Subgroups — #43274635

Order 28900.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₁₄₄₅	C₂	1	1	yes	maximal, characteristic
2	C₅²×C₂₈₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#19153590	—	5	6	no	maximal
4	D₁₄₄₅	—	5	6	no	—
5	#13133343	—	17	1	no	maximal
6	C₅×C₂₈₉	AGL(1,𝔽₅)	1	6	yes	complemented
7	#11923876	—	25	1	no	Hall
8	C₅⋊D₈₅	—	17	1	no	—
9	D₂₈₉	—	25	1	no	—
10	C₅²×C₁₇	#595	1	1	yes	characteristic
11	#66775	—	85	6	no	—
12	C₂₈₉	#1043	1	1	yes	characteristic, complemented, Sylow
13	D₈₅	—	85	6	no	—
14	#1043	—	289	1	no	Hall
15	C₅×C₁₇	#66775	1	6	yes	—
16	#595	—	425	1	no	—
17	C₅⋊D₅	—	289	1	no	—
18	D₁₇	—	425	1	no	—
19	C₅²	#11923876	1	1	yes	characteristic, complemented, Sylow
20	AGL(1,𝔽₅)	—	1445	6	no	—
21	C₁₇	#13133343	1	1	yes	characteristic
22	D₅	—	1445	6	no	—
23	C₅	#19153590	1	6	yes	complemented
24	C₄	—	7225	1	no	Sylow
25	C₂	—	7225	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₅²×C₂₈₉	C₄
Frattini	C₁₇	#13133343
socle	C₅²×C₁₇	#595
prime radical, cosocle	C₅⋊D₁₄₄₅	C₂
LCS	G ▷ C₅²×C₂₈₉
UCS	C₁

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

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