Subgroups — C₉⋊(Dic₆₁⋊C₅) #24926656

Order 10980.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₉×C₆₁⋊C₅	C₂	1	1	yes	maximal, characteristic
2	C₃⋊(Dic₆₁⋊C₅)	—	3	1	no	maximal
3	C₉×C₆₁⋊C₅	C₄	1	1	yes	characteristic, complemented, Hall
4	Dic₅₄₉	C₅	1	1	yes	maximal, characteristic, complemented, Hall
5	C₂×C₃×C₆₁⋊C₅	D₃	1	1	yes	characteristic
6	Dic₆₁⋊C₅	—	9	1	no	Hall
7	C₂×C₉×C₆₁	C₂×C₅	1	1	yes	characteristic
8	C₃×C₆₁⋊C₅	Dic₃	1	1	yes	characteristic
9	Dic₁₈₃	—	3	1	no	—
10	C₂×C₆₁⋊C₅	D₉	1	1	yes	characteristic
11	C₉×C₆₁	C₄×C₅	1	1	yes	characteristic, complemented, Hall
12	C₂×C₃×C₆₁	C₅×D₃	1	1	yes	characteristic
13	C₆₁⋊C₅	Dic₉	1	1	yes	characteristic, complemented, Hall
14	Dic₆₁	—	9	1	no	Hall
15	C₃×C₆₁	C₅×Dic₃	1	1	yes	characteristic
16	C₅×Dic₉	—	61	1	no	maximal, Hall
17	C₂×C₆₁	C₅×D₉	1	1	yes	characteristic
18	C₂×C₅×C₉	—	61	1	no	—
19	C₆₁	C₅×Dic₉	1	1	yes	characteristic, complemented, Sylow
20	C₅×Dic₃	—	183	1	no	—
21	C₅×C₉	—	61	1	no	Hall
22	Dic₉	—	61	1	no	Hall
23	C₂×C₃×C₅	—	61	1	no	—
24	C₄×C₅	—	549	1	no	Hall
25	C₂×C₉	D₆₁⋊C₅	1	1	yes	characteristic
26	C₃×C₅	—	61	1	no	—
27	Dic₃	—	183	1	no	—
28	C₂×C₅	—	61	1	no	—
29	C₉	Dic₆₁⋊C₅	1	1	yes	characteristic, complemented, Sylow
30	C₂×C₃	C₃⋊(D₆₁⋊C₅)	1	1	yes	characteristic
31	C₅	—	61	1	no	Sylow
32	C₄	—	549	1	no	Sylow
33	C₃	C₃⋊(Dic₆₁⋊C₅)	1	1	yes	characteristic
34	C₂	C₉⋊(D₆₁⋊C₅)	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.