Subgroups — C₇×#61021 #13238237

Order 1792.

1724 conjugacy classes of subgroups.

The subgroup lattice has 1258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3258	C₂	1	2	yes	maximal, complemented
4	C₇×#3257	C₂	1	2	yes	maximal, complemented
5	C₇×#3239	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3238	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3236	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3234	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3219	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3219	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3204	C₂	1	2	yes	maximal, complemented
14	C₇×#3203	C₂	1	2	yes	maximal, complemented
15	C₇×#3181	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3180	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3172	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3171	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3125	C₂	1	2	yes	maximal, complemented
20	C₇×#3124	C₂	1	2	yes	maximal, complemented
21	C₇×#3120	C₂	1	2	yes	maximal, complemented
22	C₇×#3119	C₂	1	2	yes	maximal, complemented
23	C₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#556	—	2	1	no	—
25	C₇×#555	—	2	1	no	—
26	C₇×#554	—	2	1	no	—
27	C₇×#553	—	2	1	no	—
28	C₇×#553	—	2	1	no	—
29	C₇×#553	—	2	1	no	—
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	—	2	1	no	—
35	C₇×#552	—	2	1	no	—
36	C₇×#552	—	2	1	no	—
37	C₇×#548	—	2	1	no	—
38	C₇×#548	—	2	1	no	—
39	C₇×#547	—	2	1	no	—
40	C₇×#542	C₂²	1	2	yes	—
41	C₇×#542	C₂²	1	2	yes	—
42	C₇×#541	C₂²	1	1	yes	characteristic
43	C₇×#541	C₂²	1	1	yes	characteristic
44	C₇×#540	C₂²	1	1	yes	characteristic
45	C₇×#540	C₂²	1	1	yes	characteristic
46	C₇×#537	C₂²	1	1	yes	characteristic
47	C₇×#537	C₂²	1	2	yes	—
48	C₇×#537	C₂²	1	1	yes	characteristic
49	C₇×#533	C₂²	1	1	yes	characteristic
50	C₇×#533	C₂²	1	1	yes	characteristic
51	C₇×#532	C₂²	1	1	yes	characteristic
52	C₇×#532	C₂²	1	1	yes	characteristic
53	C₇×#532	C₂²	1	1	yes	characteristic
54	C₇×#532	C₂²	1	1	yes	characteristic
55	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
56	C₇×#529	C₂²	1	1	yes	characteristic
57	C₇×#529	C₂²	1	1	yes	characteristic
58	C₇×#529	C₂²	1	1	yes	characteristic
59	C₇×#529	C₂²	1	1	yes	characteristic
60	C₂×C₇×#125	C₂²	1	1	yes	characteristic
61	C₇×#520	C₂²	1	2	yes	—
62	C₇×#520	C₂²	1	1	yes	characteristic
63	C₇×#520	C₂²	1	1	yes	characteristic
64	C₄×C₇×#41	C₂²	1	1	yes	characteristic
65	C₇×#501	C₂²	1	1	yes	characteristic
66	C₇×#501	C₂²	1	1	yes	characteristic
67	C₇×#501	C₂²	1	1	yes	characteristic
68	C₇×#501	C₂²	1	1	yes	characteristic
69	C₇×#497	C₂²	1	1	yes	characteristic
70	C₇×#497	C₂²	1	1	yes	characteristic
71	C₇×#496	C₂²	1	1	yes	characteristic
72	C₇×#496	C₂²	1	1	yes	characteristic
73	C₇×#491	C₂²	1	1	yes	characteristic
74	C₇×#491	C₂²	1	1	yes	characteristic
75	C₇×#490	C₂²	1	1	yes	characteristic
76	C₇×#490	C₂²	1	1	yes	characteristic
77	C₇×#489	C₂²	1	1	yes	characteristic
78	C₇×#489	C₂²	1	1	yes	characteristic
79	C₇×#489	C₂²	1	1	yes	characteristic
80	C₇×#489	C₂²	1	1	yes	characteristic
81	C₇×#484	C₂²	1	2	yes	—
82	C₇×#484	C₂²	1	2	yes	—
83	C₇×#483	C₂²	1	2	yes	—
84	C₇×#483	C₂²	1	2	yes	—
85	C₇×#481	C₂²	1	2	yes	—
86	C₇×#481	C₂²	1	2	yes	—
87	C₇×#480	C₂²	1	2	yes	—
88	C₇×#480	C₂²	1	2	yes	—
89	C₇×#479	C₂²	1	2	yes	—
90	C₇×#479	C₂²	1	2	yes	—
91	C₇×#478	C₂²	1	2	yes	—
92	C₇×#478	C₂²	1	2	yes	—
93	C₇×#477	C₂²	1	2	yes	—
94	C₇×#476	C₂²	1	2	yes	—
95	C₇×#475	C₂²	1	2	yes	—
96	C₇×#474	C₂²	1	2	yes	—
97	C₇×#470	C₂²	1	2	yes	—
98	C₇×#469	C₂²	1	2	yes	—
99	C₇×#468	C₂²	1	2	yes	—
100	C₇×#468	C₂²	1	2	yes	—
101	C₇×#467	C₂²	1	2	yes	—
102	C₇×#466	C₂²	1	2	yes	—
103	C₇×#465	C₂²	1	2	yes	—
104	C₇×#465	C₂²	1	2	yes	—
105	C₇×#464	C₂²	1	2	yes	—
106	C₇×#464	C₂²	1	2	yes	—
107	C₇×#463	C₂²	1	2	yes	—
108	C₇×#463	C₂²	1	2	yes	—
109	C₇×#462	C₂²	1	2	yes	—
110	C₇×#461	C₂²	1	2	yes	—
111	C₇×#460	C₂²	1	2	yes	—
112	C₇×#459	C₂²	1	2	yes	—
113	C₇×#452	C₂²	1	2	yes	—
114	C₇×#452	C₂²	1	2	yes	—
115	C₇×#452	C₂²	1	2	yes	—
116	C₇×#452	C₂²	1	2	yes	—
117	C₇×#449	C₂²	1	2	yes	—
118	C₇×#449	C₂²	1	2	yes	—
119	C₇×#449	C₂²	1	2	yes	—
120	C₇×#449	C₂²	1	2	yes	—
121	C₇×#442	C₂²	1	2	yes	—
122	C₇×#441	C₂²	1	2	yes	—
123	C₇×#440	C₂²	1	2	yes	—
124	C₇×#440	C₂²	1	2	yes	—
125	C₄×C₇×Q₁₆	C₂²	1	2	yes	—
126	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
127	C₄×C₇×SD₁₆	C₂²	1	2	yes	—
128	C₄×C₇×D₈	C₂²	1	2	yes	—
129	C₇×#433	C₂²	1	2	yes	—
130	C₇×#433	C₂²	1	2	yes	—
131	C₇×#432	C₂²	1	1	yes	characteristic
132	C₇×#432	C₂²	1	1	yes	characteristic
133	C₇×#432	C₂²	1	1	yes	characteristic
134	C₇×#432	C₂²	1	1	yes	characteristic
135	C₇×#424	C₂²	1	2	yes	—
136	C₇×#408	C₂²	1	2	yes	—
137	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
138	C₂×C₇×#97	C₂²	1	1	yes	characteristic
139	#61021	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂×C₇×#41	—	2	1	no	—
