Subgroups — C₇×#62019 #13239235

Order 1792.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1066 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
2	C₇×#3523	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3400	C₂	1	2	yes	maximal, complemented
4	C₇×#3371	C₂	1	2	yes	maximal, complemented
5	C₇×#3311	C₂	1	2	yes	maximal, complemented
6	C₇×#3310	C₂	1	2	yes	maximal, complemented
7	C₇×#3300	C₂	1	2	yes	maximal, complemented
8	C₇×D₄×SD₁₆	C₂	1	2	yes	maximal, complemented
9	C₇×#3270	C₂	1	2	yes	maximal, complemented
10	C₇×#3266	C₂	1	2	yes	maximal, complemented
11	C₇×#3258	C₂	1	2	yes	maximal, complemented
12	C₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3222	C₂	1	2	yes	maximal, complemented
14	C₇×#3215	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3121	C₂	1	2	yes	maximal, complemented
16	C₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3043	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×#137	C₂²	1	2	yes	complemented
21	C₂²×C₇×Q₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
24	C₇×#562	—	2	1	no	—
25	C₇×H(3,𝔽₄)	—	2	1	no	—
26	C₇×#559	C₂²	1	2	yes	—
27	C₇×#557	—	2	1	no	—
28	C₇×#557	C₂²	1	1	yes	characteristic, complemented
29	C₇×#557	C₂²	1	1	yes	characteristic, complemented
30	C₇×#556	—	2	1	no	—
31	C₇×#556	C₂²	1	1	yes	characteristic, complemented
32	C₇×#552	—	2	2	no	—
33	C₇×#552	C₂²	1	2	yes	complemented
34	C₇×D₄×Q₈	C₂²	1	1	yes	characteristic, complemented
35	C₇×D₄×Q₈	C₂²	1	2	yes	complemented
36	C₇×#548	C₂²	1	2	yes	—
37	C₇×#546	—	2	2	no	—
38	C₇×#546	C₂²	1	2	yes	—
39	C₇×D₄²	C₂²	1	2	yes	—
40	C₇×#542	C₂²	1	2	yes	—
41	C₇×#541	—	2	2	no	—
42	C₇×#541	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×#533	—	2	1	no	—
48	C₇×#533	C₂²	1	1	yes	characteristic, complemented
49	C₇×#532	C₂²	1	1	yes	characteristic
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×#519	C₂²	1	2	yes	complemented
54	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
55	C₇×#497	C₂²	1	2	yes	complemented
56	C₇×#497	C₂²	1	2	yes	complemented
57	C₇×#492	C₂²	1	2	yes	—
58	C₇×#490	C₂²	1	2	yes	—
59	C₇×#489	C₂²	1	2	yes	complemented
60	C₇×#488	C₂²	1	2	yes	complemented
61	C₇×#485	C₂²	1	2	yes	complemented
62	C₇×#482	C₂²	1	2	yes	—
63	C₇×#480	C₂²	1	2	yes	complemented
64	C₇×#479	C₂²	1	2	yes	complemented
65	C₇×#478	C₂²	1	2	yes	complemented
66	C₇×#477	C₂²	1	1	yes	characteristic, complemented
67	C₇×#477	C₂²	1	1	yes	characteristic, complemented
68	C₇×#476	C₂²	1	2	yes	complemented
69	C₇×#475	C₂²	1	2	yes	complemented
70	C₇×#470	C₂²	1	2	yes	complemented
71	C₇×#468	C₂²	1	2	yes	—
72	C₇×#467	C₂²	1	2	yes	complemented
73	C₇×#465	C₂²	1	2	yes	—
74	C₇×#465	C₂²	1	2	yes	complemented
75	C₇×#465	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×#464	C₂²	1	2	yes	complemented
83	C₇×#464	C₂²	1	2	yes	complemented
84	C₇×#462	C₂²	1	2	yes	complemented
85	C₇×#461	C₂²	1	2	yes	complemented
86	C₇×#461	C₂²	1	2	yes	complemented
87	C₇×#460	C₂²	1	2	yes	—
88	C₇×#460	C₂²	1	2	yes	—
89	C₇×#460	C₂²	1	1	yes	characteristic, complemented
90	C₇×#460	C₂²	1	2	yes	complemented
91	C₇×#460	C₂²	1	1	yes	characteristic, complemented
92	C₇×#452	C₂²	1	2	yes	complemented
93	C₇×#452	C₂²	1	2	yes	complemented
94	C₇×#451	C₂²	1	2	yes	complemented
95	C₇×#451	C₂²	1	2	yes	complemented
96	C₇×#450	C₂²	1	2	yes	—
97	C₇×#450	C₂²	1	2	yes	complemented
98	C₇×#450	C₂²	1	2	yes	complemented
99	C₇×#448	C₂²	1	2	yes	—
100	C₇×#448	C₂²	1	2	yes	complemented
101	C₇×#446	C₂²	1	2	yes	complemented
102	C₇×#441	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×SD₁₆	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×#418	C₂²	1	2	yes	complemented
116	C₇×#416	C₂²	1	2	yes	complemented
117	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
118	C₂×C₇×#102	C₂²	1	1	yes	characteristic
119	#62019	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂×C₇×#41	—	2	1	no	—
121	C₂×C₇×#41	C₂³	1	2	yes	—
122	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
123	C₂²×C₇×Q₈	C₂³	1	2	yes	—
124	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×D₄	—	2	2	no	—
126	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
127	C₂²×C₇×D₄	C₂³	1	2	yes	—
128	C₇×#137	—	4	4	no	—
129	C₂×C₇×Q₁₆	—	4	2	no	—
130	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
131	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
132	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
133	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
