Subgroups — C₇×#61191 #13238407

Order 1792.

2156 conjugacy classes of subgroups.

The subgroup lattice has 1298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3492	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₇×#3322	C₂	1	2	yes	maximal, complemented
5	C₇×#3314	C₂	1	2	yes	maximal, complemented
6	C₇×#3310	C₂	1	2	yes	maximal, complemented
7	C₇×#3309	C₂	1	2	yes	maximal, complemented
8	C₇×#3308	C₂	1	2	yes	maximal, complemented
9	C₇×#3300	C₂	1	2	yes	maximal, complemented
10	C₇×#3294	C₂	1	2	yes	maximal, complemented
11	C₇×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₇×#480	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3061	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3045	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3002	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#417	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
26	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×#135	C₂²	1	1	yes	characteristic
28	C₂×C₇×#135	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic, complemented
31	C₇×#554	—	2	1	no	—
32	C₇×#554	C₂²	1	2	yes	complemented
33	C₇×#553	—	2	1	no	—
34	C₇×#553	C₂²	1	2	yes	complemented
35	C₇×#552	—	2	1	no	—
36	C₇×#552	C₂²	1	2	yes	complemented
37	C₇×#550	C₂²	1	2	yes	—
38	C₇×#548	C₂²	1	2	yes	—
39	C₇×#547	—	2	1	no	—
40	C₇×#547	C₂²	1	2	yes	complemented
41	C₇×#546	—	2	2	no	—
42	C₇×#546	C₂²	1	2	yes	—
43	C₇×D₄²	—	2	2	no	—
44	C₇×D₄²	C₂²	1	2	yes	—
45	C₇×#544	C₂²	1	1	yes	characteristic, complemented
46	C₇×#539	—	2	2	no	—
47	C₇×#537	—	2	1	no	—
48	C₇×#537	C₂²	1	1	yes	characteristic
49	C₇×#537	C₂²	1	1	yes	characteristic, complemented
50	C₇×#535	—	2	1	no	—
51	C₇×#535	C₂²	1	1	yes	characteristic
52	C₇×#525	—	2	1	no	—
53	C₇×#525	—	2	2	no	—
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₇×#525	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₇×#121	—	2	1	no	—
57	C₂×C₇×#121	C₂²	1	1	yes	characteristic
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic, complemented
60	C₇×#520	C₂²	1	1	yes	characteristic, complemented
61	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
62	C₇×#490	C₂²	1	2	yes	complemented
63	C₇×#489	C₂²	1	2	yes	complemented
64	C₇×#488	C₂²	1	2	yes	complemented
65	C₇×#486	C₂²	1	2	yes	complemented
66	C₇×#485	C₂²	1	2	yes	complemented
67	C₇×#484	C₂²	1	2	yes	complemented
68	C₇×#482	C₂²	1	2	yes	complemented
69	C₇×#480	C₂²	1	2	yes	complemented
70	C₇×#480	C₂²	1	2	yes	complemented
71	C₇×#480	C₂²	1	2	yes	complemented
72	C₇×#480	C₂²	1	2	yes	complemented
73	C₇×#480	C₂²	1	2	yes	complemented
74	C₇×#479	C₂²	1	2	yes	complemented
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#477	C₂²	1	2	yes	complemented
77	C₇×#474	C₂²	1	2	yes	complemented
78	C₇×#469	C₂²	1	2	yes	complemented
79	C₇×#468	C₂²	1	2	yes	complemented
80	C₇×#468	C₂²	1	2	yes	complemented
81	C₇×#468	C₂²	1	2	yes	complemented
82	C₇×#467	C₂²	1	2	yes	complemented
83	C₇×#466	C₂²	1	2	yes	complemented
84	C₇×#466	C₂²	1	2	yes	complemented
85	C₇×#465	C₂²	1	2	yes	complemented
86	C₇×#464	C₂²	1	2	yes	complemented
87	C₇×#463	C₂²	1	2	yes	complemented
88	C₇×#460	C₂²	1	2	yes	complemented
89	C₇×#459	C₂²	1	2	yes	complemented
90	C₇×#452	C₂²	1	1	yes	characteristic, complemented
91	C₇×#452	C₂²	1	1	yes	characteristic, complemented
92	C₇×#452	C₂²	1	2	yes	complemented
93	C₇×#451	C₂²	1	1	yes	characteristic, complemented
94	C₇×#450	C₂²	1	1	yes	characteristic, complemented
95	C₇×#450	C₂²	1	2	yes	complemented
96	C₇×#449	C₂²	1	1	yes	characteristic, complemented
97	C₇×#449	C₂²	1	1	yes	characteristic, complemented
98	C₇×#449	C₂²	1	2	yes	complemented
99	C₇×#448	C₂²	1	1	yes	characteristic, complemented
100	C₇×#447	C₂²	1	1	yes	characteristic, complemented
101	C₇×#447	C₂²	1	2	yes	complemented
102	C₇×#440	C₂²	1	2	yes	complemented
103	C₇×#440	C₂²	1	2	yes	complemented
104	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×D₈	C₂²	1	2	yes	complemented
106	C₇×#436	C₂²	1	2	yes	complemented
107	C₇×#435	C₂²	1	2	yes	complemented
108	C₇×#435	C₂²	1	2	yes	complemented
109	C₇×C₈×D₄	C₂²	1	2	yes	complemented
110	C₇×#428	C₂²	1	1	yes	characteristic, complemented
111	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
112	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
113	C₇×#424	C₂²	1	1	yes	characteristic, complemented
114	C₇×#418	C₂²	1	2	yes	complemented
115	C₇×#418	C₂²	1	1	yes	characteristic, complemented
116	C₇×#417	C₂²	1	1	yes	characteristic
117	C₇×#417	C₂²	1	1	yes	characteristic
118	C₇×#417	C₂²	1	1	yes	characteristic, complemented
119	C₇×#417	C₂²	1	1	yes	characteristic, complemented
120	C₇×#417	C₂²	1	2	yes	complemented
121	C₇×#417	C₂²	1	2	yes	complemented
122	C₇×#417	C₂²	1	2	yes	complemented
123	C₇×#417	C₂²	1	1	yes	characteristic, complemented
124	C₇×#416	C₂²	1	1	yes	characteristic
125	C₇×#416	C₂²	1	1	yes	characteristic, complemented
126	C₇×#416	C₂²	1	2	yes	complemented
127	C₂×C₇×#103	C₂²	1	2	yes	complemented
128	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
129	C₂×C₇×#102	C₂²	1	2	yes	complemented
130	C₂×C₇×#102	C₂²	1	2	yes	complemented
131	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
132	C₇×#408	C₂²	1	1	yes	characteristic, complemented
133	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
134	C₇×#405	C₂²	1	1	yes	characteristic, complemented
135	#61191	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₇×H(5,𝔽₂)	—	2	4	no	—
137	C₇×H(5,𝔽₂)	—	4	2	no	—
138	C₂×C₇×#41	—	2	1	no	—
139	C₂×C₇×#41	—	2	2	no	—
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	—	2	4	no	—
143	C₂×C₇×#41	—	4	2	no	—
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂×C₇×#41	C₂³	1	1	yes	characteristic
147	C₂×C₇×#41	C₂³	1	1	yes	characteristic
148	C₂×C₇×#41	C₂³	1	2	yes	—
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂×C₇×#41	C₂³	1	1	yes	characteristic
151	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
152	C₂²×C₇×D₄	—	2	1	no	—
153	C₂²×C₇×D₄	—	2	1	no	—
