Subgroups — #45658261

Order 32700.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654824	C₂	1	1	yes	maximal, characteristic
2	#24926270	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²⋊C₃×C₁₀₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅⋊D₅₄₅	C₂×C₃	1	1	yes	characteristic
5	C₅²×C₁₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#14546126	—	15	2	no	—
7	C₃×#89137	—	25	1	no	maximal, Hall
8	D₅₄₅	—	15	2	no	—
9	C₃×D₁₀₉	—	25	1	no	—
10	C₅×C₁₀₉	—	3	2	no	—
11	#89137	—	25	1	no	Hall
12	C₃×C₁₀₉	—	25	1	no	Hall
13	#1043⋊C₃	—	109	1	no	maximal, Hall
14	D₁₀₉	—	25	1	no	—
15	(C₅⋊D₅)⋊C₃	—	109	1	no	—
16	C₁₀₉	#1043⋊C₃	1	1	yes	characteristic, complemented, Sylow
17	#1043	—	109	1	no	Hall
18	C₅²⋊C₃	#89137	1	1	yes	characteristic, complemented, Hall
19	C₅⋊D₅	—	109	1	no	—
20	C₅²	C₃×#89137	1	1	yes	characteristic, complemented, Sylow
21	AGL(1,𝔽₅)	—	1635	2	no	—
22	C₃×C₄	—	2725	1	no	Hall
23	D₅	—	1635	2	no	—
24	C₂×C₃	—	2725	1	no	—
25	C₅	—	3	2	no	—
26	C₄	—	2725	1	no	Sylow
27	C₃	—	25	1	no	Sylow
28	C₂	—	2725	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₁₀₉	C₃×C₄
prime radical	#30654824	C₂
cosocle	C₅⋊D₅₄₅	C₂×C₃
LCS	G ▷ C₅²×C₁₀₉
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.