Subgroups — C₇×#60994 #13238210

Order 1792.

1782 conjugacy classes of subgroups.

The subgroup lattice has 1294 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3254	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3251	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#3247	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#3246	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#3241	C₂	1	2	yes	maximal, complemented
8	C₇×#3237	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3233	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3221	C₂	1	2	yes	maximal, complemented
11	C₇×#3217	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3200	C₂	1	2	yes	maximal, complemented
14	C₇×#3198	C₂	1	2	yes	maximal, complemented
15	C₇×#3179	C₂	1	2	yes	maximal, complemented
16	C₇×#3174	C₂	1	2	yes	maximal, complemented
17	C₇×#3123	C₂	1	2	yes	maximal, complemented
18	C₇×#3118	C₂	1	2	yes	maximal, complemented
19	C₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3112	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#3103	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#559	—	2	1	no	—
25	C₇×#559	—	2	1	no	—
26	C₇×#550	—	2	1	no	—
27	C₇×#550	—	2	1	no	—
28	C₇×#546	—	2	1	no	—
29	C₇×#546	—	2	1	no	—
30	C₇×#546	—	2	1	no	—
31	C₇×#546	—	2	1	no	—
32	C₇×#544	C₂²	1	1	yes	characteristic, complemented
33	C₇×#542	—	2	1	no	—
34	C₇×#542	C₂²	1	1	yes	characteristic
35	C₇×#542	C₂²	1	1	yes	characteristic, complemented
36	C₇×#541	—	2	1	no	—
37	C₇×#541	C₂²	1	1	yes	characteristic
38	C₇×#541	C₂²	1	1	yes	characteristic, complemented
39	C₇×#540	C₂²	1	2	yes	—
40	C₇×#540	C₂²	1	2	yes	—
41	C₇×#539	—	2	1	no	—
42	C₇×#539	—	2	1	no	—
43	C₇×#537	C₂²	1	1	yes	characteristic
44	C₇×#536	C₂²	1	1	yes	characteristic
45	C₇×#536	C₂²	1	1	yes	characteristic, complemented
46	C₇×#535	C₂²	1	2	yes	—
47	C₇×#533	—	2	1	no	—
48	C₇×#533	C₂²	1	1	yes	characteristic
49	C₇×#533	C₂²	1	1	yes	characteristic
50	C₇×#533	C₂²	1	1	yes	characteristic, complemented
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×#127	C₂²	1	1	yes	characteristic
56	C₇×#529	—	2	1	no	—
57	C₇×#529	—	2	1	no	—
58	C₇×#529	—	2	1	no	—
59	C₇×#529	C₂²	1	1	yes	characteristic
60	C₇×#529	C₂²	1	1	yes	characteristic, complemented
61	C₇×#518	C₂²	1	2	yes	—
62	C₄×C₇×#41	C₂²	1	1	yes	characteristic
63	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
64	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₇×#501	C₂²	1	2	yes	complemented
66	C₇×#499	C₂²	1	2	yes	complemented
67	C₇×#496	C₂²	1	2	yes	—
68	C₇×#492	C₂²	1	2	yes	—
69	C₇×#491	C₂²	1	2	yes	complemented
70	C₇×#490	C₂²	1	2	yes	—
71	C₇×#488	C₂²	1	2	yes	complemented
72	C₇×#486	C₂²	1	2	yes	—
73	C₇×#485	C₂²	1	2	yes	—
74	C₇×#485	C₂²	1	2	yes	—
75	C₇×#485	C₂²	1	2	yes	—
76	C₇×#482	C₂²	1	2	yes	—
77	C₇×#482	C₂²	1	2	yes	complemented
78	C₇×#482	C₂²	1	2	yes	complemented
79	C₇×#481	C₂²	1	2	yes	complemented
80	C₇×#480	C₂²	1	2	yes	complemented
81	C₇×#478	C₂²	1	2	yes	complemented
82	C₇×#478	C₂²	1	2	yes	complemented
83	C₇×#477	C₂²	1	1	yes	characteristic, complemented
84	C₇×#477	C₂²	1	1	yes	characteristic, complemented
85	C₇×#477	C₂²	1	1	yes	characteristic, complemented
86	C₇×#476	C₂²	1	1	yes	characteristic, complemented
87	C₇×#476	C₂²	1	2	yes	complemented
88	C₇×#475	C₂²	1	1	yes	characteristic, complemented
89	C₇×#475	C₂²	1	1	yes	characteristic, complemented
90	C₇×#475	C₂²	1	1	yes	characteristic, complemented
91	C₇×#474	C₂²	1	1	yes	characteristic, complemented
92	C₇×#474	C₂²	1	2	yes	complemented
93	C₇×#469	C₂²	1	2	yes	complemented
94	C₇×#468	C₂²	1	2	yes	complemented
95	C₇×#468	C₂²	1	2	yes	complemented
96	C₇×#468	C₂²	1	2	yes	complemented
97	C₇×#466	C₂²	1	2	yes	complemented
98	C₇×#465	C₂²	1	2	yes	complemented
99	C₇×#465	C₂²	1	2	yes	complemented
100	C₇×#465	C₂²	1	2	yes	complemented
101	C₇×#463	C₂²	1	2	yes	complemented
102	C₇×#463	C₂²	1	2	yes	complemented
103	C₇×#461	C₂²	1	2	yes	complemented
104	C₇×#461	C₂²	1	2	yes	complemented
105	C₇×#460	C₂²	1	1	yes	characteristic
106	C₇×#460	C₂²	1	1	yes	characteristic
107	C₇×#460	C₂²	1	1	yes	characteristic
108	C₇×#460	C₂²	1	1	yes	characteristic
109	C₇×#460	C₂²	1	1	yes	characteristic
110	C₇×#460	C₂²	1	1	yes	characteristic
111	C₇×#459	C₂²	1	1	yes	characteristic
112	C₇×#459	C₂²	1	1	yes	characteristic
113	C₇×#450	C₂²	1	2	yes	—
114	C₇×#450	C₂²	1	2	yes	—
115	C₇×#450	C₂²	1	2	yes	—
116	C₇×#449	C₂²	1	2	yes	complemented
117	C₇×#449	C₂²	1	2	yes	complemented
118	C₇×#448	C₂²	1	2	yes	complemented
119	C₇×#448	C₂²	1	2	yes	complemented
120	C₇×#447	C₂²	1	2	yes	—
121	C₇×#442	C₂²	1	2	yes	complemented
122	C₇×#440	C₂²	1	2	yes	complemented
123	C₇×#440	C₂²	1	2	yes	complemented
124	C₇×#440	C₂²	1	2	yes	complemented
125	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
126	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
127	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
128	C₄×C₇×D₈	C₂²	1	2	yes	complemented
129	C₇×#433	C₂²	1	2	yes	—
130	C₇×#433	C₂²	1	2	yes	complemented
131	C₇×#432	C₂²	1	1	yes	characteristic
132	C₇×#432	C₂²	1	1	yes	characteristic, complemented
133	C₇×#431	C₂²	1	1	yes	characteristic
134	C₇×#431	C₂²	1	1	yes	characteristic, complemented
