Subgroups — C₇×#61212 #13238428

Order 1792.

2110 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3507	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3496	C₂	1	1	yes	maximal, characteristic
3	C₇×#3331	C₂	1	2	yes	maximal, complemented
4	C₇×#3324	C₂	1	2	yes	maximal, complemented
5	C₇×#3323	C₂	1	4	yes	maximal, complemented
6	C₇×#3302	C₂	1	2	yes	maximal, complemented
7	C₇×#3296	C₂	1	4	yes	maximal, complemented
8	C₇×#3295	C₂	1	2	yes	maximal, complemented
9	C₇×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₇×#3099	C₂	1	2	yes	maximal, complemented
11	C₇×#3077	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3063	C₂	1	2	yes	maximal, complemented
13	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₇×#3009	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₇×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
16	C₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
17	C₇×#2897	C₂	1	2	yes	maximal, complemented
18	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂×C₇×#137	C₂²	1	2	yes	complemented
20	C₂²×C₇×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₇×#131	C₂²	1	2	yes	complemented
22	C₇×#559	—	2	1	no	—
23	C₇×#557	—	2	1	no	—
24	C₇×#556	—	2	2	no	—
25	C₇×#556	C₂²	1	2	yes	complemented
26	C₇×#554	C₂²	1	2	yes	complemented
27	C₇×#552	C₂²	1	4	yes	complemented
28	C₇×#547	—	2	1	no	—
29	C₇×#547	C₂²	1	2	yes	—
30	C₇×#546	—	2	2	no	—
31	C₇×#546	C₂²	1	4	yes	—
32	C₇×D₄²	—	2	1	no	—
33	C₇×D₄²	C₂²	1	2	yes	—
34	C₇×#539	—	2	2	no	—
35	C₇×#537	C₂²	1	2	yes	—
36	C₇×#536	C₂²	1	2	yes	complemented
37	C₇×#534	—	2	2	no	—
38	C₇×#533	C₂²	1	1	yes	characteristic, complemented
39	C₇×#532	C₂²	1	1	yes	characteristic
40	C₇×#532	C₂²	1	1	yes	characteristic
41	C₇×#529	—	2	2	no	—
42	C₂×C₇×#121	—	2	2	no	—
43	C₇×#520	C₂²	1	2	yes	complemented
44	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
46	C₇×#488	C₂²	1	2	yes	complemented
47	C₇×#488	C₂²	1	2	yes	complemented
48	C₇×#487	C₂²	1	1	yes	characteristic, complemented
49	C₇×#487	C₂²	1	1	yes	characteristic, complemented
50	C₇×#486	C₂²	1	1	yes	characteristic, complemented
51	C₇×#486	C₂²	1	1	yes	characteristic, complemented
52	C₇×#485	C₂²	1	4	yes	complemented
53	C₇×#483	C₂²	1	4	yes	complemented
54	C₇×#482	C₂²	1	4	yes	complemented
55	C₇×#481	C₂²	1	4	yes	complemented
56	C₇×#478	C₂²	1	4	yes	complemented
57	C₇×#476	C₂²	1	2	yes	complemented
58	C₇×#474	C₂²	1	2	yes	complemented
59	C₇×#470	C₂²	1	4	yes	complemented
60	C₇×#468	C₂²	1	4	yes	complemented
61	C₇×#467	C₂²	1	4	yes	complemented
62	C₇×#465	C₂²	1	4	yes	complemented
63	C₇×#464	C₂²	1	4	yes	complemented
64	C₇×#462	C₂²	1	2	yes	complemented
65	C₇×#460	C₂²	1	2	yes	complemented
66	C₇×#452	C₂²	1	4	yes	complemented
67	C₇×#452	C₂²	1	4	yes	complemented
68	C₇×#450	C₂²	1	4	yes	complemented
69	C₇×#450	C₂²	1	4	yes	complemented
70	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
71	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
72	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
73	C₄×C₇×SD₁₆	C₂²	1	2	yes	complemented
74	C₇×#436	C₂²	1	2	yes	complemented
75	C₇×#436	C₂²	1	2	yes	complemented
76	C₇×C₈×D₄	C₂²	1	2	yes	complemented
77	C₇×C₈×D₄	C₂²	1	2	yes	complemented
78	C₇×#428	C₂²	1	2	yes	complemented
79	C₂×C₇×#106	C₂²	1	1	yes	characteristic, complemented
80	C₇×#423	C₂²	1	1	yes	characteristic, complemented
81	C₇×#418	C₂²	1	2	yes	—
82	C₇×#418	C₂²	1	4	yes	complemented
83	C₇×#417	C₂²	1	2	yes	complemented
84	C₇×#417	C₂²	1	4	yes	complemented
85	C₇×#416	C₂²	1	2	yes	complemented
86	C₇×#416	C₂²	1	4	yes	complemented
87	C₇×#416	C₂²	1	2	yes	complemented
88	C₂×C₇×#103	C₂²	1	1	yes	characteristic, complemented
89	C₂×C₇×#102	C₂²	1	1	yes	characteristic
90	C₂×C₇×#102	C₂²	1	4	yes	complemented
91	C₇×#408	C₂²	1	2	yes	complemented
92	C₂×C₄×C₇×C₈	C₂²	1	1	yes	characteristic, complemented
93	#61212	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
