Subgroups — C₇×#61350 #13238566

Order 1792.

1746 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3504	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3377	C₂	1	2	yes	maximal, complemented
4	C₇×#3376	C₂	1	2	yes	maximal, complemented
5	C₇×#3374	C₂	1	2	yes	maximal, complemented
6	C₇×#3372	C₂	1	2	yes	maximal, complemented
7	C₇×#3371	C₂	1	2	yes	maximal, complemented
8	C₇×#3370	C₂	1	2	yes	maximal, complemented
9	C₇×#3364	C₂	1	2	yes	maximal, complemented
10	C₇×#3360	C₂	1	2	yes	maximal, complemented
11	C₇×#3142	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3035	C₂	1	1	yes	maximal, characteristic
20	C₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2952	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×C₇×#137	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#137	C₂²	1	1	yes	characteristic
25	C₂×C₇×#135	C₂²	1	1	yes	characteristic
26	C₂×C₇×#135	C₂²	1	1	yes	characteristic
27	C₇×#559	C₂²	1	2	yes	—
28	C₇×#557	C₂²	1	2	yes	—
29	C₇×#557	C₂²	1	2	yes	—
30	C₇×#557	C₂²	1	2	yes	—
31	C₇×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	2	yes	—
33	C₇×#556	C₂²	1	2	yes	—
34	C₇×#554	—	2	1	no	—
35	C₇×#554	—	2	2	no	—
36	C₇×#554	—	2	2	no	—
37	C₇×#554	C₂²	1	2	yes	—
38	C₇×#554	C₂²	1	2	yes	—
39	C₇×#552	—	2	1	no	—
40	C₇×#552	—	2	1	no	—
41	C₇×#544	—	2	1	no	—
42	C₇×#544	—	2	1	no	—
43	C₇×#544	C₂²	1	1	yes	characteristic
44	C₇×#544	C₂²	1	1	yes	characteristic
45	C₇×#539	—	2	2	no	—
46	C₇×#536	C₂²	1	1	yes	characteristic
47	C₇×#536	C₂²	1	1	yes	characteristic
48	C₇×#533	—	2	1	no	—
49	C₇×#533	C₂²	1	1	yes	characteristic
50	C₇×#532	C₂²	1	1	yes	characteristic
51	C₇×#529	—	2	2	no	—
52	C₂×C₇×#125	—	2	1	no	—
53	C₂×C₇×#125	C₂²	1	1	yes	characteristic
54	C₇×#520	C₂²	1	1	yes	characteristic
55	C₇×#520	C₂²	1	1	yes	characteristic
56	C₇×#520	C₂²	1	1	yes	characteristic
57	C₇×#520	C₂²	1	1	yes	characteristic
58	C₄×C₇×#41	C₂²	1	1	yes	characteristic
59	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
60	C₇×#491	C₂²	1	2	yes	—
61	C₇×#491	C₂²	1	2	yes	—
62	C₇×#491	C₂²	1	2	yes	—
63	C₇×#490	C₂²	1	2	yes	—
64	C₇×#489	C₂²	1	2	yes	—
65	C₇×#489	C₂²	1	2	yes	—
66	C₇×#488	C₂²	1	2	yes	—
67	C₇×#488	C₂²	1	2	yes	—
68	C₇×#488	C₂²	1	2	yes	—
69	C₇×#488	C₂²	1	2	yes	—
70	C₇×#487	C₂²	1	2	yes	—
71	C₇×#487	C₂²	1	2	yes	—
72	C₇×#479	C₂²	1	2	yes	—
73	C₇×#479	C₂²	1	2	yes	—
74	C₇×#479	C₂²	1	2	yes	—
75	C₇×#479	C₂²	1	2	yes	—
76	C₇×#479	C₂²	1	2	yes	—
77	C₇×#479	C₂²	1	2	yes	—
78	C₇×#478	C₂²	1	2	yes	—
79	C₇×#478	C₂²	1	2	yes	—
80	C₇×#477	C₂²	1	2	yes	—
81	C₇×#476	C₂²	1	2	yes	—
82	C₇×#475	C₂²	1	2	yes	—
83	C₇×#474	C₂²	1	2	yes	—
84	C₇×#464	C₂²	1	1	yes	characteristic
85	C₇×#464	C₂²	1	1	yes	characteristic
86	C₇×#464	C₂²	1	2	yes	—
87	C₇×#464	C₂²	1	2	yes	—
88	C₇×#463	C₂²	1	1	yes	characteristic
89	C₇×#463	C₂²	1	1	yes	characteristic
90	C₇×#463	C₂²	1	2	yes	—
91	C₇×#463	C₂²	1	2	yes	—
92	C₇×#462	C₂²	1	1	yes	characteristic
93	C₇×#462	C₂²	1	2	yes	—
94	C₇×#462	C₂²	1	2	yes	—
95	C₇×#461	C₂²	1	1	yes	characteristic
96	C₇×#461	C₂²	1	2	yes	—
97	C₇×#461	C₂²	1	2	yes	—
98	C₇×#460	C₂²	1	1	yes	characteristic
99	C₇×#459	C₂²	1	1	yes	characteristic
100	C₇×#446	C₂²	1	2	yes	—
101	C₇×#446	C₂²	1	2	yes	—
102	C₇×#446	C₂²	1	2	yes	—
103	C₇×C₈×Q₈	C₂²	1	2	yes	—
104	C₇×#442	C₂²	1	2	yes	—
105	C₇×#441	C₂²	1	2	yes	—
106	C₇×#441	C₂²	1	2	yes	—
107	C₇×#440	C₂²	1	2	yes	—
108	C₇×#440	C₂²	1	2	yes	—
109	C₇×#440	C₂²	1	2	yes	—
110	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
111	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
112	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
113	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
114	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
115	C₄×C₇×D₈	C₂²	1	2	yes	—
116	C₇×#428	C₂²	1	1	yes	characteristic
117	C₂×C₇×#107	C₂²	1	1	yes	characteristic
118	C₂×C₇×#106	C₂²	1	1	yes	characteristic
119	C₇×#424	C₂²	1	1	yes	characteristic
120	C₇×#424	C₂²	1	1	yes	characteristic
121	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
122	C₇×#419	C₂²	1	1	yes	characteristic
123	C₇×#417	C₂²	1	1	yes	characteristic
124	C₇×#417	C₂²	1	1	yes	characteristic
125	C₇×#417	C₂²	1	1	yes	characteristic
126	C₇×#417	C₂²	1	1	yes	characteristic
127	C₇×#417	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic
129	C₇×#416	C₂²	1	1	yes	characteristic
130	C₂×C₇×#103	C₂²	1	1	yes	characteristic
131	C₂×C₇×#103	C₂²	1	1	yes	characteristic
132	C₇×#405	C₂²	1	1	yes	characteristic
133	C₇×#405	C₂²	1	1	yes	characteristic
134	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
135	#61350	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂³	1	1	yes	characteristic
