Subgroups — C₇×#60805 #13238021

Order 1792.

2196 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₇×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×#3219	C₂	1	4	yes	maximal, complemented
4	C₇×#3218	C₂	1	2	yes	maximal, complemented
5	C₇×#3217	C₂	1	2	yes	maximal, complemented
6	C₇×#3212	C₂	1	4	yes	maximal, complemented
7	C₇×#3211	C₂	1	4	yes	maximal, complemented
8	C₇×#3153	C₂	1	2	yes	maximal, complemented
9	C₇×#3142	C₂	1	2	yes	maximal, complemented
10	C₇×#3037	C₂	1	2	yes	maximal, complemented
11	C₇×#3036	C₂	1	2	yes	maximal, complemented
12	C₇×#3007	C₂	1	2	yes	maximal, complemented
13	C₇×#3006	C₂	1	2	yes	maximal, complemented
14	C₇×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₇×#41	C₂²	1	2	yes	—
16	C₂×C₇×#137	C₂²	1	4	yes	complemented
17	C₂×C₇×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₇×#532	—	2	1	no	—
19	C₇×#532	—	2	1	no	—
20	C₇×#532	—	2	1	no	—
21	C₇×#532	—	2	1	no	—
22	C₇×#532	C₂²	1	2	yes	—
23	C₇×#532	C₂²	1	2	yes	—
24	C₇×#532	C₂²	1	2	yes	complemented
25	C₇×#532	C₂²	1	2	yes	complemented
26	C₂×C₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₇×#127	C₂²	1	1	yes	characteristic, complemented
28	C₇×#529	—	2	1	no	—
29	C₇×#529	—	2	1	no	—
30	C₇×#529	—	2	1	no	—
31	C₇×#529	—	2	1	no	—
32	C₇×#529	C₂²	1	2	yes	—
33	C₇×#529	C₂²	1	2	yes	—
34	C₇×#529	C₂²	1	2	yes	complemented
35	C₇×#529	C₂²	1	2	yes	complemented
36	C₂×C₇×#126	—	2	1	no	—
37	C₂×C₇×#125	C₂²	1	1	yes	characteristic, complemented
38	C₂×C₇×#124	C₂²	1	2	yes	complemented
39	C₂×C₇×#124	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₇×#123	—	2	1	no	—
41	C₂×C₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₂×C₇×#121	—	2	1	no	—
43	C₂×C₇×#121	—	2	1	no	—
44	C₂×C₇×#121	C₂²	1	1	yes	characteristic
45	C₂×C₄×C₇×Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₇×D₄	—	2	1	no	—
47	C₂×C₄×C₇×D₄	—	2	1	no	—
48	C₂×C₄×C₇×D₄	—	2	1	no	—
49	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₇×#117	—	2	1	no	—
51	C₂²×C₄²×C₇	C₂²	1	1	yes	characteristic
52	C₇×#497	C₂²	1	4	yes	complemented
53	C₇×#496	C₂²	1	4	yes	complemented
54	C₇×#495	C₂²	1	8	yes	complemented
55	C₇×#491	C₂²	1	4	yes	complemented
56	C₇×#490	C₂²	1	4	yes	complemented
57	C₇×#488	C₂²	1	8	yes	complemented
58	C₇×#464	C₂²	1	8	yes	complemented
59	C₇×#463	C₂²	1	8	yes	complemented
60	C₇×#462	C₂²	1	4	yes	complemented
61	C₇×#461	C₂²	1	4	yes	complemented
62	C₇×#460	C₂²	1	4	yes	complemented
63	C₇×#459	C₂²	1	4	yes	complemented
64	C₇×#452	C₂²	1	8	yes	complemented
65	C₇×#451	C₂²	1	4	yes	complemented
66	C₇×#450	C₂²	1	4	yes	complemented
67	C₇×#449	C₂²	1	8	yes	complemented
68	C₇×#448	C₂²	1	4	yes	—
69	C₇×#447	C₂²	1	4	yes	—
70	C₇×#432	C₂²	1	2	yes	complemented
71	C₇×#432	C₂²	1	2	yes	complemented
72	C₇×#431	C₂²	1	2	yes	complemented
73	C₇×#431	C₂²	1	2	yes	complemented
74	C₇×#423	C₂²	1	2	yes	complemented
75	C₇×#417	C₂²	1	4	yes	complemented
76	C₇×#417	C₂²	1	4	yes	complemented
77	C₇×#407	C₂²	1	2	yes	—
78	C₄×C₇×M₁₆	C₂²	1	2	yes	complemented
79	#60805	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×C₇×#41	—	2	2	no	—
81	C₂×C₇×#41	—	2	2	no	—
82	C₂×C₇×#41	—	4	8	no	—
83	C₂×C₇×#41	C₂³	1	4	yes	—
84	C₂×C₇×#41	C₂³	1	4	yes	—
85	C₂²×C₇×Q₈	C₂³	1	1	yes	characteristic
86	C₂²×C₇×Q₈	C₂³	1	2	yes	—
87	C₂²×C₇×D₄	—	2	2	no	—
88	C₂²×C₇×D₄	—	2	1	no	—
89	C₂²×C₇×D₄	—	2	1	no	—
90	C₂²×C₇×D₄	—	2	1	no	—
91	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
92	C₂²×C₇×D₄	C₂³	1	2	yes	—
93	C₂³×C₄×C₇	—	2	2	no	—
94	C₂³×C₄×C₇	—	2	1	no	—
95	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
96	C₂³×C₄×C₇	D₄	1	1	yes	characteristic
97	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
98	C₇×#137	—	4	8	no	—
99	C₇×AGL(1,ℤ/8)	—	4	8	no	—
