Subgroups — C₇×#34910 #13212126

Order 1792.

2570 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₇×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2602	C₂	1	4	yes	maximal, complemented
4	C₇×#2601	C₂	1	4	yes	maximal, complemented
5	C₇×#2566	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2500	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#2499	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2432	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2431	C₂	1	1	yes	maximal, characteristic
13	C₇×#2392	C₂	1	4	yes	maximal, complemented
14	C₄×C₇×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₇×#127	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#2290	C₂	1	4	yes	maximal, complemented
19	C₄×C₇×#117	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
21	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₇×#127	C₂²	1	1	yes	characteristic
23	C₇×#529	—	2	8	no	—
24	C₂×C₇×#126	C₂²	1	2	yes	—
25	C₂×C₇×#125	C₂²	1	1	yes	characteristic
26	C₂×C₇×#124	C₂²	1	1	yes	characteristic
27	C₂×C₇×#124	C₂²	1	1	yes	characteristic
28	C₂×C₇×#124	C₂²	1	1	yes	characteristic
29	C₂×C₇×#123	C₂²	1	2	yes	—
30	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₇×#121	C₂²	1	1	yes	characteristic
32	C₄×C₇×#41	—	2	8	no	—
33	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
37	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
38	C₂×C₄×C₇×D₄	C₂²	1	4	yes	—
39	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
42	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
43	C₂×C₇×#117	C₂²	1	2	yes	—
44	C₂×C₇×#117	C₂²	1	1	yes	characteristic
45	C₂×C₇×#117	C₂²	1	2	yes	—
46	C₂×C₇×#117	C₂²	1	2	yes	—
47	C₂²×C₄²×C₇	C₂²	1	2	yes	—
48	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
49	C₇×#398	C₂²	1	4	yes	—
50	C₇×#397	C₂²	1	4	yes	—
51	C₇×#396	C₂²	1	4	yes	—
52	C₇×#396	C₂²	1	4	yes	—
53	C₇×#394	C₂²	1	4	yes	—
54	C₇×#394	C₂²	1	4	yes	—
55	C₇×#394	C₂²	1	4	yes	—
56	C₇×#392	C₂²	1	4	yes	—
57	C₇×#391	C₂²	1	1	yes	characteristic
58	C₇×#391	C₂²	1	1	yes	characteristic
59	C₇×#391	C₂²	1	1	yes	characteristic
60	C₇×#391	C₂²	1	1	yes	characteristic
61	C₇×#390	C₂²	1	1	yes	characteristic
62	C₇×#390	C₂²	1	1	yes	characteristic
63	C₇×#390	C₂²	1	1	yes	characteristic
64	C₇×#390	C₂²	1	1	yes	characteristic
65	C₇×#390	C₂²	1	4	yes	—
66	C₇×#389	C₂²	1	4	yes	—
67	C₇×#388	C₂²	1	4	yes	—
68	C₇×#388	C₂²	1	4	yes	—
69	C₇×#388	C₂²	1	4	yes	—
70	C₇×#388	C₂²	1	4	yes	—
71	C₇×#387	C₂²	1	4	yes	—
72	C₇×#387	C₂²	1	4	yes	—
73	C₇×#386	C₂²	1	4	yes	—
74	C₇×#386	C₂²	1	4	yes	—
75	C₇×#385	C₂²	1	4	yes	—
76	C₇×#385	C₂²	1	4	yes	—
77	C₇×#384	C₂²	1	1	yes	characteristic
78	C₇×#384	C₂²	1	1	yes	characteristic
79	C₇×#382	C₂²	1	1	yes	characteristic
80	C₇×#382	C₂²	1	1	yes	characteristic
81	C₄×C₇×C₄⋊C₄	C₂²	1	4	yes	—
82	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
83	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
84	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
85	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
86	C₄×C₇×C₂²⋊C₄	C₂²	1	4	yes	—
87	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
88	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