135	C₇×#423	C₂²	1	1	yes	characteristic, complemented
136	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
137	C₇×#408	C₂²	1	2	yes	—
138	C₇×#405	C₂²	1	2	yes	complemented
139	#60994	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	—	2	1	no	—
143	C₂×C₇×#41	—	2	1	no	—
144	C₂×C₇×#41	C₂³	1	1	yes	characteristic
145	C₂×C₇×#41	C₂³	1	1	yes	characteristic
146	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
147	C₂²×C₇×D₄	—	2	1	no	—
148	C₂²×C₇×D₄	—	2	1	no	—
149	C₂²×C₇×D₄	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×SD₁₆	C₂³	1	2	yes	—
154	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
155	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
156	C₂×C₇×D₈	C₂³	1	2	yes	—
157	C₂×C₇×D₈	C₂³	1	2	yes	—
158	C₂×C₇×M₁₆	C₂³	1	2	yes	—
159	C₂²×C₇×C₈	C₂³	1	2	yes	—
160	C₇×C₄⋊Q₈	—	2	1	no	—
161	C₇×C₄⋊Q₈	—	2	1	no	—
162	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
163	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
164	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
165	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
166	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
167	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
168	C₇×#127	—	2	2	no	—
169	C₇×#127	—	2	1	no	—
170	C₇×#127	—	2	1	no	—
171	C₇×#127	C₂³	1	2	yes	—
172	C₇×#127	C₂³	1	1	yes	characteristic
173	C₇×#127	C₂³	1	1	yes	characteristic
174	C₇×#126	—	2	1	no	—
175	C₇×#126	—	2	1	no	—
176	C₇×#126	—	2	1	no	—
177	C₇×#126	—	2	1	no	—
178	C₇×#126	—	2	1	no	—
179	C₇×#126	—	2	1	no	—
180	C₇×#126	—	2	1	no	—
181	C₇×#126	—	2	1	no	—
182	C₇×#125	—	2	1	no	—
183	C₇×#125	—	2	1	no	—
184	C₇×#125	—	2	1	no	—
185	C₇×#125	—	2	1	no	—
186	C₇×#125	—	2	1	no	—
187	C₇×#125	—	2	1	no	—
188	C₇×#125	—	2	1	no	—
189	C₇×#125	C₂³	1	1	yes	characteristic
190	C₇×#125	C₂³	1	2	yes	—
191	C₇×#125	C₂³	1	1	yes	characteristic
192	C₇×#124	—	2	2	no	—
193	C₇×#124	—	2	1	no	—
194	C₇×#124	—	2	1	no	—
195	C₇×#124	—	2	1	no	—
196	C₇×#124	—	2	1	no	—
197	C₇×#124	—	2	1	no	—
198	C₇×#124	—	2	1	no	—
199	C₇×#124	—	2	1	no	—
200	C₇×#124	C₂³	1	1	yes	characteristic
201	C₇×#124	C₂³	1	1	yes	characteristic
202	C₇×#123	—	2	1	no	—
203	C₇×#123	—	2	1	no	—
204	C₇×#123	—	2	1	no	—
205	C₇×#123	—	2	1	no	—
206	C₇×#123	—	2	2	no	—
207	C₇×#123	—	2	2	no	—
208	C₇×#123	—	2	2	no	—
209	C₇×#123	—	2	2	no	—
210	C₇×#123	—	2	1	no	—
211	C₇×#123	—	2	1	no	—
212	C₇×#123	—	2	1	no	—
213	C₇×#123	—	2	1	no	—
214	C₇×C₂²⋊Q₈	—	2	1	no	—
215	C₇×C₂²⋊Q₈	—	2	1	no	—
216	C₇×C₂²⋊Q₈	—	2	1	no	—
217	C₇×C₂²⋊Q₈	—	2	1	no	—
218	C₇×C₂²⋊Q₈	—	2	1	no	—
219	C₇×C₂²⋊Q₈	—	2	1	no	—
220	C₇×C₂²⋊Q₈	—	2	1	no	—
221	C₇×C₂²⋊Q₈	—	2	1	no	—
222	C₇×C₂²⋊Q₈	—	2	1	no	—
223	C₇×C₂²⋊Q₈	—	2	1	no	—
224	C₇×C₂²⋊Q₈	—	2	1	no	—
225	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
226	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
227	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
228	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
229	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
230	C₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
238	C₇×#121	—	2	2	no	—
239	C₇×#121	—	2	2	no	—
240	C₇×#121	—	2	2	no	—
241	C₇×#121	—	2	2	no	—
242	C₇×#121	C₂³	1	1	yes	characteristic
243	C₇×#121	C₂³	1	2	yes	—
244	C₇×#121	C₂³	1	2	yes	—
245	C₇×#121	C₂³	1	2	yes	—
246	C₇×#121	C₂³	1	2	yes	—
247	C₇×#121	C₂³	1	1	yes	characteristic
248	C₇×#120	—	2	2	no	—
249	C₇×#120	—	2	2	no	—
250	C₄×C₇×Q₈	—	2	1	no	—
251	C₄×C₇×Q₈	—	2	1	no	—
252	C₄×C₇×Q₈	—	2	1	no	—
253	C₄×C₇×Q₈	—	2	1	no	—
254	C₄×C₇×Q₈	—	2	1	no	—
255	C₄×C₇×Q₈	—	2	1	no	—
256	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
257	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
258	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
259	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
260	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
261	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
262	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
263	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
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	2	no	—
269	C₄×C₇×D₄	—	2	2	no	—
270	C₄×C₇×D₄	—	2	1	no	—
271	C₄×C₇×D₄	—	2	1	no	—
272	C₄×C₇×D₄	—	2	1	no	—
273	C₄×C₇×D₄	—	2	1	no	—
274	C₄×C₇×D₄	D₄	1	1	yes	characteristic
275	C₄×C₇×D₄	D₄	1	1	yes	characteristic
276	C₄×C₇×D₄	D₄	1	1	yes	characteristic
277	C₄×C₇×D₄	D₄	1	1	yes	characteristic
278	C₄×C₇×D₄	D₄	1	1	yes	characteristic
279	C₄×C₇×D₄	D₄	1	1	yes	characteristic
280	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
281	C₄×C₇×D₄	C₂³	1	2	yes	—
282	C₄×C₇×D₄	C₂³	1	2	yes	—
283	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
284	C₄×C₇×D₄	C₂³	1	2	yes	—
285	C₄×C₇×D₄	C₂³	1	2	yes	—
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	—	2	1	no	—
291	C₇×#117	C₂³	1	2	yes	—
292	C₇×#117	C₂³	1	1	yes	characteristic
293	C₇×#117	C₂³	1	1	yes	characteristic
294	C₇×#117	C₂³	1	1	yes	characteristic
295	C₇×#117	C₂³	1	1	yes	characteristic
296	C₂×C₇×C₄⋊C₄	—	2	1	no	—
297	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₄²×C₇	—	2	1	no	—
301	C₂×C₄²×C₇	—	2	1	no	—
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	1	yes	characteristic
314	C₇×C₄⋊C₈	C₂³	1	2	yes	—