100	C₂×C₇×Q₁₆	C₂³	1	8	yes	—
101	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
102	C₂×C₇×SD₁₆	C₂³	1	8	yes	—
103	C₂×C₇×D₈	C₂³	1	8	yes	—
104	C₂×C₇×M₁₆	C₂³	1	4	yes	—
105	C₇×C₄⋊Q₈	—	2	1	no	—
106	C₇×C₄⋊Q₈	—	2	1	no	—
107	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
108	C₇×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₇×#127	—	2	1	no	—
110	C₇×#127	—	2	1	no	—
111	C₇×#127	C₂³	1	2	yes	—
112	C₇×#127	C₂³	1	2	yes	—
113	C₇×#126	—	2	2	no	—
114	C₇×#126	—	2	2	no	—
115	C₇×#126	—	2	2	no	—
116	C₇×#126	—	2	2	no	—
117	C₇×#125	—	2	1	no	—
118	C₇×#125	—	2	1	no	—
119	C₇×#125	C₂³	1	2	yes	—
120	C₇×#125	C₂³	1	2	yes	—
121	C₇×#124	—	2	1	no	—
122	C₇×#124	—	2	1	no	—
123	C₇×#124	—	2	2	no	—
124	C₇×#124	—	2	2	no	—
125	C₇×#124	C₂³	1	4	yes	—
126	C₇×#124	C₂³	1	2	yes	—
127	C₇×#124	C₂³	1	2	yes	—
128	C₇×#124	C₂³	1	4	yes	—
129	C₇×#123	—	2	2	no	—
130	C₇×#123	—	2	2	no	—
131	C₇×#123	—	2	2	no	—
132	C₇×#123	—	2	2	no	—
133	C₇×C₂²⋊Q₈	—	2	1	no	—
134	C₇×C₂²⋊Q₈	—	2	1	no	—
135	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
136	C₇×C₂²⋊Q₈	C₂³	1	2	yes	—
137	C₇×#121	—	2	2	no	—
138	C₇×#121	—	2	2	no	—
139	C₇×#121	—	2	2	no	—
140	C₇×#121	—	2	2	no	—
141	C₇×#121	—	2	2	no	—
142	C₇×#121	—	2	2	no	—
143	C₇×#121	—	2	2	no	—
144	C₇×#121	—	2	2	no	—
145	C₇×#121	—	2	1	no	—
146	C₇×#121	—	2	1	no	—
147	C₇×#121	C₂³	1	2	yes	—
148	C₇×#121	C₂³	1	2	yes	—
149	C₄×C₇×Q₈	—	2	1	no	—
150	C₄×C₇×Q₈	—	2	1	no	—
151	C₄×C₇×Q₈	C₂³	1	2	yes	—
152	C₄×C₇×Q₈	C₂³	1	2	yes	—
153	C₄×C₇×D₄	—	2	2	no	—
154	C₄×C₇×D₄	—	2	2	no	—
155	C₄×C₇×D₄	—	2	2	no	—
156	C₄×C₇×D₄	—	2	2	no	—
157	C₄×C₇×D₄	—	2	2	no	—
158	C₄×C₇×D₄	—	2	2	no	—
159	C₄×C₇×D₄	—	2	2	no	—
160	C₄×C₇×D₄	—	2	2	no	—
161	C₄×C₇×D₄	—	2	2	no	—
162	C₄×C₇×D₄	—	2	2	no	—
163	C₄×C₇×D₄	—	2	2	no	—
164	C₄×C₇×D₄	—	2	2	no	—
165	C₄×C₇×D₄	—	2	1	no	—
166	C₄×C₇×D₄	—	2	1	no	—
167	C₄×C₇×D₄	C₂³	1	2	yes	—
168	C₄×C₇×D₄	C₂³	1	2	yes	—
169	C₇×#117	—	2	2	no	—
170	C₇×#117	—	2	2	no	—
171	C₇×#117	—	2	2	no	—
172	C₇×#117	—	2	2	no	—
173	C₂×C₇×C₄⋊C₄	—	2	1	no	—
174	C₂×C₇×C₄⋊C₄	—	2	1	no	—
175	C₂×C₇×C₄⋊C₄	—	2	1	no	—
176	C₂×C₇×C₄⋊C₄	—	2	1	no	—
177	C₂×C₇×C₄⋊C₄	—	2	1	no	—
178	C₂×C₇×C₄⋊C₄	—	2	1	no	—
179	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
182	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
183	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
184	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
185	C₂×C₇×C₂²⋊C₄	—	2	2	no	—
186	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
187	C₂×C₇×C₂²⋊C₄	—	2	1	no	—
188	C₂×C₄²×C₇	—	2	1	no	—
189	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
194	C₂×C₄²×C₇	D₄	1	1	yes	characteristic
195	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
199	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
200	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
201	C₇×C₄⋊C₈	C₂³	1	4	yes	—
202	C₇×C₄⋊C₈	C₂³	1	4	yes	—
203	C₇×#103	C₂³	1	8	yes	—
204	C₇×#103	C₂³	1	8	yes	—
205	C₇×#102	C₂³	1	8	yes	—
206	C₇×#102	C₂³	1	8	yes	—
207	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₇×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₇×#97	C₂³	1	4	yes	—
210	C₄×C₇×C₈	C₂³	1	4	yes	—
211	C₂×#532	C₂×C₇	1	1	yes	characteristic, complemented
212	C₂×#529	C₂×C₇	1	1	yes	characteristic, complemented
213	#3219	C₂×C₇	1	4	yes	complemented
214	#3218	C₂×C₇	1	2	yes	complemented
215	#3217	C₂×C₇	1	2	yes	complemented
216	#3212	C₂×C₇	1	4	yes	complemented
217	#3211	C₂×C₇	1	4	yes	complemented
218	#3153	C₂×C₇	1	2	yes	complemented
219	#3142	C₂×C₇	1	2	yes	complemented
220	#3037	C₂×C₇	1	2	yes	complemented
221	#3036	C₂×C₇	1	2	yes	complemented
222	#3007	C₂×C₇	1	2	yes	complemented
223	#3006	C₂×C₇	1	2	yes	complemented
