Subgroups — C₇×#62022 #13239238

Order 1792.

1892 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3522	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3403	C₂	1	2	yes	maximal, complemented
4	C₇×#3375	C₂	1	2	yes	maximal, complemented
5	C₇×#3314	C₂	1	2	yes	maximal, complemented
6	C₇×#3308	C₂	1	2	yes	maximal, complemented
7	C₇×#3294	C₂	1	2	yes	maximal, complemented
8	C₇×#3285	C₂	1	2	yes	maximal, complemented
9	C₇×#3268	C₂	1	2	yes	maximal, complemented
10	C₇×#3265	C₂	1	2	yes	maximal, complemented
11	C₇×#3262	C₂	1	2	yes	maximal, complemented
12	C₇×#3245	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3224	C₂	1	2	yes	maximal, complemented
14	C₇×#3213	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3124	C₂	1	2	yes	maximal, complemented
16	C₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3045	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×#464	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#2992	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂×C₇×#135	C₂²	1	2	yes	complemented
22	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
24	C₇×#562	—	2	1	no	—
25	C₇×H(3,𝔽₄)	—	2	1	no	—
26	C₇×#559	—	2	1	no	—
27	C₇×#559	C₂²	1	2	yes	—
28	C₇×#559	C₂²	1	1	yes	characteristic, complemented
29	C₇×Q₈²	C₂²	1	1	yes	characteristic, complemented
30	C₇×#554	—	2	1	no	—
31	C₇×#554	C₂²	1	1	yes	characteristic, complemented
32	C₇×#550	C₂²	1	1	yes	characteristic, complemented
33	C₇×#548	C₂²	1	2	yes	—
34	C₇×#548	C₂²	1	2	yes	complemented
35	C₇×#547	—	2	2	no	—
36	C₇×#547	C₂²	1	2	yes	complemented
37	C₇×#546	—	2	2	no	—
38	C₇×#546	C₂²	1	2	yes	—
39	C₇×D₄²	C₂²	1	2	yes	—
40	C₇×#542	—	2	2	no	—
41	C₇×#542	C₂²	1	2	yes	—
42	C₇×#542	C₂²	1	2	yes	complemented
43	C₇×#538	—	2	2	no	—
44	C₇×#538	—	2	1	no	—
45	C₇×#535	C₂²	1	2	yes	—
46	C₇×#534	—	2	1	no	—
47	C₇×#532	—	2	1	no	—
48	C₇×#532	C₂²	1	1	yes	characteristic
49	C₇×#532	C₂²	1	1	yes	characteristic, complemented
50	C₇×#529	—	2	1	no	—
51	C₇×#529	C₂²	1	1	yes	characteristic
52	C₂×C₇×#124	C₂²	1	1	yes	characteristic
53	C₇×#520	C₂²	1	2	yes	complemented
54	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₇×#496	C₂²	1	2	yes	—
56	C₇×#496	C₂²	1	2	yes	complemented
57	C₇×#495	C₂²	1	2	yes	complemented
58	C₇×#489	C₂²	1	2	yes	complemented
59	C₇×#489	C₂²	1	2	yes	complemented
60	C₇×#486	C₂²	1	2	yes	—
61	C₇×#484	C₂²	1	2	yes	complemented
62	C₇×#480	C₂²	1	2	yes	—
63	C₇×#480	C₂²	1	2	yes	complemented
64	C₇×#477	C₂²	1	1	yes	characteristic, complemented
65	C₇×#477	C₂²	1	2	yes	complemented
66	C₇×#477	C₂²	1	1	yes	characteristic, complemented
67	C₇×#474	C₂²	1	2	yes	complemented
68	C₇×#474	C₂²	1	2	yes	complemented
69	C₇×#474	C₂²	1	2	yes	complemented
70	C₇×#468	C₂²	1	2	yes	—
71	C₇×#468	C₂²	1	2	yes	complemented
72	C₇×#467	C₂²	1	2	yes	complemented
73	C₇×#466	C₂²	1	2	yes	—
74	C₇×#466	C₂²	1	2	yes	complemented
75	C₇×#466	C₂²	1	2	yes	complemented
76	C₇×#464	C₂²	1	2	yes	complemented
77	C₇×#464	C₂²	1	2	yes	complemented
78	C₇×#464	C₂²	1	2	yes	complemented
79	C₇×#464	C₂²	1	2	yes	complemented
80	C₇×#464	C₂²	1	2	yes	complemented
81	C₇×#464	C₂²	1	2	yes	complemented
82	C₇×#463	C₂²	1	2	yes	complemented
83	C₇×#463	C₂²	1	2	yes	complemented
84	C₇×#463	C₂²	1	2	yes	complemented
85	C₇×#463	C₂²	1	2	yes	complemented
86	C₇×#460	C₂²	1	2	yes	—
87	C₇×#460	C₂²	1	1	yes	characteristic, complemented
88	C₇×#460	C₂²	1	1	yes	characteristic, complemented
89	C₇×#459	C₂²	1	2	yes	—
90	C₇×#459	C₂²	1	2	yes	complemented
91	C₇×#459	C₂²	1	2	yes	complemented
92	C₇×#452	C₂²	1	2	yes	complemented
93	C₇×#452	C₂²	1	2	yes	complemented
94	C₇×#450	C₂²	1	2	yes	complemented
95	C₇×#449	C₂²	1	2	yes	—
96	C₇×#449	C₂²	1	2	yes	complemented
97	C₇×#448	C₂²	1	2	yes	complemented
98	C₇×#448	C₂²	1	2	yes	complemented
99	C₇×#447	C₂²	1	2	yes	—
100	C₇×#447	C₂²	1	2	yes	complemented
101	C₇×#446	C₂²	1	2	yes	complemented
102	C₇×#440	C₂²	1	2	yes	complemented
103	C₇×#440	C₂²	1	2	yes	complemented
104	C₇×#440	C₂²	1	2	yes	complemented
105	C₇×#440	C₂²	1	2	yes	complemented
106	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
107	C₄×C₇×D₈	C₂²	1	2	yes	complemented
108	C₇×#435	C₂²	1	2	yes	complemented
109	C₇×#435	C₂²	1	2	yes	complemented
110	C₇×C₈×D₄	C₂²	1	2	yes	complemented
111	C₇×#433	C₂²	1	2	yes	complemented
112	C₇×#432	C₂²	1	1	yes	characteristic, complemented
113	C₇×#424	C₂²	1	2	yes	complemented
114	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
115	C₇×#417	C₂²	1	2	yes	complemented
116	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₇×#102	C₂²	1	1	yes	characteristic
118	C₂×C₇×#102	C₂²	1	2	yes	complemented
119	#62022	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂×C₇×#41	—	2	2	no	—
121	C₂×C₇×#41	—	2	1	no	—
122	C₂×C₇×#41	—	2	1	no	—
123	C₂×C₇×#41	C₂³	1	2	yes	—
124	C₂×C₇×#41	C₂³	1	2	yes	—
125	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