154	C₂²×C₇×D₄	—	2	1	no	—
155	C₂²×C₇×D₄	—	2	2	no	—
156	C₂²×C₇×D₄	—	2	2	no	—
157	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
158	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
159	C₂²×C₇×D₄	C₂³	1	2	yes	—
160	C₂³×C₄×C₇	—	2	1	no	—
161	C₂³×C₄×C₇	—	2	1	no	—
162	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
163	C₇×AGL(1,ℤ/8)	—	4	2	no	—
164	C₇×#135	—	2	4	no	—
165	C₇×#135	—	4	2	no	—
166	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
167	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
168	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
169	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
170	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
171	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic
172	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
173	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
174	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
175	C₂×C₇×D₈	C₂³	1	2	yes	—
176	C₇×#131	—	4	2	no	—
177	C₂×C₇×M₁₆	—	4	2	no	—
178	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
179	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
180	C₂×C₇×M₁₆	C₂³	1	2	yes	—
181	C₂×C₇×M₁₆	C₂³	1	2	yes	—
182	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
183	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
184	C₂²×C₇×C₈	C₂³	1	2	yes	—
185	C₂²×C₇×C₈	C₂³	1	2	yes	—
186	C₇×C₄⋊Q₈	—	2	1	no	—
187	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
188	C₇×#127	—	2	2	no	—
189	C₇×#127	C₂³	1	2	yes	—
190	C₇×#126	—	2	2	no	—
191	C₇×#126	—	2	2	no	—
192	C₇×#125	—	2	2	no	—
193	C₇×#125	—	2	2	no	—
194	C₇×#125	—	2	1	no	—
195	C₇×#125	C₂³	1	2	yes	—
196	C₇×#124	—	2	2	no	—
197	C₇×#124	C₂³	1	2	yes	—
198	C₇×#123	—	2	2	no	—
199	C₇×#123	—	2	1	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	D₄	1	2	yes	—
205	C₇×C₂²⋊Q₈	—	2	1	no	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	—	2	2	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	D₄	1	1	yes	characteristic
213	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
216	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₇×#121	—	2	1	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	2	no	—
221	C₇×#121	—	2	2	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	1	no	—
224	C₇×#121	—	2	1	no	—
225	C₇×#121	—	2	1	no	—
226	C₇×#121	—	2	1	no	—
227	C₇×#121	—	2	1	no	—
228	C₇×#121	—	2	2	no	—
229	C₇×#121	—	2	2	no	—
230	C₇×#121	—	2	2	no	—
231	C₇×#121	—	2	2	no	—
232	C₇×#121	D₄	1	1	yes	characteristic
233	C₇×#121	D₄	1	1	yes	characteristic
234	C₇×#121	C₂³	1	1	yes	characteristic
235	C₇×#121	C₂³	1	2	yes	—
236	C₇×#121	C₂³	1	2	yes	—
237	C₇×#121	C₂³	1	2	yes	—
238	C₇×#121	C₂³	1	2	yes	—
239	C₇×#121	C₂³	1	1	yes	characteristic
240	C₇×#120	—	2	1	no	—
241	C₇×#120	—	2	2	no	—
242	C₇×#120	—	2	2	no	—
243	C₇×#120	—	2	2	no	—
244	C₇×#120	—	2	2	no	—
245	C₇×#120	D₄	1	2	yes	—
246	C₄×C₇×Q₈	—	2	1	no	—
247	C₄×C₇×Q₈	C₂³	1	2	yes	—
248	C₄×C₇×Q₈	C₂³	1	2	yes	—
249	C₄×C₇×D₄	—	2	2	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	—	2	2	no	—
252	C₄×C₇×D₄	—	2	1	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	2	no	—
255	C₄×C₇×D₄	—	2	2	no	—
256	C₄×C₇×D₄	—	2	2	no	—
257	C₄×C₇×D₄	—	2	2	no	—
258	C₄×C₇×D₄	—	2	2	no	—
259	C₄×C₇×D₄	C₂³	1	2	yes	—
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₄×C₇×D₄	C₂³	1	2	yes	—
262	C₄×C₇×D₄	C₂³	1	2	yes	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	—	2	2	no	—
266	C₇×#117	C₂³	1	2	yes	—
267	C₇×#117	C₂³	1	1	yes	characteristic
268	C₇×#117	C₂³	1	1	yes	characteristic
269	C₂×C₇×C₄⋊C₄	—	2	1	no	—
270	C₂×C₇×C₄⋊C₄	—	2	1	no	—
271	C₂×C₇×C₄⋊C₄	—	2	1	no	—
272	C₂×C₇×C₄⋊C₄	—	2	1	no	—
273	C₂×C₇×C₄⋊C₄	—	2	1	no	—
274	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
275	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
276	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
277	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
278	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
280	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
282	C₇×#107	C₂³	1	2	yes	—
283	C₇×#107	C₂³	1	2	yes	—
284	C₇×#107	C₂³	1	2	yes	—
285	C₇×#107	C₂³	1	2	yes	—
286	C₇×#107	C₂³	1	2	yes	—
287	C₇×#106	C₂³	1	2	yes	—
288	C₇×C₄⋊C₈	C₂³	1	2	yes	—
289	C₇×C₄⋊C₈	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	2	yes	—
292	C₇×#103	C₂³	1	1	yes	characteristic
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	1	yes	characteristic
295	C₇×#103	C₂³	1	1	yes	characteristic
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	2	yes	—
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×#102	C₂³	1	2	yes	—
311	C₇×#102	C₂³	1	2	yes	—
312	C₇×#102	C₂³	1	1	yes	characteristic
313	C₇×#102	C₂³	1	2	yes	—
314	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
315	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
316	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
317	C₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
318	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
319	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
320	C₇×#97	C₂³	1	2	yes	—
321	C₄×C₇×C₈	C₂³	1	2	yes	—
322	#3492	C₂×C₇	1	1	yes	characteristic, complemented
323	#3488	C₂×C₇	1	1	yes	characteristic, complemented
324	#3333	C₂×C₇	1	2	yes	complemented
325	#3322	C₂×C₇	1	2	yes	complemented
326	#3314	C₂×C₇	1	2	yes	complemented
327	#3310	C₂×C₇	1	2	yes	complemented
328	#3309	C₂×C₇	1	2	yes	complemented
329	#3308	C₂×C₇	1	2	yes	complemented
330	#3300	C₂×C₇	1	2	yes	complemented
331	#3294	C₂×C₇	1	2	yes	complemented
332	#3136	C₂×C₇	1	1	yes	characteristic, complemented
333	#3098	C₂×C₇	1	1	yes	characteristic, complemented
334	C₂×#480	C₂×C₇	1	1	yes	characteristic, complemented
335	#3083	C₂×C₇	1	1	yes	characteristic, complemented
336	#3061	C₂×C₇	1	1	yes	characteristic, complemented
337	#3055	C₂×C₇	1	1	yes	characteristic, complemented
338	#3045	C₂×C₇	1	1	yes	characteristic, complemented
339	#3012	C₂×C₇	1	1	yes	characteristic, complemented
