Subgroups — C₁₃₁×#7510 #45693394

Order 33536.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₆₄×C₁₃₁	C₂	1	2	yes	maximal
2	C₄×C₃₂×C₁₃₁	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃₂×C₁₃₁	C₄	1	1	yes	characteristic
4	C₂×C₃₂×C₁₃₁	C₂²	1	1	yes	characteristic
5	C₄×C₁₆×C₁₃₁	C₄	1	1	yes	characteristic
6	C₆₄×C₁₃₁	C₄	1	4	yes	complemented
7	C₂×C₁₆×C₁₃₁	C₈	1	1	yes	characteristic
8	C₂×C₁₆×C₁₃₁	C₂×C₄	1	1	yes	characteristic
9	C₄×C₈×C₁₃₁	C₈	1	1	yes	characteristic
10	C₃₂×C₁₃₁	C₈	1	2	yes	—
11	C₃₂×C₁₃₁	C₂×C₄	1	2	yes	—
12	C₂×C₈×C₁₃₁	C₁₆	1	1	yes	characteristic
13	C₂×C₈×C₁₃₁	C₂×C₈	1	1	yes	characteristic
14	C₄²×C₁₃₁	C₁₆	1	1	yes	characteristic
15	C₁₆×C₁₃₁	C₁₆	1	2	yes	—
16	C₁₆×C₁₃₁	C₄²	1	1	yes	characteristic
17	C₁₆×C₁₃₁	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₁₃₁	C₃₂	1	2	yes	—
19	C₂×C₄×C₁₃₁	C₂×C₁₆	1	1	yes	characteristic
20	C₈×C₁₃₁	C₃₂	1	2	yes	—
21	C₈×C₁₃₁	C₄×C₈	1	1	yes	characteristic
22	C₈×C₁₃₁	C₂×C₁₆	1	1	yes	characteristic
23	C₂²×C₁₃₁	C₂×C₃₂	1	1	yes	characteristic
24	C₄×C₁₃₁	—	2	2	no	—
25	C₄×C₁₃₁	C₄×C₁₆	1	1	yes	characteristic
26	C₄×C₁₃₁	C₂×C₃₂	1	1	yes	characteristic
27	C₂×C₁₃₁	C₄×C₃₂	1	1	yes	characteristic
28	C₂×C₁₃₁	M₁₂₈	1	2	yes	—
29	#7510	C₁₃₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₁₃₁	#7510	1	1	yes	characteristic, direct product factor, Sylow
31	C₂×C₆₄	C₂×C₁₃₁	1	2	yes	—
32	C₄×C₃₂	C₂×C₁₃₁	1	1	yes	characteristic
33	C₂×C₃₂	C₄×C₁₃₁	1	1	yes	characteristic
34	C₂×C₃₂	C₂²×C₁₃₁	1	1	yes	characteristic
35	C₄×C₁₆	C₄×C₁₃₁	1	1	yes	characteristic
36	C₆₄	C₄×C₁₃₁	1	4	yes	complemented
37	C₂×C₁₆	C₈×C₁₃₁	1	1	yes	characteristic
38	C₂×C₁₆	C₂×C₄×C₁₃₁	1	1	yes	characteristic
39	C₄×C₈	C₈×C₁₃₁	1	1	yes	characteristic
40	C₃₂	C₈×C₁₃₁	1	2	yes	—
41	C₃₂	C₂×C₄×C₁₃₁	1	2	yes	—
42	C₂×C₈	C₁₆×C₁₃₁	1	1	yes	characteristic
43	C₂×C₈	C₂×C₈×C₁₃₁	1	1	yes	characteristic
44	C₄²	C₁₆×C₁₃₁	1	1	yes	characteristic
45	C₁₆	C₁₆×C₁₃₁	1	2	yes	—
46	C₁₆	C₄²×C₁₃₁	1	1	yes	characteristic
47	C₁₆	C₂×C₈×C₁₃₁	1	1	yes	characteristic
48	C₂×C₄	C₃₂×C₁₃₁	1	2	yes	—
49	C₂×C₄	C₂×C₁₆×C₁₃₁	1	1	yes	characteristic
50	C₈	C₃₂×C₁₃₁	1	2	yes	—
51	C₈	C₄×C₈×C₁₃₁	1	1	yes	characteristic
52	C₈	C₂×C₁₆×C₁₃₁	1	1	yes	characteristic
53	C₂²	C₂×C₃₂×C₁₃₁	1	1	yes	characteristic
54	C₄	—	2	2	no	—
55	C₄	C₄×C₁₆×C₁₃₁	1	1	yes	characteristic
56	C₄	C₂×C₃₂×C₁₃₁	1	1	yes	characteristic
57	C₂	C₄×C₃₂×C₁₃₁	1	1	yes	characteristic
58	C₂	M₁₂₈×C₁₃₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₃₂×C₁₃₁	C₂²
commutator	C₂	C₄×C₃₂×C₁₃₁
Frattini, cosocle	C₂×C₃₂	C₂²×C₁₃₁
socle, prime radical	C₂²×C₁₃₁	C₂×C₃₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃₂×C₁₃₁ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₆₄×C₁₃₁	C₄	semidirect
29. #7510	C₁₃₁	direct (N × H)
30. C₁₃₁	#7510	direct (N × H)
36. C₆₄	C₄×C₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₆₄×C₁₃₁	2
C₄×C₃₂×C₁₃₁	2
#7510	131

Subgroups — C131×#7510 #45693394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃₁×#7510 #45693394