141	C₂×C₇×#41	—	2	1	no	—
142	C₂×C₇×#41	C₂³	1	2	yes	—
143	C₂×C₇×#41	C₂³	1	1	yes	characteristic
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂²×C₇×Q₈	—	2	1	no	—
147	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
148	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
149	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
150	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
151	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
152	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
153	C₂×C₇×D₈	C₂³	1	2	yes	—
154	C₂×C₇×D₈	C₂³	1	2	yes	—
155	C₂×C₇×M₁₆	C₂³	1	2	yes	—
156	C₂²×C₇×C₈	C₂³	1	2	yes	—
157	C₇×C₄⋊Q₈	—	2	1	no	—
158	C₇×C₄⋊Q₈	—	2	1	no	—
159	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
161	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
162	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×#127	C₂³	1	1	yes	characteristic
165	C₇×#127	C₂³	1	1	yes	characteristic
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×#126	—	2	1	no	—
173	C₇×#126	—	2	1	no	—
174	C₇×#126	—	2	1	no	—
175	C₇×#126	—	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	—	2	1	no	—
181	C₇×#125	—	2	1	no	—
182	C₇×#125	—	2	1	no	—
183	C₇×#125	—	2	1	no	—
184	C₇×#125	C₂³	1	1	yes	characteristic
185	C₇×#125	C₂³	1	1	yes	characteristic
186	C₇×#125	C₂³	1	1	yes	characteristic
187	C₇×#125	C₂³	1	1	yes	characteristic
188	C₇×#124	—	2	2	no	—
189	C₇×#124	—	2	2	no	—
190	C₇×#124	—	2	1	no	—
191	C₇×#124	—	2	1	no	—
192	C₇×#124	C₂³	1	1	yes	characteristic
193	C₇×#124	C₂³	1	1	yes	characteristic
194	C₇×#124	C₂³	1	2	yes	—
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×#123	—	2	1	no	—
201	C₇×#123	—	2	1	no	—
202	C₇×#123	—	2	1	no	—
203	C₇×#123	—	2	2	no	—
204	C₇×#123	—	2	2	no	—
205	C₇×C₂²⋊Q₈	—	2	1	no	—
206	C₇×C₂²⋊Q₈	—	2	1	no	—
207	C₇×C₂²⋊Q₈	—	2	2	no	—
208	C₇×C₂²⋊Q₈	—	2	1	no	—
209	C₇×C₂²⋊Q₈	—	2	1	no	—
210	C₇×C₂²⋊Q₈	—	2	2	no	—
211	C₇×C₂²⋊Q₈	—	2	2	no	—
212	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
215	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
216	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
217	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
218	C₇×#121	—	2	2	no	—
219	C₇×#121	—	2	2	no	—
220	C₇×#121	—	2	2	no	—
221	C₇×#121	—	2	1	no	—
222	C₇×#121	—	2	1	no	—
223	C₇×#121	—	2	1	no	—
224	C₇×#121	—	2	1	no	—
225	C₇×#121	—	2	1	no	—
226	C₇×#121	—	2	1	no	—
227	C₇×#121	—	2	1	no	—
228	C₇×#121	—	2	1	no	—
229	C₇×#121	—	2	1	no	—
230	C₇×#121	—	2	1	no	—
231	C₇×#121	—	2	1	no	—
232	C₇×#121	—	2	1	no	—
233	C₇×#121	—	2	1	no	—
234	C₇×#121	—	2	1	no	—
235	C₇×#121	—	2	1	no	—
236	C₇×#121	—	2	1	no	—
237	C₇×#121	C₂³	1	1	yes	characteristic
238	C₇×#121	C₂³	1	2	yes	—
239	C₇×#121	C₂³	1	1	yes	characteristic
240	C₇×#121	C₂³	1	1	yes	characteristic
241	C₇×#121	C₂³	1	2	yes	—
242	C₇×#121	C₂³	1	1	yes	characteristic
243	C₄×C₇×Q₈	—	2	1	no	—
244	C₄×C₇×Q₈	—	2	1	no	—
245	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
246	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
247	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
248	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
249	C₄×C₇×Q₈	C₂³	1	2	yes	—
250	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
251	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
252	C₄×C₇×Q₈	C₂³	1	2	yes	—
253	C₄×C₇×D₄	—	2	1	no	—
254	C₄×C₇×D₄	—	2	1	no	—
255	C₄×C₇×D₄	—	2	1	no	—
256	C₄×C₇×D₄	—	2	1	no	—
257	C₄×C₇×D₄	—	2	2	no	—
258	C₄×C₇×D₄	—	2	2	no	—
259	C₄×C₇×D₄	—	2	1	no	—
260	C₄×C₇×D₄	—	2	1	no	—
261	C₄×C₇×D₄	—	2	1	no	—
262	C₄×C₇×D₄	—	2	1	no	—
263	C₄×C₇×D₄	—	2	1	no	—
264	C₄×C₇×D₄	—	2	1	no	—
265	C₄×C₇×D₄	—	2	1	no	—
266	C₄×C₇×D₄	—	2	1	no	—
267	C₄×C₇×D₄	—	2	1	no	—
268	C₄×C₇×D₄	—	2	1	no	—
269	C₄×C₇×D₄	D₄	1	1	yes	characteristic
270	C₄×C₇×D₄	D₄	1	1	yes	characteristic
271	C₄×C₇×D₄	D₄	1	1	yes	characteristic
272	C₄×C₇×D₄	D₄	1	1	yes	characteristic
273	C₄×C₇×D₄	D₄	1	1	yes	characteristic
274	C₄×C₇×D₄	D₄	1	1	yes	characteristic
275	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
276	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
277	C₄×C₇×D₄	C₂³	1	2	yes	—
278	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
279	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
280	C₄×C₇×D₄	C₂³	1	2	yes	—
281	C₇×#117	—	2	1	no	—
282	C₇×#117	—	2	1	no	—
283	C₇×#117	—	2	1	no	—
284	C₇×#117	—	2	1	no	—
285	C₇×#117	—	2	2	no	—
286	C₇×#117	—	2	1	no	—
287	C₇×#117	—	2	1	no	—
288	C₇×#117	—	2	1	no	—
289	C₇×#117	—	2	1	no	—
290	C₇×#117	C₂³	1	1	yes	characteristic
291	C₇×#117	C₂³	1	1	yes	characteristic
292	C₇×#117	C₂³	1	1	yes	characteristic
293	C₂×C₇×C₄⋊C₄	—	2	1	no	—
294	C₂×C₇×C₄⋊C₄	—	2	1	no	—
295	C₂×C₇×C₄⋊C₄	—	2	1	no	—
296	C₂×C₇×C₄⋊C₄	—	2	2	no	—
297	C₂×C₇×C₄⋊C₄	—	2	1	no	—
298	C₂×C₇×C₄⋊C₄	—	2	1	no	—
299	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
300	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
