Subgroups — C₁₃₁×#22668 #45708552

Order 33536.

868 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×M₁₆×C₁₃₁	C₂	1	2	yes	maximal
2	C₂×#435×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×#430×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×#108×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
5	#1950×C₁₃₁	C₂	1	2	yes	maximal, complemented
6	#1855×C₁₃₁	C₂	1	2	yes	maximal, complemented
7	#1855×C₁₃₁	C₂	1	2	yes	maximal, complemented
8	#1849×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
9	#1811×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
10	#1810×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
11	#1778×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₁₃₁	C₂²	1	2	yes	—
13	C₂²×M₁₆×C₁₃₁	C₂²	1	2	yes	—
14	C₂²×M₁₆×C₁₃₁	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₃₁	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₁₃₁	C₂²	1	1	yes	characteristic
17	#436×C₁₃₁	—	2	2	no	—
18	#435×C₁₃₁	—	2	2	no	—
19	#435×C₁₃₁	—	2	2	no	—
20	#435×C₁₃₁	C₄	1	4	yes	—
21	#435×C₁₃₁	C₄	1	4	yes	—
22	C₈×D₄×C₁₃₁	—	2	2	no	—
23	#430×C₁₃₁	—	2	4	no	—
24	C₂×#108×C₁₃₁	—	2	4	no	—
25	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
26	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
27	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
28	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
29	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
30	C₂×#108×C₁₃₁	C₂²	1	2	yes	—
31	C₂×#108×C₁₃₁	C₂²	1	1	yes	characteristic
32	#423×C₁₃₁	C₂²	1	2	yes	—
33	C₂×C₄⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
34	#407×C₁₃₁	C₂²	1	2	yes	—
35	#407×C₁₃₁	C₂²	1	2	yes	—
36	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₁₃₁	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₁₃₁	C₂²	1	2	yes	—
39	C₂×#97×C₁₃₁	C₂²	1	1	yes	characteristic
40	#341×C₁₃₁	C₂²	1	2	yes	—
41	#341×C₁₃₁	C₂²	1	2	yes	—
42	#341×C₁₃₁	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₃₁	Q₈	1	1	yes	characteristic
44	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₁₃₁	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₃₁	—	2	2	no	—
47	C₂×M₁₆×C₁₃₁	—	2	2	no	—
48	C₂×M₁₆×C₁₃₁	—	2	2	no	—
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	—	4	2	no	—
53	C₂×M₁₆×C₁₃₁	—	4	2	no	—
54	C₂×M₁₆×C₁₃₁	C₂×C₄	1	4	yes	—
55	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
56	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
57	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
58	C₂×M₁₆×C₁₃₁	C₂³	1	2	yes	—
59	C₂²×C₈×C₁₃₁	—	2	2	no	—
60	C₂²×C₈×C₁₃₁	—	2	2	no	—
61	C₂²×C₈×C₁₃₁	—	2	2	no	—
62	C₂²×C₈×C₁₃₁	—	2	2	no	—
63	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
64	C₂²×C₈×C₁₃₁	C₂×C₄	1	2	yes	—
65	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₃₁	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
70	C₄×D₄×C₁₃₁	C₂×C₄	1	2	yes	—
71	C₄×D₄×C₁₃₁	D₄	1	2	yes	—
