Subgroups — C₇×#60891 #13238107

Order 1792.

1636 conjugacy classes of subgroups.

The subgroup lattice has 1072 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3504	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3461	C₂	1	1	yes	maximal, characteristic
3	C₇×#3244	C₂	1	2	yes	maximal, complemented
4	C₇×#3243	C₂	1	2	yes	maximal, complemented
5	C₇×#3242	C₂	1	2	yes	maximal, complemented
6	C₇×#3242	C₂	1	2	yes	maximal, complemented
7	C₇×#3240	C₂	1	2	yes	maximal, complemented
8	C₇×#3236	C₂	1	2	yes	maximal, complemented
9	C₇×#3232	C₂	1	2	yes	maximal, complemented
10	C₇×#3231	C₂	1	2	yes	maximal, complemented
11	C₇×#3164	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3137	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3099	C₂	1	1	yes	maximal, characteristic
16	C₇×#3098	C₂	1	1	yes	maximal, characteristic
17	C₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#479	C₂	1	1	yes	maximal, characteristic, complemented
23	C₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
24	C₇×#557	—	2	1	no	—
25	C₇×#557	—	2	1	no	—
26	C₇×#554	—	2	2	no	—
27	C₇×#554	—	2	1	no	—
28	C₇×#554	—	2	2	no	—
29	C₇×#554	—	2	1	no	—
30	C₇×#544	C₂²	1	1	yes	characteristic
31	C₇×#544	C₂²	1	1	yes	characteristic
32	C₇×#544	C₂²	1	1	yes	characteristic
33	C₇×#544	C₂²	1	2	yes	—
34	C₇×#544	C₂²	1	2	yes	—
35	C₇×#542	—	2	1	no	—
36	C₇×#542	C₂²	1	2	yes	—
37	C₇×#541	—	2	1	no	—
38	C₇×#541	C₂²	1	2	yes	—
39	C₇×#539	—	2	2	no	—
40	C₇×#537	C₂²	1	1	yes	characteristic
41	C₇×#536	C₂²	1	1	yes	characteristic
42	C₇×#536	C₂²	1	1	yes	characteristic
43	C₇×#533	—	2	1	no	—
44	C₇×#533	C₂²	1	2	yes	—
45	C₇×#533	C₂²	1	2	yes	—
46	C₇×#533	C₂²	1	1	yes	characteristic
47	C₇×#529	—	2	2	no	—
48	C₇×#529	—	2	1	no	—
49	C₇×#529	C₂²	1	2	yes	—
50	C₂×C₇×#125	C₂²	1	2	yes	—
51	C₂×C₇×#125	C₂²	1	1	yes	characteristic
52	C₇×#520	C₂²	1	1	yes	characteristic
53	C₇×#520	C₂²	1	1	yes	characteristic
54	C₄×C₇×#41	C₂²	1	1	yes	characteristic
55	C₄×C₇×#41	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
57	C₇×#501	C₂²	1	2	yes	—
58	C₇×#501	C₂²	1	2	yes	—
59	C₇×#501	C₂²	1	2	yes	—
60	C₇×#501	C₂²	1	2	yes	—
61	C₇×#500	C₂²	1	2	yes	—
62	C₇×#499	C₂²	1	2	yes	—
63	C₇×#499	C₂²	1	2	yes	—
64	C₇×#498	C₂²	1	2	yes	—
65	C₇×#491	C₂²	1	2	yes	—
66	C₇×#491	C₂²	1	2	yes	—
67	C₇×#489	C₂²	1	2	yes	—
68	C₇×#489	C₂²	1	2	yes	—
69	C₇×#488	C₂²	1	2	yes	—
70	C₇×#488	C₂²	1	2	yes	—
71	C₇×#487	C₂²	1	2	yes	—
72	C₇×#487	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×#485	C₂²	1	2	yes	—
77	C₇×#485	C₂²	1	2	yes	—
78	C₇×#485	C₂²	1	2	yes	—
79	C₇×#484	C₂²	1	2	yes	—
80	C₇×#484	C₂²	1	2	yes	—
81	C₇×#484	C₂²	1	2	yes	—
82	C₇×#483	C₂²	1	2	yes	—
83	C₇×#483	C₂²	1	2	yes	—
84	C₇×#483	C₂²	1	2	yes	—
85	C₇×#482	C₂²	1	2	yes	—
86	C₇×#482	C₂²	1	2	yes	—
87	C₇×#481	C₂²	1	2	yes	—
88	C₇×#480	C₂²	1	2	yes	—
89	C₇×#479	C₂²	1	1	yes	characteristic
90	C₇×#479	C₂²	1	2	yes	—
91	C₇×#479	C₂²	1	2	yes	—
92	C₇×#479	C₂²	1	2	yes	—
93	C₇×#479	C₂²	1	2	yes	—
94	C₇×#479	C₂²	1	1	yes	characteristic
95	C₇×#479	C₂²	1	2	yes	—
96	C₇×#479	C₂²	1	2	yes	—
97	C₇×#479	C₂²	1	2	yes	—
98	C₇×#479	C₂²	1	2	yes	—
99	C₇×#478	C₂²	1	1	yes	characteristic
100	C₇×#478	C₂²	1	2	yes	—
101	C₇×#478	C₂²	1	1	yes	characteristic
102	C₇×#478	C₂²	1	2	yes	—
103	C₇×#477	C₂²	1	1	yes	characteristic
104	C₇×#477	C₂²	1	2	yes	—
105	C₇×#476	C₂²	1	1	yes	characteristic
106	C₇×#475	C₂²	1	1	yes	characteristic
107	C₇×#475	C₂²	1	2	yes	—
108	C₇×#474	C₂²	1	1	yes	characteristic
109	C₇×#433	C₂²	1	2	yes	—
110	C₇×#433	C₂²	1	2	yes	—
111	C₇×#432	C₂²	1	2	yes	—
112	C₇×#431	C₂²	1	2	yes	—
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×#427	C₂²	1	1	yes	characteristic
118	C₇×#427	C₂²	1	1	yes	characteristic
119	C₂×C₇×#107	C₂²	1	1	yes	characteristic
120	C₂×C₇×#106	C₂²	1	1	yes	characteristic
121	C₇×#423	C₂²	1	1	yes	characteristic
122	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
123	C₇×#419	C₂²	1	1	yes	characteristic
124	C₇×#419	C₂²	1	1	yes	characteristic
125	C₇×#417	C₂²	1	1	yes	characteristic
126	C₇×#417	C₂²	1	1	yes	characteristic
127	C₇×#416	C₂²	1	1	yes	characteristic
128	C₇×#416	C₂²	1	1	yes	characteristic
129	C₂×C₇×#103	C₂²	1	1	yes	characteristic
130	C₂×C₇×#103	C₂²	1	1	yes	characteristic
131	C₇×#408	C₂²	1	1	yes	characteristic
132	C₇×#408	C₂²	1	1	yes	characteristic
133	C₇×#405	C₂²	1	1	yes	characteristic
134	C₇×#405	C₂²	1	1	yes	characteristic
135	#60891	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	C₂³	1	1	yes	characteristic
