Subgroups — C₇×#22464 #13199680

Order 1792.

1346 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#577	C₂	1	1	yes	maximal, characteristic
2	C₂×C₇×#444	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#2951	C₂	1	1	yes	maximal, characteristic, complemented
4	C₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
6	C₇×#1977	C₂	1	1	yes	maximal, characteristic, complemented
7	C₇×#1973	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#1908	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#1907	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#1883	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇×#1882	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#1816	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#1793	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#1792	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#1765	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₇×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
17	C₂×C₇×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
18	C₇×#577	—	2	4	no	—
19	C₇×#577	C₄	1	8	yes	complemented
20	C₂×C₇×#137	—	2	1	no	—
21	C₂×C₇×#137	C₂²	1	1	yes	characteristic
22	C₂×C₇×AGL(1,ℤ/8)	—	2	1	no	—
23	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
24	C₂×C₇×#135	—	2	1	no	—
25	C₂×C₇×#135	C₂²	1	1	yes	characteristic
26	C₂²×C₇×SD₁₆	—	2	1	no	—
27	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
28	C₂×C₇×#131	C₂²	1	1	yes	characteristic
29	C₂×C₇×#131	C₂²	1	1	yes	characteristic
30	C₂×C₇×#131	C₂²	1	1	yes	characteristic, complemented
31	C₇×#520	C₂²	1	1	yes	characteristic
32	C₇×#520	C₂²	1	1	yes	characteristic, complemented
33	C₇×#444	—	2	4	no	—
34	C₇×#440	—	2	1	no	—
35	C₇×#440	—	2	1	no	—
36	C₄×C₇×Q₁₆	—	2	1	no	—
37	C₄×C₇×D₈	—	2	1	no	—
38	C₂×C₇×#108	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₇×#107	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₇×#104	C₂²	1	1	yes	characteristic
41	C₂×C₇×#104	C₂²	1	1	yes	characteristic
42	C₂×C₇×#104	C₂²	1	1	yes	characteristic, complemented
43	C₇×#419	—	2	1	no	—
44	C₇×#419	C₂²	1	1	yes	characteristic, complemented
45	C₇×#418	—	2	1	no	—
46	C₇×#418	C₂²	1	1	yes	characteristic
47	C₇×#417	—	2	1	no	—
48	C₇×#417	—	2	1	no	—
49	C₇×#417	C₂²	1	1	yes	characteristic
50	C₇×#417	C₂²	1	1	yes	characteristic
51	C₇×#417	C₂²	1	1	yes	characteristic
52	C₇×#417	C₂²	1	1	yes	characteristic, complemented
53	C₇×#416	—	2	1	no	—
54	C₇×#416	—	2	1	no	—
55	C₇×#416	C₂²	1	1	yes	characteristic
56	C₂×C₇×#103	—	2	1	no	—
57	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
58	C₂×C₇×#102	—	2	1	no	—
59	C₂×C₇×#102	C₂²	1	1	yes	characteristic
60	C₂×C₇×#101	C₂²	1	1	yes	characteristic, complemented
61	C₂×C₇×#100	C₂²	1	1	yes	characteristic
62	C₇×#405	C₂²	1	1	yes	characteristic, complemented
63	C₂×C₇×#97	C₂²	1	1	yes	characteristic, complemented
64	C₇×#391	C₂²	1	1	yes	characteristic, complemented
65	C₇×#390	C₂²	1	1	yes	characteristic
66	C₇×#343	C₂²	1	1	yes	characteristic, complemented
67	C₇×#343	C₂²	1	1	yes	characteristic, complemented
68	C₇×#341	C₂²	1	1	yes	characteristic, complemented
69	C₇×#339	C₂²	1	1	yes	characteristic, complemented
70	#22464	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
71	C₇×2₋¹⁺⁴	—	2	2	no	—
72	C₇×2₋¹⁺⁴	—	2	2	no	—
73	C₇×2₋¹⁺⁴	—	4	1	no	—
74	C₇×2₋¹⁺⁴	C₂×C₄	1	4	yes	complemented
75	C₇×H(5,𝔽₂)	—	2	2	no	—
76	C₇×H(5,𝔽₂)	—	2	2	no	—
77	C₇×H(5,𝔽₂)	—	4	1	no	—
78	C₇×H(5,𝔽₂)	C₂×C₄	1	4	yes	complemented
79	C₂×C₇×#41	—	2	1	no	—
80	C₂×C₇×#41	—	2	1	no	—
81	C₂×C₇×#41	—	2	1	no	—
82	C₂×C₇×#41	—	2	1	no	—
