Subgroups — C₃×C₂²⋊(C₅²⋊C₃) #11744729

Order 900.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅²	C₃	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊(C₅²⋊C₃)	C₃	1	3	yes	maximal, direct product factor
3	C₃×C₅²⋊C₃	—	4	1	no	maximal, Hall
4	C₂×C₃×C₅²	—	3	1	no	—
5	C₂²×C₅²	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅²	A₄	1	1	yes	characteristic, complemented
7	C₅²⋊C₃	—	4	3	no	—
8	C₂²×C₃×C₅	—	3	2	no	—
9	C₂×C₅²	—	3	1	no	—
10	C₃×A₄	—	25	1	no	maximal, Hall
11	C₂×C₃×C₅	—	3	6	no	—
12	C₅²	C₃×A₄	1	1	yes	characteristic, complemented, Sylow
13	C₂²×C₅	—	3	2	no	—
14	C₃×C₅	—	3	2	no	—
15	C₂²×C₃	C₅²⋊C₃	1	1	yes	characteristic, complemented
16	A₄	—	25	3	no	—
17	C₂×C₅	—	3	6	no	—
18	C₃²	—	100	1	no	Sylow
19	C₂×C₃	—	3	1	no	—
20	C₅	—	3	2	no	—
21	C₂²	C₃×C₅²⋊C₃	1	1	yes	characteristic, complemented, Sylow
22	C₃	—	100	3	no	—
23	C₃	C₂²⋊(C₅²⋊C₃)	1	1	yes	characteristic, direct product factor
24	C₂	—	3	1	no	—

	subgroup	G/H
center, hypercenter	C₃	C₂²⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₅²	C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅²	C₃
LCS	G ▷ C₂²×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.