Subgroups — C₇×#61255 #13238471

Order 1792.

1898 conjugacy classes of subgroups.

The subgroup lattice has 1318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3475	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3355	C₂	1	2	yes	maximal, complemented
4	C₇×#3351	C₂	1	2	yes	maximal, complemented
5	C₇×#3350	C₂	1	2	yes	maximal, complemented
6	C₇×#3347	C₂	1	2	yes	maximal, complemented
7	C₇×#3346	C₂	1	2	yes	maximal, complemented
8	C₇×#3345	C₂	1	2	yes	maximal, complemented
9	C₇×#3339	C₂	1	2	yes	maximal, complemented
10	C₇×#3337	C₂	1	2	yes	maximal, complemented
11	C₇×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3094	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3093	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3092	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3055	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2911	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₇×#428	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
25	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
26	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
27	C₇×#556	C₂²	1	1	yes	characteristic, complemented
28	C₇×#555	C₂²	1	1	yes	characteristic, complemented
29	C₇×#554	C₂²	1	1	yes	characteristic, complemented
30	C₇×#553	—	2	1	no	—
31	C₇×#553	—	2	1	no	—
32	C₇×#553	—	2	1	no	—
33	C₇×#553	—	2	1	no	—
34	C₇×#553	C₂²	1	2	yes	—
35	C₇×#553	C₂²	1	2	yes	—
36	C₇×#553	C₂²	1	2	yes	—
37	C₇×#553	C₂²	1	2	yes	—
38	C₇×#553	C₂²	1	1	yes	characteristic, complemented
39	C₇×#553	C₂²	1	1	yes	characteristic, complemented
40	C₇×#552	—	2	1	no	—
41	C₇×#552	C₂²	1	1	yes	characteristic, complemented
42	C₇×#552	C₂²	1	1	yes	characteristic, complemented
43	C₇×#551	—	2	1	no	—
44	C₇×#551	—	2	1	no	—
45	C₇×#547	C₂²	1	1	yes	characteristic, complemented
46	C₇×#546	—	2	1	no	—
47	C₇×#533	C₂²	1	1	yes	characteristic
48	C₇×#529	—	2	1	no	—
49	C₇×#529	—	2	1	no	—
50	C₇×#529	—	2	1	no	—
51	C₂×C₇×#126	—	2	1	no	—
52	C₂×C₇×#125	C₂²	1	1	yes	characteristic
53	C₇×#525	C₂²	1	1	yes	characteristic
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₂×C₇×#123	—	2	1	no	—
56	C₂×C₇×#121	—	2	1	no	—
57	C₂×C₇×#121	C₂²	1	1	yes	characteristic
58	C₂×C₇×#121	C₂²	1	1	yes	characteristic
59	C₄×C₇×#41	—	2	1	no	—
60	C₄×C₇×#41	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₇×D₄	—	2	1	no	—
62	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
63	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
64	C₂×C₇×#117	C₂²	1	1	yes	characteristic
65	C₂×C₇×#117	C₂²	1	1	yes	characteristic
66	C₂×C₇×#117	C₂²	1	1	yes	characteristic
67	C₂²×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
68	C₇×#501	C₂²	1	2	yes	complemented
69	C₇×#501	C₂²	1	2	yes	complemented
70	C₇×#499	C₂²	1	2	yes	complemented
71	C₇×#499	C₂²	1	2	yes	complemented
72	C₇×#485	C₂²	1	2	yes	complemented
73	C₇×#485	C₂²	1	2	yes	complemented
74	C₇×#484	C₂²	1	2	yes	complemented
75	C₇×#483	C₂²	1	2	yes	complemented
76	C₇×#482	C₂²	1	2	yes	complemented
77	C₇×#482	C₂²	1	2	yes	complemented
78	C₇×#482	C₂²	1	2	yes	complemented
79	C₇×#482	C₂²	1	2	yes	complemented
80	C₇×#482	C₂²	1	2	yes	complemented
81	C₇×#482	C₂²	1	2	yes	complemented
82	C₇×#481	C₂²	1	2	yes	complemented
83	C₇×#481	C₂²	1	2	yes	complemented
84	C₇×#481	C₂²	1	2	yes	complemented
85	C₇×#480	C₂²	1	2	yes	complemented
86	C₇×#480	C₂²	1	2	yes	complemented
87	C₇×#480	C₂²	1	2	yes	complemented
88	C₇×#479	C₂²	1	2	yes	complemented
89	C₇×#479	C₂²	1	2	yes	complemented
90	C₇×#478	C₂²	1	2	yes	complemented
91	C₇×#478	C₂²	1	2	yes	complemented
92	C₇×#478	C₂²	1	2	yes	complemented
93	C₇×#478	C₂²	1	2	yes	complemented
94	C₇×#476	C₂²	1	2	yes	complemented
95	C₇×#474	C₂²	1	2	yes	complemented
96	C₇×#469	C₂²	1	2	yes	complemented
97	C₇×#469	C₂²	1	2	yes	complemented
98	C₇×#468	C₂²	1	2	yes	complemented
99	C₇×#468	C₂²	1	2	yes	complemented
100	C₇×#466	C₂²	1	2	yes	complemented
101	C₇×#466	C₂²	1	2	yes	complemented
102	C₇×#465	C₂²	1	2	yes	complemented
103	C₇×#465	C₂²	1	2	yes	complemented
104	C₇×#442	C₂²	1	2	yes	complemented
105	C₇×#440	C₂²	1	2	yes	complemented
106	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
107	C₄×C₇×D₈	C₂²	1	2	yes	complemented
108	C₇×#436	C₂²	1	2	yes	complemented
109	C₇×#435	C₂²	1	2	yes	complemented
110	C₇×#435	C₂²	1	2	yes	complemented
111	C₇×C₈×D₄	C₂²	1	2	yes	complemented
112	C₇×#428	C₂²	1	1	yes	characteristic
113	C₇×#428	C₂²	1	1	yes	characteristic
114	C₇×#428	C₂²	1	1	yes	characteristic
115	C₇×#428	C₂²	1	1	yes	characteristic
116	C₇×#428	C₂²	1	1	yes	characteristic
117	C₇×#428	C₂²	1	1	yes	characteristic
118	C₇×#428	C₂²	1	1	yes	characteristic
119	C₇×#428	C₂²	1	1	yes	characteristic
120	C₇×#428	C₂²	1	1	yes	characteristic
121	C₇×#428	C₂²	1	2	yes	complemented
122	C₇×#428	C₂²	1	2	yes	complemented
123	C₇×#428	C₂²	1	2	yes	complemented
124	C₇×#428	C₂²	1	2	yes	complemented
125	C₇×#427	C₂²	1	2	yes	complemented
126	C₇×#427	C₂²	1	2	yes	complemented
127	C₂×C₇×#107	C₂²	1	2	yes	complemented
128	C₂×C₇×#106	C₂²	1	2	yes	complemented
129	C₇×#423	C₂²	1	1	yes	characteristic
130	C₇×#418	C₂²	1	1	yes	characteristic
131	C₇×#418	C₂²	1	1	yes	characteristic
132	C₇×#418	C₂²	1	1	yes	characteristic
133	C₇×#417	C₂²	1	1	yes	characteristic
134	C₇×#417	C₂²	1	1	yes	characteristic
135	C₇×#417	C₂²	1	1	yes	characteristic
136	C₇×#407	C₂²	1	1	yes	characteristic
137	C₇×#407	C₂²	1	1	yes	characteristic
138	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
139	#61255	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	C₂³	1	1	yes	characteristic
142	C₂²×C₇×D₄	—	2	1	no	—
143	C₂²×C₇×D₄	—	2	1	no	—
144	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
145	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₇	—	2	1	no	—
147	C₂³×C₄×C₇	—	2	1	no	—
148	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
149	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
150	C₇×AGL(1,ℤ/8)	—	2	4	no	—
151	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₇×D₈	C₂³	1	2	yes	—
153	C₂×C₇×M₁₆	—	2	4	no	—
154	C₂×C₇×M₁₆	—	2	4	no	—