126	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
127	C₂²×C₇×D₄	—	2	2	no	—
128	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
129	C₂²×C₇×D₄	C₂³	1	2	yes	—
130	C₇×AGL(1,ℤ/8)	—	4	4	no	—
131	C₇×#135	—	4	4	no	—
132	C₂×C₇×Q₁₆	—	4	2	no	—
133	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
134	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
135	C₂×C₇×SD₁₆	—	4	2	no	—
136	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
137	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
138	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
139	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
140	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
141	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
142	C₂×C₇×D₈	C₂³	1	2	yes	—
143	C₂×C₇×D₈	C₂³	1	2	yes	—
144	C₂×C₇×D₈	C₂³	1	2	yes	—
145	C₂×C₇×D₈	C₂³	1	2	yes	—
146	C₂×C₇×M₁₆	C₂³	1	2	yes	—
147	C₂²×C₇×C₈	C₂³	1	2	yes	—
148	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
150	C₇×C₄⋊Q₈	—	2	1	no	—
151	C₇×C₄⋊Q₈	—	2	2	no	—
152	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₇×#127	—	2	1	no	—
156	C₇×#127	C₂³	1	2	yes	—
157	C₇×#127	C₂³	1	1	yes	characteristic
158	C₇×#127	C₂³	1	1	yes	characteristic
159	C₇×#126	—	2	2	no	—
160	C₇×#126	—	2	2	no	—
161	C₇×#126	D₄	1	2	yes	—
162	C₇×#125	—	2	1	no	—
163	C₇×#125	D₄	1	1	yes	characteristic
164	C₇×#124	—	2	1	no	—
165	C₇×#124	—	2	2	no	—
166	C₇×#124	—	2	2	no	—
167	C₇×#124	—	2	2	no	—
168	C₇×#124	—	2	2	no	—
169	C₇×#124	—	2	2	no	—
170	C₇×#124	—	2	1	no	—
171	C₇×#124	—	2	1	no	—
172	C₇×#124	—	2	1	no	—
173	C₇×#124	—	2	1	no	—
174	C₇×#124	D₄	1	1	yes	characteristic
175	C₇×#124	C₂³	1	2	yes	—
176	C₇×#124	C₂³	1	2	yes	—
177	C₇×#124	C₂³	1	2	yes	—
178	C₇×#124	C₂³	1	2	yes	—
179	C₇×#123	—	2	2	no	—
180	C₇×#123	—	2	2	no	—
181	C₇×#123	—	2	2	no	—
182	C₇×#123	—	2	2	no	—
183	C₇×#123	—	2	2	no	—
184	C₇×#123	—	2	2	no	—
185	C₇×#123	—	2	2	no	—
186	C₇×#123	—	2	2	no	—
187	C₇×#123	D₄	1	2	yes	—
188	C₇×C₂²⋊Q₈	—	2	2	no	—
189	C₇×C₂²⋊Q₈	—	2	2	no	—
190	C₇×C₂²⋊Q₈	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	2	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
195	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
196	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₇×#121	—	2	2	no	—
198	C₇×#121	—	2	2	no	—
199	C₇×#121	—	2	1	no	—
200	C₇×#121	—	2	1	no	—
201	C₇×#121	—	2	2	no	—
202	C₇×#121	—	2	2	no	—
203	C₇×#121	—	2	2	no	—
204	C₇×#121	—	2	2	no	—
205	C₇×#121	—	2	2	no	—
206	C₇×#121	D₄	1	1	yes	characteristic
207	C₇×#121	C₂³	1	2	yes	—
208	C₇×#121	C₂³	1	2	yes	—
209	C₇×#121	C₂³	1	2	yes	—
210	C₇×#121	C₂³	1	2	yes	—
211	C₇×#120	—	2	2	no	—
212	C₇×#120	—	2	2	no	—
213	C₇×#120	—	2	2	no	—
214	C₇×#120	—	2	2	no	—
215	C₇×#120	—	2	2	no	—
216	C₄×C₇×Q₈	—	2	1	no	—
217	C₄×C₇×Q₈	—	2	1	no	—
218	C₄×C₇×Q₈	—	2	1	no	—
219	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
220	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
221	C₄×C₇×Q₈	C₂³	1	2	yes	—
222	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
223	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
224	C₄×C₇×Q₈	C₂³	1	2	yes	—
225	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
226	C₄×C₇×D₄	—	2	1	no	—
227	C₄×C₇×D₄	—	2	1	no	—
228	C₄×C₇×D₄	—	2	1	no	—
229	C₄×C₇×D₄	—	2	2	no	—
230	C₄×C₇×D₄	—	2	2	no	—
231	C₄×C₇×D₄	—	2	2	no	—
232	C₄×C₇×D₄	—	2	2	no	—
233	C₄×C₇×D₄	—	2	2	no	—
234	C₄×C₇×D₄	—	2	1	no	—
235	C₄×C₇×D₄	—	2	1	no	—
236	C₄×C₇×D₄	C₂³	1	2	yes	—
237	C₄×C₇×D₄	C₂³	1	2	yes	—
238	C₄×C₇×D₄	C₂³	1	2	yes	—
239	C₄×C₇×D₄	C₂³	1	2	yes	—
240	C₄×C₇×D₄	C₂³	1	2	yes	—
241	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
242	C₇×#117	—	2	2	no	—
243	C₇×#117	C₂³	1	2	yes	—
244	C₂×C₇×C₄⋊C₄	—	2	1	no	—
245	C₂×C₇×C₄⋊C₄	—	2	2	no	—
246	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
247	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
248	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
249	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
250	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₄²×C₇	—	2	1	no	—
252	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
253	C₇×#107	C₂³	1	2	yes	—
254	C₇×#107	C₂³	1	2	yes	—
255	C₇×#107	C₂³	1	2	yes	—
256	C₇×#107	C₂³	1	2	yes	—
257	C₇×C₄⋊C₈	C₂³	1	2	yes	—
258	C₇×C₄⋊C₈	C₂³	1	2	yes	—
259	C₇×C₄⋊C₈	C₂³	1	2	yes	—
260	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₇×C₄⋊C₈	C₂³	1	2	yes	—
262	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
263	C₇×#103	C₂³	1	2	yes	—
264	C₇×#103	C₂³	1	2	yes	—
265	C₇×#103	C₂³	1	2	yes	—
266	C₇×#103	C₂³	1	2	yes	—
267	C₇×#103	C₂³	1	2	yes	—
268	C₇×#103	C₂³	1	2	yes	—
269	C₇×#102	C₂³	1	2	yes	—
270	C₇×#102	C₂³	1	2	yes	—
271	C₇×#102	C₂³	1	2	yes	—
272	C₇×#102	C₂³	1	2	yes	—
273	C₇×#102	C₂³	1	2	yes	—
274	C₇×#102	C₂³	1	2	yes	—
275	C₇×#102	C₂³	1	2	yes	—
276	C₇×#102	C₂³	1	2	yes	—
