Subgroups — C₁₃₁×#29858 #45715742

Order 33536.

736 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#486×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	#3079×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
3	#3038×C₁₃₁	C₂	1	1	yes	maximal, characteristic
4	#2922×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#2063×C₁₃₁	C₂	1	4	yes	maximal, complemented
6	#2051×C₁₃₁	C₂	1	4	yes	maximal, complemented
7	#1997×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1965×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1848×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₁₃₁	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₁₃₁	C₂²	1	1	yes	characteristic
12	C₂×#127×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₄×#41×C₁₃₁	C₂²	1	1	yes	characteristic
14	#486×C₁₃₁	—	2	2	no	—
15	#486×C₁₃₁	—	2	2	no	—
16	#477×C₁₃₁	—	2	1	no	—
17	#476×C₁₃₁	—	2	1	no	—
18	#475×C₁₃₁	—	2	1	no	—
19	#474×C₁₃₁	—	2	1	no	—
20	#460×C₁₃₁	—	2	1	no	—
21	#460×C₁₃₁	—	2	1	no	—
22	#459×C₁₃₁	—	2	1	no	—
23	#459×C₁₃₁	—	2	1	no	—
24	#433×C₁₃₁	—	2	2	no	—
25	#431×C₁₃₁	—	2	2	no	—
26	C₂×#108×C₁₃₁	C₂²	1	4	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	#418×C₁₃₁	C₂²	1	2	yes	—
32	#417×C₁₃₁	C₂²	1	2	yes	—
33	C₂×#102×C₁₃₁	C₂²	1	4	yes	—
34	C₂×#100×C₁₃₁	C₂²	1	4	yes	—
35	#408×C₁₃₁	C₂²	1	2	yes	—
36	C₄×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
38	#343×C₁₃₁	C₂²	1	4	yes	—
39	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
40	C₂²×Q₈×C₁₃₁	—	2	1	no	—
41	C₂²×D₄×C₁₃₁	—	2	1	no	—
42	C₂²×D₄×C₁₃₁	—	2	1	no	—
43	C₂²×D₄×C₁₃₁	C₂³	1	2	yes	—
44	AGL(1,ℤ/8)×C₁₃₁	—	4	4	no	—
45	C₂×SD₁₆×C₁₃₁	—	2	2	no	—
46	C₂×D₈×C₁₃₁	—	2	2	no	—
47	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
48	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
50	C₂²×C₈×C₁₃₁	C₂³	1	2	yes	—
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	#127×C₁₃₁	—	2	1	no	—
56	#127×C₁₃₁	—	2	1	no	—
57	#127×C₁₃₁	—	2	1	no	—
58	#127×C₁₃₁	—	2	1	no	—
59	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
60	C₄×Q₈×C₁₃₁	D₄	1	1	yes	characteristic
61	C₄×D₄×C₁₃₁	—	2	1	no	—
62	C₄×D₄×C₁₃₁	—	2	1	no	—
63	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
64	C₄×D₄×C₁₃₁	D₄	1	1	yes	characteristic
65	#117×C₁₃₁	—	2	1	no	—
66	#117×C₁₃₁	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₁₃₁	—	2	1	no	—
68	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
69	C₂×C₄²×C₁₃₁	—	2	1	no	—
70	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
71	#108×C₁₃₁	—	4	4	no	—
72	#107×C₁₃₁	—	2	2	no	—
73	#106×C₁₃₁	—	2	2	no	—
74	C₄⋊C₈×C₁₃₁	—	2	4	no	—
75	C₄⋊C₈×C₁₃₁	—	2	1	no	—
76	C₄⋊C₈×C₁₃₁	—	2	1	no	—
77	C₄⋊C₈×C₁₃₁	—	2	1	no	—
78	C₄⋊C₈×C₁₃₁	—	2	1	no	—
79	#103×C₁₃₁	—	2	2	no	—
80	#102×C₁₃₁	—	2	2	no	—
81	#102×C₁₃₁	—	2	8	no	—
82	#102×C₁₃₁	—	2	2	no	—
83	#102×C₁₃₁	—	2	2	no	—
84	#100×C₁₃₁	—	4	4	no	—
85	C₂²⋊C₈×C₁₃₁	—	2	4	no	—
86	#97×C₁₃₁	—	2	1	no	—
87	C₄×C₈×C₁₃₁	—	2	1	no	—
88	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
89	C₄×C₈×C₁₃₁	D₄	1	2	yes	—
90	C₂⁴×C₁₃₁	—	2	2	no	—
91	#41×C₁₃₁	—	2	2	no	—
92	#41×C₁₃₁	—	2	2	no	—
93	C₂×Q₈×C₁₃₁	—	4	1	no	—
94	C₂×Q₈×C₁₃₁	—	4	1	no	—
95	C₂×Q₈×C₁₃₁	—	8	2	no	—
96	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₁₃₁	—	2	1	no	—
98	C₂×D₄×C₁₃₁	—	2	2	no	—
99	C₂×D₄×C₁₃₁	—	2	2	no	—
