Subgroups — C₇×#60890 #13238106

Order 1792.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1100 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×#3460	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×#3241	C₂	1	2	yes	maximal, complemented
6	C₇×#3241	C₂	1	2	yes	maximal, complemented
7	C₇×#3240	C₂	1	2	yes	maximal, complemented
8	C₇×#3234	C₂	1	2	yes	maximal, complemented
9	C₇×#3232	C₂	1	2	yes	maximal, complemented
10	C₇×#3228	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×#3136	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3136	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3099	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
18	C₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
19	C₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₇×#478	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	2	no	—
28	C₇×#554	—	2	1	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	complemented
34	C₇×#544	C₂²	1	2	yes	complemented
35	C₇×#542	—	2	1	no	—
36	C₇×#542	C₂²	1	2	yes	—
37	C₇×#540	—	2	1	no	—
38	C₇×#540	C₂²	1	2	yes	—
39	C₇×#538	—	2	2	no	—
40	C₇×#537	C₂²	1	1	yes	characteristic
41	C₇×#535	C₂²	1	1	yes	characteristic
42	C₇×#535	C₂²	1	1	yes	characteristic
43	C₇×#533	C₂²	1	1	yes	characteristic
44	C₇×#533	C₂²	1	2	yes	complemented
45	C₇×#532	—	2	1	no	—
46	C₇×#532	C₂²	1	2	yes	—
47	C₇×#529	—	2	1	no	—
48	C₇×#529	C₂²	1	2	yes	—
49	C₂×C₇×#125	C₂²	1	1	yes	characteristic
50	C₂×C₇×#125	C₂²	1	2	yes	complemented
51	C₇×#525	—	2	2	no	—
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×D₄	C₂²	1	1	yes	characteristic
57	C₇×#501	C₂²	1	2	yes	complemented
58	C₇×#501	C₂²	1	2	yes	complemented
59	C₇×#501	C₂²	1	2	yes	complemented
60	C₇×#501	C₂²	1	2	yes	complemented
61	C₇×#500	C₂²	1	2	yes	complemented
62	C₇×#499	C₂²	1	2	yes	complemented
63	C₇×#499	C₂²	1	2	yes	complemented
64	C₇×#498	C₂²	1	2	yes	complemented
65	C₇×#490	C₂²	1	2	yes	—
66	C₇×#490	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×#486	C₂²	1	2	yes	—
72	C₇×#486	C₂²	1	2	yes	—
73	C₇×#485	C₂²	1	2	yes	complemented
74	C₇×#485	C₂²	1	2	yes	complemented
75	C₇×#484	C₂²	1	2	yes	complemented
76	C₇×#483	C₂²	1	2	yes	complemented
77	C₇×#482	C₂²	1	2	yes	—
78	C₇×#482	C₂²	1	2	yes	—
79	C₇×#482	C₂²	1	2	yes	—
80	C₇×#482	C₂²	1	2	yes	—
81	C₇×#482	C₂²	1	2	yes	complemented
82	C₇×#482	C₂²	1	2	yes	complemented
83	C₇×#481	C₂²	1	2	yes	—
84	C₇×#481	C₂²	1	2	yes	—
85	C₇×#481	C₂²	1	2	yes	complemented
86	C₇×#480	C₂²	1	2	yes	—
87	C₇×#480	C₂²	1	2	yes	—
88	C₇×#480	C₂²	1	2	yes	complemented
89	C₇×#479	C₂²	1	1	yes	characteristic, complemented
90	C₇×#479	C₂²	1	2	yes	complemented
91	C₇×#479	C₂²	1	1	yes	characteristic, complemented
92	C₇×#479	C₂²	1	2	yes	complemented
93	C₇×#478	C₂²	1	2	yes	—
94	C₇×#478	C₂²	1	2	yes	—
95	C₇×#478	C₂²	1	2	yes	—
96	C₇×#478	C₂²	1	2	yes	—
97	C₇×#478	C₂²	1	2	yes	—
98	C₇×#478	C₂²	1	2	yes	—
99	C₇×#478	C₂²	1	1	yes	characteristic, complemented
100	C₇×#478	C₂²	1	2	yes	complemented
101	C₇×#478	C₂²	1	1	yes	characteristic, complemented
102	C₇×#478	C₂²	1	2	yes	complemented
103	C₇×#477	C₂²	1	1	yes	characteristic, complemented
104	C₇×#476	C₂²	1	2	yes	—
105	C₇×#476	C₂²	1	1	yes	characteristic, complemented
106	C₇×#475	C₂²	1	1	yes	characteristic, complemented
107	C₇×#474	C₂²	1	2	yes	—
108	C₇×#474	C₂²	1	1	yes	characteristic, complemented
109	C₇×#433	C₂²	1	2	yes	complemented
110	C₇×#433	C₂²	1	2	yes	complemented
111	C₇×#432	C₂²	1	2	yes	complemented
112	C₇×#431	C₂²	1	2	yes	complemented
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×#418	C₂²	1	1	yes	characteristic
124	C₇×#418	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×#102	C₂²	1	1	yes	characteristic
130	C₂×C₇×#102	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	#60890	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
136	C₂×C₇×#41	—	2	2	no	—
137	C₂×C₇×#41	C₂³	1	1	yes	characteristic
138	C₂×C₇×#41	C₂³	1	1	yes	characteristic
139	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₇	—	2	1	no	—
141	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
142	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
143	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
144	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
145	C₇×C₄⋊Q₈	—	2	1	no	—
146	C₇×C₄⋊Q₈	—	2	1	no	—
147	C₇×C₄⋊Q₈	—	2	1	no	—
