Subgroups — C₇×#61005 #13238221

Order 1792.

1672 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3495	C₂	1	2	yes	maximal, complemented
2	C₇×#3256	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3255	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#3252	C₂	1	2	yes	maximal, complemented
5	C₇×#3244	C₂	1	2	yes	maximal, complemented
6	C₇×#3242	C₂	1	2	yes	maximal, complemented
7	C₇×#3225	C₂	1	2	yes	maximal, complemented
8	C₇×#3223	C₂	1	2	yes	maximal, complemented
9	C₇×#3197	C₂	1	1	yes	maximal, characteristic
10	C₇×#3196	C₂	1	2	yes	maximal, complemented
11	C₇×#3195	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3185	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3183	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3172	C₂	1	2	yes	maximal, complemented
15	C₇×#3127	C₂	1	2	yes	maximal, complemented
16	C₇×#3125	C₂	1	2	yes	maximal, complemented
17	C₇×#3121	C₂	1	2	yes	maximal, complemented
18	C₇×#3120	C₂	1	2	yes	maximal, complemented
19	C₇×#2921	C₂	1	1	yes	maximal, characteristic, complemented
20	C₇×#556	—	2	2	no	—
21	C₇×#554	—	2	2	no	—
22	C₇×#552	—	2	2	no	—
23	C₇×#552	—	2	2	no	—
24	C₇×#552	—	2	2	no	—
25	C₇×#552	—	2	2	no	—
26	C₇×#551	—	2	2	no	—
27	C₇×#551	—	2	2	no	—
28	C₇×#544	C₂²	1	2	yes	—
29	C₇×#542	C₂²	1	2	yes	—
30	C₇×#542	C₂²	1	2	yes	—
31	C₇×#541	C₂²	1	2	yes	—
32	C₇×#541	C₂²	1	2	yes	—
33	C₇×#536	C₂²	1	2	yes	—
34	C₇×#533	C₂²	1	2	yes	—
35	C₇×#533	C₂²	1	2	yes	—
36	C₇×#529	C₂²	1	2	yes	—
37	C₇×#529	C₂²	1	2	yes	—
38	C₇×#525	C₂²	1	2	yes	—
39	C₂×C₇×C₂²⋊Q₈	C₂²	1	2	yes	—
40	C₇×#520	C₂²	1	2	yes	—
41	C₇×#519	C₂²	1	2	yes	—
42	C₂×C₇×#117	C₂²	1	1	yes	characteristic
43	C₇×#501	C₂²	1	2	yes	complemented
44	C₇×#499	C₂²	1	1	yes	characteristic, complemented
45	C₇×#498	C₂²	1	1	yes	characteristic, complemented
46	C₇×#497	C₂²	1	2	yes	complemented
47	C₇×#495	C₂²	1	1	yes	characteristic, complemented
48	C₇×#494	C₂²	1	1	yes	characteristic, complemented
49	C₇×#491	C₂²	1	2	yes	complemented
50	C₇×#489	C₂²	1	2	yes	complemented
51	C₇×#488	C₂²	1	2	yes	complemented
52	C₇×#487	C₂²	1	2	yes	complemented
53	C₇×#485	C₂²	1	2	yes	—
54	C₇×#485	C₂²	1	2	yes	—
55	C₇×#485	C₂²	1	2	yes	—
56	C₇×#484	C₂²	1	2	yes	—
57	C₇×#483	C₂²	1	2	yes	—
58	C₇×#483	C₂²	1	2	yes	—
59	C₇×#482	C₂²	1	2	yes	—
60	C₇×#481	C₂²	1	2	yes	—
61	C₇×#479	C₂²	1	2	yes	complemented
62	C₇×#479	C₂²	1	2	yes	complemented
63	C₇×#479	C₂²	1	2	yes	complemented
64	C₇×#478	C₂²	1	2	yes	complemented
65	C₇×#477	C₂²	1	2	yes	complemented
66	C₇×#476	C₂²	1	2	yes	complemented
67	C₇×#475	C₂²	1	2	yes	complemented
68	C₇×#475	C₂²	1	2	yes	complemented
69	C₇×#470	C₂²	1	2	yes	—
70	C₇×#470	C₂²	1	2	yes	—
71	C₇×#470	C₂²	1	1	yes	characteristic
72	C₇×#470	C₂²	1	1	yes	characteristic
73	C₇×#470	C₂²	1	2	yes	—
74	C₇×#470	C₂²	1	1	yes	characteristic
75	C₇×#469	C₂²	1	1	yes	characteristic
76	C₇×#468	C₂²	1	2	yes	—
77	C₇×#468	C₂²	1	2	yes	—
78	C₇×#468	C₂²	1	2	yes	—
79	C₇×#464	C₂²	1	2	yes	complemented
80	C₇×#464	C₂²	1	2	yes	complemented
81	C₇×#464	C₂²	1	2	yes	complemented
82	C₇×#463	C₂²	1	2	yes	complemented
83	C₇×#462	C₂²	1	2	yes	complemented
84	C₇×#462	C₂²	1	2	yes	complemented
85	C₇×#462	C₂²	1	2	yes	complemented
86	C₇×#461	C₂²	1	2	yes	complemented
87	C₇×#452	C₂²	1	2	yes	—
88	C₇×#452	C₂²	1	2	yes	—
89	C₇×#452	C₂²	1	2	yes	—
90	C₇×#451	C₂²	1	2	yes	—
91	C₇×#451	C₂²	1	2	yes	—
92	C₇×#451	C₂²	1	2	yes	—
93	C₇×#449	C₂²	1	2	yes	—
94	C₇×#448	C₂²	1	2	yes	—
95	C₇×#442	C₂²	1	1	yes	characteristic, complemented
96	C₇×#441	C₂²	1	1	yes	characteristic, complemented
97	C₇×#441	C₂²	1	1	yes	characteristic, complemented
98	C₇×#441	C₂²	1	1	yes	characteristic, complemented
99	C₇×#441	C₂²	1	2	yes	complemented
100	C₇×#440	C₂²	1	2	yes	complemented
101	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
102	C₄×C₇×Q₁₆	C₂²	1	2	yes	complemented
103	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
104	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
105	C₇×#433	C₂²	1	2	yes	—
106	C₇×#433	C₂²	1	2	yes	—
107	C₇×#433	C₂²	1	2	yes	—
108	C₇×#433	C₂²	1	2	yes	—
109	C₇×#423	C₂²	1	1	yes	characteristic