277	C₇×#102	C₂³	1	2	yes	—
278	C₇×#102	C₂³	1	2	yes	—
279	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
280	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
281	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
282	C₇×#97	C₂³	1	2	yes	—
283	C₇×#97	C₂³	1	2	yes	—
284	C₄×C₇×C₈	C₂³	1	2	yes	—
285	#3558	C₂×C₇	1	1	yes	characteristic, complemented
286	#3522	C₂×C₇	1	1	yes	characteristic, complemented
287	#3403	C₂×C₇	1	2	yes	complemented
288	#3375	C₂×C₇	1	2	yes	complemented
289	#3314	C₂×C₇	1	2	yes	complemented
290	#3308	C₂×C₇	1	2	yes	complemented
291	#3294	C₂×C₇	1	2	yes	complemented
292	#3285	C₂×C₇	1	2	yes	complemented
293	#3268	C₂×C₇	1	2	yes	complemented
294	#3265	C₂×C₇	1	2	yes	complemented
295	#3262	C₂×C₇	1	2	yes	complemented
296	#3245	C₂×C₇	1	1	yes	characteristic, complemented
297	#3224	C₂×C₇	1	2	yes	complemented
298	#3213	C₂×C₇	1	1	yes	characteristic, complemented
299	#3124	C₂×C₇	1	2	yes	complemented
300	#3112	C₂×C₇	1	1	yes	characteristic, complemented
301	#3045	C₂×C₇	1	2	yes	complemented
302	C₂×#464	C₂×C₇	1	1	yes	characteristic, complemented
303	#2992	C₂×C₇	1	1	yes	characteristic, complemented
304	C₂⁴×C₇	—	2	1	no	—
305	C₂⁴×C₇	—	2	2	no	—
306	C₇×#41	—	2	4	no	—
307	C₇×#41	—	4	2	no	—
308	C₇×#41	—	4	2	no	—
309	C₇×#41	—	4	2	no	—
310	C₇×#41	—	8	2	no	—
311	C₇×#41	—	8	2	no	—
312	C₇×#41	—	8	4	no	—
313	C₂×C₇×Q₈	—	2	1	no	—
314	C₂×C₇×Q₈	—	2	1	no	—
315	C₂×C₇×Q₈	—	2	1	no	—
316	C₂×C₇×Q₈	—	2	2	no	—
317	C₂×C₇×Q₈	—	2	1	no	—
318	C₂×C₇×Q₈	—	2	2	no	—
319	C₂×C₇×Q₈	—	4	1	no	—
320	C₂×C₇×Q₈	—	4	1	no	—
321	C₂×C₇×Q₈	—	4	1	no	—
322	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
323	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
324	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
325	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
326	C₂×C₇×D₄	—	2	2	no	—
327	C₂×C₇×D₄	—	2	2	no	—
328	C₂×C₇×D₄	—	2	2	no	—
329	C₂×C₇×D₄	—	2	2	no	—
330	C₂×C₇×D₄	—	2	2	no	—
331	C₂×C₇×D₄	—	2	2	no	—
332	C₂×C₇×D₄	—	2	1	no	—
333	C₂×C₇×D₄	—	2	2	no	—
334	C₂×C₇×D₄	—	2	1	no	—
335	C₂×C₇×D₄	—	2	1	no	—
336	C₂×C₇×D₄	—	2	1	no	—
337	C₂×C₇×D₄	—	2	2	no	—
338	C₂×C₇×D₄	—	2	2	no	—
339	C₂×C₇×D₄	—	2	1	no	—
340	C₂×C₇×D₄	—	4	1	no	—
341	C₂×C₇×D₄	—	4	2	no	—
342	C₂×C₇×D₄	—	4	1	no	—
343	C₂×C₇×D₄	—	4	2	no	—
344	C₂×C₇×D₄	—	8	4	no	—
345	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
346	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
347	C₂×C₇×D₄	C₂⁴	1	2	yes	—
348	C₂×C₇×D₄	C₂⁴	1	2	yes	—
349	C₂×C₇×D₄	C₂⁴	1	2	yes	—
350	C₂²×C₄×C₇	—	2	1	no	—
351	C₂²×C₄×C₇	—	2	1	no	—
352	C₂²×C₄×C₇	—	2	1	no	—
353	C₂²×C₄×C₇	—	2	2	no	—
354	C₂²×C₄×C₇	—	2	2	no	—
355	C₂²×C₄×C₇	—	2	2	no	—
356	C₂²×C₄×C₇	—	2	2	no	—
357	C₂²×C₄×C₇	—	2	2	no	—
358	C₂²×C₄×C₇	—	2	2	no	—
359	C₂²×C₄×C₇	—	2	2	no	—
360	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
361	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
362	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
364	C₇×Q₁₆	—	2	4	no	—
365	C₇×Q₁₆	—	4	2	no	—
366	C₇×SD₁₆	—	2	4	no	—
367	C₇×SD₁₆	—	2	4	no	—
368	C₇×SD₁₆	—	4	2	no	—
369	C₇×SD₁₆	—	4	2	no	—
370	C₇×SD₁₆	—	4	2	no	—
371	C₇×SD₁₆	—	4	2	no	—
372	C₇×D₈	—	4	2	no	—
373	C₇×D₈	—	4	2	no	—
374	C₇×D₈	—	4	2	no	—
375	C₇×D₈	—	4	2	no	—
376	C₇×M₁₆	—	4	2	no	—
377	C₂×C₇×C₈	—	4	1	no	—
378	C₂×C₇×C₈	—	4	1	no	—
379	C₂×C₇×C₈	—	4	2	no	—
380	C₂×C₇×C₈	C₂⁴	1	2	yes	—
381	C₂×C₇×C₈	C₂⁴	1	2	yes	—
382	C₂×C₇×C₈	C₂⁴	1	2	yes	—
383	C₂×C₇×C₈	C₂⁴	1	2	yes	—
384	C₇×C₄⋊C₄	—	2	1	no	—
385	C₇×C₄⋊C₄	—	2	2	no	—
386	C₇×C₄⋊C₄	—	2	2	no	—
387	C₇×C₄⋊C₄	—	2	1	no	—
388	C₇×C₄⋊C₄	—	2	1	no	—
389	C₇×C₄⋊C₄	—	2	1	no	—
390	C₇×C₄⋊C₄	—	2	1	no	—
391	C₇×C₄⋊C₄	—	2	1	no	—
392	C₇×C₄⋊C₄	—	2	2	no	—
393	C₇×C₄⋊C₄	—	2	1	no	—
394	C₇×C₄⋊C₄	—	2	2	no	—
395	C₇×C₄⋊C₄	—	2	2	no	—
396	C₇×C₄⋊C₄	—	2	2	no	—
397	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
399	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
400	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
402	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
403	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
406	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
407	C₇×C₂²⋊C₄	—	2	2	no	—
408	C₇×C₂²⋊C₄	—	2	2	no	—
409	C₇×C₂²⋊C₄	—	2	2	no	—
410	C₇×C₂²⋊C₄	—	2	2	no	—
411	C₇×C₂²⋊C₄	—	2	2	no	—
412	C₇×C₂²⋊C₄	—	2	2	no	—
413	C₇×C₂²⋊C₄	—	2	2	no	—
414	C₇×C₂²⋊C₄	—	2	2	no	—
415	C₇×C₂²⋊C₄	—	2	2	no	—
416	C₇×C₂²⋊C₄	—	2	2	no	—
417	C₇×C₂²⋊C₄	—	2	2	no	—
418	C₇×C₂²⋊C₄	—	2	2	no	—
419	C₇×C₂²⋊C₄	—	2	2	no	—
420	C₇×C₂²⋊C₄	—	2	2	no	—
421	C₇×C₂²⋊C₄	—	2	2	no	—
422	C₇×C₂²⋊C₄	—	2	2	no	—
423	C₇×C₂²⋊C₄	—	2	2	no	—
424	C₇×C₂²⋊C₄	—	2	2	no	—
425	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
426	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
427	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
428	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
429	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