155	C₂×C₇×M₁₆	C₂³	1	2	yes	—
156	C₂×C₇×M₁₆	C₂³	1	2	yes	—
157	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
158	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
159	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
160	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
161	C₂²×C₇×C₈	C₂³	1	2	yes	—
162	C₂²×C₇×C₈	C₂³	1	2	yes	—
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₇×#126	—	2	2	no	—
166	C₇×#126	—	2	2	no	—
167	C₇×#126	—	2	2	no	—
168	C₇×#126	—	2	2	no	—
169	C₇×#126	—	2	1	no	—
170	C₇×#126	—	2	1	no	—
171	C₇×#126	—	2	1	no	—
172	C₇×#126	—	2	1	no	—
173	C₇×#126	—	2	1	no	—
174	C₇×#126	—	2	1	no	—
175	C₇×#125	—	2	1	no	—
176	C₇×#125	—	2	1	no	—
177	C₇×#125	—	2	1	no	—
178	C₇×#125	—	2	1	no	—
179	C₇×#125	—	2	1	no	—
180	C₇×#125	C₂³	1	1	yes	characteristic
181	C₇×#125	C₂³	1	1	yes	characteristic
182	C₇×#125	C₂³	1	2	yes	—
183	C₇×#125	C₂³	1	2	yes	—
184	C₇×#124	—	2	1	no	—
185	C₇×#124	—	2	1	no	—
186	C₇×#124	—	2	1	no	—
187	C₇×#123	—	2	1	no	—
188	C₇×#123	—	2	1	no	—
189	C₇×#123	—	2	1	no	—
190	C₇×#123	—	2	1	no	—
191	C₇×#123	—	2	2	no	—
192	C₇×#123	—	2	2	no	—
193	C₇×#123	—	2	2	no	—
194	C₇×#123	—	2	2	no	—
195	C₇×#123	—	2	1	no	—
196	C₇×#123	—	2	1	no	—
197	C₇×#123	—	2	1	no	—
198	C₇×#123	—	2	1	no	—
199	C₇×C₂²⋊Q₈	—	2	1	no	—
200	C₇×C₂²⋊Q₈	—	2	1	no	—
201	C₇×C₂²⋊Q₈	—	2	1	no	—
202	C₇×C₂²⋊Q₈	—	2	1	no	—
203	C₇×C₂²⋊Q₈	—	2	1	no	—
204	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
205	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
206	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
207	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
208	C₇×#121	—	2	2	no	—
209	C₇×#121	—	2	2	no	—
210	C₇×#121	—	2	2	no	—
211	C₇×#121	—	2	2	no	—
212	C₇×#121	—	2	1	no	—
213	C₇×#121	—	2	1	no	—
214	C₇×#121	—	2	1	no	—
215	C₇×#121	—	2	1	no	—
216	C₇×#121	—	2	1	no	—
217	C₇×#121	—	2	1	no	—
218	C₇×#121	—	2	1	no	—
219	C₇×#121	C₂³	1	1	yes	characteristic
220	C₇×#121	C₂³	1	1	yes	characteristic
221	C₇×#121	C₂³	1	2	yes	—
222	C₇×#121	C₂³	1	2	yes	—
223	C₇×#121	C₂³	1	2	yes	—
224	C₇×#121	C₂³	1	2	yes	—
225	C₇×#121	C₂³	1	1	yes	characteristic
226	C₇×#121	C₂³	1	1	yes	characteristic
227	C₇×#120	—	2	1	no	—
228	C₇×#120	—	2	1	no	—
229	C₄×C₇×Q₈	—	2	1	no	—
230	C₄×C₇×Q₈	—	2	1	no	—
231	C₄×C₇×Q₈	—	2	1	no	—
232	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
233	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
234	C₄×C₇×D₄	—	2	1	no	—
235	C₄×C₇×D₄	—	2	1	no	—
236	C₄×C₇×D₄	—	2	1	no	—
237	C₄×C₇×D₄	—	2	1	no	—
238	C₄×C₇×D₄	—	2	1	no	—
239	C₄×C₇×D₄	—	2	1	no	—
240	C₄×C₇×D₄	—	2	1	no	—
241	C₄×C₇×D₄	—	2	2	no	—
242	C₄×C₇×D₄	—	2	2	no	—
243	C₄×C₇×D₄	—	2	2	no	—
244	C₄×C₇×D₄	—	2	2	no	—
245	C₄×C₇×D₄	—	2	1	no	—
246	C₄×C₇×D₄	—	2	1	no	—
247	C₄×C₇×D₄	—	2	1	no	—
248	C₄×C₇×D₄	—	2	1	no	—
249	C₄×C₇×D₄	D₄	1	1	yes	characteristic
250	C₄×C₇×D₄	D₄	1	1	yes	characteristic
251	C₄×C₇×D₄	D₄	1	1	yes	characteristic
252	C₄×C₇×D₄	D₄	1	1	yes	characteristic
253	C₄×C₇×D₄	C₂³	1	2	yes	—
254	C₄×C₇×D₄	C₂³	1	2	yes	—
255	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
256	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
257	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
258	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
259	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
260	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
261	C₇×#117	—	2	1	no	—
262	C₇×#117	—	2	1	no	—
263	C₇×#117	—	2	1	no	—
264	C₇×#117	—	2	1	no	—
265	C₇×#117	—	2	1	no	—
266	C₇×#117	—	2	1	no	—
267	C₇×#117	—	2	1	no	—
268	C₇×#117	—	2	1	no	—
269	C₇×#117	—	2	1	no	—
270	C₇×#117	—	2	1	no	—
271	C₇×#117	C₂³	1	1	yes	characteristic
272	C₇×#117	C₂³	1	1	yes	characteristic
273	C₇×#117	C₂³	1	1	yes	characteristic
274	C₇×#117	C₂³	1	1	yes	characteristic
275	C₇×#117	C₂³	1	2	yes	—
276	C₇×#117	C₂³	1	2	yes	—
277	C₇×#117	C₂³	1	1	yes	characteristic
278	C₇×#117	C₂³	1	1	yes	characteristic
279	C₇×#117	C₂³	1	1	yes	characteristic
280	C₂×C₇×C₄⋊C₄	—	2	1	no	—
281	C₂×C₇×C₄⋊C₄	—	2	1	no	—
282	C₂×C₇×C₄⋊C₄	—	2	1	no	—
283	C₂×C₇×C₄⋊C₄	—	2	1	no	—
284	C₂×C₇×C₄⋊C₄	—	2	1	no	—
285	C₂×C₇×C₄⋊C₄	D₄	1	1	yes	characteristic
286	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
287	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
288	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
289	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
290	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
292	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
295	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
297	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
299	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
302	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
303	C₂×C₄²×C₇	—	2	1	no	—
304	C₂×C₄²×C₇	—	2	1	no	—
305	C₂×C₄²×C₇	—	2	1	no	—
306	C₂×C₄²×C₇	—	2	1	no	—
307	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
308	C₇×#107	C₂³	1	2	yes	—
309	C₇×#107	C₂³	1	2	yes	—
310	C₇×#107	C₂³	1	2	yes	—
311	C₇×#107	C₂³	1	2	yes	—
312	C₇×#107	C₂³	1	2	yes	—
313	C₇×#107	C₂³	1	2	yes	—
314	C₇×#107	C₂³	1	2	yes	—
315	C₇×#107	C₂³	1	2	yes	—
316	C₇×#107	C₂³	1	2	yes	—
317	C₇×#106	C₂³	1	2	yes	—
318	C₇×#106	C₂³	1	2	yes	—
319	C₇×#106	C₂³	1	2	yes	—
320	C₇×#106	C₂³	1	2	yes	—
321	C₇×#106	C₂³	1	2	yes	—
322	C₇×#106	C₂³	1	2	yes	—
323	C₇×#106	C₂³	1	2	yes	—
324	C₇×#106	C₂³	1	2	yes	—
325	C₇×#106	C₂³	1	2	yes	—
326	C₇×C₄⋊C₈	C₂³	1	2	yes	—
327	C₇×C₄⋊C₈	C₂³	1	2	yes	—
328	C₇×#103	C₂³	1	2	yes	—
329	C₇×#103	C₂³	1	2	yes	—
330	C₇×#103	C₂³	1	2	yes	—
331	C₇×#102	C₂³	1	2	yes	—
332	C₇×#102	C₂³	1	2	yes	—
333	C₇×#102	C₂³	1	2	yes	—
334	C₇×#102	C₂³	1	2	yes	—
335	C₇×#102	C₂³	1	2	yes	—
336	C₇×#102	C₂³	1	2	yes	—
337	C₇×#102	C₂³	1	2	yes	—
338	C₇×#102	C₂³	1	2	yes	—
339	C₇×#102	C₂³	1	2	yes	—
340	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
341	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
342	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
343	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
344	C₇×#97	C₂³	1	2	yes	—
345	C₄×C₇×C₈	C₂³	1	2	yes	—