94	C₇×H(5,𝔽₂)	—	2	8	no	—
95	C₇×H(5,𝔽₂)	—	4	4	no	—
96	C₂×C₇×#41	—	2	2	no	—
97	C₂×C₇×#41	C₂³	1	2	yes	—
98	C₂×C₇×#41	C₂³	1	4	yes	—
99	C₂×C₇×#41	C₂³	1	2	yes	—
100	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
101	C₂²×C₇×D₄	—	2	4	no	—
102	C₂²×C₇×D₄	—	2	2	no	—
103	C₂²×C₇×D₄	—	2	2	no	—
104	C₂²×C₇×D₄	C₂³	1	4	yes	—
105	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₇	—	2	1	no	—
107	C₇×#137	—	4	4	no	—
108	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
109	C₂×C₇×SD₁₆	—	2	4	no	—
110	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
111	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
112	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
113	C₇×#131	—	4	4	no	—
114	C₂×C₇×M₁₆	C₂³	1	2	yes	—
115	C₂×C₇×M₁₆	C₂³	1	4	yes	—
116	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
117	C₂²×C₇×C₈	C₂³	1	1	yes	characteristic
118	C₂²×C₇×C₈	C₂³	1	4	yes	—
119	C₇×C₄⋊Q₈	—	2	2	no	—
120	C₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
121	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
124	C₇×#127	D₄	1	1	yes	characteristic
125	C₇×#127	C₂³	1	1	yes	characteristic
126	C₇×#126	—	2	4	no	—
127	C₇×#126	—	2	4	no	—
128	C₇×#125	—	2	2	no	—
129	C₇×#125	—	2	4	no	—
130	C₇×#125	C₂³	1	2	yes	—
131	C₇×#124	—	2	2	no	—
132	C₇×#124	—	2	2	no	—
133	C₇×#124	D₄	1	2	yes	—
134	C₇×#124	C₂³	1	2	yes	—
135	C₇×#123	—	2	4	no	—
136	C₇×#123	—	2	4	no	—
137	C₇×#123	—	2	4	no	—
138	C₇×#123	—	2	4	no	—
139	C₇×C₂²⋊Q₈	—	2	2	no	—
140	C₇×C₂²⋊Q₈	—	2	1	no	—
141	C₇×C₂²⋊Q₈	—	2	1	no	—
142	C₇×C₂²⋊Q₈	—	2	4	no	—
143	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
146	C₇×#121	—	2	4	no	—
147	C₇×#121	—	2	2	no	—
148	C₇×#121	—	2	2	no	—
149	C₇×#121	—	2	1	no	—
150	C₇×#121	—	2	1	no	—
151	C₇×#121	—	2	2	no	—
152	C₇×#121	—	2	4	no	—
153	C₇×#121	D₄	1	2	yes	—
154	C₇×#121	D₄	1	2	yes	—
155	C₇×#121	C₂³	1	4	yes	—
156	C₇×#120	—	2	4	no	—
157	C₇×#120	—	2	4	no	—
158	C₄×C₇×Q₈	—	2	2	no	—
159	C₄×C₇×Q₈	—	2	2	no	—
160	C₄×C₇×Q₈	—	2	1	no	—
161	C₄×C₇×Q₈	—	2	1	no	—
162	C₄×C₇×Q₈	—	2	1	no	—
163	C₄×C₇×Q₈	—	2	1	no	—
164	C₄×C₇×Q₈	C₂³	1	2	yes	—
165	C₄×C₇×Q₈	C₂³	1	2	yes	—
166	C₄×C₇×D₄	—	2	4	no	—
167	C₄×C₇×D₄	—	2	2	no	—
168	C₄×C₇×D₄	—	2	2	no	—
169	C₄×C₇×D₄	—	2	1	no	—
170	C₄×C₇×D₄	—	2	1	no	—
171	C₄×C₇×D₄	—	2	1	no	—
172	C₄×C₇×D₄	—	2	1	no	—
173	C₄×C₇×D₄	C₂³	1	2	yes	—
174	C₄×C₇×D₄	C₂³	1	2	yes	—
175	C₄×C₇×D₄	C₂³	1	2	yes	—
176	C₄×C₇×D₄	C₂³	1	2	yes	—
177	C₇×#117	—	2	4	no	—
178	C₇×#117	C₂³	1	4	yes	—
179	C₇×#117	C₂³	1	2	yes	—
180	C₂×C₇×C₄⋊C₄	—	2	1	no	—
181	C₂×C₇×C₄⋊C₄	—	2	2	no	—
182	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	—
183	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
186	C₂×C₇×C₂²⋊C₄	—	2	4	no	—
187	C₂×C₄²×C₇	—	2	1	no	—
188	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
189	C₇×#107	C₂³	1	4	yes	—
190	C₇×#106	C₂³	1	4	yes	—
191	C₇×#106	C₂³	1	2	yes	—
192	C₇×#106	C₂³	1	2	yes	—
193	C₇×C₄⋊C₈	C₂³	1	2	yes	—
194	C₇×C₄⋊C₈	C₂³	1	2	yes	—
195	C₇×#103	C₂³	1	2	yes	—
196	C₇×#103	C₂³	1	2	yes	—
197	C₇×#103	C₂³	1	2	yes	—
198	C₇×#103	C₂³	1	2	yes	—
199	C₇×#103	C₂³	1	2	yes	—
200	C₇×#103	C₂³	1	4	yes	—
201	C₇×#103	C₂³	1	2	yes	—
202	C₇×#102	C₂³	1	2	yes	—
203	C₇×#102	C₂³	1	4	yes	—
204	C₇×#102	C₂³	1	4	yes	—
205	C₇×#102	C₂³	1	2	yes	—
206	C₇×#102	C₂³	1	4	yes	—
207	C₇×#102	C₂³	1	2	yes	—
208	C₇×#102	C₂³	1	2	yes	—
209	C₇×#102	C₂³	1	2	yes	—
210	C₇×#102	C₂³	1	2	yes	—
211	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
212	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
213	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
214	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
215	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
216	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
217	#3507	C₂×C₇	1	1	yes	characteristic, complemented
218	#3496	C₂×C₇	1	1	yes	characteristic
219	#3331	C₂×C₇	1	2	yes	complemented
