Subgroups — C₇×#61171 #13238387

Order 1792.

2174 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×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3488	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3319	C₂	1	2	yes	maximal, complemented
4	C₇×#3318	C₂	1	2	yes	maximal, complemented
5	C₇×#3309	C₂	1	2	yes	maximal, complemented
6	C₇×#3308	C₂	1	2	yes	maximal, complemented
7	C₇×#3305	C₂	1	2	yes	maximal, complemented
8	C₇×#3301	C₂	1	2	yes	maximal, complemented
9	C₇×#3297	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	C₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3041	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3006	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#2946	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2929	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#416	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
27	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic, complemented
28	C₂²×C₇×D₈	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
30	C₂³×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
31	C₇×#555	C₂²	1	2	yes	complemented
32	C₇×#553	C₂²	1	2	yes	complemented
33	C₇×#553	C₂²	1	2	yes	complemented
34	C₇×#551	—	2	2	no	—
35	C₇×#550	C₂²	1	2	yes	complemented
36	C₇×#548	C₂²	1	2	yes	complemented
37	C₇×#547	C₂²	1	2	yes	complemented
38	C₇×#546	—	2	2	no	—
39	C₇×#546	—	2	2	no	—
40	C₇×#546	C₂²	1	2	yes	complemented
41	C₇×D₄²	—	2	2	no	—
42	C₇×D₄²	C₂²	1	2	yes	complemented
43	C₇×#544	C₂²	1	1	yes	characteristic, complemented
44	C₇×#542	—	2	1	no	—
45	C₇×#540	—	2	1	no	—
46	C₇×#537	—	2	1	no	—
47	C₇×#537	C₂²	1	1	yes	characteristic
48	C₇×#535	—	2	1	no	—
49	C₇×#535	C₂²	1	1	yes	characteristic
50	C₇×#535	C₂²	1	1	yes	characteristic, complemented
51	C₇×#532	—	2	1	no	—
52	C₇×#529	—	2	1	no	—
53	C₇×#525	—	2	1	no	—
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₂×C₇×#121	—	2	1	no	—
56	C₂×C₇×#121	C₂²	1	1	yes	characteristic
57	C₂×C₇×#121	C₂²	1	1	yes	characteristic, complemented
58	C₇×#520	C₂²	1	1	yes	characteristic
59	C₇×#520	C₂²	1	1	yes	characteristic, complemented
60	C₇×#518	C₂²	1	1	yes	characteristic, complemented
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×#484	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×#481	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×#466	C₂²	1	2	yes	complemented
81	C₇×#466	C₂²	1	2	yes	complemented
82	C₇×#466	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×#463	C₂²	1	2	yes	complemented
87	C₇×#463	C₂²	1	2	yes	complemented
88	C₇×#459	C₂²	1	2	yes	complemented
89	C₇×#459	C₂²	1	2	yes	complemented
90	C₇×#449	C₂²	1	2	yes	complemented
91	C₇×#449	C₂²	1	2	yes	complemented
92	C₇×#449	C₂²	1	2	yes	complemented
93	C₇×#449	C₂²	1	2	yes	complemented
94	C₇×#448	C₂²	1	2	yes	complemented
95	C₇×#447	C₂²	1	2	yes	complemented
96	C₇×#447	C₂²	1	2	yes	complemented
97	C₇×#447	C₂²	1	2	yes	complemented
98	C₇×#442	C₂²	1	2	yes	complemented
99	C₇×#440	C₂²	1	2	yes	complemented
100	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
101	C₄×C₇×D₈	C₂²	1	2	yes	complemented
102	C₇×#435	C₂²	1	2	yes	complemented
103	C₇×#435	C₂²	1	2	yes	complemented
104	C₇×C₈×D₄	C₂²	1	2	yes	complemented
105	C₇×C₈×D₄	C₂²	1	2	yes	complemented
106	C₇×#428	C₂²	1	1	yes	characteristic, complemented
107	C₇×#428	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
109	C₇×#424	C₂²	1	1	yes	characteristic, complemented
110	C₇×#418	C₂²	1	1	yes	characteristic, complemented
111	C₇×#418	C₂²	1	1	yes	characteristic, complemented
112	C₇×#418	C₂²	1	2	yes	complemented
113	C₇×#417	C₂²	1	1	yes	characteristic
114	C₇×#417	C₂²	1	1	yes	characteristic, complemented
115	C₇×#417	C₂²	1	2	yes	complemented
116	C₇×#416	C₂²	1	1	yes	characteristic
117	C₇×#416	C₂²	1	1	yes	characteristic
118	C₇×#416	C₂²	1	1	yes	characteristic, complemented
119	C₇×#416	C₂²	1	1	yes	characteristic, complemented
120	C₇×#416	C₂²	1	2	yes	complemented
121	C₇×#416	C₂²	1	1	yes	characteristic, complemented
122	C₇×#416	C₂²	1	1	yes	characteristic, complemented
123	C₇×#416	C₂²	1	1	yes	characteristic, complemented
124	C₇×#416	C₂²	1	1	yes	characteristic, complemented
125	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
126	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
127	C₂×C₇×#102	C₂²	1	1	yes	characteristic, 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	1	yes	characteristic, complemented
131	C₂×C₇×#102	C₂²	1	1	yes	characteristic, 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	#61171	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	2	yes	—
148	C₂×C₇×#41	C₂³	1	1	yes	characteristic
149	C₂×C₇×#41	C₂³	1	1	yes	characteristic
150	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
151	C₂²×C₇×D₄	—	2	1	no	—
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	1	yes	characteristic
160	C₂²×C₇×D₄	C₂³	1	2	yes	—
161	C₂³×C₄×C₇	—	2	1	no	—
162	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
163	C₇×AGL(1,ℤ/8)	—	2	4	no	—
164	C₇×AGL(1,ℤ/8)	—	4	2	no	—
165	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
166	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
167	C₂×C₇×D₈	—	4	2	no	—
168	C₂×C₇×D₈	C₂³	1	2	yes	—