315	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
316	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
317	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
318	C₇×C₄⋊C₈	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×#102	C₂³	1	2	yes	—
334	C₇×#102	C₂³	1	2	yes	—
335	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
336	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
337	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
338	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
339	C₇×#97	C₂³	1	2	yes	—
340	C₇×#97	C₂³	1	2	yes	—
341	C₄×C₇×C₈	C₂³	1	2	yes	—
342	C₄×C₇×C₈	C₂³	1	2	yes	—
343	#3508	C₂×C₇	1	1	yes	characteristic, complemented
344	#3461	C₂×C₇	1	1	yes	characteristic, complemented
345	#3254	C₂×C₇	1	1	yes	characteristic, complemented
346	#3251	C₂×C₇	1	1	yes	characteristic, complemented
347	#3247	C₂×C₇	1	1	yes	characteristic, complemented
348	#3246	C₂×C₇	1	1	yes	characteristic, complemented
349	#3241	C₂×C₇	1	2	yes	complemented
350	#3237	C₂×C₇	1	1	yes	characteristic, complemented
351	#3233	C₂×C₇	1	1	yes	characteristic, complemented
352	#3221	C₂×C₇	1	2	yes	complemented
353	#3217	C₂×C₇	1	1	yes	characteristic, complemented
354	#3208	C₂×C₇	1	1	yes	characteristic, complemented
355	#3200	C₂×C₇	1	2	yes	complemented
356	#3198	C₂×C₇	1	2	yes	complemented
357	#3179	C₂×C₇	1	2	yes	complemented
358	#3174	C₂×C₇	1	2	yes	complemented
359	#3123	C₂×C₇	1	2	yes	complemented
360	#3118	C₂×C₇	1	2	yes	complemented
361	#3115	C₂×C₇	1	1	yes	characteristic, complemented
362	#3112	C₂×C₇	1	1	yes	characteristic, complemented
363	#3106	C₂×C₇	1	1	yes	characteristic, complemented
364	#3103	C₂×C₇	1	1	yes	characteristic, complemented
365	#2925	C₂×C₇	1	1	yes	characteristic, complemented
366	C₂⁴×C₇	—	2	2	no	—
367	C₇×#41	—	4	1	no	—
368	C₇×#41	—	4	1	no	—
369	C₇×#41	—	4	1	no	—
370	C₇×#41	—	4	1	no	—
371	C₇×#41	—	8	2	no	—
372	C₇×#41	—	8	2	no	—
373	C₇×#41	—	8	2	no	—
374	C₇×#41	—	8	2	no	—
375	C₂×C₇×Q₈	—	2	1	no	—
376	C₂×C₇×Q₈	—	2	1	no	—
377	C₂×C₇×Q₈	—	2	1	no	—
378	C₂×C₇×Q₈	—	2	1	no	—
379	C₂×C₇×Q₈	—	2	1	no	—
380	C₂×C₇×Q₈	—	4	1	no	—
381	C₂×C₇×Q₈	—	4	1	no	—
382	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
383	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
386	C₂×C₇×D₄	—	2	1	no	—
387	C₂×C₇×D₄	—	2	1	no	—
388	C₂×C₇×D₄	—	2	1	no	—
389	C₂×C₇×D₄	—	2	2	no	—
390	C₂×C₇×D₄	—	2	2	no	—
391	C₂×C₇×D₄	—	2	2	no	—
392	C₂×C₇×D₄	—	2	2	no	—
393	C₂×C₇×D₄	—	2	2	no	—
394	C₂×C₇×D₄	—	2	1	no	—
395	C₂×C₇×D₄	—	2	1	no	—
396	C₂×C₇×D₄	—	2	1	no	—
397	C₂×C₇×D₄	—	2	1	no	—
398	C₂×C₇×D₄	—	2	2	no	—
399	C₂×C₇×D₄	—	2	2	no	—
400	C₂×C₇×D₄	—	4	2	no	—
401	C₂×C₇×D₄	—	4	2	no	—
402	C₂×C₇×D₄	—	8	2	no	—
403	C₂×C₇×D₄	—	8	2	no	—
404	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
405	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
406	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
407	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
408	C₂×C₇×D₄	C₂⁴	1	2	yes	—
409	C₂×C₇×D₄	C₂⁴	1	2	yes	—
410	C₂²×C₄×C₇	—	2	1	no	—
411	C₂²×C₄×C₇	—	2	1	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	—	2	2	no	—
418	C₂²×C₄×C₇	—	2	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	C₂⁴	1	1	yes	characteristic
426	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
427	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
428	C₇×SD₁₆	—	4	2	no	—
429	C₇×SD₁₆	—	4	2	no	—
430	C₇×SD₁₆	—	4	2	no	—
431	C₇×SD₁₆	—	4	2	no	—
432	C₇×SD₁₆	—	4	2	no	—
433	C₇×SD₁₆	—	4	2	no	—
434	C₇×D₈	—	4	2	no	—
435	C₇×D₈	—	4	2	no	—
436	C₇×M₁₆	—	4	2	no	—
437	C₂×C₇×C₈	—	4	2	no	—
438	C₂×C₇×C₈	C₂⁴	1	2	yes	—
439	C₂×C₇×C₈	C₂⁴	1	2	yes	—
440	C₂×C₇×C₈	C₂⁴	1	2	yes	—
441	C₂×C₇×C₈	C₂⁴	1	2	yes	—
442	C₇×C₄⋊C₄	—	2	1	no	—
443	C₇×C₄⋊C₄	—	2	1	no	—
444	C₇×C₄⋊C₄	—	2	1	no	—
445	C₇×C₄⋊C₄	—	2	1	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	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	2	no	—
462	C₇×C₄⋊C₄	—	2	2	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	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	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	2	yes	—
480	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
481	C₇×C₂²⋊C₄	—	2	2	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	2	no	—
492	C₇×C₂²⋊C₄	—	2	2	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	1	no	—
498	C₇×C₂²⋊C₄	—	2	1	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	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	C₄²×C₇	—	2	1	no	—
512	C₄²×C₇	—	2	1	no	—
513	C₄²×C₇	—	2	1	no	—
514	C₄²×C₇	—	2	1	no	—
515	C₄²×C₇	—	2	1	no	—
516	C₄²×C₇	—	2	1	no	—
517	C₄²×C₇	—	2	1	no	—
518	C₄²×C₇	—	2	2	no	—
519	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
520	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
521	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
522	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
523	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
524	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
525	C₄²×C₇	C₂⁴	1	1	yes	characteristic
526	C₄²×C₇	C₂⁴	1	1	yes	characteristic
527	C₄²×C₇	C₂⁴	1	1	yes	characteristic
528	C₄²×C₇	C₂⁴	1	1	yes	characteristic
529	#559	—	2	1	no	—
