Subgroups — C₇×#61175 #13238391

Order 1792.

2230 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3493	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3484	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3325	C₂	1	2	yes	maximal, complemented
4	C₇×#3324	C₂	1	2	yes	maximal, complemented
5	C₇×#3323	C₂	1	2	yes	maximal, complemented
6	C₇×#3322	C₂	1	2	yes	maximal, complemented
7	C₇×#3319	C₂	1	2	yes	maximal, complemented
8	C₇×#3318	C₂	1	2	yes	maximal, complemented
9	C₇×#3311	C₂	1	2	yes	maximal, complemented
10	C₇×#3310	C₂	1	2	yes	maximal, complemented
11	C₇×#3136	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3093	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3054	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×#3003	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#418	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
25	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
26	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
27	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
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×#556	—	2	1	no	—
32	C₇×#556	C₂²	1	2	yes	complemented
33	C₇×#555	—	2	1	no	—
34	C₇×#555	C₂²	1	2	yes	complemented
35	C₇×#553	—	2	1	no	—
36	C₇×#553	C₂²	1	2	yes	complemented
37	C₇×#552	—	2	1	no	—
38	C₇×#552	C₂²	1	2	yes	complemented
39	C₇×#546	—	2	1	no	—
40	C₇×#546	—	2	1	no	—
41	C₇×#546	C₂²	1	2	yes	—
42	C₇×#546	C₂²	1	2	yes	—
43	C₇×D₄²	—	2	1	no	—
44	C₇×D₄²	—	2	1	no	—
45	C₇×D₄²	C₂²	1	2	yes	—
46	C₇×D₄²	C₂²	1	2	yes	—
47	C₇×#544	C₂²	1	1	yes	characteristic, complemented
48	C₇×#538	—	2	2	no	—
49	C₇×#537	C₂²	1	1	yes	characteristic, complemented
50	C₇×#535	C₂²	1	1	yes	characteristic
51	C₇×#535	C₂²	1	1	yes	characteristic
52	C₇×#534	—	2	2	no	—
53	C₇×#529	—	2	2	no	—
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₇×#525	C₂²	1	1	yes	characteristic
56	C₇×#525	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₇×#120	—	2	2	no	—
58	C₇×#520	C₂²	1	1	yes	characteristic, complemented
59	C₇×#520	C₂²	1	1	yes	characteristic, complemented
60	C₇×#518	C₂²	1	1	yes	characteristic
61	C₂×C₇×#117	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×#485	C₂²	1	2	yes	complemented
68	C₇×#482	C₂²	1	2	yes	complemented
69	C₇×#482	C₂²	1	2	yes	complemented
70	C₇×#482	C₂²	1	2	yes	complemented
71	C₇×#482	C₂²	1	2	yes	complemented
72	C₇×#481	C₂²	1	2	yes	complemented
73	C₇×#480	C₂²	1	2	yes	complemented
74	C₇×#478	C₂²	1	2	yes	complemented
75	C₇×#478	C₂²	1	2	yes	complemented
76	C₇×#476	C₂²	1	2	yes	complemented
77	C₇×#474	C₂²	1	2	yes	complemented
78	C₇×#470	C₂²	1	1	yes	characteristic, complemented
79	C₇×#470	C₂²	1	1	yes	characteristic, complemented
80	C₇×#469	C₂²	1	2	yes	complemented
81	C₇×#469	C₂²	1	1	yes	characteristic, complemented
82	C₇×#469	C₂²	1	1	yes	characteristic, complemented
83	C₇×#468	C₂²	1	2	yes	complemented
84	C₇×#468	C₂²	1	1	yes	characteristic, complemented
85	C₇×#468	C₂²	1	1	yes	characteristic, complemented
86	C₇×#468	C₂²	1	1	yes	characteristic, complemented
87	C₇×#468	C₂²	1	1	yes	characteristic, complemented
88	C₇×#466	C₂²	1	2	yes	complemented
89	C₇×#465	C₂²	1	2	yes	complemented
90	C₇×#464	C₂²	1	2	yes	complemented
91	C₇×#463	C₂²	1	2	yes	complemented
92	C₇×#460	C₂²	1	2	yes	complemented
93	C₇×#459	C₂²	1	2	yes	complemented
94	C₇×#452	C₂²	1	2	yes	complemented
95	C₇×#450	C₂²	1	2	yes	complemented
96	C₇×#450	C₂²	1	2	yes	complemented
97	C₇×#450	C₂²	1	2	yes	complemented
98	C₇×#449	C₂²	1	2	yes	complemented
99	C₇×#447	C₂²	1	2	yes	complemented
100	C₇×#447	C₂²	1	2	yes	complemented
101	C₇×#447	C₂²	1	2	yes	complemented
102	C₇×#442	C₂²	1	2	yes	complemented
103	C₇×#440	C₂²	1	2	yes	complemented
104	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
105	C₄×C₇×D₈	C₂²	1	2	yes	complemented
106	C₇×#436	C₂²	1	2	yes	complemented
107	C₇×#436	C₂²	1	2	yes	complemented
108	C₇×#435	C₂²	1	2	yes	complemented
109	C₇×#435	C₂²	1	2	yes	complemented
110	C₇×#428	C₂²	1	1	yes	characteristic, complemented
111	C₇×#428	C₂²	1	1	yes	characteristic, complemented
112	C₇×#427	C₂²	1	1	yes	characteristic, complemented
113	C₇×#424	C₂²	1	1	yes	characteristic, complemented
114	C₇×#418	C₂²	1	1	yes	characteristic
115	C₇×#418	C₂²	1	1	yes	characteristic, complemented
116	C₇×#418	C₂²	1	2	yes	complemented
117	C₇×#418	C₂²	1	2	yes	complemented
118	C₇×#418	C₂²	1	2	yes	complemented
119	C₇×#418	C₂²	1	2	yes	complemented
120	C₇×#418	C₂²	1	2	yes	complemented
121	C₇×#417	C₂²	1	2	yes	complemented
122	C₇×#417	C₂²	1	1	yes	characteristic, complemented
123	C₇×#417	C₂²	1	1	yes	characteristic, complemented
124	C₇×#416	C₂²	1	2	yes	complemented
125	C₇×#416	C₂²	1	1	yes	characteristic, complemented
126	C₇×#416	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₇×#102	C₂²	1	1	yes	characteristic
128	C₂×C₇×#102	C₂²	1	1	yes	characteristic
129	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₇×#102	C₂²	1	1	yes	characteristic, complemented
131	C₂×C₇×#102	C₂²	1	2	yes	complemented
132	C₇×#408	C₂²	1	1	yes	characteristic, complemented
133	C₇×#407	C₂²	1	1	yes	characteristic, complemented
134	C₇×#405	C₂²	1	1	yes	characteristic, complemented
135	#61175	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂⁵×C₇	—	2	1	no	—
137	C₇×H(5,𝔽₂)	—	2	4	no	—
138	C₇×H(5,𝔽₂)	—	4	2	no	—
139	C₂×C₇×#41	—	2	1	no	—
140	C₂×C₇×#41	C₂³	1	1	yes	characteristic
141	C₂×C₇×#41	C₂³	1	1	yes	characteristic
142	C₂×C₇×#41	C₂³	1	2	yes	—
143	C₂×C₇×#41	C₂³	1	1	yes	characteristic
144	C₂²×C₇×D₄	—	2	4	no	—
145	C₂²×C₇×D₄	—	2	2	no	—
146	C₂²×C₇×D₄	—	2	1	no	—
147	C₂²×C₇×D₄	—	2	2	no	—
148	C₂²×C₇×D₄	—	2	2	no	—
149	C₂²×C₇×D₄	—	2	1	no	—
150	C₂²×C₇×D₄	—	2	1	no	—
151	C₂²×C₇×D₄	—	2	1	no	—
152	C₂²×C₇×D₄	—	4	2	no	—
153	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
154	C₂²×C₇×D₄	C₂³	1	2	yes	—
155	C₂²×C₇×D₄	C₂³	1	2	yes	—
156	C₂²×C₇×D₄	C₂³	1	2	yes	—
157	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
158	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
159	C₇×AGL(1,ℤ/8)	—	2	4	no	—
160	C₇×AGL(1,ℤ/8)	—	4	2	no	—
161	C₇×#135	—	4	2	no	—
162	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic, complemented
163	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
