Subgroups — C₇×#62058 #13239274

Order 1792.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3400	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3363	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3331	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3308	C₂	1	2	yes	maximal, complemented
9	C₇×#3299	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3298	C₂	1	2	yes	maximal, complemented
11	C₇×#3285	C₂	1	2	yes	maximal, complemented
12	C₇×#3284	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3278	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3270	C₂	1	2	yes	maximal, complemented
15	C₇×#3258	C₂	1	2	yes	maximal, complemented
16	C₇×#3247	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3225	C₂	1	2	yes	maximal, complemented
18	C₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3120	C₂	1	2	yes	maximal, complemented
20	C₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3046	C₂	1	2	yes	maximal, complemented
22	C₂×C₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2994	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	2	yes	—
25	C₂×C₇×#135	C₂²	1	2	yes	—
26	C₂²×C₇×Q₁₆	C₂²	1	2	yes	—
27	C₇×#563	—	2	2	no	—
28	C₇×#559	—	2	1	no	—
29	C₇×#559	C₂²	1	1	yes	characteristic
30	C₇×Q₈²	C₂²	1	1	yes	characteristic
31	C₇×#557	C₂²	1	1	yes	characteristic
32	C₇×#556	C₂²	1	1	yes	characteristic
33	C₇×#554	—	2	1	no	—
34	C₇×#554	—	2	1	no	—
35	C₇×#554	C₂²	1	1	yes	characteristic
36	C₇×#553	—	2	1	no	—
37	C₇×#550	C₂²	1	1	yes	characteristic
38	C₇×D₄×Q₈	C₂²	1	2	yes	—
39	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic
40	C₇×#548	C₂²	1	2	yes	—
41	C₇×#548	C₂²	1	2	yes	—
42	C₇×#547	—	2	2	no	—
43	C₇×#547	C₂²	1	1	yes	characteristic
44	C₇×#547	C₂²	1	2	yes	—
45	C₇×#544	—	2	1	no	—
46	C₇×#542	—	2	2	no	—
47	C₇×#542	—	2	1	no	—
48	C₇×#542	C₂²	1	2	yes	—
49	C₇×#541	C₂²	1	2	yes	—
50	C₇×#539	—	2	2	no	—
51	C₇×#536	C₂²	1	2	yes	—
52	C₇×#532	—	2	1	no	—
53	C₇×#532	C₂²	1	1	yes	characteristic
54	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
55	C₇×#529	—	2	1	no	—
56	C₇×#529	C₂²	1	1	yes	characteristic
57	C₇×#529	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	2	yes	—
59	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
60	C₇×#497	C₂²	1	2	yes	—
61	C₇×#495	C₂²	1	2	yes	—
62	C₇×#492	C₂²	1	1	yes	characteristic
63	C₇×#492	C₂²	1	1	yes	characteristic
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#487	C₂²	1	1	yes	characteristic
66	C₇×#487	C₂²	1	1	yes	characteristic
67	C₇×#487	C₂²	1	2	yes	—
68	C₇×#484	C₂²	1	2	yes	—
69	C₇×#483	C₂²	1	1	yes	characteristic
70	C₇×#483	C₂²	1	2	yes	—
71	C₇×#480	C₂²	1	1	yes	characteristic
72	C₇×#479	C₂²	1	1	yes	characteristic
73	C₇×#479	C₂²	1	1	yes	characteristic
74	C₇×#478	C₂²	1	2	yes	—
75	C₇×#477	C₂²	1	1	yes	characteristic
76	C₇×#477	C₂²	1	2	yes	—
77	C₇×#476	C₂²	1	1	yes	characteristic
78	C₇×#475	C₂²	1	2	yes	—
79	C₇×#470	C₂²	1	2	yes	—
80	C₇×#468	C₂²	1	2	yes	—
81	C₇×#467	C₂²	1	2	yes	—
82	C₇×#466	C₂²	1	2	yes	—
83	C₇×#465	C₂²	1	2	yes	—
84	C₇×#465	C₂²	1	2	yes	—
85	C₇×#464	C₂²	1	1	yes	characteristic
86	C₇×#464	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	—
88	C₇×#464	C₂²	1	2	yes	—
89	C₇×#464	C₂²	1	1	yes	characteristic
90	C₇×#463	C₂²	1	2	yes	—
91	C₇×#463	C₂²	1	2	yes	—
92	C₇×#462	C₂²	1	2	yes	—
93	C₇×#462	C₂²	1	2	yes	—
94	C₇×#462	C₂²	1	1	yes	characteristic
95	C₇×#462	C₂²	1	1	yes	characteristic
96	C₇×#462	C₂²	1	1	yes	characteristic
97	C₇×#462	C₂²	1	2	yes	—
98	C₇×#462	C₂²	1	1	yes	characteristic
99	C₇×#461	C₂²	1	2	yes	—
100	C₇×#461	C₂²	1	2	yes	—
101	C₇×#461	C₂²	1	2	yes	—
102	C₇×#460	C₂²	1	1	yes	characteristic
103	C₇×#459	C₂²	1	1	yes	characteristic
104	C₇×#452	C₂²	1	2	yes	—
105	C₇×#452	C₂²	1	2	yes	—
106	C₇×#452	C₂²	1	2	yes	—
107	C₇×#451	C₂²	1	2	yes	—
108	C₇×#451	C₂²	1	1	yes	characteristic
109	C₇×#449	C₂²	1	2	yes	—
110	C₇×#448	C₂²	1	2	yes	—
111	C₇×#448	C₂²	1	2	yes	—
112	C₇×#448	C₂²	1	2	yes	—
113	C₇×#448	C₂²	1	1	yes	characteristic
114	C₇×#446	C₂²	1	1	yes	characteristic
115	C₇×C₈×Q₈	C₂²	1	1	yes	characteristic
116	C₇×#441	C₂²	1	2	yes	—
117	C₇×#440	C₂²	1	2	yes	—
118	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
119	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
120	C₄×C₇×Q₁₆	C₂²	1	1	yes	characteristic
121	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
122	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
123	C₄×C₇×SD₁₆	C₂²	1	1	yes	characteristic
124	C₇×#436	C₂²	1	1	yes	characteristic
125	C₇×#435	C₂²	1	2	yes	—
126	C₇×C₈×D₄	C₂²	1	1	yes	characteristic