148	C₇×C₄⋊Q₈	—	2	2	no	—
149	C₇×C₄⋊Q₈	—	2	2	no	—
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×#127	—	2	1	no	—
156	C₇×#127	C₂³	1	2	yes	—
157	C₇×#126	—	2	2	no	—
158	C₇×#126	—	2	2	no	—
159	C₇×#125	—	2	1	no	—
160	C₇×#125	—	2	1	no	—
161	C₇×#125	—	2	1	no	—
162	C₇×#125	—	2	2	no	—
163	C₇×#125	—	2	2	no	—
164	C₇×#125	—	2	1	no	—
165	C₇×#125	—	2	1	no	—
166	C₇×#125	—	2	2	no	—
167	C₇×#125	—	2	2	no	—
168	C₇×#125	C₂³	1	2	yes	—
169	C₇×#125	C₂³	1	2	yes	—
170	C₇×#125	C₂³	1	1	yes	characteristic
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	2	yes	—
175	C₇×#124	—	2	1	no	—
176	C₇×#124	—	2	2	no	—
177	C₇×#124	—	2	2	no	—
178	C₇×#124	C₂³	1	2	yes	—
179	C₇×#123	—	2	2	no	—
180	C₇×#123	—	2	2	no	—
181	C₇×#123	—	2	2	no	—
182	C₇×#123	—	2	2	no	—
183	C₇×C₂²⋊Q₈	—	2	1	no	—
184	C₇×C₂²⋊Q₈	—	2	1	no	—
185	C₇×C₂²⋊Q₈	—	2	1	no	—
186	C₇×C₂²⋊Q₈	—	2	2	no	—
187	C₇×C₂²⋊Q₈	—	2	2	no	—
188	C₇×C₂²⋊Q₈	—	2	2	no	—
189	C₇×C₂²⋊Q₈	—	2	2	no	—
190	C₇×C₂²⋊Q₈	—	2	2	no	—
191	C₇×C₂²⋊Q₈	—	2	2	no	—
192	C₇×C₂²⋊Q₈	—	2	2	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	C₂³	1	2	yes	—
197	C₇×#121	—	2	2	no	—
198	C₇×#121	—	2	1	no	—
199	C₇×#121	—	2	2	no	—
200	C₇×#121	—	2	1	no	—
201	C₇×#121	—	2	1	no	—
202	C₇×#121	—	2	2	no	—
203	C₇×#121	—	2	2	no	—
204	C₇×#121	C₂³	1	2	yes	—
205	C₇×#121	C₂³	1	2	yes	—
206	C₇×#121	C₂³	1	2	yes	—
207	C₇×#120	—	2	2	no	—
208	C₇×#120	—	2	2	no	—
209	C₄×C₇×Q₈	—	2	1	no	—
210	C₄×C₇×Q₈	—	2	1	no	—
211	C₄×C₇×Q₈	—	2	1	no	—
212	C₄×C₇×Q₈	—	2	1	no	—
213	C₄×C₇×Q₈	—	2	2	no	—
214	C₄×C₇×Q₈	—	2	2	no	—
215	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
216	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
217	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
218	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
219	C₄×C₇×D₄	—	2	2	no	—
220	C₄×C₇×D₄	—	2	2	no	—
221	C₄×C₇×D₄	—	2	1	no	—
222	C₄×C₇×D₄	—	2	1	no	—
223	C₄×C₇×D₄	—	2	1	no	—
224	C₄×C₇×D₄	—	2	1	no	—
225	C₄×C₇×D₄	—	2	2	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	2	yes	—
230	C₄×C₇×D₄	D₄	1	1	yes	characteristic
231	C₄×C₇×D₄	D₄	1	2	yes	—
232	C₄×C₇×D₄	D₄	1	1	yes	characteristic
233	C₄×C₇×D₄	C₂³	1	2	yes	—
234	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
235	C₄×C₇×D₄	C₂³	1	2	yes	—
236	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
237	C₇×#117	—	2	1	no	—
238	C₇×#117	—	2	2	no	—
239	C₇×#117	C₂³	1	2	yes	—
240	C₇×#117	C₂³	1	2	yes	—
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	1	yes	characteristic
245	C₇×#117	C₂³	1	2	yes	—
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×C₇×C₂²⋊C₄	—	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	2	yes	—
260	C₇×#107	C₂³	1	2	yes	—
261	C₇×#107	C₂³	1	1	yes	characteristic
262	C₇×#107	C₂³	1	1	yes	characteristic
263	C₇×#107	C₂³	1	1	yes	characteristic
264	C₇×#107	C₂³	1	1	yes	characteristic
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	2	yes	—
280	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
281	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
286	C₇×#103	C₂³	1	1	yes	characteristic
287	C₇×#103	C₂³	1	1	yes	characteristic
288	C₇×#103	C₂³	1	1	yes	characteristic
289	C₇×#103	C₂³	1	2	yes	—
290	C₇×#103	C₂³	1	2	yes	—
291	C₇×#102	C₂³	1	2	yes	—
292	C₇×#102	C₂³	1	2	yes	—
293	C₇×#102	C₂³	1	1	yes	characteristic
294	C₇×#102	C₂³	1	1	yes	characteristic
295	C₇×#102	C₂³	1	2	yes	—
296	C₇×#102	C₂³	1	2	yes	—
297	C₇×#102	C₂³	1	1	yes	characteristic
298	C₇×#102	C₂³	1	1	yes	characteristic
299	C₇×#102	C₂³	1	2	yes	—
300	C₇×#102	C₂³	1	2	yes	—
301	C₇×#102	C₂³	1	2	yes	—
302	C₇×#102	C₂³	1	2	yes	—
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	#3460	C₂×C₇	1	1	yes	characteristic
315	#3244	C₂×C₇	1	2	yes	complemented
316	#3243	C₂×C₇	1	2	yes	complemented
317	#3241	C₂×C₇	1	2	yes	complemented
318	#3241	C₂×C₇	1	2	yes	complemented
319	#3240	C₂×C₇	1	2	yes	complemented
320	#3234	C₂×C₇	1	2	yes	complemented
321	#3232	C₂×C₇	1	2	yes	complemented
322	#3228	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	#3136	C₂×C₇	1	1	yes	characteristic, complemented
326	#3136	C₂×C₇	1	1	yes	characteristic, complemented
327	#3099	C₂×C₇	1	1	yes	characteristic, complemented
328	#3098	C₂×C₇	1	1	yes	characteristic, complemented
329	#3096	C₂×C₇	1	1	yes	characteristic, complemented
330	#3096	C₂×C₇	1	1	yes	characteristic, complemented
