Subgroups — C₁₃₁×#25052 #45710936

Order 33536.

720 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3099×C₁₃₁	C₂	1	2	yes	maximal, complemented
2	#3061×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	#2951×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#2079×C₁₃₁	C₂	1	2	yes	maximal, complemented
5	#2040×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1974×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
7	#1952×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
8	#1860×C₁₃₁	C₂	1	2	yes	maximal, complemented
9	#1846×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1816×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1764×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₃₁	C₂²	1	1	yes	characteristic
13	C₂×#131×C₁₃₁	C₂²	1	1	yes	characteristic
14	#537×C₁₃₁	C₂²	1	2	yes	—
15	#520×C₁₃₁	C₂²	1	2	yes	—
16	#485×C₁₃₁	—	2	2	no	—
17	#483×C₁₃₁	—	2	2	no	—
18	#482×C₁₃₁	—	2	2	no	—
19	#481×C₁₃₁	—	2	2	no	—
20	#468×C₁₃₁	—	2	2	no	—
21	#467×C₁₃₁	—	2	1	no	—
22	#466×C₁₃₁	—	2	1	no	—
23	#440×C₁₃₁	—	2	2	no	—
24	C₄×Q₁₆×C₁₃₁	—	2	1	no	—
25	C₄×D₈×C₁₃₁	—	2	1	no	—
26	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
27	#428×C₁₃₁	C₂²	1	2	yes	—
28	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
29	C₂×#107×C₁₃₁	C₂²	1	1	yes	characteristic
30	C₂×#106×C₁₃₁	C₂²	1	2	yes	—
31	C₂×#104×C₁₃₁	C₂²	1	2	yes	—
32	C₂×#104×C₁₃₁	C₂²	1	1	yes	characteristic
33	#417×C₁₃₁	C₂²	1	2	yes	—
34	#417×C₁₃₁	C₂²	1	2	yes	—
35	#417×C₁₃₁	C₂²	1	2	yes	—
36	#416×C₁₃₁	C₂²	1	1	yes	characteristic
37	#408×C₁₃₁	C₂²	1	2	yes	—
38	#405×C₁₃₁	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
40	#382×C₁₃₁	C₂²	1	2	yes	—
41	#343×C₁₃₁	C₂²	1	2	yes	—
42	#343×C₁₃₁	C₂²	1	2	yes	—
43	#341×C₁₃₁	C₂²	1	1	yes	characteristic
44	#339×C₁₃₁	C₂²	1	1	yes	characteristic
45	C₂×#41×C₁₃₁	C₂³	1	2	yes	—
46	C₂×#41×C₁₃₁	C₂³	1	1	yes	characteristic
47	#135×C₁₃₁	—	2	2	no	—
48	#135×C₁₃₁	—	2	2	no	—
49	C₂×Q₁₆×C₁₃₁	D₄	1	1	yes	characteristic
50	C₂×SD₁₆×C₁₃₁	D₄	1	2	yes	—
51	C₂×D₈×C₁₃₁	D₄	1	1	yes	characteristic
52	#131×C₁₃₁	—	2	2	no	—
53	#131×C₁₃₁	—	2	2	no	—
54	C₂×M₁₆×C₁₃₁	—	2	1	no	—
55	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
56	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₁₃₁	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₁₃₁	—	2	1	no	—
59	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
61	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
