Subgroups — C₇×#61253 #13238469

Order 1792.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1288 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
2	C₂×C₇×#552	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3352	C₂	1	2	yes	maximal, complemented
4	C₇×#3351	C₂	1	2	yes	maximal, complemented
5	C₇×#3349	C₂	1	2	yes	maximal, complemented
6	C₇×#3348	C₂	1	2	yes	maximal, complemented
7	C₇×#3344	C₂	1	2	yes	maximal, complemented
8	C₇×#3343	C₂	1	2	yes	maximal, complemented
9	C₇×#3337	C₂	1	2	yes	maximal, complemented
10	C₇×#3336	C₂	1	2	yes	maximal, complemented
11	C₇×#3166	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3095	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3095	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×#3078	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3056	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×C₇×#137	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×#137	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
28	C₇×#555	C₂²	1	1	yes	characteristic
29	C₇×#554	C₂²	1	1	yes	characteristic
30	C₇×#553	C₂²	1	1	yes	characteristic
31	C₇×#553	C₂²	1	1	yes	characteristic
32	C₇×#552	—	2	1	no	—
33	C₇×#552	—	2	1	no	—
34	C₇×#552	—	2	1	no	—
35	C₇×#552	—	2	1	no	—
36	C₇×#552	—	2	1	no	—
37	C₇×#552	C₂²	1	2	yes	—
38	C₇×#552	C₂²	1	2	yes	—
39	C₇×#552	C₂²	1	2	yes	—
40	C₇×#552	C₂²	1	2	yes	—
41	C₇×#552	C₂²	1	1	yes	characteristic
42	C₇×#552	C₂²	1	1	yes	characteristic
43	C₇×#551	—	2	1	no	—
44	C₇×#551	—	2	1	no	—
45	C₇×#547	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
53	C₂×C₇×#125	C₂²	1	1	yes	characteristic
54	C₇×#525	C₂²	1	1	yes	characteristic
55	C₇×#525	C₂²	1	1	yes	characteristic
56	C₂×C₇×#123	—	2	1	no	—
57	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₇×C₂²⋊Q₈	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×Q₈	C₂²	1	1	yes	characteristic
62	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
63	C₂×C₇×#117	—	2	1	no	—
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×#485	C₂²	1	2	yes	complemented
75	C₇×#485	C₂²	1	2	yes	complemented
76	C₇×#485	C₂²	1	2	yes	complemented
77	C₇×#485	C₂²	1	2	yes	complemented
78	C₇×#484	C₂²	1	2	yes	complemented
79	C₇×#484	C₂²	1	2	yes	complemented
80	C₇×#484	C₂²	1	2	yes	complemented
81	C₇×#483	C₂²	1	2	yes	complemented
82	C₇×#483	C₂²	1	2	yes	complemented
83	C₇×#483	C₂²	1	2	yes	complemented
84	C₇×#482	C₂²	1	2	yes	complemented
85	C₇×#482	C₂²	1	2	yes	complemented
86	C₇×#481	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×#479	C₂²	1	2	yes	complemented
91	C₇×#479	C₂²	1	2	yes	complemented
92	C₇×#478	C₂²	1	2	yes	complemented
93	C₇×#478	C₂²	1	2	yes	complemented
94	C₇×#477	C₂²	1	2	yes	complemented
95	C₇×#475	C₂²	1	2	yes	complemented
96	C₇×#470	C₂²	1	2	yes	complemented
97	C₇×#470	C₂²	1	2	yes	complemented
98	C₇×#468	C₂²	1	2	yes	complemented
99	C₇×#468	C₂²	1	2	yes	complemented
100	C₇×#467	C₂²	1	2	yes	complemented
101	C₇×#467	C₂²	1	2	yes	complemented
102	C₇×#465	C₂²	1	2	yes	complemented
103	C₇×#465	C₂²	1	2	yes	complemented
104	C₇×#441	C₂²	1	2	yes	complemented
105	C₇×#440	C₂²	1	2	yes	complemented
106	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
107	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
108	C₇×#436	C₂²	1	2	yes	—
109	C₇×#435	C₂²	1	2	yes	—
110	C₇×#435	C₂²	1	2	yes	—
111	C₇×C₈×D₄	C₂²	1	2	yes	—
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×#419	C₂²	1	1	yes	characteristic
131	C₇×#419	C₂²	1	1	yes	characteristic
132	C₇×#419	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	#61253	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×Q₈	C₂³	1	1	yes	characteristic
143	C₂²×C₇×D₄	D₄	1	1	yes	characteristic
144	C₂³×C₄×C₇	—	2	1	no	—
145	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
146	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
147	C₇×#137	—	2	4	no	—
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₇×M₁₆	—	2	4	no	—
151	C₂×C₇×M₁₆	—	2	4	no	—
152	C₂×C₇×M₁₆	C₂³	1	2	yes	—
153	C₂×C₇×M₁₆	C₂³	1	2	yes	—
154	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
155	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
156	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
157	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
158	C₂²×C₇×C₈	C₂³	1	2	yes	—
159	C₂²×C₇×C₈	C₂³	1	2	yes	—
160	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₇×#126	—	2	1	no	—
163	C₇×#126	—	2	1	no	—
164	C₇×#126	—	2	2	no	—
165	C₇×#126	—	2	2	no	—
166	C₇×#126	—	2	2	no	—
167	C₇×#126	—	2	2	no	—
168	C₇×#126	—	2	1	no	—
169	C₇×#126	—	2	1	no	—
170	C₇×#126	—	2	1	no	—
171	C₇×#126	—	2	1	no	—
172	C₇×#125	—	2	2	no	—
173	C₇×#125	—	2	2	no	—
174	C₇×#125	—	2	2	no	—
175	C₇×#125	—	2	2	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	—	2	1	no	—
181	C₇×#125	C₂³	1	2	yes	—
182	C₇×#125	C₂³	1	2	yes	—
183	C₇×#125	C₂³	1	1	yes	characteristic
184	C₇×#125	C₂³	1	1	yes	characteristic
185	C₇×#124	—	2	1	no	—
186	C₇×#124	—	2	1	no	—
187	C₇×#124	—	2	1	no	—
188	C₇×#123	—	2	2	no	—
189	C₇×#123	—	2	2	no	—
190	C₇×#123	—	2	2	no	—
191	C₇×#123	—	2	2	no	—
