Subgroups — #11744708

Order 900.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₅⋊D₅))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²	C₄	1	1	yes	characteristic, complemented, Hall
3	#4380	—	5	2	no	maximal
4	C₃⋊(C₅⋊D₅)	—	6	2	no	—
5	#1044	—	9	1	no	maximal, Hall
6	C₃⋊D₁₅	—	5	2	no	—
7	C₃⋊D₁₅	—	10	2	no	—
8	C₃×C₅²	—	2	2	no	—
9	C₅⋊D₅	—	9	1	no	—
10	C₃²×C₅	—	2	2	no	—
11	C₃²×C₅	AGL(1,𝔽₅)	1	2	yes	complemented
12	#157	—	25	1	no	Hall
13	D₁₅	—	30	4	no	—
14	D₁₅	—	30	8	no	—
15	C₅²	#157	1	1	yes	characteristic, complemented, Sylow
16	AGL(1,𝔽₅)	—	45	2	no	—
17	C₃⋊D₃	—	25	1	no	—
18	C₃×C₅	—	2	8	no	—
19	C₃×C₅	—	2	4	no	—
20	D₅	—	45	2	no	—
21	D₅	—	90	2	no	—
22	C₃²	#1044	1	1	yes	characteristic, complemented, Sylow
23	D₃	—	150	2	no	—
24	C₅	—	2	2	no	—
25	C₅	#4380	1	2	yes	complemented
26	C₄	—	225	1	no	Sylow
27	C₃	—	2	2	no	—
28	C₂	—	225	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²	C₄
prime radical, cosocle	C₃⋊(C₃⋊(C₅⋊D₅))	C₂
LCS	G ▷ C₃²×C₅²
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.