Subgroups — C₇×#34754 #13211970

Order 1792.

2182 conjugacy classes of subgroups.

The subgroup lattice has 870 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#2518	C₂	1	2	yes	maximal, complemented
3	C₇×#2517	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2510	C₂	1	2	yes	maximal, complemented
5	C₇×#2505	C₂	1	2	yes	maximal, complemented
6	C₇×#2493	C₂	1	2	yes	maximal, complemented
7	C₇×#2488	C₂	1	2	yes	maximal, complemented
8	C₇×#2483	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2437	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2412	C₂	1	2	yes	maximal
11	C₇×#2401	C₂	1	2	yes	maximal, complemented
12	C₇×#2398	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#2395	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#123	C₂	1	2	yes	maximal, complemented
16	C₄×C₇×#120	C₂	1	1	yes	maximal, characteristic
17	C₇×#2290	C₂	1	2	yes	maximal, complemented
18	C₇×#2283	C₂	1	2	yes	maximal, complemented
19	C₂×C₄×C₇×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
20	C₂⁴×C₄×C₇	C₂²	1	1	yes	characteristic
21	C₂×C₇×#123	C₂²	1	2	yes	—
22	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₇×#120	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
26	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
27	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂²×C₄²×C₇	C₂²	1	2	yes	—
31	C₂²×C₄²×C₇	C₂²	1	2	yes	—
32	C₇×#401	C₂²	1	2	yes	complemented
33	C₇×#400	C₂²	1	1	yes	characteristic, 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×#400	C₂²	1	2	yes	complemented
38	C₇×#399	C₂²	1	1	yes	characteristic
39	C₇×#398	C₂²	1	1	yes	characteristic, complemented
40	C₇×#397	C₂²	1	1	yes	characteristic
41	C₇×#397	C₂²	1	1	yes	characteristic
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	complemented
46	C₇×#397	C₂²	1	1	yes	characteristic, complemented
47	C₇×#396	C₂²	1	2	yes	—
48	C₇×#394	C₂²	1	2	yes	—
49	C₇×#394	C₂²	1	2	yes	—
50	C₇×#393	C₂²	1	1	yes	characteristic
51	C₇×#393	C₂²	1	1	yes	characteristic, complemented
52	C₇×#391	C₂²	1	2	yes	complemented
53	C₇×#389	C₂²	1	2	yes	complemented
54	C₇×#388	C₂²	1	2	yes	complemented
55	C₇×#388	C₂²	1	2	yes	complemented
56	C₇×#388	C₂²	1	2	yes	complemented
57	C₇×#388	C₂²	1	2	yes	complemented
58	C₇×#387	C₂²	1	2	yes	complemented
59	C₇×#387	C₂²	1	2	yes	complemented
60	C₇×#387	C₂²	1	2	yes	complemented
61	C₇×#387	C₂²	1	2	yes	complemented
62	C₇×#387	C₂²	1	2	yes	complemented
63	C₇×#387	C₂²	1	2	yes	complemented
64	C₇×#386	C₂²	1	2	yes	—
65	C₇×#386	C₂²	1	2	yes	—
66	C₇×#386	C₂²	1	2	yes	—
67	C₇×#386	C₂²	1	2	yes	—
68	C₇×#386	C₂²	1	1	yes	characteristic
69	C₇×#385	C₂²	1	2	yes	—
70	C₇×#385	C₂²	1	2	yes	—
71	C₇×#385	C₂²	1	2	yes	—
72	C₇×#385	C₂²	1	2	yes	—
73	C₇×#385	C₂²	1	2	yes	—
74	C₇×#385	C₂²	1	2	yes	—
75	C₇×#385	C₂²	1	1	yes	characteristic
76	C₇×#383	C₂²	1	2	yes	complemented
77	C₇×#383	C₂²	1	2	yes	complemented
78	C₇×#382	C₂²	1	2	yes	complemented
79	C₇×#382	C₂²	1	2	yes	complemented
80	C₇×#381	C₂²	1	2	yes	—
81	C₇×#381	C₂²	1	2	yes	—
82	C₇×#381	C₂²	1	2	yes	—
83	C₇×#380	C₂²	1	2	yes	—
84	C₇×#380	C₂²	1	2	yes	—
85	C₇×#380	C₂²	1	2	yes	—
86	C₇×#379	C₂²	1	1	yes	characteristic
87	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
88	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
89	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