89	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
90	C₇×#376	C₂²	1	2	yes	—
91	C₄³×C₇	C₂²	1	1	yes	characteristic
92	C₄³×C₇	C₂²	1	1	yes	characteristic
93	#34910	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₂×C₇×#41	—	2	4	no	—
95	C₂×C₇×#41	—	2	4	no	—
96	C₂×C₇×#41	—	2	4	no	—
97	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
98	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
99	C₂²×C₇×D₄	C₂³	1	2	yes	—
100	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
101	C₂²×C₇×D₄	C₂³	1	4	yes	—
102	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
103	C₂²×C₇×D₄	C₂³	1	2	yes	—
104	C₂³×C₄×C₇	C₂³	1	2	yes	—
105	C₂³×C₄×C₇	C₂³	1	2	yes	—
106	C₂³×C₄×C₇	C₂³	1	2	yes	—
107	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₇	C₂³	1	2	yes	—
110	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
111	C₇×C₄⋊Q₈	—	2	4	no	—
112	C₇×#127	—	2	4	no	—
113	C₇×#126	—	2	8	no	—
114	C₇×#125	—	2	4	no	—
115	C₇×#124	—	2	4	no	—
116	C₇×#124	—	2	4	no	—
117	C₇×#124	—	2	4	no	—
118	C₇×#123	—	2	8	no	—
119	C₇×C₂²⋊Q₈	—	2	4	no	—
120	C₇×#121	—	2	4	no	—
121	C₄×C₇×Q₈	—	2	4	no	—
122	C₄×C₇×Q₈	—	2	4	no	—
123	C₄×C₇×Q₈	—	2	4	no	—
124	C₄×C₇×D₄	—	2	8	no	—
125	C₄×C₇×D₄	—	2	8	no	—
126	C₄×C₇×D₄	—	2	8	no	—
127	C₄×C₇×D₄	—	2	4	no	—
128	C₄×C₇×D₄	—	2	4	no	—
129	C₄×C₇×D₄	—	2	4	no	—
130	C₄×C₇×D₄	—	2	16	no	—
131	C₇×#117	—	2	4	no	—
132	C₇×#117	—	2	8	no	—
133	C₇×#117	—	2	8	no	—
134	C₇×#117	—	2	8	no	—
135	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
136	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
137	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	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	4	yes	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₇×C₄⋊C₄	C₂³	1	4	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	2	yes	—
149	C₂×C₇×C₄⋊C₄	C₂³	1	4	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	4	yes	—
153	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
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	4	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	4	yes	—
163	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
165	C₂×C₇×C₂²⋊C₄	C₂³	1	4	yes	—
166	C₂×C₄²×C₇	—	2	8	no	—
167	C₂×C₄²×C₇	D₄	1	8	yes	complemented
168	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
171	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	2	yes	—
176	C₂×C₄²×C₇	C₂³	1	2	yes	—
177	C₂×C₄²×C₇	C₂³	1	2	yes	—
178	C₂×C₄²×C₇	C₂³	1	2	yes	—
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	1	yes	characteristic
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	4	yes	—
189	C₇×#95	C₂³	1	4	yes	—
190	C₇×#95	C₂³	1	4	yes	—
191	C₇×#95	C₂³	1	4	yes	—
192	C₇×#95	C₂³	1	4	yes	—
193	C₇×#95	C₂³	1	4	yes	—
194	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
195	C₂×C₄×#41	C₂×C₇	1	1	yes	characteristic, complemented
196	#2602	C₂×C₇	1	4	yes	complemented
197	#2601	C₂×C₇	1	4	yes	complemented
198	#2566	C₂×C₇	1	1	yes	characteristic, complemented
199	#2565	C₂×C₇	1	1	yes	characteristic, complemented
200	#2545	C₂×C₇	1	1	yes	characteristic, complemented
201	#2544	C₂×C₇	1	1	yes	characteristic, complemented
