Subgroups — C₇×#34780 #13211996

Order 1792.

1848 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2524	C₂	1	2	yes	maximal, complemented
2	C₇×#2515	C₂	1	2	yes	maximal, complemented
3	C₇×#2514	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2508	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2503	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2495	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2493	C₂	1	2	yes	maximal, complemented
8	C₇×#2489	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#2486	C₂	1	1	yes	maximal, characteristic
10	C₇×#2442	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#2419	C₂	1	2	yes	maximal
12	C₇×#2417	C₂	1	1	yes	maximal, characteristic
13	C₇×#2402	C₂	1	2	yes	maximal, complemented
14	C₇×#2401	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
18	C₄×C₇×#123	C₂	1	2	yes	maximal
19	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2283	C₂	1	2	yes	maximal, complemented
21	C₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄²×C₇×D₄	C₂	1	1	yes	maximal, characteristic
23	C₂×C₄×C₇×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#125	C₂²	1	1	yes	characteristic
25	C₂×C₇×#123	C₂²	1	2	yes	—
26	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
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	C₂²×C₄²×C₇	C₂²	1	2	yes	—
36	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
37	C₇×#401	C₂²	1	2	yes	—
38	C₇×#400	C₂²	1	2	yes	—
39	C₇×#400	C₂²	1	2	yes	—
40	C₇×#400	C₂²	1	2	yes	—
41	C₇×#400	C₂²	1	2	yes	—
42	C₇×#400	C₂²	1	2	yes	—
43	C₇×#400	C₂²	1	2	yes	—
44	C₇×#400	C₂²	1	2	yes	—
45	C₇×#398	C₂²	1	2	yes	—
46	C₇×#398	C₂²	1	2	yes	—
47	C₇×#398	C₂²	1	2	yes	—
48	C₇×#398	C₂²	1	2	yes	—
49	C₇×#397	C₂²	1	2	yes	—
50	C₇×#397	C₂²	1	2	yes	—
51	C₇×#397	C₂²	1	2	yes	—
52	C₇×#396	C₂²	1	2	yes	—
53	C₇×#391	C₂²	1	1	yes	characteristic
54	C₇×#391	C₂²	1	1	yes	characteristic
55	C₇×#391	C₂²	1	1	yes	characteristic
56	C₇×#391	C₂²	1	1	yes	characteristic
57	C₇×#389	C₂²	1	1	yes	characteristic
58	C₇×#389	C₂²	1	1	yes	characteristic
59	C₇×#389	C₂²	1	1	yes	characteristic
60	C₇×#389	C₂²	1	1	yes	characteristic
61	C₇×#389	C₂²	1	1	yes	characteristic
62	C₇×#389	C₂²	1	1	yes	characteristic
63	C₇×#388	C₂²	1	2	yes	—
64	C₇×#388	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×#386	C₂²	1	2	yes	—
74	C₇×#385	C₂²	1	2	yes	—
75	C₇×#385	C₂²	1	2	yes	—
76	C₇×#385	C₂²	1	2	yes	—
77	C₇×#383	C₂²	1	2	yes	—
78	C₇×#383	C₂²	1	2	yes	—
79	C₇×#383	C₂²	1	2	yes	—
80	C₇×#382	C₂²	1	1	yes	characteristic
81	C₇×#382	C₂²	1	2	yes	—
82	C₇×#382	C₂²	1	1	yes	characteristic
83	C₇×#382	C₂²	1	1	yes	characteristic
84	C₇×#382	C₂²	1	2	yes	—
85	C₇×#381	C₂²	1	2	yes	—
86	C₇×#381	C₂²	1	2	yes	—
87	C₇×#381	C₂²	1	2	yes	—
88	C₇×#381	C₂²	1	2	yes	—
89	C₇×#380	C₂²	1	2	yes	—
90	C₇×#380	C₂²	1	1	yes	characteristic
91	C₇×#380	C₂²	1	2	yes	—
92	C₇×#380	C₂²	1	1	yes	characteristic
93	C₇×#380	C₂²	1	1	yes	characteristic
94	C₇×#380	C₂²	1	1	yes	characteristic
95	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
96	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
97	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
98	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
99	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
100	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
101	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
102	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
103	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
106	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
107	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
108	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