430	C₄²×C₇	—	2	1	no	—
431	C₄²×C₇	—	2	1	no	—
432	C₄²×C₇	—	2	1	no	—
433	C₄²×C₇	—	2	1	no	—
434	C₄²×C₇	—	2	2	no	—
435	C₄²×C₇	—	2	2	no	—
436	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
437	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₇	C₂⁴	1	2	yes	—
439	C₄²×C₇	C₂⁴	1	1	yes	characteristic
440	C₄²×C₇	C₂⁴	1	1	yes	characteristic
441	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
442	C₂×#135	C₂²×C₇	1	2	yes	complemented
443	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
444	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
445	#562	—	2	1	no	—
446	H(3,𝔽₄)	—	2	1	no	—
447	#559	—	2	1	no	—
448	#559	C₂²×C₇	1	2	yes	—
449	#559	C₂²×C₇	1	1	yes	characteristic, complemented
450	Q₈²	C₂²×C₇	1	1	yes	characteristic, complemented
451	#554	—	2	1	no	—
452	#554	C₂²×C₇	1	1	yes	characteristic, complemented
453	#550	C₂²×C₇	1	1	yes	characteristic, complemented
454	#548	C₂²×C₇	1	2	yes	—
455	#548	C₂²×C₇	1	2	yes	complemented
456	#547	—	2	2	no	—
457	#547	C₂²×C₇	1	2	yes	complemented
458	#546	—	2	2	no	—
459	#546	C₂²×C₇	1	2	yes	—
460	D₄²	C₂²×C₇	1	2	yes	—
461	#542	—	2	2	no	—
462	#542	C₂²×C₇	1	2	yes	—
463	#542	C₂²×C₇	1	2	yes	complemented
464	#538	—	2	2	no	—
465	#538	—	2	1	no	—
466	#535	C₂²×C₇	1	2	yes	—
467	#534	—	2	1	no	—
468	#532	—	2	1	no	—
469	#532	C₂²×C₇	1	1	yes	characteristic
470	#532	C₂²×C₇	1	1	yes	characteristic, complemented
471	#529	—	2	1	no	—
472	#529	C₂²×C₇	1	1	yes	characteristic
473	C₂×#124	C₂²×C₇	1	1	yes	characteristic
474	#520	C₂²×C₇	1	2	yes	complemented
475	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
476	#496	C₂²×C₇	1	2	yes	—
477	#496	C₂²×C₇	1	2	yes	complemented
478	#495	C₂²×C₇	1	2	yes	complemented
479	#489	C₂²×C₇	1	2	yes	complemented
480	#489	C₂²×C₇	1	2	yes	complemented
481	#486	C₂²×C₇	1	2	yes	—
482	#484	C₂²×C₇	1	2	yes	complemented
483	#480	C₂²×C₇	1	2	yes	—
484	#480	C₂²×C₇	1	2	yes	complemented
485	#477	C₂²×C₇	1	1	yes	characteristic, complemented
486	#477	C₂²×C₇	1	1	yes	characteristic, complemented
487	#477	C₂²×C₇	1	2	yes	complemented
488	#474	C₂²×C₇	1	2	yes	complemented
489	#474	C₂²×C₇	1	2	yes	complemented
490	#474	C₂²×C₇	1	2	yes	complemented
491	#468	C₂²×C₇	1	2	yes	—
492	#468	C₂²×C₇	1	2	yes	complemented
493	#467	C₂²×C₇	1	2	yes	complemented
494	#466	C₂²×C₇	1	2	yes	—
495	#466	C₂²×C₇	1	2	yes	complemented
496	#466	C₂²×C₇	1	2	yes	complemented
497	#464	C₂²×C₇	1	2	yes	complemented
498	#464	C₂²×C₇	1	2	yes	complemented
499	#464	C₂²×C₇	1	2	yes	complemented
500	#464	C₂²×C₇	1	2	yes	complemented
501	#464	C₂²×C₇	1	2	yes	complemented
502	#464	C₂²×C₇	1	2	yes	complemented
503	#463	C₂²×C₇	1	2	yes	complemented
504	#463	C₂²×C₇	1	2	yes	complemented
505	#463	C₂²×C₇	1	2	yes	complemented
506	#463	C₂²×C₇	1	2	yes	complemented
507	#460	C₂²×C₇	1	2	yes	—
508	#460	C₂²×C₇	1	1	yes	characteristic, complemented
509	#460	C₂²×C₇	1	1	yes	characteristic, complemented
510	#459	C₂²×C₇	1	2	yes	—
511	#459	C₂²×C₇	1	2	yes	complemented
512	#459	C₂²×C₇	1	2	yes	complemented
513	#452	C₂²×C₇	1	2	yes	complemented
514	#452	C₂²×C₇	1	2	yes	complemented
515	#450	C₂²×C₇	1	2	yes	complemented
516	#449	C₂²×C₇	1	2	yes	—
517	#449	C₂²×C₇	1	2	yes	complemented
518	#448	C₂²×C₇	1	2	yes	complemented
519	#448	C₂²×C₇	1	2	yes	complemented
520	#447	C₂²×C₇	1	2	yes	—
521	#447	C₂²×C₇	1	2	yes	complemented
522	#446	C₂²×C₇	1	2	yes	complemented
523	#440	C₂²×C₇	1	2	yes	complemented
524	#440	C₂²×C₇	1	2	yes	complemented
525	#440	C₂²×C₇	1	2	yes	complemented
526	#440	C₂²×C₇	1	2	yes	complemented
527	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
528	C₄×D₈	C₂²×C₇	1	2	yes	complemented
529	#435	C₂²×C₇	1	2	yes	complemented
530	#435	C₂²×C₇	1	2	yes	complemented
531	C₈×D₄	C₂²×C₇	1	2	yes	complemented
532	#433	C₂²×C₇	1	2	yes	complemented
533	#432	C₂²×C₇	1	1	yes	characteristic, complemented
534	#424	C₂²×C₇	1	2	yes	complemented
535	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
536	#417	C₂²×C₇	1	2	yes	complemented
537	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
538	C₂×#102	C₂²×C₇	1	1	yes	characteristic
539	C₂×#102	C₂²×C₇	1	2	yes	complemented
540	C₂³×C₇	—	2	2	no	—
541	C₂³×C₇	—	2	2	no	—
542	C₂³×C₇	—	2	2	no	—
543	C₂³×C₇	—	4	2	no	—
544	C₂³×C₇	—	8	1	no	—
545	C₂³×C₇	—	8	2	no	—
546	C₂³×C₇	—	8	2	no	—
547	C₂³×C₇	—	8	1	no	—
548	C₂³×C₇	—	8	2	no	—
549	C₂³×C₇	C₂²×D₄	1	2	yes	—
550	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
551	C₇×Q₈	—	2	1	no	—
552	C₇×Q₈	—	2	1	no	—
553	C₇×Q₈	—	2	2	no	—
554	C₇×Q₈	—	2	1	no	—
555	C₇×Q₈	—	2	2	no	—
556	C₇×Q₈	—	4	1	no	—
557	C₇×Q₈	—	4	2	no	—
558	C₇×Q₈	—	8	1	no	—
559	C₇×Q₈	—	8	1	no	—
560	C₇×Q₈	—	8	1	no	—
561	C₇×Q₈	—	8	2	no	—
562	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
563	C₇×D₄	—	2	4	no	—
564	C₇×D₄	—	2	2	no	—
565	C₇×D₄	—	2	2	no	—
566	C₇×D₄	—	2	2	no	—
567	C₇×D₄	—	2	2	no	—