346	#3475	C₂×C₇	1	1	yes	characteristic, complemented
347	C₂×#553	C₂×C₇	1	1	yes	characteristic, complemented
348	#3355	C₂×C₇	1	2	yes	complemented
349	#3351	C₂×C₇	1	2	yes	complemented
350	#3350	C₂×C₇	1	2	yes	complemented
351	#3347	C₂×C₇	1	2	yes	complemented
352	#3346	C₂×C₇	1	2	yes	complemented
353	#3345	C₂×C₇	1	2	yes	complemented
354	#3339	C₂×C₇	1	2	yes	complemented
355	#3337	C₂×C₇	1	2	yes	complemented
356	#3166	C₂×C₇	1	1	yes	characteristic, complemented
357	#3094	C₂×C₇	1	1	yes	characteristic, complemented
358	#3094	C₂×C₇	1	1	yes	characteristic, complemented
359	#3093	C₂×C₇	1	1	yes	characteristic, complemented
360	#3092	C₂×C₇	1	1	yes	characteristic, complemented
361	#3080	C₂×C₇	1	1	yes	characteristic, complemented
362	#3077	C₂×C₇	1	1	yes	characteristic, complemented
363	#3055	C₂×C₇	1	1	yes	characteristic, complemented
364	#3055	C₂×C₇	1	1	yes	characteristic, complemented
365	C₄×AGL(1,ℤ/8)	C₂×C₇	1	1	yes	characteristic, complemented
366	D₄×M₁₆	C₂×C₇	1	1	yes	characteristic, complemented
367	#2911	C₂×C₇	1	1	yes	characteristic, complemented
368	C₂×#428	C₂×C₇	1	1	yes	characteristic, complemented
369	C₂⁴×C₇	—	2	1	no	—
370	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
371	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
372	C₇×#41	—	2	2	no	—
373	C₇×#41	—	2	2	no	—
374	C₇×#41	—	4	4	no	—
375	C₂×C₇×Q₈	—	2	1	no	—
376	C₂×C₇×Q₈	—	2	1	no	—
377	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
378	C₂×C₇×D₄	—	2	1	no	—
379	C₂×C₇×D₄	—	2	1	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	1	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	1	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	4	no	—
392	C₂×C₇×D₄	—	8	2	no	—
393	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
394	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
395	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
396	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
397	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
398	C₂×C₇×D₄	C₂⁴	1	2	yes	—
399	C₂²×C₄×C₇	—	2	2	no	—
400	C₂²×C₄×C₇	—	2	2	no	—
401	C₂²×C₄×C₇	—	2	2	no	—
402	C₂²×C₄×C₇	—	2	2	no	—
403	C₂²×C₄×C₇	—	2	1	no	—
404	C₂²×C₄×C₇	—	2	1	no	—
405	C₂²×C₄×C₇	—	2	1	no	—
406	C₂²×C₄×C₇	—	2	1	no	—
407	C₂²×C₄×C₇	—	2	1	no	—
408	C₂²×C₄×C₇	—	2	1	no	—
409	C₂²×C₄×C₇	—	2	1	no	—
410	C₂²×C₄×C₇	—	2	2	no	—
411	C₂²×C₄×C₇	—	2	2	no	—
412	C₂²×C₄×C₇	—	2	1	no	—
413	C₂²×C₄×C₇	—	2	1	no	—
414	C₂²×C₄×C₇	—	2	1	no	—
415	C₂²×C₄×C₇	—	2	2	no	—
416	C₂²×C₄×C₇	—	2	2	no	—
417	C₂²×C₄×C₇	—	8	2	no	—
418	C₂²×C₄×C₇	—	8	2	no	—
419	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
424	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
425	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
426	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
427	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
428	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
429	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
432	C₇×SD₁₆	—	2	4	no	—
433	C₇×D₈	—	2	4	no	—
434	C₇×M₁₆	—	2	2	no	—
435	C₇×M₁₆	—	2	2	no	—
436	C₇×M₁₆	—	2	2	no	—
437	C₇×M₁₆	—	2	4	no	—
438	C₇×M₁₆	—	2	4	no	—
439	C₇×M₁₆	#41	1	4	yes	complemented
440	C₂×C₇×C₈	—	2	4	no	—
441	C₂×C₇×C₈	—	2	4	no	—
442	C₂×C₇×C₈	C₂⁴	1	2	yes	—
443	C₂×C₇×C₈	C₂⁴	1	2	yes	—
444	C₂×C₇×C₈	C₂⁴	1	2	yes	—
445	C₂×C₇×C₈	C₂⁴	1	2	yes	—
446	C₇×C₄⋊C₄	—	2	1	no	—
447	C₇×C₄⋊C₄	—	2	1	no	—
448	C₇×C₄⋊C₄	—	2	2	no	—
449	C₇×C₄⋊C₄	—	2	2	no	—
450	C₇×C₄⋊C₄	—	2	2	no	—
451	C₇×C₄⋊C₄	—	2	2	no	—
452	C₇×C₄⋊C₄	—	2	2	no	—
453	C₇×C₄⋊C₄	—	2	2	no	—
454	C₇×C₄⋊C₄	—	2	1	no	—
455	C₇×C₄⋊C₄	—	2	1	no	—
456	C₇×C₄⋊C₄	—	2	1	no	—
457	C₇×C₄⋊C₄	—	2	1	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	1	no	—
462	C₇×C₄⋊C₄	—	2	1	no	—
463	C₇×C₄⋊C₄	—	2	1	no	—
464	C₇×C₄⋊C₄	—	2	1	no	—
465	C₇×C₄⋊C₄	—	2	1	no	—
466	C₇×C₄⋊C₄	—	2	1	no	—
467	C₇×C₄⋊C₄	—	2	1	no	—
468	C₇×C₄⋊C₄	—	2	1	no	—
469	C₇×C₄⋊C₄	—	2	1	no	—
470	C₇×C₄⋊C₄	—	2	1	no	—
471	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
472	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
473	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
474	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
475	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
476	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
477	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
478	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
479	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
480	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
481	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
482	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
483	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
484	C₇×C₂²⋊C₄	—	2	1	no	—
485	C₇×C₂²⋊C₄	—	2	1	no	—
486	C₇×C₂²⋊C₄	—	2	1	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	1	no	—
491	C₇×C₂²⋊C₄	—	2	1	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	—	2	1	no	—
496	C₇×C₂²⋊C₄	—	2	1	no	—
497	C₇×C₂²⋊C₄	—	2	2	no	—
498	C₇×C₂²⋊C₄	—	2	2	no	—
499	C₇×C₂²⋊C₄	—	2	2	no	—
500	C₇×C₂²⋊C₄	—	2	2	no	—
501	C₇×C₂²⋊C₄	—	2	2	no	—
502	C₇×C₂²⋊C₄	—	2	2	no	—
503	C₇×C₂²⋊C₄	—	2	1	no	—
504	C₇×C₂²⋊C₄	—	2	1	no	—
505	C₇×C₂²⋊C₄	—	2	1	no	—
506	C₇×C₂²⋊C₄	—	2	1	no	—
507	C₇×C₂²⋊C₄	—	2	1	no	—
508	C₇×C₂²⋊C₄	—	2	1	no	—
509	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
510	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
511	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
512	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
513	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
514	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
515	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
516	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
517	C₄²×C₇	—	2	1	no	—
518	C₄²×C₇	—	2	1	no	—
519	C₄²×C₇	—	2	1	no	—
520	C₄²×C₇	—	2	1	no	—
521	C₄²×C₇	—	2	1	no	—
522	C₄²×C₇	—	2	1	no	—
523	C₄²×C₇	—	2	2	no	—
524	C₄²×C₇	—	2	2	no	—
525	C₄²×C₇	—	2	1	no	—
526	C₄²×C₇	—	2	1	no	—
527	C₄²×C₇	—	2	1	no	—
528	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