62	C₂²⋊Q₈×C₁₃₁	—	2	2	no	—
63	#121×C₁₃₁	—	2	2	no	—
64	#121×C₁₃₁	—	2	2	no	—
65	#121×C₁₃₁	—	4	2	no	—
66	C₄×Q₈×C₁₃₁	—	2	2	no	—
67	C₄×D₄×C₁₃₁	—	2	2	no	—
68	C₄×D₄×C₁₃₁	—	4	2	no	—
69	#117×C₁₃₁	—	2	2	no	—
70	#117×C₁₃₁	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₁₃₁	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₃₁	C₂³	1	2	yes	—
74	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
75	#108×C₁₃₁	—	2	2	no	—
76	#107×C₁₃₁	—	2	1	no	—
77	#107×C₁₃₁	—	2	1	no	—
78	#107×C₁₃₁	—	2	1	no	—
79	#107×C₁₃₁	—	2	1	no	—
80	#107×C₁₃₁	—	2	2	no	—
81	#106×C₁₃₁	—	2	2	no	—
82	#106×C₁₃₁	—	2	2	no	—
83	#106×C₁₃₁	—	2	2	no	—
84	#104×C₁₃₁	—	2	4	no	—
85	#104×C₁₃₁	—	2	2	no	—
86	#103×C₁₃₁	—	2	2	no	—
87	#103×C₁₃₁	—	2	2	no	—
88	#103×C₁₃₁	—	2	2	no	—
89	#103×C₁₃₁	D₄	1	1	yes	characteristic
90	#103×C₁₃₁	D₄	1	1	yes	characteristic
91	#102×C₁₃₁	—	2	2	no	—
92	#102×C₁₃₁	—	2	2	no	—
93	#102×C₁₃₁	—	2	2	no	—
94	#102×C₁₃₁	D₄	1	1	yes	characteristic
95	#102×C₁₃₁	D₄	1	1	yes	characteristic
96	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
97	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
98	#97×C₁₃₁	—	2	1	no	—
99	C₄×C₈×C₁₃₁	—	2	1	no	—
100	C₄×C₈×C₁₃₁	—	2	2	no	—
101	#95×C₁₃₁	—	4	2	no	—
102	#41×C₁₃₁	—	2	2	no	—
103	#41×C₁₃₁	—	2	1	no	—
104	#41×C₁₃₁	—	2	1	no	—
105	#41×C₁₃₁	—	2	1	no	—
106	#41×C₁₃₁	—	2	2	no	—
107	#41×C₁₃₁	—	2	2	no	—
108	#41×C₁₃₁	—	2	2	no	—
109	#41×C₁₃₁	—	2	1	no	—
110	C₂×Q₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
111	C₂×Q₈×C₁₃₁	C₂×D₄	1	2	yes	—
112	C₂×D₄×C₁₃₁	—	2	2	no	—
113	C₂×D₄×C₁₃₁	—	2	1	no	—
114	C₂×D₄×C₁₃₁	—	4	2	no	—
115	C₂×D₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₁₃₁	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₁₃₁	—	2	1	no	—
118	C₂²×C₄×C₁₃₁	—	2	2	no	—
119	C₂²×C₄×C₁₃₁	—	2	1	no	—
120	C₂²×C₄×C₁₃₁	—	2	2	no	—
121	C₂²×C₄×C₁₃₁	—	2	2	no	—
122	C₂²×C₄×C₁₃₁	—	4	2	no	—
123	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₁₃₁	—	2	2	no	—
125	SD₁₆×C₁₃₁	—	2	4	no	—
126	D₈×C₁₃₁	—	2	2	no	—
127	M₁₆×C₁₃₁	—	2	2	no	—
128	M₁₆×C₁₃₁	—	2	1	no	—
129	M₁₆×C₁₃₁	—	2	2	no	—
130	M₁₆×C₁₃₁	—	2	1	no	—
131	M₁₆×C₁₃₁	—	2	1	no	—
132	M₁₆×C₁₃₁	—	2	1	no	—
133	M₁₆×C₁₃₁	—	4	2	no	—
134	C₂×C₈×C₁₃₁	—	2	1	no	—
135	C₂×C₈×C₁₃₁	—	2	1	no	—
136	C₂×C₈×C₁₃₁	—	2	1	no	—
137	C₂×C₈×C₁₃₁	—	2	2	no	—
138	C₂×C₈×C₁₃₁	—	2	1	no	—
139	C₂×C₈×C₁₃₁	—	4	2	no	—
140	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₁₃₁	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₁₃₁	#41	1	2	yes	—
