Subgroups — C₇×#60557 #13237773

Order 1792.

2038 conjugacy classes of subgroups.

The subgroup lattice has 974 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3127	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3126	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3125	C₂	1	2	yes	maximal, complemented
6	C₇×#3124	C₂	1	2	yes	maximal, complemented
7	C₇×#3123	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3122	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3121	C₂	1	2	yes	maximal, complemented
10	C₇×#3120	C₂	1	2	yes	maximal, complemented
11	C₇×#3119	C₂	1	2	yes	maximal, complemented
12	C₇×#3118	C₂	1	2	yes	maximal, complemented
13	C₇×#3091	C₂	1	2	yes	maximal, complemented
14	C₇×#3076	C₂	1	2	yes	maximal, complemented
15	C₇×#3035	C₂	1	2	yes	maximal, complemented
16	C₇×#3002	C₂	1	2	yes	maximal, complemented
17	C₇×#2943	C₂	1	2	yes	maximal, complemented
18	C₄×C₇×#135	C₂	1	2	yes	maximal, complemented
19	C₂×C₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
21	C₂×C₇×#135	C₂²	1	2	yes	—
22	C₂×C₇×#135	C₂²	1	2	yes	—
23	C₇×#542	C₂²	1	2	yes	—
24	C₇×#542	C₂²	1	2	yes	complemented
25	C₇×#541	C₂²	1	1	yes	characteristic
26	C₇×#541	C₂²	1	1	yes	characteristic, complemented
27	C₇×#540	C₂²	1	1	yes	characteristic
28	C₇×#540	C₂²	1	1	yes	characteristic, complemented
29	C₇×#539	—	2	2	no	—
30	C₇×#538	—	2	2	no	—
31	C₇×#533	C₂²	1	1	yes	characteristic, complemented
32	C₇×#532	C₂²	1	1	yes	characteristic, complemented
33	C₇×#529	—	2	2	no	—
34	C₇×#529	—	2	2	no	—
35	C₇×#525	C₂²	1	2	yes	—
36	C₇×#520	—	2	2	no	—
37	C₇×#520	C₂²	1	2	yes	—
38	C₇×#520	C₂²	1	2	yes	—
39	C₇×#519	C₂²	1	1	yes	characteristic
40	C₇×#519	C₂²	1	1	yes	characteristic
41	C₇×#518	—	2	2	no	—
42	C₇×#518	C₂²	1	1	yes	characteristic
43	C₇×#518	C₂²	1	1	yes	characteristic
44	C₄×C₇×#41	—	2	2	no	—
45	C₄×C₇×#41	C₂²	1	2	yes	—
46	C₄×C₇×#41	C₂²	1	2	yes	—
47	C₄×C₇×#41	C₂²	1	2	yes	complemented
48	C₂×C₇×#117	—	2	2	no	—
49	C₂×C₇×#117	C₂²	1	1	yes	characteristic
50	C₂×C₇×#117	C₂²	1	1	yes	characteristic
51	C₇×#485	C₂²	1	2	yes	—
52	C₇×#485	C₂²	1	2	yes	—
53	C₇×#484	C₂²	1	2	yes	complemented
54	C₇×#483	C₂²	1	2	yes	complemented
55	C₇×#482	C₂²	1	2	yes	—
56	C₇×#482	C₂²	1	2	yes	—
57	C₇×#481	C₂²	1	2	yes	complemented
58	C₇×#480	C₂²	1	2	yes	complemented
59	C₇×#479	C₂²	1	2	yes	complemented
60	C₇×#479	C₂²	1	2	yes	complemented
61	C₇×#478	C₂²	1	2	yes	complemented
62	C₇×#478	C₂²	1	2	yes	complemented
63	C₇×#477	C₂²	1	2	yes	complemented
64	C₇×#476	C₂²	1	2	yes	complemented
65	C₇×#475	C₂²	1	2	yes	complemented
66	C₇×#474	C₂²	1	2	yes	complemented
67	C₇×#464	C₂²	1	2	yes	complemented
68	C₇×#464	C₂²	1	2	yes	complemented
69	C₇×#463	C₂²	1	2	yes	complemented
70	C₇×#463	C₂²	1	2	yes	complemented
71	C₇×#462	C₂²	1	2	yes	complemented
72	C₇×#461	C₂²	1	2	yes	complemented
73	C₇×#460	C₂²	1	2	yes	complemented
74	C₇×#459	C₂²	1	2	yes	complemented
75	C₇×#452	C₂²	1	2	yes	—
76	C₇×#452	C₂²	1	2	yes	—
77	C₇×#451	C₂²	1	2	yes	—
78	C₇×#450	C₂²	1	2	yes	—
79	C₇×#449	C₂²	1	2	yes	—
80	C₇×#449	C₂²	1	2	yes	—
81	C₇×#448	C₂²	1	2	yes	—
82	C₇×#447	C₂²	1	2	yes	—
83	C₇×#442	C₂²	1	2	yes	complemented
84	C₇×#442	C₂²	1	2	yes	complemented
85	C₇×#441	C₂²	1	2	yes	complemented
86	C₇×#441	C₂²	1	2	yes	complemented
87	C₇×#440	C₂²	1	2	yes	complemented
88	C₇×#440	C₂²	1	2	yes	complemented
89	C₇×#440	C₂²	1	2	yes	complemented
90	C₇×#440	C₂²	1	2	yes	complemented
91	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
92	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
93	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
94	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
95	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
96	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
97	C₄×C₇×D₈	C₂²	1	2	yes	complemented
98	C₄×C₇×D₈	C₂²	1	2	yes	complemented
99	C₇×#433	C₂²	1	2	yes	—
100	C₇×#433	C₂²	1	1	yes	characteristic
101	C₇×#433	C₂²	1	1	yes	characteristic
102	C₇×#433	C₂²	1	2	yes	complemented
103	C₇×#433	C₂²	1	1	yes	characteristic, complemented
104	C₇×#433	C₂²	1	1	yes	characteristic, complemented
105	C₇×#427	C₂²	1	2	yes	complemented
106	C₇×#427	C₂²	1	2	yes	complemented
107	C₂×C₇×C₄⋊C₈	C₂²	1	2	yes	complemented
108	C₇×#416	C₂²	1	2	yes	—
109	C₇×#416	C₂²	1	2	yes	—
110	C₇×#416	C₂²	1	2	yes	complemented
111	C₇×#416	C₂²	1	2	yes	complemented
112	C₂×C₇×C₂²⋊C₈	C₂²	1	2	yes	—
113	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
114	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