568	C₇×D₄	—	2	2	no	—
569	C₇×D₄	—	2	2	no	—
570	C₇×D₄	—	4	1	no	—
571	C₇×D₄	—	4	4	no	—
572	C₇×D₄	—	4	2	no	—
573	C₇×D₄	—	4	4	no	—
574	C₇×D₄	—	4	4	no	—
575	C₇×D₄	—	8	1	no	—
576	C₇×D₄	—	8	2	no	—
577	C₇×D₄	—	8	2	no	—
578	C₇×D₄	—	8	1	no	—
579	C₇×D₄	—	8	2	no	—
580	C₇×D₄	—	8	1	no	—
581	C₇×D₄	—	8	1	no	—
582	C₇×D₄	—	8	2	no	—
583	C₇×D₄	—	8	2	no	—
584	C₇×D₄	—	8	2	no	—
585	C₂×C₄×C₇	—	2	2	no	—
586	C₂×C₄×C₇	—	2	1	no	—
587	C₂×C₄×C₇	—	2	1	no	—
588	C₂×C₄×C₇	—	2	2	no	—
589	C₂×C₄×C₇	—	2	1	no	—
590	C₂×C₄×C₇	—	2	2	no	—
591	C₂×C₄×C₇	—	2	1	no	—
592	C₂×C₄×C₇	—	2	1	no	—
593	C₂×C₄×C₇	—	2	1	no	—
594	C₂×C₄×C₇	—	2	2	no	—
595	C₂×C₄×C₇	—	2	2	no	—
596	C₂×C₄×C₇	—	2	2	no	—
597	C₂×C₄×C₇	—	4	1	no	—
598	C₂×C₄×C₇	—	4	4	no	—
599	C₂×C₄×C₇	—	4	2	no	—
600	C₂×C₄×C₇	—	4	2	no	—
601	C₂×C₄×C₇	—	8	2	no	—
602	C₂×C₄×C₇	—	8	2	no	—
603	C₂×C₄×C₇	—	8	2	no	—
604	C₂×C₄×C₇	—	8	2	no	—
605	C₂×C₄×C₇	—	8	2	no	—
606	C₂×C₄×C₇	—	8	1	no	—
607	C₂×C₄×C₇	—	8	2	no	—
608	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
609	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
610	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
611	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
612	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
613	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
614	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
615	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
616	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
617	C₇×C₈	—	2	2	no	—
618	C₇×C₈	—	2	2	no	—
619	C₇×C₈	—	2	2	no	—
620	C₇×C₈	—	2	2	no	—
621	C₂×#41	—	2	2	no	—
622	C₂×#41	—	2	1	no	—
623	C₂×#41	—	2	1	no	—
624	C₂×#41	C₂³×C₇	1	2	yes	—
625	C₂×#41	C₂³×C₇	1	2	yes	—
626	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
627	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
628	C₂²×D₄	—	2	2	no	—
629	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
630	C₂²×D₄	C₂³×C₇	1	2	yes	—
631	AGL(1,ℤ/8)	—	4	4	no	—
632	#135	—	4	4	no	—
633	C₂×Q₁₆	—	4	2	no	—
634	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
635	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
636	C₂×SD₁₆	—	4	2	no	—
637	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
638	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
639	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
640	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
641	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
642	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
643	C₂×D₈	C₂³×C₇	1	2	yes	—
644	C₂×D₈	C₂³×C₇	1	2	yes	—
645	C₂×D₈	C₂³×C₇	1	2	yes	—
646	C₂×D₈	C₂³×C₇	1	2	yes	—
647	C₂×M₁₆	C₂³×C₇	1	2	yes	—
648	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
649	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
650	C₂²×C₈	C₂³×C₇	1	2	yes	—
651	C₄⋊Q₈	—	2	1	no	—
652	C₄⋊Q₈	—	2	2	no	—
653	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
654	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
655	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
656	#127	—	2	1	no	—
657	#127	C₂³×C₇	1	1	yes	characteristic
658	#127	C₂³×C₇	1	1	yes	characteristic
659	#127	C₂³×C₇	1	2	yes	—
660	#126	—	2	2	no	—
661	#126	—	2	2	no	—
662	#126	C₇×D₄	1	2	yes	—
663	#125	—	2	1	no	—
664	#125	C₇×D₄	1	1	yes	characteristic
665	#124	—	2	1	no	—
666	#124	—	2	2	no	—
667	#124	—	2	2	no	—
668	#124	—	2	2	no	—
669	#124	—	2	2	no	—
670	#124	—	2	2	no	—
671	#124	—	2	1	no	—
672	#124	—	2	1	no	—
673	#124	—	2	1	no	—
674	#124	—	2	1	no	—
675	#124	C₇×D₄	1	1	yes	characteristic
676	#124	C₂³×C₇	1	2	yes	—
677	#124	C₂³×C₇	1	2	yes	—
678	#124	C₂³×C₇	1	2	yes	—
679	#124	C₂³×C₇	1	2	yes	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	#123	—	2	2	no	—
683	#123	—	2	2	no	—
684	#123	—	2	2	no	—
685	#123	—	2	2	no	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	C₇×D₄	1	2	yes	—
689	C₂²⋊Q₈	—	2	2	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
696	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
697	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
698	#121	—	2	2	no	—
699	#121	—	2	2	no	—
700	#121	—	2	1	no	—
701	#121	—	2	1	no	—
702	#121	—	2	2	no	—
703	#121	—	2	2	no	—
704	#121	—	2	2	no	—
705	#121	—	2	2	no	—
706	#121	—	2	2	no	—
707	#121	C₇×D₄	1	1	yes	characteristic
708	#121	C₂³×C₇	1	2	yes	—
709	#121	C₂³×C₇	1	2	yes	—
710	#121	C₂³×C₇	1	2	yes	—
711	#121	C₂³×C₇	1	2	yes	—
712	#120	—	2	2	no	—
713	#120	—	2	2	no	—
714	#120	—	2	2	no	—
715	#120	—	2	2	no	—
716	#120	—	2	2	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	—	2	1	no	—
720	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
721	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
722	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
723	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
724	C₄×Q₈	C₂³×C₇	1	2	yes	—
725	C₄×Q₈	C₂³×C₇	1	2	yes	—