530	#559	—	2	1	no	—
531	#550	—	2	1	no	—
532	#550	—	2	1	no	—
533	#546	—	2	1	no	—
534	#546	—	2	1	no	—
535	#546	—	2	1	no	—
536	#546	—	2	1	no	—
537	#544	C₂²×C₇	1	1	yes	characteristic, complemented
538	#542	—	2	1	no	—
539	#542	C₂²×C₇	1	1	yes	characteristic
540	#542	C₂²×C₇	1	1	yes	characteristic, complemented
541	#541	—	2	1	no	—
542	#541	C₂²×C₇	1	1	yes	characteristic
543	#541	C₂²×C₇	1	1	yes	characteristic, complemented
544	#540	C₂²×C₇	1	2	yes	—
545	#540	C₂²×C₇	1	2	yes	—
546	#539	—	2	1	no	—
547	#539	—	2	1	no	—
548	#537	C₂²×C₇	1	1	yes	characteristic
549	#536	C₂²×C₇	1	1	yes	characteristic
550	#536	C₂²×C₇	1	1	yes	characteristic, complemented
551	#535	C₂²×C₇	1	2	yes	—
552	#533	—	2	1	no	—
553	#533	C₂²×C₇	1	1	yes	characteristic
554	#533	C₂²×C₇	1	1	yes	characteristic
555	#533	C₂²×C₇	1	1	yes	characteristic, complemented
556	#532	C₂²×C₇	1	1	yes	characteristic
557	#532	C₂²×C₇	1	1	yes	characteristic
558	#532	C₂²×C₇	1	1	yes	characteristic
559	#532	C₂²×C₇	1	1	yes	characteristic
560	C₂×#127	C₂²×C₇	1	1	yes	characteristic
561	#529	—	2	1	no	—
562	#529	—	2	1	no	—
563	#529	—	2	1	no	—
564	#529	C₂²×C₇	1	1	yes	characteristic
565	#529	C₂²×C₇	1	1	yes	characteristic, complemented
566	#518	C₂²×C₇	1	2	yes	—
567	C₄×#41	C₂²×C₇	1	1	yes	characteristic
568	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
569	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
570	#501	C₂²×C₇	1	2	yes	complemented
571	#499	C₂²×C₇	1	2	yes	complemented
572	#496	C₂²×C₇	1	2	yes	—
573	#492	C₂²×C₇	1	2	yes	—
574	#491	C₂²×C₇	1	2	yes	complemented
575	#490	C₂²×C₇	1	2	yes	—
576	#488	C₂²×C₇	1	2	yes	complemented
577	#486	C₂²×C₇	1	2	yes	—
578	#485	C₂²×C₇	1	2	yes	—
579	#485	C₂²×C₇	1	2	yes	—
580	#485	C₂²×C₇	1	2	yes	—
581	#482	C₂²×C₇	1	2	yes	—
582	#482	C₂²×C₇	1	2	yes	complemented
583	#482	C₂²×C₇	1	2	yes	complemented
584	#481	C₂²×C₇	1	2	yes	complemented
585	#480	C₂²×C₇	1	2	yes	complemented
586	#478	C₂²×C₇	1	2	yes	complemented
587	#478	C₂²×C₇	1	2	yes	complemented
588	#477	C₂²×C₇	1	1	yes	characteristic, complemented
589	#477	C₂²×C₇	1	1	yes	characteristic, complemented
590	#477	C₂²×C₇	1	1	yes	characteristic, complemented
591	#476	C₂²×C₇	1	1	yes	characteristic, complemented
592	#476	C₂²×C₇	1	2	yes	complemented
593	#475	C₂²×C₇	1	1	yes	characteristic, complemented
594	#475	C₂²×C₇	1	1	yes	characteristic, complemented
595	#475	C₂²×C₇	1	1	yes	characteristic, complemented
596	#474	C₂²×C₇	1	1	yes	characteristic, complemented
597	#474	C₂²×C₇	1	2	yes	complemented
598	#469	C₂²×C₇	1	2	yes	complemented
599	#468	C₂²×C₇	1	2	yes	complemented
600	#468	C₂²×C₇	1	2	yes	complemented
601	#468	C₂²×C₇	1	2	yes	complemented
602	#466	C₂²×C₇	1	2	yes	complemented
603	#465	C₂²×C₇	1	2	yes	complemented
604	#465	C₂²×C₇	1	2	yes	complemented
605	#465	C₂²×C₇	1	2	yes	complemented
606	#463	C₂²×C₇	1	2	yes	complemented
607	#463	C₂²×C₇	1	2	yes	complemented
608	#461	C₂²×C₇	1	2	yes	complemented
609	#461	C₂²×C₇	1	2	yes	complemented
610	#460	C₂²×C₇	1	1	yes	characteristic
611	#460	C₂²×C₇	1	1	yes	characteristic
612	#460	C₂²×C₇	1	1	yes	characteristic
613	#460	C₂²×C₇	1	1	yes	characteristic
614	#460	C₂²×C₇	1	1	yes	characteristic
615	#460	C₂²×C₇	1	1	yes	characteristic
616	#459	C₂²×C₇	1	1	yes	characteristic
617	#459	C₂²×C₇	1	1	yes	characteristic
618	#450	C₂²×C₇	1	2	yes	—
619	#450	C₂²×C₇	1	2	yes	—
620	#450	C₂²×C₇	1	2	yes	—
621	#449	C₂²×C₇	1	2	yes	complemented
622	#449	C₂²×C₇	1	2	yes	complemented
623	#448	C₂²×C₇	1	2	yes	complemented
624	#448	C₂²×C₇	1	2	yes	complemented
625	#447	C₂²×C₇	1	2	yes	—
626	#442	C₂²×C₇	1	2	yes	complemented
627	#440	C₂²×C₇	1	2	yes	complemented
628	#440	C₂²×C₇	1	2	yes	complemented
629	#440	C₂²×C₇	1	2	yes	complemented
630	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
631	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
632	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
633	C₄×D₈	C₂²×C₇	1	2	yes	complemented
634	#433	C₂²×C₇	1	2	yes	—
635	#433	C₂²×C₇	1	2	yes	complemented
636	#432	C₂²×C₇	1	1	yes	characteristic
637	#432	C₂²×C₇	1	1	yes	characteristic, complemented
638	#431	C₂²×C₇	1	1	yes	characteristic
639	#431	C₂²×C₇	1	1	yes	characteristic, complemented
640	#423	C₂²×C₇	1	1	yes	characteristic, complemented
641	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
642	#408	C₂²×C₇	1	2	yes	—
643	#405	C₂²×C₇	1	2	yes	complemented
644	C₂³×C₇	—	2	1	no	—
645	C₂³×C₇	—	2	2	no	—
646	C₂³×C₇	—	2	2	no	—
647	C₂³×C₇	—	4	4	no	—
648	C₂³×C₇	—	8	2	no	—
649	C₂³×C₇	—	8	2	no	—
650	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
651	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
652	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
653	C₇×Q₈	—	2	1	no	—
654	C₇×Q₈	—	2	1	no	—
655	C₇×Q₈	—	2	1	no	—
656	C₇×Q₈	—	2	1	no	—
657	C₇×Q₈	—	2	1	no	—
658	C₇×Q₈	—	2	1	no	—
659	C₇×Q₈	—	4	1	no	—
660	C₇×Q₈	—	4	2	no	—
661	C₇×Q₈	—	4	2	no	—
662	C₇×Q₈	—	4	2	no	—
663	C₇×Q₈	—	8	1	no	—
664	C₇×Q₈	—	8	1	no	—
665	C₇×D₄	—	2	1	no	—
666	C₇×D₄	—	2	1	no	—
667	C₇×D₄	—	2	2	no	—
668	C₇×D₄	—	2	2	no	—
669	C₇×D₄	—	2	2	no	—
670	C₇×D₄	—	2	2	no	—
671	C₇×D₄	—	4	1	no	—
672	C₇×D₄	—	4	1	no	—
673	C₇×D₄	—	4	1	no	—
674	C₇×D₄	—	4	4	no	—
675	C₇×D₄	—	4	2	no	—
