Subgroups — C₇×#60833 #13238049

Order 1792.

2144 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
2	C₇×#3461	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3224	C₂	1	4	yes	maximal, complemented
4	C₇×#3222	C₂	1	4	yes	maximal, complemented
5	C₇×#3217	C₂	1	2	yes	maximal, complemented
6	C₇×#3216	C₂	1	2	yes	maximal, complemented
7	C₇×#3212	C₂	1	2	yes	maximal, complemented
8	C₇×#3208	C₂	1	2	yes	maximal, complemented
9	C₇×#3154	C₂	1	2	yes	maximal, complemented
10	C₇×#3136	C₂	1	2	yes	maximal, complemented
11	C₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
12	C₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
13	C₇×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
15	C₇×#3012	C₂	1	2	yes	maximal, complemented
16	C₇×#3009	C₂	1	2	yes	maximal, complemented
17	C₇×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂×C₇×#137	C₂²	1	2	yes	complemented
20	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
21	C₂×C₇×#135	C₂²	1	2	yes	complemented
22	C₂²×C₇×SD₁₆	C₂²	1	2	yes	complemented
23	C₇×#550	—	2	1	no	—
24	C₇×#550	—	2	1	no	—
25	C₇×D₄²	—	2	1	no	—
26	C₇×D₄²	—	2	2	no	—
27	C₇×D₄²	—	2	2	no	—
28	C₇×D₄²	—	2	1	no	—
29	C₇×#544	C₂²	1	1	yes	characteristic, complemented
30	C₇×#542	—	2	1	no	—
31	C₇×#542	C₂²	1	2	yes	complemented
32	C₇×#541	—	2	1	no	—
33	C₇×#541	C₂²	1	2	yes	complemented
34	C₇×#539	—	2	2	no	—
35	C₇×#537	C₂²	1	1	yes	characteristic
36	C₇×#536	C₂²	1	1	yes	characteristic
37	C₇×#536	C₂²	1	1	yes	characteristic, complemented
38	C₇×#535	C₂²	1	4	yes	—
39	C₇×#535	C₂²	1	2	yes	—
40	C₇×#533	—	2	1	no	—
41	C₇×#533	C₂²	1	2	yes	complemented
42	C₇×#532	C₂²	1	2	yes	—
43	C₇×#532	C₂²	1	1	yes	characteristic
44	C₂×C₇×#127	C₂²	1	2	yes	—
45	C₂×C₇×#127	C₂²	1	1	yes	characteristic
46	C₇×#529	—	2	2	no	—
47	C₇×#529	—	2	1	no	—
48	C₇×#529	C₂²	1	2	yes	complemented
49	C₄×C₇×#41	C₂²	1	1	yes	characteristic
50	C₄×C₇×#41	C₂²	1	1	yes	characteristic, complemented
51	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
52	C₇×#497	C₂²	1	4	yes	complemented
53	C₇×#496	C₂²	1	4	yes	complemented
54	C₇×#495	C₂²	1	4	yes	complemented
55	C₇×#492	C₂²	1	4	yes	complemented
56	C₇×#490	C₂²	1	4	yes	complemented
57	C₇×#489	C₂²	1	4	yes	complemented
58	C₇×#488	C₂²	1	4	yes	complemented
59	C₇×#486	C₂²	1	4	yes	complemented
60	C₇×#464	C₂²	1	2	yes	complemented
61	C₇×#464	C₂²	1	4	yes	complemented
62	C₇×#463	C₂²	1	2	yes	complemented
63	C₇×#462	C₂²	1	2	yes	complemented
64	C₇×#462	C₂²	1	1	yes	characteristic, complemented
65	C₇×#461	C₂²	1	1	yes	characteristic, complemented
66	C₇×#460	C₂²	1	1	yes	characteristic, complemented
67	C₇×#460	C₂²	1	2	yes	complemented
68	C₇×#460	C₂²	1	2	yes	complemented
69	C₇×#460	C₂²	1	2	yes	complemented
70	C₇×#460	C₂²	1	2	yes	complemented
71	C₇×#460	C₂²	1	2	yes	complemented
72	C₇×#460	C₂²	1	4	yes	complemented
73	C₇×#459	C₂²	1	2	yes	complemented
74	C₇×#459	C₂²	1	1	yes	characteristic, complemented
75	C₇×#459	C₂²	1	2	yes	complemented
76	C₇×#452	C₂²	1	4	yes	complemented
77	C₇×#452	C₂²	1	4	yes	complemented
78	C₇×#452	C₂²	1	4	yes	complemented
79	C₇×#450	C₂²	1	4	yes	complemented
80	C₇×#450	C₂²	1	4	yes	complemented
81	C₇×#450	C₂²	1	4	yes	complemented
82	C₇×#449	C₂²	1	4	yes	complemented
83	C₇×#447	C₂²	1	4	yes	complemented
84	C₇×#433	C₂²	1	4	yes	complemented
85	C₇×#432	C₂²	1	2	yes	complemented
86	C₇×#431	C₂²	1	2	yes	complemented
87	C₇×#423	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₇×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
89	C₇×#418	C₂²	1	2	yes	complemented
90	C₇×#417	C₂²	1	2	yes	complemented
91	C₇×#416	C₂²	1	2	yes	complemented
92	C₂×C₇×#102	C₂²	1	2	yes	complemented
93	C₇×#408	C₂²	1	2	yes	—
94	C₇×#405	C₂²	1	2	yes	complemented
95	#60833	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₇×H(5,𝔽₂)	—	4	4	no	—
97	C₇×H(5,𝔽₂)	—	4	4	no	—
98	C₂×C₇×#41	—	2	2	no	—
99	C₂×C₇×#41	C₂³	1	2	yes	—
100	C₂×C₇×#41	C₂³	1	1	yes	characteristic
101	C₂×C₇×#41	C₂³	1	4	yes	—
102	C₂×C₇×#41	C₂³	1	1	yes	characteristic
103	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₇×D₄	—	2	4	no	—
105	C₂²×C₇×D₄	—	2	2	no	—
106	C₂²×C₇×D₄	—	2	1	no	—
107	C₂²×C₇×D₄	—	2	2	no	—
108	C₂²×C₇×D₄	—	2	1	no	—
109	C₂²×C₇×D₄	—	2	2	no	—
110	C₂²×C₇×D₄	C₂³	1	2	yes	—