164	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
165	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic, complemented
166	C₂×C₇×SD₁₆	C₂³	1	1	yes	characteristic, complemented
167	C₂×C₇×D₈	C₂³	1	2	yes	—
168	C₂×C₇×D₈	C₂³	1	2	yes	—
169	C₂×C₇×D₈	C₂³	1	1	yes	characteristic, complemented
170	C₇×#131	—	4	2	no	—
171	C₂×C₇×M₁₆	—	4	2	no	—
172	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
173	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
174	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
175	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
176	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
177	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
178	C₂×C₇×M₁₆	C₂³	1	2	yes	complemented
179	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
180	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
181	C₂²×C₇×C₈	C₂³	1	2	yes	complemented
182	C₇×C₄⋊Q₈	—	2	1	no	—
183	C₇×C₄⋊Q₈	C₂³	1	2	yes	complemented
184	C₇×#127	—	2	1	no	—
185	C₇×#127	C₂³	1	2	yes	—
186	C₇×#126	—	2	2	no	—
187	C₇×#126	—	2	2	no	—
188	C₇×#126	—	2	2	no	—
189	C₇×#126	—	2	2	no	—
190	C₇×#125	—	2	2	no	—
191	C₇×#125	—	2	1	no	—
192	C₇×#125	C₂³	1	2	yes	complemented
193	C₇×#124	—	2	1	no	—
194	C₇×#124	—	2	2	no	—
195	C₇×#124	—	2	2	no	—
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	1	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	2	no	—
207	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
208	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
212	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	complemented
214	C₇×#121	—	2	2	no	—
215	C₇×#121	—	2	1	no	—
216	C₇×#121	—	2	2	no	—
217	C₇×#121	—	2	2	no	—
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	1	no	—
221	C₇×#121	—	2	1	no	—
222	C₇×#121	—	2	2	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	D₄	1	1	yes	characteristic
225	C₇×#121	D₄	1	1	yes	characteristic
226	C₇×#121	C₂³	1	2	yes	—
227	C₇×#121	C₂³	1	1	yes	characteristic
228	C₇×#121	C₂³	1	1	yes	characteristic
229	C₇×#121	C₂³	1	1	yes	characteristic
230	C₇×#121	C₂³	1	1	yes	characteristic
231	C₇×#121	C₂³	1	2	yes	—
232	C₇×#121	C₂³	1	2	yes	complemented
233	C₇×#120	—	2	1	no	—
234	C₇×#120	—	2	1	no	—
235	C₇×#120	—	2	2	no	—
236	C₇×#120	—	2	2	no	—
237	C₇×#120	—	2	2	no	—
238	C₇×#120	—	2	2	no	—
239	C₇×#120	—	2	2	no	—
240	C₇×#120	—	2	2	no	—
241	C₇×#120	—	2	2	no	—
242	C₇×#120	—	2	2	no	—
243	C₇×#120	D₄	1	2	yes	—
244	C₄×C₇×Q₈	—	2	1	no	—
245	C₄×C₇×Q₈	—	2	2	no	—
246	C₄×C₇×Q₈	C₂³	1	2	yes	complemented
247	C₄×C₇×D₄	—	2	2	no	—
248	C₄×C₇×D₄	—	2	1	no	—
249	C₄×C₇×D₄	—	2	1	no	—
250	C₄×C₇×D₄	—	2	1	no	—
251	C₄×C₇×D₄	—	2	1	no	—
252	C₄×C₇×D₄	—	2	1	no	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	2	no	—
256	C₄×C₇×D₄	—	2	2	no	—
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₄×C₇×D₄	C₂³	1	2	yes	—
259	C₄×C₇×D₄	C₂³	1	2	yes	—
260	C₄×C₇×D₄	C₂³	1	2	yes	—
261	C₄×C₇×D₄	C₂³	1	2	yes	complemented
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	—	2	2	no	—
266	C₇×#117	—	2	2	no	—
267	C₇×#117	C₂³	1	2	yes	—
268	C₇×#117	C₂³	1	2	yes	—
269	C₇×#117	C₂³	1	1	yes	characteristic
270	C₇×#117	C₂³	1	1	yes	characteristic
271	C₇×#117	C₂³	1	1	yes	characteristic
272	C₇×#117	C₂³	1	2	yes	complemented
273	C₂×C₇×C₄⋊C₄	—	2	1	no	—
274	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
275	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
276	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	complemented
277	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
280	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₄²×C₇	—	2	1	no	—
282	C₇×#107	C₂³	1	2	yes	complemented
283	C₇×#107	C₂³	1	1	yes	characteristic, complemented
284	C₇×#107	C₂³	1	1	yes	characteristic, complemented
285	C₇×#107	C₂³	1	2	yes	complemented
286	C₇×#106	C₂³	1	1	yes	characteristic, complemented
287	C₇×#106	C₂³	1	1	yes	characteristic, complemented
288	C₇×#106	C₂³	1	2	yes	complemented
289	C₇×#106	C₂³	1	2	yes	complemented
290	C₇×C₄⋊C₈	C₂³	1	2	yes	complemented
291	C₇×C₄⋊C₈	C₂³	1	2	yes	complemented
292	C₇×#103	C₂³	1	1	yes	characteristic, complemented
293	C₇×#103	C₂³	1	1	yes	characteristic, complemented
294	C₇×#103	C₂³	1	1	yes	characteristic, complemented
295	C₇×#103	C₂³	1	1	yes	characteristic, complemented
296	C₇×#103	C₂³	1	2	yes	complemented
297	C₇×#103	C₂³	1	2	yes	complemented
298	C₇×#102	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	2	yes	—
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	2	yes	—
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	1	yes	characteristic, complemented
311	C₇×#102	C₂³	1	1	yes	characteristic, complemented
312	C₇×#102	C₂³	1	1	yes	characteristic, complemented
313	C₇×#102	C₂³	1	1	yes	characteristic, complemented
314	C₇×#102	C₂³	1	2	yes	complemented
315	C₇×#102	C₂³	1	2	yes	complemented
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
318	C₇×C₂²⋊C₈	C₂³	1	2	yes	complemented
319	C₇×C₂²⋊C₈	C₂³	1	2	yes	complemented
320	C₇×#97	C₂³	1	2	yes	complemented
321	C₄×C₇×C₈	C₂³	1	2	yes	complemented
322	#3493	C₂×C₇	1	1	yes	characteristic, complemented
323	#3484	C₂×C₇	1	1	yes	characteristic, complemented
324	#3325	C₂×C₇	1	2	yes	complemented
325	#3324	C₂×C₇	1	2	yes	complemented
326	#3323	C₂×C₇	1	2	yes	complemented
327	#3322	C₂×C₇	1	2	yes	complemented
328	#3319	C₂×C₇	1	2	yes	complemented
329	#3318	C₂×C₇	1	2	yes	complemented
330	#3311	C₂×C₇	1	2	yes	complemented
331	#3310	C₂×C₇	1	2	yes	complemented
332	#3136	C₂×C₇	1	1	yes	characteristic, complemented
333	#3096	C₂×C₇	1	1	yes	characteristic, complemented
334	#3093	C₂×C₇	1	1	yes	characteristic, complemented
335	#3081	C₂×C₇	1	1	yes	characteristic, complemented
336	#3062	C₂×C₇	1	1	yes	characteristic, complemented
337	#3054	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	#3003	C₂×C₇	1	1	yes	characteristic, complemented
341	#2946	C₂×C₇	1	1	yes	characteristic, complemented
342	#2930	C₂×C₇	1	1	yes	characteristic, complemented
343	#2897	C₂×C₇	1	1	yes	characteristic, complemented
344	C₂×#418	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	1	no	—
346	C₂⁴×C₇	—	2	2	no	—
347	C₂⁴×C₇	—	2	2	no	—
348	C₂⁴×C₇	—	2	1	no	—
349	C₂⁴×C₇	—	2	2	no	—