220	#3324	C₂×C₇	1	2	yes	complemented
221	#3323	C₂×C₇	1	4	yes	complemented
222	#3302	C₂×C₇	1	2	yes	complemented
223	#3296	C₂×C₇	1	4	yes	complemented
224	#3295	C₂×C₇	1	2	yes	complemented
225	#3131	C₂×C₇	1	1	yes	characteristic, complemented
226	#3099	C₂×C₇	1	2	yes	complemented
227	#3077	C₂×C₇	1	1	yes	characteristic, complemented
228	#3063	C₂×C₇	1	2	yes	complemented
229	#3037	C₂×C₇	1	1	yes	characteristic, complemented
230	#3009	C₂×C₇	1	2	yes	complemented
231	C₂×C₄×SD₁₆	C₂×C₇	1	1	yes	characteristic, complemented
232	#2931	C₂×C₇	1	1	yes	characteristic, complemented
233	#2897	C₂×C₇	1	2	yes	complemented
234	C₂⁴×C₇	—	2	1	no	—
235	C₂⁴×C₇	—	2	4	no	—
236	C₇×#41	—	2	4	no	—
237	C₇×#41	—	2	4	no	—
238	C₇×#41	—	2	8	no	—
239	C₇×#41	—	2	4	no	—
240	C₇×#41	—	2	4	no	—
241	C₇×#41	—	4	4	no	—
242	C₇×#41	—	4	8	no	—
243	C₂×C₇×Q₈	—	2	1	no	—
244	C₂×C₇×Q₈	—	2	1	no	—
245	C₂×C₇×Q₈	—	2	1	no	—
246	C₂×C₇×Q₈	—	2	2	no	—
247	C₂×C₇×Q₈	—	2	2	no	—
248	C₂×C₇×Q₈	C₂×D₄	1	2	yes	—
249	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
250	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
251	C₂×C₇×D₄	—	2	8	no	—
252	C₂×C₇×D₄	—	2	4	no	—
253	C₂×C₇×D₄	—	2	2	no	—
254	C₂×C₇×D₄	—	2	4	no	—
255	C₂×C₇×D₄	—	2	1	no	—
256	C₂×C₇×D₄	—	2	1	no	—
257	C₂×C₇×D₄	—	2	4	no	—
258	C₂×C₇×D₄	—	2	1	no	—
259	C₂×C₇×D₄	—	2	2	no	—
260	C₂×C₇×D₄	—	4	4	no	—
261	C₂×C₇×D₄	—	4	8	no	—
262	C₂×C₇×D₄	—	4	16	no	—
263	C₂×C₇×D₄	—	8	4	no	—
264	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
265	C₂×C₇×D₄	C₂×D₄	1	4	yes	—
266	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
267	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
268	C₂×C₇×D₄	#41	1	4	yes	—
269	C₂×C₇×D₄	C₂⁴	1	2	yes	—
270	C₂×C₇×D₄	C₂⁴	1	2	yes	—
271	C₂²×C₄×C₇	—	2	1	no	—
272	C₂²×C₄×C₇	—	2	1	no	—
273	C₂²×C₄×C₇	—	2	1	no	—
274	C₂²×C₄×C₇	—	2	4	no	—
275	C₂²×C₄×C₇	—	2	4	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	—	8	2	no	—
280	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
283	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
284	C₇×Q₁₆	—	4	4	no	—
285	C₇×SD₁₆	—	2	4	no	—
286	C₇×SD₁₆	—	2	4	no	—
287	C₇×SD₁₆	—	4	4	no	—
288	C₇×M₁₆	—	2	4	no	—
289	C₇×M₁₆	—	4	4	no	—
290	C₂×C₇×C₈	—	2	2	no	—
291	C₂×C₇×C₈	—	2	2	no	—
292	C₂×C₇×C₈	—	4	4	no	—
293	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
294	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
295	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
296	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
297	C₂×C₇×C₈	C₂⁴	1	4	yes	—
298	C₇×C₄⋊C₄	—	2	1	no	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	4	no	—
302	C₇×C₄⋊C₄	—	2	1	no	—
303	C₇×C₄⋊C₄	—	2	1	no	—
304	C₇×C₄⋊C₄	—	2	4	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	4	no	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	2	1	no	—
309	C₇×C₄⋊C₄	—	2	2	no	—
310	C₇×C₄⋊C₄	—	2	1	no	—
311	C₇×C₄⋊C₄	—	2	4	no	—
312	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
313	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
314	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
315	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
316	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
317	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
318	C₇×C₂²⋊C₄	—	2	4	no	—
319	C₇×C₂²⋊C₄	—	2	4	no	—
320	C₇×C₂²⋊C₄	—	2	2	no	—
321	C₇×C₂²⋊C₄	—	2	4	no	—
322	C₇×C₂²⋊C₄	—	2	4	no	—
323	C₇×C₂²⋊C₄	—	2	2	no	—
324	C₇×C₂²⋊C₄	—	2	2	no	—
325	C₇×C₂²⋊C₄	—	2	2	no	—
326	C₇×C₂²⋊C₄	—	2	4	no	—
327	C₇×C₂²⋊C₄	—	2	2	no	—
328	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
329	C₇×C₂²⋊C₄	C₂×D₄	1	4	yes	—
330	C₄²×C₇	—	2	2	no	—
331	C₄²×C₇	—	2	2	no	—
332	C₄²×C₇	—	2	4	no	—
333	C₄²×C₇	—	2	2	no	—
334	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₇	C₂⁴	1	1	yes	characteristic
337	C₄²×C₇	C₂⁴	1	1	yes	characteristic
338	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
339	C₂×#137	C₂²×C₇	1	2	yes	complemented