111	C₂²×C₇×D₄	C₂³	1	4	yes	—
112	C₇×#137	—	4	4	no	—
113	C₇×AGL(1,ℤ/8)	—	4	4	no	—
114	C₇×#135	—	4	4	no	—
115	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
116	C₂×C₇×Q₁₆	C₂³	1	2	yes	—
117	C₂×C₇×SD₁₆	—	4	4	no	—
118	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
119	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
122	C₂×C₇×SD₁₆	C₂³	1	2	yes	—
123	C₂×C₇×SD₁₆	C₂³	1	4	yes	—
124	C₂×C₇×D₈	C₂³	1	4	yes	—
125	C₂×C₇×D₈	C₂³	1	2	yes	—
126	C₂×C₇×M₁₆	C₂³	1	2	yes	—
127	C₂²×C₇×C₈	C₂³	1	2	yes	—
128	C₇×C₄⋊Q₈	—	2	1	no	—
129	C₇×C₄⋊Q₈	—	2	1	no	—
130	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
131	C₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
132	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
133	C₇×#127	—	2	1	no	—
134	C₇×#127	—	2	2	no	—
135	C₇×#127	—	2	1	no	—
136	C₇×#127	—	2	2	no	—
137	C₇×#127	C₂³	1	4	yes	—
138	C₇×#127	C₂³	1	1	yes	characteristic
139	C₇×#127	C₂³	1	2	yes	—
140	C₇×#127	C₂³	1	2	yes	—
141	C₇×#126	—	2	2	no	—
142	C₇×#126	—	2	2	no	—
143	C₇×#126	—	2	2	no	—
144	C₇×#126	—	2	2	no	—
145	C₇×#125	—	2	2	no	—
146	C₇×#125	—	2	1	no	—
147	C₇×#125	—	2	2	no	—
148	C₇×#125	—	2	2	no	—
149	C₇×#125	C₂³	1	2	yes	—
150	C₇×#124	—	2	1	no	—
151	C₇×#124	—	2	2	no	—
152	C₇×#124	C₂³	1	4	yes	—
153	C₇×#124	C₂³	1	2	yes	—
154	C₇×#124	C₂³	1	2	yes	—
155	C₇×#123	—	2	2	no	—
156	C₇×#123	—	2	2	no	—
157	C₇×#123	—	2	2	no	—
158	C₇×#123	—	2	2	no	—
159	C₇×C₂²⋊Q₈	—	2	1	no	—
160	C₇×C₂²⋊Q₈	—	2	2	no	—
161	C₇×C₂²⋊Q₈	—	2	1	no	—
162	C₇×C₂²⋊Q₈	—	2	1	no	—
163	C₇×C₂²⋊Q₈	—	2	2	no	—
164	C₇×C₂²⋊Q₈	—	2	2	no	—
165	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
166	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
167	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
168	C₇×#121	—	2	2	no	—
169	C₇×#121	—	2	1	no	—
170	C₇×#121	—	2	1	no	—
171	C₇×#121	—	2	2	no	—
172	C₇×#121	—	2	1	no	—
173	C₇×#121	—	2	2	no	—
174	C₇×#121	—	2	4	no	—
175	C₇×#121	—	2	2	no	—
176	C₇×#121	—	2	2	no	—
177	C₇×#121	—	2	4	no	—
178	C₇×#121	C₂³	1	2	yes	—
179	C₇×#120	—	2	4	no	—
180	C₇×#120	—	2	4	no	—
181	C₇×#120	—	2	4	no	—
182	C₄×C₇×Q₈	—	2	1	no	—
183	C₄×C₇×Q₈	—	2	1	no	—
184	C₄×C₇×Q₈	—	2	2	no	—
185	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
186	C₄×C₇×Q₈	D₄	1	1	yes	characteristic
187	C₄×C₇×Q₈	C₂³	1	2	yes	—
188	C₄×C₇×Q₈	C₂³	1	2	yes	—
189	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
190	C₄×C₇×Q₈	C₂³	1	1	yes	characteristic
191	C₄×C₇×D₄	—	2	1	no	—
192	C₄×C₇×D₄	—	2	1	no	—
193	C₄×C₇×D₄	—	2	2	no	—
194	C₄×C₇×D₄	—	2	1	no	—
195	C₄×C₇×D₄	—	2	2	no	—
196	C₄×C₇×D₄	—	2	1	no	—
197	C₄×C₇×D₄	—	2	2	no	—
198	C₄×C₇×D₄	D₄	1	1	yes	characteristic
199	C₄×C₇×D₄	D₄	1	2	yes	—
200	C₄×C₇×D₄	D₄	1	2	yes	—
201	C₄×C₇×D₄	D₄	1	1	yes	characteristic
202	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
203	C₄×C₇×D₄	C₂³	1	1	yes	characteristic
204	C₇×#117	—	2	2	no	—
205	C₇×#117	—	2	1	no	—
206	C₇×#117	—	2	2	no	—
207	C₇×#117	C₂³	1	1	yes	characteristic
208	C₇×#117	C₂³	1	1	yes	characteristic
209	C₇×#117	C₂³	1	2	yes	—
210	C₂×C₇×C₄⋊C₄	—	2	1	no	—
211	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₇	—	2	1	no	—
213	C₂×C₄²×C₇	—	2	1	no	—
214	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₇	C₂³	1	2	yes	—
216	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
217	C₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
218	C₇×C₄⋊C₈	C₂³	1	2	yes	—
219	C₇×C₄⋊C₈	C₂³	1	2	yes	—
220	C₇×C₄⋊C₈	C₂³	1	2	yes	—
221	C₇×#103	C₂³	1	2	yes	—
222	C₇×#103	C₂³	1	4	yes	—
223	C₇×#103	C₂³	1	2	yes	—
224	C₇×#102	C₂³	1	2	yes	—
225	C₇×#102	C₂³	1	4	yes	—
226	C₇×#102	C₂³	1	4	yes	—
227	C₇×#102	C₂³	1	4	yes	—
228	C₇×#102	C₂³	1	4	yes	—
229	C₇×#102	C₂³	1	4	yes	—
230	C₇×#102	C₂³	1	2	yes	—
231	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
232	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
233	C₇×#97	C₂³	1	4	yes	—
234	C₄×C₇×C₈	C₂³	1	4	yes	—
235	#3498	C₂×C₇	1	1	yes	characteristic, complemented
236	#3461	C₂×C₇	1	1	yes	characteristic, complemented
237	#3224	C₂×C₇	1	4	yes	complemented
238	#3222	C₂×C₇	1	4	yes	complemented
239	#3217	C₂×C₇	1	2	yes	complemented
240	#3216	C₂×C₇	1	2	yes	complemented
241	#3212	C₂×C₇	1	2	yes	complemented
242	#3208	C₂×C₇	1	2	yes	complemented
243	#3154	C₂×C₇	1	2	yes	complemented
244	#3136	C₂×C₇	1	2	yes	complemented