137	C₂×C₇×#41	C₂³	1	1	yes	characteristic
138	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
139	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
140	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
141	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
142	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
143	C₇×C₄⋊Q₈	—	2	1	no	—
144	C₇×C₄⋊Q₈	—	2	1	no	—
145	C₇×C₄⋊Q₈	—	2	1	no	—
146	C₇×C₄⋊Q₈	—	2	2	no	—
147	C₇×C₄⋊Q₈	—	2	1	no	—
148	C₇×C₄⋊Q₈	—	2	2	no	—
149	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
150	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
151	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
152	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
153	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
154	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₇×#126	—	2	2	no	—
156	C₇×#126	—	2	2	no	—
157	C₇×#126	—	2	2	no	—
158	C₇×#126	—	2	2	no	—
159	C₇×#125	—	2	2	no	—
160	C₇×#125	—	2	1	no	—
161	C₇×#125	—	2	2	no	—
162	C₇×#125	—	2	1	no	—
163	C₇×#125	—	2	2	no	—
164	C₇×#125	—	2	1	no	—
165	C₇×#125	—	2	2	no	—
166	C₇×#125	—	2	1	no	—
167	C₇×#125	—	2	2	no	—
168	C₇×#125	—	2	1	no	—
169	C₇×#125	—	2	2	no	—
170	C₇×#125	—	2	2	no	—
171	C₇×#125	C₂³	1	1	yes	characteristic
172	C₇×#125	C₂³	1	2	yes	—
173	C₇×#125	C₂³	1	2	yes	—
174	C₇×#125	C₂³	1	1	yes	characteristic
175	C₇×#125	C₂³	1	2	yes	—
176	C₇×#125	C₂³	1	2	yes	—
177	C₇×#125	C₂³	1	2	yes	—
178	C₇×#124	—	2	1	no	—
179	C₇×#124	—	2	2	no	—
180	C₇×#124	C₂³	1	2	yes	—
181	C₇×#123	—	2	2	no	—
182	C₇×#123	—	2	2	no	—
183	C₇×#123	—	2	2	no	—
184	C₇×#123	—	2	2	no	—
185	C₇×C₂²⋊Q₈	—	2	1	no	—
186	C₇×C₂²⋊Q₈	—	2	2	no	—
187	C₇×C₂²⋊Q₈	—	2	1	no	—
188	C₇×C₂²⋊Q₈	—	2	1	no	—
189	C₇×C₂²⋊Q₈	—	2	2	no	—
190	C₇×C₂²⋊Q₈	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	1	no	—
192	C₇×C₂²⋊Q₈	—	2	1	no	—
193	C₇×C₂²⋊Q₈	—	2	2	no	—
194	C₇×C₂²⋊Q₈	—	2	2	no	—
195	C₇×C₂²⋊Q₈	—	2	2	no	—
196	C₇×C₂²⋊Q₈	—	2	2	no	—
197	C₇×C₂²⋊Q₈	—	2	2	no	—
198	C₇×C₂²⋊Q₈	—	2	2	no	—
199	C₇×C₂²⋊Q₈	—	2	2	no	—
200	C₇×C₂²⋊Q₈	—	2	2	no	—
201	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
202	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
203	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
204	C₇×#121	—	2	2	no	—
205	C₇×#121	—	2	1	no	—
206	C₇×#121	C₂³	1	2	yes	—
207	C₄×C₇×Q₈	—	2	1	no	—
208	C₄×C₇×Q₈	—	2	1	no	—
209	C₄×C₇×Q₈	—	2	1	no	—
210	C₄×C₇×Q₈	—	2	1	no	—
211	C₄×C₇×Q₈	—	2	2	no	—
212	C₄×C₇×Q₈	—	2	1	no	—
213	C₄×C₇×Q₈	—	2	2	no	—
214	C₄×C₇×Q₈	—	2	1	no	—
215	C₄×C₇×Q₈	—	2	2	no	—
216	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
217	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
218	C₄×C₇×Q₈	C₂³	1	2	yes	—
219	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
220	C₄×C₇×Q₈	C₂³	1	2	yes	—
221	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
222	C₄×C₇×D₄	—	2	2	no	—
223	C₄×C₇×D₄	—	2	2	no	—
224	C₄×C₇×D₄	—	2	1	no	—
225	C₄×C₇×D₄	—	2	1	no	—
226	C₄×C₇×D₄	—	2	1	no	—
227	C₄×C₇×D₄	—	2	1	no	—
228	C₄×C₇×D₄	—	2	2	no	—
229	C₄×C₇×D₄	D₄	1	1	yes	characteristic
230	C₄×C₇×D₄	D₄	1	2	yes	—
231	C₄×C₇×D₄	D₄	1	2	yes	—
232	C₄×C₇×D₄	D₄	1	1	yes	characteristic
233	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
234	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
235	C₇×#117	—	2	2	no	—
236	C₇×#117	—	2	1	no	—
237	C₇×#117	—	2	2	no	—
238	C₇×#117	C₂³	1	2	yes	—
239	C₇×#117	C₂³	1	2	yes	—
240	C₇×#117	C₂³	1	1	yes	characteristic
241	C₇×#117	C₂³	1	1	yes	characteristic
242	C₇×#117	C₂³	1	1	yes	characteristic
243	C₇×#117	C₂³	1	1	yes	characteristic
244	C₇×#117	C₂³	1	2	yes	—
245	C₂×C₇×C₄⋊C₄	—	2	1	no	—
246	C₂×C₇×C₄⋊C₄	—	2	1	no	—
247	C₂×C₇×C₄⋊C₄	—	2	1	no	—
248	C₂×C₇×C₄⋊C₄	—	2	2	no	—
249	C₂×C₇×C₄⋊C₄	—	2	2	no	—
250	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
251	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
252	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
253	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
254	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
255	C₂×C₄²×C₇	—	2	1	no	—
256	C₂×C₄²×C₇	—	2	1	no	—
257	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
258	C₂×C₄²×C₇	C₂³	1	2	yes	—
259	C₇×#107	C₂³	1	1	yes	characteristic
260	C₇×#107	C₂³	1	1	yes	characteristic
261	C₇×#107	C₂³	1	1	yes	characteristic
262	C₇×#107	C₂³	1	1	yes	characteristic
263	C₇×#107	C₂³	1	2	yes	—
264	C₇×#107	C₂³	1	2	yes	—
265	C₇×#107	C₂³	1	2	yes	—
266	C₇×#107	C₂³	1	2	yes	—