134	C₂×C₇×SD₁₆	—	4	2	no	—
135	C₂×C₇×SD₁₆	—	4	4	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×SD₁₆	C₂³	1	2	yes	—
143	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
144	C₂×C₇×M₁₆	C₂³	1	2	yes	—
145	C₂²×C₇×C₈	C₂³	1	2	yes	—
146	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
147	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
148	C₇×C₄⋊Q₈	—	2	1	no	—
149	C₇×C₄⋊Q₈	—	2	1	no	—
150	C₇×C₄⋊Q₈	—	2	2	no	—
151	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
155	C₇×#127	C₂³	1	2	yes	—
156	C₇×#127	C₂³	1	1	yes	characteristic
157	C₇×#126	—	2	2	no	—
158	C₇×#126	—	2	2	no	—
159	C₇×#126	—	2	2	no	—
160	C₇×#126	—	2	2	no	—
161	C₇×#126	—	2	2	no	—
162	C₇×#126	D₄	1	2	yes	—
163	C₇×#125	—	2	1	no	—
164	C₇×#125	—	2	2	no	—
165	C₇×#125	—	2	2	no	—
166	C₇×#125	—	2	2	no	—
167	C₇×#125	—	2	2	no	—
168	C₇×#125	—	2	2	no	—
169	C₇×#125	—	2	1	no	—
170	C₇×#125	D₄	1	1	yes	characteristic
171	C₇×#125	C₂³	1	2	yes	—
172	C₇×#124	—	2	2	no	—
173	C₇×#124	—	2	1	no	—
174	C₇×#124	—	2	2	no	—
175	C₇×#124	—	2	2	no	—
176	C₇×#124	—	2	1	no	—
177	C₇×#124	—	2	1	no	—
178	C₇×#124	—	2	1	no	—
179	C₇×#124	D₄	1	1	yes	characteristic
180	C₇×#124	C₂³	1	2	yes	—
181	C₇×#124	C₂³	1	2	yes	—
182	C₇×#124	C₂³	1	2	yes	—
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	—	2	2	no	—
188	C₇×#123	D₄	1	2	yes	—
189	C₇×C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
195	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
196	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
197	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
198	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
199	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
200	C₇×#121	—	2	2	no	—
201	C₇×#121	—	2	1	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×#120	—	2	2	no	—
210	C₇×#120	—	2	2	no	—
211	C₇×#120	—	2	2	no	—
212	C₇×#120	—	2	2	no	—
213	C₇×#120	—	2	2	no	—
214	C₄×C₇×Q₈	—	2	1	no	—
215	C₄×C₇×Q₈	—	2	2	no	—
216	C₄×C₇×Q₈	—	2	2	no	—
217	C₄×C₇×Q₈	—	2	1	no	—
218	C₄×C₇×Q₈	—	2	1	no	—
219	C₄×C₇×Q₈	—	2	1	no	—
220	C₄×C₇×Q₈	—	2	1	no	—
221	C₄×C₇×Q₈	—	2	1	no	—
222	C₄×C₇×Q₈	C₂³	1	2	yes	—
223	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
224	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
225	C₄×C₇×Q₈	C₂³	1	2	yes	—
226	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
227	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
228	C₄×C₇×Q₈	C₂³	1	2	yes	—
229	C₄×C₇×Q₈	C₂³	1	2	yes	—
230	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
231	C₄×C₇×D₄	—	2	2	no	—
232	C₄×C₇×D₄	—	2	1	no	—
233	C₄×C₇×D₄	—	2	2	no	—
234	C₄×C₇×D₄	—	2	2	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	1	yes	characteristic
240	C₇×#117	—	2	1	no	—
241	C₇×#117	—	2	2	no	—
242	C₇×#117	—	2	2	no	—
243	C₇×#117	—	2	2	no	—
244	C₇×#117	C₂³	1	2	yes	—
245	C₇×#117	C₂³	1	2	yes	—
246	C₂×C₇×C₄⋊C₄	—	2	1	no	—
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×#106	C₂³	1	2	yes	—
256	C₇×#106	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	1	yes	characteristic
260	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
261	C₇×C₄⋊C₈	C₂³	1	2	yes	—
262	C₇×C₄⋊C₈	C₂³	1	2	yes	—
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×#103	C₂³	1	2	yes	—
270	C₇×#103	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
286	#3523	C₂×C₇	1	1	yes	characteristic, complemented
287	#3400	C₂×C₇	1	2	yes	complemented
288	#3371	C₂×C₇	1	2	yes	complemented
289	#3311	C₂×C₇	1	2	yes	complemented
290	#3310	C₂×C₇	1	2	yes	complemented
291	#3300	C₂×C₇	1	2	yes	complemented
292	D₄×SD₁₆	C₂×C₇	1	2	yes	complemented
293	#3270	C₂×C₇	1	2	yes	complemented
294	#3266	C₂×C₇	1	2	yes	complemented
295	#3258	C₂×C₇	1	2	yes	complemented
296	#3246	C₂×C₇	1	1	yes	characteristic, complemented
297	#3222	C₂×C₇	1	2	yes	complemented
298	#3215	C₂×C₇	1	1	yes	characteristic, complemented
299	#3121	C₂×C₇	1	2	yes	complemented
300	#3112	C₂×C₇	1	1	yes	characteristic, complemented
301	#3043	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	—	4	2	no	—
307	C₇×#41	—	4	2	no	—
308	C₇×#41	—	8	2	no	—
309	C₂×C₇×Q₈	—	2	1	no	—
310	C₂×C₇×Q₈	—	2	2	no	—
311	C₂×C₇×Q₈	—	2	1	no	—
312	C₂×C₇×Q₈	—	2	1	no	—
313	C₂×C₇×Q₈	—	2	1	no	—
314	C₂×C₇×Q₈	—	2	2	no	—
315	C₂×C₇×Q₈	—	2	4	no	—
316	C₂×C₇×Q₈	—	4	1	no	—
317	C₂×C₇×Q₈	—	4	2	no	—
318	C₂×C₇×Q₈	—	4	1	no	—
319	C₂×C₇×Q₈	—	4	1	no	—
320	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
