Subgroups — C₁₃₁×#29860 #45715744

Order 33536.

678 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#488×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3080×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#3040×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2922×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2064×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#2063×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#2052×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#2051×C₁₃₁	C₂	1	2	yes	maximal
9	#1998×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1967×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1848×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×AGL(1,ℤ/8)×C₁₃₁	C₂²	1	1	yes	characteristic
14	C₂×#125×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂×#124×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
17	#488×C₁₃₁	—	2	2	no	—
18	#488×C₁₃₁	—	2	2	no	—
19	#479×C₁₃₁	—	2	2	no	—
20	#478×C₁₃₁	—	2	2	no	—
21	#464×C₁₃₁	—	2	2	no	—
22	#463×C₁₃₁	—	2	2	no	—
23	#433×C₁₃₁	—	2	2	no	—
24	#431×C₁₃₁	—	2	2	no	—
25	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
26	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
27	#428×C₁₃₁	C₂²	1	2	yes	—
28	#424×C₁₃₁	C₂²	1	2	yes	—
29	#423×C₁₃₁	C₂²	1	1	yes	characteristic
30	#423×C₁₃₁	C₂²	1	1	yes	characteristic
31	#419×C₁₃₁	C₂²	1	1	yes	characteristic
32	#418×C₁₃₁	C₂²	1	1	yes	characteristic
33	#417×C₁₃₁	C₂²	1	2	yes	—
34	C₂×#103×C₁₃₁	C₂²	1	2	yes	—
35	C₂×#102×C₁₃₁	C₂²	1	2	yes	—
36	C₂×#101×C₁₃₁	C₂²	1	2	yes	—
37	C₂×#100×C₁₃₁	C₂²	1	2	yes	—
38	#408×C₁₃₁	C₂²	1	2	yes	—
39	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
41	#343×C₁₃₁	C₂²	1	2	yes	—
42	#343×C₁₃₁	C₂²	1	2	yes	—
43	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₁₃₁	C₂³	1	1	yes	characteristic
46	#137×C₁₃₁	—	4	2	no	—
47	AGL(1,ℤ/8)×C₁₃₁	—	4	2	no	—
48	C₂×Q₁₆×C₁₃₁	—	2	1	no	—
49	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
50	C₂×SD₁₆×C₁₃₁	—	2	1	no	—
51	C₂×D₈×C₁₃₁	—	2	1	no	—
52	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
53	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
54	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
57	#125×C₁₃₁	—	2	2	no	—
58	#125×C₁₃₁	—	2	1	no	—
59	#125×C₁₃₁	—	2	1	no	—
60	#124×C₁₃₁	—	2	2	no	—
61	#124×C₁₃₁	—	2	1	no	—
62	#124×C₁₃₁	—	2	1	no	—
63	C₄×Q₈×C₁₃₁	D₄	1	2	yes	—
64	C₄×D₄×C₁₃₁	—	2	2	no	—
65	C₄×D₄×C₁₃₁	D₄	1	2	yes	—
66	#117×C₁₃₁	—	2	1	no	—
67	#117×C₁₃₁	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
69	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₁₃₁	—	2	2	no	—
71	C₂×C₄²×C₁₃₁	—	2	1	no	—
72	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
73	#108×C₁₃₁	—	4	2	no	—
74	#108×C₁₃₁	—	4	2	no	—
75	#107×C₁₃₁	—	2	2	no	—
76	#106×C₁₃₁	—	2	2	no	—
77	C₄⋊C₈×C₁₃₁	—	2	4	no	—
78	C₄⋊C₈×C₁₃₁	—	2	2	no	—
79	C₄⋊C₈×C₁₃₁	—	2	2	no	—
80	#103×C₁₃₁	—	2	2	no	—
81	#103×C₁₃₁	—	2	4	no	—
82	#103×C₁₃₁	—	2	2	no	—
83	#102×C₁₃₁	—	2	2	no	—
84	#102×C₁₃₁	—	2	4	no	—
85	#102×C₁₃₁	—	2	2	no	—
86	#101×C₁₃₁	—	4	2	no	—
87	#100×C₁₃₁	—	4	2	no	—
88	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
89	#97×C₁₃₁	—	2	1	no	—
90	C₄×C₈×C₁₃₁	—	2	1	no	—
91	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