110	C₇×#423	C₂²	1	1	yes	characteristic
111	C₇×#407	C₂²	1	1	yes	characteristic
112	C₇×#407	C₂²	1	1	yes	characteristic
113	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
114	C₄×C₇×M₁₆	C₂²	1	1	yes	characteristic
115	#61005	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
116	C₂×C₇×#41	C₂³	1	2	yes	—
117	C₂²×C₇×Q₈	C₂³	1	2	yes	—
118	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
119	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
120	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
121	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
122	C₂×C₇×Q₁₆	C₂³	1	1	yes	characteristic
123	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
124	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
125	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
126	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
127	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
128	C₂×C₇×D₈	C₂³	1	1	yes	characteristic
129	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
130	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
131	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
132	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
133	C₇×C₄⋊Q₈	—	2	2	no	—
134	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
135	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
136	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₇×#126	—	2	2	no	—
139	C₇×#126	—	2	2	no	—
140	C₇×#126	—	2	2	no	—
141	C₇×#126	—	2	2	no	—
142	C₇×#126	—	2	2	no	—
143	C₇×#126	—	2	2	no	—
144	C₇×#126	—	2	2	no	—
145	C₇×#126	—	2	2	no	—
146	C₇×#125	—	2	2	no	—
147	C₇×#125	—	2	2	no	—
148	C₇×#125	—	2	2	no	—
149	C₇×#125	—	2	2	no	—
150	C₇×#125	—	2	2	no	—
151	C₇×#125	—	2	2	no	—
152	C₇×#125	—	2	2	no	—
153	C₇×#125	C₂³	1	2	yes	—
154	C₇×#125	C₂³	1	2	yes	—
155	C₇×#124	—	2	2	no	—
156	C₇×#124	—	2	2	no	—
157	C₇×#124	C₂³	1	2	yes	—
158	C₇×#124	C₂³	1	2	yes	—
159	C₇×#123	—	2	2	no	—
160	C₇×#123	—	2	2	no	—
161	C₇×#123	—	2	2	no	—
162	C₇×#123	—	2	2	no	—
163	C₇×#123	—	2	2	no	—
164	C₇×#123	—	2	2	no	—
165	C₇×#123	—	2	2	no	—
166	C₇×C₂²⋊Q₈	—	2	2	no	—
167	C₇×C₂²⋊Q₈	—	2	2	no	—
168	C₇×C₂²⋊Q₈	—	2	2	no	—
169	C₇×C₂²⋊Q₈	—	2	2	no	—
170	C₇×C₂²⋊Q₈	—	2	2	no	—
171	C₇×C₂²⋊Q₈	—	2	2	no	—
172	C₇×C₂²⋊Q₈	—	2	2	no	—
173	C₇×C₂²⋊Q₈	—	2	2	no	—
174	C₇×C₂²⋊Q₈	—	2	2	no	—
175	C₇×C₂²⋊Q₈	—	2	2	no	—
176	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
177	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
179	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
180	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
181	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
182	C₇×#121	C₂³	1	2	yes	—
183	C₇×#121	C₂³	1	2	yes	—
184	C₇×#120	—	2	2	no	—
185	C₄×C₇×Q₈	—	2	2	no	—
186	C₄×C₇×Q₈	—	2	2	no	—
187	C₄×C₇×Q₈	—	2	2	no	—
188	C₄×C₇×Q₈	—	2	2	no	—
189	C₄×C₇×Q₈	C₂³	1	2	yes	—
190	C₄×C₇×Q₈	C₂³	1	2	yes	—
191	C₄×C₇×Q₈	C₂³	1	2	yes	—
192	C₄×C₇×Q₈	C₂³	1	2	yes	—
193	C₄×C₇×Q₈	C₂³	1	2	yes	—
194	C₄×C₇×Q₈	C₂³	1	2	yes	—
195	C₄×C₇×D₄	—	2	2	no	—
196	C₄×C₇×D₄	—	2	2	no	—
197	C₄×C₇×D₄	—	2	2	no	—
198	C₄×C₇×D₄	—	2	2	no	—
199	C₄×C₇×D₄	—	2	2	no	—
200	C₄×C₇×D₄	—	2	2	no	—
201	C₄×C₇×D₄	C₂³	1	2	yes	—
202	C₄×C₇×D₄	C₂³	1	2	yes	—
203	C₇×#117	—	2	2	no	—
204	C₇×#117	—	2	2	no	—
205	C₇×#117	—	2	2	no	—
206	C₇×#117	—	2	2	no	—
207	C₇×#117	—	2	2	no	—
208	C₇×#117	—	2	2	no	—
209	C₇×#117	—	2	2	no	—
210	C₇×#117	D₄	1	2	yes	—
211	C₇×#117	D₄	1	2	yes	—
212	C₇×#117	C₂³	1	2	yes	—
213	C₇×#117	C₂³	1	2	yes	—
214	C₇×#117	C₂³	1	2	yes	—
215	C₂×C₇×C₄⋊C₄	—	2	2	no	—
216	C₂×C₇×C₄⋊C₄	—	2	2	no	—
217	C₂×C₇×C₄⋊C₄	D₄	1	2	yes	—
218	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
219	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
220	C₂×C₇×C₂²⋊C₄	D₄	1	2	yes	—
221	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
222	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
223	C₇×#107	C₂³	1	2	yes	—
224	C₇×#107	C₂³	1	2	yes	—
225	C₇×#107	C₂³	1	2	yes	—
226	C₇×#106	C₂³	1	1	yes	characteristic
227	C₇×#106	C₂³	1	2	yes	—
228	C₇×#106	C₂³	1	1	yes	characteristic
229	C₇×#106	C₂³	1	1	yes	characteristic
230	C₇×#106	C₂³	1	2	yes	—