115	#60557	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂×C₇×#41	—	2	8	no	—
117	C₂×C₇×#41	—	2	1	no	—
118	C₂×C₇×#41	—	2	1	no	—
119	C₂×C₇×#41	C₂³	1	2	yes	—
120	C₂×C₇×#41	C₂³	1	2	yes	—
121	C₂×C₇×#41	C₂³	1	2	yes	—
122	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
123	C₂²×C₇×D₄	—	2	1	no	—
124	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
125	C₂³×C₄×C₇	—	2	1	no	—
126	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
127	C₇×#135	—	2	8	no	—
128	C₇×#135	—	2	8	no	—
129	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
130	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
131	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
132	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
133	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
134	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
135	C₂×C₇×D₈	C₂³	1	2	yes	—
136	C₂×C₇×D₈	C₂³	1	2	yes	—
137	C₂²×C₇×C₈	C₂³	1	2	yes	—
138	C₂²×C₇×C₈	C₂³	1	2	yes	—
139	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
140	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
141	C₇×#127	C₂³	1	1	yes	characteristic
142	C₇×#126	—	2	2	no	—
143	C₇×#126	—	2	2	no	—
144	C₇×#126	—	2	2	no	—
145	C₇×#126	—	2	2	no	—
146	C₇×#125	—	2	2	no	—
147	C₇×#125	—	2	2	no	—
148	C₇×#125	C₂³	1	1	yes	characteristic
149	C₇×#125	C₂³	1	1	yes	characteristic
150	C₇×#124	—	2	2	no	—
151	C₇×#124	—	2	2	no	—
152	C₇×#124	C₂³	1	2	yes	—
153	C₇×#123	—	2	2	no	—
154	C₇×#123	—	2	2	no	—
155	C₇×#123	—	2	2	no	—
156	C₇×#123	—	2	2	no	—
157	C₇×#123	—	2	2	no	—
158	C₇×C₂²⋊Q₈	—	2	2	no	—
159	C₇×C₂²⋊Q₈	—	2	2	no	—
160	C₇×C₂²⋊Q₈	—	2	2	no	—
161	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
162	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
163	C₇×#121	—	2	2	no	—
164	C₇×#121	—	2	2	no	—
165	C₇×#121	—	2	2	no	—
166	C₇×#121	C₂³	1	2	yes	—
167	C₇×#121	C₂³	1	2	yes	—
168	C₇×#120	—	2	2	no	—
169	C₄×C₇×Q₈	—	2	2	no	—
170	C₄×C₇×Q₈	—	2	2	no	—
171	C₄×C₇×Q₈	—	2	2	no	—
172	C₄×C₇×Q₈	C₂³	1	2	yes	—
173	C₄×C₇×Q₈	C₂³	1	2	yes	—
174	C₄×C₇×Q₈	C₂³	1	2	yes	—
175	C₄×C₇×Q₈	C₂³	1	2	yes	—
176	C₄×C₇×Q₈	C₂³	1	2	yes	—
177	C₄×C₇×Q₈	C₂³	1	2	yes	—
178	C₄×C₇×D₄	—	2	2	no	—
179	C₄×C₇×D₄	—	2	2	no	—
180	C₄×C₇×D₄	—	2	2	no	—
181	C₄×C₇×D₄	—	2	2	no	—
182	C₄×C₇×D₄	—	2	2	no	—
183	C₄×C₇×D₄	—	2	2	no	—
184	C₄×C₇×D₄	—	2	2	no	—
185	C₄×C₇×D₄	—	2	2	no	—
186	C₄×C₇×D₄	—	2	2	no	—
187	C₄×C₇×D₄	—	2	2	no	—
188	C₄×C₇×D₄	—	2	2	no	—
189	C₄×C₇×D₄	—	2	2	no	—
190	C₄×C₇×D₄	—	2	2	no	—
191	C₄×C₇×D₄	—	2	2	no	—
192	C₄×C₇×D₄	—	2	2	no	—
193	C₄×C₇×D₄	C₂³	1	2	yes	—
194	C₄×C₇×D₄	C₂³	1	2	yes	—
195	C₄×C₇×D₄	C₂³	1	2	yes	—
196	C₄×C₇×D₄	C₂³	1	2	yes	—
197	C₄×C₇×D₄	C₂³	1	2	yes	—
198	C₄×C₇×D₄	C₂³	1	2	yes	—
199	C₇×#117	—	2	1	no	—
200	C₇×#117	—	2	1	no	—
201	C₇×#117	—	2	2	no	—
202	C₇×#117	—	2	2	no	—
203	C₇×#117	—	2	2	no	—
204	C₇×#117	—	2	2	no	—
205	C₇×#117	—	2	2	no	—
206	C₇×#117	—	2	2	no	—
207	C₇×#117	—	2	2	no	—
208	C₇×#117	D₄	1	2	yes	—
209	C₇×#117	D₄	1	2	yes	—
210	C₇×#117	C₂³	1	1	yes	characteristic
211	C₇×#117	C₂³	1	1	yes	characteristic
212	C₇×#117	C₂³	1	2	yes	—
213	C₇×#117	C₂³	1	2	yes	—
214	C₇×#117	C₂³	1	1	yes	characteristic
215	C₇×#117	C₂³	1	1	yes	characteristic
216	C₇×#117	C₂³	1	1	yes	characteristic
217	C₇×#117	C₂³	1	1	yes	characteristic
218	C₂×C₇×C₄⋊C₄	—	2	2	no	—
219	C₂×C₇×C₄⋊C₄	—	2	2	no	—
220	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
221	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
222	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
223	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
224	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
225	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
226	C₂×C₄²×C₇	—	2	1	no	—
227	C₂×C₄²×C₇	—	2	2	no	—
228	C₂×C₄²×C₇	—	2	2	no	—
229	C₂×C₄²×C₇	—	2	2	no	—
230	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
231	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
232	C₇×#107	C₂³	1	2	yes	—
233	C₇×#107	C₂³	1	2	yes	—
234	C₇×#107	C₂³	1	2	yes	—
235	C₇×#107	C₂³	1	2	yes	—
236	C₇×#106	C₂³	1	2	yes	—
237	C₇×#106	C₂³	1	2	yes	—
238	C₇×#106	C₂³	1	2	yes	—
239	C₇×#106	C₂³	1	2	yes	—
240	C₇×C₄⋊C₈	C₂³	1	2	yes	—
241	C₇×C₄⋊C₈	C₂³	1	2	yes	—
242	C₇×C₄⋊C₈	C₂³	1	2	yes	—
243	C₇×C₄⋊C₈	C₂³	1	2	yes	—
244	C₇×#103	C₂³	1	2	yes	—
245	C₇×#103	C₂³	1	2	yes	—
246	C₇×#103	C₂³	1	2	yes	—
247	C₇×#103	C₂³	1	2	yes	—
248	C₇×#103	C₂³	1	2	yes	—
249	C₇×#103	C₂³	1	2	yes	—
250	C₇×#103	C₂³	1	2	yes	—
251	C₇×#103	C₂³	1	2	yes	—
252	C₇×#102	C₂³	1	2	yes	—
