Subgroups — C₇×#36638 #13213854

Order 1792.

2082 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#2866	C₂	1	2	yes	maximal, complemented
2	C₇×#2865	C₂	1	2	yes	maximal, complemented
3	C₇×#2864	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2863	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2861	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#2860	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#2855	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#2854	C₂	1	1	yes	maximal, characteristic
9	C₇×#2853	C₂	1	2	yes	maximal, complemented
10	C₇×#2852	C₂	1	2	yes	maximal, complemented
11	C₇×#2851	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#2850	C₂	1	1	yes	maximal, characteristic
13	C₄×C₇×#125	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₇×#126	C₂	1	2	yes	maximal, complemented
15	C₄×C₇×#124	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₇×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×C₇×#123	C₂	1	2	yes	maximal, complemented
18	C₄×C₇×#121	C₂	1	1	yes	maximal, characteristic
19	C₇×#2298	C₂	1	2	yes	maximal, complemented
20	C₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
21	C₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
22	C₇×#2290	C₂	1	2	yes	maximal, complemented
23	C₂×C₄³×C₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₇×#126	C₂²	1	2	yes	—
25	C₂×C₇×#125	C₂²	1	1	yes	characteristic
26	C₂×C₇×#124	C₂²	1	1	yes	characteristic
27	C₂×C₇×#123	C₂²	1	2	yes	—
28	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₇×#121	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₇×D₄	C₂²	1	2	yes	—
32	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
33	C₂×C₇×#117	C₂²	1	2	yes	—
34	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
39	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
41	C₇×#391	C₂²	1	1	yes	characteristic
42	C₇×#391	C₂²	1	1	yes	characteristic
43	C₇×#391	C₂²	1	1	yes	characteristic
44	C₇×#391	C₂²	1	1	yes	characteristic
45	C₇×#390	C₂²	1	1	yes	characteristic
46	C₇×#390	C₂²	1	1	yes	characteristic
47	C₇×#390	C₂²	1	1	yes	characteristic
48	C₇×#390	C₂²	1	1	yes	characteristic
49	C₇×#389	C₂²	1	1	yes	characteristic
50	C₇×#389	C₂²	1	1	yes	characteristic
51	C₇×#389	C₂²	1	1	yes	characteristic
52	C₇×#389	C₂²	1	1	yes	characteristic
53	C₇×#389	C₂²	1	1	yes	characteristic
54	C₇×#389	C₂²	1	1	yes	characteristic
55	C₇×#389	C₂²	1	1	yes	characteristic
56	C₇×#389	C₂²	1	1	yes	characteristic
57	C₇×#388	C₂²	1	2	yes	—
58	C₇×#388	C₂²	1	2	yes	—
59	C₇×#388	C₂²	1	2	yes	—
60	C₇×#388	C₂²	1	2	yes	—
61	C₇×#388	C₂²	1	2	yes	—
62	C₇×#388	C₂²	1	2	yes	—
63	C₇×#388	C₂²	1	2	yes	—
64	C₇×#388	C₂²	1	2	yes	—
65	C₇×#388	C₂²	1	2	yes	—
66	C₇×#388	C₂²	1	2	yes	—
67	C₇×#388	C₂²	1	2	yes	—
68	C₇×#388	C₂²	1	2	yes	—
69	C₇×#388	C₂²	1	2	yes	—
70	C₇×#388	C₂²	1	2	yes	—
71	C₇×#388	C₂²	1	2	yes	—
72	C₇×#388	C₂²	1	2	yes	—
73	C₇×#387	C₂²	1	2	yes	—
74	C₇×#387	C₂²	1	2	yes	—
75	C₇×#387	C₂²	1	2	yes	—
76	C₇×#387	C₂²	1	2	yes	—
77	C₇×#387	C₂²	1	2	yes	—
78	C₇×#387	C₂²	1	2	yes	—
79	C₇×#387	C₂²	1	2	yes	—
80	C₇×#387	C₂²	1	2	yes	—
81	C₇×#387	C₂²	1	2	yes	—
82	C₇×#387	C₂²	1	2	yes	—
83	C₇×#387	C₂²	1	2	yes	—
84	C₇×#387	C₂²	1	2	yes	—
85	C₇×#387	C₂²	1	2	yes	—
86	C₇×#387	C₂²	1	2	yes	—
87	C₇×#387	C₂²	1	2	yes	—
88	C₇×#387	C₂²	1	2	yes	—
89	C₇×#386	C₂²	1	2	yes	—
90	C₇×#386	C₂²	1	2	yes	—
91	C₇×#386	C₂²	1	2	yes	—
92	C₇×#386	C₂²	1	2	yes	—
93	C₇×#385	C₂²	1	2	yes	—
94	C₇×#385	C₂²	1	2	yes	—
95	C₇×#385	C₂²	1	2	yes	—
96	C₇×#385	C₂²	1	2	yes	—
97	C₇×#383	C₂²	1	2	yes	—
98	C₇×#382	C₂²	1	1	yes	characteristic
99	C₇×#382	C₂²	1	1	yes	characteristic
100	C₇×#381	C₂²	1	2	yes	—
101	C₇×#380	C₂²	1	1	yes	characteristic
102	C₇×#380	C₂²	1	1	yes	characteristic
103	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
104	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
105	C₄×C₇×C₄⋊C₄	C₂²	1	1	yes	characteristic
106	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
107	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
108	C₄×C₇×C₄⋊C₄	C₂²	1	2	yes	—
109	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
110	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