676	C₇×D₄	—	4	2	no	—
677	C₇×D₄	—	4	2	no	—
678	C₇×D₄	—	4	2	no	—
679	C₇×D₄	—	4	2	no	—
680	C₇×D₄	—	8	2	no	—
681	C₇×D₄	—	8	2	no	—
682	C₇×D₄	—	8	1	no	—
683	C₇×D₄	—	8	1	no	—
684	C₇×D₄	—	8	2	no	—
685	C₇×D₄	—	8	2	no	—
686	C₇×D₄	—	8	2	no	—
687	C₇×D₄	—	8	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	1	no	—
703	C₂×C₄×C₇	—	2	1	no	—
704	C₂×C₄×C₇	—	2	2	no	—
705	C₂×C₄×C₇	—	2	2	no	—
706	C₂×C₄×C₇	—	4	1	no	—
707	C₂×C₄×C₇	—	4	1	no	—
708	C₂×C₄×C₇	—	4	1	no	—
709	C₂×C₄×C₇	—	4	2	no	—
710	C₂×C₄×C₇	—	4	2	no	—
711	C₂×C₄×C₇	—	4	2	no	—
712	C₂×C₄×C₇	—	8	1	no	—
713	C₂×C₄×C₇	—	8	2	no	—
714	C₂×C₄×C₇	—	8	2	no	—
715	C₂×C₄×C₇	—	8	2	no	—
716	C₂×C₄×C₇	—	8	2	no	—
717	C₂×C₄×C₇	—	8	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
724	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
730	C₇×C₈	—	2	2	no	—
731	C₇×C₈	—	2	2	no	—
732	C₇×C₈	—	2	2	no	—
733	C₇×C₈	—	2	2	no	—
734	C₂×#41	—	2	1	no	—
735	C₂×#41	—	2	1	no	—
736	C₂×#41	—	2	1	no	—
737	C₂×#41	—	2	1	no	—
738	C₂×#41	C₂³×C₇	1	1	yes	characteristic
739	C₂×#41	C₂³×C₇	1	1	yes	characteristic
740	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
741	C₂²×D₄	—	2	1	no	—
742	C₂²×D₄	—	2	1	no	—
743	C₂²×D₄	C₂³×C₇	1	2	yes	—
744	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
745	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
746	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
747	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
750	C₂×D₈	C₂³×C₇	1	2	yes	—
751	C₂×D₈	C₂³×C₇	1	2	yes	—
752	C₂×M₁₆	C₂³×C₇	1	2	yes	—
753	C₂²×C₈	C₂³×C₇	1	2	yes	—
754	C₄⋊Q₈	—	2	1	no	—
755	C₄⋊Q₈	—	2	1	no	—
756	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
757	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
758	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
759	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
760	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
761	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
762	#127	—	2	2	no	—
763	#127	—	2	1	no	—
764	#127	—	2	1	no	—
765	#127	C₂³×C₇	1	1	yes	characteristic
766	#127	C₂³×C₇	1	1	yes	characteristic
767	#127	C₂³×C₇	1	2	yes	—
768	#126	—	2	1	no	—
769	#126	—	2	1	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	—	2	1	no	—
782	#125	—	2	1	no	—
783	#125	C₂³×C₇	1	1	yes	characteristic
784	#125	C₂³×C₇	1	1	yes	characteristic
785	#125	C₂³×C₇	1	2	yes	—
786	#124	—	2	2	no	—
787	#124	—	2	1	no	—
788	#124	—	2	1	no	—
789	#124	—	2	1	no	—
790	#124	—	2	1	no	—
791	#124	—	2	1	no	—
792	#124	—	2	1	no	—
793	#124	—	2	1	no	—
794	#124	C₂³×C₇	1	1	yes	characteristic
795	#124	C₂³×C₇	1	1	yes	characteristic
796	#123	—	2	1	no	—
797	#123	—	2	1	no	—
798	#123	—	2	1	no	—
799	#123	—	2	1	no	—
800	#123	—	2	2	no	—
801	#123	—	2	2	no	—
802	#123	—	2	2	no	—
803	#123	—	2	2	no	—
804	#123	—	2	1	no	—
805	#123	—	2	1	no	—
806	#123	—	2	1	no	—
807	#123	—	2	1	no	—
808	C₂²⋊Q₈	—	2	1	no	—
809	C₂²⋊Q₈	—	2	1	no	—
810	C₂²⋊Q₈	—	2	1	no	—
811	C₂²⋊Q₈	—	2	1	no	—
812	C₂²⋊Q₈	—	2	1	no	—
813	C₂²⋊Q₈	—	2	1	no	—
814	C₂²⋊Q₈	—	2	1	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	2	1	no	—
818	C₂²⋊Q₈	—	2	1	no	—
819	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
820	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
821	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
822	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
823	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
824	C₂²⋊Q₈	C₂³×C₇	1	1	yes	characteristic
825	#121	—	2	1	no	—
826	#121	—	2	1	no	—
827	#121	—	2	1	no	—
828	#121	—	2	1	no	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	1	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	C₂³×C₇	1	1	yes	characteristic
837	#121	C₂³×C₇	1	1	yes	characteristic
838	#121	C₂³×C₇	1	2	yes	—
839	#121	C₂³×C₇	1	2	yes	—
840	#121	C₂³×C₇	1	2	yes	—
841	#121	C₂³×C₇	1	2	yes	—
842	#120	—	2	2	no	—
843	#120	—	2	2	no	—
844	C₄×Q₈	—	2	1	no	—
845	C₄×Q₈	—	2	1	no	—
846	C₄×Q₈	—	2	1	no	—
847	C₄×Q₈	—	2	1	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
851	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
852	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
853	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
854	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
855	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
856	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
857	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	1	no	—
865	C₄×D₄	—	2	1	no	—
866	C₄×D₄	—	2	1	no	—
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	C₇×D₄	1	1	yes	characteristic
869	C₄×D₄	C₇×D₄	1	1	yes	characteristic
870	C₄×D₄	C₇×D₄	1	1	yes	characteristic
871	C₄×D₄	C₇×D₄	1	1	yes	characteristic
872	C₄×D₄	C₇×D₄	1	1	yes	characteristic
873	C₄×D₄	C₇×D₄	1	1	yes	characteristic
874	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
875	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
876	C₄×D₄	C₂³×C₇	1	2	yes	—
877	C₄×D₄	C₂³×C₇	1	2	yes	—
878	C₄×D₄	C₂³×C₇	1	2	yes	—
879	C₄×D₄	C₂³×C₇	1	2	yes	—
880	#117	—	2	1	no	—
881	#117	—	2	1	no	—
882	#117	—	2	1	no	—
883	#117	—	2	1	no	—
884	#117	—	2	1	no	—
885	#117	C₂³×C₇	1	1	yes	characteristic
886	#117	C₂³×C₇	1	2	yes	—
887	#117	C₂³×C₇	1	1	yes	characteristic
