Subgroups — C₇×#34432 #13211648

Order 1792.

2010 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#544	C₂	1	1	yes	maximal, characteristic
2	C₇×#2382	C₂	1	2	yes	maximal, complemented
3	C₇×#2381	C₂	1	2	yes	maximal, complemented
4	C₇×#2371	C₂	1	2	yes	maximal, complemented
5	C₇×#2368	C₂	1	2	yes	maximal
6	C₇×#2365	C₂	1	2	yes	maximal, complemented
7	C₇×#2360	C₂	1	2	yes	maximal
8	C₇×#2343	C₂	1	2	yes	maximal
9	C₇×#2343	C₂	1	2	yes	maximal
10	C₇×#2336	C₂	1	2	yes	maximal, complemented
11	C₇×#2336	C₂	1	2	yes	maximal, complemented
12	C₇×#2331	C₂	1	2	yes	maximal, complemented
13	C₇×#2329	C₂	1	1	yes	maximal, characteristic
14	C₇×#2329	C₂	1	1	yes	maximal, characteristic
15	C₇×#2327	C₂	1	2	yes	maximal, complemented
16	C₇×#2313	C₂	1	1	yes	maximal, characteristic
17	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
18	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
19	C₂×C₇×#387	C₂	1	1	yes	maximal, characteristic
20	C₇×#544	C₄	1	16	yes	complemented
21	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
22	C₂×C₇×C₄⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₇×#125	C₂²	1	2	yes	—
24	C₂×C₇×#125	C₂²	1	2	yes	—
25	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	2	yes	—
31	C₂×C₇×#117	C₂²	1	2	yes	—
32	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
33	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
35	C₇×#391	C₂²	1	1	yes	characteristic
36	C₇×#391	C₂²	1	1	yes	characteristic
37	C₇×#391	C₂²	1	2	yes	—
38	C₇×#391	C₂²	1	2	yes	—
39	C₇×#391	C₂²	1	2	yes	—
40	C₇×#391	C₂²	1	2	yes	—
41	C₇×#391	C₂²	1	2	yes	—
42	C₇×#389	C₂²	1	1	yes	characteristic
43	C₇×#389	C₂²	1	1	yes	characteristic
44	C₇×#389	C₂²	1	2	yes	—
45	C₇×#389	C₂²	1	2	yes	—
46	C₇×#389	C₂²	1	2	yes	—
47	C₇×#389	C₂²	1	2	yes	—
48	C₇×#389	C₂²	1	2	yes	—
49	C₇×#387	C₂²	1	2	yes	—
50	C₇×#387	C₂²	1	2	yes	—
51	C₇×#387	C₂²	1	2	yes	—
52	C₇×#387	C₂²	1	2	yes	—
53	C₇×#387	C₂²	1	2	yes	—
54	C₇×#387	C₂²	1	2	yes	—
55	C₇×#387	C₂²	1	2	yes	—
56	C₇×#387	C₂²	1	2	yes	—
57	C₇×#387	C₂²	1	2	yes	—
58	C₇×#387	C₂²	1	2	yes	—
59	C₇×#387	C₂²	1	2	yes	—
60	C₇×#387	C₂²	1	2	yes	—
61	C₇×#387	C₂²	1	2	yes	—
62	C₇×#387	C₂²	1	2	yes	—
63	C₇×#387	C₂²	1	2	yes	—
64	C₇×#387	C₂²	1	2	yes	—
65	C₇×#387	C₂²	1	2	yes	—
66	C₇×#387	C₂²	1	2	yes	—
67	C₇×#387	C₂²	1	2	yes	—
68	C₇×#387	C₂²	1	2	yes	—
69	C₇×#387	C₂²	1	2	yes	—
70	C₇×#387	C₂²	1	2	yes	—
71	C₇×#387	C₂²	1	2	yes	—
72	C₇×#387	C₂²	1	2	yes	—
73	C₇×#387	C₂²	1	2	yes	—
74	C₇×#387	C₂²	1	2	yes	—
75	C₇×#387	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	2	yes	—
77	C₇×#385	C₂²	1	2	yes	—
78	C₇×#385	C₂²	1	2	yes	—
79	C₇×#385	C₂²	1	2	yes	—
80	C₇×#385	C₂²	1	2	yes	—
81	C₇×#383	C₂²	1	2	yes	—
82	C₇×#383	C₂²	1	2	yes	—
83	C₇×#382	C₂²	1	2	yes	—
84	C₇×#382	C₂²	1	2	yes	—
85	C₇×#381	C₂²	1	2	yes	—
86	C₇×#380	C₂²	1	1	yes	characteristic
87	C₇×#380	C₂²	1	1	yes	characteristic
88	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
89	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
90	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
91	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
92	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
93	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
94	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
95	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₇×C₄⋊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	2	yes	—