267	C₇×#107	C₂³	1	2	yes	—
268	C₇×#107	C₂³	1	2	yes	—
269	C₇×#106	C₂³	1	1	yes	characteristic
270	C₇×#106	C₂³	1	1	yes	characteristic
271	C₇×#106	C₂³	1	2	yes	—
272	C₇×#106	C₂³	1	2	yes	—
273	C₇×#106	C₂³	1	1	yes	characteristic
274	C₇×#106	C₂³	1	1	yes	characteristic
275	C₇×#106	C₂³	1	2	yes	—
276	C₇×#106	C₂³	1	2	yes	—
277	C₇×#106	C₂³	1	2	yes	—
278	C₇×#106	C₂³	1	2	yes	—
279	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
280	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
283	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
284	C₇×C₄⋊C₈	C₂³	1	2	yes	—
285	C₇×#103	C₂³	1	2	yes	—
286	C₇×#103	C₂³	1	1	yes	characteristic
287	C₇×#103	C₂³	1	1	yes	characteristic
288	C₇×#103	C₂³	1	2	yes	—
289	C₇×#103	C₂³	1	1	yes	characteristic
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#103	C₂³	1	1	yes	characteristic
292	C₇×#103	C₂³	1	2	yes	—
293	C₇×#103	C₂³	1	2	yes	—
294	C₇×#103	C₂³	1	2	yes	—
295	C₇×#103	C₂³	1	2	yes	—
296	C₇×#103	C₂³	1	2	yes	—
297	C₇×#103	C₂³	1	2	yes	—
298	C₇×#103	C₂³	1	2	yes	—
299	C₇×#102	C₂³	1	1	yes	characteristic
300	C₇×#102	C₂³	1	1	yes	characteristic
301	C₇×#102	C₂³	1	1	yes	characteristic
302	C₇×#102	C₂³	1	1	yes	characteristic
303	C₇×#102	C₂³	1	2	yes	—
304	C₇×#102	C₂³	1	2	yes	—
305	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
306	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
307	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
308	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
309	C₇×#97	C₂³	1	2	yes	—
310	C₇×#97	C₂³	1	2	yes	—
311	C₄×C₇×C₈	C₂³	1	2	yes	—
312	C₄×C₇×C₈	C₂³	1	2	yes	—
313	#3504	C₂×C₇	1	1	yes	characteristic, complemented
314	#3461	C₂×C₇	1	1	yes	characteristic
315	#3244	C₂×C₇	1	2	yes	complemented
316	#3243	C₂×C₇	1	2	yes	complemented
317	#3242	C₂×C₇	1	2	yes	complemented
318	#3242	C₂×C₇	1	2	yes	complemented
319	#3240	C₂×C₇	1	2	yes	complemented
320	#3236	C₂×C₇	1	2	yes	complemented
321	#3232	C₂×C₇	1	2	yes	complemented
322	#3231	C₂×C₇	1	2	yes	complemented
323	#3164	C₂×C₇	1	1	yes	characteristic, complemented
324	#3163	C₂×C₇	1	1	yes	characteristic, complemented
325	#3137	C₂×C₇	1	1	yes	characteristic, complemented
326	#3137	C₂×C₇	1	1	yes	characteristic, complemented
327	#3099	C₂×C₇	1	1	yes	characteristic
328	#3098	C₂×C₇	1	1	yes	characteristic
329	#3097	C₂×C₇	1	1	yes	characteristic, complemented
330	#3097	C₂×C₇	1	1	yes	characteristic, complemented
331	#3080	C₂×C₇	1	1	yes	characteristic, complemented
332	#3078	C₂×C₇	1	1	yes	characteristic, complemented
333	#3076	C₂×C₇	1	1	yes	characteristic, complemented
334	C₂×#479	C₂×C₇	1	1	yes	characteristic, complemented
335	#2925	C₂×C₇	1	1	yes	characteristic, complemented
336	C₇×#41	—	2	2	no	—
337	C₇×#41	—	2	2	no	—
338	C₇×#41	—	2	2	no	—
339	C₇×#41	—	2	2	no	—
340	C₂×C₇×Q₈	—	2	1	no	—
341	C₂×C₇×Q₈	—	2	2	no	—
342	C₂×C₇×Q₈	—	2	1	no	—
343	C₂×C₇×Q₈	—	2	1	no	—
344	C₂×C₇×Q₈	—	2	2	no	—
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	—	2	2	no	—
348	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
349	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
350	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
351	C₂×C₇×D₄	—	2	1	no	—
352	C₂×C₇×D₄	—	2	2	no	—
353	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
354	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
355	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₇	—	2	1	no	—
357	C₂²×C₄×C₇	—	2	1	no	—
358	C₂²×C₄×C₇	—	2	2	no	—
359	C₂²×C₄×C₇	—	2	2	no	—
360	C₂²×C₄×C₇	—	2	1	no	—
361	C₂²×C₄×C₇	—	2	1	no	—
362	C₂²×C₄×C₇	—	2	1	no	—
363	C₂²×C₄×C₇	—	2	1	no	—
364	C₂²×C₄×C₇	—	2	1	no	—
365	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
366	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
367	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
368	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
369	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
371	C₇×M₁₆	—	2	2	no	—
372	C₇×M₁₆	—	2	2	no	—
373	C₂×C₇×C₈	—	2	2	no	—
374	C₂×C₇×C₈	—	2	2	no	—
375	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
376	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
377	C₂×C₇×C₈	C₂⁴	1	2	yes	—
378	C₂×C₇×C₈	C₂⁴	1	2	yes	—
379	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
380	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
381	C₇×C₄⋊C₄	—	2	2	no	—
382	C₇×C₄⋊C₄	—	2	1	no	—
383	C₇×C₄⋊C₄	—	2	2	no	—
384	C₇×C₄⋊C₄	—	2	1	no	—
385	C₇×C₄⋊C₄	—	2	2	no	—
386	C₇×C₄⋊C₄	—	2	2	no	—