127	C₇×C₈×D₄	C₂²	1	2	yes	—
128	C₇×#433	C₂²	1	2	yes	—
129	C₇×#431	C₂²	1	1	yes	characteristic
130	C₇×#424	C₂²	1	2	yes	—
131	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
132	C₇×#417	C₂²	1	2	yes	—
133	C₂×C₇×#103	C₂²	1	2	yes	—
134	C₂×C₇×#103	C₂²	1	2	yes	—
135	#62058	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	2	no	—
137	C₂×C₇×#41	—	2	1	no	—
138	C₂×C₇×#41	C₂³	1	2	yes	—
139	C₂×C₇×#41	C₂³	1	2	yes	—
140	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
141	C₂²×C₇×Q₈	C₂³	1	2	yes	—
142	C₂²×C₇×Q₈	C₂³	1	2	yes	—
143	C₇×#137	—	4	4	no	—
144	C₇×#135	—	4	4	no	—
145	C₂×C₇×Q₁₆	—	4	4	no	—
146	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
150	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
151	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
152	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
153	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
157	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
159	C₂×C₇×D₈	C₂³	1	2	yes	—
160	C₂×C₇×M₁₆	C₂³	1	2	yes	—
161	C₂²×C₇×C₈	C₂³	1	2	yes	—
162	C₂²×C₇×C₈	C₂³	1	2	yes	—
163	C₇×C₄⋊Q₈	—	2	1	no	—
164	C₇×C₄⋊Q₈	—	2	2	no	—
165	C₇×C₄⋊Q₈	—	2	1	no	—
166	C₇×C₄⋊Q₈	—	2	2	no	—
167	C₇×C₄⋊Q₈	—	2	1	no	—
168	C₇×C₄⋊Q₈	—	2	1	no	—
169	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
170	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
171	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
172	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
173	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
174	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
175	C₇×#127	—	2	1	no	—
176	C₇×#127	C₂³	1	1	yes	characteristic
177	C₇×#126	—	2	2	no	—
178	C₇×#126	—	2	2	no	—
179	C₇×#126	—	2	2	no	—
180	C₇×#126	—	2	2	no	—
181	C₇×#126	—	2	1	no	—
182	C₇×#126	D₄	1	2	yes	—
183	C₇×#125	—	2	1	no	—
184	C₇×#125	—	2	2	no	—
185	C₇×#125	—	2	2	no	—
186	C₇×#125	—	2	2	no	—
187	C₇×#125	—	2	1	no	—
188	C₇×#125	D₄	1	1	yes	characteristic
189	C₇×#125	C₂³	1	1	yes	characteristic
190	C₇×#124	—	2	1	no	—
191	C₇×#124	—	2	2	no	—
192	C₇×#124	—	2	2	no	—
193	C₇×#124	—	2	2	no	—
194	C₇×#124	—	2	1	no	—
195	C₇×#124	D₄	1	1	yes	characteristic
196	C₇×#124	C₂³	1	2	yes	—
197	C₇×#124	C₂³	1	2	yes	—
198	C₇×#124	C₂³	1	1	yes	characteristic
199	C₇×#123	—	2	1	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×#123	—	2	2	no	—
206	C₇×#123	—	2	2	no	—
207	C₇×#123	D₄	1	2	yes	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	—	2	2	no	—
214	C₇×C₂²⋊Q₈	—	2	2	no	—
215	C₇×C₂²⋊Q₈	—	2	2	no	—
216	C₇×C₂²⋊Q₈	—	2	2	no	—
217	C₇×C₂²⋊Q₈	—	2	2	no	—
218	C₇×C₂²⋊Q₈	—	2	2	no	—
219	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
220	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
221	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
222	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
223	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	1	no	—
227	C₇×#121	—	2	1	no	—
228	C₇×#121	—	2	2	no	—
229	C₇×#121	D₄	1	1	yes	characteristic
230	C₇×#121	C₂³	1	1	yes	characteristic
231	C₇×#121	C₂³	1	2	yes	—
232	C₇×#121	C₂³	1	2	yes	—
233	C₄×C₇×Q₈	—	2	1	no	—
234	C₄×C₇×Q₈	—	2	1	no	—
235	C₄×C₇×Q₈	—	2	1	no	—
236	C₄×C₇×Q₈	—	2	1	no	—
237	C₄×C₇×Q₈	C₂³	1	2	yes	—
238	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
239	C₄×C₇×Q₈	C₂³	1	2	yes	—
240	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
241	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
242	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
243	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
244	C₄×C₇×Q₈	C₂³	1	2	yes	—
245	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	1	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	—	2	2	no	—
253	C₄×C₇×D₄	—	2	2	no	—
254	C₄×C₇×D₄	—	2	2	no	—
255	C₄×C₇×D₄	—	2	2	no	—
256	C₄×C₇×D₄	—	2	1	no	—
257	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₄×C₇×D₄	C₂³	1	2	yes	—
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
262	C₇×#117	—	2	2	no	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	C₂³	1	2	yes	—
266	C₂×C₇×C₄⋊C₄	—	2	1	no	—
267	C₂×C₇×C₄⋊C₄	—	2	1	no	—
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	—	2	2	no	—
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
273	C₂×C₄²×C₇	—	2	1	no	—
274	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
275	C₇×#107	C₂³	1	2	yes	—
276	C₇×#107	C₂³	1	1	yes	characteristic
277	C₇×#107	C₂³	1	1	yes	characteristic
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×#106	C₂³	1	1	yes	characteristic
280	C₇×#106	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×C₄⋊C₈	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