340	#3002	C₂×C₇	1	1	yes	characteristic, complemented
341	#2951	C₂×C₇	1	1	yes	characteristic, complemented
342	#2933	C₂×C₇	1	1	yes	characteristic, complemented
343	#2897	C₂×C₇	1	1	yes	characteristic, complemented
344	C₂×#417	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	1	no	—
346	C₂⁴×C₇	—	2	2	no	—
347	C₂⁴×C₇	—	2	1	no	—
348	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
349	C₇×#41	—	2	2	no	—
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	2	no	—
353	C₇×#41	—	2	4	no	—
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	2	2	no	—
357	C₇×#41	—	2	2	no	—
358	C₇×#41	—	2	2	no	—
359	C₇×#41	—	4	4	no	—
360	C₇×#41	—	4	1	no	—
361	C₇×#41	—	4	1	no	—
362	C₇×#41	—	4	2	no	—
363	C₇×#41	—	4	4	no	—
364	C₇×#41	—	4	4	no	—
365	C₇×#41	—	8	4	no	—
366	C₇×#41	#41	1	4	yes	complemented
367	C₂×C₇×Q₈	—	2	1	no	—
368	C₂×C₇×Q₈	—	2	2	no	—
369	C₂×C₇×Q₈	—	2	2	no	—
370	C₂×C₇×Q₈	—	4	1	no	—
371	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
372	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
374	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
375	C₂×C₇×D₄	—	2	1	no	—
376	C₂×C₇×D₄	—	2	2	no	—
377	C₂×C₇×D₄	—	2	4	no	—
378	C₂×C₇×D₄	—	2	1	no	—
379	C₂×C₇×D₄	—	2	1	no	—
380	C₂×C₇×D₄	—	2	2	no	—
381	C₂×C₇×D₄	—	2	1	no	—
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	1	no	—
384	C₂×C₇×D₄	—	2	2	no	—
385	C₂×C₇×D₄	—	2	1	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	2	2	no	—
388	C₂×C₇×D₄	—	2	2	no	—
389	C₂×C₇×D₄	—	2	1	no	—
390	C₂×C₇×D₄	—	2	2	no	—
391	C₂×C₇×D₄	—	2	1	no	—
392	C₂×C₇×D₄	—	2	2	no	—
393	C₂×C₇×D₄	—	2	2	no	—
394	C₂×C₇×D₄	—	2	2	no	—
395	C₂×C₇×D₄	—	2	2	no	—
396	C₂×C₇×D₄	—	4	1	no	—
397	C₂×C₇×D₄	—	4	2	no	—
398	C₂×C₇×D₄	—	4	4	no	—
399	C₂×C₇×D₄	—	4	8	no	—
400	C₂×C₇×D₄	—	4	4	no	—
401	C₂×C₇×D₄	—	8	4	no	—
402	C₂×C₇×D₄	—	8	2	no	—
403	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
404	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
405	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
406	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
407	C₂×C₇×D₄	C₂⁴	1	2	yes	—
408	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
409	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
410	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
411	C₂²×C₄×C₇	—	2	1	no	—
412	C₂²×C₄×C₇	—	2	2	no	—
413	C₂²×C₄×C₇	—	2	2	no	—
414	C₂²×C₄×C₇	—	2	2	no	—
415	C₂²×C₄×C₇	—	2	1	no	—
416	C₂²×C₄×C₇	—	2	1	no	—
417	C₂²×C₄×C₇	—	2	1	no	—
418	C₂²×C₄×C₇	—	2	2	no	—
419	C₂²×C₄×C₇	—	2	1	no	—
420	C₂²×C₄×C₇	—	2	2	no	—
421	C₂²×C₄×C₇	—	2	1	no	—
422	C₂²×C₄×C₇	—	2	1	no	—
423	C₂²×C₄×C₇	—	2	1	no	—
424	C₂²×C₄×C₇	—	2	2	no	—
425	C₂²×C₄×C₇	—	2	1	no	—
426	C₂²×C₄×C₇	—	2	2	no	—
427	C₂²×C₄×C₇	—	2	2	no	—
428	C₂²×C₄×C₇	—	4	4	no	—
429	C₂²×C₄×C₇	—	8	2	no	—
430	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
431	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
432	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
433	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
436	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
437	C₇×Q₁₆	—	2	2	no	—
438	C₇×Q₁₆	—	4	1	no	—
439	C₇×SD₁₆	—	2	2	no	—
440	C₇×SD₁₆	—	2	2	no	—
441	C₇×SD₁₆	—	4	1	no	—
442	C₇×SD₁₆	—	4	1	no	—
443	C₇×SD₁₆	—	4	2	no	—
444	C₇×D₈	—	2	2	no	—
445	C₇×D₈	—	4	1	no	—
446	C₇×D₈	—	4	2	no	—
447	C₇×M₁₆	—	2	2	no	—
448	C₇×M₁₆	—	2	2	no	—
449	C₇×M₁₆	—	4	2	no	—
450	C₇×M₁₆	—	4	2	no	—
451	C₂×C₇×C₈	—	2	2	no	—
452	C₂×C₇×C₈	—	2	2	no	—
453	C₂×C₇×C₈	—	4	2	no	—
454	C₂×C₇×C₈	—	4	2	no	—
455	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
456	C₂×C₇×C₈	C₂⁴	1	2	yes	—
457	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
458	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
459	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
460	C₂×C₇×C₈	C₂⁴	1	2	yes	—
461	C₇×C₄⋊C₄	—	2	1	no	—
462	C₇×C₄⋊C₄	—	2	1	no	—
463	C₇×C₄⋊C₄	—	2	2	no	—
464	C₇×C₄⋊C₄	—	2	2	no	—
465	C₇×C₄⋊C₄	—	2	1	no	—
466	C₇×C₄⋊C₄	—	2	2	no	—
467	C₇×C₄⋊C₄	—	2	2	no	—
468	C₇×C₄⋊C₄	—	2	2	no	—
469	C₇×C₄⋊C₄	—	2	2	no	—
470	C₇×C₄⋊C₄	—	2	2	no	—
471	C₇×C₄⋊C₄	—	2	2	no	—
472	C₇×C₄⋊C₄	—	2	1	no	—
473	C₇×C₄⋊C₄	—	2	2	no	—
474	C₇×C₄⋊C₄	—	2	2	no	—
475	C₇×C₄⋊C₄	—	2	1	no	—
476	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
477	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
478	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
479	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
480	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
481	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
482	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
483	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
484	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
485	C₇×C₂²⋊C₄	—	2	2	no	—
486	C₇×C₂²⋊C₄	—	2	1	no	—
487	C₇×C₂²⋊C₄	—	2	1	no	—
488	C₇×C₂²⋊C₄	—	2	2	no	—
489	C₇×C₂²⋊C₄	—	2	1	no	—
490	C₇×C₂²⋊C₄	—	2	2	no	—
491	C₇×C₂²⋊C₄	—	2	2	no	—
492	C₇×C₂²⋊C₄	—	2	2	no	—
493	C₇×C₂²⋊C₄	—	2	2	no	—
494	C₇×C₂²⋊C₄	—	2	2	no	—
495	C₇×C₂²⋊C₄	—	2	2	no	—
496	C₇×C₂²⋊C₄	—	2	2	no	—
497	C₇×C₂²⋊C₄	—	2	2	no	—
498	C₇×C₂²⋊C₄	—	2	2	no	—
499	C₇×C₂²⋊C₄	—	2	1	no	—
500	C₇×C₂²⋊C₄	—	2	1	no	—
501	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
502	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
503	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
504	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
505	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
506	C₄²×C₇	—	2	2	no	—
507	C₄²×C₇	—	2	2	no	—
508	C₄²×C₇	—	2	2	no	—
509	C₄²×C₇	—	2	1	no	—
510	C₄²×C₇	C₂⁴	1	2	yes	—
511	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
512	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
513	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic, complemented
514	C₂×#135	C₂²×C₇	1	1	yes	characteristic
515	C₂×#135	C₂²×C₇	1	1	yes	characteristic, complemented
516	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
517	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
518	#554	—	2	1	no	—
