Subgroups — C₇×#22889 #13200105

Order 1792.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3002	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#443	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2933	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₇×#421	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2880	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1975	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1937	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1929	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1897	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1876	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1876	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1866	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1855	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1765	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₇×#41	C₂²	1	1	yes	characteristic
17	C₂×C₇×#135	C₂²	1	1	yes	characteristic
18	C₂×C₇×#135	C₂²	1	1	yes	characteristic
19	C₂×C₇×#131	C₂²	1	1	yes	characteristic
20	C₂×C₇×#131	C₂²	1	1	yes	characteristic
21	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
22	C₂²×C₇×M₁₆	C₂²	1	1	yes	characteristic
23	C₇×#525	C₂²	1	1	yes	characteristic
24	C₂×C₇×#117	C₂²	1	1	yes	characteristic
25	C₇×#452	C₄	1	1	yes	characteristic, complemented
26	C₇×#452	C₄	1	1	yes	characteristic, complemented
27	C₇×#451	C₄	1	1	yes	characteristic, complemented
28	C₇×#450	C₄	1	1	yes	characteristic, complemented
29	C₇×#449	C₄	1	1	yes	characteristic, complemented
30	C₇×#449	C₄	1	1	yes	characteristic, complemented
31	C₇×#448	C₄	1	1	yes	characteristic, complemented
32	C₇×#447	C₄	1	1	yes	characteristic, complemented
33	C₇×#443	—	2	4	no	—
34	C₇×#436	—	2	1	no	—
35	C₇×#435	—	2	1	no	—
36	C₇×#435	—	2	1	no	—
37	C₇×C₈×D₄	—	2	1	no	—
38	C₂×C₇×#108	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₇×#108	C₂²	1	1	yes	characteristic, complemented
40	C₇×#424	C₂²	1	1	yes	characteristic, complemented
41	C₇×#421	—	2	4	no	—
42	C₂×C₇×#104	C₂²	1	1	yes	characteristic
43	C₂×C₇×#104	C₂²	1	1	yes	characteristic
44	C₂×C₇×#104	C₂²	1	1	yes	characteristic
45	C₂×C₇×#104	C₂²	1	1	yes	characteristic
46	C₂×C₇×#104	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₇×#104	C₂²	1	1	yes	characteristic, complemented
48	C₇×#416	C₂²	1	1	yes	characteristic
49	C₇×#416	C₂²	1	1	yes	characteristic
50	C₇×#408	—	2	1	no	—
51	C₇×#408	—	2	1	no	—
52	C₇×#408	C₂²	1	1	yes	characteristic
53	C₇×#408	C₂²	1	1	yes	characteristic
54	C₇×#408	C₂²	1	1	yes	characteristic, complemented
55	C₇×#407	—	2	1	no	—
56	C₇×#407	C₂²	1	1	yes	characteristic
57	C₂×C₇×C₂²⋊C₈	—	2	1	no	—
58	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₂×C₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
60	C₇×#405	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
62	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
63	C₇×#341	C₂²	1	1	yes	characteristic, complemented
64	C₇×#341	C₂²	1	1	yes	characteristic, complemented
65	C₇×#339	C₂²	1	1	yes	characteristic, complemented
66	C₇×#339	C₂²	1	1	yes	characteristic, complemented
67	C₇×#336	C₂²	1	1	yes	characteristic, complemented
68	C₇×#336	C₂²	1	1	yes	characteristic, complemented
69	#22889	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
70	C₂×C₇×#41	—	2	1	no	—
71	C₂×C₇×#41	—	2	1	no	—
72	C₂×C₇×#41	—	2	2	no	—
73	C₂×C₇×#41	—	2	2	no	—
74	C₂×C₇×#41	—	4	1	no	—
75	C₂×C₇×#41	—	4	1	no	—
76	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
77	C₂×C₇×#41	C₂×C₄	1	1	yes	characteristic
78	C₂×C₇×#41	C₂³	1	1	yes	characteristic
79	C₂×C₇×#41	C₂³	1	1	yes	characteristic
80	C₂×C₇×#41	C₂³	1	1	yes	characteristic
81	C₂²×C₇×Q₈	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₇×D₄	—	2	1	no	—
83	C₂²×C₇×D₄	C₂×C₄	1	1	yes	characteristic