202	#2500	C₂×C₇	1	1	yes	characteristic, complemented
203	#2499	C₂×C₇	1	1	yes	characteristic, complemented
204	#2432	C₂×C₇	1	1	yes	characteristic, complemented
205	#2431	C₂×C₇	1	1	yes	characteristic
206	#2392	C₂×C₇	1	4	yes	complemented
207	C₄×C₄⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
208	C₄×#127	C₂×C₇	1	1	yes	characteristic, complemented
209	C₄×#124	C₂×C₇	1	1	yes	characteristic, complemented
210	C₄×#124	C₂×C₇	1	1	yes	characteristic, complemented
211	#2290	C₂×C₇	1	4	yes	complemented
212	C₄×#117	C₂×C₇	1	1	yes	characteristic, complemented
213	C₂⁴×C₇	C₂⁴	1	2	yes	—
214	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
215	C₂⁴×C₇	C₂⁴	1	2	yes	—
216	C₇×#41	—	2	32	no	—
217	C₂×C₇×Q₈	—	2	2	no	—
218	C₂×C₇×Q₈	—	2	2	no	—
219	C₂×C₇×Q₈	—	2	2	no	—
220	C₂×C₇×Q₈	—	2	2	no	—
221	C₂×C₇×Q₈	—	2	2	no	—
222	C₂×C₇×Q₈	#41	1	4	yes	—
223	C₂×C₇×D₄	—	2	4	no	—
224	C₂×C₇×D₄	—	2	4	no	—
225	C₂×C₇×D₄	—	2	4	no	—
226	C₂×C₇×D₄	—	2	8	no	—
227	C₂×C₇×D₄	—	2	2	no	—
228	C₂×C₇×D₄	—	2	2	no	—
229	C₂×C₇×D₄	—	2	4	no	—
230	C₂×C₇×D₄	—	2	2	no	—
231	C₂×C₇×D₄	—	2	8	no	—
232	C₂×C₇×D₄	—	2	2	no	—
233	C₂×C₇×D₄	—	2	2	no	—
234	C₂×C₇×D₄	—	4	4	no	—
235	C₂×C₇×D₄	—	4	4	no	—
236	C₂×C₇×D₄	#41	1	4	yes	—
237	C₂²×C₄×C₇	—	2	4	no	—
238	C₂²×C₄×C₇	—	2	4	no	—
239	C₂²×C₄×C₇	—	2	4	no	—
240	C₂²×C₄×C₇	—	2	4	no	—
241	C₂²×C₄×C₇	—	2	2	no	—
242	C₂²×C₄×C₇	—	2	2	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	8	no	—
247	C₂²×C₄×C₇	—	2	8	no	—
248	C₂²×C₄×C₇	—	4	2	no	—
249	C₂²×C₄×C₇	—	4	4	no	—
250	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
251	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
252	C₂²×C₄×C₇	C₂×D₄	1	4	yes	—
253	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
261	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
263	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
268	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
269	C₇×C₄⋊C₄	—	2	4	no	—
270	C₇×C₄⋊C₄	—	2	4	no	—
271	C₇×C₄⋊C₄	—	2	2	no	—
272	C₇×C₄⋊C₄	—	2	2	no	—
273	C₇×C₄⋊C₄	—	2	4	no	—
274	C₇×C₄⋊C₄	—	2	4	no	—
275	C₇×C₄⋊C₄	—	2	2	no	—
276	C₇×C₄⋊C₄	—	2	4	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	8	no	—
282	C₇×C₄⋊C₄	—	2	8	no	—
283	C₇×C₄⋊C₄	—	4	4	no	—
284	C₇×C₂²⋊C₄	—	2	4	no	—
285	C₇×C₂²⋊C₄	—	2	4	no	—
286	C₇×C₂²⋊C₄	—	2	8	no	—
287	C₇×C₂²⋊C₄	—	2	4	no	—
288	C₇×C₂²⋊C₄	—	2	4	no	—
289	C₇×C₂²⋊C₄	—	2	4	no	—
290	C₇×C₂²⋊C₄	—	2	4	no	—
291	C₇×C₂²⋊C₄	—	2	4	no	—
292	C₇×C₂²⋊C₄	—	2	4	no	—
293	C₇×C₂²⋊C₄	—	2	4	no	—
294	C₇×C₂²⋊C₄	—	2	4	no	—
295	C₇×C₂²⋊C₄	—	2	8	no	—
296	C₇×C₂²⋊C₄	—	2	8	no	—
297	C₇×C₂²⋊C₄	—	2	8	no	—
298	C₇×C₂²⋊C₄	—	4	4	no	—
299	C₇×C₂²⋊C₄	—	4	4	no	—
300	C₄²×C₇	—	2	4	no	—
301	C₄²×C₇	—	2	4	no	—
302	C₄²×C₇	—	2	4	no	—
303	C₄²×C₇	—	2	4	no	—
304	C₄²×C₇	—	2	4	no	—
305	C₄²×C₇	—	2	2	no	—
306	C₄²×C₇	—	2	2	no	—
307	C₄²×C₇	—	2	2	no	—
308	C₄²×C₇	—	2	2	no	—
309	C₄²×C₇	—	4	2	no	—
310	C₄²×C₇	—	4	2	no	—
311	C₄²×C₇	C₂×D₄	1	4	yes	—
312	C₄²×C₇	C₂×D₄	1	4	yes	—
313	C₄²×C₇	C₂×D₄	1	4	yes	—
314	C₄²×C₇	C₂×D₄	1	4	yes	—
315	C₄²×C₇	#41	1	8	yes	complemented
316	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
317	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
318	C₂×#127	C₂²×C₇	1	1	yes	characteristic