83	C₂×C₇×#41	—	4	1	no	—
84	C₂×C₇×#41	C₂³	1	1	yes	characteristic
85	C₂×C₇×#41	C₂³	1	1	yes	characteristic
86	C₂×C₇×#41	C₂³	1	1	yes	characteristic
87	C₂²×C₇×Q₈	—	2	1	no	—
88	C₂²×C₇×Q₈	—	2	1	no	—
89	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
90	C₂²×C₇×D₄	—	2	1	no	—
91	C₂²×C₇×D₄	—	2	1	no	—
92	C₂²×C₇×D₄	—	4	1	no	—
93	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
94	C₇×#137	—	2	2	no	—
95	C₇×#137	—	2	8	no	—
96	C₇×#137	C₂×C₄	1	4	yes	complemented
97	C₇×AGL(1,ℤ/8)	—	2	2	no	—
98	C₇×AGL(1,ℤ/8)	—	2	8	no	—
99	C₇×AGL(1,ℤ/8)	C₂×C₄	1	4	yes	complemented
100	C₇×#135	—	2	8	no	—
101	C₇×#135	C₂×C₄	1	4	yes	—
102	C₇×#135	D₄	1	4	yes	—
103	C₂×C₇×Q₁₆	—	2	1	no	—
104	C₂×C₇×Q₁₆	D₄	1	1	yes	characteristic
105	C₂×C₇×SD₁₆	—	2	1	no	—
106	C₂×C₇×SD₁₆	—	2	1	no	—
107	C₂×C₇×SD₁₆	—	2	8	no	—
108	C₂×C₇×SD₁₆	—	2	1	no	—
109	C₂×C₇×SD₁₆	—	2	1	no	—
110	C₂×C₇×SD₁₆	—	2	2	no	—
111	C₂×C₇×SD₁₆	C₂×C₄	1	4	yes	complemented
112	C₂×C₇×SD₁₆	D₄	1	1	yes	characteristic
113	C₂×C₇×SD₁₆	D₄	1	1	yes	characteristic
114	C₂×C₇×D₈	—	2	1	no	—
115	C₂×C₇×D₈	D₄	1	1	yes	characteristic
116	C₇×#131	—	2	2	no	—
117	C₇×#131	—	2	2	no	—
118	C₇×#131	—	2	2	no	—
119	C₇×#131	—	4	1	no	—
120	C₇×#131	—	4	1	no	—
121	C₇×#131	C₂×C₄	1	4	yes	complemented
122	C₂×C₇×M₁₆	—	2	1	no	—
123	C₂×C₇×M₁₆	—	2	1	no	—
124	C₂×C₇×M₁₆	—	2	1	no	—
125	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
126	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
127	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
128	C₂×C₇×M₁₆	C₂³	1	1	yes	characteristic
129	C₂²×C₇×C₈	—	2	1	no	—
130	C₂²×C₇×C₈	—	2	1	no	—
131	C₂²×C₇×C₈	—	2	1	no	—
132	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
133	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
134	C₄×C₇×Q₈	—	2	1	no	—
135	C₄×C₇×Q₈	—	2	1	no	—
136	C₄×C₇×D₄	—	2	1	no	—
137	C₄×C₇×D₄	—	2	1	no	—
138	C₄×C₇×D₄	—	4	1	no	—
139	C₄×C₇×D₄	—	4	1	no	—
140	C₇×#117	—	2	1	no	—
141	C₇×#117	—	2	1	no	—
142	C₇×#117	C₂³	1	1	yes	characteristic
143	C₂×C₇×C₄⋊C₄	—	2	1	no	—
144	C₂×C₇×C₄⋊C₄	—	2	1	no	—
145	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₇×C₂²⋊C₄	—	4	1	no	—
148	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
149	C₇×#108	—	2	2	no	—
150	C₇×#107	—	2	1	no	—
151	C₇×#107	—	2	1	no	—
152	C₇×#104	—	2	2	no	—
153	C₇×#104	—	2	2	no	—
154	C₇×#104	—	2	2	no	—
155	C₇×#103	—	2	1	no	—
156	C₇×#103	—	2	1	no	—
157	C₇×#103	—	2	1	no	—
158	C₇×#103	—	2	1	no	—
159	C₇×#103	—	2	1	no	—
160	C₇×#103	—	2	1	no	—
161	C₇×#103	—	2	1	no	—
162	C₇×#103	—	2	1	no	—
163	C₇×#103	D₄	1	1	yes	characteristic
164	C₇×#103	D₄	1	1	yes	characteristic
165	C₇×#102	—	2	1	no	—
166	C₇×#102	—	2	1	no	—
167	C₇×#102	—	2	1	no	—
168	C₇×#102	—	2	1	no	—
169	C₇×#102	—	2	1	no	—
170	C₇×#102	—	2	1	no	—
171	C₇×#102	—	2	1	no	—
172	C₇×#102	—	2	1	no	—
173	C₇×#102	D₄	1	1	yes	characteristic
174	C₇×#102	D₄	1	1	yes	characteristic
175	C₇×#101	—	4	1	no	—
176	C₇×#100	—	4	1	no	—
177	C₇×#97	—	2	2	no	—
178	C₇×#97	—	2	1	no	—
179	C₄×C₇×C₈	—	2	1	no	—
180	C₇×#95	—	4	1	no	—
181	C₂×#577	C₂×C₇	1	1	yes	characteristic
182	C₂×#444	C₂×C₇	1	1	yes	characteristic, complemented
183	#2951	C₂×C₇	1	1	yes	characteristic, complemented
184	#2898	C₂×C₇	1	1	yes	characteristic, complemented
185	#2897	C₂×C₇	1	1	yes	characteristic, complemented
186	#1977	C₂×C₇	1	1	yes	characteristic, complemented
187	#1973	C₂×C₇	1	1	yes	characteristic, complemented
188	#1908	C₂×C₇	1	1	yes	characteristic, complemented
189	#1907	C₂×C₇	1	1	yes	characteristic, complemented
190	#1883	C₂×C₇	1	1	yes	characteristic, complemented
191	#1882	C₂×C₇	1	1	yes	characteristic, complemented