109	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
110	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
111	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
114	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
115	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
116	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
117	C₄×C₇×C₂²⋊C₄	C₂²	1	1	yes	characteristic
118	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
119	C₇×#376	C₂²	1	2	yes	—
120	C₇×#376	C₂²	1	2	yes	—
121	C₂×C₇×#95	C₂²	1	2	yes	—
122	C₄³×C₇	C₂²	1	1	yes	characteristic
123	#34780	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
126	C₂³×C₄×C₇	C₂³	1	2	yes	—
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇	C₂³	1	2	yes	—
131	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₇×#125	—	2	4	no	—
135	C₇×#123	—	2	8	no	—
136	C₇×C₂²⋊Q₈	—	2	4	no	—
137	C₇×C₂²⋊Q₈	—	2	4	no	—
138	C₄×C₇×Q₈	—	2	4	no	—
139	C₄×C₇×D₄	—	2	4	no	—
140	C₄×C₇×D₄	—	2	4	no	—
141	C₄×C₇×D₄	—	2	4	no	—
142	C₂×C₇×C₄⋊C₄	—	2	4	no	—
143	C₂×C₇×C₄⋊C₄	—	2	4	no	—
144	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	1	yes	characteristic
153	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
162	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
168	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
169	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
170	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
171	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
172	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
179	C₂×C₄²×C₇	—	2	8	no	—
180	C₂×C₄²×C₇	—	2	4	no	—
181	C₂×C₄²×C₇	—	2	4	no	—
182	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
184	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
185	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇	C₂³	1	2	yes	—
190	C₂×C₄²×C₇	C₂³	1	2	yes	—
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	2	yes	—
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	2	yes	—
197	C₂×C₄²×C₇	C₂³	1	2	yes	—
198	C₂×C₄²×C₇	C₂³	1	2	yes	—
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
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	C₇×#95	C₂³	1	2	yes	—
211	C₇×#95	C₂³	1	2	yes	—
212	C₇×#95	C₂³	1	2	yes	—
213	C₇×#95	C₂³	1	1	yes	characteristic
214	C₇×#95	C₂³	1	1	yes	characteristic
215	C₇×#95	C₂³	1	1	yes	characteristic
216	C₇×#95	C₂³	1	1	yes	characteristic
217	C₇×#95	C₂³	1	1	yes	characteristic
218	C₇×#95	C₂³	1	1	yes	characteristic
219	C₇×#95	C₂³	1	2	yes	—
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	2	yes	—
222	C₇×#95	C₂³	1	2	yes	—
223	C₇×#95	C₂³	1	2	yes	—
224	C₇×#95	C₂³	1	2	yes	—
225	C₇×#95	C₂³	1	2	yes	—
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	2	yes	—
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	#2524	C₂×C₇	1	2	yes	complemented
237	#2515	C₂×C₇	1	2	yes	complemented
238	#2514	C₂×C₇	1	1	yes	characteristic, complemented
239	#2508	C₂×C₇	1	1	yes	characteristic, complemented
240	#2503	C₂×C₇	1	1	yes	characteristic, complemented
241	#2495	C₂×C₇	1	1	yes	characteristic, complemented
242	#2493	C₂×C₇	1	2	yes	complemented
243	#2489	C₂×C₇	1	1	yes	characteristic, complemented
244	#2486	C₂×C₇	1	1	yes	characteristic
245	#2442	C₂×C₇	1	1	yes	characteristic, complemented
246	#2419	C₂×C₇	1	2	yes	—
247	#2417	C₂×C₇	1	1	yes	characteristic
248	#2402	C₂×C₇	1	2	yes	complemented
249	#2401	C₂×C₇	1	2	yes	complemented
250	C₄×#125	C₂×C₇	1	1	yes	characteristic, complemented
251	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
252	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
253	C₄×#123	C₂×C₇	1	2	yes	—
