Subgroups — C₁₃₁×#21242 #45707126

Order 33536.

1474 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#575×C₁₃₁	C₂	1	1	yes	maximal, characteristic
2	C₂×#430×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#421×C₁₃₁	C₂	1	2	yes	maximal, complemented
4	C₂×#408×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	C₂×#405×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#1975×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	#1974×C₁₃₁	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₁₃₁	C₂²	1	2	yes	—
9	#575×C₁₃₁	—	2	4	no	—
10	#575×C₁₃₁	—	2	4	no	—
11	C₂×#137×C₁₃₁	C₄	1	4	yes	complemented
12	C₂×AGL(1,ℤ/8)×C₁₃₁	C₄	1	4	yes	complemented
13	C₂×#135×C₁₃₁	C₂²	1	4	yes	—
14	C₂²×M₁₆×C₁₃₁	C₂²	1	2	yes	—
15	C₂²×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
17	C₂×#117×C₁₃₁	C₂²	1	1	yes	characteristic
18	#430×C₁₃₁	—	2	4	no	—
19	C₂×#108×C₁₃₁	C₂²	1	4	yes	complemented
20	#421×C₁₃₁	—	2	8	no	—
21	C₂×#104×C₁₃₁	C₂²	1	8	yes	complemented
22	#408×C₁₃₁	—	2	4	no	—
23	#408×C₁₃₁	C₂²	1	4	yes	complemented
24	#408×C₁₃₁	C₂²	1	4	yes	complemented
25	C₂×C₂²⋊C₈×C₁₃₁	—	2	4	no	—
26	#405×C₁₃₁	—	2	4	no	—
27	C₂×#97×C₁₃₁	C₂²	1	2	yes	complemented
28	C₂×C₄×C₈×C₁₃₁	C₂²	1	2	yes	complemented
29	C₂×#41×C₁₃₁	—	2	2	no	—
30	C₂×#41×C₁₃₁	—	2	2	no	—
31	C₂×#41×C₁₃₁	—	2	4	no	—
32	C₂×#41×C₁₃₁	—	2	4	no	—
33	C₂×#41×C₁₃₁	—	2	4	no	—
34	C₂×#41×C₁₃₁	—	2	4	no	—
35	C₂×#41×C₁₃₁	C₂×C₄	1	4	yes	—
36	C₂×#41×C₁₃₁	C₂³	1	4	yes	—
37	C₂²×Q₈×C₁₃₁	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₁₃₁	—	2	2	no	—
39	C₂²×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₃₁	—	2	2	no	—
41	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
42	#137×C₁₃₁	—	2	16	no	—
43	AGL(1,ℤ/8)×C₁₃₁	—	2	16	no	—
44	#135×C₁₃₁	—	2	8	no	—
45	#135×C₁₃₁	—	2	8	no	—
46	C₂×Q₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
47	C₂×SD₁₆×C₁₃₁	C₂×C₄	1	8	yes	—
48	C₂×D₈×C₁₃₁	C₂×C₄	1	4	yes	—
49	C₂×M₁₆×C₁₃₁	—	2	2	no	—
50	C₂×M₁₆×C₁₃₁	—	2	4	no	—
51	C₂×M₁₆×C₁₃₁	—	2	4	no	—
52	C₂×M₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
53	C₂×M₁₆×C₁₃₁	D₄	1	4	yes	—
54	C₂×M₁₆×C₁₃₁	D₄	1	4	yes	—
55	C₂×M₁₆×C₁₃₁	C₂³	1	4	yes	—
56	C₂²×C₈×C₁₃₁	—	2	2	no	—
57	C₂²×C₈×C₁₃₁	—	2	2	no	—
58	C₂²×C₈×C₁₃₁	—	2	2	no	—
59	C₂²×C₈×C₁₃₁	D₄	1	4	yes	—
60	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
63	#117×C₁₃₁	—	2	2	no	—
64	#117×C₁₃₁	D₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₁₃₁	—	2	1	no	—
67	C₂×C₄²×C₁₃₁	C₂³	1	2	yes	—
68	#108×C₁₃₁	—	2	8	no	—
69	#104×C₁₃₁	—	2	16	no	—
70	C₂²⋊C₈×C₁₃₁	—	2	8	no	—
71	C₂²⋊C₈×C₁₃₁	—	2	8	no	—
72	#97×C₁₃₁	—	2	4	no	—