231	C₇×#106	C₂³	1	2	yes	—
232	C₇×#106	C₂³	1	1	yes	characteristic
233	C₇×C₄⋊C₈	C₂³	1	2	yes	—
234	C₇×C₄⋊C₈	C₂³	1	2	yes	—
235	C₇×C₄⋊C₈	C₂³	1	2	yes	—
236	C₇×C₄⋊C₈	C₂³	1	2	yes	—
237	C₇×#103	C₂³	1	2	yes	—
238	C₇×#103	C₂³	1	2	yes	—
239	C₇×#103	C₂³	1	2	yes	—
240	C₇×#103	C₂³	1	2	yes	—
241	C₇×#103	C₂³	1	2	yes	—
242	C₇×#103	C₂³	1	2	yes	—
243	C₇×#103	C₂³	1	2	yes	—
244	C₇×#103	C₂³	1	2	yes	—
245	C₇×#103	C₂³	1	2	yes	—
246	C₇×#103	C₂³	1	2	yes	—
247	C₇×#103	C₂³	1	2	yes	—
248	C₇×#103	C₂³	1	2	yes	—
249	C₇×#102	C₂³	1	2	yes	—
250	C₇×#102	C₂³	1	2	yes	—
251	C₇×#102	C₂³	1	2	yes	—
252	C₇×#102	C₂³	1	2	yes	—
253	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
254	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
255	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
256	C₇×C₂²⋊C₈	C₂³	1	2	yes	—
257	C₇×#97	C₂³	1	2	yes	—
258	C₇×#97	C₂³	1	1	yes	characteristic
259	C₇×#97	C₂³	1	1	yes	characteristic
260	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
261	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
262	C₄×C₇×C₈	C₂³	1	2	yes	—
263	#3495	C₂×C₇	1	2	yes	complemented
264	#3256	C₂×C₇	1	1	yes	characteristic, complemented
265	#3255	C₂×C₇	1	1	yes	characteristic, complemented
266	#3252	C₂×C₇	1	2	yes	complemented
267	#3244	C₂×C₇	1	2	yes	complemented
268	#3242	C₂×C₇	1	2	yes	complemented
269	#3225	C₂×C₇	1	2	yes	complemented
270	#3223	C₂×C₇	1	2	yes	complemented
271	#3197	C₂×C₇	1	1	yes	characteristic
272	#3196	C₂×C₇	1	2	yes	complemented
273	#3195	C₂×C₇	1	1	yes	characteristic, complemented
274	#3185	C₂×C₇	1	1	yes	characteristic, complemented
275	#3183	C₂×C₇	1	1	yes	characteristic, complemented
276	#3172	C₂×C₇	1	2	yes	complemented
277	#3127	C₂×C₇	1	2	yes	complemented
278	#3125	C₂×C₇	1	2	yes	complemented
279	#3121	C₂×C₇	1	2	yes	complemented
280	#3120	C₂×C₇	1	2	yes	complemented
281	#2921	C₂×C₇	1	1	yes	characteristic, complemented
282	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
283	C₇×#41	—	4	2	no	—
284	C₇×#41	—	4	2	no	—
285	C₂×C₇×Q₈	—	2	2	no	—
286	C₂×C₇×Q₈	—	2	2	no	—
287	C₂×C₇×Q₈	—	2	2	no	—
288	C₂×C₇×Q₈	—	4	2	no	—
289	C₂×C₇×Q₈	—	4	2	no	—
290	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
291	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
292	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
293	C₂×C₇×D₄	—	2	2	no	—
294	C₂×C₇×D₄	—	2	2	no	—
295	C₂×C₇×D₄	—	2	2	no	—
296	C₂×C₇×D₄	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₇	—	2	2	no	—
298	C₂²×C₄×C₇	—	2	2	no	—
299	C₂²×C₄×C₇	—	2	2	no	—
300	C₂²×C₄×C₇	—	2	2	no	—
301	C₂²×C₄×C₇	—	2	2	no	—
302	C₂²×C₄×C₇	—	4	1	no	—
303	C₂²×C₄×C₇	—	4	1	no	—
304	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
305	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
306	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
307	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₇×Q₁₆	—	4	1	no	—
311	C₇×Q₁₆	—	4	2	no	—
312	C₇×Q₁₆	—	4	2	no	—
313	C₇×Q₁₆	—	4	1	no	—
314	C₇×Q₁₆	—	4	2	no	—
315	C₇×Q₁₆	—	4	1	no	—
316	C₇×SD₁₆	—	4	2	no	—
317	C₇×SD₁₆	—	4	2	no	—
318	C₇×SD₁₆	—	4	2	no	—
319	C₇×D₈	—	4	1	no	—
320	C₇×M₁₆	—	4	1	no	—
321	C₇×M₁₆	—	4	1	no	—
322	C₇×M₁₆	—	4	1	no	—
323	C₇×M₁₆	—	4	1	no	—
324	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
325	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
326	C₂×C₇×C₈	C₂⁴	1	2	yes	—
327	C₂×C₇×C₈	C₂⁴	1	2	yes	—
328	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
329	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
330	C₇×C₄⋊C₄	—	2	2	no	—
331	C₇×C₄⋊C₄	—	2	2	no	—
332	C₇×C₄⋊C₄	—	2	2	no	—
333	C₇×C₄⋊C₄	—	2	2	no	—
334	C₇×C₄⋊C₄	—	2	2	no	—
335	C₇×C₄⋊C₄	—	2	2	no	—
336	C₇×C₄⋊C₄	—	2	2	no	—
337	C₇×C₄⋊C₄	—	2	2	no	—
338	C₇×C₄⋊C₄	—	2	2	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	—	2	2	no	—
344	C₇×C₄⋊C₄	—	2	2	no	—
345	C₇×C₄⋊C₄	—	2	2	no	—
346	C₇×C₄⋊C₄	—	2	2	no	—
347	C₇×C₄⋊C₄	—	2	2	no	—
348	C₇×C₄⋊C₄	—	2	2	no	—
349	C₇×C₄⋊C₄	—	2	2	no	—
350	C₇×C₄⋊C₄	—	2	2	no	—
351	C₇×C₄⋊C₄	—	2	2	no	—
352	C₇×C₄⋊C₄	—	2	2	no	—
353	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
354	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