245	#3038	C₂×C₇	1	1	yes	characteristic, complemented
246	#3037	C₂×C₇	1	1	yes	characteristic, complemented
247	#3035	C₂×C₇	1	1	yes	characteristic, complemented
248	C₂×#460	C₂×C₇	1	1	yes	characteristic, complemented
249	#3012	C₂×C₇	1	2	yes	complemented
250	#3009	C₂×C₇	1	2	yes	complemented
251	#2925	C₂×C₇	1	1	yes	characteristic, complemented
252	C₂⁴×C₇	—	2	4	no	—
253	C₂⁴×C₇	—	2	2	no	—
254	C₇×#41	—	2	2	no	—
255	C₇×#41	—	2	2	no	—
256	C₇×#41	—	2	2	no	—
257	C₇×#41	—	2	4	no	—
258	C₇×#41	—	2	2	no	—
259	C₇×#41	—	2	4	no	—
260	C₇×#41	—	4	4	no	—
261	C₇×#41	—	4	4	no	—
262	C₇×#41	—	4	8	no	—
263	C₂×C₇×Q₈	—	2	1	no	—
264	C₂×C₇×Q₈	—	2	2	no	—
265	C₂×C₇×Q₈	—	2	2	no	—
266	C₂×C₇×Q₈	—	2	2	no	—
267	C₂×C₇×Q₈	C₂×D₄	1	1	yes	characteristic
268	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
269	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
270	C₂×C₇×Q₈	C₂⁴	1	1	yes	characteristic
271	C₂×C₇×D₄	—	2	1	no	—
272	C₂×C₇×D₄	—	2	4	no	—
273	C₂×C₇×D₄	—	2	2	no	—
274	C₂×C₇×D₄	—	2	2	no	—
275	C₂×C₇×D₄	—	2	1	no	—
276	C₂×C₇×D₄	—	2	2	no	—
277	C₂×C₇×D₄	—	2	1	no	—
278	C₂×C₇×D₄	—	2	2	no	—
279	C₂×C₇×D₄	—	2	4	no	—
280	C₂×C₇×D₄	—	2	2	no	—
281	C₂×C₇×D₄	—	2	2	no	—
282	C₂×C₇×D₄	—	2	2	no	—
283	C₂×C₇×D₄	—	2	4	no	—
284	C₂×C₇×D₄	—	2	4	no	—
285	C₂×C₇×D₄	—	2	4	no	—
286	C₂×C₇×D₄	—	2	4	no	—
287	C₂×C₇×D₄	—	4	4	no	—
288	C₂×C₇×D₄	—	4	4	no	—
289	C₂×C₇×D₄	—	4	16	no	—
290	C₂×C₇×D₄	—	4	8	no	—
291	C₂×C₇×D₄	—	8	2	no	—
292	C₂×C₇×D₄	—	8	4	no	—
293	C₂×C₇×D₄	—	8	2	no	—
294	C₂×C₇×D₄	—	8	4	no	—
295	C₂×C₇×D₄	C₂×D₄	1	2	yes	—
296	C₂×C₇×D₄	C₂×D₄	1	1	yes	characteristic
297	C₂×C₇×D₄	C₂⁴	1	4	yes	—
298	C₂×C₇×D₄	C₂⁴	1	2	yes	—
299	C₂×C₇×D₄	C₂⁴	1	1	yes	characteristic
300	C₂²×C₄×C₇	—	2	1	no	—
301	C₂²×C₄×C₇	—	2	1	no	—
302	C₂²×C₄×C₇	—	2	1	no	—
303	C₂²×C₄×C₇	—	2	1	no	—
304	C₂²×C₄×C₇	—	2	4	no	—
305	C₂²×C₄×C₇	—	2	2	no	—
306	C₂²×C₄×C₇	—	2	1	no	—
307	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
308	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
309	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
310	C₂²×C₄×C₇	C₂×D₄	1	2	yes	—
311	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
313	C₇×Q₁₆	—	4	2	no	—
314	C₇×Q₁₆	—	4	4	no	—
315	C₇×SD₁₆	—	4	4	no	—
316	C₇×SD₁₆	—	4	4	no	—
317	C₇×SD₁₆	—	4	2	no	—
318	C₇×SD₁₆	—	4	2	no	—
319	C₇×SD₁₆	—	4	4	no	—
320	C₇×SD₁₆	—	4	4	no	—
321	C₇×D₈	—	4	2	no	—
322	C₇×D₈	—	4	4	no	—
323	C₇×M₁₆	—	2	4	no	—
324	C₂×C₇×C₈	—	2	4	no	—
325	C₂×C₇×C₈	C₂⁴	1	2	yes	—
326	C₂×C₇×C₈	C₂⁴	1	4	yes	—
327	C₂×C₇×C₈	C₂⁴	1	2	yes	—
328	C₇×C₄⋊C₄	—	2	2	no	—
329	C₇×C₄⋊C₄	—	2	2	no	—
330	C₇×C₄⋊C₄	—	2	1	no	—
331	C₇×C₄⋊C₄	—	2	1	no	—
332	C₇×C₄⋊C₄	—	2	1	no	—
333	C₇×C₄⋊C₄	—	2	2	no	—
334	C₇×C₄⋊C₄	—	2	2	no	—
335	C₇×C₄⋊C₄	—	2	2	no	—
336	C₇×C₄⋊C₄	—	2	2	no	—
337	C₇×C₄⋊C₄	—	2	1	no	—
338	C₇×C₄⋊C₄	—	2	1	no	—
339	C₇×C₄⋊C₄	—	2	2	no	—
340	C₇×C₄⋊C₄	—	2	2	no	—
341	C₇×C₄⋊C₄	—	2	2	no	—
342	C₇×C₄⋊C₄	—	2	2	no	—
343	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
344	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
345	C₇×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
346	C₇×C₄⋊C₄	C₂×D₄	1	2	yes	—
347	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
348	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
349	C₇×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
350	C₇×C₂²⋊C₄	—	2	2	no	—
351	C₇×C₂²⋊C₄	—	2	2	no	—
352	C₇×C₂²⋊C₄	—	2	1	no	—
353	C₇×C₂²⋊C₄	—	2	2	no	—
354	C₇×C₂²⋊C₄	—	2	1	no	—
355	C₇×C₂²⋊C₄	—	2	1	no	—
356	C₇×C₂²⋊C₄	—	2	2	no	—
357	C₇×C₂²⋊C₄	—	2	2	no	—
358	C₇×C₂²⋊C₄	—	2	2	no	—
359	C₇×C₂²⋊C₄	—	2	2	no	—
360	C₇×C₂²⋊C₄	—	2	4	no	—
361	C₇×C₂²⋊C₄	—	2	4	no	—
362	C₇×C₂²⋊C₄	—	2	2	no	—
363	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
364	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
365	C₇×C₂²⋊C₄	C₂×D₄	1	2	yes	—
366	C₄²×C₇	—	2	2	no	—
367	C₄²×C₇	—	2	1	no	—
368	C₄²×C₇	—	2	1	no	—
369	C₄²×C₇	—	2	1	no	—
370	C₄²×C₇	—	2	2	no	—
371	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
373	C₄²×C₇	C₂×D₄	1	2	yes	—
374	C₄²×C₇	C₂×D₄	1	2	yes	—
375	C₄²×C₇	C₂⁴	1	2	yes	—
376	C₄²×C₇	C₂⁴	1	1	yes	characteristic
377	C₄²×C₇	C₂⁴	1	1	yes	characteristic
378	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
379	C₂×#137	C₂²×C₇	1	2	yes	complemented