192	C₇×#123	—	2	1	no	—
193	C₇×#123	—	2	1	no	—
194	C₇×#123	—	2	1	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×#123	—	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	—	2	1	no	—
205	C₇×C₂²⋊Q₈	—	2	1	no	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
207	C₇×C₂²⋊Q₈	—	2	1	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
210	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
211	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
212	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
215	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₇×#121	—	2	1	no	—
218	C₇×#121	—	2	1	no	—
219	C₇×#121	—	2	1	no	—
220	C₇×#121	C₂³	1	1	yes	characteristic
221	C₇×#121	C₂³	1	1	yes	characteristic
222	C₇×#121	C₂³	1	1	yes	characteristic
223	C₇×#121	C₂³	1	1	yes	characteristic
224	C₇×#120	—	2	1	no	—
225	C₇×#120	—	2	1	no	—
226	C₄×C₇×Q₈	—	2	1	no	—
227	C₄×C₇×Q₈	—	2	1	no	—
228	C₄×C₇×Q₈	—	2	1	no	—
229	C₄×C₇×Q₈	—	2	1	no	—
230	C₄×C₇×Q₈	—	2	1	no	—
231	C₄×C₇×Q₈	C₂³	1	2	yes	—
232	C₄×C₇×Q₈	C₂³	1	2	yes	—
233	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
234	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	1	no	—
242	C₄×C₇×D₄	—	2	1	no	—
243	C₄×C₇×D₄	—	2	1	no	—
244	C₄×C₇×D₄	D₄	1	1	yes	characteristic
245	C₄×C₇×D₄	D₄	1	1	yes	characteristic
246	C₄×C₇×D₄	D₄	1	1	yes	characteristic
247	C₄×C₇×D₄	D₄	1	1	yes	characteristic
248	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
249	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
250	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
251	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
252	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
253	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
254	C₇×#117	—	2	1	no	—
255	C₇×#117	—	2	1	no	—
256	C₇×#117	—	2	1	no	—
257	C₇×#117	—	2	1	no	—
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	—	2	2	no	—
263	C₇×#117	—	2	2	no	—
264	C₇×#117	—	2	2	no	—
265	C₇×#117	—	2	1	no	—
266	C₇×#117	—	2	1	no	—
267	C₇×#117	—	2	1	no	—
268	C₇×#117	C₂³	1	2	yes	—
269	C₇×#117	C₂³	1	2	yes	—
270	C₇×#117	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
276	C₇×#117	C₂³	1	1	yes	characteristic
277	C₂×C₇×C₄⋊C₄	—	2	1	no	—
278	C₂×C₇×C₄⋊C₄	—	2	1	no	—
279	C₂×C₇×C₄⋊C₄	—	2	1	no	—
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	2	yes	—
287	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
288	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	D₄	1	1	yes	characteristic
301	C₂×C₇×C₂²⋊C₄	D₄	1	1	yes	characteristic
302	C₂×C₄²×C₇	—	2	1	no	—
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×#103	C₂³	1	2	yes	—
332	C₇×#103	C₂³	1	2	yes	—
333	C₇×#103	C₂³	1	2	yes	—
334	C₇×#103	C₂³	1	2	yes	—
335	C₇×#103	C₂³	1	2	yes	—
336	C₇×#103	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
347	C₂×#552	C₂×C₇	1	1	yes	characteristic, complemented
348	#3352	C₂×C₇	1	2	yes	complemented
349	#3351	C₂×C₇	1	2	yes	complemented
350	#3349	C₂×C₇	1	2	yes	complemented
351	#3348	C₂×C₇	1	2	yes	complemented
352	#3344	C₂×C₇	1	2	yes	complemented
353	#3343	C₂×C₇	1	2	yes	complemented
354	#3337	C₂×C₇	1	2	yes	complemented
355	#3336	C₂×C₇	1	2	yes	complemented
356	#3166	C₂×C₇	1	1	yes	characteristic, complemented
357	#3095	C₂×C₇	1	1	yes	characteristic, complemented
358	#3095	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	#3078	C₂×C₇	1	1	yes	characteristic, complemented
363	#3056	C₂×C₇	1	1	yes	characteristic, complemented
364	#3056	C₂×C₇	1	1	yes	characteristic, complemented
365	C₄×#137	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	C₂×D₄	1	1	yes	characteristic
370	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
371	C₇×#41	—	2	2	no	—
372	C₇×#41	—	2	2	no	—
373	C₇×#41	—	4	4	no	—
374	C₂×C₇×Q₈	—	2	1	no	—
375	C₂×C₇×Q₈	—	2	1	no	—
376	C₂×C₇×Q₈	—	2	1	no	—
377	C₂×C₇×Q₈	—	2	2	no	—
378	C₂×C₇×Q₈	—	2	2	no	—
379	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
380	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₇×D₄	—	2	1	no	—
382	C₂×C₇×D₄	—	2	1	no	—
383	C₂×C₇×D₄	—	2	1	no	—
384	C₂×C₇×D₄	—	2	1	no	—
385	C₂×C₇×D₄	—	2	1	no	—
386	C₂×C₇×D₄	—	4	2	no	—
387	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
388	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
389	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
390	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
391	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
392	C₂²×C₄×C₇	—	2	2	no	—
393	C₂²×C₄×C₇	—	2	2	no	—
394	C₂²×C₄×C₇	—	2	2	no	—
395	C₂²×C₄×C₇	—	2	2	no	—
396	C₂²×C₄×C₇	—	2	1	no	—
397	C₂²×C₄×C₇	—	2	1	no	—
398	C₂²×C₄×C₇	—	2	1	no	—
399	C₂²×C₄×C₇	—	2	1	no	—
400	C₂²×C₄×C₇	—	2	1	no	—
401	C₂²×C₄×C₇	—	2	1	no	—
402	C₂²×C₄×C₇	—	2	2	no	—
403	C₂²×C₄×C₇	—	2	2	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	—	4	4	no	—
410	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
411	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
412	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
413	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
414	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