529	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
530	C₄²×C₇	C₂⁴	1	1	yes	characteristic
531	C₄²×C₇	C₂⁴	1	1	yes	characteristic
532	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
533	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
534	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
535	#556	C₂²×C₇	1	1	yes	characteristic, complemented
536	#555	C₂²×C₇	1	1	yes	characteristic, complemented
537	#554	C₂²×C₇	1	1	yes	characteristic, complemented
538	#553	—	2	1	no	—
539	#553	—	2	1	no	—
540	#553	—	2	1	no	—
541	#553	—	2	1	no	—
542	#553	C₂²×C₇	1	2	yes	—
543	#553	C₂²×C₇	1	2	yes	—
544	#553	C₂²×C₇	1	2	yes	—
545	#553	C₂²×C₇	1	2	yes	—
546	#553	C₂²×C₇	1	1	yes	characteristic, complemented
547	#553	C₂²×C₇	1	1	yes	characteristic, complemented
548	#552	—	2	1	no	—
549	#552	C₂²×C₇	1	1	yes	characteristic, complemented
550	#552	C₂²×C₇	1	1	yes	characteristic, complemented
551	#551	—	2	1	no	—
552	#551	—	2	1	no	—
553	#547	C₂²×C₇	1	1	yes	characteristic, complemented
554	#546	—	2	1	no	—
555	#533	C₂²×C₇	1	1	yes	characteristic
556	#529	—	2	1	no	—
557	#529	—	2	1	no	—
558	#529	—	2	1	no	—
559	C₂×#126	—	2	1	no	—
560	C₂×#125	C₂²×C₇	1	1	yes	characteristic
561	#525	C₂²×C₇	1	1	yes	characteristic
562	#525	C₂²×C₇	1	1	yes	characteristic
563	C₂×#123	—	2	1	no	—
564	C₂×#121	—	2	1	no	—
565	C₂×#121	C₂²×C₇	1	1	yes	characteristic
566	C₂×#121	C₂²×C₇	1	1	yes	characteristic
567	C₄×#41	—	2	1	no	—
568	C₄×#41	C₂²×C₇	1	1	yes	characteristic
569	C₂×C₄×D₄	—	2	1	no	—
570	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
571	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
572	C₂×#117	C₂²×C₇	1	1	yes	characteristic
573	C₂×#117	C₂²×C₇	1	1	yes	characteristic
574	C₂×#117	C₂²×C₇	1	1	yes	characteristic
575	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
576	#501	C₂²×C₇	1	2	yes	complemented
577	#501	C₂²×C₇	1	2	yes	complemented
578	#499	C₂²×C₇	1	2	yes	complemented
579	#499	C₂²×C₇	1	2	yes	complemented
580	#485	C₂²×C₇	1	2	yes	complemented
581	#485	C₂²×C₇	1	2	yes	complemented
582	#484	C₂²×C₇	1	2	yes	complemented
583	#483	C₂²×C₇	1	2	yes	complemented
584	#482	C₂²×C₇	1	2	yes	complemented
585	#482	C₂²×C₇	1	2	yes	complemented
586	#482	C₂²×C₇	1	2	yes	complemented
587	#482	C₂²×C₇	1	2	yes	complemented
588	#482	C₂²×C₇	1	2	yes	complemented
589	#482	C₂²×C₇	1	2	yes	complemented
590	#481	C₂²×C₇	1	2	yes	complemented
591	#481	C₂²×C₇	1	2	yes	complemented
592	#481	C₂²×C₇	1	2	yes	complemented
593	#480	C₂²×C₇	1	2	yes	complemented
594	#480	C₂²×C₇	1	2	yes	complemented
595	#480	C₂²×C₇	1	2	yes	complemented
596	#479	C₂²×C₇	1	2	yes	complemented
597	#479	C₂²×C₇	1	2	yes	complemented
598	#478	C₂²×C₇	1	2	yes	complemented
599	#478	C₂²×C₇	1	2	yes	complemented
600	#478	C₂²×C₇	1	2	yes	complemented
601	#478	C₂²×C₇	1	2	yes	complemented
602	#476	C₂²×C₇	1	2	yes	complemented
603	#474	C₂²×C₇	1	2	yes	complemented
604	#469	C₂²×C₇	1	2	yes	complemented
605	#469	C₂²×C₇	1	2	yes	complemented
606	#468	C₂²×C₇	1	2	yes	complemented
607	#468	C₂²×C₇	1	2	yes	complemented
608	#466	C₂²×C₇	1	2	yes	complemented
609	#466	C₂²×C₇	1	2	yes	complemented
610	#465	C₂²×C₇	1	2	yes	complemented
611	#465	C₂²×C₇	1	2	yes	complemented
612	#442	C₂²×C₇	1	2	yes	complemented
613	#440	C₂²×C₇	1	2	yes	complemented
614	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
615	C₄×D₈	C₂²×C₇	1	2	yes	complemented
616	#436	C₂²×C₇	1	2	yes	complemented
617	#435	C₂²×C₇	1	2	yes	complemented
618	#435	C₂²×C₇	1	2	yes	complemented
619	C₈×D₄	C₂²×C₇	1	2	yes	complemented
620	#428	C₂²×C₇	1	1	yes	characteristic
621	#428	C₂²×C₇	1	1	yes	characteristic
622	#428	C₂²×C₇	1	1	yes	characteristic
623	#428	C₂²×C₇	1	1	yes	characteristic
624	#428	C₂²×C₇	1	1	yes	characteristic
625	#428	C₂²×C₇	1	1	yes	characteristic
626	#428	C₂²×C₇	1	1	yes	characteristic
627	#428	C₂²×C₇	1	1	yes	characteristic
628	#428	C₂²×C₇	1	1	yes	characteristic
629	#428	C₂²×C₇	1	2	yes	complemented
630	#428	C₂²×C₇	1	2	yes	complemented
631	#428	C₂²×C₇	1	2	yes	complemented
632	#428	C₂²×C₇	1	2	yes	complemented
633	#427	C₂²×C₇	1	2	yes	complemented
634	#427	C₂²×C₇	1	2	yes	complemented
635	C₂×#107	C₂²×C₇	1	2	yes	complemented
636	C₂×#106	C₂²×C₇	1	2	yes	complemented
637	#423	C₂²×C₇	1	1	yes	characteristic
638	#418	C₂²×C₇	1	1	yes	characteristic
639	#418	C₂²×C₇	1	1	yes	characteristic
640	#418	C₂²×C₇	1	1	yes	characteristic
641	#417	C₂²×C₇	1	1	yes	characteristic
642	#417	C₂²×C₇	1	1	yes	characteristic
643	#417	C₂²×C₇	1	1	yes	characteristic
644	#407	C₂²×C₇	1	1	yes	characteristic
645	#407	C₂²×C₇	1	1	yes	characteristic
646	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
647	C₂³×C₇	—	2	2	no	—
648	C₂³×C₇	—	2	2	no	—
649	C₂³×C₇	—	2	2	no	—
650	C₂³×C₇	—	2	1	no	—
651	C₂³×C₇	—	2	2	no	—
652	C₂³×C₇	—	4	1	no	—
653	C₂³×C₇	—	4	1	no	—
654	C₂³×C₇	—	4	1	no	—
655	C₂³×C₇	—	4	2	no	—
656	C₂³×C₇	—	4	2	no	—
657	C₂³×C₇	—	4	2	no	—
658	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
659	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
660	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
661	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
662	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
663	C₇×Q₈	—	2	1	no	—
664	C₇×Q₈	—	2	1	no	—
665	C₇×Q₈	—	4	2	no	—
666	C₇×Q₈	—	8	1	no	—
667	C₇×D₄	—	2	2	no	—
668	C₇×D₄	—	2	2	no	—
669	C₇×D₄	—	2	1	no	—
670	C₇×D₄	—	2	2	no	—
671	C₇×D₄	—	2	2	no	—
672	C₇×D₄	—	2	1	no	—
673	C₇×D₄	—	4	1	no	—
674	C₇×D₄	—	4	1	no	—
675	C₇×D₄	—	4	4	no	—
676	C₇×D₄	—	4	2	no	—
677	C₇×D₄	—	4	2	no	—
678	C₇×D₄	—	4	4	no	—
679	C₇×D₄	—	4	2	no	—
680	C₇×D₄	—	4	2	no	—
681	C₇×D₄	—	8	1	no	—
682	C₇×D₄	—	8	1	no	—
683	C₇×D₄	—	8	2	no	—
684	C₇×D₄	—	8	2	no	—
685	C₂×C₄×C₇	—	2	2	no	—
686	C₂×C₄×C₇	—	2	2	no	—
687	C₂×C₄×C₇	—	2	2	no	—
688	C₂×C₄×C₇	—	2	2	no	—
689	C₂×C₄×C₇	—	2	2	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	1	no	—
696	C₂×C₄×C₇	—	2	1	no	—
697	C₂×C₄×C₇	—	2	1	no	—
698	C₂×C₄×C₇	—	2	1	no	—
699	C₂×C₄×C₇	—	2	1	no	—
700	C₂×C₄×C₇	—	2	1	no	—
701	C₂×C₄×C₇	—	2	1	no	—
702	C₂×C₄×C₇	—	2	2	no	—
