Subgroups — C₇×#36760 #13213976

Order 1792.

1662 conjugacy classes of subgroups.

The subgroup lattice has 876 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×#2798	C₂	1	2	yes	maximal, complemented
4	C₇×#2783	C₂	1	2	yes	maximal, complemented
5	C₇×#2772	C₂	1	2	yes	maximal, complemented
6	C₇×#2754	C₂	1	2	yes	maximal, complemented
7	C₇×#2725	C₂	1	2	yes	maximal, complemented
8	C₇×#2725	C₂	1	2	yes	maximal, complemented
9	C₇×#2721	C₂	1	2	yes	maximal, complemented
10	C₇×#2716	C₂	1	2	yes	maximal, complemented
11	C₇×#2626	C₂	1	1	yes	maximal, characteristic
12	C₇×#2626	C₂	1	1	yes	maximal, characteristic
13	C₇×#2505	C₂	1	2	yes	maximal, complemented
14	C₇×#2480	C₂	1	2	yes	maximal
15	C₇×#2480	C₂	1	2	yes	maximal
16	C₇×#2473	C₂	1	2	yes	maximal, complemented
17	C₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2329	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×C₇×#388	C₂	1	1	yes	maximal, characteristic
20	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₇×#126	C₂²	1	2	yes	—
22	C₂×C₇×#126	C₂²	1	2	yes	—
23	C₂×C₇×#125	C₂²	1	2	yes	complemented
24	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
31	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
32	C₇×#400	C₂²	1	2	yes	complemented
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×#399	C₂²	1	2	yes	—
37	C₇×#399	C₂²	1	2	yes	—
38	C₇×#398	C₂²	1	2	yes	complemented
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×#397	C₂²	1	2	yes	—
43	C₇×#397	C₂²	1	2	yes	—
44	C₇×#397	C₂²	1	2	yes	—
45	C₇×#397	C₂²	1	2	yes	—
46	C₇×#397	C₂²	1	2	yes	—
47	C₇×#397	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×#396	C₂²	1	2	yes	—
52	C₇×#396	C₂²	1	2	yes	—
53	C₇×#396	C₂²	1	2	yes	—
54	C₇×#393	C₂²	1	2	yes	—
55	C₇×#393	C₂²	1	2	yes	—
56	C₇×#391	C₂²	1	2	yes	complemented
57	C₇×#391	C₂²	1	2	yes	complemented
58	C₇×#391	C₂²	1	1	yes	characteristic, complemented
59	C₇×#391	C₂²	1	1	yes	characteristic, 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	2	yes	complemented
66	C₇×#389	C₂²	1	2	yes	complemented
67	C₇×#389	C₂²	1	1	yes	characteristic, complemented
68	C₇×#388	C₂²	1	2	yes	—
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×#388	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	complemented
79	C₇×#387	C₂²	1	2	yes	complemented
80	C₇×#387	C₂²	1	2	yes	complemented
81	C₇×#387	C₂²	1	2	yes	complemented
82	C₇×#387	C₂²	1	2	yes	complemented
83	C₇×#387	C₂²	1	2	yes	complemented
84	C₇×#387	C₂²	1	2	yes	complemented
85	C₇×#387	C₂²	1	2	yes	complemented
86	C₇×#387	C₂²	1	2	yes	complemented
87	C₇×#387	C₂²	1	2	yes	complemented
88	C₇×#385	C₂²	1	2	yes	—
89	C₇×#385	C₂²	1	2	yes	—
90	C₇×#385	C₂²	1	2	yes	—
91	C₇×#385	C₂²	1	2	yes	—
92	C₇×#385	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#384	C₂²	1	1	yes	characteristic, complemented
95	C₇×#382	C₂²	1	2	yes	complemented
96	C₇×#382	C₂²	1	1	yes	characteristic, complemented
97	C₇×#380	C₂²	1	2	yes	—
98	C₇×#380	C₂²	1	2	yes	—
99	C₇×#380	C₂²	1	1	yes	characteristic
100	C₇×#380	C₂²	1	1	yes	characteristic