254	#2295	C₂×C₇	1	1	yes	characteristic, complemented
255	#2283	C₂×C₇	1	2	yes	complemented
256	#2283	C₂×C₇	1	1	yes	characteristic, complemented
257	C₄²×D₄	C₂×C₇	1	1	yes	characteristic
258	C₂×C₄×C₄⋊C₄	C₂×C₇	1	1	yes	characteristic, complemented
259	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
260	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
261	C₂×C₇×Q₈	—	2	2	no	—
262	C₂×C₇×Q₈	—	2	2	no	—
263	C₂×C₇×Q₈	—	2	2	no	—
264	C₂×C₇×D₄	—	2	2	no	—
265	C₂×C₇×D₄	—	2	2	no	—
266	C₂×C₇×D₄	#41	1	4	yes	—
267	C₂²×C₄×C₇	—	2	2	no	—
268	C₂²×C₄×C₇	—	2	2	no	—
269	C₂²×C₄×C₇	—	2	2	no	—
270	C₂²×C₄×C₇	—	2	2	no	—
271	C₂²×C₄×C₇	—	2	4	no	—
272	C₂²×C₄×C₇	—	2	4	no	—
273	C₂²×C₄×C₇	—	2	4	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	4	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	4	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	2	no	—
284	C₂²×C₄×C₇	—	2	2	no	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	4	1	no	—
287	C₂²×C₄×C₇	—	4	1	no	—
288	C₂²×C₄×C₇	—	4	2	no	—
289	C₂²×C₄×C₇	#41	1	4	yes	—
290	C₂²×C₄×C₇	#41	1	4	yes	—
291	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
295	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
296	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
312	C₇×C₄⋊C₄	—	2	4	no	—
313	C₇×C₄⋊C₄	—	2	4	no	—
314	C₇×C₄⋊C₄	—	2	2	no	—
315	C₇×C₄⋊C₄	—	2	2	no	—
316	C₇×C₄⋊C₄	—	2	2	no	—
317	C₇×C₄⋊C₄	—	2	2	no	—
318	C₇×C₄⋊C₄	—	2	2	no	—
319	C₇×C₄⋊C₄	—	2	2	no	—
320	C₇×C₄⋊C₄	—	2	2	no	—
321	C₇×C₄⋊C₄	—	2	4	no	—
322	C₇×C₄⋊C₄	—	2	2	no	—
323	C₇×C₄⋊C₄	—	2	4	no	—
324	C₇×C₄⋊C₄	—	2	4	no	—
325	C₇×C₄⋊C₄	—	2	4	no	—
326	C₇×C₄⋊C₄	—	2	4	no	—
327	C₇×C₄⋊C₄	—	2	4	no	—
328	C₇×C₄⋊C₄	—	2	4	no	—
329	C₇×C₄⋊C₄	—	2	2	no	—
330	C₇×C₄⋊C₄	—	4	2	no	—
331	C₇×C₄⋊C₄	—	4	2	no	—
332	C₇×C₄⋊C₄	—	4	2	no	—
333	C₇×C₄⋊C₄	—	4	2	no	—
334	C₇×C₄⋊C₄	#41	1	4	yes	—
335	C₇×C₂²⋊C₄	—	2	2	no	—
336	C₇×C₂²⋊C₄	—	2	2	no	—
337	C₇×C₂²⋊C₄	—	2	2	no	—
338	C₇×C₂²⋊C₄	—	2	2	no	—
339	C₇×C₂²⋊C₄	—	2	4	no	—
340	C₇×C₂²⋊C₄	—	2	4	no	—
341	C₇×C₂²⋊C₄	—	2	4	no	—
342	C₇×C₂²⋊C₄	—	2	4	no	—
343	C₇×C₂²⋊C₄	—	2	2	no	—
344	C₇×C₂²⋊C₄	—	2	2	no	—
345	C₇×C₂²⋊C₄	—	2	4	no	—
346	C₇×C₂²⋊C₄	—	4	2	no	—
347	C₄²×C₇	—	2	2	no	—
348	C₄²×C₇	—	2	4	no	—
349	C₄²×C₇	—	2	2	no	—
350	C₄²×C₇	—	2	4	no	—
351	C₄²×C₇	—	2	2	no	—
352	C₄²×C₇	—	2	4	no	—
353	C₄²×C₇	—	2	2	no	—
354	C₄²×C₇	—	2	2	no	—
355	C₄²×C₇	—	2	4	no	—
356	C₄²×C₇	—	2	2	no	—
357	C₄²×C₇	—	2	2	no	—
358	C₄²×C₇	—	2	2	no	—
359	C₄²×C₇	—	2	2	no	—
360	C₄²×C₇	—	2	4	no	—
361	C₄²×C₇	—	2	2	no	—
362	C₄²×C₇	—	2	2	no	—
363	C₄²×C₇	—	2	4	no	—
364	C₄²×C₇	—	4	1	no	—
365	C₄²×C₇	#41	1	4	yes	—
366	C₂×#125	C₂²×C₇	1	1	yes	characteristic
367	C₂×#123	C₂²×C₇	1	2	yes	—
368	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
369	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
370	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
372	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
373	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
374	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
375	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
376	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
377	C₂²×C₄²	C₂²×C₇	1	2	yes	—
378	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
379	#401	C₂²×C₇	1	2	yes	—
380	#400	C₂²×C₇	1	2	yes	—
381	#400	C₂²×C₇	1	2	yes	—
382	#400	C₂²×C₇	1	2	yes	—
383	#400	C₂²×C₇	1	2	yes	—
384	#400	C₂²×C₇	1	2	yes	—
385	#400	C₂²×C₇	1	2	yes	—
386	#400	C₂²×C₇	1	2	yes	—
387	#398	C₂²×C₇	1	2	yes	—
388	#398	C₂²×C₇	1	2	yes	—
389	#398	C₂²×C₇	1	2	yes	—
390	#398	C₂²×C₇	1	2	yes	—
391	#397	C₂²×C₇	1	2	yes	—
392	#397	C₂²×C₇	1	2	yes	—
393	#397	C₂²×C₇	1	2	yes	—
394	#396	C₂²×C₇	1	2	yes	—
395	#391	C₂²×C₇	1	1	yes	characteristic