224	#2920	C₂×C₇	1	1	yes	characteristic, complemented
225	C₂⁴×C₇	—	2	1	no	—
226	C₂⁴×C₇	—	2	2	no	—
227	C₂⁴×C₇	C₂×D₄	1	1	yes	characteristic
228	C₇×#41	—	2	8	no	—
229	C₇×#41	—	2	8	no	—
230	C₇×#41	—	4	4	no	—
231	C₇×#41	—	4	4	no	—
232	C₇×#41	—	4	8	no	—
233	C₇×#41	—	4	8	no	—
234	C₂×C₇×Q₈	—	2	1	no	—
235	C₂×C₇×Q₈	—	2	2	no	—
236	C₂×C₇×Q₈	—	2	4	no	—
237	C₂×C₇×Q₈	—	4	4	no	—
238	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
239	C₂×C₇×Q₈	C₂⁴	1	2	yes	—
240	C₂×C₇×D₄	—	2	2	no	—
241	C₂×C₇×D₄	—	2	2	no	—
242	C₂×C₇×D₄	—	2	4	no	—
243	C₂×C₇×D₄	—	2	4	no	—
244	C₂×C₇×D₄	—	2	1	no	—
245	C₂×C₇×D₄	—	2	2	no	—
246	C₂×C₇×D₄	—	2	2	no	—
247	C₂×C₇×D₄	—	2	2	no	—
248	C₂×C₇×D₄	—	2	2	no	—
249	C₂×C₇×D₄	—	2	2	no	—
250	C₂×C₇×D₄	—	2	4	no	—
251	C₂×C₇×D₄	—	4	4	no	—
252	C₂×C₇×D₄	—	4	4	no	—
253	C₂×C₇×D₄	—	4	4	no	—
254	C₂×C₇×D₄	—	4	4	no	—
255	C₂×C₇×D₄	—	4	8	no	—
256	C₂×C₇×D₄	C₂⁴	1	4	yes	—
257	C₂×C₇×D₄	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₇	—	2	4	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	—	2	2	no	—
263	C₂²×C₄×C₇	—	2	2	no	—
264	C₂²×C₄×C₇	—	2	2	no	—
265	C₂²×C₄×C₇	—	2	4	no	—
266	C₂²×C₄×C₇	—	2	4	no	—
267	C₂²×C₄×C₇	—	4	2	no	—
268	C₂²×C₄×C₇	—	4	2	no	—
269	C₂²×C₄×C₇	—	4	4	no	—
270	C₂²×C₄×C₇	—	4	8	no	—
271	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
273	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
274	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
275	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
276	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
277	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
278	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
279	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
280	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
281	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₇	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
289	C₇×Q₁₆	—	4	8	no	—
290	C₇×SD₁₆	—	4	8	no	—
291	C₇×SD₁₆	—	4	8	no	—
292	C₇×D₈	—	4	8	no	—
293	C₇×M₁₆	—	2	8	no	—
294	C₂×C₇×C₈	C₂⁴	1	8	yes	—
295	C₇×C₄⋊C₄	—	2	2	no	—
296	C₇×C₄⋊C₄	—	2	2	no	—
297	C₇×C₄⋊C₄	—	2	2	no	—
298	C₇×C₄⋊C₄	—	2	2	no	—
299	C₇×C₄⋊C₄	—	2	2	no	—
300	C₇×C₄⋊C₄	—	2	2	no	—
301	C₇×C₄⋊C₄	—	2	2	no	—
302	C₇×C₄⋊C₄	—	2	2	no	—
303	C₇×C₄⋊C₄	—	2	2	no	—
304	C₇×C₄⋊C₄	—	2	2	no	—
305	C₇×C₄⋊C₄	—	2	2	no	—
306	C₇×C₄⋊C₄	—	2	2	no	—
307	C₇×C₄⋊C₄	—	2	1	no	—
308	C₇×C₄⋊C₄	—	2	1	no	—
309	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
310	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
311	C₇×C₂²⋊C₄	—	2	2	no	—
312	C₇×C₂²⋊C₄	—	2	2	no	—
313	C₇×C₂²⋊C₄	—	2	2	no	—
314	C₇×C₂²⋊C₄	—	2	2	no	—
315	C₇×C₂²⋊C₄	—	2	2	no	—
316	C₇×C₂²⋊C₄	—	2	2	no	—
317	C₇×C₂²⋊C₄	—	2	4	no	—
318	C₇×C₂²⋊C₄	—	2	4	no	—
319	C₇×C₂²⋊C₄	—	2	4	no	—
320	C₇×C₂²⋊C₄	—	2	4	no	—
321	C₇×C₂²⋊C₄	—	2	2	no	—
322	C₇×C₂²⋊C₄	—	2	2	no	—
323	C₇×C₂²⋊C₄	—	2	2	no	—
324	C₇×C₂²⋊C₄	—	2	2	no	—
325	C₄²×C₇	—	2	2	no	—
326	C₄²×C₇	—	2	2	no	—
327	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
328	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
329	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
330	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
331	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₇	C₂⁴	1	1	yes	characteristic
340	C₄²×C₇	C₂⁴	1	1	yes	characteristic
341	C₄²×C₇	C₂⁴	1	1	yes	characteristic
342	C₄²×C₇	C₂⁴	1	1	yes	characteristic
343	C₂²×#41	C₂²×C₇	1	2	yes	—
344	C₂×#137	C₂²×C₇	1	4	yes	complemented
345	C₂×AGL(1,ℤ/8)	C₂²×C₇	1	4	yes	complemented
346	#532	—	2	1	no	—
347	#532	—	2	1	no	—
348	#532	—	2	1	no	—
349	#532	—	2	1	no	—
350	#532	C₂²×C₇	1	2	yes	—
351	#532	C₂²×C₇	1	2	yes	—
352	#532	C₂²×C₇	1	2	yes	complemented
353	#532	C₂²×C₇	1	2	yes	complemented