387	C₇×C₄⋊C₄	—	2	2	no	—
388	C₇×C₄⋊C₄	—	2	2	no	—
389	C₇×C₄⋊C₄	—	2	2	no	—
390	C₇×C₄⋊C₄	—	2	2	no	—
391	C₇×C₄⋊C₄	—	2	2	no	—
392	C₇×C₄⋊C₄	—	2	2	no	—
393	C₇×C₄⋊C₄	—	2	2	no	—
394	C₇×C₄⋊C₄	—	2	2	no	—
395	C₇×C₄⋊C₄	—	2	1	no	—
396	C₇×C₄⋊C₄	—	2	1	no	—
397	C₇×C₄⋊C₄	—	2	1	no	—
398	C₇×C₄⋊C₄	—	2	1	no	—
399	C₇×C₄⋊C₄	—	2	1	no	—
400	C₇×C₄⋊C₄	—	2	2	no	—
401	C₇×C₄⋊C₄	—	2	2	no	—
402	C₇×C₄⋊C₄	—	2	2	no	—
403	C₇×C₄⋊C₄	—	2	2	no	—
404	C₇×C₄⋊C₄	—	2	2	no	—
405	C₇×C₄⋊C₄	—	2	1	no	—
406	C₇×C₄⋊C₄	—	2	1	no	—
407	C₇×C₄⋊C₄	—	2	2	no	—
408	C₇×C₄⋊C₄	—	2	1	no	—
409	C₇×C₄⋊C₄	—	2	1	no	—
410	C₇×C₄⋊C₄	—	2	2	no	—
411	C₇×C₄⋊C₄	—	2	2	no	—
412	C₇×C₄⋊C₄	—	2	2	no	—
413	C₇×C₄⋊C₄	—	2	2	no	—
414	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
415	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
416	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
417	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
418	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
419	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
420	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
422	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
423	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
424	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
425	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
426	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
427	C₇×C₂²⋊C₄	—	2	2	no	—
428	C₇×C₂²⋊C₄	—	2	2	no	—
429	C₇×C₂²⋊C₄	—	2	2	no	—
430	C₇×C₂²⋊C₄	—	2	2	no	—
431	C₇×C₂²⋊C₄	—	2	1	no	—
432	C₇×C₂²⋊C₄	—	2	1	no	—
433	C₇×C₂²⋊C₄	—	2	1	no	—
434	C₇×C₂²⋊C₄	—	2	2	no	—
435	C₇×C₂²⋊C₄	—	2	1	no	—
436	C₇×C₂²⋊C₄	—	2	1	no	—
437	C₇×C₂²⋊C₄	—	2	2	no	—
438	C₇×C₂²⋊C₄	—	2	2	no	—
439	C₇×C₂²⋊C₄	—	2	2	no	—
440	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
441	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
442	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
443	C₄²×C₇	—	2	2	no	—
444	C₄²×C₇	—	2	1	no	—
445	C₄²×C₇	—	2	1	no	—
446	C₄²×C₇	—	2	1	no	—
447	C₄²×C₇	—	2	2	no	—
448	C₄²×C₇	—	2	2	no	—
449	C₄²×C₇	—	2	2	no	—
450	C₄²×C₇	—	2	1	no	—
451	C₄²×C₇	—	2	1	no	—
452	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
453	C₄²×C₇	C₂×D₄	1	2	yes	—
454	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₇	C₂×D₄	1	2	yes	—
456	C₄²×C₇	C₂⁴	1	2	yes	—
457	C₄²×C₇	C₂⁴	1	1	yes	characteristic
458	C₄²×C₇	C₂⁴	1	1	yes	characteristic
459	#557	—	2	1	no	—
460	#557	—	2	1	no	—
461	#554	—	2	2	no	—
462	#554	—	2	1	no	—
463	#554	—	2	2	no	—
464	#554	—	2	1	no	—
465	#544	C₂²×C₇	1	1	yes	characteristic
466	#544	C₂²×C₇	1	1	yes	characteristic
467	#544	C₂²×C₇	1	1	yes	characteristic
468	#544	C₂²×C₇	1	2	yes	—
469	#544	C₂²×C₇	1	2	yes	—
470	#542	—	2	1	no	—
471	#542	C₂²×C₇	1	2	yes	—
472	#541	—	2	1	no	—
473	#541	C₂²×C₇	1	2	yes	—
474	#539	—	2	2	no	—
475	#537	C₂²×C₇	1	1	yes	characteristic
476	#536	C₂²×C₇	1	1	yes	characteristic
477	#536	C₂²×C₇	1	1	yes	characteristic
478	#533	—	2	1	no	—
479	#533	C₂²×C₇	1	2	yes	—
480	#533	C₂²×C₇	1	1	yes	characteristic
481	#533	C₂²×C₇	1	2	yes	—
482	#529	—	2	2	no	—
483	#529	—	2	1	no	—
484	#529	C₂²×C₇	1	2	yes	—
485	C₂×#125	C₂²×C₇	1	1	yes	characteristic
486	C₂×#125	C₂²×C₇	1	2	yes	—
487	#520	C₂²×C₇	1	1	yes	characteristic
488	#520	C₂²×C₇	1	1	yes	characteristic
489	C₄×#41	C₂²×C₇	1	1	yes	characteristic
490	C₄×#41	C₂²×C₇	1	1	yes	characteristic
491	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
492	#501	C₂²×C₇	1	2	yes	—
493	#501	C₂²×C₇	1	2	yes	—
494	#501	C₂²×C₇	1	2	yes	—
495	#501	C₂²×C₇	1	2	yes	—
496	#500	C₂²×C₇	1	2	yes	—
497	#499	C₂²×C₇	1	2	yes	—
498	#499	C₂²×C₇	1	2	yes	—
499	#498	C₂²×C₇	1	2	yes	—
500	#491	C₂²×C₇	1	2	yes	—
501	#491	C₂²×C₇	1	2	yes	—
502	#489	C₂²×C₇	1	2	yes	—
503	#489	C₂²×C₇	1	2	yes	—
504	#488	C₂²×C₇	1	2	yes	—
505	#488	C₂²×C₇	1	2	yes	—
506	#487	C₂²×C₇	1	2	yes	—
507	#487	C₂²×C₇	1	2	yes	—
508	#485	C₂²×C₇	1	2	yes	—
509	#485	C₂²×C₇	1	2	yes	—
510	#485	C₂²×C₇	1	2	yes	—
511	#485	C₂²×C₇	1	2	yes	—
512	#485	C₂²×C₇	1	2	yes	—
513	#485	C₂²×C₇	1	2	yes	—
514	#484	C₂²×C₇	1	2	yes	—
515	#484	C₂²×C₇	1	2	yes	—
516	#484	C₂²×C₇	1	2	yes	—
517	#483	C₂²×C₇	1	2	yes	—
518	#483	C₂²×C₇	1	2	yes	—
519	#483	C₂²×C₇	1	2	yes	—
520	#482	C₂²×C₇	1	2	yes	—
521	#482	C₂²×C₇	1	2	yes	—
522	#481	C₂²×C₇	1	2	yes	—
523	#480	C₂²×C₇	1	2	yes	—
524	#479	C₂²×C₇	1	2	yes	—
525	#479	C₂²×C₇	1	2	yes	—
526	#479	C₂²×C₇	1	2	yes	—
527	#479	C₂²×C₇	1	2	yes	—
528	#479	C₂²×C₇	1	1	yes	characteristic
