Subgroups — Dic₁₂₀ #91085

Order 480.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₀	C₂	1	2	yes	maximal
2	C₃×C₅×C₁₆	C₂	1	1	yes	maximal, characteristic
3	Dic₄₀	—	3	1	no	maximal, Hall
4	Dic₃₀	—	2	2	no	—
5	C₃×C₅×C₈	C₂²	1	1	yes	characteristic
6	Dic₂₄	—	5	1	no	maximal, Hall
7	Dic₂₀	—	3	2	no	—
8	C₅×C₁₆	D₃	1	1	yes	characteristic
9	C₃×C₄×C₅	D₄	1	1	yes	characteristic
10	Dic₁₅	—	4	2	no	—
11	Dic₁₂	—	5	2	no	—
12	C₃×C₁₆	D₅	1	1	yes	characteristic
13	Dic₁₀	—	6	2	no	—
14	C₅×C₈	C₂×D₃	1	1	yes	characteristic
15	Q₃₂	—	15	1	no	Sylow
16	C₂×C₃×C₅	D₈	1	1	yes	characteristic
17	Dic₆	—	10	2	no	—
18	C₃×C₈	C₂×D₅	1	1	yes	characteristic
19	C₄×C₅	D₁₂	1	1	yes	characteristic
20	Dic₅	—	12	2	no	—
21	Q₁₆	—	15	2	no	—
22	C₁₆	D₁₅	1	1	yes	characteristic
23	C₃×C₅	Q₃₂	1	1	yes	characteristic, complemented, Hall
24	C₃×C₄	D₂₀	1	1	yes	characteristic
25	Dic₃	—	20	2	no	—
26	C₂×C₅	D₂₄	1	1	yes	characteristic
27	Q₈	—	30	2	no	—
28	C₈	C₂×D₁₅	1	1	yes	characteristic
29	C₂×C₃	D₄₀	1	1	yes	characteristic
30	C₅	Dic₂₄	1	1	yes	characteristic, complemented, Sylow
31	C₄	—	60	2	no	—
32	C₄	D₆₀	1	1	yes	characteristic
33	C₃	Dic₄₀	1	1	yes	characteristic, complemented, Sylow
34	C₂	D₁₂₀	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.