253	C₇×#102	C₂³	1	2	yes	—
254	C₇×#102	C₂³	1	2	yes	—
255	C₇×#102	C₂³	1	2	yes	—
256	C₇×#102	C₂³	1	2	yes	—
257	C₇×#102	C₂³	1	2	yes	—
258	C₇×#102	C₂³	1	2	yes	—
259	C₇×#102	C₂³	1	2	yes	—
260	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
261	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
262	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
263	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
264	C₇×#97	C₂³	1	1	yes	characteristic
265	C₇×#97	C₂³	1	2	yes	—
266	C₇×#97	C₂³	1	1	yes	characteristic
267	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
268	C₄×C₇×C₈	C₂³	1	2	yes	—
269	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
270	#3455	C₂×C₇	1	1	yes	characteristic, complemented
271	#3428	C₂×C₇	1	1	yes	characteristic, complemented
272	#3127	C₂×C₇	1	1	yes	characteristic, complemented
273	#3126	C₂×C₇	1	1	yes	characteristic, complemented
274	#3125	C₂×C₇	1	2	yes	complemented
275	#3124	C₂×C₇	1	2	yes	complemented
276	#3123	C₂×C₇	1	1	yes	characteristic, complemented
277	#3122	C₂×C₇	1	1	yes	characteristic, complemented
278	#3121	C₂×C₇	1	2	yes	complemented
279	#3120	C₂×C₇	1	2	yes	complemented
280	#3119	C₂×C₇	1	2	yes	complemented
281	#3118	C₂×C₇	1	2	yes	complemented
282	#3091	C₂×C₇	1	2	yes	complemented
283	#3076	C₂×C₇	1	2	yes	complemented
284	#3035	C₂×C₇	1	2	yes	complemented
285	#3002	C₂×C₇	1	2	yes	complemented
286	#2943	C₂×C₇	1	2	yes	complemented
287	C₄×#135	C₂×C₇	1	2	yes	complemented
288	C₂×#433	C₂×C₇	1	1	yes	characteristic, complemented
289	C₂⁴×C₇	—	2	1	no	—
290	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
291	C₇×#41	—	2	8	no	—
292	C₇×#41	—	2	8	no	—
293	C₇×#41	—	2	4	no	—
294	C₇×#41	—	2	4	no	—
295	C₇×#41	—	2	4	no	—
296	C₇×#41	—	2	4	no	—
297	C₇×#41	—	2	4	no	—
298	C₇×#41	#41	1	8	yes	—
299	C₂×C₇×Q₈	—	2	4	no	—
300	C₂×C₇×Q₈	—	2	1	no	—
301	C₂×C₇×Q₈	—	2	2	no	—
302	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
303	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
304	C₂×C₇×D₄	—	2	8	no	—
305	C₂×C₇×D₄	—	2	2	no	—
306	C₂×C₇×D₄	—	2	2	no	—
307	C₂×C₇×D₄	—	2	4	no	—
308	C₂×C₇×D₄	—	2	2	no	—
309	C₂×C₇×D₄	—	2	2	no	—
310	C₂×C₇×D₄	—	2	2	no	—
311	C₂×C₇×D₄	—	2	1	no	—
312	C₂×C₇×D₄	—	2	2	no	—
313	C₂×C₇×D₄	C₂⁴	1	2	yes	—
314	C₂×C₇×D₄	C₂⁴	1	2	yes	—
315	C₂²×C₄×C₇	—	2	8	no	—
316	C₂²×C₄×C₇	—	2	1	no	—
317	C₂²×C₄×C₇	—	2	2	no	—
318	C₂²×C₄×C₇	—	2	2	no	—
319	C₂²×C₄×C₇	—	2	4	no	—
320	C₂²×C₄×C₇	—	2	2	no	—
321	C₂²×C₄×C₇	—	2	2	no	—
322	C₂²×C₄×C₇	—	2	2	no	—
323	C₂²×C₄×C₇	—	2	2	no	—
324	C₂²×C₄×C₇	—	2	2	no	—
325	C₂²×C₄×C₇	—	2	2	no	—
326	C₂²×C₄×C₇	—	2	2	no	—
327	C₂²×C₄×C₇	—	2	2	no	—
328	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
332	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
333	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
334	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
336	C₇×Q₁₆	—	2	4	no	—
337	C₇×Q₁₆	—	2	4	no	—
338	C₇×SD₁₆	—	2	4	no	—
339	C₇×SD₁₆	—	2	4	no	—
340	C₇×SD₁₆	—	2	4	no	—
341	C₇×SD₁₆	—	2	4	no	—
342	C₇×D₈	—	2	4	no	—
343	C₇×D₈	—	2	4	no	—
344	C₂×C₇×C₈	—	2	4	no	—
345	C₂×C₇×C₈	—	2	4	no	—
346	C₂×C₇×C₈	C₂⁴	1	2	yes	—
347	C₂×C₇×C₈	C₂⁴	1	2	yes	—
348	C₂×C₇×C₈	C₂⁴	1	2	yes	—
349	C₂×C₇×C₈	C₂⁴	1	2	yes	—
350	C₇×C₄⋊C₄	—	2	2	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	—	2	2	no	—
354	C₇×C₄⋊C₄	—	2	2	no	—
355	C₇×C₄⋊C₄	—	2	2	no	—
356	C₇×C₄⋊C₄	—	2	2	no	—
357	C₇×C₄⋊C₄	—	2	2	no	—
358	C₇×C₄⋊C₄	—	2	2	no	—
359	C₇×C₄⋊C₄	—	2	2	no	—
360	C₇×C₄⋊C₄	—	2	2	no	—
361	C₇×C₄⋊C₄	—	2	2	no	—
362	C₇×C₄⋊C₄	—	2	2	no	—
363	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
364	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
365	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
366	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
367	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
368	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
369	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
370	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
371	C₇×C₂²⋊C₄	—	2	1	no	—
372	C₇×C₂²⋊C₄	—	2	1	no	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	2	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	—	2	2	no	—
377	C₇×C₂²⋊C₄	—	2	2	no	—
378	C₇×C₂²⋊C₄	—	2	2	no	—
379	C₇×C₂²⋊C₄	—	2	2	no	—
380	C₇×C₂²⋊C₄	—	2	2	no	—
381	C₇×C₂²⋊C₄	—	2	2	no	—
382	C₇×C₂²⋊C₄	—	2	2	no	—
383	C₇×C₂²⋊C₄	—	2	2	no	—
384	C₇×C₂²⋊C₄	—	2	2	no	—
385	C₇×C₂²⋊C₄	—	2	2	no	—
386	C₇×C₂²⋊C₄	—	2	2	no	—
387	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