102	C₇×#376	C₂²	1	2	yes	—
103	C₇×#376	C₂²	1	2	yes	—
104	C₂×C₇×#95	C₂²	1	1	yes	characteristic
105	C₂×C₇×#95	C₂²	1	1	yes	characteristic
106	C₂×C₇×#95	C₂²	1	1	yes	characteristic
107	C₂×C₇×#95	C₂²	1	1	yes	characteristic
108	#34432	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
110	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
111	C₂²×C₇×Q₈	C₂³	1	2	yes	—
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	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₇×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
120	C₇×C₄⋊Q₈	C₂×C₄	1	16	yes	complemented
121	C₇×#125	C₂×C₄	1	16	yes	complemented
122	C₇×#125	C₂×C₄	1	16	yes	complemented
123	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
124	C₇×C₂²⋊Q₈	C₂×C₄	1	8	yes	—
125	C₇×C₂²⋊Q₈	C₂×C₄	1	16	yes	—
126	C₄×C₇×Q₈	—	4	2	no	—
127	C₄×C₇×Q₈	—	4	2	no	—
128	C₄×C₇×Q₈	—	4	4	no	—
129	C₇×#117	C₂×C₄	1	16	yes	—
130	C₂×C₇×C₄⋊C₄	—	4	2	no	—
131	C₂×C₇×C₄⋊C₄	C₂×C₄	1	8	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	2	yes	—
142	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	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×C₄²×C₇	—	4	2	no	—
162	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
163	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₇	C₂³	1	2	yes	—
165	C₂×C₄²×C₇	C₂³	1	2	yes	—
166	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	2	yes	—
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	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	C₇×#95	C₂³	1	2	yes	—
209	C₇×#95	C₂³	1	2	yes	—
210	C₂×#544	C₂×C₇	1	1	yes	characteristic
211	#2382	C₂×C₇	1	2	yes	complemented
212	#2381	C₂×C₇	1	2	yes	complemented
213	#2371	C₂×C₇	1	2	yes	complemented
214	#2368	C₂×C₇	1	2	yes	—
215	#2365	C₂×C₇	1	2	yes	complemented
216	#2360	C₂×C₇	1	2	yes	—
217	#2343	C₂×C₇	1	2	yes	—
218	#2343	C₂×C₇	1	2	yes	—
219	#2336	C₂×C₇	1	2	yes	complemented
220	#2336	C₂×C₇	1	2	yes	complemented
221	#2331	C₂×C₇	1	2	yes	complemented
222	#2329	C₂×C₇	1	1	yes	characteristic
223	#2329	C₂×C₇	1	1	yes	characteristic
224	#2327	C₂×C₇	1	2	yes	complemented
225	#2313	C₂×C₇	1	1	yes	characteristic
226	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
227	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic
228	C₂×#387	C₂×C₇	1	1	yes	characteristic
229	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
230	C₂×C₇×Q₈	—	4	1	no	—
231	C₂×C₇×Q₈	—	4	1	no	—
232	C₂×C₇×Q₈	—	4	2	no	—
233	C₂×C₇×Q₈	—	4	2	no	—
234	C₂×C₇×Q₈	—	4	1	no	—
235	C₂×C₇×Q₈	—	4	1	no	—
236	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
237	C₂×C₇×Q₈	C₂²×C₄	1	4	yes	—
238	C₂×C₇×Q₈	C₂²×C₄	1	8	yes	—
239	C₂²×C₄×C₇	—	2	2	no	—
240	C₂²×C₄×C₇	—	2	2	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	—	4	1	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	C₂²×C₄	1	4	yes	—
258	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
259	C₂²×C₄×C₇	C₂²×C₄	1	4	yes	—
260	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
262	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
273	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
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	—	4	2	no	—
282	C₇×C₄⋊C₄	—	4	2	no	—
283	C₇×C₄⋊C₄	—	4	2	no	—
284	C₇×C₄⋊C₄	—	4	2	no	—
285	C₇×C₄⋊C₄	—	4	1	no	—
286	C₇×C₄⋊C₄	—	4	1	no	—
287	C₇×C₄⋊C₄	—	4	2	no	—
288	C₇×C₄⋊C₄	—	4	1	no	—
289	C₇×C₄⋊C₄	—	4	1	no	—