287	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
288	C₇×#103	C₂³	1	1	yes	characteristic
289	C₇×#103	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	1	yes	characteristic
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	1	yes	characteristic
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#103	C₂³	1	2	yes	—
302	C₇×#103	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	1	yes	characteristic
307	C₇×#102	C₂³	1	1	yes	characteristic
308	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
309	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
310	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
311	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
314	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3552	C₂×C₇	1	1	yes	characteristic, complemented
317	#3522	C₂×C₇	1	1	yes	characteristic, complemented
318	#3400	C₂×C₇	1	1	yes	characteristic, complemented
319	#3394	C₂×C₇	1	1	yes	characteristic, complemented
320	#3369	C₂×C₇	1	1	yes	characteristic, complemented
321	#3363	C₂×C₇	1	1	yes	characteristic, complemented
322	#3331	C₂×C₇	1	1	yes	characteristic, complemented
323	#3308	C₂×C₇	1	2	yes	complemented
324	#3299	C₂×C₇	1	1	yes	characteristic, complemented
325	#3298	C₂×C₇	1	2	yes	complemented
326	#3285	C₂×C₇	1	2	yes	complemented
327	#3284	C₂×C₇	1	1	yes	characteristic, complemented
328	#3278	C₂×C₇	1	1	yes	characteristic, complemented
329	#3270	C₂×C₇	1	2	yes	complemented
330	#3258	C₂×C₇	1	2	yes	complemented
331	#3247	C₂×C₇	1	1	yes	characteristic, complemented
332	#3225	C₂×C₇	1	2	yes	complemented
333	#3206	C₂×C₇	1	1	yes	characteristic, complemented
334	#3120	C₂×C₇	1	2	yes	complemented
335	#3108	C₂×C₇	1	1	yes	characteristic, complemented
336	#3046	C₂×C₇	1	2	yes	complemented
337	C₂×#462	C₂×C₇	1	1	yes	characteristic, complemented
338	#2994	C₂×C₇	1	1	yes	characteristic, complemented
339	C₇×#41	—	2	4	no	—
340	C₇×#41	—	4	2	no	—
341	C₇×#41	—	4	2	no	—
342	C₇×#41	—	4	2	no	—
343	C₇×#41	—	8	2	no	—
344	C₇×#41	—	8	4	no	—
345	C₂×C₇×Q₈	—	2	1	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	2	no	—
349	C₂×C₇×Q₈	—	2	1	no	—
350	C₂×C₇×Q₈	—	2	2	no	—
351	C₂×C₇×Q₈	—	4	1	no	—
352	C₂×C₇×Q₈	—	4	2	no	—
353	C₂×C₇×Q₈	—	4	2	no	—
354	C₂×C₇×Q₈	—	4	2	no	—
355	C₂×C₇×Q₈	—	4	2	no	—
356	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
357	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
358	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
359	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
360	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
361	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
362	C₂×C₇×D₄	—	2	1	no	—
363	C₂×C₇×D₄	—	2	2	no	—
364	C₂×C₇×D₄	—	2	2	no	—
365	C₂×C₇×D₄	—	2	2	no	—
366	C₂×C₇×D₄	—	2	2	no	—
367	C₂×C₇×D₄	—	2	1	no	—
368	C₂×C₇×D₄	—	2	1	no	—
369	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
370	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
371	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
372	C₂×C₇×D₄	C₂⁴	1	2	yes	—
373	C₂²×C₄×C₇	—	2	1	no	—
374	C₂²×C₄×C₇	—	2	1	no	—
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	—	2	2	no	—
377	C₂²×C₄×C₇	—	2	2	no	—
378	C₂²×C₄×C₇	—	2	1	no	—
379	C₂²×C₄×C₇	—	2	2	no	—
380	C₂²×C₄×C₇	—	2	2	no	—
381	C₂²×C₄×C₇	—	2	2	no	—
382	C₂²×C₄×C₇	—	2	2	no	—
383	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
384	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
385	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
386	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
387	C₇×Q₁₆	—	2	4	no	—
388	C₇×Q₁₆	—	2	4	no	—
389	C₇×Q₁₆	—	2	2	no	—
390	C₇×Q₁₆	—	4	2	no	—
391	C₇×Q₁₆	—	4	2	no	—
392	C₇×Q₁₆	—	4	1	no	—
393	C₇×SD₁₆	—	2	2	no	—
394	C₇×SD₁₆	—	4	2	no	—
395	C₇×SD₁₆	—	4	1	no	—
396	C₇×SD₁₆	—	4	2	no	—
397	C₇×SD₁₆	—	4	2	no	—
398	C₇×SD₁₆	—	4	2	no	—
399	C₇×SD₁₆	—	4	2	no	—
400	C₇×D₈	—	4	2	no	—
401	C₇×M₁₆	—	4	2	no	—
402	C₂×C₇×C₈	—	4	2	no	—
403	C₂×C₇×C₈	—	4	2	no	—
404	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
405	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
406	C₂×C₇×C₈	C₂⁴	1	2	yes	—
407	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
409	C₂×C₇×C₈	C₂⁴	1	2	yes	—
410	C₇×C₄⋊C₄	—	2	1	no	—
411	C₇×C₄⋊C₄	—	2	1	no	—
412	C₇×C₄⋊C₄	—	2	2	no	—
413	C₇×C₄⋊C₄	—	2	1	no	—
414	C₇×C₄⋊C₄	—	2	2	no	—
415	C₇×C₄⋊C₄	—	2	1	no	—
416	C₇×C₄⋊C₄	—	2	1	no	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	1	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	2	2	no	—