101	C₇×#379	C₂²	1	2	yes	—
102	C₇×#379	C₂²	1	2	yes	—
103	C₄×C₇×C₂²⋊C₄	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	#36760	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂⁵×C₇	C₂³	1	1	yes	characteristic
109	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
116	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
117	C₇×C₄⋊Q₈	—	4	2	no	—
118	C₇×#126	—	4	4	no	—
119	C₇×#126	—	4	4	no	—
120	C₇×#125	—	4	2	no	—
121	C₇×#125	—	4	4	no	—
122	C₇×C₂²⋊Q₈	—	2	4	no	—
123	C₇×C₂²⋊Q₈	—	2	4	no	—
124	C₂×C₇×C₄⋊C₄	—	4	2	no	—
125	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
126	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
127	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
128	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
129	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
133	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
134	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
140	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	2	yes	—
148	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
152	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
153	C₂×C₇×C₂²⋊C₄	—	4	2	no	—
154	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
156	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
158	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
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×C₄²×C₇	—	4	2	no	—
173	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
177	C₂×C₄²×C₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₇	C₂³	1	2	yes	—
179	C₂×C₄²×C₇	C₂³	1	2	yes	—
180	C₂×C₄²×C₇	C₂³	1	2	yes	—
181	C₇×#95	C₂³	1	2	yes	—
182	C₇×#95	C₂³	1	2	yes	—
183	C₇×#95	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	#2857	C₂×C₇	1	1	yes	characteristic, complemented
208	#2851	C₂×C₇	1	1	yes	characteristic, complemented
209	#2798	C₂×C₇	1	2	yes	complemented
210	#2783	C₂×C₇	1	2	yes	complemented
211	#2772	C₂×C₇	1	2	yes	complemented
212	#2754	C₂×C₇	1	2	yes	complemented
213	#2725	C₂×C₇	1	2	yes	complemented
214	#2725	C₂×C₇	1	2	yes	complemented
215	#2721	C₂×C₇	1	2	yes	complemented
216	#2716	C₂×C₇	1	2	yes	complemented
217	#2626	C₂×C₇	1	1	yes	characteristic
218	#2626	C₂×C₇	1	1	yes	characteristic
219	#2505	C₂×C₇	1	2	yes	complemented
220	#2480	C₂×C₇	1	2	yes	—
221	#2480	C₂×C₇	1	2	yes	—
222	#2473	C₂×C₇	1	2	yes	complemented
223	#2329	C₂×C₇	1	1	yes	characteristic, complemented
224	#2329	C₂×C₇	1	1	yes	characteristic, complemented
225	C₂×#388	C₂×C₇	1	1	yes	characteristic
226	C₂⁴×C₇	—	2	2	no	—
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	C₂⁴	1	2	yes	—
234	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
235	C₂×C₇×Q₈	—	2	2	no	—
236	C₂×C₇×Q₈	—	2	2	no	—
237	C₂×C₇×Q₈	—	4	1	no	—
238	C₂×C₇×Q₈	—	4	1	no	—
239	C₂×C₇×Q₈	—	4	1	no	—
240	C₂×C₇×Q₈	—	4	1	no	—
241	C₂²×C₄×C₇	—	2	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	1	no	—
256	C₂²×C₄×C₇	—	4	1	no	—
257	C₂²×C₄×C₇	—	4	1	no	—
258	C₂²×C₄×C₇	#41	1	4	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