73	C₄×C₈×C₁₃₁	—	2	4	no	—
74	C₂⁴×C₁₃₁	—	2	2	no	—
75	C₂⁴×C₁₃₁	#41	1	1	yes	characteristic
76	#41×C₁₃₁	—	2	8	no	—
77	#41×C₁₃₁	—	2	8	no	—
78	#41×C₁₃₁	—	2	4	no	—
79	#41×C₁₃₁	—	2	4	no	—
80	#41×C₁₃₁	—	2	4	no	—
81	#41×C₁₃₁	—	2	4	no	—
82	#41×C₁₃₁	—	4	4	no	—
83	#41×C₁₃₁	—	4	4	no	—
84	#41×C₁₃₁	—	4	4	no	—
85	#41×C₁₃₁	—	4	4	no	—
86	C₂×Q₈×C₁₃₁	—	2	2	no	—
87	C₂×Q₈×C₁₃₁	—	2	4	no	—
88	C₂×Q₈×C₁₃₁	—	2	4	no	—
89	C₂×Q₈×C₁₃₁	C₂²×C₄	1	4	yes	—
90	C₂×D₄×C₁₃₁	—	2	4	no	—
91	C₂×D₄×C₁₃₁	—	2	4	no	—
92	C₂×D₄×C₁₃₁	—	2	4	no	—
93	C₂×D₄×C₁₃₁	—	2	4	no	—
94	C₂×D₄×C₁₃₁	—	2	2	no	—
95	C₂×D₄×C₁₃₁	—	4	4	no	—
96	C₂×D₄×C₁₃₁	—	4	4	no	—
97	C₂×D₄×C₁₃₁	C₂²×C₄	1	4	yes	—
98	C₂²×C₄×C₁₃₁	—	2	2	no	—
99	C₂²×C₄×C₁₃₁	—	2	2	no	—
100	C₂²×C₄×C₁₃₁	—	2	4	no	—
101	C₂²×C₄×C₁₃₁	—	2	4	no	—
102	C₂²×C₄×C₁₃₁	—	4	4	no	—
103	C₂²×C₄×C₁₃₁	—	4	4	no	—
104	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
110	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
111	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
112	Q₁₆×C₁₃₁	—	2	8	no	—
113	SD₁₆×C₁₃₁	—	2	16	no	—
114	D₈×C₁₃₁	—	2	8	no	—
115	M₁₆×C₁₃₁	—	2	4	no	—
116	M₁₆×C₁₃₁	—	2	4	no	—
117	M₁₆×C₁₃₁	—	4	4	no	—
118	M₁₆×C₁₃₁	C₂²⋊C₄	1	16	yes	—
119	C₂×C₈×C₁₃₁	—	2	8	no	—
120	C₂×C₈×C₁₃₁	—	2	1	no	—
121	C₂×C₈×C₁₃₁	—	2	1	no	—
122	C₂×C₈×C₁₃₁	—	2	1	no	—
123	C₂×C₈×C₁₃₁	—	2	1	no	—
124	C₂×C₈×C₁₃₁	—	2	4	no	—
125	C₂×C₈×C₁₃₁	—	4	4	no	—
126	C₂×C₈×C₁₃₁	C₂²×C₄	1	4	yes	—
127	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
130	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
131	C₄⋊C₄×C₁₃₁	—	2	4	no	—
132	C₂²⋊C₄×C₁₃₁	—	2	4	no	—
133	C₄²×C₁₃₁	—	2	2	no	—
134	C₄²×C₁₃₁	C₂×D₄	1	4	yes	—
135	C₂³×C₁₃₁	—	2	4	no	—
136	C₂³×C₁₃₁	—	4	2	no	—
137	C₂³×C₁₃₁	—	4	8	no	—
138	C₂³×C₁₃₁	—	4	4	no	—
139	C₂³×C₁₃₁	C₄×D₄	1	2	yes	—
140	C₂³×C₁₃₁	#121	1	2	yes	—
141	C₂³×C₁₃₁	#124	1	2	yes	—
142	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
143	Q₈×C₁₃₁	—	2	4	no	—
144	Q₈×C₁₃₁	—	2	4	no	—
145	Q₈×C₁₃₁	—	4	4	no	—
146	D₄×C₁₃₁	—	2	4	no	—
147	D₄×C₁₃₁	—	2	4	no	—
148	D₄×C₁₃₁	—	4	4	no	—
149	D₄×C₁₃₁	—	4	4	no	—
150	D₄×C₁₃₁	—	4	8	no	—
151	D₄×C₁₃₁	—	4	4	no	—
152	C₂×C₄×C₁₃₁	—	2	4	no	—
153	C₂×C₄×C₁₃₁	—	2	4	no	—
154	C₂×C₄×C₁₃₁	—	4	4	no	—
155	C₂×C₄×C₁₃₁	—	4	4	no	—
156	C₂×C₄×C₁₃₁	—	4	4	no	—
157	C₂×C₄×C₁₃₁	—	4	4	no	—
158	C₂×C₄×C₁₃₁	—	4	8	no	—
159	C₂×C₄×C₁₃₁	C₂×C₂²⋊C₄	1	4	yes	—
160	C₂×C₄×C₁₃₁	C₄×D₄	1	4	yes	—
161	C₂×C₄×C₁₃₁	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₁₃₁	#121	1	4	yes	—
163	C₂×C₄×C₁₃₁	#121	1	2	yes	—
164	C₂×C₄×C₁₃₁	#124	1	2	yes	—
165	C₂×C₄×C₁₃₁	#127	1	4	yes	—
166	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
