Subgroups — #30632552

Order 16068.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃⋊C₃×C₁₀₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃₃₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₁₀₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₁₀₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₀₃	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₁₀₃	—	13	1	no	maximal, Hall
7	C₂×C₃×C₁₀₃	—	26	1	no	—
8	Dic₁₀₃	—	13	1	no	Hall
9	C₃×C₁₀₃	—	26	1	no	Hall
10	C₂×C₁₀₃	D₁₃⋊C₃	1	1	yes	characteristic
11	Dic₁₃⋊C₃	—	103	1	no	maximal, Hall
12	C₁₀₃	Dic₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₁₃⋊C₃	D₁₀₃	1	1	yes	characteristic
14	Dic₁₃	—	103	1	no	Hall
15	C₁₃⋊C₃	Dic₁₀₃	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₃	C₃×D₁₀₃	1	1	yes	characteristic
17	C₁₃	C₃×Dic₁₀₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1339	1	no	Hall
19	C₂×C₃	—	26	1	no	—
20	C₄	—	1339	1	no	Sylow
21	C₃	—	26	1	no	Sylow
22	C₂	(C₁₃⋊C₃)⋊D₁₀₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₁₃⋊C₃)⋊D₁₀₃
commutator, hypocenter	C₁₃×C₁₀₃	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₃×C₁₀₃	C₂×C₃
prime radical	C₂×C₁₃⋊C₃×C₁₀₃	C₂
LCS	G ▷ C₁₃×C₁₀₃
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.