Subgroups — C₂×C₃⋊(C₃⋊D₁₅) #10587458

Order 540.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃³×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃⋊(C₃⋊D₁₅)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊D₁₅	—	3	13	no	maximal
4	C₃³×C₅	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃⋊(C₃⋊D₃)	—	5	1	no	maximal, Hall
6	C₂×C₃²×C₅	D₃	1	13	yes	complemented
7	C₃⋊D₁₅	—	3	26	no	—
8	C₂×D₁₅	—	9	13	no	—
9	C₂×C₃³	D₅	1	1	yes	characteristic, complemented
10	C₃⋊(C₃⋊D₃)	—	5	2	no	—
11	C₃²×C₅	C₂×D₃	1	13	yes	complemented
12	C₂×C₃⋊D₃	—	15	13	no	—
13	C₂×C₃×C₅	C₃⋊D₃	1	13	yes	complemented
14	D₁₅	—	9	26	no	—
15	C₃³	C₂×D₅	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₅	—	27	1	no	Hall
17	C₂×C₃²	D₁₅	1	13	yes	complemented
18	C₃⋊D₃	—	15	26	no	—
19	C₃×C₅	C₂×C₃⋊D₃	1	13	yes	complemented
20	C₂×D₃	—	45	13	no	—
21	C₂×C₅	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
22	D₅	—	27	2	no	—
23	C₃²	C₂×D₁₅	1	13	yes	complemented
24	C₂×C₃	C₃⋊D₁₅	1	13	yes	complemented
25	D₃	—	45	26	no	—
26	C₅	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented, Sylow
27	C₂²	—	135	1	no	Sylow
28	C₃	C₂×C₃⋊D₁₅	1	13	yes	complemented
29	C₂	—	135	2	no	—
30	C₂	C₃⋊(C₃⋊D₁₅)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₃⋊D₁₅)
commutator, cosocle, hypocenter	C₃³×C₅	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₃³×C₅	C₂
LCS	G ▷ C₃³×C₅
UCS	C₁ ◁ C₂

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.