421	C₇×C₄⋊C₄	—	2	2	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	1	no	—
424	C₇×C₄⋊C₄	—	2	1	no	—
425	C₇×C₄⋊C₄	—	2	1	no	—
426	C₇×C₄⋊C₄	—	2	1	no	—
427	C₇×C₄⋊C₄	—	2	2	no	—
428	C₇×C₄⋊C₄	—	2	2	no	—
429	C₇×C₄⋊C₄	—	2	2	no	—
430	C₇×C₄⋊C₄	—	2	1	no	—
431	C₇×C₄⋊C₄	—	2	2	no	—
432	C₇×C₄⋊C₄	—	2	2	no	—
433	C₇×C₄⋊C₄	—	2	2	no	—
434	C₇×C₄⋊C₄	—	2	2	no	—
435	C₇×C₄⋊C₄	—	2	1	no	—
436	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
437	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
438	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
439	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
440	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
441	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
442	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
443	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
444	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
445	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
446	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
447	C₇×C₂²⋊C₄	—	2	1	no	—
448	C₇×C₂²⋊C₄	—	2	2	no	—
449	C₇×C₂²⋊C₄	—	2	2	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	2	no	—
454	C₇×C₂²⋊C₄	—	2	1	no	—
455	C₇×C₂²⋊C₄	—	2	1	no	—
456	C₇×C₂²⋊C₄	—	2	2	no	—
457	C₇×C₂²⋊C₄	—	2	2	no	—
458	C₇×C₂²⋊C₄	—	2	2	no	—
459	C₇×C₂²⋊C₄	—	2	1	no	—
460	C₇×C₂²⋊C₄	—	2	2	no	—
461	C₇×C₂²⋊C₄	—	2	2	no	—
462	C₇×C₂²⋊C₄	—	2	1	no	—
463	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
464	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
465	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
466	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
467	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
468	C₄²×C₇	—	2	1	no	—
469	C₄²×C₇	—	2	1	no	—
470	C₄²×C₇	—	2	1	no	—
471	C₄²×C₇	—	2	1	no	—
472	C₄²×C₇	—	2	2	no	—
473	C₄²×C₇	—	2	1	no	—
474	C₄²×C₇	—	2	2	no	—
475	C₄²×C₇	—	2	2	no	—
476	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
477	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
478	C₄²×C₇	C₂⁴	1	1	yes	characteristic
479	C₄²×C₇	C₂⁴	1	2	yes	—
480	C₄²×C₇	C₂⁴	1	1	yes	characteristic
481	C₂×#137	C₂²×C₇	1	2	yes	—
482	C₂×#135	C₂²×C₇	1	2	yes	—
483	C₂²×Q₁₆	C₂²×C₇	1	2	yes	—
484	#563	—	2	2	no	—
485	#559	—	2	1	no	—
486	#559	C₂²×C₇	1	1	yes	characteristic
487	Q₈²	C₂²×C₇	1	1	yes	characteristic
488	#557	C₂²×C₇	1	1	yes	characteristic
489	#556	C₂²×C₇	1	1	yes	characteristic
490	#554	—	2	1	no	—
491	#554	—	2	1	no	—
492	#554	C₂²×C₇	1	1	yes	characteristic
493	#553	—	2	1	no	—
494	#550	C₂²×C₇	1	1	yes	characteristic
495	D₄×Q₈	C₂²×C₇	1	2	yes	—
496	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic
497	#548	C₂²×C₇	1	2	yes	—
498	#548	C₂²×C₇	1	2	yes	—
499	#547	—	2	2	no	—
500	#547	C₂²×C₇	1	1	yes	characteristic
501	#547	C₂²×C₇	1	2	yes	—
502	#544	—	2	1	no	—
503	#542	—	2	2	no	—
504	#542	—	2	1	no	—
505	#542	C₂²×C₇	1	2	yes	—
506	#541	C₂²×C₇	1	2	yes	—
507	#539	—	2	2	no	—
508	#536	C₂²×C₇	1	2	yes	—
509	#532	—	2	1	no	—
510	#532	C₂²×C₇	1	1	yes	characteristic
511	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
512	#529	—	2	1	no	—
513	#529	C₂²×C₇	1	1	yes	characteristic
514	#529	C₂²×C₇	1	1	yes	characteristic
515	#520	C₂²×C₇	1	2	yes	—
516	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
517	#497	C₂²×C₇	1	2	yes	—
518	#495	C₂²×C₇	1	2	yes	—
519	#492	C₂²×C₇	1	1	yes	characteristic
520	#492	C₂²×C₇	1	1	yes	characteristic
521	#489	C₂²×C₇	1	2	yes	—
522	#487	C₂²×C₇	1	1	yes	characteristic
523	#487	C₂²×C₇	1	2	yes	—
524	#487	C₂²×C₇	1	1	yes	characteristic
525	#484	C₂²×C₇	1	2	yes	—
526	#483	C₂²×C₇	1	2	yes	—
527	#483	C₂²×C₇	1	1	yes	characteristic
528	#480	C₂²×C₇	1	1	yes	characteristic
529	#479	C₂²×C₇	1	1	yes	characteristic
530	#479	C₂²×C₇	1	1	yes	characteristic
531	#478	C₂²×C₇	1	2	yes	—
532	#477	C₂²×C₇	1	1	yes	characteristic
533	#477	C₂²×C₇	1	2	yes	—
534	#476	C₂²×C₇	1	1	yes	characteristic
535	#475	C₂²×C₇	1	2	yes	—
536	#470	C₂²×C₇	1	2	yes	—
537	#468	C₂²×C₇	1	2	yes	—
538	#467	C₂²×C₇	1	2	yes	—
539	#466	C₂²×C₇	1	2	yes	—
540	#465	C₂²×C₇	1	2	yes	—
541	#465	C₂²×C₇	1	2	yes	—
542	#464	C₂²×C₇	1	1	yes	characteristic
543	#464	C₂²×C₇	1	1	yes	characteristic
544	#464	C₂²×C₇	1	2	yes	—
545	#464	C₂²×C₇	1	2	yes	—
546	#464	C₂²×C₇	1	2	yes	—
547	#463	C₂²×C₇	1	2	yes	—
548	#463	C₂²×C₇	1	2	yes	—
549	#462	C₂²×C₇	1	1	yes	characteristic
550	#462	C₂²×C₇	1	2	yes	—
551	#462	C₂²×C₇	1	1	yes	characteristic
552	#462	C₂²×C₇	1	1	yes	characteristic
553	#462	C₂²×C₇	1	2	yes	—
554	#462	C₂²×C₇	1	1	yes	characteristic
555	#462	C₂²×C₇	1	2	yes	—
556	#461	C₂²×C₇	1	2	yes	—