319	#529	—	2	8	no	—
320	C₂×#126	C₂²×C₇	1	2	yes	—
321	C₂×#125	C₂²×C₇	1	1	yes	characteristic
322	C₂×#124	C₂²×C₇	1	1	yes	characteristic
323	C₂×#124	C₂²×C₇	1	1	yes	characteristic
324	C₂×#124	C₂²×C₇	1	1	yes	characteristic
325	C₂×#123	C₂²×C₇	1	2	yes	—
326	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
327	C₂×#121	C₂²×C₇	1	1	yes	characteristic
328	C₄×#41	—	2	8	no	—
329	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
330	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
332	C₂×C₄×D₄	C₂²×C₇	1	4	yes	—
333	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
334	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
335	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
336	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
337	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
338	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
339	C₂×#117	C₂²×C₇	1	2	yes	—
340	C₂×#117	C₂²×C₇	1	2	yes	—
341	C₂×#117	C₂²×C₇	1	1	yes	characteristic
342	C₂×#117	C₂²×C₇	1	2	yes	—
343	C₂²×C₄²	C₂²×C₇	1	2	yes	—
344	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
345	#398	C₂²×C₇	1	4	yes	—
346	#397	C₂²×C₇	1	4	yes	—
347	#396	C₂²×C₇	1	4	yes	—
348	#396	C₂²×C₇	1	4	yes	—
349	#394	C₂²×C₇	1	4	yes	—
350	#394	C₂²×C₇	1	4	yes	—
351	#394	C₂²×C₇	1	4	yes	—
352	#392	C₂²×C₇	1	4	yes	—
353	#391	C₂²×C₇	1	1	yes	characteristic
354	#391	C₂²×C₇	1	1	yes	characteristic
355	#391	C₂²×C₇	1	1	yes	characteristic
356	#391	C₂²×C₇	1	1	yes	characteristic
357	#390	C₂²×C₇	1	1	yes	characteristic
358	#390	C₂²×C₇	1	4	yes	—
359	#390	C₂²×C₇	1	1	yes	characteristic
360	#390	C₂²×C₇	1	1	yes	characteristic
361	#390	C₂²×C₇	1	1	yes	characteristic
362	#389	C₂²×C₇	1	4	yes	—
363	#388	C₂²×C₇	1	4	yes	—
364	#388	C₂²×C₇	1	4	yes	—
365	#388	C₂²×C₇	1	4	yes	—
366	#388	C₂²×C₇	1	4	yes	—
367	#387	C₂²×C₇	1	4	yes	—
368	#387	C₂²×C₇	1	4	yes	—
369	#386	C₂²×C₇	1	4	yes	—
370	#386	C₂²×C₇	1	4	yes	—
371	#385	C₂²×C₇	1	4	yes	—
372	#385	C₂²×C₇	1	4	yes	—
373	#384	C₂²×C₇	1	1	yes	characteristic
374	#384	C₂²×C₇	1	1	yes	characteristic
375	#382	C₂²×C₇	1	1	yes	characteristic
376	#382	C₂²×C₇	1	1	yes	characteristic
377	C₄×C₄⋊C₄	C₂²×C₇	1	4	yes	—
378	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
379	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
380	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
382	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
383	C₄×C₂²⋊C₄	C₂²×C₇	1	4	yes	—
384	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
385	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
386	#376	C₂²×C₇	1	2	yes	—
387	C₄³	C₂²×C₇	1	1	yes	characteristic
388	C₄³	C₂²×C₇	1	1	yes	characteristic
389	C₂³×C₇	—	2	2	no	—
390	C₂³×C₇	—	2	2	no	—
391	C₂³×C₇	—	2	4	no	—
392	C₂³×C₇	—	2	1	no	—
393	C₂³×C₇	—	2	1	no	—
394	C₂³×C₇	—	2	2	no	—
395	C₂³×C₇	—	2	4	no	—
396	C₂³×C₇	—	2	2	no	—
397	C₂³×C₇	—	2	2	no	—
398	C₂³×C₇	—	2	2	no	—
399	C₂³×C₇	—	2	4	no	—
400	C₂³×C₇	—	2	2	no	—
401	C₂³×C₇	—	2	4	no	—
402	C₂³×C₇	C₂²×D₄	1	2	yes	—
403	C₂³×C₇	C₂×#41	1	4	yes	—
404	C₂³×C₇	C₂⁵	1	1	yes	characteristic
405	C₇×Q₈	—	2	8	no	—
406	C₇×Q₈	—	4	4	no	—
407	C₇×D₄	—	2	16	no	—
