Subgroups — C₃²×C₅⋊D₅×D₃₇ #45686398

Order 33300.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₅²×D₃₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃²×C₃₇×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₅⋊D₁₈₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅⋊D₅×D₃₇	C₃	1	4	yes	maximal, direct product factor
5	C₃²×C₅²×C₃₇	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃²×D₅×D₃₇	—	5	6	no	maximal
7	C₃×C₅⋊D₁₈₅	C₂×C₃	1	4	yes	complemented
8	C₃×C₃₇×C₅⋊D₅	C₂×C₃	1	4	yes	complemented
9	C₃×C₅²×D₃₇	C₂×C₃	1	4	yes	complemented
10	C₅⋊D₅×D₃₇	C₃²	1	1	yes	characteristic, direct product factor, Hall
11	C₃²×D₁₈₅	—	5	6	no	—
12	C₃²×D₅×C₃₇	—	5	6	no	—
13	C₃²×C₅×D₃₇	D₅	1	6	yes	complemented
14	C₃×C₅²×C₃₇	C₂²×C₃	1	4	yes	complemented
15	C₃×D₅×D₃₇	—	5	24	no	—
16	C₅⋊D₁₈₅	C₂×C₃²	1	1	yes	characteristic, complemented
17	C₃₇×C₅⋊D₅	C₂×C₃²	1	1	yes	characteristic, complemented
18	C₅²×D₃₇	C₂×C₃²	1	1	yes	characteristic, complemented
19	C₃²×C₅×C₃₇	C₂×D₅	1	6	yes	complemented
20	C₂×C₃²×D₃₇	—	25	1	no	Hall
21	C₃×D₁₈₅	—	5	24	no	—
22	C₃×D₅×C₃₇	—	5	24	no	—
23	C₃×C₅×D₃₇	C₃×D₅	1	24	yes	complemented
24	C₅²×C₃₇	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
25	C₂×C₃²×C₅⋊D₅	—	37	1	no	maximal, Hall
26	D₅×D₃₇	—	5	6	no	—
27	C₂×C₃²×C₃₇	—	25	1	no	—
28	C₃²×D₃₇	—	25	1	no	—
29	C₃²×D₃₇	C₅⋊D₅	1	1	yes	characteristic, direct product factor
30	C₃×C₅×C₃₇	C₂×C₃×D₅	1	24	yes	complemented
31	C₂×C₃²×C₅²	—	37	1	no	—
32	C₃²×C₅⋊D₅	—	37	1	no	—
33	C₃²×C₅⋊D₅	D₃₇	1	1	yes	characteristic, direct product factor
34	C₂×C₃×D₃₇	—	25	4	no	—
35	D₁₈₅	—	5	6	no	—
36	C₅×D₃₇	C₃²×D₅	1	6	yes	complemented
37	D₅×C₃₇	—	5	6	no	—
38	C₃²×C₃₇	C₂×C₅⋊D₅	1	1	yes	characteristic, complemented, Hall
39	C₂×C₃×C₅⋊D₅	—	37	4	no	—
40	C₃²×C₅²	C₂×D₃₇	1	1	yes	characteristic, complemented, Hall
41	C₂×C₃×C₃₇	—	25	4	no	—
42	C₃×D₃₇	—	25	4	no	—
43	C₃×D₃₇	C₃×C₅⋊D₅	1	4	yes	direct product factor
44	C₅×C₃₇	C₂×C₃²×D₅	1	6	yes	complemented
45	C₂×C₃²×D₅	—	185	6	no	—
46	C₂×C₃×C₅²	—	37	4	no	—
47	C₃×C₅⋊D₅	—	37	4	no	—
48	C₃×C₅⋊D₅	C₃×D₃₇	1	4	yes	direct product factor
49	C₂×D₃₇	—	25	1	no	Hall
50	C₃×C₃₇	C₂×C₃×C₅⋊D₅	1	4	yes	complemented
51	C₂×C₅⋊D₅	—	37	1	no	Hall
52	C₂×C₃²×C₅	—	37	6	no	—
53	C₃²×D₅	—	5	6	no	—
54	C₃²×D₅	—	185	6	no	—
55	C₃×C₅²	C₂×C₃×D₃₇	1	4	yes	complemented
56	C₂×C₃₇	—	25	1	no	—
57	D₃₇	—	25	1	no	—
58	D₃₇	C₃²×C₅⋊D₅	1	1	yes	characteristic, direct product factor
59	C₂×C₃×D₅	—	185	24	no	—
60	C₂×C₅²	—	37	1	no	—
61	C₅⋊D₅	—	37	1	no	—
62	C₅⋊D₅	C₃²×D₃₇	1	1	yes	characteristic, direct product factor
63	C₃²×C₅	D₅×D₃₇	1	6	yes	complemented
64	C₃₇	C₂×C₃²×C₅⋊D₅	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₃²	—	925	1	no	Hall
66	C₂×C₃×C₅	—	37	24	no	—
67	C₃×D₅	—	5	24	no	—
68	C₃×D₅	—	185	24	no	—
69	C₅²	C₂×C₃²×D₃₇	1	1	yes	characteristic, complemented, Sylow
70	C₂×D₅	—	185	6	no	—
71	C₂×C₃²	—	25	1	no	—
72	C₂×C₃²	—	37	1	no	—
73	C₂×C₃²	—	925	1	no	—
74	C₃×C₅	C₃×D₅×D₃₇	1	24	yes	complemented
75	C₂²×C₃	—	925	4	no	—
76	C₂×C₅	—	37	6	no	—
77	D₅	—	5	6	no	—
78	D₅	—	185	6	no	—
79	C₃²	C₅⋊D₅×D₃₇	1	1	yes	characteristic, direct product factor, Sylow
80	C₂×C₃	—	25	4	no	—
81	C₂×C₃	—	37	4	no	—
82	C₂×C₃	—	925	4	no	—
83	C₅	C₃²×D₅×D₃₇	1	6	yes	complemented
84	C₂²	—	925	1	no	Sylow
85	C₃	C₃×C₅⋊D₅×D₃₇	1	4	yes	direct product factor
86	C₂	—	25	1	no	—
87	C₂	—	37	1	no	—
88	C₂	—	925	1	no	—