321	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
322	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
323	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
324	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
325	C₂×C₇×D₄	—	2	2	no	—
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	1	no	—
330	C₂×C₇×D₄	—	2	1	no	—
331	C₂×C₇×D₄	—	2	1	no	—
332	C₂×C₇×D₄	—	2	2	no	—
333	C₂×C₇×D₄	—	2	2	no	—
334	C₂×C₇×D₄	—	4	1	no	—
335	C₂×C₇×D₄	—	4	2	no	—
336	C₂×C₇×D₄	—	4	1	no	—
337	C₂×C₇×D₄	—	4	2	no	—
338	C₂×C₇×D₄	—	8	4	no	—
339	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
340	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
341	C₂×C₇×D₄	C₂⁴	1	2	yes	—
342	C₂×C₇×D₄	C₂⁴	1	2	yes	—
343	C₂²×C₄×C₇	—	2	1	no	—
344	C₂²×C₄×C₇	—	2	1	no	—
345	C₂²×C₄×C₇	—	2	2	no	—
346	C₂²×C₄×C₇	—	2	1	no	—
347	C₂²×C₄×C₇	—	2	2	no	—
348	C₂²×C₄×C₇	—	2	2	no	—
349	C₂²×C₄×C₇	—	2	2	no	—
350	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
351	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
352	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
353	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
354	C₇×Q₁₆	—	2	4	no	—
355	C₇×Q₁₆	—	4	2	no	—
356	C₇×Q₁₆	—	4	2	no	—
357	C₇×Q₁₆	—	4	2	no	—
358	C₇×SD₁₆	—	2	4	no	—
359	C₇×SD₁₆	—	2	4	no	—
360	C₇×SD₁₆	—	4	2	no	—
361	C₇×SD₁₆	—	4	2	no	—
362	C₇×SD₁₆	—	4	2	no	—
363	C₇×SD₁₆	—	4	2	no	—
364	C₇×SD₁₆	—	4	2	no	—
365	C₇×SD₁₆	—	4	2	no	—
366	C₇×M₁₆	—	4	2	no	—
367	C₂×C₇×C₈	—	4	1	no	—
368	C₂×C₇×C₈	—	4	2	no	—
369	C₂×C₇×C₈	—	4	1	no	—
370	C₂×C₇×C₈	C₂⁴	1	2	yes	—
371	C₂×C₇×C₈	C₂⁴	1	2	yes	—
372	C₂×C₇×C₈	C₂⁴	1	2	yes	—
373	C₂×C₇×C₈	C₂⁴	1	2	yes	—
374	C₇×C₄⋊C₄	—	2	1	no	—
375	C₇×C₄⋊C₄	—	2	1	no	—
376	C₇×C₄⋊C₄	—	2	1	no	—
377	C₇×C₄⋊C₄	—	2	1	no	—
378	C₇×C₄⋊C₄	—	2	1	no	—
379	C₇×C₄⋊C₄	—	2	2	no	—
380	C₇×C₄⋊C₄	—	2	2	no	—
381	C₇×C₄⋊C₄	—	2	2	no	—
382	C₇×C₄⋊C₄	—	2	1	no	—
383	C₇×C₄⋊C₄	—	2	2	no	—
384	C₇×C₄⋊C₄	—	2	1	no	—
385	C₇×C₄⋊C₄	—	2	2	no	—
386	C₇×C₄⋊C₄	—	2	1	no	—
387	C₇×C₄⋊C₄	—	2	2	no	—
388	C₇×C₄⋊C₄	—	2	1	no	—
389	C₇×C₄⋊C₄	—	2	2	no	—
390	C₇×C₄⋊C₄	—	2	2	no	—
391	C₇×C₄⋊C₄	—	2	2	no	—
392	C₇×C₄⋊C₄	—	2	2	no	—
393	C₇×C₄⋊C₄	—	2	2	no	—
394	C₇×C₄⋊C₄	—	2	2	no	—
395	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
396	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
397	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
398	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
400	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
401	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
402	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
403	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
404	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
405	C₇×C₂²⋊C₄	—	2	2	no	—
406	C₇×C₂²⋊C₄	—	2	2	no	—
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	C₂×D₄	1	2	yes	—
421	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
422	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
423	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
424	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
425	C₄²×C₇	—	2	1	no	—
426	C₄²×C₇	—	2	1	no	—
427	C₄²×C₇	—	2	1	no	—
428	C₄²×C₇	—	2	1	no	—
429	C₄²×C₇	—	2	2	no	—
430	C₄²×C₇	—	2	2	no	—
431	C₄²×C₇	—	2	2	no	—
432	C₄²×C₇	—	2	2	no	—
433	C₄²×C₇	—	2	2	no	—
434	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
435	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
436	C₄²×C₇	C₂⁴	1	2	yes	—
437	C₄²×C₇	C₂⁴	1	1	yes	characteristic
438	C₄²×C₇	C₂⁴	1	1	yes	characteristic
439	C₂×#137	C₂²×C₇	1	2	yes	complemented
440	C₂²×Q₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
441	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
442	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
443	#562	—	2	1	no	—
444	H(3,𝔽₄)	—	2	1	no	—
445	#559	C₂²×C₇	1	2	yes	—
446	#557	—	2	1	no	—
447	#557	C₂²×C₇	1	1	yes	characteristic, complemented
448	#557	C₂²×C₇	1	1	yes	characteristic, complemented
449	#556	—	2	1	no	—
450	#556	C₂²×C₇	1	1	yes	characteristic, complemented
451	#552	—	2	2	no	—
452	#552	C₂²×C₇	1	2	yes	complemented
453	D₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
454	D₄×Q₈	C₂²×C₇	1	2	yes	complemented
455	#548	C₂²×C₇	1	2	yes	—
456	#546	—	2	2	no	—
457	#546	C₂²×C₇	1	2	yes	—
458	D₄²	C₂²×C₇	1	2	yes	—
459	#542	C₂²×C₇	1	2	yes	—
460	#541	—	2	2	no	—
461	#541	C₂²×C₇	1	2	yes	complemented
462	#538	—	2	2	no	—
463	#538	—	2	1	no	—
464	#535	C₂²×C₇	1	2	yes	—
465	#534	—	2	1	no	—