703	C₂×C₄×C₇	—	2	1	no	—
704	C₂×C₄×C₇	—	2	1	no	—
705	C₂×C₄×C₇	—	2	1	no	—
706	C₂×C₄×C₇	—	2	1	no	—
707	C₂×C₄×C₇	—	2	2	no	—
708	C₂×C₄×C₇	—	2	2	no	—
709	C₂×C₄×C₇	—	4	1	no	—
710	C₂×C₄×C₇	—	4	1	no	—
711	C₂×C₄×C₇	—	4	2	no	—
712	C₂×C₄×C₇	—	4	2	no	—
713	C₂×C₄×C₇	—	4	2	no	—
714	C₂×C₄×C₇	—	4	2	no	—
715	C₂×C₄×C₇	—	4	2	no	—
716	C₂×C₄×C₇	—	4	2	no	—
717	C₂×C₄×C₇	—	4	2	no	—
718	C₂×C₄×C₇	—	8	1	no	—
719	C₂×C₄×C₇	—	8	2	no	—
720	C₂×C₄×C₇	—	8	2	no	—
721	C₂×C₄×C₇	—	8	1	no	—
722	C₂×C₄×C₇	—	8	1	no	—
723	C₂×C₄×C₇	—	8	2	no	—
724	C₂×C₄×C₇	—	8	2	no	—
725	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
726	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
727	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
728	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
729	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
730	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
731	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
732	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
733	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
734	C₂×C₄×C₇	C₂×#41	1	2	yes	—
735	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
736	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
737	C₇×C₈	—	2	2	no	—
738	C₇×C₈	—	2	2	no	—
739	C₇×C₈	—	2	2	no	—
740	C₇×C₈	C₂×#41	1	4	yes	—
741	C₂×#41	—	2	1	no	—
742	C₂×#41	C₂³×C₇	1	1	yes	characteristic
743	C₂²×D₄	—	2	1	no	—
744	C₂²×D₄	—	2	1	no	—
745	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
746	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
747	C₂³×C₄	—	2	1	no	—
748	C₂³×C₄	—	2	1	no	—
749	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
750	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
751	AGL(1,ℤ/8)	—	2	4	no	—
752	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
753	C₂×D₈	C₂³×C₇	1	2	yes	—
754	C₂×M₁₆	—	2	4	no	—
755	C₂×M₁₆	—	2	4	no	—
756	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
757	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
758	C₂×M₁₆	C₂³×C₇	1	2	yes	—
759	C₂×M₁₆	C₂³×C₇	1	2	yes	—
760	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
761	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
762	C₂²×C₈	C₂³×C₇	1	2	yes	—
763	C₂²×C₈	C₂³×C₇	1	2	yes	—
764	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
765	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
766	#126	—	2	2	no	—
767	#126	—	2	2	no	—
768	#126	—	2	2	no	—
769	#126	—	2	2	no	—
770	#126	—	2	1	no	—
771	#126	—	2	1	no	—
772	#126	—	2	1	no	—
773	#126	—	2	1	no	—
774	#126	—	2	1	no	—
775	#126	—	2	1	no	—
776	#125	—	2	1	no	—
777	#125	—	2	1	no	—
778	#125	—	2	1	no	—
779	#125	—	2	1	no	—
780	#125	—	2	1	no	—
781	#125	C₂³×C₇	1	2	yes	—
782	#125	C₂³×C₇	1	2	yes	—
783	#125	C₂³×C₇	1	1	yes	characteristic
784	#125	C₂³×C₇	1	1	yes	characteristic
785	#124	—	2	1	no	—
786	#124	—	2	1	no	—
787	#124	—	2	1	no	—
788	#123	—	2	1	no	—
789	#123	—	2	1	no	—
790	#123	—	2	1	no	—
791	#123	—	2	1	no	—
792	#123	—	2	2	no	—
793	#123	—	2	2	no	—
794	#123	—	2	2	no	—
795	#123	—	2	2	no	—
796	#123	—	2	1	no	—
797	#123	—	2	1	no	—
798	#123	—	2	1	no	—
799	#123	—	2	1	no	—
800	C₂²⋊Q₈	—	2	1	no	—
801	C₂²⋊Q₈	—	2	1	no	—
802	C₂²⋊Q₈	—	2	1	no	—
803	C₂²⋊Q₈	—	2	1	no	—
804	C₂²⋊Q₈	—	2	1	no	—
805	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
806	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
807	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
808	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
809	#121	—	2	2	no	—
810	#121	—	2	2	no	—
811	#121	—	2	2	no	—
812	#121	—	2	2	no	—
813	#121	—	2	1	no	—
814	#121	—	2	1	no	—
815	#121	—	2	1	no	—
816	#121	—	2	1	no	—
817	#121	—	2	1	no	—
818	#121	—	2	1	no	—
819	#121	—	2	1	no	—
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	1	yes	characteristic
825	#121	C₂³×C₇	1	1	yes	characteristic
826	#121	C₂³×C₇	1	1	yes	characteristic
827	#121	C₂³×C₇	1	1	yes	characteristic
828	#120	—	2	1	no	—
829	#120	—	2	1	no	—
830	C₄×Q₈	—	2	1	no	—
831	C₄×Q₈	—	2	1	no	—
832	C₄×Q₈	—	2	1	no	—
833	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
834	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
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	1	no	—
841	C₄×D₄	—	2	1	no	—
842	C₄×D₄	—	2	2	no	—
843	C₄×D₄	—	2	2	no	—
844	C₄×D₄	—	2	2	no	—
845	C₄×D₄	—	2	2	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	—	2	1	no	—
848	C₄×D₄	—	2	1	no	—
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	C₇×D₄	1	1	yes	characteristic
851	C₄×D₄	C₇×D₄	1	1	yes	characteristic
852	C₄×D₄	C₇×D₄	1	1	yes	characteristic
853	C₄×D₄	C₇×D₄	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₇	1	2	yes	—
855	C₄×D₄	C₂³×C₇	1	2	yes	—
856	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
857	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
858	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
859	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
860	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
861	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
862	#117	—	2	1	no	—
863	#117	—	2	1	no	—
864	#117	—	2	1	no	—
865	#117	—	2	1	no	—
866	#117	—	2	1	no	—
867	#117	—	2	1	no	—
868	#117	—	2	1	no	—
869	#117	—	2	1	no	—
870	#117	—	2	1	no	—
871	#117	—	2	1	no	—
872	#117	C₂³×C₇	1	1	yes	characteristic
873	#117	C₂³×C₇	1	1	yes	characteristic
874	#117	C₂³×C₇	1	1	yes	characteristic
875	#117	C₂³×C₇	1	1	yes	characteristic
876	#117	C₂³×C₇	1	1	yes	characteristic
877	#117	C₂³×C₇	1	2	yes	—
878	#117	C₂³×C₇	1	2	yes	—
879	#117	C₂³×C₇	1	1	yes	characteristic
880	#117	C₂³×C₇	1	1	yes	characteristic
881	C₂×C₄⋊C₄	—	2	1	no	—
882	C₂×C₄⋊C₄	—	2	1	no	—
883	C₂×C₄⋊C₄	—	2	1	no	—
884	C₂×C₄⋊C₄	—	2	1	no	—
885	C₂×C₄⋊C₄	—	2	1	no	—
886	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
887	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
888	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
889	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
890	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
891	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
