Subgroups — C₂×C₃×C₃⋊(D₁₃₁⋊C₅) #37556092

Order 23580.

88 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, complemented
2	C₃×C₃⋊(D₁₃₁⋊C₅)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊(D₁₃₁⋊C₅)	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃×D₁₃₁⋊C₅	—	3	1	no	maximal
5	C₃²×C₁₃₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₃×D₃₉₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
7	C₃⋊(D₁₃₁⋊C₅)	C₂×C₃	1	2	yes	direct product factor
8	C₃×D₁₃₁⋊C₅	—	3	2	no	—
9	C₂×C₃×C₁₃₁⋊C₅	—	2	1	no	—
10	C₂×C₃×C₁₃₁⋊C₅	D₃	1	1	yes	characteristic, complemented
11	C₂×C₃×C₁₃₁⋊C₅	C₂×C₃	1	1	yes	characteristic, complemented
12	C₂×D₁₃₁⋊C₅	—	3	1	no	Hall
13	C₃×D₃₉₃	C₂×C₅	1	2	yes	complemented
14	C₂×C₃²×C₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented
15	C₃×C₁₃₁⋊C₅	—	2	1	no	—
16	C₃×C₁₃₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented
17	C₃×C₁₃₁⋊C₅	C₂²×C₃	1	1	yes	characteristic, complemented
18	C₂×D₃₉₃	C₃×C₅	1	1	yes	characteristic, complemented
19	C₂×C₃×D₁₃₁	—	3	1	no	—
20	C₂×C₁₃₁⋊C₅	C₃×D₃	1	1	yes	characteristic, complemented
21	D₁₃₁⋊C₅	—	3	2	no	—
22	C₃²×C₁₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
23	C₂×C₃×C₁₃₁	—	2	1	no	—
24	C₂×C₃×C₁₃₁	C₅×D₃	1	1	yes	characteristic, complemented
25	C₂×C₃×C₁₃₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented
26	D₃₉₃	C₂×C₃×C₅	1	2	yes	complemented
27	C₃×D₁₃₁	—	3	2	no	—
28	C₁₃₁⋊C₅	C₂×C₃×D₃	1	1	yes	characteristic, complemented, Hall
29	C₂×D₁₃₁	—	3	1	no	Hall
30	C₃×C₁₃₁	—	2	1	no	—
31	C₃×C₁₃₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
32	C₃×C₁₃₁	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
33	C₂×C₁₃₁	C₃×C₅×D₃	1	1	yes	characteristic, complemented
34	D₁₃₁	—	3	2	no	—
35	C₂×C₃×C₅×D₃	—	131	1	no	maximal, Hall
36	C₁₃₁	C₂×C₃×C₅×D₃	1	1	yes	characteristic, complemented, Sylow
37	C₂×C₃²×C₅	—	131	1	no	—
38	C₃×C₅×D₃	—	131	2	no	—
39	C₂²×C₃×C₅	—	393	1	no	—
40	C₂×C₅×D₃	—	131	1	no	—
41	C₃²×C₅	—	131	1	no	Hall
42	C₂×C₃×D₃	—	655	1	no	Hall
43	C₂×C₃×C₅	—	262	1	no	—
44	C₂×C₃×C₅	—	131	1	no	—
45	C₂×C₃×C₅	—	131	1	no	—
46	C₂×C₃×C₅	—	393	2	no	—
47	C₅×D₃	—	131	2	no	—
48	C₂²×C₅	—	393	1	no	Hall
49	C₂×C₃²	D₁₃₁⋊C₅	1	1	yes	characteristic, complemented