172	C₈×C₁₃₁	—	2	2	no	—
173	C₈×C₁₃₁	—	2	2	no	—
174	C₈×C₁₃₁	—	4	4	no	—
175	C₈×C₁₃₁	C₂×C₂²⋊C₄	1	8	yes	—
176	C₂²×C₁₃₁	—	2	2	no	—
177	C₂²×C₁₃₁	—	2	4	no	—
178	C₂²×C₁₃₁	—	4	2	no	—
179	C₂²×C₁₃₁	—	4	2	no	—
180	C₂²×C₁₃₁	—	4	8	no	—
181	C₂²×C₁₃₁	—	4	4	no	—
182	C₂²×C₁₃₁	—	8	8	no	—
183	C₂²×C₁₃₁	#390	1	4	yes	—
184	C₂²×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
186	C₂²×C₁₃₁	C₂×#124	1	1	yes	characteristic
187	C₄×C₁₃₁	—	4	4	no	—
188	C₄×C₁₃₁	—	4	4	no	—
189	C₄×C₁₃₁	#390	1	4	yes	—
190	C₄×C₁₃₁	C₂²×C₂²⋊C₄	1	1	yes	characteristic
191	C₄×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₁₃₁	C₂×#121	1	1	yes	characteristic
193	C₄×C₁₃₁	C₂×#127	1	1	yes	characteristic
194	C₂×C₁₃₁	—	2	1	no	—
195	C₂×C₁₃₁	—	2	4	no	—
196	C₂×C₁₃₁	—	2	1	no	—
197	C₂×C₁₃₁	—	8	4	no	—
198	C₂×C₁₃₁	C₂×#390	1	1	yes	characteristic
199	C₂×C₁₃₁	#2955	1	2	yes	—
200	#21242	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₁₃₁	#21242	1	1	yes	characteristic, direct product factor, Sylow
202	C₂×#575	C₂×C₁₃₁	1	1	yes	characteristic
203	C₂×#430	C₂×C₁₃₁	1	1	yes	characteristic, complemented
204	C₂×#421	C₂×C₁₃₁	1	2	yes	complemented
205	C₂×#408	C₂×C₁₃₁	1	2	yes	complemented
206	C₂×#405	C₂×C₁₃₁	1	1	yes	characteristic, complemented
207	#1975	C₂×C₁₃₁	1	4	yes	complemented
208	#1974	C₂×C₁₃₁	1	4	yes	complemented
209	C₂²×#41	C₂²×C₁₃₁	1	2	yes	—
210	#575	—	2	4	no	—
211	#575	—	2	4	no	—
212	C₂×#137	C₄×C₁₃₁	1	4	yes	complemented
213	C₂×AGL(1,ℤ/8)	C₄×C₁₃₁	1	4	yes	complemented
214	C₂×#135	C₂²×C₁₃₁	1	4	yes	—
215	C₂²×M₁₆	C₂²×C₁₃₁	1	2	yes	—
216	C₂²×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
217	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
218	C₂×#117	C₂²×C₁₃₁	1	1	yes	characteristic
219	#430	—	2	4	no	—
220	C₂×#108	C₂²×C₁₃₁	1	4	yes	complemented
221	#421	—	2	8	no	—
222	C₂×#104	C₂²×C₁₃₁	1	8	yes	complemented
223	#408	—	2	4	no	—
224	#408	C₂²×C₁₃₁	1	4	yes	complemented
225	#408	C₂²×C₁₃₁	1	4	yes	complemented
226	C₂×C₂²⋊C₈	—	2	4	no	—
227	#405	—	2	4	no	—
228	C₂×#97	C₂²×C₁₃₁	1	2	yes	complemented
229	C₂×C₄×C₈	C₂²×C₁₃₁	1	2	yes	complemented
230	C₂×#41	—	2	2	no	—
231	C₂×#41	—	2	2	no	—
232	C₂×#41	—	2	4	no	—
233	C₂×#41	—	2	4	no	—
234	C₂×#41	—	2	4	no	—
235	C₂×#41	—	2	4	no	—
236	C₂×#41	C₂×C₄×C₁₃₁	1	4	yes	—
237	C₂×#41	C₂³×C₁₃₁	1	4	yes	—
238	C₂²×Q₈	C₂×C₄×C₁₃₁	1	2	yes	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
241	C₂³×C₄	—	2	2	no	—
242	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
243	#137	—	2	16	no	—
244	AGL(1,ℤ/8)	—	2	16	no	—
245	#135	—	2	8	no	—
246	#135	—	2	8	no	—