415	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
416	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
417	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
418	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
419	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
420	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
421	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
422	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
423	C₇×Q₁₆	—	2	4	no	—
424	C₇×SD₁₆	—	2	4	no	—
425	C₇×M₁₆	—	2	2	no	—
426	C₇×M₁₆	—	2	2	no	—
427	C₇×M₁₆	—	2	2	no	—
428	C₇×M₁₆	—	2	4	no	—
429	C₇×M₁₆	—	2	4	no	—
430	C₇×M₁₆	#41	1	4	yes	complemented
431	C₂×C₇×C₈	—	2	4	no	—
432	C₂×C₇×C₈	—	2	4	no	—
433	C₂×C₇×C₈	C₂⁴	1	2	yes	—
434	C₂×C₇×C₈	C₂⁴	1	2	yes	—
435	C₂×C₇×C₈	C₂⁴	1	2	yes	—
436	C₂×C₇×C₈	C₂⁴	1	2	yes	—
437	C₇×C₄⋊C₄	—	2	1	no	—
438	C₇×C₄⋊C₄	—	2	1	no	—
439	C₇×C₄⋊C₄	—	2	2	no	—
440	C₇×C₄⋊C₄	—	2	2	no	—
441	C₇×C₄⋊C₄	—	2	2	no	—
442	C₇×C₄⋊C₄	—	2	2	no	—
443	C₇×C₄⋊C₄	—	2	2	no	—
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	2	no	—
446	C₇×C₄⋊C₄	—	2	2	no	—
447	C₇×C₄⋊C₄	—	2	2	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	1	no	—
452	C₇×C₄⋊C₄	—	2	1	no	—
453	C₇×C₄⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
472	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
473	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
474	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
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×C₂²⋊C₄	—	2	1	no	—
482	C₇×C₂²⋊C₄	—	2	2	no	—
483	C₇×C₂²⋊C₄	—	2	2	no	—
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	1	no	—
488	C₇×C₂²⋊C₄	—	2	1	no	—
489	C₇×C₂²⋊C₄	—	2	1	no	—
490	C₇×C₂²⋊C₄	—	2	2	no	—
491	C₇×C₂²⋊C₄	—	2	2	no	—
492	C₇×C₂²⋊C₄	—	2	2	no	—
493	C₇×C₂²⋊C₄	—	2	2	no	—
494	C₇×C₂²⋊C₄	—	2	1	no	—
495	C₇×C₂²⋊C₄	—	2	1	no	—
496	C₇×C₂²⋊C₄	—	2	1	no	—
497	C₇×C₂²⋊C₄	—	2	1	no	—
498	C₇×C₂²⋊C₄	—	2	1	no	—
499	C₇×C₂²⋊C₄	—	2	1	no	—
500	C₇×C₂²⋊C₄	—	2	1	no	—
501	C₇×C₂²⋊C₄	—	2	1	no	—
502	C₇×C₂²⋊C₄	—	2	1	no	—
503	C₇×C₂²⋊C₄	—	2	1	no	—
504	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
505	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
506	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
507	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
508	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₇	—	2	1	no	—
513	C₄²×C₇	—	2	1	no	—
514	C₄²×C₇	—	2	1	no	—
515	C₄²×C₇	—	2	2	no	—
516	C₄²×C₇	—	2	2	no	—
517	C₄²×C₇	—	2	1	no	—
518	C₄²×C₇	—	2	2	no	—
519	C₄²×C₇	—	2	2	no	—
520	C₄²×C₇	—	2	1	no	—
521	C₄²×C₇	—	2	1	no	—
522	C₄²×C₇	—	2	1	no	—
523	C₄²×C₇	—	2	1	no	—
524	C₄²×C₇	—	2	1	no	—
525	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
526	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
527	C₄²×C₇	C₂⁴	1	1	yes	characteristic
528	C₄²×C₇	C₂⁴	1	1	yes	characteristic
529	C₂×#137	C₂²×C₇	1	1	yes	characteristic
530	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
531	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
532	#556	C₂²×C₇	1	1	yes	characteristic
533	#555	C₂²×C₇	1	1	yes	characteristic
534	#554	C₂²×C₇	1	1	yes	characteristic
535	#553	C₂²×C₇	1	1	yes	characteristic
536	#553	C₂²×C₇	1	1	yes	characteristic
537	#552	—	2	1	no	—
538	#552	—	2	1	no	—
539	#552	—	2	1	no	—
540	#552	—	2	1	no	—
541	#552	—	2	1	no	—
542	#552	C₂²×C₇	1	1	yes	characteristic
543	#552	C₂²×C₇	1	2	yes	—
544	#552	C₂²×C₇	1	2	yes	—
545	#552	C₂²×C₇	1	2	yes	—
546	#552	C₂²×C₇	1	2	yes	—
547	#552	C₂²×C₇	1	1	yes	characteristic
548	#551	—	2	1	no	—
549	#551	—	2	1	no	—
550	#547	C₂²×C₇	1	1	yes	characteristic
551	#546	—	2	1	no	—
552	#533	C₂²×C₇	1	1	yes	characteristic
553	#529	—	2	1	no	—
554	#529	—	2	1	no	—
555	#529	—	2	1	no	—
556	C₂×#126	—	2	1	no	—
557	C₂×#125	—	2	1	no	—
558	C₂×#125	C₂²×C₇	1	1	yes	characteristic
559	#525	C₂²×C₇	1	1	yes	characteristic
560	#525	C₂²×C₇	1	1	yes	characteristic
561	C₂×#123	—	2	1	no	—
562	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
563	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
564	C₄×#41	—	2	1	no	—
565	C₄×#41	C₂²×C₇	1	1	yes	characteristic
566	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
567	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
568	C₂×#117	—	2	1	no	—
569	C₂×#117	C₂²×C₇	1	1	yes	characteristic
570	C₂×#117	C₂²×C₇	1	1	yes	characteristic
571	C₂×#117	C₂²×C₇	1	1	yes	characteristic
572	C₂²×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
573	#501	C₂²×C₇	1	2	yes	complemented
574	#501	C₂²×C₇	1	2	yes	complemented
575	#499	C₂²×C₇	1	2	yes	complemented
576	#499	C₂²×C₇	1	2	yes	complemented
577	#485	C₂²×C₇	1	2	yes	complemented
578	#485	C₂²×C₇	1	2	yes	complemented
579	#485	C₂²×C₇	1	2	yes	complemented
580	#485	C₂²×C₇	1	2	yes	complemented
581	#485	C₂²×C₇	1	2	yes	complemented
582	#485	C₂²×C₇	1	2	yes	complemented
583	#484	C₂²×C₇	1	2	yes	complemented
584	#484	C₂²×C₇	1	2	yes	complemented
585	#484	C₂²×C₇	1	2	yes	complemented
586	#483	C₂²×C₇	1	2	yes	complemented
587	#483	C₂²×C₇	1	2	yes	complemented
588	#483	C₂²×C₇	1	2	yes	complemented
589	#482	C₂²×C₇	1	2	yes	complemented