137	C₂×C₇×#41	C₂³	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	1	yes	characteristic
139	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
140	C₇×#137	—	2	4	no	—
141	C₇×#135	—	2	4	no	—
142	C₇×#135	—	2	4	no	—
143	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
144	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
145	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
146	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
147	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
148	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
149	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
150	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
152	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
153	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
154	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
155	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
156	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
157	C₇×C₄⋊Q₈	—	2	2	no	—
158	C₇×C₄⋊Q₈	—	2	2	no	—
159	C₇×C₄⋊Q₈	—	2	1	no	—
160	C₇×C₄⋊Q₈	—	2	1	no	—
161	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
162	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
164	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
165	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
167	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
168	C₇×#127	C₂³	1	1	yes	characteristic
169	C₇×#126	—	2	2	no	—
170	C₇×#126	—	2	2	no	—
171	C₇×#126	—	2	2	no	—
172	C₇×#126	—	2	2	no	—
173	C₇×#125	—	2	1	no	—
174	C₇×#125	—	2	1	no	—
175	C₇×#125	—	2	2	no	—
176	C₇×#125	—	2	2	no	—
177	C₇×#125	—	2	2	no	—
178	C₇×#125	—	2	2	no	—
179	C₇×#125	—	2	2	no	—
180	C₇×#125	—	2	2	no	—
181	C₇×#125	—	2	2	no	—
182	C₇×#125	—	2	1	no	—
183	C₇×#125	—	2	1	no	—
184	C₇×#125	D₄	1	1	yes	characteristic
185	C₇×#125	D₄	1	1	yes	characteristic
186	C₇×#125	C₂³	1	2	yes	—
187	C₇×#125	C₂³	1	2	yes	—
188	C₇×#125	C₂³	1	2	yes	—
189	C₇×#125	C₂³	1	2	yes	—
190	C₇×#124	—	2	2	no	—
191	C₇×#124	C₂³	1	1	yes	characteristic
192	C₇×#124	C₂³	1	1	yes	characteristic
193	C₇×#124	C₂³	1	2	yes	—
194	C₇×#124	C₂³	1	2	yes	—
195	C₇×#123	—	2	2	no	—
196	C₇×#123	—	2	2	no	—
197	C₇×#123	—	2	2	no	—
198	C₇×#123	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	—	2	2	no	—
201	C₇×C₂²⋊Q₈	—	2	2	no	—
202	C₇×C₂²⋊Q₈	—	2	2	no	—
203	C₇×C₂²⋊Q₈	—	2	2	no	—
204	C₇×C₂²⋊Q₈	—	2	2	no	—
205	C₇×C₂²⋊Q₈	—	2	1	no	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	2	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	—	2	2	no	—
213	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
214	C₇×C₂²⋊Q₈	D₄	1	2	yes	—
215	C₇×#121	—	2	1	no	—
216	C₇×#121	—	2	1	no	—
217	C₄×C₇×Q₈	—	2	2	no	—
218	C₄×C₇×Q₈	—	2	2	no	—
219	C₄×C₇×Q₈	—	2	2	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	2	yes	—
224	C₄×C₇×Q₈	C₂³	1	2	yes	—
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	2	yes	—
231	C₄×C₇×Q₈	C₂³	1	2	yes	—
232	C₄×C₇×D₄	—	2	1	no	—
233	C₄×C₇×D₄	—	2	1	no	—
234	C₄×C₇×D₄	—	2	2	no	—
235	C₄×C₇×D₄	—	2	2	no	—
236	C₄×C₇×D₄	—	2	2	no	—
237	C₄×C₇×D₄	—	2	2	no	—
238	C₄×C₇×D₄	—	2	2	no	—
239	C₄×C₇×D₄	—	2	1	no	—
240	C₄×C₇×D₄	—	2	1	no	—
241	C₄×C₇×D₄	C₂³	1	2	yes	—
242	C₄×C₇×D₄	C₂³	1	2	yes	—
243	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
244	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
245	C₄×C₇×D₄	C₂³	1	2	yes	—
246	C₄×C₇×D₄	C₂³	1	2	yes	—
247	C₇×#117	—	2	1	no	—
248	C₇×#117	—	2	1	no	—
249	C₇×#117	—	2	1	no	—
250	C₇×#117	—	2	1	no	—
251	C₇×#117	—	2	2	no	—
252	C₇×#117	—	2	2	no	—
253	C₇×#117	—	2	1	no	—
254	C₇×#117	C₂³	1	1	yes	characteristic
255	C₇×#117	C₂³	1	1	yes	characteristic
256	C₇×#117	C₂³	1	1	yes	characteristic
257	C₂×C₇×C₄⋊C₄	—	2	1	no	—
258	C₂×C₇×C₄⋊C₄	—	2	1	no	—
259	C₂×C₇×C₄⋊C₄	—	2	1	no	—
260	C₂×C₇×C₄⋊C₄	—	2	1	no	—
261	C₂×C₇×C₄⋊C₄	—	2	1	no	—
262	C₂×C₇×C₄⋊C₄	—	2	1	no	—
263	C₂×C₇×C₄⋊C₄	—	2	1	no	—
264	C₂×C₇×C₄⋊C₄	—	2	2	no	—
265	C₂×C₇×C₄⋊C₄	—	2	2	no	—
266	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
267	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
268	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₄²×C₇	—	2	1	no	—
270	C₂×C₄²×C₇	—	2	1	no	—
271	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
272	C₇×#107	C₂³	1	2	yes	—
273	C₇×#107	C₂³	1	2	yes	—
274	C₇×#107	C₂³	1	2	yes	—
275	C₇×#106	C₂³	1	2	yes	—
276	C₇×#106	C₂³	1	2	yes	—
277	C₇×#106	C₂³	1	2	yes	—
278	C₇×C₄⋊C₈	C₂³	1	2	yes	—
279	C₇×C₄⋊C₈	C₂³	1	2	yes	—
280	C₇×C₄⋊C₈	C₂³	1	2	yes	—
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