290	C₇×C₄⋊C₄	—	4	2	no	—
291	C₇×C₄⋊C₄	—	4	2	no	—
292	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
293	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
294	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
295	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
296	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
297	C₇×C₄⋊C₄	C₂²×C₄	1	4	yes	—
298	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
299	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
300	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
301	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
302	C₇×C₄⋊C₄	C₂²×C₄	1	8	yes	—
303	C₇×C₂²⋊C₄	—	2	4	no	—
304	C₇×C₂²⋊C₄	—	2	4	no	—
305	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
306	C₇×C₂²⋊C₄	C₂²×C₄	1	8	yes	—
307	C₄²×C₇	—	2	2	no	—
308	C₄²×C₇	—	2	2	no	—
309	C₄²×C₇	—	2	4	no	—
310	C₄²×C₇	—	2	4	no	—
311	C₄²×C₇	—	4	1	no	—
312	C₄²×C₇	—	4	1	no	—
313	C₄²×C₇	—	4	2	no	—
314	C₄²×C₇	—	4	2	no	—
315	C₄²×C₇	—	4	2	no	—
316	C₄²×C₇	—	4	2	no	—
317	C₄²×C₇	—	4	2	no	—
318	C₄²×C₇	—	4	2	no	—
319	C₄²×C₇	—	4	2	no	—
320	C₄²×C₇	—	4	2	no	—
321	C₄²×C₇	C₂²×C₄	1	8	yes	—
322	C₄²×C₇	C₂²×C₄	1	8	yes	—
323	#544	C₄×C₇	1	16	yes	complemented
324	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
325	C₂×C₄⋊Q₈	C₂²×C₇	1	2	yes	—
326	C₂×#125	C₂²×C₇	1	2	yes	—
327	C₂×#125	C₂²×C₇	1	2	yes	—
328	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
329	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
330	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
331	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
332	C₂×C₄×Q₈	C₂²×C₇	1	2	yes	—
333	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
334	C₂×#117	C₂²×C₇	1	2	yes	—
335	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
336	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
337	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
338	#391	C₂²×C₇	1	2	yes	—
339	#391	C₂²×C₇	1	2	yes	—
340	#391	C₂²×C₇	1	2	yes	—
341	#391	C₂²×C₇	1	1	yes	characteristic
342	#391	C₂²×C₇	1	2	yes	—
343	#391	C₂²×C₇	1	2	yes	—
344	#391	C₂²×C₇	1	1	yes	characteristic
345	#389	C₂²×C₇	1	2	yes	—
346	#389	C₂²×C₇	1	2	yes	—
347	#389	C₂²×C₇	1	2	yes	—
348	#389	C₂²×C₇	1	1	yes	characteristic
349	#389	C₂²×C₇	1	2	yes	—
350	#389	C₂²×C₇	1	2	yes	—
351	#389	C₂²×C₇	1	1	yes	characteristic
352	#387	C₂²×C₇	1	2	yes	—
353	#387	C₂²×C₇	1	2	yes	—
354	#387	C₂²×C₇	1	2	yes	—
355	#387	C₂²×C₇	1	2	yes	—
356	#387	C₂²×C₇	1	2	yes	—
357	#387	C₂²×C₇	1	2	yes	—
358	#387	C₂²×C₇	1	2	yes	—
359	#387	C₂²×C₇	1	2	yes	—
360	#387	C₂²×C₇	1	2	yes	—
361	#387	C₂²×C₇	1	2	yes	—
362	#387	C₂²×C₇	1	2	yes	—
363	#387	C₂²×C₇	1	2	yes	—
364	#387	C₂²×C₇	1	2	yes	—
365	#387	C₂²×C₇	1	2	yes	—
366	#387	C₂²×C₇	1	2	yes	—
367	#387	C₂²×C₇	1	2	yes	—
368	#387	C₂²×C₇	1	2	yes	—
369	#387	C₂²×C₇	1	2	yes	—
370	#387	C₂²×C₇	1	2	yes	—
371	#387	C₂²×C₇	1	2	yes	—
372	#387	C₂²×C₇	1	2	yes	—
373	#387	C₂²×C₇	1	2	yes	—
374	#387	C₂²×C₇	1	2	yes	—
375	#387	C₂²×C₇	1	2	yes	—
376	#387	C₂²×C₇	1	2	yes	—
377	#387	C₂²×C₇	1	2	yes	—
378	#387	C₂²×C₇	1	2	yes	—
379	#387	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	2	yes	—
384	#383	C₂²×C₇	1	2	yes	—
385	#383	C₂²×C₇	1	2	yes	—
386	#382	C₂²×C₇	1	2	yes	—
387	#382	C₂²×C₇	1	2	yes	—
388	#381	C₂²×C₇	1	2	yes	—
389	#380	C₂²×C₇	1	1	yes	characteristic
390	#380	C₂²×C₇	1	1	yes	characteristic
391	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