892	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
893	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
894	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
895	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
896	C₂×C₂²⋊C₄	—	2	1	no	—
897	C₂×C₂²⋊C₄	—	2	1	no	—
898	C₂×C₂²⋊C₄	—	2	1	no	—
899	C₂×C₂²⋊C₄	—	2	1	no	—
900	C₂×C₂²⋊C₄	—	2	1	no	—
901	C₂×C₂²⋊C₄	—	2	1	no	—
902	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
903	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
904	C₂×C₄²	—	2	1	no	—
905	C₂×C₄²	—	2	1	no	—
906	C₂×C₄²	—	2	1	no	—
907	C₂×C₄²	—	2	1	no	—
908	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
909	#107	C₂³×C₇	1	2	yes	—
910	#107	C₂³×C₇	1	2	yes	—
911	#107	C₂³×C₇	1	2	yes	—
912	#107	C₂³×C₇	1	2	yes	—
913	#107	C₂³×C₇	1	2	yes	—
914	#107	C₂³×C₇	1	2	yes	—
915	#107	C₂³×C₇	1	2	yes	—
916	#107	C₂³×C₇	1	2	yes	—
917	#107	C₂³×C₇	1	2	yes	—
918	#106	C₂³×C₇	1	2	yes	—
919	#106	C₂³×C₇	1	2	yes	—
920	#106	C₂³×C₇	1	2	yes	—
921	#106	C₂³×C₇	1	2	yes	—
922	#106	C₂³×C₇	1	2	yes	—
923	#106	C₂³×C₇	1	2	yes	—
924	#106	C₂³×C₇	1	2	yes	—
925	#106	C₂³×C₇	1	2	yes	—
926	#106	C₂³×C₇	1	2	yes	—
927	C₄⋊C₈	C₂³×C₇	1	2	yes	—
928	C₄⋊C₈	C₂³×C₇	1	2	yes	—
929	#103	C₂³×C₇	1	2	yes	—
930	#103	C₂³×C₇	1	2	yes	—
931	#103	C₂³×C₇	1	2	yes	—
932	#102	C₂³×C₇	1	2	yes	—
933	#102	C₂³×C₇	1	2	yes	—
934	#102	C₂³×C₇	1	2	yes	—
935	#102	C₂³×C₇	1	2	yes	—
936	#102	C₂³×C₇	1	2	yes	—
937	#102	C₂³×C₇	1	2	yes	—
938	#102	C₂³×C₇	1	2	yes	—
939	#102	C₂³×C₇	1	2	yes	—
940	#102	C₂³×C₇	1	2	yes	—
941	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
942	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
943	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
944	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
945	#97	C₂³×C₇	1	2	yes	—
946	C₄×C₈	C₂³×C₇	1	2	yes	—
947	C₂²×C₇	—	2	1	no	—
948	C₂²×C₇	—	2	1	no	—
949	C₂²×C₇	—	2	1	no	—
950	C₂²×C₇	—	2	1	no	—
951	C₂²×C₇	—	2	1	no	—
952	C₂²×C₇	—	2	1	no	—
953	C₂²×C₇	—	2	1	no	—
954	C₂²×C₇	—	2	1	no	—
955	C₂²×C₇	—	2	1	no	—
956	C₂²×C₇	—	2	1	no	—
957	C₂²×C₇	—	2	1	no	—
958	C₂²×C₇	—	2	1	no	—
959	C₂²×C₇	—	2	1	no	—
960	C₂²×C₇	—	4	4	no	—
961	C₂²×C₇	—	4	2	no	—
962	C₂²×C₇	—	4	1	no	—
963	C₂²×C₇	—	4	1	no	—
964	C₂²×C₇	—	4	2	no	—
965	C₂²×C₇	—	4	1	no	—
966	C₂²×C₇	—	4	2	no	—
967	C₂²×C₇	—	8	2	no	—
968	C₂²×C₇	—	8	4	no	—
969	C₂²×C₇	#547	1	2	yes	—
970	C₂²×C₇	#575	1	2	yes	—
971	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
972	C₄×C₇	—	2	1	no	—
973	C₄×C₇	—	2	1	no	—
974	C₄×C₇	—	2	1	no	—
975	C₄×C₇	—	2	1	no	—
976	C₄×C₇	—	2	1	no	—
977	C₄×C₇	—	2	1	no	—
978	C₄×C₇	—	2	1	no	—
979	C₄×C₇	—	2	1	no	—
980	C₄×C₇	—	4	2	no	—
981	C₄×C₇	—	4	2	no	—
982	C₄×C₇	—	4	1	no	—
983	C₄×C₇	—	4	1	no	—
984	C₄×C₇	—	4	1	no	—
985	C₄×C₇	—	4	1	no	—
986	C₄×C₇	—	4	1	no	—
987	C₄×C₇	—	4	2	no	—
988	C₄×C₇	—	4	1	no	—
989	C₄×C₇	—	4	1	no	—
990	C₄×C₇	#547	1	2	yes	—
991	C₄×C₇	C₂²×#41	1	1	yes	characteristic
992	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
993	C₂⁴	—	2	1	no	—
994	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
995	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
996	#41	—	2	2	no	—
997	#41	—	2	2	no	—
998	#41	—	4	4	no	—
999	C₂×Q₈	—	2	1	no	—
1000	C₂×Q₈	—	2	1	no	—
1001	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
1002	C₂×D₄	—	2	1	no	—
1003	C₂×D₄	—	2	1	no	—
1004	C₂×D₄	—	2	1	no	—
1005	C₂×D₄	—	2	2	no	—
1006	C₂×D₄	—	2	2	no	—
1007	C₂×D₄	—	2	1	no	—
1008	C₂×D₄	—	2	1	no	—
1009	C₂×D₄	—	2	2	no	—
1010	C₂×D₄	—	2	2	no	—
1011	C₂×D₄	—	2	1	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	2	2	no	—
1014	C₂×D₄	—	4	2	no	—
1015	C₂×D₄	—	4	4	no	—
1016	C₂×D₄	—	8	2	no	—
1017	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1018	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1019	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1020	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1021	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1022	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1023	C₂²×C₄	—	2	2	no	—
1024	C₂²×C₄	—	2	2	no	—
1025	C₂²×C₄	—	2	2	no	—
1026	C₂²×C₄	—	2	2	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	1	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	2	no	—
1036	C₂²×C₄	—	2	1	no	—
1037	C₂²×C₄	—	2	1	no	—
1038	C₂²×C₄	—	2	1	no	—
1039	C₂²×C₄	—	2	2	no	—
1040	C₂²×C₄	—	2	2	no	—
1041	C₂²×C₄	—	8	2	no	—
1042	C₂²×C₄	—	8	2	no	—
1043	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1044	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1045	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1046	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1047	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1048	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1049	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1050	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1051	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1052	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1053	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1054	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1055	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1056	SD₁₆	—	2	4	no	—
1057	D₈	—	2	4	no	—
1058	M₁₆	—	2	2	no	—
1059	M₁₆	—	2	2	no	—
1060	M₁₆	—	2	2	no	—
1061	M₁₆	—	2	4	no	—
1062	M₁₆	—	2	4	no	—
1063	M₁₆	C₇×#41	1	4	yes	complemented
1064	C₂×C₈	—	2	4	no	—
1065	C₂×C₈	—	2	4	no	—
1066	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1067	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1068	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1069	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	2	no	—
1073	C₄⋊C₄	—	2	2	no	—
1074	C₄⋊C₄	—	2	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	2	no	—
1077	C₄⋊C₄	—	2	2	no	—
1078	C₄⋊C₄	—	2	1	no	—
1079	C₄⋊C₄	—	2	1	no	—
1080	C₄⋊C₄	—	2	1	no	—
1081	C₄⋊C₄	—	2	1	no	—
1082	C₄⋊C₄	—	2	1	no	—
1083	C₄⋊C₄	—	2	1	no	—
1084	C₄⋊C₄	—	2	1	no	—
1085	C₄⋊C₄	—	2	1	no	—
1086	C₄⋊C₄	—	2	1	no	—
1087	C₄⋊C₄	—	2	1	no	—
1088	C₄⋊C₄	—	2	1	no	—
1089	C₄⋊C₄	—	2	1	no	—