145	C₂×C₈×C₁₃₁	#41	1	2	yes	—
146	C₄⋊C₄×C₁₃₁	—	2	2	no	—
147	C₄⋊C₄×C₁₃₁	—	2	2	no	—
148	C₄⋊C₄×C₁₃₁	—	2	2	no	—
149	C₄⋊C₄×C₁₃₁	—	2	2	no	—
150	C₄⋊C₄×C₁₃₁	—	4	2	no	—
151	C₄⋊C₄×C₁₃₁	—	4	2	no	—
152	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
153	C₄⋊C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
154	C₂²⋊C₄×C₁₃₁	—	2	1	no	—
155	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
156	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
157	C₂²⋊C₄×C₁₃₁	—	4	2	no	—
158	C₄²×C₁₃₁	—	2	1	no	—
159	C₄²×C₁₃₁	—	2	1	no	—
160	C₄²×C₁₃₁	—	4	2	no	—
161	C₄²×C₁₃₁	#41	1	2	yes	—
162	C₂³×C₁₃₁	—	2	2	no	—
163	C₂³×C₁₃₁	—	2	1	no	—
164	C₂³×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
165	Q₈×C₁₃₁	—	2	2	no	—
166	Q₈×C₁₃₁	—	2	1	no	—
167	Q₈×C₁₃₁	—	2	1	no	—
168	Q₈×C₁₃₁	—	2	2	no	—
169	D₄×C₁₃₁	—	2	2	no	—
170	D₄×C₁₃₁	—	2	1	no	—
171	D₄×C₁₃₁	—	2	1	no	—
172	D₄×C₁₃₁	—	2	2	no	—
173	D₄×C₁₃₁	—	4	2	no	—
174	D₄×C₁₃₁	—	4	1	no	—
175	D₄×C₁₃₁	—	4	2	no	—
176	D₄×C₁₃₁	—	4	1	no	—
177	D₄×C₁₃₁	—	16	2	no	—
178	C₂×C₄×C₁₃₁	—	2	1	no	—
179	C₂×C₄×C₁₃₁	—	2	1	no	—
180	C₂×C₄×C₁₃₁	—	2	2	no	—
181	C₂×C₄×C₁₃₁	—	2	1	no	—
182	C₂×C₄×C₁₃₁	—	2	2	no	—
183	C₂×C₄×C₁₃₁	—	4	1	no	—
184	C₂×C₄×C₁₃₁	—	4	1	no	—
185	C₂×C₄×C₁₃₁	—	4	1	no	—
186	C₂×C₄×C₁₃₁	—	4	2	no	—
187	C₂×C₄×C₁₃₁	—	4	2	no	—
188	C₂×C₄×C₁₃₁	—	4	1	no	—
189	C₂×C₄×C₁₃₁	—	4	2	no	—
190	C₂×C₄×C₁₃₁	—	4	2	no	—
191	C₂×C₄×C₁₃₁	—	8	2	no	—
192	C₂×C₄×C₁₃₁	—	8	2	no	—
193	C₂×C₄×C₁₃₁	—	16	2	no	—
194	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
200	C₈×C₁₃₁	—	2	1	no	—
201	C₈×C₁₃₁	—	2	1	no	—
202	C₈×C₁₃₁	—	4	1	no	—
203	C₈×C₁₃₁	—	4	2	no	—
204	C₈×C₁₃₁	—	4	1	no	—
205	C₈×C₁₃₁	#123	1	2	yes	—
206	C₈×C₁₃₁	#123	1	2	yes	—
207	C₂²×C₁₃₁	—	2	1	no	—
208	C₂²×C₁₃₁	—	2	1	no	—
209	C₂²×C₁₃₁	—	4	1	no	—
210	C₂²×C₁₃₁	—	4	2	no	—
211	C₂²×C₁₃₁	—	4	2	no	—
212	C₂²×C₁₃₁	—	4	1	no	—
213	C₂²×C₁₃₁	—	4	2	no	—
214	C₂²×C₁₃₁	—	4	1	no	—
215	C₂²×C₁₃₁	#542	1	1	yes	characteristic
216	C₂²×C₁₃₁	D₄²	1	1	yes	characteristic
217	C₂²×C₁₃₁	#553	1	1	yes	characteristic
218	C₄×C₁₃₁	—	4	2	no	—
219	C₄×C₁₃₁	—	4	2	no	—
220	C₄×C₁₃₁	—	4	1	no	—
221	C₄×C₁₃₁	—	4	1	no	—
222	C₄×C₁₃₁	—	4	1	no	—
223	C₄×C₁₃₁	—	8	2	no	—
224	C₄×C₁₃₁	—	8	2	no	—
225	C₄×C₁₃₁	C₂×#123	1	1	yes	characteristic
226	C₄×C₁₃₁	#532	1	1	yes	characteristic
227	C₄×C₁₃₁	#547	1	1	yes	characteristic
228	C₄×C₁₃₁	#547	1	1	yes	characteristic
229	C₂×C₁₃₁	—	2	1	no	—
230	C₂×C₁₃₁	—	2	1	no	—
231	C₂×C₁₃₁	—	8	2	no	—
232	C₂×C₁₃₁	—	8	1	no	—
