Subgroups — C₁₃⋊C₃×C₁₆₃⋊C₃ #34040177

Order 19071.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263773	C₃	1	1	yes	maximal, characteristic, complemented
2	#20263772	C₃	1	1	yes	maximal, characteristic, complemented
3	C₁₃×C₁₆₃⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
4	C₁₃⋊C₃×C₁₆₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₁₃×C₁₆₃	C₃²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₆₃⋊C₃	—	13	1	no	maximal, Hall
7	C₃×C₁₆₃	—	13	1	no	—
8	C₁₆₃⋊C₃	—	13	1	no	—
9	C₁₆₃⋊C₃	—	13	1	no	—
10	C₁₆₃⋊C₃	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor
11	C₁₆₃	C₃×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₁₃⋊C₃	—	163	1	no	maximal, Hall
13	C₃×C₁₃	—	163	1	no	—
14	C₁₃⋊C₃	—	163	1	no	—
15	C₁₃⋊C₃	—	163	1	no	—
16	C₁₃⋊C₃	C₁₆₃⋊C₃	1	1	yes	characteristic, direct product factor
17	C₁₃	C₃×C₁₆₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃²	—	2119	1	no	Sylow
19	C₃	—	13	1	no	—
20	C₃	—	2119	1	no	—
21	C₃	—	2119	1	no	—
22	C₃	—	163	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃×C₁₆₃	C₃²
LCS	G ▷ C₁₃×C₁₆₃
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.