192	#1816	C₂×C₇	1	1	yes	characteristic, complemented
193	#1793	C₂×C₇	1	1	yes	characteristic, complemented
194	#1792	C₂×C₇	1	1	yes	characteristic, complemented
195	#1765	C₂×C₇	1	1	yes	characteristic, complemented
196	C₂⁴×C₇	—	2	1	no	—
197	C₂⁴×C₇	—	4	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	—	2	4	no	—
205	C₇×#41	—	2	4	no	—
206	C₇×#41	—	2	4	no	—
207	C₇×#41	—	2	4	no	—
208	C₇×#41	—	4	4	no	—
209	C₇×#41	—	4	2	no	—
210	C₇×#41	—	4	2	no	—
211	C₇×#41	—	4	2	no	—
212	C₇×#41	—	4	2	no	—
213	C₇×#41	—	4	4	no	—
214	C₇×#41	C₂²×C₄	1	2	yes	—
215	C₇×#41	C₂²×C₄	1	2	yes	—
216	C₇×#41	C₂²×C₄	1	2	yes	—
217	C₇×#41	C₂×D₄	1	2	yes	—
218	C₇×#41	C₂×D₄	1	2	yes	—
219	C₇×#41	#41	1	2	yes	—
220	C₂×C₇×Q₈	—	2	1	no	—
221	C₂×C₇×Q₈	—	2	4	no	—
222	C₂×C₇×Q₈	—	2	4	no	—
223	C₂×C₇×Q₈	—	2	1	no	—
224	C₂×C₇×Q₈	—	2	1	no	—
225	C₂×C₇×Q₈	—	2	1	no	—
226	C₂×C₇×Q₈	—	2	1	no	—
227	C₂×C₇×Q₈	—	4	1	no	—
228	C₂×C₇×Q₈	—	4	2	no	—
229	C₂×C₇×Q₈	—	4	2	no	—
230	C₂×C₇×Q₈	C₂²×C₄	1	2	yes	—
231	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
232	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
233	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
234	C₂×C₇×D₄	—	2	1	no	—
235	C₂×C₇×D₄	—	2	1	no	—
236	C₂×C₇×D₄	—	2	1	no	—
237	C₂×C₇×D₄	—	2	4	no	—
238	C₂×C₇×D₄	—	2	4	no	—
239	C₂×C₇×D₄	—	2	1	no	—
240	C₂×C₇×D₄	—	2	1	no	—
241	C₂×C₇×D₄	—	2	1	no	—
242	C₂×C₇×D₄	—	2	1	no	—
243	C₂×C₇×D₄	—	2	1	no	—
244	C₂×C₇×D₄	—	4	2	no	—
245	C₂×C₇×D₄	—	4	2	no	—
246	C₂×C₇×D₄	—	4	1	no	—
247	C₂×C₇×D₄	—	4	1	no	—
248	C₂×C₇×D₄	—	4	4	no	—
249	C₂×C₇×D₄	—	4	4	no	—
250	C₂×C₇×D₄	—	4	1	no	—
251	C₂×C₇×D₄	C₂²×C₄	1	2	yes	—
252	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
253	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
254	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₇	—	2	1	no	—
256	C₂²×C₄×C₇	—	2	1	no	—
257	C₂²×C₄×C₇	—	2	1	no	—
258	C₂²×C₄×C₇	—	2	1	no	—
259	C₂²×C₄×C₇	—	2	1	no	—
260	C₂²×C₄×C₇	—	2	1	no	—
261	C₂²×C₄×C₇	—	2	1	no	—
262	C₂²×C₄×C₇	—	4	1	no	—
263	C₂²×C₄×C₇	—	4	1	no	—
264	C₂²×C₄×C₇	—	4	1	no	—
265	C₂²×C₄×C₇	—	4	1	no	—
266	C₂²×C₄×C₇	—	4	1	no	—
267	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
268	C₇×Q₁₆	—	2	4	no	—
269	C₇×Q₁₆	C₂²⋊C₄	1	4	yes	complemented
270	C₇×SD₁₆	—	2	4	no	—
271	C₇×SD₁₆	—	2	4	no	—
272	C₇×SD₁₆	—	2	4	no	—
273	C₇×SD₁₆	—	2	4	no	—
274	C₇×SD₁₆	C₂²⋊C₄	1	4	yes	complemented
275	C₇×SD₁₆	C₂²⋊C₄	1	4	yes	complemented
276	C₇×D₈	—	2	4	no	—
277	C₇×D₈	C₂²⋊C₄	1	4	yes	complemented
278	C₇×M₁₆	—	2	1	no	—
279	C₇×M₁₆	—	2	4	no	—
280	C₇×M₁₆	—	2	1	no	—
281	C₇×M₁₆	—	2	1	no	—
282	C₇×M₁₆	—	2	1	no	—
283	C₇×M₁₆	—	2	1	no	—
284	C₇×M₁₆	—	2	1	no	—
285	C₇×M₁₆	—	2	1	no	—
286	C₇×M₁₆	—	4	2	no	—
287	C₇×M₁₆	—	4	2	no	—
288	C₇×M₁₆	C₂²×C₄	1	2	yes	—
289	C₂×C₇×C₈	—	2	1	no	—
290	C₂×C₇×C₈	—	2	1	no	—
291	C₂×C₇×C₈	—	2	1	no	—
292	C₂×C₇×C₈	—	2	4	no	—
293	C₂×C₇×C₈	—	2	1	no	—
294	C₂×C₇×C₈	—	2	1	no	—
295	C₂×C₇×C₈	—	2	1	no	—
296	C₂×C₇×C₈	—	4	2	no	—
297	C₂×C₇×C₈	—	4	2	no	—
298	C₂×C₇×C₈	C₂²×C₄	1	2	yes	—
299	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
300	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
301	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
302	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
303	C₂×C₇×C₈	C₂×D₄	1	2	yes	—
304	C₇×C₄⋊C₄	—	2	1	no	—
305	C₇×C₄⋊C₄	—	2	1	no	—
306	C₇×C₄⋊C₄	—	2	1	no	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	4	1	no	—
309	C₇×C₄⋊C₄	—	4	1	no	—
310	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
311	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
312	C₇×C₂²⋊C₄	—	2	1	no	—
313	C₇×C₂²⋊C₄	—	4	1	no	—
314	C₇×C₂²⋊C₄	—	4	1	no	—