590	#482	C₂²×C₇	1	2	yes	complemented
591	#481	C₂²×C₇	1	2	yes	complemented
592	#480	C₂²×C₇	1	2	yes	complemented
593	#479	C₂²×C₇	1	2	yes	complemented
594	#479	C₂²×C₇	1	2	yes	complemented
595	#479	C₂²×C₇	1	2	yes	complemented
596	#479	C₂²×C₇	1	2	yes	complemented
597	#478	C₂²×C₇	1	2	yes	complemented
598	#478	C₂²×C₇	1	2	yes	complemented
599	#477	C₂²×C₇	1	2	yes	complemented
600	#475	C₂²×C₇	1	2	yes	complemented
601	#470	C₂²×C₇	1	2	yes	complemented
602	#470	C₂²×C₇	1	2	yes	complemented
603	#468	C₂²×C₇	1	2	yes	complemented
604	#468	C₂²×C₇	1	2	yes	complemented
605	#467	C₂²×C₇	1	2	yes	complemented
606	#467	C₂²×C₇	1	2	yes	complemented
607	#465	C₂²×C₇	1	2	yes	complemented
608	#465	C₂²×C₇	1	2	yes	complemented
609	#441	C₂²×C₇	1	2	yes	complemented
610	#440	C₂²×C₇	1	2	yes	complemented
611	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
612	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
613	#436	C₂²×C₇	1	2	yes	—
614	#435	C₂²×C₇	1	2	yes	—
615	#435	C₂²×C₇	1	2	yes	—
616	C₈×D₄	C₂²×C₇	1	2	yes	—
617	#428	C₂²×C₇	1	1	yes	characteristic
618	#428	C₂²×C₇	1	1	yes	characteristic
619	#428	C₂²×C₇	1	1	yes	characteristic
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	2	yes	complemented
627	#428	C₂²×C₇	1	2	yes	complemented
628	#428	C₂²×C₇	1	2	yes	complemented
629	#428	C₂²×C₇	1	2	yes	complemented
630	#427	C₂²×C₇	1	2	yes	complemented
631	#427	C₂²×C₇	1	2	yes	complemented
632	C₂×#107	C₂²×C₇	1	2	yes	complemented
633	C₂×#106	C₂²×C₇	1	2	yes	complemented
634	#423	C₂²×C₇	1	1	yes	characteristic
635	#419	C₂²×C₇	1	1	yes	characteristic
636	#419	C₂²×C₇	1	1	yes	characteristic
637	#419	C₂²×C₇	1	1	yes	characteristic
638	#417	C₂²×C₇	1	1	yes	characteristic
639	#417	C₂²×C₇	1	1	yes	characteristic
640	#417	C₂²×C₇	1	1	yes	characteristic
641	#407	C₂²×C₇	1	1	yes	characteristic
642	#407	C₂²×C₇	1	1	yes	characteristic
643	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
644	C₂³×C₇	—	2	2	no	—
645	C₂³×C₇	—	2	2	no	—
646	C₂³×C₇	—	2	2	no	—
647	C₂³×C₇	—	2	1	no	—
648	C₂³×C₇	—	4	1	no	—
649	C₂³×C₇	—	4	1	no	—
650	C₂³×C₇	—	4	1	no	—
651	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
652	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
653	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
654	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
655	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
656	C₇×Q₈	—	2	2	no	—
657	C₇×Q₈	—	2	1	no	—
658	C₇×Q₈	—	2	2	no	—
659	C₇×Q₈	—	2	1	no	—
660	C₇×Q₈	—	4	2	no	—
661	C₇×Q₈	—	4	2	no	—
662	C₇×Q₈	—	8	1	no	—
663	C₇×D₄	—	2	2	no	—
664	C₇×D₄	—	2	2	no	—
665	C₇×D₄	—	2	1	no	—
666	C₇×D₄	—	2	1	no	—
667	C₇×D₄	—	4	1	no	—
668	C₇×D₄	—	4	1	no	—
669	C₇×D₄	—	4	2	no	—
670	C₇×D₄	—	4	2	no	—
671	C₇×D₄	—	4	2	no	—
672	C₇×D₄	—	8	1	no	—
673	C₇×D₄	—	8	1	no	—
674	C₂×C₄×C₇	—	2	2	no	—
675	C₂×C₄×C₇	—	2	2	no	—
676	C₂×C₄×C₇	—	2	2	no	—
677	C₂×C₄×C₇	—	2	2	no	—
678	C₂×C₄×C₇	—	2	2	no	—
679	C₂×C₄×C₇	—	2	2	no	—
680	C₂×C₄×C₇	—	2	1	no	—
681	C₂×C₄×C₇	—	2	1	no	—
682	C₂×C₄×C₇	—	2	1	no	—
683	C₂×C₄×C₇	—	2	1	no	—
684	C₂×C₄×C₇	—	2	1	no	—
685	C₂×C₄×C₇	—	2	1	no	—
686	C₂×C₄×C₇	—	2	1	no	—
687	C₂×C₄×C₇	—	2	1	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	2	no	—
692	C₂×C₄×C₇	—	2	1	no	—
693	C₂×C₄×C₇	—	2	2	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	2	no	—
699	C₂×C₄×C₇	—	4	1	no	—
700	C₂×C₄×C₇	—	4	1	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	—	4	2	no	—
705	C₂×C₄×C₇	—	4	4	no	—
706	C₂×C₄×C₇	—	4	2	no	—
707	C₂×C₄×C₇	—	4	2	no	—
708	C₂×C₄×C₇	—	4	4	no	—
709	C₂×C₄×C₇	—	4	2	no	—
710	C₂×C₄×C₇	—	4	2	no	—
711	C₂×C₄×C₇	—	8	1	no	—
712	C₂×C₄×C₇	—	8	1	no	—
713	C₂×C₄×C₇	—	8	1	no	—
714	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
715	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
716	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
717	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
718	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
719	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
720	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
721	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
722	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
723	C₂×C₄×C₇	C₂×#41	1	2	yes	—
724	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
725	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
726	C₇×C₈	—	2	2	no	—
727	C₇×C₈	—	2	2	no	—
728	C₇×C₈	—	2	2	no	—
729	C₇×C₈	C₂×#41	1	4	yes	—
730	C₂×#41	—	2	1	no	—
731	C₂×#41	C₂³×C₇	1	1	yes	characteristic
732	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
733	C₂²×D₄	C₇×D₄	1	1	yes	characteristic
734	C₂³×C₄	—	2	1	no	—
735	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
736	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
737	#137	—	2	4	no	—
738	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
739	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
740	C₂×M₁₆	—	2	4	no	—
741	C₂×M₁₆	—	2	4	no	—
742	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
743	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
744	C₂×M₁₆	C₂³×C₇	1	2	yes	—
745	C₂×M₁₆	C₂³×C₇	1	2	yes	—