388	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
389	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
390	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
391	C₄²×C₇	—	2	2	no	—
392	C₄²×C₇	—	2	2	no	—
393	C₄²×C₇	—	2	2	no	—
394	C₄²×C₇	—	2	2	no	—
395	C₄²×C₇	—	2	1	no	—
396	C₄²×C₇	—	2	1	no	—
397	C₄²×C₇	—	2	2	no	—
398	C₄²×C₇	—	2	2	no	—
399	C₄²×C₇	—	2	2	no	—
400	C₄²×C₇	—	2	2	no	—
401	C₄²×C₇	C₂×D₄	1	2	yes	—
402	C₄²×C₇	C₂×D₄	1	2	yes	—
403	C₄²×C₇	C₂⁴	1	1	yes	characteristic
404	C₄²×C₇	C₂⁴	1	1	yes	characteristic
405	C₄²×C₇	C₂⁴	1	1	yes	characteristic
406	C₄²×C₇	C₂⁴	1	1	yes	characteristic
407	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
408	C₂×#135	C₂²×C₇	1	2	yes	—
409	C₂×#135	C₂²×C₇	1	2	yes	—
410	#542	C₂²×C₇	1	2	yes	—
411	#542	C₂²×C₇	1	2	yes	complemented
412	#541	C₂²×C₇	1	1	yes	characteristic
413	#541	C₂²×C₇	1	1	yes	characteristic, complemented
414	#540	C₂²×C₇	1	1	yes	characteristic
415	#540	C₂²×C₇	1	1	yes	characteristic, complemented
416	#539	—	2	2	no	—
417	#538	—	2	2	no	—
418	#533	C₂²×C₇	1	1	yes	characteristic, complemented
419	#532	C₂²×C₇	1	1	yes	characteristic, complemented
420	#529	—	2	2	no	—
421	#529	—	2	2	no	—
422	#525	C₂²×C₇	1	2	yes	—
423	#520	—	2	2	no	—
424	#520	C₂²×C₇	1	2	yes	—
425	#520	C₂²×C₇	1	2	yes	—
426	#519	C₂²×C₇	1	1	yes	characteristic
427	#519	C₂²×C₇	1	1	yes	characteristic
428	#518	—	2	2	no	—
429	#518	C₂²×C₇	1	1	yes	characteristic
430	#518	C₂²×C₇	1	1	yes	characteristic
431	C₄×#41	—	2	2	no	—
432	C₄×#41	C₂²×C₇	1	2	yes	—
433	C₄×#41	C₂²×C₇	1	2	yes	—
434	C₄×#41	C₂²×C₇	1	2	yes	complemented
435	C₂×#117	—	2	2	no	—
436	C₂×#117	C₂²×C₇	1	1	yes	characteristic
437	C₂×#117	C₂²×C₇	1	1	yes	characteristic
438	#485	C₂²×C₇	1	2	yes	—
439	#485	C₂²×C₇	1	2	yes	—
440	#484	C₂²×C₇	1	2	yes	complemented
441	#483	C₂²×C₇	1	2	yes	complemented
442	#482	C₂²×C₇	1	2	yes	—
443	#482	C₂²×C₇	1	2	yes	—
444	#481	C₂²×C₇	1	2	yes	complemented
445	#480	C₂²×C₇	1	2	yes	complemented
446	#479	C₂²×C₇	1	2	yes	complemented
447	#479	C₂²×C₇	1	2	yes	complemented
448	#478	C₂²×C₇	1	2	yes	complemented
449	#478	C₂²×C₇	1	2	yes	complemented
450	#477	C₂²×C₇	1	2	yes	complemented
451	#476	C₂²×C₇	1	2	yes	complemented
452	#475	C₂²×C₇	1	2	yes	complemented
453	#474	C₂²×C₇	1	2	yes	complemented
454	#464	C₂²×C₇	1	2	yes	complemented
455	#464	C₂²×C₇	1	2	yes	complemented
456	#463	C₂²×C₇	1	2	yes	complemented
457	#463	C₂²×C₇	1	2	yes	complemented
458	#462	C₂²×C₇	1	2	yes	complemented
459	#461	C₂²×C₇	1	2	yes	complemented
460	#460	C₂²×C₇	1	2	yes	complemented
461	#459	C₂²×C₇	1	2	yes	complemented
462	#452	C₂²×C₇	1	2	yes	—
463	#452	C₂²×C₇	1	2	yes	—
464	#451	C₂²×C₇	1	2	yes	—
465	#450	C₂²×C₇	1	2	yes	—
466	#449	C₂²×C₇	1	2	yes	—
467	#449	C₂²×C₇	1	2	yes	—
468	#448	C₂²×C₇	1	2	yes	—
469	#447	C₂²×C₇	1	2	yes	—
470	#442	C₂²×C₇	1	2	yes	complemented
471	#442	C₂²×C₇	1	2	yes	complemented
472	#441	C₂²×C₇	1	2	yes	complemented
473	#441	C₂²×C₇	1	2	yes	complemented
474	#440	C₂²×C₇	1	2	yes	complemented
475	#440	C₂²×C₇	1	2	yes	complemented
476	#440	C₂²×C₇	1	2	yes	complemented
477	#440	C₂²×C₇	1	2	yes	complemented
478	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
479	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
480	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
481	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
482	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
483	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
484	C₄×D₈	C₂²×C₇	1	2	yes	complemented
485	C₄×D₈	C₂²×C₇	1	2	yes	complemented
486	#433	C₂²×C₇	1	2	yes	—
487	#433	C₂²×C₇	1	1	yes	characteristic
488	#433	C₂²×C₇	1	1	yes	characteristic
489	#433	C₂²×C₇	1	2	yes	complemented
490	#433	C₂²×C₇	1	1	yes	characteristic, complemented
491	#433	C₂²×C₇	1	1	yes	characteristic, complemented
492	#427	C₂²×C₇	1	2	yes	complemented
493	#427	C₂²×C₇	1	2	yes	complemented
494	C₂×C₄⋊C₈	C₂²×C₇	1	2	yes	complemented
495	#416	C₂²×C₇	1	2	yes	—
496	#416	C₂²×C₇	1	2	yes	—
497	#416	C₂²×C₇	1	2	yes	complemented
498	#416	C₂²×C₇	1	2	yes	complemented
499	C₂×C₂²⋊C₈	C₂²×C₇	1	2	yes	—
500	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
501	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
502	C₂³×C₇	—	2	4	no	—
503	C₂³×C₇	—	2	2	no	—
504	C₂³×C₇	—	2	2	no	—
505	C₂³×C₇	—	2	2	no	—
506	C₂³×C₇	—	4	2	no	—
507	C₂³×C₇	—	8	2	no	—
508	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
509	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
510	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