285	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
286	C₇×#103	C₂³	1	1	yes	characteristic
287	C₇×#103	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	1	yes	characteristic
289	C₇×#103	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	1	yes	characteristic
291	C₇×#103	C₂³	1	1	yes	characteristic
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#103	C₂³	1	2	yes	—
300	C₇×#103	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	2	yes	—
303	C₇×#102	C₂³	1	1	yes	characteristic
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	1	yes	characteristic
306	C₇×#102	C₂³	1	1	yes	characteristic
307	C₇×#102	C₂³	1	2	yes	—
308	C₇×#102	C₂³	1	2	yes	—
309	C₇×#102	C₂³	1	2	yes	—
310	C₇×#97	C₂³	1	2	yes	—
311	C₇×#97	C₂³	1	2	yes	—
312	C₇×#97	C₂³	1	2	yes	—
313	C₄×C₇×C₈	C₂³	1	2	yes	—
314	C₄×C₇×C₈	C₂³	1	2	yes	—
315	C₄×C₇×C₈	C₂³	1	2	yes	—
316	#3507	C₂×C₇	1	1	yes	characteristic, complemented
317	#3504	C₂×C₇	1	1	yes	characteristic, complemented
318	#3377	C₂×C₇	1	2	yes	complemented
319	#3376	C₂×C₇	1	2	yes	complemented
320	#3374	C₂×C₇	1	2	yes	complemented
321	#3372	C₂×C₇	1	2	yes	complemented
322	#3371	C₂×C₇	1	2	yes	complemented
323	#3370	C₂×C₇	1	2	yes	complemented
324	#3364	C₂×C₇	1	2	yes	complemented
325	#3360	C₂×C₇	1	2	yes	complemented
326	#3142	C₂×C₇	1	1	yes	characteristic, complemented
327	#3137	C₂×C₇	1	1	yes	characteristic, complemented
328	#3137	C₂×C₇	1	1	yes	characteristic, complemented
329	#3084	C₂×C₇	1	1	yes	characteristic, complemented
330	#3083	C₂×C₇	1	1	yes	characteristic, complemented
331	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
332	#3046	C₂×C₇	1	1	yes	characteristic, complemented
333	#3046	C₂×C₇	1	1	yes	characteristic, complemented
334	#3035	C₂×C₇	1	1	yes	characteristic
335	#2962	C₂×C₇	1	1	yes	characteristic, complemented
336	#2952	C₂×C₇	1	1	yes	characteristic, complemented
337	#2951	C₂×C₇	1	1	yes	characteristic, complemented
338	C₄×#137	C₂×C₇	1	1	yes	characteristic, complemented
339	C₇×#41	—	2	2	no	—
340	C₇×#41	—	2	2	no	—
341	C₇×#41	—	2	2	no	—
342	C₇×#41	—	2	2	no	—
343	C₇×#41	—	2	2	no	—
344	C₇×#41	#41	1	4	yes	—
345	C₂×C₇×Q₈	—	2	1	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	—	2	2	no	—
349	C₂×C₇×Q₈	—	2	2	no	—
350	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
351	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
352	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
353	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
354	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
355	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
356	C₂×C₇×D₄	—	2	1	no	—
357	C₂×C₇×D₄	—	2	1	no	—
358	C₂×C₇×D₄	—	2	1	no	—
359	C₂×C₇×D₄	—	2	1	no	—
360	C₂×C₇×D₄	—	2	1	no	—
361	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
362	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
363	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
364	C₂²×C₄×C₇	—	2	1	no	—
365	C₂²×C₄×C₇	—	2	1	no	—
366	C₂²×C₄×C₇	—	2	1	no	—
367	C₂²×C₄×C₇	—	2	1	no	—
368	C₂²×C₄×C₇	—	2	1	no	—
369	C₂²×C₄×C₇	—	2	1	no	—
370	C₂²×C₄×C₇	—	2	1	no	—
371	C₂²×C₄×C₇	—	2	1	no	—
372	C₂²×C₄×C₇	—	2	1	no	—
373	C₂²×C₄×C₇	—	2	2	no	—
374	C₂²×C₄×C₇	—	2	2	no	—
375	C₂²×C₄×C₇	—	2	2	no	—
376	C₂²×C₄×C₇	—	2	2	no	—
377	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
378	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
379	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
380	C₇×Q₁₆	—	2	2	no	—
381	C₇×Q₁₆	—	2	2	no	—
382	C₇×Q₁₆	—	2	4	no	—
383	C₇×SD₁₆	—	2	2	no	—
384	C₇×SD₁₆	—	2	2	no	—
385	C₇×SD₁₆	—	2	2	no	—
386	C₇×SD₁₆	—	2	2	no	—
387	C₇×SD₁₆	—	2	4	no	—
388	C₇×D₈	—	2	2	no	—
389	C₇×D₈	—	2	2	no	—
390	C₇×M₁₆	—	2	2	no	—
391	C₇×M₁₆	—	2	2	no	—
392	C₂×C₇×C₈	—	2	2	no	—
393	C₂×C₇×C₈	—	2	2	no	—
394	C₂×C₇×C₈	C₂⁴	1	2	yes	—
395	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
396	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
397	C₂×C₇×C₈	C₂⁴	1	2	yes	—
398	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
399	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
400	C₇×C₄⋊C₄	—	2	1	no	—
401	C₇×C₄⋊C₄	—	2	2	no	—
402	C₇×C₄⋊C₄	—	2	2	no	—
403	C₇×C₄⋊C₄	—	2	1	no	—
404	C₇×C₄⋊C₄	—	2	1	no	—
405	C₇×C₄⋊C₄	—	2	2	no	—
406	C₇×C₄⋊C₄	—	2	2	no	—
407	C₇×C₄⋊C₄	—	2	2	no	—
408	C₇×C₄⋊C₄	—	2	2	no	—
409	C₇×C₄⋊C₄	—	2	2	no	—
410	C₇×C₄⋊C₄	—	2	2	no	—
411	C₇×C₄⋊C₄	—	2	2	no	—
412	C₇×C₄⋊C₄	—	2	2	no	—
413	C₇×C₄⋊C₄	—	2	2	no	—
414	C₇×C₄⋊C₄	—	2	2	no	—
415	C₇×C₄⋊C₄	—	2	2	no	—
416	C₇×C₄⋊C₄	—	2	2	no	—
417	C₇×C₄⋊C₄	—	2	1	no	—
418	C₇×C₄⋊C₄	—	2	1	no	—
419	C₇×C₄⋊C₄	—	2	2	no	—
420	C₇×C₄⋊C₄	—	2	2	no	—
421	C₇×C₄⋊C₄	—	2	1	no	—