350	C₂⁴×C₇	—	4	4	no	—
351	C₂⁴×C₇	—	8	2	no	—
352	C₂⁴×C₇	—	8	2	no	—
353	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
354	C₇×#41	—	2	2	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	2	4	no	—
357	C₇×#41	—	2	2	no	—
358	C₇×#41	—	2	2	no	—
359	C₇×#41	—	2	2	no	—
360	C₇×#41	—	2	2	no	—
361	C₇×#41	—	4	2	no	—
362	C₇×#41	—	4	4	no	—
363	C₂×C₇×Q₈	—	2	2	no	—
364	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
365	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
366	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
367	C₂×C₇×D₄	—	2	4	no	—
368	C₂×C₇×D₄	—	2	4	no	—
369	C₂×C₇×D₄	—	2	4	no	—
370	C₂×C₇×D₄	—	2	1	no	—
371	C₂×C₇×D₄	—	2	1	no	—
372	C₂×C₇×D₄	—	2	1	no	—
373	C₂×C₇×D₄	—	2	1	no	—
374	C₂×C₇×D₄	—	2	2	no	—
375	C₂×C₇×D₄	—	2	1	no	—
376	C₂×C₇×D₄	—	2	1	no	—
377	C₂×C₇×D₄	—	2	2	no	—
378	C₂×C₇×D₄	—	2	2	no	—
379	C₂×C₇×D₄	—	2	2	no	—
380	C₂×C₇×D₄	—	2	1	no	—
381	C₂×C₇×D₄	—	2	2	no	—
382	C₂×C₇×D₄	—	2	2	no	—
383	C₂×C₇×D₄	—	2	2	no	—
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	2	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	2	no	—
390	C₂×C₇×D₄	—	4	2	no	—
391	C₂×C₇×D₄	—	4	2	no	—
392	C₂×C₇×D₄	—	4	2	no	—
393	C₂×C₇×D₄	—	4	4	no	—
394	C₂×C₇×D₄	—	4	4	no	—
395	C₂×C₇×D₄	—	4	4	no	—
396	C₂×C₇×D₄	—	4	4	no	—
397	C₂×C₇×D₄	—	4	8	no	—
398	C₂×C₇×D₄	—	8	4	no	—
399	C₂×C₇×D₄	—	8	4	no	—
400	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
401	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
402	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
403	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
404	C₂×C₇×D₄	#41	1	4	yes	—
405	C₂×C₇×D₄	C₂⁴	1	2	yes	—
406	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
407	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
408	C₂×C₇×D₄	C₂⁴	1	2	yes	—
409	C₂²×C₄×C₇	—	2	2	no	—
410	C₂²×C₄×C₇	—	2	2	no	—
411	C₂²×C₄×C₇	—	2	1	no	—
412	C₂²×C₄×C₇	—	2	1	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	2	no	—
418	C₂²×C₄×C₇	—	2	2	no	—
419	C₂²×C₄×C₇	—	2	2	no	—
420	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
421	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
422	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
423	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
424	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
425	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
426	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
427	C₇×Q₁₆	—	4	1	no	—
428	C₇×SD₁₆	—	2	4	no	—
429	C₇×SD₁₆	—	4	2	no	—
430	C₇×SD₁₆	—	4	1	no	—
431	C₇×SD₁₆	—	4	1	no	—
432	C₇×D₈	—	2	4	no	—
433	C₇×D₈	—	4	2	no	—
434	C₇×D₈	—	4	1	no	—
435	C₇×M₁₆	—	2	2	no	—
436	C₇×M₁₆	—	2	2	no	—
437	C₇×M₁₆	—	4	1	no	—
438	C₇×M₁₆	—	4	1	no	—
439	C₇×M₁₆	—	4	1	no	—
440	C₇×M₁₆	—	4	1	no	—
441	C₇×M₁₆	—	4	2	no	—
442	C₂×C₇×C₈	—	2	2	no	—
443	C₂×C₇×C₈	—	2	2	no	—
444	C₂×C₇×C₈	—	4	2	no	—
445	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
446	C₂×C₇×C₈	C₂⁴	1	2	yes	—
447	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
448	C₂×C₇×C₈	C₂⁴	1	2	yes	—
449	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
450	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
451	C₇×C₄⋊C₄	—	2	1	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	—	2	1	no	—
454	C₇×C₄⋊C₄	—	2	2	no	—
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	2	no	—
457	C₇×C₄⋊C₄	—	2	2	no	—
458	C₇×C₄⋊C₄	—	2	1	no	—
459	C₇×C₄⋊C₄	—	2	1	no	—
460	C₇×C₄⋊C₄	—	2	1	no	—
461	C₇×C₄⋊C₄	—	2	2	no	—
462	C₇×C₄⋊C₄	—	2	2	no	—
463	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
464	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
465	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
466	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
467	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
468	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
469	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
470	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
471	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
472	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
473	C₇×C₂²⋊C₄	—	2	1	no	—
474	C₇×C₂²⋊C₄	—	2	1	no	—
475	C₇×C₂²⋊C₄	—	2	1	no	—
476	C₇×C₂²⋊C₄	—	2	2	no	—
477	C₇×C₂²⋊C₄	—	2	2	no	—
478	C₇×C₂²⋊C₄	—	2	2	no	—
479	C₇×C₂²⋊C₄	—	2	1	no	—
480	C₇×C₂²⋊C₄	—	2	2	no	—
481	C₇×C₂²⋊C₄	—	2	1	no	—
482	C₇×C₂²⋊C₄	—	2	1	no	—
483	C₇×C₂²⋊C₄	—	2	2	no	—
484	C₇×C₂²⋊C₄	—	2	2	no	—
485	C₇×C₂²⋊C₄	—	2	2	no	—
486	C₇×C₂²⋊C₄	—	2	2	no	—
487	C₇×C₂²⋊C₄	—	2	2	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	1	no	—
493	C₇×C₂²⋊C₄	—	2	1	no	—
494	C₇×C₂²⋊C₄	—	2	1	no	—
495	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
496	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
497	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
498	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
499	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
500	C₄²×C₇	—	2	2	no	—
501	C₄²×C₇	—	2	2	no	—
502	C₄²×C₇	—	2	2	no	—
503	C₄²×C₇	—	2	2	no	—
504	C₄²×C₇	—	2	1	no	—
505	C₄²×C₇	—	2	1	no	—
506	C₄²×C₇	C₂⁴	1	2	yes	—
507	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
508	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
509	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
510	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic, complemented
511	C₂×#135	C₂²×C₇	1	1	yes	characteristic, complemented
512	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
513	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic, complemented
514	#556	—	2	1	no	—
515	#556	C₂²×C₇	1	2	yes	complemented
516	#555	—	2	1	no	—
517	#555	C₂²×C₇	1	2	yes	complemented
518	#553	—	2	1	no	—
519	#553	C₂²×C₇	1	2	yes	complemented
520	#552	—	2	1	no	—
521	#552	C₂²×C₇	1	2	yes	complemented
522	#546	—	2	1	no	—
523	#546	—	2	1	no	—
524	#546	C₂²×C₇	1	2	yes	—
525	#546	C₂²×C₇	1	2	yes	—
526	D₄²	—	2	1	no	—
527	D₄²	—	2	1	no	—
528	D₄²	C₂²×C₇	1	2	yes	—
529	D₄²	C₂²×C₇	1	2	yes	—
530	#544	C₂²×C₇	1	1	yes	characteristic, complemented
531	#538	—	2	2	no	—
532	#537	C₂²×C₇	1	1	yes	characteristic, complemented
533	#535	C₂²×C₇	1	1	yes	characteristic
534	#535	C₂²×C₇	1	1	yes	characteristic
535	#534	—	2	2	no	—
536	#529	—	2	2	no	—
537	#525	C₂²×C₇	1	1	yes	characteristic