746	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
747	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
748	C₂²×C₈	C₂³×C₇	1	2	yes	—
749	C₂²×C₈	C₂³×C₇	1	2	yes	—
750	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
751	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
752	#126	—	2	1	no	—
753	#126	—	2	1	no	—
754	#126	—	2	2	no	—
755	#126	—	2	2	no	—
756	#126	—	2	2	no	—
757	#126	—	2	2	no	—
758	#126	—	2	1	no	—
759	#126	—	2	1	no	—
760	#126	—	2	1	no	—
761	#126	—	2	1	no	—
762	#125	—	2	2	no	—
763	#125	—	2	2	no	—
764	#125	—	2	2	no	—
765	#125	—	2	2	no	—
766	#125	—	2	1	no	—
767	#125	—	2	1	no	—
768	#125	—	2	1	no	—
769	#125	—	2	1	no	—
770	#125	—	2	1	no	—
771	#125	C₂³×C₇	1	2	yes	—
772	#125	C₂³×C₇	1	2	yes	—
773	#125	C₂³×C₇	1	1	yes	characteristic
774	#125	C₂³×C₇	1	1	yes	characteristic
775	#124	—	2	1	no	—
776	#124	—	2	1	no	—
777	#124	—	2	1	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	2	2	no	—
782	#123	—	2	1	no	—
783	#123	—	2	1	no	—
784	#123	—	2	1	no	—
785	#123	—	2	1	no	—
786	#123	—	2	1	no	—
787	#123	—	2	1	no	—
788	#123	—	2	1	no	—
789	#123	—	2	1	no	—
790	C₂²⋊Q₈	—	2	1	no	—
791	C₂²⋊Q₈	—	2	1	no	—
792	C₂²⋊Q₈	—	2	1	no	—
793	C₂²⋊Q₈	—	2	1	no	—
794	C₂²⋊Q₈	—	2	1	no	—
795	C₂²⋊Q₈	—	2	1	no	—
796	C₂²⋊Q₈	—	2	1	no	—
797	C₂²⋊Q₈	—	2	1	no	—
798	C₂²⋊Q₈	—	2	1	no	—
799	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
800	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
801	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
802	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
803	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
804	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
805	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
806	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
807	#121	—	2	1	no	—
808	#121	—	2	1	no	—
809	#121	—	2	1	no	—
810	#121	C₂³×C₇	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	#120	—	2	1	no	—
815	#120	—	2	1	no	—
816	C₄×Q₈	—	2	1	no	—
817	C₄×Q₈	—	2	1	no	—
818	C₄×Q₈	—	2	1	no	—
819	C₄×Q₈	—	2	1	no	—
820	C₄×Q₈	—	2	1	no	—
821	C₄×Q₈	C₂³×C₇	1	2	yes	—
822	C₄×Q₈	C₂³×C₇	1	2	yes	—
823	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
824	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
825	C₄×D₄	—	2	1	no	—
826	C₄×D₄	—	2	1	no	—
827	C₄×D₄	—	2	1	no	—
828	C₄×D₄	—	2	1	no	—
829	C₄×D₄	—	2	1	no	—
830	C₄×D₄	—	2	1	no	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	C₇×D₄	1	1	yes	characteristic
835	C₄×D₄	C₇×D₄	1	1	yes	characteristic
836	C₄×D₄	C₇×D₄	1	1	yes	characteristic
837	C₄×D₄	C₇×D₄	1	1	yes	characteristic
838	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
839	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
840	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
841	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
842	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
843	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
844	#117	—	2	1	no	—
845	#117	—	2	1	no	—
846	#117	—	2	1	no	—
847	#117	—	2	1	no	—
848	#117	—	2	1	no	—
849	#117	—	2	1	no	—
850	#117	—	2	1	no	—
851	#117	—	2	2	no	—
852	#117	—	2	2	no	—
853	#117	—	2	2	no	—
854	#117	—	2	2	no	—
855	#117	—	2	1	no	—
856	#117	—	2	1	no	—
857	#117	—	2	1	no	—
858	#117	C₂³×C₇	1	1	yes	characteristic
859	#117	C₂³×C₇	1	1	yes	characteristic
860	#117	C₂³×C₇	1	1	yes	characteristic
861	#117	C₂³×C₇	1	2	yes	—
862	#117	C₂³×C₇	1	2	yes	—
863	#117	C₂³×C₇	1	1	yes	characteristic
864	#117	C₂³×C₇	1	1	yes	characteristic
865	#117	C₂³×C₇	1	1	yes	characteristic
866	#117	C₂³×C₇	1	1	yes	characteristic
867	C₂×C₄⋊C₄	—	2	1	no	—
868	C₂×C₄⋊C₄	—	2	1	no	—
869	C₂×C₄⋊C₄	—	2	1	no	—
870	C₂×C₄⋊C₄	—	2	1	no	—
871	C₂×C₄⋊C₄	—	2	1	no	—
872	C₂×C₄⋊C₄	—	2	1	no	—
873	C₂×C₄⋊C₄	—	2	1	no	—
874	C₂×C₄⋊C₄	—	2	1	no	—
875	C₂×C₄⋊C₄	C₇×D₄	1	1	yes	characteristic
876	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
877	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
879	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
880	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
881	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
882	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
884	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	2	1	no	—
887	C₂×C₂²⋊C₄	—	2	1	no	—
888	C₂×C₂²⋊C₄	—	2	1	no	—
889	C₂×C₂²⋊C₄	—	2	1	no	—
890	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
891	C₂×C₂²⋊C₄	C₇×D₄	1	1	yes	characteristic
892	C₂×C₄²	—	2	1	no	—
893	C₂×C₄²	—	2	1	no	—
894	C₂×C₄²	—	2	1	no	—
895	C₂×C₄²	—	2	1	no	—
896	C₂×C₄²	—	2	1	no	—
897	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
898	#107	C₂³×C₇	1	2	yes	—
899	#107	C₂³×C₇	1	2	yes	—
900	#107	C₂³×C₇	1	2	yes	—
901	#107	C₂³×C₇	1	2	yes	—
902	#107	C₂³×C₇	1	2	yes	—
903	#107	C₂³×C₇	1	2	yes	—
904	#107	C₂³×C₇	1	2	yes	—
905	#107	C₂³×C₇	1	2	yes	—
906	#107	C₂³×C₇	1	2	yes	—
907	#106	C₂³×C₇	1	2	yes	—
908	#106	C₂³×C₇	1	2	yes	—
909	#106	C₂³×C₇	1	2	yes	—
910	#106	C₂³×C₇	1	2	yes	—
911	#106	C₂³×C₇	1	2	yes	—
912	#106	C₂³×C₇	1	2	yes	—
913	#106	C₂³×C₇	1	2	yes	—
914	#106	C₂³×C₇	1	2	yes	—
915	#106	C₂³×C₇	1	2	yes	—