111	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
112	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
113	C₄×C₇×C₂²⋊C₄	C₂²	1	2	yes	—
114	C₇×#376	C₂²	1	2	yes	—
115	C₄³×C₇	C₂²	1	1	yes	characteristic
116	C₄³×C₇	C₂²	1	1	yes	characteristic
117	C₄³×C₇	C₂²	1	1	yes	characteristic
118	C₄³×C₇	C₂²	1	1	yes	characteristic
119	C₄³×C₇	C₂²	1	1	yes	characteristic
120	C₄³×C₇	C₂²	1	1	yes	characteristic
121	C₄³×C₇	C₂²	1	1	yes	characteristic
122	C₄³×C₇	C₂²	1	1	yes	characteristic
123	#36638	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
124	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
125	C₂²×C₇×D₄	C₂³	1	2	yes	—
126	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
127	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
129	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
131	C₂³×C₄×C₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
135	C₇×#126	—	2	8	no	—
136	C₇×#125	—	2	4	no	—
137	C₇×#124	—	2	4	no	—
138	C₇×#123	—	2	8	no	—
139	C₇×C₂²⋊Q₈	—	2	4	no	—
140	C₇×#121	—	2	4	no	—
141	C₄×C₇×Q₈	—	2	4	no	—
142	C₄×C₇×D₄	—	2	8	no	—
143	C₄×C₇×D₄	—	2	4	no	—
144	C₇×#117	—	2	8	no	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
146	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
147	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
149	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
152	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
153	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
154	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
155	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
156	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
160	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
161	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
162	C₂×C₇×C₄⋊C₄	C₂³	1	2	yes	—
163	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
167	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
175	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
177	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
178	C₂×C₄²×C₇	—	2	4	no	—
179	C₂×C₄²×C₇	—	2	4	no	—
180	C₂×C₄²×C₇	—	2	4	no	—
181	C₂×C₄²×C₇	—	2	4	no	—
182	C₂×C₄²×C₇	—	2	4	no	—
183	C₂×C₄²×C₇	—	2	4	no	—
184	C₂×C₄²×C₇	—	2	4	no	—
185	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
186	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
187	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
190	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
191	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
192	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
193	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
202	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
203	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
204	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
205	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
206	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
208	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
209	C₂×C₄²×C₇	C₂³	1	2	yes	—
210	C₂×C₄²×C₇	C₂³	1	2	yes	—
211	C₂×C₄²×C₇	C₂³	1	2	yes	—
212	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
213	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
216	C₇×#95	C₂³	1	2	yes	—
217	C₇×#95	C₂³	1	2	yes	—
218	C₇×#95	C₂³	1	2	yes	—
219	C₇×#95	C₂³	1	2	yes	—
220	C₇×#95	C₂³	1	2	yes	—
221	C₇×#95	C₂³	1	2	yes	—
222	C₇×#95	C₂³	1	2	yes	—
223	C₇×#95	C₂³	1	2	yes	—
224	C₇×#95	C₂³	1	2	yes	—
225	C₇×#95	C₂³	1	2	yes	—
226	C₇×#95	C₂³	1	2	yes	—
227	C₇×#95	C₂³	1	2	yes	—
228	C₇×#95	C₂³	1	2	yes	—
229	C₇×#95	C₂³	1	2	yes	—
230	C₇×#95	C₂³	1	2	yes	—
231	C₇×#95	C₂³	1	2	yes	—
232	C₇×#95	C₂³	1	2	yes	—
233	C₇×#95	C₂³	1	2	yes	—
234	C₇×#95	C₂³	1	2	yes	—
235	C₇×#95	C₂³	1	2	yes	—
236	C₇×#95	C₂³	1	2	yes	—
237	C₇×#95	C₂³	1	2	yes	—
238	C₇×#95	C₂³	1	2	yes	—
239	C₇×#95	C₂³	1	2	yes	—
240	#2866	C₂×C₇	1	2	yes	complemented
241	#2865	C₂×C₇	1	2	yes	complemented
242	#2864	C₂×C₇	1	1	yes	characteristic, complemented
243	#2863	C₂×C₇	1	1	yes	characteristic, complemented
244	#2861	C₂×C₇	1	1	yes	characteristic, complemented
245	#2860	C₂×C₇	1	1	yes	characteristic, complemented