355	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
356	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
357	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
358	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
359	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
360	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
361	C₇×C₂²⋊C₄	—	2	2	no	—
362	C₇×C₂²⋊C₄	—	2	2	no	—
363	C₇×C₂²⋊C₄	—	2	2	no	—
364	C₇×C₂²⋊C₄	—	2	2	no	—
365	C₇×C₂²⋊C₄	—	2	2	no	—
366	C₇×C₂²⋊C₄	—	2	2	no	—
367	C₇×C₂²⋊C₄	—	2	2	no	—
368	C₇×C₂²⋊C₄	—	2	2	no	—
369	C₇×C₂²⋊C₄	—	2	2	no	—
370	C₇×C₂²⋊C₄	—	2	2	no	—
371	C₇×C₂²⋊C₄	—	2	2	no	—
372	C₇×C₂²⋊C₄	—	2	2	no	—
373	C₇×C₂²⋊C₄	—	2	2	no	—
374	C₇×C₂²⋊C₄	—	2	2	no	—
375	C₇×C₂²⋊C₄	—	2	2	no	—
376	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
377	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
378	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
379	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
380	C₄²×C₇	—	2	2	no	—
381	C₄²×C₇	—	2	2	no	—
382	C₄²×C₇	—	2	2	no	—
383	C₄²×C₇	—	2	2	no	—
384	C₄²×C₇	—	2	2	no	—
385	C₄²×C₇	—	2	2	no	—
386	C₄²×C₇	—	2	2	no	—
387	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₇	C₂×D₄	1	2	yes	—
389	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₇	C₂⁴	1	1	yes	characteristic
391	C₄²×C₇	C₂⁴	1	1	yes	characteristic
392	C₄²×C₇	C₂⁴	1	2	yes	—
393	#556	—	2	2	no	—
394	#554	—	2	2	no	—
395	#552	—	2	2	no	—
396	#552	—	2	2	no	—
397	#552	—	2	2	no	—
398	#552	—	2	2	no	—
399	#551	—	2	2	no	—
400	#551	—	2	2	no	—
401	#544	C₂²×C₇	1	2	yes	—
402	#542	C₂²×C₇	1	2	yes	—
403	#542	C₂²×C₇	1	2	yes	—
404	#541	C₂²×C₇	1	2	yes	—
405	#541	C₂²×C₇	1	2	yes	—
406	#536	C₂²×C₇	1	2	yes	—
407	#533	C₂²×C₇	1	2	yes	—
408	#533	C₂²×C₇	1	2	yes	—
409	#529	C₂²×C₇	1	2	yes	—
410	#529	C₂²×C₇	1	2	yes	—
411	#525	C₂²×C₇	1	2	yes	—
412	C₂×C₂²⋊Q₈	C₂²×C₇	1	2	yes	—
413	#520	C₂²×C₇	1	2	yes	—
414	#519	C₂²×C₇	1	2	yes	—
415	C₂×#117	C₂²×C₇	1	1	yes	characteristic
416	#501	C₂²×C₇	1	2	yes	complemented
417	#499	C₂²×C₇	1	1	yes	characteristic, complemented
418	#498	C₂²×C₇	1	1	yes	characteristic, complemented
419	#497	C₂²×C₇	1	2	yes	complemented
420	#495	C₂²×C₇	1	1	yes	characteristic, complemented
421	#494	C₂²×C₇	1	1	yes	characteristic, complemented
422	#491	C₂²×C₇	1	2	yes	complemented
423	#489	C₂²×C₇	1	2	yes	complemented
424	#488	C₂²×C₇	1	2	yes	complemented
425	#487	C₂²×C₇	1	2	yes	complemented
426	#485	C₂²×C₇	1	2	yes	—
427	#485	C₂²×C₇	1	2	yes	—
428	#485	C₂²×C₇	1	2	yes	—
429	#484	C₂²×C₇	1	2	yes	—
430	#483	C₂²×C₇	1	2	yes	—
431	#483	C₂²×C₇	1	2	yes	—
432	#482	C₂²×C₇	1	2	yes	—
433	#481	C₂²×C₇	1	2	yes	—
434	#479	C₂²×C₇	1	2	yes	complemented
435	#479	C₂²×C₇	1	2	yes	complemented
436	#479	C₂²×C₇	1	2	yes	complemented
437	#478	C₂²×C₇	1	2	yes	complemented
438	#477	C₂²×C₇	1	2	yes	complemented
439	#476	C₂²×C₇	1	2	yes	complemented
440	#475	C₂²×C₇	1	2	yes	complemented
441	#475	C₂²×C₇	1	2	yes	complemented
442	#470	C₂²×C₇	1	2	yes	—
443	#470	C₂²×C₇	1	2	yes	—
444	#470	C₂²×C₇	1	1	yes	characteristic
445	#470	C₂²×C₇	1	1	yes	characteristic
446	#470	C₂²×C₇	1	2	yes	—
447	#470	C₂²×C₇	1	1	yes	characteristic
448	#469	C₂²×C₇	1	1	yes	characteristic
449	#468	C₂²×C₇	1	2	yes	—
450	#468	C₂²×C₇	1	2	yes	—
451	#468	C₂²×C₇	1	2	yes	—
452	#464	C₂²×C₇	1	2	yes	complemented
453	#464	C₂²×C₇	1	2	yes	complemented
454	#464	C₂²×C₇	1	2	yes	complemented
455	#463	C₂²×C₇	1	2	yes	complemented
456	#462	C₂²×C₇	1	2	yes	complemented
457	#462	C₂²×C₇	1	2	yes	complemented
458	#462	C₂²×C₇	1	2	yes	complemented
459	#461	C₂²×C₇	1	2	yes	complemented
460	#452	C₂²×C₇	1	2	yes	—
461	#452	C₂²×C₇	1	2	yes	—
462	#452	C₂²×C₇	1	2	yes	—
463	#451	C₂²×C₇	1	2	yes	—
464	#451	C₂²×C₇	1	2	yes	—
465	#451	C₂²×C₇	1	2	yes	—
466	#449	C₂²×C₇	1	2	yes	—
467	#448	C₂²×C₇	1	2	yes	—
468	#442	C₂²×C₇	1	1	yes	characteristic, complemented
469	#441	C₂²×C₇	1	1	yes	characteristic, complemented
470	#441	C₂²×C₇	1	1	yes	characteristic, complemented
471	#441	C₂²×C₇	1	2	yes	complemented
472	#441	C₂²×C₇	1	1	yes	characteristic, complemented
473	#440	C₂²×C₇	1	2	yes	complemented
