Subgroups — C₂×#1719×C₁₃₁ #45705495

Order 33536.

850 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#500×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#492×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#487×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#487×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#486×C₁₃₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#486×C₁₃₁	C₂	1	1	yes	maximal, characteristic
7	#1719×C₁₃₁	C₂	1	8	yes	maximal, direct product factor
8	C₂×#322×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×SD₁₆×C₁₃₁	—	2	2	no	—
10	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
14	#500×C₁₃₁	—	2	2	no	—
15	#500×C₁₃₁	C₂²	1	4	yes	complemented
16	#492×C₁₃₁	—	2	2	no	—
17	#492×C₁₃₁	C₂²	1	4	yes	—
18	#487×C₁₃₁	—	2	2	no	—
19	#487×C₁₃₁	—	2	2	no	—
20	#487×C₁₃₁	C₂²	1	4	yes	complemented
21	#487×C₁₃₁	C₂²	1	4	yes	complemented
22	#486×C₁₃₁	—	2	2	no	—
23	#486×C₁₃₁	—	2	2	no	—
24	#486×C₁₃₁	C₂²	1	4	yes	—
25	#486×C₁₃₁	C₂²	1	4	yes	—
26	C₂×#107×C₁₃₁	—	2	2	no	—
27	C₂×#103×C₁₃₁	—	2	2	no	—
28	C₂×#103×C₁₃₁	—	2	2	no	—
29	C₂×#102×C₁₃₁	—	2	2	no	—
30	C₂×#102×C₁₃₁	—	2	2	no	—
31	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
34	#322×C₁₃₁	C₂²	1	4	yes	complemented
35	C₂²×Q₈×C₁₃₁	—	2	1	no	—
36	C₂²×Q₈×C₁₃₁	—	2	1	no	—
37	C₂²×Q₈×C₁₃₁	—	2	1	no	—
38	C₂²×D₄×C₁₃₁	—	2	1	no	—
39	C₂²×D₄×C₁₃₁	—	2	1	no	—
40	C₂²×D₄×C₁₃₁	—	2	1	no	—
41	C₂×SD₁₆×C₁₃₁	—	2	8	no	—
42	C₂×SD₁₆×C₁₃₁	—	4	8	no	—
43	C₂²×C₈×C₁₃₁	D₄	1	2	yes	—
44	C₂²×C₈×C₁₃₁	D₄	1	2	yes	—
45	C₂²×C₈×C₁₃₁	D₄	1	2	yes	—
46	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
47	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
48	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
49	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
50	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
51	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
52	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
53	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
54	C₄⋊Q₈×C₁₃₁	—	2	1	no	—
55	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
56	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
57	C₄⋊Q₈×C₁₃₁	C₂³	1	2	yes	—
58	#127×C₁₃₁	—	2	1	no	—
59	#127×C₁₃₁	—	2	1	no	—
60	#127×C₁₃₁	—	2	1	no	—
61	#127×C₁₃₁	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
68	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
69	#107×C₁₃₁	—	2	8	no	—
70	#103×C₁₃₁	—	2	8	no	—
71	#103×C₁₃₁	—	2	8	no	—
72	#102×C₁₃₁	—	2	8	no	—
73	#102×C₁₃₁	—	2	8	no	—
74	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
75	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
76	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
77	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
78	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
79	C₄×C₈×C₁₃₁	C₂³	1	2	yes	—
80	C₂⁴×C₁₃₁	—	4	1	no	—
81	C₂×Q₈×C₁₃₁	—	2	2	no	—
82	C₂×Q₈×C₁₃₁	—	2	2	no	—