72	C₄×D₄×C₁₃₁	D₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₃₁	Q₈	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₁₃₁	Q₈	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₁₃₁	Q₈	1	1	yes	characteristic
76	C₂×C₄²×C₁₃₁	C₂³	1	1	yes	characteristic
77	#108×C₁₃₁	—	2	4	no	—
78	#108×C₁₃₁	—	2	4	no	—
79	#108×C₁₃₁	—	2	2	no	—
80	#108×C₁₃₁	—	2	2	no	—
81	#108×C₁₃₁	—	2	2	no	—
82	#108×C₁₃₁	—	4	2	no	—
83	#108×C₁₃₁	D₄	1	4	yes	complemented
84	C₄⋊C₈×C₁₃₁	—	2	2	no	—
85	C₄⋊C₈×C₁₃₁	—	2	2	no	—
86	C₄⋊C₈×C₁₃₁	C₂×C₄	1	4	yes	—
87	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
88	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
89	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
90	C₂²⋊C₈×C₁₃₁	—	2	2	no	—
91	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	4	yes	—
92	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
93	C₂²⋊C₈×C₁₃₁	C₂×C₄	1	2	yes	—
94	#97×C₁₃₁	—	2	2	no	—
95	#97×C₁₃₁	C₂×C₄	1	4	yes	—
96	C₄×C₈×C₁₃₁	—	2	2	no	—
97	C₂⁴×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
98	C₂⁴×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
99	C₂×D₄×C₁₃₁	—	4	2	no	—
100	C₂×D₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
101	C₂×D₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
102	C₂²×C₄×C₁₃₁	—	2	1	no	—
103	C₂²×C₄×C₁₃₁	—	2	1	no	—
104	C₂²×C₄×C₁₃₁	—	2	1	no	—
105	C₂²×C₄×C₁₃₁	—	2	1	no	—
106	C₂²×C₄×C₁₃₁	—	2	1	no	—
107	C₂²×C₄×C₁₃₁	—	2	1	no	—
108	C₂²×C₄×C₁₃₁	—	2	1	no	—
109	C₂²×C₄×C₁₃₁	—	2	1	no	—
110	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₃₁	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃₁	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₃₁	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₁₃₁	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
118	C₂²×C₄×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
119	C₂²×C₄×C₁₃₁	C₂×Q₈	1	1	yes	characteristic
120	C₂²×C₄×C₁₃₁	C₂⁴	1	1	yes	characteristic
121	M₁₆×C₁₃₁	—	2	2	no	—
122	M₁₆×C₁₃₁	—	2	8	no	—
123	M₁₆×C₁₃₁	—	2	2	no	—
124	M₁₆×C₁₃₁	—	2	2	no	—
125	M₁₆×C₁₃₁	—	2	2	no	—
126	M₁₆×C₁₃₁	—	2	2	no	—
127	M₁₆×C₁₃₁	—	2	2	no	—
128	M₁₆×C₁₃₁	—	2	2	no	—
129	M₁₆×C₁₃₁	—	4	4	no	—
130	M₁₆×C₁₃₁	—	4	4	no	—
131	M₁₆×C₁₃₁	C₂×D₄	1	4	yes	—
132	C₂×C₈×C₁₃₁	—	2	1	no	—
133	C₂×C₈×C₁₃₁	—	2	1	no	—
134	C₂×C₈×C₁₃₁	—	2	2	no	—
135	C₂×C₈×C₁₃₁	—	2	1	no	—
136	C₂×C₈×C₁₃₁	—	2	1	no	—
137	C₂×C₈×C₁₃₁	—	2	1	no	—
138	C₂×C₈×C₁₃₁	—	2	1	no	—
139	C₂×C₈×C₁₃₁	—	2	4	no	—
140	C₂×C₈×C₁₃₁	—	2	4	no	—
141	C₂×C₈×C₁₃₁	—	2	2	no	—
142	C₂×C₈×C₁₃₁	—	2	2	no	—
143	C₂×C₈×C₁₃₁	—	2	2	no	—
144	C₂×C₈×C₁₃₁	—	4	4	no	—
145	C₂×C₈×C₁₃₁	—	4	4	no	—
146	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
149	C₂×C₈×C₁₃₁	C₂²×C₄	1	2	yes	—
150	C₂×C₈×C₁₃₁	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₃₁	#41	1	2	yes	—
152	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
153	C₄⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