474	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
475	C₄×Q₁₆	C₂²×C₇	1	2	yes	complemented
476	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
477	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
478	#433	C₂²×C₇	1	2	yes	—
479	#433	C₂²×C₇	1	2	yes	—
480	#433	C₂²×C₇	1	2	yes	—
481	#433	C₂²×C₇	1	2	yes	—
482	#423	C₂²×C₇	1	1	yes	characteristic
483	#423	C₂²×C₇	1	1	yes	characteristic
484	#407	C₂²×C₇	1	1	yes	characteristic
485	#407	C₂²×C₇	1	1	yes	characteristic
486	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
487	C₄×M₁₆	C₂²×C₇	1	1	yes	characteristic
488	C₂³×C₇	—	2	2	no	—
489	C₂³×C₇	—	4	1	no	—
490	C₂³×C₇	—	4	2	no	—
491	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
492	C₂³×C₇	C₂²×D₄	1	2	yes	—
493	C₇×Q₈	—	2	2	no	—
494	C₇×Q₈	—	2	2	no	—
495	C₇×Q₈	—	2	2	no	—
496	C₇×Q₈	—	2	2	no	—
497	C₇×Q₈	—	2	2	no	—
498	C₇×Q₈	—	2	2	no	—
499	C₇×Q₈	—	4	4	no	—
500	C₇×Q₈	—	8	2	no	—
501	C₇×Q₈	—	8	2	no	—
502	C₇×D₄	—	2	2	no	—
503	C₇×D₄	—	2	2	no	—
504	C₇×D₄	—	4	4	no	—
505	C₇×D₄	—	4	4	no	—
506	C₇×D₄	—	8	2	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	1	no	—
509	C₂×C₄×C₇	—	2	2	no	—
510	C₂×C₄×C₇	—	2	2	no	—
511	C₂×C₄×C₇	—	2	2	no	—
512	C₂×C₄×C₇	—	2	2	no	—
513	C₂×C₄×C₇	—	2	2	no	—
514	C₂×C₄×C₇	—	2	2	no	—
515	C₂×C₄×C₇	—	2	2	no	—
516	C₂×C₄×C₇	—	2	2	no	—
517	C₂×C₄×C₇	—	2	2	no	—
518	C₂×C₄×C₇	—	4	1	no	—
519	C₂×C₄×C₇	—	4	2	no	—
520	C₂×C₄×C₇	—	4	2	no	—
521	C₂×C₄×C₇	—	4	2	no	—
522	C₂×C₄×C₇	—	4	4	no	—
523	C₂×C₄×C₇	—	4	4	no	—
524	C₂×C₄×C₇	—	8	2	no	—
525	C₂×C₄×C₇	—	8	2	no	—
526	C₂×C₄×C₇	—	8	2	no	—
527	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
528	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
529	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
530	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
531	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
534	C₇×C₈	—	2	1	no	—
535	C₇×C₈	—	2	1	no	—
536	C₇×C₈	—	2	2	no	—
537	C₇×C₈	—	2	2	no	—
538	C₇×C₈	—	2	1	no	—
539	C₇×C₈	—	2	1	no	—
540	C₂×#41	C₂³×C₇	1	2	yes	—
541	C₂²×Q₈	C₂³×C₇	1	2	yes	—
542	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
543	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
544	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
545	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
546	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
547	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
548	C₂×Q₁₆	C₂³×C₇	1	1	yes	characteristic
549	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
552	C₂×D₈	C₂³×C₇	1	1	yes	characteristic
553	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
554	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
555	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
556	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
557	C₄⋊Q₈	—	2	2	no	—
558	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
559	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
560	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
561	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
562	#126	—	2	2	no	—
563	#126	—	2	2	no	—
564	#126	—	2	2	no	—
565	#126	—	2	2	no	—
566	#126	—	2	2	no	—
567	#126	—	2	2	no	—
568	#126	—	2	2	no	—
569	#126	—	2	2	no	—
570	#125	—	2	2	no	—
571	#125	—	2	2	no	—
572	#125	—	2	2	no	—
573	#125	—	2	2	no	—
574	#125	—	2	2	no	—
575	#125	—	2	2	no	—
576	#125	—	2	2	no	—
577	#125	C₂³×C₇	1	2	yes	—
578	#125	C₂³×C₇	1	2	yes	—
579	#124	—	2	2	no	—
580	#124	—	2	2	no	—
581	#124	C₂³×C₇	1	2	yes	—
582	#124	C₂³×C₇	1	2	yes	—
583	#123	—	2	2	no	—
584	#123	—	2	2	no	—
585	#123	—	2	2	no	—
586	#123	—	2	2	no	—
587	#123	—	2	2	no	—
588	#123	—	2	2	no	—
589	#123	—	2	2	no	—
590	C₂²⋊Q₈	—	2	2	no	—
591	C₂²⋊Q₈	—	2	2	no	—
592	C₂²⋊Q₈	—	2	2	no	—
593	C₂²⋊Q₈	—	2	2	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	2	no	—
596	C₂²⋊Q₈	—	2	2	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	—	2	2	no	—
600	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
601	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
602	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