83	C₂×Q₈×C₁₃₁	—	2	2	no	—
84	C₂×Q₈×C₁₃₁	—	4	1	no	—
85	C₂×Q₈×C₁₃₁	—	4	1	no	—
86	C₂×Q₈×C₁₃₁	—	4	1	no	—
87	C₂×Q₈×C₁₃₁	—	4	4	no	—
88	C₂×Q₈×C₁₃₁	—	4	4	no	—
89	C₂×Q₈×C₁₃₁	—	4	4	no	—
90	C₂×D₄×C₁₃₁	—	2	2	no	—
91	C₂×D₄×C₁₃₁	—	2	2	no	—
92	C₂×D₄×C₁₃₁	—	2	2	no	—
93	C₂×D₄×C₁₃₁	—	4	1	no	—
94	C₂×D₄×C₁₃₁	—	4	1	no	—
95	C₂×D₄×C₁₃₁	—	4	1	no	—
96	C₂×D₄×C₁₃₁	—	4	4	no	—
97	C₂×D₄×C₁₃₁	—	4	4	no	—
98	C₂×D₄×C₁₃₁	—	4	4	no	—
99	C₂²×C₄×C₁₃₁	—	4	1	no	—
100	C₂²×C₄×C₁₃₁	—	4	1	no	—
101	C₂²×C₄×C₁₃₁	—	4	1	no	—
102	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
105	SD₁₆×C₁₃₁	—	4	16	no	—
106	C₂×C₈×C₁₃₁	—	2	4	no	—
107	C₂×C₈×C₁₃₁	—	2	4	no	—
108	C₂×C₈×C₁₃₁	—	2	4	no	—
109	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
110	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
111	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
112	C₄⋊C₄×C₁₃₁	—	2	2	no	—
113	C₄⋊C₄×C₁₃₁	—	2	2	no	—
114	C₄⋊C₄×C₁₃₁	—	2	2	no	—
115	C₄⋊C₄×C₁₃₁	—	2	2	no	—
116	C₄⋊C₄×C₁₃₁	—	2	2	no	—
117	C₄⋊C₄×C₁₃₁	—	2	2	no	—
118	C₄⋊C₄×C₁₃₁	—	4	1	no	—
119	C₄⋊C₄×C₁₃₁	—	4	1	no	—
120	C₄⋊C₄×C₁₃₁	—	4	1	no	—
121	C₄⋊C₄×C₁₃₁	—	4	1	no	—
122	C₄⋊C₄×C₁₃₁	—	4	1	no	—
123	C₄⋊C₄×C₁₃₁	—	4	1	no	—
124	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₁₃₁	C₂⁴	1	1	yes	characteristic
128	C₂³×C₁₃₁	—	4	2	no	—
129	C₂³×C₁₃₁	—	8	2	no	—
130	C₂³×C₁₃₁	—	8	2	no	—
131	C₂³×C₁₃₁	—	8	2	no	—
132	C₂³×C₁₃₁	#127	1	1	yes	characteristic
133	Q₈×C₁₃₁	—	4	4	no	—
134	Q₈×C₁₃₁	—	4	4	no	—
135	Q₈×C₁₃₁	—	4	4	no	—
136	Q₈×C₁₃₁	—	8	2	no	—
137	Q₈×C₁₃₁	—	8	2	no	—
138	Q₈×C₁₃₁	—	8	2	no	—
139	D₄×C₁₃₁	—	4	4	no	—
140	D₄×C₁₃₁	—	4	4	no	—
141	D₄×C₁₃₁	—	4	4	no	—
142	D₄×C₁₃₁	—	8	2	no	—
143	D₄×C₁₃₁	—	8	2	no	—
144	D₄×C₁₃₁	—	8	2	no	—
145	C₂×C₄×C₁₃₁	—	4	2	no	—
146	C₂×C₄×C₁₃₁	—	4	2	no	—
147	C₂×C₄×C₁₃₁	—	4	2	no	—
148	C₂×C₄×C₁₃₁	—	8	2	no	—
149	C₂×C₄×C₁₃₁	—	8	2	no	—
150	C₂×C₄×C₁₃₁	—	8	2	no	—
151	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
152	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
153	C₂×C₄×C₁₃₁	#127	1	1	yes	characteristic
154	C₂×C₄×C₁₃₁	#135	1	4	yes	—
155	C₂×C₄×C₁₃₁	AGL(1,ℤ/8)	1	4	yes	—
156	C₂×C₄×C₁₃₁	#137	1	4	yes	—
157	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
160	C₈×C₁₃₁	—	2	4	no	—
161	C₈×C₁₃₁	—	2	4	no	—
162	C₈×C₁₃₁	—	2	4	no	—
163	C₂²×C₁₃₁	—	8	2	no	—
164	C₂²×C₁₃₁	—	8	2	no	—
165	C₂²×C₁₃₁	—	8	2	no	—
166	C₂²×C₁₃₁	—	16	4	no	—
167	C₂²×C₁₃₁	#495	1	2	yes	—
168	C₂²×C₁₃₁	#496	1	2	yes	—
169	C₂²×C₁₃₁	#497	1	2	yes	—
170	C₂²×C₁₃₁	C₂×#127	1	1	yes	characteristic
171	C₄×C₁₃₁	—	8	2	no	—
172	C₄×C₁₃₁	—	8	2	no	—
173	C₄×C₁₃₁	—	8	2	no	—
174	C₄×C₁₃₁	#495	1	2	yes	—
175	C₄×C₁₃₁	#496	1	2	yes	—
176	C₄×C₁₃₁	#497	1	2	yes	—
177	C₄×C₁₃₁	C₂×#135	1	2	yes	—
178	C₄×C₁₃₁	C₂×AGL(1,ℤ/8)	1	2	yes	—
179	C₄×C₁₃₁	C₂×#137	1	2	yes	—
180	C₂×C₁₃₁	—	16	2	no	—
181	C₂×C₁₃₁	#1719	1	4	yes	direct product factor
182	C₂×C₁₃₁	C₂×#495	1	1	yes	characteristic
183	C₂×C₁₃₁	C₂×#496	1	1	yes	characteristic
184	C₂×C₁₃₁	C₂×#497	1	1	yes	characteristic