422	C₇×C₄⋊C₄	—	2	1	no	—
423	C₇×C₄⋊C₄	—	2	2	no	—
424	C₇×C₄⋊C₄	—	2	2	no	—
425	C₇×C₄⋊C₄	—	2	2	no	—
426	C₇×C₄⋊C₄	—	2	2	no	—
427	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
428	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
429	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
430	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
431	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
432	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
433	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
434	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
435	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
436	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
437	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
438	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
439	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
440	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
441	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
442	C₇×C₂²⋊C₄	—	2	1	no	—
443	C₇×C₂²⋊C₄	—	2	1	no	—
444	C₇×C₂²⋊C₄	—	2	1	no	—
445	C₇×C₂²⋊C₄	—	2	1	no	—
446	C₇×C₂²⋊C₄	—	2	1	no	—
447	C₇×C₂²⋊C₄	—	2	2	no	—
448	C₇×C₂²⋊C₄	—	2	2	no	—
449	C₇×C₂²⋊C₄	—	2	2	no	—
450	C₇×C₂²⋊C₄	—	2	2	no	—
451	C₇×C₂²⋊C₄	—	2	2	no	—
452	C₇×C₂²⋊C₄	—	2	2	no	—
453	C₇×C₂²⋊C₄	—	2	1	no	—
454	C₇×C₂²⋊C₄	—	2	1	no	—
455	C₇×C₂²⋊C₄	—	2	2	no	—
456	C₇×C₂²⋊C₄	—	2	2	no	—
457	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
458	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
459	C₄²×C₇	—	2	2	no	—
460	C₄²×C₇	—	2	1	no	—
461	C₄²×C₇	—	2	2	no	—
462	C₄²×C₇	—	2	1	no	—
463	C₄²×C₇	—	2	1	no	—
464	C₄²×C₇	—	2	2	no	—
465	C₄²×C₇	—	2	2	no	—
466	C₄²×C₇	—	2	2	no	—
467	C₄²×C₇	—	2	2	no	—
468	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
469	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
470	C₄²×C₇	C₂⁴	1	1	yes	characteristic
471	C₄²×C₇	C₂⁴	1	2	yes	—
472	C₄²×C₇	C₂⁴	1	2	yes	—
473	C₄²×C₇	C₂⁴	1	1	yes	characteristic
474	C₂×#137	C₂²×C₇	1	1	yes	characteristic
475	C₂×#135	C₂²×C₇	1	1	yes	characteristic
476	C₂×#135	C₂²×C₇	1	1	yes	characteristic
477	#559	C₂²×C₇	1	2	yes	—
478	#557	C₂²×C₇	1	2	yes	—
479	#557	C₂²×C₇	1	2	yes	—
480	#557	C₂²×C₇	1	2	yes	—
481	#556	—	2	1	no	—
482	#556	C₂²×C₇	1	2	yes	—
483	#556	C₂²×C₇	1	2	yes	—
484	#554	—	2	1	no	—
485	#554	—	2	2	no	—
486	#554	—	2	2	no	—
487	#554	C₂²×C₇	1	2	yes	—
488	#554	C₂²×C₇	1	2	yes	—
489	#552	—	2	1	no	—
490	#552	—	2	1	no	—
491	#544	—	2	1	no	—
492	#544	—	2	1	no	—
493	#544	C₂²×C₇	1	1	yes	characteristic
494	#544	C₂²×C₇	1	1	yes	characteristic
495	#539	—	2	2	no	—
496	#536	C₂²×C₇	1	1	yes	characteristic
497	#536	C₂²×C₇	1	1	yes	characteristic
498	#533	—	2	1	no	—
499	#533	C₂²×C₇	1	1	yes	characteristic
500	#532	C₂²×C₇	1	1	yes	characteristic
501	#529	—	2	2	no	—
502	C₂×#125	—	2	1	no	—
503	C₂×#125	C₂²×C₇	1	1	yes	characteristic
504	#520	C₂²×C₇	1	1	yes	characteristic
505	#520	C₂²×C₇	1	1	yes	characteristic
506	#520	C₂²×C₇	1	1	yes	characteristic
507	#520	C₂²×C₇	1	1	yes	characteristic
508	C₄×#41	C₂²×C₇	1	1	yes	characteristic
509	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
510	#491	C₂²×C₇	1	2	yes	—
511	#491	C₂²×C₇	1	2	yes	—
512	#491	C₂²×C₇	1	2	yes	—
513	#490	C₂²×C₇	1	2	yes	—
514	#489	C₂²×C₇	1	2	yes	—
515	#489	C₂²×C₇	1	2	yes	—
516	#488	C₂²×C₇	1	2	yes	—
517	#488	C₂²×C₇	1	2	yes	—
518	#488	C₂²×C₇	1	2	yes	—
519	#488	C₂²×C₇	1	2	yes	—
520	#487	C₂²×C₇	1	2	yes	—
521	#487	C₂²×C₇	1	2	yes	—
522	#479	C₂²×C₇	1	2	yes	—
523	#479	C₂²×C₇	1	2	yes	—
524	#479	C₂²×C₇	1	2	yes	—
525	#479	C₂²×C₇	1	2	yes	—
526	#479	C₂²×C₇	1	2	yes	—
527	#479	C₂²×C₇	1	2	yes	—
528	#478	C₂²×C₇	1	2	yes	—
529	#478	C₂²×C₇	1	2	yes	—
530	#477	C₂²×C₇	1	2	yes	—
531	#476	C₂²×C₇	1	2	yes	—
532	#475	C₂²×C₇	1	2	yes	—
533	#474	C₂²×C₇	1	2	yes	—
534	#464	C₂²×C₇	1	1	yes	characteristic
535	#464	C₂²×C₇	1	2	yes	—
536	#464	C₂²×C₇	1	2	yes	—
537	#464	C₂²×C₇	1	1	yes	characteristic
538	#463	C₂²×C₇	1	1	yes	characteristic
539	#463	C₂²×C₇	1	2	yes	—
540	#463	C₂²×C₇	1	2	yes	—
541	#463	C₂²×C₇	1	1	yes	characteristic
542	#462	C₂²×C₇	1	2	yes	—
543	#462	C₂²×C₇	1	1	yes	characteristic
544	#462	C₂²×C₇	1	2	yes	—
545	#461	C₂²×C₇	1	2	yes	—
546	#461	C₂²×C₇	1	1	yes	characteristic
547	#461	C₂²×C₇	1	2	yes	—
548	#460	C₂²×C₇	1	1	yes	characteristic
549	#459	C₂²×C₇	1	1	yes	characteristic
550	#446	C₂²×C₇	1	2	yes	—
551	#446	C₂²×C₇	1	2	yes	—
552	#446	C₂²×C₇	1	2	yes	—
553	C₈×Q₈	C₂²×C₇	1	2	yes	—
554	#442	C₂²×C₇	1	2	yes	—
555	#441	C₂²×C₇	1	2	yes	—
556	#441	C₂²×C₇	1	2	yes	—
557	#440	C₂²×C₇	1	2	yes	—
558	#440	C₂²×C₇	1	2	yes	—
559	#440	C₂²×C₇	1	2	yes	—