331	#3080	C₂×C₇	1	1	yes	characteristic, complemented
332	#3077	C₂×C₇	1	1	yes	characteristic, complemented
333	#3076	C₂×C₇	1	1	yes	characteristic, complemented
334	C₂×#478	C₂×C₇	1	1	yes	characteristic, complemented
335	#2925	C₂×C₇	1	1	yes	characteristic, complemented
336	C₂⁴×C₇	—	2	1	no	—
337	C₇×#41	—	2	2	no	—
338	C₇×#41	—	2	2	no	—
339	C₇×#41	—	2	2	no	—
340	C₇×#41	—	2	2	no	—
341	C₇×#41	—	8	4	no	—
342	C₂×C₇×Q₈	—	2	1	no	—
343	C₂×C₇×Q₈	—	2	2	no	—
344	C₂×C₇×Q₈	—	2	1	no	—
345	C₂×C₇×Q₈	—	2	2	no	—
346	C₂×C₇×Q₈	—	2	2	no	—
347	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
348	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
349	C₂×C₇×D₄	—	2	1	no	—
350	C₂×C₇×D₄	—	2	2	no	—
351	C₂×C₇×D₄	—	2	2	no	—
352	C₂×C₇×D₄	—	2	2	no	—
353	C₂×C₇×D₄	—	2	1	no	—
354	C₂×C₇×D₄	—	2	2	no	—
355	C₂×C₇×D₄	—	2	2	no	—
356	C₂×C₇×D₄	—	2	2	no	—
357	C₂×C₇×D₄	—	2	2	no	—
358	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
359	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
360	C₂×C₇×D₄	C₂⁴	1	2	yes	—
361	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
362	C₂²×C₄×C₇	—	2	1	no	—
363	C₂²×C₄×C₇	—	2	2	no	—
364	C₂²×C₄×C₇	—	2	2	no	—
365	C₂²×C₄×C₇	—	2	1	no	—
366	C₂²×C₄×C₇	—	2	1	no	—
367	C₂²×C₄×C₇	—	2	1	no	—
368	C₂²×C₄×C₇	—	2	1	no	—
369	C₂²×C₄×C₇	—	2	2	no	—
370	C₂²×C₄×C₇	—	2	1	no	—
371	C₂²×C₄×C₇	—	2	2	no	—
372	C₂²×C₄×C₇	—	8	2	no	—
373	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
374	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
377	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
378	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
379	C₇×M₁₆	—	2	2	no	—
380	C₇×M₁₆	—	2	2	no	—
381	C₂×C₇×C₈	—	2	2	no	—
382	C₂×C₇×C₈	—	2	2	no	—
383	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
384	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
385	C₂×C₇×C₈	C₂⁴	1	2	yes	—
386	C₂×C₇×C₈	C₂⁴	1	2	yes	—
387	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
388	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
389	C₇×C₄⋊C₄	—	2	2	no	—
390	C₇×C₄⋊C₄	—	2	1	no	—
391	C₇×C₄⋊C₄	—	2	2	no	—
392	C₇×C₄⋊C₄	—	2	1	no	—
393	C₇×C₄⋊C₄	—	2	2	no	—
394	C₇×C₄⋊C₄	—	2	2	no	—
395	C₇×C₄⋊C₄	—	2	2	no	—
396	C₇×C₄⋊C₄	—	2	2	no	—
397	C₇×C₄⋊C₄	—	2	2	no	—
398	C₇×C₄⋊C₄	—	2	2	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	1	no	—
403	C₇×C₄⋊C₄	—	2	1	no	—
404	C₇×C₄⋊C₄	—	2	1	no	—
405	C₇×C₄⋊C₄	—	2	1	no	—
406	C₇×C₄⋊C₄	—	2	2	no	—
407	C₇×C₄⋊C₄	—	2	2	no	—
408	C₇×C₄⋊C₄	—	2	2	no	—
409	C₇×C₄⋊C₄	—	2	2	no	—
410	C₇×C₄⋊C₄	—	2	1	no	—
411	C₇×C₄⋊C₄	—	2	1	no	—
412	C₇×C₄⋊C₄	—	2	1	no	—
413	C₇×C₄⋊C₄	—	2	2	no	—
414	C₇×C₄⋊C₄	—	2	1	no	—
415	C₇×C₄⋊C₄	—	2	2	no	—
416	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
417	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
418	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
419	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
420	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
421	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
422	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
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	2	yes	—
427	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
428	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
429	C₇×C₂²⋊C₄	—	2	1	no	—
430	C₇×C₂²⋊C₄	—	2	2	no	—
431	C₇×C₂²⋊C₄	—	2	2	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	2	no	—
436	C₇×C₂²⋊C₄	—	2	2	no	—
437	C₇×C₂²⋊C₄	—	2	1	no	—
438	C₇×C₂²⋊C₄	—	2	1	no	—
439	C₇×C₂²⋊C₄	—	2	2	no	—
440	C₇×C₂²⋊C₄	—	2	2	no	—
441	C₇×C₂²⋊C₄	—	2	2	no	—
442	C₇×C₂²⋊C₄	—	2	2	no	—
443	C₇×C₂²⋊C₄	—	2	2	no	—
444	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
445	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
446	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
447	C₄²×C₇	—	2	1	no	—
448	C₄²×C₇	—	2	1	no	—
449	C₄²×C₇	—	2	1	no	—
450	C₄²×C₇	—	2	2	no	—
451	C₄²×C₇	—	2	2	no	—
452	C₄²×C₇	—	2	1	no	—
453	C₄²×C₇	—	2	1	no	—
454	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
455	C₄²×C₇	C₂×D₄	1	2	yes	—
456	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
457	C₄²×C₇	C₂×D₄	1	2	yes	—
458	C₄²×C₇	C₂⁴	1	2	yes	—
459	C₄²×C₇	C₂⁴	1	1	yes	characteristic
460	C₄²×C₇	C₂⁴	1	1	yes	characteristic
461	#557	—	2	1	no	—
462	#557	—	2	1	no	—
463	#554	—	2	2	no	—
464	#554	—	2	2	no	—
465	#554	—	2	1	no	—
466	#554	—	2	1	no	—
467	#544	C₂²×C₇	1	1	yes	characteristic
