Subgroups — #67077

Order 360.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₄₅	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₅×Dic₉	C₂	1	1	yes	maximal, characteristic
4	#1204	—	3	1	no	maximal
5	C₂×C₅×C₉	C₂²	1	1	yes	characteristic
6	Dic₁₈	—	5	1	no	maximal, Hall
7	Dic₁₅	—	3	1	no	—
8	C₃×Dic₅	D₃	1	1	yes	characteristic
9	C₅×Dic₃	—	3	1	no	—
10	C₅×C₉	Q₈	1	1	yes	characteristic, complemented, Hall
11	Dic₁₀	—	9	1	no	Hall
12	C₄×C₉	—	5	1	no	—
13	Dic₉	—	5	1	no	—
14	Dic₉	D₅	1	1	yes	characteristic
15	C₂×C₃×C₅	C₂×D₃	1	1	yes	characteristic
16	Dic₆	—	15	1	no	—
17	C₄×C₅	—	9	1	no	—
18	Dic₅	—	9	1	no	—
19	Dic₅	D₉	1	1	yes	characteristic
20	C₂×C₉	C₂×D₅	1	1	yes	characteristic
21	C₃×C₅	Dic₆	1	1	yes	characteristic
22	C₃×C₄	—	5	1	no	—
23	Dic₃	—	3	1	no	—
24	Dic₃	—	15	1	no	—
25	C₂×C₅	C₂×D₉	1	1	yes	characteristic
26	C₉	Dic₁₀	1	1	yes	characteristic, complemented, Sylow
27	Q₈	—	45	1	no	Sylow
28	C₂×C₃	D₃×D₅	1	1	yes	characteristic
29	C₅	Dic₁₈	1	1	yes	characteristic, complemented, Sylow
30	C₄	—	5	1	no	—
31	C₄	—	9	1	no	—
32	C₄	—	45	1	no	—
33	C₃	#1204	1	1	yes	characteristic
34	C₂	D₅×D₉	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.