408	C₇×D₄	—	2	8	no	—
409	C₇×D₄	—	4	16	no	—
410	C₇×D₄	—	4	8	no	—
411	C₇×D₄	—	4	4	no	—
412	C₂×C₄×C₇	—	2	16	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	2	no	—
415	C₂×C₄×C₇	—	2	2	no	—
416	C₂×C₄×C₇	—	2	2	no	—
417	C₂×C₄×C₇	—	2	1	no	—
418	C₂×C₄×C₇	—	2	1	no	—
419	C₂×C₄×C₇	—	2	2	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	8	no	—
425	C₂×C₄×C₇	—	2	8	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	2	no	—
428	C₂×C₄×C₇	—	2	2	no	—
429	C₂×C₄×C₇	—	2	2	no	—
430	C₂×C₄×C₇	—	2	2	no	—
431	C₂×C₄×C₇	—	2	2	no	—
432	C₂×C₄×C₇	—	2	2	no	—
433	C₂×C₄×C₇	—	2	2	no	—
434	C₂×C₄×C₇	—	2	2	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	4	no	—
437	C₂×C₄×C₇	—	2	4	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	4	no	—
442	C₂×C₄×C₇	—	2	4	no	—
443	C₂×C₄×C₇	—	4	4	no	—
444	C₂×C₄×C₇	—	4	8	no	—
445	C₂×C₄×C₇	—	4	8	no	—
446	C₂×C₄×C₇	—	4	8	no	—
447	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
448	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
449	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
450	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
451	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
452	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
453	C₂×C₄×C₇	C₂×#41	1	4	yes	—
454	C₂×C₄×C₇	C₂×#41	1	4	yes	—
455	C₂×C₄×C₇	C₂×#41	1	4	yes	—
456	C₂×C₄×C₇	C₂×#41	1	2	yes	—
457	C₂×C₄×C₇	C₂×#41	1	2	yes	—
458	C₂×C₄×C₇	C₂×#41	1	4	yes	—
459	C₂×#41	—	2	4	no	—
460	C₂×#41	—	2	4	no	—
461	C₂×#41	—	2	4	no	—
462	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
463	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
464	C₂²×D₄	C₂³×C₇	1	2	yes	—
465	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
466	C₂²×D₄	C₂³×C₇	1	4	yes	—
467	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
468	C₂²×D₄	C₂³×C₇	1	2	yes	—
469	C₂³×C₄	C₂³×C₇	1	2	yes	—
470	C₂³×C₄	C₂³×C₇	1	2	yes	—
471	C₂³×C₄	C₂³×C₇	1	2	yes	—
472	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
473	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
474	C₂³×C₄	C₂³×C₇	1	2	yes	—
475	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
476	C₄⋊Q₈	—	2	4	no	—
477	#127	—	2	4	no	—
478	#126	—	2	8	no	—
479	#125	—	2	4	no	—
480	#124	—	2	4	no	—
481	#124	—	2	4	no	—
482	#124	—	2	4	no	—
483	#123	—	2	8	no	—
484	C₂²⋊Q₈	—	2	4	no	—
485	#121	—	2	4	no	—
486	C₄×Q₈	—	2	4	no	—
487	C₄×Q₈	—	2	4	no	—
488	C₄×Q₈	—	2	4	no	—
489	C₄×D₄	—	2	8	no	—
490	C₄×D₄	—	2	8	no	—
491	C₄×D₄	—	2	8	no	—
492	C₄×D₄	—	2	4	no	—
493	C₄×D₄	—	2	4	no	—
494	C₄×D₄	—	2	4	no	—
495	C₄×D₄	—	2	16	no	—
496	#117	—	2	4	no	—
497	#117	—	2	8	no	—
498	#117	—	2	8	no	—
499	#117	—	2	8	no	—
500	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
501	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
502	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
503	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
504	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
505	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
507	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
509	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
511	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