354	C₂×C₄⋊Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
355	C₂×#127	C₂²×C₇	1	1	yes	characteristic, complemented
356	#529	—	2	1	no	—
357	#529	—	2	1	no	—
358	#529	—	2	1	no	—
359	#529	—	2	1	no	—
360	#529	C₂²×C₇	1	2	yes	—
361	#529	C₂²×C₇	1	2	yes	—
362	#529	C₂²×C₇	1	2	yes	complemented
363	#529	C₂²×C₇	1	2	yes	complemented
364	C₂×#126	—	2	1	no	—
365	C₂×#125	C₂²×C₇	1	1	yes	characteristic, complemented
366	C₂×#124	C₂²×C₇	1	1	yes	characteristic, complemented
367	C₂×#124	C₂²×C₇	1	2	yes	complemented
368	C₂×#123	—	2	1	no	—
369	C₂×C₂²⋊Q₈	C₂²×C₇	1	1	yes	characteristic
370	C₂×#121	—	2	1	no	—
371	C₂×#121	—	2	1	no	—
372	C₂×#121	C₂²×C₇	1	1	yes	characteristic
373	C₂×C₄×Q₈	C₂²×C₇	1	1	yes	characteristic, complemented
374	C₂×C₄×D₄	—	2	1	no	—
375	C₂×C₄×D₄	—	2	1	no	—
376	C₂×C₄×D₄	—	2	1	no	—
377	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
378	C₂×#117	—	2	1	no	—
379	C₂²×C₄²	C₂²×C₇	1	1	yes	characteristic
380	#497	C₂²×C₇	1	4	yes	complemented
381	#496	C₂²×C₇	1	4	yes	complemented
382	#495	C₂²×C₇	1	8	yes	complemented
383	#491	C₂²×C₇	1	4	yes	complemented
384	#490	C₂²×C₇	1	4	yes	complemented
385	#488	C₂²×C₇	1	8	yes	complemented
386	#464	C₂²×C₇	1	8	yes	complemented
387	#463	C₂²×C₇	1	8	yes	complemented
388	#462	C₂²×C₇	1	4	yes	complemented
389	#461	C₂²×C₇	1	4	yes	complemented
390	#460	C₂²×C₇	1	4	yes	complemented
391	#459	C₂²×C₇	1	4	yes	complemented
392	#452	C₂²×C₇	1	8	yes	complemented
393	#451	C₂²×C₇	1	4	yes	complemented
394	#450	C₂²×C₇	1	4	yes	complemented
395	#449	C₂²×C₇	1	8	yes	complemented
396	#448	C₂²×C₇	1	4	yes	—
397	#447	C₂²×C₇	1	4	yes	—
398	#432	C₂²×C₇	1	2	yes	complemented
399	#432	C₂²×C₇	1	2	yes	complemented
400	#431	C₂²×C₇	1	2	yes	complemented
401	#431	C₂²×C₇	1	2	yes	complemented
402	#423	C₂²×C₇	1	2	yes	complemented
403	#417	C₂²×C₇	1	4	yes	complemented
404	#417	C₂²×C₇	1	4	yes	complemented
405	#407	C₂²×C₇	1	2	yes	—
406	C₄×M₁₆	C₂²×C₇	1	2	yes	complemented
407	C₂³×C₇	—	2	2	no	—
408	C₂³×C₇	—	2	2	no	—
409	C₂³×C₇	—	2	2	no	—
410	C₂³×C₇	—	2	4	no	—
411	C₂³×C₇	—	4	1	no	—
412	C₂³×C₇	—	4	4	no	—
413	C₂³×C₇	—	4	2	no	—
414	C₂³×C₇	—	4	4	no	—
415	C₂³×C₇	—	4	2	no	—
416	C₂³×C₇	—	4	2	no	—
417	C₂³×C₇	—	4	4	no	—
418	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
419	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
420	C₂³×C₇	C₂²×D₄	1	1	yes	characteristic
421	C₇×Q₈	—	2	4	no	—
422	C₇×Q₈	—	2	4	no	—
423	C₇×Q₈	—	2	4	no	—
424	C₇×Q₈	—	4	4	no	—
425	C₇×Q₈	—	4	2	no	—
426	C₇×D₄	—	2	4	no	—
427	C₇×D₄	—	2	4	no	—
428	C₇×D₄	—	2	4	no	—
429	C₇×D₄	—	4	4	no	—
430	C₇×D₄	—	4	4	no	—
431	C₇×D₄	—	4	4	no	—
432	C₇×D₄	—	4	4	no	—
433	C₇×D₄	—	4	4	no	—
434	C₇×D₄	—	4	8	no	—
435	C₇×D₄	—	4	8	no	—
436	C₇×D₄	—	4	4	no	—
437	C₇×D₄	—	4	2	no	—
438	C₇×D₄	—	4	4	no	—
439	C₂×C₄×C₇	—	2	2	no	—
440	C₂×C₄×C₇	—	2	2	no	—
441	C₂×C₄×C₇	—	2	2	no	—
442	C₂×C₄×C₇	—	2	2	no	—
443	C₂×C₄×C₇	—	2	2	no	—
444	C₂×C₄×C₇	—	2	2	no	—
445	C₂×C₄×C₇	—	2	2	no	—
446	C₂×C₄×C₇	—	2	2	no	—
447	C₂×C₄×C₇	—	2	2	no	—
448	C₂×C₄×C₇	—	2	2	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	4	no	—
453	C₂×C₄×C₇	—	4	1	no	—
454	C₂×C₄×C₇	—	4	1	no	—
455	C₂×C₄×C₇	—	4	1	no	—
456	C₂×C₄×C₇	—	4	1	no	—
457	C₂×C₄×C₇	—	4	1	no	—
458	C₂×C₄×C₇	—	4	1	no	—
459	C₂×C₄×C₇	—	4	1	no	—
460	C₂×C₄×C₇	—	4	4	no	—
461	C₂×C₄×C₇	—	4	8	no	—
462	C₂×C₄×C₇	—	4	2	no	—
463	C₂×C₄×C₇	—	4	4	no	—
464	C₂×C₄×C₇	—	4	2	no	—
465	C₂×C₄×C₇	—	4	2	no	—
466	C₂×C₄×C₇	—	4	8	no	—
467	C₂×C₄×C₇	—	4	4	no	—
468	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₇	H(5,𝔽₂)	1	4	yes	—
480	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
481	C₇×C₈	—	2	8	no	—
482	C₂×#41	—	2	2	no	—
483	C₂×#41	—	2	2	no	—
484	C₂×#41	—	4	8	no	—
485	C₂×#41	C₂³×C₇	1	4	yes	—
