Subgroups — D₁₂₀ #6707

Order 240.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₀	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄₀	—	3	1	no	maximal, Hall
4	C₂×D₁₅	—	2	2	no	—
5	C₃×C₄×C₅	C₂²	1	1	yes	characteristic
6	D₂₄	—	5	1	no	maximal, Hall
7	D₂₀	—	3	2	no	—
8	C₅×C₈	D₃	1	1	yes	characteristic, complemented
9	C₂×C₃×C₅	D₄	1	1	yes	characteristic
10	D₁₅	—	4	2	no	—
11	D₁₂	—	5	2	no	—
12	C₃×C₈	D₅	1	1	yes	characteristic, complemented
13	C₂×D₅	—	6	2	no	—
14	C₄×C₅	C₂×D₃	1	1	yes	characteristic
15	D₈	—	15	1	no	Sylow
16	C₃×C₅	D₈	1	1	yes	characteristic, complemented, Hall
17	C₂×D₃	—	10	2	no	—
18	C₃×C₄	C₂×D₅	1	1	yes	characteristic
19	C₂×C₅	D₁₂	1	1	yes	characteristic
20	D₅	—	12	2	no	—
21	D₄	—	15	2	no	—
22	C₈	D₁₅	1	1	yes	characteristic, complemented
23	C₂×C₃	D₂₀	1	1	yes	characteristic
24	D₃	—	20	2	no	—
25	C₅	D₂₄	1	1	yes	characteristic, complemented, Sylow
26	C₂²	—	30	2	no	—
27	C₄	C₂×D₁₅	1	1	yes	characteristic
28	C₃	D₄₀	1	1	yes	characteristic, complemented, Sylow
29	C₂	—	60	2	no	—
30	C₂	D₆₀	1	1	yes	characteristic

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.