Subgroups — A₄⋊D₁₃ #64632

Order 312.

22 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	A₄×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²⋊D₁₃	—	3	1	no	maximal, Hall
3	D₃₉	—	4	1	no	maximal
4	C₂²×C₁₃	D₃	1	1	yes	characteristic, complemented
5	C₂×D₁₃	—	3	1	no	—
6	Dic₁₃	—	3	1	no	—
7	C₃×C₁₃	—	4	1	no	Hall
8	C₂×C₁₃	—	3	1	no	—
9	D₁₃	—	6	1	no	—
10	S₄	—	13	1	no	maximal, Hall
11	C₁₃	S₄	1	1	yes	characteristic, complemented, Sylow
12	A₄	D₁₃	1	1	yes	characteristic, complemented
13	D₄	—	39	1	no	Sylow
14	D₃	—	52	1	no	—
15	C₂²	—	39	1	no	—
16	C₂²	D₃₉	1	1	yes	characteristic, complemented
17	C₄	—	39	1	no	—
18	C₃	—	4	1	no	Sylow
19	C₂	—	3	1	no	—
20	C₂	—	78	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	A₄×C₁₃	C₂
Fitting, socle	C₂²×C₁₃	D₃
LCS	G ▷ A₄×C₁₃
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.