Subgroups — #49147074

Order 36900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₃⋊D₃×C₄₁	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#20301658	—	5	6	no	maximal
4	C₅²×D₃×C₄₁	—	6	2	no	—
5	#16861497	—	9	1	no	maximal, Hall
6	C₅×C₃⋊D₃×C₄₁	D₅	1	6	yes	—
7	C₃×C₅²×C₄₁	—	2	2	no	—
8	C₂×C₅²×C₄₁	—	9	1	no	—
9	C₃²×C₅×C₄₁	Dic₅	1	6	yes	complemented
10	#13093288	—	25	1	no	Hall
11	C₅×D₃×C₄₁	—	6	12	no	—
12	C₅²×C₄₁	#157	1	1	yes	characteristic, complemented, Hall
13	#11744710	—	41	1	no	maximal, Hall
14	Dic₂₀₅	—	45	6	no	—
15	C₃⋊D₃×C₄₁	C₅⋊D₅	1	1	yes	characteristic
16	C₃×C₅×C₄₁	—	2	12	no	—
17	C₅²×C₃⋊D₃	D₄₁	1	1	yes	characteristic
18	C₂×C₅×C₄₁	—	9	6	no	—
19	C₃²×C₄₁	#1039	1	1	yes	characteristic, complemented, Hall
20	D₃×C₄₁	—	6	2	no	—
21	C₃²×C₅²	Dic₄₁	1	1	yes	characteristic, complemented, Hall
22	C₅×C₄₁	#4379	1	6	yes	complemented
23	#4379	—	205	6	no	—
24	Dic₄₁	—	225	1	no	Hall
25	C₅²×D₃	—	6	2	no	—
26	C₃×C₄₁	—	2	2	no	—
27	#1039	—	369	1	no	Hall
28	C₅×C₃⋊D₃	D₂₀₅	1	6	yes	—
29	C₂×C₄₁	—	9	1	no	—
30	C₃×C₅²	—	2	2	no	—
31	C₂×C₅²	—	9	1	no	—
32	C₃²×C₅	Dic₂₀₅	1	6	yes	complemented
33	C₄₁	#11744710	1	1	yes	characteristic, complemented, Sylow
34	#157	—	1025	1	no	Hall
35	C₅×D₃	—	6	12	no	—
36	C₅²	#13093288	1	1	yes	characteristic, complemented, Sylow
37	Dic₅	—	1845	6	no	—
38	C₃⋊D₃	C₅⋊D₂₀₅	1	1	yes	characteristic
39	C₃×C₅	—	2	12	no	—
40	C₂×C₅	—	9	6	no	—
41	C₃²	#16861497	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6	2	no	—
43	C₅	#20301658	1	6	yes	complemented
44	C₄	—	9225	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₄₁	C₄
prime radical, cosocle	C₅²×C₃⋊D₃×C₄₁	C₂
LCS	G ▷ C₃²×C₅²×C₄₁
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₄₁	C₄	semidirect
9. C₃²×C₅×C₄₁	Dic₅	semidirect
12. C₅²×C₄₁	#157	semidirect
19. C₃²×C₄₁	#1039	semidirect
21. C₃²×C₅²	Dic₄₁	semidirect
22. C₅×C₄₁	#4379	semidirect
32. C₃²×C₅	Dic₂₀₅	semidirect
33. C₄₁	#11744710	semidirect
36. C₅²	#13093288	semidirect
41. C₃²	#16861497	semidirect
43. C₅	#20301658	semidirect

Maximal subgroups

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

subgroup	index
C₅²×C₃⋊D₃×C₄₁	2
#20301658	5
#16861497	9
#11744710	41