392	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
393	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
394	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
395	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
396	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
397	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
398	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
399	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
400	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
401	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
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	#376	C₂²×C₇	1	2	yes	—
406	#376	C₂²×C₇	1	2	yes	—
407	C₂×#95	C₂²×C₇	1	1	yes	characteristic
408	C₂×#95	C₂²×C₇	1	1	yes	characteristic
409	C₂×#95	C₂²×C₇	1	1	yes	characteristic
410	C₂×#95	C₂²×C₇	1	1	yes	characteristic
411	C₂³×C₇	—	2	1	no	—
412	C₂³×C₇	—	2	1	no	—
413	C₂³×C₇	—	2	1	no	—
414	C₂³×C₇	—	2	1	no	—
415	C₂³×C₇	C₂³×C₄	1	2	yes	—
416	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
417	C₂³×C₇	2₋¹⁺⁴	1	2	yes	—
418	C₂³×C₇	C₂⁵	1	1	yes	characteristic
419	C₇×Q₈	—	4	4	no	—
420	C₇×Q₈	—	4	4	no	—
421	C₇×Q₈	—	4	8	no	—
422	C₂×C₄×C₇	—	2	8	no	—
423	C₂×C₄×C₇	—	2	1	no	—
424	C₂×C₄×C₇	—	2	1	no	—
425	C₂×C₄×C₇	—	2	1	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	1	no	—
434	C₂×C₄×C₇	—	2	1	no	—
435	C₂×C₄×C₇	—	2	2	no	—
436	C₂×C₄×C₇	—	2	1	no	—
437	C₂×C₄×C₇	—	2	2	no	—
438	C₂×C₄×C₇	—	2	2	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	1	no	—
441	C₂×C₄×C₇	—	2	1	no	—
442	C₂×C₄×C₇	—	2	2	no	—
443	C₂×C₄×C₇	—	2	2	no	—
444	C₂×C₄×C₇	—	2	1	no	—
445	C₂×C₄×C₇	—	2	2	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	2	no	—
453	C₂×C₄×C₇	—	2	2	no	—
454	C₂×C₄×C₇	—	2	1	no	—
455	C₂×C₄×C₇	—	2	2	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	1	no	—
467	C₂×C₄×C₇	—	4	4	no	—
468	C₂×C₄×C₇	—	4	4	no	—
469	C₂×C₄×C₇	—	4	4	no	—
470	C₂×C₄×C₇	—	4	4	no	—
471	C₂×C₄×C₇	—	8	2	no	—
472	C₂×C₄×C₇	—	8	2	no	—
473	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
474	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
475	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
476	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
477	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
478	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
479	C₂×C₄×C₇	C₂³×C₄	1	2	yes	—
480	C₂×C₄×C₇	C₂³×C₄	1	4	yes	—
481	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
482	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
483	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
484	C₂²×Q₈	C₂³×C₇	1	2	yes	—
485	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
486	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
489	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
490	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
491	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
492	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
493	C₄⋊Q₈	C₂×C₄×C₇	1	16	yes	complemented
494	C₄⋊Q₈	C₂×C₄×C₇	1	16	yes	complemented
495	#125	C₂×C₄×C₇	1	16	yes	complemented
496	#125	C₂×C₄×C₇	1	16	yes	complemented
497	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
498	C₂²⋊Q₈	C₂×C₄×C₇	1	8	yes	—
499	C₂²⋊Q₈	C₂×C₄×C₇	1	16	yes	—
500	C₄×Q₈	—	4	2	no	—
501	C₄×Q₈	—	4	2	no	—
502	C₄×Q₈	—	4	4	no	—