468	#544	C₂²×C₇	1	1	yes	characteristic
469	#544	C₂²×C₇	1	1	yes	characteristic
470	#544	C₂²×C₇	1	2	yes	complemented
471	#544	C₂²×C₇	1	2	yes	complemented
472	#542	—	2	1	no	—
473	#542	C₂²×C₇	1	2	yes	—
474	#540	—	2	1	no	—
475	#540	C₂²×C₇	1	2	yes	—
476	#538	—	2	2	no	—
477	#537	C₂²×C₇	1	1	yes	characteristic
478	#535	C₂²×C₇	1	1	yes	characteristic
479	#535	C₂²×C₇	1	1	yes	characteristic
480	#533	C₂²×C₇	1	1	yes	characteristic
481	#533	C₂²×C₇	1	2	yes	complemented
482	#532	—	2	1	no	—
483	#532	C₂²×C₇	1	2	yes	—
484	#529	—	2	1	no	—
485	#529	C₂²×C₇	1	2	yes	—
486	C₂×#125	C₂²×C₇	1	1	yes	characteristic
487	C₂×#125	C₂²×C₇	1	2	yes	complemented
488	#525	—	2	2	no	—
489	#520	C₂²×C₇	1	1	yes	characteristic
490	#520	C₂²×C₇	1	1	yes	characteristic
491	C₄×#41	C₂²×C₇	1	1	yes	characteristic
492	C₄×#41	C₂²×C₇	1	1	yes	characteristic
493	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
494	#501	C₂²×C₇	1	2	yes	complemented
495	#501	C₂²×C₇	1	2	yes	complemented
496	#501	C₂²×C₇	1	2	yes	complemented
497	#501	C₂²×C₇	1	2	yes	complemented
498	#500	C₂²×C₇	1	2	yes	complemented
499	#499	C₂²×C₇	1	2	yes	complemented
500	#499	C₂²×C₇	1	2	yes	complemented
501	#498	C₂²×C₇	1	2	yes	complemented
502	#490	C₂²×C₇	1	2	yes	—
503	#490	C₂²×C₇	1	2	yes	—
504	#489	C₂²×C₇	1	2	yes	—
505	#489	C₂²×C₇	1	2	yes	—
506	#488	C₂²×C₇	1	2	yes	—
507	#488	C₂²×C₇	1	2	yes	—
508	#486	C₂²×C₇	1	2	yes	—
509	#486	C₂²×C₇	1	2	yes	—
510	#485	C₂²×C₇	1	2	yes	complemented
511	#485	C₂²×C₇	1	2	yes	complemented
512	#484	C₂²×C₇	1	2	yes	complemented
513	#483	C₂²×C₇	1	2	yes	complemented
514	#482	C₂²×C₇	1	2	yes	—
515	#482	C₂²×C₇	1	2	yes	—
516	#482	C₂²×C₇	1	2	yes	—
517	#482	C₂²×C₇	1	2	yes	—
518	#482	C₂²×C₇	1	2	yes	complemented
519	#482	C₂²×C₇	1	2	yes	complemented
520	#481	C₂²×C₇	1	2	yes	—
521	#481	C₂²×C₇	1	2	yes	—
522	#481	C₂²×C₇	1	2	yes	complemented
523	#480	C₂²×C₇	1	2	yes	—
524	#480	C₂²×C₇	1	2	yes	—
525	#480	C₂²×C₇	1	2	yes	complemented
526	#479	C₂²×C₇	1	1	yes	characteristic, complemented
527	#479	C₂²×C₇	1	1	yes	characteristic, complemented
528	#479	C₂²×C₇	1	2	yes	complemented
529	#479	C₂²×C₇	1	2	yes	complemented
530	#478	C₂²×C₇	1	2	yes	—
531	#478	C₂²×C₇	1	2	yes	—
532	#478	C₂²×C₇	1	2	yes	—
533	#478	C₂²×C₇	1	2	yes	—
534	#478	C₂²×C₇	1	2	yes	—
535	#478	C₂²×C₇	1	2	yes	—
536	#478	C₂²×C₇	1	1	yes	characteristic, complemented
537	#478	C₂²×C₇	1	1	yes	characteristic, complemented
538	#478	C₂²×C₇	1	2	yes	complemented
539	#478	C₂²×C₇	1	2	yes	complemented
540	#477	C₂²×C₇	1	1	yes	characteristic, complemented
541	#476	C₂²×C₇	1	2	yes	—
542	#476	C₂²×C₇	1	1	yes	characteristic, complemented
543	#475	C₂²×C₇	1	1	yes	characteristic, complemented
544	#474	C₂²×C₇	1	2	yes	—
545	#474	C₂²×C₇	1	1	yes	characteristic, complemented
546	#433	C₂²×C₇	1	2	yes	complemented
547	#433	C₂²×C₇	1	2	yes	complemented
548	#432	C₂²×C₇	1	2	yes	complemented
549	#431	C₂²×C₇	1	2	yes	complemented
550	#428	C₂²×C₇	1	1	yes	characteristic
551	#428	C₂²×C₇	1	1	yes	characteristic
552	#428	C₂²×C₇	1	1	yes	characteristic
553	#428	C₂²×C₇	1	1	yes	characteristic
554	#427	C₂²×C₇	1	1	yes	characteristic
555	#427	C₂²×C₇	1	1	yes	characteristic
556	C₂×#107	C₂²×C₇	1	1	yes	characteristic
557	C₂×#106	C₂²×C₇	1	1	yes	characteristic
558	#423	C₂²×C₇	1	1	yes	characteristic
559	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic
560	#418	C₂²×C₇	1	1	yes	characteristic
561	#418	C₂²×C₇	1	1	yes	characteristic
562	#417	C₂²×C₇	1	1	yes	characteristic
563	#417	C₂²×C₇	1	1	yes	characteristic
564	#416	C₂²×C₇	1	1	yes	characteristic
565	#416	C₂²×C₇	1	1	yes	characteristic
566	C₂×#102	C₂²×C₇	1	1	yes	characteristic
567	C₂×#102	C₂²×C₇	1	1	yes	characteristic
568	#408	C₂²×C₇	1	1	yes	characteristic
569	#408	C₂²×C₇	1	1	yes	characteristic
570	#405	C₂²×C₇	1	1	yes	characteristic
571	#405	C₂²×C₇	1	1	yes	characteristic
572	C₂³×C₇	—	2	2	no	—
573	C₂³×C₇	—	2	1	no	—
574	C₂³×C₇	—	4	2	no	—
575	C₂³×C₇	—	8	1	no	—
576	C₂³×C₇	—	8	1	no	—
577	C₂³×C₇	C₂²×D₄	1	2	yes	—
578	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
579	C₇×Q₈	—	2	2	no	—
580	C₇×Q₈	—	2	1	no	—
581	C₇×Q₈	—	2	1	no	—
582	C₇×Q₈	—	8	1	no	—
583	C₇×Q₈	—	8	2	no	—
584	C₇×Q₈	—	8	1	no	—
585	C₇×Q₈	—	8	2	no	—
586	C₇×Q₈	—	8	2	no	—
587	C₇×D₄	—	2	4	no	—
588	C₇×D₄	—	2	2	no	—
589	C₇×D₄	—	2	2	no	—
590	C₇×D₄	—	2	2	no	—
591	C₇×D₄	—	2	1	no	—