380	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	2	yes	complemented
381	C₂×#135	C₂²×C₇	1	2	yes	complemented
382	C₂²×SD₁₆	C₂²×C₇	1	2	yes	complemented
383	#550	—	2	1	no	—
384	#550	—	2	1	no	—
385	D₄²	—	2	1	no	—
386	D₄²	—	2	2	no	—
387	D₄²	—	2	2	no	—
388	D₄²	—	2	1	no	—
389	#544	C₂²×C₇	1	1	yes	characteristic, complemented
390	#542	—	2	1	no	—
391	#542	C₂²×C₇	1	2	yes	complemented
392	#541	—	2	1	no	—
393	#541	C₂²×C₇	1	2	yes	complemented
394	#539	—	2	2	no	—
395	#537	C₂²×C₇	1	1	yes	characteristic
396	#536	C₂²×C₇	1	1	yes	characteristic
397	#536	C₂²×C₇	1	1	yes	characteristic, complemented
398	#535	C₂²×C₇	1	2	yes	—
399	#535	C₂²×C₇	1	4	yes	—
400	#533	—	2	1	no	—
401	#533	C₂²×C₇	1	2	yes	complemented
402	#532	C₂²×C₇	1	2	yes	—
403	#532	C₂²×C₇	1	1	yes	characteristic
404	C₂×#127	C₂²×C₇	1	2	yes	—
405	C₂×#127	C₂²×C₇	1	1	yes	characteristic
406	#529	—	2	2	no	—
407	#529	—	2	1	no	—
408	#529	C₂²×C₇	1	2	yes	complemented
409	C₄×#41	C₂²×C₇	1	1	yes	characteristic
410	C₄×#41	C₂²×C₇	1	1	yes	characteristic, complemented
411	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
412	#497	C₂²×C₇	1	4	yes	complemented
413	#496	C₂²×C₇	1	4	yes	complemented
414	#495	C₂²×C₇	1	4	yes	complemented
415	#492	C₂²×C₇	1	4	yes	complemented
416	#490	C₂²×C₇	1	4	yes	complemented
417	#489	C₂²×C₇	1	4	yes	complemented
418	#488	C₂²×C₇	1	4	yes	complemented
419	#486	C₂²×C₇	1	4	yes	complemented
420	#464	C₂²×C₇	1	2	yes	complemented
421	#464	C₂²×C₇	1	4	yes	complemented
422	#463	C₂²×C₇	1	2	yes	complemented
423	#462	C₂²×C₇	1	2	yes	complemented
424	#462	C₂²×C₇	1	1	yes	characteristic, complemented
425	#461	C₂²×C₇	1	1	yes	characteristic, complemented
426	#460	C₂²×C₇	1	1	yes	characteristic, complemented
427	#460	C₂²×C₇	1	2	yes	complemented
428	#460	C₂²×C₇	1	2	yes	complemented
429	#460	C₂²×C₇	1	2	yes	complemented
430	#460	C₂²×C₇	1	2	yes	complemented
431	#460	C₂²×C₇	1	2	yes	complemented
432	#460	C₂²×C₇	1	4	yes	complemented
433	#459	C₂²×C₇	1	2	yes	complemented
434	#459	C₂²×C₇	1	1	yes	characteristic, complemented
435	#459	C₂²×C₇	1	2	yes	complemented
436	#452	C₂²×C₇	1	4	yes	complemented
437	#452	C₂²×C₇	1	4	yes	complemented
438	#452	C₂²×C₇	1	4	yes	complemented
439	#450	C₂²×C₇	1	4	yes	complemented
440	#450	C₂²×C₇	1	4	yes	complemented
441	#450	C₂²×C₇	1	4	yes	complemented
442	#449	C₂²×C₇	1	4	yes	complemented
443	#447	C₂²×C₇	1	4	yes	complemented
444	#433	C₂²×C₇	1	4	yes	complemented
445	#432	C₂²×C₇	1	2	yes	complemented
446	#431	C₂²×C₇	1	2	yes	complemented
447	#423	C₂²×C₇	1	1	yes	characteristic, complemented
448	C₂×C₄⋊C₈	C₂²×C₇	1	1	yes	characteristic, complemented
449	#418	C₂²×C₇	1	2	yes	complemented
450	#417	C₂²×C₇	1	2	yes	complemented
451	#416	C₂²×C₇	1	2	yes	complemented
452	C₂×#102	C₂²×C₇	1	2	yes	complemented
453	#408	C₂²×C₇	1	2	yes	—
454	#405	C₂²×C₇	1	2	yes	complemented
455	C₂³×C₇	—	2	1	no	—
456	C₂³×C₇	—	2	4	no	—
457	C₂³×C₇	—	2	2	no	—
458	C₂³×C₇	—	4	8	no	—
459	C₂³×C₇	—	4	4	no	—
460	C₂³×C₇	—	8	2	no	—
461	C₂³×C₇	—	8	2	no	—
462	C₂³×C₇	—	8	4	no	—
463	C₂³×C₇	—	8	4	no	—
464	C₂³×C₇	C₂²×D₄	1	2	yes	—
465	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
466	C₇×Q₈	—	2	2	no	—
467	C₇×Q₈	—	2	2	no	—
468	C₇×Q₈	—	2	1	no	—
469	C₇×Q₈	—	2	2	no	—
470	C₇×Q₈	—	2	1	no	—
471	C₇×Q₈	—	2	2	no	—
472	C₇×Q₈	—	2	2	no	—
473	C₇×Q₈	—	4	2	no	—
474	C₇×Q₈	—	8	2	no	—
475	C₇×D₄	—	2	4	no	—
476	C₇×D₄	—	2	2	no	—
477	C₇×D₄	—	2	1	no	—
478	C₇×D₄	—	2	1	no	—
479	C₇×D₄	—	2	4	no	—
480	C₇×D₄	—	2	2	no	—
481	C₇×D₄	—	2	4	no	—
482	C₇×D₄	—	2	2	no	—
483	C₇×D₄	—	4	8	no	—
484	C₇×D₄	—	4	4	no	—
485	C₇×D₄	—	4	2	no	—
486	C₇×D₄	—	4	8	no	—
487	C₇×D₄	—	4	4	no	—
488	C₇×D₄	—	4	2	no	—
489	C₇×D₄	—	4	4	no	—
490	C₇×D₄	—	4	4	no	—
491	C₇×D₄	—	4	2	no	—
492	C₇×D₄	—	8	2	no	—
493	C₇×D₄	—	8	4	no	—
494	C₇×D₄	—	8	2	no	—
495	C₇×D₄	—	8	4	no	—
496	C₇×D₄	—	8	2	no	—
497	C₂×C₄×C₇	—	2	2	no	—
498	C₂×C₄×C₇	—	2	4	no	—
499	C₂×C₄×C₇	—	2	2	no	—
500	C₂×C₄×C₇	—	2	2	no	—
501	C₂×C₄×C₇	—	2	1	no	—
502	C₂×C₄×C₇	—	2	2	no	—
503	C₂×C₄×C₇	—	2	1	no	—
504	C₂×C₄×C₇	—	2	1	no	—
505	C₂×C₄×C₇	—	2	2	no	—
506	C₂×C₄×C₇	—	2	2	no	—
507	C₂×C₄×C₇	—	4	1	no	—
508	C₂×C₄×C₇	—	4	2	no	—
509	C₂×C₄×C₇	—	4	8	no	—
510	C₂×C₄×C₇	—	4	2	no	—
511	C₂×C₄×C₇	—	4	4	no	—
512	C₂×C₄×C₇	—	4	2	no	—
513	C₂×C₄×C₇	—	4	2	no	—
514	C₂×C₄×C₇	—	8	1	no	—