90	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	complemented
91	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
92	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
93	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
94	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
95	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
96	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
97	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
101	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
102	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
103	C₇×#376	C₂²	1	1	yes	characteristic, complemented
104	C₇×#376	C₂²	1	2	yes	complemented
105	C₂×C₇×#95	C₂²	1	2	yes	—
106	C₂×C₇×#95	C₂²	1	2	yes	—
107	#34754	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×D₄	C₂³	1	2	yes	—
111	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
112	C₂³×C₄×C₇	—	2	8	no	—
113	C₂³×C₄×C₇	—	4	2	no	—
114	C₂³×C₄×C₇	C₂³	1	2	yes	—
115	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
116	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
117	C₂³×C₄×C₇	C₂³	1	2	yes	—
118	C₂³×C₄×C₇	C₂³	1	2	yes	—
119	C₂³×C₄×C₇	C₂³	1	2	yes	—
120	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₇	C₂³	1	2	yes	—
122	C₂³×C₄×C₇	C₂³	1	2	yes	—
123	C₇×#123	—	2	8	no	—
124	C₇×C₂²⋊Q₈	—	2	8	no	—
125	C₇×#120	—	2	4	no	—
126	C₄×C₇×Q₈	—	4	2	no	—
127	C₄×C₇×D₄	—	2	8	no	—
128	C₄×C₇×D₄	—	4	2	no	—
129	C₇×#117	—	4	2	no	—
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	2	yes	—
136	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
137	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
138	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
139	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
140	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
141	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
143	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
144	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
145	C₂×C₇×C₂²⋊C₄	—	2	8	no	—
146	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
148	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
164	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
165	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₄²×C₇	—	2	8	no	—
167	C₂×C₄²×C₇	—	4	4	no	—
168	C₂×C₄²×C₇	C₂³	1	2	yes	—
169	C₂×C₄²×C₇	C₂³	1	2	yes	—
170	C₂×C₄²×C₇	C₂³	1	2	yes	—
171	C₂×C₄²×C₇	C₂³	1	2	yes	—
172	C₂×C₄²×C₇	C₂³	1	2	yes	—
173	C₂×C₄²×C₇	C₂³	1	2	yes	—
174	C₂×C₄²×C₇	C₂³	1	2	yes	—
175	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₇	C₂³	1	2	yes	—
178	C₇×#95	C₂³	1	2	yes	—
179	C₇×#95	C₂³	1	2	yes	—
180	C₇×#95	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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
197	C₇×#95	C₂³	1	2	yes	—
198	C₇×#95	C₂³	1	2	yes	—
199	C₇×#95	C₂³	1	1	yes	characteristic
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	#2523	C₂×C₇	1	1	yes	characteristic, complemented
209	#2518	C₂×C₇	1	2	yes	complemented
210	#2517	C₂×C₇	1	1	yes	characteristic, complemented
211	#2510	C₂×C₇	1	2	yes	complemented
212	#2505	C₂×C₇	1	2	yes	complemented
213	#2493	C₂×C₇	1	2	yes	complemented
214	#2488	C₂×C₇	1	2	yes	complemented
215	#2483	C₂×C₇	1	1	yes	characteristic, complemented
216	#2437	C₂×C₇	1	1	yes	characteristic, complemented