396	#391	C₂²×C₇	1	1	yes	characteristic
397	#391	C₂²×C₇	1	1	yes	characteristic
398	#391	C₂²×C₇	1	1	yes	characteristic
399	#389	C₂²×C₇	1	1	yes	characteristic
400	#389	C₂²×C₇	1	1	yes	characteristic
401	#389	C₂²×C₇	1	1	yes	characteristic
402	#389	C₂²×C₇	1	1	yes	characteristic
403	#389	C₂²×C₇	1	1	yes	characteristic
404	#389	C₂²×C₇	1	1	yes	characteristic
405	#388	C₂²×C₇	1	2	yes	—
406	#388	C₂²×C₇	1	2	yes	—
407	#387	C₂²×C₇	1	2	yes	—
408	#387	C₂²×C₇	1	2	yes	—
409	#387	C₂²×C₇	1	2	yes	—
410	#387	C₂²×C₇	1	2	yes	—
411	#387	C₂²×C₇	1	2	yes	—
412	#387	C₂²×C₇	1	2	yes	—
413	#387	C₂²×C₇	1	2	yes	—
414	#387	C₂²×C₇	1	2	yes	—
415	#386	C₂²×C₇	1	2	yes	—
416	#385	C₂²×C₇	1	2	yes	—
417	#385	C₂²×C₇	1	2	yes	—
418	#385	C₂²×C₇	1	2	yes	—
419	#383	C₂²×C₇	1	2	yes	—
420	#383	C₂²×C₇	1	2	yes	—
421	#383	C₂²×C₇	1	2	yes	—
422	#382	C₂²×C₇	1	1	yes	characteristic
423	#382	C₂²×C₇	1	1	yes	characteristic
424	#382	C₂²×C₇	1	2	yes	—
425	#382	C₂²×C₇	1	1	yes	characteristic
426	#382	C₂²×C₇	1	2	yes	—
427	#381	C₂²×C₇	1	2	yes	—
428	#381	C₂²×C₇	1	2	yes	—
429	#381	C₂²×C₇	1	2	yes	—
430	#381	C₂²×C₇	1	2	yes	—
431	#380	C₂²×C₇	1	2	yes	—
432	#380	C₂²×C₇	1	1	yes	characteristic
433	#380	C₂²×C₇	1	2	yes	—
434	#380	C₂²×C₇	1	1	yes	characteristic
435	#380	C₂²×C₇	1	1	yes	characteristic
436	#380	C₂²×C₇	1	1	yes	characteristic
437	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
438	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
439	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
440	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
441	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
442	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
443	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
444	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
445	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
446	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
447	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
448	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
449	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
450	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
451	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
452	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
453	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
454	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
455	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
456	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
457	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
458	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
459	C₄×C₂²⋊C₄	C₂²×C₇	1	1	yes	characteristic
460	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
461	#376	C₂²×C₇	1	2	yes	—
462	#376	C₂²×C₇	1	2	yes	—
463	C₂×#95	C₂²×C₇	1	2	yes	—
464	C₄³	C₂²×C₇	1	1	yes	characteristic
465	C₂³×C₇	—	2	1	no	—
466	C₂³×C₇	—	2	1	no	—
467	C₂³×C₇	—	2	1	no	—
468	C₂³×C₇	—	2	1	no	—
469	C₂³×C₇	—	2	1	no	—
470	C₂³×C₇	—	2	1	no	—
471	C₂³×C₇	—	2	1	no	—
472	C₂³×C₇	—	2	1	no	—
473	C₂³×C₇	—	2	1	no	—
474	C₂³×C₇	—	2	1	no	—
475	C₂³×C₇	C₂×#41	1	2	yes	—
476	C₂³×C₇	C₂×#41	1	2	yes	—
477	C₂³×C₇	C₂×#41	1	2	yes	—
478	C₂³×C₇	C₂×#41	1	2	yes	—
479	C₂³×C₇	C₂⁵	1	1	yes	characteristic
480	C₇×Q₈	—	4	4	no	—
481	C₇×D₄	—	2	8	no	—
482	C₂×C₄×C₇	—	2	1	no	—
483	C₂×C₄×C₇	—	2	1	no	—
484	C₂×C₄×C₇	—	2	2	no	—
485	C₂×C₄×C₇	—	2	1	no	—
486	C₂×C₄×C₇	—	2	1	no	—
487	C₂×C₄×C₇	—	2	1	no	—
488	C₂×C₄×C₇	—	2	1	no	—
489	C₂×C₄×C₇	—	2	1	no	—
490	C₂×C₄×C₇	—	2	1	no	—
491	C₂×C₄×C₇	—	2	2	no	—
492	C₂×C₄×C₇	—	2	8	no	—
493	C₂×C₄×C₇	—	2	8	no	—
494	C₂×C₄×C₇	—	2	2	no	—
495	C₂×C₄×C₇	—	2	2	no	—
496	C₂×C₄×C₇	—	2	1	no	—