592	C₇×D₄	—	2	1	no	—
593	C₇×D₄	—	4	2	no	—
594	C₇×D₄	—	4	2	no	—
595	C₇×D₄	—	8	2	no	—
596	C₇×D₄	—	8	2	no	—
597	C₇×D₄	—	8	2	no	—
598	C₇×D₄	—	8	2	no	—
599	C₇×D₄	—	8	2	no	—
600	C₂×C₄×C₇	—	2	2	no	—
601	C₂×C₄×C₇	—	2	2	no	—
602	C₂×C₄×C₇	—	2	1	no	—
603	C₂×C₄×C₇	—	2	1	no	—
604	C₂×C₄×C₇	—	2	1	no	—
605	C₂×C₄×C₇	—	2	1	no	—
606	C₂×C₄×C₇	—	2	1	no	—
607	C₂×C₄×C₇	—	2	2	no	—
608	C₂×C₄×C₇	—	2	1	no	—
609	C₂×C₄×C₇	—	2	2	no	—
610	C₂×C₄×C₇	—	2	1	no	—
611	C₂×C₄×C₇	—	2	2	no	—
612	C₂×C₄×C₇	—	4	1	no	—
613	C₂×C₄×C₇	—	4	1	no	—
614	C₂×C₄×C₇	—	4	2	no	—
615	C₂×C₄×C₇	—	4	2	no	—
616	C₂×C₄×C₇	—	4	4	no	—
617	C₂×C₄×C₇	—	4	2	no	—
618	C₂×C₄×C₇	—	4	2	no	—
619	C₂×C₄×C₇	—	8	1	no	—
620	C₂×C₄×C₇	—	8	2	no	—
621	C₂×C₄×C₇	—	8	1	no	—
622	C₂×C₄×C₇	—	8	2	no	—
623	C₂×C₄×C₇	—	8	1	no	—
624	C₂×C₄×C₇	—	8	2	no	—
625	C₂×C₄×C₇	—	8	1	no	—
626	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
627	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
628	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
629	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
630	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
631	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
632	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
633	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
634	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
635	C₂×C₄×C₇	2₋¹⁺⁴	1	2	yes	—
636	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
637	C₇×C₈	—	2	1	no	—
638	C₇×C₈	—	2	1	no	—
639	C₇×C₈	—	2	1	no	—
640	C₇×C₈	—	2	1	no	—
641	C₇×C₈	—	2	2	no	—
642	C₇×C₈	—	2	2	no	—
643	C₂×#41	—	2	2	no	—
644	C₂×#41	C₂³×C₇	1	1	yes	characteristic
645	C₂×#41	C₂³×C₇	1	1	yes	characteristic
646	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
647	C₂³×C₄	—	2	1	no	—
648	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
649	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
650	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
651	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
652	C₄⋊Q₈	—	2	1	no	—
653	C₄⋊Q₈	—	2	1	no	—
654	C₄⋊Q₈	—	2	1	no	—
655	C₄⋊Q₈	—	2	2	no	—
656	C₄⋊Q₈	—	2	2	no	—
657	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
658	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
659	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
660	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
661	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
662	#127	—	2	1	no	—
663	#127	C₂³×C₇	1	2	yes	—
664	#126	—	2	2	no	—
665	#126	—	2	2	no	—
666	#125	—	2	1	no	—
667	#125	—	2	1	no	—
668	#125	—	2	1	no	—
669	#125	—	2	2	no	—
670	#125	—	2	2	no	—
671	#125	—	2	1	no	—
672	#125	—	2	1	no	—
673	#125	—	2	2	no	—
674	#125	—	2	2	no	—
675	#125	C₂³×C₇	1	2	yes	—
676	#125	C₂³×C₇	1	2	yes	—
677	#125	C₂³×C₇	1	1	yes	characteristic
678	#125	C₂³×C₇	1	2	yes	—
679	#125	C₂³×C₇	1	2	yes	—
680	#125	C₂³×C₇	1	2	yes	—
681	#125	C₂³×C₇	1	1	yes	characteristic
682	#124	—	2	1	no	—
683	#124	—	2	2	no	—
684	#124	—	2	2	no	—
685	#124	C₂³×C₇	1	2	yes	—
686	#123	—	2	2	no	—
687	#123	—	2	2	no	—
688	#123	—	2	2	no	—
689	#123	—	2	2	no	—
690	C₂²⋊Q₈	—	2	1	no	—
691	C₂²⋊Q₈	—	2	1	no	—
692	C₂²⋊Q₈	—	2	1	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	—	2	2	no	—
699	C₂²⋊Q₈	—	2	2	no	—
700	C₂²⋊Q₈	—	2	2	no	—
701	C₂²⋊Q₈	—	2	2	no	—
702	C₂²⋊Q₈	—	2	2	no	—
703	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
704	#121	—	2	2	no	—
705	#121	—	2	1	no	—
706	#121	—	2	2	no	—
707	#121	—	2	1	no	—
708	#121	—	2	1	no	—
709	#121	—	2	2	no	—
710	#121	—	2	2	no	—
711	#121	C₂³×C₇	1	2	yes	—
712	#121	C₂³×C₇	1	2	yes	—
713	#121	C₂³×C₇	1	2	yes	—
714	#120	—	2	2	no	—
715	#120	—	2	2	no	—
716	C₄×Q₈	—	2	1	no	—
717	C₄×Q₈	—	2	1	no	—
718	C₄×Q₈	—	2	1	no	—
719	C₄×Q₈	—	2	1	no	—
720	C₄×Q₈	—	2	2	no	—
721	C₄×Q₈	—	2	2	no	—
722	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
723	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
724	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
725	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
726	C₄×D₄	—	2	2	no	—
727	C₄×D₄	—	2	2	no	—
728	C₄×D₄	—	2	1	no	—
729	C₄×D₄	—	2	1	no	—
730	C₄×D₄	—	2	1	no	—
731	C₄×D₄	—	2	1	no	—
732	C₄×D₄	—	2	2	no	—
733	C₄×D₄	—	2	1	no	—
734	C₄×D₄	—	2	1	no	—
735	C₄×D₄	—	2	2	no	—
736	C₄×D₄	C₇×D₄	1	2	yes	—
737	C₄×D₄	C₇×D₄	1	1	yes	characteristic
738	C₄×D₄	C₇×D₄	1	2	yes	—
739	C₄×D₄	C₇×D₄	1	1	yes	characteristic