515	C₂×C₄×C₇	—	8	1	no	—
516	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
519	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
520	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
521	C₂×C₄×C₇	C₂²×D₄	1	2	yes	—
522	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
523	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
524	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
525	C₂×C₄×C₇	H(5,𝔽₂)	1	2	yes	—
526	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
527	C₇×C₈	—	2	2	no	—
528	C₇×C₈	—	2	2	no	—
529	C₇×C₈	—	2	4	no	—
530	H(5,𝔽₂)	—	4	4	no	—
531	H(5,𝔽₂)	—	4	4	no	—
532	C₂×#41	—	2	2	no	—
533	C₂×#41	C₂³×C₇	1	1	yes	characteristic
534	C₂×#41	C₂³×C₇	1	2	yes	—
535	C₂×#41	C₂³×C₇	1	4	yes	—
536	C₂×#41	C₂³×C₇	1	1	yes	characteristic
537	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
538	C₂²×D₄	—	2	4	no	—
539	C₂²×D₄	—	2	2	no	—
540	C₂²×D₄	—	2	1	no	—
541	C₂²×D₄	—	2	2	no	—
542	C₂²×D₄	—	2	1	no	—
543	C₂²×D₄	—	2	2	no	—
544	C₂²×D₄	C₂³×C₇	1	2	yes	—
545	C₂²×D₄	C₂³×C₇	1	4	yes	—
546	#137	—	4	4	no	—
547	AGL(1,ℤ/8)	—	4	4	no	—
548	#135	—	4	4	no	—
549	C₂×Q₁₆	C₂³×C₇	1	2	yes	—
550	C₂×Q₁₆	C₂³×C₇	1	4	yes	—
551	C₂×SD₁₆	—	4	4	no	—
552	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
553	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
554	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
555	C₂×SD₁₆	C₂³×C₇	1	2	yes	—
556	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
557	C₂×SD₁₆	C₂³×C₇	1	4	yes	—
558	C₂×D₈	C₂³×C₇	1	2	yes	—
559	C₂×D₈	C₂³×C₇	1	4	yes	—
560	C₂×M₁₆	C₂³×C₇	1	2	yes	—
561	C₂²×C₈	C₂³×C₇	1	2	yes	—
562	C₄⋊Q₈	—	2	1	no	—
563	C₄⋊Q₈	—	2	1	no	—
564	C₄⋊Q₈	C₂³×C₇	1	1	yes	characteristic
565	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
566	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
567	#127	—	2	1	no	—
568	#127	—	2	2	no	—
569	#127	—	2	1	no	—
570	#127	—	2	2	no	—
571	#127	C₂³×C₇	1	1	yes	characteristic
572	#127	C₂³×C₇	1	2	yes	—
573	#127	C₂³×C₇	1	2	yes	—
574	#127	C₂³×C₇	1	4	yes	—
575	#126	—	2	2	no	—
576	#126	—	2	2	no	—
577	#126	—	2	2	no	—
578	#126	—	2	2	no	—
579	#125	—	2	2	no	—
580	#125	—	2	1	no	—
581	#125	—	2	2	no	—
582	#125	—	2	2	no	—
583	#125	C₂³×C₇	1	2	yes	—
584	#124	—	2	1	no	—
585	#124	—	2	2	no	—
586	#124	C₂³×C₇	1	2	yes	—
587	#124	C₂³×C₇	1	2	yes	—
588	#124	C₂³×C₇	1	4	yes	—
589	#123	—	2	2	no	—
590	#123	—	2	2	no	—
591	#123	—	2	2	no	—
592	#123	—	2	2	no	—
593	C₂²⋊Q₈	—	2	1	no	—
594	C₂²⋊Q₈	—	2	2	no	—
595	C₂²⋊Q₈	—	2	1	no	—
596	C₂²⋊Q₈	—	2	1	no	—
597	C₂²⋊Q₈	—	2	2	no	—
598	C₂²⋊Q₈	—	2	2	no	—
599	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
600	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
601	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
602	#121	—	2	2	no	—
603	#121	—	2	1	no	—
604	#121	—	2	1	no	—
605	#121	—	2	2	no	—
606	#121	—	2	1	no	—
607	#121	—	2	2	no	—
608	#121	—	2	2	no	—
609	#121	—	2	4	no	—
610	#121	—	2	2	no	—
611	#121	—	2	4	no	—
612	#121	C₂³×C₇	1	2	yes	—
613	#120	—	2	4	no	—
614	#120	—	2	4	no	—
615	#120	—	2	4	no	—
616	C₄×Q₈	—	2	1	no	—
617	C₄×Q₈	—	2	1	no	—
618	C₄×Q₈	—	2	2	no	—
619	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
620	C₄×Q₈	C₇×D₄	1	1	yes	characteristic
621	C₄×Q₈	C₂³×C₇	1	2	yes	—
622	C₄×Q₈	C₂³×C₇	1	2	yes	—
623	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
624	C₄×Q₈	C₂³×C₇	1	1	yes	characteristic
625	C₄×D₄	—	2	1	no	—
626	C₄×D₄	—	2	1	no	—
627	C₄×D₄	—	2	2	no	—
628	C₄×D₄	—	2	1	no	—
629	C₄×D₄	—	2	2	no	—
630	C₄×D₄	—	2	1	no	—
631	C₄×D₄	—	2	2	no	—
632	C₄×D₄	C₇×D₄	1	1	yes	characteristic
633	C₄×D₄	C₇×D₄	1	2	yes	—
634	C₄×D₄	C₇×D₄	1	2	yes	—
635	C₄×D₄	C₇×D₄	1	1	yes	characteristic
636	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
637	C₄×D₄	C₂³×C₇	1	1	yes	characteristic
638	#117	—	2	2	no	—
639	#117	—	2	1	no	—
640	#117	—	2	2	no	—
641	#117	C₂³×C₇	1	1	yes	characteristic
642	#117	C₂³×C₇	1	1	yes	characteristic
643	#117	C₂³×C₇	1	2	yes	—
644	C₂×C₄⋊C₄	—	2	1	no	—
645	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
646	C₂×C₄²	—	2	1	no	—
647	C₂×C₄²	—	2	1	no	—
648	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
649	C₂×C₄²	C₂³×C₇	1	2	yes	—
650	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
651	C₄⋊C₈	C₂³×C₇	1	1	yes	characteristic
652	C₄⋊C₈	C₂³×C₇	1	2	yes	—
