Subgroups — C₂²×D₁₅ #1236

Order 120.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₁₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×D₅	—	3	1	no	maximal, Hall
4	C₂×C₃×C₅	C₂²	1	3	yes	complemented
5	D₁₅	C₂²	1	4	yes	direct product factor
6	C₂²×D₃	—	5	1	no	maximal, Hall
7	C₂²×C₅	D₃	1	1	yes	characteristic, complemented
8	C₂×D₅	—	3	6	no	—
9	C₃×C₅	C₂³	1	1	yes	characteristic, complemented, Hall
10	C₂²×C₃	D₅	1	1	yes	characteristic, complemented
11	C₂×D₃	—	5	6	no	—
12	C₂×C₅	C₂×D₃	1	3	yes	complemented
13	D₅	—	3	4	no	—
14	C₂³	—	15	1	no	Sylow
15	C₂×C₃	C₂×D₅	1	3	yes	complemented
16	D₃	—	5	4	no	—
17	C₅	C₂²×D₃	1	1	yes	characteristic, complemented, Sylow
18	C₂²	—	15	6	no	—
19	C₂²	D₁₅	1	1	yes	characteristic, direct product factor
20	C₃	C₂²×D₅	1	1	yes	characteristic, complemented, Sylow
21	C₂	—	15	4	no	—
22	C₂	C₂×D₁₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂³
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₅	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₂²

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.