916	C₄⋊C₈	C₂³×C₇	1	2	yes	—
917	C₄⋊C₈	C₂³×C₇	1	2	yes	—
918	#103	C₂³×C₇	1	2	yes	—
919	#103	C₂³×C₇	1	2	yes	—
920	#103	C₂³×C₇	1	2	yes	—
921	#103	C₂³×C₇	1	2	yes	—
922	#103	C₂³×C₇	1	2	yes	—
923	#103	C₂³×C₇	1	2	yes	—
924	#103	C₂³×C₇	1	2	yes	—
925	#103	C₂³×C₇	1	2	yes	—
926	#103	C₂³×C₇	1	2	yes	—
927	#102	C₂³×C₇	1	2	yes	—
928	#102	C₂³×C₇	1	2	yes	—
929	#102	C₂³×C₇	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
931	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
932	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
933	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
934	#97	C₂³×C₇	1	2	yes	—
935	C₄×C₈	C₂³×C₇	1	2	yes	—
936	C₂²×C₇	—	2	1	no	—
937	C₂²×C₇	—	2	1	no	—
938	C₂²×C₇	—	2	1	no	—
939	C₂²×C₇	—	2	1	no	—
940	C₂²×C₇	—	2	1	no	—
941	C₂²×C₇	—	2	1	no	—
942	C₂²×C₇	—	2	1	no	—
943	C₂²×C₇	—	2	1	no	—
944	C₂²×C₇	—	2	1	no	—
945	C₂²×C₇	—	2	1	no	—
946	C₂²×C₇	—	2	1	no	—
947	C₂²×C₇	—	2	1	no	—
948	C₂²×C₇	—	2	1	no	—
949	C₂²×C₇	—	4	4	no	—
950	C₂²×C₇	—	4	1	no	—
951	C₂²×C₇	—	4	1	no	—
952	C₂²×C₇	—	4	1	no	—
953	C₂²×C₇	—	8	2	no	—
954	C₂²×C₇	#547	1	2	yes	—
955	C₂²×C₇	#575	1	2	yes	—
956	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
957	C₄×C₇	—	2	1	no	—
958	C₄×C₇	—	2	1	no	—
959	C₄×C₇	—	2	1	no	—
960	C₄×C₇	—	2	1	no	—
961	C₄×C₇	—	2	1	no	—
962	C₄×C₇	—	2	1	no	—
963	C₄×C₇	—	2	1	no	—
964	C₄×C₇	—	2	1	no	—
965	C₄×C₇	—	4	2	no	—
966	C₄×C₇	—	4	1	no	—
967	C₄×C₇	—	4	1	no	—
968	C₄×C₇	—	4	1	no	—
969	C₄×C₇	—	4	1	no	—
970	C₄×C₇	—	4	2	no	—
971	C₄×C₇	—	4	1	no	—
972	C₄×C₇	—	4	2	no	—
973	C₄×C₇	—	4	2	no	—
974	C₄×C₇	—	4	1	no	—
975	C₄×C₇	—	4	1	no	—
976	C₄×C₇	#547	1	2	yes	—
977	C₄×C₇	C₂²×#41	1	1	yes	characteristic
978	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
979	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
980	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
981	#41	—	2	2	no	—
982	#41	—	2	2	no	—
983	#41	—	4	4	no	—
984	C₂×Q₈	—	2	1	no	—
985	C₂×Q₈	—	2	1	no	—
986	C₂×Q₈	—	2	1	no	—
987	C₂×Q₈	—	2	2	no	—
988	C₂×Q₈	—	2	2	no	—
989	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
990	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
991	C₂×D₄	—	2	1	no	—
992	C₂×D₄	—	2	1	no	—
993	C₂×D₄	—	2	1	no	—
994	C₂×D₄	—	2	1	no	—
995	C₂×D₄	—	2	1	no	—
996	C₂×D₄	—	4	2	no	—
997	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
998	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
999	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1000	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
1001	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
1002	C₂²×C₄	—	2	2	no	—
1003	C₂²×C₄	—	2	2	no	—
1004	C₂²×C₄	—	2	2	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	1	no	—
1007	C₂²×C₄	—	2	1	no	—
1008	C₂²×C₄	—	2	1	no	—
1009	C₂²×C₄	—	2	1	no	—
1010	C₂²×C₄	—	2	1	no	—
1011	C₂²×C₄	—	2	1	no	—
1012	C₂²×C₄	—	2	2	no	—
1013	C₂²×C₄	—	2	2	no	—
1014	C₂²×C₄	—	2	1	no	—
1015	C₂²×C₄	—	2	1	no	—
1016	C₂²×C₄	—	2	1	no	—
1017	C₂²×C₄	—	2	1	no	—
1018	C₂²×C₄	—	2	1	no	—
1019	C₂²×C₄	—	4	4	no	—
1020	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1021	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1022	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1023	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1024	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1025	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1026	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1027	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1028	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1029	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1030	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1031	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1032	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1033	Q₁₆	—	2	4	no	—
1034	SD₁₆	—	2	4	no	—
1035	M₁₆	—	2	2	no	—
1036	M₁₆	—	2	2	no	—
1037	M₁₆	—	2	2	no	—
1038	M₁₆	—	2	4	no	—
1039	M₁₆	—	2	4	no	—
1040	M₁₆	C₇×#41	1	4	yes	complemented
1041	C₂×C₈	—	2	4	no	—
1042	C₂×C₈	—	2	4	no	—
1043	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1044	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1045	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1046	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	2	no	—
1051	C₄⋊C₄	—	2	2	no	—
1052	C₄⋊C₄	—	2	2	no	—
1053	C₄⋊C₄	—	2	2	no	—
1054	C₄⋊C₄	—	2	2	no	—
1055	C₄⋊C₄	—	2	2	no	—
1056	C₄⋊C₄	—	2	2	no	—
1057	C₄⋊C₄	—	2	2	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	—	2	2	no	—
1061	C₄⋊C₄	—	2	1	no	—
1062	C₄⋊C₄	—	2	1	no	—
1063	C₄⋊C₄	—	2	1	no	—
1064	C₄⋊C₄	—	2	1	no	—
1065	C₄⋊C₄	—	2	1	no	—
1066	C₄⋊C₄	—	2	1	no	—
1067	C₄⋊C₄	—	2	1	no	—
1068	C₄⋊C₄	—	2	1	no	—
1069	C₄⋊C₄	—	2	1	no	—
1070	C₄⋊C₄	—	2	1	no	—
1071	C₄⋊C₄	—	2	1	no	—
1072	C₄⋊C₄	—	2	1	no	—
1073	C₄⋊C₄	—	2	1	no	—
1074	C₄⋊C₄	—	2	1	no	—
1075	C₄⋊C₄	—	2	1	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	no	—