497	C₂×C₄×C₇	—	2	1	no	—
498	C₂×C₄×C₇	—	2	2	no	—
499	C₂×C₄×C₇	—	2	1	no	—
500	C₂×C₄×C₇	—	2	1	no	—
501	C₂×C₄×C₇	—	2	1	no	—
502	C₂×C₄×C₇	—	2	1	no	—
503	C₂×C₄×C₇	—	2	1	no	—
504	C₂×C₄×C₇	—	2	2	no	—
505	C₂×C₄×C₇	—	2	1	no	—
506	C₂×C₄×C₇	—	2	1	no	—
507	C₂×C₄×C₇	—	2	2	no	—
508	C₂×C₄×C₇	—	2	2	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	1	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	2	2	no	—
519	C₂×C₄×C₇	—	2	2	no	—
520	C₂×C₄×C₇	—	2	2	no	—
521	C₂×C₄×C₇	—	2	2	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	2	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	2	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	2	no	—
528	C₂×C₄×C₇	—	2	1	no	—
529	C₂×C₄×C₇	—	2	1	no	—
530	C₂×C₄×C₇	—	2	1	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	1	no	—
535	C₂×C₄×C₇	—	2	1	no	—
536	C₂×C₄×C₇	—	4	4	no	—
537	C₂×C₄×C₇	—	4	4	no	—
538	C₂×C₄×C₇	—	4	8	no	—
539	C₂×C₄×C₇	—	4	8	no	—
540	C₂×C₄×C₇	—	4	4	no	—
541	C₂×C₄×C₇	—	4	4	no	—
542	C₂×C₄×C₇	C₂×#41	1	2	yes	—
543	C₂×C₄×C₇	C₂×#41	1	2	yes	—
544	C₂×C₄×C₇	C₂×#41	1	2	yes	—
545	C₂×C₄×C₇	C₂×#41	1	2	yes	—
546	C₂×C₄×C₇	C₂×#41	1	4	yes	—
547	C₂×C₄×C₇	C₂×#41	1	2	yes	—
548	C₂×C₄×C₇	C₂×#41	1	2	yes	—
549	C₂×C₄×C₇	C₂×#41	1	2	yes	—
550	C₂×C₄×C₇	C₂×#41	1	2	yes	—
551	C₂×C₄×C₇	C₂×#41	1	2	yes	—
552	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
553	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
554	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
555	C₂³×C₄	C₂³×C₇	1	2	yes	—
556	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₇	1	2	yes	—
559	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
562	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
563	#125	—	2	4	no	—
564	#123	—	2	8	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	—	2	4	no	—
567	C₄×Q₈	—	2	4	no	—
568	C₄×D₄	—	2	4	no	—
569	C₄×D₄	—	2	4	no	—
570	C₄×D₄	—	2	4	no	—
571	C₂×C₄⋊C₄	—	2	4	no	—
572	C₂×C₄⋊C₄	—	2	4	no	—
573	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
574	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
575	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
577	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
579	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
580	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
581	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
583	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
585	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
586	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
587	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
588	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
589	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
590	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
591	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
592	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
595	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
597	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
599	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
608	C₂×C₄²	—	2	8	no	—
609	C₂×C₄²	—	2	4	no	—
610	C₂×C₄²	—	2	4	no	—
611	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
612	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
613	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
614	C₂×C₄²	C₂³×C₇	1	2	yes	—
615	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
616	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
617	C₂×C₄²	C₂³×C₇	1	2	yes	—
618	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
619	C₂×C₄²	C₂³×C₇	1	2	yes	—
620	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₇	1	2	yes	—