260	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
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	1	yes	characteristic
274	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
276	C₇×C₄⋊C₄	—	2	2	no	—
277	C₇×C₄⋊C₄	—	2	2	no	—
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	4	no	—
283	C₇×C₄⋊C₄	—	2	4	no	—
284	C₇×C₄⋊C₄	—	2	4	no	—
285	C₇×C₄⋊C₄	—	4	2	no	—
286	C₇×C₄⋊C₄	—	4	1	no	—
287	C₇×C₄⋊C₄	—	4	1	no	—
288	C₇×C₄⋊C₄	—	4	2	no	—
289	C₇×C₄⋊C₄	—	4	2	no	—
290	C₇×C₄⋊C₄	—	4	2	no	—
291	C₇×C₄⋊C₄	—	4	2	no	—
292	C₇×C₄⋊C₄	—	4	2	no	—
293	C₇×C₄⋊C₄	—	4	1	no	—
294	C₇×C₄⋊C₄	—	4	1	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×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	4	no	—
305	C₇×C₂²⋊C₄	—	2	4	no	—
306	C₇×C₂²⋊C₄	—	2	4	no	—
307	C₇×C₂²⋊C₄	—	2	4	no	—
308	C₇×C₂²⋊C₄	—	2	4	no	—
309	C₇×C₂²⋊C₄	—	2	4	no	—
310	C₇×C₂²⋊C₄	—	4	2	no	—
311	C₇×C₂²⋊C₄	—	4	2	no	—
312	C₇×C₂²⋊C₄	—	4	2	no	—
313	C₇×C₂²⋊C₄	—	4	2	no	—
314	C₇×C₂²⋊C₄	—	4	2	no	—
315	C₇×C₂²⋊C₄	—	4	2	no	—
316	C₇×C₂²⋊C₄	—	4	2	no	—
317	C₇×C₂²⋊C₄	—	4	2	no	—
318	C₇×C₂²⋊C₄	—	4	2	no	—
319	C₇×C₂²⋊C₄	—	4	2	no	—
320	C₄²×C₇	—	2	2	no	—
321	C₄²×C₇	—	2	2	no	—
322	C₄²×C₇	—	4	1	no	—
323	C₄²×C₇	—	4	1	no	—
324	C₄²×C₇	—	4	2	no	—
325	C₄²×C₇	—	4	2	no	—
326	C₄²×C₇	—	4	2	no	—
327	C₄²×C₇	—	4	2	no	—
328	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
329	C₂×#126	C₂²×C₇	1	2	yes	—
330	C₂×#126	C₂²×C₇	1	2	yes	—
331	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
332	C₂×#125	C₂²×C₇	1	2	yes	complemented
333	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
334	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
335	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
336	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
337	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
338	C₂²×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
339	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
340	#400	C₂²×C₇	1	2	yes	complemented
341	#400	C₂²×C₇	1	2	yes	complemented
342	#400	C₂²×C₇	1	2	yes	complemented
343	#400	C₂²×C₇	1	2	yes	complemented
344	#399	C₂²×C₇	1	2	yes	—
345	#399	C₂²×C₇	1	2	yes	—
346	#398	C₂²×C₇	1	2	yes	complemented
347	#398	C₂²×C₇	1	2	yes	complemented
348	#398	C₂²×C₇	1	2	yes	complemented
349	#398	C₂²×C₇	1	2	yes	complemented
350	#397	C₂²×C₇	1	2	yes	—
351	#397	C₂²×C₇	1	2	yes	—
352	#397	C₂²×C₇	1	2	yes	—
353	#397	C₂²×C₇	1	2	yes	—
354	#397	C₂²×C₇	1	2	yes	—
355	#397	C₂²×C₇	1	2	yes	—
356	#396	C₂²×C₇	1	2	yes	—
357	#396	C₂²×C₇	1	2	yes	—
358	#396	C₂²×C₇	1	2	yes	—
359	#396	C₂²×C₇	1	2	yes	—
360	#396	C₂²×C₇	1	2	yes	—
361	#396	C₂²×C₇	1	2	yes	—
362	#393	C₂²×C₇	1	2	yes	—
363	#393	C₂²×C₇	1	2	yes	—
364	#391	C₂²×C₇	1	2	yes	complemented
365	#391	C₂²×C₇	1	2	yes	complemented
366	#391	C₂²×C₇	1	1	yes	characteristic, complemented
367	#391	C₂²×C₇	1	1	yes	characteristic, complemented
368	#389	C₂²×C₇	1	2	yes	complemented
369	#389	C₂²×C₇	1	2	yes	complemented
370	#389	C₂²×C₇	1	1	yes	characteristic, complemented