726	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
727	C₄×D₄	—	2	1	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	2	no	—
731	C₄×D₄	—	2	2	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	2	no	—
734	C₄×D₄	—	2	2	no	—
735	C₄×D₄	—	2	1	no	—
736	C₄×D₄	—	2	1	no	—
737	C₄×D₄	C₂³×C₇	1	2	yes	—
738	C₄×D₄	C₂³×C₇	1	2	yes	—
739	C₄×D₄	C₂³×C₇	1	2	yes	—
740	C₄×D₄	C₂³×C₇	1	2	yes	—
741	C₄×D₄	C₂³×C₇	1	2	yes	—
742	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
743	#117	—	2	2	no	—
744	#117	C₂³×C₇	1	2	yes	—
745	C₂×C₄⋊C₄	—	2	1	no	—
746	C₂×C₄⋊C₄	—	2	2	no	—
747	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
749	C₂×C₂²⋊C₄	—	2	1	no	—
750	C₂×C₂²⋊C₄	—	2	1	no	—
751	C₂×C₂²⋊C₄	—	2	2	no	—
752	C₂×C₄²	—	2	1	no	—
753	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
754	#107	C₂³×C₇	1	2	yes	—
755	#107	C₂³×C₇	1	2	yes	—
756	#107	C₂³×C₇	1	2	yes	—
757	#107	C₂³×C₇	1	2	yes	—
758	C₄⋊C₈	C₂³×C₇	1	2	yes	—
759	C₄⋊C₈	C₂³×C₇	1	2	yes	—
760	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
761	C₄⋊C₈	C₂³×C₇	1	2	yes	—
762	C₄⋊C₈	C₂³×C₇	1	2	yes	—
763	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
764	#103	C₂³×C₇	1	2	yes	—
765	#103	C₂³×C₇	1	2	yes	—
766	#103	C₂³×C₇	1	2	yes	—
767	#103	C₂³×C₇	1	2	yes	—
768	#103	C₂³×C₇	1	2	yes	—
769	#103	C₂³×C₇	1	2	yes	—
770	#102	C₂³×C₇	1	2	yes	—
771	#102	C₂³×C₇	1	2	yes	—
772	#102	C₂³×C₇	1	2	yes	—
773	#102	C₂³×C₇	1	2	yes	—
774	#102	C₂³×C₇	1	2	yes	—
775	#102	C₂³×C₇	1	2	yes	—
776	#102	C₂³×C₇	1	2	yes	—
777	#102	C₂³×C₇	1	2	yes	—
778	#102	C₂³×C₇	1	2	yes	—
779	#102	C₂³×C₇	1	2	yes	—
780	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
781	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
782	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
783	#97	C₂³×C₇	1	2	yes	—
784	#97	C₂³×C₇	1	2	yes	—
785	C₄×C₈	C₂³×C₇	1	2	yes	—
786	C₂²×C₇	—	2	1	no	—
787	C₂²×C₇	—	2	1	no	—
788	C₂²×C₇	—	2	2	no	—
789	C₂²×C₇	—	2	2	no	—
790	C₂²×C₇	—	2	2	no	—
791	C₂²×C₇	—	4	2	no	—
792	C₂²×C₇	—	4	2	no	—
793	C₂²×C₇	—	4	2	no	—
794	C₂²×C₇	—	4	2	no	—
795	C₂²×C₇	—	4	2	no	—
796	C₂²×C₇	—	4	2	no	—
797	C₂²×C₇	—	4	2	no	—
798	C₂²×C₇	—	4	2	no	—
799	C₂²×C₇	—	4	2	no	—
800	C₂²×C₇	—	16	2	no	—
801	C₂²×C₇	—	16	4	no	—
802	C₂²×C₇	#576	1	2	yes	—
803	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
804	C₄×C₇	—	2	1	no	—
805	C₄×C₇	—	2	1	no	—
806	C₄×C₇	—	2	2	no	—
807	C₄×C₇	—	2	2	no	—
808	C₄×C₇	—	2	1	no	—
809	C₄×C₇	—	2	2	no	—
810	C₄×C₇	—	2	1	no	—
811	C₄×C₇	—	2	1	no	—
812	C₄×C₇	—	2	2	no	—
813	C₄×C₇	—	4	1	no	—
814	C₄×C₇	—	4	2	no	—
815	C₄×C₇	—	4	1	no	—
816	C₄×C₇	—	4	1	no	—
817	C₄×C₇	—	4	2	no	—
818	C₄×C₇	—	4	2	no	—
819	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
820	C₄×C₇	#585	1	1	yes	characteristic
821	C₂⁴	—	2	1	no	—
822	C₂⁴	—	2	2	no	—
823	#41	—	2	4	no	—
824	#41	—	4	2	no	—
825	#41	—	4	2	no	—
826	#41	—	4	2	no	—
827	#41	—	8	2	no	—
828	#41	—	8	2	no	—
829	#41	—	8	4	no	—
830	C₂×Q₈	—	2	1	no	—
831	C₂×Q₈	—	2	1	no	—
832	C₂×Q₈	—	2	1	no	—
833	C₂×Q₈	—	2	2	no	—
834	C₂×Q₈	—	2	1	no	—
835	C₂×Q₈	—	2	2	no	—
836	C₂×Q₈	—	4	1	no	—
837	C₂×Q₈	—	4	1	no	—
838	C₂×Q₈	—	4	1	no	—
839	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
840	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
841	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
842	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
843	C₂×D₄	—	2	2	no	—
844	C₂×D₄	—	2	2	no	—
845	C₂×D₄	—	2	2	no	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	2	2	no	—
848	C₂×D₄	—	2	2	no	—
849	C₂×D₄	—	2	1	no	—
850	C₂×D₄	—	2	2	no	—
851	C₂×D₄	—	2	1	no	—
852	C₂×D₄	—	2	1	no	—
853	C₂×D₄	—	2	1	no	—
854	C₂×D₄	—	2	2	no	—
855	C₂×D₄	—	2	2	no	—
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	4	1	no	—
858	C₂×D₄	—	4	2	no	—
859	C₂×D₄	—	4	1	no	—
860	C₂×D₄	—	4	2	no	—
861	C₂×D₄	—	8	4	no	—
862	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
863	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
864	C₂×D₄	C₂⁴×C₇	1	2	yes	—
865	C₂×D₄	C₂⁴×C₇	1	2	yes	—
866	C₂×D₄	C₂⁴×C₇	1	2	yes	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	no	—
873	C₂²×C₄	—	2	2	no	—
874	C₂²×C₄	—	2	2	no	—
875	C₂²×C₄	—	2	2	no	—
876	C₂²×C₄	—	2	2	no	—
877	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
878	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
881	Q₁₆	—	2	4	no	—
882	Q₁₆	—	4	2	no	—
883	SD₁₆	—	2	4	no	—
884	SD₁₆	—	2	4	no	—
885	SD₁₆	—	4	2	no	—
886	SD₁₆	—	4	2	no	—
887	SD₁₆	—	4	2	no	—
888	SD₁₆	—	4	2	no	—
889	D₈	—	4	2	no	—
890	D₈	—	4	2	no	—
891	D₈	—	4	2	no	—
892	D₈	—	4	2	no	—
893	M₁₆	—	4	2	no	—
894	C₂×C₈	—	4	1	no	—
895	C₂×C₈	—	4	1	no	—
896	C₂×C₈	—	4	2	no	—
897	C₂×C₈	C₂⁴×C₇	1	2	yes	—
898	C₂×C₈	C₂⁴×C₇	1	2	yes	—
899	C₂×C₈	C₂⁴×C₇	1	2	yes	—
900	C₂×C₈	C₂⁴×C₇	1	2	yes	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	2	2	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
915	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