653	C₄⋊C₈	C₂³×C₇	1	2	yes	—
654	C₄⋊C₈	C₂³×C₇	1	2	yes	—
655	#103	C₂³×C₇	1	2	yes	—
656	#103	C₂³×C₇	1	2	yes	—
657	#103	C₂³×C₇	1	4	yes	—
658	#102	C₂³×C₇	1	4	yes	—
659	#102	C₂³×C₇	1	4	yes	—
660	#102	C₂³×C₇	1	2	yes	—
661	#102	C₂³×C₇	1	2	yes	—
662	#102	C₂³×C₇	1	4	yes	—
663	#102	C₂³×C₇	1	4	yes	—
664	#102	C₂³×C₇	1	4	yes	—
665	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
666	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
667	#97	C₂³×C₇	1	4	yes	—
668	C₄×C₈	C₂³×C₇	1	4	yes	—
669	C₂²×C₇	—	2	1	no	—
670	C₂²×C₇	—	2	1	no	—
671	C₂²×C₇	—	2	2	no	—
672	C₂²×C₇	—	2	2	no	—
673	C₂²×C₇	—	2	2	no	—
674	C₂²×C₇	—	4	1	no	—
675	C₂²×C₇	—	4	4	no	—
676	C₂²×C₇	—	4	2	no	—
677	C₂²×C₇	—	4	4	no	—
678	C₂²×C₇	—	4	2	no	—
679	C₂²×C₇	—	4	1	no	—
680	C₂²×C₇	—	4	1	no	—
681	C₂²×C₇	—	4	4	no	—
682	C₂²×C₇	—	4	2	no	—
683	C₂²×C₇	—	16	4	no	—
684	C₂²×C₇	—	16	8	no	—
685	C₂²×C₇	#535	1	2	yes	—
686	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
687	C₄×C₇	—	2	1	no	—
688	C₄×C₇	—	2	1	no	—
689	C₄×C₇	—	2	2	no	—
690	C₄×C₇	—	2	2	no	—
691	C₄×C₇	—	2	1	no	—
692	C₄×C₇	—	2	2	no	—
693	C₄×C₇	—	4	2	no	—
694	C₄×C₇	—	4	1	no	—
695	C₄×C₇	—	4	2	no	—
696	C₄×C₇	—	4	1	no	—
697	C₄×C₇	—	4	2	no	—
698	C₄×C₇	—	4	1	no	—
699	C₄×C₇	#535	1	2	yes	—
700	C₄×C₇	#577	1	2	yes	—
701	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
702	C₄×C₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
703	C₂⁴	—	2	4	no	—
704	C₂⁴	—	2	2	no	—
705	#41	—	2	2	no	—
706	#41	—	2	2	no	—
707	#41	—	2	2	no	—
708	#41	—	2	4	no	—
709	#41	—	2	2	no	—
710	#41	—	2	4	no	—
711	#41	—	4	4	no	—
712	#41	—	4	4	no	—
713	#41	—	4	8	no	—
714	C₂×Q₈	—	2	1	no	—
715	C₂×Q₈	—	2	2	no	—
716	C₂×Q₈	—	2	2	no	—
717	C₂×Q₈	—	2	2	no	—
718	C₂×Q₈	C₂×C₇×D₄	1	1	yes	characteristic
719	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
720	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
721	C₂×Q₈	C₂⁴×C₇	1	1	yes	characteristic
722	C₂×D₄	—	2	1	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	1	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	1	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	4	no	—
731	C₂×D₄	—	2	2	no	—
732	C₂×D₄	—	2	2	no	—
733	C₂×D₄	—	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	4	no	—
738	C₂×D₄	—	4	4	no	—
739	C₂×D₄	—	4	4	no	—
740	C₂×D₄	—	4	16	no	—
741	C₂×D₄	—	4	8	no	—
742	C₂×D₄	—	8	2	no	—
743	C₂×D₄	—	8	4	no	—
744	C₂×D₄	—	8	2	no	—
745	C₂×D₄	—	8	4	no	—
746	C₂×D₄	C₂×C₇×D₄	1	2	yes	—
747	C₂×D₄	C₂×C₇×D₄	1	1	yes	characteristic
748	C₂×D₄	C₂⁴×C₇	1	4	yes	—
749	C₂×D₄	C₂⁴×C₇	1	2	yes	—
750	C₂×D₄	C₂⁴×C₇	1	1	yes	characteristic
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	1	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	—	2	2	no	—
757	C₂²×C₄	—	2	1	no	—
758	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
759	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
760	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
761	C₂²×C₄	C₂×C₇×D₄	1	2	yes	—
762	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
763	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
764	Q₁₆	—	4	2	no	—
765	Q₁₆	—	4	4	no	—
766	SD₁₆	—	4	4	no	—
767	SD₁₆	—	4	4	no	—
768	SD₁₆	—	4	2	no	—
769	SD₁₆	—	4	2	no	—
770	SD₁₆	—	4	4	no	—
771	SD₁₆	—	4	4	no	—
772	D₈	—	4	2	no	—
773	D₈	—	4	4	no	—
774	M₁₆	—	2	4	no	—
775	C₂×C₈	—	2	4	no	—
776	C₂×C₈	C₂⁴×C₇	1	2	yes	—
777	C₂×C₈	C₂⁴×C₇	1	4	yes	—
778	C₂×C₈	C₂⁴×C₇	1	2	yes	—
779	C₄⋊C₄	—	2	2	no	—
780	C₄⋊C₄	—	2	2	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	2	no	—
785	C₄⋊C₄	—	2	2	no	—
786	C₄⋊C₄	—	2	2	no	—
787	C₄⋊C₄	—	2	2	no	—
788	C₄⋊C₄	—	2	1	no	—
789	C₄⋊C₄	—	2	1	no	—
790	C₄⋊C₄	—	2	2	no	—
791	C₄⋊C₄	—	2	2	no	—
792	C₄⋊C₄	—	2	2	no	—
793	C₄⋊C₄	—	2	2	no	—
794	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
795	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
796	C₄⋊C₄	C₂×C₇×D₄	1	1	yes	characteristic
797	C₄⋊C₄	C₂×C₇×D₄	1	2	yes	—
798	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
799	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
800	C₄⋊C₄	C₂⁴×C₇	1	1	yes	characteristic
801	C₂²⋊C₄	—	2	2	no	—
802	C₂²⋊C₄	—	2	2	no	—
803	C₂²⋊C₄	—	2	1	no	—
804	C₂²⋊C₄	—	2	2	no	—
805	C₂²⋊C₄	—	2	1	no	—
806	C₂²⋊C₄	—	2	1	no	—
807	C₂²⋊C₄	—	2	2	no	—
808	C₂²⋊C₄	—	2	2	no	—
809	C₂²⋊C₄	—	2	2	no	—