315	C₇×C₂²⋊C₄	—	8	2	no	—
316	C₄²×C₇	—	2	1	no	—
317	C₄²×C₇	—	2	1	no	—
318	C₄²×C₇	—	2	1	no	—
319	C₄²×C₇	—	4	1	no	—
320	C₄²×C₇	—	4	1	no	—
321	C₂×2₋¹⁺⁴	C₂²×C₇	1	1	yes	characteristic
322	C₂×H(5,𝔽₂)	C₂²×C₇	1	1	yes	characteristic
323	#577	—	2	4	no	—
324	#577	C₄×C₇	1	8	yes	complemented
325	C₂×#137	—	2	1	no	—
326	C₂×#137	C₂²×C₇	1	1	yes	characteristic
327	C₂×AGL(1,ℤ/8)	—	2	1	no	—
328	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	1	yes	characteristic
329	C₂×#135	—	2	1	no	—
330	C₂×#135	C₂²×C₇	1	1	yes	characteristic
331	C₂²×SD₁₆	—	2	1	no	—
332	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
333	C₂×#131	C₂²×C₇	1	1	yes	characteristic
334	C₂×#131	C₂²×C₇	1	1	yes	characteristic
335	C₂×#131	C₂²×C₇	1	1	yes	characteristic, complemented
336	#520	C₂²×C₇	1	1	yes	characteristic
337	#520	C₂²×C₇	1	1	yes	characteristic, complemented
338	#444	—	2	4	no	—
339	#440	—	2	1	no	—
340	#440	—	2	1	no	—
341	C₄×Q₁₆	—	2	1	no	—
342	C₄×D₈	—	2	1	no	—
343	C₂×#108	C₂²×C₇	1	1	yes	characteristic, complemented
344	C₂×#107	C₂²×C₇	1	1	yes	characteristic, complemented
345	C₂×#104	C₂²×C₇	1	1	yes	characteristic
346	C₂×#104	C₂²×C₇	1	1	yes	characteristic
347	C₂×#104	C₂²×C₇	1	1	yes	characteristic, complemented
348	#419	—	2	1	no	—
349	#419	C₂²×C₇	1	1	yes	characteristic, complemented
350	#418	—	2	1	no	—
351	#418	C₂²×C₇	1	1	yes	characteristic
352	#417	—	2	1	no	—
353	#417	—	2	1	no	—
354	#417	C₂²×C₇	1	1	yes	characteristic
355	#417	C₂²×C₇	1	1	yes	characteristic
356	#417	C₂²×C₇	1	1	yes	characteristic
357	#417	C₂²×C₇	1	1	yes	characteristic, complemented
358	#416	—	2	1	no	—
359	#416	—	2	1	no	—
360	#416	C₂²×C₇	1	1	yes	characteristic
361	C₂×#103	—	2	1	no	—
362	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
363	C₂×#102	—	2	1	no	—
364	C₂×#102	C₂²×C₇	1	1	yes	characteristic
365	C₂×#101	C₂²×C₇	1	1	yes	characteristic, complemented
366	C₂×#100	C₂²×C₇	1	1	yes	characteristic
367	#405	C₂²×C₇	1	1	yes	characteristic, complemented
368	C₂×#97	C₂²×C₇	1	1	yes	characteristic, complemented
369	#391	C₂²×C₇	1	1	yes	characteristic, complemented
370	#390	C₂²×C₇	1	1	yes	characteristic
371	#343	C₂²×C₇	1	1	yes	characteristic, complemented
372	#343	C₂²×C₇	1	1	yes	characteristic, complemented
373	#341	C₂²×C₇	1	1	yes	characteristic, complemented
374	#339	C₂²×C₇	1	1	yes	characteristic, complemented
375	C₂³×C₇	—	2	1	no	—
376	C₂³×C₇	—	2	1	no	—
377	C₂³×C₇	—	2	1	no	—
378	C₂³×C₇	—	2	2	no	—
379	C₂³×C₇	—	4	4	no	—
380	C₂³×C₇	—	4	1	no	—
381	C₂³×C₇	—	4	1	no	—
382	C₂³×C₇	—	8	1	no	—
383	C₂³×C₇	—	8	1	no	—
384	C₂³×C₇	—	16	1	no	—
385	C₂³×C₇	—	16	1	no	—
386	C₂³×C₇	H(5,𝔽₂)	1	1	yes	characteristic
387	C₇×Q₈	—	2	1	no	—
388	C₇×Q₈	—	2	1	no	—
389	C₇×Q₈	—	2	1	no	—
390	C₇×Q₈	—	2	2	no	—
391	C₇×Q₈	—	2	2	no	—
392	C₇×Q₈	—	4	4	no	—
393	C₇×Q₈	—	4	1	no	—
394	C₇×Q₈	—	4	1	no	—
395	C₇×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
396	C₇×Q₈	C₂×C₂²⋊C₄	1	2	yes	—
397	C₇×Q₈	C₄×D₄	1	2	yes	—
398	C₇×D₄	—	2	2	no	—
399	C₇×D₄	—	2	2	no	—
400	C₇×D₄	—	2	2	no	—
401	C₇×D₄	—	2	2	no	—
402	C₇×D₄	—	2	2	no	—
403	C₇×D₄	—	2	2	no	—
404	C₇×D₄	—	2	2	no	—
405	C₇×D₄	—	2	2	no	—
406	C₇×D₄	—	2	1	no	—
407	C₇×D₄	—	2	1	no	—
408	C₇×D₄	—	2	1	no	—
409	C₇×D₄	—	4	4	no	—
410	C₇×D₄	—	4	4	no	—
411	C₇×D₄	—	4	4	no	—
412	C₇×D₄	—	4	1	no	—
413	C₇×D₄	—	4	1	no	—
414	C₇×D₄	C₂×C₂²⋊C₄	1	2	yes	—
415	C₇×D₄	C₂×C₂²⋊C₄	1	2	yes	—
416	C₇×D₄	C₄×D₄	1	2	yes	—
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	—	2	2	no	—
422	C₂×C₄×C₇	—	2	2	no	—
423	C₂×C₄×C₇	—	2	2	no	—
424	C₂×C₄×C₇	—	2	2	no	—
425	C₂×C₄×C₇	—	2	2	no	—
426	C₂×C₄×C₇	—	2	2	no	—
427	C₂×C₄×C₇	—	2	1	no	—
