Subgroups — #45685919

Order 33300.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₃⋊D₇₅	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₂₅×C₃₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#20269167	—	5	1	no	maximal
4	C₃₇×D₇₅	—	6	2	no	—
5	#16814856	—	9	1	no	maximal, Hall
6	C₃₇×C₃⋊D₁₅	—	5	1	no	—
7	C₃×C₂₅×C₃₇	—	2	2	no	—
8	C₃₇×D₂₅	—	9	1	no	—
9	C₃²×C₅×C₃₇	AGL(1,𝔽₅)	1	1	yes	characteristic
10	#13050653	—	25	1	no	Hall
11	D₁₅×C₃₇	—	30	2	no	—
12	C₂₅×C₃₇	#157	1	1	yes	characteristic, complemented, Hall
13	#11744621	—	37	1	no	maximal, Hall
14	#10625193	—	45	1	no	—
15	C₃⋊D₃×C₃₇	—	25	1	no	—
16	C₃×C₅×C₃₇	—	2	2	no	—
17	C₃⋊D₇₅	D₃₇	1	1	yes	characteristic
18	D₅×C₃₇	—	45	1	no	—
19	C₃²×C₃₇	#1035	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₂₅	Dic₃₇	1	1	yes	characteristic, complemented, Hall
21	D₃×C₃₇	—	150	2	no	—
22	C₅×C₃₇	#4380	1	1	yes	characteristic
23	#4380	—	185	1	no	—
24	D₇₅	—	6	2	no	—
25	Dic₃₇	—	225	1	no	Hall
26	C₃×C₃₇	—	2	2	no	—
27	#1035	—	333	1	no	Hall
28	C₃⋊D₁₅	—	5	1	no	—
29	C₃×C₂₅	—	2	2	no	—
30	C₂×C₃₇	—	225	1	no	—
31	D₂₅	—	9	1	no	—
32	C₃²×C₅	#10625193	1	1	yes	characteristic
33	C₃₇	#11744621	1	1	yes	characteristic, complemented, Sylow
34	#157	—	925	1	no	Hall
35	D₁₅	—	30	2	no	—
36	C₂₅	#13050653	1	1	yes	characteristic, complemented, Sylow
37	AGL(1,𝔽₅)	—	1665	1	no	—
38	C₃⋊D₃	—	25	1	no	—
39	C₃×C₅	—	2	2	no	—
40	D₅	—	45	1	no	—
41	C₃²	#16814856	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	150	2	no	—
43	C₅	#20269167	1	1	yes	characteristic
44	C₄	—	8325	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	225	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₃²×C₂₅×C₃₇	C₄
Frattini	C₅	#20269167
socle	C₃²×C₅×C₃₇	AGL(1,𝔽₅)
prime radical, cosocle	C₃₇×C₃⋊D₇₅	C₂
LCS	G ▷ C₃²×C₂₅×C₃₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₂₅×C₃₇	C₄	semidirect
12. C₂₅×C₃₇	#157	semidirect
19. C₃²×C₃₇	#1035	semidirect
20. C₃²×C₂₅	Dic₃₇	semidirect
33. C₃₇	#11744621	semidirect
36. C₂₅	#13050653	semidirect
41. C₃²	#16814856	semidirect

Maximal subgroups

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

subgroup	index
C₃₇×C₃⋊D₇₅	2
#20269167	5
#16814856	9
#11744621	37