557	#461	C₂²×C₇	1	2	yes	—
558	#461	C₂²×C₇	1	2	yes	—
559	#460	C₂²×C₇	1	1	yes	characteristic
560	#459	C₂²×C₇	1	1	yes	characteristic
561	#452	C₂²×C₇	1	2	yes	—
562	#452	C₂²×C₇	1	2	yes	—
563	#452	C₂²×C₇	1	2	yes	—
564	#451	C₂²×C₇	1	1	yes	characteristic
565	#451	C₂²×C₇	1	2	yes	—
566	#449	C₂²×C₇	1	2	yes	—
567	#448	C₂²×C₇	1	1	yes	characteristic
568	#448	C₂²×C₇	1	2	yes	—
569	#448	C₂²×C₇	1	2	yes	—
570	#448	C₂²×C₇	1	2	yes	—
571	#446	C₂²×C₇	1	1	yes	characteristic
572	C₈×Q₈	C₂²×C₇	1	1	yes	characteristic
573	#441	C₂²×C₇	1	2	yes	—
574	#440	C₂²×C₇	1	2	yes	—
575	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
576	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
577	C₄×Q₁₆	C₂²×C₇	1	1	yes	characteristic
578	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
579	C₄×SD₁₆	C₂²×C₇	1	1	yes	characteristic
580	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
581	#436	C₂²×C₇	1	1	yes	characteristic
582	#435	C₂²×C₇	1	2	yes	—
583	C₈×D₄	C₂²×C₇	1	1	yes	characteristic
584	C₈×D₄	C₂²×C₇	1	2	yes	—
585	#433	C₂²×C₇	1	2	yes	—
586	#431	C₂²×C₇	1	1	yes	characteristic
587	#424	C₂²×C₇	1	2	yes	—
588	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
589	#417	C₂²×C₇	1	2	yes	—
590	C₂×#103	C₂²×C₇	1	2	yes	—
591	C₂×#103	C₂²×C₇	1	2	yes	—
592	C₂³×C₇	—	2	1	no	—
593	C₂³×C₇	—	2	2	no	—
594	C₂³×C₇	C₂²×D₄	1	2	yes	—
595	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
596	C₇×Q₈	—	2	2	no	—
597	C₇×Q₈	—	2	1	no	—
598	C₇×Q₈	—	2	1	no	—
599	C₇×Q₈	—	2	2	no	—
600	C₇×Q₈	—	2	2	no	—
601	C₇×Q₈	—	2	1	no	—
602	C₇×Q₈	—	2	1	no	—
603	C₇×Q₈	—	2	2	no	—
604	C₇×Q₈	—	2	2	no	—
605	C₇×Q₈	—	2	1	no	—
606	C₇×Q₈	—	4	2	no	—
607	C₇×Q₈	—	8	2	no	—
608	C₇×Q₈	—	8	2	no	—
609	C₇×Q₈	—	8	1	no	—
610	C₇×Q₈	—	8	2	no	—
611	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
612	C₇×D₄	—	2	4	no	—
613	C₇×D₄	—	2	2	no	—
614	C₇×D₄	—	2	1	no	—
615	C₇×D₄	—	2	2	no	—
616	C₇×D₄	—	2	2	no	—
617	C₇×D₄	—	2	1	no	—
618	C₇×D₄	—	4	4	no	—
619	C₇×D₄	—	4	2	no	—
620	C₇×D₄	—	4	4	no	—
621	C₇×D₄	—	4	2	no	—
622	C₇×D₄	—	8	1	no	—
623	C₇×D₄	—	8	2	no	—
624	C₇×D₄	—	8	2	no	—
625	C₂×C₄×C₇	—	2	2	no	—
626	C₂×C₄×C₇	—	2	1	no	—
627	C₂×C₄×C₇	—	2	2	no	—
628	C₂×C₄×C₇	—	2	1	no	—
629	C₂×C₄×C₇	—	2	2	no	—
630	C₂×C₄×C₇	—	2	1	no	—
631	C₂×C₄×C₇	—	2	2	no	—
632	C₂×C₄×C₇	—	2	1	no	—
633	C₂×C₄×C₇	—	2	1	no	—
634	C₂×C₄×C₇	—	2	1	no	—
635	C₂×C₄×C₇	—	2	1	no	—
636	C₂×C₄×C₇	—	2	1	no	—
637	C₂×C₄×C₇	—	2	1	no	—
638	C₂×C₄×C₇	—	2	2	no	—
639	C₂×C₄×C₇	—	2	2	no	—
640	C₂×C₄×C₇	—	2	2	no	—
641	C₂×C₄×C₇	—	4	4	no	—
642	C₂×C₄×C₇	—	4	2	no	—
643	C₂×C₄×C₇	—	4	2	no	—
644	C₂×C₄×C₇	—	4	2	no	—
645	C₂×C₄×C₇	—	8	2	no	—
646	C₂×C₄×C₇	—	8	2	no	—
647	C₂×C₄×C₇	—	8	2	no	—
648	C₂×C₄×C₇	—	8	2	no	—
649	C₂×C₄×C₇	—	8	2	no	—
650	C₂×C₄×C₇	—	8	2	no	—
651	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
652	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
653	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
654	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
655	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
656	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
657	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
658	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
659	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
660	C₇×C₈	—	2	2	no	—
661	C₇×C₈	—	2	1	no	—
662	C₇×C₈	—	2	2	no	—
663	C₇×C₈	—	2	1	no	—
664	C₇×C₈	—	2	1	no	—
665	C₇×C₈	—	2	1	no	—
666	C₂×#41	—	2	2	no	—
667	C₂×#41	—	2	1	no	—
668	C₂×#41	C₂³×C₇	1	2	yes	—
669	C₂×#41	C₂³×C₇	1	2	yes	—
670	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
671	C₂²×Q₈	C₂³×C₇	1	2	yes	—
672	C₂²×Q₈	C₂³×C₇	1	2	yes	—
673	#137	—	4	4	no	—
674	#135	—	4	4	no	—
675	C₂×Q₁₆	—	4	4	no	—
676	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
677	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
678	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
679	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
680	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
681	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
682	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
683	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
684	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
686	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
688	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
689	C₂×D₈	C₂³×C₇	1	2	yes	—
690	C₂×M₁₆	C₂³×C₇	1	2	yes	—
691	C₂²×C₈	C₂³×C₇	1	2	yes	—
692	C₂²×C₈	C₂³×C₇	1	2	yes	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	2	2	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	—	2	1	no	—