511	C₇×Q₈	—	2	4	no	—
512	C₇×Q₈	—	2	2	no	—
513	C₇×Q₈	—	2	2	no	—
514	C₇×Q₈	—	2	2	no	—
515	C₇×Q₈	—	8	2	no	—
516	C₇×Q₈	C₂×#41	1	4	yes	—
517	C₇×D₄	—	2	8	no	—
518	C₇×D₄	—	2	4	no	—
519	C₇×D₄	—	2	8	no	—
520	C₇×D₄	—	2	2	no	—
521	C₇×D₄	—	2	2	no	—
522	C₇×D₄	—	2	2	no	—
523	C₇×D₄	—	4	4	no	—
524	C₇×D₄	—	8	2	no	—
525	C₇×D₄	—	8	2	no	—
526	C₇×D₄	—	8	2	no	—
527	C₇×D₄	C₂×#41	1	4	yes	—
528	C₂×C₄×C₇	—	2	4	no	—
529	C₂×C₄×C₇	—	2	8	no	—
530	C₂×C₄×C₇	—	2	2	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	8	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	2	no	—
537	C₂×C₄×C₇	—	2	2	no	—
538	C₂×C₄×C₇	—	2	2	no	—
539	C₂×C₄×C₇	—	2	2	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	4	2	no	—
543	C₂×C₄×C₇	—	4	2	no	—
544	C₂×C₄×C₇	—	4	4	no	—
545	C₂×C₄×C₇	—	8	2	no	—
546	C₂×C₄×C₇	—	8	2	no	—
547	C₂×C₄×C₇	—	8	2	no	—
548	C₂×C₄×C₇	—	8	2	no	—
549	C₂×C₄×C₇	—	8	2	no	—
550	C₂×C₄×C₇	—	8	2	no	—
551	C₂×C₄×C₇	—	8	2	no	—
552	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
554	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
556	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
557	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
558	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
559	C₂×C₄×C₇	C₂×#41	1	4	yes	—
560	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
561	C₇×C₈	—	2	2	no	—
562	C₇×C₈	—	2	2	no	—
563	C₇×C₈	—	2	2	no	—
564	C₇×C₈	—	2	2	no	—
565	C₂×#41	—	2	8	no	—
566	C₂×#41	—	2	1	no	—
567	C₂×#41	—	2	1	no	—
568	C₂×#41	C₂³×C₇	1	2	yes	—
569	C₂×#41	C₂³×C₇	1	2	yes	—
570	C₂×#41	C₂³×C₇	1	2	yes	—
571	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
572	C₂²×D₄	—	2	1	no	—
573	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
574	C₂³×C₄	—	2	1	no	—
575	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
576	#135	—	2	8	no	—
577	#135	—	2	8	no	—
578	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
579	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
580	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
581	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
582	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
583	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
584	C₂×D₈	C₂³×C₇	1	2	yes	—
585	C₂×D₈	C₂³×C₇	1	2	yes	—
586	C₂²×C₈	C₂³×C₇	1	2	yes	—
587	C₂²×C₈	C₂³×C₇	1	2	yes	—
588	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
589	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
590	#127	C₂³×C₇	1	1	yes	characteristic
591	#126	—	2	2	no	—
592	#126	—	2	2	no	—
593	#126	—	2	2	no	—
594	#126	—	2	2	no	—
595	#125	—	2	2	no	—
596	#125	—	2	2	no	—
597	#125	C₂³×C₇	1	1	yes	characteristic
598	#125	C₂³×C₇	1	1	yes	characteristic
599	#124	—	2	2	no	—
600	#124	—	2	2	no	—
601	#124	C₂³×C₇	1	2	yes	—
602	#123	—	2	2	no	—
603	#123	—	2	2	no	—
604	#123	—	2	2	no	—
605	#123	—	2	2	no	—
606	#123	—	2	2	no	—
607	C₂²⋊Q₈	—	2	2	no	—
608	C₂²⋊Q₈	—	2	2	no	—
609	C₂²⋊Q₈	—	2	2	no	—
610	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
611	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
612	#121	—	2	2	no	—
613	#121	—	2	2	no	—
614	#121	—	2	2	no	—
615	#121	C₂³×C₇	1	2	yes	—
616	#121	C₂³×C₇	1	2	yes	—
617	#120	—	2	2	no	—
618	C₄×Q₈	—	2	2	no	—
619	C₄×Q₈	—	2	2	no	—
620	C₄×Q₈	—	2	2	no	—
621	C₄×Q₈	C₂³×C₇	1	2	yes	—
622	C₄×Q₈	C₂³×C₇	1	2	yes	—
623	C₄×Q₈	C₂³×C₇	1	2	yes	—
624	C₄×Q₈	C₂³×C₇	1	2	yes	—
625	C₄×Q₈	C₂³×C₇	1	2	yes	—
626	C₄×Q₈	C₂³×C₇	1	2	yes	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	2	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	2	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	—	2	2	no	—
633	C₄×D₄	—	2	2	no	—
634	C₄×D₄	—	2	2	no	—
635	C₄×D₄	—	2	2	no	—
636	C₄×D₄	—	2	2	no	—
637	C₄×D₄	—	2	2	no	—
638	C₄×D₄	—	2	2	no	—
639	C₄×D₄	—	2	2	no	—
640	C₄×D₄	—	2	2	no	—
641	C₄×D₄	—	2	2	no	—
642	C₄×D₄	C₂³×C₇	1	2	yes	—
643	C₄×D₄	C₂³×C₇	1	2	yes	—
644	C₄×D₄	C₂³×C₇	1	2	yes	—
645	C₄×D₄	C₂³×C₇	1	2	yes	—
646	C₄×D₄	C₂³×C₇	1	2	yes	—
647	C₄×D₄	C₂³×C₇	1	2	yes	—
648	#117	—	2	1	no	—
649	#117	—	2	1	no	—
650	#117	—	2	2	no	—
651	#117	—	2	2	no	—
652	#117	—	2	2	no	—
653	#117	—	2	2	no	—
654	#117	—	2	2	no	—
655	#117	—	2	2	no	—
656	#117	—	2	2	no	—
657	#117	C₇×D₄	1	2	yes	—
658	#117	C₇×D₄	1	2	yes	—
659	#117	C₂³×C₇	1	2	yes	—
660	#117	C₂³×C₇	1	1	yes	characteristic
661	#117	C₂³×C₇	1	1	yes	characteristic
662	#117	C₂³×C₇	1	2	yes	—
663	#117	C₂³×C₇	1	1	yes	characteristic
664	#117	C₂³×C₇	1	1	yes	characteristic
665	#117	C₂³×C₇	1	1	yes	characteristic