740	C₄×D₄	C₂³×C₇	1	2	yes	—
741	C₄×D₄	C₂³×C₇	1	2	yes	—
742	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
743	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
744	#117	—	2	1	no	—
745	#117	—	2	2	no	—
746	#117	C₂³×C₇	1	1	yes	characteristic
747	#117	C₂³×C₇	1	1	yes	characteristic
748	#117	C₂³×C₇	1	1	yes	characteristic
749	#117	C₂³×C₇	1	2	yes	—
750	#117	C₂³×C₇	1	2	yes	—
751	#117	C₂³×C₇	1	1	yes	characteristic
752	#117	C₂³×C₇	1	2	yes	—
753	C₂×C₄⋊C₄	—	2	1	no	—
754	C₂×C₄⋊C₄	—	2	1	no	—
755	C₂×C₄⋊C₄	—	2	2	no	—
756	C₂×C₄⋊C₄	—	2	2	no	—
757	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
758	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
759	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
760	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
761	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
762	C₂×C₂²⋊C₄	—	2	1	no	—
763	C₂×C₄²	—	2	1	no	—
764	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
765	C₂×C₄²	C₂³×C₇	1	2	yes	—
766	#107	C₂³×C₇	1	2	yes	—
767	#107	C₂³×C₇	1	2	yes	—
768	#107	C₂³×C₇	1	1	yes	characteristic
769	#107	C₂³×C₇	1	1	yes	characteristic
770	#107	C₂³×C₇	1	1	yes	characteristic
771	#107	C₂³×C₇	1	1	yes	characteristic
772	#107	C₂³×C₇	1	2	yes	—
773	#107	C₂³×C₇	1	2	yes	—
774	#107	C₂³×C₇	1	2	yes	—
775	#107	C₂³×C₇	1	2	yes	—
776	#106	C₂³×C₇	1	2	yes	—
777	#106	C₂³×C₇	1	2	yes	—
778	#106	C₂³×C₇	1	1	yes	characteristic
779	#106	C₂³×C₇	1	1	yes	characteristic
780	#106	C₂³×C₇	1	1	yes	characteristic
781	#106	C₂³×C₇	1	1	yes	characteristic
782	#106	C₂³×C₇	1	2	yes	—
783	#106	C₂³×C₇	1	2	yes	—
784	#106	C₂³×C₇	1	2	yes	—
785	#106	C₂³×C₇	1	2	yes	—
786	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
787	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
788	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
789	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
790	C₄⋊C₈	C₂³×C₇	1	2	yes	—
791	C₄⋊C₈	C₂³×C₇	1	2	yes	—
792	#103	C₂³×C₇	1	1	yes	characteristic
793	#103	C₂³×C₇	1	1	yes	characteristic
794	#103	C₂³×C₇	1	1	yes	characteristic
795	#103	C₂³×C₇	1	1	yes	characteristic
796	#103	C₂³×C₇	1	2	yes	—
797	#103	C₂³×C₇	1	2	yes	—
798	#102	C₂³×C₇	1	2	yes	—
799	#102	C₂³×C₇	1	2	yes	—
800	#102	C₂³×C₇	1	2	yes	—
801	#102	C₂³×C₇	1	2	yes	—
802	#102	C₂³×C₇	1	1	yes	characteristic
803	#102	C₂³×C₇	1	1	yes	characteristic
804	#102	C₂³×C₇	1	1	yes	characteristic
805	#102	C₂³×C₇	1	1	yes	characteristic
806	#102	C₂³×C₇	1	2	yes	—
807	#102	C₂³×C₇	1	2	yes	—
808	#102	C₂³×C₇	1	2	yes	—
809	#102	C₂³×C₇	1	2	yes	—
810	#102	C₂³×C₇	1	2	yes	—
811	#102	C₂³×C₇	1	2	yes	—
812	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
813	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
814	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
815	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
816	#97	C₂³×C₇	1	2	yes	—
817	#97	C₂³×C₇	1	2	yes	—
818	C₄×C₈	C₂³×C₇	1	2	yes	—
819	C₄×C₈	C₂³×C₇	1	2	yes	—
820	C₂²×C₇	—	2	1	no	—
821	C₂²×C₇	—	2	1	no	—
822	C₂²×C₇	—	2	2	no	—
823	C₂²×C₇	—	2	2	no	—
824	C₂²×C₇	—	2	2	no	—
825	C₂²×C₇	—	4	1	no	—
826	C₂²×C₇	—	4	2	no	—
827	C₂²×C₇	—	4	2	no	—
828	C₂²×C₇	—	4	1	no	—
829	C₂²×C₇	—	4	1	no	—
830	C₂²×C₇	—	4	2	no	—
831	C₂²×C₇	—	8	4	no	—
832	C₂²×C₇	#536	1	2	yes	—
833	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
834	C₄×C₇	—	2	1	no	—
835	C₄×C₇	—	2	1	no	—
836	C₄×C₇	—	2	2	no	—
837	C₄×C₇	—	2	1	no	—
838	C₄×C₇	—	2	1	no	—
839	C₄×C₇	—	2	2	no	—
840	C₄×C₇	—	2	2	no	—
841	C₄×C₇	—	4	2	no	—
842	C₄×C₇	—	4	1	no	—
843	C₄×C₇	—	4	1	no	—
844	C₄×C₇	—	4	1	no	—
845	C₄×C₇	—	4	2	no	—
846	C₄×C₇	—	4	1	no	—
847	C₄×C₇	—	4	2	no	—
848	C₄×C₇	—	4	1	no	—
849	C₄×C₇	—	4	1	no	—
850	C₄×C₇	—	4	1	no	—
851	C₄×C₇	#536	1	2	yes	—
852	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
853	C₄×C₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
854	C₂⁴	—	2	1	no	—
855	#41	—	2	2	no	—
856	#41	—	2	2	no	—
857	#41	—	2	2	no	—
858	#41	—	2	2	no	—
859	#41	—	8	4	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
866	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
867	C₂×D₄	—	2	1	no	—
868	C₂×D₄	—	2	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	2	1	no	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	2	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
877	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