486	C₂×#41	C₂³×C₇	1	4	yes	—
487	C₂²×Q₈	C₂³×C₇	1	1	yes	characteristic
488	C₂²×Q₈	C₂³×C₇	1	2	yes	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	—	2	2	no	—
491	C₂²×D₄	—	2	1	no	—
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
494	C₂²×D₄	C₂³×C₇	1	2	yes	—
495	C₂³×C₄	—	2	1	no	—
496	C₂³×C₄	—	2	2	no	—
497	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
498	C₂³×C₄	C₇×D₄	1	1	yes	characteristic
499	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
500	#137	—	4	8	no	—
501	AGL(1,ℤ/8)	—	4	8	no	—
502	C₂×Q₁₆	C₂³×C₇	1	8	yes	—
503	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
504	C₂×SD₁₆	C₂³×C₇	1	8	yes	—
505	C₂×D₈	C₂³×C₇	1	8	yes	—
506	C₂×M₁₆	C₂³×C₇	1	4	yes	—
507	C₄⋊Q₈	—	2	1	no	—
508	C₄⋊Q₈	—	2	1	no	—
509	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
510	C₄⋊Q₈	C₂³×C₇	1	2	yes	—
511	#127	—	2	1	no	—
512	#127	—	2	1	no	—
513	#127	C₂³×C₇	1	2	yes	—
514	#127	C₂³×C₇	1	2	yes	—
515	#126	—	2	2	no	—
516	#126	—	2	2	no	—
517	#126	—	2	2	no	—
518	#126	—	2	2	no	—
519	#125	—	2	1	no	—
520	#125	—	2	1	no	—
521	#125	C₂³×C₇	1	2	yes	—
522	#125	C₂³×C₇	1	2	yes	—
523	#124	—	2	1	no	—
524	#124	—	2	1	no	—
525	#124	—	2	2	no	—
526	#124	—	2	2	no	—
527	#124	C₂³×C₇	1	2	yes	—
528	#124	C₂³×C₇	1	2	yes	—
529	#124	C₂³×C₇	1	4	yes	—
530	#124	C₂³×C₇	1	4	yes	—
531	#123	—	2	2	no	—
532	#123	—	2	2	no	—
533	#123	—	2	2	no	—
534	#123	—	2	2	no	—
535	C₂²⋊Q₈	—	2	1	no	—
536	C₂²⋊Q₈	—	2	1	no	—
537	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
538	C₂²⋊Q₈	C₂³×C₇	1	2	yes	—
539	#121	—	2	2	no	—
540	#121	—	2	2	no	—
541	#121	—	2	2	no	—
542	#121	—	2	2	no	—
543	#121	—	2	2	no	—
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	2	2	no	—
547	#121	—	2	1	no	—
548	#121	—	2	1	no	—
549	#121	C₂³×C₇	1	2	yes	—
550	#121	C₂³×C₇	1	2	yes	—
551	C₄×Q₈	—	2	1	no	—
552	C₄×Q₈	—	2	1	no	—
553	C₄×Q₈	C₂³×C₇	1	2	yes	—
554	C₄×Q₈	C₂³×C₇	1	2	yes	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	2	no	—
560	C₄×D₄	—	2	2	no	—
561	C₄×D₄	—	2	2	no	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	C₂³×C₇	1	2	yes	—
570	C₄×D₄	C₂³×C₇	1	2	yes	—
571	#117	—	2	2	no	—
572	#117	—	2	2	no	—
573	#117	—	2	2	no	—
574	#117	—	2	2	no	—
575	C₂×C₄⋊C₄	—	2	1	no	—
576	C₂×C₄⋊C₄	—	2	1	no	—
577	C₂×C₄⋊C₄	—	2	1	no	—
578	C₂×C₄⋊C₄	—	2	1	no	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
582	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
583	C₂×C₂²⋊C₄	—	2	1	no	—
584	C₂×C₂²⋊C₄	—	2	1	no	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	2	no	—
587	C₂×C₂²⋊C₄	—	2	2	no	—
588	C₂×C₂²⋊C₄	—	2	1	no	—
589	C₂×C₂²⋊C₄	—	2	1	no	—
590	C₂×C₄²	—	2	1	no	—
591	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
592	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
593	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
594	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
595	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
596	C₂×C₄²	C₇×D₄	1	1	yes	characteristic
597	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
598	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
599	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
600	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
601	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
602	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
603	C₄⋊C₈	C₂³×C₇	1	4	yes	—
604	C₄⋊C₈	C₂³×C₇	1	4	yes	—
605	#103	C₂³×C₇	1	8	yes	—
606	#103	C₂³×C₇	1	8	yes	—
607	#102	C₂³×C₇	1	8	yes	—
608	#102	C₂³×C₇	1	8	yes	—
609	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
610	C₂²⋊C₈	C₂³×C₇	1	4	yes	—
611	#97	C₂³×C₇	1	4	yes	—
612	C₄×C₈	C₂³×C₇	1	4	yes	—
613	C₂²×C₇	—	2	1	no	—
614	C₂²×C₇	—	2	1	no	—
615	C₂²×C₇	—	2	1	no	—
616	C₂²×C₇	—	2	1	no	—