340	C₂²×SD₁₆	C₂²×C₇	1	1	yes	characteristic
341	C₂×#131	C₂²×C₇	1	2	yes	complemented
342	#559	—	2	1	no	—
343	#557	—	2	1	no	—
344	#556	—	2	2	no	—
345	#556	C₂²×C₇	1	2	yes	complemented
346	#554	C₂²×C₇	1	2	yes	complemented
347	#552	C₂²×C₇	1	4	yes	complemented
348	#547	—	2	1	no	—
349	#547	C₂²×C₇	1	2	yes	—
350	#546	—	2	2	no	—
351	#546	C₂²×C₇	1	4	yes	—
352	D₄²	—	2	1	no	—
353	D₄²	C₂²×C₇	1	2	yes	—
354	#539	—	2	2	no	—
355	#537	C₂²×C₇	1	2	yes	—
356	#536	C₂²×C₇	1	2	yes	complemented
357	#534	—	2	2	no	—
358	#533	C₂²×C₇	1	1	yes	characteristic, complemented
359	#532	C₂²×C₇	1	1	yes	characteristic
360	#532	C₂²×C₇	1	1	yes	characteristic
361	#529	—	2	2	no	—
362	C₂×#121	—	2	2	no	—
363	#520	C₂²×C₇	1	2	yes	complemented
364	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
365	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
366	#488	C₂²×C₇	1	2	yes	complemented
367	#488	C₂²×C₇	1	2	yes	complemented
368	#487	C₂²×C₇	1	1	yes	characteristic, complemented
369	#487	C₂²×C₇	1	1	yes	characteristic, complemented
370	#486	C₂²×C₇	1	1	yes	characteristic, complemented
371	#486	C₂²×C₇	1	1	yes	characteristic, complemented
372	#485	C₂²×C₇	1	4	yes	complemented
373	#483	C₂²×C₇	1	4	yes	complemented
374	#482	C₂²×C₇	1	4	yes	complemented
375	#481	C₂²×C₇	1	4	yes	complemented
376	#478	C₂²×C₇	1	4	yes	complemented
377	#476	C₂²×C₇	1	2	yes	complemented
378	#474	C₂²×C₇	1	2	yes	complemented
379	#470	C₂²×C₇	1	4	yes	complemented
380	#468	C₂²×C₇	1	4	yes	complemented
381	#467	C₂²×C₇	1	4	yes	complemented
382	#465	C₂²×C₇	1	4	yes	complemented
383	#464	C₂²×C₇	1	4	yes	complemented
384	#462	C₂²×C₇	1	2	yes	complemented
385	#460	C₂²×C₇	1	2	yes	complemented
386	#452	C₂²×C₇	1	4	yes	complemented
387	#452	C₂²×C₇	1	4	yes	complemented
388	#450	C₂²×C₇	1	4	yes	complemented
389	#450	C₂²×C₇	1	4	yes	complemented
390	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
391	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
392	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
393	C₄×SD₁₆	C₂²×C₇	1	2	yes	complemented
394	#436	C₂²×C₇	1	2	yes	complemented
395	#436	C₂²×C₇	1	2	yes	complemented
396	C₈×D₄	C₂²×C₇	1	2	yes	complemented
397	C₈×D₄	C₂²×C₇	1	2	yes	complemented
398	#428	C₂²×C₇	1	2	yes	complemented
399	C₂×#106	C₂²×C₇	1	1	yes	characteristic, complemented
400	#423	C₂²×C₇	1	1	yes	characteristic, complemented
401	#418	C₂²×C₇	1	2	yes	—
402	#418	C₂²×C₇	1	4	yes	complemented
403	#417	C₂²×C₇	1	4	yes	complemented
404	#417	C₂²×C₇	1	2	yes	complemented
405	#416	C₂²×C₇	1	2	yes	complemented
406	#416	C₂²×C₇	1	2	yes	complemented
407	#416	C₂²×C₇	1	4	yes	complemented
408	C₂×#103	C₂²×C₇	1	1	yes	characteristic, complemented
409	C₂×#102	C₂²×C₇	1	1	yes	characteristic
410	C₂×#102	C₂²×C₇	1	4	yes	complemented
411	#408	C₂²×C₇	1	2	yes	complemented
412	C₂×C₄×C₈	C₂²×C₇	1	1	yes	characteristic, complemented
413	C₂³×C₇	—	2	2	no	—
414	C₂³×C₇	—	2	4	no	—
415	C₂³×C₇	—	2	2	no	—
416	C₂³×C₇	—	4	8	no	—
417	C₂³×C₇	—	8	1	no	—
418	C₂³×C₇	—	8	1	no	—
419	C₂³×C₇	—	8	4	no	—
420	C₂³×C₇	—	8	4	no	—
421	C₂³×C₇	C₂²×D₄	1	4	yes	—
422	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
423	C₇×Q₈	—	2	4	no	—
424	C₇×Q₈	—	2	2	no	—
425	C₇×Q₈	—	2	2	no	—
426	C₇×Q₈	—	2	2	no	—
427	C₇×Q₈	—	2	2	no	—
428	C₇×Q₈	—	4	2	no	—
429	C₇×Q₈	—	4	2	no	—
430	C₇×Q₈	—	8	1	no	—
431	C₇×D₄	—	2	8	no	—
432	C₇×D₄	—	2	4	no	—
433	C₇×D₄	—	2	4	no	—
434	C₇×D₄	—	2	4	no	—
435	C₇×D₄	—	2	2	no	—
436	C₇×D₄	—	2	2	no	—
437	C₇×D₄	—	2	2	no	—
438	C₇×D₄	—	4	2	no	—
439	C₇×D₄	—	4	8	no	—
440	C₇×D₄	—	4	8	no	—
441	C₇×D₄	—	4	4	no	—
442	C₇×D₄	—	4	2	no	—
443	C₇×D₄	—	8	1	no	—
444	C₇×D₄	—	8	4	no	—
445	C₇×D₄	C₂×#41	1	4	yes	—
446	C₂×C₄×C₇	—	2	2	no	—
447	C₂×C₄×C₇	—	2	4	no	—
448	C₂×C₄×C₇	—	2	4	no	—
449	C₂×C₄×C₇	—	2	2	no	—
450	C₂×C₄×C₇	—	2	2	no	—
451	C₂×C₄×C₇	—	2	2	no	—
452	C₂×C₄×C₇	—	2	2	no	—
453	C₂×C₄×C₇	—	2	2	no	—
454	C₂×C₄×C₇	—	2	2	no	—
455	C₂×C₄×C₇	—	4	1	no	—