154	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
155	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
156	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
157	C₂²⋊C₄×C₁₃₁	C₄⋊C₄	1	2	yes	—
158	C₄²×C₁₃₁	C₂²×C₄	1	2	yes	—
159	C₄²×C₁₃₁	C₂×D₄	1	2	yes	—
160	C₂³×C₁₃₁	—	2	1	no	—
161	C₂³×C₁₃₁	—	2	1	no	—
162	C₂³×C₁₃₁	—	2	2	no	—
163	C₂³×C₁₃₁	—	2	1	no	—
164	C₂³×C₁₃₁	—	2	1	no	—
165	C₂³×C₁₃₁	—	4	1	no	—
166	C₂³×C₁₃₁	—	4	1	no	—
167	C₂³×C₁₃₁	—	4	1	no	—
168	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
169	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
170	C₂³×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂³×C₁₃₁	C₂²×Q₈	1	1	yes	characteristic
172	D₄×C₁₃₁	—	2	4	no	—
173	D₄×C₁₃₁	—	4	2	no	—
174	C₂×C₄×C₁₃₁	—	2	1	no	—
175	C₂×C₄×C₁₃₁	—	2	1	no	—
176	C₂×C₄×C₁₃₁	—	2	1	no	—
177	C₂×C₄×C₁₃₁	—	2	1	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	1	no	—
183	C₂×C₄×C₁₃₁	—	2	2	no	—
184	C₂×C₄×C₁₃₁	—	2	1	no	—
185	C₂×C₄×C₁₃₁	—	2	2	no	—
186	C₂×C₄×C₁₃₁	—	2	1	no	—
187	C₂×C₄×C₁₃₁	—	2	1	no	—
188	C₂×C₄×C₁₃₁	—	2	1	no	—
189	C₂×C₄×C₁₃₁	—	2	2	no	—
190	C₂×C₄×C₁₃₁	—	4	1	no	—
191	C₂×C₄×C₁₃₁	—	4	1	no	—
192	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
193	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
194	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
195	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₄×C₁₃₁	C₂×C₄⋊C₄	1	2	yes	—
197	C₂×C₄×C₁₃₁	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃₁	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃₁	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₁₃₁	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₁₃₁	2₋¹⁺⁴	1	1	yes	characteristic
203	C₈×C₁₃₁	—	2	2	no	—
204	C₈×C₁₃₁	—	2	2	no	—
205	C₈×C₁₃₁	—	2	2	no	—
206	C₈×C₁₃₁	—	2	4	no	—
207	C₈×C₁₃₁	—	4	2	no	—
208	C₈×C₁₃₁	—	4	2	no	—
209	C₈×C₁₃₁	—	4	2	no	—
210	C₈×C₁₃₁	C₄×D₄	1	4	yes	—
211	C₂²×C₁₃₁	—	2	1	no	—
212	C₂²×C₁₃₁	—	2	1	no	—
213	C₂²×C₁₃₁	—	2	1	no	—
214	C₂²×C₁₃₁	—	2	1	no	—
215	C₂²×C₁₃₁	—	2	1	no	—
216	C₂²×C₁₃₁	—	2	2	no	—
217	C₂²×C₁₃₁	—	2	2	no	—
218	C₂²×C₁₃₁	—	2	1	no	—
219	C₂²×C₁₃₁	—	2	1	no	—
220	C₂²×C₁₃₁	—	2	2	no	—
221	C₂²×C₁₃₁	—	4	2	no	—
222	C₂²×C₁₃₁	—	4	2	no	—
223	C₂²×C₁₃₁	—	8	1	no	—
224	C₂²×C₁₃₁	—	8	1	no	—
225	C₂²×C₁₃₁	#430	1	2	yes	complemented
226	C₂²×C₁₃₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
227	C₂²×C₁₃₁	D₄×Q₈	1	1	yes	characteristic
228	C₂²×C₁₃₁	#554	1	1	yes	characteristic
229	C₄×C₁₃₁	—	2	1	no	—
230	C₄×C₁₃₁	—	2	1	no	—
231	C₄×C₁₃₁	—	2	2	no	—
232	C₄×C₁₃₁	—	2	2	no	—
233	C₄×C₁₃₁	—	2	2	no	—
234	C₄×C₁₃₁	C₂×C₄×D₄	1	1	yes	characteristic
235	C₄×C₁₃₁	#520	1	1	yes	characteristic
236	C₄×C₁₃₁	D₄²	1	1	yes	characteristic
237	C₄×C₁₃₁	#547	1	1	yes	characteristic
238	C₂×C₁₃₁	—	2	1	no	—
239	C₂×C₁₃₁	—	2	1	no	—
240	C₂×C₁₃₁	—	2	2	no	—
241	C₂×C₁₃₁	—	4	1	no	—
242	C₂×C₁₃₁	—	4	2	no	—
243	C₂×C₁₃₁	D₄×C₄⋊C₄	1	1	yes	characteristic