246	#2855	C₂×C₇	1	1	yes	characteristic, complemented
247	#2854	C₂×C₇	1	1	yes	characteristic
248	#2853	C₂×C₇	1	2	yes	complemented
249	#2852	C₂×C₇	1	2	yes	complemented
250	#2851	C₂×C₇	1	1	yes	characteristic, complemented
251	#2850	C₂×C₇	1	1	yes	characteristic
252	C₄×#125	C₂×C₇	1	1	yes	characteristic, complemented
253	C₄×#126	C₂×C₇	1	2	yes	complemented
254	C₄×#124	C₂×C₇	1	1	yes	characteristic, complemented
255	C₄×C₂²⋊Q₈	C₂×C₇	1	1	yes	characteristic, complemented
256	C₄×#123	C₂×C₇	1	2	yes	complemented
257	C₄×#121	C₂×C₇	1	1	yes	characteristic
258	#2298	C₂×C₇	1	2	yes	complemented
259	#2295	C₂×C₇	1	1	yes	characteristic, complemented
260	#2293	C₂×C₇	1	1	yes	characteristic, complemented
261	#2290	C₂×C₇	1	2	yes	complemented
262	C₂×C₄³	C₂×C₇	1	1	yes	characteristic, complemented
263	C₂⁴×C₇	C₂⁴	1	2	yes	—
264	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	—	2	2	no	—
268	C₂×C₇×D₄	—	2	4	no	—
269	C₂×C₇×D₄	—	2	4	no	—
270	C₂×C₇×D₄	—	2	4	no	—
271	C₂×C₇×D₄	—	2	2	no	—
272	C₂×C₇×D₄	—	2	2	no	—
273	C₂×C₇×D₄	—	2	2	no	—
274	C₂²×C₄×C₇	—	2	2	no	—
275	C₂²×C₄×C₇	—	2	2	no	—
276	C₂²×C₄×C₇	—	2	2	no	—
277	C₂²×C₄×C₇	—	2	2	no	—
278	C₂²×C₄×C₇	—	2	2	no	—
279	C₂²×C₄×C₇	—	2	2	no	—
280	C₂²×C₄×C₇	—	2	2	no	—
281	C₂²×C₄×C₇	—	2	2	no	—
282	C₂²×C₄×C₇	—	2	2	no	—
283	C₂²×C₄×C₇	—	2	2	no	—
284	C₂²×C₄×C₇	—	2	2	no	—
285	C₂²×C₄×C₇	—	2	2	no	—
286	C₂²×C₄×C₇	—	2	2	no	—
287	C₂²×C₄×C₇	—	2	2	no	—
288	C₂²×C₄×C₇	—	2	2	no	—
289	C₂²×C₄×C₇	—	2	2	no	—
290	C₂²×C₄×C₇	—	2	2	no	—
291	C₂²×C₄×C₇	—	2	2	no	—
292	C₂²×C₄×C₇	—	2	4	no	—
293	C₂²×C₄×C₇	—	2	4	no	—
294	C₂²×C₄×C₇	—	2	4	no	—
295	C₂²×C₄×C₇	#41	1	4	yes	—
296	C₂²×C₄×C₇	#41	1	4	yes	—
297	C₂²×C₄×C₇	#41	1	4	yes	—
298	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
300	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
303	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
312	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
317	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
319	C₇×C₄⋊C₄	—	2	4	no	—
320	C₇×C₄⋊C₄	—	2	4	no	—
321	C₇×C₄⋊C₄	—	2	4	no	—
322	C₇×C₄⋊C₄	—	2	2	no	—
323	C₇×C₄⋊C₄	—	2	2	no	—
324	C₇×C₄⋊C₄	—	2	4	no	—
325	C₇×C₄⋊C₄	—	2	2	no	—
326	C₇×C₄⋊C₄	—	2	2	no	—
327	C₇×C₄⋊C₄	—	2	4	no	—
328	C₇×C₄⋊C₄	—	2	4	no	—
329	C₇×C₄⋊C₄	—	2	4	no	—
330	C₇×C₄⋊C₄	—	2	4	no	—
331	C₇×C₄⋊C₄	—	2	4	no	—
332	C₇×C₄⋊C₄	—	2	2	no	—
333	C₇×C₄⋊C₄	—	2	2	no	—
334	C₇×C₄⋊C₄	—	2	4	no	—
335	C₇×C₄⋊C₄	—	2	4	no	—
336	C₇×C₄⋊C₄	—	2	4	no	—
337	C₇×C₂²⋊C₄	—	2	4	no	—
338	C₇×C₂²⋊C₄	—	2	4	no	—
339	C₇×C₂²⋊C₄	—	2	4	no	—
340	C₇×C₂²⋊C₄	—	2	4	no	—
341	C₇×C₂²⋊C₄	—	2	4	no	—
342	C₇×C₂²⋊C₄	—	2	4	no	—
343	C₇×C₂²⋊C₄	—	2	4	no	—
344	C₇×C₂²⋊C₄	—	2	4	no	—
345	C₇×C₂²⋊C₄	—	2	4	no	—
346	C₇×C₂²⋊C₄	—	2	4	no	—
347	C₇×C₂²⋊C₄	—	2	4	no	—
348	C₇×C₂²⋊C₄	—	2	4	no	—
349	C₇×C₂²⋊C₄	—	2	4	no	—
350	C₇×C₂²⋊C₄	—	2	4	no	—
351	C₇×C₂²⋊C₄	—	2	4	no	—
352	C₄²×C₇	—	2	2	no	—
353	C₄²×C₇	—	2	2	no	—
354	C₄²×C₇	—	2	2	no	—
355	C₄²×C₇	—	2	2	no	—
356	C₄²×C₇	—	2	2	no	—
357	C₄²×C₇	—	2	2	no	—
358	C₄²×C₇	—	2	2	no	—
359	C₄²×C₇	—	2	2	no	—
360	C₄²×C₇	—	2	2	no	—
361	C₄²×C₇	—	2	2	no	—
362	C₄²×C₇	—	2	2	no	—
363	C₄²×C₇	—	2	2	no	—
364	C₄²×C₇	—	2	2	no	—
365	C₄²×C₇	—	2	2	no	—
366	C₄²×C₇	—	2	2	no	—
367	C₄²×C₇	—	2	2	no	—
368	C₄²×C₇	—	2	2	no	—
369	C₄²×C₇	—	2	2	no	—
370	C₄²×C₇	—	2	2	no	—
371	C₄²×C₇	—	2	2	no	—
372	C₄²×C₇	—	2	2	no	—
373	C₄²×C₇	—	2	2	no	—
374	C₄²×C₇	—	2	2	no	—
375	C₄²×C₇	—	2	2	no	—
376	C₄²×C₇	—	2	4	no	—
377	C₄²×C₇	—	2	4	no	—
378	C₄²×C₇	—	2	4	no	—
379	C₄²×C₇	#41	1	4	yes	—
380	C₄²×C₇	#41	1	4	yes	—
381	C₄²×C₇	#41	1	4	yes	—
382	C₄²×C₇	#41	1	4	yes	—
383	C₂×#126	C₂²×C₇	1	2	yes	—
384	C₂×#125	C₂²×C₇	1	1	yes	characteristic
385	C₂×#124	C₂²×C₇	1	1	yes	characteristic
386	C₂×#123	C₂²×C₇	1	2	yes	—
387	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
388	C₂×#121	C₂²×C₇	1	1	yes	characteristic
389	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic
390	C₂×C₄×D₄	C₂²×C₇	1	2	yes	—
391	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
392	C₂×#117	C₂²×C₇	1	2	yes	—
393	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
394	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
395	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
396	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