100	C₂×D₄×C₁₃₁	—	2	4	no	—
101	C₂×D₄×C₁₃₁	—	2	4	no	—
102	C₂×D₄×C₁₃₁	—	4	1	no	—
103	C₂×D₄×C₁₃₁	—	4	1	no	—
104	C₂×D₄×C₁₃₁	—	4	1	no	—
105	C₂×D₄×C₁₃₁	—	4	1	no	—
106	C₂×D₄×C₁₃₁	—	8	2	no	—
107	C₂×D₄×C₁₃₁	—	8	2	no	—
108	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₃₁	—	2	1	no	—
110	C₂²×C₄×C₁₃₁	—	2	1	no	—
111	C₂²×C₄×C₁₃₁	—	2	1	no	—
112	C₂²×C₄×C₁₃₁	—	2	2	no	—
113	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₁	#41	1	1	yes	characteristic
115	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
116	SD₁₆×C₁₃₁	—	4	4	no	—
117	D₈×C₁₃₁	—	4	4	no	—
118	M₁₆×C₁₃₁	—	2	2	no	—
119	M₁₆×C₁₃₁	—	2	4	no	—
120	M₁₆×C₁₃₁	—	2	4	no	—
121	M₁₆×C₁₃₁	—	2	2	no	—
122	C₂×C₈×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	2	no	—
127	C₂×C₈×C₁₃₁	C₂×D₄	1	4	yes	—
128	C₄⋊C₄×C₁₃₁	—	2	1	no	—
129	C₄⋊C₄×C₁₃₁	—	2	1	no	—
130	C₄⋊C₄×C₁₃₁	—	2	2	no	—
131	C₄⋊C₄×C₁₃₁	—	2	2	no	—
132	C₄⋊C₄×C₁₃₁	—	4	1	no	—
133	C₄⋊C₄×C₁₃₁	—	4	1	no	—
134	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
135	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
136	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
137	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
138	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
139	C₄²×C₁₃₁	—	2	1	no	—
140	C₄²×C₁₃₁	—	2	1	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	1	yes	characteristic
145	C₄²×C₁₃₁	C₂×D₄	1	1	yes	characteristic
146	C₂³×C₁₃₁	—	2	1	no	—
147	C₂³×C₁₃₁	—	4	2	no	—
148	C₂³×C₁₃₁	—	4	4	no	—
149	C₂³×C₁₃₁	—	8	2	no	—
150	C₂³×C₁₃₁	—	8	2	no	—
151	C₂³×C₁₃₁	C₂×#41	1	1	yes	characteristic
152	Q₈×C₁₃₁	—	2	1	no	—
153	Q₈×C₁₃₁	—	2	1	no	—
154	Q₈×C₁₃₁	—	8	2	no	—
155	Q₈×C₁₃₁	—	8	2	no	—
156	D₄×C₁₃₁	—	2	1	no	—
157	D₄×C₁₃₁	—	2	1	no	—
158	D₄×C₁₃₁	—	4	2	no	—
159	D₄×C₁₃₁	—	4	2	no	—
160	D₄×C₁₃₁	—	4	2	no	—
161	D₄×C₁₃₁	—	4	4	no	—
162	D₄×C₁₃₁	—	8	2	no	—
163	D₄×C₁₃₁	—	8	2	no	—
164	D₄×C₁₃₁	—	8	2	no	—
165	D₄×C₁₃₁	—	8	2	no	—
166	C₂×C₄×C₁₃₁	—	2	2	no	—
167	C₂×C₄×C₁₃₁	—	2	2	no	—
168	C₂×C₄×C₁₃₁	—	2	1	no	—
169	C₂×C₄×C₁₃₁	—	2	1	no	—
170	C₂×C₄×C₁₃₁	—	2	1	no	—
171	C₂×C₄×C₁₃₁	—	4	2	no	—
172	C₂×C₄×C₁₃₁	—	4	2	no	—
173	C₂×C₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	4	2	no	—
175	C₂×C₄×C₁₃₁	—	8	2	no	—
176	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
177	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
178	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₃₁	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	2	yes	—
183	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	2	yes	—
184	C₈×C₁₃₁	—	2	4	no	—
185	C₈×C₁₃₁	—	4	2	no	—
186	C₈×C₁₃₁	—	4	2	no	—
187	C₈×C₁₃₁	—	4	2	no	—
188	C₂²×C₁₃₁	—	2	1	no	—
189	C₂²×C₁₃₁	—	2	1	no	—
190	C₂²×C₁₃₁	—	4	1	no	—
191	C₂²×C₁₃₁	—	4	1	no	—
192	C₂²×C₁₃₁	—	4	1	no	—
193	C₂²×C₁₃₁	—	8	2	no	—
194	C₂²×C₁₃₁	—	8	2	no	—
195	C₂²×C₁₃₁	—	8	2	no	—
196	C₂²×C₁₃₁	—	16	4	no	—
197	C₂²×C₁₃₁	C₂×#121	1	1	yes	characteristic
198	C₂²×C₁₃₁	#542	1	2	yes	—
199	C₄×C₁₃₁	—	2	1	no	—
200	C₄×C₁₃₁	—	2	1	no	—
201	C₄×C₁₃₁	—	4	1	no	—
202	C₄×C₁₃₁	—	4	1	no	—
203	C₄×C₁₃₁	—	4	1	no	—
204	C₄×C₁₃₁	—	8	2	no	—
205	C₄×C₁₃₁	#471	1	2	yes	—
206	C₄×C₁₃₁	#472	1	2	yes	—
207	C₄×C₁₃₁	#535	1	1	yes	characteristic
208	C₄×C₁₃₁	#536	1	1	yes	characteristic
209	C₄×C₁₃₁	#537	1	2	yes	—
210	C₂×C₁₃₁	—	2	2	no	—
211	C₂×C₁₃₁	—	8	1	no	—