519	#554	C₂²×C₇	1	2	yes	complemented
520	#553	—	2	1	no	—
521	#553	C₂²×C₇	1	2	yes	complemented
522	#552	—	2	1	no	—
523	#552	C₂²×C₇	1	2	yes	complemented
524	#550	C₂²×C₇	1	2	yes	—
525	#548	C₂²×C₇	1	2	yes	—
526	#547	—	2	1	no	—
527	#547	C₂²×C₇	1	2	yes	complemented
528	#546	—	2	2	no	—
529	#546	C₂²×C₇	1	2	yes	—
530	D₄²	—	2	2	no	—
531	D₄²	C₂²×C₇	1	2	yes	—
532	#544	C₂²×C₇	1	1	yes	characteristic, complemented
533	#539	—	2	2	no	—
534	#537	—	2	1	no	—
535	#537	C₂²×C₇	1	1	yes	characteristic
536	#537	C₂²×C₇	1	1	yes	characteristic, complemented
537	#535	—	2	1	no	—
538	#535	C₂²×C₇	1	1	yes	characteristic
539	#525	—	2	1	no	—
540	#525	—	2	2	no	—
541	#525	C₂²×C₇	1	1	yes	characteristic
542	#525	C₂²×C₇	1	1	yes	characteristic, complemented
543	C₂×#121	—	2	1	no	—
544	C₂×#121	C₂²×C₇	1	1	yes	characteristic
545	#520	C₂²×C₇	1	1	yes	characteristic
546	#520	C₂²×C₇	1	1	yes	characteristic, complemented
547	#520	C₂²×C₇	1	1	yes	characteristic, complemented
548	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic, complemented
549	#490	C₂²×C₇	1	2	yes	complemented
550	#489	C₂²×C₇	1	2	yes	complemented
551	#488	C₂²×C₇	1	2	yes	complemented
552	#486	C₂²×C₇	1	2	yes	complemented
553	#485	C₂²×C₇	1	2	yes	complemented
554	#484	C₂²×C₇	1	2	yes	complemented
555	#482	C₂²×C₇	1	2	yes	complemented
556	#480	C₂²×C₇	1	2	yes	complemented
557	#480	C₂²×C₇	1	2	yes	complemented
558	#480	C₂²×C₇	1	2	yes	complemented
559	#480	C₂²×C₇	1	2	yes	complemented
560	#480	C₂²×C₇	1	2	yes	complemented
561	#479	C₂²×C₇	1	2	yes	complemented
562	#478	C₂²×C₇	1	2	yes	complemented
563	#477	C₂²×C₇	1	2	yes	complemented
564	#474	C₂²×C₇	1	2	yes	complemented
565	#469	C₂²×C₇	1	2	yes	complemented
566	#468	C₂²×C₇	1	2	yes	complemented
567	#468	C₂²×C₇	1	2	yes	complemented
568	#468	C₂²×C₇	1	2	yes	complemented
569	#467	C₂²×C₇	1	2	yes	complemented
570	#466	C₂²×C₇	1	2	yes	complemented
571	#466	C₂²×C₇	1	2	yes	complemented
572	#465	C₂²×C₇	1	2	yes	complemented
573	#464	C₂²×C₇	1	2	yes	complemented
574	#463	C₂²×C₇	1	2	yes	complemented
575	#460	C₂²×C₇	1	2	yes	complemented
576	#459	C₂²×C₇	1	2	yes	complemented
577	#452	C₂²×C₇	1	1	yes	characteristic, complemented
578	#452	C₂²×C₇	1	2	yes	complemented
579	#452	C₂²×C₇	1	1	yes	characteristic, complemented
580	#451	C₂²×C₇	1	1	yes	characteristic, complemented
581	#450	C₂²×C₇	1	1	yes	characteristic, complemented
582	#450	C₂²×C₇	1	2	yes	complemented
583	#449	C₂²×C₇	1	1	yes	characteristic, complemented
584	#449	C₂²×C₇	1	1	yes	characteristic, complemented
585	#449	C₂²×C₇	1	2	yes	complemented
586	#448	C₂²×C₇	1	1	yes	characteristic, complemented
587	#447	C₂²×C₇	1	1	yes	characteristic, complemented
588	#447	C₂²×C₇	1	2	yes	complemented
589	#440	C₂²×C₇	1	2	yes	complemented
590	#440	C₂²×C₇	1	2	yes	complemented
591	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
592	C₄×D₈	C₂²×C₇	1	2	yes	complemented
593	#436	C₂²×C₇	1	2	yes	complemented
594	#435	C₂²×C₇	1	2	yes	complemented
595	#435	C₂²×C₇	1	2	yes	complemented
596	C₈×D₄	C₂²×C₇	1	2	yes	complemented
597	#428	C₂²×C₇	1	1	yes	characteristic, complemented
598	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
599	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
600	#424	C₂²×C₇	1	1	yes	characteristic, complemented
601	#418	C₂²×C₇	1	1	yes	characteristic, complemented
602	#418	C₂²×C₇	1	2	yes	complemented
603	#417	C₂²×C₇	1	1	yes	characteristic
604	#417	C₂²×C₇	1	1	yes	characteristic
605	#417	C₂²×C₇	1	2	yes	complemented
606	#417	C₂²×C₇	1	2	yes	complemented
607	#417	C₂²×C₇	1	1	yes	characteristic, complemented
608	#417	C₂²×C₇	1	1	yes	characteristic, complemented
609	#417	C₂²×C₇	1	2	yes	complemented
610	#417	C₂²×C₇	1	1	yes	characteristic, complemented
611	#416	C₂²×C₇	1	1	yes	characteristic
612	#416	C₂²×C₇	1	1	yes	characteristic, complemented
613	#416	C₂²×C₇	1	2	yes	complemented
614	C₂×#103	C₂²×C₇	1	2	yes	complemented
615	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
616	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
617	C₂×#102	C₂²×C₇	1	2	yes	complemented
618	C₂×#102	C₂²×C₇	1	2	yes	complemented
619	#408	C₂²×C₇	1	1	yes	characteristic, complemented
620	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
621	#405	C₂²×C₇	1	1	yes	characteristic, complemented
622	C₂³×C₇	—	2	2	no	—
623	C₂³×C₇	—	2	2	no	—
624	C₂³×C₇	—	2	1	no	—
625	C₂³×C₇	—	2	1	no	—
626	C₂³×C₇	—	2	2	no	—
627	C₂³×C₇	—	2	1	no	—
628	C₂³×C₇	—	4	1	no	—
629	C₂³×C₇	—	4	2	no	—
630	C₂³×C₇	—	4	4	no	—
631	C₂³×C₇	—	4	2	no	—
632	C₂³×C₇	—	4	2	no	—
633	C₂³×C₇	—	8	1	no	—
634	C₂³×C₇	—	8	1	no	—
635	C₂³×C₇	—	8	2	no	—
636	C₂³×C₇	—	8	1	no	—
637	C₂³×C₇	—	8	2	no	—
638	C₂³×C₇	C₂²×D₄	1	2	yes	—
639	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
640	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
641	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
642	C₇×Q₈	—	2	2	no	—
643	C₇×Q₈	—	2	1	no	—
644	C₇×Q₈	—	2	1	no	—
645	C₇×Q₈	—	2	1	no	—
646	C₇×Q₈	—	2	1	no	—
647	C₇×Q₈	—	2	1	no	—
648	C₇×Q₈	—	4	2	no	—
649	C₇×Q₈	—	8	2	no	—
650	C₇×Q₈	C₂×#41	1	2	yes	—
651	C₇×D₄	—	2	4	no	—
652	C₇×D₄	—	2	4	no	—
653	C₇×D₄	—	2	4	no	—
654	C₇×D₄	—	2	2	no	—
655	C₇×D₄	—	2	1	no	—
656	C₇×D₄	—	2	2	no	—
657	C₇×D₄	—	2	1	no	—
658	C₇×D₄	—	2	1	no	—
659	C₇×D₄	—	2	1	no	—
660	C₇×D₄	—	2	2	no	—
661	C₇×D₄	—	2	1	no	—
662	C₇×D₄	—	4	2	no	—
663	C₇×D₄	—	4	4	no	—
664	C₇×D₄	—	4	2	no	—
665	C₇×D₄	—	4	4	no	—
666	C₇×D₄	—	4	2	no	—
667	C₇×D₄	—	4	2	no	—
668	C₇×D₄	—	4	2	no	—
669	C₇×D₄	—	4	2	no	—
670	C₇×D₄	—	4	2	no	—
671	C₇×D₄	—	4	4	no	—
672	C₇×D₄	—	4	2	no	—
673	C₇×D₄	—	4	2	no	—
674	C₇×D₄	—	8	2	no	—
675	C₇×D₄	—	8	2	no	—
676	C₇×D₄	—	8	2	no	—
677	C₇×D₄	—	8	2	no	—
678	C₇×D₄	—	8	2	no	—
679	C₇×D₄	C₂×#41	1	2	yes	—
680	C₂×C₄×C₇	—	2	2	no	—
681	C₂×C₄×C₇	—	2	1	no	—
682	C₂×C₄×C₇	—	2	2	no	—
683	C₂×C₄×C₇	—	2	2	no	—
684	C₂×C₄×C₇	—	2	4	no	—
685	C₂×C₄×C₇	—	2	1	no	—
686	C₂×C₄×C₇	—	2	1	no	—
687	C₂×C₄×C₇	—	2	2	no	—
688	C₂×C₄×C₇	—	2	1	no	—
689	C₂×C₄×C₇	—	2	2	no	—
690	C₂×C₄×C₇	—	2	1	no	—
691	C₂×C₄×C₇	—	2	1	no	—