244	C₂×C₁₃₁	C₂×#430	1	1	yes	characteristic
245	C₂×C₁₃₁	#2916	1	1	yes	characteristic
246	#22668	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
247	C₁₃₁	#22668	1	1	yes	characteristic, direct product factor, Sylow
248	D₄×M₁₆	C₂×C₁₃₁	1	2	yes	—
249	C₂×#435	C₂×C₁₃₁	1	1	yes	characteristic
250	C₂×#430	C₂×C₁₃₁	1	1	yes	characteristic, complemented
251	C₂²×#108	C₂×C₁₃₁	1	1	yes	characteristic, complemented
252	#1950	C₂×C₁₃₁	1	2	yes	complemented
253	#1855	C₂×C₁₃₁	1	2	yes	complemented
254	#1855	C₂×C₁₃₁	1	2	yes	complemented
255	#1849	C₂×C₁₃₁	1	1	yes	characteristic, complemented
256	#1811	C₂×C₁₃₁	1	1	yes	characteristic, complemented
257	#1810	C₂×C₁₃₁	1	1	yes	characteristic, complemented
258	#1778	C₂×C₁₃₁	1	1	yes	characteristic, complemented
259	C₂²×M₁₆	C₂²×C₁₃₁	1	2	yes	—
260	C₂²×M₁₆	C₂²×C₁₃₁	1	2	yes	—
261	C₂²×M₁₆	C₂²×C₁₃₁	1	1	yes	characteristic
262	C₂³×C₈	C₂²×C₁₃₁	1	1	yes	characteristic
263	C₂×C₄×D₄	C₂²×C₁₃₁	1	1	yes	characteristic
264	#436	—	2	2	no	—
265	#435	—	2	2	no	—
266	#435	—	2	2	no	—
267	#435	C₄×C₁₃₁	1	4	yes	—
268	#435	C₄×C₁₃₁	1	4	yes	—
269	C₈×D₄	—	2	2	no	—
270	#430	—	2	4	no	—
271	C₂×#108	—	2	4	no	—
272	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
273	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
274	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
275	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
276	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
277	C₂×#108	C₂²×C₁₃₁	1	2	yes	—
278	C₂×#108	C₂²×C₁₃₁	1	1	yes	characteristic
279	#423	C₂²×C₁₃₁	1	2	yes	—
280	C₂×C₄⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
281	#407	C₂²×C₁₃₁	1	2	yes	—
282	#407	C₂²×C₁₃₁	1	2	yes	—
283	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	C₂²×C₁₃₁	1	1	yes	characteristic
285	C₄×M₁₆	C₂²×C₁₃₁	1	2	yes	—
286	C₂×#97	C₂²×C₁₃₁	1	1	yes	characteristic
287	#341	C₂²×C₁₃₁	1	2	yes	—
288	#341	C₂²×C₁₃₁	1	2	yes	—
289	#341	C₂²×C₁₃₁	1	2	yes	—
290	C₂²×D₄	Q₈×C₁₃₁	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
292	C₂³×C₄	C₂³×C₁₃₁	1	1	yes	characteristic
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	2	2	no	—
297	C₂×M₁₆	—	2	4	no	—
298	C₂×M₁₆	—	2	4	no	—
299	C₂×M₁₆	—	4	2	no	—
300	C₂×M₁₆	—	4	2	no	—
301	C₂×M₁₆	C₂×C₄×C₁₃₁	1	4	yes	—
302	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
303	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
304	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
305	C₂×M₁₆	C₂³×C₁₃₁	1	2	yes	—
306	C₂²×C₈	—	2	2	no	—
307	C₂²×C₈	—	2	2	no	—
308	C₂²×C₈	—	2	2	no	—
309	C₂²×C₈	—	2	2	no	—
310	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
311	C₂²×C₈	C₂×C₄×C₁₃₁	1	2	yes	—
312	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
313	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
314	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
315	C₂²×C₈	C₂³×C₁₃₁	1	1	yes	characteristic
316	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