371	#389	C₂²×C₇	1	1	yes	characteristic, complemented
372	#389	C₂²×C₇	1	2	yes	complemented
373	#389	C₂²×C₇	1	2	yes	complemented
374	#389	C₂²×C₇	1	2	yes	complemented
375	#389	C₂²×C₇	1	2	yes	complemented
376	#388	C₂²×C₇	1	2	yes	—
377	#388	C₂²×C₇	1	2	yes	—
378	#388	C₂²×C₇	1	2	yes	—
379	#388	C₂²×C₇	1	2	yes	—
380	#388	C₂²×C₇	1	2	yes	—
381	#388	C₂²×C₇	1	2	yes	—
382	#388	C₂²×C₇	1	2	yes	—
383	#388	C₂²×C₇	1	2	yes	—
384	#388	C₂²×C₇	1	2	yes	—
385	#388	C₂²×C₇	1	2	yes	—
386	#387	C₂²×C₇	1	2	yes	complemented
387	#387	C₂²×C₇	1	2	yes	complemented
388	#387	C₂²×C₇	1	2	yes	complemented
389	#387	C₂²×C₇	1	2	yes	complemented
390	#387	C₂²×C₇	1	2	yes	complemented
391	#387	C₂²×C₇	1	2	yes	complemented
392	#387	C₂²×C₇	1	2	yes	complemented
393	#387	C₂²×C₇	1	2	yes	complemented
394	#387	C₂²×C₇	1	2	yes	complemented
395	#387	C₂²×C₇	1	2	yes	complemented
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	#384	C₂²×C₇	1	1	yes	characteristic, complemented
403	#382	C₂²×C₇	1	1	yes	characteristic, complemented
404	#382	C₂²×C₇	1	2	yes	complemented
405	#380	C₂²×C₇	1	1	yes	characteristic
406	#380	C₂²×C₇	1	1	yes	characteristic
407	#380	C₂²×C₇	1	2	yes	—
408	#380	C₂²×C₇	1	2	yes	—
409	#379	C₂²×C₇	1	2	yes	—
410	#379	C₂²×C₇	1	2	yes	—
411	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
412	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
413	C₂×#95	C₂²×C₇	1	1	yes	characteristic
414	C₂×#95	C₂²×C₇	1	1	yes	characteristic
415	C₂³×C₇	—	2	1	no	—
416	C₂³×C₇	—	2	1	no	—
417	C₂³×C₇	—	2	1	no	—
418	C₂³×C₇	—	2	1	no	—
419	C₂³×C₇	—	2	2	no	—
420	C₂³×C₇	—	2	2	no	—
421	C₂³×C₇	—	2	2	no	—
422	C₂³×C₇	—	2	2	no	—
423	C₂³×C₇	—	2	2	no	—
424	C₂³×C₇	—	2	2	no	—
425	C₂³×C₇	—	2	2	no	—
426	C₂³×C₇	—	4	4	no	—
427	C₂³×C₇	—	4	4	no	—
428	C₂³×C₇	—	4	4	no	—
429	C₂³×C₇	—	8	2	no	—
430	C₂³×C₇	—	8	2	no	—
431	C₂³×C₇	—	8	2	no	—
432	C₂³×C₇	—	8	2	no	—
433	C₂³×C₇	C₂×#41	1	2	yes	—
434	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
435	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
436	C₂³×C₇	C₂⁵	1	1	yes	characteristic
437	C₇×Q₈	—	8	2	no	—
438	C₇×Q₈	—	8	2	no	—
439	C₂×C₄×C₇	—	2	1	no	—
440	C₂×C₄×C₇	—	2	1	no	—
441	C₂×C₄×C₇	—	2	1	no	—
442	C₂×C₄×C₇	—	2	1	no	—
443	C₂×C₄×C₇	—	2	1	no	—
444	C₂×C₄×C₇	—	2	1	no	—
445	C₂×C₄×C₇	—	2	1	no	—
446	C₂×C₄×C₇	—	2	1	no	—
447	C₂×C₄×C₇	—	2	2	no	—
448	C₂×C₄×C₇	—	2	2	no	—
449	C₂×C₄×C₇	—	2	2	no	—
450	C₂×C₄×C₇	—	2	2	no	—
451	C₂×C₄×C₇	—	2	2	no	—
452	C₂×C₄×C₇	—	2	1	no	—
453	C₂×C₄×C₇	—	2	1	no	—
454	C₂×C₄×C₇	—	2	2	no	—
455	C₂×C₄×C₇	—	2	2	no	—
456	C₂×C₄×C₇	—	2	2	no	—
457	C₂×C₄×C₇	—	2	2	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	1	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	2	no	—
469	C₂×C₄×C₇	—	2	2	no	—
470	C₂×C₄×C₇	—	2	2	no	—
471	C₂×C₄×C₇	—	2	1	no	—
472	C₂×C₄×C₇	—	2	1	no	—
473	C₂×C₄×C₇	—	2	2	no	—
474	C₂×C₄×C₇	—	2	2	no	—
475	C₂×C₄×C₇	—	2	2	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	2	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	1	no	—
486	C₂×C₄×C₇	—	4	4	no	—
487	C₂×C₄×C₇	—	4	4	no	—