50	C₃×D₃	—	655	2	no	—
51	C₃×C₅	—	262	1	no	—
52	C₃×C₅	—	131	1	no	—
53	C₃×C₅	—	131	1	no	—
54	C₂²×C₃	—	1965	1	no	—
55	C₂×D₃	—	655	1	no	—
56	C₂×C₅	—	131	1	no	—
57	C₂×C₅	—	393	2	no	—
58	C₃²	C₂×D₁₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
59	C₂×C₃	—	2	1	no	—
60	C₂×C₃	—	1965	2	no	—
61	C₂×C₃	C₃×D₁₃₁⋊C₅	1	1	yes	characteristic, complemented
62	C₂×C₃	C₃⋊(D₁₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
63	D₃	—	655	2	no	—
64	C₅	—	131	1	no	Sylow
65	C₂²	—	1965	1	no	Sylow
66	C₃	—	2	1	no	—
67	C₃	C₂×C₃×D₁₃₁⋊C₅	1	1	yes	characteristic, complemented
68	C₃	C₂×C₃⋊(D₁₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
69	C₂	—	1965	2	no	—
70	C₂	C₃×C₃⋊(D₁₃₁⋊C₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃	C₃⋊(D₁₃₁⋊C₅)
commutator, cosocle, hypocenter	C₃×C₁₃₁	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₁₃₁	C₂×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
1. C₂×C₃²×C₁₃₁⋊C₅	C₂	semidirect
2. C₃×C₃⋊(D₁₃₁⋊C₅)	C₂	direct (N × H)
3. C₂×C₃⋊(D₁₃₁⋊C₅)	C₃	direct (N × H)
5. C₃²×C₁₃₁⋊C₅	C₂²	semidirect
6. C₂×C₃×D₃₉₃	C₅	semidirect
7. C₃⋊(D₁₃₁⋊C₅)	C₂×C₃	direct (N × H)
10. C₂×C₃×C₁₃₁⋊C₅	D₃	semidirect
11. C₂×C₃×C₁₃₁⋊C₅	C₂×C₃	semidirect
13. C₃×D₃₉₃	C₂×C₅	semidirect
14. C₂×C₃²×C₁₃₁	C₂×C₅	semidirect
16. C₃×C₁₃₁⋊C₅	C₂×D₃	semidirect
17. C₃×C₁₃₁⋊C₅	C₂²×C₃	semidirect
18. C₂×D₃₉₃	C₃×C₅	semidirect
20. C₂×C₁₃₁⋊C₅	C₃×D₃	semidirect
22. C₃²×C₁₃₁	C₂²×C₅	semidirect
24. C₂×C₃×C₁₃₁	C₅×D₃	semidirect
25. C₂×C₃×C₁₃₁	C₂×C₃×C₅	semidirect
26. D₃₉₃	C₂×C₃×C₅	semidirect
28. C₁₃₁⋊C₅	C₂×C₃×D₃	semidirect
31. C₃×C₁₃₁	C₂×C₅×D₃	semidirect
32. C₃×C₁₃₁	C₂²×C₃×C₅	semidirect
33. C₂×C₁₃₁	C₃×C₅×D₃	semidirect
36. C₁₃₁	C₂×C₃×C₅×D₃	semidirect
49. C₂×C₃²	D₁₃₁⋊C₅	semidirect
58. C₃²	C₂×D₁₃₁⋊C₅	semidirect
61. C₂×C₃	C₃×D₁₃₁⋊C₅	semidirect
62. C₂×C₃	C₃⋊(D₁₃₁⋊C₅)	direct (N × H)
67. C₃	C₂×C₃×D₁₃₁⋊C₅	semidirect
68. C₃	C₂×C₃⋊(D₁₃₁⋊C₅)	direct (N × H)
70. C₂	C₃×C₃⋊(D₁₃₁⋊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
C₃×C₃⋊(D₁₃₁⋊C₅)	2
C₂×C₃⋊(D₁₃₁⋊C₅)	3
C₂×C₃×D₁₃₁⋊C₅	3
C₂×C₃×D₃₉₃	5
C₂×C₃×C₅×D₃	131

Subgroups — C2×C3×C3⋊(D131⋊C5) #37556092

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₃⋊(D₁₃₁⋊C₅) #37556092