217	#2412	C₂×C₇	1	2	yes	—
218	#2401	C₂×C₇	1	2	yes	complemented
219	#2398	C₂×C₇	1	1	yes	characteristic, complemented
220	#2395	C₂×C₇	1	1	yes	characteristic, complemented
221	C₄×C₂²⋊Q₈	C₂×C₇	1	2	yes	complemented
222	C₄×#123	C₂×C₇	1	2	yes	complemented
223	C₄×#120	C₂×C₇	1	1	yes	characteristic
224	#2290	C₂×C₇	1	2	yes	complemented
225	#2283	C₂×C₇	1	2	yes	complemented
226	C₂×C₄×C₂²⋊C₄	C₂×C₇	1	2	yes	complemented
227	C₂⁴×C₇	—	2	4	no	—
228	C₂⁴×C₇	—	2	4	no	—
229	C₂⁴×C₇	—	4	1	no	—
230	C₂⁴×C₇	—	4	1	no	—
231	C₂⁴×C₇	#41	1	4	yes	—
232	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
234	C₂⁴×C₇	C₂⁴	1	2	yes	—
235	C₂×C₇×Q₈	—	2	4	no	—
236	C₂×C₇×Q₈	—	4	1	no	—
237	C₂×C₇×D₄	—	2	4	no	—
238	C₂×C₇×D₄	—	2	2	no	—
239	C₂×C₇×D₄	—	2	4	no	—
240	C₂×C₇×D₄	—	2	4	no	—
241	C₂×C₇×D₄	—	4	1	no	—
242	C₂×C₇×D₄	—	4	1	no	—
243	C₂²×C₄×C₇	—	2	4	no	—
244	C₂²×C₄×C₇	—	2	4	no	—
245	C₂²×C₄×C₇	—	2	4	no	—
246	C₂²×C₄×C₇	—	2	4	no	—
247	C₂²×C₄×C₇	—	2	4	no	—
248	C₂²×C₄×C₇	—	2	4	no	—
249	C₂²×C₄×C₇	—	2	4	no	—
250	C₂²×C₄×C₇	—	2	4	no	—
251	C₂²×C₄×C₇	—	2	4	no	—
252	C₂²×C₄×C₇	—	2	4	no	—
253	C₂²×C₄×C₇	—	2	4	no	—
254	C₂²×C₄×C₇	—	2	4	no	—
255	C₂²×C₄×C₇	—	2	4	no	—
256	C₂²×C₄×C₇	—	2	4	no	—
257	C₂²×C₄×C₇	—	2	4	no	—
258	C₂²×C₄×C₇	—	2	2	no	—
259	C₂²×C₄×C₇	—	2	2	no	—
260	C₂²×C₄×C₇	—	4	2	no	—
261	C₂²×C₄×C₇	—	4	2	no	—
262	C₂²×C₄×C₇	—	4	1	no	—
263	C₂²×C₄×C₇	—	4	2	no	—
264	C₂²×C₄×C₇	—	4	2	no	—
265	C₂²×C₄×C₇	—	4	2	no	—
266	C₂²×C₄×C₇	—	4	16	no	—
267	C₂²×C₄×C₇	#41	1	8	yes	—
268	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
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	1	yes	characteristic
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	2	yes	—
282	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	—	2	4	no	—
288	C₇×C₄⋊C₄	—	2	4	no	—
289	C₇×C₄⋊C₄	—	2	4	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	1	no	—
296	C₇×C₄⋊C₄	—	4	2	no	—
297	C₇×C₄⋊C₄	—	4	1	no	—
298	C₇×C₂²⋊C₄	—	2	4	no	—
299	C₇×C₂²⋊C₄	—	2	4	no	—
300	C₇×C₂²⋊C₄	—	2	4	no	—
301	C₇×C₂²⋊C₄	—	2	4	no	—
302	C₇×C₂²⋊C₄	—	2	4	no	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	2	no	—
305	C₇×C₂²⋊C₄	—	2	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	—	2	4	no	—
311	C₇×C₂²⋊C₄	—	2	4	no	—
312	C₇×C₂²⋊C₄	—	4	1	no	—
313	C₇×C₂²⋊C₄	—	4	2	no	—
314	C₇×C₂²⋊C₄	—	4	2	no	—
315	C₇×C₂²⋊C₄	—	4	1	no	—
316	C₇×C₂²⋊C₄	—	4	1	no	—
317	C₇×C₂²⋊C₄	#41	1	8	yes	—
318	C₄²×C₇	—	2	4	no	—
319	C₄²×C₇	—	2	4	no	—
320	C₄²×C₇	—	2	4	no	—
321	C₄²×C₇	—	2	4	no	—
322	C₄²×C₇	—	2	4	no	—
323	C₄²×C₇	—	2	4	no	—
324	C₄²×C₇	—	2	4	no	—
325	C₄²×C₇	—	2	2	no	—
326	C₄²×C₇	—	4	2	no	—
327	C₄²×C₇	—	4	2	no	—
328	C₂⁴×C₄	C₂²×C₇	1	1	yes	characteristic
329	C₂×#123	C₂²×C₇	1	2	yes	—
330	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
331	C₂×#120	C₂²×C₇	1	1	yes	characteristic
332	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
333	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
334	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
335	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
336	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
337	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
338	C₂²×C₄²	C₂²×C₇	1	2	yes	—
339	C₂²×C₄²	C₂²×C₇	1	2	yes	—
340	#401	C₂²×C₇	1	2	yes	complemented
341	#400	C₂²×C₇	1	1	yes	characteristic, complemented
342	#400	C₂²×C₇	1	2	yes	complemented