560	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
561	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
562	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
563	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
564	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
565	C₄×D₈	C₂²×C₇	1	2	yes	—
566	#428	C₂²×C₇	1	1	yes	characteristic
567	C₂×#107	C₂²×C₇	1	1	yes	characteristic
568	C₂×#106	C₂²×C₇	1	1	yes	characteristic
569	#424	C₂²×C₇	1	1	yes	characteristic
570	#424	C₂²×C₇	1	1	yes	characteristic
571	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
572	#419	C₂²×C₇	1	1	yes	characteristic
573	#417	C₂²×C₇	1	1	yes	characteristic
574	#417	C₂²×C₇	1	1	yes	characteristic
575	#417	C₂²×C₇	1	1	yes	characteristic
576	#417	C₂²×C₇	1	1	yes	characteristic
577	#417	C₂²×C₇	1	1	yes	characteristic
578	#416	C₂²×C₇	1	1	yes	characteristic
579	#416	C₂²×C₇	1	1	yes	characteristic
580	C₂×#103	C₂²×C₇	1	1	yes	characteristic
581	C₂×#103	C₂²×C₇	1	1	yes	characteristic
582	#405	C₂²×C₇	1	1	yes	characteristic
583	#405	C₂²×C₇	1	1	yes	characteristic
584	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
585	C₂³×C₇	—	2	1	no	—
586	C₂³×C₇	—	2	1	no	—
587	C₂³×C₇	—	2	1	no	—
588	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
589	C₇×Q₈	—	2	1	no	—
590	C₇×Q₈	—	2	2	no	—
591	C₇×Q₈	—	2	1	no	—
592	C₇×Q₈	—	2	1	no	—
593	C₇×Q₈	—	2	2	no	—
594	C₇×Q₈	—	2	1	no	—
595	C₇×Q₈	—	2	1	no	—
596	C₇×Q₈	—	4	2	no	—
597	C₇×Q₈	—	4	2	no	—
598	C₇×Q₈	—	4	2	no	—
599	C₇×Q₈	—	8	2	no	—
600	C₇×Q₈	—	8	2	no	—
601	C₇×Q₈	C₂×#41	1	2	yes	—
602	C₇×D₄	—	2	4	no	—
603	C₇×D₄	—	2	1	no	—
604	C₇×D₄	—	2	1	no	—
605	C₇×D₄	—	2	1	no	—
606	C₇×D₄	—	2	1	no	—
607	C₇×D₄	—	2	1	no	—
608	C₇×D₄	—	4	2	no	—
609	C₇×D₄	—	4	2	no	—
610	C₇×D₄	—	4	2	no	—
611	C₇×D₄	—	8	1	no	—
612	C₇×D₄	C₂×#41	1	2	yes	—
613	C₂×C₄×C₇	—	2	1	no	—
614	C₂×C₄×C₇	—	2	4	no	—
615	C₂×C₄×C₇	—	2	2	no	—
616	C₂×C₄×C₇	—	2	2	no	—
617	C₂×C₄×C₇	—	2	1	no	—
618	C₂×C₄×C₇	—	2	1	no	—
619	C₂×C₄×C₇	—	2	1	no	—
620	C₂×C₄×C₇	—	2	1	no	—
621	C₂×C₄×C₇	—	2	2	no	—
622	C₂×C₄×C₇	—	2	2	no	—
623	C₂×C₄×C₇	—	4	1	no	—
624	C₂×C₄×C₇	—	4	1	no	—
625	C₂×C₄×C₇	—	4	2	no	—
626	C₂×C₄×C₇	—	4	2	no	—
627	C₂×C₄×C₇	—	4	2	no	—
628	C₂×C₄×C₇	—	8	1	no	—
629	C₂×C₄×C₇	—	8	2	no	—
630	C₂×C₄×C₇	—	8	2	no	—
631	C₂×C₄×C₇	—	8	2	no	—
632	C₂×C₄×C₇	—	8	1	no	—
633	C₂×C₄×C₇	—	8	2	no	—
634	C₂×C₄×C₇	—	8	1	no	—
635	C₂×C₄×C₇	—	8	1	no	—
636	C₂×C₄×C₇	—	8	1	no	—
637	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
638	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
639	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
640	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
641	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
642	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
643	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
644	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
645	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
646	C₂×C₄×C₇	C₂×#41	1	2	yes	—
647	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
648	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
649	C₇×C₈	—	2	1	no	—
650	C₇×C₈	—	2	1	no	—
651	C₇×C₈	—	2	1	no	—
652	C₇×C₈	—	2	1	no	—
653	C₇×C₈	—	2	2	no	—
654	C₇×C₈	—	2	2	no	—
655	C₂×#41	C₂³×C₇	1	1	yes	characteristic
656	C₂×#41	C₂³×C₇	1	1	yes	characteristic
657	C₂×#41	C₂³×C₇	1	1	yes	characteristic
658	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
659	#137	—	2	4	no	—
660	#135	—	2	4	no	—
661	#135	—	2	4	no	—
662	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
663	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
664	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
665	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
666	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
667	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
668	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
669	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
670	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
671	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
672	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
673	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
674	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
675	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
676	C₄⋊Q₈	—	2	2	no	—
677	C₄⋊Q₈	—	2	2	no	—
678	C₄⋊Q₈	—	2	1	no	—
679	C₄⋊Q₈	—	2	1	no	—
680	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
681	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
682	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