692	C₂×C₄×C₇	—	2	1	no	—
693	C₂×C₄×C₇	—	2	2	no	—
694	C₂×C₄×C₇	—	2	2	no	—
695	C₂×C₄×C₇	—	2	1	no	—
696	C₂×C₄×C₇	—	2	1	no	—
697	C₂×C₄×C₇	—	2	2	no	—
698	C₂×C₄×C₇	—	4	2	no	—
699	C₂×C₄×C₇	—	4	4	no	—
700	C₂×C₄×C₇	—	4	2	no	—
701	C₂×C₄×C₇	—	4	2	no	—
702	C₂×C₄×C₇	—	4	4	no	—
703	C₂×C₄×C₇	—	4	2	no	—
704	C₂×C₄×C₇	—	4	2	no	—
705	C₂×C₄×C₇	—	8	2	no	—
706	C₂×C₄×C₇	—	8	2	no	—
707	C₂×C₄×C₇	—	8	1	no	—
708	C₂×C₄×C₇	—	8	2	no	—
709	C₂×C₄×C₇	—	8	1	no	—
710	C₂×C₄×C₇	—	8	1	no	—
711	C₂×C₄×C₇	—	8	2	no	—
712	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
713	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
714	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
715	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
716	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
717	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
718	C₂×C₄×C₇	C₂×#41	1	2	yes	—
719	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
720	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
721	C₇×C₈	—	2	1	no	—
722	C₇×C₈	—	2	1	no	—
723	C₇×C₈	—	2	1	no	—
724	C₇×C₈	—	2	1	no	—
725	C₇×C₈	—	2	2	no	—
726	C₇×C₈	—	2	2	no	—
727	H(5,𝔽₂)	—	2	4	no	—
728	H(5,𝔽₂)	—	4	2	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	—	2	2	no	—
731	C₂×#41	—	2	1	no	—
732	C₂×#41	—	2	1	no	—
733	C₂×#41	—	2	4	no	—
734	C₂×#41	—	4	2	no	—
735	C₂×#41	C₂³×C₇	1	1	yes	characteristic
736	C₂×#41	C₂³×C₇	1	1	yes	characteristic
737	C₂×#41	C₂³×C₇	1	1	yes	characteristic
738	C₂×#41	C₂³×C₇	1	2	yes	—
739	C₂×#41	C₂³×C₇	1	1	yes	characteristic
740	C₂×#41	C₂³×C₇	1	1	yes	characteristic
741	C₂×#41	C₂³×C₇	1	1	yes	characteristic
742	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	—	2	1	no	—
745	C₂²×D₄	—	2	1	no	—
746	C₂²×D₄	—	2	2	no	—
747	C₂²×D₄	—	2	2	no	—
748	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
749	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
750	C₂²×D₄	C₂³×C₇	1	2	yes	—
751	C₂³×C₄	—	2	1	no	—
752	C₂³×C₄	—	2	1	no	—
753	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
754	AGL(1,ℤ/8)	—	4	2	no	—
755	#135	—	2	4	no	—
756	#135	—	4	2	no	—
757	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
758	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
759	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
760	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
761	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
762	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic
763	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
764	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
765	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
766	C₂×D₈	C₂³×C₇	1	2	yes	—
767	#131	—	4	2	no	—
768	C₂×M₁₆	—	4	2	no	—
769	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
770	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
771	C₂×M₁₆	C₂³×C₇	1	2	yes	—
772	C₂×M₁₆	C₂³×C₇	1	2	yes	—
773	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
774	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
775	C₂²×C₈	C₂³×C₇	1	2	yes	—
776	C₂²×C₈	C₂³×C₇	1	2	yes	—
777	C₄⋊Q₈	—	2	1	no	—
778	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
779	#127	—	2	2	no	—
780	#127	C₂³×C₇	1	2	yes	—
781	#126	—	2	2	no	—
782	#126	—	2	2	no	—
783	#125	—	2	2	no	—
784	#125	—	2	2	no	—
785	#125	—	2	1	no	—
786	#125	C₂³×C₇	1	2	yes	—
787	#124	—	2	2	no	—
788	#124	C₂³×C₇	1	2	yes	—
789	#123	—	2	2	no	—
790	#123	—	2	1	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	C₇×D₄	1	2	yes	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	2	no	—
799	C₂²⋊Q₈	—	2	2	no	—
800	C₂²⋊Q₈	—	2	2	no	—
801	C₂²⋊Q₈	—	2	2	no	—
802	C₂²⋊Q₈	—	2	2	no	—
803	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
804	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
805	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
806	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
807	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
808	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
809	#121	—	2	1	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	2	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	1	no	—
818	#121	—	2	1	no	—
819	#121	—	2	2	no	—
820	#121	—	2	2	no	—
821	#121	—	2	2	no	—
822	#121	—	2	2	no	—
823	#121	C₇×D₄	1	1	yes	characteristic
824	#121	C₇×D₄	1	1	yes	characteristic
825	#121	C₂³×C₇	1	2	yes	—
826	#121	C₂³×C₇	1	2	yes	—
827	#121	C₂³×C₇	1	1	yes	characteristic
828	#121	C₂³×C₇	1	1	yes	characteristic
829	#121	C₂³×C₇	1	2	yes	—
830	#121	C₂³×C₇	1	2	yes	—
831	#120	—	2	1	no	—
832	#120	—	2	2	no	—
833	#120	—	2	2	no	—
834	#120	—	2	2	no	—
835	#120	—	2	2	no	—
836	#120	C₇×D₄	1	2	yes	—
837	C₄×Q₈	—	2	1	no	—
838	C₄×Q₈	C₂³×C₇	1	2	yes	—
839	C₄×Q₈	C₂³×C₇	1	2	yes	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	2	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	2	no	—
847	C₄×D₄	—	2	2	no	—
848	C₄×D₄	—	2	2	no	—
849	C₄×D₄	—	2	2	no	—
850	C₄×D₄	C₂³×C₇	1	2	yes	—
851	C₄×D₄	C₂³×C₇	1	2	yes	—
852	C₄×D₄	C₂³×C₇	1	2	yes	—
853	C₄×D₄	C₂³×C₇	1	2	yes	—
854	#117	—	2	1	no	—
855	#117	—	2	1	no	—
856	#117	—	2	2	no	—
857	#117	C₂³×C₇	1	1	yes	characteristic
858	#117	C₂³×C₇	1	2	yes	—
859	#117	C₂³×C₇	1	1	yes	characteristic
860	C₂×C₄⋊C₄	—	2	1	no	—
861	C₂×C₄⋊C₄	—	2	1	no	—
862	C₂×C₄⋊C₄	—	2	1	no	—
863	C₂×C₄⋊C₄	—	2	1	no	—
864	C₂×C₄⋊C₄	—	2	1	no	—
865	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
866	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
867	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
868	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
869	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
870	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
871	C₂×C₂²⋊C₄	—	2	1	no	—
872	C₂×C₂²⋊C₄	—	2	2	no	—
873	#107	C₂³×C₇	1	2	yes	—
874	#107	C₂³×C₇	1	2	yes	—
875	#107	C₂³×C₇	1	2	yes	—
876	#107	C₂³×C₇	1	2	yes	—
877	#107	C₂³×C₇	1	2	yes	—
878	#106	C₂³×C₇	1	2	yes	—
879	C₄⋊C₈	C₂³×C₇	1	2	yes	—
880	C₄⋊C₈	C₂³×C₇	1	2	yes	—
881	#103	C₂³×C₇	1	2	yes	—
882	#103	C₂³×C₇	1	2	yes	—