456	C₂×C₄×C₇	—	4	8	no	—
457	C₂×C₄×C₇	—	4	2	no	—
458	C₂×C₄×C₇	—	4	4	no	—
459	C₂×C₄×C₇	—	4	4	no	—
460	C₂×C₄×C₇	—	8	2	no	—
461	C₂×C₄×C₇	—	8	1	no	—
462	C₂×C₄×C₇	—	8	4	no	—
463	C₂×C₄×C₇	—	8	1	no	—
464	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₇	C₂²×D₄	1	4	yes	—
466	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₇	C₂×#41	1	2	yes	—
471	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
472	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
473	C₇×C₈	—	2	1	no	—
474	C₇×C₈	—	2	1	no	—
475	C₇×C₈	—	2	1	no	—
476	C₇×C₈	—	2	1	no	—
477	C₇×C₈	—	2	4	no	—
478	H(5,𝔽₂)	—	2	8	no	—
479	H(5,𝔽₂)	—	4	4	no	—
480	C₂×#41	—	2	2	no	—
481	C₂×#41	C₂³×C₇	1	2	yes	—
482	C₂×#41	C₂³×C₇	1	4	yes	—
483	C₂×#41	C₂³×C₇	1	2	yes	—
484	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
485	C₂²×D₄	—	2	4	no	—
486	C₂²×D₄	—	2	2	no	—
487	C₂²×D₄	—	2	2	no	—
488	C₂²×D₄	C₂³×C₇	1	4	yes	—
489	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
490	C₂³×C₄	—	2	1	no	—
491	#137	—	4	4	no	—
492	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
493	C₂×SD₁₆	—	2	4	no	—
494	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
495	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
496	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
497	#131	—	4	4	no	—
498	C₂×M₁₆	C₂³×C₇	1	2	yes	—
499	C₂×M₁₆	C₂³×C₇	1	4	yes	—
500	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
501	C₂²×C₈	C₂³×C₇	1	1	yes	characteristic
502	C₂²×C₈	C₂³×C₇	1	4	yes	—
503	C₄⋊Q₈	—	2	2	no	—
504	C₄⋊Q₈	C₇×D₄	1	1	yes	characteristic
505	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
506	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
507	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
508	#127	C₇×D₄	1	1	yes	characteristic
509	#127	C₂³×C₇	1	1	yes	characteristic
510	#126	—	2	4	no	—
511	#126	—	2	4	no	—
512	#125	—	2	2	no	—
513	#125	—	2	4	no	—
514	#125	C₂³×C₇	1	2	yes	—
515	#124	—	2	2	no	—
516	#124	—	2	2	no	—
517	#124	C₇×D₄	1	2	yes	—
518	#124	C₂³×C₇	1	2	yes	—
519	#123	—	2	4	no	—
520	#123	—	2	4	no	—
521	#123	—	2	4	no	—
522	#123	—	2	4	no	—
523	C₂²⋊Q₈	—	2	2	no	—
524	C₂²⋊Q₈	—	2	1	no	—
525	C₂²⋊Q₈	—	2	1	no	—
526	C₂²⋊Q₈	—	2	4	no	—
527	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
528	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
529	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
530	#121	—	2	4	no	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	2	1	no	—
534	#121	—	2	1	no	—
535	#121	—	2	2	no	—
536	#121	—	2	4	no	—
537	#121	C₇×D₄	1	2	yes	—
538	#121	C₇×D₄	1	2	yes	—
539	#121	C₂³×C₇	1	4	yes	—
540	#120	—	2	4	no	—
541	#120	—	2	4	no	—
542	C₄×Q₈	—	2	2	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	1	no	—
545	C₄×Q₈	—	2	1	no	—
546	C₄×Q₈	—	2	1	no	—
547	C₄×Q₈	—	2	1	no	—
548	C₄×Q₈	C₂³×C₇	1	2	yes	—
549	C₄×Q₈	C₂³×C₇	1	2	yes	—
550	C₄×D₄	—	2	4	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	1	no	—
554	C₄×D₄	—	2	1	no	—
555	C₄×D₄	—	2	1	no	—
556	C₄×D₄	—	2	1	no	—
557	C₄×D₄	C₂³×C₇	1	2	yes	—
558	C₄×D₄	C₂³×C₇	1	2	yes	—
559	C₄×D₄	C₂³×C₇	1	2	yes	—
560	C₄×D₄	C₂³×C₇	1	2	yes	—
561	#117	—	2	4	no	—
562	#117	C₂³×C₇	1	2	yes	—
563	#117	C₂³×C₇	1	4	yes	—
564	C₂×C₄⋊C₄	—	2	1	no	—
565	C₂×C₄⋊C₄	—	2	2	no	—
566	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
567	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
568	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	—
569	C₂×C₂²⋊C₄	—	2	1	no	—
570	C₂×C₂²⋊C₄	—	2	4	no	—
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
573	#107	C₂³×C₇	1	4	yes	—
574	#106	C₂³×C₇	1	2	yes	—
575	#106	C₂³×C₇	1	2	yes	—
576	#106	C₂³×C₇	1	4	yes	—
577	C₄⋊C₈	C₂³×C₇	1	2	yes	—
578	C₄⋊C₈	C₂³×C₇	1	2	yes	—
579	#103	C₂³×C₇	1	2	yes	—
580	#103	C₂³×C₇	1	2	yes	—
581	#103	C₂³×C₇	1	2	yes	—
582	#103	C₂³×C₇	1	4	yes	—
583	#103	C₂³×C₇	1	2	yes	—
584	#103	C₂³×C₇	1	2	yes	—
585	#103	C₂³×C₇	1	2	yes	—
586	#102	C₂³×C₇	1	2	yes	—