169	C₂×C₇×D₈	C₂³	1	2	yes	—
170	C₂×C₇×D₈	C₂³	1	2	yes	—
171	C₂×C₇×D₈	C₂³	1	2	yes	—
172	C₇×#131	—	4	2	no	—
173	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
174	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
175	C₂×C₇×M₁₆	C₂³	1	2	yes	—
176	C₂²×C₇×C₈	—	4	2	no	—
177	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
178	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
179	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
180	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
181	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
182	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
183	C₂²×C₇×C₈	C₂³	1	2	yes	—
184	C₇×C₄⋊Q₈	—	2	1	no	—
185	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
186	C₇×#127	—	2	1	no	—
187	C₇×#127	—	2	2	no	—
188	C₇×#127	C₂³	1	2	yes	—
189	C₇×#126	—	2	2	no	—
190	C₇×#126	—	2	2	no	—
191	C₇×#125	—	2	1	no	—
192	C₇×#125	C₂³	1	2	yes	—
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	2	no	—
200	C₇×#123	—	2	2	no	—
201	C₇×#123	—	2	2	no	—
202	C₇×#123	—	2	2	no	—
203	C₇×#123	D₄	1	2	yes	—
204	C₇×C₂²⋊Q₈	—	2	1	no	—
205	C₇×C₂²⋊Q₈	—	2	2	no	—
206	C₇×C₂²⋊Q₈	—	2	2	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
209	C₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
211	C₇×#121	—	2	1	no	—
212	C₇×#121	—	2	2	no	—
213	C₇×#121	—	2	2	no	—
214	C₇×#121	—	2	2	no	—
215	C₇×#121	—	2	2	no	—
216	C₇×#121	—	2	2	no	—
217	C₇×#121	—	2	1	no	—
218	C₇×#121	—	2	1	no	—
219	C₇×#121	—	2	1	no	—
220	C₇×#121	—	2	1	no	—
221	C₇×#121	—	2	1	no	—
222	C₇×#121	—	2	1	no	—
223	C₇×#121	—	2	2	no	—
224	C₇×#121	—	2	2	no	—
225	C₇×#121	—	2	2	no	—
226	C₇×#121	—	2	2	no	—
227	C₇×#121	D₄	1	1	yes	characteristic
228	C₇×#121	D₄	1	1	yes	characteristic
229	C₇×#121	C₂³	1	2	yes	—
230	C₇×#121	C₂³	1	2	yes	—
231	C₇×#121	C₂³	1	2	yes	—
232	C₇×#121	C₂³	1	2	yes	—
233	C₇×#121	C₂³	1	2	yes	—
234	C₇×#121	C₂³	1	2	yes	—
235	C₇×#121	C₂³	1	2	yes	—
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	D₄	1	2	yes	—
242	C₄×C₇×Q₈	—	2	1	no	—
243	C₄×C₇×Q₈	C₂³	1	2	yes	—
244	C₄×C₇×D₄	—	2	1	no	—
245	C₄×C₇×D₄	—	2	2	no	—
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	2	no	—
249	C₄×C₇×D₄	—	2	2	no	—
250	C₄×C₇×D₄	—	2	2	no	—
251	C₄×C₇×D₄	—	2	2	no	—
252	C₄×C₇×D₄	—	2	2	no	—
253	C₄×C₇×D₄	C₂³	1	2	yes	—
254	C₄×C₇×D₄	C₂³	1	2	yes	—
255	C₄×C₇×D₄	C₂³	1	2	yes	—
256	C₄×C₇×D₄	C₂³	1	2	yes	—
257	C₄×C₇×D₄	C₂³	1	2	yes	—
258	C₇×#117	—	2	1	no	—
259	C₇×#117	—	2	1	no	—
260	C₇×#117	—	2	1	no	—
261	C₇×#117	—	2	2	no	—
262	C₇×#117	C₂³	1	1	yes	characteristic
263	C₇×#117	C₂³	1	1	yes	characteristic
264	C₇×#117	C₂³	1	2	yes	—
265	C₇×#117	C₂³	1	1	yes	characteristic
266	C₇×#117	C₂³	1	1	yes	characteristic
267	C₇×#117	C₂³	1	1	yes	characteristic
268	C₂×C₇×C₄⋊C₄	—	2	1	no	—
269	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
270	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
271	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
272	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
273	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
274	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
275	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
276	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
277	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
278	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
279	C₂×C₄²×C₇	—	2	1	no	—
280	C₇×#107	C₂³	1	2	yes	—
281	C₇×#107	C₂³	1	2	yes	—
282	C₇×#107	C₂³	1	2	yes	—
283	C₇×#107	C₂³	1	2	yes	—
284	C₇×#106	C₂³	1	2	yes	—
285	C₇×#106	C₂³	1	2	yes	—
286	C₇×C₄⋊C₈	C₂³	1	2	yes	—
287	C₇×C₄⋊C₈	C₂³	1	2	yes	—
288	C₇×#103	C₂³	1	1	yes	characteristic
289	C₇×#103	C₂³	1	1	yes	characteristic
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
297	C₇×#103	C₂³	1	1	yes	characteristic
298	C₇×#102	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
305	C₇×#102	C₂³	1	2	yes	—
306	C₇×#102	C₂³	1	1	yes	characteristic
307	C₇×#102	C₂³	1	1	yes	characteristic
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	2	yes	—
313	C₇×#102	C₂³	1	1	yes	characteristic
314	C₇×#102	C₂³	1	1	yes	characteristic
315	C₇×#102	C₂³	1	1	yes	characteristic
316	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
317	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
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	#3494	C₂×C₇	1	1	yes	characteristic, complemented
323	#3488	C₂×C₇	1	1	yes	characteristic, complemented
324	#3319	C₂×C₇	1	2	yes	complemented
325	#3318	C₂×C₇	1	2	yes	complemented
326	#3309	C₂×C₇	1	2	yes	complemented
327	#3308	C₂×C₇	1	2	yes	complemented
328	#3305	C₂×C₇	1	2	yes	complemented
329	#3301	C₂×C₇	1	2	yes	complemented
330	#3297	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	#3094	C₂×C₇	1	1	yes	characteristic, complemented
335	#3083	C₂×C₇	1	1	yes	characteristic, complemented
336	#3062	C₂×C₇	1	1	yes	characteristic, complemented
337	C₂×#466	C₂×C₇	1	1	yes	characteristic, complemented
338	#3041	C₂×C₇	1	1	yes	characteristic, complemented
339	#3008	C₂×C₇	1	1	yes	characteristic, complemented
340	#3006	C₂×C₇	1	1	yes	characteristic, complemented
341	#2946	C₂×C₇	1	1	yes	characteristic, complemented
342	#2929	C₂×C₇	1	1	yes	characteristic, complemented