185	C₂×#1719	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₁₃₁	C₂×#1719	1	1	yes	characteristic, direct product factor, Sylow
187	C₂×#500	C₂×C₁₃₁	1	1	yes	characteristic, complemented
188	C₂×#492	C₂×C₁₃₁	1	1	yes	characteristic
189	C₂×#487	C₂×C₁₃₁	1	1	yes	characteristic, complemented
190	C₂×#487	C₂×C₁₃₁	1	1	yes	characteristic, complemented
191	C₂×#486	C₂×C₁₃₁	1	1	yes	characteristic
192	C₂×#486	C₂×C₁₃₁	1	1	yes	characteristic
193	#1719	C₂×C₁₃₁	1	8	yes	direct product factor
194	C₂×#322	C₂×C₁₃₁	1	1	yes	characteristic, complemented
195	C₂²×SD₁₆	—	2	2	no	—
196	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
197	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
198	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
199	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
200	#500	—	2	2	no	—
201	#500	C₂²×C₁₃₁	1	4	yes	complemented
202	#492	—	2	2	no	—
203	#492	C₂²×C₁₃₁	1	4	yes	—
204	#487	—	2	2	no	—
205	#487	—	2	2	no	—
206	#487	C₂²×C₁₃₁	1	4	yes	complemented
207	#487	C₂²×C₁₃₁	1	4	yes	complemented
208	#486	—	2	2	no	—
209	#486	—	2	2	no	—
210	#486	C₂²×C₁₃₁	1	4	yes	—
211	#486	C₂²×C₁₃₁	1	4	yes	—
212	C₂×#107	—	2	2	no	—
213	C₂×#103	—	2	2	no	—
214	C₂×#103	—	2	2	no	—
215	C₂×#102	—	2	2	no	—
216	C₂×#102	—	2	2	no	—
217	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
220	#322	C₂²×C₁₃₁	1	4	yes	complemented
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×Q₈	—	2	1	no	—
223	C₂²×Q₈	—	2	1	no	—
224	C₂²×D₄	—	2	1	no	—
225	C₂²×D₄	—	2	1	no	—
226	C₂²×D₄	—	2	1	no	—
227	C₂×SD₁₆	—	2	8	no	—
228	C₂×SD₁₆	—	4	8	no	—
229	C₂²×C₈	D₄×C₁₃₁	1	2	yes	—
230	C₂²×C₈	D₄×C₁₃₁	1	2	yes	—
231	C₂²×C₈	D₄×C₁₃₁	1	2	yes	—
232	C₄⋊Q₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	—	2	1	no	—
241	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
242	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
243	C₄⋊Q₈	C₂³×C₁₃₁	1	2	yes	—
244	#127	—	2	1	no	—
245	#127	—	2	1	no	—
246	#127	—	2	1	no	—
247	#127	C₂³×C₁₃₁	1	2	yes	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
255	#107	—	2	8	no	—
256	#103	—	2	8	no	—
257	#103	—	2	8	no	—
258	#102	—	2	8	no	—
259	#102	—	2	8	no	—
260	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
261	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
262	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
263	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
264	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
265	C₄×C₈	C₂³×C₁₃₁	1	2	yes	—
266	C₂⁴	—	4	1	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	4	1	no	—
271	C₂×Q₈	—	4	1	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×Q₈	—	4	4	no	—
274	C₂×Q₈	—	4	4	no	—
275	C₂×Q₈	—	4	4	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	4	no	—
283	C₂×D₄	—	4	4	no	—
284	C₂×D₄	—	4	4	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
289	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