84	C₂³×C₄×C₇	—	2	1	no	—
85	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
86	C₇×#135	—	2	2	no	—
87	C₇×#135	—	2	2	no	—
88	C₇×#135	—	4	1	no	—
89	C₇×#135	—	4	1	no	—
90	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
91	C₂×C₇×Q₁₆	C₂×C₄	1	1	yes	characteristic
92	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
93	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
94	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
95	C₂×C₇×SD₁₆	C₂×C₄	1	1	yes	characteristic
96	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
97	C₂×C₇×D₈	C₂×C₄	1	1	yes	characteristic
98	C₇×#131	—	2	2	no	—
99	C₇×#131	—	2	2	no	—
100	C₇×#131	—	2	2	no	—
101	C₇×#131	—	4	1	no	—
102	C₇×#131	—	4	1	no	—
103	C₇×#131	—	4	1	no	—
104	C₂×C₇×M₁₆	—	2	1	no	—
105	C₂×C₇×M₁₆	—	2	1	no	—
106	C₂×C₇×M₁₆	—	2	1	no	—
107	C₂×C₇×M₁₆	—	2	1	no	—
108	C₂×C₇×M₁₆	—	2	2	no	—
109	C₂×C₇×M₁₆	—	4	1	no	—
110	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
111	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
112	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
113	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
114	C₂²×C₇×C₈	—	2	1	no	—
115	C₂²×C₇×C₈	—	2	1	no	—
116	C₂²×C₇×C₈	—	2	1	no	—
117	C₂²×C₇×C₈	—	2	1	no	—
118	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
119	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
120	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
121	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
122	C₇×#123	—	2	1	no	—
123	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
124	C₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
125	C₇×#121	C₂×C₄	1	1	yes	characteristic
126	C₇×#121	C₂×C₄	1	1	yes	characteristic
127	C₇×#120	—	2	1	no	—
128	C₄×C₇×D₄	—	2	1	no	—
129	C₄×C₇×D₄	—	2	1	no	—
130	C₇×#117	—	2	2	no	—
131	C₇×#117	—	4	1	no	—
132	C₇×#117	C₂³	1	1	yes	characteristic
133	C₂×C₇×C₄⋊C₄	—	2	1	no	—
134	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
137	C₇×#108	—	2	2	no	—
138	C₇×#108	—	4	1	no	—
139	C₇×C₄⋊C₈	—	2	1	no	—
140	C₇×C₄⋊C₈	—	2	1	no	—
141	C₇×#104	—	2	2	no	—
142	C₇×#104	—	2	2	no	—
143	C₇×#104	—	2	2	no	—
144	C₇×#104	—	2	2	no	—
145	C₇×#104	—	4	1	no	—
146	C₇×#104	D₄	1	4	yes	complemented
147	C₇×#103	C₂×C₄	1	1	yes	characteristic
148	C₇×#103	C₂×C₄	1	1	yes	characteristic
149	C₇×#103	C₂×C₄	1	1	yes	characteristic
150	C₇×#103	C₂×C₄	1	1	yes	characteristic
151	C₇×#102	C₂×C₄	1	1	yes	characteristic
152	C₇×#102	C₂×C₄	1	1	yes	characteristic
153	C₇×#102	C₂×C₄	1	1	yes	characteristic
154	C₇×#102	C₂×C₄	1	1	yes	characteristic
155	C₇×C₂²⋊C₈	—	2	1	no	—
156	C₇×C₂²⋊C₈	—	2	1	no	—
157	C₇×C₂²⋊C₈	—	2	1	no	—
158	C₇×C₂²⋊C₈	—	2	1	no	—
159	C₇×C₂²⋊C₈	—	2	1	no	—
160	C₇×C₂²⋊C₈	—	2	1	no	—
161	C₇×C₂²⋊C₈	—	2	1	no	—
162	C₇×C₂²⋊C₈	—	2	1	no	—
163	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
164	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
165	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
166	C₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
167	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
168	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
169	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
170	C₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
171	C₇×#97	—	2	1	no	—
172	C₇×#97	—	4	1	no	—
173	C₄×C₇×C₈	—	2	1	no	—
174	C₄×C₇×C₈	—	2	2	no	—
175	#3002	C₂×C₇	1	1	yes	characteristic
176	C₂×#443	C₂×C₇	1	1	yes	characteristic, complemented
177	#2933	C₂×C₇	1	1	yes	characteristic, complemented
178	C₂×#421	C₂×C₇	1	1	yes	characteristic, complemented
179	#2880	C₂×C₇	1	1	yes	characteristic, complemented
180	#1975	C₂×C₇	1	1	yes	characteristic, complemented
181	#1937	C₂×C₇	1	1	yes	characteristic, complemented
182	#1929	C₂×C₇	1	1	yes	characteristic, complemented
183	#1897	C₂×C₇	1	1	yes	characteristic, complemented