466	#533	—	2	1	no	—
467	#533	C₂²×C₇	1	1	yes	characteristic, complemented
468	#532	C₂²×C₇	1	1	yes	characteristic
469	#529	—	2	1	no	—
470	#529	C₂²×C₇	1	1	yes	characteristic
471	C₂×#124	C₂²×C₇	1	1	yes	characteristic
472	#519	C₂²×C₇	1	2	yes	complemented
473	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
474	#497	C₂²×C₇	1	2	yes	complemented
475	#497	C₂²×C₇	1	2	yes	complemented
476	#492	C₂²×C₇	1	2	yes	—
477	#490	C₂²×C₇	1	2	yes	—
478	#489	C₂²×C₇	1	2	yes	complemented
479	#488	C₂²×C₇	1	2	yes	complemented
480	#485	C₂²×C₇	1	2	yes	complemented
481	#482	C₂²×C₇	1	2	yes	—
482	#480	C₂²×C₇	1	2	yes	complemented
483	#479	C₂²×C₇	1	2	yes	complemented
484	#478	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	#476	C₂²×C₇	1	2	yes	complemented
488	#475	C₂²×C₇	1	2	yes	complemented
489	#470	C₂²×C₇	1	2	yes	complemented
490	#468	C₂²×C₇	1	2	yes	—
491	#467	C₂²×C₇	1	2	yes	complemented
492	#465	C₂²×C₇	1	2	yes	—
493	#465	C₂²×C₇	1	2	yes	complemented
494	#465	C₂²×C₇	1	2	yes	complemented
495	#464	C₂²×C₇	1	2	yes	complemented
496	#464	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	#462	C₂²×C₇	1	2	yes	complemented
504	#461	C₂²×C₇	1	2	yes	complemented
505	#461	C₂²×C₇	1	2	yes	complemented
506	#460	C₂²×C₇	1	2	yes	—
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	#460	C₂²×C₇	1	2	yes	complemented
511	#452	C₂²×C₇	1	2	yes	complemented
512	#452	C₂²×C₇	1	2	yes	complemented
513	#451	C₂²×C₇	1	2	yes	complemented
514	#451	C₂²×C₇	1	2	yes	complemented
515	#450	C₂²×C₇	1	2	yes	—
516	#450	C₂²×C₇	1	2	yes	complemented
517	#450	C₂²×C₇	1	2	yes	complemented
518	#448	C₂²×C₇	1	2	yes	—
519	#448	C₂²×C₇	1	2	yes	complemented
520	#446	C₂²×C₇	1	2	yes	complemented
521	#441	C₂²×C₇	1	2	yes	complemented
522	#440	C₂²×C₇	1	2	yes	complemented
523	#440	C₂²×C₇	1	2	yes	complemented
524	#440	C₂²×C₇	1	2	yes	complemented
525	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
526	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
527	#435	C₂²×C₇	1	2	yes	complemented
528	#435	C₂²×C₇	1	2	yes	complemented
529	C₈×D₄	C₂²×C₇	1	2	yes	complemented
530	#433	C₂²×C₇	1	2	yes	complemented
531	#432	C₂²×C₇	1	1	yes	characteristic, complemented
532	#424	C₂²×C₇	1	2	yes	complemented
533	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
534	#418	C₂²×C₇	1	2	yes	complemented
535	#416	C₂²×C₇	1	2	yes	complemented
536	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
537	C₂×#102	C₂²×C₇	1	1	yes	characteristic
538	C₂³×C₇	—	2	2	no	—
539	C₂³×C₇	—	2	2	no	—
540	C₂³×C₇	—	4	2	no	—
541	C₂³×C₇	—	8	1	no	—
542	C₂³×C₇	—	8	2	no	—
543	C₂³×C₇	—	8	2	no	—
544	C₂³×C₇	—	8	1	no	—
545	C₂³×C₇	—	8	2	no	—
546	C₂³×C₇	C₂²×D₄	1	2	yes	—
547	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
548	C₇×Q₈	—	2	1	no	—
549	C₇×Q₈	—	2	2	no	—
550	C₇×Q₈	—	2	1	no	—
551	C₇×Q₈	—	2	2	no	—
552	C₇×Q₈	—	2	1	no	—
553	C₇×Q₈	—	2	2	no	—
554	C₇×Q₈	—	2	2	no	—
555	C₇×Q₈	—	4	1	no	—
556	C₇×Q₈	—	4	4	no	—
557	C₇×Q₈	—	4	2	no	—
558	C₇×Q₈	—	4	2	no	—
559	C₇×Q₈	—	8	1	no	—
560	C₇×Q₈	—	8	1	no	—
561	C₇×Q₈	H(5,𝔽₂)	1	2	yes	—
562	C₇×D₄	—	2	4	no	—
563	C₇×D₄	—	2	2	no	—
564	C₇×D₄	—	2	2	no	—
565	C₇×D₄	—	2	2	no	—
566	C₇×D₄	—	2	2	no	—
567	C₇×D₄	—	4	1	no	—
568	C₇×D₄	—	4	4	no	—
569	C₇×D₄	—	8	1	no	—
570	C₇×D₄	—	8	2	no	—
571	C₇×D₄	—	8	2	no	—
572	C₇×D₄	—	8	1	no	—
573	C₇×D₄	—	8	2	no	—
574	C₇×D₄	—	8	1	no	—
575	C₇×D₄	—	8	2	no	—
576	C₇×D₄	—	8	2	no	—
577	C₂×C₄×C₇	—	2	2	no	—
578	C₂×C₄×C₇	—	2	1	no	—
579	C₂×C₄×C₇	—	2	1	no	—
580	C₂×C₄×C₇	—	2	2	no	—
581	C₂×C₄×C₇	—	2	1	no	—
582	C₂×C₄×C₇	—	2	2	no	—
583	C₂×C₄×C₇	—	2	1	no	—
584	C₂×C₄×C₇	—	2	2	no	—
585	C₂×C₄×C₇	—	2	1	no	—
586	C₂×C₄×C₇	—	2	1	no	—
587	C₂×C₄×C₇	—	2	2	no	—
588	C₂×C₄×C₇	—	2	2	no	—
589	C₂×C₄×C₇	—	2	2	no	—
590	C₂×C₄×C₇	—	4	1	no	—
591	C₂×C₄×C₇	—	4	2	no	—
592	C₂×C₄×C₇	—	4	4	no	—
593	C₂×C₄×C₇	—	4	2	no	—
594	C₂×C₄×C₇	—	8	2	no	—
595	C₂×C₄×C₇	—	8	2	no	—
596	C₂×C₄×C₇	—	8	2	no	—
597	C₂×C₄×C₇	—	8	1	no	—
598	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
599	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
600	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
601	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
602	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
603	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
604	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
605	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
606	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