617	C₂²×C₇	—	2	1	no	—
618	C₂²×C₇	—	2	1	no	—
619	C₂²×C₇	—	2	1	no	—
620	C₂²×C₇	—	4	4	no	—
621	C₂²×C₇	—	4	4	no	—
622	C₂²×C₇	—	4	2	no	—
623	C₂²×C₇	—	4	2	no	—
624	C₂²×C₇	—	4	4	no	—
625	C₂²×C₇	—	4	2	no	—
626	C₂²×C₇	—	4	4	no	—
627	C₂²×C₇	—	8	8	no	—
628	C₂²×C₇	—	8	4	no	—
629	C₂²×C₇	#535	1	2	yes	—
630	C₂²×C₇	#575	1	2	yes	—
631	C₂²×C₇	C₂³×D₄	1	1	yes	characteristic
632	C₄×C₇	—	2	1	no	—
633	C₄×C₇	—	2	1	no	—
634	C₄×C₇	—	2	1	no	—
635	C₄×C₇	—	2	1	no	—
636	C₄×C₇	—	2	1	no	—
637	C₄×C₇	—	2	1	no	—
638	C₄×C₇	—	2	1	no	—
639	C₄×C₇	—	2	1	no	—
640	C₄×C₇	—	2	1	no	—
641	C₄×C₇	—	4	4	no	—
642	C₄×C₇	—	4	2	no	—
643	C₄×C₇	—	4	2	no	—
644	C₄×C₇	—	4	2	no	—
645	C₄×C₇	#535	1	2	yes	—
646	C₄×C₇	#575	1	2	yes	—
647	C₄×C₇	C₂×H(5,𝔽₂)	1	2	yes	—
648	C₂⁴	—	2	1	no	—
649	C₂⁴	—	2	2	no	—
650	C₂⁴	C₂×C₇×D₄	1	1	yes	characteristic
651	#41	—	2	8	no	—
652	#41	—	2	8	no	—
653	#41	—	4	4	no	—
654	#41	—	4	4	no	—
655	#41	—	4	8	no	—
656	#41	—	4	8	no	—
657	C₂×Q₈	—	2	1	no	—
658	C₂×Q₈	—	2	2	no	—
659	C₂×Q₈	—	2	4	no	—
660	C₂×Q₈	—	4	4	no	—
661	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
662	C₂×Q₈	C₂⁴×C₇	1	2	yes	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	2	no	—
665	C₂×D₄	—	2	4	no	—
666	C₂×D₄	—	2	4	no	—
667	C₂×D₄	—	2	1	no	—
668	C₂×D₄	—	2	2	no	—
669	C₂×D₄	—	2	2	no	—
670	C₂×D₄	—	2	2	no	—
671	C₂×D₄	—	2	2	no	—
672	C₂×D₄	—	2	2	no	—
673	C₂×D₄	—	2	4	no	—
674	C₂×D₄	—	4	4	no	—
675	C₂×D₄	—	4	4	no	—
676	C₂×D₄	—	4	4	no	—
677	C₂×D₄	—	4	8	no	—
678	C₂×D₄	—	4	4	no	—
679	C₂×D₄	C₂⁴×C₇	1	4	yes	—
680	C₂×D₄	C₂⁴×C₇	1	2	yes	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	1	no	—
683	C₂²×C₄	—	2	1	no	—
684	C₂²×C₄	—	2	1	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	4	no	—
689	C₂²×C₄	—	2	4	no	—
690	C₂²×C₄	—	4	2	no	—
691	C₂²×C₄	—	4	2	no	—
692	C₂²×C₄	—	4	4	no	—
693	C₂²×C₄	—	4	8	no	—
694	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
695	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
696	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
697	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
698	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
699	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
700	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
701	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
702	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
703	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
704	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
705	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
706	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
707	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
708	C₂²×C₄	C₂×C₇×D₄	1	1	yes	characteristic
709	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
710	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
712	Q₁₆	—	4	8	no	—
713	SD₁₆	—	4	8	no	—
714	SD₁₆	—	4	8	no	—
715	D₈	—	4	8	no	—
716	M₁₆	—	2	8	no	—
717	C₂×C₈	C₂⁴×C₇	1	8	yes	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	2	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	2	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	—	2	2	no	—
728	C₄⋊C₄	—	2	2	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	1	no	—
731	C₄⋊C₄	—	2	1	no	—
732	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	2	no	—
737	C₂²⋊C₄	—	2	2	no	—
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	4	no	—
741	C₂²⋊C₄	—	2	4	no	—
742	C₂²⋊C₄	—	2	4	no	—
743	C₂²⋊C₄	—	2	4	no	—
744	C₂²⋊C₄	—	2	2	no	—
745	C₂²⋊C₄	—	2	2	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₄²	—	2	2	no	—
749	C₄²	—	2	2	no	—
750	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
751	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