529	#479	C₂²×C₇	1	1	yes	characteristic
530	#479	C₂²×C₇	1	2	yes	—
531	#479	C₂²×C₇	1	2	yes	—
532	#479	C₂²×C₇	1	2	yes	—
533	#479	C₂²×C₇	1	2	yes	—
534	#478	C₂²×C₇	1	1	yes	characteristic
535	#478	C₂²×C₇	1	1	yes	characteristic
536	#478	C₂²×C₇	1	2	yes	—
537	#478	C₂²×C₇	1	2	yes	—
538	#477	C₂²×C₇	1	1	yes	characteristic
539	#477	C₂²×C₇	1	2	yes	—
540	#476	C₂²×C₇	1	1	yes	characteristic
541	#475	C₂²×C₇	1	1	yes	characteristic
542	#475	C₂²×C₇	1	2	yes	—
543	#474	C₂²×C₇	1	1	yes	characteristic
544	#433	C₂²×C₇	1	2	yes	—
545	#433	C₂²×C₇	1	2	yes	—
546	#432	C₂²×C₇	1	2	yes	—
547	#431	C₂²×C₇	1	2	yes	—
548	#428	C₂²×C₇	1	1	yes	characteristic
549	#428	C₂²×C₇	1	1	yes	characteristic
550	#428	C₂²×C₇	1	1	yes	characteristic
551	#428	C₂²×C₇	1	1	yes	characteristic
552	#427	C₂²×C₇	1	1	yes	characteristic
553	#427	C₂²×C₇	1	1	yes	characteristic
554	C₂×#107	C₂²×C₇	1	1	yes	characteristic
555	C₂×#106	C₂²×C₇	1	1	yes	characteristic
556	#423	C₂²×C₇	1	1	yes	characteristic
557	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
558	#419	C₂²×C₇	1	1	yes	characteristic
559	#419	C₂²×C₇	1	1	yes	characteristic
560	#417	C₂²×C₇	1	1	yes	characteristic
561	#417	C₂²×C₇	1	1	yes	characteristic
562	#416	C₂²×C₇	1	1	yes	characteristic
563	#416	C₂²×C₇	1	1	yes	characteristic
564	C₂×#103	C₂²×C₇	1	1	yes	characteristic
565	C₂×#103	C₂²×C₇	1	1	yes	characteristic
566	#408	C₂²×C₇	1	1	yes	characteristic
567	#408	C₂²×C₇	1	1	yes	characteristic
568	#405	C₂²×C₇	1	1	yes	characteristic
569	#405	C₂²×C₇	1	1	yes	characteristic
570	C₂³×C₇	—	2	1	no	—
571	C₂³×C₇	C₂²×D₄	1	2	yes	—
572	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
573	C₇×Q₈	—	2	2	no	—
574	C₇×Q₈	—	2	2	no	—
575	C₇×Q₈	—	2	2	no	—
576	C₇×Q₈	—	2	1	no	—
577	C₇×Q₈	—	2	1	no	—
578	C₇×Q₈	—	4	2	no	—
579	C₇×Q₈	—	8	1	no	—
580	C₇×Q₈	—	8	2	no	—
581	C₇×Q₈	—	8	2	no	—
582	C₇×Q₈	—	8	1	no	—
583	C₇×Q₈	—	8	2	no	—
584	C₇×D₄	—	2	4	no	—
585	C₇×D₄	—	2	2	no	—
586	C₇×D₄	—	2	1	no	—
587	C₇×D₄	—	2	1	no	—
588	C₇×D₄	—	4	2	no	—
589	C₇×D₄	—	8	2	no	—
590	C₂×C₄×C₇	—	2	2	no	—
591	C₂×C₄×C₇	—	2	2	no	—
592	C₂×C₄×C₇	—	2	1	no	—
593	C₂×C₄×C₇	—	2	1	no	—
594	C₂×C₄×C₇	—	2	1	no	—
595	C₂×C₄×C₇	—	2	2	no	—
596	C₂×C₄×C₇	—	2	1	no	—
597	C₂×C₄×C₇	—	2	1	no	—
598	C₂×C₄×C₇	—	2	2	no	—
599	C₂×C₄×C₇	—	2	2	no	—
600	C₂×C₄×C₇	—	2	1	no	—
601	C₂×C₄×C₇	—	2	2	no	—
602	C₂×C₄×C₇	—	2	1	no	—
603	C₂×C₄×C₇	—	4	1	no	—
604	C₂×C₄×C₇	—	4	2	no	—
605	C₂×C₄×C₇	—	4	1	no	—
606	C₂×C₄×C₇	—	4	2	no	—
607	C₂×C₄×C₇	—	4	2	no	—
608	C₂×C₄×C₇	—	4	2	no	—
609	C₂×C₄×C₇	—	4	2	no	—
610	C₂×C₄×C₇	—	8	1	no	—
611	C₂×C₄×C₇	—	8	1	no	—
612	C₂×C₄×C₇	—	8	2	no	—
613	C₂×C₄×C₇	—	8	1	no	—
614	C₂×C₄×C₇	—	8	1	no	—
615	C₂×C₄×C₇	—	8	2	no	—
616	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
617	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
618	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
619	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
620	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
621	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
622	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
623	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
624	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
625	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
626	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
627	C₇×C₈	—	2	1	no	—
628	C₇×C₈	—	2	1	no	—
629	C₇×C₈	—	2	1	no	—
630	C₇×C₈	—	2	1	no	—
631	C₇×C₈	—	2	2	no	—
632	C₇×C₈	—	2	2	no	—
633	C₂×#41	C₂³×C₇	1	1	yes	characteristic
634	C₂×#41	C₂³×C₇	1	1	yes	characteristic
635	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
636	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
637	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
638	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
639	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
640	C₄⋊Q₈	—	2	1	no	—
641	C₄⋊Q₈	—	2	1	no	—
642	C₄⋊Q₈	—	2	1	no	—
643	C₄⋊Q₈	—	2	2	no	—
644	C₄⋊Q₈	—	2	1	no	—
645	C₄⋊Q₈	—	2	2	no	—
646	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
647	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
648	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
649	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
650	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
651	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
652	#126	—	2	2	no	—
653	#126	—	2	2	no	—
654	#126	—	2	2	no	—
655	#126	—	2	2	no	—
656	#125	—	2	2	no	—
657	#125	—	2	1	no	—