291	SD₁₆	—	4	16	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	2	4	no	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
296	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
297	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
311	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
313	C₄²	C₂⁴×C₁₃₁	1	1	yes	characteristic
314	C₂³	—	4	2	no	—
315	C₂³	—	8	2	no	—
316	C₂³	—	8	2	no	—
317	C₂³	—	8	2	no	—
318	C₂³	#127×C₁₃₁	1	1	yes	characteristic
319	Q₈	—	4	4	no	—
320	Q₈	—	4	4	no	—
321	Q₈	—	4	4	no	—
322	Q₈	—	8	2	no	—
323	Q₈	—	8	2	no	—
324	Q₈	—	8	2	no	—
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	D₄	—	8	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	8	2	no	—
335	C₂×C₄	—	8	2	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
338	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
339	C₂×C₄	#127×C₁₃₁	1	1	yes	characteristic
340	C₂×C₄	#135×C₁₃₁	1	4	yes	—
341	C₂×C₄	AGL(1,ℤ/8)×C₁₃₁	1	4	yes	—
342	C₂×C₄	#137×C₁₃₁	1	4	yes	—
343	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
344	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
346	C₈	—	2	4	no	—
347	C₈	—	2	4	no	—
348	C₈	—	2	4	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	16	4	no	—
353	C₂²	#495×C₁₃₁	1	2	yes	—
354	C₂²	#496×C₁₃₁	1	2	yes	—
355	C₂²	#497×C₁₃₁	1	2	yes	—
356	C₂²	C₂×#127×C₁₃₁	1	1	yes	characteristic
357	C₄	—	8	2	no	—
358	C₄	—	8	2	no	—
359	C₄	—	8	2	no	—
360	C₄	#495×C₁₃₁	1	2	yes	—
361	C₄	#496×C₁₃₁	1	2	yes	—
362	C₄	#497×C₁₃₁	1	2	yes	—
363	C₄	C₂×#135×C₁₃₁	1	2	yes	—
364	C₄	C₂×AGL(1,ℤ/8)×C₁₃₁	1	2	yes	—
365	C₄	C₂×#137×C₁₃₁	1	2	yes	—
366	C₂	—	16	2	no	—
367	C₂	#1719×C₁₃₁	1	4	yes	direct product factor
368	C₂	C₂×#495×C₁₃₁	1	1	yes	characteristic
369	C₂	C₂×#496×C₁₃₁	1	1	yes	characteristic
370	C₂	C₂×#497×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₃₁	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃₁
prime radical	C₂×#127×C₁₃₁	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#500×C₁₃₁	C₂	semidirect
3. C₂×#487×C₁₃₁	C₂	semidirect
4. C₂×#487×C₁₃₁	C₂	semidirect
7. #1719×C₁₃₁	C₂	direct (N × H)
8. C₂×#322×C₁₃₁	C₂	semidirect
15. #500×C₁₃₁	C₂²	semidirect
20. #487×C₁₃₁	C₂²	semidirect
21. #487×C₁₃₁	C₂²	semidirect
34. #322×C₁₃₁	C₂²	semidirect
181. C₂×C₁₃₁	#1719	direct (N × H)
185. C₂×#1719	C₁₃₁	direct (N × H)
186. C₁₃₁	C₂×#1719	direct (N × H)
187. C₂×#500	C₂×C₁₃₁	semidirect
189. C₂×#487	C₂×C₁₃₁	semidirect
190. C₂×#487	C₂×C₁₃₁	semidirect
193. #1719	C₂×C₁₃₁	direct (N × H)
194. C₂×#322	C₂×C₁₃₁	semidirect
201. #500	C₂²×C₁₃₁	semidirect
206. #487	C₂²×C₁₃₁	semidirect
207. #487	C₂²×C₁₃₁	semidirect
220. #322	C₂²×C₁₃₁	semidirect
367. C₂	#1719×C₁₃₁	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×#500×C₁₃₁	2
C₂×#492×C₁₃₁	2
C₂×#487×C₁₃₁	2
C₂×#486×C₁₃₁	2
#1719×C₁₃₁	2
C₂×#322×C₁₃₁	2
C₂×#1719	131

Subgroups — C2×#1719×C131 #45705495

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1719×C₁₃₁ #45705495