607	C₇×C₈	—	2	2	no	—
608	C₇×C₈	—	2	2	no	—
609	C₇×C₈	—	2	2	no	—
610	C₇×C₈	—	2	2	no	—
611	C₂×#41	—	2	1	no	—
612	C₂×#41	C₂³×C₇	1	2	yes	—
613	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
614	C₂²×Q₈	C₂³×C₇	1	2	yes	—
615	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
616	C₂²×D₄	—	2	2	no	—
617	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
618	C₂²×D₄	C₂³×C₇	1	2	yes	—
619	#137	—	4	4	no	—
620	C₂×Q₁₆	—	4	2	no	—
621	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
622	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
623	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
624	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
625	C₂×SD₁₆	—	4	2	no	—
626	C₂×SD₁₆	—	4	4	no	—
627	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
628	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
629	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
630	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
631	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
632	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
633	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
634	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
635	C₂×M₁₆	C₂³×C₇	1	2	yes	—
636	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
637	C₂²×C₈	C₂³×C₇	1	2	yes	—
638	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
639	C₄⋊Q₈	—	2	1	no	—
640	C₄⋊Q₈	—	2	1	no	—
641	C₄⋊Q₈	—	2	2	no	—
642	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
643	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
644	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
645	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
646	#127	C₂³×C₇	1	1	yes	characteristic
647	#127	C₂³×C₇	1	2	yes	—
648	#126	—	2	2	no	—
649	#126	—	2	2	no	—
650	#126	—	2	2	no	—
651	#126	—	2	2	no	—
652	#126	—	2	2	no	—
653	#126	C₇×D₄	1	2	yes	—
654	#125	—	2	1	no	—
655	#125	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	2	no	—
658	#125	—	2	2	no	—
659	#125	—	2	2	no	—
660	#125	—	2	1	no	—
661	#125	C₇×D₄	1	1	yes	characteristic
662	#125	C₂³×C₇	1	2	yes	—
663	#124	—	2	2	no	—
664	#124	—	2	1	no	—
665	#124	—	2	2	no	—
666	#124	—	2	2	no	—
667	#124	—	2	1	no	—
668	#124	—	2	1	no	—
669	#124	—	2	1	no	—
670	#124	C₇×D₄	1	1	yes	characteristic
671	#124	C₂³×C₇	1	2	yes	—
672	#124	C₂³×C₇	1	2	yes	—
673	#124	C₂³×C₇	1	2	yes	—
674	#123	—	2	2	no	—
675	#123	—	2	2	no	—
676	#123	—	2	2	no	—
677	#123	—	2	2	no	—
678	#123	—	2	2	no	—
679	#123	C₇×D₄	1	2	yes	—
680	C₂²⋊Q₈	—	2	1	no	—
681	C₂²⋊Q₈	—	2	2	no	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	2	2	no	—
686	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
687	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
688	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
689	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
690	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
691	#121	—	2	2	no	—
692	#121	—	2	1	no	—
693	#121	—	2	2	no	—
694	#121	—	2	2	no	—
695	#121	—	2	2	no	—
696	#121	—	2	2	no	—
697	#121	C₇×D₄	1	1	yes	characteristic
698	#121	C₂³×C₇	1	2	yes	—
699	#121	C₂³×C₇	1	2	yes	—
700	#120	—	2	2	no	—
701	#120	—	2	2	no	—
702	#120	—	2	2	no	—
703	#120	—	2	2	no	—
704	#120	—	2	2	no	—
705	C₄×Q₈	—	2	1	no	—
706	C₄×Q₈	—	2	2	no	—
707	C₄×Q₈	—	2	2	no	—
708	C₄×Q₈	—	2	1	no	—
709	C₄×Q₈	—	2	1	no	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	—	2	1	no	—
712	C₄×Q₈	—	2	1	no	—
713	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
714	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
715	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
716	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
717	C₄×Q₈	C₂³×C₇	1	2	yes	—
718	C₄×Q₈	C₂³×C₇	1	2	yes	—
719	C₄×Q₈	C₂³×C₇	1	2	yes	—
720	C₄×Q₈	C₂³×C₇	1	2	yes	—
721	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
722	C₄×D₄	—	2	2	no	—
723	C₄×D₄	—	2	1	no	—
724	C₄×D₄	—	2	2	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	—	2	1	no	—
727	C₄×D₄	C₂³×C₇	1	2	yes	—
728	C₄×D₄	C₂³×C₇	1	2	yes	—
729	C₄×D₄	C₂³×C₇	1	2	yes	—
730	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
731	#117	—	2	1	no	—
732	#117	—	2	2	no	—
733	#117	—	2	2	no	—
734	#117	—	2	2	no	—
735	#117	C₂³×C₇	1	2	yes	—
736	#117	C₂³×C₇	1	2	yes	—
737	C₂×C₄⋊C₄	—	2	1	no	—
738	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
739	C₂×C₂²⋊C₄	—	2	1	no	—
740	C₂×C₂²⋊C₄	—	2	1	no	—