603	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
604	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
605	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
606	#121	C₂³×C₇	1	2	yes	—
607	#121	C₂³×C₇	1	2	yes	—
608	#120	—	2	2	no	—
609	C₄×Q₈	—	2	2	no	—
610	C₄×Q₈	—	2	2	no	—
611	C₄×Q₈	—	2	2	no	—
612	C₄×Q₈	—	2	2	no	—
613	C₄×Q₈	C₂³×C₇	1	2	yes	—
614	C₄×Q₈	C₂³×C₇	1	2	yes	—
615	C₄×Q₈	C₂³×C₇	1	2	yes	—
616	C₄×Q₈	C₂³×C₇	1	2	yes	—
617	C₄×Q₈	C₂³×C₇	1	2	yes	—
618	C₄×Q₈	C₂³×C₇	1	2	yes	—
619	C₄×D₄	—	2	2	no	—
620	C₄×D₄	—	2	2	no	—
621	C₄×D₄	—	2	2	no	—
622	C₄×D₄	—	2	2	no	—
623	C₄×D₄	—	2	2	no	—
624	C₄×D₄	—	2	2	no	—
625	C₄×D₄	C₂³×C₇	1	2	yes	—
626	C₄×D₄	C₂³×C₇	1	2	yes	—
627	#117	—	2	2	no	—
628	#117	—	2	2	no	—
629	#117	—	2	2	no	—
630	#117	—	2	2	no	—
631	#117	—	2	2	no	—
632	#117	—	2	2	no	—
633	#117	—	2	2	no	—
634	#117	C₇×D₄	1	2	yes	—
635	#117	C₇×D₄	1	2	yes	—
636	#117	C₂³×C₇	1	2	yes	—
637	#117	C₂³×C₇	1	2	yes	—
638	#117	C₂³×C₇	1	2	yes	—
639	C₂×C₄⋊C₄	—	2	2	no	—
640	C₂×C₄⋊C₄	—	2	2	no	—
641	C₂×C₄⋊C₄	C₇×D₄	1	2	yes	—
642	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
643	C₂×C₂²⋊C₄	—	2	2	no	—
644	C₂×C₂²⋊C₄	C₇×D₄	1	2	yes	—
645	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
647	#107	C₂³×C₇	1	2	yes	—
648	#107	C₂³×C₇	1	2	yes	—
649	#107	C₂³×C₇	1	2	yes	—
650	#106	C₂³×C₇	1	2	yes	—
651	#106	C₂³×C₇	1	2	yes	—
652	#106	C₂³×C₇	1	1	yes	characteristic
653	#106	C₂³×C₇	1	1	yes	characteristic
654	#106	C₂³×C₇	1	2	yes	—
655	#106	C₂³×C₇	1	1	yes	characteristic
656	#106	C₂³×C₇	1	1	yes	characteristic
657	C₄⋊C₈	C₂³×C₇	1	2	yes	—
658	C₄⋊C₈	C₂³×C₇	1	2	yes	—
659	C₄⋊C₈	C₂³×C₇	1	2	yes	—
660	C₄⋊C₈	C₂³×C₇	1	2	yes	—
661	#103	C₂³×C₇	1	2	yes	—
662	#103	C₂³×C₇	1	2	yes	—
663	#103	C₂³×C₇	1	2	yes	—
664	#103	C₂³×C₇	1	2	yes	—
665	#103	C₂³×C₇	1	2	yes	—
666	#103	C₂³×C₇	1	2	yes	—
667	#103	C₂³×C₇	1	2	yes	—
668	#103	C₂³×C₇	1	2	yes	—
669	#103	C₂³×C₇	1	2	yes	—
670	#103	C₂³×C₇	1	2	yes	—
671	#103	C₂³×C₇	1	2	yes	—
672	#103	C₂³×C₇	1	2	yes	—
673	#102	C₂³×C₇	1	2	yes	—
674	#102	C₂³×C₇	1	2	yes	—
675	#102	C₂³×C₇	1	2	yes	—
676	#102	C₂³×C₇	1	2	yes	—
677	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
678	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
679	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
680	C₂²⋊C₈	C₂³×C₇	1	2	yes	—
681	#97	C₂³×C₇	1	1	yes	characteristic
682	#97	C₂³×C₇	1	1	yes	characteristic
683	#97	C₂³×C₇	1	2	yes	—
684	C₄×C₈	C₂³×C₇	1	2	yes	—
685	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
686	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
687	C₂²×C₇	—	2	2	no	—
688	C₂²×C₇	—	2	2	no	—
689	C₂²×C₇	—	2	2	no	—
690	C₂²×C₇	—	2	2	no	—
691	C₂²×C₇	—	2	1	no	—
692	C₂²×C₇	—	4	2	no	—
693	C₂²×C₇	—	4	2	no	—
694	C₂²×C₇	—	4	2	no	—
695	C₂²×C₇	—	8	2	no	—
696	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
697	C₄×C₇	—	2	2	no	—
698	C₄×C₇	—	2	2	no	—
699	C₄×C₇	—	2	2	no	—
700	C₄×C₇	—	2	2	no	—
701	C₄×C₇	—	2	2	no	—
702	C₄×C₇	—	2	1	no	—
703	C₄×C₇	—	4	2	no	—
704	C₄×C₇	—	4	2	no	—
705	C₄×C₇	—	4	2	no	—
706	C₄×C₇	—	4	2	no	—
707	C₄×C₇	—	4	2	no	—
708	C₄×C₇	—	4	2	no	—
709	C₄×C₇	—	4	2	no	—
710	C₄×C₇	#585	1	1	yes	characteristic
711	C₄×C₇	#585	1	1	yes	characteristic
712	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
713	#41	—	4	2	no	—
714	#41	—	4	2	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	2	no	—
718	C₂×Q₈	—	4	2	no	—
719	C₂×Q₈	—	4	2	no	—
720	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
721	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
722	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	C₂⁴×C₇	1	2	yes	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	2	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	4	1	no	—
733	C₂²×C₄	—	4	1	no	—
734	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
735	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
736	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
737	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
738	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
739	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
740	Q₁₆	—	4	1	no	—
741	Q₁₆	—	4	2	no	—