301	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
302	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
303	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
304	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
305	C₇×#107	C₂³	1	2	yes	—
306	C₇×#107	C₂³	1	2	yes	—
307	C₇×#107	C₂³	1	2	yes	—
308	C₇×#107	C₂³	1	2	yes	—
309	C₇×#106	C₂³	1	2	yes	—
310	C₇×#106	C₂³	1	2	yes	—
311	C₇×#106	C₂³	1	2	yes	—
312	C₇×#106	C₂³	1	2	yes	—
313	C₇×C₄⋊C₈	C₂³	1	2	yes	—
314	C₇×C₄⋊C₈	C₂³	1	2	yes	—
315	C₇×C₄⋊C₈	C₂³	1	2	yes	—
316	C₇×C₄⋊C₈	C₂³	1	2	yes	—
317	C₇×#103	C₂³	1	2	yes	—
318	C₇×#103	C₂³	1	2	yes	—
319	C₇×#103	C₂³	1	2	yes	—
320	C₇×#103	C₂³	1	2	yes	—
321	C₇×#103	C₂³	1	2	yes	—
322	C₇×#103	C₂³	1	2	yes	—
323	C₇×#103	C₂³	1	2	yes	—
324	C₇×#103	C₂³	1	2	yes	—
325	C₇×#102	C₂³	1	2	yes	—
326	C₇×#102	C₂³	1	2	yes	—
327	C₇×#102	C₂³	1	2	yes	—
328	C₇×#102	C₂³	1	2	yes	—
329	C₇×#102	C₂³	1	2	yes	—
330	C₇×#102	C₂³	1	2	yes	—
331	C₇×#102	C₂³	1	2	yes	—
332	C₇×#102	C₂³	1	2	yes	—
333	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
334	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
335	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₇×#97	C₂³	1	1	yes	characteristic
338	C₇×#97	C₂³	1	1	yes	characteristic
339	C₇×#97	C₂³	1	1	yes	characteristic
340	C₇×#97	C₂³	1	1	yes	characteristic
341	C₇×#97	C₂³	1	2	yes	—
342	C₄×C₇×C₈	C₂³	1	2	yes	—
343	#3512	C₂×C₇	1	1	yes	characteristic, complemented
344	#3511	C₂×C₇	1	1	yes	characteristic, complemented
345	#3258	C₂×C₇	1	2	yes	complemented
346	#3257	C₂×C₇	1	2	yes	complemented
347	#3239	C₂×C₇	1	1	yes	characteristic, complemented
348	#3238	C₂×C₇	1	1	yes	characteristic, complemented
349	#3236	C₂×C₇	1	1	yes	characteristic, complemented
350	#3234	C₂×C₇	1	1	yes	characteristic, complemented
351	#3219	C₂×C₇	1	1	yes	characteristic, complemented
352	#3219	C₂×C₇	1	1	yes	characteristic, complemented
353	#3216	C₂×C₇	1	1	yes	characteristic, complemented
354	#3214	C₂×C₇	1	1	yes	characteristic, complemented
355	#3204	C₂×C₇	1	2	yes	complemented
356	#3203	C₂×C₇	1	2	yes	complemented
357	#3181	C₂×C₇	1	1	yes	characteristic, complemented
358	#3180	C₂×C₇	1	1	yes	characteristic, complemented
359	#3172	C₂×C₇	1	1	yes	characteristic, complemented
360	#3171	C₂×C₇	1	1	yes	characteristic, complemented
361	#3125	C₂×C₇	1	2	yes	complemented
362	#3124	C₂×C₇	1	2	yes	complemented
363	#3120	C₂×C₇	1	2	yes	complemented
364	#3119	C₂×C₇	1	2	yes	complemented
365	#2923	C₂×C₇	1	1	yes	characteristic, complemented
366	C₇×#41	—	4	2	no	—
367	C₇×#41	—	4	2	no	—
368	C₇×#41	—	4	2	no	—
369	C₇×#41	—	4	2	no	—
370	C₇×#41	—	4	2	no	—
371	C₇×#41	—	8	2	no	—
372	C₇×#41	—	8	2	no	—
373	C₂×C₇×Q₈	—	2	1	no	—
374	C₂×C₇×Q₈	—	2	1	no	—
375	C₂×C₇×Q₈	—	2	2	no	—
376	C₂×C₇×Q₈	—	8	2	no	—
377	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
378	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
379	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
381	C₂×C₇×D₄	—	2	2	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	—	2	1	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	—	2	1	no	—
391	C₂×C₇×D₄	—	2	1	no	—
392	C₂×C₇×D₄	—	2	1	no	—
393	C₂×C₇×D₄	—	2	1	no	—
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	2	yes	—
398	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
399	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
410	C₂²×C₄×C₇	—	2	2	no	—
411	C₂²×C₄×C₇	—	2	2	no	—
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	C₇×Q₁₆	—	4	2	no	—
422	C₇×Q₁₆	—	4	2	no	—
423	C₇×SD₁₆	—	4	2	no	—
424	C₇×SD₁₆	—	4	2	no	—
425	C₇×SD₁₆	—	4	2	no	—
426	C₇×SD₁₆	—	4	2	no	—
427	C₇×D₈	—	4	2	no	—
428	C₇×D₈	—	4	2	no	—
429	C₇×M₁₆	—	4	2	no	—
430	C₂×C₇×C₈	—	4	2	no	—
431	C₂×C₇×C₈	C₂⁴	1	2	yes	—
432	C₂×C₇×C₈	C₂⁴	1	2	yes	—
433	C₂×C₇×C₈	C₂⁴	1	2	yes	—
434	C₂×C₇×C₈	C₂⁴	1	2	yes	—
435	C₇×C₄⋊C₄	—	2	1	no	—
436	C₇×C₄⋊C₄	—	2	1	no	—
437	C₇×C₄⋊C₄	—	2	2	no	—
438	C₇×C₄⋊C₄	—	2	1	no	—
439	C₇×C₄⋊C₄	—	2	1	no	—
440	C₇×C₄⋊C₄	—	2	1	no	—
441	C₇×C₄⋊C₄	—	2	1	no	—
442	C₇×C₄⋊C₄	—	2	1	no	—
443	C₇×C₄⋊C₄	—	2	1	no	—
444	C₇×C₄⋊C₄	—	2	2	no	—
445	C₇×C₄⋊C₄	—	2	2	no	—
446	C₇×C₄⋊C₄	—	2	1	no	—
447	C₇×C₄⋊C₄	—	2	1	no	—
448	C₇×C₄⋊C₄	—	2	1	no	—
449	C₇×C₄⋊C₄	—	2	1	no	—
450	C₇×C₄⋊C₄	—	2	1	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	2	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	2	no	—
464	C₇×C₄⋊C₄	—	2	2	no	—
465	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
466	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
467	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
472	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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×C₂²⋊C₄	—	2	2	no	—
478	C₇×C₂²⋊C₄	—	2	2	no	—
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	1	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	2	no	—
490	C₇×C₂²⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
