Subgroups — C₂×C₂²⋊(C₁₃⋊C₃) #64641

Order 312.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊(C₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×C₁₃⋊C₃	—	4	1	no	maximal
4	C₂²×C₁₃	—	3	1	no	—
5	C₂²×C₁₃	—	3	1	no	—
6	C₂²×C₁₃	C₂×C₃	1	1	yes	characteristic, complemented
7	C₁₃⋊C₃	—	4	1	no	Hall
8	C₂×C₁₃	—	3	1	no	—
9	C₂×C₁₃	—	3	1	no	—
10	C₂×C₁₃	A₄	1	1	yes	characteristic, complemented
11	C₂×A₄	—	13	1	no	maximal, Hall
12	C₁₃	C₂×A₄	1	1	yes	characteristic, complemented, Sylow
13	A₄	—	13	1	no	—
14	C₂³	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃	—	52	1	no	—
16	C₂²	—	3	1	no	—
17	C₂²	—	3	1	no	—
18	C₂²	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
19	C₃	—	52	1	no	Sylow
20	C₂	—	3	1	no	—
21	C₂	—	3	1	no	—
22	C₂	C₂²⋊(C₁₃⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₂²⋊(C₁₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₃	C₂×C₃
Frattini	C₁	G
Fitting, socle	C₂³×C₁₃	C₃
LCS	G ▷ C₂²×C₁₃
UCS	C₁ ◁ C₂

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.