Subgroups — #1200

Order 120.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₅	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅	C₂²	1	1	yes	characteristic
6	D₁₅	C₄	1	2	yes	complemented
7	C₄×D₃	—	5	1	no	maximal, Hall
8	C₂×D₅	—	3	1	no	—
9	C₄×C₅	—	3	1	no	—
10	Dic₅	D₃	1	1	yes	characteristic, complemented
11	C₃×C₅	C₂×C₄	1	1	yes	characteristic, complemented, Hall
12	C₂×D₃	—	5	1	no	—
13	C₃×C₄	—	5	1	no	—
14	Dic₃	D₅	1	1	yes	characteristic, complemented
15	C₂×C₅	C₂×D₃	1	1	yes	characteristic
16	D₅	—	3	2	no	—
17	C₂×C₄	—	15	1	no	Sylow
18	C₂×C₃	C₂×D₅	1	1	yes	characteristic
19	D₃	—	5	2	no	—
20	C₅	C₄×D₃	1	1	yes	characteristic, complemented, Sylow
21	C₂²	—	15	1	no	—
22	C₄	—	3	1	no	—
23	C₄	—	5	1	no	—
24	C₃	C₄×D₅	1	1	yes	characteristic, complemented, Sylow
25	C₂	—	15	2	no	—
26	C₂	D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₅	C₂²
prime radical	C₂×D₁₅	C₂
LCS	G ▷ C₃×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.