397	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
398	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
399	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
400	#391	C₂²×C₇	1	1	yes	characteristic
401	#391	C₂²×C₇	1	1	yes	characteristic
402	#391	C₂²×C₇	1	1	yes	characteristic
403	#391	C₂²×C₇	1	1	yes	characteristic
404	#390	C₂²×C₇	1	1	yes	characteristic
405	#390	C₂²×C₇	1	1	yes	characteristic
406	#390	C₂²×C₇	1	1	yes	characteristic
407	#390	C₂²×C₇	1	1	yes	characteristic
408	#389	C₂²×C₇	1	1	yes	characteristic
409	#389	C₂²×C₇	1	1	yes	characteristic
410	#389	C₂²×C₇	1	1	yes	characteristic
411	#389	C₂²×C₇	1	1	yes	characteristic
412	#389	C₂²×C₇	1	1	yes	characteristic
413	#389	C₂²×C₇	1	1	yes	characteristic
414	#389	C₂²×C₇	1	1	yes	characteristic
415	#389	C₂²×C₇	1	1	yes	characteristic
416	#388	C₂²×C₇	1	2	yes	—
417	#388	C₂²×C₇	1	2	yes	—
418	#388	C₂²×C₇	1	2	yes	—
419	#388	C₂²×C₇	1	2	yes	—
420	#388	C₂²×C₇	1	2	yes	—
421	#388	C₂²×C₇	1	2	yes	—
422	#388	C₂²×C₇	1	2	yes	—
423	#388	C₂²×C₇	1	2	yes	—
424	#388	C₂²×C₇	1	2	yes	—
425	#388	C₂²×C₇	1	2	yes	—
426	#388	C₂²×C₇	1	2	yes	—
427	#388	C₂²×C₇	1	2	yes	—
428	#388	C₂²×C₇	1	2	yes	—
429	#388	C₂²×C₇	1	2	yes	—
430	#388	C₂²×C₇	1	2	yes	—
431	#388	C₂²×C₇	1	2	yes	—
432	#387	C₂²×C₇	1	2	yes	—
433	#387	C₂²×C₇	1	2	yes	—
434	#387	C₂²×C₇	1	2	yes	—
435	#387	C₂²×C₇	1	2	yes	—
436	#387	C₂²×C₇	1	2	yes	—
437	#387	C₂²×C₇	1	2	yes	—
438	#387	C₂²×C₇	1	2	yes	—
439	#387	C₂²×C₇	1	2	yes	—
440	#387	C₂²×C₇	1	2	yes	—
441	#387	C₂²×C₇	1	2	yes	—
442	#387	C₂²×C₇	1	2	yes	—
443	#387	C₂²×C₇	1	2	yes	—
444	#387	C₂²×C₇	1	2	yes	—
445	#387	C₂²×C₇	1	2	yes	—
446	#387	C₂²×C₇	1	2	yes	—
447	#387	C₂²×C₇	1	2	yes	—
448	#386	C₂²×C₇	1	2	yes	—
449	#386	C₂²×C₇	1	2	yes	—
450	#386	C₂²×C₇	1	2	yes	—
451	#386	C₂²×C₇	1	2	yes	—
452	#385	C₂²×C₇	1	2	yes	—
453	#385	C₂²×C₇	1	2	yes	—
454	#385	C₂²×C₇	1	2	yes	—
455	#385	C₂²×C₇	1	2	yes	—
456	#383	C₂²×C₇	1	2	yes	—
457	#382	C₂²×C₇	1	1	yes	characteristic
458	#382	C₂²×C₇	1	1	yes	characteristic
459	#381	C₂²×C₇	1	2	yes	—
460	#380	C₂²×C₇	1	1	yes	characteristic
461	#380	C₂²×C₇	1	1	yes	characteristic
462	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
463	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
464	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
465	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
466	C₄×C₄⋊C₄	C₂²×C₇	1	1	yes	characteristic
467	C₄×C₄⋊C₄	C₂²×C₇	1	2	yes	—
468	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
469	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
470	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
471	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
472	C₄×C₂²⋊C₄	C₂²×C₇	1	2	yes	—
473	#376	C₂²×C₇	1	2	yes	—
474	C₄³	C₂²×C₇	1	1	yes	characteristic
475	C₄³	C₂²×C₇	1	1	yes	characteristic
476	C₄³	C₂²×C₇	1	1	yes	characteristic
477	C₄³	C₂²×C₇	1	1	yes	characteristic
478	C₄³	C₂²×C₇	1	1	yes	characteristic
479	C₄³	C₂²×C₇	1	1	yes	characteristic
480	C₄³	C₂²×C₇	1	1	yes	characteristic
481	C₄³	C₂²×C₇	1	1	yes	characteristic
482	C₂³×C₇	—	2	1	no	—
483	C₂³×C₇	—	2	1	no	—
484	C₂³×C₇	—	2	1	no	—
485	C₂³×C₇	—	2	1	no	—
486	C₂³×C₇	—	2	2	no	—
487	C₂³×C₇	—	2	2	no	—
488	C₂³×C₇	—	2	2	no	—
489	C₂³×C₇	—	2	2	no	—
490	C₂³×C₇	—	2	2	no	—
491	C₂³×C₇	—	2	2	no	—
492	C₂³×C₇	—	2	2	no	—
493	C₂³×C₇	C₂×#41	1	2	yes	—
494	C₂³×C₇	C₂×#41	1	2	yes	—
495	C₂³×C₇	C₂×#41	1	2	yes	—
496	C₂³×C₇	C₂⁵	1	1	yes	characteristic
497	C₇×Q₈	—	4	4	no	—
498	C₇×D₄	—	4	8	no	—
499	C₇×D₄	—	4	4	no	—
500	C₂×C₄×C₇	—	2	8	no	—
501	C₂×C₄×C₇	—	2	8	no	—
502	C₂×C₄×C₇	—	2	8	no	—
503	C₂×C₄×C₇	—	2	8	no	—
504	C₂×C₄×C₇	—	2	8	no	—
505	C₂×C₄×C₇	—	2	1	no	—
506	C₂×C₄×C₇	—	2	1	no	—
507	C₂×C₄×C₇	—	2	1	no	—
508	C₂×C₄×C₇	—	2	1	no	—
509	C₂×C₄×C₇	—	2	1	no	—
510	C₂×C₄×C₇	—	2	1	no	—
511	C₂×C₄×C₇	—	2	1	no	—
512	C₂×C₄×C₇	—	2	1	no	—
513	C₂×C₄×C₇	—	2	1	no	—
514	C₂×C₄×C₇	—	2	1	no	—
515	C₂×C₄×C₇	—	2	1	no	—
516	C₂×C₄×C₇	—	2	1	no	—
517	C₂×C₄×C₇	—	2	1	no	—
518	C₂×C₄×C₇	—	2	1	no	—
519	C₂×C₄×C₇	—	2	1	no	—
520	C₂×C₄×C₇	—	2	1	no	—
521	C₂×C₄×C₇	—	2	1	no	—
522	C₂×C₄×C₇	—	2	1	no	—
523	C₂×C₄×C₇	—	2	1	no	—
524	C₂×C₄×C₇	—	2	1	no	—
525	C₂×C₄×C₇	—	2	1	no	—