184	#1876	C₂×C₇	1	1	yes	characteristic, complemented
185	#1876	C₂×C₇	1	1	yes	characteristic, complemented
186	#1866	C₂×C₇	1	1	yes	characteristic, complemented
187	#1855	C₂×C₇	1	1	yes	characteristic, complemented
188	#1765	C₂×C₇	1	1	yes	characteristic, complemented
189	#1750	C₂×C₇	1	1	yes	characteristic, complemented
190	C₂⁴×C₇	—	2	1	no	—
191	C₂⁴×C₇	#41	1	1	yes	characteristic
192	C₇×#41	—	2	1	no	—
193	C₇×#41	—	2	1	no	—
194	C₇×#41	—	2	2	no	—
195	C₇×#41	—	2	2	no	—
196	C₇×#41	—	2	1	no	—
197	C₇×#41	—	2	1	no	—
198	C₇×#41	—	2	1	no	—
199	C₇×#41	—	2	1	no	—
200	C₇×#41	—	2	1	no	—
201	C₇×#41	—	2	1	no	—
202	C₇×#41	—	2	1	no	—
203	C₇×#41	—	2	1	no	—
204	C₇×#41	—	4	2	no	—
205	C₇×#41	—	4	2	no	—
206	C₇×#41	—	4	1	no	—
207	C₇×#41	—	4	1	no	—
208	C₇×#41	—	4	2	no	—
209	C₇×#41	—	4	2	no	—
210	C₇×#41	C₂×D₄	1	2	yes	—
211	C₇×#41	#41	1	2	yes	—
212	C₂×C₇×Q₈	—	2	1	no	—
213	C₂×C₇×Q₈	—	2	2	no	—
214	C₂×C₇×Q₈	—	4	1	no	—
215	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
216	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
217	C₂×C₇×Q₈	C₂²×C₄	1	1	yes	characteristic
218	C₂×C₇×D₄	—	2	1	no	—
219	C₂×C₇×D₄	—	2	2	no	—
220	C₂×C₇×D₄	—	2	1	no	—
221	C₂×C₇×D₄	—	2	1	no	—
222	C₂×C₇×D₄	—	2	1	no	—
223	C₂×C₇×D₄	—	2	1	no	—
224	C₂×C₇×D₄	—	2	1	no	—
225	C₂×C₇×D₄	—	2	1	no	—
226	C₂×C₇×D₄	—	2	1	no	—
227	C₂×C₇×D₄	—	4	1	no	—
228	C₂×C₇×D₄	—	4	2	no	—
229	C₂×C₇×D₄	—	4	2	no	—
230	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
231	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
232	C₂×C₇×D₄	C₂²×C₄	1	1	yes	characteristic
233	C₂²×C₄×C₇	—	2	1	no	—
234	C₂²×C₄×C₇	—	2	1	no	—
235	C₂²×C₄×C₇	—	2	1	no	—
236	C₂²×C₄×C₇	—	2	1	no	—
237	C₂²×C₄×C₇	—	2	1	no	—
238	C₂²×C₄×C₇	—	2	1	no	—
239	C₂²×C₄×C₇	—	2	1	no	—
240	C₂²×C₄×C₇	—	2	1	no	—
241	C₂²×C₄×C₇	—	2	1	no	—
242	C₂²×C₄×C₇	—	2	1	no	—
243	C₂²×C₄×C₇	—	2	1	no	—
244	C₂²×C₄×C₇	—	2	1	no	—
245	C₂²×C₄×C₇	—	4	2	no	—
246	C₂²×C₄×C₇	—	4	2	no	—
247	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
248	C₂²×C₄×C₇	C₂²×C₄	1	1	yes	characteristic
249	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
250	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₇	#41	1	1	yes	characteristic
252	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
253	C₇×Q₁₆	—	2	2	no	—
254	C₇×Q₁₆	—	4	1	no	—
255	C₇×SD₁₆	—	2	2	no	—
256	C₇×SD₁₆	—	2	2	no	—
257	C₇×SD₁₆	—	4	1	no	—
258	C₇×SD₁₆	—	4	1	no	—
259	C₇×D₈	—	2	2	no	—
260	C₇×D₈	—	4	1	no	—
261	C₇×M₁₆	—	2	1	no	—
262	C₇×M₁₆	—	2	1	no	—
263	C₇×M₁₆	—	2	1	no	—
264	C₇×M₁₆	—	2	1	no	—
265	C₇×M₁₆	—	2	1	no	—
266	C₇×M₁₆	—	2	1	no	—
267	C₇×M₁₆	—	2	1	no	—
268	C₇×M₁₆	—	4	2	no	—
269	C₇×M₁₆	—	4	2	no	—
270	C₇×M₁₆	—	4	2	no	—
271	C₇×M₁₆	—	4	2	no	—
272	C₇×M₁₆	C₂×D₄	1	2	yes	—
273	C₂×C₇×C₈	—	2	1	no	—
274	C₂×C₇×C₈	—	2	1	no	—
275	C₂×C₇×C₈	—	2	1	no	—
276	C₂×C₇×C₈	—	2	1	no	—
277	C₂×C₇×C₈	—	2	1	no	—
278	C₂×C₇×C₈	—	2	1	no	—
279	C₂×C₇×C₈	—	2	1	no	—
280	C₂×C₇×C₈	—	2	1	no	—
281	C₂×C₇×C₈	—	2	1	no	—
282	C₂×C₇×C₈	—	2	1	no	—
283	C₂×C₇×C₈	—	2	1	no	—
284	C₂×C₇×C₈	—	2	1	no	—
285	C₂×C₇×C₈	—	4	2	no	—
286	C₂×C₇×C₈	—	4	2	no	—
287	C₂×C₇×C₈	—	4	2	no	—
288	C₂×C₇×C₈	—	4	2	no	—
289	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
290	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
291	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
292	C₂×C₇×C₈	C₂²×C₄	1	1	yes	characteristic
293	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
294	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
295	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
296	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
297	C₇×C₄⋊C₄	—	2	1	no	—
298	C₇×C₄⋊C₄	—	2	1	no	—
299	C₇×C₄⋊C₄	—	4	2	no	—
300	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
301	C₇×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
302	C₇×C₂²⋊C₄	—	2	1	no	—
303	C₇×C₂²⋊C₄	—	2	1	no	—
304	C₇×C₂²⋊C₄	—	2	1	no	—