683	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
684	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
685	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
686	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
687	#127	C₂³×C₇	1	1	yes	characteristic
688	#126	—	2	2	no	—
689	#126	—	2	2	no	—
690	#126	—	2	2	no	—
691	#126	—	2	2	no	—
692	#125	—	2	1	no	—
693	#125	—	2	1	no	—
694	#125	—	2	2	no	—
695	#125	—	2	2	no	—
696	#125	—	2	2	no	—
697	#125	—	2	2	no	—
698	#125	—	2	2	no	—
699	#125	—	2	2	no	—
700	#125	—	2	2	no	—
701	#125	—	2	1	no	—
702	#125	—	2	1	no	—
703	#125	C₇×D₄	1	1	yes	characteristic
704	#125	C₇×D₄	1	1	yes	characteristic
705	#125	C₂³×C₇	1	2	yes	—
706	#125	C₂³×C₇	1	2	yes	—
707	#125	C₂³×C₇	1	2	yes	—
708	#125	C₂³×C₇	1	2	yes	—
709	#124	—	2	2	no	—
710	#124	C₂³×C₇	1	1	yes	characteristic
711	#124	C₂³×C₇	1	1	yes	characteristic
712	#124	C₂³×C₇	1	2	yes	—
713	#124	C₂³×C₇	1	2	yes	—
714	#123	—	2	2	no	—
715	#123	—	2	2	no	—
716	#123	—	2	2	no	—
717	#123	—	2	2	no	—
718	C₂²⋊Q₈	—	2	2	no	—
719	C₂²⋊Q₈	—	2	2	no	—
720	C₂²⋊Q₈	—	2	2	no	—
721	C₂²⋊Q₈	—	2	2	no	—
722	C₂²⋊Q₈	—	2	2	no	—
723	C₂²⋊Q₈	—	2	2	no	—
724	C₂²⋊Q₈	—	2	1	no	—
725	C₂²⋊Q₈	—	2	1	no	—
726	C₂²⋊Q₈	—	2	1	no	—
727	C₂²⋊Q₈	—	2	1	no	—
728	C₂²⋊Q₈	—	2	2	no	—
729	C₂²⋊Q₈	—	2	2	no	—
730	C₂²⋊Q₈	—	2	2	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
733	C₂²⋊Q₈	C₇×D₄	1	2	yes	—
734	#121	—	2	1	no	—
735	#121	—	2	1	no	—
736	C₄×Q₈	—	2	2	no	—
737	C₄×Q₈	—	2	2	no	—
738	C₄×Q₈	—	2	2	no	—
739	C₄×Q₈	—	2	1	no	—
740	C₄×Q₈	—	2	1	no	—
741	C₄×Q₈	C₂³×C₇	1	2	yes	—
742	C₄×Q₈	C₂³×C₇	1	2	yes	—
743	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
744	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
745	C₄×Q₈	C₂³×C₇	1	2	yes	—
746	C₄×Q₈	C₂³×C₇	1	2	yes	—
747	C₄×Q₈	C₂³×C₇	1	2	yes	—
748	C₄×Q₈	C₂³×C₇	1	2	yes	—
749	C₄×Q₈	C₂³×C₇	1	2	yes	—
750	C₄×Q₈	C₂³×C₇	1	2	yes	—
751	C₄×D₄	—	2	1	no	—
752	C₄×D₄	—	2	1	no	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	2	no	—
758	C₄×D₄	—	2	1	no	—
759	C₄×D₄	—	2	1	no	—
760	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
761	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
762	C₄×D₄	C₂³×C₇	1	2	yes	—
763	C₄×D₄	C₂³×C₇	1	2	yes	—
764	C₄×D₄	C₂³×C₇	1	2	yes	—
765	C₄×D₄	C₂³×C₇	1	2	yes	—
766	#117	—	2	1	no	—
767	#117	—	2	1	no	—
768	#117	—	2	1	no	—
769	#117	—	2	1	no	—
770	#117	—	2	2	no	—
771	#117	—	2	2	no	—
772	#117	—	2	1	no	—
773	#117	C₂³×C₇	1	1	yes	characteristic
774	#117	C₂³×C₇	1	1	yes	characteristic
775	#117	C₂³×C₇	1	1	yes	characteristic
776	C₂×C₄⋊C₄	—	2	1	no	—
777	C₂×C₄⋊C₄	—	2	1	no	—
778	C₂×C₄⋊C₄	—	2	1	no	—
779	C₂×C₄⋊C₄	—	2	1	no	—
780	C₂×C₄⋊C₄	—	2	1	no	—
781	C₂×C₄⋊C₄	—	2	1	no	—
782	C₂×C₄⋊C₄	—	2	1	no	—
783	C₂×C₄⋊C₄	—	2	2	no	—
784	C₂×C₄⋊C₄	—	2	2	no	—
785	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
786	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
787	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
788	C₂×C₄²	—	2	1	no	—
789	C₂×C₄²	—	2	1	no	—
790	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
791	#107	C₂³×C₇	1	2	yes	—
792	#107	C₂³×C₇	1	2	yes	—
793	#107	C₂³×C₇	1	2	yes	—
794	#106	C₂³×C₇	1	2	yes	—
795	#106	C₂³×C₇	1	2	yes	—
796	#106	C₂³×C₇	1	2	yes	—
797	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
798	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
799	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
800	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
801	C₄⋊C₈	C₂³×C₇	1	2	yes	—
802	C₄⋊C₈	C₂³×C₇	1	2	yes	—
803	C₄⋊C₈	C₂³×C₇	1	2	yes	—
804	C₄⋊C₈	C₂³×C₇	1	2	yes	—
805	#103	C₂³×C₇	1	2	yes	—
806	#103	C₂³×C₇	1	2	yes	—
807	#103	C₂³×C₇	1	2	yes	—
808	#103	C₂³×C₇	1	2	yes	—
809	#103	C₂³×C₇	1	1	yes	characteristic
810	#103	C₂³×C₇	1	1	yes	characteristic
811	#103	C₂³×C₇	1	1	yes	characteristic
812	#103	C₂³×C₇	1	1	yes	characteristic
813	#103	C₂³×C₇	1	2	yes	—
814	#103	C₂³×C₇	1	2	yes	—
815	#103	C₂³×C₇	1	2	yes	—
816	#103	C₂³×C₇	1	2	yes	—
817	#103	C₂³×C₇	1	2	yes	—
818	#103	C₂³×C₇	1	2	yes	—
819	#103	C₂³×C₇	1	2	yes	—
820	#102	C₂³×C₇	1	1	yes	characteristic
821	#102	C₂³×C₇	1	1	yes	characteristic
822	#102	C₂³×C₇	1	1	yes	characteristic
823	#102	C₂³×C₇	1	1	yes	characteristic
824	#102	C₂³×C₇	1	2	yes	—
825	#102	C₂³×C₇	1	2	yes	—
826	#102	C₂³×C₇	1	2	yes	—
827	#102	C₂³×C₇	1	2	yes	—
828	#102	C₂³×C₇	1	2	yes	—
829	#97	C₂³×C₇	1	2	yes	—
830	#97	C₂³×C₇	1	2	yes	—
831	#97	C₂³×C₇	1	2	yes	—
832	C₄×C₈	C₂³×C₇	1	2	yes	—
833	C₄×C₈	C₂³×C₇	1	2	yes	—
834	C₄×C₈	C₂³×C₇	1	2	yes	—
835	C₂²×C₇	—	2	1	no	—
836	C₂²×C₇	—	2	1	no	—
837	C₂²×C₇	—	2	2	no	—
838	C₂²×C₇	—	4	1	no	—
