Subgroups — C₃×Dic₃×C₁₃₁⋊C₅ #37556067

Order 23580.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×C₁₃₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	Dic₃×C₁₃₁⋊C₅	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×C₄×C₁₃₁⋊C₅	—	3	1	no	maximal
4	C₃²×C₁₃₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×Dic₃×C₁₃₁	C₅	1	1	yes	maximal, characteristic, complemented, Hall
6	C₂×C₃×C₁₃₁⋊C₅	—	2	1	no	—
7	C₂×C₃×C₁₃₁⋊C₅	D₃	1	1	yes	characteristic
8	C₂×C₃×C₁₃₁⋊C₅	C₂×C₃	1	1	yes	characteristic
9	C₄×C₁₃₁⋊C₅	—	3	1	no	Hall
10	C₂×C₃²×C₁₃₁	C₂×C₅	1	1	yes	characteristic
11	C₃×C₁₃₁⋊C₅	—	2	1	no	—
12	C₃×C₁₃₁⋊C₅	Dic₃	1	1	yes	characteristic, direct product factor
13	C₃×C₁₃₁⋊C₅	C₃×C₄	1	1	yes	characteristic, complemented
14	C₃×C₄×C₁₃₁	—	3	1	no	—
15	Dic₃×C₁₃₁	C₃×C₅	1	1	yes	characteristic, complemented
16	C₂×C₁₃₁⋊C₅	C₃×D₃	1	1	yes	characteristic
17	C₃²×C₁₃₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
18	C₂×C₃×C₁₃₁	—	2	1	no	—
19	C₂×C₃×C₁₃₁	C₅×D₃	1	1	yes	characteristic
20	C₂×C₃×C₁₃₁	C₂×C₃×C₅	1	1	yes	characteristic
21	C₁₃₁⋊C₅	C₃×Dic₃	1	1	yes	characteristic, direct product factor, Hall
22	C₄×C₁₃₁	—	3	1	no	Hall
23	C₃×C₁₃₁	—	2	1	no	—
24	C₃×C₁₃₁	C₅×Dic₃	1	1	yes	characteristic, complemented
25	C₃×C₁₃₁	C₃×C₄×C₅	1	1	yes	characteristic, complemented
26	C₂×C₁₃₁	C₃×C₅×D₃	1	1	yes	characteristic
27	C₃×C₅×Dic₃	—	131	1	no	maximal, Hall
28	C₁₃₁	C₃×C₅×Dic₃	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃²×C₅	—	131	1	no	—
30	C₃×C₄×C₅	—	393	1	no	—
31	C₅×Dic₃	—	131	1	no	—
32	C₃²×C₅	—	131	1	no	Hall
33	C₃×Dic₃	C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor, Hall
34	C₂×C₃×C₅	—	262	1	no	—
35	C₂×C₃×C₅	—	131	1	no	—
36	C₂×C₃×C₅	—	131	1	no	—
37	C₄×C₅	—	393	1	no	Hall
38	C₂×C₃²	C₂×C₁₃₁⋊C₅	1	1	yes	characteristic
39	C₃×C₅	—	262	1	no	—
40	C₃×C₅	—	131	1	no	—
41	C₃×C₅	—	131	1	no	—
42	C₃×C₄	—	3	1	no	—
43	Dic₃	C₃×C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor
44	C₂×C₅	—	131	1	no	—
45	C₃²	C₄×C₁₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
46	C₂×C₃	—	2	1	no	—
47	C₂×C₃	C₂×C₃×C₁₃₁⋊C₅	1	1	yes	characteristic
48	C₂×C₃	D₃×C₁₃₁⋊C₅	1	1	yes	characteristic
49	C₅	—	131	1	no	Sylow
50	C₄	—	3	1	no	Sylow
51	C₃	—	2	1	no	—
52	C₃	C₃×C₄×C₁₃₁⋊C₅	1	1	yes	characteristic, complemented
53	C₃	Dic₃×C₁₃₁⋊C₅	1	1	yes	characteristic, direct product factor
54	C₂	C₃×D₃×C₁₃₁⋊C₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	D₃×C₁₃₁⋊C₅
commutator, hypocenter	C₃×C₁₃₁	C₃×C₄×C₅
Frattini	C₂	C₃×D₃×C₁₃₁⋊C₅
Fitting, socle	C₂×C₃²×C₁₃₁	C₂×C₅
prime radical	C₂×C₃²×C₁₃₁⋊C₅	C₂
cosocle	C₂×C₃×C₁₃₁	C₂×C₃×C₅
LCS	G ▷ C₃×C₁₃₁
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
2. Dic₃×C₁₃₁⋊C₅	C₃	direct (N × H)
4. C₃²×C₁₃₁⋊C₅	C₄	semidirect
5. C₃×Dic₃×C₁₃₁	C₅	semidirect
12. C₃×C₁₃₁⋊C₅	Dic₃	direct (N × H)
13. C₃×C₁₃₁⋊C₅	C₃×C₄	semidirect
15. Dic₃×C₁₃₁	C₃×C₅	semidirect
17. C₃²×C₁₃₁	C₄×C₅	semidirect
21. C₁₃₁⋊C₅	C₃×Dic₃	direct (N × H)
24. C₃×C₁₃₁	C₅×Dic₃	semidirect
25. C₃×C₁₃₁	C₃×C₄×C₅	semidirect
28. C₁₃₁	C₃×C₅×Dic₃	semidirect
33. C₃×Dic₃	C₁₃₁⋊C₅	direct (N × H)
43. Dic₃	C₃×C₁₃₁⋊C₅	direct (N × H)
45. C₃²	C₄×C₁₃₁⋊C₅	semidirect
52. C₃	C₃×C₄×C₁₃₁⋊C₅	semidirect
53. C₃	Dic₃×C₁₃₁⋊C₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃²×C₁₃₁⋊C₅	2
Dic₃×C₁₃₁⋊C₅	3
C₃×C₄×C₁₃₁⋊C₅	3
C₃×Dic₃×C₁₃₁	5
C₃×C₅×Dic₃	131

Subgroups — C3×Dic3×C131⋊C5 #37556067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×Dic₃×C₁₃₁⋊C₅ #37556067