428	C₂×C₄×C₇	—	2	1	no	—
429	C₂×C₄×C₇	—	4	4	no	—
430	C₂×C₄×C₇	—	4	4	no	—
431	C₂×C₄×C₇	—	4	4	no	—
432	C₂×C₄×C₇	—	4	1	no	—
433	C₂×C₄×C₇	—	4	1	no	—
434	C₂×C₄×C₇	—	4	1	no	—
435	C₂×C₄×C₇	—	4	1	no	—
436	C₂×C₄×C₇	—	4	1	no	—
437	C₂×C₄×C₇	—	4	1	no	—
438	C₂×C₄×C₇	—	4	1	no	—
439	C₂×C₄×C₇	—	8	1	no	—
440	C₂×C₄×C₇	—	8	1	no	—
441	C₂×C₄×C₇	—	16	1	no	—
442	C₂×C₄×C₇	—	16	1	no	—
443	C₂×C₄×C₇	C₂³×C₄	1	1	yes	characteristic
444	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
445	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₇	C₂×#41	1	1	yes	characteristic
448	C₂×C₄×C₇	H(5,𝔽₂)	1	1	yes	characteristic
449	C₇×C₈	—	2	2	no	—
450	C₇×C₈	—	2	1	no	—
451	C₇×C₈	—	2	1	no	—
452	C₇×C₈	—	4	1	no	—
453	C₇×C₈	—	4	1	no	—
454	C₇×C₈	—	4	1	no	—
455	C₇×C₈	C₂×C₂²⋊C₄	1	2	yes	—
456	C₇×C₈	C₂×C₂²⋊C₄	1	2	yes	—
457	2₋¹⁺⁴	—	2	2	no	—
458	2₋¹⁺⁴	—	2	2	no	—
459	2₋¹⁺⁴	—	4	1	no	—
460	2₋¹⁺⁴	C₂×C₄×C₇	1	4	yes	complemented
461	H(5,𝔽₂)	—	2	2	no	—
462	H(5,𝔽₂)	—	2	2	no	—
463	H(5,𝔽₂)	—	4	1	no	—
464	H(5,𝔽₂)	C₂×C₄×C₇	1	4	yes	complemented
465	C₂×#41	—	2	1	no	—
466	C₂×#41	—	2	1	no	—
467	C₂×#41	—	2	1	no	—
468	C₂×#41	—	2	1	no	—
469	C₂×#41	—	4	1	no	—
470	C₂×#41	C₂³×C₇	1	1	yes	characteristic
471	C₂×#41	C₂³×C₇	1	1	yes	characteristic
472	C₂×#41	C₂³×C₇	1	1	yes	characteristic
473	C₂²×Q₈	—	2	1	no	—
474	C₂²×Q₈	—	2	1	no	—
475	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
476	C₂²×D₄	—	2	1	no	—
477	C₂²×D₄	—	2	1	no	—
478	C₂²×D₄	—	4	1	no	—
479	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
480	#137	—	2	2	no	—
481	#137	—	2	8	no	—
482	#137	C₂×C₄×C₇	1	4	yes	complemented
483	AGL(1,ℤ/8)	—	2	2	no	—
484	AGL(1,ℤ/8)	—	2	8	no	—
485	AGL(1,ℤ/8)	C₂×C₄×C₇	1	4	yes	complemented
486	#135	—	2	8	no	—
487	#135	C₂×C₄×C₇	1	4	yes	—
488	#135	C₇×D₄	1	4	yes	—
489	C₂×Q₁₆	—	2	1	no	—
490	C₂×Q₁₆	C₇×D₄	1	1	yes	characteristic
491	C₂×SD₁₆	—	2	1	no	—
492	C₂×SD₁₆	—	2	1	no	—
493	C₂×SD₁₆	—	2	8	no	—
494	C₂×SD₁₆	—	2	1	no	—
495	C₂×SD₁₆	—	2	1	no	—
496	C₂×SD₁₆	—	2	2	no	—
497	C₂×SD₁₆	C₂×C₄×C₇	1	4	yes	complemented
498	C₂×SD₁₆	C₇×D₄	1	1	yes	characteristic
499	C₂×SD₁₆	C₇×D₄	1	1	yes	characteristic
500	C₂×D₈	—	2	1	no	—
501	C₂×D₈	C₇×D₄	1	1	yes	characteristic
502	#131	—	2	2	no	—
503	#131	—	2	2	no	—
504	#131	—	2	2	no	—
505	#131	—	4	1	no	—
506	#131	—	4	1	no	—
507	#131	C₂×C₄×C₇	1	4	yes	complemented
508	C₂×M₁₆	—	2	1	no	—
509	C₂×M₁₆	—	2	1	no	—
510	C₂×M₁₆	—	2	1	no	—
511	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
512	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
513	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
514	C₂×M₁₆	C₂³×C₇	1	1	yes	characteristic
515	C₂²×C₈	—	2	1	no	—
516	C₂²×C₈	—	2	1	no	—
517	C₂²×C₈	—	2	1	no	—
518	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
520	C₄×Q₈	—	2	1	no	—
521	C₄×Q₈	—	2	1	no	—
522	C₄×D₄	—	2	1	no	—
523	C₄×D₄	—	2	1	no	—
524	C₄×D₄	—	4	1	no	—
525	C₄×D₄	—	4	1	no	—
526	#117	—	2	1	no	—
527	#117	—	2	1	no	—
528	#117	C₂³×C₇	1	1	yes	characteristic
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	1	no	—
531	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
532	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
533	C₂×C₂²⋊C₄	—	4	1	no	—
534	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
535	#108	—	2	2	no	—
536	#107	—	2	1	no	—
537	#107	—	2	1	no	—
538	#104	—	2	2	no	—
539	#104	—	2	2	no	—
540	#104	—	2	2	no	—
541	#103	—	2	1	no	—
542	#103	—	2	1	no	—
543	#103	—	2	1	no	—
544	#103	—	2	1	no	—
545	#103	—	2	1	no	—
546	#103	—	2	1	no	—
547	#103	—	2	1	no	—
548	#103	—	2	1	no	—
549	#103	C₇×D₄	1	1	yes	characteristic
550	#103	C₇×D₄	1	1	yes	characteristic