538	#525	C₂²×C₇	1	1	yes	characteristic
539	#525	C₂²×C₇	1	1	yes	characteristic, complemented
540	C₂×#120	—	2	2	no	—
541	#520	C₂²×C₇	1	1	yes	characteristic, complemented
542	#520	C₂²×C₇	1	1	yes	characteristic, complemented
543	#518	C₂²×C₇	1	1	yes	characteristic
544	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
545	#490	C₂²×C₇	1	2	yes	complemented
546	#489	C₂²×C₇	1	2	yes	complemented
547	#488	C₂²×C₇	1	2	yes	complemented
548	#486	C₂²×C₇	1	2	yes	complemented
549	#485	C₂²×C₇	1	2	yes	complemented
550	#485	C₂²×C₇	1	2	yes	complemented
551	#482	C₂²×C₇	1	2	yes	complemented
552	#482	C₂²×C₇	1	2	yes	complemented
553	#482	C₂²×C₇	1	2	yes	complemented
554	#482	C₂²×C₇	1	2	yes	complemented
555	#481	C₂²×C₇	1	2	yes	complemented
556	#480	C₂²×C₇	1	2	yes	complemented
557	#478	C₂²×C₇	1	2	yes	complemented
558	#478	C₂²×C₇	1	2	yes	complemented
559	#476	C₂²×C₇	1	2	yes	complemented
560	#474	C₂²×C₇	1	2	yes	complemented
561	#470	C₂²×C₇	1	1	yes	characteristic, complemented
562	#470	C₂²×C₇	1	1	yes	characteristic, complemented
563	#469	C₂²×C₇	1	2	yes	complemented
564	#469	C₂²×C₇	1	1	yes	characteristic, complemented
565	#469	C₂²×C₇	1	1	yes	characteristic, complemented
566	#468	C₂²×C₇	1	2	yes	complemented
567	#468	C₂²×C₇	1	1	yes	characteristic, complemented
568	#468	C₂²×C₇	1	1	yes	characteristic, complemented
569	#468	C₂²×C₇	1	1	yes	characteristic, complemented
570	#468	C₂²×C₇	1	1	yes	characteristic, 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	2	yes	complemented
578	#450	C₂²×C₇	1	2	yes	complemented
579	#450	C₂²×C₇	1	2	yes	complemented
580	#450	C₂²×C₇	1	2	yes	complemented
581	#449	C₂²×C₇	1	2	yes	complemented
582	#447	C₂²×C₇	1	2	yes	complemented
583	#447	C₂²×C₇	1	2	yes	complemented
584	#447	C₂²×C₇	1	2	yes	complemented
585	#442	C₂²×C₇	1	2	yes	complemented
586	#440	C₂²×C₇	1	2	yes	complemented
587	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
588	C₄×D₈	C₂²×C₇	1	2	yes	complemented
589	#436	C₂²×C₇	1	2	yes	complemented
590	#436	C₂²×C₇	1	2	yes	complemented
591	#435	C₂²×C₇	1	2	yes	complemented
592	#435	C₂²×C₇	1	2	yes	complemented
593	#428	C₂²×C₇	1	1	yes	characteristic, complemented
594	#428	C₂²×C₇	1	1	yes	characteristic, complemented
595	#427	C₂²×C₇	1	1	yes	characteristic, complemented
596	#424	C₂²×C₇	1	1	yes	characteristic, complemented
597	#418	C₂²×C₇	1	1	yes	characteristic
598	#418	C₂²×C₇	1	1	yes	characteristic, complemented
599	#418	C₂²×C₇	1	2	yes	complemented
600	#418	C₂²×C₇	1	2	yes	complemented
601	#418	C₂²×C₇	1	2	yes	complemented
602	#418	C₂²×C₇	1	2	yes	complemented
603	#418	C₂²×C₇	1	2	yes	complemented
604	#417	C₂²×C₇	1	2	yes	complemented
605	#417	C₂²×C₇	1	1	yes	characteristic, complemented
606	#417	C₂²×C₇	1	1	yes	characteristic, complemented
607	#416	C₂²×C₇	1	2	yes	complemented
608	#416	C₂²×C₇	1	1	yes	characteristic, complemented
609	#416	C₂²×C₇	1	1	yes	characteristic, complemented
610	C₂×#102	C₂²×C₇	1	1	yes	characteristic
611	C₂×#102	C₂²×C₇	1	1	yes	characteristic
612	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
613	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
614	C₂×#102	C₂²×C₇	1	2	yes	complemented
615	#408	C₂²×C₇	1	1	yes	characteristic, complemented
616	#407	C₂²×C₇	1	1	yes	characteristic, complemented
617	#405	C₂²×C₇	1	1	yes	characteristic, complemented
618	C₂³×C₇	—	2	2	no	—
619	C₂³×C₇	—	2	2	no	—
620	C₂³×C₇	—	2	4	no	—
621	C₂³×C₇	—	2	1	no	—
622	C₂³×C₇	—	2	2	no	—
623	C₂³×C₇	—	2	1	no	—
624	C₂³×C₇	—	4	1	no	—
625	C₂³×C₇	—	4	1	no	—
626	C₂³×C₇	—	4	4	no	—
627	C₂³×C₇	—	4	4	no	—
628	C₂³×C₇	—	4	4	no	—
629	C₂³×C₇	—	4	4	no	—
630	C₂³×C₇	—	4	4	no	—
631	C₂³×C₇	—	4	2	no	—
632	C₂³×C₇	—	8	1	no	—
633	C₂³×C₇	—	8	1	no	—
634	C₂³×C₇	—	8	1	no	—
635	C₂³×C₇	—	8	1	no	—
636	C₂³×C₇	—	8	2	no	—
637	C₂³×C₇	—	8	2	no	—
638	C₂³×C₇	—	8	2	no	—
639	C₂³×C₇	—	8	2	no	—
640	C₂³×C₇	—	8	16	no	—
641	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
642	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
643	C₂³×C₇	C₂²×D₄	1	2	yes	—
644	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
645	C₇×Q₈	—	2	2	no	—
646	C₇×Q₈	—	2	1	no	—
647	C₇×Q₈	—	2	1	no	—
648	C₇×Q₈	—	2	1	no	—
649	C₇×Q₈	—	2	1	no	—
650	C₇×Q₈	—	8	2	no	—
651	C₇×D₄	—	2	4	no	—
652	C₇×D₄	—	2	4	no	—
653	C₇×D₄	—	2	2	no	—
654	C₇×D₄	—	2	1	no	—
655	C₇×D₄	—	2	2	no	—
656	C₇×D₄	—	2	1	no	—
657	C₇×D₄	—	2	2	no	—
658	C₇×D₄	—	2	1	no	—
659	C₇×D₄	—	2	2	no	—
660	C₇×D₄	—	2	1	no	—
661	C₇×D₄	—	4	2	no	—
662	C₇×D₄	—	4	2	no	—
663	C₇×D₄	—	4	4	no	—
664	C₇×D₄	—	4	4	no	—
665	C₇×D₄	—	4	4	no	—
666	C₇×D₄	—	4	4	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	2	no	—
672	C₇×D₄	—	8	2	no	—
673	C₇×D₄	—	8	2	no	—
674	C₇×D₄	—	8	1	no	—
675	C₇×D₄	—	8	2	no	—
676	C₇×D₄	—	8	1	no	—
677	C₇×D₄	—	8	2	no	—
678	C₇×D₄	—	8	2	no	—
679	C₇×D₄	C₂×#41	1	4	yes	—
680	C₂×C₄×C₇	—	2	2	no	—
681	C₂×C₄×C₇	—	2	2	no	—
682	C₂×C₄×C₇	—	2	2	no	—
683	C₂×C₄×C₇	—	2	1	no	—
684	C₂×C₄×C₇	—	2	1	no	—
685	C₂×C₄×C₇	—	2	2	no	—
686	C₂×C₄×C₇	—	2	2	no	—
687	C₂×C₄×C₇	—	2	1	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	2	no	—
693	C₂×C₄×C₇	—	2	1	no	—
694	C₂×C₄×C₇	—	2	1	no	—
695	C₂×C₄×C₇	—	2	1	no	—
696	C₂×C₄×C₇	—	2	1	no	—
697	C₂×C₄×C₇	—	4	4	no	—
698	C₂×C₄×C₇	—	4	2	no	—
699	C₂×C₄×C₇	—	4	2	no	—
700	C₂×C₄×C₇	—	8	2	no	—
701	C₂×C₄×C₇	—	8	2	no	—
702	C₂×C₄×C₇	—	8	2	no	—
703	C₂×C₄×C₇	—	8	1	no	—
704	C₂×C₄×C₇	—	8	2	no	—
705	C₂×C₄×C₇	—	8	1	no	—
706	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
707	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
708	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
709	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
710	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
711	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
712	C₂×C₄×C₇	C₂×#41	1	2	yes	—
713	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
714	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
715	C₇×C₈	—	2	2	no	—
716	C₇×C₈	—	2	1	no	—
717	C₇×C₈	—	2	1	no	—
718	C₇×C₈	—	2	1	no	—
719	C₇×C₈	—	2	1	no	—
720	C₇×C₈	—	2	2	no	—
721	C₂⁵	—	2	1	no	—
722	H(5,𝔽₂)	—	2	4	no	—
723	H(5,𝔽₂)	—	4	2	no	—
724	C₂×#41	—	2	1	no	—
725	C₂×#41	C₂³×C₇	1	1	yes	characteristic
726	C₂×#41	C₂³×C₇	1	1	yes	characteristic
727	C₂×#41	C₂³×C₇	1	2	yes	—