233	C₂×C₁₃₁	#2422	1	1	yes	characteristic
234	C₂×C₁₃₁	#3290	1	1	yes	characteristic
235	C₂×C₁₃₁	#3290	1	1	yes	characteristic
236	#25052	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₁₃₁	#25052	1	1	yes	characteristic, direct product factor, Sylow
238	#3099	C₂×C₁₃₁	1	2	yes	complemented
239	#3061	C₂×C₁₃₁	1	1	yes	characteristic
240	#2951	C₂×C₁₃₁	1	1	yes	characteristic, complemented
241	#2079	C₂×C₁₃₁	1	2	yes	complemented
242	#2040	C₂×C₁₃₁	1	2	yes	complemented
243	#1974	C₂×C₁₃₁	1	1	yes	characteristic, complemented
244	#1952	C₂×C₁₃₁	1	1	yes	characteristic, complemented
245	#1860	C₂×C₁₃₁	1	2	yes	complemented
246	#1846	C₂×C₁₃₁	1	1	yes	characteristic, complemented
247	#1816	C₂×C₁₃₁	1	1	yes	characteristic, complemented
248	#1764	C₂×C₁₃₁	1	1	yes	characteristic, complemented
249	C₂×#135	C₂²×C₁₃₁	1	1	yes	characteristic
250	C₂×#131	C₂²×C₁₃₁	1	1	yes	characteristic
251	#537	C₂²×C₁₃₁	1	2	yes	—
252	#520	C₂²×C₁₃₁	1	2	yes	—
253	#485	—	2	2	no	—
254	#483	—	2	2	no	—
255	#482	—	2	2	no	—
256	#481	—	2	2	no	—
257	#468	—	2	2	no	—
258	#467	—	2	1	no	—
259	#466	—	2	1	no	—
260	#440	—	2	2	no	—
261	C₄×Q₁₆	—	2	1	no	—
262	C₄×D₈	—	2	1	no	—
263	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
264	#428	C₂²×C₁₃₁	1	2	yes	—
265	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
266	C₂×#107	C₂²×C₁₃₁	1	1	yes	characteristic
267	C₂×#106	C₂²×C₁₃₁	1	2	yes	—
268	C₂×#104	C₂²×C₁₃₁	1	2	yes	—
269	C₂×#104	C₂²×C₁₃₁	1	1	yes	characteristic
270	#417	C₂²×C₁₃₁	1	2	yes	—
271	#417	C₂²×C₁₃₁	1	2	yes	—
272	#417	C₂²×C₁₃₁	1	2	yes	—
273	#416	C₂²×C₁₃₁	1	1	yes	characteristic
274	#408	C₂²×C₁₃₁	1	2	yes	—
275	#405	C₂²×C₁₃₁	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
277	#382	C₂²×C₁₃₁	1	2	yes	—
278	#343	C₂²×C₁₃₁	1	2	yes	—
279	#343	C₂²×C₁₃₁	1	2	yes	—
280	#341	C₂²×C₁₃₁	1	1	yes	characteristic
281	#339	C₂²×C₁₃₁	1	1	yes	characteristic
282	C₂×#41	C₂³×C₁₃₁	1	2	yes	—
283	C₂×#41	C₂³×C₁₃₁	1	1	yes	characteristic
284	#135	—	2	2	no	—
285	#135	—	2	2	no	—
286	C₂×Q₁₆	D₄×C₁₃₁	1	1	yes	characteristic
287	C₂×SD₁₆	D₄×C₁₃₁	1	2	yes	—
288	C₂×D₈	D₄×C₁₃₁	1	1	yes	characteristic
289	#131	—	2	2	no	—
290	#131	—	2	2	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
293	C₂×M₁₆	C₂³×C₁₃₁	1	1	yes	characteristic
294	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
295	C₂²×C₈	—	2	1	no	—
296	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	—	2	2	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	#121	—	4	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×D₄	—	2	2	no	—