741	C₂×C₂²⋊C₄	—	2	2	no	—
742	C₂×C₄²	—	2	1	no	—
743	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
744	#107	C₂³×C₇	1	2	yes	—
745	#107	C₂³×C₇	1	2	yes	—
746	#106	C₂³×C₇	1	2	yes	—
747	#106	C₂³×C₇	1	2	yes	—
748	C₄⋊C₈	C₂³×C₇	1	2	yes	—
749	C₄⋊C₈	C₂³×C₇	1	2	yes	—
750	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
751	C₄⋊C₈	C₂³×C₇	1	2	yes	—
752	C₄⋊C₈	C₂³×C₇	1	2	yes	—
753	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
754	#103	C₂³×C₇	1	2	yes	—
755	#103	C₂³×C₇	1	2	yes	—
756	#103	C₂³×C₇	1	2	yes	—
757	#103	C₂³×C₇	1	2	yes	—
758	#103	C₂³×C₇	1	2	yes	—
759	#103	C₂³×C₇	1	2	yes	—
760	#103	C₂³×C₇	1	2	yes	—
761	#103	C₂³×C₇	1	2	yes	—
762	#102	C₂³×C₇	1	2	yes	—
763	#102	C₂³×C₇	1	2	yes	—
764	#102	C₂³×C₇	1	2	yes	—
765	#102	C₂³×C₇	1	2	yes	—
766	#102	C₂³×C₇	1	2	yes	—
767	#102	C₂³×C₇	1	2	yes	—
768	#102	C₂³×C₇	1	2	yes	—
769	#102	C₂³×C₇	1	2	yes	—
770	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
771	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
772	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
773	#97	C₂³×C₇	1	2	yes	—
774	#97	C₂³×C₇	1	2	yes	—
775	C₄×C₈	C₂³×C₇	1	2	yes	—
776	C₂²×C₇	—	2	1	no	—
777	C₂²×C₇	—	2	1	no	—
778	C₂²×C₇	—	2	2	no	—
779	C₂²×C₇	—	2	2	no	—
780	C₂²×C₇	—	2	2	no	—
781	C₂²×C₇	—	4	2	no	—
782	C₂²×C₇	—	4	2	no	—
783	C₂²×C₇	—	4	2	no	—
784	C₂²×C₇	—	4	2	no	—
785	C₂²×C₇	—	4	2	no	—
786	C₂²×C₇	—	4	2	no	—
787	C₂²×C₇	—	16	2	no	—
788	C₂²×C₇	—	16	4	no	—
789	C₂²×C₇	#577	1	2	yes	—
790	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
791	C₄×C₇	—	2	1	no	—
792	C₄×C₇	—	2	1	no	—
793	C₄×C₇	—	2	2	no	—
794	C₄×C₇	—	2	2	no	—
795	C₄×C₇	—	2	1	no	—
796	C₄×C₇	—	2	2	no	—
797	C₄×C₇	—	2	1	no	—
798	C₄×C₇	—	2	1	no	—
799	C₄×C₇	—	2	2	no	—
800	C₄×C₇	—	4	2	no	—
801	C₄×C₇	—	4	2	no	—
802	C₄×C₇	—	4	1	no	—
803	C₄×C₇	—	4	2	no	—
804	C₄×C₇	—	4	1	no	—
805	C₄×C₇	—	4	1	no	—
806	C₄×C₇	—	4	2	no	—
807	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
808	C₄×C₇	#585	1	1	yes	characteristic
809	C₂⁴	—	2	1	no	—
810	C₂⁴	—	2	2	no	—
811	#41	—	4	2	no	—
812	#41	—	4	2	no	—
813	#41	—	8	2	no	—
814	C₂×Q₈	—	2	1	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	2	1	no	—
817	C₂×Q₈	—	2	1	no	—
818	C₂×Q₈	—	2	1	no	—
819	C₂×Q₈	—	2	2	no	—
820	C₂×Q₈	—	2	4	no	—
821	C₂×Q₈	—	4	1	no	—
822	C₂×Q₈	—	4	2	no	—
823	C₂×Q₈	—	4	1	no	—
824	C₂×Q₈	—	4	1	no	—
825	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
826	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
827	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
828	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
829	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	2	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	1	no	—
836	C₂×D₄	—	2	1	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	4	1	no	—
840	C₂×D₄	—	4	2	no	—
841	C₂×D₄	—	4	1	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	8	4	no	—
844	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
845	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
846	C₂×D₄	C₂⁴×C₇	1	2	yes	—
847	C₂×D₄	C₂⁴×C₇	1	2	yes	—
848	C₂²×C₄	—	2	1	no	—
849	C₂²×C₄	—	2	1	no	—
850	C₂²×C₄	—	2	2	no	—
851	C₂²×C₄	—	2	1	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
856	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
857	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
858	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
859	Q₁₆	—	2	4	no	—
860	Q₁₆	—	4	2	no	—
861	Q₁₆	—	4	2	no	—
862	Q₁₆	—	4	2	no	—
863	SD₁₆	—	2	4	no	—
864	SD₁₆	—	2	4	no	—
865	SD₁₆	—	4	2	no	—
866	SD₁₆	—	4	2	no	—
867	SD₁₆	—	4	2	no	—
868	SD₁₆	—	4	2	no	—
869	SD₁₆	—	4	2	no	—
870	SD₁₆	—	4	2	no	—
871	M₁₆	—	4	2	no	—
872	C₂×C₈	—	4	1	no	—
873	C₂×C₈	—	4	2	no	—
874	C₂×C₈	—	4	1	no	—
875	C₂×C₈	C₂⁴×C₇	1	2	yes	—
876	C₂×C₈	C₂⁴×C₇	1	2	yes	—
877	C₂×C₈	C₂⁴×C₇	1	2	yes	—
878	C₂×C₈	C₂⁴×C₇	1	2	yes	—
879	C₄⋊C₄	—	2	1	no	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	2	1	no	—
882	C₄⋊C₄	—	2	1	no	—
883	C₄⋊C₄	—	2	1	no	—
884	C₄⋊C₄	—	2	2	no	—
885	C₄⋊C₄	—	2	2	no	—
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	1	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	1	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
901	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
902	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
903	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
904	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
