Subgroups — C₅×C₂²⋊(C₆₁⋊C₉) #24926713

Order 10980.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×C₆₁	C₃	1	1	yes	maximal, characteristic
2	C₅×C₆₁⋊C₉	—	4	1	no	maximal, Hall
3	C₂²⋊(C₆₁⋊C₉)	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂×C₃×C₅×C₆₁	—	3	1	no	—
5	C₂²×C₅×C₆₁	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅×C₆₁	A₄	1	1	yes	characteristic
7	C₂²×C₃×C₆₁	C₃×C₅	1	1	yes	characteristic
8	C₂×C₅×C₆₁	—	3	1	no	—
9	C₆₁⋊C₉	—	4	1	no	Hall
10	C₂×C₃×C₆₁	—	3	1	no	—
11	C₅×C₆₁	C₂²⋊C₉	1	1	yes	characteristic, complemented, Hall
12	C₂²×C₆₁	C₅×C₉	1	1	yes	characteristic, complemented, Hall
13	C₃×C₆₁	C₅×A₄	1	1	yes	characteristic
14	C₅×C₂²⋊C₉	—	61	1	no	maximal, Hall
15	C₂×C₆₁	—	3	1	no	—
16	C₆₁	C₅×C₂²⋊C₉	1	1	yes	characteristic, complemented, Sylow
17	C₂²×C₃×C₅	C₆₁⋊C₃	1	1	yes	characteristic
18	C₅×C₉	—	244	1	no	Hall
19	C₂²⋊C₉	—	61	1	no	Hall
20	C₂×C₃×C₅	—	3	1	no	—
21	C₂²×C₅	C₆₁⋊C₉	1	1	yes	characteristic, complemented, Hall
22	C₃×C₅	C₂²⋊(C₆₁⋊C₃)	1	1	yes	characteristic
23	C₂²×C₃	C₅×C₆₁⋊C₃	1	1	yes	characteristic
24	C₂×C₅	—	3	1	no	—
25	C₉	—	244	1	no	Sylow
26	C₂×C₃	—	3	1	no	—
27	C₅	C₂²⋊(C₆₁⋊C₉)	1	1	yes	characteristic, direct product factor, Sylow
28	C₂²	C₅×C₆₁⋊C₉	1	1	yes	characteristic, complemented, Sylow
29	C₃	C₅×C₂²⋊(C₆₁⋊C₃)	1	1	yes	characteristic
30	C₂	—	3	1	no	—

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.