551	#102	—	2	1	no	—
552	#102	—	2	1	no	—
553	#102	—	2	1	no	—
554	#102	—	2	1	no	—
555	#102	—	2	1	no	—
556	#102	—	2	1	no	—
557	#102	—	2	1	no	—
558	#102	—	2	1	no	—
559	#102	C₇×D₄	1	1	yes	characteristic
560	#102	C₇×D₄	1	1	yes	characteristic
561	#101	—	4	1	no	—
562	#100	—	4	1	no	—
563	#97	—	2	2	no	—
564	#97	—	2	1	no	—
565	C₄×C₈	—	2	1	no	—
566	#95	—	4	1	no	—
567	C₂²×C₇	—	2	1	no	—
568	C₂²×C₇	—	2	1	no	—
569	C₂²×C₇	—	2	2	no	—
570	C₂²×C₇	—	2	2	no	—
571	C₂²×C₇	—	2	2	no	—
572	C₂²×C₇	—	4	1	no	—
573	C₂²×C₇	—	4	1	no	—
574	C₂²×C₇	—	4	1	no	—
575	C₂²×C₇	—	4	1	no	—
576	C₂²×C₇	—	4	1	no	—
577	C₂²×C₇	—	4	1	no	—
578	C₂²×C₇	—	4	2	no	—
579	C₂²×C₇	—	8	2	no	—
580	C₂²×C₇	—	8	1	no	—
581	C₂²×C₇	—	8	1	no	—
582	C₂²×C₇	—	16	1	no	—
583	C₂²×C₇	—	16	4	no	—
584	C₂²×C₇	#518	1	1	yes	characteristic
585	C₂²×C₇	D₄²	1	1	yes	characteristic
586	C₂²×C₇	#546	1	1	yes	characteristic
587	C₄×C₇	—	2	2	no	—
588	C₄×C₇	—	2	2	no	—
589	C₄×C₇	—	2	2	no	—
590	C₄×C₇	—	4	2	no	—
591	C₄×C₇	—	4	1	no	—
592	C₄×C₇	—	4	1	no	—
593	C₄×C₇	—	8	1	no	—
594	C₄×C₇	—	8	1	no	—
595	C₄×C₇	—	8	1	no	—
596	C₄×C₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
597	C₄×C₇	C₂×C₄×D₄	1	1	yes	characteristic
598	C₄×C₇	D₄²	1	1	yes	characteristic
599	C₄×C₇	#546	1	1	yes	characteristic
600	C₂⁴	—	2	1	no	—
601	C₂⁴	—	4	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	—	2	4	no	—
609	#41	—	2	4	no	—
610	#41	—	2	4	no	—
611	#41	—	2	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	2	no	—
614	#41	—	4	2	no	—
615	#41	—	4	2	no	—
616	#41	—	4	2	no	—
617	#41	—	4	4	no	—
618	#41	C₂²×C₄×C₇	1	2	yes	—
619	#41	C₂²×C₄×C₇	1	2	yes	—
620	#41	C₂²×C₄×C₇	1	2	yes	—
621	#41	C₂×C₇×D₄	1	2	yes	—
622	#41	C₂×C₇×D₄	1	2	yes	—
623	#41	C₇×#41	1	2	yes	—
624	C₂×Q₈	—	2	1	no	—
625	C₂×Q₈	—	2	4	no	—
626	C₂×Q₈	—	2	4	no	—
627	C₂×Q₈	—	2	1	no	—
628	C₂×Q₈	—	2	1	no	—
629	C₂×Q₈	—	2	1	no	—
630	C₂×Q₈	—	2	1	no	—
631	C₂×Q₈	—	4	1	no	—
632	C₂×Q₈	—	4	2	no	—
633	C₂×Q₈	—	4	2	no	—
634	C₂×Q₈	C₂²×C₄×C₇	1	2	yes	—
635	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
636	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
637	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
638	C₂×D₄	—	2	1	no	—
639	C₂×D₄	—	2	1	no	—
640	C₂×D₄	—	2	1	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	1	no	—
644	C₂×D₄	—	2	1	no	—
645	C₂×D₄	—	2	1	no	—
646	C₂×D₄	—	2	1	no	—
647	C₂×D₄	—	2	1	no	—
648	C₂×D₄	—	4	2	no	—
649	C₂×D₄	—	4	2	no	—
650	C₂×D₄	—	4	1	no	—
651	C₂×D₄	—	4	1	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	—	4	1	no	—
655	C₂×D₄	C₂²×C₄×C₇	1	2	yes	—
656	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
657	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
658	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
659	C₂²×C₄	—	2	1	no	—
660	C₂²×C₄	—	2	1	no	—
661	C₂²×C₄	—	2	1	no	—
662	C₂²×C₄	—	2	1	no	—
663	C₂²×C₄	—	2	1	no	—
664	C₂²×C₄	—	2	1	no	—
665	C₂²×C₄	—	2	1	no	—
666	C₂²×C₄	—	4	1	no	—
667	C₂²×C₄	—	4	1	no	—
668	C₂²×C₄	—	4	1	no	—
669	C₂²×C₄	—	4	1	no	—
670	C₂²×C₄	—	4	1	no	—
671	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
672	Q₁₆	—	2	4	no	—
673	Q₁₆	C₇×C₂²⋊C₄	1	4	yes	complemented
674	SD₁₆	—	2	4	no	—
675	SD₁₆	—	2	4	no	—
676	SD₁₆	—	2	4	no	—
677	SD₁₆	—	2	4	no	—
678	SD₁₆	C₇×C₂²⋊C₄	1	4	yes	complemented
679	SD₁₆	C₇×C₂²⋊C₄	1	4	yes	complemented
680	D₈	—	2	4	no	—
681	D₈	C₇×C₂²⋊C₄	1	4	yes	complemented
682	M₁₆	—	2	1	no	—
683	M₁₆	—	2	4	no	—
684	M₁₆	—	2	1	no	—
685	M₁₆	—	2	1	no	—
686	M₁₆	—	2	1	no	—
687	M₁₆	—	2	1	no	—
688	M₁₆	—	2	1	no	—
689	M₁₆	—	2	1	no	—
690	M₁₆	—	4	2	no	—
691	M₁₆	—	4	2	no	—
692	M₁₆	C₂²×C₄×C₇	1	2	yes	—
693	C₂×C₈	—	2	1	no	—
