Subgroups — D₃×C₃⋊(D₁₃₁⋊C₅) #37556086

Order 23580.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(D₁₃₁⋊C₅))	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₃×C₁₃₁⋊C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃⋊(D₁₃₁⋊C₅)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃⋊(D₁₃₁⋊C₅)	—	3	1	no	maximal
5	D₃×D₁₃₁⋊C₅	—	3	1	no	maximal
6	C₃²×C₁₃₁⋊C₅	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×D₃₉₃	C₅	1	1	yes	maximal, characteristic, complemented, Hall
8	C₃⋊(D₁₃₁⋊C₅)	—	3	1	no	—
9	C₃⋊(D₁₃₁⋊C₅)	—	3	1	no	—
10	C₃⋊(D₁₃₁⋊C₅)	—	6	1	no	—
11	C₃⋊(D₁₃₁⋊C₅)	D₃	1	1	yes	characteristic, direct product factor
12	D₃×C₁₃₁⋊C₅	D₃	1	1	yes	characteristic, complemented
13	C₃×D₁₃₁⋊C₅	—	3	1	no	—
14	C₂×C₃×C₁₃₁⋊C₅	—	3	1	no	—
15	C₂×D₁₃₁⋊C₅	—	9	1	no	Hall
16	C₃⋊D₃₉₃	C₂×C₅	1	1	yes	characteristic, complemented
17	C₃×D₃₉₃	C₂×C₅	1	1	yes	characteristic, complemented
18	C₃×D₃×C₁₃₁	C₂×C₅	1	1	yes	characteristic, complemented
19	C₃×C₁₃₁⋊C₅	—	2	1	no	—
20	C₃×C₁₃₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₁₃₁⋊C₅	C₂×D₃	1	1	yes	characteristic, complemented
22	C₂×D₃₉₃	—	3	1	no	—
23	D₃×D₁₃₁	—	3	1	no	—
24	C₂×C₁₃₁⋊C₅	—	3	1	no	—
25	D₁₃₁⋊C₅	—	3	1	no	—
26	D₁₃₁⋊C₅	—	9	1	no	—
27	C₃²×C₁₃₁	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₃₁	—	3	1	no	—
29	D₃₉₃	—	3	1	no	—
30	D₃₉₃	—	3	1	no	—
31	D₃₉₃	—	6	1	no	—
32	D₃₉₃	C₅×D₃	1	1	yes	characteristic, complemented
33	C₃×D₁₃₁	—	3	1	no	—
34	D₃×C₁₃₁	C₅×D₃	1	1	yes	characteristic, complemented
35	C₁₃₁⋊C₅	D₃²	1	1	yes	characteristic, complemented, Hall
36	C₂×D₁₃₁	—	9	1	no	Hall
37	C₃×C₁₃₁	—	2	1	no	—
38	C₃×C₁₃₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
39	C₃×C₁₃₁	C₂×C₅×D₃	1	1	yes	characteristic, complemented
40	C₂×C₁₃₁	—	3	1	no	—
41	D₁₃₁	—	3	1	no	—
42	D₁₃₁	—	9	1	no	—
43	C₅×D₃²	—	131	1	no	maximal, Hall
44	C₁₃₁	C₅×D₃²	1	1	yes	characteristic, complemented, Sylow
45	C₅×C₃⋊D₃	—	131	1	no	—
46	C₃×C₅×D₃	—	131	1	no	—
47	C₃×C₅×D₃	—	131	1	no	—
48	C₂×C₅×D₃	—	393	1	no	—
49	C₂×C₅×D₃	—	393	1	no	—
50	C₃²×C₅	—	131	1	no	Hall
51	D₃²	—	131	1	no	Hall
52	C₂×C₃×C₅	—	393	1	no	—