502	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
503	C₇×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₄²×C₇	—	2	1	no	—
508	C₄²×C₇	—	2	1	no	—
509	C₄²×C₇	—	2	1	no	—
510	C₄²×C₇	—	2	1	no	—
511	C₄²×C₇	—	2	2	no	—
512	C₄²×C₇	—	2	2	no	—
513	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
514	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
515	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
516	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
517	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
518	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
519	C₄²×C₇	C₂⁴	1	1	yes	characteristic
520	C₄²×C₇	C₂⁴	1	1	yes	characteristic
521	C₄²×C₇	C₂⁴	1	1	yes	characteristic
522	C₄²×C₇	C₂⁴	1	1	yes	characteristic
523	#556	—	2	1	no	—
524	#555	—	2	1	no	—
525	#554	—	2	1	no	—
526	#553	—	2	1	no	—
527	#553	—	2	1	no	—
528	#553	—	2	1	no	—
529	#553	—	2	1	no	—
530	#553	—	2	1	no	—
531	#553	—	2	1	no	—
532	#553	—	2	1	no	—
533	#553	—	2	1	no	—
534	#552	—	2	1	no	—
535	#552	—	2	1	no	—
536	#548	—	2	1	no	—
537	#548	—	2	1	no	—
538	#547	—	2	1	no	—
539	#542	C₂²×C₇	1	2	yes	—
540	#542	C₂²×C₇	1	2	yes	—
541	#541	C₂²×C₇	1	1	yes	characteristic
542	#541	C₂²×C₇	1	1	yes	characteristic
543	#540	C₂²×C₇	1	1	yes	characteristic
544	#540	C₂²×C₇	1	1	yes	characteristic
545	#537	C₂²×C₇	1	1	yes	characteristic
546	#537	C₂²×C₇	1	2	yes	—
547	#537	C₂²×C₇	1	1	yes	characteristic
548	#533	C₂²×C₇	1	1	yes	characteristic
549	#533	C₂²×C₇	1	1	yes	characteristic
550	#532	C₂²×C₇	1	1	yes	characteristic
551	#532	C₂²×C₇	1	1	yes	characteristic
552	#532	C₂²×C₇	1	1	yes	characteristic
553	#532	C₂²×C₇	1	1	yes	characteristic
554	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic
555	#529	C₂²×C₇	1	1	yes	characteristic
556	#529	C₂²×C₇	1	1	yes	characteristic
557	#529	C₂²×C₇	1	1	yes	characteristic
558	#529	C₂²×C₇	1	1	yes	characteristic
559	C₂×#125	C₂²×C₇	1	1	yes	characteristic
560	#520	C₂²×C₇	1	2	yes	—
561	#520	C₂²×C₇	1	1	yes	characteristic
562	#520	C₂²×C₇	1	1	yes	characteristic
563	C₄×#41	C₂²×C₇	1	1	yes	characteristic
564	#501	C₂²×C₇	1	1	yes	characteristic
565	#501	C₂²×C₇	1	1	yes	characteristic
566	#501	C₂²×C₇	1	1	yes	characteristic
567	#501	C₂²×C₇	1	1	yes	characteristic
568	#497	C₂²×C₇	1	1	yes	characteristic
569	#497	C₂²×C₇	1	1	yes	characteristic
570	#496	C₂²×C₇	1	1	yes	characteristic
571	#496	C₂²×C₇	1	1	yes	characteristic
572	#491	C₂²×C₇	1	1	yes	characteristic
573	#491	C₂²×C₇	1	1	yes	characteristic
574	#490	C₂²×C₇	1	1	yes	characteristic
575	#490	C₂²×C₇	1	1	yes	characteristic
576	#489	C₂²×C₇	1	1	yes	characteristic
577	#489	C₂²×C₇	1	1	yes	characteristic
578	#489	C₂²×C₇	1	1	yes	characteristic
579	#489	C₂²×C₇	1	1	yes	characteristic
580	#484	C₂²×C₇	1	2	yes	—
581	#484	C₂²×C₇	1	2	yes	—
582	#483	C₂²×C₇	1	2	yes	—
583	#483	C₂²×C₇	1	2	yes	—
584	#481	C₂²×C₇	1	2	yes	—
585	#481	C₂²×C₇	1	2	yes	—
586	#480	C₂²×C₇	1	2	yes	—
587	#480	C₂²×C₇	1	2	yes	—
588	#479	C₂²×C₇	1	2	yes	—
589	#479	C₂²×C₇	1	2	yes	—
590	#478	C₂²×C₇	1	2	yes	—
591	#478	C₂²×C₇	1	2	yes	—
592	#477	C₂²×C₇	1	2	yes	—
593	#476	C₂²×C₇	1	2	yes	—
594	#475	C₂²×C₇	1	2	yes	—
595	#474	C₂²×C₇	1	2	yes	—
596	#470	C₂²×C₇	1	2	yes	—
597	#469	C₂²×C₇	1	2	yes	—
598	#468	C₂²×C₇	1	2	yes	—
599	#468	C₂²×C₇	1	2	yes	—
600	#467	C₂²×C₇	1	2	yes	—
601	#466	C₂²×C₇	1	2	yes	—
602	#465	C₂²×C₇	1	2	yes	—
603	#465	C₂²×C₇	1	2	yes	—
604	#464	C₂²×C₇	1	2	yes	—
605	#464	C₂²×C₇	1	2	yes	—
606	#463	C₂²×C₇	1	2	yes	—
607	#463	C₂²×C₇	1	2	yes	—
608	#462	C₂²×C₇	1	2	yes	—
609	#461	C₂²×C₇	1	2	yes	—
610	#460	C₂²×C₇	1	2	yes	—
611	#459	C₂²×C₇	1	2	yes	—
612	#452	C₂²×C₇	1	2	yes	—
613	#452	C₂²×C₇	1	2	yes	—
614	#452	C₂²×C₇	1	2	yes	—
615	#452	C₂²×C₇	1	2	yes	—
616	#449	C₂²×C₇	1	2	yes	—
617	#449	C₂²×C₇	1	2	yes	—
618	#449	C₂²×C₇	1	2	yes	—
619	#449	C₂²×C₇	1	2	yes	—
620	#442	C₂²×C₇	1	2	yes	—
621	#441	C₂²×C₇	1	2	yes	—
622	#440	C₂²×C₇	1	2	yes	—
623	#440	C₂²×C₇	1	2	yes	—
624	C₄×Q₁₆	C₂²×C₇	1	2	yes	—
625	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
626	C₄×SD₁₆	C₂²×C₇	1	2	yes	—
627	C₄×D₈	C₂²×C₇	1	2	yes	—
628	#433	C₂²×C₇	1	2	yes	—
629	#433	C₂²×C₇	1	2	yes	—
630	#432	C₂²×C₇	1	1	yes	characteristic
631	#432	C₂²×C₇	1	1	yes	characteristic
632	#432	C₂²×C₇	1	1	yes	characteristic
633	#432	C₂²×C₇	1	1	yes	characteristic
634	#424	C₂²×C₇	1	2	yes	—
635	#408	C₂²×C₇	1	2	yes	—
636	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
637	C₂×#97	C₂²×C₇	1	1	yes	characteristic
638	C₂³×C₇	—	2	2	no	—
639	C₂³×C₇	—	2	1	no	—
640	C₂³×C₇	—	2	1	no	—
641	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
642	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
643	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
644	C₇×Q₈	—	2	2	no	—
645	C₇×Q₈	—	2	2	no	—
646	C₇×Q₈	—	2	2	no	—
647	C₇×Q₈	—	2	2	no	—
648	C₇×Q₈	—	4	1	no	—
649	C₇×Q₈	—	4	2	no	—
650	C₇×Q₈	—	4	2	no	—
651	C₇×Q₈	—	8	2	no	—
