Subgroups — A₄×C₈₅₉⋊C₃ #44525698

Order 30924.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈₅₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	A₄×C₈₅₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊(C₈₅₉⋊C₃)	C₃	1	2	yes	maximal, complemented
4	C₃×C₈₅₉⋊C₃	—	4	1	no	maximal, Hall
5	C₂×C₈₅₉⋊C₃	—	3	1	no	—
6	C₂²×C₈₅₉	C₃²	1	1	yes	characteristic, complemented, Hall
7	C₃×C₈₅₉	—	4	1	no	—
8	C₈₅₉⋊C₃	—	4	2	no	—
9	C₈₅₉⋊C₃	A₄	1	1	yes	characteristic, direct product factor
10	C₂×C₈₅₉	—	3	1	no	—
11	C₈₅₉	C₃×A₄	1	1	yes	characteristic, complemented, Sylow
12	C₃×A₄	—	859	1	no	maximal, Hall
13	C₂²×C₃	—	859	1	no	—
14	A₄	—	859	2	no	—
15	A₄	C₈₅₉⋊C₃	1	1	yes	characteristic, direct product factor
16	C₃²	—	3436	1	no	Sylow
17	C₂×C₃	—	2577	1	no	—
18	C₂²	C₃×C₈₅₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₃	—	4	1	no	—
20	C₃	—	859	1	no	—
21	C₃	—	3436	2	no	—
22	C₂	—	3	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₈₅₉	C₃²
LCS	G ▷ C₂²×C₈₅₉
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.