305	C₇×C₂²⋊C₄	—	2	1	no	—
306	C₇×C₂²⋊C₄	—	2	1	no	—
307	C₇×C₂²⋊C₄	—	4	2	no	—
308	C₄²×C₇	—	2	1	no	—
309	C₄²×C₇	—	2	1	no	—
310	C₄²×C₇	—	2	1	no	—
311	C₄²×C₇	—	2	1	no	—
312	C₄²×C₇	C₂×D₄	1	2	yes	—
313	C₂²×#41	C₂²×C₇	1	1	yes	characteristic
314	C₂×#135	C₂²×C₇	1	1	yes	characteristic
315	C₂×#135	C₂²×C₇	1	1	yes	characteristic
316	C₂×#131	C₂²×C₇	1	1	yes	characteristic
317	C₂×#131	C₂²×C₇	1	1	yes	characteristic
318	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
319	C₂²×M₁₆	C₂²×C₇	1	1	yes	characteristic
320	#525	C₂²×C₇	1	1	yes	characteristic
321	C₂×#117	C₂²×C₇	1	1	yes	characteristic
322	#452	C₄×C₇	1	1	yes	characteristic, complemented
323	#452	C₄×C₇	1	1	yes	characteristic, complemented
324	#451	C₄×C₇	1	1	yes	characteristic, complemented
325	#450	C₄×C₇	1	1	yes	characteristic, complemented
326	#449	C₄×C₇	1	1	yes	characteristic, complemented
327	#449	C₄×C₇	1	1	yes	characteristic, complemented
328	#448	C₄×C₇	1	1	yes	characteristic, complemented
329	#447	C₄×C₇	1	1	yes	characteristic, complemented
330	#443	—	2	4	no	—
331	#436	—	2	1	no	—
332	#435	—	2	1	no	—
333	#435	—	2	1	no	—
334	C₈×D₄	—	2	1	no	—
335	C₂×#108	C₂²×C₇	1	1	yes	characteristic, complemented
336	C₂×#108	C₂²×C₇	1	1	yes	characteristic, complemented
337	#424	C₂²×C₇	1	1	yes	characteristic, complemented
338	#421	—	2	4	no	—
339	C₂×#104	C₂²×C₇	1	1	yes	characteristic
340	C₂×#104	C₂²×C₇	1	1	yes	characteristic
341	C₂×#104	C₂²×C₇	1	1	yes	characteristic
342	C₂×#104	C₂²×C₇	1	1	yes	characteristic
343	C₂×#104	C₂²×C₇	1	1	yes	characteristic, complemented
344	C₂×#104	C₂²×C₇	1	1	yes	characteristic, complemented
345	#416	C₂²×C₇	1	1	yes	characteristic
346	#416	C₂²×C₇	1	1	yes	characteristic
347	#408	—	2	1	no	—
348	#408	—	2	1	no	—
349	#408	C₂²×C₇	1	1	yes	characteristic
350	#408	C₂²×C₇	1	1	yes	characteristic
351	#408	C₂²×C₇	1	1	yes	characteristic, complemented
352	#407	—	2	1	no	—
353	#407	C₂²×C₇	1	1	yes	characteristic
354	C₂×C₂²⋊C₈	—	2	1	no	—
355	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
356	C₂×C₂²⋊C₈	C₂²×C₇	1	1	yes	characteristic
357	#405	C₂²×C₇	1	1	yes	characteristic, complemented
358	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
359	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
360	#341	C₂²×C₇	1	1	yes	characteristic, complemented
361	#341	C₂²×C₇	1	1	yes	characteristic, complemented
362	#339	C₂²×C₇	1	1	yes	characteristic, complemented
363	#339	C₂²×C₇	1	1	yes	characteristic, complemented
364	#336	C₂²×C₇	1	1	yes	characteristic, complemented
365	#336	C₂²×C₇	1	1	yes	characteristic, complemented
366	C₂³×C₇	—	2	1	no	—
367	C₂³×C₇	—	2	1	no	—
368	C₂³×C₇	—	2	1	no	—
369	C₂³×C₇	—	2	1	no	—
370	C₂³×C₇	—	2	1	no	—
371	C₂³×C₇	—	4	1	no	—
372	C₂³×C₇	—	4	1	no	—
373	C₂³×C₇	—	4	2	no	—
374	C₂³×C₇	—	4	2	no	—
375	C₂³×C₇	—	8	1	no	—
376	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
377	C₂³×C₇	C₄×D₄	1	1	yes	characteristic
378	C₂³×C₇	C₂×#41	1	1	yes	characteristic
379	C₇×Q₈	—	2	1	no	—
380	C₇×Q₈	—	2	1	no	—
381	C₇×Q₈	—	2	1	no	—
382	C₇×Q₈	—	2	1	no	—
383	C₇×Q₈	—	2	1	no	—
384	C₇×Q₈	—	4	2	no	—
385	C₇×Q₈	C₄×D₄	1	2	yes	—
386	C₇×D₄	—	2	2	no	—
387	C₇×D₄	—	2	2	no	—
388	C₇×D₄	—	2	1	no	—
389	C₇×D₄	—	2	1	no	—
390	C₇×D₄	—	2	1	no	—
391	C₇×D₄	—	2	1	no	—
392	C₇×D₄	—	2	1	no	—
393	C₇×D₄	—	4	2	no	—
394	C₇×D₄	—	4	2	no	—
395	C₇×D₄	—	4	2	no	—
396	C₇×D₄	—	4	2	no	—
397	C₇×D₄	—	4	1	no	—
398	C₇×D₄	—	4	1	no	—
399	C₇×D₄	—	4	1	no	—
400	C₇×D₄	—	4	1	no	—
401	C₇×D₄	—	8	1	no	—
402	C₇×D₄	C₄×D₄	1	2	yes	—
403	C₂×C₄×C₇	—	2	1	no	—
404	C₂×C₄×C₇	—	2	1	no	—
405	C₂×C₄×C₇	—	2	1	no	—
406	C₂×C₄×C₇	—	2	1	no	—
407	C₂×C₄×C₇	—	2	1	no	—
408	C₂×C₄×C₇	—	2	1	no	—
409	C₂×C₄×C₇	—	2	1	no	—
410	C₂×C₄×C₇	—	2	1	no	—
411	C₂×C₄×C₇	—	2	2	no	—
412	C₂×C₄×C₇	—	2	1	no	—
413	C₂×C₄×C₇	—	2	2	no	—
414	C₂×C₄×C₇	—	2	1	no	—
415	C₂×C₄×C₇	—	2	1	no	—
416	C₂×C₄×C₇	—	2	1	no	—