343	#2897	C₂×C₇	1	1	yes	characteristic, complemented
344	C₂×#416	C₂×C₇	1	1	yes	characteristic, complemented
345	C₂⁴×C₇	—	2	1	no	—
346	C₂⁴×C₇	—	2	1	no	—
347	C₂⁴×C₇	—	2	2	no	—
348	C₂⁴×C₇	—	2	1	no	—
349	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
350	C₇×#41	—	2	2	no	—
351	C₇×#41	—	2	2	no	—
352	C₇×#41	—	2	2	no	—
353	C₇×#41	—	2	2	no	—
354	C₇×#41	—	2	4	no	—
355	C₇×#41	—	2	2	no	—
356	C₇×#41	—	2	2	no	—
357	C₇×#41	—	2	2	no	—
358	C₇×#41	—	4	4	no	—
359	C₇×#41	—	4	1	no	—
360	C₇×#41	—	4	1	no	—
361	C₇×#41	—	4	2	no	—
362	C₇×#41	—	4	4	no	—
363	C₇×#41	—	4	4	no	—
364	C₇×#41	—	8	4	no	—
365	C₇×#41	#41	1	4	yes	complemented
366	C₂×C₇×Q₈	—	2	1	no	—
367	C₂×C₇×Q₈	—	2	2	no	—
368	C₂×C₇×Q₈	—	2	2	no	—
369	C₂×C₇×Q₈	—	4	1	no	—
370	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
371	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
372	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
373	C₂×C₇×D₄	—	2	1	no	—
374	C₂×C₇×D₄	—	2	2	no	—
375	C₂×C₇×D₄	—	2	4	no	—
376	C₂×C₇×D₄	—	2	2	no	—
377	C₂×C₇×D₄	—	2	2	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	2	no	—
383	C₂×C₇×D₄	—	2	2	no	—
384	C₂×C₇×D₄	—	2	2	no	—
385	C₂×C₇×D₄	—	2	2	no	—
386	C₂×C₇×D₄	—	2	2	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	1	no	—
389	C₂×C₇×D₄	—	2	2	no	—
390	C₂×C₇×D₄	—	2	1	no	—
391	C₂×C₇×D₄	—	2	2	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	—	2	2	no	—
397	C₂×C₇×D₄	—	4	1	no	—
398	C₂×C₇×D₄	—	4	2	no	—
399	C₂×C₇×D₄	—	4	4	no	—
400	C₂×C₇×D₄	—	4	8	no	—
401	C₂×C₇×D₄	—	4	4	no	—
402	C₂×C₇×D₄	—	8	4	no	—
403	C₂×C₇×D₄	—	8	2	no	—
404	C₂×C₇×D₄	—	8	2	no	—
405	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
406	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
407	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
408	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
409	C₂×C₇×D₄	C₂⁴	1	2	yes	—
410	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
411	C₂×C₇×D₄	C₂⁴	1	2	yes	—
412	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
413	C₂²×C₄×C₇	—	2	1	no	—
414	C₂²×C₄×C₇	—	2	2	no	—
415	C₂²×C₄×C₇	—	2	2	no	—
416	C₂²×C₄×C₇	—	2	1	no	—
417	C₂²×C₄×C₇	—	2	1	no	—
418	C₂²×C₄×C₇	—	2	1	no	—
419	C₂²×C₄×C₇	—	2	1	no	—
420	C₂²×C₄×C₇	—	2	1	no	—
421	C₂²×C₄×C₇	—	2	2	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	—	2	2	no	—
429	C₂²×C₄×C₇	—	4	4	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	2	yes	—
435	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
437	C₇×SD₁₆	—	2	4	no	—
438	C₇×SD₁₆	—	4	2	no	—
439	C₇×D₈	—	2	4	no	—
440	C₇×D₈	—	4	2	no	—
441	C₇×D₈	—	4	2	no	—
442	C₇×D₈	—	4	2	no	—
443	C₇×M₁₆	—	2	2	no	—
444	C₇×M₁₆	—	2	2	no	—
445	C₇×M₁₆	—	4	2	no	—
446	C₂×C₇×C₈	—	2	2	no	—
447	C₂×C₇×C₈	—	2	2	no	—
448	C₂×C₇×C₈	—	4	1	no	—
449	C₂×C₇×C₈	—	4	1	no	—
450	C₂×C₇×C₈	—	4	1	no	—
451	C₂×C₇×C₈	—	4	1	no	—
452	C₂×C₇×C₈	—	4	2	no	—
453	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
454	C₂×C₇×C₈	C₂⁴	1	2	yes	—
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	C₇×C₄⋊C₄	—	2	1	no	—
460	C₇×C₄⋊C₄	—	2	2	no	—
461	C₇×C₄⋊C₄	—	2	1	no	—
462	C₇×C₄⋊C₄	—	2	1	no	—
463	C₇×C₄⋊C₄	—	2	1	no	—
464	C₇×C₄⋊C₄	—	2	2	no	—
465	C₇×C₄⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
470	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
471	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
472	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
473	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
474	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
475	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
476	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
477	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
478	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
479	C₇×C₂²⋊C₄	—	2	1	no	—
480	C₇×C₂²⋊C₄	—	2	1	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	2	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	C₂×D₄	1	2	yes	—
498	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
499	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
500	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
501	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
502	C₄²×C₇	—	2	1	no	—
503	C₄²×C₇	—	2	1	no	—
504	C₄²×C₇	—	2	1	no	—
505	C₄²×C₇	—	2	1	no	—
506	C₄²×C₇	—	2	2	no	—
507	C₄²×C₇	—	2	2	no	—
508	C₄²×C₇	C₂⁴	1	2	yes	—
509	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
510	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
511	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
512	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic, complemented
513	C₂²×D₈	C₂²×C₇	1	1	yes	characteristic, complemented
514	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
515	C₂³×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
516	#555	C₂²×C₇	1	2	yes	complemented
517	#553	C₂²×C₇	1	2	yes	complemented
518	#553	C₂²×C₇	1	2	yes	complemented
519	#551	—	2	2	no	—
520	#550	C₂²×C₇	1	2	yes	complemented
521	#548	C₂²×C₇	1	2	yes	complemented
522	#547	C₂²×C₇	1	2	yes	complemented
523	#546	—	2	2	no	—
524	#546	—	2	2	no	—
525	#546	C₂²×C₇	1	2	yes	complemented
526	D₄²	—	2	2	no	—
527	D₄²	C₂²×C₇	1	2	yes	complemented
528	#544	C₂²×C₇	1	1	yes	characteristic, complemented
529	#542	—	2	1	no	—
530	#540	—	2	1	no	—
