Subgroups — #1043⋊(C₆₁⋊C₃) #32913055

Order 18300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₅⋊D₅)⋊(C₆₁⋊C₃)	C₂	1	1	yes	maximal, characteristic
2	C₆₁×#1043	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²⋊(C₆₁⋊C₃)	C₄	1	1	yes	characteristic, complemented, Hall
4	C₅⋊D₅×C₆₁	C₂×C₃	1	1	yes	characteristic
5	C₅²×C₆₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	AGL(1,𝔽₅)×C₆₁	—	15	2	no	—
7	C₄×C₆₁⋊C₃	—	25	1	no	maximal, Hall
8	D₅×C₆₁	—	15	2	no	—
9	C₂×C₆₁⋊C₃	—	25	1	no	—
10	C₅×C₆₁	—	3	2	no	—
11	#1043⋊C₃	—	61	1	no	maximal, Hall
12	C₄×C₆₁	—	25	1	no	Hall
13	C₆₁⋊C₃	—	100	1	no	Hall
14	(C₅⋊D₅)⋊C₃	—	61	1	no	—
15	C₂×C₆₁	—	25	1	no	—
16	#1043	C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₅²⋊C₃	—	61	1	no	Hall
18	C₆₁	#1043⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₅⋊D₅	C₂×C₆₁⋊C₃	1	1	yes	characteristic
20	C₅²	C₄×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	AGL(1,𝔽₅)	—	15	2	no	—
22	C₃×C₄	—	1525	1	no	Hall
23	D₅	—	15	2	no	—
24	C₂×C₃	—	1525	1	no	—
25	C₅	—	3	2	no	—
26	C₄	—	25	1	no	Sylow
27	C₃	—	6100	1	no	Sylow
28	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₆₁	C₃×C₄
prime radical	(C₅⋊D₅)⋊(C₆₁⋊C₃)	C₂
cosocle	C₅⋊D₅×C₆₁	C₂×C₃
LCS	G ▷ C₅²×C₆₁
UCS	C₁

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.