Subgroups — Dic₁₈₀ #10623596

Order 720.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₉₀	C₂	1	2	yes	maximal
2	C₅×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	Dic₆₀	—	3	1	no	maximal
4	C₄×C₅×C₉	C₂²	1	1	yes	characteristic
5	Dic₄₅	—	2	2	no	—
6	Dic₃₆	—	5	1	no	maximal, Hall
7	Dic₃₀	—	3	2	no	—
8	C₃×C₅×C₈	D₃	1	1	yes	characteristic
9	C₂×C₅×C₉	D₄	1	1	yes	characteristic
10	Dic₂₀	—	9	1	no	Hall
11	Dic₁₈	—	5	2	no	—
12	C₈×C₉	D₅	1	1	yes	characteristic
13	C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
14	Dic₁₅	—	6	2	no	—
15	Dic₁₂	—	15	1	no	—
16	C₅×C₉	Q₁₆	1	1	yes	characteristic, complemented, Hall
17	Dic₁₀	—	9	2	no	—
18	C₅×C₈	D₉	1	1	yes	characteristic
19	C₄×C₉	C₂×D₅	1	1	yes	characteristic
20	Dic₉	—	10	2	no	—
21	C₂×C₃×C₅	D₁₂	1	1	yes	characteristic
22	Dic₆	—	15	2	no	—
23	C₃×C₈	D₁₅	1	1	yes	characteristic
24	C₄×C₅	C₂×D₉	1	1	yes	characteristic
25	Dic₅	—	18	2	no	—
26	C₂×C₉	D₂₀	1	1	yes	characteristic
27	Q₁₆	—	45	1	no	Sylow
28	C₃×C₅	Dic₁₂	1	1	yes	characteristic
29	C₃×C₄	C₂×D₁₅	1	1	yes	characteristic
30	Dic₃	—	30	2	no	—
31	C₂×C₅	D₃₆	1	1	yes	characteristic
32	C₉	Dic₂₀	1	1	yes	characteristic, complemented, Sylow
33	Q₈	—	45	2	no	—
34	C₈	D₄₅	1	1	yes	characteristic
35	C₂×C₃	D₆₀	1	1	yes	characteristic
36	C₅	Dic₃₆	1	1	yes	characteristic, complemented, Sylow
37	C₄	—	90	2	no	—
38	C₄	C₂×D₄₅	1	1	yes	characteristic
39	C₃	Dic₆₀	1	1	yes	characteristic
40	C₂	D₁₈₀	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.