531	#537	—	2	1	no	—
532	#537	C₂²×C₇	1	1	yes	characteristic
533	#535	—	2	1	no	—
534	#535	C₂²×C₇	1	1	yes	characteristic
535	#535	C₂²×C₇	1	1	yes	characteristic, complemented
536	#532	—	2	1	no	—
537	#529	—	2	1	no	—
538	#525	—	2	1	no	—
539	#525	C₂²×C₇	1	1	yes	characteristic
540	C₂×#121	—	2	1	no	—
541	C₂×#121	C₂²×C₇	1	1	yes	characteristic
542	C₂×#121	C₂²×C₇	1	1	yes	characteristic, complemented
543	#520	C₂²×C₇	1	1	yes	characteristic
544	#520	C₂²×C₇	1	1	yes	characteristic, complemented
545	#518	C₂²×C₇	1	1	yes	characteristic, complemented
546	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
547	#490	C₂²×C₇	1	2	yes	complemented
548	#489	C₂²×C₇	1	2	yes	complemented
549	#488	C₂²×C₇	1	2	yes	complemented
550	#486	C₂²×C₇	1	2	yes	complemented
551	#485	C₂²×C₇	1	2	yes	complemented
552	#484	C₂²×C₇	1	2	yes	complemented
553	#482	C₂²×C₇	1	2	yes	complemented
554	#482	C₂²×C₇	1	2	yes	complemented
555	#482	C₂²×C₇	1	2	yes	complemented
556	#481	C₂²×C₇	1	2	yes	complemented
557	#480	C₂²×C₇	1	2	yes	complemented
558	#480	C₂²×C₇	1	2	yes	complemented
559	#479	C₂²×C₇	1	2	yes	complemented
560	#478	C₂²×C₇	1	2	yes	complemented
561	#477	C₂²×C₇	1	2	yes	complemented
562	#474	C₂²×C₇	1	2	yes	complemented
563	#469	C₂²×C₇	1	2	yes	complemented
564	#468	C₂²×C₇	1	2	yes	complemented
565	#466	C₂²×C₇	1	2	yes	complemented
566	#466	C₂²×C₇	1	2	yes	complemented
567	#466	C₂²×C₇	1	2	yes	complemented
568	#466	C₂²×C₇	1	2	yes	complemented
569	#466	C₂²×C₇	1	2	yes	complemented
570	#465	C₂²×C₇	1	2	yes	complemented
571	#463	C₂²×C₇	1	2	yes	complemented
572	#463	C₂²×C₇	1	2	yes	complemented
573	#459	C₂²×C₇	1	2	yes	complemented
574	#459	C₂²×C₇	1	2	yes	complemented
575	#449	C₂²×C₇	1	2	yes	complemented
576	#449	C₂²×C₇	1	2	yes	complemented
577	#449	C₂²×C₇	1	2	yes	complemented
578	#449	C₂²×C₇	1	2	yes	complemented
579	#448	C₂²×C₇	1	2	yes	complemented
580	#447	C₂²×C₇	1	2	yes	complemented
581	#447	C₂²×C₇	1	2	yes	complemented
582	#447	C₂²×C₇	1	2	yes	complemented
583	#442	C₂²×C₇	1	2	yes	complemented
584	#440	C₂²×C₇	1	2	yes	complemented
585	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
586	C₄×D₈	C₂²×C₇	1	2	yes	complemented
587	#435	C₂²×C₇	1	2	yes	complemented
588	#435	C₂²×C₇	1	2	yes	complemented
589	C₈×D₄	C₂²×C₇	1	2	yes	complemented
590	C₈×D₄	C₂²×C₇	1	2	yes	complemented
591	#428	C₂²×C₇	1	1	yes	characteristic, complemented
592	#428	C₂²×C₇	1	1	yes	characteristic, complemented
593	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
594	#424	C₂²×C₇	1	1	yes	characteristic, complemented
595	#418	C₂²×C₇	1	1	yes	characteristic, complemented
596	#418	C₂²×C₇	1	1	yes	characteristic, complemented
597	#418	C₂²×C₇	1	2	yes	complemented
598	#417	C₂²×C₇	1	1	yes	characteristic
599	#417	C₂²×C₇	1	1	yes	characteristic, complemented
600	#417	C₂²×C₇	1	2	yes	complemented
601	#416	C₂²×C₇	1	1	yes	characteristic
602	#416	C₂²×C₇	1	1	yes	characteristic
603	#416	C₂²×C₇	1	1	yes	characteristic, complemented
604	#416	C₂²×C₇	1	1	yes	characteristic, complemented
605	#416	C₂²×C₇	1	1	yes	characteristic, complemented
606	#416	C₂²×C₇	1	1	yes	characteristic, complemented
607	#416	C₂²×C₇	1	1	yes	characteristic, complemented
608	#416	C₂²×C₇	1	1	yes	characteristic, complemented
609	#416	C₂²×C₇	1	2	yes	complemented
610	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
611	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
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	1	yes	characteristic, complemented
615	C₂×#102	C₂²×C₇	1	2	yes	complemented
616	C₂×#102	C₂²×C₇	1	1	yes	characteristic, complemented
617	#408	C₂²×C₇	1	1	yes	characteristic, complemented
618	#407	C₂²×C₇	1	1	yes	characteristic, complemented
619	#405	C₂²×C₇	1	1	yes	characteristic, complemented
620	C₂³×C₇	—	2	2	no	—
621	C₂³×C₇	—	2	2	no	—
622	C₂³×C₇	—	2	1	no	—
623	C₂³×C₇	—	2	2	no	—
624	C₂³×C₇	—	2	2	no	—
625	C₂³×C₇	—	2	1	no	—
626	C₂³×C₇	—	4	1	no	—
627	C₂³×C₇	—	4	2	no	—
628	C₂³×C₇	—	4	4	no	—
629	C₂³×C₇	—	4	2	no	—
630	C₂³×C₇	—	4	2	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	2	no	—
636	C₂³×C₇	—	8	1	no	—
637	C₂³×C₇	—	8	1	no	—
638	C₂³×C₇	—	8	2	no	—
639	C₂³×C₇	C₂²×D₄	1	2	yes	—
640	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
641	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
642	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
643	C₇×Q₈	—	2	2	no	—
644	C₇×Q₈	—	2	1	no	—
645	C₇×Q₈	—	2	1	no	—
646	C₇×Q₈	—	2	1	no	—
647	C₇×Q₈	—	4	2	no	—
648	C₇×Q₈	—	8	2	no	—
649	C₇×Q₈	C₂×#41	1	2	yes	—
650	C₇×D₄	—	2	4	no	—
651	C₇×D₄	—	2	4	no	—
652	C₇×D₄	—	2	4	no	—
653	C₇×D₄	—	2	2	no	—
654	C₇×D₄	—	2	2	no	—
655	C₇×D₄	—	2	2	no	—
656	C₇×D₄	—	2	1	no	—
657	C₇×D₄	—	2	1	no	—
658	C₇×D₄	—	2	2	no	—
659	C₇×D₄	—	2	2	no	—
660	C₇×D₄	—	2	1	no	—
661	C₇×D₄	—	4	2	no	—
662	C₇×D₄	—	4	4	no	—
663	C₇×D₄	—	4	2	no	—
664	C₇×D₄	—	4	4	no	—
665	C₇×D₄	—	4	2	no	—
666	C₇×D₄	—	4	2	no	—
667	C₇×D₄	—	4	2	no	—
668	C₇×D₄	—	4	4	no	—
669	C₇×D₄	—	4	4	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	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	1	no	—
690	C₂×C₄×C₇	—	2	2	no	—
691	C₂×C₄×C₇	—	2	1	no	—
692	C₂×C₄×C₇	—	2	1	no	—
693	C₂×C₄×C₇	—	2	1	no	—
694	C₂×C₄×C₇	—	2	1	no	—
695	C₂×C₄×C₇	—	2	2	no	—