317	C₄×D₄	C₂×C₄×C₁₃₁	1	2	yes	—
318	C₄×D₄	D₄×C₁₃₁	1	2	yes	—
319	C₄×D₄	D₄×C₁₃₁	1	2	yes	—
320	C₂×C₄⋊C₄	Q₈×C₁₃₁	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	Q₈×C₁₃₁	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	Q₈×C₁₃₁	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₁₃₁	1	1	yes	characteristic
324	#108	—	2	4	no	—
325	#108	—	2	4	no	—
326	#108	—	2	2	no	—
327	#108	—	2	2	no	—
328	#108	—	2	2	no	—
329	#108	—	4	2	no	—
330	#108	D₄×C₁₃₁	1	4	yes	complemented
331	C₄⋊C₈	—	2	2	no	—
332	C₄⋊C₈	—	2	2	no	—
333	C₄⋊C₈	C₂×C₄×C₁₃₁	1	4	yes	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	C₂²⋊C₈	—	2	2	no	—
337	C₂²⋊C₈	—	2	2	no	—
338	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	4	yes	—
339	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
340	C₂²⋊C₈	C₂×C₄×C₁₃₁	1	2	yes	—
341	#97	—	2	2	no	—
342	#97	C₂×C₄×C₁₃₁	1	4	yes	—
343	C₄×C₈	—	2	2	no	—
344	C₂⁴	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
345	C₂⁴	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
346	C₂×D₄	—	4	2	no	—
347	C₂×D₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
348	C₂×D₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
358	C₂²×C₄	C₂²×C₄×C₁₃₁	1	1	yes	characteristic
359	C₂²×C₄	C₂²×C₄×C₁₃₁	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₄×C₁₃₁	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₁₃₁	1	1	yes	characteristic
363	C₂²×C₄	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
364	C₂²×C₄	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
365	C₂²×C₄	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
366	C₂²×C₄	C₂×Q₈×C₁₃₁	1	1	yes	characteristic
367	C₂²×C₄	C₂⁴×C₁₃₁	1	1	yes	characteristic
368	M₁₆	—	2	2	no	—
369	M₁₆	—	2	8	no	—
370	M₁₆	—	2	2	no	—
371	M₁₆	—	2	2	no	—
372	M₁₆	—	2	2	no	—
373	M₁₆	—	2	2	no	—
374	M₁₆	—	2	2	no	—
375	M₁₆	—	2	2	no	—
376	M₁₆	—	4	4	no	—
377	M₁₆	—	4	4	no	—
378	M₁₆	C₂×D₄×C₁₃₁	1	4	yes	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	2	1	no	—
382	C₂×C₈	—	2	1	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	4	4	no	—
392	C₂×C₈	—	4	4	no	—
393	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
394	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
395	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
396	C₂×C₈	C₂²×C₄×C₁₃₁	1	2	yes	—
397	C₂×C₈	C₂×D₄×C₁₃₁	1	2	yes	—
398	C₂×C₈	#41×C₁₃₁	1	2	yes	—
399	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
400	C₄⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
401	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
402	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
403	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
404	C₂²⋊C₄	C₄⋊C₄×C₁₃₁	1	2	yes	—
405	C₄²	C₂²×C₄×C₁₃₁	1	2	yes	—
406	C₄²	C₂×D₄×C₁₃₁	1	2	yes	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
416	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