883	#103	C₂³×C₇	1	2	yes	—
884	#103	C₂³×C₇	1	2	yes	—
885	#103	C₂³×C₇	1	1	yes	characteristic
886	#103	C₂³×C₇	1	1	yes	characteristic
887	#103	C₂³×C₇	1	1	yes	characteristic
888	#103	C₂³×C₇	1	1	yes	characteristic
889	#103	C₂³×C₇	1	2	yes	—
890	#102	C₂³×C₇	1	1	yes	characteristic
891	#102	C₂³×C₇	1	2	yes	—
892	#102	C₂³×C₇	1	2	yes	—
893	#102	C₂³×C₇	1	2	yes	—
894	#102	C₂³×C₇	1	2	yes	—
895	#102	C₂³×C₇	1	2	yes	—
896	#102	C₂³×C₇	1	2	yes	—
897	#102	C₂³×C₇	1	2	yes	—
898	#102	C₂³×C₇	1	2	yes	—
899	#102	C₂³×C₇	1	2	yes	—
900	#102	C₂³×C₇	1	1	yes	characteristic
901	#102	C₂³×C₇	1	2	yes	—
902	#102	C₂³×C₇	1	1	yes	characteristic
903	#102	C₂³×C₇	1	1	yes	characteristic
904	#102	C₂³×C₇	1	2	yes	—
905	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
906	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
907	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
908	C₂²⋊C₈	C₂³×C₇	1	1	yes	characteristic
909	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
910	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
911	#97	C₂³×C₇	1	2	yes	—
912	C₄×C₈	C₂³×C₇	1	2	yes	—
913	C₂²×C₇	—	2	1	no	—
914	C₂²×C₇	—	2	1	no	—
915	C₂²×C₇	—	2	1	no	—
916	C₂²×C₇	—	2	1	no	—
917	C₂²×C₇	—	2	1	no	—
918	C₂²×C₇	—	2	2	no	—
919	C₂²×C₇	—	2	1	no	—
920	C₂²×C₇	—	2	2	no	—
921	C₂²×C₇	—	2	2	no	—
922	C₂²×C₇	—	2	1	no	—
923	C₂²×C₇	—	2	2	no	—
924	C₂²×C₇	—	4	4	no	—
925	C₂²×C₇	—	4	1	no	—
926	C₂²×C₇	—	4	1	no	—
927	C₂²×C₇	—	4	1	no	—
928	C₂²×C₇	—	4	1	no	—
929	C₂²×C₇	—	4	2	no	—
930	C₂²×C₇	—	4	1	no	—
931	C₂²×C₇	—	4	2	no	—
932	C₂²×C₇	—	4	1	no	—
933	C₂²×C₇	—	4	1	no	—
934	C₂²×C₇	—	4	2	no	—
935	C₂²×C₇	—	4	1	no	—
936	C₂²×C₇	—	8	4	no	—
937	C₂²×C₇	—	16	2	no	—
938	C₂²×C₇	—	16	4	no	—
939	C₂²×C₇	#546	1	2	yes	—
940	C₂²×C₇	#576	1	2	yes	—
941	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
942	C₄×C₇	—	2	2	no	—
943	C₄×C₇	—	2	1	no	—
944	C₄×C₇	—	2	1	no	—
945	C₄×C₇	—	2	2	no	—
946	C₄×C₇	—	2	2	no	—
947	C₄×C₇	—	2	2	no	—
948	C₄×C₇	—	4	1	no	—
949	C₄×C₇	—	4	1	no	—
950	C₄×C₇	—	4	1	no	—
951	C₄×C₇	—	4	2	no	—
952	C₄×C₇	—	4	2	no	—
953	C₄×C₇	—	4	2	no	—
954	C₄×C₇	—	4	1	no	—
955	C₄×C₇	#546	1	2	yes	—
956	C₄×C₇	C₂²×#41	1	1	yes	characteristic
957	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
958	C₂⁴	—	2	1	no	—
959	C₂⁴	—	2	2	no	—
960	C₂⁴	—	2	1	no	—
961	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
962	#41	—	2	2	no	—
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	2	2	no	—
966	#41	—	2	4	no	—
967	#41	—	2	2	no	—
968	#41	—	2	2	no	—
969	#41	—	2	2	no	—
970	#41	—	2	2	no	—
971	#41	—	2	2	no	—
972	#41	—	4	4	no	—
973	#41	—	4	1	no	—
974	#41	—	4	1	no	—
975	#41	—	4	2	no	—
976	#41	—	4	4	no	—
977	#41	—	4	4	no	—
978	#41	—	8	4	no	—
979	#41	C₇×#41	1	4	yes	complemented
980	C₂×Q₈	—	2	1	no	—
981	C₂×Q₈	—	2	2	no	—
982	C₂×Q₈	—	2	2	no	—
983	C₂×Q₈	—	4	1	no	—
984	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
985	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
986	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
987	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	4	no	—
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	2	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	2	1	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	1	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	2	no	—
1001	C₂×D₄	—	2	2	no	—
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	2	no	—
1008	C₂×D₄	—	2	2	no	—
1009	C₂×D₄	—	4	1	no	—
1010	C₂×D₄	—	4	2	no	—
1011	C₂×D₄	—	4	4	no	—
1012	C₂×D₄	—	4	8	no	—
1013	C₂×D₄	—	4	4	no	—
1014	C₂×D₄	—	8	4	no	—
1015	C₂×D₄	—	8	2	no	—
1016	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1017	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1018	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1019	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1020	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1021	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1022	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1023	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	2	no	—
1027	C₂²×C₄	—	2	2	no	—
1028	C₂²×C₄	—	2	1	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	2	no	—
1034	C₂²×C₄	—	2	1	no	—
1035	C₂²×C₄	—	2	1	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	2	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	4	4	no	—
1042	C₂²×C₄	—	8	2	no	—
1043	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1044	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1045	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1046	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1047	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1048	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1049	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1050	Q₁₆	—	2	2	no	—
1051	Q₁₆	—	4	1	no	—
1052	SD₁₆	—	2	2	no	—
1053	SD₁₆	—	2	2	no	—
1054	SD₁₆	—	4	1	no	—
1055	SD₁₆	—	4	1	no	—
1056	SD₁₆	—	4	2	no	—
1057	D₈	—	2	2	no	—
1058	D₈	—	4	1	no	—
1059	D₈	—	4	2	no	—
1060	M₁₆	—	2	2	no	—
1061	M₁₆	—	2	2	no	—
1062	M₁₆	—	4	2	no	—
1063	M₁₆	—	4	2	no	—
1064	C₂×C₈	—	2	2	no	—
1065	C₂×C₈	—	2	2	no	—
1066	C₂×C₈	—	4	2	no	—
1067	C₂×C₈	—	4	2	no	—
1068	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1069	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1070	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1071	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1072	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1073	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	2	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	—	2	2	no	—
1083	C₄⋊C₄	—	2	2	no	—
1084	C₄⋊C₄	—	2	2	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	2	no	—
1087	C₄⋊C₄	—	2	2	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1090	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1091	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1092	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1093	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1094	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1095	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1096	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1097	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	1	no	—