694	C₂×C₈	—	2	1	no	—
695	C₂×C₈	—	2	1	no	—
696	C₂×C₈	—	2	4	no	—
697	C₂×C₈	—	2	1	no	—
698	C₂×C₈	—	2	1	no	—
699	C₂×C₈	—	2	1	no	—
700	C₂×C₈	—	4	2	no	—
701	C₂×C₈	—	4	2	no	—
702	C₂×C₈	C₂²×C₄×C₇	1	2	yes	—
703	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
704	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
705	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
706	C₂×C₈	C₂×C₇×D₄	1	1	yes	characteristic
707	C₂×C₈	C₂×C₇×D₄	1	2	yes	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	—	2	1	no	—
712	C₄⋊C₄	—	4	1	no	—
713	C₄⋊C₄	—	4	1	no	—
714	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
715	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
716	C₂²⋊C₄	—	2	1	no	—
717	C₂²⋊C₄	—	4	1	no	—
718	C₂²⋊C₄	—	4	1	no	—
719	C₂²⋊C₄	—	8	2	no	—
720	C₄²	—	2	1	no	—
721	C₄²	—	2	1	no	—
722	C₄²	—	2	1	no	—
723	C₄²	—	4	1	no	—
724	C₄²	—	4	1	no	—
725	C₂×C₇	—	2	1	no	—
726	C₂×C₇	—	2	1	no	—
727	C₂×C₇	—	4	2	no	—
728	C₂×C₇	—	4	2	no	—
729	C₂×C₇	—	4	2	no	—
730	C₂×C₇	—	8	2	no	—
731	C₂×C₇	D₄×C₂²⋊C₄	1	1	yes	characteristic
732	C₂×C₇	#3288	1	1	yes	characteristic
733	C₂×C₇	#3289	1	1	yes	characteristic
734	C₂³	—	2	1	no	—
735	C₂³	—	2	1	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	2	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	1	no	—
740	C₂³	—	4	1	no	—
741	C₂³	—	8	1	no	—
742	C₂³	—	8	1	no	—
743	C₂³	—	16	1	no	—
744	C₂³	—	16	1	no	—
745	C₂³	C₇×H(5,𝔽₂)	1	1	yes	characteristic
746	Q₈	—	2	1	no	—
747	Q₈	—	2	1	no	—
748	Q₈	—	2	1	no	—
749	Q₈	—	2	2	no	—
750	Q₈	—	2	2	no	—
751	Q₈	—	4	4	no	—
752	Q₈	—	4	1	no	—
753	Q₈	—	4	1	no	—
754	Q₈	C₂×C₇×C₂²⋊C₄	1	2	yes	—
755	Q₈	C₂×C₇×C₂²⋊C₄	1	2	yes	—
756	Q₈	C₄×C₇×D₄	1	2	yes	—
757	D₄	—	2	2	no	—
758	D₄	—	2	2	no	—
759	D₄	—	2	2	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	2	no	—
764	D₄	—	2	2	no	—
765	D₄	—	2	1	no	—
766	D₄	—	2	1	no	—
767	D₄	—	2	1	no	—
768	D₄	—	4	4	no	—
769	D₄	—	4	4	no	—
770	D₄	—	4	4	no	—
771	D₄	—	4	1	no	—
772	D₄	—	4	1	no	—
773	D₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
774	D₄	C₂×C₇×C₂²⋊C₄	1	2	yes	—
775	D₄	C₄×C₇×D₄	1	2	yes	—
776	C₂×C₄	—	2	1	no	—
777	C₂×C₄	—	2	1	no	—
778	C₂×C₄	—	2	1	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	1	no	—
787	C₂×C₄	—	2	1	no	—
788	C₂×C₄	—	4	4	no	—
789	C₂×C₄	—	4	4	no	—
790	C₂×C₄	—	4	4	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	1	no	—
793	C₂×C₄	—	4	1	no	—
794	C₂×C₄	—	4	1	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	1	no	—
797	C₂×C₄	—	4	1	no	—
798	C₂×C₄	—	8	1	no	—
799	C₂×C₄	—	8	1	no	—
800	C₂×C₄	—	16	1	no	—
801	C₂×C₄	—	16	1	no	—
802	C₂×C₄	C₂³×C₄×C₇	1	1	yes	characteristic
803	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
804	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
805	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
806	C₂×C₄	C₂×C₇×#41	1	1	yes	characteristic
807	C₂×C₄	C₇×H(5,𝔽₂)	1	1	yes	characteristic
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	C₈	C₂×C₇×C₂²⋊C₄	1	2	yes	—
815	C₈	C₂×C₇×C₂²⋊C₄	1	2	yes	—
816	C₇	#22464	1	1	yes	characteristic, direct product factor, Sylow
817	C₂²	—	2	1	no	—
818	C₂²	—	2	1	no	—
819	C₂²	—	2	2	no	—
820	C₂²	—	2	2	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	4	1	no	—
823	C₂²	—	4	1	no	—
824	C₂²	—	4	1	no	—
825	C₂²	—	4	1	no	—
826	C₂²	—	4	1	no	—
827	C₂²	—	4	1	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	8	2	no	—
830	C₂²	—	8	1	no	—
831	C₂²	—	8	1	no	—
832	C₂²	—	16	1	no	—
833	C₂²	—	16	4	no	—
834	C₂²	C₇×#518	1	1	yes	characteristic
835	C₂²	C₇×D₄²	1	1	yes	characteristic
836	C₂²	C₇×#546	1	1	yes	characteristic
837	C₄	—	2	2	no	—
838	C₄	—	2	2	no	—
