Subgroups — Dic₉₀ #67095

Order 360.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₉	C₂	1	1	yes	maximal, characteristic
2	Dic₄₅	C₂	1	2	yes	maximal
3	Dic₃₀	—	3	1	no	maximal
4	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
5	Dic₁₈	—	5	1	no	maximal, Hall
6	C₃×C₄×C₅	D₃	1	1	yes	characteristic
7	Dic₁₅	—	3	2	no	—
8	C₅×C₉	Q₈	1	1	yes	characteristic, complemented, Hall
9	Dic₁₀	—	9	1	no	Hall
10	C₄×C₉	D₅	1	1	yes	characteristic
11	Dic₉	—	5	2	no	—
12	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic
13	Dic₆	—	15	1	no	—
14	C₄×C₅	D₉	1	1	yes	characteristic
15	Dic₅	—	9	2	no	—
16	C₂×C₉	C₂×D₅	1	1	yes	characteristic
17	C₃×C₅	Dic₆	1	1	yes	characteristic
18	C₃×C₄	D₁₅	1	1	yes	characteristic
19	Dic₃	—	15	2	no	—
20	C₂×C₅	C₂×D₉	1	1	yes	characteristic
21	C₉	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
22	Q₈	—	45	1	no	Sylow
23	C₂×C₃	C₂×D₁₅	1	1	yes	characteristic
24	C₅	Dic₁₈	1	1	yes	characteristic, complemented, Sylow
25	C₄	—	45	2	no	—
26	C₄	D₄₅	1	1	yes	characteristic
27	C₃	Dic₃₀	1	1	yes	characteristic
28	C₂	C₂×D₄₅	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.