1078	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1079	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1080	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1081	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1082	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1083	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1084	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1085	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
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	1	yes	characteristic
1090	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	1	no	—
1095	C₂²⋊C₄	—	2	1	no	—
1096	C₂²⋊C₄	—	2	1	no	—
1097	C₂²⋊C₄	—	2	1	no	—
1098	C₂²⋊C₄	—	2	1	no	—
1099	C₂²⋊C₄	—	2	1	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	1	no	—
1105	C₂²⋊C₄	—	2	1	no	—
1106	C₂²⋊C₄	—	2	1	no	—
1107	C₂²⋊C₄	—	2	1	no	—
1108	C₂²⋊C₄	—	2	1	no	—
1109	C₂²⋊C₄	—	2	1	no	—
1110	C₂²⋊C₄	—	2	1	no	—
1111	C₂²⋊C₄	—	2	1	no	—
1112	C₂²⋊C₄	—	2	1	no	—
1113	C₂²⋊C₄	—	2	1	no	—
1114	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1115	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1116	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1117	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1118	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1119	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1120	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1121	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1122	C₄²	—	2	1	no	—
1123	C₄²	—	2	1	no	—
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	2	no	—
1126	C₄²	—	2	2	no	—
1127	C₄²	—	2	1	no	—
1128	C₄²	—	2	2	no	—
1129	C₄²	—	2	2	no	—
1130	C₄²	—	2	1	no	—
1131	C₄²	—	2	1	no	—
1132	C₄²	—	2	1	no	—
1133	C₄²	—	2	1	no	—
1134	C₄²	—	2	1	no	—
1135	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1136	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1137	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1138	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1139	C₂×C₇	—	2	2	no	—
1140	C₂×C₇	—	2	2	no	—
1141	C₂×C₇	—	4	1	no	—
1142	C₂×C₇	—	4	1	no	—
1143	C₂×C₇	—	4	1	no	—
1144	C₂×C₇	—	8	1	no	—
1145	C₂×C₇	C₂×#547	1	1	yes	characteristic
1146	C₂×C₇	C₂×#575	1	1	yes	characteristic
1147	C₂×C₇	#3586	1	1	yes	characteristic
1148	C₂³	—	2	2	no	—
1149	C₂³	—	2	2	no	—
1150	C₂³	—	2	2	no	—
1151	C₂³	—	2	1	no	—
1152	C₂³	—	4	1	no	—
1153	C₂³	—	4	1	no	—
1154	C₂³	—	4	1	no	—
1155	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1156	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1157	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1158	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1159	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1160	Q₈	—	2	2	no	—
1161	Q₈	—	2	1	no	—
1162	Q₈	—	2	2	no	—
1163	Q₈	—	2	1	no	—
1164	Q₈	—	4	2	no	—
1165	Q₈	—	4	2	no	—
1166	Q₈	—	8	1	no	—
1167	D₄	—	2	2	no	—
1168	D₄	—	2	2	no	—
1169	D₄	—	2	1	no	—
1170	D₄	—	2	1	no	—
1171	D₄	—	4	1	no	—
1172	D₄	—	4	1	no	—
1173	D₄	—	4	2	no	—
1174	D₄	—	4	2	no	—
1175	D₄	—	4	2	no	—
1176	D₄	—	8	1	no	—
1177	D₄	—	8	1	no	—
1178	C₂×C₄	—	2	2	no	—
1179	C₂×C₄	—	2	2	no	—
1180	C₂×C₄	—	2	1	no	—
1181	C₂×C₄	—	2	1	no	—
1182	C₂×C₄	—	2	1	no	—
1183	C₂×C₄	—	2	1	no	—
1184	C₂×C₄	—	2	1	no	—
1185	C₂×C₄	—	2	1	no	—
1186	C₂×C₄	—	2	1	no	—
1187	C₂×C₄	—	2	1	no	—
1188	C₂×C₄	—	2	2	no	—
1189	C₂×C₄	—	2	2	no	—
1190	C₂×C₄	—	2	2	no	—
1191	C₂×C₄	—	2	2	no	—
1192	C₂×C₄	—	2	1	no	—
1193	C₂×C₄	—	2	1	no	—
1194	C₂×C₄	—	2	2	no	—
1195	C₂×C₄	—	2	2	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	1	no	—
1201	C₂×C₄	—	2	1	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	4	1	no	—
1204	C₂×C₄	—	4	1	no	—
1205	C₂×C₄	—	4	2	no	—
1206	C₂×C₄	—	4	2	no	—
1207	C₂×C₄	—	4	2	no	—
1208	C₂×C₄	—	4	2	no	—
1209	C₂×C₄	—	4	4	no	—
1210	C₂×C₄	—	4	2	no	—
1211	C₂×C₄	—	4	2	no	—
1212	C₂×C₄	—	4	4	no	—
1213	C₂×C₄	—	4	2	no	—
1214	C₂×C₄	—	4	2	no	—
1215	C₂×C₄	—	8	1	no	—
1216	C₂×C₄	—	8	1	no	—
1217	C₂×C₄	—	8	1	no	—
1218	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1219	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1220	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1221	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1222	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1223	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1224	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1225	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1226	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1227	C₂×C₄	C₂×C₇×#41	1	2	yes	—
1228	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1229	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1230	C₈	—	2	2	no	—
1231	C₈	—	2	2	no	—
1232	C₈	—	2	2	no	—
1233	C₈	C₂×C₇×#41	1	4	yes	—
1234	C₇	#61253	1	1	yes	characteristic, direct product factor, Sylow
1235	C₂²	—	2	1	no	—
1236	C₂²	—	2	1	no	—
1237	C₂²	—	2	1	no	—
1238	C₂²	—	2	1	no	—
1239	C₂²	—	2	1	no	—
1240	C₂²	—	2	1	no	—
1241	C₂²	—	2	1	no	—
1242	C₂²	—	2	1	no	—
1243	C₂²	—	2	1	no	—
1244	C₂²	—	2	1	no	—
1245	C₂²	—	2	1	no	—
1246	C₂²	—	2	1	no	—
1247	C₂²	—	2	1	no	—
1248	C₂²	—	4	4	no	—
1249	C₂²	—	4	1	no	—
1250	C₂²	—	4	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	8	2	no	—
1253	C₂²	C₇×#547	1	2	yes	—
1254	C₂²	C₇×#575	1	2	yes	—