417	C₂×C₄×C₇	—	2	1	no	—
418	C₂×C₄×C₇	—	2	1	no	—
419	C₂×C₄×C₇	—	2	1	no	—
420	C₂×C₄×C₇	—	2	2	no	—
421	C₂×C₄×C₇	—	4	2	no	—
422	C₂×C₄×C₇	—	4	2	no	—
423	C₂×C₄×C₇	—	4	2	no	—
424	C₂×C₄×C₇	—	4	1	no	—
425	C₂×C₄×C₇	—	4	1	no	—
426	C₂×C₄×C₇	—	4	1	no	—
427	C₂×C₄×C₇	—	4	1	no	—
428	C₂×C₄×C₇	—	4	1	no	—
429	C₂×C₄×C₇	—	4	1	no	—
430	C₂×C₄×C₇	—	4	1	no	—
431	C₂×C₄×C₇	—	4	1	no	—
432	C₂×C₄×C₇	—	4	1	no	—
433	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
434	C₂×C₄×C₇	C₄×D₄	1	1	yes	characteristic
435	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
436	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
437	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
438	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
439	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
440	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
441	C₇×C₈	—	2	1	no	—
442	C₇×C₈	—	2	1	no	—
443	C₇×C₈	—	2	1	no	—
444	C₇×C₈	—	2	1	no	—
445	C₇×C₈	—	2	1	no	—
446	C₇×C₈	—	2	1	no	—
447	C₇×C₈	—	2	2	no	—
448	C₇×C₈	—	2	1	no	—
449	C₇×C₈	—	2	1	no	—
450	C₇×C₈	—	4	1	no	—
451	C₇×C₈	—	4	1	no	—
452	C₇×C₈	—	4	1	no	—
453	C₂×#41	—	2	1	no	—
454	C₂×#41	—	2	1	no	—
455	C₂×#41	—	2	2	no	—
456	C₂×#41	—	2	2	no	—
457	C₂×#41	—	4	1	no	—
458	C₂×#41	—	4	1	no	—
459	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
460	C₂×#41	C₂×C₄×C₇	1	1	yes	characteristic
461	C₂×#41	C₂³×C₇	1	1	yes	characteristic
462	C₂×#41	C₂³×C₇	1	1	yes	characteristic
463	C₂×#41	C₂³×C₇	1	1	yes	characteristic
464	C₂²×Q₈	C₂×C₄×C₇	1	1	yes	characteristic
465	C₂²×D₄	—	2	1	no	—
466	C₂²×D₄	C₂×C₄×C₇	1	1	yes	characteristic
467	C₂³×C₄	—	2	1	no	—
468	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
469	#135	—	2	2	no	—
470	#135	—	2	2	no	—
471	#135	—	4	1	no	—
472	#135	—	4	1	no	—
473	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
474	C₂×Q₁₆	C₂×C₄×C₇	1	1	yes	characteristic
475	C₂×SD₁₆	C₂×C₄×C₇	1	1	yes	characteristic
476	C₂×SD₁₆	C₂×C₄×C₇	1	1	yes	characteristic
477	C₂×SD₁₆	C₂×C₄×C₇	1	1	yes	characteristic
478	C₂×SD₁₆	C₂×C₄×C₇	1	1	yes	characteristic
479	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
480	C₂×D₈	C₂×C₄×C₇	1	1	yes	characteristic
481	#131	—	2	2	no	—
482	#131	—	2	2	no	—
483	#131	—	2	2	no	—
484	#131	—	4	1	no	—
485	#131	—	4	1	no	—
486	#131	—	4	1	no	—
487	C₂×M₁₆	—	2	1	no	—
488	C₂×M₁₆	—	2	1	no	—
489	C₂×M₁₆	—	2	1	no	—
490	C₂×M₁₆	—	2	1	no	—
491	C₂×M₁₆	—	2	2	no	—
492	C₂×M₁₆	—	4	1	no	—
493	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
494	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
495	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
496	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
497	C₂²×C₈	—	2	1	no	—
498	C₂²×C₈	—	2	1	no	—
499	C₂²×C₈	—	2	1	no	—
500	C₂²×C₈	—	2	1	no	—
501	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
503	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
504	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
505	#123	—	2	1	no	—
506	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
507	C₂²⋊Q₈	C₂×C₄×C₇	1	1	yes	characteristic
508	#121	C₂×C₄×C₇	1	1	yes	characteristic
509	#121	C₂×C₄×C₇	1	1	yes	characteristic
510	#120	—	2	1	no	—
511	C₄×D₄	—	2	1	no	—
512	C₄×D₄	—	2	1	no	—
513	#117	—	2	2	no	—
514	#117	—	4	1	no	—
515	#117	C₂³×C₇	1	1	yes	characteristic
516	C₂×C₄⋊C₄	—	2	1	no	—
517	C₂×C₂²⋊C₄	—	2	1	no	—
518	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
519	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
520	#108	—	2	2	no	—
521	#108	—	4	1	no	—
522	C₄⋊C₈	—	2	1	no	—
523	C₄⋊C₈	—	2	1	no	—
524	#104	—	2	2	no	—
525	#104	—	2	2	no	—
526	#104	—	2	2	no	—
527	#104	—	2	2	no	—
528	#104	—	4	1	no	—
529	#104	C₇×D₄	1	4	yes	complemented
530	#103	C₂×C₄×C₇	1	1	yes	characteristic
531	#103	C₂×C₄×C₇	1	1	yes	characteristic
532	#103	C₂×C₄×C₇	1	1	yes	characteristic
533	#103	C₂×C₄×C₇	1	1	yes	characteristic