526	C₂×C₄×C₇	—	2	1	no	—
527	C₂×C₄×C₇	—	2	1	no	—
528	C₂×C₄×C₇	—	2	1	no	—
529	C₂×C₄×C₇	—	2	8	no	—
530	C₂×C₄×C₇	—	2	8	no	—
531	C₂×C₄×C₇	—	2	2	no	—
532	C₂×C₄×C₇	—	2	2	no	—
533	C₂×C₄×C₇	—	2	2	no	—
534	C₂×C₄×C₇	—	2	2	no	—
535	C₂×C₄×C₇	—	2	2	no	—
536	C₂×C₄×C₇	—	2	2	no	—
537	C₂×C₄×C₇	—	2	2	no	—
538	C₂×C₄×C₇	—	2	2	no	—
539	C₂×C₄×C₇	—	2	2	no	—
540	C₂×C₄×C₇	—	2	2	no	—
541	C₂×C₄×C₇	—	2	2	no	—
542	C₂×C₄×C₇	—	2	2	no	—
543	C₂×C₄×C₇	—	2	2	no	—
544	C₂×C₄×C₇	—	2	2	no	—
545	C₂×C₄×C₇	—	2	2	no	—
546	C₂×C₄×C₇	—	2	2	no	—
547	C₂×C₄×C₇	—	2	2	no	—
548	C₂×C₄×C₇	—	2	2	no	—
549	C₂×C₄×C₇	—	2	2	no	—
550	C₂×C₄×C₇	—	2	2	no	—
551	C₂×C₄×C₇	—	2	2	no	—
552	C₂×C₄×C₇	—	4	8	no	—
553	C₂×C₄×C₇	C₂×#41	1	2	yes	—
554	C₂×C₄×C₇	C₂×#41	1	2	yes	—
555	C₂×C₄×C₇	C₂×#41	1	2	yes	—
556	C₂×C₄×C₇	C₂×#41	1	2	yes	—
557	C₂×C₄×C₇	C₂×#41	1	2	yes	—
558	C₂×C₄×C₇	C₂×#41	1	2	yes	—
559	C₂×C₄×C₇	C₂×#41	1	2	yes	—
560	C₂×C₄×C₇	C₂×#41	1	2	yes	—
561	C₂×C₄×C₇	C₂×#41	1	2	yes	—
562	C₂×C₄×C₇	C₂×#41	1	2	yes	—
563	C₂×C₄×C₇	C₂×#41	1	2	yes	—
564	C₂×C₄×C₇	C₂×#41	1	2	yes	—
565	C₂×C₄×C₇	C₂×#41	1	2	yes	—
566	C₂×C₄×C₇	C₂×#41	1	2	yes	—
567	C₂×C₄×C₇	C₂×#41	1	2	yes	—
568	C₂×C₄×C₇	C₂×#41	1	2	yes	—
569	C₂×C₄×C₇	C₂×#41	1	2	yes	—
570	C₂×C₄×C₇	C₂×#41	1	2	yes	—
571	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
572	C₂²×D₄	C₂³×C₇	1	2	yes	—
573	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
574	C₂³×C₄	C₂³×C₇	1	2	yes	—
575	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
576	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
577	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
578	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
579	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
580	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
581	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
582	#126	—	2	8	no	—
583	#125	—	2	4	no	—
584	#124	—	2	4	no	—
585	#123	—	2	8	no	—
586	C₂²⋊Q₈	—	2	4	no	—
587	#121	—	2	4	no	—
588	C₄×Q₈	—	2	4	no	—
589	C₄×D₄	—	2	8	no	—
590	C₄×D₄	—	2	4	no	—
591	#117	—	2	8	no	—
592	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
593	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
594	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
596	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
597	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
598	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
599	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
601	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
602	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
603	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
605	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
606	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
607	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
608	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
609	C₂×C₄⋊C₄	C₂³×C₇	1	2	yes	—
610	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
611	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
612	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
613	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
614	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
615	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
616	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
617	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
618	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
619	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
620	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
621	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
622	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
623	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
624	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
625	C₂×C₄²	—	2	4	no	—
626	C₂×C₄²	—	2	4	no	—
627	C₂×C₄²	—	2	4	no	—
628	C₂×C₄²	—	2	4	no	—
629	C₂×C₄²	—	2	4	no	—
630	C₂×C₄²	—	2	4	no	—
631	C₂×C₄²	—	2	4	no	—
632	C₂×C₄²	C₂³×C₇	1	2	yes	—
633	C₂×C₄²	C₂³×C₇	1	2	yes	—
634	C₂×C₄²	C₂³×C₇	1	2	yes	—
635	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
636	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