699	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
700	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
704	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
705	#127	—	2	1	no	—
706	#127	C₂³×C₇	1	1	yes	characteristic
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	1	no	—
712	#126	C₇×D₄	1	2	yes	—
713	#125	—	2	1	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	1	no	—
718	#125	C₇×D₄	1	1	yes	characteristic
719	#125	C₂³×C₇	1	1	yes	characteristic
720	#124	—	2	1	no	—
721	#124	—	2	2	no	—
722	#124	—	2	2	no	—
723	#124	—	2	2	no	—
724	#124	—	2	1	no	—
725	#124	C₇×D₄	1	1	yes	characteristic
726	#124	C₂³×C₇	1	1	yes	characteristic
727	#124	C₂³×C₇	1	2	yes	—
728	#124	C₂³×C₇	1	2	yes	—
729	#123	—	2	1	no	—
730	#123	—	2	2	no	—
731	#123	—	2	2	no	—
732	#123	—	2	2	no	—
733	#123	—	2	2	no	—
734	#123	—	2	2	no	—
735	#123	—	2	2	no	—
736	#123	—	2	2	no	—
737	#123	C₇×D₄	1	2	yes	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	2	no	—
740	C₂²⋊Q₈	—	2	2	no	—
741	C₂²⋊Q₈	—	2	2	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
750	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
751	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
752	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
753	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
754	#121	—	2	2	no	—
755	#121	—	2	2	no	—
756	#121	—	2	1	no	—
757	#121	—	2	1	no	—
758	#121	—	2	2	no	—
759	#121	C₇×D₄	1	1	yes	characteristic
760	#121	C₂³×C₇	1	1	yes	characteristic
761	#121	C₂³×C₇	1	2	yes	—
762	#121	C₂³×C₇	1	2	yes	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
768	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
769	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
770	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
771	C₄×Q₈	C₂³×C₇	1	2	yes	—
772	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₇	1	2	yes	—
774	C₄×Q₈	C₂³×C₇	1	2	yes	—
775	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	2	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	—	2	1	no	—
780	C₄×D₄	—	2	1	no	—
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	2	no	—
783	C₄×D₄	—	2	2	no	—
784	C₄×D₄	—	2	2	no	—
785	C₄×D₄	—	2	2	no	—
786	C₄×D₄	—	2	1	no	—
787	C₄×D₄	C₂³×C₇	1	2	yes	—
788	C₄×D₄	C₂³×C₇	1	2	yes	—
789	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
790	C₄×D₄	C₂³×C₇	1	2	yes	—
791	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
792	#117	—	2	2	no	—
793	#117	—	2	1	no	—
794	#117	—	2	1	no	—
795	#117	C₂³×C₇	1	2	yes	—
796	C₂×C₄⋊C₄	—	2	1	no	—
797	C₂×C₄⋊C₄	—	2	1	no	—
798	C₂×C₄⋊C₄	—	2	1	no	—
799	C₂×C₄⋊C₄	—	2	2	no	—
800	C₂×C₄⋊C₄	—	2	1	no	—
801	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
802	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
803	C₂×C₄²	—	2	1	no	—
804	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
805	#107	C₂³×C₇	1	1	yes	characteristic
806	#107	C₂³×C₇	1	2	yes	—
807	#107	C₂³×C₇	1	1	yes	characteristic
808	#106	C₂³×C₇	1	1	yes	characteristic
809	#106	C₂³×C₇	1	1	yes	characteristic
810	#106	C₂³×C₇	1	2	yes	—
811	C₄⋊C₈	C₂³×C₇	1	2	yes	—
812	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
813	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
814	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
815	C₄⋊C₈	C₂³×C₇	1	2	yes	—
816	C₄⋊C₈	C₂³×C₇	1	2	yes	—
817	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
818	#103	C₂³×C₇	1	2	yes	—
819	#103	C₂³×C₇	1	1	yes	characteristic
820	#103	C₂³×C₇	1	2	yes	—
821	#103	C₂³×C₇	1	2	yes	—
822	#103	C₂³×C₇	1	2	yes	—
823	#103	C₂³×C₇	1	2	yes	—
824	#103	C₂³×C₇	1	2	yes	—
825	#103	C₂³×C₇	1	2	yes	—
826	#103	C₂³×C₇	1	1	yes	characteristic
827	#103	C₂³×C₇	1	1	yes	characteristic
828	#103	C₂³×C₇	1	1	yes	characteristic
829	#103	C₂³×C₇	1	1	yes	characteristic
830	#103	C₂³×C₇	1	2	yes	—
831	#103	C₂³×C₇	1	1	yes	characteristic
832	#103	C₂³×C₇	1	2	yes	—
833	#102	C₂³×C₇	1	1	yes	characteristic
834	#102	C₂³×C₇	1	2	yes	—
835	#102	C₂³×C₇	1	1	yes	characteristic
836	#102	C₂³×C₇	1	2	yes	—
837	#102	C₂³×C₇	1	2	yes	—
838	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
839	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
840	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
841	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
842	#97	C₂³×C₇	1	2	yes	—
843	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
844	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
845	C₄×C₈	C₂³×C₇	1	2	yes	—
846	C₂²×C₇	—	2	1	no	—
847	C₂²×C₇	—	2	1	no	—
848	C₂²×C₇	—	2	2	no	—
849	C₂²×C₇	—	2	2	no	—