488	C₂×C₄×C₇	—	4	4	no	—
489	C₂×C₄×C₇	—	4	4	no	—
490	C₂×C₄×C₇	—	8	2	no	—
491	C₂×C₄×C₇	—	8	2	no	—
492	C₂×C₄×C₇	C₂×#41	1	2	yes	—
493	C₂×C₄×C₇	C₂×#41	1	2	yes	—
494	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
495	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
496	C₂⁵	C₂³×C₇	1	1	yes	characteristic
497	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
498	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
500	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
501	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
504	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
505	C₄⋊Q₈	—	4	2	no	—
506	#126	—	4	4	no	—
507	#126	—	4	4	no	—
508	#125	—	4	2	no	—
509	#125	—	4	4	no	—
510	C₂²⋊Q₈	—	2	4	no	—
511	C₂²⋊Q₈	—	2	4	no	—
512	C₂×C₄⋊C₄	—	4	2	no	—
513	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
514	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
517	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
518	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
522	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
523	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
533	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	4	no	—
540	C₂×C₂²⋊C₄	—	4	2	no	—
541	C₂×C₂²⋊C₄	—	4	2	no	—
542	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
543	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
544	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
545	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
546	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
547	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
548	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
549	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
550	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
552	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
553	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
554	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
555	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
556	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
557	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
558	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
559	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
560	C₂×C₄²	—	4	2	no	—
561	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
562	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
563	C₂×C₄²	C₂³×C₇	1	2	yes	—
564	C₂×C₄²	C₂³×C₇	1	2	yes	—
565	C₂×C₄²	C₂³×C₇	1	2	yes	—
566	C₂×C₄²	C₂³×C₇	1	2	yes	—
567	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
568	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
569	#95	C₂³×C₇	1	2	yes	—
570	#95	C₂³×C₇	1	2	yes	—
571	#95	C₂³×C₇	1	2	yes	—
572	#95	C₂³×C₇	1	2	yes	—
573	#95	C₂³×C₇	1	2	yes	—
574	#95	C₂³×C₇	1	2	yes	—
575	#95	C₂³×C₇	1	2	yes	—
576	#95	C₂³×C₇	1	2	yes	—
577	#95	C₂³×C₇	1	2	yes	—
578	#95	C₂³×C₇	1	2	yes	—
579	#95	C₂³×C₇	1	2	yes	—
580	#95	C₂³×C₇	1	2	yes	—