637	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
638	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
639	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
640	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
641	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
642	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
643	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
644	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
645	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
646	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
647	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
648	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
650	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
651	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
652	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
653	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
654	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
655	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
656	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
657	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
658	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
659	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
660	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
661	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
662	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
663	#95	C₂³×C₇	1	2	yes	—
664	#95	C₂³×C₇	1	2	yes	—
665	#95	C₂³×C₇	1	2	yes	—
666	#95	C₂³×C₇	1	2	yes	—
667	#95	C₂³×C₇	1	2	yes	—
668	#95	C₂³×C₇	1	2	yes	—
669	#95	C₂³×C₇	1	2	yes	—
670	#95	C₂³×C₇	1	2	yes	—
671	#95	C₂³×C₇	1	2	yes	—
672	#95	C₂³×C₇	1	2	yes	—
673	#95	C₂³×C₇	1	2	yes	—
674	#95	C₂³×C₇	1	2	yes	—
675	#95	C₂³×C₇	1	2	yes	—
676	#95	C₂³×C₇	1	2	yes	—
677	#95	C₂³×C₇	1	2	yes	—
678	#95	C₂³×C₇	1	2	yes	—
679	#95	C₂³×C₇	1	2	yes	—
680	#95	C₂³×C₇	1	2	yes	—
681	#95	C₂³×C₇	1	2	yes	—
682	#95	C₂³×C₇	1	2	yes	—
683	#95	C₂³×C₇	1	2	yes	—
684	#95	C₂³×C₇	1	2	yes	—
685	#95	C₂³×C₇	1	2	yes	—
686	#95	C₂³×C₇	1	2	yes	—
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	2	no	—
692	C₂²×C₇	—	2	2	no	—
693	C₂²×C₇	—	4	2	no	—
694	C₂²×C₇	—	4	2	no	—
695	C₂²×C₇	—	4	2	no	—
696	C₂²×C₇	—	4	2	no	—
697	C₂²×C₇	—	4	2	no	—
698	C₂²×C₇	—	4	2	no	—
699	C₂²×C₇	—	4	2	no	—
700	C₂²×C₇	#529	1	4	yes	—
701	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
702	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
703	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
704	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
705	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
706	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
707	C₂²×C₇	C₂²×#41	1	1	yes	characteristic
708	C₄×C₇	—	2	2	no	—
709	C₄×C₇	—	2	2	no	—
710	C₄×C₇	—	2	2	no	—
711	C₄×C₇	—	2	2	no	—
712	C₄×C₇	—	2	2	no	—
713	C₄×C₇	—	2	2	no	—
714	C₄×C₇	—	2	2	no	—
715	C₄×C₇	—	2	2	no	—
716	C₄×C₇	—	2	2	no	—
717	C₄×C₇	—	2	2	no	—
718	C₄×C₇	—	2	2	no	—
719	C₄×C₇	—	2	2	no	—
720	C₄×C₇	—	4	2	no	—
721	C₄×C₇	—	4	2	no	—
722	C₄×C₇	—	4	2	no	—
723	C₄×C₇	—	4	2	no	—
724	C₄×C₇	—	4	2	no	—
725	C₄×C₇	—	4	2	no	—
726	C₄×C₇	—	4	2	no	—
727	C₄×C₇	#529	1	4	yes	—
728	C₄×C₇	#529	1	4	yes	—
729	C₂⁴	C₂⁴×C₇	1	2	yes	—
730	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
731	C₂×Q₈	—	2	2	no	—
732	C₂×Q₈	—	2	2	no	—
733	C₂×Q₈	—	2	2	no	—
734	C₂×D₄	—	2	4	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	2	4	no	—
737	C₂×D₄	—	2	2	no	—
738	C₂×D₄	—	2	2	no	—
739	C₂×D₄	—	2	2	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	2	no	—
742	C₂²×C₄	—	2	2	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	2	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	2	no	—
750	C₂²×C₄	—	2	2	no	—
751	C₂²×C₄	—	2	2	no	—
752	C₂²×C₄	—	2	2	no	—
753	C₂²×C₄	—	2	2	no	—
754	C₂²×C₄	—	2	2	no	—
755	C₂²×C₄	—	2	2	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	2	no	—
758	C₂²×C₄	—	2	4	no	—
759	C₂²×C₄	—	2	4	no	—
760	C₂²×C₄	—	2	4	no	—
761	C₂²×C₄	C₇×#41	1	4	yes	—
762	C₂²×C₄	C₇×#41	1	4	yes	—
763	C₂²×C₄	C₇×#41	1	4	yes	—
764	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