905	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
906	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
907	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
908	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
909	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	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	—	2	2	no	—
924	C₂²⋊C₄	—	2	2	no	—
925	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
926	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
927	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
928	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
929	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
930	C₄²	—	2	1	no	—
931	C₄²	—	2	1	no	—
932	C₄²	—	2	1	no	—
933	C₄²	—	2	1	no	—
934	C₄²	—	2	2	no	—
935	C₄²	—	2	2	no	—
936	C₄²	—	2	2	no	—
937	C₄²	—	2	2	no	—
938	C₄²	—	2	2	no	—
939	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
940	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
941	C₄²	C₂⁴×C₇	1	2	yes	—
942	C₄²	C₂⁴×C₇	1	1	yes	characteristic
943	C₄²	C₂⁴×C₇	1	1	yes	characteristic
944	C₂×C₇	—	2	2	no	—
945	C₂×C₇	—	4	2	no	—
946	C₂×C₇	—	8	2	no	—
947	C₂×C₇	—	8	2	no	—
948	C₂×C₇	#3488	1	1	yes	characteristic
949	C₂×C₇	C₂×#577	1	1	yes	characteristic
950	C₂×C₇	#3586	1	1	yes	characteristic
951	C₂³	—	2	2	no	—
952	C₂³	—	2	2	no	—
953	C₂³	—	4	2	no	—
954	C₂³	—	8	1	no	—
955	C₂³	—	8	2	no	—
956	C₂³	—	8	2	no	—
957	C₂³	—	8	1	no	—
958	C₂³	—	8	2	no	—
959	C₂³	C₂²×C₇×D₄	1	2	yes	—
960	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
961	Q₈	—	2	1	no	—
962	Q₈	—	2	2	no	—
963	Q₈	—	2	1	no	—
964	Q₈	—	2	2	no	—
965	Q₈	—	2	1	no	—
966	Q₈	—	2	2	no	—
967	Q₈	—	2	2	no	—
968	Q₈	—	4	1	no	—
969	Q₈	—	4	4	no	—
970	Q₈	—	4	2	no	—
971	Q₈	—	4	2	no	—
972	Q₈	—	8	1	no	—
973	Q₈	—	8	1	no	—
974	Q₈	C₇×H(5,𝔽₂)	1	2	yes	—
975	D₄	—	2	4	no	—
976	D₄	—	2	2	no	—
977	D₄	—	2	2	no	—
978	D₄	—	2	2	no	—
979	D₄	—	2	2	no	—
980	D₄	—	4	1	no	—
981	D₄	—	4	4	no	—
982	D₄	—	8	1	no	—
983	D₄	—	8	2	no	—
984	D₄	—	8	2	no	—
985	D₄	—	8	1	no	—
986	D₄	—	8	2	no	—
987	D₄	—	8	1	no	—
988	D₄	—	8	2	no	—
989	D₄	—	8	2	no	—
990	C₂×C₄	—	2	1	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	2	no	—
1003	C₂×C₄	—	4	1	no	—
1004	C₂×C₄	—	4	2	no	—
1005	C₂×C₄	—	4	4	no	—
1006	C₂×C₄	—	4	2	no	—
1007	C₂×C₄	—	8	2	no	—
1008	C₂×C₄	—	8	2	no	—
1009	C₂×C₄	—	8	2	no	—
1010	C₂×C₄	—	8	1	no	—
1011	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1012	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1013	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1014	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1015	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1016	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1017	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1018	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1019	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1020	C₈	—	2	2	no	—
1021	C₈	—	2	2	no	—
1022	C₈	—	2	2	no	—
1023	C₈	—	2	2	no	—
1024	C₇	#62019	1	1	yes	characteristic, direct product factor, Sylow
1025	C₂²	—	2	1	no	—
1026	C₂²	—	2	1	no	—
1027	C₂²	—	2	2	no	—
1028	C₂²	—	2	2	no	—
1029	C₂²	—	2	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	2	no	—
1032	C₂²	—	4	2	no	—
1033	C₂²	—	4	2	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	2	no	—
1036	C₂²	—	16	2	no	—
1037	C₂²	—	16	4	no	—
1038	C₂²	C₇×#577	1	2	yes	—
1039	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1040	C₄	—	2	1	no	—
1041	C₄	—	2	1	no	—
1042	C₄	—	2	2	no	—
1043	C₄	—	2	1	no	—
1044	C₄	—	2	1	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	2	no	—
1049	C₄	—	4	1	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	2	no	—
1056	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1057	C₄	C₇×#585	1	1	yes	characteristic
1058	C₂	—	2	2	no	—
1059	C₂	—	4	2	no	—
1060	C₂	—	8	2	no	—
1061	C₂	—	8	2	no	—
1062	C₂	C₇×#3488	1	1	yes	characteristic
1063	C₂	C₂×C₇×#577	1	1	yes	characteristic
1064	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3558	C₂
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
2. C₇×#3523	C₂	semidirect
3. C₇×#3400	C₂	semidirect
4. C₇×#3371	C₂	semidirect
5. C₇×#3311	C₂	semidirect
6. C₇×#3310	C₂	semidirect
7. C₇×#3300	C₂	semidirect
8. C₇×D₄×SD₁₆	C₂	semidirect
9. C₇×#3270	C₂	semidirect
10. C₇×#3266	C₂	semidirect
11. C₇×#3258	C₂	semidirect
12. C₇×#3246	C₂	semidirect
13. C₇×#3222	C₂	semidirect
14. C₇×#3215	C₂	semidirect
15. C₇×#3121	C₂	semidirect