343	#400	C₂²×C₇	1	2	yes	complemented
344	#400	C₂²×C₇	1	2	yes	complemented
345	#400	C₂²×C₇	1	2	yes	complemented
346	#399	C₂²×C₇	1	1	yes	characteristic
347	#398	C₂²×C₇	1	1	yes	characteristic, complemented
348	#397	C₂²×C₇	1	1	yes	characteristic
349	#397	C₂²×C₇	1	1	yes	characteristic
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	complemented
354	#397	C₂²×C₇	1	1	yes	characteristic, complemented
355	#396	C₂²×C₇	1	2	yes	—
356	#394	C₂²×C₇	1	2	yes	—
357	#394	C₂²×C₇	1	2	yes	—
358	#393	C₂²×C₇	1	1	yes	characteristic
359	#393	C₂²×C₇	1	1	yes	characteristic, complemented
360	#391	C₂²×C₇	1	2	yes	complemented
361	#389	C₂²×C₇	1	2	yes	complemented
362	#388	C₂²×C₇	1	2	yes	complemented
363	#388	C₂²×C₇	1	2	yes	complemented
364	#388	C₂²×C₇	1	2	yes	complemented
365	#388	C₂²×C₇	1	2	yes	complemented
366	#387	C₂²×C₇	1	2	yes	complemented
367	#387	C₂²×C₇	1	2	yes	complemented
368	#387	C₂²×C₇	1	2	yes	complemented
369	#387	C₂²×C₇	1	2	yes	complemented
370	#387	C₂²×C₇	1	2	yes	complemented
371	#387	C₂²×C₇	1	2	yes	complemented
372	#386	C₂²×C₇	1	2	yes	—
373	#386	C₂²×C₇	1	2	yes	—
374	#386	C₂²×C₇	1	2	yes	—
375	#386	C₂²×C₇	1	2	yes	—
376	#386	C₂²×C₇	1	1	yes	characteristic
377	#385	C₂²×C₇	1	2	yes	—
378	#385	C₂²×C₇	1	2	yes	—
379	#385	C₂²×C₇	1	2	yes	—
380	#385	C₂²×C₇	1	2	yes	—
381	#385	C₂²×C₇	1	2	yes	—
382	#385	C₂²×C₇	1	2	yes	—
383	#385	C₂²×C₇	1	1	yes	characteristic
384	#383	C₂²×C₇	1	2	yes	complemented
385	#383	C₂²×C₇	1	2	yes	complemented
386	#382	C₂²×C₇	1	2	yes	complemented
387	#382	C₂²×C₇	1	2	yes	complemented
388	#381	C₂²×C₇	1	2	yes	—
389	#381	C₂²×C₇	1	2	yes	—
390	#381	C₂²×C₇	1	2	yes	—
391	#380	C₂²×C₇	1	2	yes	—
392	#380	C₂²×C₇	1	2	yes	—
393	#380	C₂²×C₇	1	2	yes	—
394	#379	C₂²×C₇	1	1	yes	characteristic
395	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
396	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
397	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
398	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	complemented
399	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
400	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
401	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
402	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
403	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
404	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
405	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
406	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
407	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
408	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
409	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
410	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
411	#376	C₂²×C₇	1	1	yes	characteristic, complemented
412	#376	C₂²×C₇	1	2	yes	complemented
413	C₂×#95	C₂²×C₇	1	2	yes	—
414	C₂×#95	C₂²×C₇	1	2	yes	—
415	C₂³×C₇	—	2	2	no	—
416	C₂³×C₇	—	2	2	no	—
417	C₂³×C₇	—	2	2	no	—
418	C₂³×C₇	—	2	2	no	—
419	C₂³×C₇	—	2	16	no	—
420	C₂³×C₇	—	2	2	no	—
421	C₂³×C₇	—	2	2	no	—
422	C₂³×C₇	—	2	1	no	—
423	C₂³×C₇	—	2	1	no	—
424	C₂³×C₇	—	2	2	no	—
425	C₂³×C₇	—	2	2	no	—
426	C₂³×C₇	—	2	1	no	—
427	C₂³×C₇	—	2	1	no	—
428	C₂³×C₇	—	2	1	no	—
429	C₂³×C₇	—	4	4	no	—
430	C₂³×C₇	—	4	4	no	—
431	C₂³×C₇	—	4	8	no	—
432	C₂³×C₇	—	4	4	no	—
433	C₂³×C₇	C₂×#41	1	2	yes	—