728	C₂×#41	C₂³×C₇	1	1	yes	characteristic
729	C₂²×D₄	—	2	4	no	—
730	C₂²×D₄	—	2	2	no	—
731	C₂²×D₄	—	2	1	no	—
732	C₂²×D₄	—	2	2	no	—
733	C₂²×D₄	—	2	2	no	—
734	C₂²×D₄	—	2	1	no	—
735	C₂²×D₄	—	2	1	no	—
736	C₂²×D₄	—	2	1	no	—
737	C₂²×D₄	—	4	2	no	—
738	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
739	C₂²×D₄	C₂³×C₇	1	2	yes	—
740	C₂²×D₄	C₂³×C₇	1	2	yes	—
741	C₂²×D₄	C₂³×C₇	1	2	yes	—
742	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
743	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
744	AGL(1,ℤ/8)	—	2	4	no	—
745	AGL(1,ℤ/8)	—	4	2	no	—
746	#135	—	4	2	no	—
747	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic, complemented
748	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
750	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic, complemented
751	C₂×SD₁₆	C₂³×C₇	1	1	yes	characteristic, complemented
752	C₂×D₈	C₂³×C₇	1	2	yes	—
753	C₂×D₈	C₂³×C₇	1	2	yes	—
754	C₂×D₈	C₂³×C₇	1	1	yes	characteristic, complemented
755	#131	—	4	2	no	—
756	C₂×M₁₆	—	4	2	no	—
757	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
758	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
759	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
760	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
761	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
762	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
763	C₂×M₁₆	C₂³×C₇	1	2	yes	complemented
764	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
765	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
766	C₂²×C₈	C₂³×C₇	1	2	yes	complemented
767	C₄⋊Q₈	—	2	1	no	—
768	C₄⋊Q₈	C₂³×C₇	1	2	yes	complemented
769	#127	—	2	1	no	—
770	#127	C₂³×C₇	1	2	yes	—
771	#126	—	2	2	no	—
772	#126	—	2	2	no	—
773	#126	—	2	2	no	—
774	#126	—	2	2	no	—
775	#125	—	2	2	no	—
776	#125	—	2	1	no	—
777	#125	C₂³×C₇	1	2	yes	complemented
778	#124	—	2	1	no	—
779	#124	—	2	2	no	—
780	#124	—	2	2	no	—
781	#124	—	2	2	no	—
782	#124	C₂³×C₇	1	2	yes	—
783	#123	—	2	2	no	—
784	#123	—	2	1	no	—
785	#123	—	2	1	no	—
786	#123	—	2	2	no	—
787	#123	—	2	2	no	—
788	#123	—	2	2	no	—
789	#123	C₇×D₄	1	2	yes	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	2	no	—
792	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
793	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
794	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
795	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
796	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
797	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
798	C₂²⋊Q₈	C₂³×C₇	1	2	yes	complemented
799	#121	—	2	2	no	—
800	#121	—	2	1	no	—
801	#121	—	2	2	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	no	—
807	#121	—	2	2	no	—
808	#121	—	2	2	no	—
809	#121	C₇×D₄	1	1	yes	characteristic
810	#121	C₇×D₄	1	1	yes	characteristic
811	#121	C₂³×C₇	1	1	yes	characteristic
812	#121	C₂³×C₇	1	1	yes	characteristic
813	#121	C₂³×C₇	1	1	yes	characteristic
814	#121	C₂³×C₇	1	1	yes	characteristic
815	#121	C₂³×C₇	1	2	yes	—
816	#121	C₂³×C₇	1	2	yes	—
817	#121	C₂³×C₇	1	2	yes	complemented
818	#120	—	2	1	no	—
819	#120	—	2	1	no	—
820	#120	—	2	2	no	—
821	#120	—	2	2	no	—
822	#120	—	2	2	no	—
823	#120	—	2	2	no	—
824	#120	—	2	2	no	—
825	#120	—	2	2	no	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	#120	C₇×D₄	1	2	yes	—
829	C₄×Q₈	—	2	1	no	—
830	C₄×Q₈	—	2	2	no	—
831	C₄×Q₈	C₂³×C₇	1	2	yes	complemented
832	C₄×D₄	—	2	2	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	1	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	1	no	—
839	C₄×D₄	—	2	1	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	C₂³×C₇	1	2	yes	—
843	C₄×D₄	C₂³×C₇	1	2	yes	—
844	C₄×D₄	C₂³×C₇	1	2	yes	—
845	C₄×D₄	C₂³×C₇	1	2	yes	—
846	C₄×D₄	C₂³×C₇	1	2	yes	complemented
847	#117	—	2	1	no	—
848	#117	—	2	1	no	—
849	#117	—	2	1	no	—
850	#117	—	2	2	no	—
851	#117	—	2	2	no	—
852	#117	C₂³×C₇	1	2	yes	—
853	#117	C₂³×C₇	1	2	yes	—
854	#117	C₂³×C₇	1	1	yes	characteristic
855	#117	C₂³×C₇	1	1	yes	characteristic
856	#117	C₂³×C₇	1	1	yes	characteristic
857	#117	C₂³×C₇	1	2	yes	complemented
858	C₂×C₄⋊C₄	—	2	1	no	—
859	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
860	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
861	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	complemented
862	C₂×C₂²⋊C₄	—	2	1	no	—
863	C₂×C₂²⋊C₄	—	2	2	no	—
864	C₂×C₂²⋊C₄	—	2	2	no	—
865	C₂×C₂²⋊C₄	—	2	2	no	—
866	C₂×C₄²	—	2	1	no	—
867	#107	C₂³×C₇	1	1	yes	characteristic, complemented
868	#107	C₂³×C₇	1	1	yes	characteristic, complemented
869	#107	C₂³×C₇	1	2	yes	complemented
870	#107	C₂³×C₇	1	2	yes	complemented
871	#106	C₂³×C₇	1	1	yes	characteristic, complemented
872	#106	C₂³×C₇	1	1	yes	characteristic, complemented
873	#106	C₂³×C₇	1	2	yes	complemented
874	#106	C₂³×C₇	1	2	yes	complemented
875	C₄⋊C₈	C₂³×C₇	1	2	yes	complemented
876	C₄⋊C₈	C₂³×C₇	1	2	yes	complemented
877	#103	C₂³×C₇	1	1	yes	characteristic, complemented
878	#103	C₂³×C₇	1	2	yes	complemented
879	#103	C₂³×C₇	1	1	yes	characteristic, complemented
880	#103	C₂³×C₇	1	1	yes	characteristic, complemented
881	#103	C₂³×C₇	1	1	yes	characteristic, complemented
882	#103	C₂³×C₇	1	2	yes	complemented
883	#102	C₂³×C₇	1	2	yes	—
884	#102	C₂³×C₇	1	2	yes	—
885	#102	C₂³×C₇	1	2	yes	—
886	#102	C₂³×C₇	1	2	yes	—
887	#102	C₂³×C₇	1	2	yes	—
888	#102	C₂³×C₇	1	2	yes	—
889	#102	C₂³×C₇	1	2	yes	—
890	#102	C₂³×C₇	1	2	yes	—
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	1	yes	characteristic, complemented
896	#102	C₂³×C₇	1	2	yes	complemented
897	#102	C₂³×C₇	1	1	yes	characteristic, complemented
898	#102	C₂³×C₇	1	1	yes	characteristic, complemented
899	#102	C₂³×C₇	1	1	yes	characteristic, complemented
900	#102	C₂³×C₇	1	2	yes	complemented
901	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₇	1	2	yes	complemented
904	C₂²⋊C₈	C₂³×C₇	1	2	yes	complemented
905	#97	C₂³×C₇	1	2	yes	complemented
906	C₄×C₈	C₂³×C₇	1	2	yes	complemented
907	C₂²×C₇	—	2	1	no	—
908	C₂²×C₇	—	2	1	no	—
909	C₂²×C₇	—	2	2	no	—
910	C₂²×C₇	—	2	1	no	—
911	C₂²×C₇	—	2	1	no	—
912	C₂²×C₇	—	2	2	no	—
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	2	no	—
918	C₂²×C₇	—	2	4	no	—
919	C₂²×C₇	—	4	4	no	—
920	C₂²×C₇	—	4	2	no	—
921	C₂²×C₇	—	4	2	no	—