839	C₄	—	2	2	no	—
840	C₄	—	4	1	no	—
841	C₄	—	4	1	no	—
842	C₄	—	4	2	no	—
843	C₄	—	8	1	no	—
844	C₄	—	8	1	no	—
845	C₄	—	8	1	no	—
846	C₄	C₂²×C₇×C₂²⋊C₄	1	1	yes	characteristic
847	C₄	C₂×C₄×C₇×D₄	1	1	yes	characteristic
848	C₄	C₇×D₄²	1	1	yes	characteristic
849	C₄	C₇×#546	1	1	yes	characteristic
850	C₂	—	2	1	no	—
851	C₂	—	2	1	no	—
852	C₂	—	4	2	no	—
853	C₂	—	4	2	no	—
854	C₂	—	4	2	no	—
855	C₂	—	8	2	no	—
856	C₂	C₇×D₄×C₂²⋊C₄	1	1	yes	characteristic
857	C₂	C₇×#3288	1	1	yes	characteristic
858	C₂	C₇×#3289	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	D₄²
commutator	C₂×C₄	C₂³×C₄×C₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#577	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₄×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₇×#444	C₂	semidirect
3. C₇×#2951	C₂	semidirect
4. C₇×#2898	C₂	semidirect
5. C₇×#2897	C₂	semidirect
6. C₇×#1977	C₂	semidirect
7. C₇×#1973	C₂	semidirect
8. C₇×#1908	C₂	semidirect
9. C₇×#1907	C₂	semidirect
10. C₇×#1883	C₂	semidirect
11. C₇×#1882	C₂	semidirect
12. C₇×#1816	C₂	semidirect
13. C₇×#1793	C₂	semidirect
14. C₇×#1792	C₂	semidirect
15. C₇×#1765	C₂	semidirect
19. C₇×#577	C₄	semidirect
30. C₂×C₇×#131	C₂²	semidirect
32. C₇×#520	C₂²	semidirect
38. C₂×C₇×#108	C₂²	semidirect
39. C₂×C₇×#107	C₂²	semidirect
42. C₂×C₇×#104	C₂²	semidirect
44. C₇×#419	C₂²	semidirect
52. C₇×#417	C₂²	semidirect
57. C₂×C₇×#103	C₂²	semidirect
60. C₂×C₇×#101	C₂²	semidirect
62. C₇×#405	C₂²	semidirect
63. C₂×C₇×#97	C₂²	semidirect
64. C₇×#391	C₂²	semidirect
66. C₇×#343	C₂²	semidirect
67. C₇×#343	C₂²	semidirect
68. C₇×#341	C₂²	semidirect
69. C₇×#339	C₂²	semidirect
70. #22464	C₇	direct (N × H)
74. C₇×2₋¹⁺⁴	C₂×C₄	semidirect
78. C₇×H(5,𝔽₂)	C₂×C₄	semidirect
96. C₇×#137	C₂×C₄	semidirect
99. C₇×AGL(1,ℤ/8)	C₂×C₄	semidirect
111. C₂×C₇×SD₁₆	C₂×C₄	semidirect
121. C₇×#131	C₂×C₄	semidirect
182. C₂×#444	C₂×C₇	semidirect
183. #2951	C₂×C₇	semidirect
184. #2898	C₂×C₇	semidirect
185. #2897	C₂×C₇	semidirect
186. #1977	C₂×C₇	semidirect
187. #1973	C₂×C₇	semidirect
188. #1908	C₂×C₇	semidirect
189. #1907	C₂×C₇	semidirect
190. #1883	C₂×C₇	semidirect
191. #1882	C₂×C₇	semidirect
192. #1816	C₂×C₇	semidirect
193. #1793	C₂×C₇	semidirect
194. #1792	C₂×C₇	semidirect
195. #1765	C₂×C₇	semidirect
269. C₇×Q₁₆	C₂²⋊C₄	semidirect
274. C₇×SD₁₆	C₂²⋊C₄	semidirect
275. C₇×SD₁₆	C₂²⋊C₄	semidirect
277. C₇×D₈	C₂²⋊C₄	semidirect
324. #577	C₄×C₇	semidirect
335. C₂×#131	C₂²×C₇	semidirect
337. #520	C₂²×C₇	semidirect
343. C₂×#108	C₂²×C₇	semidirect
344. C₂×#107	C₂²×C₇	semidirect
347. C₂×#104	C₂²×C₇	semidirect
349. #419	C₂²×C₇	semidirect
357. #417	C₂²×C₇	semidirect
362. C₂×#103	C₂²×C₇	semidirect
365. C₂×#101	C₂²×C₇	semidirect
367. #405	C₂²×C₇	semidirect
368. C₂×#97	C₂²×C₇	semidirect
369. #391	C₂²×C₇	semidirect
371. #343	C₂²×C₇	semidirect
372. #343	C₂²×C₇	semidirect
373. #341	C₂²×C₇	semidirect
374. #339	C₂²×C₇	semidirect
460. 2₋¹⁺⁴	C₂×C₄×C₇	semidirect
464. H(5,𝔽₂)	C₂×C₄×C₇	semidirect
482. #137	C₂×C₄×C₇	semidirect
485. AGL(1,ℤ/8)	C₂×C₄×C₇	semidirect
497. C₂×SD₁₆	C₂×C₄×C₇	semidirect
507. #131	C₂×C₄×C₇	semidirect
673. Q₁₆	C₇×C₂²⋊C₄	semidirect
678. SD₁₆	C₇×C₂²⋊C₄	semidirect
679. SD₁₆	C₇×C₂²⋊C₄	semidirect
681. D₈	C₇×C₂²⋊C₄	semidirect
816. C₇	#22464	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₇×#577	2
C₂×C₇×#444	2
C₇×#2951	2
C₇×#2898	2
C₇×#2897	2
C₇×#1977	2
C₇×#1973	2
C₇×#1908	2
C₇×#1907	2
C₇×#1883	2
C₇×#1882	2
C₇×#1816	2
C₇×#1793	2
C₇×#1792	2
C₇×#1765	2
#22464	7

Subgroups — C7×#22464 #13199680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#22464 #13199680