Subgroups — #1202

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, complemented
2	C₂×C₃×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₂₀	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅	C₂²	1	1	yes	characteristic
6	D₁₅	—	2	1	no	—
7	C₃×D₅	—	2	1	no	—
8	#67	—	5	1	no	maximal, Hall
9	C₂×D₅	—	3	1	no	—
10	C₂×D₅	D₃	1	1	yes	characteristic, complemented
11	C₄×C₅	—	3	1	no	—
12	C₃×C₅	D₄	1	1	yes	characteristic, complemented, Hall
13	C₂²×C₃	—	5	1	no	—
14	C₂×D₃	—	5	1	no	—
15	Dic₃	D₅	1	1	yes	characteristic, complemented
16	C₂×C₅	C₂×D₃	1	1	yes	characteristic
17	D₅	—	2	1	no	—
18	D₅	—	6	1	no	—
19	D₄	—	15	1	no	Sylow
20	C₂×C₃	—	10	1	no	—
21	C₂×C₃	C₂×D₅	1	1	yes	characteristic
22	D₃	—	10	1	no	—
23	C₅	#67	1	1	yes	characteristic, complemented, Sylow
24	C₂²	—	5	1	no	—
25	C₂²	—	15	1	no	—
26	C₄	—	3	1	no	—
27	C₃	D₂₀	1	1	yes	characteristic, complemented, Sylow
28	C₂	—	10	1	no	—
29	C₂	—	30	1	no	—
30	C₂	D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₅
commutator, Fitting, socle, cosocle	C₂×C₃×C₅	C₂²
hypocenter	C₃×C₅	D₄
LCS	G ▷ C₂×C₃×C₅ ▷ 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.