92	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
93	C₂⁴×C₁₃₁	—	2	1	no	—
94	#41×C₁₃₁	—	2	2	no	—
95	#41×C₁₃₁	—	2	2	no	—
96	C₂×Q₈×C₁₃₁	—	2	1	no	—
97	C₂×Q₈×C₁₃₁	—	2	1	no	—
98	C₂×Q₈×C₁₃₁	—	2	2	no	—
99	C₂×Q₈×C₁₃₁	—	2	2	no	—
100	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₁₃₁	—	2	1	no	—
102	C₂×D₄×C₁₃₁	—	2	1	no	—
103	C₂×D₄×C₁₃₁	—	2	1	no	—
104	C₂×D₄×C₁₃₁	—	2	2	no	—
105	C₂×D₄×C₁₃₁	—	2	2	no	—
106	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₃₁	—	2	2	no	—
108	C₂²×C₄×C₁₃₁	—	2	1	no	—
109	C₂²×C₄×C₁₃₁	—	2	1	no	—
110	C₂²×C₄×C₁₃₁	—	2	2	no	—
111	C₂²×C₄×C₁₃₁	#41	1	2	yes	—
112	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
113	Q₁₆×C₁₃₁	—	4	2	no	—
114	SD₁₆×C₁₃₁	—	4	2	no	—
115	SD₁₆×C₁₃₁	—	4	2	no	—
116	D₈×C₁₃₁	—	4	2	no	—
117	M₁₆×C₁₃₁	—	2	2	no	—
118	M₁₆×C₁₃₁	—	2	2	no	—
119	M₁₆×C₁₃₁	—	2	2	no	—
120	M₁₆×C₁₃₁	—	2	2	no	—
121	M₁₆×C₁₃₁	—	2	2	no	—
122	M₁₆×C₁₃₁	—	2	2	no	—
123	C₂×C₈×C₁₃₁	—	2	2	no	—
124	C₂×C₈×C₁₃₁	—	2	2	no	—
125	C₂×C₈×C₁₃₁	—	2	2	no	—
126	C₂×C₈×C₁₃₁	—	2	1	no	—
127	C₂×C₈×C₁₃₁	—	2	2	no	—
128	C₂×C₈×C₁₃₁	—	2	1	no	—
129	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₁₃₁	—	2	2	no	—
131	C₄⋊C₄×C₁₃₁	—	2	2	no	—
132	C₄⋊C₄×C₁₃₁	—	2	2	no	—
133	C₄⋊C₄×C₁₃₁	—	4	2	no	—
134	C₄⋊C₄×C₁₃₁	—	4	2	no	—
135	C₄⋊C₄×C₁₃₁	C₂×D₄	1	2	yes	—
136	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
137	C₂²⋊C₄×C₁₃₁	—	2	2	no	—
138	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
139	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
140	C₄²×C₁₃₁	—	2	2	no	—
141	C₄²×C₁₃₁	—	2	1	no	—
142	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
144	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
145	C₂³×C₁₃₁	—	2	1	no	—
146	C₂³×C₁₃₁	—	4	1	no	—
147	C₂³×C₁₃₁	—	4	2	no	—
148	C₂³×C₁₃₁	—	8	2	no	—
149	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
150	Q₈×C₁₃₁	—	2	1	no	—
151	Q₈×C₁₃₁	—	2	1	no	—
152	Q₈×C₁₃₁	—	4	1	no	—
153	Q₈×C₁₃₁	—	4	1	no	—
154	Q₈×C₁₃₁	—	4	2	no	—
155	D₄×C₁₃₁	—	2	1	no	—
156	D₄×C₁₃₁	—	2	1	no	—
157	D₄×C₁₃₁	—	4	2	no	—
158	D₄×C₁₃₁	—	4	1	no	—
159	D₄×C₁₃₁	—	4	1	no	—
160	D₄×C₁₃₁	—	4	2	no	—
161	C₂×C₄×C₁₃₁	—	2	2	no	—
162	C₂×C₄×C₁₃₁	—	2	1	no	—
163	C₂×C₄×C₁₃₁	—	4	2	no	—
164	C₂×C₄×C₁₃₁	—	4	4	no	—
165	C₂×C₄×C₁₃₁	—	4	2	no	—
166	C₂×C₄×C₁₃₁	—	4	1	no	—
167	C₂×C₄×C₁₃₁	—	4	2	no	—
168	C₂×C₄×C₁₃₁	—	4	2	no	—
169	C₂×C₄×C₁₃₁	—	8	2	no	—
170	C₂×C₄×C₁₃₁	#121	1	2	yes	—
171	C₂×C₄×C₁₃₁	#121	1	2	yes	—
172	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
175	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
176	C₈×C₁₃₁	—	2	4	no	—
177	C₈×C₁₃₁	—	4	2	no	—
178	C₈×C₁₃₁	—	4	1	no	—
179	C₈×C₁₃₁	—	4	1	no	—
180	C₈×C₁₃₁	—	4	2	no	—
181	C₂²×C₁₃₁	—	2	2	no	—
182	C₂²×C₁₃₁	—	4	1	no	—
183	C₂²×C₁₃₁	—	4	2	no	—
184	C₂²×C₁₃₁	—	8	1	no	—
185	C₂²×C₁₃₁	—	8	2	no	—
186	C₂²×C₁₃₁	—	16	2	no	—
187	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
188	C₂²×C₁₃₁	#542	1	2	yes	—
189	C₄×C₁₃₁	—	2	2	no	—
190	C₄×C₁₃₁	—	2	2	no	—
191	C₄×C₁₃₁	—	4	1	no	—
192	C₄×C₁₃₁	—	4	2	no	—
193	C₄×C₁₃₁	—	8	1	no	—
194	C₄×C₁₃₁	—	8	2	no	—
195	C₄×C₁₃₁	#535	1	1	yes	characteristic
196	C₄×C₁₃₁	#536	1	1	yes	characteristic
197	C₄×C₁₃₁	#537	1	2	yes	—
198	C₂×C₁₃₁	—	2	2	no	—
199	C₂×C₁₃₁	—	8	1	no	—
200	C₂×C₁₃₁	—	16	1	no	—
201	C₂×C₁₃₁	#2620	1	1	yes	characteristic