839	C₂²×C₇	—	4	1	no	—
840	C₂²×C₇	—	4	1	no	—
841	C₂²×C₇	—	4	1	no	—
842	C₂²×C₇	—	4	1	no	—
843	C₂²×C₇	—	4	1	no	—
844	C₂²×C₇	—	4	1	no	—
845	C₂²×C₇	—	4	1	no	—
846	C₂²×C₇	#548	1	2	yes	—
847	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
848	C₄×C₇	—	2	1	no	—
849	C₄×C₇	—	2	1	no	—
850	C₄×C₇	—	2	2	no	—
851	C₄×C₇	—	2	2	no	—
852	C₄×C₇	—	2	1	no	—
853	C₄×C₇	—	2	1	no	—
854	C₄×C₇	—	2	2	no	—
855	C₄×C₇	—	2	2	no	—
856	C₄×C₇	—	2	2	no	—
857	C₄×C₇	—	4	2	no	—
858	C₄×C₇	—	4	2	no	—
859	C₄×C₇	—	4	1	no	—
860	C₄×C₇	—	4	2	no	—
861	C₄×C₇	—	4	1	no	—
862	C₄×C₇	—	4	1	no	—
863	C₄×C₇	—	4	1	no	—
864	C₄×C₇	—	4	2	no	—
865	C₄×C₇	#548	1	2	yes	—
866	C₄×C₇	C₂²×#41	1	1	yes	characteristic
867	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
868	#41	—	2	2	no	—
869	#41	—	2	2	no	—
870	#41	—	2	2	no	—
871	#41	—	2	2	no	—
872	#41	—	2	2	no	—
873	#41	C₇×#41	1	4	yes	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	2	2	no	—
876	C₂×Q₈	—	2	2	no	—
877	C₂×Q₈	—	2	2	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
880	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
881	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
882	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
883	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
884	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
885	C₂×D₄	—	2	1	no	—
886	C₂×D₄	—	2	1	no	—
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	2	1	no	—
890	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
891	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
892	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
893	C₂²×C₄	—	2	1	no	—
894	C₂²×C₄	—	2	1	no	—
895	C₂²×C₄	—	2	1	no	—
896	C₂²×C₄	—	2	1	no	—
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	1	no	—
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	2	no	—
903	C₂²×C₄	—	2	2	no	—
904	C₂²×C₄	—	2	2	no	—
905	C₂²×C₄	—	2	2	no	—
906	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
907	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
908	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
909	Q₁₆	—	2	2	no	—
910	Q₁₆	—	2	2	no	—
911	Q₁₆	—	2	4	no	—
912	SD₁₆	—	2	2	no	—
913	SD₁₆	—	2	2	no	—
914	SD₁₆	—	2	2	no	—
915	SD₁₆	—	2	2	no	—
916	SD₁₆	—	2	4	no	—
917	D₈	—	2	2	no	—
918	D₈	—	2	2	no	—
919	M₁₆	—	2	2	no	—
920	M₁₆	—	2	2	no	—
921	C₂×C₈	—	2	2	no	—
922	C₂×C₈	—	2	2	no	—
923	C₂×C₈	C₂⁴×C₇	1	2	yes	—
924	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
925	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
926	C₂×C₈	C₂⁴×C₇	1	2	yes	—
927	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
928	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	2	no	—
938	C₄⋊C₄	—	2	2	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	2	no	—
941	C₄⋊C₄	—	2	2	no	—
942	C₄⋊C₄	—	2	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	2	no	—
945	C₄⋊C₄	—	2	2	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	2	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
957	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
958	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
959	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
960	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
961	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
962	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
963	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
964	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
965	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
966	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
967	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
968	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
969	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	2	2	no	—
979	C₂²⋊C₄	—	2	2	no	—
980	C₂²⋊C₄	—	2	2	no	—
981	C₂²⋊C₄	—	2	2	no	—
982	C₂²⋊C₄	—	2	1	no	—
983	C₂²⋊C₄	—	2	1	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
987	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
988	C₄²	—	2	2	no	—
989	C₄²	—	2	1	no	—
990	C₄²	—	2	2	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	2	no	—
994	C₄²	—	2	2	no	—
995	C₄²	—	2	2	no	—
996	C₄²	—	2	2	no	—
997	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
998	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
999	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1000	C₄²	C₂⁴×C₇	1	2	yes	—
1001	C₄²	C₂⁴×C₇	1	2	yes	—
1002	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1003	C₂×C₇	—	2	2	no	—
1004	C₂×C₇	—	4	2	no	—
1005	C₂×C₇	—	8	1	no	—
1006	C₂×C₇	—	8	1	no	—
1007	C₂×C₇	C₂×#548	1	1	yes	characteristic