434	C₂³×C₇	C₂×#41	1	4	yes	—
435	C₂³×C₇	C₂×#41	1	4	yes	—
436	C₂³×C₇	C₂×#41	1	4	yes	—
437	C₂³×C₇	C₂⁵	1	1	yes	characteristic
438	C₇×Q₈	—	4	4	no	—
439	C₇×D₄	—	4	4	no	—
440	C₇×D₄	—	4	8	no	—
441	C₂×C₄×C₇	—	2	2	no	—
442	C₂×C₄×C₇	—	2	2	no	—
443	C₂×C₄×C₇	—	2	2	no	—
444	C₂×C₄×C₇	—	2	2	no	—
445	C₂×C₄×C₇	—	2	2	no	—
446	C₂×C₄×C₇	—	2	2	no	—
447	C₂×C₄×C₇	—	2	16	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	2	no	—
453	C₂×C₄×C₇	—	2	2	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	1	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	2	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	1	no	—
473	C₂×C₄×C₇	—	2	1	no	—
474	C₂×C₄×C₇	—	2	1	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	—	4	4	no	—
482	C₂×C₄×C₇	—	4	8	no	—
483	C₂×C₄×C₇	—	4	8	no	—
484	C₂×C₄×C₇	—	4	8	no	—
485	C₂×C₄×C₇	—	4	8	no	—
486	C₂×C₄×C₇	—	4	8	no	—
487	C₂×C₄×C₇	—	4	4	no	—
488	C₂×C₄×C₇	—	4	4	no	—
489	C₂×C₄×C₇	C₂×#41	1	4	yes	—
490	C₂×C₄×C₇	C₂×#41	1	4	yes	—
491	C₂×C₄×C₇	C₂×#41	1	4	yes	—
492	C₂×C₄×C₇	C₂×#41	1	4	yes	—
493	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
494	C₂⁵	C₂³×C₇	1	1	yes	characteristic
495	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
496	C₂²×D₄	C₂³×C₇	1	2	yes	—
497	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
498	C₂³×C₄	—	2	8	no	—
499	C₂³×C₄	—	4	2	no	—
500	C₂³×C₄	C₂³×C₇	1	2	yes	—
501	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
502	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
503	C₂³×C₄	C₂³×C₇	1	2	yes	—
504	C₂³×C₄	C₂³×C₇	1	2	yes	—
505	C₂³×C₄	C₂³×C₇	1	2	yes	—
506	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
507	C₂³×C₄	C₂³×C₇	1	2	yes	—
508	C₂³×C₄	C₂³×C₇	1	2	yes	—
509	#123	—	2	8	no	—
510	C₂²⋊Q₈	—	2	8	no	—
511	#120	—	2	4	no	—
512	C₄×Q₈	—	4	2	no	—
513	C₄×D₄	—	2	8	no	—
514	C₄×D₄	—	4	2	no	—
515	#117	—	4	2	no	—
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	1	yes	characteristic
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	1	yes	characteristic
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×C₂²⋊C₄	—	2	8	no	—
531	C₂×C₂²⋊C₄	—	2	8	no	—
532	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
533	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
534	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
535	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
536	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
537	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
538	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
539	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
540	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
541	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
542	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
548	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
549	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
550	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
551	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
552	C₂×C₄²	—	2	8	no	—
553	C₂×C₄²	—	4	4	no	—
554	C₂×C₄²	C₂³×C₇	1	2	yes	—
555	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
556	C₂×C₄²	C₂³×C₇	1	2	yes	—
557	C₂×C₄²	C₂³×C₇	1	2	yes	—
558	C₂×C₄²	C₂³×C₇	1	2	yes	—
559	C₂×C₄²	C₂³×C₇	1	2	yes	—
560	C₂×C₄²	C₂³×C₇	1	2	yes	—
561	C₂×C₄²	C₂³×C₇	1	2	yes	—
562	C₂×C₄²	C₂³×C₇	1	2	yes	—