696	C₂×C₄×C₇	—	2	2	no	—
697	C₂×C₄×C₇	—	2	1	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	2	no	—
703	C₂×C₄×C₇	—	4	2	no	—
704	C₂×C₄×C₇	—	8	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	1	no	—
709	C₂×C₄×C₇	—	8	1	no	—
710	C₂×C₄×C₇	—	8	2	no	—
711	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
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	C₂×#41	1	2	yes	—
718	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
719	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
720	C₇×C₈	—	2	2	no	—
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	H(5,𝔽₂)	—	2	4	no	—
727	H(5,𝔽₂)	—	4	2	no	—
728	C₂×#41	—	2	1	no	—
729	C₂×#41	—	2	2	no	—
730	C₂×#41	—	2	1	no	—
731	C₂×#41	—	2	1	no	—
732	C₂×#41	—	2	4	no	—
733	C₂×#41	—	4	2	no	—
734	C₂×#41	C₂³×C₇	1	1	yes	characteristic
735	C₂×#41	C₂³×C₇	1	1	yes	characteristic
736	C₂×#41	C₂³×C₇	1	2	yes	—
737	C₂×#41	C₂³×C₇	1	1	yes	characteristic
738	C₂×#41	C₂³×C₇	1	1	yes	characteristic
739	C₂×#41	C₂³×C₇	1	1	yes	characteristic
740	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
741	C₂²×D₄	—	2	1	no	—
742	C₂²×D₄	—	2	1	no	—
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	—	2	1	no	—
745	C₂²×D₄	—	2	2	no	—
746	C₂²×D₄	—	2	2	no	—
747	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
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	C₂³×C₇	1	1	yes	characteristic
753	AGL(1,ℤ/8)	—	2	4	no	—
754	AGL(1,ℤ/8)	—	4	2	no	—
755	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
756	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
757	C₂×D₈	—	4	2	no	—
758	C₂×D₈	C₂³×C₇	1	2	yes	—
759	C₂×D₈	C₂³×C₇	1	2	yes	—
760	C₂×D₈	C₂³×C₇	1	2	yes	—
761	C₂×D₈	C₂³×C₇	1	2	yes	—
762	#131	—	4	2	no	—
763	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
764	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
765	C₂×M₁₆	C₂³×C₇	1	2	yes	—
766	C₂²×C₈	—	4	2	no	—
767	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
768	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
769	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
770	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
771	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
772	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
773	C₂²×C₈	C₂³×C₇	1	2	yes	—
774	C₄⋊Q₈	—	2	1	no	—
775	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
776	#127	—	2	1	no	—
777	#127	—	2	2	no	—
778	#127	C₂³×C₇	1	2	yes	—
779	#126	—	2	2	no	—
780	#126	—	2	2	no	—
781	#125	—	2	1	no	—
782	#125	C₂³×C₇	1	2	yes	—
783	#124	—	2	1	no	—
784	#124	—	2	2	no	—
785	#124	—	2	2	no	—
786	#124	—	2	2	no	—
787	#124	C₂³×C₇	1	2	yes	—
788	#123	—	2	2	no	—
789	#123	—	2	2	no	—
790	#123	—	2	2	no	—
791	#123	—	2	2	no	—
792	#123	—	2	2	no	—
793	#123	C₇×D₄	1	2	yes	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	2	no	—
796	C₂²⋊Q₈	—	2	2	no	—
797	C₂²⋊Q₈	—	2	2	no	—
798	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
799	C₂²⋊Q₈	C₇×D₄	1	1	yes	characteristic
800	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
801	#121	—	2	1	no	—
802	#121	—	2	2	no	—
803	#121	—	2	2	no	—
804	#121	—	2	2	no	—
805	#121	—	2	2	no	—
806	#121	—	2	2	no	—
807	#121	—	2	1	no	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	—	2	1	no	—
811	#121	—	2	1	no	—
812	#121	—	2	1	no	—
813	#121	—	2	2	no	—
814	#121	—	2	2	no	—
815	#121	—	2	2	no	—
816	#121	—	2	2	no	—
817	#121	C₇×D₄	1	1	yes	characteristic
818	#121	C₇×D₄	1	1	yes	characteristic
819	#121	C₂³×C₇	1	2	yes	—
820	#121	C₂³×C₇	1	2	yes	—
821	#121	C₂³×C₇	1	2	yes	—
822	#121	C₂³×C₇	1	2	yes	—
823	#121	C₂³×C₇	1	2	yes	—
824	#121	C₂³×C₇	1	2	yes	—
825	#121	C₂³×C₇	1	2	yes	—
826	#120	—	2	2	no	—
827	#120	—	2	2	no	—
828	#120	—	2	2	no	—
829	#120	—	2	2	no	—
830	#120	—	2	2	no	—
831	#120	C₇×D₄	1	2	yes	—
832	C₄×Q₈	—	2	1	no	—
833	C₄×Q₈	C₂³×C₇	1	2	yes	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	1	no	—
837	C₄×D₄	—	2	1	no	—
838	C₄×D₄	—	2	2	no	—
839	C₄×D₄	—	2	2	no	—
840	C₄×D₄	—	2	2	no	—
841	C₄×D₄	—	2	2	no	—
842	C₄×D₄	—	2	2	no	—
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	—
847	C₄×D₄	C₂³×C₇	1	2	yes	—
848	#117	—	2	1	no	—
849	#117	—	2	1	no	—
850	#117	—	2	1	no	—
851	#117	—	2	2	no	—
852	#117	C₂³×C₇	1	1	yes	characteristic
853	#117	C₂³×C₇	1	1	yes	characteristic
854	#117	C₂³×C₇	1	1	yes	characteristic
855	#117	C₂³×C₇	1	1	yes	characteristic
856	#117	C₂³×C₇	1	2	yes	—
857	#117	C₂³×C₇	1	1	yes	characteristic
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	1	yes	characteristic
862	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
863	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
864	C₂×C₂²⋊C₄	—	2	1	no	—
865	C₂×C₂²⋊C₄	—	2	1	no	—
866	C₂×C₂²⋊C₄	—	2	1	no	—
867	C₂×C₂²⋊C₄	—	2	2	no	—
868	C₂×C₂²⋊C₄	—	2	2	no	—
869	C₂×C₄²	—	2	1	no	—
870	#107	C₂³×C₇	1	2	yes	—
871	#107	C₂³×C₇	1	2	yes	—
872	#107	C₂³×C₇	1	2	yes	—
873	#107	C₂³×C₇	1	2	yes	—
874	#106	C₂³×C₇	1	2	yes	—
875	#106	C₂³×C₇	1	2	yes	—
876	C₄⋊C₈	C₂³×C₇	1	2	yes	—
877	C₄⋊C₈	C₂³×C₇	1	2	yes	—
878	#103	C₂³×C₇	1	1	yes	characteristic
879	#103	C₂³×C₇	1	1	yes	characteristic
880	#103	C₂³×C₇	1	1	yes	characteristic
881	#103	C₂³×C₇	1	1	yes	characteristic
882	#103	C₂³×C₇	1	1	yes	characteristic
883	#103	C₂³×C₇	1	1	yes	characteristic
884	#103	C₂³×C₇	1	1	yes	characteristic