1100	C₂²⋊C₄	—	2	1	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	2	no	—
1107	C₂²⋊C₄	—	2	2	no	—
1108	C₂²⋊C₄	—	2	2	no	—
1109	C₂²⋊C₄	—	2	2	no	—
1110	C₂²⋊C₄	—	2	2	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1115	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1116	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1117	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1118	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1119	C₄²	—	2	2	no	—
1120	C₄²	—	2	2	no	—
1121	C₄²	—	2	2	no	—
1122	C₄²	—	2	1	no	—
1123	C₄²	C₂⁴×C₇	1	2	yes	—
1124	C₂×C₇	—	2	2	no	—
1125	C₂×C₇	—	2	2	no	—
1126	C₂×C₇	—	4	1	no	—
1127	C₂×C₇	—	4	2	no	—
1128	C₂×C₇	—	4	2	no	—
1129	C₂×C₇	—	8	1	no	—
1130	C₂×C₇	—	8	1	no	—
1131	C₂×C₇	—	8	2	no	—
1132	C₂×C₇	C₂×#546	1	1	yes	characteristic
1133	C₂×C₇	C₂×#576	1	1	yes	characteristic
1134	C₂×C₇	#3586	1	1	yes	characteristic
1135	C₂³	—	2	1	no	—
1136	C₂³	—	2	2	no	—
1137	C₂³	—	2	2	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	2	2	no	—
1140	C₂³	—	2	1	no	—
1141	C₂³	—	4	1	no	—
1142	C₂³	—	4	2	no	—
1143	C₂³	—	4	4	no	—
1144	C₂³	—	4	2	no	—
1145	C₂³	—	4	2	no	—
1146	C₂³	—	8	1	no	—
1147	C₂³	—	8	1	no	—
1148	C₂³	—	8	2	no	—
1149	C₂³	—	8	1	no	—
1150	C₂³	—	8	2	no	—
1151	C₂³	C₂²×C₇×D₄	1	2	yes	—
1152	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1153	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1154	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1155	Q₈	—	2	1	no	—
1156	Q₈	—	2	2	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	2	1	no	—
1160	Q₈	—	2	1	no	—
1161	Q₈	—	4	2	no	—
1162	Q₈	—	8	2	no	—
1163	Q₈	C₂×C₇×#41	1	2	yes	—
1164	D₄	—	2	4	no	—
1165	D₄	—	2	4	no	—
1166	D₄	—	2	4	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	2	1	no	—
1172	D₄	—	2	2	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	2	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	4	4	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	4	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	2	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	4	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	2	no	—
1190	D₄	—	8	2	no	—
1191	D₄	—	8	2	no	—
1192	D₄	C₂×C₇×#41	1	2	yes	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	2	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	4	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	2	no	—
1207	C₂×C₄	—	2	2	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	4	no	—
1213	C₂×C₄	—	4	2	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	4	4	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	8	2	no	—
1219	C₂×C₄	—	8	2	no	—
1220	C₂×C₄	—	8	1	no	—
1221	C₂×C₄	—	8	2	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	—	8	1	no	—
1224	C₂×C₄	—	8	2	no	—
1225	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1226	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1227	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1228	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1229	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1230	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1231	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1232	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1233	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1234	C₈	—	2	1	no	—
1235	C₈	—	2	1	no	—
1236	C₈	—	2	1	no	—
1237	C₈	—	2	1	no	—
1238	C₈	—	2	2	no	—
1239	C₈	—	2	2	no	—
1240	C₇	#61191	1	1	yes	characteristic, direct product factor, Sylow
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	2	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	2	2	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	2	no	—
1251	C₂²	—	2	2	no	—
1252	C₂²	—	4	4	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	1	no	—
1255	C₂²	—	4	1	no	—
1256	C₂²	—	4	2	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	1	no	—
1260	C₂²	—	4	2	no	—
1261	C₂²	—	4	1	no	—
1262	C₂²	—	4	2	no	—
1263	C₂²	—	4	1	no	—
1264	C₂²	—	8	4	no	—
1265	C₂²	—	16	2	no	—
1266	C₂²	—	16	4	no	—
1267	C₂²	C₇×#546	1	2	yes	—
1268	C₂²	C₇×#576	1	2	yes	—
1269	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1270	C₄	—	2	2	no	—
1271	C₄	—	2	2	no	—
1272	C₄	—	2	1	no	—
1273	C₄	—	2	1	no	—
1274	C₄	—	2	2	no	—
1275	C₄	—	2	2	no	—
1276	C₄	—	4	2	no	—
1277	C₄	—	4	2	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	1	no	—
1280	C₄	—	4	1	no	—
1281	C₄	—	4	1	no	—
1282	C₄	—	4	1	no	—
1283	C₄	C₇×#546	1	2	yes	—
1284	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1285	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1286	C₂	—	2	2	no	—
1287	C₂	—	2	2	no	—
1288	C₂	—	4	1	no	—
1289	C₂	—	4	2	no	—
1290	C₂	—	4	2	no	—
1291	C₂	—	8	1	no	—
1292	C₂	—	8	2	no	—
1293	C₂	—	8	1	no	—
1294	C₂	C₂×C₇×#546	1	1	yes	characteristic
1295	C₂	C₂×C₇×#576	1	1	yes	characteristic
1296	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3492	C₂	semidirect
2. C₇×#3488	C₂	semidirect
3. C₇×#3333	C₂	semidirect
4. C₇×#3322	C₂	semidirect
5. C₇×#3314	C₂	semidirect
6. C₇×#3310	C₂	semidirect
7. C₇×#3309	C₂	semidirect
8. C₇×#3308	C₂	semidirect
9. C₇×#3300	C₂	semidirect
10. C₇×#3294	C₂	semidirect
11. C₇×#3136	C₂	semidirect
12. C₇×#3098	C₂	semidirect
13. C₂×C₇×#480	C₂	semidirect
14. C₇×#3083	C₂	semidirect
15. C₇×#3061	C₂	semidirect
16. C₇×#3055	C₂	semidirect
17. C₇×#3045	C₂	semidirect
18. C₇×#3012	C₂	semidirect
19. C₇×#3002	C₂	semidirect
20. C₇×#2951	C₂	semidirect
21. C₇×#2933	C₂	semidirect
22. C₇×#2897	C₂	semidirect
23. C₂×C₇×#417	C₂	semidirect
26. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂×C₇×#135	C₂²	semidirect
29. C₂×C₇×#131	C₂²	semidirect
30. C₂²×C₇×M₁₆	C₂²	semidirect
32. C₇×#554	C₂²	semidirect
34. C₇×#553	C₂²	semidirect
36. C₇×#552	C₂²	semidirect