916	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
917	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
918	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
919	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
920	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
921	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
922	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
923	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	—	2	2	no	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	2	2	no	—
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	2	no	—
941	C₂²⋊C₄	—	2	2	no	—
942	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
943	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
944	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
945	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
946	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
947	C₄²	—	2	1	no	—
948	C₄²	—	2	1	no	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	1	no	—
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
954	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
955	C₄²	C₂⁴×C₇	1	2	yes	—
956	C₄²	C₂⁴×C₇	1	1	yes	characteristic
957	C₄²	C₂⁴×C₇	1	1	yes	characteristic
958	C₂×C₇	—	2	2	no	—
959	C₂×C₇	—	4	2	no	—
960	C₂×C₇	—	8	2	no	—
961	C₂×C₇	—	8	2	no	—
962	C₂×C₇	—	8	2	no	—
963	C₂×C₇	#3488	1	1	yes	characteristic
964	C₂×C₇	C₂×#576	1	1	yes	characteristic
965	C₂×C₇	#3586	1	1	yes	characteristic
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	4	2	no	—
970	C₂³	—	8	1	no	—
971	C₂³	—	8	2	no	—
972	C₂³	—	8	2	no	—
973	C₂³	—	8	1	no	—
974	C₂³	—	8	2	no	—
975	C₂³	C₂²×C₇×D₄	1	2	yes	—
976	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
977	Q₈	—	2	1	no	—
978	Q₈	—	2	1	no	—
979	Q₈	—	2	2	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	2	no	—
982	Q₈	—	4	1	no	—
983	Q₈	—	4	2	no	—
984	Q₈	—	8	1	no	—
985	Q₈	—	8	1	no	—
986	Q₈	—	8	1	no	—
987	Q₈	—	8	2	no	—
988	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
989	D₄	—	2	4	no	—
990	D₄	—	2	2	no	—
991	D₄	—	2	2	no	—
992	D₄	—	2	2	no	—
993	D₄	—	2	2	no	—
994	D₄	—	2	2	no	—
995	D₄	—	2	2	no	—
996	D₄	—	4	1	no	—
997	D₄	—	4	4	no	—
998	D₄	—	4	2	no	—
999	D₄	—	4	4	no	—
1000	D₄	—	4	4	no	—
1001	D₄	—	8	1	no	—
1002	D₄	—	8	2	no	—
1003	D₄	—	8	2	no	—
1004	D₄	—	8	1	no	—
1005	D₄	—	8	2	no	—
1006	D₄	—	8	1	no	—
1007	D₄	—	8	1	no	—
1008	D₄	—	8	2	no	—
1009	D₄	—	8	2	no	—
1010	D₄	—	8	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	2	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	4	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	4	2	no	—
1027	C₂×C₄	—	8	2	no	—
1028	C₂×C₄	—	8	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	1	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1035	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1036	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1037	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1038	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1039	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1040	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1041	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1042	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1043	C₈	—	2	2	no	—
1044	C₈	—	2	2	no	—
1045	C₈	—	2	2	no	—
1046	C₈	—	2	2	no	—
1047	C₇	#62022	1	1	yes	characteristic, direct product factor, Sylow
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	2	2	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	4	2	no	—
1054	C₂²	—	4	2	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	2	no	—
1057	C₂²	—	4	2	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	4	2	no	—
1062	C₂²	—	16	2	no	—
1063	C₂²	—	16	4	no	—
1064	C₂²	C₇×#576	1	2	yes	—
1065	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	1	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	2	2	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1082	C₄	C₇×#585	1	1	yes	characteristic
1083	C₂	—	2	2	no	—
1084	C₂	—	4	2	no	—
1085	C₂	—	8	2	no	—
1086	C₂	—	8	2	no	—
1087	C₂	—	8	2	no	—
1088	C₂	C₇×#3488	1	1	yes	characteristic
1089	C₂	C₂×C₇×#576	1	1	yes	characteristic
1090	C₂	C₇×#3586	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×#3558	C₂	semidirect
2. C₇×#3522	C₂	semidirect
3. C₇×#3403	C₂	semidirect
4. C₇×#3375	C₂	semidirect
5. C₇×#3314	C₂	semidirect
6. C₇×#3308	C₂	semidirect
7. C₇×#3294	C₂	semidirect
8. C₇×#3285	C₂	semidirect
9. C₇×#3268	C₂	semidirect
10. C₇×#3265	C₂	semidirect
11. C₇×#3262	C₂	semidirect
12. C₇×#3245	C₂	semidirect
13. C₇×#3224	C₂	semidirect
14. C₇×#3213	C₂	semidirect
15. C₇×#3124	C₂	semidirect
16. C₇×#3112	C₂	semidirect
17. C₇×#3045	C₂	semidirect
18. C₂×C₇×#464	C₂	semidirect
19. C₇×#2992	C₂	semidirect
20. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₇×#135	C₂²	semidirect