885	#103	C₂³×C₇	1	1	yes	characteristic
886	#103	C₂³×C₇	1	2	yes	—
887	#103	C₂³×C₇	1	2	yes	—
888	#102	C₂³×C₇	1	1	yes	characteristic
889	#102	C₂³×C₇	1	2	yes	—
890	#102	C₂³×C₇	1	1	yes	characteristic
891	#102	C₂³×C₇	1	1	yes	characteristic
892	#102	C₂³×C₇	1	1	yes	characteristic
893	#102	C₂³×C₇	1	1	yes	characteristic
894	#102	C₂³×C₇	1	1	yes	characteristic
895	#102	C₂³×C₇	1	1	yes	characteristic
896	#102	C₂³×C₇	1	1	yes	characteristic
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	2	yes	—
901	#102	C₂³×C₇	1	2	yes	—
902	#102	C₂³×C₇	1	2	yes	—
903	#102	C₂³×C₇	1	2	yes	—
904	#102	C₂³×C₇	1	2	yes	—
905	#102	C₂³×C₇	1	2	yes	—
906	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
907	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
908	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
909	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
910	#97	C₂³×C₇	1	2	yes	—
911	C₄×C₈	C₂³×C₇	1	2	yes	—
912	C₂²×C₇	—	2	1	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	1	no	—
919	C₂²×C₇	—	2	2	no	—
920	C₂²×C₇	—	2	2	no	—
921	C₂²×C₇	—	2	2	no	—
922	C₂²×C₇	—	2	1	no	—
923	C₂²×C₇	—	4	4	no	—
924	C₂²×C₇	—	4	1	no	—
925	C₂²×C₇	—	4	1	no	—
926	C₂²×C₇	—	4	2	no	—
927	C₂²×C₇	—	4	1	no	—
928	C₂²×C₇	—	4	2	no	—
929	C₂²×C₇	—	4	1	no	—
930	C₂²×C₇	—	4	2	no	—
931	C₂²×C₇	—	4	2	no	—
932	C₂²×C₇	—	4	2	no	—
933	C₂²×C₇	—	4	2	no	—
934	C₂²×C₇	—	4	1	no	—
935	C₂²×C₇	—	8	4	no	—
936	C₂²×C₇	—	16	2	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	1	no	—
952	C₄×C₇	—	4	1	no	—
953	C₄×C₇	—	4	2	no	—
954	C₄×C₇	—	4	2	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	1	no	—
960	C₂⁴	—	2	2	no	—
961	C₂⁴	—	2	1	no	—
962	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
963	#41	—	2	2	no	—
964	#41	—	2	2	no	—
965	#41	—	2	2	no	—
966	#41	—	2	2	no	—
967	#41	—	2	4	no	—
968	#41	—	2	2	no	—
969	#41	—	2	2	no	—
970	#41	—	2	2	no	—
971	#41	—	4	4	no	—
972	#41	—	4	1	no	—
973	#41	—	4	1	no	—
974	#41	—	4	2	no	—
975	#41	—	4	4	no	—
976	#41	—	4	4	no	—
977	#41	—	8	4	no	—
978	#41	C₇×#41	1	4	yes	complemented
979	C₂×Q₈	—	2	1	no	—
980	C₂×Q₈	—	2	2	no	—
981	C₂×Q₈	—	2	2	no	—
982	C₂×Q₈	—	4	1	no	—
983	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
984	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
985	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	2	no	—
988	C₂×D₄	—	2	4	no	—
989	C₂×D₄	—	2	2	no	—
990	C₂×D₄	—	2	2	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	2	no	—
996	C₂×D₄	—	2	2	no	—
997	C₂×D₄	—	2	2	no	—
998	C₂×D₄	—	2	2	no	—
999	C₂×D₄	—	2	2	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	2	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	—	2	2	no	—
1010	C₂×D₄	—	4	1	no	—
1011	C₂×D₄	—	4	2	no	—
1012	C₂×D₄	—	4	4	no	—
1013	C₂×D₄	—	4	8	no	—
1014	C₂×D₄	—	4	4	no	—
1015	C₂×D₄	—	8	4	no	—
1016	C₂×D₄	—	8	2	no	—
1017	C₂×D₄	—	8	2	no	—
1018	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1019	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1020	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1021	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
1022	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1023	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1024	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1025	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	2	no	—
1028	C₂²×C₄	—	2	2	no	—
1029	C₂²×C₄	—	2	1	no	—
1030	C₂²×C₄	—	2	1	no	—
1031	C₂²×C₄	—	2	1	no	—
1032	C₂²×C₄	—	2	1	no	—
1033	C₂²×C₄	—	2	1	no	—
1034	C₂²×C₄	—	2	2	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	—	2	2	no	—
1042	C₂²×C₄	—	4	4	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	2	yes	—
1048	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1049	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1050	SD₁₆	—	2	4	no	—
1051	SD₁₆	—	4	2	no	—
1052	D₈	—	2	4	no	—
1053	D₈	—	4	2	no	—
1054	D₈	—	4	2	no	—
1055	D₈	—	4	2	no	—
1056	M₁₆	—	2	2	no	—
1057	M₁₆	—	2	2	no	—
1058	M₁₆	—	4	2	no	—
1059	C₂×C₈	—	2	2	no	—
1060	C₂×C₈	—	2	2	no	—
1061	C₂×C₈	—	4	1	no	—
1062	C₂×C₈	—	4	1	no	—
1063	C₂×C₈	—	4	1	no	—
1064	C₂×C₈	—	4	1	no	—
1065	C₂×C₈	—	4	2	no	—
1066	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
1067	C₂×C₈	C₂⁴×C₇	1	2	yes	—
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	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	2	no	—
1079	C₄⋊C₄	—	2	2	no	—
1080	C₄⋊C₄	—	2	2	no	—
1081	C₄⋊C₄	—	2	2	no	—
1082	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1083	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1084	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1085	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
1086	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1087	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1088	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1089	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1090	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1091	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1092	C₂²⋊C₄	—	2	1	no	—
1093	C₂²⋊C₄	—	2	1	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	2	no	—
1097	C₂²⋊C₄	—	2	2	no	—
1098	C₂²⋊C₄	—	2	2	no	—
1099	C₂²⋊C₄	—	2	2	no	—
1100	C₂²⋊C₄	—	2	2	no	—
1101	C₂²⋊C₄	—	2	2	no	—
