Subgroups — C₂²×C₁₃⋊C₃×C₁₅₇ #37587658

Order 24492.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊C₃×C₁₅₇	C₂	1	3	yes	maximal, direct product factor
2	C₂²×C₁₃×C₁₅₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₁₅₇	C₂²	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₁₃×C₁₅₇	C₂×C₃	1	3	yes	complemented
5	C₁₃×C₁₅₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
6	C₂²×C₃×C₁₅₇	—	13	1	no	maximal, Hall
7	C₂×C₃×C₁₅₇	—	13	3	no	—
8	C₂²×C₁₅₇	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₅₇	—	13	1	no	Hall
10	C₂×C₁₅₇	C₂×C₁₃⋊C₃	1	3	yes	direct product factor
11	C₁₅₇	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
12	C₂²×C₁₃⋊C₃	C₁₅₇	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₁₃⋊C₃	C₂×C₁₅₇	1	3	yes	direct product factor
14	C₂²×C₁₃	C₃×C₁₅₇	1	1	yes	characteristic, complemented, Hall
15	C₁₃⋊C₃	C₂²×C₁₅₇	1	1	yes	characteristic, direct product factor, Hall
16	C₂×C₁₃	C₂×C₃×C₁₅₇	1	3	yes	complemented
17	C₁₃	C₂²×C₃×C₁₅₇	1	1	yes	characteristic, complemented, Sylow
18	C₂²×C₃	—	13	1	no	Hall
19	C₂×C₃	—	13	3	no	—
20	C₂²	C₁₃⋊C₃×C₁₅₇	1	1	yes	characteristic, direct product factor, Sylow
21	C₃	—	13	1	no	Sylow
22	C₂	C₂×C₁₃⋊C₃×C₁₅₇	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₁₅₇	C₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂²×C₃×C₁₅₇
Frattini	C₁	G
Fitting, socle	C₂²×C₁₃×C₁₅₇	C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂²×C₁₅₇

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.