666	#117	C₂³×C₇	1	1	yes	characteristic
667	C₂×C₄⋊C₄	—	2	2	no	—
668	C₂×C₄⋊C₄	—	2	2	no	—
669	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
670	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
671	C₂×C₂²⋊C₄	—	2	1	no	—
672	C₂×C₂²⋊C₄	—	2	2	no	—
673	C₂×C₂²⋊C₄	—	2	2	no	—
674	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
675	C₂×C₄²	—	2	1	no	—
676	C₂×C₄²	—	2	2	no	—
677	C₂×C₄²	—	2	2	no	—
678	C₂×C₄²	—	2	2	no	—
679	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
680	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
681	#107	C₂³×C₇	1	2	yes	—
682	#107	C₂³×C₇	1	2	yes	—
683	#107	C₂³×C₇	1	2	yes	—
684	#107	C₂³×C₇	1	2	yes	—
685	#106	C₂³×C₇	1	2	yes	—
686	#106	C₂³×C₇	1	2	yes	—
687	#106	C₂³×C₇	1	2	yes	—
688	#106	C₂³×C₇	1	2	yes	—
689	C₄⋊C₈	C₂³×C₇	1	2	yes	—
690	C₄⋊C₈	C₂³×C₇	1	2	yes	—
691	C₄⋊C₈	C₂³×C₇	1	2	yes	—
692	C₄⋊C₈	C₂³×C₇	1	2	yes	—
693	#103	C₂³×C₇	1	2	yes	—
694	#103	C₂³×C₇	1	2	yes	—
695	#103	C₂³×C₇	1	2	yes	—
696	#103	C₂³×C₇	1	2	yes	—
697	#103	C₂³×C₇	1	2	yes	—
698	#103	C₂³×C₇	1	2	yes	—
699	#103	C₂³×C₇	1	2	yes	—
700	#103	C₂³×C₇	1	2	yes	—
701	#102	C₂³×C₇	1	2	yes	—
702	#102	C₂³×C₇	1	2	yes	—
703	#102	C₂³×C₇	1	2	yes	—
704	#102	C₂³×C₇	1	2	yes	—
705	#102	C₂³×C₇	1	2	yes	—
706	#102	C₂³×C₇	1	2	yes	—
707	#102	C₂³×C₇	1	2	yes	—
708	#102	C₂³×C₇	1	2	yes	—
709	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
710	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
711	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
712	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
713	#97	C₂³×C₇	1	1	yes	characteristic
714	#97	C₂³×C₇	1	2	yes	—
715	#97	C₂³×C₇	1	1	yes	characteristic
716	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
717	C₄×C₈	C₂³×C₇	1	2	yes	—
718	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
719	C₂²×C₇	—	2	2	no	—
720	C₂²×C₇	—	2	2	no	—
721	C₂²×C₇	—	2	2	no	—
722	C₂²×C₇	—	2	1	no	—
723	C₂²×C₇	—	2	1	no	—
724	C₂²×C₇	—	2	4	no	—
725	C₂²×C₇	—	4	2	no	—
726	C₂²×C₇	—	4	2	no	—
727	C₂²×C₇	—	4	2	no	—
728	C₂²×C₇	—	4	2	no	—
729	C₂²×C₇	—	4	2	no	—
730	C₂²×C₇	—	8	2	no	—
731	C₂²×C₇	—	8	4	no	—
732	C₂²×C₇	#525	1	2	yes	—
733	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
734	C₄×C₇	—	2	2	no	—
735	C₄×C₇	—	2	2	no	—
736	C₄×C₇	—	2	2	no	—
737	C₄×C₇	—	2	2	no	—
738	C₄×C₇	—	2	1	no	—
739	C₄×C₇	—	2	4	no	—
740	C₄×C₇	—	2	1	no	—
741	C₄×C₇	—	4	2	no	—
742	C₄×C₇	—	4	2	no	—
743	C₄×C₇	—	4	2	no	—
744	C₄×C₇	—	4	2	no	—
745	C₄×C₇	—	4	2	no	—
746	C₄×C₇	#525	1	2	yes	—
747	C₄×C₇	C₂²×#41	1	2	yes	—
748	C₂⁴	—	2	1	no	—
749	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
750	#41	—	2	8	no	—
751	#41	—	2	8	no	—
752	#41	—	2	4	no	—
753	#41	—	2	4	no	—
754	#41	—	2	4	no	—
755	#41	—	2	4	no	—
756	#41	—	2	4	no	—
757	#41	C₇×#41	1	8	yes	—
758	C₂×Q₈	—	2	4	no	—
759	C₂×Q₈	—	2	1	no	—
760	C₂×Q₈	—	2	2	no	—
761	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
762	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
763	C₂×D₄	—	2	8	no	—
764	C₂×D₄	—	2	2	no	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	2	4	no	—
767	C₂×D₄	—	2	2	no	—
768	C₂×D₄	—	2	2	no	—
769	C₂×D₄	—	2	2	no	—
770	C₂×D₄	—	2	1	no	—
771	C₂×D₄	—	2	2	no	—
772	C₂×D₄	C₂⁴×C₇	1	2	yes	—
773	C₂×D₄	C₂⁴×C₇	1	2	yes	—
774	C₂²×C₄	—	2	8	no	—
775	C₂²×C₄	—	2	1	no	—
776	C₂²×C₄	—	2	2	no	—
777	C₂²×C₄	—	2	2	no	—
778	C₂²×C₄	—	2	4	no	—
779	C₂²×C₄	—	2	2	no	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	2	2	no	—
782	C₂²×C₄	—	2	2	no	—
783	C₂²×C₄	—	2	2	no	—
784	C₂²×C₄	—	2	2	no	—
785	C₂²×C₄	—	2	2	no	—
786	C₂²×C₄	—	2	2	no	—
787	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
788	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
789	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
790	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
791	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
792	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
793	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
794	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
795	Q₁₆	—	2	4	no	—
796	Q₁₆	—	2	4	no	—
797	SD₁₆	—	2	4	no	—
798	SD₁₆	—	2	4	no	—
799	SD₁₆	—	2	4	no	—
800	SD₁₆	—	2	4	no	—
801	D₈	—	2	4	no	—
802	D₈	—	2	4	no	—
803	C₂×C₈	—	2	4	no	—
804	C₂×C₈	—	2	4	no	—
805	C₂×C₈	C₂⁴×C₇	1	2	yes	—
806	C₂×C₈	C₂⁴×C₇	1	2	yes	—
807	C₂×C₈	C₂⁴×C₇	1	2	yes	—
808	C₂×C₈	C₂⁴×C₇	1	2	yes	—
809	C₄⋊C₄	—	2	2	no	—
810	C₄⋊C₄	—	2	2	no	—
811	C₄⋊C₄	—	2	2	no	—
812	C₄⋊C₄	—	2	2	no	—
813	C₄⋊C₄	—	2	2	no	—
814	C₄⋊C₄	—	2	2	no	—
815	C₄⋊C₄	—	2	2	no	—
816	C₄⋊C₄	—	2	2	no	—