247	C₂×Q₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
248	C₂×SD₁₆	C₂×C₄×C₁₃₁	1	8	yes	—
249	C₂×D₈	C₂×C₄×C₁₃₁	1	4	yes	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	4	no	—
252	C₂×M₁₆	—	2	4	no	—
253	C₂×M₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
254	C₂×M₁₆	D₄×C₁₃₁	1	4	yes	—
255	C₂×M₁₆	D₄×C₁₃₁	1	4	yes	—
256	C₂×M₁₆	C₂³×C₁₃₁	1	4	yes	—
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	2	2	no	—
259	C₂²×C₈	—	2	2	no	—
260	C₂²×C₈	D₄×C₁₃₁	1	4	yes	—
261	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
264	#117	—	2	2	no	—
265	#117	D₄×C₁₃₁	1	4	yes	—
266	C₂×C₄⋊C₄	—	2	1	no	—
267	C₂×C₂²⋊C₄	—	2	1	no	—
268	C₂×C₄²	C₂³×C₁₃₁	1	2	yes	—
269	#108	—	2	8	no	—
270	#104	—	2	16	no	—
271	C₂²⋊C₈	—	2	8	no	—
272	C₂²⋊C₈	—	2	8	no	—
273	#97	—	2	4	no	—
274	C₄×C₈	—	2	4	no	—
275	C₂⁴	—	2	2	no	—
276	C₂⁴	#41×C₁₃₁	1	1	yes	characteristic
277	#41	—	2	8	no	—
278	#41	—	2	8	no	—
279	#41	—	2	4	no	—
280	#41	—	2	4	no	—
281	#41	—	2	4	no	—
282	#41	—	2	4	no	—
283	#41	—	4	4	no	—
284	#41	—	4	4	no	—
285	#41	—	4	4	no	—
286	#41	—	4	4	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	C₂²×C₄×C₁₃₁	1	4	yes	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂×D₄	—	2	4	no	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	C₂²×C₄×C₁₃₁	1	4	yes	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	4	4	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
308	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
310	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
311	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
313	Q₁₆	—	2	8	no	—
314	SD₁₆	—	2	16	no	—
315	D₈	—	2	8	no	—
316	M₁₆	—	2	4	no	—
317	M₁₆	—	2	4	no	—
318	M₁₆	—	4	4	no	—
319	M₁₆	C₂²⋊C₄×C₁₃₁	1	16	yes	—
320	C₂×C₈	—	2	8	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	4	4	no	—
327	C₂×C₈	C₂²×C₄×C₁₃₁	1	4	yes	—
328	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
329	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
330	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
331	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
332	C₄⋊C₄	—	2	4	no	—
333	C₂²⋊C₄	—	2	4	no	—
334	C₄²	—	2	2	no	—
335	C₄²	C₂×D₄×C₁₃₁	1	4	yes	—
336	C₂³	—	2	4	no	—
337	C₂³	—	4	2	no	—
338	C₂³	—	4	8	no	—
339	C₂³	—	4	4	no	—
340	C₂³	C₄×D₄×C₁₃₁	1	2	yes	—
341	C₂³	#121×C₁₃₁	1	2	yes	—
342	C₂³	#124×C₁₃₁	1	2	yes	—
343	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
344	Q₈	—	2	4	no	—
345	Q₈	—	2	4	no	—
346	Q₈	—	4	4	no	—
347	D₄	—	2	4	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	8	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	4	4	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	C₂×C₂²⋊C₄×C₁₃₁	1	4	yes	—