587	#102	C₂³×C₇	1	2	yes	—
588	#102	C₂³×C₇	1	2	yes	—
589	#102	C₂³×C₇	1	4	yes	—
590	#102	C₂³×C₇	1	4	yes	—
591	#102	C₂³×C₇	1	4	yes	—
592	#102	C₂³×C₇	1	2	yes	—
593	#102	C₂³×C₇	1	2	yes	—
594	#102	C₂³×C₇	1	2	yes	—
595	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
596	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
597	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
598	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
599	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
600	C₄×C₈	C₂³×C₇	1	1	yes	characteristic
601	C₂²×C₇	—	2	1	no	—
602	C₂²×C₇	—	2	1	no	—
603	C₂²×C₇	—	2	4	no	—
604	C₂²×C₇	—	2	4	no	—
605	C₂²×C₇	—	2	4	no	—
606	C₂²×C₇	—	2	4	no	—
607	C₂²×C₇	—	4	2	no	—
608	C₂²×C₇	—	4	2	no	—
609	C₂²×C₇	—	4	2	no	—
610	C₂²×C₇	—	4	2	no	—
611	C₂²×C₇	—	4	2	no	—
612	C₂²×C₇	—	8	4	no	—
613	C₂²×C₇	—	16	8	no	—
614	C₂²×C₇	#546	1	2	yes	—
615	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
616	C₄×C₇	—	2	1	no	—
617	C₄×C₇	—	2	1	no	—
618	C₄×C₇	—	2	4	no	—
619	C₄×C₇	—	2	1	no	—
620	C₄×C₇	—	4	2	no	—
621	C₄×C₇	—	4	2	no	—
622	C₄×C₇	—	4	2	no	—
623	C₄×C₇	—	4	2	no	—
624	C₄×C₇	—	4	2	no	—
625	C₄×C₇	—	4	2	no	—
626	C₄×C₇	#546	1	2	yes	—
627	C₄×C₇	#577	1	2	yes	—
628	C₄×C₇	C₂²×#41	1	1	yes	characteristic
629	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
630	C₂⁴	—	2	1	no	—
631	C₂⁴	—	2	4	no	—
632	#41	—	2	4	no	—
633	#41	—	2	4	no	—
634	#41	—	2	8	no	—
635	#41	—	2	4	no	—
636	#41	—	2	4	no	—
637	#41	—	4	4	no	—
638	#41	—	4	8	no	—
639	C₂×Q₈	—	2	1	no	—
640	C₂×Q₈	—	2	1	no	—
641	C₂×Q₈	—	2	1	no	—
642	C₂×Q₈	—	2	2	no	—
643	C₂×Q₈	—	2	2	no	—
644	C₂×Q₈	C₂×C₇×D₄	1	2	yes	—
645	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
646	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	2	4	no	—
649	C₂×D₄	—	2	2	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	1	no	—
652	C₂×D₄	—	2	1	no	—
653	C₂×D₄	—	2	4	no	—
654	C₂×D₄	—	2	1	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	8	no	—
658	C₂×D₄	—	4	16	no	—
659	C₂×D₄	—	8	4	no	—
660	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
661	C₂×D₄	C₂×C₇×D₄	1	4	yes	—
662	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
663	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
664	C₂×D₄	C₇×#41	1	4	yes	—
665	C₂×D₄	C₂⁴×C₇	1	2	yes	—
666	C₂×D₄	C₂⁴×C₇	1	2	yes	—
667	C₂²×C₄	—	2	1	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	4	no	—
671	C₂²×C₄	—	2	4	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	8	2	no	—
676	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
677	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
678	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
679	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
680	Q₁₆	—	4	4	no	—
681	SD₁₆	—	2	4	no	—
682	SD₁₆	—	2	4	no	—
683	SD₁₆	—	4	4	no	—
684	M₁₆	—	2	4	no	—
685	M₁₆	—	4	4	no	—
686	C₂×C₈	—	2	2	no	—
687	C₂×C₈	—	2	2	no	—
688	C₂×C₈	—	4	4	no	—
689	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
690	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
691	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
692	C₂×C₈	C₂⁴×C₇	1	1	yes	characteristic
693	C₂×C₈	C₂⁴×C₇	1	4	yes	—
694	C₄⋊C₄	—	2	1	no	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	1	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	4	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	1	no	—
707	C₄⋊C₄	—	2	4	no	—
708	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
709	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
710	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
711	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
712	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
713	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	2	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	2	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	4	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