534	#102	C₂×C₄×C₇	1	1	yes	characteristic
535	#102	C₂×C₄×C₇	1	1	yes	characteristic
536	#102	C₂×C₄×C₇	1	1	yes	characteristic
537	#102	C₂×C₄×C₇	1	1	yes	characteristic
538	C₂²⋊C₈	—	2	1	no	—
539	C₂²⋊C₈	—	2	1	no	—
540	C₂²⋊C₈	—	2	1	no	—
541	C₂²⋊C₈	—	2	1	no	—
542	C₂²⋊C₈	—	2	1	no	—
543	C₂²⋊C₈	—	2	1	no	—
544	C₂²⋊C₈	—	2	1	no	—
545	C₂²⋊C₈	—	2	1	no	—
546	C₂²⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
547	C₂²⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
548	C₂²⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
549	C₂²⋊C₈	C₂×C₄×C₇	1	1	yes	characteristic
550	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
551	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
552	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
553	C₂²⋊C₈	C₇×D₄	1	1	yes	characteristic
554	#97	—	2	1	no	—
555	#97	—	4	1	no	—
556	C₄×C₈	—	2	1	no	—
557	C₄×C₈	—	2	2	no	—
558	C₂²×C₇	—	2	1	no	—
559	C₂²×C₇	—	2	1	no	—
560	C₂²×C₇	—	2	1	no	—
561	C₂²×C₇	—	2	1	no	—
562	C₂²×C₇	—	2	2	no	—
563	C₂²×C₇	—	2	1	no	—
564	C₂²×C₇	—	2	1	no	—
565	C₂²×C₇	—	2	1	no	—
566	C₂²×C₇	—	2	1	no	—
567	C₂²×C₇	—	4	1	no	—
568	C₂²×C₇	—	4	1	no	—
569	C₂²×C₇	—	4	1	no	—
570	C₂²×C₇	—	4	1	no	—
571	C₂²×C₇	—	4	1	no	—
572	C₂²×C₇	—	4	1	no	—
573	C₂²×C₇	—	4	1	no	—
574	C₂²×C₇	—	4	1	no	—
575	C₂²×C₇	—	8	1	no	—
576	C₂²×C₇	—	8	1	no	—
577	C₂²×C₇	—	8	4	no	—
578	C₂²×C₇	C₂×C₄×D₄	1	1	yes	characteristic
579	C₂²×C₇	#546	1	1	yes	characteristic
580	C₂²×C₇	#551	1	1	yes	characteristic
581	C₄×C₇	—	2	1	no	—
582	C₄×C₇	—	2	1	no	—
583	C₄×C₇	—	2	2	no	—
584	C₄×C₇	—	4	2	no	—
585	C₄×C₇	—	4	1	no	—
586	C₄×C₇	—	4	1	no	—
587	C₄×C₇	—	4	1	no	—
588	C₄×C₇	—	4	1	no	—
589	C₄×C₇	—	8	1	no	—
590	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
591	C₄×C₇	#518	1	1	yes	characteristic
592	C₄×C₇	D₄²	1	1	yes	characteristic
593	C₄×C₇	#546	1	1	yes	characteristic
594	C₂⁴	—	2	1	no	—
595	C₂⁴	C₇×#41	1	1	yes	characteristic
596	#41	—	2	1	no	—
597	#41	—	2	1	no	—
598	#41	—	2	2	no	—
599	#41	—	2	2	no	—
600	#41	—	2	1	no	—
601	#41	—	2	1	no	—
602	#41	—	2	1	no	—
603	#41	—	2	1	no	—
604	#41	—	2	1	no	—
605	#41	—	2	1	no	—
606	#41	—	2	1	no	—
607	#41	—	2	1	no	—
608	#41	—	4	2	no	—
609	#41	—	4	2	no	—
610	#41	—	4	1	no	—
611	#41	—	4	1	no	—
612	#41	—	4	2	no	—
613	#41	—	4	2	no	—
614	#41	C₂×C₇×D₄	1	2	yes	—
615	#41	C₇×#41	1	2	yes	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	2	no	—
618	C₂×Q₈	—	4	1	no	—
619	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
620	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
621	C₂×Q₈	C₂²×C₄×C₇	1	1	yes	characteristic
622	C₂×D₄	—	2	1	no	—
623	C₂×D₄	—	2	2	no	—
624	C₂×D₄	—	2	1	no	—
625	C₂×D₄	—	2	1	no	—
626	C₂×D₄	—	2	1	no	—
627	C₂×D₄	—	2	1	no	—
628	C₂×D₄	—	2	1	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	4	1	no	—
632	C₂×D₄	—	4	2	no	—
633	C₂×D₄	—	4	2	no	—
634	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
635	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
636	C₂×D₄	C₂²×C₄×C₇	1	1	yes	characteristic
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	1	no	—
642	C₂²×C₄	—	2	1	no	—
643	C₂²×C₄	—	2	1	no	—
644	C₂²×C₄	—	2	1	no	—
645	C₂²×C₄	—	2	1	no	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	1	no	—
648	C₂²×C₄	—	2	1	no	—
649	C₂²×C₄	—	4	2	no	—
650	C₂²×C₄	—	4	2	no	—
651	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
652	C₂²×C₄	C₂²×C₄×C₇	1	1	yes	characteristic
653	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
654	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
655	C₂²×C₄	C₇×#41	1	1	yes	characteristic
656	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
657	Q₁₆	—	2	2	no	—
658	Q₁₆	—	4	1	no	—
659	SD₁₆	—	2	2	no	—
660	SD₁₆	—	2	2	no	—
661	SD₁₆	—	4	1	no	—
662	SD₁₆	—	4	1	no	—
663	D₈	—	2	2	no	—
664	D₈	—	4	1	no	—
665	M₁₆	—	2	1	no	—
666	M₁₆	—	2	1	no	—
667	M₁₆	—	2	1	no	—
