Subgroups — #45656359

Order 32580.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊(#13108656⋊C₂)	C₂	1	1	yes	maximal, characteristic
2	C₃×#16813738	C₃	1	1	yes	maximal, characteristic
3	C₅×#13108656	C₄	1	1	yes	characteristic, complemented, Hall
4	#20266771	—	5	1	no	maximal, Hall
5	C₃×D₉₀₅	C₂×C₃	1	1	yes	characteristic
6	#16813738	C₉	1	1	yes	characteristic, complemented, Hall
7	#13108656⋊C₂	—	5	1	no	—
8	C₃×C₅×C₁₈₁	C₃×C₄	1	1	yes	characteristic
9	C₃×#10624382	—	5	1	no	—
10	D₉₀₅	C₂×C₉	1	1	yes	characteristic
11	#13108656	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	C₃×D₁₈₁	—	5	1	no	—
13	C₅×C₁₈₁	C₄×C₉	1	1	yes	characteristic, complemented, Hall
14	#10624382	—	5	1	no	Hall
15	C₃×C₁₈₁	C₃×AGL(1,𝔽₅)	1	1	yes	characteristic
16	D₁₈₁	—	5	1	no	—
17	C₁₈₁	C₉×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Sylow
18	C₉×AGL(1,𝔽₅)	—	181	1	no	maximal, Hall
19	C₉×D₅	—	181	1	no	—
20	C₃×AGL(1,𝔽₅)	—	181	1	no	—
21	C₅×C₉	—	181	1	no	Hall
22	C₄×C₉	—	905	1	no	Hall
23	C₃×D₅	—	181	1	no	—
24	AGL(1,𝔽₅)	—	181	1	no	Hall
25	C₂×C₉	—	905	1	no	—
26	C₃×C₅	#10624382⋊C₃	1	1	yes	characteristic
27	C₃×C₄	—	905	1	no	—
28	D₅	—	181	1	no	—
29	C₉	—	181	1	no	Sylow
30	C₂×C₃	—	905	1	no	—
31	C₅	#20266771	1	1	yes	characteristic, complemented, Sylow
32	C₄	—	905	1	no	Sylow
33	C₃	#16813738⋊C₃	1	1	yes	characteristic
34	C₂	—	905	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	#16813738⋊C₃
commutator, hypocenter	C₅×C₁₈₁	C₄×C₉
Fitting, socle	C₃×C₅×C₁₈₁	C₃×C₄
prime radical, cosocle	C₃×D₉₀₅	C₂×C₃
LCS	G ▷ C₅×C₁₈₁
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.