765	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
766	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
767	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
768	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
769	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
770	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
771	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
772	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
773	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
774	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
775	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
776	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
777	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
778	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
779	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
780	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
781	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
782	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
783	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
784	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
785	C₄⋊C₄	—	2	4	no	—
786	C₄⋊C₄	—	2	4	no	—
787	C₄⋊C₄	—	2	4	no	—
788	C₄⋊C₄	—	2	2	no	—
789	C₄⋊C₄	—	2	2	no	—
790	C₄⋊C₄	—	2	4	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	4	no	—
794	C₄⋊C₄	—	2	4	no	—
795	C₄⋊C₄	—	2	4	no	—
796	C₄⋊C₄	—	2	4	no	—
797	C₄⋊C₄	—	2	4	no	—
798	C₄⋊C₄	—	2	2	no	—
799	C₄⋊C₄	—	2	2	no	—
800	C₄⋊C₄	—	2	4	no	—
801	C₄⋊C₄	—	2	4	no	—
802	C₄⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	—	2	4	no	—
804	C₂²⋊C₄	—	2	4	no	—
805	C₂²⋊C₄	—	2	4	no	—
806	C₂²⋊C₄	—	2	4	no	—
807	C₂²⋊C₄	—	2	4	no	—
808	C₂²⋊C₄	—	2	4	no	—
809	C₂²⋊C₄	—	2	4	no	—
810	C₂²⋊C₄	—	2	4	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	4	no	—
814	C₂²⋊C₄	—	2	4	no	—
815	C₂²⋊C₄	—	2	4	no	—
816	C₂²⋊C₄	—	2	4	no	—
817	C₂²⋊C₄	—	2	4	no	—
818	C₄²	—	2	2	no	—
819	C₄²	—	2	2	no	—
820	C₄²	—	2	2	no	—
821	C₄²	—	2	2	no	—
822	C₄²	—	2	2	no	—
823	C₄²	—	2	2	no	—
824	C₄²	—	2	2	no	—
825	C₄²	—	2	2	no	—
826	C₄²	—	2	2	no	—
827	C₄²	—	2	2	no	—
828	C₄²	—	2	2	no	—
829	C₄²	—	2	2	no	—
830	C₄²	—	2	2	no	—
831	C₄²	—	2	2	no	—
832	C₄²	—	2	2	no	—
833	C₄²	—	2	2	no	—
834	C₄²	—	2	2	no	—
835	C₄²	—	2	2	no	—
836	C₄²	—	2	2	no	—
837	C₄²	—	2	2	no	—
838	C₄²	—	2	2	no	—
839	C₄²	—	2	2	no	—
840	C₄²	—	2	2	no	—
841	C₄²	—	2	2	no	—
842	C₄²	—	2	4	no	—
843	C₄²	—	2	4	no	—
844	C₄²	—	2	4	no	—
845	C₄²	C₇×#41	1	4	yes	—
846	C₄²	C₇×#41	1	4	yes	—
847	C₄²	C₇×#41	1	4	yes	—
848	C₄²	C₇×#41	1	4	yes	—
849	C₂×C₇	—	2	4	no	—
850	C₂×C₇	—	8	2	no	—
851	C₂×C₇	C₂×#529	1	1	yes	characteristic
852	C₂×C₇	C₂×#529	1	1	yes	characteristic
853	C₂×C₇	C₂×#529	1	1	yes	characteristic
854	C₂×C₇	#3444	1	1	yes	characteristic
855	C₂×C₇	#3444	1	1	yes	characteristic
856	C₂×C₇	#3444	1	1	yes	characteristic
857	C₂×C₇	#3444	1	1	yes	characteristic
858	C₂³	—	2	1	no	—
859	C₂³	—	2	1	no	—
860	C₂³	—	2	1	no	—
861	C₂³	—	2	1	no	—
862	C₂³	—	2	2	no	—
863	C₂³	—	2	2	no	—
864	C₂³	—	2	2	no	—
865	C₂³	—	2	2	no	—
866	C₂³	—	2	2	no	—
867	C₂³	—	2	2	no	—
868	C₂³	—	2	2	no	—
869	C₂³	C₂×C₇×#41	1	2	yes	—
870	C₂³	C₂×C₇×#41	1	2	yes	—
871	C₂³	C₂×C₇×#41	1	2	yes	—
872	C₂³	C₂⁵×C₇	1	1	yes	characteristic
873	Q₈	—	4	4	no	—
874	D₄	—	4	8	no	—
875	D₄	—	4	4	no	—
876	C₂×C₄	—	2	8	no	—
877	C₂×C₄	—	2	8	no	—
878	C₂×C₄	—	2	8	no	—
879	C₂×C₄	—	2	8	no	—
880	C₂×C₄	—	2	1	no	—
881	C₂×C₄	—	2	1	no	—
882	C₂×C₄	—	2	1	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	1	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	1	no	—
888	C₂×C₄	—	2	1	no	—
889	C₂×C₄	—	2	1	no	—
890	C₂×C₄	—	2	1	no	—
891	C₂×C₄	—	2	1	no	—
892	C₂×C₄	—	2	1	no	—
893	C₂×C₄	—	2	1	no	—
894	C₂×C₄	—	2	1	no	—
895	C₂×C₄	—	2	1	no	—
896	C₂×C₄	—	2	1	no	—
897	C₂×C₄	—	2	1	no	—
898	C₂×C₄	—	2	1	no	—
899	C₂×C₄	—	2	1	no	—
900	C₂×C₄	—	2	1	no	—
901	C₂×C₄	—	2	1	no	—
902	C₂×C₄	—	2	1	no	—
903	C₂×C₄	—	2	1	no	—
904	C₂×C₄	—	2	8	no	—
905	C₂×C₄	—	2	8	no	—
906	C₂×C₄	—	2	8	no	—
907	C₂×C₄	—	2	2	no	—
908	C₂×C₄	—	2	2	no	—
909	C₂×C₄	—	2	2	no	—
910	C₂×C₄	—	2	2	no	—
911	C₂×C₄	—	2	2	no	—
912	C₂×C₄	—	2	2	no	—
913	C₂×C₄	—	2	2	no	—
914	C₂×C₄	—	2	2	no	—