850	C₂²×C₇	—	2	2	no	—
851	C₂²×C₇	—	4	2	no	—
852	C₂²×C₇	—	4	1	no	—
853	C₂²×C₇	—	4	2	no	—
854	C₂²×C₇	—	4	1	no	—
855	C₂²×C₇	—	4	1	no	—
856	C₂²×C₇	—	4	2	no	—
857	C₂²×C₇	#577	1	2	yes	—
858	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
859	C₄×C₇	—	2	2	no	—
860	C₄×C₇	—	2	1	no	—
861	C₄×C₇	—	2	2	no	—
862	C₄×C₇	—	2	1	no	—
863	C₄×C₇	—	2	1	no	—
864	C₄×C₇	—	2	2	no	—
865	C₄×C₇	—	2	1	no	—
866	C₄×C₇	—	2	2	no	—
867	C₄×C₇	—	4	1	no	—
868	C₄×C₇	—	4	2	no	—
869	C₄×C₇	—	4	1	no	—
870	C₄×C₇	—	4	2	no	—
871	C₄×C₇	—	4	1	no	—
872	C₄×C₇	—	4	1	no	—
873	C₄×C₇	—	4	2	no	—
874	C₄×C₇	—	4	1	no	—
875	C₄×C₇	—	4	1	no	—
876	C₄×C₇	#578	1	2	yes	—
877	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
878	C₄×C₇	#585	1	1	yes	characteristic
879	#41	—	2	4	no	—
880	#41	—	4	2	no	—
881	#41	—	4	2	no	—
882	#41	—	4	2	no	—
883	#41	—	8	2	no	—
884	#41	—	8	4	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	2	1	no	—
890	C₂×Q₈	—	2	2	no	—
891	C₂×Q₈	—	4	1	no	—
892	C₂×Q₈	—	4	2	no	—
893	C₂×Q₈	—	4	2	no	—
894	C₂×Q₈	—	4	2	no	—
895	C₂×Q₈	—	4	2	no	—
896	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
897	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
898	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
899	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
900	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
901	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
902	C₂×D₄	—	2	1	no	—
903	C₂×D₄	—	2	2	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	2	2	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
910	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
911	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
912	C₂×D₄	C₂⁴×C₇	1	2	yes	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	2	2	no	—
917	C₂²×C₄	—	2	2	no	—
918	C₂²×C₄	—	2	1	no	—
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
924	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
925	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
926	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
927	Q₁₆	—	2	4	no	—
928	Q₁₆	—	2	4	no	—
929	Q₁₆	—	2	2	no	—
930	Q₁₆	—	4	2	no	—
931	Q₁₆	—	4	2	no	—
932	Q₁₆	—	4	1	no	—
933	SD₁₆	—	2	2	no	—
934	SD₁₆	—	4	2	no	—
935	SD₁₆	—	4	1	no	—
936	SD₁₆	—	4	2	no	—
937	SD₁₆	—	4	2	no	—
938	SD₁₆	—	4	2	no	—
939	SD₁₆	—	4	2	no	—
940	D₈	—	4	2	no	—
941	M₁₆	—	4	2	no	—
942	C₂×C₈	—	4	2	no	—
943	C₂×C₈	—	4	2	no	—
944	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
945	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
946	C₂×C₈	C₂⁴×C₇	1	2	yes	—
947	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
948	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
949	C₂×C₈	C₂⁴×C₇	1	2	yes	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	1	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	2	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	2	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
977	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
978	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
979	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
980	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
981	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
982	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
983	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
984	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
986	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	2	2	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	2	1	no	—
995	C₂²⋊C₄	—	2	1	no	—
996	C₂²⋊C₄	—	2	2	no	—
997	C₂²⋊C₄	—	2	2	no	—
998	C₂²⋊C₄	—	2	2	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1004	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1005	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1006	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1007	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1008	C₄²	—	2	1	no	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1017	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1018	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1019	C₄²	C₂⁴×C₇	1	2	yes	—
1020	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1021	C₂×C₇	—	2	2	no	—
1022	C₂×C₇	—	4	2	no	—
1023	C₂×C₇	—	8	2	no	—
1024	C₂×C₇	—	8	1	no	—
1025	C₂×C₇	#3488	1	1	yes	characteristic
1026	C₂×C₇	C₂×#577	1	1	yes	characteristic
1027	C₂×C₇	C₂×#578	1	1	yes	characteristic
1028	C₂³	—	2	1	no	—
1029	C₂³	—	2	2	no	—
1030	C₂³	C₂²×C₇×D₄	1	2	yes	—