810	C₂²⋊C₄	—	2	2	no	—
811	C₂²⋊C₄	—	2	4	no	—
812	C₂²⋊C₄	—	2	4	no	—
813	C₂²⋊C₄	—	2	2	no	—
814	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
815	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
816	C₂²⋊C₄	C₂×C₇×D₄	1	2	yes	—
817	C₄²	—	2	2	no	—
818	C₄²	—	2	1	no	—
819	C₄²	—	2	1	no	—
820	C₄²	—	2	1	no	—
821	C₄²	—	2	2	no	—
822	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
823	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
824	C₄²	C₂×C₇×D₄	1	2	yes	—
825	C₄²	C₂×C₇×D₄	1	2	yes	—
826	C₄²	C₂⁴×C₇	1	2	yes	—
827	C₄²	C₂⁴×C₇	1	1	yes	characteristic
828	C₄²	C₂⁴×C₇	1	1	yes	characteristic
829	C₂×C₇	—	2	2	no	—
830	C₂×C₇	—	4	2	no	—
831	C₂×C₇	—	8	1	no	—
832	C₂×C₇	—	8	4	no	—
833	C₂×C₇	—	8	2	no	—
834	C₂×C₇	C₂×#535	1	1	yes	characteristic
835	C₂×C₇	C₂×#577	1	1	yes	characteristic
836	C₂×C₇	#3585	1	1	yes	characteristic
837	C₂³	—	2	1	no	—
838	C₂³	—	2	4	no	—
839	C₂³	—	2	2	no	—
840	C₂³	—	4	8	no	—
841	C₂³	—	4	4	no	—
842	C₂³	—	8	2	no	—
843	C₂³	—	8	2	no	—
844	C₂³	—	8	4	no	—
845	C₂³	—	8	4	no	—
846	C₂³	C₂²×C₇×D₄	1	2	yes	—
847	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
848	Q₈	—	2	2	no	—
849	Q₈	—	2	2	no	—
850	Q₈	—	2	1	no	—
851	Q₈	—	2	2	no	—
852	Q₈	—	2	1	no	—
853	Q₈	—	2	2	no	—
854	Q₈	—	2	2	no	—
855	Q₈	—	4	2	no	—
856	Q₈	—	8	2	no	—
857	D₄	—	2	4	no	—
858	D₄	—	2	1	no	—
859	D₄	—	2	1	no	—
860	D₄	—	2	4	no	—
861	D₄	—	2	2	no	—
862	D₄	—	2	4	no	—
863	D₄	—	2	2	no	—
864	D₄	—	2	2	no	—
865	D₄	—	4	8	no	—
866	D₄	—	4	4	no	—
867	D₄	—	4	2	no	—
868	D₄	—	4	8	no	—
869	D₄	—	4	4	no	—
870	D₄	—	4	2	no	—
871	D₄	—	4	4	no	—
872	D₄	—	4	4	no	—
873	D₄	—	4	2	no	—
874	D₄	—	8	2	no	—
875	D₄	—	8	4	no	—
876	D₄	—	8	2	no	—
877	D₄	—	8	4	no	—
878	D₄	—	8	2	no	—
879	C₂×C₄	—	2	2	no	—
880	C₂×C₄	—	2	2	no	—
881	C₂×C₄	—	2	2	no	—
882	C₂×C₄	—	2	4	no	—
883	C₂×C₄	—	2	1	no	—
884	C₂×C₄	—	2	2	no	—
885	C₂×C₄	—	2	1	no	—
886	C₂×C₄	—	2	1	no	—
887	C₂×C₄	—	2	2	no	—
888	C₂×C₄	—	2	2	no	—
889	C₂×C₄	—	4	1	no	—
890	C₂×C₄	—	4	2	no	—
891	C₂×C₄	—	4	8	no	—
892	C₂×C₄	—	4	2	no	—
893	C₂×C₄	—	4	4	no	—
894	C₂×C₄	—	4	2	no	—
895	C₂×C₄	—	4	2	no	—
896	C₂×C₄	—	8	1	no	—
897	C₂×C₄	—	8	1	no	—
898	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
899	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
900	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
901	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
902	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
903	C₂×C₄	C₂²×C₇×D₄	1	2	yes	—
904	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
905	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
906	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
907	C₂×C₄	C₇×H(5,𝔽₂)	1	2	yes	—
908	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
909	C₈	—	2	2	no	—
910	C₈	—	2	2	no	—
911	C₈	—	2	4	no	—
912	C₇	#60833	1	1	yes	characteristic, direct product factor, Sylow
913	C₂²	—	2	1	no	—
914	C₂²	—	2	1	no	—
915	C₂²	—	2	2	no	—
916	C₂²	—	2	2	no	—
917	C₂²	—	2	2	no	—
918	C₂²	—	4	1	no	—
919	C₂²	—	4	4	no	—
920	C₂²	—	4	2	no	—
921	C₂²	—	4	1	no	—
922	C₂²	—	4	4	no	—
923	C₂²	—	4	2	no	—
924	C₂²	—	4	4	no	—
925	C₂²	—	4	2	no	—
926	C₂²	—	4	1	no	—
927	C₂²	—	16	4	no	—
928	C₂²	—	16	8	no	—
929	C₂²	C₇×#535	1	2	yes	—
930	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
931	C₄	—	2	1	no	—
932	C₄	—	2	2	no	—
933	C₄	—	2	1	no	—
934	C₄	—	2	1	no	—
935	C₄	—	2	2	no	—
936	C₄	—	2	2	no	—
937	C₄	—	4	1	no	—
938	C₄	—	4	2	no	—
939	C₄	—	4	1	no	—
940	C₄	—	4	2	no	—
941	C₄	—	4	1	no	—
942	C₄	—	4	2	no	—
943	C₄	C₇×#535	1	2	yes	—
944	C₄	C₇×#577	1	2	yes	—
945	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
946	C₄	C₂×C₇×H(5,𝔽₂)	1	1	yes	characteristic
947	C₂	—	2	2	no	—
948	C₂	—	4	2	no	—
949	C₂	—	8	4	no	—
950	C₂	—	8	2	no	—
951	C₂	—	8	1	no	—
952	C₂	C₂×C₇×#535	1	1	yes	characteristic
953	C₂	C₂×C₇×#577	1	1	yes	characteristic
954	C₂	C₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₄×C₇×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₇×#3498	C₂	semidirect
2. C₇×#3461	C₂	semidirect
3. C₇×#3224	C₂	semidirect
4. C₇×#3222	C₂	semidirect
5. C₇×#3217	C₂	semidirect
6. C₇×#3216	C₂	semidirect
7. C₇×#3212	C₂	semidirect
8. C₇×#3208	C₂	semidirect
9. C₇×#3154	C₂	semidirect
10. C₇×#3136	C₂	semidirect
11. C₇×#3038	C₂	semidirect
12. C₇×#3037	C₂	semidirect