512	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
514	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
515	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
516	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₇	1	4	yes	—
531	C₂×C₄²	—	2	8	no	—
532	C₂×C₄²	C₇×D₄	1	8	yes	complemented
533	C₂×C₄²	C₂³×C₇	1	2	yes	—
534	C₂×C₄²	C₂³×C₇	1	2	yes	—
535	C₂×C₄²	C₂³×C₇	1	2	yes	—
536	C₂×C₄²	C₂³×C₇	1	2	yes	—
537	C₂×C₄²	C₂³×C₇	1	2	yes	—
538	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
540	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
541	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₇	1	2	yes	—
543	C₂×C₄²	C₂³×C₇	1	2	yes	—
544	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₇	1	2	yes	—
549	#95	C₂³×C₇	1	2	yes	—
550	#95	C₂³×C₇	1	2	yes	—
551	#95	C₂³×C₇	1	2	yes	—
552	#95	C₂³×C₇	1	2	yes	—
553	#95	C₂³×C₇	1	4	yes	—
554	#95	C₂³×C₇	1	4	yes	—
555	#95	C₂³×C₇	1	4	yes	—
556	#95	C₂³×C₇	1	4	yes	—
557	#95	C₂³×C₇	1	4	yes	—
558	#95	C₂³×C₇	1	4	yes	—
559	C₂²×C₇	—	2	2	no	—
560	C₂²×C₇	—	2	4	no	—
561	C₂²×C₇	—	2	2	no	—
562	C₂²×C₇	—	2	2	no	—
563	C₂²×C₇	—	2	8	no	—
564	C₂²×C₇	—	4	2	no	—
565	C₂²×C₇	—	4	2	no	—
566	C₂²×C₇	—	4	2	no	—
567	C₂²×C₇	—	4	2	no	—
568	C₂²×C₇	—	4	4	no	—
569	C₂²×C₇	—	4	2	no	—
570	C₂²×C₇	—	4	2	no	—
571	C₂²×C₇	—	4	2	no	—
572	C₂²×C₇	—	4	4	no	—
573	C₂²×C₇	—	4	4	no	—
574	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
575	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
576	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
577	C₂²×C₇	C₂²×#41	1	2	yes	—
578	C₂²×C₇	#585	1	2	yes	—
579	C₄×C₇	—	2	2	no	—
580	C₄×C₇	—	2	4	no	—
581	C₄×C₇	—	2	2	no	—
582	C₄×C₇	—	2	2	no	—
583	C₄×C₇	—	2	2	no	—
584	C₄×C₇	—	2	4	no	—
585	C₄×C₇	—	2	4	no	—
586	C₄×C₇	—	4	2	no	—
587	C₄×C₇	—	4	2	no	—
588	C₄×C₇	—	4	2	no	—
589	C₄×C₇	—	4	2	no	—
590	C₄×C₇	—	4	2	no	—
591	C₄×C₇	—	4	2	no	—
592	C₄×C₇	—	4	2	no	—
593	C₄×C₇	#525	1	4	yes	—
594	C₄×C₇	#532	1	4	yes	—
595	C₂⁴	C₂⁴×C₇	1	2	yes	—
596	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
597	C₂⁴	C₂⁴×C₇	1	2	yes	—
598	#41	—	2	32	no	—
599	C₂×Q₈	—	2	2	no	—
600	C₂×Q₈	—	2	2	no	—
601	C₂×Q₈	—	2	2	no	—
602	C₂×Q₈	—	2	2	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	C₇×#41	1	4	yes	—
605	C₂×D₄	—	2	4	no	—
606	C₂×D₄	—	2	4	no	—
607	C₂×D₄	—	2	4	no	—
608	C₂×D₄	—	2	8	no	—
609	C₂×D₄	—	2	2	no	—
610	C₂×D₄	—	2	2	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	2	no	—
613	C₂×D₄	—	2	8	no	—
614	C₂×D₄	—	2	2	no	—
615	C₂×D₄	—	2	2	no	—
616	C₂×D₄	—	4	4	no	—
617	C₂×D₄	—	4	4	no	—
618	C₂×D₄	C₇×#41	1	4	yes	—
619	C₂²×C₄	—	2	4	no	—
620	C₂²×C₄	—	2	4	no	—
621	C₂²×C₄	—	2	4	no	—
622	C₂²×C₄	—	2	4	no	—
623	C₂²×C₄	—	2	2	no	—
624	C₂²×C₄	—	2	2	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	4	no	—
628	C₂²×C₄	—	2	8	no	—
629	C₂²×C₄	—	2	8	no	—
630	C₂²×C₄	—	4	2	no	—
631	C₂²×C₄	—	4	4	no	—
632	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
633	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
634	C₂²×C₄	C₂×C₇×D₄	1	4	yes	—
635	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
636	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
637	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