742	Q₁₆	—	4	2	no	—
743	Q₁₆	—	4	1	no	—
744	Q₁₆	—	4	2	no	—
745	Q₁₆	—	4	1	no	—
746	SD₁₆	—	4	2	no	—
747	SD₁₆	—	4	2	no	—
748	SD₁₆	—	4	2	no	—
749	D₈	—	4	1	no	—
750	M₁₆	—	4	1	no	—
751	M₁₆	—	4	1	no	—
752	M₁₆	—	4	1	no	—
753	M₁₆	—	4	1	no	—
754	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
755	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
756	C₂×C₈	C₂⁴×C₇	1	2	yes	—
757	C₂×C₈	C₂⁴×C₇	1	2	yes	—
758	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
759	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	2	no	—
762	C₄⋊C₄	—	2	2	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	2	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	2	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	2	no	—
772	C₄⋊C₄	—	2	2	no	—
773	C₄⋊C₄	—	2	2	no	—
774	C₄⋊C₄	—	2	2	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	2	no	—
782	C₄⋊C₄	—	2	2	no	—
783	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
784	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
785	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
786	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
787	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
788	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
789	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
790	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	2	no	—
796	C₂²⋊C₄	—	2	2	no	—
797	C₂²⋊C₄	—	2	2	no	—
798	C₂²⋊C₄	—	2	2	no	—
799	C₂²⋊C₄	—	2	2	no	—
800	C₂²⋊C₄	—	2	2	no	—
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	2	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	2	no	—
806	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
807	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
808	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
809	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
810	C₄²	—	2	2	no	—
811	C₄²	—	2	2	no	—
812	C₄²	—	2	2	no	—
813	C₄²	—	2	2	no	—
814	C₄²	—	2	2	no	—
815	C₄²	—	2	2	no	—
816	C₄²	—	2	2	no	—
817	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
818	C₄²	C₂×C₇×D₄	1	2	yes	—
819	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
820	C₄²	C₂⁴×C₇	1	1	yes	characteristic
821	C₄²	C₂⁴×C₇	1	1	yes	characteristic
822	C₄²	C₂⁴×C₇	1	2	yes	—
823	C₂×C₇	—	4	1	no	—
824	C₂×C₇	—	4	2	no	—
825	C₂×C₇	—	8	2	no	—
826	C₂×C₇	#3449	1	1	yes	characteristic
827	C₂×C₇	#3586	1	2	yes	—
828	C₂³	—	2	2	no	—
829	C₂³	—	4	1	no	—
830	C₂³	—	4	2	no	—
831	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
832	C₂³	C₂²×C₇×D₄	1	2	yes	—
833	Q₈	—	2	2	no	—
834	Q₈	—	2	2	no	—
835	Q₈	—	2	2	no	—
836	Q₈	—	2	2	no	—
837	Q₈	—	2	2	no	—
838	Q₈	—	2	2	no	—
839	Q₈	—	4	4	no	—
840	Q₈	—	8	2	no	—
841	Q₈	—	8	2	no	—
842	D₄	—	2	2	no	—
843	D₄	—	2	2	no	—
844	D₄	—	4	4	no	—
845	D₄	—	4	4	no	—
846	D₄	—	8	2	no	—
847	C₂×C₄	—	2	1	no	—
848	C₂×C₄	—	2	1	no	—
849	C₂×C₄	—	2	2	no	—
850	C₂×C₄	—	2	2	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	2	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	2	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	2	no	—
858	C₂×C₄	—	4	1	no	—
859	C₂×C₄	—	4	2	no	—
860	C₂×C₄	—	4	2	no	—
861	C₂×C₄	—	4	2	no	—
862	C₂×C₄	—	4	4	no	—
863	C₂×C₄	—	4	4	no	—
864	C₂×C₄	—	8	2	no	—
865	C₂×C₄	—	8	2	no	—
866	C₂×C₄	—	8	2	no	—
867	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
868	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
869	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
870	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
871	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
872	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
873	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
874	C₈	—	2	1	no	—
875	C₈	—	2	1	no	—
876	C₈	—	2	2	no	—
877	C₈	—	2	2	no	—
878	C₈	—	2	1	no	—
879	C₈	—	2	1	no	—
880	C₇	#61005	1	1	yes	characteristic, direct product factor, Sylow
881	C₂²	—	2	2	no	—
882	C₂²	—	2	2	no	—
883	C₂²	—	2	2	no	—
884	C₂²	—	2	2	no	—
885	C₂²	—	2	1	no	—
886	C₂²	—	4	2	no	—
887	C₂²	—	4	2	no	—
888	C₂²	—	4	2	no	—
889	C₂²	—	8	2	no	—
890	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
891	C₄	—	2	2	no	—