668	M₁₆	—	2	1	no	—
669	M₁₆	—	2	1	no	—
670	M₁₆	—	2	1	no	—
671	M₁₆	—	2	1	no	—
672	M₁₆	—	4	2	no	—
673	M₁₆	—	4	2	no	—
674	M₁₆	—	4	2	no	—
675	M₁₆	—	4	2	no	—
676	M₁₆	C₂×C₇×D₄	1	2	yes	—
677	C₂×C₈	—	2	1	no	—
678	C₂×C₈	—	2	1	no	—
679	C₂×C₈	—	2	1	no	—
680	C₂×C₈	—	2	1	no	—
681	C₂×C₈	—	2	1	no	—
682	C₂×C₈	—	2	1	no	—
683	C₂×C₈	—	2	1	no	—
684	C₂×C₈	—	2	1	no	—
685	C₂×C₈	—	2	1	no	—
686	C₂×C₈	—	2	1	no	—
687	C₂×C₈	—	2	1	no	—
688	C₂×C₈	—	2	1	no	—
689	C₂×C₈	—	4	2	no	—
690	C₂×C₈	—	4	2	no	—
691	C₂×C₈	—	4	2	no	—
692	C₂×C₈	—	4	2	no	—
693	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
694	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
695	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
696	C₂×C₈	C₂²×C₄×C₇	1	1	yes	characteristic
697	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
698	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
699	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
700	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
701	C₄⋊C₄	—	2	1	no	—
702	C₄⋊C₄	—	2	1	no	—
703	C₄⋊C₄	—	4	2	no	—
704	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
705	C₄⋊C₄	C₂²×C₄×C₇	1	1	yes	characteristic
706	C₂²⋊C₄	—	2	1	no	—
707	C₂²⋊C₄	—	2	1	no	—
708	C₂²⋊C₄	—	2	1	no	—
709	C₂²⋊C₄	—	2	1	no	—
710	C₂²⋊C₄	—	2	1	no	—
711	C₂²⋊C₄	—	4	2	no	—
712	C₄²	—	2	1	no	—
713	C₄²	—	2	1	no	—
714	C₄²	—	2	1	no	—
715	C₄²	—	2	1	no	—
716	C₄²	C₂×C₇×D₄	1	2	yes	—
717	C₂×C₇	—	2	1	no	—
718	C₂×C₇	—	2	1	no	—
719	C₂×C₇	—	4	1	no	—
720	C₂×C₇	—	4	1	no	—
721	C₂×C₇	—	4	2	no	—
722	C₂×C₇	—	8	1	no	—
723	C₂×C₇	—	8	1	no	—
724	C₂×C₇	#2358	1	1	yes	characteristic
725	C₂×C₇	#2955	1	1	yes	characteristic
726	C₂×C₇	#2957	1	1	yes	characteristic
727	C₂³	—	2	1	no	—
728	C₂³	—	2	1	no	—
729	C₂³	—	2	1	no	—
730	C₂³	—	2	1	no	—
731	C₂³	—	2	1	no	—
732	C₂³	—	4	1	no	—
733	C₂³	—	4	1	no	—
734	C₂³	—	4	2	no	—
735	C₂³	—	4	2	no	—
736	C₂³	—	8	1	no	—
737	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
738	C₂³	C₄×C₇×D₄	1	1	yes	characteristic
739	C₂³	C₂×C₇×#41	1	1	yes	characteristic
740	Q₈	—	2	1	no	—
741	Q₈	—	2	1	no	—
742	Q₈	—	2	1	no	—
743	Q₈	—	2	1	no	—
744	Q₈	—	2	1	no	—
745	Q₈	—	4	2	no	—
746	Q₈	C₄×C₇×D₄	1	2	yes	—
747	D₄	—	2	2	no	—
748	D₄	—	2	2	no	—
749	D₄	—	2	1	no	—
750	D₄	—	2	1	no	—
751	D₄	—	2	1	no	—
752	D₄	—	2	1	no	—
753	D₄	—	2	1	no	—
754	D₄	—	4	2	no	—
755	D₄	—	4	2	no	—
756	D₄	—	4	2	no	—
757	D₄	—	4	2	no	—
758	D₄	—	4	1	no	—
759	D₄	—	4	1	no	—
760	D₄	—	4	1	no	—
761	D₄	—	4	1	no	—
762	D₄	—	8	1	no	—
763	D₄	C₄×C₇×D₄	1	2	yes	—
764	C₂×C₄	—	2	1	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	2	1	no	—
767	C₂×C₄	—	2	1	no	—
768	C₂×C₄	—	2	1	no	—
769	C₂×C₄	—	2	1	no	—
770	C₂×C₄	—	2	1	no	—
771	C₂×C₄	—	2	1	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	1	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	1	no	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	1	no	—
780	C₂×C₄	—	2	1	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	4	2	no	—
783	C₂×C₄	—	4	2	no	—
784	C₂×C₄	—	4	2	no	—
785	C₂×C₄	—	4	1	no	—
786	C₂×C₄	—	4	1	no	—
787	C₂×C₄	—	4	1	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
795	C₂×C₄	C₄×C₇×D₄	1	1	yes	characteristic
796	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
797	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
798	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
799	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
800	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
801	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
802	C₈	—	2	1	no	—
803	C₈	—	2	1	no	—
804	C₈	—	2	1	no	—
805	C₈	—	2	1	no	—
806	C₈	—	2	1	no	—
807	C₈	—	2	1	no	—
808	C₈	—	2	2	no	—
809	C₈	—	2	1	no	—
810	C₈	—	2	1	no	—
811	C₈	—	4	1	no	—
812	C₈	—	4	1	no	—
813	C₈	—	4	1	no	—
814	C₇	#22889	1	1	yes	characteristic, direct product factor, Sylow
815	C₂²	—	2	1	no	—
816	C₂²	—	2	1	no	—