53	C₂×C₃×C₅	—	393	1	no	—
54	C₅×D₃	—	786	1	no	—
55	C₅×D₃	—	131	1	no	—
56	C₅×D₃	—	131	1	no	—
57	C₅×D₃	—	393	1	no	—
58	C₅×D₃	—	393	1	no	—
59	C₂²×C₅	—	1179	1	no	Hall
60	C₃⋊D₃	—	131	1	no	—
61	C₃×D₃	—	131	1	no	—
62	C₃×D₃	D₁₃₁⋊C₅	1	1	yes	characteristic, complemented
63	C₃×C₅	—	262	1	no	—
64	C₃×C₅	—	131	1	no	—
65	C₃×C₅	—	131	1	no	—
66	C₂×D₃	—	393	1	no	—
67	C₂×D₃	—	393	1	no	—
68	C₂×C₅	—	393	1	no	—
69	C₂×C₅	—	393	1	no	—
70	C₂×C₅	—	1179	1	no	—
71	C₃²	C₂×D₁₃₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	3	1	no	—
73	C₂×C₃	—	393	1	no	—
74	D₃	—	786	1	no	—
75	D₃	—	131	1	no	—
76	D₃	—	393	1	no	—
77	D₃	—	393	1	no	—
78	D₃	C₃⋊(D₁₃₁⋊C₅)	1	1	yes	characteristic, direct product factor
79	C₅	—	131	1	no	Sylow
80	C₂²	—	1179	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₁₃₁⋊C₅	1	1	yes	characteristic, complemented
83	C₃	C₂×C₃⋊(D₁₃₁⋊C₅)	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	393	1	no	—
86	C₂	—	1179	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₁₃₁	C₂²×C₅
LCS	G ▷ C₃²×C₁₃₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊(C₃⋊(D₁₃₁⋊C₅))	C₂	semidirect
2. C₃×D₃×C₁₃₁⋊C₅	C₂	semidirect
3. C₃×C₃⋊(D₁₃₁⋊C₅)	C₂	semidirect
6. C₃²×C₁₃₁⋊C₅	C₂²	semidirect
7. D₃×D₃₉₃	C₅	semidirect
11. C₃⋊(D₁₃₁⋊C₅)	D₃	direct (N × H)
12. D₃×C₁₃₁⋊C₅	D₃	semidirect
16. C₃⋊D₃₉₃	C₂×C₅	semidirect
17. C₃×D₃₉₃	C₂×C₅	semidirect
18. C₃×D₃×C₁₃₁	C₂×C₅	semidirect
20. C₃×C₁₃₁⋊C₅	C₂×D₃	semidirect
21. C₃×C₁₃₁⋊C₅	C₂×D₃	semidirect
27. C₃²×C₁₃₁	C₂²×C₅	semidirect
32. D₃₉₃	C₅×D₃	semidirect
34. D₃×C₁₃₁	C₅×D₃	semidirect
35. C₁₃₁⋊C₅	D₃²	semidirect
38. C₃×C₁₃₁	C₂×C₅×D₃	semidirect
39. C₃×C₁₃₁	C₂×C₅×D₃	semidirect
44. C₁₃₁	C₅×D₃²	semidirect
62. C₃×D₃	D₁₃₁⋊C₅	semidirect
71. C₃²	C₂×D₁₃₁⋊C₅	semidirect
78. D₃	C₃⋊(D₁₃₁⋊C₅)	direct (N × H)
82. C₃	D₃×D₁₃₁⋊C₅	semidirect
83. C₃	C₂×C₃⋊(D₁₃₁⋊C₅)	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₃⋊(D₁₃₁⋊C₅))	2
C₃×D₃×C₁₃₁⋊C₅	2
C₃×C₃⋊(D₁₃₁⋊C₅)	2
C₂×C₃⋊(D₁₃₁⋊C₅)	3
D₃×D₁₃₁⋊C₅	3
D₃×D₃₉₃	5
C₅×D₃²	131

Subgroups — D3×C3⋊(D131⋊C5) #37556086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×C₃⋊(D₁₃₁⋊C₅) #37556086