Subgroups — #49147076

Order 36900.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₅⋊D₂₀₅))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	#20301653	—	5	6	no	maximal
4	C₃⋊(C₅⋊D₂₀₅)	—	6	2	no	—
5	#16861518	—	9	1	no	maximal, Hall
6	C₃⋊D₆₁₅	—	5	6	no	—
7	C₃×C₅²×C₄₁	—	2	2	no	—
8	C₅⋊D₂₀₅	—	9	1	no	—
9	C₃²×C₅×C₄₁	AGL(1,𝔽₅)	1	6	yes	complemented
10	#13093287	—	25	1	no	Hall
11	D₆₁₅	—	30	12	no	—
12	C₅²×C₄₁	#157	1	1	yes	characteristic, complemented, Hall
13	#11744707	—	41	1	no	maximal, Hall
14	#11717961	—	45	6	no	—
15	C₃⋊D₁₂₃	—	25	1	no	—
16	C₃×C₅×C₄₁	—	2	12	no	—
17	C₃⋊(C₃⋊(C₅⋊D₅))	—	41	1	no	—
18	D₂₀₅	—	45	6	no	—
19	C₃²×C₄₁	#1043	1	1	yes	characteristic, complemented, Hall
20	D₁₂₃	—	150	2	no	—
21	C₃²×C₅²	#4223	1	1	yes	characteristic, complemented, Hall
22	C₅×C₄₁	#4380	1	6	yes	complemented
23	#4380	—	205	6	no	—
24	#4223	—	225	1	no	Hall
25	C₃⋊(C₅⋊D₅)	—	246	2	no	—
26	C₃×C₄₁	—	2	2	no	—
27	#1043	—	369	1	no	Hall
28	C₃⋊D₁₅	—	205	6	no	—
29	D₄₁	—	225	1	no	—
30	C₃×C₅²	—	2	2	no	—
31	C₅⋊D₅	—	369	1	no	—
32	C₃²×C₅	#11717961	1	6	yes	complemented
33	C₄₁	#11744707	1	1	yes	characteristic, complemented, Sylow
34	#157	—	1025	1	no	Hall
35	D₁₅	—	1230	12	no	—
36	C₅²	#13093287	1	1	yes	characteristic, complemented, Sylow
37	AGL(1,𝔽₅)	—	1845	6	no	—
38	C₃⋊D₃	—	1025	1	no	—
39	C₃×C₅	—	2	12	no	—
40	D₅	—	1845	6	no	—
41	C₃²	#16861518	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	6150	2	no	—
43	C₅	#20301653	1	6	yes	complemented
44	C₄	—	9225	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	9225	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₄₁	C₄
prime radical, cosocle	C₃⋊(C₃⋊(C₅⋊D₂₀₅))	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	AGL(1,𝔽₅)	semidirect
12. C₅²×C₄₁	#157	semidirect
19. C₃²×C₄₁	#1043	semidirect
21. C₃²×C₅²	#4223	semidirect
22. C₅×C₄₁	#4380	semidirect
32. C₃²×C₅	#11717961	semidirect
33. C₄₁	#11744707	semidirect
36. C₅²	#13093287	semidirect
41. C₃²	#16861518	semidirect
43. C₅	#20301653	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₃⋊(C₅⋊D₂₀₅))	2
#20301653	5
#16861518	9
#11744707	41