922	C₂²×C₇	—	4	1	no	—
923	C₂²×C₇	—	4	1	no	—
924	C₂²×C₇	—	4	1	no	—
925	C₂²×C₇	—	4	1	no	—
926	C₂²×C₇	—	4	2	no	—
927	C₂²×C₇	—	4	2	no	—
928	C₂²×C₇	—	4	1	no	—
929	C₂²×C₇	—	4	1	no	—
930	C₂²×C₇	—	4	2	no	—
931	C₂²×C₇	—	8	4	no	—
932	C₂²×C₇	—	8	4	no	—
933	C₂²×C₇	—	8	8	no	—
934	C₂²×C₇	—	8	8	no	—
935	C₂²×C₇	—	16	4	no	—
936	C₂²×C₇	#546	1	2	yes	—
937	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
938	C₄×C₇	—	2	2	no	—
939	C₄×C₇	—	2	2	no	—
940	C₄×C₇	—	2	1	no	—
941	C₄×C₇	—	2	1	no	—
942	C₄×C₇	—	2	2	no	—
943	C₄×C₇	—	4	2	no	—
944	C₄×C₇	—	4	1	no	—
945	C₄×C₇	—	4	1	no	—
946	C₄×C₇	—	4	1	no	—
947	C₄×C₇	—	4	2	no	—
948	C₄×C₇	—	4	1	no	—
949	C₄×C₇	—	4	1	no	—
950	C₄×C₇	—	4	1	no	—
951	C₄×C₇	#546	1	2	yes	—
952	C₄×C₇	C₂²×#41	1	1	yes	characteristic
953	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
954	C₂⁴	—	2	1	no	—
955	C₂⁴	—	2	2	no	—
956	C₂⁴	—	2	2	no	—
957	C₂⁴	—	2	1	no	—
958	C₂⁴	—	2	2	no	—
959	C₂⁴	—	4	4	no	—
960	C₂⁴	—	8	2	no	—
961	C₂⁴	—	8	2	no	—
962	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	2	4	no	—
966	#41	—	2	2	no	—
967	#41	—	2	2	no	—
968	#41	—	2	2	no	—
969	#41	—	2	2	no	—
970	#41	—	4	2	no	—
971	#41	—	4	4	no	—
972	C₂×Q₈	—	2	2	no	—
973	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
974	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
975	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
976	C₂×D₄	—	2	4	no	—
977	C₂×D₄	—	2	4	no	—
978	C₂×D₄	—	2	4	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	1	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	2	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	2	no	—
989	C₂×D₄	—	2	1	no	—
990	C₂×D₄	—	2	2	no	—
991	C₂×D₄	—	2	2	no	—
992	C₂×D₄	—	2	2	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	2	no	—
995	C₂×D₄	—	2	2	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	4	2	no	—
1000	C₂×D₄	—	4	2	no	—
1001	C₂×D₄	—	4	2	no	—
1002	C₂×D₄	—	4	4	no	—
1003	C₂×D₄	—	4	4	no	—
1004	C₂×D₄	—	4	4	no	—
1005	C₂×D₄	—	4	4	no	—
1006	C₂×D₄	—	4	8	no	—
1007	C₂×D₄	—	8	4	no	—
1008	C₂×D₄	—	8	4	no	—
1009	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1010	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1011	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1012	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1013	C₂×D₄	C₇×#41	1	4	yes	—
1014	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1015	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1016	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1017	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1018	C₂²×C₄	—	2	2	no	—
1019	C₂²×C₄	—	2	2	no	—
1020	C₂²×C₄	—	2	1	no	—
1021	C₂²×C₄	—	2	1	no	—
1022	C₂²×C₄	—	2	2	no	—
1023	C₂²×C₄	—	2	2	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	2	no	—
1027	C₂²×C₄	—	2	2	no	—
1028	C₂²×C₄	—	2	2	no	—
1029	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1030	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1031	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1032	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1033	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1034	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
1035	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1036	Q₁₆	—	4	1	no	—
1037	SD₁₆	—	2	4	no	—
1038	SD₁₆	—	4	2	no	—
1039	SD₁₆	—	4	1	no	—
1040	SD₁₆	—	4	1	no	—
1041	D₈	—	2	4	no	—
1042	D₈	—	4	2	no	—
1043	D₈	—	4	1	no	—
1044	M₁₆	—	2	2	no	—
1045	M₁₆	—	2	2	no	—
1046	M₁₆	—	4	1	no	—
1047	M₁₆	—	4	1	no	—
1048	M₁₆	—	4	1	no	—
1049	M₁₆	—	4	1	no	—
1050	M₁₆	—	4	2	no	—
1051	C₂×C₈	—	2	2	no	—
1052	C₂×C₈	—	2	2	no	—
1053	C₂×C₈	—	4	2	no	—
1054	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1055	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1056	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1057	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1058	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1059	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1060	C₄⋊C₄	—	2	1	no	—
1061	C₄⋊C₄	—	2	2	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	2	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	2	no	—
1066	C₄⋊C₄	—	2	2	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	2	no	—
1071	C₄⋊C₄	—	2	2	no	—
1072	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1073	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1074	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1075	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1076	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1077	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1078	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1079	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1080	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1081	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	1	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	2	no	—
1087	C₂²⋊C₄	—	2	2	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	2	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	1	no	—
1103	C₂²⋊C₄	—	2	1	no	—
1104	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1105	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1106	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1107	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1108	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1109	C₄²	—	2	2	no	—
1110	C₄²	—	2	2	no	—
1111	C₄²	—	2	2	no	—
1112	C₄²	—	2	2	no	—
1113	C₄²	—	2	1	no	—
1114	C₄²	—	2	1	no	—
1115	C₄²	C₂⁴×C₇	1	2	yes	—
1116	C₂×C₇	—	2	2	no	—
1117	C₂×C₇	—	4	1	no	—
1118	C₂×C₇	—	4	1	no	—
1119	C₂×C₇	—	4	2	no	—
1120	C₂×C₇	—	4	4	no	—
1121	C₂×C₇	—	8	1	no	—
1122	C₂×C₇	—	8	2	no	—
1123	C₂×C₇	—	8	1	no	—
1124	C₂×C₇	C₂×#546	1	1	yes	characteristic
1125	C₂×C₇	#3585	1	1	yes	characteristic
1126	C₂×C₇	#3585	1	1	yes	characteristic
1127	C₂³	—	2	2	no	—
1128	C₂³	—	2	2	no	—
1129	C₂³	—	2	4	no	—
1130	C₂³	—	2	1	no	—
1131	C₂³	—	2	2	no	—
1132	C₂³	—	2	1	no	—
1133	C₂³	—	4	1	no	—
1134	C₂³	—	4	1	no	—
1135	C₂³	—	4	4	no	—
1136	C₂³	—	4	4	no	—
1137	C₂³	—	4	4	no	—
1138	C₂³	—	4	4	no	—
1139	C₂³	—	4	4	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	8	1	no	—
1142	C₂³	—	8	1	no	—
1143	C₂³	—	8	1	no	—
1144	C₂³	—	8	1	no	—