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	C₂²×C₇	—	2	2	no	—
596	C₂²×C₇	—	2	2	no	—
597	C₂²×C₇	—	2	2	no	—
598	C₂²×C₇	—	2	2	no	—
599	C₂²×C₇	—	2	2	no	—
600	C₂²×C₇	—	2	2	no	—
601	C₂²×C₇	—	4	2	no	—
602	C₂²×C₇	—	4	2	no	—
603	C₂²×C₇	—	4	2	no	—
604	C₂²×C₇	—	4	2	no	—
605	C₂²×C₇	—	4	2	no	—
606	C₂²×C₇	—	4	2	no	—
607	C₂²×C₇	—	4	2	no	—
608	C₂²×C₇	—	8	8	no	—
609	C₂²×C₇	#541	1	4	yes	—
610	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
611	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
612	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
613	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
614	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
615	C₂²×C₇	#585	1	1	yes	characteristic
616	C₂²×C₇	#585	1	1	yes	characteristic
617	C₄×C₇	—	2	2	no	—
618	C₄×C₇	—	2	2	no	—
619	C₄×C₇	—	2	2	no	—
620	C₄×C₇	—	2	2	no	—
621	C₄×C₇	—	4	2	no	—
622	C₄×C₇	—	4	2	no	—
623	C₄×C₇	—	4	2	no	—
624	C₄×C₇	—	4	2	no	—
625	C₄×C₇	—	4	2	no	—
626	C₄×C₇	—	4	2	no	—
627	C₄×C₇	—	4	1	no	—
628	C₄×C₇	—	4	2	no	—
629	C₄×C₇	—	4	1	no	—
630	C₄×C₇	—	4	2	no	—
631	C₄×C₇	—	4	2	no	—
632	C₄×C₇	—	4	2	no	—
633	C₄×C₇	—	4	2	no	—
634	C₂⁴	—	2	2	no	—
635	C₂⁴	—	2	2	no	—
636	C₂⁴	—	2	2	no	—
637	C₂⁴	—	4	1	no	—
638	C₂⁴	—	4	1	no	—
639	C₂⁴	—	4	1	no	—
640	C₂⁴	—	4	1	no	—
641	C₂⁴	C₂⁴×C₇	1	2	yes	—
642	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	—	2	2	no	—
645	C₂×Q₈	—	4	1	no	—
646	C₂×Q₈	—	4	1	no	—
647	C₂×Q₈	—	4	1	no	—
648	C₂×Q₈	—	4	1	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	4	1	no	—
657	C₂²×C₄	—	4	1	no	—
658	C₂²×C₄	—	4	1	no	—
659	C₂²×C₄	—	4	1	no	—
660	C₂²×C₄	—	4	1	no	—
661	C₂²×C₄	—	4	1	no	—
662	C₂²×C₄	—	4	1	no	—
663	C₂²×C₄	—	4	1	no	—
664	C₂²×C₄	—	4	1	no	—
665	C₂²×C₄	—	4	1	no	—
666	C₂²×C₄	C₇×#41	1	4	yes	—
667	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
668	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
669	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
670	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
671	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
673	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
674	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
675	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
676	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
677	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
681	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
682	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
684	C₄⋊C₄	—	2	2	no	—
685	C₄⋊C₄	—	2	2	no	—
686	C₄⋊C₄	—	2	4	no	—
687	C₄⋊C₄	—	2	4	no	—
688	C₄⋊C₄	—	2	4	no	—
689	C₄⋊C₄	—	2	4	no	—
690	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	4	2	no	—
694	C₄⋊C₄	—	4	1	no	—
695	C₄⋊C₄	—	4	1	no	—
696	C₄⋊C₄	—	4	2	no	—
697	C₄⋊C₄	—	4	2	no	—
698	C₄⋊C₄	—	4	2	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	2	no	—
701	C₄⋊C₄	—	4	1	no	—
702	C₄⋊C₄	—	4	1	no	—
703	C₄⋊C₄	—	4	2	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	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	4	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	4	2	no	—
