Subgroups — #16861520⋊C₃ #27134242

Order 12300.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×(C₅⋊D₅)⋊C₃	C₂	1	1	yes	maximal, characteristic
2	#16861520	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₄₁×C₅²⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₄₁×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
5	C₅²×C₄₁	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	#11717963	—	15	2	no	—
7	C₃×Dic₄₁	—	25	1	no	maximal, Hall
8	D₅×C₄₁	—	15	2	no	—
9	#1043⋊C₃	—	41	1	no	maximal, Hall
10	C₂×C₃×C₄₁	—	25	1	no	—
11	C₅×C₄₁	—	3	2	no	—
12	Dic₄₁	—	25	1	no	Hall
13	(C₅⋊D₅)⋊C₃	D₄₁	1	1	yes	characteristic
14	C₃×C₄₁	—	25	1	no	Hall
15	#1043	—	41	1	no	Hall
16	C₂×C₄₁	—	25	1	no	—
17	C₅²⋊C₃	Dic₄₁	1	1	yes	characteristic, complemented, Hall
18	C₅⋊D₅	C₃×D₄₁	1	1	yes	characteristic
19	C₄₁	#1043⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₅²	C₃×Dic₄₁	1	1	yes	characteristic, complemented, Sylow
21	AGL(1,𝔽₅)	—	615	2	no	—
22	C₃×C₄	—	1025	1	no	Hall
23	D₅	—	15	2	no	—
24	C₂×C₃	—	25	1	no	—
25	C₅	—	3	2	no	—
26	C₄	—	1025	1	no	Sylow
27	C₃	—	25	1	no	Sylow
28	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₄₁	C₃×C₄
prime radical	C₄₁×(C₅⋊D₅)⋊C₃	C₂
cosocle	C₄₁×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₄₁
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.