915	C₂×C₄	—	2	2	no	—
916	C₂×C₄	—	2	2	no	—
917	C₂×C₄	—	2	2	no	—
918	C₂×C₄	—	2	2	no	—
919	C₂×C₄	—	2	2	no	—
920	C₂×C₄	—	2	2	no	—
921	C₂×C₄	—	2	2	no	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	2	no	—
924	C₂×C₄	—	2	2	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	2	2	no	—
927	C₂×C₄	—	2	2	no	—
928	C₂×C₄	—	4	8	no	—
929	C₂×C₄	C₂×C₇×#41	1	2	yes	—
930	C₂×C₄	C₂×C₇×#41	1	2	yes	—
931	C₂×C₄	C₂×C₇×#41	1	2	yes	—
932	C₂×C₄	C₂×C₇×#41	1	2	yes	—
933	C₂×C₄	C₂×C₇×#41	1	2	yes	—
934	C₂×C₄	C₂×C₇×#41	1	2	yes	—
935	C₂×C₄	C₂×C₇×#41	1	2	yes	—
936	C₂×C₄	C₂×C₇×#41	1	2	yes	—
937	C₂×C₄	C₂×C₇×#41	1	2	yes	—
938	C₂×C₄	C₂×C₇×#41	1	2	yes	—
939	C₂×C₄	C₂×C₇×#41	1	2	yes	—
940	C₂×C₄	C₂×C₇×#41	1	2	yes	—
941	C₂×C₄	C₂×C₇×#41	1	2	yes	—
942	C₂×C₄	C₂×C₇×#41	1	2	yes	—
943	C₂×C₄	C₂×C₇×#41	1	2	yes	—
944	C₂×C₄	C₂×C₇×#41	1	2	yes	—
945	C₂×C₄	C₂×C₇×#41	1	2	yes	—
946	C₂×C₄	C₂×C₇×#41	1	2	yes	—
947	C₇	#36638	1	1	yes	characteristic, direct product factor, Sylow
948	C₂²	—	2	2	no	—
949	C₂²	—	2	2	no	—
950	C₂²	—	2	2	no	—
951	C₂²	—	2	2	no	—
952	C₂²	—	2	2	no	—
953	C₂²	—	2	2	no	—
954	C₂²	—	4	2	no	—
955	C₂²	—	4	2	no	—
956	C₂²	—	4	2	no	—
957	C₂²	—	4	2	no	—
958	C₂²	—	4	2	no	—
959	C₂²	—	4	2	no	—
960	C₂²	—	4	2	no	—
961	C₂²	C₇×#529	1	4	yes	—
962	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
963	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
964	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
965	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
966	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
967	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
968	C₂²	C₂²×C₇×#41	1	1	yes	characteristic
969	C₄	—	2	2	no	—
970	C₄	—	2	2	no	—
971	C₄	—	2	2	no	—
972	C₄	—	2	2	no	—
973	C₄	—	2	2	no	—
974	C₄	—	2	2	no	—
975	C₄	—	2	2	no	—
976	C₄	—	2	2	no	—
977	C₄	—	2	2	no	—
978	C₄	—	2	2	no	—
979	C₄	—	2	2	no	—
980	C₄	—	2	2	no	—
981	C₄	—	4	2	no	—
982	C₄	—	4	2	no	—
983	C₄	—	4	2	no	—
984	C₄	—	4	2	no	—
985	C₄	—	4	2	no	—
986	C₄	—	4	2	no	—
987	C₄	—	4	2	no	—
988	C₄	C₇×#529	1	4	yes	—
989	C₄	C₇×#529	1	4	yes	—
990	C₂	—	2	4	no	—
991	C₂	—	8	2	no	—
992	C₂	C₂×C₇×#529	1	1	yes	characteristic
993	C₂	C₂×C₇×#529	1	1	yes	characteristic
994	C₂	C₂×C₇×#529	1	1	yes	characteristic
995	C₂	C₇×#3444	1	1	yes	characteristic
996	C₂	C₇×#3444	1	1	yes	characteristic
997	C₂	C₇×#3444	1	1	yes	characteristic
998	C₂	C₇×#3444	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₇
socle	C₂³×C₇	C₂⁵
prime radical	C₂×C₇×#121	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#2866	C₂	semidirect
2. C₇×#2865	C₂	semidirect
3. C₇×#2864	C₂	semidirect
4. C₇×#2863	C₂	semidirect
5. C₇×#2861	C₂	semidirect
6. C₇×#2860	C₂	semidirect
7. C₇×#2855	C₂	semidirect
9. C₇×#2853	C₂	semidirect
10. C₇×#2852	C₂	semidirect
11. C₇×#2851	C₂	semidirect
13. C₄×C₇×#125	C₂	semidirect
14. C₄×C₇×#126	C₂	semidirect
15. C₄×C₇×#124	C₂	semidirect
16. C₄×C₇×C₂²⋊Q₈	C₂	semidirect
17. C₄×C₇×#123	C₂	semidirect
19. C₇×#2298	C₂	semidirect
20. C₇×#2295	C₂	semidirect
21. C₇×#2293	C₂	semidirect
22. C₇×#2290	C₂	semidirect
23. C₂×C₄³×C₇	C₂	semidirect
123. #36638	C₇	direct (N × H)
240. #2866	C₂×C₇	semidirect
241. #2865	C₂×C₇	semidirect
242. #2864	C₂×C₇	semidirect
243. #2863	C₂×C₇	semidirect
244. #2861	C₂×C₇	semidirect
245. #2860	C₂×C₇	semidirect
246. #2855	C₂×C₇	semidirect
248. #2853	C₂×C₇	semidirect
249. #2852	C₂×C₇	semidirect
250. #2851	C₂×C₇	semidirect
252. C₄×#125	C₂×C₇	semidirect
253. C₄×#126	C₂×C₇	semidirect
254. C₄×#124	C₂×C₇	semidirect
255. C₄×C₂²⋊Q₈	C₂×C₇	semidirect
256. C₄×#123	C₂×C₇	semidirect
258. #2298	C₂×C₇	semidirect
259. #2295	C₂×C₇	semidirect
260. #2293	C₂×C₇	semidirect
261. #2290	C₂×C₇	semidirect
262. C₂×C₄³	C₂×C₇	semidirect
947. C₇	#36638	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×#2866	2
C₇×#2865	2
C₇×#2864	2
C₇×#2863	2
C₇×#2861	2
C₇×#2860	2
C₇×#2855	2
C₇×#2854	2
C₇×#2853	2
C₇×#2852	2
C₇×#2851	2
C₇×#2850	2
C₄×C₇×#125	2
C₄×C₇×#126	2
C₄×C₇×#124	2
C₄×C₇×C₂²⋊Q₈	2
C₄×C₇×#123	2
C₄×C₇×#121	2
C₇×#2298	2
C₇×#2295	2
C₇×#2293	2
C₇×#2290	2
C₂×C₄³×C₇	2
#36638	7

Subgroups — C7×#36638 #13213854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#36638 #13213854