202	C₂×C₁₃₁	#3067	1	2	yes	—
203	#29860	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
204	C₁₃₁	#29860	1	1	yes	characteristic, direct product factor, Sylow
205	C₂×#488	C₂×C₁₃₁	1	1	yes	characteristic, complemented
206	#3080	C₂×C₁₃₁	1	1	yes	characteristic, complemented
207	#3040	C₂×C₁₃₁	1	1	yes	characteristic
208	#2922	C₂×C₁₃₁	1	1	yes	characteristic, complemented
209	#2064	C₂×C₁₃₁	1	2	yes	complemented
210	#2063	C₂×C₁₃₁	1	2	yes	complemented
211	#2052	C₂×C₁₃₁	1	2	yes	complemented
212	#2051	C₂×C₁₃₁	1	2	yes	—
213	#1998	C₂×C₁₃₁	1	1	yes	characteristic, complemented
214	#1967	C₂×C₁₃₁	1	1	yes	characteristic, complemented
215	#1848	C₂×C₁₃₁	1	1	yes	characteristic, complemented
216	C₂×#137	C₂²×C₁₃₁	1	1	yes	characteristic
217	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₁	1	1	yes	characteristic
218	C₂×#125	C₂²×C₁₃₁	1	1	yes	characteristic
219	C₂×#124	C₂²×C₁₃₁	1	1	yes	characteristic
220	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
221	#488	—	2	2	no	—
222	#488	—	2	2	no	—
223	#479	—	2	2	no	—
224	#478	—	2	2	no	—
225	#464	—	2	2	no	—
226	#463	—	2	2	no	—
227	#433	—	2	2	no	—
228	#431	—	2	2	no	—
229	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
230	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
231	#428	C₂²×C₁₃₁	1	2	yes	—
232	#424	C₂²×C₁₃₁	1	2	yes	—
233	#423	C₂²×C₁₃₁	1	1	yes	characteristic
234	#423	C₂²×C₁₃₁	1	1	yes	characteristic
235	#419	C₂²×C₁₃₁	1	1	yes	characteristic
236	#418	C₂²×C₁₃₁	1	1	yes	characteristic
237	#417	C₂²×C₁₃₁	1	2	yes	—
238	C₂×#103	C₂²×C₁₃₁	1	2	yes	—
239	C₂×#102	C₂²×C₁₃₁	1	2	yes	—
240	C₂×#101	C₂²×C₁₃₁	1	2	yes	—
241	C₂×#100	C₂²×C₁₃₁	1	2	yes	—
242	#408	C₂²×C₁₃₁	1	2	yes	—
243	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
244	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
245	#343	C₂²×C₁₃₁	1	2	yes	—
246	#343	C₂²×C₁₃₁	1	2	yes	—
247	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
248	C₂²×Q₈	C₂³×C₁₃₁	1	1	yes	characteristic
249	C₂²×D₄	C₂³×C₁₃₁	1	1	yes	characteristic
250	#137	—	4	2	no	—
251	AGL(1,ℤ/8)	—	4	2	no	—
252	C₂×Q₁₆	—	2	1	no	—
253	C₂×SD₁₆	—	2	1	no	—
254	C₂×SD₁₆	—	2	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
257	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
258	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
259	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
260	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
261	#125	—	2	2	no	—
262	#125	—	2	1	no	—
263	#125	—	2	1	no	—
264	#124	—	2	2	no	—
265	#124	—	2	1	no	—
266	#124	—	2	1	no	—
267	C₄×Q₈	D₄×C₁₃₁	1	2	yes	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	D₄×C₁₃₁	1	2	yes	—
270	#117	—	2	1	no	—
271	#117	C₂³×C₁₃₁	1	1	yes	characteristic
272	C₂×C₄⋊C₄	—	2	2	no	—
273	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₄²	—	2	1	no	—
276	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
277	#108	—	4	2	no	—
278	#108	—	4	2	no	—
279	#107	—	2	2	no	—
280	#106	—	2	2	no	—
281	C₄⋊C₈	—	2	4	no	—
282	C₄⋊C₈	—	2	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	#103	—	2	2	no	—
285	#103	—	2	4	no	—
286	#103	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	4	no	—
289	#102	—	2	2	no	—
290	#101	—	4	2	no	—
291	#100	—	4	2	no	—