1102	C₂²⋊C₄	—	2	2	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	C₂×C₇×D₄	1	2	yes	—
1111	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1112	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1113	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1114	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
1115	C₄²	—	2	1	no	—
1116	C₄²	—	2	1	no	—
1117	C₄²	—	2	1	no	—
1118	C₄²	—	2	1	no	—
1119	C₄²	—	2	2	no	—
1120	C₄²	—	2	2	no	—
1121	C₄²	C₂⁴×C₇	1	2	yes	—
1122	C₂×C₇	—	2	2	no	—
1123	C₂×C₇	—	2	2	no	—
1124	C₂×C₇	—	4	1	no	—
1125	C₂×C₇	—	4	2	no	—
1126	C₂×C₇	—	4	2	no	—
1127	C₂×C₇	—	8	1	no	—
1128	C₂×C₇	—	8	2	no	—
1129	C₂×C₇	—	8	2	no	—
1130	C₂×C₇	C₂×#546	1	1	yes	characteristic
1131	C₂×C₇	C₂×#576	1	1	yes	characteristic
1132	C₂×C₇	#3584	1	1	yes	characteristic
1133	C₂³	—	2	1	no	—
1134	C₂³	—	2	2	no	—
1135	C₂³	—	2	2	no	—
1136	C₂³	—	2	2	no	—
1137	C₂³	—	2	2	no	—
1138	C₂³	—	2	1	no	—
1139	C₂³	—	4	1	no	—
1140	C₂³	—	4	2	no	—
1141	C₂³	—	4	4	no	—
1142	C₂³	—	4	2	no	—
1143	C₂³	—	4	2	no	—
1144	C₂³	—	4	2	no	—
1145	C₂³	—	8	1	no	—
1146	C₂³	—	8	1	no	—
1147	C₂³	—	8	1	no	—
1148	C₂³	—	8	2	no	—
1149	C₂³	—	8	1	no	—
1150	C₂³	—	8	1	no	—
1151	C₂³	—	8	2	no	—
1152	C₂³	C₂²×C₇×D₄	1	2	yes	—
1153	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1154	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1155	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1156	Q₈	—	2	1	no	—
1157	Q₈	—	2	2	no	—
1158	Q₈	—	2	1	no	—
1159	Q₈	—	2	1	no	—
1160	Q₈	—	4	2	no	—
1161	Q₈	—	8	2	no	—
1162	Q₈	C₂×C₇×#41	1	2	yes	—
1163	D₄	—	2	4	no	—
1164	D₄	—	2	4	no	—
1165	D₄	—	2	4	no	—
1166	D₄	—	2	2	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	1	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	2	no	—
1171	D₄	—	2	2	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	2	2	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	4	no	—
1176	D₄	—	4	2	no	—
1177	D₄	—	4	4	no	—
1178	D₄	—	4	2	no	—
1179	D₄	—	4	2	no	—
1180	D₄	—	4	2	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	4	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	8	2	no	—
1186	D₄	—	8	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	1	no	—
1200	C₂×C₄	—	2	2	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	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	2	no	—
1209	C₂×C₄	—	2	2	no	—
1210	C₂×C₄	—	2	1	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	2	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	8	2	no	—
1218	C₂×C₄	—	8	2	no	—
1219	C₂×C₄	—	8	2	no	—
1220	C₂×C₄	—	8	1	no	—
1221	C₂×C₄	—	8	1	no	—
1222	C₂×C₄	—	8	1	no	—
1223	C₂×C₄	—	8	2	no	—
1224	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
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	C₂×C₇×#41	1	2	yes	—
1231	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
1232	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1233	C₈	—	2	2	no	—
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	C₇	#61171	1	1	yes	characteristic, direct product factor, Sylow
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	2	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	2	no	—
1248	C₂²	—	2	1	no	—
1249	C₂²	—	2	2	no	—
1250	C₂²	—	2	2	no	—
1251	C₂²	—	4	4	no	—
1252	C₂²	—	4	1	no	—
1253	C₂²	—	4	1	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	2	no	—
1258	C₂²	—	4	1	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	—	4	1	no	—
1261	C₂²	—	4	2	no	—
1262	C₂²	—	4	2	no	—
1263	C₂²	—	8	4	no	—
1264	C₂²	—	16	2	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	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	2	no	—
1279	C₄	—	4	2	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	2	no	—
1294	C₂	C₂×C₇×#546	1	1	yes	characteristic
1295	C₂	C₂×C₇×#576	1	1	yes	characteristic
1296	C₂	C₇×#3584	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×#3494	C₂	semidirect
2. C₇×#3488	C₂	semidirect
3. C₇×#3319	C₂	semidirect
4. C₇×#3318	C₂	semidirect
5. C₇×#3309	C₂	semidirect
6. C₇×#3308	C₂	semidirect
7. C₇×#3305	C₂	semidirect
8. C₇×#3301	C₂	semidirect
9. C₇×#3297	C₂	semidirect
10. C₇×#3294	C₂	semidirect
11. C₇×#3136	C₂	semidirect
12. C₇×#3098	C₂	semidirect
13. C₇×#3094	C₂	semidirect
14. C₇×#3083	C₂	semidirect
15. C₇×#3062	C₂	semidirect
16. C₂×C₇×#466	C₂	semidirect
17. C₇×#3041	C₂	semidirect
18. C₇×#3008	C₂	semidirect
19. C₇×#3006	C₂	semidirect
20. C₇×#2946	C₂	semidirect
21. C₇×#2929	C₂	semidirect
22. C₇×#2897	C₂	semidirect
23. C₂×C₇×#416	C₂	semidirect
27. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
28. C₂²×C₇×D₈	C₂²	semidirect
29. C₂×C₇×#131	C₂²	semidirect
30. C₂³×C₇×C₈	C₂²	semidirect
31. C₇×#555	C₂²	semidirect
32. C₇×#553	C₂²	semidirect
33. C₇×#553	C₂²	semidirect
35. C₇×#550	C₂²	semidirect
36. C₇×#548	C₂²	semidirect
37. C₇×#547	C₂²	semidirect
40. C₇×#546	C₂²	semidirect
42. C₇×D₄²	C₂²	semidirect
43. C₇×#544	C₂²	semidirect
50. C₇×#535	C₂²	semidirect
57. C₂×C₇×#121	C₂²	semidirect
59. C₇×#520	C₂²	semidirect
60. C₇×#518	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×#484	C₂²	semidirect
68. C₇×#482	C₂²	semidirect
69. C₇×#482	C₂²	semidirect
70. C₇×#482	C₂²	semidirect
71. C₇×#481	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×#466	C₂²	semidirect
