Subgroups — #29506056

Order 15300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₅⋊D₈₅))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#15690391	—	5	6	no	maximal
4	C₃⋊(C₅⋊D₈₅)	—	6	2	no	—
5	#13133344	—	9	1	no	maximal, Hall
6	C₃⋊D₂₅₅	—	5	6	no	—
7	C₃×C₅²×C₁₇	—	2	2	no	—
8	#11744707	—	17	1	no	maximal, Hall
9	C₅⋊D₈₅	—	9	1	no	—
10	C₃²×C₅×C₁₇	AGL(1,𝔽₅)	1	6	yes	complemented
11	#10597479	—	25	1	no	Hall
12	D₂₅₅	—	30	12	no	—
13	C₃⋊(C₃⋊(C₅⋊D₅))	—	17	1	no	—
14	C₅²×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
15	#66776	—	45	6	no	—
16	C₃⋊D₅₁	—	25	1	no	—
17	C₃×C₅×C₁₇	—	2	12	no	—
18	C₃²×C₅²	#595	1	1	yes	characteristic, complemented, Hall
19	#4380	—	85	6	no	—
20	D₈₅	—	45	6	no	—
21	C₃²×C₁₇	#1043	1	1	yes	characteristic, complemented, Hall
22	C₃⋊(C₅⋊D₅)	—	102	2	no	—
23	D₅₁	—	150	2	no	—
24	#1043	—	153	1	no	Hall
25	C₃⋊D₁₅	—	85	6	no	—
26	C₅×C₁₇	#4380	1	6	yes	complemented
27	C₃×C₅²	—	2	2	no	—
28	#595	—	225	1	no	Hall
29	C₃×C₁₇	—	2	2	no	—
30	C₅⋊D₅	—	153	1	no	—
31	C₃²×C₅	#66776	1	6	yes	complemented
32	#157	—	425	1	no	Hall
33	D₁₇	—	225	1	no	—
34	D₁₅	—	510	12	no	—
35	C₅²	#10597479	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	765	6	no	—
37	C₃⋊D₃	—	425	1	no	—
38	C₁₇	#11744707	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	2	12	no	—
40	D₅	—	765	6	no	—
41	C₃²	#13133344	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	2550	2	no	—
43	C₅	#15690391	1	6	yes	complemented
44	C₄	—	3825	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	3825	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₇	C₄
prime radical, cosocle	C₃⋊(C₃⋊(C₅⋊D₈₅))	C₂
LCS	G ▷ C₃²×C₅²×C₁₇
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₁₇	C₄	semidirect
10. C₃²×C₅×C₁₇	AGL(1,𝔽₅)	semidirect
14. C₅²×C₁₇	#157	semidirect
18. C₃²×C₅²	#595	semidirect
21. C₃²×C₁₇	#1043	semidirect
26. C₅×C₁₇	#4380	semidirect
31. C₃²×C₅	#66776	semidirect
35. C₅²	#10597479	semidirect
38. C₁₇	#11744707	semidirect
41. C₃²	#13133344	semidirect
43. C₅	#15690391	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⋊D₈₅))	2
#15690391	5
#13133344	9
#11744707	17