	subgroup	G/H
center, hypercenter	C₃²	C₅⋊D₅×D₃₇
commutator, cosocle, hypocenter	C₅²×C₃₇	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₃²×C₅²×C₃₇	C₂²
LCS	G ▷ C₅²×C₃₇
UCS	C₁ ◁ C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×C₅²×D₃₇	C₂	semidirect
2. C₃²×C₃₇×C₅⋊D₅	C₂	semidirect
3. C₃²×C₅⋊D₁₈₅	C₂	semidirect
4. C₃×C₅⋊D₅×D₃₇	C₃	direct (N × H)
5. C₃²×C₅²×C₃₇	C₂²	semidirect
7. C₃×C₅⋊D₁₈₅	C₂×C₃	semidirect
8. C₃×C₃₇×C₅⋊D₅	C₂×C₃	semidirect
9. C₃×C₅²×D₃₇	C₂×C₃	semidirect
10. C₅⋊D₅×D₃₇	C₃²	direct (N × H)
13. C₃²×C₅×D₃₇	D₅	semidirect
14. C₃×C₅²×C₃₇	C₂²×C₃	semidirect
16. C₅⋊D₁₈₅	C₂×C₃²	semidirect
17. C₃₇×C₅⋊D₅	C₂×C₃²	semidirect
18. C₅²×D₃₇	C₂×C₃²	semidirect
19. C₃²×C₅×C₃₇	C₂×D₅	semidirect
23. C₃×C₅×D₃₇	C₃×D₅	semidirect
24. C₅²×C₃₇	C₂²×C₃²	semidirect
29. C₃²×D₃₇	C₅⋊D₅	direct (N × H)
30. C₃×C₅×C₃₇	C₂×C₃×D₅	semidirect
33. C₃²×C₅⋊D₅	D₃₇	direct (N × H)
36. C₅×D₃₇	C₃²×D₅	semidirect
38. C₃²×C₃₇	C₂×C₅⋊D₅	semidirect
40. C₃²×C₅²	C₂×D₃₇	semidirect
43. C₃×D₃₇	C₃×C₅⋊D₅	direct (N × H)
44. C₅×C₃₇	C₂×C₃²×D₅	semidirect
48. C₃×C₅⋊D₅	C₃×D₃₇	direct (N × H)
50. C₃×C₃₇	C₂×C₃×C₅⋊D₅	semidirect
55. C₃×C₅²	C₂×C₃×D₃₇	semidirect
58. D₃₇	C₃²×C₅⋊D₅	direct (N × H)
62. C₅⋊D₅	C₃²×D₃₇	direct (N × H)
63. C₃²×C₅	D₅×D₃₇	semidirect
64. C₃₇	C₂×C₃²×C₅⋊D₅	semidirect
69. C₅²	C₂×C₃²×D₃₇	semidirect
74. C₃×C₅	C₃×D₅×D₃₇	semidirect
79. C₃²	C₅⋊D₅×D₃₇	direct (N × H)
83. C₅	C₃²×D₅×D₃₇	semidirect
85. C₃	C₃×C₅⋊D₅×D₃₇	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×C₅²×D₃₇	2
C₃²×C₃₇×C₅⋊D₅	2
C₃²×C₅⋊D₁₈₅	2
C₃×C₅⋊D₅×D₃₇	3
C₃²×D₅×D₃₇	5
C₂×C₃²×C₅⋊D₅	37

Subgroups — C32×C5⋊D5×D37 #45686398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×C₅⋊D₅×D₃₇ #45686398