652	C₇×D₄	—	2	2	no	—
653	C₇×D₄	—	2	2	no	—
654	C₇×D₄	—	2	2	no	—
655	C₇×D₄	—	2	2	no	—
656	C₇×D₄	—	4	1	no	—
657	C₇×D₄	—	4	1	no	—
658	C₇×D₄	—	4	1	no	—
659	C₇×D₄	—	4	2	no	—
660	C₇×D₄	—	4	2	no	—
661	C₇×D₄	—	4	4	no	—
662	C₇×D₄	—	4	2	no	—
663	C₇×D₄	—	4	2	no	—
664	C₇×D₄	—	8	1	no	—
665	C₇×D₄	—	8	1	no	—
666	C₇×D₄	—	8	1	no	—
667	C₇×D₄	—	8	1	no	—
668	C₇×D₄	—	8	1	no	—
669	C₇×D₄	—	8	1	no	—
670	C₇×D₄	—	8	2	no	—
671	C₇×D₄	—	8	2	no	—
672	C₂×C₄×C₇	—	2	2	no	—
673	C₂×C₄×C₇	—	2	2	no	—
674	C₂×C₄×C₇	—	2	2	no	—
675	C₂×C₄×C₇	—	2	1	no	—
676	C₂×C₄×C₇	—	2	1	no	—
677	C₂×C₄×C₇	—	2	2	no	—
678	C₂×C₄×C₇	—	2	1	no	—
679	C₂×C₄×C₇	—	2	1	no	—
680	C₂×C₄×C₇	—	2	1	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	—	4	1	no	—
685	C₂×C₄×C₇	—	4	1	no	—
686	C₂×C₄×C₇	—	4	1	no	—
687	C₂×C₄×C₇	—	4	1	no	—
688	C₂×C₄×C₇	—	4	1	no	—
689	C₂×C₄×C₇	—	4	1	no	—
690	C₂×C₄×C₇	—	4	4	no	—
691	C₂×C₄×C₇	—	4	2	no	—
692	C₂×C₄×C₇	—	4	2	no	—
693	C₂×C₄×C₇	—	8	1	no	—
694	C₂×C₄×C₇	—	8	1	no	—
695	C₂×C₄×C₇	—	8	1	no	—
696	C₂×C₄×C₇	—	8	1	no	—
697	C₂×C₄×C₇	—	8	2	no	—
698	C₂×C₄×C₇	—	8	2	no	—
699	C₂×C₄×C₇	—	8	1	no	—
700	C₂×C₄×C₇	—	8	1	no	—
701	C₂×C₄×C₇	—	8	2	no	—
702	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
703	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
704	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
705	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
706	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
707	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
708	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
709	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
710	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
711	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
712	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
713	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
714	C₇×C₈	—	2	2	no	—
715	C₇×C₈	—	2	2	no	—
716	C₇×C₈	—	2	2	no	—
717	C₇×C₈	—	2	2	no	—
718	C₂×#41	—	2	1	no	—
719	C₂×#41	—	2	1	no	—
720	C₂×#41	C₂³×C₇	1	2	yes	—
721	C₂×#41	C₂³×C₇	1	1	yes	characteristic
722	C₂×#41	C₂³×C₇	1	1	yes	characteristic
723	C₂×#41	C₂³×C₇	1	1	yes	characteristic
724	C₂²×Q₈	—	2	1	no	—
725	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
726	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
727	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
728	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
729	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
730	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
731	C₂×D₈	C₂³×C₇	1	2	yes	—
732	C₂×D₈	C₂³×C₇	1	2	yes	—
733	C₂×M₁₆	C₂³×C₇	1	2	yes	—
734	C₂²×C₈	C₂³×C₇	1	2	yes	—
735	C₄⋊Q₈	—	2	1	no	—
736	C₄⋊Q₈	—	2	1	no	—
737	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
738	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
739	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
740	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
741	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
742	#127	C₂³×C₇	1	1	yes	characteristic
743	#127	C₂³×C₇	1	1	yes	characteristic
744	#126	—	2	2	no	—
745	#126	—	2	2	no	—
746	#126	—	2	1	no	—
747	#126	—	2	1	no	—
748	#126	—	2	1	no	—
749	#126	—	2	1	no	—
750	#126	—	2	1	no	—
751	#126	—	2	1	no	—
752	#126	—	2	1	no	—
753	#126	—	2	1	no	—
754	#125	—	2	1	no	—
755	#125	—	2	1	no	—
756	#125	—	2	1	no	—
757	#125	—	2	1	no	—
758	#125	—	2	1	no	—
759	#125	—	2	1	no	—
760	#125	—	2	1	no	—
761	#125	—	2	1	no	—
762	#125	C₂³×C₇	1	1	yes	characteristic
763	#125	C₂³×C₇	1	1	yes	characteristic
764	#125	C₂³×C₇	1	1	yes	characteristic
765	#125	C₂³×C₇	1	1	yes	characteristic
766	#124	—	2	2	no	—
767	#124	—	2	2	no	—
768	#124	—	2	1	no	—
769	#124	—	2	1	no	—
770	#124	C₂³×C₇	1	1	yes	characteristic
771	#124	C₂³×C₇	1	1	yes	characteristic
772	#124	C₂³×C₇	1	2	yes	—
773	#123	—	2	1	no	—
774	#123	—	2	1	no	—
775	#123	—	2	1	no	—
776	#123	—	2	1	no	—
777	#123	—	2	1	no	—
778	#123	—	2	1	no	—
779	#123	—	2	1	no	—
780	#123	—	2	1	no	—
781	#123	—	2	2	no	—
782	#123	—	2	2	no	—
783	C₂²⋊Q₈	—	2	1	no	—
784	C₂²⋊Q₈	—	2	1	no	—
785	C₂²⋊Q₈	—	2	2	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	2	2	no	—
790	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
791	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
792	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
793	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
794	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
795	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
796	#121	—	2	2	no	—
797	#121	—	2	2	no	—
798	#121	—	2	2	no	—
799	#121	—	2	1	no	—
800	#121	—	2	1	no	—
801	#121	—	2	1	no	—
802	#121	—	2	1	no	—
803	#121	—	2	1	no	—
804	#121	—	2	1	no	—
805	#121	—	2	1	no	—
806	#121	—	2	1	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	1	no	—
814	#121	—	2	1	no	—
815	#121	C₂³×C₇	1	1	yes	characteristic
816	#121	C₂³×C₇	1	1	yes	characteristic