305	C₄×D₄	—	4	2	no	—
306	#117	—	2	2	no	—
307	#117	C₂³×C₁₃₁	1	1	yes	characteristic
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₁₃₁	1	2	yes	—
311	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
312	#108	—	2	2	no	—
313	#107	—	2	1	no	—
314	#107	—	2	1	no	—
315	#107	—	2	1	no	—
316	#107	—	2	1	no	—
317	#107	—	2	2	no	—
318	#106	—	2	2	no	—
319	#106	—	2	2	no	—
320	#106	—	2	2	no	—
321	#104	—	2	4	no	—
322	#104	—	2	2	no	—
323	#103	—	2	2	no	—
324	#103	—	2	2	no	—
325	#103	—	2	2	no	—
326	#103	D₄×C₁₃₁	1	1	yes	characteristic
327	#103	D₄×C₁₃₁	1	1	yes	characteristic
328	#102	—	2	2	no	—
329	#102	—	2	2	no	—
330	#102	—	2	2	no	—
331	#102	D₄×C₁₃₁	1	1	yes	characteristic
332	#102	D₄×C₁₃₁	1	1	yes	characteristic
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	#97	—	2	1	no	—
336	C₄×C₈	—	2	1	no	—
337	C₄×C₈	—	2	2	no	—
338	#95	—	4	2	no	—
339	#41	—	2	2	no	—
340	#41	—	2	1	no	—
341	#41	—	2	1	no	—
342	#41	—	2	1	no	—
343	#41	—	2	2	no	—
344	#41	—	2	2	no	—
345	#41	—	2	2	no	—
346	#41	—	2	1	no	—
347	C₂×Q₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
348	C₂×Q₈	C₂×D₄×C₁₃₁	1	2	yes	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
353	C₂×D₄	C₂×D₄×C₁₃₁	1	2	yes	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
361	Q₁₆	—	2	2	no	—
362	SD₁₆	—	2	4	no	—
363	D₈	—	2	2	no	—
364	M₁₆	—	2	2	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	2	1	no	—
368	M₁₆	—	2	1	no	—
369	M₁₆	—	2	1	no	—
370	M₁₆	—	4	2	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	4	2	no	—
377	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
378	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
379	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
380	C₂×C₈	C₂×D₄×C₁₃₁	1	1	yes	characteristic
381	C₂×C₈	#41×C₁₃₁	1	2	yes	—
382	C₂×C₈	#41×C₁₃₁	1	2	yes	—
383	C₄⋊C₄	—	2	2	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
390	C₄⋊C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₄²	—	2	1	no	—
396	C₄²	—	2	1	no	—
397	C₄²	—	4	2	no	—
398	C₄²	#41×C₁₃₁	1	2	yes	—
399	C₂³	—	2	2	no	—
400	C₂³	—	2	1	no	—
401	C₂³	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
402	Q₈	—	2	2	no	—
403	Q₈	—	2	1	no	—
404	Q₈	—	2	1	no	—
405	Q₈	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	2	1	no	—
408	D₄	—	2	1	no	—
409	D₄	—	2	2	no	—
410	D₄	—	4	2	no	—
411	D₄	—	4	1	no	—
412	D₄	—	4	2	no	—