1255	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1256	C₄	—	2	1	no	—
1257	C₄	—	2	1	no	—
1258	C₄	—	2	1	no	—
1259	C₄	—	2	1	no	—
1260	C₄	—	2	1	no	—
1261	C₄	—	2	1	no	—
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	4	1	no	—
1265	C₄	—	4	2	no	—
1266	C₄	—	4	2	no	—
1267	C₄	—	4	1	no	—
1268	C₄	—	4	1	no	—
1269	C₄	—	4	2	no	—
1270	C₄	—	4	1	no	—
1271	C₄	—	4	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	1	no	—
1274	C₄	—	4	2	no	—
1275	C₄	C₇×#547	1	2	yes	—
1276	C₄	C₂²×C₇×#41	1	1	yes	characteristic
1277	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1278	C₂	—	2	2	no	—
1279	C₂	—	2	2	no	—
1280	C₂	—	4	1	no	—
1281	C₂	—	4	1	no	—
1282	C₂	—	4	1	no	—
1283	C₂	—	8	1	no	—
1284	C₂	C₂×C₇×#547	1	1	yes	characteristic
1285	C₂	C₂×C₇×#575	1	1	yes	characteristic
1286	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3475	C₂
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
2. C₂×C₇×#552	C₂	semidirect
3. C₇×#3352	C₂	semidirect
4. C₇×#3351	C₂	semidirect
5. C₇×#3349	C₂	semidirect
6. C₇×#3348	C₂	semidirect
7. C₇×#3344	C₂	semidirect
8. C₇×#3343	C₂	semidirect
9. C₇×#3337	C₂	semidirect
10. C₇×#3336	C₂	semidirect
11. C₇×#3166	C₂	semidirect
12. C₇×#3095	C₂	semidirect
13. C₇×#3095	C₂	semidirect
14. C₇×#3093	C₂	semidirect
15. C₇×#3092	C₂	semidirect
16. C₇×#3080	C₂	semidirect
17. C₇×#3078	C₂	semidirect
18. C₇×#3056	C₂	semidirect
19. C₇×#3056	C₂	semidirect
20. C₄×C₇×#137	C₂	semidirect
21. C₇×D₄×M₁₆	C₂	semidirect
22. C₇×#2911	C₂	semidirect
23. C₂×C₇×#428	C₂	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×#485	C₂²	semidirect
75. C₇×#485	C₂²	semidirect
76. C₇×#485	C₂²	semidirect
77. C₇×#485	C₂²	semidirect
78. C₇×#484	C₂²	semidirect
79. C₇×#484	C₂²	semidirect
80. C₇×#484	C₂²	semidirect
81. C₇×#483	C₂²	semidirect
82. C₇×#483	C₂²	semidirect
83. C₇×#483	C₂²	semidirect
84. C₇×#482	C₂²	semidirect
85. C₇×#482	C₂²	semidirect
86. C₇×#481	C₂²	semidirect
87. C₇×#480	C₂²	semidirect
88. C₇×#479	C₂²	semidirect
89. C₇×#479	C₂²	semidirect
90. C₇×#479	C₂²	semidirect
91. C₇×#479	C₂²	semidirect
92. C₇×#478	C₂²	semidirect
93. C₇×#478	C₂²	semidirect
94. C₇×#477	C₂²	semidirect
95. C₇×#475	C₂²	semidirect
96. C₇×#470	C₂²	semidirect
97. C₇×#470	C₂²	semidirect
98. C₇×#468	C₂²	semidirect
99. C₇×#468	C₂²	semidirect
100. C₇×#467	C₂²	semidirect
101. C₇×#467	C₂²	semidirect
102. C₇×#465	C₂²	semidirect
103. C₇×#465	C₂²	semidirect
104. C₇×#441	C₂²	semidirect
105. C₇×#440	C₂²	semidirect
106. C₄×C₇×Q₁₆	C₂²	semidirect
107. C₄×C₇×SD₁₆	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. #61253	C₇	direct (N × H)
347. C₂×#552	C₂×C₇	semidirect
348. #3352	C₂×C₇	semidirect
349. #3351	C₂×C₇	semidirect
350. #3349	C₂×C₇	semidirect
351. #3348	C₂×C₇	semidirect
352. #3344	C₂×C₇	semidirect
353. #3343	C₂×C₇	semidirect
354. #3337	C₂×C₇	semidirect
355. #3336	C₂×C₇	semidirect
356. #3166	C₂×C₇	semidirect
357. #3095	C₂×C₇	semidirect
358. #3095	C₂×C₇	semidirect
359. #3093	C₂×C₇	semidirect
360. #3092	C₂×C₇	semidirect
361. #3080	C₂×C₇	semidirect
362. #3078	C₂×C₇	semidirect
363. #3056	C₂×C₇	semidirect
364. #3056	C₂×C₇	semidirect
365. C₄×#137	C₂×C₇	semidirect
366. D₄×M₁₆	C₂×C₇	semidirect
367. #2911	C₂×C₇	semidirect
368. C₂×#428	C₂×C₇	semidirect
430. C₇×M₁₆	#41	semidirect
573. #501	C₂²×C₇	semidirect
574. #501	C₂²×C₇	semidirect
575. #499	C₂²×C₇	semidirect
576. #499	C₂²×C₇	semidirect
577. #485	C₂²×C₇	semidirect
578. #485	C₂²×C₇	semidirect
579. #485	C₂²×C₇	semidirect
580. #485	C₂²×C₇	semidirect
581. #485	C₂²×C₇	semidirect
582. #485	C₂²×C₇	semidirect
583. #484	C₂²×C₇	semidirect
584. #484	C₂²×C₇	semidirect
585. #484	C₂²×C₇	semidirect
586. #483	C₂²×C₇	semidirect
587. #483	C₂²×C₇	semidirect
588. #483	C₂²×C₇	semidirect
589. #482	C₂²×C₇	semidirect
590. #482	C₂²×C₇	semidirect
591. #481	C₂²×C₇	semidirect
592. #480	C₂²×C₇	semidirect
593. #479	C₂²×C₇	semidirect
594. #479	C₂²×C₇	semidirect
595. #479	C₂²×C₇	semidirect
596. #479	C₂²×C₇	semidirect
597. #478	C₂²×C₇	semidirect
598. #478	C₂²×C₇	semidirect
599. #477	C₂²×C₇	semidirect
600. #475	C₂²×C₇	semidirect
601. #470	C₂²×C₇	semidirect
602. #470	C₂²×C₇	semidirect
603. #468	C₂²×C₇	semidirect
604. #468	C₂²×C₇	semidirect
605. #467	C₂²×C₇	semidirect
606. #467	C₂²×C₇	semidirect
607. #465	C₂²×C₇	semidirect
608. #465	C₂²×C₇	semidirect
609. #441	C₂²×C₇	semidirect
610. #440	C₂²×C₇	semidirect
611. C₄×Q₁₆	C₂²×C₇	semidirect
612. C₄×SD₁₆	C₂²×C₇	semidirect
626. #428	C₂²×C₇	semidirect
627. #428	C₂²×C₇	semidirect
628. #428	C₂²×C₇	semidirect
629. #428	C₂²×C₇	semidirect
630. #427	C₂²×C₇	semidirect
631. #427	C₂²×C₇	semidirect
632. C₂×#107	C₂²×C₇	semidirect
633. C₂×#106	C₂²×C₇	semidirect
1040. M₁₆	C₇×#41	semidirect
1234. C₇	#61253	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×#552	2
C₇×#3352	2
C₇×#3351	2
C₇×#3349	2
C₇×#3348	2
C₇×#3344	2
C₇×#3343	2
C₇×#3337	2
C₇×#3336	2
C₇×#3166	2
C₇×#3095	2
C₇×#3093	2
C₇×#3092	2
C₇×#3080	2
C₇×#3078	2
C₇×#3056	2
C₄×C₇×#137	2
C₇×D₄×M₁₆	2
C₇×#2911	2
C₂×C₇×#428	2
#61253	7

Subgroups — C7×#61253 #13238469

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61253 #13238469