361	C₂×C₄	C₄×D₄×C₁₃₁	1	2	yes	—
362	C₂×C₄	C₄×D₄×C₁₃₁	1	4	yes	—
363	C₂×C₄	#121×C₁₃₁	1	2	yes	—
364	C₂×C₄	#121×C₁₃₁	1	4	yes	—
365	C₂×C₄	#124×C₁₃₁	1	2	yes	—
366	C₂×C₄	#127×C₁₃₁	1	4	yes	—
367	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
369	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
373	C₈	—	2	2	no	—
374	C₈	—	2	2	no	—
375	C₈	—	4	4	no	—
376	C₈	C₂×C₂²⋊C₄×C₁₃₁	1	8	yes	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	8	no	—
383	C₂²	—	8	8	no	—
384	C₂²	#390×C₁₃₁	1	4	yes	—
385	C₂²	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
386	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
387	C₂²	C₂×#124×C₁₃₁	1	1	yes	characteristic
388	C₄	—	4	4	no	—
389	C₄	—	4	4	no	—
390	C₄	#390×C₁₃₁	1	4	yes	—
391	C₄	C₂²×C₂²⋊C₄×C₁₃₁	1	1	yes	characteristic
392	C₄	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
393	C₄	C₂×#121×C₁₃₁	1	1	yes	characteristic
394	C₄	C₂×#127×C₁₃₁	1	1	yes	characteristic
395	C₂	—	2	1	no	—
396	C₂	—	2	4	no	—
397	C₂	—	2	1	no	—
398	C₂	—	8	4	no	—
399	C₂	C₂×#390×C₁₃₁	1	1	yes	characteristic
400	C₂	#2955×C₁₃₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂×C₄×D₄
prime radical	C₂×#575×C₁₃₁	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂³×C₈×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#430×C₁₃₁	C₂	semidirect
3. C₂×#421×C₁₃₁	C₂	semidirect
4. C₂×#408×C₁₃₁	C₂	semidirect
5. C₂×#405×C₁₃₁	C₂	semidirect
6. #1975×C₁₃₁	C₂	semidirect
7. #1974×C₁₃₁	C₂	semidirect
11. C₂×#137×C₁₃₁	C₄	semidirect
12. C₂×AGL(1,ℤ/8)×C₁₃₁	C₄	semidirect
19. C₂×#108×C₁₃₁	C₂²	semidirect
21. C₂×#104×C₁₃₁	C₂²	semidirect
23. #408×C₁₃₁	C₂²	semidirect
24. #408×C₁₃₁	C₂²	semidirect
27. C₂×#97×C₁₃₁	C₂²	semidirect
28. C₂×C₄×C₈×C₁₃₁	C₂²	semidirect
200. #21242	C₁₃₁	direct (N × H)
201. C₁₃₁	#21242	direct (N × H)
203. C₂×#430	C₂×C₁₃₁	semidirect
204. C₂×#421	C₂×C₁₃₁	semidirect
205. C₂×#408	C₂×C₁₃₁	semidirect
206. C₂×#405	C₂×C₁₃₁	semidirect
207. #1975	C₂×C₁₃₁	semidirect
208. #1974	C₂×C₁₃₁	semidirect
212. C₂×#137	C₄×C₁₃₁	semidirect
213. C₂×AGL(1,ℤ/8)	C₄×C₁₃₁	semidirect
220. C₂×#108	C₂²×C₁₃₁	semidirect
222. C₂×#104	C₂²×C₁₃₁	semidirect
224. #408	C₂²×C₁₃₁	semidirect
225. #408	C₂²×C₁₃₁	semidirect
228. C₂×#97	C₂²×C₁₃₁	semidirect
229. C₂×C₄×C₈	C₂²×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#575×C₁₃₁	2
C₂×#430×C₁₃₁	2
C₂×#421×C₁₃₁	2
C₂×#408×C₁₃₁	2
C₂×#405×C₁₃₁	2
#1975×C₁₃₁	2
#1974×C₁₃₁	2
#21242	131

Subgroups — C131×#21242 #45707126

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#21242 #45707126