Subgroups — #29506057

Order 15300.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×C₃⋊(C₃⋊(C₅⋊D₅))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₁₇	C₄	1	1	yes	characteristic, complemented, Hall
3	#15690392	—	5	6	no	maximal
4	C₁₇×C₃⋊(C₅⋊D₅)	—	6	2	no	—
5	#13133345	—	9	1	no	maximal, Hall
6	C₁₇×C₃⋊D₁₅	—	5	6	no	—
7	C₃×C₅²×C₁₇	—	2	2	no	—
8	#11744707	—	17	1	no	maximal, Hall
9	C₁₇×C₅⋊D₅	—	9	1	no	—
10	C₃²×C₅×C₁₇	AGL(1,𝔽₅)	1	6	yes	complemented
11	#10597480	—	25	1	no	Hall
12	C₁₇×D₁₅	—	30	12	no	—
13	C₃⋊(C₃⋊(C₅⋊D₅))	D₁₇	1	1	yes	characteristic
14	C₅²×C₁₇	#157	1	1	yes	characteristic, complemented, Hall
15	#66774	—	45	6	no	—
16	C₁₇×C₃⋊D₃	—	25	1	no	—
17	C₃×C₅×C₁₇	—	2	12	no	—
18	C₃²×C₅²	Dic₁₇	1	1	yes	characteristic, complemented, Hall
19	#4380	—	85	6	no	—
20	D₅×C₁₇	—	45	6	no	—
21	C₃²×C₁₇	#1043	1	1	yes	characteristic, complemented, Hall
22	C₃⋊(C₅⋊D₅)	—	6	2	no	—
23	D₃×C₁₇	—	150	2	no	—
24	#1043	—	153	1	no	Hall
25	C₃⋊D₁₅	—	5	6	no	—
26	C₅×C₁₇	#4380	1	6	yes	complemented
27	C₃×C₅²	—	2	2	no	—
28	Dic₁₇	—	225	1	no	Hall
29	C₃×C₁₇	—	2	2	no	—
30	C₅⋊D₅	—	9	1	no	—
31	C₃²×C₅	#66774	1	6	yes	complemented
32	#157	—	425	1	no	Hall
33	C₂×C₁₇	—	225	1	no	—
34	D₁₅	—	30	12	no	—
35	C₅²	#10597480	1	1	yes	characteristic, complemented, Sylow
36	AGL(1,𝔽₅)	—	765	6	no	—
37	C₃⋊D₃	—	25	1	no	—
38	C₁₇	#11744707	1	1	yes	characteristic, complemented, Sylow
39	C₃×C₅	—	2	12	no	—
40	D₅	—	45	6	no	—
41	C₃²	#13133345	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	150	2	no	—
43	C₅	#15690392	1	6	yes	complemented
44	C₄	—	3825	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	225	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₁₇	C₄
prime radical, cosocle	C₁₇×C₃⋊(C₃⋊(C₅⋊D₅))	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	Dic₁₇	semidirect
21. C₃²×C₁₇	#1043	semidirect
26. C₅×C₁₇	#4380	semidirect
31. C₃²×C₅	#66774	semidirect
35. C₅²	#10597480	semidirect
38. C₁₇	#11744707	semidirect
41. C₃²	#13133345	semidirect
43. C₅	#15690392	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×C₃⋊(C₃⋊(C₅⋊D₅))	2
#15690392	5
#13133345	9
#11744707	17