13. C₇×#3035	C₂	semidirect
14. C₂×C₇×#460	C₂	semidirect
15. C₇×#3012	C₂	semidirect
16. C₇×#3009	C₂	semidirect
17. C₇×#2925	C₂	semidirect
19. C₂×C₇×#137	C₂²	semidirect
20. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
21. C₂×C₇×#135	C₂²	semidirect
22. C₂²×C₇×SD₁₆	C₂²	semidirect
29. C₇×#544	C₂²	semidirect
31. C₇×#542	C₂²	semidirect
33. C₇×#541	C₂²	semidirect
37. C₇×#536	C₂²	semidirect
41. C₇×#533	C₂²	semidirect
48. C₇×#529	C₂²	semidirect
50. C₄×C₇×#41	C₂²	semidirect
51. C₂×C₄×C₇×Q₈	C₂²	semidirect
52. C₇×#497	C₂²	semidirect
53. C₇×#496	C₂²	semidirect
54. C₇×#495	C₂²	semidirect
55. C₇×#492	C₂²	semidirect
56. C₇×#490	C₂²	semidirect
57. C₇×#489	C₂²	semidirect
58. C₇×#488	C₂²	semidirect
59. C₇×#486	C₂²	semidirect
60. C₇×#464	C₂²	semidirect
61. C₇×#464	C₂²	semidirect
62. C₇×#463	C₂²	semidirect
63. C₇×#462	C₂²	semidirect
64. C₇×#462	C₂²	semidirect
65. C₇×#461	C₂²	semidirect
66. C₇×#460	C₂²	semidirect
67. C₇×#460	C₂²	semidirect
68. C₇×#460	C₂²	semidirect
69. C₇×#460	C₂²	semidirect
70. C₇×#460	C₂²	semidirect
71. C₇×#460	C₂²	semidirect
72. C₇×#460	C₂²	semidirect
73. C₇×#459	C₂²	semidirect
74. C₇×#459	C₂²	semidirect
75. C₇×#459	C₂²	semidirect
76. C₇×#452	C₂²	semidirect
77. C₇×#452	C₂²	semidirect
78. C₇×#452	C₂²	semidirect
79. C₇×#450	C₂²	semidirect
80. C₇×#450	C₂²	semidirect
81. C₇×#450	C₂²	semidirect
82. C₇×#449	C₂²	semidirect
83. C₇×#447	C₂²	semidirect
84. C₇×#433	C₂²	semidirect
85. C₇×#432	C₂²	semidirect
86. C₇×#431	C₂²	semidirect
87. C₇×#423	C₂²	semidirect
88. C₂×C₇×C₄⋊C₈	C₂²	semidirect
89. C₇×#418	C₂²	semidirect
90. C₇×#417	C₂²	semidirect
91. C₇×#416	C₂²	semidirect
92. C₂×C₇×#102	C₂²	semidirect
94. C₇×#405	C₂²	semidirect
95. #60833	C₇	direct (N × H)
235. #3498	C₂×C₇	semidirect
236. #3461	C₂×C₇	semidirect
237. #3224	C₂×C₇	semidirect
238. #3222	C₂×C₇	semidirect
239. #3217	C₂×C₇	semidirect
240. #3216	C₂×C₇	semidirect
241. #3212	C₂×C₇	semidirect
242. #3208	C₂×C₇	semidirect
243. #3154	C₂×C₇	semidirect
244. #3136	C₂×C₇	semidirect
245. #3038	C₂×C₇	semidirect
246. #3037	C₂×C₇	semidirect
247. #3035	C₂×C₇	semidirect
248. C₂×#460	C₂×C₇	semidirect
249. #3012	C₂×C₇	semidirect
250. #3009	C₂×C₇	semidirect
251. #2925	C₂×C₇	semidirect
379. C₂×#137	C₂²×C₇	semidirect
380. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
381. C₂×#135	C₂²×C₇	semidirect
382. C₂²×SD₁₆	C₂²×C₇	semidirect
389. #544	C₂²×C₇	semidirect
391. #542	C₂²×C₇	semidirect
393. #541	C₂²×C₇	semidirect
397. #536	C₂²×C₇	semidirect
401. #533	C₂²×C₇	semidirect
408. #529	C₂²×C₇	semidirect
410. C₄×#41	C₂²×C₇	semidirect
411. C₂×C₄×Q₈	C₂²×C₇	semidirect
412. #497	C₂²×C₇	semidirect
413. #496	C₂²×C₇	semidirect
414. #495	C₂²×C₇	semidirect
415. #492	C₂²×C₇	semidirect
416. #490	C₂²×C₇	semidirect
417. #489	C₂²×C₇	semidirect
418. #488	C₂²×C₇	semidirect
419. #486	C₂²×C₇	semidirect
420. #464	C₂²×C₇	semidirect
421. #464	C₂²×C₇	semidirect
422. #463	C₂²×C₇	semidirect
423. #462	C₂²×C₇	semidirect
424. #462	C₂²×C₇	semidirect
425. #461	C₂²×C₇	semidirect
426. #460	C₂²×C₇	semidirect
427. #460	C₂²×C₇	semidirect
428. #460	C₂²×C₇	semidirect
429. #460	C₂²×C₇	semidirect
430. #460	C₂²×C₇	semidirect
431. #460	C₂²×C₇	semidirect
432. #460	C₂²×C₇	semidirect
433. #459	C₂²×C₇	semidirect
434. #459	C₂²×C₇	semidirect
435. #459	C₂²×C₇	semidirect
436. #452	C₂²×C₇	semidirect
437. #452	C₂²×C₇	semidirect
438. #452	C₂²×C₇	semidirect
439. #450	C₂²×C₇	semidirect
440. #450	C₂²×C₇	semidirect
441. #450	C₂²×C₇	semidirect
442. #449	C₂²×C₇	semidirect
443. #447	C₂²×C₇	semidirect
444. #433	C₂²×C₇	semidirect
445. #432	C₂²×C₇	semidirect
446. #431	C₂²×C₇	semidirect
447. #423	C₂²×C₇	semidirect
448. C₂×C₄⋊C₈	C₂²×C₇	semidirect
449. #418	C₂²×C₇	semidirect
450. #417	C₂²×C₇	semidirect
451. #416	C₂²×C₇	semidirect
452. C₂×#102	C₂²×C₇	semidirect
454. #405	C₂²×C₇	semidirect
912. C₇	#60833	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×#3498	2
C₇×#3461	2
C₇×#3224	2
C₇×#3222	2
C₇×#3217	2
C₇×#3216	2
C₇×#3212	2
C₇×#3208	2
C₇×#3154	2
C₇×#3136	2
C₇×#3038	2
C₇×#3037	2
C₇×#3035	2
C₂×C₇×#460	2
C₇×#3012	2
C₇×#3009	2
C₇×#2925	2
#60833	7

Subgroups — C7×#60833 #13238049

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60833 #13238049