292	C₂²⋊C₈	—	2	4	no	—
293	#97	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
296	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
297	C₂⁴	—	2	1	no	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	—	2	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	#41×C₁₃₁	1	2	yes	—
316	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
317	Q₁₆	—	4	2	no	—
318	SD₁₆	—	4	2	no	—
319	SD₁₆	—	4	2	no	—
320	D₈	—	4	2	no	—
321	M₁₆	—	2	2	no	—
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	2	2	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	4	2	no	—
338	C₄⋊C₄	—	4	2	no	—
339	C₄⋊C₄	C₂×D₄×C₁₃₁	1	2	yes	—
340	C₂²⋊C₄	—	2	1	no	—
341	C₂²⋊C₄	—	2	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	1	no	—
346	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
347	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
348	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
349	C₂³	—	2	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	8	2	no	—
353	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
354	Q₈	—	2	1	no	—
355	Q₈	—	2	1	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	4	2	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	1	no	—
363	D₄	—	4	1	no	—
364	D₄	—	4	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	#121×C₁₃₁	1	2	yes	—
375	C₂×C₄	#121×C₁₃₁	1	2	yes	—
376	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
377	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
378	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
379	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
380	C₈	—	2	4	no	—
381	C₈	—	4	1	no	—
382	C₈	—	4	1	no	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	1	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	16	2	no	—
391	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
392	C₂²	#542×C₁₃₁	1	2	yes	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	1	no	—
399	C₄	#535×C₁₃₁	1	1	yes	characteristic
400	C₄	#536×C₁₃₁	1	1	yes	characteristic
401	C₄	#537×C₁₃₁	1	2	yes	—
402	C₂	—	2	2	no	—
403	C₂	—	8	1	no	—
404	C₂	—	16	1	no	—
405	C₂	#2620×C₁₃₁	1	1	yes	characteristic
406	C₂	#3067×C₁₃₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	C₂×AGL(1,ℤ/8)×C₁₃₁	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂×C₄²×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#488×C₁₃₁	C₂	semidirect
2. #3080×C₁₃₁	C₂	semidirect
4. #2922×C₁₃₁	C₂	semidirect
5. #2064×C₁₃₁	C₂	semidirect
6. #2063×C₁₃₁	C₂	semidirect
7. #2052×C₁₃₁	C₂	semidirect
9. #1998×C₁₃₁	C₂	semidirect
10. #1967×C₁₃₁	C₂	semidirect
11. #1848×C₁₃₁	C₂	semidirect
203. #29860	C₁₃₁	direct (N × H)
204. C₁₃₁	#29860	direct (N × H)
205. C₂×#488	C₂×C₁₃₁	semidirect
206. #3080	C₂×C₁₃₁	semidirect
208. #2922	C₂×C₁₃₁	semidirect
209. #2064	C₂×C₁₃₁	semidirect
210. #2063	C₂×C₁₃₁	semidirect
211. #2052	C₂×C₁₃₁	semidirect
213. #1998	C₂×C₁₃₁	semidirect
214. #1967	C₂×C₁₃₁	semidirect
215. #1848	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×#488×C₁₃₁	2
#3080×C₁₃₁	2
#3040×C₁₃₁	2
#2922×C₁₃₁	2
#2064×C₁₃₁	2
#2063×C₁₃₁	2
#2052×C₁₃₁	2
#2051×C₁₃₁	2
#1998×C₁₃₁	2
#1967×C₁₃₁	2
#1848×C₁₃₁	2
#29860	131

Subgroups — C131×#29860 #45715744

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29860 #45715744