622	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
623	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
624	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
625	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
626	C₂×C₄²	C₂³×C₇	1	2	yes	—
627	C₂×C₄²	C₂³×C₇	1	2	yes	—
628	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
629	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
630	#95	C₂³×C₇	1	2	yes	—
631	#95	C₂³×C₇	1	2	yes	—
632	#95	C₂³×C₇	1	2	yes	—
633	#95	C₂³×C₇	1	2	yes	—
634	#95	C₂³×C₇	1	2	yes	—
635	#95	C₂³×C₇	1	2	yes	—
636	#95	C₂³×C₇	1	2	yes	—
637	#95	C₂³×C₇	1	2	yes	—
638	#95	C₂³×C₇	1	2	yes	—
639	#95	C₂³×C₇	1	2	yes	—
640	#95	C₂³×C₇	1	2	yes	—
641	#95	C₂³×C₇	1	2	yes	—
642	#95	C₂³×C₇	1	1	yes	characteristic
643	#95	C₂³×C₇	1	1	yes	characteristic
644	#95	C₂³×C₇	1	1	yes	characteristic
645	#95	C₂³×C₇	1	1	yes	characteristic
646	#95	C₂³×C₇	1	1	yes	characteristic
647	#95	C₂³×C₇	1	1	yes	characteristic
648	#95	C₂³×C₇	1	2	yes	—
649	#95	C₂³×C₇	1	2	yes	—
650	#95	C₂³×C₇	1	2	yes	—
651	#95	C₂³×C₇	1	2	yes	—
652	#95	C₂³×C₇	1	2	yes	—
653	#95	C₂³×C₇	1	2	yes	—
654	#95	C₂³×C₇	1	2	yes	—
655	#95	C₂³×C₇	1	2	yes	—
656	#95	C₂³×C₇	1	2	yes	—
657	#95	C₂³×C₇	1	2	yes	—
658	#95	C₂³×C₇	1	2	yes	—
659	#95	C₂³×C₇	1	2	yes	—
660	#95	C₂³×C₇	1	2	yes	—
661	#95	C₂³×C₇	1	2	yes	—
662	#95	C₂³×C₇	1	2	yes	—
663	#95	C₂³×C₇	1	2	yes	—
664	#95	C₂³×C₇	1	2	yes	—
665	C₂²×C₇	—	2	2	no	—
666	C₂²×C₇	—	2	2	no	—
667	C₂²×C₇	—	2	2	no	—
668	C₂²×C₇	—	2	2	no	—
669	C₂²×C₇	—	2	2	no	—
670	C₂²×C₇	—	2	2	no	—
671	C₂²×C₇	—	2	2	no	—
672	C₂²×C₇	—	2	2	no	—
673	C₂²×C₇	—	2	2	no	—
674	C₂²×C₇	—	4	1	no	—
675	C₂²×C₇	—	4	1	no	—
676	C₂²×C₇	—	4	1	no	—
677	C₂²×C₇	—	4	1	no	—
678	C₂²×C₇	#529	1	4	yes	—
679	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
680	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
681	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
682	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
683	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
684	C₂²×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
685	C₂²×C₇	#585	1	1	yes	characteristic
686	C₄×C₇	—	2	2	no	—
687	C₄×C₇	—	2	2	no	—
688	C₄×C₇	—	2	2	no	—
689	C₄×C₇	—	2	2	no	—
690	C₄×C₇	—	2	4	no	—
691	C₄×C₇	—	4	2	no	—
692	C₄×C₇	—	4	2	no	—
693	C₄×C₇	—	4	1	no	—
694	C₄×C₇	—	4	2	no	—
695	C₄×C₇	—	4	1	no	—
696	C₄×C₇	—	4	2	no	—
697	C₄×C₇	—	4	1	no	—
698	C₄×C₇	—	4	1	no	—
699	C₄×C₇	—	4	2	no	—
700	C₄×C₇	—	4	2	no	—
701	C₄×C₇	—	4	1	no	—
702	C₄×C₇	—	4	1	no	—
703	C₄×C₇	—	4	1	no	—
704	C₄×C₇	—	4	2	no	—
705	C₄×C₇	#529	1	4	yes	—
706	C₄×C₇	#552	1	4	yes	—
707	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
708	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
709	C₂×Q₈	—	2	2	no	—
710	C₂×Q₈	—	2	2	no	—
711	C₂×Q₈	—	2	2	no	—
712	C₂×D₄	—	2	2	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	C₇×#41	1	4	yes	—
715	C₂²×C₄	—	2	2	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	2	2	no	—
718	C₂²×C₄	—	2	2	no	—
719	C₂²×C₄	—	2	4	no	—
720	C₂²×C₄	—	2	4	no	—
721	C₂²×C₄	—	2	4	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	2	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	4	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	2	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	4	1	no	—
735	C₂²×C₄	—	4	1	no	—
736	C₂²×C₄	—	4	2	no	—
737	C₂²×C₄	C₇×#41	1	4	yes	—
738	C₂²×C₄	C₇×#41	1	4	yes	—
739	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
741	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
742	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
743	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
744	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