892	C₄	—	2	2	no	—
893	C₄	—	2	2	no	—
894	C₄	—	2	2	no	—
895	C₄	—	2	2	no	—
896	C₄	—	2	1	no	—
897	C₄	—	4	2	no	—
898	C₄	—	4	2	no	—
899	C₄	—	4	2	no	—
900	C₄	—	4	2	no	—
901	C₄	—	4	2	no	—
902	C₄	—	4	2	no	—
903	C₄	—	4	2	no	—
904	C₄	C₇×#585	1	1	yes	characteristic
905	C₄	C₇×#585	1	1	yes	characteristic
906	C₂	—	4	1	no	—
907	C₂	—	4	2	no	—
908	C₂	—	8	2	no	—
909	C₂	C₇×#3449	1	1	yes	characteristic
910	C₂	C₇×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3197	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂×C₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3495	C₂	semidirect
2. C₇×#3256	C₂	semidirect
3. C₇×#3255	C₂	semidirect
4. C₇×#3252	C₂	semidirect
5. C₇×#3244	C₂	semidirect
6. C₇×#3242	C₂	semidirect
7. C₇×#3225	C₂	semidirect
8. C₇×#3223	C₂	semidirect
10. C₇×#3196	C₂	semidirect
11. C₇×#3195	C₂	semidirect
12. C₇×#3185	C₂	semidirect
13. C₇×#3183	C₂	semidirect
14. C₇×#3172	C₂	semidirect
15. C₇×#3127	C₂	semidirect
16. C₇×#3125	C₂	semidirect
17. C₇×#3121	C₂	semidirect
18. C₇×#3120	C₂	semidirect
19. C₇×#2921	C₂	semidirect
43. C₇×#501	C₂²	semidirect
44. C₇×#499	C₂²	semidirect
45. C₇×#498	C₂²	semidirect
46. C₇×#497	C₂²	semidirect
47. C₇×#495	C₂²	semidirect
48. C₇×#494	C₂²	semidirect
49. C₇×#491	C₂²	semidirect
50. C₇×#489	C₂²	semidirect
51. C₇×#488	C₂²	semidirect
52. C₇×#487	C₂²	semidirect
61. C₇×#479	C₂²	semidirect
62. C₇×#479	C₂²	semidirect
63. C₇×#479	C₂²	semidirect
64. C₇×#478	C₂²	semidirect
65. C₇×#477	C₂²	semidirect
66. C₇×#476	C₂²	semidirect
67. C₇×#475	C₂²	semidirect
68. C₇×#475	C₂²	semidirect
79. C₇×#464	C₂²	semidirect
80. C₇×#464	C₂²	semidirect
81. C₇×#464	C₂²	semidirect
82. C₇×#463	C₂²	semidirect
83. C₇×#462	C₂²	semidirect
84. C₇×#462	C₂²	semidirect
85. C₇×#462	C₂²	semidirect
86. C₇×#461	C₂²	semidirect
95. C₇×#442	C₂²	semidirect
96. C₇×#441	C₂²	semidirect
97. C₇×#441	C₂²	semidirect
98. C₇×#441	C₂²	semidirect
99. C₇×#441	C₂²	semidirect
100. C₇×#440	C₂²	semidirect
101. C₄×C₇×Q₁₆	C₂²	semidirect
102. C₄×C₇×Q₁₆	C₂²	semidirect
103. C₄×C₇×SD₁₆	C₂²	semidirect
104. C₄×C₇×SD₁₆	C₂²	semidirect
115. #61005	C₇	direct (N × H)
263. #3495	C₂×C₇	semidirect
264. #3256	C₂×C₇	semidirect
265. #3255	C₂×C₇	semidirect
266. #3252	C₂×C₇	semidirect
267. #3244	C₂×C₇	semidirect
268. #3242	C₂×C₇	semidirect
269. #3225	C₂×C₇	semidirect
270. #3223	C₂×C₇	semidirect
272. #3196	C₂×C₇	semidirect
273. #3195	C₂×C₇	semidirect
274. #3185	C₂×C₇	semidirect
275. #3183	C₂×C₇	semidirect
276. #3172	C₂×C₇	semidirect
277. #3127	C₂×C₇	semidirect
278. #3125	C₂×C₇	semidirect
279. #3121	C₂×C₇	semidirect
280. #3120	C₂×C₇	semidirect
281. #2921	C₂×C₇	semidirect
416. #501	C₂²×C₇	semidirect
417. #499	C₂²×C₇	semidirect
418. #498	C₂²×C₇	semidirect
419. #497	C₂²×C₇	semidirect
420. #495	C₂²×C₇	semidirect
421. #494	C₂²×C₇	semidirect
422. #491	C₂²×C₇	semidirect
423. #489	C₂²×C₇	semidirect
424. #488	C₂²×C₇	semidirect
425. #487	C₂²×C₇	semidirect
434. #479	C₂²×C₇	semidirect
435. #479	C₂²×C₇	semidirect
436. #479	C₂²×C₇	semidirect
437. #478	C₂²×C₇	semidirect
438. #477	C₂²×C₇	semidirect
439. #476	C₂²×C₇	semidirect
440. #475	C₂²×C₇	semidirect
441. #475	C₂²×C₇	semidirect
452. #464	C₂²×C₇	semidirect
453. #464	C₂²×C₇	semidirect
454. #464	C₂²×C₇	semidirect
455. #463	C₂²×C₇	semidirect
456. #462	C₂²×C₇	semidirect
457. #462	C₂²×C₇	semidirect
458. #462	C₂²×C₇	semidirect
459. #461	C₂²×C₇	semidirect
468. #442	C₂²×C₇	semidirect
469. #441	C₂²×C₇	semidirect
470. #441	C₂²×C₇	semidirect
471. #441	C₂²×C₇	semidirect
472. #441	C₂²×C₇	semidirect
473. #440	C₂²×C₇	semidirect
474. C₄×Q₁₆	C₂²×C₇	semidirect
475. C₄×Q₁₆	C₂²×C₇	semidirect
476. C₄×SD₁₆	C₂²×C₇	semidirect
477. C₄×SD₁₆	C₂²×C₇	semidirect
880. C₇	#61005	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×#3495	2
C₇×#3256	2
C₇×#3255	2
C₇×#3252	2
C₇×#3244	2
C₇×#3242	2
C₇×#3225	2
C₇×#3223	2
C₇×#3197	2
C₇×#3196	2
C₇×#3195	2
C₇×#3185	2
C₇×#3183	2
C₇×#3172	2
C₇×#3127	2
C₇×#3125	2
C₇×#3121	2
C₇×#3120	2
C₇×#2921	2
#61005	7

Subgroups — C7×#61005 #13238221

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61005 #13238221