Subgroups — D₄₅⋊D₁₃₁ #37556055

Order 23580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄₅×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₁₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×D₆₅₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₅⋊D₁₃₁	—	3	1	no	maximal
5	C₅×C₉×C₁₃₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₉×D₁₃₁	—	5	1	no	maximal, Hall
7	D₁₅×C₁₃₁	—	3	1	no	—
8	C₅×D₃₉₃	—	3	1	no	—
9	C₃×D₆₅₅	D₃	1	1	yes	characteristic
10	D₅×D₁₃₁	—	9	1	no	Hall
11	D₁₁₇₉	D₅	1	1	yes	characteristic, complemented
12	C₉×D₁₃₁	—	5	1	no	—
13	D₉×C₁₃₁	—	5	1	no	—
14	C₃×C₅×C₁₃₁	C₂×D₃	1	1	yes	characteristic
15	D₃×D₁₃₁	—	15	1	no	—
16	D₆₅₅	D₉	1	1	yes	characteristic, complemented
17	C₅×D₁₃₁	—	9	1	no	—
18	D₅×C₁₃₁	—	9	1	no	—
19	C₉×C₁₃₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	D₃₉₃	—	3	1	no	—
21	C₃×D₁₃₁	—	5	1	no	—
22	D₃×C₁₃₁	—	15	1	no	—
23	C₅×C₁₃₁	C₂×D₉	1	1	yes	characteristic, complemented, Hall
24	C₂×D₁₃₁	—	45	1	no	Hall
25	C₃×C₁₃₁	D₃×D₅	1	1	yes	characteristic
26	C₂×C₁₃₁	—	45	1	no	—
27	D₁₃₁	—	5	1	no	—
28	D₁₃₁	—	9	1	no	—
29	D₅×D₉	—	131	1	no	maximal, Hall
30	C₁₃₁	D₅×D₉	1	1	yes	characteristic, complemented, Sylow
31	D₄₅	D₁₃₁	1	1	yes	characteristic, complemented
32	C₉×D₅	—	131	1	no	—
33	C₅×D₉	—	131	1	no	—
34	D₃×D₅	—	393	1	no	—
35	C₅×C₉	C₂×D₁₃₁	1	1	yes	characteristic, complemented, Hall
36	C₂×D₉	—	655	1	no	Hall
37	D₁₅	—	3	1	no	—
38	C₃×D₅	—	131	1	no	—
39	C₅×D₃	—	393	1	no	—
40	C₂×D₅	—	1179	1	no	Hall
41	C₂×C₉	—	655	1	no	—
42	D₉	—	5	1	no	—
43	D₉	—	131	1	no	—
44	C₃×C₅	D₃×D₁₃₁	1	1	yes	characteristic
45	C₂×D₃	—	1965	1	no	—
46	C₂×C₅	—	1179	1	no	—
47	D₅	—	9	1	no	—
48	D₅	—	131	1	no	—
49	C₉	D₅×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
50	C₂×C₃	—	655	1	no	—
51	D₃	—	15	1	no	—
52	D₃	—	393	1	no	—
53	C₅	D₉×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
54	C₂²	—	5895	1	no	Sylow
55	C₃	D₁₅⋊D₁₃₁	1	1	yes	characteristic
56	C₂	—	45	1	no	—
57	C₂	—	655	1	no	—
58	C₂	—	1179	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₅×C₉×C₁₃₁	C₂²
Frattini	C₃	D₁₅⋊D₁₃₁
socle	C₃×C₅×C₁₃₁	C₂×D₃
LCS	G ▷ C₅×C₉×C₁₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₄₅×C₁₃₁	C₂	semidirect
2. C₅×D₁₁₇₉	C₂	semidirect
3. C₉×D₆₅₅	C₂	semidirect
5. C₅×C₉×C₁₃₁	C₂²	semidirect
11. D₁₁₇₉	D₅	semidirect
16. D₆₅₅	D₉	semidirect
19. C₉×C₁₃₁	C₂×D₅	semidirect
23. C₅×C₁₃₁	C₂×D₉	semidirect
30. C₁₃₁	D₅×D₉	semidirect
31. D₄₅	D₁₃₁	semidirect
35. C₅×C₉	C₂×D₁₃₁	semidirect
49. C₉	D₅×D₁₃₁	semidirect
53. C₅	D₉×D₁₃₁	semidirect

Maximal subgroups

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

subgroup	index
D₄₅×C₁₃₁	2
C₅×D₁₁₇₉	2
C₉×D₆₅₅	2
D₁₅⋊D₁₃₁	3
D₉×D₁₃₁	5
D₅×D₉	131

Subgroups — D45⋊D131 #37556055

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₅⋊D₁₃₁ #37556055