817	C₄⋊C₄	—	2	2	no	—
818	C₄⋊C₄	—	2	2	no	—
819	C₄⋊C₄	—	2	2	no	—
820	C₄⋊C₄	—	2	2	no	—
821	C₄⋊C₄	—	2	2	no	—
822	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
823	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
824	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
825	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
826	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
827	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
828	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
829	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
830	C₂²⋊C₄	—	2	1	no	—
831	C₂²⋊C₄	—	2	1	no	—
832	C₂²⋊C₄	—	2	2	no	—
833	C₂²⋊C₄	—	2	2	no	—
834	C₂²⋊C₄	—	2	2	no	—
835	C₂²⋊C₄	—	2	2	no	—
836	C₂²⋊C₄	—	2	2	no	—
837	C₂²⋊C₄	—	2	2	no	—
838	C₂²⋊C₄	—	2	2	no	—
839	C₂²⋊C₄	—	2	2	no	—
840	C₂²⋊C₄	—	2	2	no	—
841	C₂²⋊C₄	—	2	2	no	—
842	C₂²⋊C₄	—	2	2	no	—
843	C₂²⋊C₄	—	2	2	no	—
844	C₂²⋊C₄	—	2	2	no	—
845	C₂²⋊C₄	—	2	2	no	—
846	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
847	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
848	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
849	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
850	C₄²	—	2	2	no	—
851	C₄²	—	2	2	no	—
852	C₄²	—	2	2	no	—
853	C₄²	—	2	2	no	—
854	C₄²	—	2	2	no	—
855	C₄²	—	2	1	no	—
856	C₄²	—	2	1	no	—
857	C₄²	—	2	2	no	—
858	C₄²	—	2	2	no	—
859	C₄²	—	2	2	no	—
860	C₄²	C₂×C₇×D₄	1	2	yes	—
861	C₄²	C₂×C₇×D₄	1	2	yes	—
862	C₄²	C₂⁴×C₇	1	1	yes	characteristic
863	C₄²	C₂⁴×C₇	1	1	yes	characteristic
864	C₄²	C₂⁴×C₇	1	1	yes	characteristic
865	C₄²	C₂⁴×C₇	1	1	yes	characteristic
866	C₂×C₇	—	2	2	no	—
867	C₂×C₇	—	4	1	no	—
868	C₂×C₇	—	4	1	no	—
869	C₂×C₇	—	4	4	no	—
870	C₂×C₇	—	8	2	no	—
871	C₂×C₇	C₂×#525	1	1	yes	characteristic
872	C₂×C₇	#3584	1	2	yes	—
873	C₂³	—	2	4	no	—
874	C₂³	—	2	2	no	—
875	C₂³	—	2	2	no	—
876	C₂³	—	2	2	no	—
877	C₂³	—	4	2	no	—
878	C₂³	—	8	2	no	—
879	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
880	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
881	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
882	Q₈	—	2	4	no	—
883	Q₈	—	2	2	no	—
884	Q₈	—	2	2	no	—
885	Q₈	—	2	2	no	—
886	Q₈	—	8	2	no	—
887	Q₈	C₂×C₇×#41	1	4	yes	—
888	D₄	—	2	8	no	—
889	D₄	—	2	4	no	—
890	D₄	—	2	8	no	—
891	D₄	—	2	2	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	4	4	no	—
895	D₄	—	8	2	no	—
896	D₄	—	8	2	no	—
897	D₄	—	8	2	no	—
898	D₄	C₂×C₇×#41	1	4	yes	—
899	C₂×C₄	—	2	4	no	—
900	C₂×C₄	—	2	8	no	—
901	C₂×C₄	—	2	2	no	—
902	C₂×C₄	—	2	2	no	—
903	C₂×C₄	—	2	2	no	—
904	C₂×C₄	—	2	2	no	—
905	C₂×C₄	—	2	2	no	—
906	C₂×C₄	—	2	8	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	4	2	no	—
914	C₂×C₄	—	4	2	no	—
915	C₂×C₄	—	4	4	no	—
916	C₂×C₄	—	8	2	no	—
917	C₂×C₄	—	8	2	no	—
918	C₂×C₄	—	8	2	no	—
919	C₂×C₄	—	8	2	no	—
920	C₂×C₄	—	8	2	no	—
921	C₂×C₄	—	8	2	no	—
922	C₂×C₄	—	8	2	no	—
923	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
924	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
925	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
926	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
927	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
928	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
929	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
930	C₂×C₄	C₂×C₇×#41	1	4	yes	—
931	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
932	C₈	—	2	2	no	—
933	C₈	—	2	2	no	—
934	C₈	—	2	2	no	—
935	C₈	—	2	2	no	—
936	C₇	#60557	1	1	yes	characteristic, direct product factor, Sylow
937	C₂²	—	2	2	no	—
938	C₂²	—	2	2	no	—
939	C₂²	—	2	2	no	—
940	C₂²	—	2	1	no	—
941	C₂²	—	2	1	no	—
942	C₂²	—	2	4	no	—
943	C₂²	—	4	2	no	—
944	C₂²	—	4	2	no	—
945	C₂²	—	4	2	no	—
946	C₂²	—	4	2	no	—
947	C₂²	—	4	2	no	—
948	C₂²	—	8	2	no	—
949	C₂²	—	8	4	no	—
950	C₂²	C₇×#525	1	2	yes	—
951	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
952	C₄	—	2	2	no	—
953	C₄	—	2	2	no	—
954	C₄	—	2	2	no	—
955	C₄	—	2	2	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	4	no	—
958	C₄	—	2	1	no	—
959	C₄	—	4	2	no	—
960	C₄	—	4	2	no	—
961	C₄	—	4	2	no	—
962	C₄	—	4	2	no	—
963	C₄	—	4	2	no	—
964	C₄	C₇×#525	1	2	yes	—
965	C₄	C₂²×C₇×#41	1	2	yes	—
966	C₂	—	2	2	no	—
967	C₂	—	4	1	no	—
968	C₂	—	4	1	no	—
969	C₂	—	4	4	no	—
970	C₂	—	8	2	no	—
971	C₂	C₂×C₇×#525	1	1	yes	characteristic
972	C₂	C₇×#3584	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
socle	C₂²×C₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3455	C₂	semidirect
2. C₇×#3428	C₂	semidirect
3. C₇×#3127	C₂	semidirect