417	C₂³	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
418	C₂³	C₂²×Q₈×C₁₃₁	1	1	yes	characteristic
419	D₄	—	2	4	no	—
420	D₄	—	4	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
440	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
441	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
442	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
443	C₂×C₄	C₂×C₄⋊C₄×C₁₃₁	1	2	yes	—
444	C₂×C₄	C₂³×C₄×C₁₃₁	1	1	yes	characteristic
445	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
446	C₂×C₄	C₂²×D₄×C₁₃₁	1	1	yes	characteristic
447	C₂×C₄	C₂×#41×C₁₃₁	1	1	yes	characteristic
448	C₂×C₄	H(5,𝔽₂)×C₁₃₁	1	1	yes	characteristic
449	C₂×C₄	2₋¹⁺⁴×C₁₃₁	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	—	2	4	no	—
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	4	2	no	—
457	C₈	C₄×D₄×C₁₃₁	1	4	yes	—
458	C₂²	—	2	1	no	—
459	C₂²	—	2	1	no	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	#430×C₁₃₁	1	2	yes	complemented
473	C₂²	C₂²×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
474	C₂²	D₄×Q₈×C₁₃₁	1	1	yes	characteristic
475	C₂²	#554×C₁₃₁	1	1	yes	characteristic
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	C₂×C₄×D₄×C₁₃₁	1	1	yes	characteristic
482	C₄	#520×C₁₃₁	1	1	yes	characteristic
483	C₄	D₄²×C₁₃₁	1	1	yes	characteristic
484	C₄	#547×C₁₃₁	1	1	yes	characteristic
485	C₂	—	2	1	no	—
486	C₂	—	2	1	no	—
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	4	2	no	—
490	C₂	D₄×C₄⋊C₄×C₁₃₁	1	1	yes	characteristic
491	C₂	C₂×#430×C₁₃₁	1	1	yes	characteristic
492	C₂	#2916×C₁₃₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₃₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₃₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃₁
socle	C₂²×C₁₃₁	C₂²×C₄⋊C₄
prime radical	C₂²×D₄×C₁₃₁	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃₁ ◁ C₂×C₄×D₄×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#430×C₁₃₁	C₂	semidirect
4. C₂²×#108×C₁₃₁	C₂	semidirect
5. #1950×C₁₃₁	C₂	semidirect
6. #1855×C₁₃₁	C₂	semidirect
7. #1855×C₁₃₁	C₂	semidirect
8. #1849×C₁₃₁	C₂	semidirect
9. #1811×C₁₃₁	C₂	semidirect
10. #1810×C₁₃₁	C₂	semidirect
11. #1778×C₁₃₁	C₂	semidirect
83. #108×C₁₃₁	D₄	semidirect
225. C₂²×C₁₃₁	#430	semidirect
246. #22668	C₁₃₁	direct (N × H)
247. C₁₃₁	#22668	direct (N × H)
250. C₂×#430	C₂×C₁₃₁	semidirect
251. C₂²×#108	C₂×C₁₃₁	semidirect
252. #1950	C₂×C₁₃₁	semidirect
253. #1855	C₂×C₁₃₁	semidirect
254. #1855	C₂×C₁₃₁	semidirect
255. #1849	C₂×C₁₃₁	semidirect
256. #1811	C₂×C₁₃₁	semidirect
257. #1810	C₂×C₁₃₁	semidirect
258. #1778	C₂×C₁₃₁	semidirect
330. #108	D₄×C₁₃₁	semidirect
472. C₂²	#430×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
D₄×M₁₆×C₁₃₁	2
C₂×#435×C₁₃₁	2
C₂×#430×C₁₃₁	2
C₂²×#108×C₁₃₁	2
#1950×C₁₃₁	2
#1855×C₁₃₁	2
#1849×C₁₃₁	2
#1811×C₁₃₁	2
#1810×C₁₃₁	2
#1778×C₁₃₁	2
#22668	131

Subgroups — C131×#22668 #45708552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#22668 #45708552