817	#121	C₂³×C₇	1	1	yes	characteristic
818	#121	C₂³×C₇	1	1	yes	characteristic
819	#121	C₂³×C₇	1	2	yes	—
820	#121	C₂³×C₇	1	2	yes	—
821	C₄×Q₈	—	2	1	no	—
822	C₄×Q₈	—	2	1	no	—
823	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
824	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
825	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
826	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
827	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
828	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
829	C₄×Q₈	C₂³×C₇	1	2	yes	—
830	C₄×Q₈	C₂³×C₇	1	2	yes	—
831	C₄×D₄	—	2	1	no	—
832	C₄×D₄	—	2	1	no	—
833	C₄×D₄	—	2	1	no	—
834	C₄×D₄	—	2	1	no	—
835	C₄×D₄	—	2	2	no	—
836	C₄×D₄	—	2	2	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	1	no	—
843	C₄×D₄	—	2	1	no	—
844	C₄×D₄	—	2	1	no	—
845	C₄×D₄	—	2	1	no	—
846	C₄×D₄	—	2	1	no	—
847	C₄×D₄	C₇×D₄	1	1	yes	characteristic
848	C₄×D₄	C₇×D₄	1	1	yes	characteristic
849	C₄×D₄	C₇×D₄	1	1	yes	characteristic
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	C₂³×C₇	1	1	yes	characteristic
854	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
855	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
856	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
857	C₄×D₄	C₂³×C₇	1	2	yes	—
858	C₄×D₄	C₂³×C₇	1	2	yes	—
859	#117	—	2	1	no	—
860	#117	—	2	1	no	—
861	#117	—	2	1	no	—
862	#117	—	2	1	no	—
863	#117	—	2	2	no	—
864	#117	—	2	1	no	—
865	#117	—	2	1	no	—
866	#117	—	2	1	no	—
867	#117	—	2	1	no	—
868	#117	C₂³×C₇	1	1	yes	characteristic
869	#117	C₂³×C₇	1	1	yes	characteristic
870	#117	C₂³×C₇	1	1	yes	characteristic
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	2	no	—
875	C₂×C₄⋊C₄	—	2	1	no	—
876	C₂×C₄⋊C₄	—	2	1	no	—
877	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
878	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
879	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
880	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
881	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
882	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
883	#107	C₂³×C₇	1	2	yes	—
884	#107	C₂³×C₇	1	2	yes	—
885	#107	C₂³×C₇	1	2	yes	—
886	#107	C₂³×C₇	1	2	yes	—
887	#106	C₂³×C₇	1	2	yes	—
888	#106	C₂³×C₇	1	2	yes	—
889	#106	C₂³×C₇	1	2	yes	—
890	#106	C₂³×C₇	1	2	yes	—
891	C₄⋊C₈	C₂³×C₇	1	2	yes	—
892	C₄⋊C₈	C₂³×C₇	1	2	yes	—
893	C₄⋊C₈	C₂³×C₇	1	2	yes	—
894	C₄⋊C₈	C₂³×C₇	1	2	yes	—
895	#103	C₂³×C₇	1	2	yes	—
896	#103	C₂³×C₇	1	2	yes	—
897	#103	C₂³×C₇	1	2	yes	—
898	#103	C₂³×C₇	1	2	yes	—
899	#103	C₂³×C₇	1	2	yes	—
900	#103	C₂³×C₇	1	2	yes	—
901	#103	C₂³×C₇	1	2	yes	—
902	#103	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	#102	C₂³×C₇	1	2	yes	—
907	#102	C₂³×C₇	1	2	yes	—
908	#102	C₂³×C₇	1	2	yes	—
909	#102	C₂³×C₇	1	2	yes	—
910	#102	C₂³×C₇	1	2	yes	—
911	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
912	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
913	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
914	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
915	#97	C₂³×C₇	1	1	yes	characteristic
916	#97	C₂³×C₇	1	1	yes	characteristic
917	#97	C₂³×C₇	1	2	yes	—
918	#97	C₂³×C₇	1	1	yes	characteristic
919	#97	C₂³×C₇	1	1	yes	characteristic
920	C₄×C₈	C₂³×C₇	1	2	yes	—
921	C₂²×C₇	—	2	1	no	—
922	C₂²×C₇	—	2	1	no	—
923	C₂²×C₇	—	2	1	no	—
924	C₂²×C₇	—	2	1	no	—
925	C₂²×C₇	—	2	1	no	—
926	C₂²×C₇	—	2	1	no	—
927	C₂²×C₇	—	2	1	no	—
928	C₂²×C₇	—	2	1	no	—
929	C₂²×C₇	—	2	1	no	—
930	C₂²×C₇	—	4	2	no	—
931	C₂²×C₇	—	4	1	no	—
932	C₂²×C₇	—	4	1	no	—
933	C₂²×C₇	—	4	1	no	—
934	C₂²×C₇	—	4	2	no	—
935	C₂²×C₇	—	4	1	no	—
936	C₂²×C₇	—	4	2	no	—
937	C₂²×C₇	—	4	1	no	—
938	C₂²×C₇	—	4	1	no	—
939	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
940	C₄×C₇	—	2	1	no	—
941	C₄×C₇	—	2	1	no	—
942	C₄×C₇	—	2	1	no	—
943	C₄×C₇	—	2	1	no	—
944	C₄×C₇	—	2	1	no	—
945	C₄×C₇	—	2	1	no	—
946	C₄×C₇	—	2	1	no	—
947	C₄×C₇	—	2	1	no	—
948	C₄×C₇	—	2	1	no	—
949	C₄×C₇	—	2	1	no	—
950	C₄×C₇	—	2	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	—	4	1	no	—
956	C₄×C₇	—	4	1	no	—
957	C₄×C₇	—	4	2	no	—
958	C₄×C₇	—	4	1	no	—
959	C₄×C₇	—	4	1	no	—
960	C₄×C₇	#585	1	2	yes	—
961	#41	—	4	2	no	—
962	#41	—	4	2	no	—
963	#41	—	4	2	no	—
964	#41	—	4	2	no	—
965	#41	—	4	2	no	—
966	#41	—	8	2	no	—
967	#41	—	8	2	no	—
968	C₂×Q₈	—	2	1	no	—
969	C₂×Q₈	—	2	1	no	—
970	C₂×Q₈	—	2	2	no	—
971	C₂×Q₈	—	8	2	no	—
972	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
973	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
974	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
975	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	2	1	no	—
978	C₂×D₄	—	2	1	no	—
979	C₂×D₄	—	2	1	no	—
980	C₂×D₄	—	2	1	no	—
981	C₂×D₄	—	2	1	no	—
982	C₂×D₄	—	2	1	no	—
983	C₂×D₄	—	2	2	no	—
984	C₂×D₄	—	2	2	no	—
985	C₂×D₄	—	2	1	no	—
986	C₂×D₄	—	2	1	no	—
987	C₂×D₄	—	2	1	no	—
988	C₂×D₄	—	2	1	no	—