40. C₇×#547	C₂²	semidirect
45. C₇×#544	C₂²	semidirect
49. C₇×#537	C₂²	semidirect
55. C₇×#525	C₂²	semidirect
59. C₇×#520	C₂²	semidirect
60. C₇×#520	C₂²	semidirect
61. C₂²×C₇×C₄⋊C₄	C₂²	semidirect
62. C₇×#490	C₂²	semidirect
63. C₇×#489	C₂²	semidirect
64. C₇×#488	C₂²	semidirect
65. C₇×#486	C₂²	semidirect
66. C₇×#485	C₂²	semidirect
67. C₇×#484	C₂²	semidirect
68. C₇×#482	C₂²	semidirect
69. C₇×#480	C₂²	semidirect
70. C₇×#480	C₂²	semidirect
71. C₇×#480	C₂²	semidirect
72. C₇×#480	C₂²	semidirect
73. C₇×#480	C₂²	semidirect
74. C₇×#479	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#477	C₂²	semidirect
77. C₇×#474	C₂²	semidirect
78. C₇×#469	C₂²	semidirect
79. C₇×#468	C₂²	semidirect
80. C₇×#468	C₂²	semidirect
81. C₇×#468	C₂²	semidirect
82. C₇×#467	C₂²	semidirect
83. C₇×#466	C₂²	semidirect
84. C₇×#466	C₂²	semidirect
85. C₇×#465	C₂²	semidirect
86. C₇×#464	C₂²	semidirect
87. C₇×#463	C₂²	semidirect
88. C₇×#460	C₂²	semidirect
89. C₇×#459	C₂²	semidirect
90. C₇×#452	C₂²	semidirect
91. C₇×#452	C₂²	semidirect
92. C₇×#452	C₂²	semidirect
93. C₇×#451	C₂²	semidirect
94. C₇×#450	C₂²	semidirect
95. C₇×#450	C₂²	semidirect
96. C₇×#449	C₂²	semidirect
97. C₇×#449	C₂²	semidirect
98. C₇×#449	C₂²	semidirect
99. C₇×#448	C₂²	semidirect
100. C₇×#447	C₂²	semidirect
101. C₇×#447	C₂²	semidirect
102. C₇×#440	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₄×C₇×Q₁₆	C₂²	semidirect
105. C₄×C₇×D₈	C₂²	semidirect
106. C₇×#436	C₂²	semidirect
107. C₇×#435	C₂²	semidirect
108. C₇×#435	C₂²	semidirect
109. C₇×C₈×D₄	C₂²	semidirect
110. C₇×#428	C₂²	semidirect
111. C₂×C₇×#107	C₂²	semidirect
112. C₂×C₇×#107	C₂²	semidirect
113. C₇×#424	C₂²	semidirect
114. C₇×#418	C₂²	semidirect
115. C₇×#418	C₂²	semidirect
118. C₇×#417	C₂²	semidirect
119. C₇×#417	C₂²	semidirect
120. C₇×#417	C₂²	semidirect
121. C₇×#417	C₂²	semidirect
122. C₇×#417	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
125. C₇×#416	C₂²	semidirect
126. C₇×#416	C₂²	semidirect
127. C₂×C₇×#103	C₂²	semidirect
128. C₂×C₇×#102	C₂²	semidirect
129. C₂×C₇×#102	C₂²	semidirect
130. C₂×C₇×#102	C₂²	semidirect
131. C₂×C₇×#102	C₂²	semidirect
132. C₇×#408	C₂²	semidirect
133. C₂×C₇×C₂²⋊C₈	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #61191	C₇	direct (N × H)
322. #3492	C₂×C₇	semidirect
323. #3488	C₂×C₇	semidirect
324. #3333	C₂×C₇	semidirect
325. #3322	C₂×C₇	semidirect
326. #3314	C₂×C₇	semidirect
327. #3310	C₂×C₇	semidirect
328. #3309	C₂×C₇	semidirect
329. #3308	C₂×C₇	semidirect
330. #3300	C₂×C₇	semidirect
331. #3294	C₂×C₇	semidirect
332. #3136	C₂×C₇	semidirect
333. #3098	C₂×C₇	semidirect
334. C₂×#480	C₂×C₇	semidirect
335. #3083	C₂×C₇	semidirect
336. #3061	C₂×C₇	semidirect
337. #3055	C₂×C₇	semidirect
338. #3045	C₂×C₇	semidirect
339. #3012	C₂×C₇	semidirect
340. #3002	C₂×C₇	semidirect
341. #2951	C₂×C₇	semidirect
342. #2933	C₂×C₇	semidirect
343. #2897	C₂×C₇	semidirect
344. C₂×#417	C₂×C₇	semidirect
366. C₇×#41	#41	semidirect
513. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
515. C₂×#135	C₂²×C₇	semidirect
516. C₂×#131	C₂²×C₇	semidirect
517. C₂²×M₁₆	C₂²×C₇	semidirect
519. #554	C₂²×C₇	semidirect
521. #553	C₂²×C₇	semidirect
523. #552	C₂²×C₇	semidirect
527. #547	C₂²×C₇	semidirect
532. #544	C₂²×C₇	semidirect
536. #537	C₂²×C₇	semidirect
542. #525	C₂²×C₇	semidirect
546. #520	C₂²×C₇	semidirect
547. #520	C₂²×C₇	semidirect
548. C₂²×C₄⋊C₄	C₂²×C₇	semidirect
549. #490	C₂²×C₇	semidirect
550. #489	C₂²×C₇	semidirect
551. #488	C₂²×C₇	semidirect
552. #486	C₂²×C₇	semidirect
553. #485	C₂²×C₇	semidirect
554. #484	C₂²×C₇	semidirect
555. #482	C₂²×C₇	semidirect
556. #480	C₂²×C₇	semidirect
557. #480	C₂²×C₇	semidirect
558. #480	C₂²×C₇	semidirect
559. #480	C₂²×C₇	semidirect
560. #480	C₂²×C₇	semidirect
561. #479	C₂²×C₇	semidirect
562. #478	C₂²×C₇	semidirect
563. #477	C₂²×C₇	semidirect
564. #474	C₂²×C₇	semidirect
565. #469	C₂²×C₇	semidirect
566. #468	C₂²×C₇	semidirect
567. #468	C₂²×C₇	semidirect
568. #468	C₂²×C₇	semidirect
569. #467	C₂²×C₇	semidirect
570. #466	C₂²×C₇	semidirect
571. #466	C₂²×C₇	semidirect
572. #465	C₂²×C₇	semidirect
573. #464	C₂²×C₇	semidirect
574. #463	C₂²×C₇	semidirect
575. #460	C₂²×C₇	semidirect
576. #459	C₂²×C₇	semidirect
577. #452	C₂²×C₇	semidirect
578. #452	C₂²×C₇	semidirect
579. #452	C₂²×C₇	semidirect
580. #451	C₂²×C₇	semidirect
581. #450	C₂²×C₇	semidirect
582. #450	C₂²×C₇	semidirect
583. #449	C₂²×C₇	semidirect
584. #449	C₂²×C₇	semidirect
585. #449	C₂²×C₇	semidirect
586. #448	C₂²×C₇	semidirect
587. #447	C₂²×C₇	semidirect
588. #447	C₂²×C₇	semidirect
589. #440	C₂²×C₇	semidirect
590. #440	C₂²×C₇	semidirect
591. C₄×Q₁₆	C₂²×C₇	semidirect
592. C₄×D₈	C₂²×C₇	semidirect
593. #436	C₂²×C₇	semidirect
594. #435	C₂²×C₇	semidirect
595. #435	C₂²×C₇	semidirect
596. C₈×D₄	C₂²×C₇	semidirect
597. #428	C₂²×C₇	semidirect
598. C₂×#107	C₂²×C₇	semidirect
599. C₂×#107	C₂²×C₇	semidirect
600. #424	C₂²×C₇	semidirect
601. #418	C₂²×C₇	semidirect
602. #418	C₂²×C₇	semidirect
605. #417	C₂²×C₇	semidirect
606. #417	C₂²×C₇	semidirect
607. #417	C₂²×C₇	semidirect
608. #417	C₂²×C₇	semidirect
609. #417	C₂²×C₇	semidirect
610. #417	C₂²×C₇	semidirect
612. #416	C₂²×C₇	semidirect
613. #416	C₂²×C₇	semidirect
614. C₂×#103	C₂²×C₇	semidirect
615. C₂×#102	C₂²×C₇	semidirect
616. C₂×#102	C₂²×C₇	semidirect
617. C₂×#102	C₂²×C₇	semidirect
618. C₂×#102	C₂²×C₇	semidirect
619. #408	C₂²×C₇	semidirect
620. C₂×C₂²⋊C₈	C₂²×C₇	semidirect
621. #405	C₂²×C₇	semidirect
979. #41	C₇×#41	semidirect
1240. C₇	#61191	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×#3492	2
C₇×#3488	2
C₇×#3333	2
C₇×#3322	2
C₇×#3314	2
C₇×#3310	2
C₇×#3309	2
C₇×#3308	2
C₇×#3300	2
C₇×#3294	2
C₇×#3136	2
C₇×#3098	2
C₂×C₇×#480	2
C₇×#3083	2
C₇×#3061	2
C₇×#3055	2
C₇×#3045	2
C₇×#3012	2
C₇×#3002	2
C₇×#2951	2
C₇×#2933	2
C₇×#2897	2
C₂×C₇×#417	2
#61191	7

Subgroups — C7×#61191 #13238407

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61191 #13238407