752	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
753	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
754	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
755	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
756	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
757	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
758	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
759	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
760	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
761	C₄²	C₂×C₇×D₄	1	1	yes	characteristic
762	C₄²	C₂⁴×C₇	1	1	yes	characteristic
763	C₄²	C₂⁴×C₇	1	1	yes	characteristic
764	C₄²	C₂⁴×C₇	1	1	yes	characteristic
765	C₄²	C₂⁴×C₇	1	1	yes	characteristic
766	C₂×C₇	—	2	2	no	—
767	C₂×C₇	—	2	2	no	—
768	C₂×C₇	—	4	1	no	—
769	C₂×C₇	—	8	4	no	—
770	C₂×C₇	—	8	2	no	—
771	C₂×C₇	C₂×#535	1	1	yes	characteristic
772	C₂×C₇	C₂×#575	1	1	yes	characteristic
773	C₂×C₇	C₂×#575	1	1	yes	characteristic
774	C₂³	—	2	2	no	—
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	4	no	—
778	C₂³	—	4	1	no	—
779	C₂³	—	4	4	no	—
780	C₂³	—	4	2	no	—
781	C₂³	—	4	4	no	—
782	C₂³	—	4	2	no	—
783	C₂³	—	4	2	no	—
784	C₂³	—	4	4	no	—
785	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
786	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
787	C₂³	C₂²×C₇×D₄	1	1	yes	characteristic
788	Q₈	—	2	4	no	—
789	Q₈	—	2	4	no	—
790	Q₈	—	2	4	no	—
791	Q₈	—	4	4	no	—
792	Q₈	—	4	2	no	—
793	D₄	—	2	4	no	—
794	D₄	—	2	4	no	—
795	D₄	—	2	4	no	—
796	D₄	—	4	4	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	4	no	—
799	D₄	—	4	4	no	—
800	D₄	—	4	4	no	—
801	D₄	—	4	8	no	—
802	D₄	—	4	8	no	—
803	D₄	—	4	4	no	—
804	D₄	—	4	2	no	—
805	D₄	—	4	4	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	4	no	—
820	C₂×C₄	—	4	1	no	—
821	C₂×C₄	—	4	1	no	—
822	C₂×C₄	—	4	1	no	—
823	C₂×C₄	—	4	1	no	—
824	C₂×C₄	—	4	1	no	—
825	C₂×C₄	—	4	1	no	—
826	C₂×C₄	—	4	1	no	—
827	C₂×C₄	—	4	4	no	—
828	C₂×C₄	—	4	8	no	—
829	C₂×C₄	—	4	2	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	2	no	—
832	C₂×C₄	—	4	2	no	—
833	C₂×C₄	—	4	8	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
836	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
837	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
838	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
839	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
840	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
841	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
842	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
843	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
844	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
845	C₂×C₄	C₂²×C₇×D₄	1	1	yes	characteristic
846	C₂×C₄	C₇×H(5,𝔽₂)	1	4	yes	—
847	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
848	C₈	—	2	8	no	—
849	C₇	#60805	1	1	yes	characteristic, direct product factor, Sylow
850	C₂²	—	2	1	no	—
851	C₂²	—	2	1	no	—
852	C₂²	—	2	1	no	—
853	C₂²	—	2	1	no	—
854	C₂²	—	2	1	no	—
855	C₂²	—	2	1	no	—
856	C₂²	—	2	1	no	—
857	C₂²	—	4	4	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	4	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	4	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	8	8	no	—
865	C₂²	—	8	4	no	—
866	C₂²	C₇×#535	1	2	yes	—
867	C₂²	C₇×#575	1	2	yes	—
868	C₂²	C₂³×C₇×D₄	1	1	yes	characteristic
869	C₄	—	2	1	no	—
870	C₄	—	2	1	no	—
871	C₄	—	2	1	no	—
872	C₄	—	2	1	no	—
873	C₄	—	2	1	no	—
874	C₄	—	2	1	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	4	2	no	—
879	C₄	—	4	2	no	—
880	C₄	—	4	4	no	—
881	C₄	—	4	2	no	—
882	C₄	C₇×#535	1	2	yes	—
883	C₄	C₇×#575	1	2	yes	—
884	C₄	C₂×C₇×H(5,𝔽₂)	1	2	yes	—