878	C₂×D₄	C₂⁴×C₇	1	2	yes	—
879	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	1	no	—
886	C₂²×C₄	—	2	1	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	8	2	no	—
891	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
892	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
893	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
894	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
895	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
896	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
897	M₁₆	—	2	2	no	—
898	M₁₆	—	2	2	no	—
899	C₂×C₈	—	2	2	no	—
900	C₂×C₈	—	2	2	no	—
901	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
902	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₇	1	2	yes	—
904	C₂×C₈	C₂⁴×C₇	1	2	yes	—
905	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	1	no	—
929	C₄⋊C₄	—	2	1	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	1	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
935	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
936	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
937	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
938	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
939	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
940	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
941	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
942	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
943	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
944	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
945	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
947	C₂²⋊C₄	—	2	1	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
963	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
964	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
973	C₄²	C₂×C₇×D₄	1	2	yes	—
974	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
975	C₄²	C₂×C₇×D₄	1	2	yes	—
976	C₄²	C₂⁴×C₇	1	2	yes	—
977	C₄²	C₂⁴×C₇	1	1	yes	characteristic
978	C₄²	C₂⁴×C₇	1	1	yes	characteristic
979	C₂×C₇	—	2	2	no	—
980	C₂×C₇	—	4	2	no	—
981	C₂×C₇	—	8	1	no	—
982	C₂×C₇	—	8	2	no	—
983	C₂×C₇	C₂×#536	1	1	yes	characteristic
984	C₂×C₇	#3584	1	1	yes	characteristic
985	C₂×C₇	#3585	1	1	yes	characteristic
986	C₂³	—	2	2	no	—
987	C₂³	—	2	1	no	—
988	C₂³	—	4	2	no	—
989	C₂³	—	8	1	no	—
990	C₂³	—	8	1	no	—
991	C₂³	C₂²×C₇×D₄	1	2	yes	—
992	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	8	1	no	—
997	Q₈	—	8	2	no	—
998	Q₈	—	8	1	no	—
999	Q₈	—	8	2	no	—
1000	Q₈	—	8	2	no	—
1001	D₄	—	2	4	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	2	1	no	—
1006	D₄	—	2	2	no	—
1007	D₄	—	4	2	no	—
1008	D₄	—	4	2	no	—
1009	D₄	—	8	2	no	—
1010	D₄	—	8	2	no	—
1011	D₄	—	8	2	no	—
1012	D₄	—	8	2	no	—
1013	D₄	—	8	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	2	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	4	1	no	—
1027	C₂×C₄	—	4	1	no	—
1028	C₂×C₄	—	4	2	no	—
1029	C₂×C₄	—	4	2	no	—
1030	C₂×C₄	—	4	4	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	4	2	no	—
1033	C₂×C₄	—	8	1	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	8	1	no	—
1036	C₂×C₄	—	8	2	no	—
1037	C₂×C₄	—	8	1	no	—
1038	C₂×C₄	—	8	2	no	—
1039	C₂×C₄	—	8	1	no	—
1040	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1041	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1042	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1043	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1044	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1045	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1046	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
1047	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
1048	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1049	C₂×C₄	C₇×2₋¹⁺⁴	1	2	yes	—
1050	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
1051	C₈	—	2	1	no	—
1052	C₈	—	2	1	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	2	no	—
1056	C₈	—	2	2	no	—
1057	C₇	#60890	1	1	yes	characteristic, direct product factor, Sylow
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	4	1	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	1	no	—
1067	C₂²	—	4	1	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	8	4	no	—
1070	C₂²	C₇×#536	1	2	yes	—