888	#117	C₂³×C₇	1	1	yes	characteristic
889	#117	C₂³×C₇	1	1	yes	characteristic
890	C₂×C₄⋊C₄	—	2	1	no	—
891	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
892	C₂×C₂²⋊C₄	—	2	2	no	—
893	C₂×C₂²⋊C₄	—	2	2	no	—
894	C₂×C₄²	—	2	1	no	—
895	C₂×C₄²	—	2	1	no	—
896	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
897	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
898	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
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	#106	C₂³×C₇	1	2	yes	—
904	#106	C₂³×C₇	1	2	yes	—
905	#106	C₂³×C₇	1	2	yes	—
906	#106	C₂³×C₇	1	2	yes	—
907	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
908	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
909	C₄⋊C₈	C₂³×C₇	1	2	yes	—
910	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
911	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
912	C₄⋊C₈	C₂³×C₇	1	2	yes	—
913	#103	C₂³×C₇	1	2	yes	—
914	#103	C₂³×C₇	1	2	yes	—
915	#103	C₂³×C₇	1	2	yes	—
916	#103	C₂³×C₇	1	2	yes	—
917	#103	C₂³×C₇	1	2	yes	—
918	#103	C₂³×C₇	1	2	yes	—
919	#102	C₂³×C₇	1	2	yes	—
920	#102	C₂³×C₇	1	2	yes	—
921	#102	C₂³×C₇	1	2	yes	—
922	#102	C₂³×C₇	1	2	yes	—
923	#102	C₂³×C₇	1	2	yes	—
924	#102	C₂³×C₇	1	2	yes	—
925	#102	C₂³×C₇	1	2	yes	—
926	#102	C₂³×C₇	1	2	yes	—
927	#102	C₂³×C₇	1	2	yes	—
928	#102	C₂³×C₇	1	2	yes	—
929	C₂²⋊C₈	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	#97	C₂³×C₇	1	2	yes	—
934	#97	C₂³×C₇	1	2	yes	—
935	C₄×C₈	C₂³×C₇	1	2	yes	—
936	C₄×C₈	C₂³×C₇	1	2	yes	—
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	—	4	2	no	—
947	C₂²×C₇	—	4	2	no	—
948	C₂²×C₇	—	4	1	no	—
949	C₂²×C₇	—	4	1	no	—
950	C₂²×C₇	—	4	2	no	—
951	C₂²×C₇	—	4	2	no	—
952	C₂²×C₇	—	4	1	no	—
953	C₂²×C₇	—	4	2	no	—
954	C₂²×C₇	—	4	2	no	—
955	C₂²×C₇	—	16	4	no	—
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	—	2	1	no	—
966	C₄×C₇	—	2	1	no	—
967	C₄×C₇	—	4	2	no	—
968	C₄×C₇	—	4	1	no	—
969	C₄×C₇	—	4	1	no	—
970	C₄×C₇	—	4	1	no	—
971	C₄×C₇	—	4	1	no	—
972	C₄×C₇	—	4	1	no	—
973	C₄×C₇	—	4	1	no	—
974	C₄×C₇	—	4	1	no	—
975	C₄×C₇	—	4	2	no	—
976	C₄×C₇	#577	1	2	yes	—
977	C₄×C₇	#585	1	1	yes	characteristic
978	C₄×C₇	#585	1	1	yes	characteristic
979	C₂⁴	—	2	2	no	—
980	#41	—	4	1	no	—
981	#41	—	4	1	no	—
982	#41	—	4	1	no	—
983	#41	—	4	1	no	—
984	#41	—	8	2	no	—
985	#41	—	8	2	no	—
986	#41	—	8	2	no	—
987	#41	—	8	2	no	—
988	C₂×Q₈	—	2	1	no	—
989	C₂×Q₈	—	2	1	no	—
990	C₂×Q₈	—	2	1	no	—
991	C₂×Q₈	—	2	1	no	—
992	C₂×Q₈	—	2	1	no	—
993	C₂×Q₈	—	4	1	no	—
994	C₂×Q₈	—	4	1	no	—
995	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
996	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
997	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
998	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
999	C₂×D₄	—	2	1	no	—
1000	C₂×D₄	—	2	1	no	—
1001	C₂×D₄	—	2	1	no	—
1002	C₂×D₄	—	2	2	no	—
1003	C₂×D₄	—	2	2	no	—
1004	C₂×D₄	—	2	2	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	1	no	—
1010	C₂×D₄	—	2	1	no	—
1011	C₂×D₄	—	2	2	no	—
1012	C₂×D₄	—	2	2	no	—
1013	C₂×D₄	—	4	2	no	—
1014	C₂×D₄	—	4	2	no	—
1015	C₂×D₄	—	8	2	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	C₂⁴×C₇	1	1	yes	characteristic
1021	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1022	C₂×D₄	C₂⁴×C₇	1	2	yes	—
1023	C₂²×C₄	—	2	1	no	—
1024	C₂²×C₄	—	2	1	no	—
1025	C₂²×C₄	—	2	1	no	—
1026	C₂²×C₄	—	2	1	no	—
1027	C₂²×C₄	—	2	1	no	—
1028	C₂²×C₄	—	2	2	no	—
1029	C₂²×C₄	—	2	2	no	—
1030	C₂²×C₄	—	2	2	no	—
1031	C₂²×C₄	—	2	2	no	—
1032	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1033	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1034	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1035	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1036	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1037	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
1038	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1039	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1040	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
1041	SD₁₆	—	4	2	no	—
1042	SD₁₆	—	4	2	no	—
1043	SD₁₆	—	4	2	no	—
1044	SD₁₆	—	4	2	no	—
1045	SD₁₆	—	4	2	no	—
1046	SD₁₆	—	4	2	no	—
1047	D₈	—	4	2	no	—
1048	D₈	—	4	2	no	—
1049	M₁₆	—	4	2	no	—
1050	C₂×C₈	—	4	2	no	—
1051	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1052	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1053	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1054	C₂×C₈	C₂⁴×C₇	1	2	yes	—
1055	C₄⋊C₄	—	2	1	no	—
1056	C₄⋊C₄	—	2	1	no	—
1057	C₄⋊C₄	—	2	1	no	—
1058	C₄⋊C₄	—	2	1	no	—
1059	C₄⋊C₄	—	2	1	no	—
1060	C₄⋊C₄	—	2	1	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	2	no	—
1075	C₄⋊C₄	—	2	2	no	—
1076	C₄⋊C₄	—	2	1	no	—
1077	C₄⋊C₄	—	2	1	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	C₂×C₇×D₄	1	1	yes	characteristic
1083	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1084	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1085	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1086	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1087	C₄⋊C₄	C₂×C₇×D₄	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	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