4. C₇×#3126	C₂	semidirect
5. C₇×#3125	C₂	semidirect
6. C₇×#3124	C₂	semidirect
7. C₇×#3123	C₂	semidirect
8. C₇×#3122	C₂	semidirect
9. C₇×#3121	C₂	semidirect
10. C₇×#3120	C₂	semidirect
11. C₇×#3119	C₂	semidirect
12. C₇×#3118	C₂	semidirect
13. C₇×#3091	C₂	semidirect
14. C₇×#3076	C₂	semidirect
15. C₇×#3035	C₂	semidirect
16. C₇×#3002	C₂	semidirect
17. C₇×#2943	C₂	semidirect
18. C₄×C₇×#135	C₂	semidirect
19. C₂×C₇×#433	C₂	semidirect
24. C₇×#542	C₂²	semidirect
26. C₇×#541	C₂²	semidirect
28. C₇×#540	C₂²	semidirect
31. C₇×#533	C₂²	semidirect
32. C₇×#532	C₂²	semidirect
47. C₄×C₇×#41	C₂²	semidirect
53. C₇×#484	C₂²	semidirect
54. C₇×#483	C₂²	semidirect
57. C₇×#481	C₂²	semidirect
58. C₇×#480	C₂²	semidirect
59. C₇×#479	C₂²	semidirect
60. C₇×#479	C₂²	semidirect
61. C₇×#478	C₂²	semidirect
62. C₇×#478	C₂²	semidirect
63. C₇×#477	C₂²	semidirect
64. C₇×#476	C₂²	semidirect
65. C₇×#475	C₂²	semidirect
66. C₇×#474	C₂²	semidirect
67. C₇×#464	C₂²	semidirect
68. C₇×#464	C₂²	semidirect
69. C₇×#463	C₂²	semidirect
70. C₇×#463	C₂²	semidirect
71. C₇×#462	C₂²	semidirect
72. C₇×#461	C₂²	semidirect
73. C₇×#460	C₂²	semidirect
74. C₇×#459	C₂²	semidirect
83. C₇×#442	C₂²	semidirect
84. C₇×#442	C₂²	semidirect
85. C₇×#441	C₂²	semidirect
86. C₇×#441	C₂²	semidirect
87. C₇×#440	C₂²	semidirect
88. C₇×#440	C₂²	semidirect
89. C₇×#440	C₂²	semidirect
90. C₇×#440	C₂²	semidirect
91. C₄×C₇×Q₁₆	C₂²	semidirect
92. C₄×C₇×Q₁₆	C₂²	semidirect
93. C₄×C₇×SD₁₆	C₂²	semidirect
94. C₄×C₇×SD₁₆	C₂²	semidirect
95. C₄×C₇×SD₁₆	C₂²	semidirect
96. C₄×C₇×SD₁₆	C₂²	semidirect
97. C₄×C₇×D₈	C₂²	semidirect
98. C₄×C₇×D₈	C₂²	semidirect
102. C₇×#433	C₂²	semidirect
103. C₇×#433	C₂²	semidirect
104. C₇×#433	C₂²	semidirect
105. C₇×#427	C₂²	semidirect
106. C₇×#427	C₂²	semidirect
107. C₂×C₇×C₄⋊C₈	C₂²	semidirect
110. C₇×#416	C₂²	semidirect
111. C₇×#416	C₂²	semidirect
113. C₂×C₇×#97	C₂²	semidirect
114. C₂×C₄×C₇×C₈	C₂²	semidirect
115. #60557	C₇	direct (N × H)
270. #3455	C₂×C₇	semidirect
271. #3428	C₂×C₇	semidirect
272. #3127	C₂×C₇	semidirect
273. #3126	C₂×C₇	semidirect
274. #3125	C₂×C₇	semidirect
275. #3124	C₂×C₇	semidirect
276. #3123	C₂×C₇	semidirect
277. #3122	C₂×C₇	semidirect
278. #3121	C₂×C₇	semidirect
279. #3120	C₂×C₇	semidirect
280. #3119	C₂×C₇	semidirect
281. #3118	C₂×C₇	semidirect
282. #3091	C₂×C₇	semidirect
283. #3076	C₂×C₇	semidirect
284. #3035	C₂×C₇	semidirect
285. #3002	C₂×C₇	semidirect
286. #2943	C₂×C₇	semidirect
287. C₄×#135	C₂×C₇	semidirect
288. C₂×#433	C₂×C₇	semidirect
411. #542	C₂²×C₇	semidirect
413. #541	C₂²×C₇	semidirect
415. #540	C₂²×C₇	semidirect
418. #533	C₂²×C₇	semidirect
419. #532	C₂²×C₇	semidirect
434. C₄×#41	C₂²×C₇	semidirect
440. #484	C₂²×C₇	semidirect
441. #483	C₂²×C₇	semidirect
444. #481	C₂²×C₇	semidirect
445. #480	C₂²×C₇	semidirect
446. #479	C₂²×C₇	semidirect
447. #479	C₂²×C₇	semidirect
448. #478	C₂²×C₇	semidirect
449. #478	C₂²×C₇	semidirect
450. #477	C₂²×C₇	semidirect
451. #476	C₂²×C₇	semidirect
452. #475	C₂²×C₇	semidirect
453. #474	C₂²×C₇	semidirect
454. #464	C₂²×C₇	semidirect
455. #464	C₂²×C₇	semidirect
456. #463	C₂²×C₇	semidirect
457. #463	C₂²×C₇	semidirect
458. #462	C₂²×C₇	semidirect
459. #461	C₂²×C₇	semidirect
460. #460	C₂²×C₇	semidirect
461. #459	C₂²×C₇	semidirect
470. #442	C₂²×C₇	semidirect
471. #442	C₂²×C₇	semidirect
472. #441	C₂²×C₇	semidirect
473. #441	C₂²×C₇	semidirect
474. #440	C₂²×C₇	semidirect
475. #440	C₂²×C₇	semidirect
476. #440	C₂²×C₇	semidirect
477. #440	C₂²×C₇	semidirect
478. C₄×Q₁₆	C₂²×C₇	semidirect
479. C₄×Q₁₆	C₂²×C₇	semidirect
480. C₄×SD₁₆	C₂²×C₇	semidirect
481. C₄×SD₁₆	C₂²×C₇	semidirect
482. C₄×SD₁₆	C₂²×C₇	semidirect
483. C₄×SD₁₆	C₂²×C₇	semidirect
484. C₄×D₈	C₂²×C₇	semidirect
485. C₄×D₈	C₂²×C₇	semidirect
489. #433	C₂²×C₇	semidirect
490. #433	C₂²×C₇	semidirect
491. #433	C₂²×C₇	semidirect
492. #427	C₂²×C₇	semidirect
493. #427	C₂²×C₇	semidirect
494. C₂×C₄⋊C₈	C₂²×C₇	semidirect
497. #416	C₂²×C₇	semidirect
498. #416	C₂²×C₇	semidirect
500. C₂×#97	C₂²×C₇	semidirect
501. C₂×C₄×C₈	C₂²×C₇	semidirect
936. C₇	#60557	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×#3455	2
C₇×#3428	2
C₇×#3127	2
C₇×#3126	2
C₇×#3125	2
C₇×#3124	2
C₇×#3123	2
C₇×#3122	2
C₇×#3121	2
C₇×#3120	2
C₇×#3119	2
C₇×#3118	2
C₇×#3091	2
C₇×#3076	2
C₇×#3035	2
C₇×#3002	2
C₇×#2943	2
C₄×C₇×#135	2
C₂×C₇×#433	2
#60557	7

Subgroups — C7×#60557 #13237773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60557 #13237773