16. C₇×#3112	C₂	semidirect
17. C₇×#3043	C₂	semidirect
18. C₂×C₇×#464	C₂	semidirect
19. C₇×#2992	C₂	semidirect
20. C₂×C₇×#137	C₂²	semidirect
21. C₂²×C₇×Q₁₆	C₂²	semidirect
23. C₂²×C₇×SD₁₆	C₂²	semidirect
28. C₇×#557	C₂²	semidirect
29. C₇×#557	C₂²	semidirect
31. C₇×#556	C₂²	semidirect
33. C₇×#552	C₂²	semidirect
34. C₇×D₄×Q₈	C₂²	semidirect
35. C₇×D₄×Q₈	C₂²	semidirect
42. C₇×#541	C₂²	semidirect
48. C₇×#533	C₂²	semidirect
53. C₇×#519	C₂²	semidirect
54. C₂×C₄×C₇×Q₈	C₂²	semidirect
55. C₇×#497	C₂²	semidirect
56. C₇×#497	C₂²	semidirect
59. C₇×#489	C₂²	semidirect
60. C₇×#488	C₂²	semidirect
61. C₇×#485	C₂²	semidirect
63. C₇×#480	C₂²	semidirect
64. C₇×#479	C₂²	semidirect
65. C₇×#478	C₂²	semidirect
66. C₇×#477	C₂²	semidirect
67. C₇×#477	C₂²	semidirect
68. C₇×#476	C₂²	semidirect
69. C₇×#475	C₂²	semidirect
70. C₇×#470	C₂²	semidirect
72. C₇×#467	C₂²	semidirect
74. C₇×#465	C₂²	semidirect
75. C₇×#465	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×#464	C₂²	semidirect
83. C₇×#464	C₂²	semidirect
84. C₇×#462	C₂²	semidirect
85. C₇×#461	C₂²	semidirect
86. C₇×#461	C₂²	semidirect
89. C₇×#460	C₂²	semidirect
90. C₇×#460	C₂²	semidirect
91. C₇×#460	C₂²	semidirect
92. C₇×#452	C₂²	semidirect
93. C₇×#452	C₂²	semidirect
94. C₇×#451	C₂²	semidirect
95. C₇×#451	C₂²	semidirect
97. C₇×#450	C₂²	semidirect
98. C₇×#450	C₂²	semidirect
100. C₇×#448	C₂²	semidirect
101. C₇×#446	C₂²	semidirect
102. C₇×#441	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×SD₁₆	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×#418	C₂²	semidirect
116. C₇×#416	C₂²	semidirect
117. C₂×C₇×#103	C₂²	semidirect
119. #62019	C₇	direct (N × H)
286. #3523	C₂×C₇	semidirect
287. #3400	C₂×C₇	semidirect
288. #3371	C₂×C₇	semidirect
289. #3311	C₂×C₇	semidirect
290. #3310	C₂×C₇	semidirect
291. #3300	C₂×C₇	semidirect
292. D₄×SD₁₆	C₂×C₇	semidirect
293. #3270	C₂×C₇	semidirect
294. #3266	C₂×C₇	semidirect
295. #3258	C₂×C₇	semidirect
296. #3246	C₂×C₇	semidirect
297. #3222	C₂×C₇	semidirect
298. #3215	C₂×C₇	semidirect
299. #3121	C₂×C₇	semidirect
300. #3112	C₂×C₇	semidirect
301. #3043	C₂×C₇	semidirect
302. C₂×#464	C₂×C₇	semidirect
303. #2992	C₂×C₇	semidirect
439. C₂×#137	C₂²×C₇	semidirect
440. C₂²×Q₁₆	C₂²×C₇	semidirect
442. C₂²×SD₁₆	C₂²×C₇	semidirect
447. #557	C₂²×C₇	semidirect
448. #557	C₂²×C₇	semidirect
450. #556	C₂²×C₇	semidirect
452. #552	C₂²×C₇	semidirect
453. D₄×Q₈	C₂²×C₇	semidirect
454. D₄×Q₈	C₂²×C₇	semidirect
461. #541	C₂²×C₇	semidirect
467. #533	C₂²×C₇	semidirect
472. #519	C₂²×C₇	semidirect
473. C₂×C₄×Q₈	C₂²×C₇	semidirect
474. #497	C₂²×C₇	semidirect
475. #497	C₂²×C₇	semidirect
478. #489	C₂²×C₇	semidirect
479. #488	C₂²×C₇	semidirect
480. #485	C₂²×C₇	semidirect
482. #480	C₂²×C₇	semidirect
483. #479	C₂²×C₇	semidirect
484. #478	C₂²×C₇	semidirect
485. #477	C₂²×C₇	semidirect
486. #477	C₂²×C₇	semidirect
487. #476	C₂²×C₇	semidirect
488. #475	C₂²×C₇	semidirect
489. #470	C₂²×C₇	semidirect
491. #467	C₂²×C₇	semidirect
493. #465	C₂²×C₇	semidirect
494. #465	C₂²×C₇	semidirect
495. #464	C₂²×C₇	semidirect
496. #464	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. #462	C₂²×C₇	semidirect
504. #461	C₂²×C₇	semidirect
505. #461	C₂²×C₇	semidirect
508. #460	C₂²×C₇	semidirect
509. #460	C₂²×C₇	semidirect
510. #460	C₂²×C₇	semidirect
511. #452	C₂²×C₇	semidirect
512. #452	C₂²×C₇	semidirect
513. #451	C₂²×C₇	semidirect
514. #451	C₂²×C₇	semidirect
516. #450	C₂²×C₇	semidirect
517. #450	C₂²×C₇	semidirect
519. #448	C₂²×C₇	semidirect
520. #446	C₂²×C₇	semidirect
521. #441	C₂²×C₇	semidirect
522. #440	C₂²×C₇	semidirect
523. #440	C₂²×C₇	semidirect
524. #440	C₂²×C₇	semidirect
525. C₄×Q₁₆	C₂²×C₇	semidirect
526. C₄×SD₁₆	C₂²×C₇	semidirect
527. #435	C₂²×C₇	semidirect
528. #435	C₂²×C₇	semidirect
529. C₈×D₄	C₂²×C₇	semidirect
530. #433	C₂²×C₇	semidirect
531. #432	C₂²×C₇	semidirect
532. #424	C₂²×C₇	semidirect
533. C₂×C₄⋊C₈	C₂²×C₇	semidirect
534. #418	C₂²×C₇	semidirect
535. #416	C₂²×C₇	semidirect
536. C₂×#103	C₂²×C₇	semidirect
1024. C₇	#62019	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×#3523	2
C₇×#3400	2
C₇×#3371	2
C₇×#3311	2
C₇×#3310	2
C₇×#3300	2
C₇×D₄×SD₁₆	2
C₇×#3270	2
C₇×#3266	2
C₇×#3258	2
C₇×#3246	2
C₇×#3222	2
C₇×#3215	2
C₇×#3121	2
C₇×#3112	2
C₇×#3043	2
C₂×C₇×#464	2
C₇×#2992	2
#62019	7

Subgroups — C7×#62019 #13239235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62019 #13239235