503	#117	C₂×C₄×C₇	1	16	yes	—
504	C₂×C₄⋊C₄	—	4	2	no	—
505	C₂×C₄⋊C₄	C₂×C₄×C₇	1	8	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	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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	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	2	yes	—
524	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
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×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
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×C₄²	—	4	2	no	—
536	C₂×C₄²	C₂³×C₇	1	2	yes	—
537	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
538	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₇	1	2	yes	—
540	C₂×C₄²	C₂³×C₇	1	2	yes	—
541	C₂×C₄²	C₂³×C₇	1	2	yes	—
542	C₂×C₄²	C₂³×C₇	1	2	yes	—
543	C₂×C₄²	C₂³×C₇	1	2	yes	—
544	C₂×C₄²	C₂³×C₇	1	2	yes	—
545	C₂×C₄²	C₂³×C₇	1	2	yes	—
546	C₂×C₄²	C₂³×C₇	1	2	yes	—
547	C₂×C₄²	C₂³×C₇	1	2	yes	—
548	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
549	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
550	C₂×C₄²	C₂³×C₇	1	2	yes	—
551	C₂×C₄²	C₂³×C₇	1	2	yes	—
552	#95	C₂³×C₇	1	2	yes	—
553	#95	C₂³×C₇	1	2	yes	—
554	#95	C₂³×C₇	1	2	yes	—
555	#95	C₂³×C₇	1	2	yes	—
556	#95	C₂³×C₇	1	2	yes	—
557	#95	C₂³×C₇	1	2	yes	—
558	#95	C₂³×C₇	1	2	yes	—
559	#95	C₂³×C₇	1	2	yes	—
560	#95	C₂³×C₇	1	2	yes	—
561	#95	C₂³×C₇	1	2	yes	—
562	#95	C₂³×C₇	1	2	yes	—
563	#95	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	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	C₂²×C₇	—	2	2	no	—
585	C₂²×C₇	—	2	2	no	—
586	C₂²×C₇	—	2	2	no	—
587	C₂²×C₇	—	2	2	no	—
588	C₂²×C₇	—	2	2	no	—
589	C₂²×C₇	—	2	2	no	—
590	C₂²×C₇	#519	1	4	yes	—
591	C₂²×C₇	C₂⁴×C₄	1	1	yes	characteristic
592	C₂²×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
593	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
594	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
595	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
596	C₂²×C₇	#585	1	1	yes	characteristic
597	C₂²×C₇	#585	1	1	yes	characteristic
598	C₄×C₇	—	2	4	no	—
599	C₄×C₇	—	2	2	no	—
600	C₄×C₇	—	2	2	no	—
601	C₄×C₇	—	2	4	no	—
602	C₄×C₇	—	2	4	no	—
603	C₄×C₇	—	2	4	no	—
604	C₄×C₇	—	2	4	no	—
605	C₄×C₇	—	2	4	no	—
606	C₄×C₇	—	2	2	no	—
607	C₄×C₇	—	2	2	no	—
608	C₄×C₇	—	4	2	no	—
609	C₄×C₇	—	4	1	no	—
610	C₄×C₇	—	4	2	no	—
611	C₄×C₇	—	4	2	no	—
612	C₄×C₇	—	4	1	no	—
613	C₄×C₇	—	4	2	no	—
614	C₄×C₇	—	4	2	no	—
615	C₄×C₇	—	4	2	no	—
616	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
617	C₂×Q₈	—	4	1	no	—
618	C₂×Q₈	—	4	1	no	—
619	C₂×Q₈	—	4	2	no	—
620	C₂×Q₈	—	4	2	no	—
621	C₂×Q₈	—	4	1	no	—
622	C₂×Q₈	—	4	1	no	—
623	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
624	C₂×Q₈	C₂²×C₄×C₇	1	4	yes	—
625	C₂×Q₈	C₂²×C₄×C₇	1	8	yes	—
626	C₂²×C₄	—	2	2	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	2	no	—
629	C₂²×C₄	—	2	2	no	—
630	C₂²×C₄	—	2	2	no	—
631	C₂²×C₄	—	2	2	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	4	1	no	—
635	C₂²×C₄	—	4	1	no	—
636	C₂²×C₄	—	4	1	no	—
637	C₂²×C₄	—	4	1	no	—
638	C₂²×C₄	—	4	1	no	—
639	C₂²×C₄	—	4	1	no	—
640	C₂²×C₄	—	4	1	no	—
641	C₂²×C₄	—	4	1	no	—
642	C₂²×C₄	—	4	1	no	—
643	C₂²×C₄	—	4	1	no	—
644	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
645	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
646	C₂²×C₄	C₂²×C₄×C₇	1	4	yes	—
647	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
