Subgroups — (C₄₃⋊C₃)⋊#1043 #27166404

Order 12900.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊D₅×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₄₃⋊#1043	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₄₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	—	5	6	no	maximal
5	C₄₃×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
6	D₅×C₄₃⋊C₃	—	5	6	no	—
7	C₅²×C₄₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
8	C₄₃⋊AGL(1,𝔽₅)	—	5	6	no	—
9	C₅×C₄₃⋊C₃	AGL(1,𝔽₅)	1	6	yes	complemented
10	(C₄₃⋊C₃)⋊C₄	—	25	1	no	Hall
11	D₅×C₄₃	—	5	6	no	—
12	C₃×#1043	—	43	1	no	maximal, Hall
13	C₂×C₄₃⋊C₃	—	25	1	no	—
14	C₅×C₄₃	C₃×AGL(1,𝔽₅)	1	6	yes	complemented
15	Dic₄₃	—	25	1	no	Hall
16	C₃×C₅⋊D₅	—	43	1	no	—
17	C₄₃⋊C₃	#1043	1	1	yes	characteristic, complemented, Hall
18	#1043	—	43	1	no	Hall
19	C₂×C₄₃	—	25	1	no	—
20	C₃×C₅²	—	43	1	no	Hall
21	C₃×AGL(1,𝔽₅)	—	215	6	no	—
22	C₅⋊D₅	D₄₃⋊C₃	1	1	yes	characteristic
23	C₄₃	C₃×#1043	1	1	yes	characteristic, complemented, Sylow
24	C₃×D₅	—	215	6	no	—
25	C₅²	(C₄₃⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
26	AGL(1,𝔽₅)	—	215	6	no	—
27	C₃×C₅	—	43	6	no	—
28	C₃×C₄	—	1075	1	no	Hall
29	D₅	—	5	6	no	—
30	C₂×C₃	—	1075	1	no	—
31	C₅	(C₄₃⋊C₃)⋊AGL(1,𝔽₅)	1	6	yes	complemented
32	C₄	—	1075	1	no	Sylow
33	C₃	—	43	1	no	Sylow
34	C₂	—	25	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₅²×C₄₃	C₃×C₄
prime radical	C₅⋊D₅×C₄₃⋊C₃	C₂
cosocle	C₄₃×C₅⋊D₅	C₂×C₃
LCS	G ▷ C₅²×C₄₃
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.