745	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
748	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
749	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
750	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
751	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
752	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
753	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
754	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
755	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
756	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
759	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
760	C₄⋊C₄	—	2	4	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	4	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	4	no	—
772	C₄⋊C₄	—	2	4	no	—
773	C₄⋊C₄	—	2	4	no	—
774	C₄⋊C₄	—	2	4	no	—
775	C₄⋊C₄	—	2	4	no	—
776	C₄⋊C₄	—	2	4	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	4	2	no	—
779	C₄⋊C₄	—	4	2	no	—
780	C₄⋊C₄	—	4	2	no	—
781	C₄⋊C₄	—	4	2	no	—
782	C₄⋊C₄	C₇×#41	1	4	yes	—
783	C₂²⋊C₄	—	2	2	no	—
784	C₂²⋊C₄	—	2	2	no	—
785	C₂²⋊C₄	—	2	2	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	4	no	—
788	C₂²⋊C₄	—	2	4	no	—
789	C₂²⋊C₄	—	2	4	no	—
790	C₂²⋊C₄	—	2	4	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	4	no	—
794	C₂²⋊C₄	—	4	2	no	—
795	C₄²	—	2	2	no	—
796	C₄²	—	2	4	no	—
797	C₄²	—	2	2	no	—
798	C₄²	—	2	4	no	—
799	C₄²	—	2	2	no	—
800	C₄²	—	2	4	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	2	no	—
803	C₄²	—	2	4	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	2	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	2	no	—
808	C₄²	—	2	4	no	—
809	C₄²	—	2	2	no	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	4	no	—
812	C₄²	—	4	1	no	—
813	C₄²	C₇×#41	1	4	yes	—
814	C₂×C₇	—	2	4	no	—
815	C₂×C₇	—	4	2	no	—
816	C₂×C₇	C₂×#529	1	1	yes	characteristic
817	C₂×C₇	C₂×#529	1	1	yes	characteristic
818	C₂×C₇	#3461	1	1	yes	characteristic
819	C₂×C₇	C₂×#552	1	1	yes	characteristic
820	C₂×C₇	#3475	1	1	yes	characteristic
821	C₂×C₇	#3475	1	1	yes	characteristic
822	C₂×C₇	#3482	1	1	yes	characteristic
823	C₂³	—	2	1	no	—
824	C₂³	—	2	1	no	—
825	C₂³	—	2	1	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	1	no	—
828	C₂³	—	2	1	no	—
829	C₂³	—	2	1	no	—
830	C₂³	—	2	1	no	—
831	C₂³	—	2	1	no	—
832	C₂³	—	2	1	no	—
833	C₂³	C₂×C₇×#41	1	2	yes	—
834	C₂³	C₂×C₇×#41	1	2	yes	—
835	C₂³	C₂×C₇×#41	1	2	yes	—
836	C₂³	C₂×C₇×#41	1	2	yes	—
837	C₂³	C₂⁵×C₇	1	1	yes	characteristic
838	Q₈	—	4	4	no	—
839	D₄	—	2	8	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	1	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	2	1	no	—
844	C₂×C₄	—	2	1	no	—
845	C₂×C₄	—	2	1	no	—
846	C₂×C₄	—	2	1	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	8	no	—
851	C₂×C₄	—	2	8	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	1	no	—
855	C₂×C₄	—	2	1	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	1	no	—
858	C₂×C₄	—	2	1	no	—
859	C₂×C₄	—	2	1	no	—
860	C₂×C₄	—	2	1	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	2	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	2	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	2	no	—
872	C₂×C₄	—	2	1	no	—
873	C₂×C₄	—	2	1	no	—
874	C₂×C₄	—	2	1	no	—
875	C₂×C₄	—	2	2	no	—
876	C₂×C₄	—	2	2	no	—
877	C₂×C₄	—	2	2	no	—
878	C₂×C₄	—	2	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	2	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	2	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	2	no	—
890	C₂×C₄	—	2	2	no	—
891	C₂×C₄	—	2	2	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	4	4	no	—
895	C₂×C₄	—	4	4	no	—
896	C₂×C₄	—	4	8	no	—