413	D₄	—	4	1	no	—
414	D₄	—	16	2	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	—	16	2	no	—
431	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
433	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
436	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
437	C₈	—	2	1	no	—
438	C₈	—	2	1	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	2	no	—
441	C₈	—	4	1	no	—
442	C₈	#123×C₁₃₁	1	2	yes	—
443	C₈	#123×C₁₃₁	1	2	yes	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	4	2	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	2	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	#542×C₁₃₁	1	1	yes	characteristic
453	C₂²	D₄²×C₁₃₁	1	1	yes	characteristic
454	C₂²	#553×C₁₃₁	1	1	yes	characteristic
455	C₄	—	4	2	no	—
456	C₄	—	4	1	no	—
457	C₄	—	4	1	no	—
458	C₄	—	4	2	no	—
459	C₄	—	4	1	no	—
460	C₄	—	8	2	no	—
461	C₄	—	8	2	no	—
462	C₄	C₂×#123×C₁₃₁	1	1	yes	characteristic
463	C₄	#532×C₁₃₁	1	1	yes	characteristic
464	C₄	#547×C₁₃₁	1	1	yes	characteristic
465	C₄	#547×C₁₃₁	1	1	yes	characteristic
466	C₂	—	2	1	no	—
467	C₂	—	2	1	no	—
468	C₂	—	8	2	no	—
469	C₂	—	8	1	no	—
470	C₂	#2422×C₁₃₁	1	1	yes	characteristic
471	C₂	#3290×C₁₃₁	1	1	yes	characteristic
472	C₂	#3290×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₃₁	D₄²
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
prime radical	#3061×C₁₃₁	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃₁ ◁ C₂²×C₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. #3099×C₁₃₁	C₂	semidirect
3. #2951×C₁₃₁	C₂	semidirect
4. #2079×C₁₃₁	C₂	semidirect
5. #2040×C₁₃₁	C₂	semidirect
6. #1974×C₁₃₁	C₂	semidirect
7. #1952×C₁₃₁	C₂	semidirect
8. #1860×C₁₃₁	C₂	semidirect
9. #1846×C₁₃₁	C₂	semidirect
10. #1816×C₁₃₁	C₂	semidirect
11. #1764×C₁₃₁	C₂	semidirect
236. #25052	C₁₃₁	direct (N × H)
237. C₁₃₁	#25052	direct (N × H)
238. #3099	C₂×C₁₃₁	semidirect
240. #2951	C₂×C₁₃₁	semidirect
241. #2079	C₂×C₁₃₁	semidirect
242. #2040	C₂×C₁₃₁	semidirect
243. #1974	C₂×C₁₃₁	semidirect
244. #1952	C₂×C₁₃₁	semidirect
245. #1860	C₂×C₁₃₁	semidirect
246. #1846	C₂×C₁₃₁	semidirect
247. #1816	C₂×C₁₃₁	semidirect
248. #1764	C₂×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
#3099×C₁₃₁	2
#3061×C₁₃₁	2
#2951×C₁₃₁	2
#2079×C₁₃₁	2
#2040×C₁₃₁	2
#1974×C₁₃₁	2
#1952×C₁₃₁	2
#1860×C₁₃₁	2
#1846×C₁₃₁	2
#1816×C₁₃₁	2
#1764×C₁₃₁	2
#25052	131

Subgroups — C131×#25052 #45710936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#25052 #45710936