212	C₂×C₁₃₁	—	16	2	no	—
213	C₂×C₁₃₁	#2620	1	1	yes	characteristic
214	C₂×C₁₃₁	C₂×#471	1	1	yes	characteristic
215	C₂×C₁₃₁	C₂×#472	1	1	yes	characteristic
216	#29858	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₁₃₁	#29858	1	1	yes	characteristic, direct product factor, Sylow
218	C₂×#486	C₂×C₁₃₁	1	1	yes	characteristic, complemented
219	#3079	C₂×C₁₃₁	1	1	yes	characteristic, complemented
220	#3038	C₂×C₁₃₁	1	1	yes	characteristic
221	#2922	C₂×C₁₃₁	1	1	yes	characteristic, complemented
222	#2063	C₂×C₁₃₁	1	4	yes	complemented
223	#2051	C₂×C₁₃₁	1	4	yes	complemented
224	#1997	C₂×C₁₃₁	1	1	yes	characteristic, complemented
225	#1965	C₂×C₁₃₁	1	1	yes	characteristic, complemented
226	#1848	C₂×C₁₃₁	1	1	yes	characteristic, complemented
227	C₂×AGL(1,ℤ/8)	C₂²×C₁₃₁	1	2	yes	—
228	C₂×C₄⋊Q₈	C₂²×C₁₃₁	1	1	yes	characteristic
229	C₂×#127	C₂²×C₁₃₁	1	1	yes	characteristic
230	C₄×#41	C₂²×C₁₃₁	1	1	yes	characteristic
231	#486	—	2	2	no	—
232	#486	—	2	2	no	—
233	#477	—	2	1	no	—
234	#476	—	2	1	no	—
235	#475	—	2	1	no	—
236	#474	—	2	1	no	—
237	#460	—	2	1	no	—
238	#460	—	2	1	no	—
239	#459	—	2	1	no	—
240	#459	—	2	1	no	—
241	#433	—	2	2	no	—
242	#431	—	2	2	no	—
243	C₂×#108	C₂²×C₁₃₁	1	4	yes	—
244	#428	C₂²×C₁₃₁	1	2	yes	—
245	#424	C₂²×C₁₃₁	1	2	yes	—
246	#423	C₂²×C₁₃₁	1	1	yes	characteristic
247	#423	C₂²×C₁₃₁	1	1	yes	characteristic
248	#418	C₂²×C₁₃₁	1	2	yes	—
249	#417	C₂²×C₁₃₁	1	2	yes	—
250	C₂×#102	C₂²×C₁₃₁	1	4	yes	—
251	C₂×#100	C₂²×C₁₃₁	1	4	yes	—
252	#408	C₂²×C₁₃₁	1	2	yes	—
253	C₄×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
254	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
255	#343	C₂²×C₁₃₁	1	4	yes	—
256	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×D₄	—	2	1	no	—
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	C₂³×C₁₃₁	1	2	yes	—
261	AGL(1,ℤ/8)	—	4	4	no	—
262	C₂×SD₁₆	—	2	2	no	—
263	C₂×D₈	—	2	2	no	—
264	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
265	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
266	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
267	C₂²×C₈	C₂³×C₁₃₁	1	2	yes	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	#127	—	2	1	no	—
273	#127	—	2	1	no	—
274	#127	—	2	1	no	—
275	#127	—	2	1	no	—
276	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
277	C₄×Q₈	D₄×C₁₃₁	1	1	yes	characteristic
278	C₄×D₄	—	2	1	no	—
279	C₄×D₄	—	2	1	no	—
280	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
281	C₄×D₄	D₄×C₁₃₁	1	1	yes	characteristic
282	#117	—	2	1	no	—
283	#117	C₂³×C₁₃₁	1	1	yes	characteristic
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
288	#108	—	4	4	no	—
289	#107	—	2	2	no	—
290	#106	—	2	2	no	—
291	C₄⋊C₈	—	2	4	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	2	1	no	—
296	#103	—	2	2	no	—
297	#102	—	2	2	no	—
298	#102	—	2	8	no	—
299	#102	—	2	2	no	—
300	#102	—	2	2	no	—
301	#100	—	4	4	no	—
302	C₂²⋊C₈	—	2	4	no	—
303	#97	—	2	1	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
306	C₄×C₈	D₄×C₁₃₁	1	2	yes	—
307	C₂⁴	—	2	2	no	—
308	#41	—	2	2	no	—
309	#41	—	2	2	no	—
310	C₂×Q₈	—	4	1	no	—
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	—	8	2	no	—
313	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