81. C₇×#466	C₂²	semidirect
82. C₇×#466	C₂²	semidirect
83. C₇×#466	C₂²	semidirect
84. C₇×#466	C₂²	semidirect
85. C₇×#465	C₂²	semidirect
86. C₇×#463	C₂²	semidirect
87. C₇×#463	C₂²	semidirect
88. C₇×#459	C₂²	semidirect
89. C₇×#459	C₂²	semidirect
90. C₇×#449	C₂²	semidirect
91. C₇×#449	C₂²	semidirect
92. C₇×#449	C₂²	semidirect
93. C₇×#449	C₂²	semidirect
94. C₇×#448	C₂²	semidirect
95. C₇×#447	C₂²	semidirect
96. C₇×#447	C₂²	semidirect
97. C₇×#447	C₂²	semidirect
98. C₇×#442	C₂²	semidirect
99. C₇×#440	C₂²	semidirect
100. C₄×C₇×SD₁₆	C₂²	semidirect
101. C₄×C₇×D₈	C₂²	semidirect
102. C₇×#435	C₂²	semidirect
103. C₇×#435	C₂²	semidirect
104. C₇×C₈×D₄	C₂²	semidirect
105. C₇×C₈×D₄	C₂²	semidirect
106. C₇×#428	C₂²	semidirect
107. C₇×#428	C₂²	semidirect
108. C₂×C₇×#107	C₂²	semidirect
109. C₇×#424	C₂²	semidirect
110. C₇×#418	C₂²	semidirect
111. C₇×#418	C₂²	semidirect
112. C₇×#418	C₂²	semidirect
114. C₇×#417	C₂²	semidirect
115. C₇×#417	C₂²	semidirect
118. C₇×#416	C₂²	semidirect
119. C₇×#416	C₂²	semidirect
120. C₇×#416	C₂²	semidirect
121. C₇×#416	C₂²	semidirect
122. C₇×#416	C₂²	semidirect
123. C₇×#416	C₂²	semidirect
124. C₇×#416	C₂²	semidirect
125. C₂×C₇×#103	C₂²	semidirect
126. C₂×C₇×#103	C₂²	semidirect
127. C₂×C₇×#102	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. C₇×#407	C₂²	semidirect
134. C₇×#405	C₂²	semidirect
135. #61171	C₇	direct (N × H)
322. #3494	C₂×C₇	semidirect
323. #3488	C₂×C₇	semidirect
324. #3319	C₂×C₇	semidirect
325. #3318	C₂×C₇	semidirect
326. #3309	C₂×C₇	semidirect
327. #3308	C₂×C₇	semidirect
328. #3305	C₂×C₇	semidirect
329. #3301	C₂×C₇	semidirect
330. #3297	C₂×C₇	semidirect
331. #3294	C₂×C₇	semidirect
332. #3136	C₂×C₇	semidirect
333. #3098	C₂×C₇	semidirect
334. #3094	C₂×C₇	semidirect
335. #3083	C₂×C₇	semidirect
336. #3062	C₂×C₇	semidirect
337. C₂×#466	C₂×C₇	semidirect
338. #3041	C₂×C₇	semidirect
339. #3008	C₂×C₇	semidirect
340. #3006	C₂×C₇	semidirect
341. #2946	C₂×C₇	semidirect
342. #2929	C₂×C₇	semidirect
343. #2897	C₂×C₇	semidirect
344. C₂×#416	C₂×C₇	semidirect
365. C₇×#41	#41	semidirect
512. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
513. C₂²×D₈	C₂²×C₇	semidirect
514. C₂×#131	C₂²×C₇	semidirect
515. C₂³×C₈	C₂²×C₇	semidirect
516. #555	C₂²×C₇	semidirect
517. #553	C₂²×C₇	semidirect
518. #553	C₂²×C₇	semidirect
520. #550	C₂²×C₇	semidirect
521. #548	C₂²×C₇	semidirect
522. #547	C₂²×C₇	semidirect
525. #546	C₂²×C₇	semidirect
527. D₄²	C₂²×C₇	semidirect
528. #544	C₂²×C₇	semidirect
535. #535	C₂²×C₇	semidirect
542. C₂×#121	C₂²×C₇	semidirect
544. #520	C₂²×C₇	semidirect
545. #518	C₂²×C₇	semidirect
546. C₂×#117	C₂²×C₇	semidirect
547. #490	C₂²×C₇	semidirect
548. #489	C₂²×C₇	semidirect
549. #488	C₂²×C₇	semidirect
550. #486	C₂²×C₇	semidirect
551. #485	C₂²×C₇	semidirect
552. #484	C₂²×C₇	semidirect
553. #482	C₂²×C₇	semidirect
554. #482	C₂²×C₇	semidirect
555. #482	C₂²×C₇	semidirect
556. #481	C₂²×C₇	semidirect
557. #480	C₂²×C₇	semidirect
558. #480	C₂²×C₇	semidirect
559. #479	C₂²×C₇	semidirect
560. #478	C₂²×C₇	semidirect
561. #477	C₂²×C₇	semidirect
562. #474	C₂²×C₇	semidirect
563. #469	C₂²×C₇	semidirect
564. #468	C₂²×C₇	semidirect
565. #466	C₂²×C₇	semidirect
566. #466	C₂²×C₇	semidirect
567. #466	C₂²×C₇	semidirect
568. #466	C₂²×C₇	semidirect
569. #466	C₂²×C₇	semidirect
570. #465	C₂²×C₇	semidirect
571. #463	C₂²×C₇	semidirect
572. #463	C₂²×C₇	semidirect
573. #459	C₂²×C₇	semidirect
574. #459	C₂²×C₇	semidirect
575. #449	C₂²×C₇	semidirect
576. #449	C₂²×C₇	semidirect
577. #449	C₂²×C₇	semidirect
578. #449	C₂²×C₇	semidirect
579. #448	C₂²×C₇	semidirect
580. #447	C₂²×C₇	semidirect
581. #447	C₂²×C₇	semidirect
582. #447	C₂²×C₇	semidirect
583. #442	C₂²×C₇	semidirect
584. #440	C₂²×C₇	semidirect
585. C₄×SD₁₆	C₂²×C₇	semidirect
586. C₄×D₈	C₂²×C₇	semidirect
587. #435	C₂²×C₇	semidirect
588. #435	C₂²×C₇	semidirect
589. C₈×D₄	C₂²×C₇	semidirect
590. C₈×D₄	C₂²×C₇	semidirect
591. #428	C₂²×C₇	semidirect
592. #428	C₂²×C₇	semidirect
593. C₂×#107	C₂²×C₇	semidirect
594. #424	C₂²×C₇	semidirect
595. #418	C₂²×C₇	semidirect
596. #418	C₂²×C₇	semidirect
597. #418	C₂²×C₇	semidirect
599. #417	C₂²×C₇	semidirect
600. #417	C₂²×C₇	semidirect
603. #416	C₂²×C₇	semidirect
604. #416	C₂²×C₇	semidirect
605. #416	C₂²×C₇	semidirect
606. #416	C₂²×C₇	semidirect
607. #416	C₂²×C₇	semidirect
608. #416	C₂²×C₇	semidirect
609. #416	C₂²×C₇	semidirect
610. C₂×#103	C₂²×C₇	semidirect
611. C₂×#103	C₂²×C₇	semidirect
612. C₂×#102	C₂²×C₇	semidirect
613. C₂×#102	C₂²×C₇	semidirect
614. C₂×#102	C₂²×C₇	semidirect
615. C₂×#102	C₂²×C₇	semidirect
616. C₂×#102	C₂²×C₇	semidirect
617. #408	C₂²×C₇	semidirect
618. #407	C₂²×C₇	semidirect
619. #405	C₂²×C₇	semidirect
978. #41	C₇×#41	semidirect
1239. C₇	#61171	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×#3494	2
C₇×#3488	2
C₇×#3319	2
C₇×#3318	2
C₇×#3309	2
C₇×#3308	2
C₇×#3305	2
C₇×#3301	2
C₇×#3297	2
C₇×#3294	2
C₇×#3136	2
C₇×#3098	2
C₇×#3094	2
C₇×#3083	2
C₇×#3062	2
C₂×C₇×#466	2
C₇×#3041	2
C₇×#3008	2
C₇×#3006	2
C₇×#2946	2
C₇×#2929	2
C₇×#2897	2
C₂×C₇×#416	2
#61171	7

Subgroups — C7×#61171 #13238387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61171 #13238387