Subgroups — #16813737⋊C₃ #24925813

Order 10860.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(D₁₈₁⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	#16813737	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅×C₁₈₁⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	#10624382⋊C₃	—	5	1	no	maximal, Hall
5	D₉₀₅	C₂×C₃	1	1	yes	characteristic
6	D₁₈₁⋊C₃	—	5	1	no	—
7	C₅×C₁₈₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	#10624382	—	5	1	no	Hall
9	C₁₈₁⋊C₃	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
10	D₁₈₁	—	5	1	no	—
11	C₁₈₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
12	C₃×AGL(1,𝔽₅)	—	181	1	no	maximal, Hall
13	C₃×D₅	—	181	1	no	—
14	AGL(1,𝔽₅)	—	181	1	no	Hall
15	C₃×C₅	—	181	1	no	Hall
16	C₃×C₄	—	905	1	no	Hall
17	D₅	—	181	1	no	—
18	C₂×C₃	—	905	1	no	—
19	C₅	#10624382⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₄	—	905	1	no	Sylow
21	C₃	—	181	1	no	Sylow
22	C₂	—	905	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅×C₁₈₁	C₃×C₄
prime radical	C₅⋊(D₁₈₁⋊C₃)	C₂
cosocle	D₉₀₅	C₂×C₃
LCS	G ▷ C₅×C₁₈₁
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.