638	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
639	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
640	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
641	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
642	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
643	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
644	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
645	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
646	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
647	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
649	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
650	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
651	C₄⋊C₄	—	2	4	no	—
652	C₄⋊C₄	—	2	4	no	—
653	C₄⋊C₄	—	2	2	no	—
654	C₄⋊C₄	—	2	2	no	—
655	C₄⋊C₄	—	2	4	no	—
656	C₄⋊C₄	—	2	4	no	—
657	C₄⋊C₄	—	2	2	no	—
658	C₄⋊C₄	—	2	4	no	—
659	C₄⋊C₄	—	2	2	no	—
660	C₄⋊C₄	—	2	4	no	—
661	C₄⋊C₄	—	2	4	no	—
662	C₄⋊C₄	—	2	4	no	—
663	C₄⋊C₄	—	2	8	no	—
664	C₄⋊C₄	—	2	8	no	—
665	C₄⋊C₄	—	4	4	no	—
666	C₂²⋊C₄	—	2	4	no	—
667	C₂²⋊C₄	—	2	4	no	—
668	C₂²⋊C₄	—	2	8	no	—
669	C₂²⋊C₄	—	2	4	no	—
670	C₂²⋊C₄	—	2	4	no	—
671	C₂²⋊C₄	—	2	4	no	—
672	C₂²⋊C₄	—	2	4	no	—
673	C₂²⋊C₄	—	2	4	no	—
674	C₂²⋊C₄	—	2	4	no	—
675	C₂²⋊C₄	—	2	4	no	—
676	C₂²⋊C₄	—	2	4	no	—
677	C₂²⋊C₄	—	2	8	no	—
678	C₂²⋊C₄	—	2	8	no	—
679	C₂²⋊C₄	—	2	8	no	—
680	C₂²⋊C₄	—	4	4	no	—
681	C₂²⋊C₄	—	4	4	no	—
682	C₄²	—	2	4	no	—
683	C₄²	—	2	4	no	—
684	C₄²	—	2	4	no	—
685	C₄²	—	2	4	no	—
686	C₄²	—	2	4	no	—
687	C₄²	—	2	2	no	—
688	C₄²	—	2	2	no	—
689	C₄²	—	2	2	no	—
690	C₄²	—	2	2	no	—
691	C₄²	—	4	2	no	—
692	C₄²	—	4	2	no	—
693	C₄²	C₂×C₇×D₄	1	4	yes	—
694	C₄²	C₂×C₇×D₄	1	4	yes	—
695	C₄²	C₂×C₇×D₄	1	4	yes	—
696	C₄²	C₂×C₇×D₄	1	4	yes	—
697	C₄²	C₇×#41	1	8	yes	complemented
698	C₂×C₇	—	4	2	no	—
699	C₂×C₇	—	4	4	no	—
700	C₂×C₇	—	8	2	no	—
701	C₂×C₇	C₂×#525	1	1	yes	characteristic
702	C₂×C₇	C₂×#532	1	1	yes	characteristic
703	C₂×C₇	#3449	1	1	yes	characteristic
704	C₂×C₇	#3475	1	2	yes	—
705	C₂×C₇	#3480	1	2	yes	—
706	C₂³	—	2	2	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	4	no	—
709	C₂³	—	2	1	no	—
710	C₂³	—	2	1	no	—
711	C₂³	—	2	2	no	—
712	C₂³	—	2	4	no	—
713	C₂³	—	2	2	no	—
714	C₂³	—	2	2	no	—
715	C₂³	—	2	2	no	—
716	C₂³	—	2	4	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	4	no	—
719	C₂³	C₂²×C₇×D₄	1	2	yes	—
720	C₂³	C₂×C₇×#41	1	4	yes	—
721	C₂³	C₂⁵×C₇	1	1	yes	characteristic
722	Q₈	—	2	8	no	—
723	Q₈	—	4	4	no	—
724	D₄	—	2	16	no	—
725	D₄	—	2	8	no	—
726	D₄	—	4	16	no	—
727	D₄	—	4	8	no	—
728	D₄	—	4	4	no	—
729	C₂×C₄	—	2	16	no	—
730	C₂×C₄	—	2	2	no	—
731	C₂×C₄	—	2	2	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	1	no	—
735	C₂×C₄	—	2	1	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	8	no	—
742	C₂×C₄	—	2	8	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	4	no	—
759	C₂×C₄	—	2	4	no	—
760	C₂×C₄	—	4	4	no	—
761	C₂×C₄	—	4	8	no	—
762	C₂×C₄	—	4	8	no	—
763	C₂×C₄	—	4	8	no	—
764	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
765	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
766	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