989	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
990	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
991	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
992	C₂×D₄	C₂⁴×C₇	1	2	yes	—
993	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
994	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
995	C₂²×C₄	—	2	1	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	—	2	1	no	—
1004	C₂²×C₄	—	2	1	no	—
1005	C₂²×C₄	—	2	2	no	—
1006	C₂²×C₄	—	2	2	no	—
1007	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1008	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1009	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1010	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1011	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1012	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1013	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1014	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1015	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1016	Q₁₆	—	4	2	no	—
1017	Q₁₆	—	4	2	no	—
1018	SD₁₆	—	4	2	no	—
1019	SD₁₆	—	4	2	no	—
1020	SD₁₆	—	4	2	no	—
1021	SD₁₆	—	4	2	no	—
1022	D₈	—	4	2	no	—
1023	D₈	—	4	2	no	—
1024	M₁₆	—	4	2	no	—
1025	C₂×C₈	—	4	2	no	—
1026	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1027	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1028	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1029	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	2	no	—
1040	C₄⋊C₄	—	2	2	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	1	no	—
1043	C₄⋊C₄	—	2	1	no	—
1044	C₄⋊C₄	—	2	1	no	—
1045	C₄⋊C₄	—	2	1	no	—
1046	C₄⋊C₄	—	2	1	no	—
1047	C₄⋊C₄	—	2	1	no	—
1048	C₄⋊C₄	—	2	1	no	—
1049	C₄⋊C₄	—	2	2	no	—
1050	C₄⋊C₄	—	2	1	no	—
1051	C₄⋊C₄	—	2	1	no	—
1052	C₄⋊C₄	—	2	1	no	—
1053	C₄⋊C₄	—	2	1	no	—
1054	C₄⋊C₄	—	2	1	no	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	2	no	—
1059	C₄⋊C₄	—	2	2	no	—
1060	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1061	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1062	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1063	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1064	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1065	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1066	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1067	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1068	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1069	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1070	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1071	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	—	2	1	no	—
1075	C₂²⋊C₄	—	2	1	no	—
1076	C₂²⋊C₄	—	2	1	no	—
1077	C₂²⋊C₄	—	2	1	no	—
1078	C₂²⋊C₄	—	2	1	no	—
1079	C₂²⋊C₄	—	2	1	no	—
1080	C₂²⋊C₄	—	2	1	no	—
1081	C₂²⋊C₄	—	2	1	no	—
1082	C₂²⋊C₄	—	2	1	no	—
1083	C₂²⋊C₄	—	2	1	no	—
1084	C₂²⋊C₄	—	2	2	no	—
1085	C₂²⋊C₄	—	2	2	no	—
1086	C₂²⋊C₄	—	2	1	no	—
1087	C₂²⋊C₄	—	2	1	no	—
1088	C₂²⋊C₄	—	2	1	no	—
1089	C₂²⋊C₄	—	2	1	no	—
1090	C₂²⋊C₄	—	2	1	no	—
1091	C₂²⋊C₄	—	2	1	no	—
1092	C₂²⋊C₄	—	2	2	no	—
1093	C₂²⋊C₄	—	2	2	no	—
1094	C₂²⋊C₄	—	2	2	no	—
1095	C₂²⋊C₄	—	2	2	no	—
1096	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1097	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1098	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1099	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1100	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1101	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1102	C₄²	—	2	1	no	—
1103	C₄²	—	2	1	no	—
1104	C₄²	—	2	1	no	—
1105	C₄²	—	2	1	no	—
1106	C₄²	—	2	2	no	—
1107	C₄²	—	2	2	no	—
1108	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1109	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1110	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1111	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1112	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1113	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1114	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1115	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1116	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1117	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1118	C₂×C₇	—	4	1	no	—
1119	C₂×C₇	—	4	1	no	—
1120	C₂×C₇	—	4	1	no	—
1121	C₂×C₇	—	8	2	no	—
1122	C₂×C₇	—	8	1	no	—
1123	C₂×C₇	—	8	1	no	—
1124	C₂×C₇	#3449	1	1	yes	characteristic
1125	C₂×C₇	#3585	1	1	yes	characteristic
1126	C₂×C₇	#3586	1	1	yes	characteristic
1127	C₂³	—	2	2	no	—
1128	C₂³	—	2	1	no	—
1129	C₂³	—	2	1	no	—
1130	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1131	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1132	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
1133	Q₈	—	2	2	no	—
1134	Q₈	—	2	2	no	—
1135	Q₈	—	2	2	no	—
1136	Q₈	—	2	2	no	—
1137	Q₈	—	4	1	no	—
1138	Q₈	—	4	2	no	—