314	C₂×D₄	—	2	1	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	4	1	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	1	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	8	2	no	—
324	C₂×D₄	—	8	2	no	—
325	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
331	C₂²×C₄	#41×C₁₃₁	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
333	SD₁₆	—	4	4	no	—
334	D₈	—	4	4	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	—	2	4	no	—
337	M₁₆	—	2	4	no	—
338	M₁₆	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	C₂×D₄×C₁₃₁	1	4	yes	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	1	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
352	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
360	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
361	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
362	C₄²	C₂×D₄×C₁₃₁	1	1	yes	characteristic
363	C₂³	—	2	1	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	8	2	no	—
367	C₂³	—	8	2	no	—
368	C₂³	C₂×#41×C₁₃₁	1	1	yes	characteristic
369	Q₈	—	2	1	no	—
370	Q₈	—	2	1	no	—
371	Q₈	—	8	2	no	—
372	Q₈	—	8	2	no	—
373	D₄	—	2	1	no	—
374	D₄	—	2	1	no	—
375	D₄	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	4	no	—
379	D₄	—	8	2	no	—
380	D₄	—	8	2	no	—
381	D₄	—	8	2	no	—
382	D₄	—	8	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	8	2	no	—
393	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
394	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
395	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
396	C₂×C₄	#121×C₁₃₁	1	1	yes	characteristic
397	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
399	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	2	yes	—
400	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	2	yes	—
401	C₈	—	2	4	no	—
402	C₈	—	4	2	no	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	4	1	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	—	16	4	no	—
414	C₂²	C₂×#121×C₁₃₁	1	1	yes	characteristic
415	C₂²	#542×C₁₃₁	1	2	yes	—
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	8	2	no	—
422	C₄	#471×C₁₃₁	1	2	yes	—
423	C₄	#472×C₁₃₁	1	2	yes	—
424	C₄	#535×C₁₃₁	1	1	yes	characteristic
425	C₄	#536×C₁₃₁	1	1	yes	characteristic
426	C₄	#537×C₁₃₁	1	2	yes	—
427	C₂	—	2	2	no	—
428	C₂	—	8	1	no	—
429	C₂	—	16	2	no	—
430	C₂	#2620×C₁₃₁	1	1	yes	characteristic
431	C₂	C₂×#471×C₁₃₁	1	1	yes	characteristic
432	C₂	C₂×#472×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	#3038×C₁₃₁	C₂
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×#486×C₁₃₁	C₂	semidirect
2. #3079×C₁₃₁	C₂	semidirect
4. #2922×C₁₃₁	C₂	semidirect
5. #2063×C₁₃₁	C₂	semidirect
6. #2051×C₁₃₁	C₂	semidirect
7. #1997×C₁₃₁	C₂	semidirect
8. #1965×C₁₃₁	C₂	semidirect
9. #1848×C₁₃₁	C₂	semidirect
216. #29858	C₁₃₁	direct (N × H)
217. C₁₃₁	#29858	direct (N × H)
218. C₂×#486	C₂×C₁₃₁	semidirect
219. #3079	C₂×C₁₃₁	semidirect
221. #2922	C₂×C₁₃₁	semidirect
222. #2063	C₂×C₁₃₁	semidirect
223. #2051	C₂×C₁₃₁	semidirect
224. #1997	C₂×C₁₃₁	semidirect
225. #1965	C₂×C₁₃₁	semidirect
226. #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×#486×C₁₃₁	2
#3079×C₁₃₁	2
#3038×C₁₃₁	2
#2922×C₁₃₁	2
#2063×C₁₃₁	2
#2051×C₁₃₁	2
#1997×C₁₃₁	2
#1965×C₁₃₁	2
#1848×C₁₃₁	2
#29858	131

Subgroups — C131×#29858 #45715742

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#29858 #45715742