1092	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1093	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
1094	C₂²⋊C₄	—	2	2	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	1	no	—
1101	C₂²⋊C₄	—	2	1	no	—
1102	C₂²⋊C₄	—	2	2	no	—
1103	C₂²⋊C₄	—	2	2	no	—
1104	C₂²⋊C₄	—	2	2	no	—
1105	C₂²⋊C₄	—	2	2	no	—
1106	C₂²⋊C₄	—	2	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	2	no	—
1113	C₂²⋊C₄	—	2	2	no	—
1114	C₂²⋊C₄	—	2	2	no	—
1115	C₂²⋊C₄	—	2	2	no	—
1116	C₂²⋊C₄	—	2	1	no	—
1117	C₂²⋊C₄	—	2	1	no	—
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	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1123	C₂²⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
1124	C₄²	—	2	1	no	—
1125	C₄²	—	2	1	no	—
1126	C₄²	—	2	1	no	—
1127	C₄²	—	2	1	no	—
1128	C₄²	—	2	1	no	—
1129	C₄²	—	2	1	no	—
1130	C₄²	—	2	1	no	—
1131	C₄²	—	2	2	no	—
1132	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1133	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1134	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1135	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1136	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1137	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
1138	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1139	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1140	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1141	C₄²	C₂⁴×C₇	1	1	yes	characteristic
1142	C₂×C₇	—	4	1	no	—
1143	C₂×C₇	—	4	1	no	—
1144	C₂×C₇	—	4	1	no	—
1145	C₂×C₇	—	8	1	no	—
1146	C₂×C₇	—	8	2	no	—
1147	C₂×C₇	—	8	2	no	—
1148	C₂×C₇	#3449	1	1	yes	characteristic
1149	C₂×C₇	C₂×#577	1	1	yes	characteristic
1150	C₂×C₇	#3585	1	1	yes	characteristic
1151	C₂³	—	2	1	no	—
1152	C₂³	—	2	2	no	—
1153	C₂³	—	2	2	no	—
1154	C₂³	—	4	4	no	—
1155	C₂³	—	8	2	no	—
1156	C₂³	—	8	2	no	—
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	1	no	—
1161	Q₈	—	2	1	no	—
1162	Q₈	—	2	1	no	—
1163	Q₈	—	2	1	no	—
1164	Q₈	—	2	1	no	—
1165	Q₈	—	2	1	no	—
1166	Q₈	—	4	1	no	—
1167	Q₈	—	4	2	no	—
1168	Q₈	—	4	2	no	—
1169	Q₈	—	4	2	no	—
1170	Q₈	—	8	1	no	—
1171	Q₈	—	8	1	no	—
1172	D₄	—	2	1	no	—
1173	D₄	—	2	1	no	—
1174	D₄	—	2	2	no	—
1175	D₄	—	2	2	no	—
1176	D₄	—	2	2	no	—
1177	D₄	—	2	2	no	—
1178	D₄	—	4	1	no	—
1179	D₄	—	4	1	no	—
1180	D₄	—	4	1	no	—
1181	D₄	—	4	4	no	—
1182	D₄	—	4	2	no	—
1183	D₄	—	4	2	no	—
1184	D₄	—	4	2	no	—
1185	D₄	—	4	2	no	—
1186	D₄	—	4	2	no	—
1187	D₄	—	8	2	no	—
1188	D₄	—	8	2	no	—
1189	D₄	—	8	1	no	—
1190	D₄	—	8	1	no	—
1191	D₄	—	8	2	no	—
1192	D₄	—	8	2	no	—
1193	D₄	—	8	2	no	—
1194	D₄	—	8	2	no	—
1195	C₂×C₄	—	2	1	no	—
1196	C₂×C₄	—	2	1	no	—
1197	C₂×C₄	—	2	1	no	—
1198	C₂×C₄	—	2	1	no	—
1199	C₂×C₄	—	2	1	no	—
1200	C₂×C₄	—	2	1	no	—
1201	C₂×C₄	—	2	2	no	—
1202	C₂×C₄	—	2	2	no	—
1203	C₂×C₄	—	2	2	no	—
1204	C₂×C₄	—	2	1	no	—
1205	C₂×C₄	—	2	1	no	—
1206	C₂×C₄	—	2	1	no	—
1207	C₂×C₄	—	2	1	no	—
1208	C₂×C₄	—	2	1	no	—
1209	C₂×C₄	—	2	1	no	—
1210	C₂×C₄	—	2	1	no	—
1211	C₂×C₄	—	2	2	no	—
1212	C₂×C₄	—	2	2	no	—
1213	C₂×C₄	—	4	1	no	—
1214	C₂×C₄	—	4	1	no	—
1215	C₂×C₄	—	4	1	no	—
1216	C₂×C₄	—	4	2	no	—
1217	C₂×C₄	—	4	2	no	—
1218	C₂×C₄	—	4	2	no	—
1219	C₂×C₄	—	8	1	no	—
1220	C₂×C₄	—	8	2	no	—
1221	C₂×C₄	—	8	2	no	—
1222	C₂×C₄	—	8	2	no	—
1223	C₂×C₄	—	8	2	no	—
1224	C₂×C₄	—	8	1	no	—
1225	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1226	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1227	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1228	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1229	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1230	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1231	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1232	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1233	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1234	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1235	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1236	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1237	C₈	—	2	2	no	—
1238	C₈	—	2	2	no	—
1239	C₈	—	2	2	no	—
1240	C₈	—	2	2	no	—
1241	C₇	#60994	1	1	yes	characteristic, direct product factor, Sylow
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	—	2	1	no	—
1249	C₂²	—	2	1	no	—
1250	C₂²	—	2	1	no	—
1251	C₂²	—	4	1	no	—
1252	C₂²	—	4	2	no	—
1253	C₂²	—	4	2	no	—
1254	C₂²	—	4	2	no	—
1255	C₂²	—	4	2	no	—
1256	C₂²	—	4	1	no	—
1257	C₂²	—	4	1	no	—
1258	C₂²	—	4	2	no	—
1259	C₂²	—	4	2	no	—
1260	C₂²	—	16	4	no	—
1261	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1262	C₄	—	2	1	no	—
1263	C₄	—	2	1	no	—
1264	C₄	—	2	1	no	—
1265	C₄	—	2	1	no	—
1266	C₄	—	2	1	no	—
1267	C₄	—	2	1	no	—
1268	C₄	—	2	1	no	—
1269	C₄	—	2	1	no	—
1270	C₄	—	2	1	no	—
1271	C₄	—	2	1	no	—
1272	C₄	—	4	1	no	—
1273	C₄	—	4	2	no	—
1274	C₄	—	4	2	no	—
1275	C₄	—	4	1	no	—
1276	C₄	—	4	1	no	—
1277	C₄	—	4	1	no	—
1278	C₄	—	4	1	no	—
1279	C₄	—	4	1	no	—
1280	C₄	—	4	1	no	—
1281	C₄	C₇×#577	1	2	yes	—
1282	C₄	C₇×#585	1	1	yes	characteristic
1283	C₄	C₇×#585	1	1	yes	characteristic
1284	C₂	—	4	1	no	—
1285	C₂	—	4	1	no	—
1286	C₂	—	4	1	no	—
1287	C₂	—	8	2	no	—
1288	C₂	—	8	2	no	—
1289	C₂	—	8	1	no	—
1290	C₂	C₇×#3449	1	1	yes	characteristic
1291	C₂	C₂×C₇×#577	1	1	yes	characteristic