658	#125	—	2	2	no	—
659	#125	—	2	1	no	—
660	#125	—	2	2	no	—
661	#125	—	2	1	no	—
662	#125	—	2	2	no	—
663	#125	—	2	1	no	—
664	#125	—	2	1	no	—
665	#125	—	2	2	no	—
666	#125	—	2	2	no	—
667	#125	—	2	2	no	—
668	#125	C₂³×C₇	1	2	yes	—
669	#125	C₂³×C₇	1	1	yes	characteristic
670	#125	C₂³×C₇	1	2	yes	—
671	#125	C₂³×C₇	1	2	yes	—
672	#125	C₂³×C₇	1	2	yes	—
673	#125	C₂³×C₇	1	2	yes	—
674	#125	C₂³×C₇	1	1	yes	characteristic
675	#124	—	2	1	no	—
676	#124	—	2	2	no	—
677	#124	C₂³×C₇	1	2	yes	—
678	#123	—	2	2	no	—
679	#123	—	2	2	no	—
680	#123	—	2	2	no	—
681	#123	—	2	2	no	—
682	C₂²⋊Q₈	—	2	1	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	1	no	—
685	C₂²⋊Q₈	—	2	1	no	—
686	C₂²⋊Q₈	—	2	2	no	—
687	C₂²⋊Q₈	—	2	2	no	—
688	C₂²⋊Q₈	—	2	1	no	—
689	C₂²⋊Q₈	—	2	1	no	—
690	C₂²⋊Q₈	—	2	2	no	—
691	C₂²⋊Q₈	—	2	2	no	—
692	C₂²⋊Q₈	—	2	2	no	—
693	C₂²⋊Q₈	—	2	2	no	—
694	C₂²⋊Q₈	—	2	2	no	—
695	C₂²⋊Q₈	—	2	2	no	—
696	C₂²⋊Q₈	—	2	2	no	—
697	C₂²⋊Q₈	—	2	2	no	—
698	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
699	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
700	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
701	#121	—	2	2	no	—
702	#121	—	2	1	no	—
703	#121	C₂³×C₇	1	2	yes	—
704	C₄×Q₈	—	2	1	no	—
705	C₄×Q₈	—	2	1	no	—
706	C₄×Q₈	—	2	1	no	—
707	C₄×Q₈	—	2	1	no	—
708	C₄×Q₈	—	2	2	no	—
709	C₄×Q₈	—	2	1	no	—
710	C₄×Q₈	—	2	1	no	—
711	C₄×Q₈	—	2	2	no	—
712	C₄×Q₈	—	2	2	no	—
713	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
714	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
715	C₄×Q₈	C₂³×C₇	1	2	yes	—
716	C₄×Q₈	C₂³×C₇	1	2	yes	—
717	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
718	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
719	C₄×D₄	—	2	2	no	—
720	C₄×D₄	—	2	2	no	—
721	C₄×D₄	—	2	1	no	—
722	C₄×D₄	—	2	1	no	—
723	C₄×D₄	—	2	1	no	—
724	C₄×D₄	—	2	1	no	—
725	C₄×D₄	—	2	2	no	—
726	C₄×D₄	C₇×D₄	1	1	yes	characteristic
727	C₄×D₄	C₇×D₄	1	2	yes	—
728	C₄×D₄	C₇×D₄	1	2	yes	—
729	C₄×D₄	C₇×D₄	1	1	yes	characteristic
730	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
731	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
732	#117	—	2	2	no	—
733	#117	—	2	1	no	—
734	#117	—	2	2	no	—
735	#117	C₂³×C₇	1	1	yes	characteristic
736	#117	C₂³×C₇	1	1	yes	characteristic
737	#117	C₂³×C₇	1	1	yes	characteristic
738	#117	C₂³×C₇	1	2	yes	—
739	#117	C₂³×C₇	1	2	yes	—
740	#117	C₂³×C₇	1	1	yes	characteristic
741	#117	C₂³×C₇	1	2	yes	—
742	C₂×C₄⋊C₄	—	2	1	no	—
743	C₂×C₄⋊C₄	—	2	1	no	—
744	C₂×C₄⋊C₄	—	2	1	no	—
745	C₂×C₄⋊C₄	—	2	2	no	—
746	C₂×C₄⋊C₄	—	2	2	no	—
747	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
748	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
749	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
750	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
751	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
752	C₂×C₄²	—	2	1	no	—
753	C₂×C₄²	—	2	1	no	—
754	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
755	C₂×C₄²	C₂³×C₇	1	2	yes	—
756	#107	C₂³×C₇	1	2	yes	—
757	#107	C₂³×C₇	1	2	yes	—
758	#107	C₂³×C₇	1	1	yes	characteristic
759	#107	C₂³×C₇	1	1	yes	characteristic
760	#107	C₂³×C₇	1	1	yes	characteristic
761	#107	C₂³×C₇	1	1	yes	characteristic
762	#107	C₂³×C₇	1	2	yes	—
763	#107	C₂³×C₇	1	2	yes	—
764	#107	C₂³×C₇	1	2	yes	—
765	#107	C₂³×C₇	1	2	yes	—
766	#106	C₂³×C₇	1	2	yes	—
767	#106	C₂³×C₇	1	2	yes	—
768	#106	C₂³×C₇	1	1	yes	characteristic
769	#106	C₂³×C₇	1	1	yes	characteristic
770	#106	C₂³×C₇	1	1	yes	characteristic
771	#106	C₂³×C₇	1	1	yes	characteristic
772	#106	C₂³×C₇	1	2	yes	—
773	#106	C₂³×C₇	1	2	yes	—
774	#106	C₂³×C₇	1	2	yes	—
775	#106	C₂³×C₇	1	2	yes	—
776	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
777	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
778	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
779	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
780	C₄⋊C₈	C₂³×C₇	1	2	yes	—
781	C₄⋊C₈	C₂³×C₇	1	2	yes	—
782	#103	C₂³×C₇	1	2	yes	—
783	#103	C₂³×C₇	1	2	yes	—
784	#103	C₂³×C₇	1	2	yes	—
785	#103	C₂³×C₇	1	2	yes	—
786	#103	C₂³×C₇	1	1	yes	characteristic
787	#103	C₂³×C₇	1	1	yes	characteristic
788	#103	C₂³×C₇	1	1	yes	characteristic
789	#103	C₂³×C₇	1	1	yes	characteristic
790	#103	C₂³×C₇	1	2	yes	—
791	#103	C₂³×C₇	1	2	yes	—
792	#103	C₂³×C₇	1	2	yes	—
793	#103	C₂³×C₇	1	2	yes	—
794	#103	C₂³×C₇	1	2	yes	—
795	#103	C₂³×C₇	1	2	yes	—
796	#102	C₂³×C₇	1	1	yes	characteristic
797	#102	C₂³×C₇	1	1	yes	characteristic
798	#102	C₂³×C₇	1	1	yes	characteristic