1071	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	2	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	2	2	no	—
1078	C₄	—	2	2	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	4	2	no	—
1084	C₄	—	4	1	no	—
1085	C₄	—	4	2	no	—
1086	C₄	—	4	1	no	—
1087	C₄	—	4	1	no	—
1088	C₄	—	4	1	no	—
1089	C₄	C₇×#536	1	2	yes	—
1090	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1091	C₄	C₂×C₇×2₋¹⁺⁴	1	1	yes	characteristic
1092	C₂	—	2	2	no	—
1093	C₂	—	4	2	no	—
1094	C₂	—	8	2	no	—
1095	C₂	—	8	1	no	—
1096	C₂	C₂×C₇×#536	1	1	yes	characteristic
1097	C₂	C₇×#3584	1	1	yes	characteristic
1098	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3460	C₂
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×#3241	C₂	semidirect
6. C₇×#3241	C₂	semidirect
7. C₇×#3240	C₂	semidirect
8. C₇×#3234	C₂	semidirect
9. C₇×#3232	C₂	semidirect
10. C₇×#3228	C₂	semidirect
11. C₇×#3164	C₂	semidirect
12. C₇×#3163	C₂	semidirect
13. C₇×#3136	C₂	semidirect
14. C₇×#3136	C₂	semidirect
15. C₇×#3099	C₂	semidirect
16. C₇×#3098	C₂	semidirect
17. C₇×#3096	C₂	semidirect
18. C₇×#3096	C₂	semidirect
19. C₇×#3080	C₂	semidirect
20. C₇×#3077	C₂	semidirect
21. C₇×#3076	C₂	semidirect
22. C₂×C₇×#478	C₂	semidirect
23. C₇×#2925	C₂	semidirect
33. C₇×#544	C₂²	semidirect
34. C₇×#544	C₂²	semidirect
44. C₇×#533	C₂²	semidirect
50. C₂×C₇×#125	C₂²	semidirect
57. C₇×#501	C₂²	semidirect
58. C₇×#501	C₂²	semidirect
59. C₇×#501	C₂²	semidirect
60. C₇×#501	C₂²	semidirect
61. C₇×#500	C₂²	semidirect
62. C₇×#499	C₂²	semidirect
63. C₇×#499	C₂²	semidirect
64. C₇×#498	C₂²	semidirect
73. C₇×#485	C₂²	semidirect
74. C₇×#485	C₂²	semidirect
75. C₇×#484	C₂²	semidirect
76. C₇×#483	C₂²	semidirect
81. C₇×#482	C₂²	semidirect
82. C₇×#482	C₂²	semidirect
85. C₇×#481	C₂²	semidirect
88. C₇×#480	C₂²	semidirect
89. C₇×#479	C₂²	semidirect
90. C₇×#479	C₂²	semidirect
91. C₇×#479	C₂²	semidirect
92. C₇×#479	C₂²	semidirect
99. C₇×#478	C₂²	semidirect
100. C₇×#478	C₂²	semidirect
101. C₇×#478	C₂²	semidirect
102. C₇×#478	C₂²	semidirect
103. C₇×#477	C₂²	semidirect
105. C₇×#476	C₂²	semidirect
106. C₇×#475	C₂²	semidirect
108. C₇×#474	C₂²	semidirect
109. C₇×#433	C₂²	semidirect
110. C₇×#433	C₂²	semidirect
111. C₇×#432	C₂²	semidirect
112. C₇×#431	C₂²	semidirect
135. #60890	C₇	direct (N × H)
313. #3504	C₂×C₇	semidirect
315. #3244	C₂×C₇	semidirect
316. #3243	C₂×C₇	semidirect
317. #3241	C₂×C₇	semidirect
318. #3241	C₂×C₇	semidirect
319. #3240	C₂×C₇	semidirect
320. #3234	C₂×C₇	semidirect
321. #3232	C₂×C₇	semidirect
322. #3228	C₂×C₇	semidirect
323. #3164	C₂×C₇	semidirect
324. #3163	C₂×C₇	semidirect
325. #3136	C₂×C₇	semidirect
326. #3136	C₂×C₇	semidirect
327. #3099	C₂×C₇	semidirect
328. #3098	C₂×C₇	semidirect
329. #3096	C₂×C₇	semidirect
330. #3096	C₂×C₇	semidirect
331. #3080	C₂×C₇	semidirect
332. #3077	C₂×C₇	semidirect
333. #3076	C₂×C₇	semidirect
334. C₂×#478	C₂×C₇	semidirect
335. #2925	C₂×C₇	semidirect
470. #544	C₂²×C₇	semidirect
471. #544	C₂²×C₇	semidirect
481. #533	C₂²×C₇	semidirect
487. C₂×#125	C₂²×C₇	semidirect
494. #501	C₂²×C₇	semidirect
495. #501	C₂²×C₇	semidirect
496. #501	C₂²×C₇	semidirect
497. #501	C₂²×C₇	semidirect
498. #500	C₂²×C₇	semidirect
499. #499	C₂²×C₇	semidirect
500. #499	C₂²×C₇	semidirect
501. #498	C₂²×C₇	semidirect
510. #485	C₂²×C₇	semidirect
511. #485	C₂²×C₇	semidirect
512. #484	C₂²×C₇	semidirect
513. #483	C₂²×C₇	semidirect
518. #482	C₂²×C₇	semidirect
519. #482	C₂²×C₇	semidirect
522. #481	C₂²×C₇	semidirect
525. #480	C₂²×C₇	semidirect
526. #479	C₂²×C₇	semidirect
527. #479	C₂²×C₇	semidirect
528. #479	C₂²×C₇	semidirect
529. #479	C₂²×C₇	semidirect
536. #478	C₂²×C₇	semidirect
537. #478	C₂²×C₇	semidirect
538. #478	C₂²×C₇	semidirect
539. #478	C₂²×C₇	semidirect
540. #477	C₂²×C₇	semidirect
542. #476	C₂²×C₇	semidirect
543. #475	C₂²×C₇	semidirect
545. #474	C₂²×C₇	semidirect
546. #433	C₂²×C₇	semidirect
547. #433	C₂²×C₇	semidirect
548. #432	C₂²×C₇	semidirect
549. #431	C₂²×C₇	semidirect
1057. C₇	#60890	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×#3460	2
C₇×#3244	2
C₇×#3243	2
C₇×#3241	2
C₇×#3240	2
C₇×#3234	2
C₇×#3232	2
C₇×#3228	2
C₇×#3164	2
C₇×#3163	2
C₇×#3136	2
C₇×#3099	2
C₇×#3098	2
C₇×#3096	2
C₇×#3080	2
C₇×#3077	2
C₇×#3076	2
C₂×C₇×#478	2
C₇×#2925	2
#60890	7

Subgroups — C7×#60890 #13238106

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60890 #13238106