563	C₂×C₄²	C₂³×C₇	1	2	yes	—
564	#95	C₂³×C₇	1	2	yes	—
565	#95	C₂³×C₇	1	2	yes	—
566	#95	C₂³×C₇	1	2	yes	—
567	#95	C₂³×C₇	1	2	yes	—
568	#95	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
583	#95	C₂³×C₇	1	2	yes	—
584	#95	C₂³×C₇	1	2	yes	—
585	#95	C₂³×C₇	1	1	yes	characteristic
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	C₂²×C₇	—	2	4	no	—
595	C₂²×C₇	—	2	4	no	—
596	C₂²×C₇	—	2	4	no	—
597	C₂²×C₇	—	2	4	no	—
598	C₂²×C₇	—	2	4	no	—
599	C₂²×C₇	—	2	4	no	—
600	C₂²×C₇	—	2	4	no	—
601	C₂²×C₇	—	2	2	no	—
602	C₂²×C₇	—	4	16	no	—
603	C₂²×C₇	—	4	1	no	—
604	C₂²×C₇	—	4	2	no	—
605	C₂²×C₇	—	4	1	no	—
606	C₂²×C₇	—	4	2	no	—
607	C₂²×C₇	—	4	1	no	—
608	C₂²×C₇	—	4	1	no	—
609	C₂²×C₇	—	4	2	no	—
610	C₂²×C₇	—	4	1	no	—
611	C₂²×C₇	#529	1	8	yes	—
612	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
613	C₂²×C₇	C₂²×#41	1	2	yes	—
614	C₂²×C₇	C₂²×#41	1	2	yes	—
615	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂²×C₇	#585	1	1	yes	characteristic
617	C₄×C₇	—	2	4	no	—
618	C₄×C₇	—	2	4	no	—
619	C₄×C₇	—	2	4	no	—
620	C₄×C₇	—	4	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	1	no	—
626	C₄×C₇	—	4	1	no	—
627	C₄×C₇	—	4	1	no	—
628	C₄×C₇	—	4	2	no	—
629	C₄×C₇	—	4	2	no	—
630	C₄×C₇	—	4	2	no	—
631	C₄×C₇	—	4	1	no	—
632	C₄×C₇	#551	1	4	yes	—
633	C₂⁴	—	2	4	no	—
634	C₂⁴	—	2	4	no	—
635	C₂⁴	—	4	1	no	—
636	C₂⁴	—	4	1	no	—
637	C₂⁴	C₇×#41	1	4	yes	—
638	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
639	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
640	C₂⁴	C₂⁴×C₇	1	2	yes	—
641	C₂×Q₈	—	2	4	no	—
642	C₂×Q₈	—	4	1	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	2	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	4	1	no	—
648	C₂×D₄	—	4	1	no	—
649	C₂²×C₄	—	2	4	no	—
650	C₂²×C₄	—	2	4	no	—
651	C₂²×C₄	—	2	4	no	—
652	C₂²×C₄	—	2	4	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	2	4	no	—
655	C₂²×C₄	—	2	4	no	—
656	C₂²×C₄	—	2	4	no	—
657	C₂²×C₄	—	2	4	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	4	no	—
662	C₂²×C₄	—	2	4	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	4	2	no	—
667	C₂²×C₄	—	4	2	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	16	no	—
673	C₂²×C₄	C₇×#41	1	8	yes	—
674	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
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	2	yes	—
681	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
684	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
685	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
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	C₄⋊C₄	—	2	4	no	—
691	C₄⋊C₄	—	2	4	no	—
692	C₄⋊C₄	—	2	4	no	—
693	C₄⋊C₄	—	2	4	no	—
694	C₄⋊C₄	—	2	4	no	—
695	C₄⋊C₄	—	2	4	no	—
696	C₄⋊C₄	—	4	1	no	—
697	C₄⋊C₄	—	4	1	no	—
698	C₄⋊C₄	—	4	1	no	—
699	C₄⋊C₄	—	4	2	no	—
700	C₄⋊C₄	—	4	1	no	—
701	C₄⋊C₄	—	4	2	no	—
702	C₄⋊C₄	—	4	2	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₂²⋊C₄	—	2	4	no	—
705	C₂²⋊C₄	—	2	4	no	—
706	C₂²⋊C₄	—	2	4	no	—
707	C₂²⋊C₄	—	2	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	2	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	1	no	—
720	C₂²⋊C₄	—	4	1	no	—
721	C₂²⋊C₄	—	4	1	no	—
722	C₂²⋊C₄	—	4	2	no	—
723	C₂²⋊C₄	C₇×#41	1	8	yes	—
724	C₄²	—	2	4	no	—
725	C₄²	—	2	4	no	—
726	C₄²	—	2	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	4	no	—
730	C₄²	—	2	4	no	—
731	C₄²	—	2	2	no	—
732	C₄²	—	4	2	no	—