1145	C₂³	—	8	2	no	—
1146	C₂³	—	8	2	no	—
1147	C₂³	—	8	2	no	—
1148	C₂³	—	8	2	no	—
1149	C₂³	—	8	16	no	—
1150	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1151	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1152	C₂³	C₂²×C₇×D₄	1	2	yes	—
1153	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1154	Q₈	—	2	2	no	—
1155	Q₈	—	2	1	no	—
1156	Q₈	—	2	1	no	—
1157	Q₈	—	2	1	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	8	2	no	—
1160	D₄	—	2	4	no	—
1161	D₄	—	2	1	no	—
1162	D₄	—	2	2	no	—
1163	D₄	—	2	1	no	—
1164	D₄	—	2	2	no	—
1165	D₄	—	2	1	no	—
1166	D₄	—	2	2	no	—
1167	D₄	—	2	1	no	—
1168	D₄	—	2	4	no	—
1169	D₄	—	2	2	no	—
1170	D₄	—	4	2	no	—
1171	D₄	—	4	2	no	—
1172	D₄	—	4	4	no	—
1173	D₄	—	4	4	no	—
1174	D₄	—	4	4	no	—
1175	D₄	—	4	4	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	2	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	8	2	no	—
1182	D₄	—	8	2	no	—
1183	D₄	—	8	1	no	—
1184	D₄	—	8	2	no	—
1185	D₄	—	8	1	no	—
1186	D₄	—	8	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	C₂×C₇×#41	1	4	yes	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	1	no	—
1191	C₂×C₄	—	2	1	no	—
1192	C₂×C₄	—	2	2	no	—
1193	C₂×C₄	—	2	2	no	—
1194	C₂×C₄	—	2	1	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	2	no	—
1197	C₂×C₄	—	2	2	no	—
1198	C₂×C₄	—	2	2	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	1	no	—
1203	C₂×C₄	—	2	1	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	4	4	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	8	2	no	—
1210	C₂×C₄	—	8	2	no	—
1211	C₂×C₄	—	8	2	no	—
1212	C₂×C₄	—	8	1	no	—
1213	C₂×C₄	—	8	2	no	—
1214	C₂×C₄	—	8	1	no	—
1215	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1216	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1217	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1218	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1219	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1220	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1221	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1222	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1223	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1224	C₈	—	2	2	no	—
1225	C₈	—	2	1	no	—
1226	C₈	—	2	1	no	—
1227	C₈	—	2	1	no	—
1228	C₈	—	2	1	no	—
1229	C₈	—	2	2	no	—
1230	C₇	#61175	1	1	yes	characteristic, direct product factor, Sylow
1231	C₂²	—	2	1	no	—
1232	C₂²	—	2	1	no	—
1233	C₂²	—	2	2	no	—
1234	C₂²	—	2	1	no	—
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	2	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	2	no	—
1242	C₂²	—	2	4	no	—
1243	C₂²	—	4	4	no	—
1244	C₂²	—	4	2	no	—
1245	C₂²	—	4	2	no	—
1246	C₂²	—	4	1	no	—
1247	C₂²	—	4	1	no	—
1248	C₂²	—	4	1	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	2	no	—
1251	C₂²	—	4	2	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	8	4	no	—
1256	C₂²	—	8	4	no	—
1257	C₂²	—	8	8	no	—
1258	C₂²	—	8	8	no	—
1259	C₂²	—	16	4	no	—
1260	C₂²	C₇×#546	1	2	yes	—
1261	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1262	C₄	—	2	2	no	—
1263	C₄	—	2	2	no	—
1264	C₄	—	2	1	no	—
1265	C₄	—	2	1	no	—
1266	C₄	—	2	2	no	—
1267	C₄	—	4	2	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	1	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	2	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	1	no	—
1275	C₄	C₇×#546	1	2	yes	—
1276	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1277	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
1278	C₂	—	2	2	no	—
1279	C₂	—	4	1	no	—
1280	C₂	—	4	1	no	—
1281	C₂	—	4	2	no	—
1282	C₂	—	4	4	no	—
1283	C₂	—	8	2	no	—
1284	C₂	—	8	1	no	—
1285	C₂	—	8	1	no	—
1286	C₂	C₂×C₇×#546	1	1	yes	characteristic
1287	C₂	C₇×#3585	1	1	yes	characteristic
1288	C₂	C₇×#3585	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×#3493	C₂	semidirect
2. C₇×#3484	C₂	semidirect
3. C₇×#3325	C₂	semidirect
4. C₇×#3324	C₂	semidirect
5. C₇×#3323	C₂	semidirect
6. C₇×#3322	C₂	semidirect
7. C₇×#3319	C₂	semidirect
8. C₇×#3318	C₂	semidirect
9. C₇×#3311	C₂	semidirect
10. C₇×#3310	C₂	semidirect
11. C₇×#3136	C₂	semidirect
12. C₇×#3096	C₂	semidirect
13. C₇×#3093	C₂	semidirect
14. C₇×#3081	C₂	semidirect
15. C₇×#3062	C₂	semidirect
16. C₇×#3054	C₂	semidirect
17. C₇×#3045	C₂	semidirect
18. C₇×#3012	C₂	semidirect
19. C₇×#3003	C₂	semidirect
20. C₇×#2946	C₂	semidirect
21. C₇×#2930	C₂	semidirect
22. C₇×#2897	C₂	semidirect
23. C₂×C₇×#418	C₂	semidirect
27. 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×#556	C₂²	semidirect
34. C₇×#555	C₂²	semidirect
36. C₇×#553	C₂²	semidirect
38. C₇×#552	C₂²	semidirect
47. C₇×#544	C₂²	semidirect
49. C₇×#537	C₂²	semidirect
56. C₇×#525	C₂²	semidirect
58. C₇×#520	C₂²	semidirect
59. C₇×#520	C₂²	semidirect
61. C₂×C₇×#117	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×#485	C₂²	semidirect
68. C₇×#482	C₂²	semidirect
69. C₇×#482	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#482	C₂²	semidirect
72. C₇×#481	C₂²	semidirect
73. C₇×#480	C₂²	semidirect
74. C₇×#478	C₂²	semidirect
75. C₇×#478	C₂²	semidirect
76. C₇×#476	C₂²	semidirect
77. C₇×#474	C₂²	semidirect
78. C₇×#470	C₂²	semidirect
79. C₇×#470	C₂²	semidirect
80. C₇×#469	C₂²	semidirect
81. C₇×#469	C₂²	semidirect
82. C₇×#469	C₂²	semidirect
83. C₇×#468	C₂²	semidirect
84. C₇×#468	C₂²	semidirect
85. C₇×#468	C₂²	semidirect
86. C₇×#468	C₂²	semidirect
87. C₇×#468	C₂²	semidirect
88. C₇×#466	C₂²	semidirect
89. C₇×#465	C₂²	semidirect
90. C₇×#464	C₂²	semidirect
91. C₇×#463	C₂²	semidirect
92. C₇×#460	C₂²	semidirect
93. C₇×#459	C₂²	semidirect
94. C₇×#452	C₂²	semidirect
95. C₇×#450	C₂²	semidirect
96. C₇×#450	C₂²	semidirect
97. C₇×#450	C₂²	semidirect
98. C₇×#449	C₂²	semidirect
99. C₇×#447	C₂²	semidirect
100. C₇×#447	C₂²	semidirect
101. C₇×#447	C₂²	semidirect
102. C₇×#442	C₂²	semidirect
103. C₇×#440	C₂²	semidirect
104. C₄×C₇×SD₁₆	C₂²	semidirect
105. C₄×C₇×D₈	C₂²	semidirect
106. C₇×#436	C₂²	semidirect
107. C₇×#436	C₂²	semidirect
108. C₇×#435	C₂²	semidirect
109. C₇×#435	C₂²	semidirect
110. C₇×#428	C₂²	semidirect
111. C₇×#428	C₂²	semidirect
112. C₇×#427	C₂²	semidirect
113. C₇×#424	C₂²	semidirect
115. C₇×#418	C₂²	semidirect
116. C₇×#418	C₂²	semidirect
117. C₇×#418	C₂²	semidirect