648	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
649	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
650	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
651	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
652	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
653	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
656	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
657	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
658	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
659	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
660	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
661	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
662	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
665	C₄⋊C₄	—	2	4	no	—
666	C₄⋊C₄	—	2	4	no	—
667	C₄⋊C₄	—	2	4	no	—
668	C₄⋊C₄	—	4	2	no	—
669	C₄⋊C₄	—	4	1	no	—
670	C₄⋊C₄	—	4	1	no	—
671	C₄⋊C₄	—	4	2	no	—
672	C₄⋊C₄	—	4	2	no	—
673	C₄⋊C₄	—	4	2	no	—
674	C₄⋊C₄	—	4	2	no	—
675	C₄⋊C₄	—	4	2	no	—
676	C₄⋊C₄	—	4	1	no	—
677	C₄⋊C₄	—	4	1	no	—
678	C₄⋊C₄	—	4	2	no	—
679	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
680	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
681	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
682	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
683	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
684	C₄⋊C₄	C₂²×C₄×C₇	1	4	yes	—
685	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
686	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
687	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
688	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
689	C₄⋊C₄	C₂²×C₄×C₇	1	8	yes	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	4	no	—
692	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
693	C₂²⋊C₄	C₂²×C₄×C₇	1	8	yes	—
694	C₄²	—	2	2	no	—
695	C₄²	—	2	2	no	—
696	C₄²	—	2	4	no	—
697	C₄²	—	2	4	no	—
698	C₄²	—	4	1	no	—
699	C₄²	—	4	1	no	—
700	C₄²	—	4	2	no	—
701	C₄²	—	4	2	no	—
702	C₄²	—	4	2	no	—
703	C₄²	—	4	2	no	—
704	C₄²	—	4	2	no	—
705	C₄²	—	4	2	no	—
706	C₄²	—	4	2	no	—
707	C₄²	—	4	2	no	—
708	C₄²	C₂²×C₄×C₇	1	8	yes	—
709	C₄²	C₂²×C₄×C₇	1	8	yes	—
710	C₂×C₇	—	2	4	no	—
711	C₂×C₇	C₂×#519	1	1	yes	characteristic
712	C₂×C₇	C₄×H(5,𝔽₂)	1	1	yes	characteristic
713	C₂×C₇	C₄×2₋¹⁺⁴	1	1	yes	characteristic
714	C₂×C₇	#3535	1	1	yes	characteristic
715	C₂×C₇	#3538	1	1	yes	characteristic
716	C₂×C₇	#3563	1	1	yes	characteristic
717	C₂×C₇	#3564	1	1	yes	characteristic
718	C₂³	—	2	1	no	—
719	C₂³	—	2	1	no	—
720	C₂³	—	2	1	no	—
721	C₂³	—	2	1	no	—
722	C₂³	C₂³×C₄×C₇	1	2	yes	—
723	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
724	C₂³	C₇×2₋¹⁺⁴	1	2	yes	—
725	C₂³	C₂⁵×C₇	1	1	yes	characteristic
726	Q₈	—	4	4	no	—
727	Q₈	—	4	4	no	—
728	Q₈	—	4	8	no	—
729	C₂×C₄	—	2	1	no	—
730	C₂×C₄	—	2	1	no	—
731	C₂×C₄	—	2	1	no	—
732	C₂×C₄	—	2	2	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	2	no	—
739	C₂×C₄	—	2	1	no	—
740	C₂×C₄	—	2	1	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	1	no	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	2	no	—
745	C₂×C₄	—	2	2	no	—
746	C₂×C₄	—	2	1	no	—
747	C₂×C₄	—	2	1	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	8	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	1	no	—
752	C₂×C₄	—	2	2	no	—
753	C₂×C₄	—	2	1	no	—
754	C₂×C₄	—	2	2	no	—
755	C₂×C₄	—	2	2	no	—
756	C₂×C₄	—	2	2	no	—