719	C₂²⋊C₄	—	4	2	no	—
720	C₂²⋊C₄	—	4	2	no	—
721	C₂²⋊C₄	—	4	2	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	—	4	2	no	—
724	C₂²⋊C₄	—	4	2	no	—
725	C₂²⋊C₄	—	4	2	no	—
726	C₂²⋊C₄	—	4	2	no	—
727	C₂²⋊C₄	—	4	2	no	—
728	C₄²	—	2	2	no	—
729	C₄²	—	2	2	no	—
730	C₄²	—	4	1	no	—
731	C₄²	—	4	1	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₄²	—	4	2	no	—
735	C₄²	—	4	2	no	—
736	C₂×C₇	—	2	4	no	—
737	C₂×C₇	—	8	2	no	—
738	C₂×C₇	C₂×#541	1	1	yes	characteristic
739	C₂×C₇	#3505	1	1	yes	characteristic
740	C₂×C₇	#3506	1	1	yes	characteristic
741	C₂×C₇	#3535	1	1	yes	characteristic
742	C₂×C₇	#3536	1	1	yes	characteristic
743	C₂×C₇	#3561	1	1	yes	characteristic
744	C₂×C₇	#3564	1	1	yes	characteristic
745	C₂³	—	2	1	no	—
746	C₂³	—	2	1	no	—
747	C₂³	—	2	1	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	4	4	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	4	no	—
759	C₂³	—	8	2	no	—
760	C₂³	—	8	2	no	—
761	C₂³	—	8	2	no	—
762	C₂³	—	8	2	no	—
763	C₂³	C₂×C₇×#41	1	2	yes	—
764	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
765	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
766	C₂³	C₂⁵×C₇	1	1	yes	characteristic
767	Q₈	—	8	2	no	—
768	Q₈	—	8	2	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	1	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	1	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	1	no	—
783	C₂×C₄	—	2	1	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	1	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	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	1	no	—
803	C₂×C₄	—	2	1	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	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	2	no	—
815	C₂×C₄	—	2	1	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	4	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	—	8	2	no	—
822	C₂×C₄	C₂×C₇×#41	1	2	yes	—
823	C₂×C₄	C₂×C₇×#41	1	2	yes	—
824	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
825	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
826	C₇	#36760	1	1	yes	characteristic, direct product factor, Sylow
827	C₂²	—	2	2	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	8	8	no	—
841	C₂²	C₇×#541	1	4	yes	—
842	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
843	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
845	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
846	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
847	C₂²	C₇×#585	1	1	yes	characteristic
848	C₂²	C₇×#585	1	1	yes	characteristic
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	2	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	1	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	2	no	—
865	C₄	—	4	2	no	—
866	C₂	—	2	4	no	—
867	C₂	—	8	2	no	—
868	C₂	C₂×C₇×#541	1	1	yes	characteristic
869	C₂	C₇×#3505	1	1	yes	characteristic
870	C₂	C₇×#3506	1	1	yes	characteristic
871	C₂	C₇×#3535	1	1	yes	characteristic
872	C₂	C₇×#3536	1	1	yes	characteristic
873	C₂	C₇×#3561	1	1	yes	characteristic