118. C₇×#418	C₂²	semidirect
119. C₇×#418	C₂²	semidirect
120. C₇×#418	C₂²	semidirect
121. C₇×#417	C₂²	semidirect
122. C₇×#417	C₂²	semidirect
123. C₇×#417	C₂²	semidirect
124. C₇×#416	C₂²	semidirect
125. C₇×#416	C₂²	semidirect
126. C₇×#416	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. C₇×#407	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #61175	C₇	direct (N × H)
162. C₂×C₇×Q₁₆	C₂³	semidirect
165. C₂×C₇×SD₁₆	C₂³	semidirect
166. C₂×C₇×SD₁₆	C₂³	semidirect
169. C₂×C₇×D₈	C₂³	semidirect
178. C₂×C₇×M₁₆	C₂³	semidirect
181. C₂²×C₇×C₈	C₂³	semidirect
183. C₇×C₄⋊Q₈	C₂³	semidirect
192. C₇×#125	C₂³	semidirect
213. C₇×C₂²⋊Q₈	C₂³	semidirect
232. C₇×#121	C₂³	semidirect
246. C₄×C₇×Q₈	C₂³	semidirect
261. C₄×C₇×D₄	C₂³	semidirect
272. C₇×#117	C₂³	semidirect
276. C₂×C₇×C₄⋊C₄	C₂³	semidirect
282. C₇×#107	C₂³	semidirect
283. C₇×#107	C₂³	semidirect
284. C₇×#107	C₂³	semidirect
285. C₇×#107	C₂³	semidirect
286. C₇×#106	C₂³	semidirect
287. C₇×#106	C₂³	semidirect
288. C₇×#106	C₂³	semidirect
289. C₇×#106	C₂³	semidirect
290. C₇×C₄⋊C₈	C₂³	semidirect
291. C₇×C₄⋊C₈	C₂³	semidirect
292. C₇×#103	C₂³	semidirect
293. C₇×#103	C₂³	semidirect
294. C₇×#103	C₂³	semidirect
295. C₇×#103	C₂³	semidirect
296. C₇×#103	C₂³	semidirect
297. C₇×#103	C₂³	semidirect
310. C₇×#102	C₂³	semidirect
311. C₇×#102	C₂³	semidirect
312. C₇×#102	C₂³	semidirect
313. C₇×#102	C₂³	semidirect
314. C₇×#102	C₂³	semidirect
315. C₇×#102	C₂³	semidirect
318. C₇×C₂²⋊C₈	C₂³	semidirect
319. C₇×C₂²⋊C₈	C₂³	semidirect
320. C₇×#97	C₂³	semidirect
321. C₄×C₇×C₈	C₂³	semidirect
322. #3493	C₂×C₇	semidirect
323. #3484	C₂×C₇	semidirect
324. #3325	C₂×C₇	semidirect
325. #3324	C₂×C₇	semidirect
326. #3323	C₂×C₇	semidirect
327. #3322	C₂×C₇	semidirect
328. #3319	C₂×C₇	semidirect
329. #3318	C₂×C₇	semidirect
330. #3311	C₂×C₇	semidirect
331. #3310	C₂×C₇	semidirect
332. #3136	C₂×C₇	semidirect
333. #3096	C₂×C₇	semidirect
334. #3093	C₂×C₇	semidirect
335. #3081	C₂×C₇	semidirect
336. #3062	C₂×C₇	semidirect
337. #3054	C₂×C₇	semidirect
338. #3045	C₂×C₇	semidirect
339. #3012	C₂×C₇	semidirect
340. #3003	C₂×C₇	semidirect
341. #2946	C₂×C₇	semidirect
342. #2930	C₂×C₇	semidirect
343. #2897	C₂×C₇	semidirect
344. C₂×#418	C₂×C₇	semidirect
510. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
511. C₂×#135	C₂²×C₇	semidirect
512. C₂×#131	C₂²×C₇	semidirect
513. C₂²×M₁₆	C₂²×C₇	semidirect
515. #556	C₂²×C₇	semidirect
517. #555	C₂²×C₇	semidirect
519. #553	C₂²×C₇	semidirect
521. #552	C₂²×C₇	semidirect
530. #544	C₂²×C₇	semidirect
532. #537	C₂²×C₇	semidirect
539. #525	C₂²×C₇	semidirect
541. #520	C₂²×C₇	semidirect
542. #520	C₂²×C₇	semidirect
544. C₂×#117	C₂²×C₇	semidirect
545. #490	C₂²×C₇	semidirect
546. #489	C₂²×C₇	semidirect
547. #488	C₂²×C₇	semidirect
548. #486	C₂²×C₇	semidirect
549. #485	C₂²×C₇	semidirect
550. #485	C₂²×C₇	semidirect
551. #482	C₂²×C₇	semidirect
552. #482	C₂²×C₇	semidirect
553. #482	C₂²×C₇	semidirect
554. #482	C₂²×C₇	semidirect
555. #481	C₂²×C₇	semidirect
556. #480	C₂²×C₇	semidirect
557. #478	C₂²×C₇	semidirect
558. #478	C₂²×C₇	semidirect
559. #476	C₂²×C₇	semidirect
560. #474	C₂²×C₇	semidirect
561. #470	C₂²×C₇	semidirect
562. #470	C₂²×C₇	semidirect
563. #469	C₂²×C₇	semidirect
564. #469	C₂²×C₇	semidirect
565. #469	C₂²×C₇	semidirect
566. #468	C₂²×C₇	semidirect
567. #468	C₂²×C₇	semidirect
568. #468	C₂²×C₇	semidirect
569. #468	C₂²×C₇	semidirect
570. #468	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. #450	C₂²×C₇	semidirect
579. #450	C₂²×C₇	semidirect
580. #450	C₂²×C₇	semidirect
581. #449	C₂²×C₇	semidirect
582. #447	C₂²×C₇	semidirect
583. #447	C₂²×C₇	semidirect
584. #447	C₂²×C₇	semidirect
585. #442	C₂²×C₇	semidirect
586. #440	C₂²×C₇	semidirect
587. C₄×SD₁₆	C₂²×C₇	semidirect
588. C₄×D₈	C₂²×C₇	semidirect
589. #436	C₂²×C₇	semidirect
590. #436	C₂²×C₇	semidirect
591. #435	C₂²×C₇	semidirect
592. #435	C₂²×C₇	semidirect
593. #428	C₂²×C₇	semidirect
594. #428	C₂²×C₇	semidirect
595. #427	C₂²×C₇	semidirect
596. #424	C₂²×C₇	semidirect
598. #418	C₂²×C₇	semidirect
599. #418	C₂²×C₇	semidirect
600. #418	C₂²×C₇	semidirect
601. #418	C₂²×C₇	semidirect
602. #418	C₂²×C₇	semidirect
603. #418	C₂²×C₇	semidirect
604. #417	C₂²×C₇	semidirect
605. #417	C₂²×C₇	semidirect
606. #417	C₂²×C₇	semidirect
607. #416	C₂²×C₇	semidirect
608. #416	C₂²×C₇	semidirect
609. #416	C₂²×C₇	semidirect
612. C₂×#102	C₂²×C₇	semidirect
613. C₂×#102	C₂²×C₇	semidirect
614. C₂×#102	C₂²×C₇	semidirect
615. #408	C₂²×C₇	semidirect
616. #407	C₂²×C₇	semidirect
617. #405	C₂²×C₇	semidirect
747. C₂×Q₁₆	C₂³×C₇	semidirect
750. C₂×SD₁₆	C₂³×C₇	semidirect
751. C₂×SD₁₆	C₂³×C₇	semidirect
754. C₂×D₈	C₂³×C₇	semidirect
763. C₂×M₁₆	C₂³×C₇	semidirect
766. C₂²×C₈	C₂³×C₇	semidirect
768. C₄⋊Q₈	C₂³×C₇	semidirect
777. #125	C₂³×C₇	semidirect
798. C₂²⋊Q₈	C₂³×C₇	semidirect
817. #121	C₂³×C₇	semidirect
831. C₄×Q₈	C₂³×C₇	semidirect
846. C₄×D₄	C₂³×C₇	semidirect
857. #117	C₂³×C₇	semidirect
861. C₂×C₄⋊C₄	C₂³×C₇	semidirect
867. #107	C₂³×C₇	semidirect
868. #107	C₂³×C₇	semidirect
869. #107	C₂³×C₇	semidirect
870. #107	C₂³×C₇	semidirect
871. #106	C₂³×C₇	semidirect
872. #106	C₂³×C₇	semidirect
873. #106	C₂³×C₇	semidirect
874. #106	C₂³×C₇	semidirect
875. C₄⋊C₈	C₂³×C₇	semidirect
876. C₄⋊C₈	C₂³×C₇	semidirect
877. #103	C₂³×C₇	semidirect
878. #103	C₂³×C₇	semidirect
879. #103	C₂³×C₇	semidirect
880. #103	C₂³×C₇	semidirect
881. #103	C₂³×C₇	semidirect
882. #103	C₂³×C₇	semidirect
895. #102	C₂³×C₇	semidirect
896. #102	C₂³×C₇	semidirect
897. #102	C₂³×C₇	semidirect
898. #102	C₂³×C₇	semidirect
899. #102	C₂³×C₇	semidirect
900. #102	C₂³×C₇	semidirect
903. C₂²⋊C₈	C₂³×C₇	semidirect
904. C₂²⋊C₈	C₂³×C₇	semidirect
905. #97	C₂³×C₇	semidirect
906. C₄×C₈	C₂³×C₇	semidirect
1230. C₇	#61175	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×#3493	2
C₇×#3484	2
C₇×#3325	2
C₇×#3324	2
C₇×#3323	2
C₇×#3322	2
C₇×#3319	2
C₇×#3318	2
C₇×#3311	2
C₇×#3310	2
C₇×#3136	2
C₇×#3096	2
C₇×#3093	2
C₇×#3081	2
C₇×#3062	2
C₇×#3054	2
C₇×#3045	2
C₇×#3012	2
C₇×#3003	2
C₇×#2946	2
C₇×#2930	2
C₇×#2897	2
C₂×C₇×#418	2
#61175	7

Subgroups — C7×#61175 #13238391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61175 #13238391