₂×C₇	semidirect
216. #2704	C₂×C₇	semidirect
217. #2704	C₂×C₇	semidirect
218. #2659	C₂×C₇	semidirect
219. #2646	C₂×C₇	semidirect
220. #2549	C₂×C₇	semidirect
221. #2442	C₂×C₇	semidirect
335. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
336. C₂×#125	C₂²×C₇	semidirect
337. C₂×#125	C₂²×C₇	semidirect
348. #400	C₂²×C₇	semidirect
349. #400	C₂²×C₇	semidirect
350. #400	C₂²×C₇	semidirect
351. #400	C₂²×C₇	semidirect
354. #398	C₂²×C₇	semidirect
355. #398	C₂²×C₇	semidirect
356. #398	C₂²×C₇	semidirect
357. #398	C₂²×C₇	semidirect
358. #398	C₂²×C₇	semidirect
359. #398	C₂²×C₇	semidirect
360. #398	C₂²×C₇	semidirect
361. #398	C₂²×C₇	semidirect
366. #395	C₂²×C₇	semidirect
367. #395	C₂²×C₇	semidirect
368. #395	C₂²×C₇	semidirect
369. #395	C₂²×C₇	semidirect
372. #391	C₂²×C₇	semidirect
373. #391	C₂²×C₇	semidirect
374. #391	C₂²×C₇	semidirect
375. #389	C₂²×C₇	semidirect
376. #389	C₂²×C₇	semidirect
377. #389	C₂²×C₇	semidirect
378. #389	C₂²×C₇	semidirect
379. #389	C₂²×C₇	semidirect
380. #389	C₂²×C₇	semidirect
381. #389	C₂²×C₇	semidirect
382. #389	C₂²×C₇	semidirect
383. #389	C₂²×C₇	semidirect
392. #387	C₂²×C₇	semidirect
393. #387	C₂²×C₇	semidirect
406. #384	C₂²×C₇	semidirect
407. #382	C₂²×C₇	semidirect
408. #382	C₂²×C₇	semidirect
557. C₂×C₂²⋊C₄	C₇×Q₈	semidirect
844. C₇	#36750	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×#2857	2
C₇×#2851	2
C₇×#2807	2
C₇×#2788	2
C₇×#2768	2
C₇×#2763	2
C₇×#2729	2
C₇×#2720	2
C₇×#2704	2
C₇×#2659	2
C₇×#2646	2
C₇×#2549	2
C₇×#2442	2
C₇×#2437	2
C₇×#2315	2
C₇×#2312	2
C₂×C₇×#388	2
#36750	7

Subgroups — C7×#36750 #13213966

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36750 #13213966