Subgroups — D₉×D₁₃₁⋊C₅ #37556039

Order 23580.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
1. C₉⋊(D₁₃₁⋊C₅)	C₂	semidirect
2. D₉×C₁₃₁⋊C₅	C₂	semidirect
3. C₉×D₁₃₁⋊C₅	C₂	semidirect
5. C₉×C₁₃₁⋊C₅	C₂²	semidirect
6. D₉×D₁₃₁	C₅	semidirect
11. D₁₁₇₉	C₂×C₅	semidirect
12. C₉×D₁₃₁	C₂×C₅	semidirect
13. D₉×C₁₃₁	C₂×C₅	semidirect
18. D₁₃₁⋊C₅	D₉	direct (N × H)
19. C₉×C₁₃₁	C₂²×C₅	semidirect
23. C₁₃₁⋊C₅	C₂×D₉	semidirect
28. D₁₃₁	C₅×D₉	semidirect
30. C₁₃₁	C₂×C₅×D₉	semidirect
43. D₉	D₁₃₁⋊C₅	direct (N × H)
49. C₉	C₂×D₁₃₁⋊C₅	semidirect

Maximal subgroups

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

subgroup	index
C₉⋊(D₁₃₁⋊C₅)	2
D₉×C₁₃₁⋊C₅	2
C₉×D₁₃₁⋊C₅	2
D₃×D₁₃₁⋊C₅	3
D₉×D₁₃₁	5
C₂×C₅×D₉	131

Subgroups — D9×D131⋊C5 #37556039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×D₁₃₁⋊C₅ #37556039