1008	C₂×C₇	#3584	1	1	yes	characteristic
1009	C₂×C₇	#3586	1	1	yes	characteristic
1010	C₂³	—	2	1	no	—
1011	C₂³	—	2	1	no	—
1012	C₂³	—	2	1	no	—
1013	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	2	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	2	2	no	—
1019	Q₈	—	2	1	no	—
1020	Q₈	—	2	1	no	—
1021	Q₈	—	4	2	no	—
1022	Q₈	—	4	2	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	8	2	no	—
1025	Q₈	—	8	2	no	—
1026	Q₈	C₂×C₇×#41	1	2	yes	—
1027	D₄	—	2	4	no	—
1028	D₄	—	2	1	no	—
1029	D₄	—	2	1	no	—
1030	D₄	—	2	1	no	—
1031	D₄	—	2	1	no	—
1032	D₄	—	2	1	no	—
1033	D₄	—	4	2	no	—
1034	D₄	—	4	2	no	—
1035	D₄	—	4	2	no	—
1036	D₄	—	8	1	no	—
1037	D₄	C₂×C₇×#41	1	2	yes	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	4	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	2	no	—
1047	C₂×C₄	—	2	2	no	—
1048	C₂×C₄	—	4	1	no	—
1049	C₂×C₄	—	4	1	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	4	2	no	—
1053	C₂×C₄	—	8	1	no	—
1054	C₂×C₄	—	8	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	1	no	—
1058	C₂×C₄	—	8	2	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	8	1	no	—
1061	C₂×C₄	—	8	1	no	—
1062	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1063	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1064	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1065	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1066	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1067	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1068	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1069	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1070	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1071	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1072	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1073	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	2	no	—
1079	C₈	—	2	2	no	—
1080	C₇	#61350	1	1	yes	characteristic, direct product factor, Sylow
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	2	no	—
1084	C₂²	—	4	1	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	4	1	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	C₇×#548	1	2	yes	—
1093	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	2	no	—
1097	C₄	—	2	2	no	—
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	2	2	no	—
1103	C₄	—	4	2	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	1	no	—
1109	C₄	—	4	1	no	—
1110	C₄	—	4	2	no	—
1111	C₄	C₇×#548	1	2	yes	—
1112	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1113	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1114	C₂	—	2	2	no	—
1115	C₂	—	4	2	no	—
1116	C₂	—	8	1	no	—
1117	C₂	—	8	1	no	—
1118	C₂	C₂×C₇×#548	1	1	yes	characteristic
1119	C₂	C₇×#3584	1	1	yes	characteristic
1120	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×#3035	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3507	C₂	semidirect
2. C₇×#3504	C₂	semidirect
3. C₇×#3377	C₂	semidirect
4. C₇×#3376	C₂	semidirect
5. C₇×#3374	C₂	semidirect
6. C₇×#3372	C₂	semidirect
7. C₇×#3371	C₂	semidirect
8. C₇×#3370	C₂	semidirect
9. C₇×#3364	C₂	semidirect
10. C₇×#3360	C₂	semidirect
11. C₇×#3142	C₂	semidirect
12. C₇×#3137	C₂	semidirect
13. C₇×#3137	C₂	semidirect
14. C₇×#3084	C₂	semidirect
15. C₇×#3083	C₂	semidirect
16. C₂×C₇×#479	C₂	semidirect
17. C₇×#3046	C₂	semidirect
18. C₇×#3046	C₂	semidirect
20. C₇×#2962	C₂	semidirect
21. C₇×#2952	C₂	semidirect
22. C₇×#2951	C₂	semidirect
23. C₄×C₇×#137	C₂	semidirect
135. #61350	C₇	direct (N × H)
316. #3507	C₂×C₇	semidirect
317. #3504	C₂×C₇	semidirect
318. #3377	C₂×C₇	semidirect
319. #3376	C₂×C₇	semidirect
320. #3374	C₂×C₇	semidirect
321. #3372	C₂×C₇	semidirect
322. #3371	C₂×C₇	semidirect
323. #3370	C₂×C₇	semidirect
324. #3364	C₂×C₇	semidirect
325. #3360	C₂×C₇	semidirect
326. #3142	C₂×C₇	semidirect
327. #3137	C₂×C₇	semidirect
328. #3137	C₂×C₇	semidirect
329. #3084	C₂×C₇	semidirect
330. #3083	C₂×C₇	semidirect
331. C₂×#479	C₂×C₇	semidirect
332. #3046	C₂×C₇	semidirect
333. #3046	C₂×C₇	semidirect
335. #2962	C₂×C₇	semidirect
336. #2952	C₂×C₇	semidirect
337. #2951	C₂×C₇	semidirect
338. C₄×#137	C₂×C₇	semidirect
1080. C₇	#61350	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×#3507	2
C₇×#3504	2
C₇×#3377	2
C₇×#3376	2
C₇×#3374	2
C₇×#3372	2
C₇×#3371	2
C₇×#3370	2
C₇×#3364	2
C₇×#3360	2
C₇×#3142	2
C₇×#3137	2
C₇×#3084	2
C₇×#3083	2
C₂×C₇×#479	2
C₇×#3046	2
C₇×#3035	2
C₇×#2962	2
C₇×#2952	2
C₇×#2951	2
C₄×C₇×#137	2
#61350	7

Subgroups — C7×#61350 #13238566

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61350 #13238566