1031	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1032	Q₈	—	2	1	no	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	2	1	no	—
1038	Q₈	—	2	1	no	—
1039	Q₈	—	2	2	no	—
1040	Q₈	—	2	2	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	4	2	no	—
1043	Q₈	—	8	2	no	—
1044	Q₈	—	8	2	no	—
1045	Q₈	—	8	1	no	—
1046	Q₈	—	8	2	no	—
1047	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
1048	D₄	—	2	4	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	2	2	no	—
1051	D₄	—	2	2	no	—
1052	D₄	—	2	1	no	—
1053	D₄	—	2	2	no	—
1054	D₄	—	4	4	no	—
1055	D₄	—	4	2	no	—
1056	D₄	—	4	4	no	—
1057	D₄	—	4	2	no	—
1058	D₄	—	8	1	no	—
1059	D₄	—	8	2	no	—
1060	D₄	—	8	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	2	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	1	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	2	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	2	no	—
1077	C₂×C₄	—	4	4	no	—
1078	C₂×C₄	—	4	2	no	—
1079	C₂×C₄	—	4	2	no	—
1080	C₂×C₄	—	4	2	no	—
1081	C₂×C₄	—	8	2	no	—
1082	C₂×C₄	—	8	2	no	—
1083	C₂×C₄	—	8	2	no	—
1084	C₂×C₄	—	8	2	no	—
1085	C₂×C₄	—	8	2	no	—
1086	C₂×C₄	—	8	2	no	—
1087	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1088	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1089	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1090	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1091	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1092	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1093	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1094	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1095	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1096	C₈	—	2	2	no	—
1097	C₈	—	2	1	no	—
1098	C₈	—	2	2	no	—
1099	C₈	—	2	1	no	—
1100	C₈	—	2	1	no	—
1101	C₈	—	2	1	no	—
1102	C₇	#62058	1	1	yes	characteristic, direct product factor, Sylow
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	4	2	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	4	1	no	—
1111	C₂²	—	4	2	no	—
1112	C₂²	—	4	2	no	—
1113	C₂²	—	4	1	no	—
1114	C₂²	C₇×#577	1	2	yes	—
1115	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	2	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	2	2	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	2	no	—
1124	C₄	—	4	1	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	1	no	—
1130	C₄	—	4	2	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	2	no	—
1133	C₄	C₇×#578	1	2	yes	—
1134	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1135	C₄	C₇×#585	1	1	yes	characteristic
1136	C₂	—	2	2	no	—
1137	C₂	—	4	2	no	—
1138	C₂	—	8	2	no	—
1139	C₂	—	8	1	no	—
1140	C₂	C₇×#3488	1	1	yes	characteristic
1141	C₂	C₂×C₇×#577	1	1	yes	characteristic
1142	C₂	C₂×C₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#529 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3552	C₂	semidirect
2. C₇×#3522	C₂	semidirect
3. C₇×#3400	C₂	semidirect
4. C₇×#3394	C₂	semidirect
5. C₇×#3369	C₂	semidirect
6. C₇×#3363	C₂	semidirect
7. C₇×#3331	C₂	semidirect
8. C₇×#3308	C₂	semidirect
9. C₇×#3299	C₂	semidirect
10. C₇×#3298	C₂	semidirect
11. C₇×#3285	C₂	semidirect
12. C₇×#3284	C₂	semidirect
13. C₇×#3278	C₂	semidirect
14. C₇×#3270	C₂	semidirect
15. C₇×#3258	C₂	semidirect
16. C₇×#3247	C₂	semidirect
17. C₇×#3225	C₂	semidirect
18. C₇×#3206	C₂	semidirect
19. C₇×#3120	C₂	semidirect
20. C₇×#3108	C₂	semidirect
21. C₇×#3046	C₂	semidirect
22. C₂×C₇×#462	C₂	semidirect
23. C₇×#2994	C₂	semidirect
135. #62058	C₇	direct (N × H)
316. #3552	C₂×C₇	semidirect
317. #3522	C₂×C₇	semidirect
318. #3400	C₂×C₇	semidirect
319. #3394	C₂×C₇	semidirect
320. #3369	C₂×C₇	semidirect
321. #3363	C₂×C₇	semidirect
322. #3331	C₂×C₇	semidirect
323. #3308	C₂×C₇	semidirect
324. #3299	C₂×C₇	semidirect
325. #3298	C₂×C₇	semidirect
326. #3285	C₂×C₇	semidirect
327. #3284	C₂×C₇	semidirect
328. #3278	C₂×C₇	semidirect
329. #3270	C₂×C₇	semidirect
330. #3258	C₂×C₇	semidirect
331. #3247	C₂×C₇	semidirect
332. #3225	C₂×C₇	semidirect
333. #3206	C₂×C₇	semidirect
334. #3120	C₂×C₇	semidirect
335. #3108	C₂×C₇	semidirect
336. #3046	C₂×C₇	semidirect
337. C₂×#462	C₂×C₇	semidirect
338. #2994	C₂×C₇	semidirect
1102. C₇	#62058	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×#3552	2
C₇×#3522	2
C₇×#3400	2
C₇×#3394	2
C₇×#3369	2
C₇×#3363	2
C₇×#3331	2
C₇×#3308	2
C₇×#3299	2
C₇×#3298	2
C₇×#3285	2
C₇×#3284	2
C₇×#3278	2
C₇×#3270	2
C₇×#3258	2
C₇×#3247	2
C₇×#3225	2
C₇×#3206	2
C₇×#3120	2
C₇×#3108	2
C₇×#3046	2
C₂×C₇×#462	2
C₇×#2994	2
#62058	7

Subgroups — C7×#62058 #13239274

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62058 #13239274