725	C₂²⋊C₄	C₂×C₇×D₄	1	4	yes	—
726	C₄²	—	2	2	no	—
727	C₄²	—	2	2	no	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	2	no	—
730	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
731	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
732	C₄²	C₂⁴×C₇	1	1	yes	characteristic
733	C₄²	C₂⁴×C₇	1	1	yes	characteristic
734	C₂×C₇	—	2	2	no	—
735	C₂×C₇	—	4	4	no	—
736	C₂×C₇	—	4	4	no	—
737	C₂×C₇	—	8	2	no	—
738	C₂×C₇	C₂×#546	1	1	yes	characteristic
739	C₂×C₇	C₂×#577	1	1	yes	characteristic
740	C₂×C₇	#3584	1	1	yes	characteristic
741	C₂³	—	2	2	no	—
742	C₂³	—	2	4	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	4	8	no	—
745	C₂³	—	8	1	no	—
746	C₂³	—	8	1	no	—
747	C₂³	—	8	4	no	—
748	C₂³	—	8	4	no	—
749	C₂³	C₂²×C₇×D₄	1	4	yes	—
750	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
751	Q₈	—	2	4	no	—
752	Q₈	—	2	2	no	—
753	Q₈	—	2	2	no	—
754	Q₈	—	2	2	no	—
755	Q₈	—	2	2	no	—
756	Q₈	—	4	2	no	—
757	Q₈	—	4	2	no	—
758	Q₈	—	8	1	no	—
759	D₄	—	2	8	no	—
760	D₄	—	2	2	no	—
761	D₄	—	2	2	no	—
762	D₄	—	2	2	no	—
763	D₄	—	2	4	no	—
764	D₄	—	2	4	no	—
765	D₄	—	2	4	no	—
766	D₄	—	4	2	no	—
767	D₄	—	4	8	no	—
768	D₄	—	4	8	no	—
769	D₄	—	4	4	no	—
770	D₄	—	4	2	no	—
771	D₄	—	8	1	no	—
772	D₄	—	8	4	no	—
773	D₄	C₂×C₇×#41	1	4	yes	—
774	C₂×C₄	—	2	4	no	—
775	C₂×C₄	—	2	4	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	no	—
778	C₂×C₄	—	2	2	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	—	4	1	no	—
784	C₂×C₄	—	4	8	no	—
785	C₂×C₄	—	4	2	no	—
786	C₂×C₄	—	4	4	no	—
787	C₂×C₄	—	4	4	no	—
788	C₂×C₄	—	8	2	no	—
789	C₂×C₄	—	8	1	no	—
790	C₂×C₄	—	8	4	no	—
791	C₂×C₄	—	8	1	no	—
792	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
793	C₂×C₄	C₂²×C₇×D₄	1	4	yes	—
794	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
795	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
796	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
797	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
798	C₂×C₄	C₂×C₇×#41	1	2	yes	—
799	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
800	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
801	C₈	—	2	1	no	—
802	C₈	—	2	1	no	—
803	C₈	—	2	1	no	—
804	C₈	—	2	1	no	—
805	C₈	—	2	4	no	—
806	C₇	#61212	1	1	yes	characteristic, direct product factor, Sylow
807	C₂²	—	2	1	no	—
808	C₂²	—	2	1	no	—
809	C₂²	—	2	4	no	—
810	C₂²	—	2	4	no	—
811	C₂²	—	2	4	no	—
812	C₂²	—	2	4	no	—
813	C₂²	—	4	2	no	—
814	C₂²	—	4	2	no	—
815	C₂²	—	4	2	no	—
816	C₂²	—	4	2	no	—
817	C₂²	—	4	2	no	—
818	C₂²	—	8	4	no	—
819	C₂²	—	16	8	no	—
820	C₂²	C₇×#546	1	2	yes	—
821	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
822	C₄	—	2	1	no	—
823	C₄	—	2	1	no	—
824	C₄	—	2	1	no	—
825	C₄	—	2	4	no	—
826	C₄	—	4	2	no	—
827	C₄	—	4	2	no	—
828	C₄	—	4	2	no	—
829	C₄	—	4	2	no	—
830	C₄	—	4	2	no	—
831	C₄	—	4	2	no	—
832	C₄	C₇×#546	1	2	yes	—
833	C₄	C₇×#577	1	2	yes	—
834	C₄	C₂²×C₇×#41	1	1	yes	characteristic
835	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
836	C₂	—	2	2	no	—
837	C₂	—	4	4	no	—
838	C₂	—	4	4	no	—
839	C₂	—	8	2	no	—
840	C₂	C₂×C₇×#546	1	1	yes	characteristic
841	C₂	C₂×C₇×#577	1	1	yes	characteristic
842	C₂	C₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
prime radical	C₇×#3496	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₇×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3507	C₂	semidirect
3. C₇×#3331	C₂	semidirect
4. C₇×#3324	C₂	semidirect
5. C₇×#3323	C₂	semidirect
6. C₇×#3302	C₂	semidirect
7. C₇×#3296	C₂	semidirect
8. C₇×#3295	C₂	semidirect
9. C₇×#3131	C₂	semidirect
10. C₇×#3099	C₂	semidirect
11. C₇×#3077	C₂	semidirect
12. C₇×#3063	C₂	semidirect
13. C₇×#3037	C₂	semidirect
14. C₇×#3009	C₂	semidirect
15. C₂×C₄×C₇×SD₁₆	C₂	semidirect
16. C₇×#2931	C₂	semidirect
17. C₇×#2897	C₂	semidirect
19. C₂×C₇×#137	C₂²	semidirect
21. C₂×C₇×#131	C₂²	semidirect
25. C₇×#556	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
27. C₇×#552	C₂²	semidirect
