Subgroups — C₃×D₃₇₀₅ #36372731

Order 22230.

72 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	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×D₁₂₃₅	—	3	1	no	maximal
4	C₃×D₇₄₁	—	5	1	no	maximal, Hall
5	C₃×C₅×C₁₃×C₁₉	—	2	1	no	—
6	C₃×C₅×C₁₃×C₁₉	D₃	1	1	yes	characteristic, complemented
7	C₃×C₅×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
8	D₁₂₃₅	—	3	1	no	Hall
9	C₃²×C₁₃×C₁₉	D₅	1	1	yes	characteristic, complemented, Hall
10	C₃×D₂₈₅	—	13	1	no	maximal, Hall
11	D₇₄₁	—	5	1	no	—
12	C₃×D₂₄₇	—	15	1	no	—
13	C₅×C₁₃×C₁₉	C₃×D₃	1	1	yes	characteristic, complemented, Hall
14	C₃×D₁₉₅	—	19	1	no	maximal, Hall
15	C₃²×C₅×C₁₉	D₁₃	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₃×C₁₉	—	2	1	no	—
17	C₃×C₁₃×C₁₉	C₃×D₅	1	1	yes	characteristic, complemented
18	C₃×C₁₃×C₁₉	D₁₅	1	1	yes	characteristic, complemented
19	C₃²×C₅×C₁₃	D₁₉	1	1	yes	characteristic, complemented, Hall
20	D₂₈₅	—	13	1	no	—
21	C₃×D₉₅	—	39	1	no	—
22	D₂₄₇	—	15	1	no	Hall
23	D₁₉₅	—	19	1	no	—
24	C₃×D₆₅	—	57	1	no	—
25	C₃×D₅₇	—	65	1	no	Hall
26	C₃×C₅×C₁₉	—	2	1	no	—
27	C₃×C₅×C₁₉	C₃×D₁₃	1	1	yes	characteristic, complemented
28	C₃×C₅×C₁₉	D₃₉	1	1	yes	characteristic, complemented
29	C₁₃×C₁₉	C₃×D₁₅	1	1	yes	characteristic, complemented, Hall
30	C₃×D₃₉	—	95	1	no	Hall
31	C₃×C₅×C₁₃	—	2	1	no	—
32	C₃×C₅×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
33	C₃×C₅×C₁₃	D₅₇	1	1	yes	characteristic, complemented
34	D₉₅	—	39	1	no	Hall
35	C₃²×C₁₉	D₆₅	1	1	yes	characteristic, complemented, Hall
36	D₆₅	—	57	1	no	Hall
37	C₃²×C₁₃	D₉₅	1	1	yes	characteristic, complemented, Hall
38	D₅₇	—	65	1	no	—
39	C₃×D₁₉	—	195	1	no	—
40	C₅×C₁₉	C₃×D₃₉	1	1	yes	characteristic, complemented, Hall
41	C₃×D₁₅	—	247	1	no	Hall
42	D₃₉	—	95	1	no	—
43	C₃×D₁₃	—	285	1	no	—
44	C₅×C₁₃	C₃×D₅₇	1	1	yes	characteristic, complemented, Hall
45	C₃×C₁₉	—	2	1	no	—
46	C₃×C₁₉	C₃×D₆₅	1	1	yes	characteristic, complemented
47	C₃×C₁₉	D₁₉₅	1	1	yes	characteristic, complemented
48	C₃²×C₅	D₂₄₇	1	1	yes	characteristic, complemented, Hall
49	C₃×C₁₃	—	2	1	no	—
50	C₃×C₁₃	C₃×D₉₅	1	1	yes	characteristic, complemented
51	C₃×C₁₃	D₂₈₅	1	1	yes	characteristic, complemented
52	D₁₉	—	195	1	no	Hall
53	D₁₅	—	247	1	no	—
54	C₃×D₅	—	741	1	no	—
55	D₁₃	—	285	1	no	Hall
56	C₁₉	C₃×D₁₉₅	1	1	yes	characteristic, complemented, Sylow
57	C₃×D₃	—	1235	1	no	Hall
58	C₃×C₅	—	2	1	no	—
59	C₃×C₅	C₃×D₂₄₇	1	1	yes	characteristic, complemented
60	C₃×C₅	D₇₄₁	1	1	yes	characteristic, complemented
61	C₁₃	C₃×D₂₈₅	1	1	yes	characteristic, complemented, Sylow
62	D₅	—	741	1	no	Hall
63	C₃²	D₁₂₃₅	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₃	—	3705	1	no	—
65	D₃	—	1235	1	no	—
66	C₅	C₃×D₇₄₁	1	1	yes	characteristic, complemented, Sylow
67	C₃	—	2	1	no	—
68	C₃	C₃×D₁₂₃₅	1	1	yes	characteristic, complemented
69	C₃	D₃₇₀₅	1	1	yes	characteristic, direct product factor
70	C₂	—	3705	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₃	D₃₇₀₅
commutator, cosocle, hypocenter	C₃×C₅×C₁₃×C₁₉	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃×C₁₉	C₂
LCS	G ▷ C₃×C₅×C₁₃×C₁₉
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅×C₁₃×C₁₉	C₂	semidirect
2. D₃₇₀₅	C₃	direct (N × H)
6. C₃×C₅×C₁₃×C₁₉	D₃	semidirect
7. C₃×C₅×C₁₃×C₁₉	C₂×C₃	semidirect
9. C₃²×C₁₃×C₁₉	D₅	semidirect
13. C₅×C₁₃×C₁₉	C₃×D₃	semidirect
15. C₃²×C₅×C₁₉	D₁₃	semidirect
17. C₃×C₁₃×C₁₉	C₃×D₅	semidirect
18. C₃×C₁₃×C₁₉	D₁₅	semidirect
19. C₃²×C₅×C₁₃	D₁₉	semidirect
27. C₃×C₅×C₁₉	C₃×D₁₃	semidirect
28. C₃×C₅×C₁₉	D₃₉	semidirect
29. C₁₃×C₁₉	C₃×D₁₅	semidirect
32. C₃×C₅×C₁₃	C₃×D₁₉	semidirect
33. C₃×C₅×C₁₃	D₅₇	semidirect
35. C₃²×C₁₉	D₆₅	semidirect
37. C₃²×C₁₃	D₉₅	semidirect
40. C₅×C₁₉	C₃×D₃₉	semidirect
44. C₅×C₁₃	C₃×D₅₇	semidirect
46. C₃×C₁₉	C₃×D₆₅	semidirect
47. C₃×C₁₉	D₁₉₅	semidirect
48. C₃²×C₅	D₂₄₇	semidirect
50. C₃×C₁₃	C₃×D₉₅	semidirect
51. C₃×C₁₃	D₂₈₅	semidirect
56. C₁₉	C₃×D₁₉₅	semidirect
59. C₃×C₅	C₃×D₂₄₇	semidirect
60. C₃×C₅	D₇₄₁	semidirect
61. C₁₃	C₃×D₂₈₅	semidirect
63. C₃²	D₁₂₃₅	semidirect
66. C₅	C₃×D₇₄₁	semidirect
68. C₃	C₃×D₁₂₃₅	semidirect
69. C₃	D₃₇₀₅	direct (N × H)

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×D₁₂₃₅	3
C₃×D₇₄₁	5
C₃×D₂₈₅	13
C₃×D₁₉₅	19

Subgroups — C3×D3705 #36372731

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃₇₀₅ #36372731