733	C₄²	—	4	2	no	—
734	C₂×C₇	—	2	8	no	—
735	C₂×C₇	—	4	2	no	—
736	C₂×C₇	—	8	1	no	—
737	C₂×C₇	C₂×#529	1	2	yes	—
738	C₂×C₇	#3459	1	1	yes	characteristic
739	C₂×C₇	C₂×#551	1	1	yes	characteristic
740	C₂×C₇	#3475	1	2	yes	—
741	C₂×C₇	#3481	1	1	yes	characteristic
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	1	no	—
749	C₂³	—	2	1	no	—
750	C₂³	—	2	16	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	1	no	—
754	C₂³	—	2	1	no	—
755	C₂³	—	2	1	no	—
756	C₂³	—	4	4	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	8	no	—
759	C₂³	—	4	4	no	—
760	C₂³	C₂×C₇×#41	1	2	yes	—
761	C₂³	C₂×C₇×#41	1	4	yes	—
762	C₂³	C₂×C₇×#41	1	4	yes	—
763	C₂³	C₂×C₇×#41	1	4	yes	—
764	C₂³	C₂⁵×C₇	1	1	yes	characteristic
765	Q₈	—	4	4	no	—
766	D₄	—	4	4	no	—
767	D₄	—	4	8	no	—
768	C₂×C₄	—	2	2	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	16	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	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	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	1	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	2	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	1	no	—
800	C₂×C₄	—	2	1	no	—
801	C₂×C₄	—	2	1	no	—
802	C₂×C₄	—	2	1	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	—	4	4	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	8	no	—
811	C₂×C₄	—	4	8	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	—	4	8	no	—
814	C₂×C₄	—	4	4	no	—
815	C₂×C₄	—	4	4	no	—
816	C₂×C₄	C₂×C₇×#41	1	4	yes	—
817	C₂×C₄	C₂×C₇×#41	1	4	yes	—
818	C₂×C₄	C₂×C₇×#41	1	4	yes	—
819	C₂×C₄	C₂×C₇×#41	1	4	yes	—
820	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
821	C₇	#34754	1	1	yes	characteristic, direct product factor, Sylow
822	C₂²	—	2	4	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	4	no	—
826	C₂²	—	2	4	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	4	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	4	16	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	1	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	1	no	—
836	C₂²	—	4	1	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	1	no	—
839	C₂²	C₇×#529	1	8	yes	—
840	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
841	C₂²	C₂²×C₇×#41	1	2	yes	—
842	C₂²	C₂²×C₇×#41	1	2	yes	—
843	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
844	C₂²	C₇×#585	1	1	yes	characteristic
845	C₄	—	2	4	no	—
846	C₄	—	2	4	no	—
847	C₄	—	2	4	no	—
848	C₄	—	4	2	no	—
849	C₄	—	4	2	no	—
850	C₄	—	4	2	no	—
851	C₄	—	4	2	no	—
852	C₄	—	4	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	1	no	—
855	C₄	—	4	1	no	—
856	C₄	—	4	2	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	C₇×#551	1	4	yes	—
861	C₂	—	2	8	no	—
862	C₂	—	4	2	no	—
863	C₂	—	8	1	no	—
864	C₂	C₂×C₇×#529	1	2	yes	—
865	C₂	C₇×#3459	1	1	yes	characteristic
866	C₂	C₂×C₇×#551	1	1	yes	characteristic
867	C₂	C₇×#3475	1	2	yes	—
868	C₂	C₇×#3481	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₂×C₇×#120	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2523	C₂	semidirect
2. C₇×#2518	C₂	semidirect
3. C₇×#2517	C₂	semidirect
4. C₇×#2510	C₂	semidirect
5. C₇×#2505	C₂	semidirect
6. C₇×#2493	C₂	semidirect
7. C₇×#2488	C₂	semidirect
8. C₇×#2483	C₂	semidirect
9. C₇×#2437	C₂	semidirect
11. C₇×#2401	C₂	semidirect
12. C₇×#2398	C₂	semidirect
13. C₇×#2395	C₂	semidirect
14. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
15. C₄×C₇×#123	C₂	semidirect
17. C₇×#2290	C₂	semidirect
18. C₇×#2283	C₂	semidirect
19. C₂×C₄×C₇×C₂²⋊C₄	C₂	semidirect
24. C₂×C₄×C₇×Q₈	C₂²	semidirect
27. C₂×C₇×#117	C₂²	semidirect
32. C₇×#401	C₂²	semidirect
33. C₇×#400	C₂²	semidirect
34. C₇×#400	C₂²	semidirect
35. C₇×#400	C₂²	semidirect
36. C₇×#400	C₂²	semidirect
37. C₇×#400	C₂²	semidirect
39. C₇×#398	C₂²	semidirect
45. C₇×#397	C₂²	semidirect
46. C₇×#397	C₂²	semidirect
51. C₇×#393	C₂²	semidirect
52. C₇×#391	C₂²	semidirect
53. C₇×#389	C₂²	semidirect
54. C₇×#388	C₂²	semidirect
55. C₇×#388	C₂²	semidirect
56. C₇×#388	C₂²	semidirect
57. C₇×#388	C₂²	semidirect
58. C₇×#387	C₂²	semidirect
59. C₇×#387	C₂²	semidirect
60. C₇×#387	C₂²	semidirect
61. C₇×#387	C₂²	semidirect
62. C₇×#387	C₂²	semidirect
63. C₇×#387	C₂²	semidirect
76. C₇×#383	C₂²	semidirect
77. C₇×#383	C₂²	semidirect
78. C₇×#382	C₂²	semidirect
79. C₇×#382	C₂²	semidirect
87. C₄×C₇×C₄⋊C₄	C₂²	semidirect
88. C₄×C₇×C₄⋊C₄	C₂²	semidirect
89. C₄×C₇×C₄⋊C₄	C₂²	semidirect
90. C₄×C₇×C₄⋊C₄	C₂²	semidirect
101. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
102. C₄×C₇×C₂²⋊C₄	C₂²	semidirect
103. C₇×#376	C₂²	semidirect
104. C₇×#376	C₂²	semidirect
107. #34754	C₇	direct (N × H)
208. #2523	C₂×C₇	semidirect
209. #2518	C₂×C₇	semidirect
210. #2517	C₂×C₇	semidirect
211. #2510	C₂×C₇	semidirect
212. #2505	C₂×C₇	semidirect
213. #2493	C₂×C₇	semidirect
214. #2488	C₂×C₇	semidirect
215. #2483	C₂×C₇	semidirect
216. #2437	C₂×C₇	semidirect
218. #2401	C₂×C₇	semidirect
219. #2398	C₂×C₇	semidirect
220. #2395	C₂×C₇	semidirect
221. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
222. C₄×#123	C₂×C₇	semidirect
224. #2290	C₂×C₇	semidirect
225. #2283	C₂×C₇	semidirect
226. C₂×C₄×C₂²⋊C₄	C₂×C₇	semidirect
332. C₂×C₄×Q₈	C₂²×C₇	semidirect
335. C₂×#117	C₂²×C₇	semidirect
340. #401	C₂²×C₇	semidirect
341. #400	C₂²×C₇	semidirect
342. #400	C₂²×C₇	semidirect
343. #400	C₂²×C₇	semidirect
344. #400	C₂²×C₇	semidirect
345. #400	C₂²×C₇	semidirect
347. #398	C₂²×C₇	semidirect
353. #397	C₂²×C₇	semidirect
354. #397	C₂²×C₇	semidirect
359. #393	C₂²×C₇	semidirect
360. #391	C₂²×C₇	semidirect
361. #389	C₂²×C₇	semidirect
362. #388	C₂²×C₇	semidirect
363. #388	C₂²×C₇	semidirect
364. #388	C₂²×C₇	semidirect
365. #388	C₂²×C₇	semidirect
366. #387	C₂²×C₇	semidirect
367. #387	C₂²×C₇	semidirect
368. #387	C₂²×C₇	semidirect
369. #387	C₂²×C₇	semidirect
370. #387	C₂²×C₇	semidirect
371. #387	C₂²×C₇	semidirect
384. #383	C₂²×C₇	semidirect
385. #383	C₂²×C₇	semidirect
386. #382	C₂²×C₇	semidirect
387. #382	C₂²×C₇	semidirect
395. C₄×C₄⋊C₄	C₂²×C₇	semidirect
396. C₄×C₄⋊C₄	C₂²×C₇	semidirect
397. C₄×C₄⋊C₄	C₂²×C₇	semidirect
398. C₄×C₄⋊C₄	C₂²×C₇	semidirect
409. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
410. C₄×C₂²⋊C₄	C₂²×C₇	semidirect
411. #376	C₂²×C₇	semidirect
412. #376	C₂²×C₇	semidirect
821. C₇	#34754	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×#2523	2
C₇×#2518	2
C₇×#2517	2
C₇×#2510	2
C₇×#2505	2
C₇×#2493	2
C₇×#2488	2
C₇×#2483	2
C₇×#2437	2
C₇×#2412	2
C₇×#2401	2
C₇×#2398	2
C₇×#2395	2
C₄×C₇×C₂²⋊Q₈	2
C₄×C₇×#123	2
C₄×C₇×#120	2
C₇×#2290	2
C₇×#2283	2
C₂×C₄×C₇×C₂²⋊C₄	2
#34754	7

Subgroups — C7×#34754 #13211970

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34754 #13211970