767	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
768	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
769	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
770	C₂×C₄	C₂×C₇×#41	1	4	yes	—
771	C₂×C₄	C₂×C₇×#41	1	4	yes	—
772	C₂×C₄	C₂×C₇×#41	1	4	yes	—
773	C₂×C₄	C₂×C₇×#41	1	2	yes	—
774	C₂×C₄	C₂×C₇×#41	1	2	yes	—
775	C₂×C₄	C₂×C₇×#41	1	4	yes	—
776	C₇	#34910	1	1	yes	characteristic, direct product factor, Sylow
777	C₂²	—	2	2	no	—
778	C₂²	—	2	4	no	—
779	C₂²	—	2	2	no	—
780	C₂²	—	2	2	no	—
781	C₂²	—	2	8	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	4	4	no	—
787	C₂²	—	4	2	no	—
788	C₂²	—	4	2	no	—
789	C₂²	—	4	2	no	—
790	C₂²	—	4	4	no	—
791	C₂²	—	4	4	no	—
792	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
793	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
794	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
795	C₂²	C₂²×C₇×#41	1	2	yes	—
796	C₂²	C₇×#585	1	2	yes	—
797	C₄	—	2	2	no	—
798	C₄	—	2	4	no	—
799	C₄	—	2	2	no	—
800	C₄	—	2	2	no	—
801	C₄	—	2	2	no	—
802	C₄	—	2	4	no	—
803	C₄	—	2	4	no	—
804	C₄	—	4	2	no	—
805	C₄	—	4	2	no	—
806	C₄	—	4	2	no	—
807	C₄	—	4	2	no	—
808	C₄	—	4	2	no	—
809	C₄	—	4	2	no	—
810	C₄	—	4	2	no	—
811	C₄	C₇×#525	1	4	yes	—
812	C₄	C₇×#532	1	4	yes	—
813	C₂	—	4	2	no	—
814	C₂	—	4	4	no	—
815	C₂	—	8	2	no	—
816	C₂	C₂×C₇×#525	1	1	yes	characteristic
817	C₂	C₂×C₇×#532	1	1	yes	characteristic
818	C₂	C₇×#3449	1	1	yes	characteristic
819	C₂	C₇×#3475	1	2	yes	—
820	C₂	C₇×#3480	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₇×#2431	C₂
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. C₂×C₇×#529	C₂	semidirect
2. C₂×C₄×C₇×#41	C₂	semidirect
3. C₇×#2602	C₂	semidirect
4. C₇×#2601	C₂	semidirect
5. C₇×#2566	C₂	semidirect
6. C₇×#2565	C₂	semidirect
7. C₇×#2545	C₂	semidirect
8. C₇×#2544	C₂	semidirect
9. C₇×#2500	C₂	semidirect
10. C₇×#2499	C₂	semidirect
11. C₇×#2432	C₂	semidirect
13. C₇×#2392	C₂	semidirect
14. C₄×C₇×C₄⋊Q₈	C₂	semidirect
15. C₄×C₇×#127	C₂	semidirect
16. C₄×C₇×#124	C₂	semidirect
17. C₄×C₇×#124	C₂	semidirect
18. C₇×#2290	C₂	semidirect
19. C₄×C₇×#117	C₂	semidirect
93. #34910	C₇	direct (N × H)
167. C₂×C₄²×C₇	D₄	semidirect
194. C₂×#529	C₂×C₇	semidirect
195. C₂×C₄×#41	C₂×C₇	semidirect
196. #2602	C₂×C₇	semidirect
197. #2601	C₂×C₇	semidirect
198. #2566	C₂×C₇	semidirect
199. #2565	C₂×C₇	semidirect
200. #2545	C₂×C₇	semidirect
201. #2544	C₂×C₇	semidirect
202. #2500	C₂×C₇	semidirect
203. #2499	C₂×C₇	semidirect
204. #2432	C₂×C₇	semidirect
206. #2392	C₂×C₇	semidirect
207. C₄×C₄⋊Q₈	C₂×C₇	semidirect
208. C₄×#127	C₂×C₇	semidirect
209. C₄×#124	C₂×C₇	semidirect
210. C₄×#124	C₂×C₇	semidirect
211. #2290	C₂×C₇	semidirect
212. C₄×#117	C₂×C₇	semidirect
315. C₄²×C₇	#41	semidirect
532. C₂×C₄²	C₇×D₄	semidirect
697. C₄²	C₇×#41	semidirect
776. C₇	#34910	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#529	2
C₂×C₄×C₇×#41	2
C₇×#2602	2
C₇×#2601	2
C₇×#2566	2
C₇×#2565	2
C₇×#2545	2
C₇×#2544	2
C₇×#2500	2
C₇×#2499	2
C₇×#2432	2
C₇×#2431	2
C₇×#2392	2
C₄×C₇×C₄⋊Q₈	2
C₄×C₇×#127	2
C₄×C₇×#124	2
C₇×#2290	2
C₄×C₇×#117	2
#34910	7

Subgroups — C7×#34910 #13212126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34910 #13212126