874	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×#2798	C₂	semidirect
4. C₇×#2783	C₂	semidirect
5. C₇×#2772	C₂	semidirect
6. C₇×#2754	C₂	semidirect
7. C₇×#2725	C₂	semidirect
8. C₇×#2725	C₂	semidirect
9. C₇×#2721	C₂	semidirect
10. C₇×#2716	C₂	semidirect
13. C₇×#2505	C₂	semidirect
16. C₇×#2473	C₂	semidirect
17. C₇×#2329	C₂	semidirect
18. C₇×#2329	C₂	semidirect
20. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
23. C₂×C₇×#125	C₂²	semidirect
24. C₂×C₇×#125	C₂²	semidirect
32. C₇×#400	C₂²	semidirect
33. C₇×#400	C₂²	semidirect
34. C₇×#400	C₂²	semidirect
35. C₇×#400	C₂²	semidirect
38. C₇×#398	C₂²	semidirect
39. C₇×#398	C₂²	semidirect
40. C₇×#398	C₂²	semidirect
41. C₇×#398	C₂²	semidirect
56. C₇×#391	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
78. C₇×#387	C₂²	semidirect
79. C₇×#387	C₂²	semidirect
80. C₇×#387	C₂²	semidirect
81. C₇×#387	C₂²	semidirect
82. C₇×#387	C₂²	semidirect
83. C₇×#387	C₂²	semidirect
84. C₇×#387	C₂²	semidirect
85. C₇×#387	C₂²	semidirect
86. C₇×#387	C₂²	semidirect
87. C₇×#387	C₂²	semidirect
94. C₇×#384	C₂²	semidirect
95. C₇×#382	C₂²	semidirect
96. C₇×#382	C₂²	semidirect
107. #36760	C₇	direct (N × H)
207. #2857	C₂×C₇	semidirect
208. #2851	C₂×C₇	semidirect
209. #2798	C₂×C₇	semidirect
210. #2783	C₂×C₇	semidirect
211. #2772	C₂×C₇	semidirect
212. #2754	C₂×C₇	semidirect
213. #2725	C₂×C₇	semidirect
214. #2725	C₂×C₇	semidirect
215. #2721	C₂×C₇	semidirect
216. #2716	C₂×C₇	semidirect
219. #2505	C₂×C₇	semidirect
222. #2473	C₂×C₇	semidirect
223. #2329	C₂×C₇	semidirect
224. #2329	C₂×C₇	semidirect
328. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
331. C₂×#125	C₂²×C₇	semidirect
332. C₂×#125	C₂²×C₇	semidirect
340. #400	C₂²×C₇	semidirect
341. #400	C₂²×C₇	semidirect
342. #400	C₂²×C₇	semidirect
343. #400	C₂²×C₇	semidirect
346. #398	C₂²×C₇	semidirect
347. #398	C₂²×C₇	semidirect
348. #398	C₂²×C₇	semidirect
349. #398	C₂²×C₇	semidirect
364. #391	C₂²×C₇	semidirect
365. #391	C₂²×C₇	semidirect
366. #391	C₂²×C₇	semidirect
367. #391	C₂²×C₇	semidirect
368. #389	C₂²×C₇	semidirect
369. #389	C₂²×C₇	semidirect
370. #389	C₂²×C₇	semidirect
371. #389	C₂²×C₇	semidirect
372. #389	C₂²×C₇	semidirect
373. #389	C₂²×C₇	semidirect
374. #389	C₂²×C₇	semidirect
375. #389	C₂²×C₇	semidirect
386. #387	C₂²×C₇	semidirect
387. #387	C₂²×C₇	semidirect
388. #387	C₂²×C₇	semidirect
389. #387	C₂²×C₇	semidirect
390. #387	C₂²×C₇	semidirect
391. #387	C₂²×C₇	semidirect
392. #387	C₂²×C₇	semidirect
393. #387	C₂²×C₇	semidirect
394. #387	C₂²×C₇	semidirect
395. #387	C₂²×C₇	semidirect
402. #384	C₂²×C₇	semidirect
403. #382	C₂²×C₇	semidirect
404. #382	C₂²×C₇	semidirect
826. C₇	#36760	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×#2798	2
C₇×#2783	2
C₇×#2772	2
C₇×#2754	2
C₇×#2725	2
C₇×#2721	2
C₇×#2716	2
C₇×#2626	2
C₇×#2505	2
C₇×#2480	2
C₇×#2473	2
C₇×#2329	2
C₂×C₇×#388	2
#36760	7

Subgroups — C7×#36760 #13213976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36760 #13213976