Subgroups — #6053⋊C₉ #14268077

Order 1800.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1043⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×#6053	C₃	1	1	yes	maximal, characteristic
3	(C₅⋊D₅)⋊C₉	C₄	1	1	yes	characteristic
4	C₃×#1043	C₂×C₃	1	1	yes	characteristic
5	C₅²⋊C₉	C₈	1	1	yes	characteristic, complemented, Hall
6	#6053	C₉	1	1	yes	characteristic, complemented, Hall
7	C₃×C₅⋊D₅	C₃×C₄	1	1	yes	characteristic
8	#1043	C₂×C₉	1	1	yes	characteristic
9	C₃×C₅²	C₃×C₈	1	1	yes	characteristic
10	C₈×C₉	—	25	1	no	maximal, Hall
11	C₃×AGL(1,𝔽₅)	—	30	1	no	—
12	C₅⋊D₅	C₄×C₉	1	1	yes	characteristic
13	C₄×C₉	—	25	1	no	—
14	C₃×D₅	—	30	1	no	—
15	C₅²	C₈×C₉	1	1	yes	characteristic, complemented, Sylow
16	C₃×C₈	—	25	1	no	—
17	AGL(1,𝔽₅)	—	30	1	no	—
18	C₂×C₉	—	25	1	no	—
19	C₃×C₅	—	6	1	no	—
20	C₃×C₄	—	25	1	no	—
21	D₅	—	30	1	no	—
22	C₉	—	25	1	no	Sylow
23	C₈	—	25	1	no	Sylow
24	C₂×C₃	—	25	1	no	—
25	C₅	—	6	1	no	—
26	C₄	—	25	1	no	—
27	C₃	AGL(1,𝔽₂₅)	1	1	yes	characteristic
28	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	AGL(1,𝔽₂₅)
commutator, hypocenter	C₅²	C₈×C₉
Fitting, socle	C₃×C₅²	C₃×C₈
prime radical	C₃×C₅⋊D₅	C₃×C₄
cosocle	C₃×#1043	C₂×C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃

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.