799	#102	C₂³×C₇	1	1	yes	characteristic
800	#102	C₂³×C₇	1	2	yes	—
801	#102	C₂³×C₇	1	2	yes	—
802	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
803	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
804	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
805	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
806	#97	C₂³×C₇	1	2	yes	—
807	#97	C₂³×C₇	1	2	yes	—
808	C₄×C₈	C₂³×C₇	1	2	yes	—
809	C₄×C₈	C₂³×C₇	1	2	yes	—
810	C₂²×C₇	—	2	1	no	—
811	C₂²×C₇	—	2	1	no	—
812	C₂²×C₇	—	2	2	no	—
813	C₂²×C₇	—	2	2	no	—
814	C₂²×C₇	—	2	2	no	—
815	C₂²×C₇	—	4	1	no	—
816	C₂²×C₇	—	4	1	no	—
817	C₂²×C₇	—	4	1	no	—
818	C₂²×C₇	#536	1	2	yes	—
819	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
820	C₄×C₇	—	2	1	no	—
821	C₄×C₇	—	2	1	no	—
822	C₄×C₇	—	2	2	no	—
823	C₄×C₇	—	2	1	no	—
824	C₄×C₇	—	2	1	no	—
825	C₄×C₇	—	2	2	no	—
826	C₄×C₇	—	2	2	no	—
827	C₄×C₇	—	4	2	no	—
828	C₄×C₇	—	4	1	no	—
829	C₄×C₇	—	4	2	no	—
830	C₄×C₇	—	4	1	no	—
831	C₄×C₇	—	4	1	no	—
832	C₄×C₇	—	4	1	no	—
833	C₄×C₇	—	4	2	no	—
834	C₄×C₇	—	4	1	no	—
835	C₄×C₇	—	4	1	no	—
836	C₄×C₇	—	4	1	no	—
837	C₄×C₇	—	4	2	no	—
838	C₄×C₇	#536	1	2	yes	—
839	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
840	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
841	#41	—	2	2	no	—
842	#41	—	2	2	no	—
843	#41	—	2	2	no	—
844	#41	—	2	2	no	—
845	C₂×Q₈	—	2	1	no	—
846	C₂×Q₈	—	2	2	no	—
847	C₂×Q₈	—	2	1	no	—
848	C₂×Q₈	—	2	1	no	—
849	C₂×Q₈	—	2	2	no	—
850	C₂×Q₈	—	2	2	no	—
851	C₂×Q₈	—	2	2	no	—
852	C₂×Q₈	—	2	2	no	—
853	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
854	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
855	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
856	C₂×D₄	—	2	1	no	—
857	C₂×D₄	—	2	2	no	—
858	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
859	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
860	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
861	C₂²×C₄	—	2	1	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	2	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	1	no	—
866	C₂²×C₄	—	2	1	no	—
867	C₂²×C₄	—	2	1	no	—
868	C₂²×C₄	—	2	1	no	—
869	C₂²×C₄	—	2	1	no	—
870	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
871	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
872	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
873	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
875	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
876	M₁₆	—	2	2	no	—
877	M₁₆	—	2	2	no	—
878	C₂×C₈	—	2	2	no	—
879	C₂×C₈	—	2	2	no	—
880	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
881	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
882	C₂×C₈	C₂⁴×C₇	1	2	yes	—
883	C₂×C₈	C₂⁴×C₇	1	2	yes	—
884	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
885	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
886	C₄⋊C₄	—	2	2	no	—
887	C₄⋊C₄	—	2	1	no	—
888	C₄⋊C₄	—	2	2	no	—
889	C₄⋊C₄	—	2	1	no	—
890	C₄⋊C₄	—	2	2	no	—
891	C₄⋊C₄	—	2	2	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
920	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
921	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
922	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
923	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
924	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
925	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
926	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
927	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
928	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
929	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
930	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
932	C₂²⋊C₄	—	2	2	no	—
933	C₂²⋊C₄	—	2	2	no	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	1	no	—
937	C₂²⋊C₄	—	2	1	no	—
938	C₂²⋊C₄	—	2	1	no	—
939	C₂²⋊C₄	—	2	2	no	—
940	C₂²⋊C₄	—	2	1	no	—
941	C₂²⋊C₄	—	2	1	no	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
946	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
947	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
948	C₄²	—	2	2	no	—
949	C₄²	—	2	1	no	—
950	C₄²	—	2	1	no	—
951	C₄²	—	2	1	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	2	1	no	—
956	C₄²	—	2	1	no	—
957	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
958	C₄²	C₂×C₇×D₄	1	2	yes	—
959	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
960	C₄²	C₂×C₇×D₄	1	2	yes	—
961	C₄²	C₂⁴×C₇	1	2	yes	—