1292	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 ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3508	C₂	semidirect
2. C₇×#3461	C₂	semidirect
3. C₇×#3254	C₂	semidirect
4. C₇×#3251	C₂	semidirect
5. C₇×#3247	C₂	semidirect
6. C₇×#3246	C₂	semidirect
7. C₇×#3241	C₂	semidirect
8. C₇×#3237	C₂	semidirect
9. C₇×#3233	C₂	semidirect
10. C₇×#3221	C₂	semidirect
11. C₇×#3217	C₂	semidirect
12. C₇×#3208	C₂	semidirect
13. C₇×#3200	C₂	semidirect
14. C₇×#3198	C₂	semidirect
15. C₇×#3179	C₂	semidirect
16. C₇×#3174	C₂	semidirect
17. C₇×#3123	C₂	semidirect
18. C₇×#3118	C₂	semidirect
19. C₇×#3115	C₂	semidirect
20. C₇×#3112	C₂	semidirect
21. C₇×#3106	C₂	semidirect
22. C₇×#3103	C₂	semidirect
23. C₇×#2925	C₂	semidirect
32. C₇×#544	C₂²	semidirect
35. C₇×#542	C₂²	semidirect
38. C₇×#541	C₂²	semidirect
45. C₇×#536	C₂²	semidirect
50. C₇×#533	C₂²	semidirect
60. C₇×#529	C₂²	semidirect
63. C₄×C₇×#41	C₂²	semidirect
64. C₂×C₄×C₇×Q₈	C₂²	semidirect
65. C₇×#501	C₂²	semidirect
66. C₇×#499	C₂²	semidirect
69. C₇×#491	C₂²	semidirect
71. C₇×#488	C₂²	semidirect
77. C₇×#482	C₂²	semidirect
78. C₇×#482	C₂²	semidirect
79. C₇×#481	C₂²	semidirect
80. C₇×#480	C₂²	semidirect
81. C₇×#478	C₂²	semidirect
82. C₇×#478	C₂²	semidirect
83. C₇×#477	C₂²	semidirect
84. C₇×#477	C₂²	semidirect
85. C₇×#477	C₂²	semidirect
86. C₇×#476	C₂²	semidirect
87. C₇×#476	C₂²	semidirect
88. C₇×#475	C₂²	semidirect
89. C₇×#475	C₂²	semidirect
90. C₇×#475	C₂²	semidirect
91. C₇×#474	C₂²	semidirect
92. C₇×#474	C₂²	semidirect
93. C₇×#469	C₂²	semidirect
94. C₇×#468	C₂²	semidirect
95. C₇×#468	C₂²	semidirect
96. C₇×#468	C₂²	semidirect
97. C₇×#466	C₂²	semidirect
98. C₇×#465	C₂²	semidirect
99. C₇×#465	C₂²	semidirect
100. C₇×#465	C₂²	semidirect
101. C₇×#463	C₂²	semidirect
102. C₇×#463	C₂²	semidirect
103. C₇×#461	C₂²	semidirect
104. C₇×#461	C₂²	semidirect
116. C₇×#449	C₂²	semidirect
117. C₇×#449	C₂²	semidirect
118. C₇×#448	C₂²	semidirect
119. C₇×#448	C₂²	semidirect
121. C₇×#442	C₂²	semidirect
122. C₇×#440	C₂²	semidirect
123. C₇×#440	C₂²	semidirect
124. C₇×#440	C₂²	semidirect
125. C₄×C₇×SD₁₆	C₂²	semidirect
126. C₄×C₇×SD₁₆	C₂²	semidirect
127. C₄×C₇×SD₁₆	C₂²	semidirect
128. C₄×C₇×D₈	C₂²	semidirect
130. C₇×#433	C₂²	semidirect
132. C₇×#432	C₂²	semidirect
134. C₇×#431	C₂²	semidirect
135. C₇×#423	C₂²	semidirect
136. C₂×C₇×C₄⋊C₈	C₂²	semidirect
138. C₇×#405	C₂²	semidirect
139. #60994	C₇	direct (N × H)
343. #3508	C₂×C₇	semidirect
344. #3461	C₂×C₇	semidirect
345. #3254	C₂×C₇	semidirect
346. #3251	C₂×C₇	semidirect
347. #3247	C₂×C₇	semidirect
348. #3246	C₂×C₇	semidirect
349. #3241	C₂×C₇	semidirect
350. #3237	C₂×C₇	semidirect
351. #3233	C₂×C₇	semidirect
352. #3221	C₂×C₇	semidirect
353. #3217	C₂×C₇	semidirect
354. #3208	C₂×C₇	semidirect
355. #3200	C₂×C₇	semidirect
356. #3198	C₂×C₇	semidirect
357. #3179	C₂×C₇	semidirect
358. #3174	C₂×C₇	semidirect
359. #3123	C₂×C₇	semidirect
360. #3118	C₂×C₇	semidirect
361. #3115	C₂×C₇	semidirect
362. #3112	C₂×C₇	semidirect
363. #3106	C₂×C₇	semidirect
364. #3103	C₂×C₇	semidirect
365. #2925	C₂×C₇	semidirect
537. #544	C₂²×C₇	semidirect
540. #542	C₂²×C₇	semidirect
543. #541	C₂²×C₇	semidirect
550. #536	C₂²×C₇	semidirect
555. #533	C₂²×C₇	semidirect
565. #529	C₂²×C₇	semidirect
568. C₄×#41	C₂²×C₇	semidirect
569. C₂×C₄×Q₈	C₂²×C₇	semidirect
570. #501	C₂²×C₇	semidirect
571. #499	C₂²×C₇	semidirect
574. #491	C₂²×C₇	semidirect
576. #488	C₂²×C₇	semidirect
582. #482	C₂²×C₇	semidirect
583. #482	C₂²×C₇	semidirect
584. #481	C₂²×C₇	semidirect
585. #480	C₂²×C₇	semidirect
586. #478	C₂²×C₇	semidirect
587. #478	C₂²×C₇	semidirect
588. #477	C₂²×C₇	semidirect
589. #477	C₂²×C₇	semidirect
590. #477	C₂²×C₇	semidirect
591. #476	C₂²×C₇	semidirect
592. #476	C₂²×C₇	semidirect
593. #475	C₂²×C₇	semidirect
594. #475	C₂²×C₇	semidirect
595. #475	C₂²×C₇	semidirect
596. #474	C₂²×C₇	semidirect
597. #474	C₂²×C₇	semidirect
598. #469	C₂²×C₇	semidirect
599. #468	C₂²×C₇	semidirect
600. #468	C₂²×C₇	semidirect
601. #468	C₂²×C₇	semidirect
602. #466	C₂²×C₇	semidirect
603. #465	C₂²×C₇	semidirect
604. #465	C₂²×C₇	semidirect
605. #465	C₂²×C₇	semidirect
606. #463	C₂²×C₇	semidirect
607. #463	C₂²×C₇	semidirect
608. #461	C₂²×C₇	semidirect
609. #461	C₂²×C₇	semidirect
621. #449	C₂²×C₇	semidirect
622. #449	C₂²×C₇	semidirect
623. #448	C₂²×C₇	semidirect
624. #448	C₂²×C₇	semidirect
626. #442	C₂²×C₇	semidirect
627. #440	C₂²×C₇	semidirect
628. #440	C₂²×C₇	semidirect
629. #440	C₂²×C₇	semidirect
630. C₄×SD₁₆	C₂²×C₇	semidirect
631. C₄×SD₁₆	C₂²×C₇	semidirect
632. C₄×SD₁₆	C₂²×C₇	semidirect
633. C₄×D₈	C₂²×C₇	semidirect
635. #433	C₂²×C₇	semidirect
637. #432	C₂²×C₇	semidirect
639. #431	C₂²×C₇	semidirect
640. #423	C₂²×C₇	semidirect
641. C₂×C₄⋊C₈	C₂²×C₇	semidirect
643. #405	C₂²×C₇	semidirect
1241. C₇	#60994	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×#3508	2
C₇×#3461	2
C₇×#3254	2
C₇×#3251	2
C₇×#3247	2
C₇×#3246	2
C₇×#3241	2
C₇×#3237	2
C₇×#3233	2
C₇×#3221	2
C₇×#3217	2
C₇×#3208	2
C₇×#3200	2
C₇×#3198	2
C₇×#3179	2
C₇×#3174	2
C₇×#3123	2
C₇×#3118	2
C₇×#3115	2
C₇×#3112	2
C₇×#3106	2
C₇×#3103	2
C₇×#2925	2
#60994	7

Subgroups — C7×#60994 #13238210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60994 #13238210