897	C₂×C₄	—	4	8	no	—
898	C₂×C₄	—	4	4	no	—
899	C₂×C₄	—	4	4	no	—
900	C₂×C₄	C₂×C₇×#41	1	2	yes	—
901	C₂×C₄	C₂×C₇×#41	1	2	yes	—
902	C₂×C₄	C₂×C₇×#41	1	2	yes	—
903	C₂×C₄	C₂×C₇×#41	1	2	yes	—
904	C₂×C₄	C₂×C₇×#41	1	4	yes	—
905	C₂×C₄	C₂×C₇×#41	1	2	yes	—
906	C₂×C₄	C₂×C₇×#41	1	2	yes	—
907	C₂×C₄	C₂×C₇×#41	1	2	yes	—
908	C₂×C₄	C₂×C₇×#41	1	2	yes	—
909	C₂×C₄	C₂×C₇×#41	1	2	yes	—
910	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
911	C₇	#34780	1	1	yes	characteristic, direct product factor, Sylow
912	C₂²	—	2	2	no	—
913	C₂²	—	2	2	no	—
914	C₂²	—	2	2	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	2	2	no	—
919	C₂²	—	2	2	no	—
920	C₂²	—	2	2	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	1	no	—
923	C₂²	—	4	1	no	—
924	C₂²	—	4	1	no	—
925	C₂²	C₇×#529	1	4	yes	—
926	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
927	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
928	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
929	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
930	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
931	C₂²	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
932	C₂²	C₇×#585	1	1	yes	characteristic
933	C₄	—	2	2	no	—
934	C₄	—	2	2	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	2	4	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	2	no	—
940	C₄	—	4	1	no	—
941	C₄	—	4	2	no	—
942	C₄	—	4	1	no	—
943	C₄	—	4	2	no	—
944	C₄	—	4	1	no	—
945	C₄	—	4	2	no	—
946	C₄	—	4	1	no	—
947	C₄	—	4	1	no	—
948	C₄	—	4	1	no	—
949	C₄	—	4	2	no	—
950	C₄	—	4	1	no	—
951	C₄	—	4	2	no	—
952	C₄	C₇×#529	1	4	yes	—
953	C₄	C₇×#552	1	4	yes	—
954	C₂	—	2	4	no	—
955	C₂	—	4	2	no	—
956	C₂	C₂×C₇×#529	1	1	yes	characteristic
957	C₂	C₂×C₇×#529	1	1	yes	characteristic
958	C₂	C₇×#3461	1	1	yes	characteristic
959	C₂	C₂×C₇×#552	1	1	yes	characteristic
960	C₂	C₇×#3475	1	1	yes	characteristic
961	C₂	C₇×#3475	1	1	yes	characteristic
962	C₂	C₇×#3482	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₂²×C₇×D₄	C₂³
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×#2524	C₂	semidirect
2. C₇×#2515	C₂	semidirect
3. C₇×#2514	C₂	semidirect
4. C₇×#2508	C₂	semidirect
5. C₇×#2503	C₂	semidirect
6. C₇×#2495	C₂	semidirect
7. C₇×#2493	C₂	semidirect
8. C₇×#2489	C₂	semidirect
10. C₇×#2442	C₂	semidirect
13. C₇×#2402	C₂	semidirect
14. C₇×#2401	C₂	semidirect
15. C₄×C₇×#125	C₂	semidirect
16. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
17. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
19. C₇×#2295	C₂	semidirect
20. C₇×#2283	C₂	semidirect
21. C₇×#2283	C₂	semidirect
23. C₂×C₄×C₇×C₄⋊C₄	C₂	semidirect
123. #34780	C₇	direct (N × H)
236. #2524	C₂×C₇	semidirect
237. #2515	C₂×C₇	semidirect
238. #2514	C₂×C₇	semidirect
239. #2508	C₂×C₇	semidirect
240. #2503	C₂×C₇	semidirect
241. #2495	C₂×C₇	semidirect
242. #2493	C₂×C₇	semidirect
243. #2489	C₂×C₇	semidirect
245. #2442	C₂×C₇	semidirect
248. #2402	C₂×C₇	semidirect
249. #2401	C₂×C₇	semidirect
250. C₄×#125	C₂×C₇	semidirect
251. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
252. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
254. #2295	C₂×C₇	semidirect
255. #2283	C₂×C₇	semidirect
256. #2283	C₂×C₇	semidirect
258. C₂×C₄×C₄⋊C₄	C₂×C₇	semidirect
911. C₇	#34780	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×#2524	2
C₇×#2515	2
C₇×#2514	2
C₇×#2508	2
C₇×#2503	2
C₇×#2495	2
C₇×#2493	2
C₇×#2489	2
C₇×#2486	2
C₇×#2442	2
C₇×#2419	2
C₇×#2417	2
C₇×#2402	2
C₇×#2401	2
C₄×C₇×#125	2
C₄×C₇×C₂²⋊Q₈	2
C₄×C₇×#123	2
C₇×#2295	2
C₇×#2283	2
C₄²×C₇×D₄	2
C₂×C₄×C₇×C₄⋊C₄	2
#34780	7

Subgroups — C7×#34780 #13211996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#34780 #13211996