22. C₂²×C₇×Q₁₆	C₂²	semidirect
28. C₇×#559	C₂²	semidirect
29. C₇×Q₈²	C₂²	semidirect
31. C₇×#554	C₂²	semidirect
32. C₇×#550	C₂²	semidirect
34. C₇×#548	C₂²	semidirect
36. C₇×#547	C₂²	semidirect
42. C₇×#542	C₂²	semidirect
49. C₇×#532	C₂²	semidirect
53. C₇×#520	C₂²	semidirect
54. C₂×C₄×C₇×Q₈	C₂²	semidirect
56. C₇×#496	C₂²	semidirect
57. C₇×#495	C₂²	semidirect
58. C₇×#489	C₂²	semidirect
59. C₇×#489	C₂²	semidirect
61. C₇×#484	C₂²	semidirect
63. C₇×#480	C₂²	semidirect
64. C₇×#477	C₂²	semidirect
65. C₇×#477	C₂²	semidirect
66. C₇×#477	C₂²	semidirect
67. C₇×#474	C₂²	semidirect
68. C₇×#474	C₂²	semidirect
69. C₇×#474	C₂²	semidirect
71. C₇×#468	C₂²	semidirect
72. C₇×#467	C₂²	semidirect
74. C₇×#466	C₂²	semidirect
75. C₇×#466	C₂²	semidirect
76. C₇×#464	C₂²	semidirect
77. C₇×#464	C₂²	semidirect
78. C₇×#464	C₂²	semidirect
79. C₇×#464	C₂²	semidirect
80. C₇×#464	C₂²	semidirect
81. C₇×#464	C₂²	semidirect
82. C₇×#463	C₂²	semidirect
83. C₇×#463	C₂²	semidirect
84. C₇×#463	C₂²	semidirect
85. C₇×#463	C₂²	semidirect
87. C₇×#460	C₂²	semidirect
88. C₇×#460	C₂²	semidirect
90. C₇×#459	C₂²	semidirect
91. C₇×#459	C₂²	semidirect
92. C₇×#452	C₂²	semidirect
93. C₇×#452	C₂²	semidirect
94. C₇×#450	C₂²	semidirect
96. C₇×#449	C₂²	semidirect
97. C₇×#448	C₂²	semidirect
98. C₇×#448	C₂²	semidirect
100. C₇×#447	C₂²	semidirect
101. C₇×#446	C₂²	semidirect
102. C₇×#440	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₇×#440	C₂²	semidirect
105. C₇×#440	C₂²	semidirect
106. C₄×C₇×Q₁₆	C₂²	semidirect
107. C₄×C₇×D₈	C₂²	semidirect
108. C₇×#435	C₂²	semidirect
109. C₇×#435	C₂²	semidirect
110. C₇×C₈×D₄	C₂²	semidirect
111. C₇×#433	C₂²	semidirect
112. C₇×#432	C₂²	semidirect
113. C₇×#424	C₂²	semidirect
114. C₂×C₇×C₄⋊C₈	C₂²	semidirect
115. C₇×#417	C₂²	semidirect
116. C₂×C₇×#103	C₂²	semidirect
118. C₂×C₇×#102	C₂²	semidirect
119. #62022	C₇	direct (N × H)
285. #3558	C₂×C₇	semidirect
286. #3522	C₂×C₇	semidirect
287. #3403	C₂×C₇	semidirect
288. #3375	C₂×C₇	semidirect
289. #3314	C₂×C₇	semidirect
290. #3308	C₂×C₇	semidirect
291. #3294	C₂×C₇	semidirect
292. #3285	C₂×C₇	semidirect
293. #3268	C₂×C₇	semidirect
294. #3265	C₂×C₇	semidirect
295. #3262	C₂×C₇	semidirect
296. #3245	C₂×C₇	semidirect
297. #3224	C₂×C₇	semidirect
298. #3213	C₂×C₇	semidirect
299. #3124	C₂×C₇	semidirect
300. #3112	C₂×C₇	semidirect
301. #3045	C₂×C₇	semidirect
302. C₂×#464	C₂×C₇	semidirect
303. #2992	C₂×C₇	semidirect
441. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
442. C₂×#135	C₂²×C₇	semidirect
443. C₂²×Q₁₆	C₂²×C₇	semidirect
449. #559	C₂²×C₇	semidirect
450. Q₈²	C₂²×C₇	semidirect
452. #554	C₂²×C₇	semidirect
453. #550	C₂²×C₇	semidirect
455. #548	C₂²×C₇	semidirect
457. #547	C₂²×C₇	semidirect
463. #542	C₂²×C₇	semidirect
470. #532	C₂²×C₇	semidirect
474. #520	C₂²×C₇	semidirect
475. C₂×C₄×Q₈	C₂²×C₇	semidirect
477. #496	C₂²×C₇	semidirect
478. #495	C₂²×C₇	semidirect
479. #489	C₂²×C₇	semidirect
480. #489	C₂²×C₇	semidirect
482. #484	C₂²×C₇	semidirect
484. #480	C₂²×C₇	semidirect
485. #477	C₂²×C₇	semidirect
486. #477	C₂²×C₇	semidirect
487. #477	C₂²×C₇	semidirect
488. #474	C₂²×C₇	semidirect
489. #474	C₂²×C₇	semidirect
490. #474	C₂²×C₇	semidirect
492. #468	C₂²×C₇	semidirect
493. #467	C₂²×C₇	semidirect
495. #466	C₂²×C₇	semidirect
496. #466	C₂²×C₇	semidirect
497. #464	C₂²×C₇	semidirect
498. #464	C₂²×C₇	semidirect
499. #464	C₂²×C₇	semidirect
500. #464	C₂²×C₇	semidirect
501. #464	C₂²×C₇	semidirect
502. #464	C₂²×C₇	semidirect
503. #463	C₂²×C₇	semidirect
504. #463	C₂²×C₇	semidirect
505. #463	C₂²×C₇	semidirect
506. #463	C₂²×C₇	semidirect
508. #460	C₂²×C₇	semidirect
509. #460	C₂²×C₇	semidirect
511. #459	C₂²×C₇	semidirect
512. #459	C₂²×C₇	semidirect
513. #452	C₂²×C₇	semidirect
514. #452	C₂²×C₇	semidirect
515. #450	C₂²×C₇	semidirect
517. #449	C₂²×C₇	semidirect
518. #448	C₂²×C₇	semidirect
519. #448	C₂²×C₇	semidirect
521. #447	C₂²×C₇	semidirect
522. #446	C₂²×C₇	semidirect
523. #440	C₂²×C₇	semidirect
524. #440	C₂²×C₇	semidirect
525. #440	C₂²×C₇	semidirect
526. #440	C₂²×C₇	semidirect
527. C₄×Q₁₆	C₂²×C₇	semidirect
528. C₄×D₈	C₂²×C₇	semidirect
529. #435	C₂²×C₇	semidirect
530. #435	C₂²×C₇	semidirect
531. C₈×D₄	C₂²×C₇	semidirect
532. #433	C₂²×C₇	semidirect
533. #432	C₂²×C₇	semidirect
534. #424	C₂²×C₇	semidirect
535. C₂×C₄⋊C₈	C₂²×C₇	semidirect
536. #417	C₂²×C₇	semidirect
537. C₂×#103	C₂²×C₇	semidirect
539. C₂×#102	C₂²×C₇	semidirect
1047. C₇	#62022	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×#3558	2
C₇×#3522	2
C₇×#3403	2
C₇×#3375	2
C₇×#3314	2
C₇×#3308	2
C₇×#3294	2
C₇×#3285	2
C₇×#3268	2
C₇×#3265	2
C₇×#3262	2
C₇×#3245	2
C₇×#3224	2
C₇×#3213	2
C₇×#3124	2
C₇×#3112	2
C₇×#3045	2
C₂×C₇×#464	2
C₇×#2992	2
#62022	7

Subgroups — C7×#62022 #13239238

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62022 #13239238