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	1	no	—
822	C₂²	—	2	1	no	—
823	C₂²	—	2	2	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	1	no	—
829	C₂²	—	4	1	no	—
830	C₂²	—	4	1	no	—
831	C₂²	—	4	1	no	—
832	C₂²	—	8	1	no	—
833	C₂²	—	8	1	no	—
834	C₂²	—	8	4	no	—
835	C₂²	C₂×C₄×C₇×D₄	1	1	yes	characteristic
836	C₂²	C₇×#546	1	1	yes	characteristic
837	C₂²	C₇×#551	1	1	yes	characteristic
838	C₄	—	2	1	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	2	no	—
841	C₄	—	4	2	no	—
842	C₄	—	4	1	no	—
843	C₄	—	4	1	no	—
844	C₄	—	4	1	no	—
845	C₄	—	4	1	no	—
846	C₄	—	8	1	no	—
847	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
848	C₄	C₇×#518	1	1	yes	characteristic
849	C₄	C₇×D₄²	1	1	yes	characteristic
850	C₄	C₇×#546	1	1	yes	characteristic
851	C₂	—	2	1	no	—
852	C₂	—	2	1	no	—
853	C₂	—	4	1	no	—
854	C₂	—	4	1	no	—
855	C₂	—	4	2	no	—
856	C₂	—	8	1	no	—
857	C₂	—	8	1	no	—
858	C₂	C₇×#2358	1	1	yes	characteristic
859	C₂	C₇×#2955	1	1	yes	characteristic
860	C₂	C₇×#2957	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
socle	C₂²×C₇	C₂×C₄×D₄
prime radical	C₇×#3002	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₇ ◁ C₂×C₇×C₂²⋊C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#443	C₂	semidirect
3. C₇×#2933	C₂	semidirect
4. C₂×C₇×#421	C₂	semidirect
5. C₇×#2880	C₂	semidirect
6. C₇×#1975	C₂	semidirect
7. C₇×#1937	C₂	semidirect
8. C₇×#1929	C₂	semidirect
9. C₇×#1897	C₂	semidirect
10. C₇×#1876	C₂	semidirect
11. C₇×#1876	C₂	semidirect
12. C₇×#1866	C₂	semidirect
13. C₇×#1855	C₂	semidirect
14. C₇×#1765	C₂	semidirect
15. C₇×#1750	C₂	semidirect
21. C₂×C₇×#131	C₂²	semidirect
25. C₇×#452	C₄	semidirect
26. C₇×#452	C₄	semidirect
27. C₇×#451	C₄	semidirect
28. C₇×#450	C₄	semidirect
29. C₇×#449	C₄	semidirect
30. C₇×#449	C₄	semidirect
31. C₇×#448	C₄	semidirect
32. C₇×#447	C₄	semidirect
38. C₂×C₇×#108	C₂²	semidirect
39. C₂×C₇×#108	C₂²	semidirect
40. C₇×#424	C₂²	semidirect
46. C₂×C₇×#104	C₂²	semidirect
47. C₂×C₇×#104	C₂²	semidirect
54. C₇×#408	C₂²	semidirect
60. C₇×#405	C₂²	semidirect
61. C₂×C₇×#97	C₂²	semidirect
62. C₂×C₄×C₇×C₈	C₂²	semidirect
63. C₇×#341	C₂²	semidirect
64. C₇×#341	C₂²	semidirect
65. C₇×#339	C₂²	semidirect
66. C₇×#339	C₂²	semidirect
67. C₇×#336	C₂²	semidirect
68. C₇×#336	C₂²	semidirect
69. #22889	C₇	direct (N × H)
146. C₇×#104	D₄	semidirect
176. C₂×#443	C₂×C₇	semidirect
177. #2933	C₂×C₇	semidirect
178. C₂×#421	C₂×C₇	semidirect
179. #2880	C₂×C₇	semidirect
180. #1975	C₂×C₇	semidirect
181. #1937	C₂×C₇	semidirect
182. #1929	C₂×C₇	semidirect
183. #1897	C₂×C₇	semidirect
184. #1876	C₂×C₇	semidirect
185. #1876	C₂×C₇	semidirect
186. #1866	C₂×C₇	semidirect
187. #1855	C₂×C₇	semidirect
188. #1765	C₂×C₇	semidirect
189. #1750	C₂×C₇	semidirect
318. C₂×#131	C₂²×C₇	semidirect
322. #452	C₄×C₇	semidirect
323. #452	C₄×C₇	semidirect
324. #451	C₄×C₇	semidirect
325. #450	C₄×C₇	semidirect
326. #449	C₄×C₇	semidirect
327. #449	C₄×C₇	semidirect
328. #448	C₄×C₇	semidirect
329. #447	C₄×C₇	semidirect
335. C₂×#108	C₂²×C₇	semidirect
336. C₂×#108	C₂²×C₇	semidirect
337. #424	C₂²×C₇	semidirect
343. C₂×#104	C₂²×C₇	semidirect
344. C₂×#104	C₂²×C₇	semidirect
351. #408	C₂²×C₇	semidirect
357. #405	C₂²×C₇	semidirect
358. C₂×#97	C₂²×C₇	semidirect
359. C₂×C₄×C₈	C₂²×C₇	semidirect
360. #341	C₂²×C₇	semidirect
361. #341	C₂²×C₇	semidirect
362. #339	C₂²×C₇	semidirect
363. #339	C₂²×C₇	semidirect
364. #336	C₂²×C₇	semidirect
365. #336	C₂²×C₇	semidirect
529. #104	C₇×D₄	semidirect
814. C₇	#22889	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×#3002	2
C₂×C₇×#443	2
C₇×#2933	2
C₂×C₇×#421	2
C₇×#2880	2
C₇×#1975	2
C₇×#1937	2
C₇×#1929	2
C₇×#1897	2
C₇×#1876	2
C₇×#1866	2
C₇×#1855	2
C₇×#1765	2
C₇×#1750	2
#22889	7

Subgroups — C7×#22889 #13200105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22889 #13200105