1090	C₄⋊C₄	—	2	1	no	—
1091	C₄⋊C₄	—	2	1	no	—
1092	C₄⋊C₄	—	2	1	no	—
1093	C₄⋊C₄	—	2	1	no	—
1094	C₄⋊C₄	—	2	1	no	—
1095	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1096	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1097	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1098	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1099	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1100	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1101	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1102	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1103	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1104	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1105	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1106	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1107	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	2	no	—
1112	C₂²⋊C₄	—	2	2	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	—	2	1	no	—
1115	C₂²⋊C₄	—	2	1	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
1118	C₂²⋊C₄	—	2	1	no	—
1119	C₂²⋊C₄	—	2	1	no	—
1120	C₂²⋊C₄	—	2	1	no	—
1121	C₂²⋊C₄	—	2	2	no	—
1122	C₂²⋊C₄	—	2	2	no	—
1123	C₂²⋊C₄	—	2	2	no	—
1124	C₂²⋊C₄	—	2	2	no	—
1125	C₂²⋊C₄	—	2	2	no	—
1126	C₂²⋊C₄	—	2	2	no	—
1127	C₂²⋊C₄	—	2	1	no	—
1128	C₂²⋊C₄	—	2	1	no	—
1129	C₂²⋊C₄	—	2	1	no	—
1130	C₂²⋊C₄	—	2	1	no	—
1131	C₂²⋊C₄	—	2	1	no	—
1132	C₂²⋊C₄	—	2	1	no	—
1133	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1134	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1135	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1136	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1137	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1138	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1139	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1140	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1141	C₄²	—	2	1	no	—
1142	C₄²	—	2	1	no	—
1143	C₄²	—	2	1	no	—
1144	C₄²	—	2	1	no	—
1145	C₄²	—	2	1	no	—
1146	C₄²	—	2	1	no	—
1147	C₄²	—	2	2	no	—
1148	C₄²	—	2	2	no	—
1149	C₄²	—	2	1	no	—
1150	C₄²	—	2	1	no	—
1151	C₄²	—	2	1	no	—
1152	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1153	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1154	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1155	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1156	C₂×C₇	—	2	2	no	—
1157	C₂×C₇	—	2	2	no	—
1158	C₂×C₇	—	4	1	no	—
1159	C₂×C₇	—	4	1	no	—
1160	C₂×C₇	—	4	1	no	—
1161	C₂×C₇	—	8	1	no	—
1162	C₂×C₇	—	8	2	no	—
1163	C₂×C₇	C₂×#547	1	1	yes	characteristic
1164	C₂×C₇	C₂×#575	1	1	yes	characteristic
1165	C₂×C₇	#3585	1	1	yes	characteristic
1166	C₂³	—	2	2	no	—
1167	C₂³	—	2	2	no	—
1168	C₂³	—	2	2	no	—
1169	C₂³	—	2	1	no	—
1170	C₂³	—	2	2	no	—
1171	C₂³	—	4	1	no	—
1172	C₂³	—	4	1	no	—
1173	C₂³	—	4	1	no	—
1174	C₂³	—	4	2	no	—
1175	C₂³	—	4	2	no	—
1176	C₂³	—	4	2	no	—
1177	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1178	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1179	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1180	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1181	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1182	Q₈	—	2	1	no	—
1183	Q₈	—	2	1	no	—
1184	Q₈	—	4	2	no	—
1185	Q₈	—	8	1	no	—
1186	D₄	—	2	2	no	—
1187	D₄	—	2	2	no	—
1188	D₄	—	2	1	no	—
1189	D₄	—	2	2	no	—
1190	D₄	—	2	2	no	—
1191	D₄	—	2	1	no	—
1192	D₄	—	4	1	no	—
1193	D₄	—	4	1	no	—
1194	D₄	—	4	4	no	—
1195	D₄	—	4	2	no	—
1196	D₄	—	4	2	no	—
1197	D₄	—	4	4	no	—
1198	D₄	—	4	2	no	—
1199	D₄	—	4	2	no	—
1200	D₄	—	8	1	no	—
1201	D₄	—	8	1	no	—
1202	D₄	—	8	2	no	—
1203	D₄	—	8	2	no	—
1204	C₂×C₄	—	2	2	no	—
1205	C₂×C₄	—	2	2	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	1	no	—
1212	C₂×C₄	—	2	1	no	—
1213	C₂×C₄	—	2	1	no	—
1214	C₂×C₄	—	2	2	no	—
1215	C₂×C₄	—	2	2	no	—
1216	C₂×C₄	—	2	2	no	—
1217	C₂×C₄	—	2	2	no	—
1218	C₂×C₄	—	2	1	no	—
1219	C₂×C₄	—	2	1	no	—
1220	C₂×C₄	—	2	1	no	—
1221	C₂×C₄	—	2	2	no	—
1222	C₂×C₄	—	2	1	no	—
1223	C₂×C₄	—	2	1	no	—
1224	C₂×C₄	—	2	1	no	—
1225	C₂×C₄	—	2	1	no	—
1226	C₂×C₄	—	2	2	no	—
1227	C₂×C₄	—	2	2	no	—
1228	C₂×C₄	—	4	1	no	—
1229	C₂×C₄	—	4	1	no	—
1230	C₂×C₄	—	4	2	no	—
1231	C₂×C₄	—	4	2	no	—
1232	C₂×C₄	—	4	2	no	—
1233	C₂×C₄	—	4	2	no	—
1234	C₂×C₄	—	4	2	no	—
1235	C₂×C₄	—	4	2	no	—
1236	C₂×C₄	—	4	2	no	—
1237	C₂×C₄	—	8	1	no	—
1238	C₂×C₄	—	8	2	no	—
1239	C₂×C₄	—	8	2	no	—
1240	C₂×C₄	—	8	1	no	—
1241	C₂×C₄	—	8	1	no	—
1242	C₂×C₄	—	8	2	no	—
1243	C₂×C₄	—	8	2	no	—
1244	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1245	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1246	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1247	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1248	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1249	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1250	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1251	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1252	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1253	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1254	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1255	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1256	C₈	—	2	2	no	—
1257	C₈	—	2	2	no	—
1258	C₈	—	2	2	no	—
1259	C₈	C₂×C₇×#41	1	4	yes	—
1260	C₇	#61255	1	1	yes	characteristic, direct product factor, Sylow
1261	C₂²	—	2	1	no	—
1262	C₂²	—	2	1	no	—
1263	C₂²	—	2	1	no	—
1264	C₂²	—	2	1	no	—
1265	C₂²	—	2	1	no	—
1266	C₂²	—	2	1	no	—
1267	C₂²	—	2	1	no	—
1268	C₂²	—	2	1	no	—
1269	C₂²	—	2	1	no	—
1270	C₂²	—	2	1	no	—
1271	C₂²	—	2	1	no	—
1272	C₂²	—	2	1	no	—
1273	C₂²	—	2	1	no	—
1274	C₂²	—	4	4	no	—
1275	C₂²	—	4	1	no	—
1276	C₂²	—	4	2	no	—
1277	C₂²	—	4	2	no	—
1278	C₂²	—	4	1	no	—
1279	C₂²	—	4	1	no	—
1280	C₂²	—	4	2	no	—
1281	C₂²	—	8	2	no	—
1282	C₂²	—	8	4	no	—
1283	C₂²	C₇×#547	1	2	yes	—
1284	C₂²	C₇×#575	1	2	yes	—
1285	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1286	C₄	—	2	1	no	—
1287	C₄	—	2	1	no	—
1288	C₄	—	2	1	no	—
1289	C₄	—	2	1	no	—
1290	C₄	—	2	1	no	—
1291	C₄	—	2	1	no	—