36. C₇×#536	C₂²	semidirect
38. C₇×#533	C₂²	semidirect
43. C₇×#520	C₂²	semidirect
44. C₂×C₄×C₇×Q₈	C₂²	semidirect
46. C₇×#488	C₂²	semidirect
47. C₇×#488	C₂²	semidirect
48. C₇×#487	C₂²	semidirect
49. C₇×#487	C₂²	semidirect
50. C₇×#486	C₂²	semidirect
51. C₇×#486	C₂²	semidirect
52. C₇×#485	C₂²	semidirect
53. C₇×#483	C₂²	semidirect
54. C₇×#482	C₂²	semidirect
55. C₇×#481	C₂²	semidirect
56. C₇×#478	C₂²	semidirect
57. C₇×#476	C₂²	semidirect
58. C₇×#474	C₂²	semidirect
59. C₇×#470	C₂²	semidirect
60. C₇×#468	C₂²	semidirect
61. C₇×#467	C₂²	semidirect
62. C₇×#465	C₂²	semidirect
63. C₇×#464	C₂²	semidirect
64. C₇×#462	C₂²	semidirect
65. C₇×#460	C₂²	semidirect
66. C₇×#452	C₂²	semidirect
67. C₇×#452	C₂²	semidirect
68. C₇×#450	C₂²	semidirect
69. C₇×#450	C₂²	semidirect
70. C₄×C₇×SD₁₆	C₂²	semidirect
71. C₄×C₇×SD₁₆	C₂²	semidirect
72. C₄×C₇×SD₁₆	C₂²	semidirect
73. C₄×C₇×SD₁₆	C₂²	semidirect
74. C₇×#436	C₂²	semidirect
75. C₇×#436	C₂²	semidirect
76. C₇×C₈×D₄	C₂²	semidirect
77. C₇×C₈×D₄	C₂²	semidirect
78. C₇×#428	C₂²	semidirect
79. C₂×C₇×#106	C₂²	semidirect
80. C₇×#423	C₂²	semidirect
82. C₇×#418	C₂²	semidirect
83. C₇×#417	C₂²	semidirect
84. C₇×#417	C₂²	semidirect
85. C₇×#416	C₂²	semidirect
86. C₇×#416	C₂²	semidirect
87. C₇×#416	C₂²	semidirect
88. C₂×C₇×#103	C₂²	semidirect
90. C₂×C₇×#102	C₂²	semidirect
91. C₇×#408	C₂²	semidirect
92. C₂×C₄×C₇×C₈	C₂²	semidirect
93. #61212	C₇	direct (N × H)
217. #3507	C₂×C₇	semidirect
219. #3331	C₂×C₇	semidirect
220. #3324	C₂×C₇	semidirect
221. #3323	C₂×C₇	semidirect
222. #3302	C₂×C₇	semidirect
223. #3296	C₂×C₇	semidirect
224. #3295	C₂×C₇	semidirect
225. #3131	C₂×C₇	semidirect
226. #3099	C₂×C₇	semidirect
227. #3077	C₂×C₇	semidirect
228. #3063	C₂×C₇	semidirect
229. #3037	C₂×C₇	semidirect
230. #3009	C₂×C₇	semidirect
231. C₂×C₄×SD₁₆	C₂×C₇	semidirect
232. #2931	C₂×C₇	semidirect
233. #2897	C₂×C₇	semidirect
339. C₂×#137	C₂²×C₇	semidirect
341. C₂×#131	C₂²×C₇	semidirect
345. #556	C₂²×C₇	semidirect
346. #554	C₂²×C₇	semidirect
347. #552	C₂²×C₇	semidirect
356. #536	C₂²×C₇	semidirect
358. #533	C₂²×C₇	semidirect
363. #520	C₂²×C₇	semidirect
364. C₂×C₄×Q₈	C₂²×C₇	semidirect
366. #488	C₂²×C₇	semidirect
367. #488	C₂²×C₇	semidirect
368. #487	C₂²×C₇	semidirect
369. #487	C₂²×C₇	semidirect
370. #486	C₂²×C₇	semidirect
371. #486	C₂²×C₇	semidirect
372. #485	C₂²×C₇	semidirect
373. #483	C₂²×C₇	semidirect
374. #482	C₂²×C₇	semidirect
375. #481	C₂²×C₇	semidirect
376. #478	C₂²×C₇	semidirect
377. #476	C₂²×C₇	semidirect
378. #474	C₂²×C₇	semidirect
379. #470	C₂²×C₇	semidirect
380. #468	C₂²×C₇	semidirect
381. #467	C₂²×C₇	semidirect
382. #465	C₂²×C₇	semidirect
383. #464	C₂²×C₇	semidirect
384. #462	C₂²×C₇	semidirect
385. #460	C₂²×C₇	semidirect
386. #452	C₂²×C₇	semidirect
387. #452	C₂²×C₇	semidirect
388. #450	C₂²×C₇	semidirect
389. #450	C₂²×C₇	semidirect
390. C₄×SD₁₆	C₂²×C₇	semidirect
391. C₄×SD₁₆	C₂²×C₇	semidirect
392. C₄×SD₁₆	C₂²×C₇	semidirect
393. C₄×SD₁₆	C₂²×C₇	semidirect
394. #436	C₂²×C₇	semidirect
395. #436	C₂²×C₇	semidirect
396. C₈×D₄	C₂²×C₇	semidirect
397. C₈×D₄	C₂²×C₇	semidirect
398. #428	C₂²×C₇	semidirect
399. C₂×#106	C₂²×C₇	semidirect
400. #423	C₂²×C₇	semidirect
402. #418	C₂²×C₇	semidirect
403. #417	C₂²×C₇	semidirect
404. #417	C₂²×C₇	semidirect
405. #416	C₂²×C₇	semidirect
406. #416	C₂²×C₇	semidirect
407. #416	C₂²×C₇	semidirect
408. C₂×#103	C₂²×C₇	semidirect
410. C₂×#102	C₂²×C₇	semidirect
411. #408	C₂²×C₇	semidirect
412. C₂×C₄×C₈	C₂²×C₇	semidirect
806. C₇	#61212	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×#3507	2
C₇×#3496	2
C₇×#3331	2
C₇×#3324	2
C₇×#3323	2
C₇×#3302	2
C₇×#3296	2
C₇×#3295	2
C₇×#3131	2
C₇×#3099	2
C₇×#3077	2
C₇×#3063	2
C₇×#3037	2
C₇×#3009	2
C₂×C₄×C₇×SD₁₆	2
C₇×#2931	2
C₇×#2897	2
#61212	7

Subgroups — C7×#61212 #13238428

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#61212 #13238428