962	C₄²	C₂⁴×C₇	1	1	yes	characteristic
963	C₄²	C₂⁴×C₇	1	1	yes	characteristic
964	C₂×C₇	—	2	2	no	—
965	C₂×C₇	—	4	2	no	—
966	C₂×C₇	—	8	1	no	—
967	C₂×C₇	C₂×#536	1	1	yes	characteristic
968	C₂×C₇	#3584	1	1	yes	characteristic
969	C₂×C₇	#3586	1	1	yes	characteristic
970	C₂³	—	2	1	no	—
971	C₂³	C₂²×C₇×D₄	1	2	yes	—
972	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
973	Q₈	—	2	2	no	—
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	2	1	no	—
977	Q₈	—	2	1	no	—
978	Q₈	—	4	2	no	—
979	Q₈	—	8	1	no	—
980	Q₈	—	8	2	no	—
981	Q₈	—	8	2	no	—
982	Q₈	—	8	1	no	—
983	Q₈	—	8	2	no	—
984	D₄	—	2	4	no	—
985	D₄	—	2	1	no	—
986	D₄	—	2	1	no	—
987	D₄	—	2	2	no	—
988	D₄	—	4	2	no	—
989	D₄	—	8	2	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	2	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	2	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	4	1	no	—
1004	C₂×C₄	—	4	2	no	—
1005	C₂×C₄	—	4	1	no	—
1006	C₂×C₄	—	4	2	no	—
1007	C₂×C₄	—	4	2	no	—
1008	C₂×C₄	—	4	2	no	—
1009	C₂×C₄	—	4	2	no	—
1010	C₂×C₄	—	8	1	no	—
1011	C₂×C₄	—	8	1	no	—
1012	C₂×C₄	—	8	2	no	—
1013	C₂×C₄	—	8	1	no	—
1014	C₂×C₄	—	8	1	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1017	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1018	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1019	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1020	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1021	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1022	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1023	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1024	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1025	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1026	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	2	no	—
1032	C₈	—	2	2	no	—
1033	C₇	#60891	1	1	yes	characteristic, direct product factor, Sylow
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	2	no	—
1037	C₂²	—	2	2	no	—
1038	C₂²	—	2	2	no	—
1039	C₂²	—	4	1	no	—
1040	C₂²	—	4	1	no	—
1041	C₂²	—	4	1	no	—
1042	C₂²	C₇×#536	1	2	yes	—
1043	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1044	C₄	—	2	1	no	—
1045	C₄	—	2	1	no	—
1046	C₄	—	2	2	no	—
1047	C₄	—	2	1	no	—
1048	C₄	—	2	1	no	—
1049	C₄	—	2	2	no	—
1050	C₄	—	2	2	no	—
1051	C₄	—	4	2	no	—
1052	C₄	—	4	1	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	1	no	—
1055	C₄	—	4	1	no	—
1056	C₄	—	4	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	2	no	—
1062	C₄	C₇×#536	1	2	yes	—
1063	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1064	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1065	C₂	—	2	2	no	—
1066	C₂	—	4	2	no	—
1067	C₂	—	8	1	no	—
1068	C₂	C₂×C₇×#536	1	1	yes	characteristic
1069	C₂	C₇×#3584	1	1	yes	characteristic
1070	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×#537	C₂²
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×#3504	C₂	semidirect
3. C₇×#3244	C₂	semidirect
4. C₇×#3243	C₂	semidirect
5. C₇×#3242	C₂	semidirect
6. C₇×#3242	C₂	semidirect
7. C₇×#3240	C₂	semidirect
8. C₇×#3236	C₂	semidirect
9. C₇×#3232	C₂	semidirect
10. C₇×#3231	C₂	semidirect
11. C₇×#3164	C₂	semidirect
12. C₇×#3163	C₂	semidirect
13. C₇×#3137	C₂	semidirect
14. C₇×#3137	C₂	semidirect
17. C₇×#3097	C₂	semidirect
18. C₇×#3097	C₂	semidirect
19. C₇×#3080	C₂	semidirect
20. C₇×#3078	C₂	semidirect
21. C₇×#3076	C₂	semidirect
22. C₂×C₇×#479	C₂	semidirect
23. C₇×#2925	C₂	semidirect
135. #60891	C₇	direct (N × H)
313. #3504	C₂×C₇	semidirect
315. #3244	C₂×C₇	semidirect
316. #3243	C₂×C₇	semidirect
317. #3242	C₂×C₇	semidirect
318. #3242	C₂×C₇	semidirect
319. #3240	C₂×C₇	semidirect
320. #3236	C₂×C₇	semidirect
321. #3232	C₂×C₇	semidirect
322. #3231	C₂×C₇	semidirect
323. #3164	C₂×C₇	semidirect
324. #3163	C₂×C₇	semidirect
325. #3137	C₂×C₇	semidirect
326. #3137	C₂×C₇	semidirect
329. #3097	C₂×C₇	semidirect
330. #3097	C₂×C₇	semidirect
331. #3080	C₂×C₇	semidirect
332. #3078	C₂×C₇	semidirect
333. #3076	C₂×C₇	semidirect
334. C₂×#479	C₂×C₇	semidirect
335. #2925	C₂×C₇	semidirect
1033. C₇	#60891	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×#3504	2
C₇×#3461	2
C₇×#3244	2
C₇×#3243	2
C₇×#3242	2
C₇×#3240	2
C₇×#3236	2
C₇×#3232	2
C₇×#3231	2
C₇×#3164	2
C₇×#3163	2
C₇×#3137	2
C₇×#3099	2
C₇×#3098	2
C₇×#3097	2
C₇×#3080	2
C₇×#3078	2
C₇×#3076	2
C₂×C₇×#479	2
C₇×#2925	2
#60891	7

Subgroups — C7×#60891 #13238107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60891 #13238107