885	C₂	—	2	2	no	—
886	C₂	—	2	2	no	—
887	C₂	—	4	1	no	—
888	C₂	—	8	2	no	—
889	C₂	—	8	4	no	—
890	C₂	C₂×C₇×#535	1	1	yes	characteristic
891	C₂	C₂×C₇×#575	1	1	yes	characteristic
892	C₂	C₂×C₇×#575	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 ◁ C₂²×C₄²×C₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₇×#532	C₂	semidirect
2. C₂×C₇×#529	C₂	semidirect
3. C₇×#3219	C₂	semidirect
4. C₇×#3218	C₂	semidirect
5. C₇×#3217	C₂	semidirect
6. C₇×#3212	C₂	semidirect
7. C₇×#3211	C₂	semidirect
8. C₇×#3153	C₂	semidirect
9. C₇×#3142	C₂	semidirect
10. C₇×#3037	C₂	semidirect
11. C₇×#3036	C₂	semidirect
12. C₇×#3007	C₂	semidirect
13. C₇×#3006	C₂	semidirect
14. C₇×#2920	C₂	semidirect
16. C₂×C₇×#137	C₂²	semidirect
17. C₂×C₇×AGL(1,ℤ/8)	C₂²	semidirect
24. C₇×#532	C₂²	semidirect
25. C₇×#532	C₂²	semidirect
26. C₂×C₇×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₇×#127	C₂²	semidirect
34. C₇×#529	C₂²	semidirect
35. C₇×#529	C₂²	semidirect
37. C₂×C₇×#125	C₂²	semidirect
38. C₂×C₇×#124	C₂²	semidirect
39. C₂×C₇×#124	C₂²	semidirect
45. C₂×C₄×C₇×Q₈	C₂²	semidirect
49. C₂×C₄×C₇×D₄	C₂²	semidirect
52. C₇×#497	C₂²	semidirect
53. C₇×#496	C₂²	semidirect
54. C₇×#495	C₂²	semidirect
55. C₇×#491	C₂²	semidirect
56. C₇×#490	C₂²	semidirect
57. C₇×#488	C₂²	semidirect
58. C₇×#464	C₂²	semidirect
59. C₇×#463	C₂²	semidirect
60. C₇×#462	C₂²	semidirect
61. C₇×#461	C₂²	semidirect
62. C₇×#460	C₂²	semidirect
63. C₇×#459	C₂²	semidirect
64. C₇×#452	C₂²	semidirect
65. C₇×#451	C₂²	semidirect
66. C₇×#450	C₂²	semidirect
67. C₇×#449	C₂²	semidirect
70. C₇×#432	C₂²	semidirect
71. C₇×#432	C₂²	semidirect
72. C₇×#431	C₂²	semidirect
73. C₇×#431	C₂²	semidirect
74. C₇×#423	C₂²	semidirect
75. C₇×#417	C₂²	semidirect
76. C₇×#417	C₂²	semidirect
78. C₄×C₇×M₁₆	C₂²	semidirect
79. #60805	C₇	direct (N × H)
211. C₂×#532	C₂×C₇	semidirect
212. C₂×#529	C₂×C₇	semidirect
213. #3219	C₂×C₇	semidirect
214. #3218	C₂×C₇	semidirect
215. #3217	C₂×C₇	semidirect
216. #3212	C₂×C₇	semidirect
217. #3211	C₂×C₇	semidirect
218. #3153	C₂×C₇	semidirect
219. #3142	C₂×C₇	semidirect
220. #3037	C₂×C₇	semidirect
221. #3036	C₂×C₇	semidirect
222. #3007	C₂×C₇	semidirect
223. #3006	C₂×C₇	semidirect
224. #2920	C₂×C₇	semidirect
344. C₂×#137	C₂²×C₇	semidirect
345. C₂×AGL(1,ℤ/8)	C₂²×C₇	semidirect
352. #532	C₂²×C₇	semidirect
353. #532	C₂²×C₇	semidirect
354. C₂×C₄⋊Q₈	C₂²×C₇	semidirect
355. C₂×#127	C₂²×C₇	semidirect
362. #529	C₂²×C₇	semidirect
363. #529	C₂²×C₇	semidirect
365. C₂×#125	C₂²×C₇	semidirect
366. C₂×#124	C₂²×C₇	semidirect
367. C₂×#124	C₂²×C₇	semidirect
373. C₂×C₄×Q₈	C₂²×C₇	semidirect
377. C₂×C₄×D₄	C₂²×C₇	semidirect
380. #497	C₂²×C₇	semidirect
381. #496	C₂²×C₇	semidirect
382. #495	C₂²×C₇	semidirect
383. #491	C₂²×C₇	semidirect
384. #490	C₂²×C₇	semidirect
385. #488	C₂²×C₇	semidirect
386. #464	C₂²×C₇	semidirect
387. #463	C₂²×C₇	semidirect
388. #462	C₂²×C₇	semidirect
389. #461	C₂²×C₇	semidirect
390. #460	C₂²×C₇	semidirect
391. #459	C₂²×C₇	semidirect
392. #452	C₂²×C₇	semidirect
393. #451	C₂²×C₇	semidirect
394. #450	C₂²×C₇	semidirect
395. #449	C₂²×C₇	semidirect
398. #432	C₂²×C₇	semidirect
399. #432	C₂²×C₇	semidirect
400. #431	C₂²×C₇	semidirect
401. #431	C₂²×C₇	semidirect
402. #423	C₂²×C₇	semidirect
403. #417	C₂²×C₇	semidirect
404. #417	C₂²×C₇	semidirect
406. C₄×M₁₆	C₂²×C₇	semidirect
849. C₇	#60805	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×#532	2
C₂×C₇×#529	2
C₇×#3219	2
C₇×#3218	2
C₇×#3217	2
C₇×#3212	2
C₇×#3211	2
C₇×#3153	2
C₇×#3142	2
C₇×#3037	2
C₇×#3036	2
C₇×#3007	2
C₇×#3006	2
C₇×#2920	2
#60805	7

Subgroups — C7×#60805 #13238021

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#60805 #13238021