757	C₂×C₄	—	2	2	no	—
758	C₂×C₄	—	2	2	no	—
759	C₂×C₄	—	2	2	no	—
760	C₂×C₄	—	2	2	no	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	2	no	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	2	no	—
767	C₂×C₄	—	2	2	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	1	no	—
774	C₂×C₄	—	4	4	no	—
775	C₂×C₄	—	4	4	no	—
776	C₂×C₄	—	4	4	no	—
777	C₂×C₄	—	4	4	no	—
778	C₂×C₄	—	8	2	no	—
779	C₂×C₄	—	8	2	no	—
780	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
781	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
782	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
783	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
784	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
785	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
786	C₂×C₄	C₂³×C₄×C₇	1	2	yes	—
787	C₂×C₄	C₂³×C₄×C₇	1	4	yes	—
788	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
789	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
790	C₇	#34432	1	1	yes	characteristic, direct product factor, Sylow
791	C₂²	—	2	2	no	—
792	C₂²	—	2	2	no	—
793	C₂²	—	2	2	no	—
794	C₂²	—	2	2	no	—
795	C₂²	—	2	2	no	—
796	C₂²	—	2	2	no	—
797	C₂²	C₇×#519	1	4	yes	—
798	C₂²	C₂⁴×C₄×C₇	1	1	yes	characteristic
799	C₂²	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
800	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
801	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
802	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
803	C₂²	C₇×#585	1	1	yes	characteristic
804	C₂²	C₇×#585	1	1	yes	characteristic
805	C₄	—	2	4	no	—
806	C₄	—	2	2	no	—
807	C₄	—	2	2	no	—
808	C₄	—	2	4	no	—
809	C₄	—	2	4	no	—
810	C₄	—	2	4	no	—
811	C₄	—	2	4	no	—
812	C₄	—	2	4	no	—
813	C₄	—	2	2	no	—
814	C₄	—	2	2	no	—
815	C₄	—	4	2	no	—
816	C₄	—	4	2	no	—
817	C₄	—	4	2	no	—
818	C₄	—	4	1	no	—
819	C₄	—	4	2	no	—
820	C₄	—	4	2	no	—
821	C₄	—	4	1	no	—
822	C₄	—	4	2	no	—
823	C₂	—	2	4	no	—
824	C₂	C₂×C₇×#519	1	1	yes	characteristic
825	C₂	C₄×C₇×H(5,𝔽₂)	1	1	yes	characteristic
826	C₂	C₄×C₇×2₋¹⁺⁴	1	1	yes	characteristic
827	C₂	C₇×#3535	1	1	yes	characteristic
828	C₂	C₇×#3538	1	1	yes	characteristic
829	C₂	C₇×#3563	1	1	yes	characteristic
830	C₂	C₇×#3564	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₇×#2382	C₂	semidirect
3. C₇×#2381	C₂	semidirect
4. C₇×#2371	C₂	semidirect
6. C₇×#2365	C₂	semidirect
10. C₇×#2336	C₂	semidirect
11. C₇×#2336	C₂	semidirect
12. C₇×#2331	C₂	semidirect
15. C₇×#2327	C₂	semidirect
20. C₇×#544	C₄	semidirect
108. #34432	C₇	direct (N × H)
119. C₇×C₄⋊Q₈	C₂×C₄	semidirect
120. C₇×C₄⋊Q₈	C₂×C₄	semidirect
121. C₇×#125	C₂×C₄	semidirect
122. C₇×#125	C₂×C₄	semidirect
211. #2382	C₂×C₇	semidirect
212. #2381	C₂×C₇	semidirect
213. #2371	C₂×C₇	semidirect
215. #2365	C₂×C₇	semidirect
219. #2336	C₂×C₇	semidirect
220. #2336	C₂×C₇	semidirect
221. #2331	C₂×C₇	semidirect
224. #2327	C₂×C₇	semidirect
323. #544	C₄×C₇	semidirect
493. C₄⋊Q₈	C₂×C₄×C₇	semidirect
494. C₄⋊Q₈	C₂×C₄×C₇	semidirect
495. #125	C₂×C₄×C₇	semidirect
496. #125	C₂×C₄×C₇	semidirect
790. C₇	#34432	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×#544	2
C₇×#2382	2
C₇×#2381	2
C₇×#2371	2
C₇×#2368	2
C₇×#2365	2
C₇×#2360	2
C₇×#2343	2
C₇×#2336	2
C₇×#2331	2
C₇×#2329	2
C₇×#2327	2
C₇×#2313	2
C₄×C₇×C₂²⋊Q₈	2
C₂×C₇×#387	2
#34432	7

Subgroups — C7×#34432 #13211648

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34432 #13211648