1292	C₄	—	2	1	no	—
1293	C₄	—	2	1	no	—
1294	C₄	—	4	1	no	—
1295	C₄	—	4	2	no	—
1296	C₄	—	4	1	no	—
1297	C₄	—	4	1	no	—
1298	C₄	—	4	2	no	—
1299	C₄	—	4	2	no	—
1300	C₄	—	4	1	no	—
1301	C₄	—	4	1	no	—
1302	C₄	—	4	1	no	—
1303	C₄	—	4	1	no	—
1304	C₄	C₇×#547	1	2	yes	—
1305	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1306	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1307	C₂	—	2	2	no	—
1308	C₂	—	2	2	no	—
1309	C₂	—	4	1	no	—
1310	C₂	—	4	1	no	—
1311	C₂	—	4	1	no	—
1312	C₂	—	8	2	no	—
1313	C₂	—	8	1	no	—
1314	C₂	C₂×C₇×#547	1	1	yes	characteristic
1315	C₂	C₂×C₇×#575	1	1	yes	characteristic
1316	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 ◁ C₂×C₄×C₇×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3475	C₂	semidirect
2. C₂×C₇×#553	C₂	semidirect
3. C₇×#3355	C₂	semidirect
4. C₇×#3351	C₂	semidirect
5. C₇×#3350	C₂	semidirect
6. C₇×#3347	C₂	semidirect
7. C₇×#3346	C₂	semidirect
8. C₇×#3345	C₂	semidirect
9. C₇×#3339	C₂	semidirect
10. C₇×#3337	C₂	semidirect
11. C₇×#3166	C₂	semidirect
12. C₇×#3094	C₂	semidirect
13. C₇×#3094	C₂	semidirect
14. C₇×#3093	C₂	semidirect
15. C₇×#3092	C₂	semidirect
16. C₇×#3080	C₂	semidirect
17. C₇×#3077	C₂	semidirect
18. C₇×#3055	C₂	semidirect
19. C₇×#3055	C₂	semidirect
20. C₄×C₇×AGL(1,ℤ/8)	C₂	semidirect
21. C₇×D₄×M₁₆	C₂	semidirect
22. C₇×#2911	C₂	semidirect
23. C₂×C₇×#428	C₂	semidirect
27. C₇×#556	C₂²	semidirect
28. C₇×#555	C₂²	semidirect
29. C₇×#554	C₂²	semidirect
38. C₇×#553	C₂²	semidirect
39. C₇×#553	C₂²	semidirect
41. C₇×#552	C₂²	semidirect
42. C₇×#552	C₂²	semidirect
45. C₇×#547	C₂²	semidirect
68. C₇×#501	C₂²	semidirect
69. C₇×#501	C₂²	semidirect
70. C₇×#499	C₂²	semidirect
71. C₇×#499	C₂²	semidirect
72. C₇×#485	C₂²	semidirect
73. C₇×#485	C₂²	semidirect
74. C₇×#484	C₂²	semidirect
75. C₇×#483	C₂²	semidirect
76. C₇×#482	C₂²	semidirect
77. C₇×#482	C₂²	semidirect
78. C₇×#482	C₂²	semidirect
79. C₇×#482	C₂²	semidirect
80. C₇×#482	C₂²	semidirect
81. C₇×#482	C₂²	semidirect
82. C₇×#481	C₂²	semidirect
83. C₇×#481	C₂²	semidirect
84. C₇×#481	C₂²	semidirect
85. C₇×#480	C₂²	semidirect
86. C₇×#480	C₂²	semidirect
87. C₇×#480	C₂²	semidirect
88. C₇×#479	C₂²	semidirect
89. C₇×#479	C₂²	semidirect
90. C₇×#478	C₂²	semidirect
91. C₇×#478	C₂²	semidirect
92. C₇×#478	C₂²	semidirect
93. C₇×#478	C₂²	semidirect
94. C₇×#476	C₂²	semidirect
95. C₇×#474	C₂²	semidirect
96. C₇×#469	C₂²	semidirect
97. C₇×#469	C₂²	semidirect
98. C₇×#468	C₂²	semidirect
99. C₇×#468	C₂²	semidirect
100. C₇×#466	C₂²	semidirect
101. C₇×#466	C₂²	semidirect
102. C₇×#465	C₂²	semidirect
103. C₇×#465	C₂²	semidirect
104. C₇×#442	C₂²	semidirect
105. C₇×#440	C₂²	semidirect
106. C₄×C₇×SD₁₆	C₂²	semidirect
107. C₄×C₇×D₈	C₂²	semidirect
108. C₇×#436	C₂²	semidirect
109. C₇×#435	C₂²	semidirect
110. C₇×#435	C₂²	semidirect
111. C₇×C₈×D₄	C₂²	semidirect
121. C₇×#428	C₂²	semidirect
122. C₇×#428	C₂²	semidirect
123. C₇×#428	C₂²	semidirect
124. C₇×#428	C₂²	semidirect
125. C₇×#427	C₂²	semidirect
126. C₇×#427	C₂²	semidirect
127. C₂×C₇×#107	C₂²	semidirect
128. C₂×C₇×#106	C₂²	semidirect
139. #61255	C₇	direct (N × H)
346. #3475	C₂×C₇	semidirect
347. C₂×#553	C₂×C₇	semidirect
348. #3355	C₂×C₇	semidirect
349. #3351	C₂×C₇	semidirect
350. #3350	C₂×C₇	semidirect
351. #3347	C₂×C₇	semidirect
352. #3346	C₂×C₇	semidirect
353. #3345	C₂×C₇	semidirect
354. #3339	C₂×C₇	semidirect
355. #3337	C₂×C₇	semidirect
356. #3166	C₂×C₇	semidirect
357. #3094	C₂×C₇	semidirect
358. #3094	C₂×C₇	semidirect
359. #3093	C₂×C₇	semidirect
360. #3092	C₂×C₇	semidirect
361. #3080	C₂×C₇	semidirect
362. #3077	C₂×C₇	semidirect
363. #3055	C₂×C₇	semidirect
364. #3055	C₂×C₇	semidirect
365. C₄×AGL(1,ℤ/8)	C₂×C₇	semidirect
366. D₄×M₁₆	C₂×C₇	semidirect
367. #2911	C₂×C₇	semidirect
368. C₂×#428	C₂×C₇	semidirect
439. C₇×M₁₆	#41	semidirect
535. #556	C₂²×C₇	semidirect
536. #555	C₂²×C₇	semidirect
537. #554	C₂²×C₇	semidirect
546. #553	C₂²×C₇	semidirect
547. #553	C₂²×C₇	semidirect
549. #552	C₂²×C₇	semidirect
550. #552	C₂²×C₇	semidirect
553. #547	C₂²×C₇	semidirect
576. #501	C₂²×C₇	semidirect
577. #501	C₂²×C₇	semidirect
578. #499	C₂²×C₇	semidirect
579. #499	C₂²×C₇	semidirect
580. #485	C₂²×C₇	semidirect
581. #485	C₂²×C₇	semidirect
582. #484	C₂²×C₇	semidirect
583. #483	C₂²×C₇	semidirect
584. #482	C₂²×C₇	semidirect
585. #482	C₂²×C₇	semidirect
586. #482	C₂²×C₇	semidirect
587. #482	C₂²×C₇	semidirect
588. #482	C₂²×C₇	semidirect
589. #482	C₂²×C₇	semidirect
590. #481	C₂²×C₇	semidirect
591. #481	C₂²×C₇	semidirect
592. #481	C₂²×C₇	semidirect
593. #480	C₂²×C₇	semidirect
594. #480	C₂²×C₇	semidirect
595. #480	C₂²×C₇	semidirect
596. #479	C₂²×C₇	semidirect
597. #479	C₂²×C₇	semidirect
598. #478	C₂²×C₇	semidirect
599. #478	C₂²×C₇	semidirect
600. #478	C₂²×C₇	semidirect
601. #478	C₂²×C₇	semidirect
602. #476	C₂²×C₇	semidirect
603. #474	C₂²×C₇	semidirect
604. #469	C₂²×C₇	semidirect
605. #469	C₂²×C₇	semidirect
606. #468	C₂²×C₇	semidirect
607. #468	C₂²×C₇	semidirect
608. #466	C₂²×C₇	semidirect
609. #466	C₂²×C₇	semidirect
610. #465	C₂²×C₇	semidirect
611. #465	C₂²×C₇	semidirect
612. #442	C₂²×C₇	semidirect
613. #440	C₂²×C₇	semidirect
614. C₄×SD₁₆	C₂²×C₇	semidirect
615. C₄×D₈	C₂²×C₇	semidirect
616. #436	C₂²×C₇	semidirect
617. #435	C₂²×C₇	semidirect
618. #435	C₂²×C₇	semidirect
619. C₈×D₄	C₂²×C₇	semidirect
629. #428	C₂²×C₇	semidirect
630. #428	C₂²×C₇	semidirect
631. #428	C₂²×C₇	semidirect
632. #428	C₂²×C₇	semidirect
633. #427	C₂²×C₇	semidirect
634. #427	C₂²×C₇	semidirect
635. C₂×#107	C₂²×C₇	semidirect
636. C₂×#106	C₂²×C₇	semidirect
1063. M₁₆	C₇×#41	semidirect
1260. C₇	#61255	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×#3475	2
C₂×C₇×#553	2
C₇×#3355	2
C₇×#3351	2
C₇×#3350	2
C₇×#3347	2
C₇×#3346	2
C₇×#3345	2
C₇×#3339	2
C₇×#3337	2
C₇×#3166	2
C₇×#3094	2
C₇×#3093	2
C₇×#3092	2
C₇×#3080	2
C₇×#3077	2
C₇×#3055	2
C₄×C₇×AGL(1,ℤ/8)	2
C₇×D₄×M₁₆	2
C₇×#2911	2
C₂×C₇×#428	2
#61255	7

Subgroups — C7×#61255 #13238471

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61255 #13238471