1139	Q₈	—	4	2	no	—
1140	Q₈	—	8	2	no	—
1141	D₄	—	2	2	no	—
1142	D₄	—	2	2	no	—
1143	D₄	—	2	2	no	—
1144	D₄	—	2	2	no	—
1145	D₄	—	4	1	no	—
1146	D₄	—	4	1	no	—
1147	D₄	—	4	1	no	—
1148	D₄	—	4	2	no	—
1149	D₄	—	4	2	no	—
1150	D₄	—	4	4	no	—
1151	D₄	—	4	2	no	—
1152	D₄	—	4	2	no	—
1153	D₄	—	8	1	no	—
1154	D₄	—	8	1	no	—
1155	D₄	—	8	1	no	—
1156	D₄	—	8	1	no	—
1157	D₄	—	8	1	no	—
1158	D₄	—	8	1	no	—
1159	D₄	—	8	2	no	—
1160	D₄	—	8	2	no	—
1161	C₂×C₄	—	2	2	no	—
1162	C₂×C₄	—	2	2	no	—
1163	C₂×C₄	—	2	2	no	—
1164	C₂×C₄	—	2	1	no	—
1165	C₂×C₄	—	2	1	no	—
1166	C₂×C₄	—	2	2	no	—
1167	C₂×C₄	—	2	1	no	—
1168	C₂×C₄	—	2	1	no	—
1169	C₂×C₄	—	2	1	no	—
1170	C₂×C₄	—	2	1	no	—
1171	C₂×C₄	—	2	2	no	—
1172	C₂×C₄	—	2	2	no	—
1173	C₂×C₄	—	4	1	no	—
1174	C₂×C₄	—	4	1	no	—
1175	C₂×C₄	—	4	1	no	—
1176	C₂×C₄	—	4	1	no	—
1177	C₂×C₄	—	4	1	no	—
1178	C₂×C₄	—	4	1	no	—
1179	C₂×C₄	—	4	4	no	—
1180	C₂×C₄	—	4	2	no	—
1181	C₂×C₄	—	4	2	no	—
1182	C₂×C₄	—	8	1	no	—
1183	C₂×C₄	—	8	1	no	—
1184	C₂×C₄	—	8	1	no	—
1185	C₂×C₄	—	8	1	no	—
1186	C₂×C₄	—	8	2	no	—
1187	C₂×C₄	—	8	2	no	—
1188	C₂×C₄	—	8	1	no	—
1189	C₂×C₄	—	8	1	no	—
1190	C₂×C₄	—	8	2	no	—
1191	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1192	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1193	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1194	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1195	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1196	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1197	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1198	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1199	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1200	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1201	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1202	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1203	C₈	—	2	2	no	—
1204	C₈	—	2	2	no	—
1205	C₈	—	2	2	no	—
1206	C₈	—	2	2	no	—
1207	C₇	#61021	1	1	yes	characteristic, direct product factor, Sylow
1208	C₂²	—	2	1	no	—
1209	C₂²	—	2	1	no	—
1210	C₂²	—	2	1	no	—
1211	C₂²	—	2	1	no	—
1212	C₂²	—	2	1	no	—
1213	C₂²	—	2	1	no	—
1214	C₂²	—	2	1	no	—
1215	C₂²	—	2	1	no	—
1216	C₂²	—	2	1	no	—
1217	C₂²	—	4	2	no	—
1218	C₂²	—	4	1	no	—
1219	C₂²	—	4	1	no	—
1220	C₂²	—	4	1	no	—
1221	C₂²	—	4	2	no	—
1222	C₂²	—	4	1	no	—
1223	C₂²	—	4	2	no	—
1224	C₂²	—	4	1	no	—
1225	C₂²	—	4	1	no	—
1226	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1227	C₄	—	2	1	no	—
1228	C₄	—	2	1	no	—
1229	C₄	—	2	1	no	—
1230	C₄	—	2	1	no	—
1231	C₄	—	2	1	no	—
1232	C₄	—	2	1	no	—
1233	C₄	—	2	1	no	—
1234	C₄	—	2	1	no	—
1235	C₄	—	2	1	no	—
1236	C₄	—	2	1	no	—
1237	C₄	—	2	1	no	—
1238	C₄	—	4	2	no	—
1239	C₄	—	4	2	no	—
1240	C₄	—	4	1	no	—
1241	C₄	—	4	1	no	—
1242	C₄	—	4	1	no	—
1243	C₄	—	4	1	no	—
1244	C₄	—	4	2	no	—
1245	C₄	—	4	1	no	—
1246	C₄	—	4	1	no	—
1247	C₄	C₇×#585	1	2	yes	—
1248	C₂	—	4	1	no	—
1249	C₂	—	4	1	no	—
1250	C₂	—	4	1	no	—
1251	C₂	—	8	2	no	—
1252	C₂	—	8	1	no	—
1253	C₂	—	8	1	no	—
1254	C₂	C₇×#3449	1	1	yes	characteristic
1255	C₂	C₇×#3585	1	1	yes	characteristic
1256	C₂	C₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3512	C₂	semidirect
2. C₇×#3511	C₂	semidirect
3. C₇×#3258	C₂	semidirect
4. C₇×#3257	C₂	semidirect
5. C₇×#3239	C₂	semidirect
6. C₇×#3238	C₂	semidirect
7. C₇×#3236	C₂	semidirect
8. C₇×#3234	C₂	semidirect
9. C₇×#3219	C₂	semidirect
10. C₇×#3219	C₂	semidirect
11. C₇×#3216	C₂	semidirect
12. C₇×#3214	C₂	semidirect
13. C₇×#3204	C₂	semidirect
14. C₇×#3203	C₂	semidirect
15. C₇×#3181	C₂	semidirect
16. C₇×#3180	C₂	semidirect
17. C₇×#3172	C₂	semidirect
18. C₇×#3171	C₂	semidirect
19. C₇×#3125	C₂	semidirect
20. C₇×#3124	C₂	semidirect
21. C₇×#3120	C₂	semidirect
22. C₇×#3119	C₂	semidirect
23. C₇×#2923	C₂	semidirect
139. #61021	C₇	direct (N × H)
343. #3512	C₂×C₇	semidirect
344. #3511	C₂×C₇	semidirect
345. #3258	C₂×C₇	semidirect
346. #3257	C₂×C₇	semidirect
347. #3239	C₂×C₇	semidirect
348. #3238	C₂×C₇	semidirect
349. #3236	C₂×C₇	semidirect
350. #3234	C₂×C₇	semidirect
351. #3219	C₂×C₇	semidirect
352. #3219	C₂×C₇	semidirect
353. #3216	C₂×C₇	semidirect
354. #3214	C₂×C₇	semidirect
355. #3204	C₂×C₇	semidirect
356. #3203	C₂×C₇	semidirect
357. #3181	C₂×C₇	semidirect
358. #3180	C₂×C₇	semidirect
359. #3172	C₂×C₇	semidirect
360. #3171	C₂×C₇	semidirect
361. #3125	C₂×C₇	semidirect
362. #3124	C₂×C₇	semidirect
363. #3120	C₂×C₇	semidirect
364. #3119	C₂×C₇	semidirect
365. #2923	C₂×C₇	semidirect
1207. C₇	#61021	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×#3512	2
C₇×#3511	2
C₇×#3258	2
C₇×#3257	2
C₇×#3239	2
C₇×#3238	2
C₇×#3236	2
C₇×#3234	2
C₇×#3219	2
C₇×#3216	2
C₇×#3214	2
C₇×#3204	2
C₇×#3203	2
C₇×#3181	2
C₇×#3180	2
C₇×#3172	2
C₇×#3171	2
C₇×#3125	2
C₇×#3124	2
C₇×#3120	2
C₇×#3119	2
C₇×#2923	2
#61021	7

Subgroups — C7×#61021 #13238237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61021 #13238237