Subgroups — C₃⋊D₃₇₀₅ #36372739

Order 22230.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅×C₁₃×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	D₃₇₀₅	—	3	4	no	maximal
3	C₃⋊D₇₄₁	—	5	1	no	maximal, Hall
4	C₃×C₅×C₁₃×C₁₉	D₃	1	4	yes	complemented
5	D₁₂₃₅	—	9	1	no	Hall
6	C₃²×C₁₃×C₁₉	D₅	1	1	yes	characteristic, complemented, Hall
7	C₃⋊D₂₈₅	—	13	1	no	maximal, Hall
8	D₇₄₁	—	15	4	no	—
9	C₅×C₁₃×C₁₉	C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
10	C₃⋊D₁₉₅	—	19	1	no	maximal, Hall
11	C₃²×C₅×C₁₉	D₁₃	1	1	yes	characteristic, complemented, Hall
12	C₃×C₁₃×C₁₉	D₁₅	1	4	yes	complemented
13	C₃²×C₅×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
14	D₂₈₅	—	39	4	no	—
15	D₂₄₇	—	45	1	no	Hall
16	D₁₉₅	—	57	4	no	—
17	C₃⋊D₅₇	—	65	1	no	Hall
18	C₃×C₅×C₁₉	D₃₉	1	4	yes	complemented
19	C₁₃×C₁₉	C₃⋊D₁₅	1	1	yes	characteristic, complemented, Hall
20	C₃⋊D₃₉	—	95	1	no	Hall
21	C₃×C₅×C₁₃	D₅₇	1	4	yes	complemented
22	D₉₅	—	117	1	no	Hall
23	C₃²×C₁₉	D₆₅	1	1	yes	characteristic, complemented, Hall
24	D₆₅	—	171	1	no	Hall
25	C₃²×C₁₃	D₉₅	1	1	yes	characteristic, complemented, Hall
26	D₅₇	—	195	4	no	—
27	C₅×C₁₉	C₃⋊D₃₉	1	1	yes	characteristic, complemented, Hall
28	C₃⋊D₁₅	—	247	1	no	Hall
29	D₃₉	—	285	4	no	—
30	C₅×C₁₃	C₃⋊D₅₇	1	1	yes	characteristic, complemented, Hall
31	C₃×C₁₉	D₁₉₅	1	4	yes	complemented
32	C₃²×C₅	D₂₄₇	1	1	yes	characteristic, complemented, Hall
33	C₃×C₁₃	D₂₈₅	1	4	yes	complemented
34	D₁₉	—	585	1	no	Hall
35	D₁₅	—	741	4	no	—
36	D₁₃	—	855	1	no	Hall
37	C₁₉	C₃⋊D₁₉₅	1	1	yes	characteristic, complemented, Sylow
38	C₃⋊D₃	—	1235	1	no	Hall
39	C₃×C₅	D₇₄₁	1	4	yes	complemented
40	C₁₃	C₃⋊D₂₈₅	1	1	yes	characteristic, complemented, Sylow
41	D₅	—	2223	1	no	Hall
42	C₃²	D₁₂₃₅	1	1	yes	characteristic, complemented, Sylow
43	D₃	—	3705	4	no	—
44	C₅	C₃⋊D₇₄₁	1	1	yes	characteristic, complemented, Sylow
45	C₃	D₃₇₀₅	1	4	yes	complemented
46	C₂	—	11115	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₃²×C₅×C₁₃×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃×C₁₉	C₂	semidirect
4. C₃×C₅×C₁₃×C₁₉	D₃	semidirect
6. C₃²×C₁₃×C₁₉	D₅	semidirect
9. C₅×C₁₃×C₁₉	C₃⋊D₃	semidirect
11. C₃²×C₅×C₁₉	D₁₃	semidirect
12. C₃×C₁₃×C₁₉	D₁₅	semidirect
13. C₃²×C₅×C₁₃	D₁₉	semidirect
18. C₃×C₅×C₁₉	D₃₉	semidirect
19. C₁₃×C₁₉	C₃⋊D₁₅	semidirect
21. C₃×C₅×C₁₃	D₅₇	semidirect
23. C₃²×C₁₉	D₆₅	semidirect
25. C₃²×C₁₃	D₉₅	semidirect
27. C₅×C₁₉	C₃⋊D₃₉	semidirect
30. C₅×C₁₃	C₃⋊D₅₇	semidirect
31. C₃×C₁₉	D₁₉₅	semidirect
32. C₃²×C₅	D₂₄₇	semidirect
33. C₃×C₁₃	D₂₈₅	semidirect
37. C₁₉	C₃⋊D₁₉₅	semidirect
39. C₃×C₅	D₇₄₁	semidirect
40. C₁₃	C₃⋊D₂₈₅	semidirect
42. C₃²	D₁₂₃₅	semidirect
44. C₅	C₃⋊D₇₄₁	semidirect
45. C₃	D₃₇₀₅	semidirect

Maximal subgroups

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

subgroup	index
C₃²×C₅×C₁₃×C₁₉	2
D₃₇₀₅	3
C₃⋊D₇₄₁	5
C₃⋊D₂₈₅	13
C₃⋊D₁₉₅	19

Subgroups — C3⋊D3705 #36372739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃⋊D₃₇₀₅ #36372739