Subgroups — #1204

Order 120.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₁₅	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
4	Dic₁₀	—	3	1	no	maximal, Hall
5	C₂×C₃×C₅	C₂²	1	1	yes	characteristic
6	Dic₆	—	5	1	no	maximal, Hall
7	C₄×C₅	—	3	1	no	—
8	Dic₅	—	3	1	no	—
9	Dic₅	D₃	1	1	yes	characteristic
10	C₃×C₅	Q₈	1	1	yes	characteristic, complemented, Hall
11	C₃×C₄	—	5	1	no	—
12	Dic₃	—	5	1	no	—
13	Dic₃	D₅	1	1	yes	characteristic
14	C₂×C₅	C₂×D₃	1	1	yes	characteristic
15	Q₈	—	15	1	no	Sylow
16	C₂×C₃	C₂×D₅	1	1	yes	characteristic
17	C₅	Dic₆	1	1	yes	characteristic, complemented, Sylow
18	C₄	—	3	1	no	—
19	C₄	—	5	1	no	—
20	C₄	—	15	1	no	—
21	C₃	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
22	C₂	D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₅
commutator, Fitting, socle, prime radical, cosocle	C₂×C₃×C₅	C₂²
hypocenter	C₃×C₅	Q₈
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.