Subgroups — Dic₁₃×C₁₀₉⋊C₃ #30684261

Order 17004.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₀₉⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₁₃×C₁₀₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃×C₁₀₉⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×C₁₀₉	C₂×C₃	1	1	yes	characteristic
5	C₁₃×C₁₀₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₄×C₁₀₉⋊C₃	—	13	1	no	maximal, Hall
7	C₂×C₁₀₉⋊C₃	D₁₃	1	1	yes	characteristic
8	C₄×C₁₀₉	—	13	1	no	Hall
9	C₁₀₉⋊C₃	Dic₁₃	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₀₉	C₃×D₁₃	1	1	yes	characteristic
11	C₃×Dic₁₃	—	109	1	no	maximal, Hall
12	C₁₀₉	C₃×Dic₁₃	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₃	—	109	1	no	—
14	Dic₁₃	C₁₀₉⋊C₃	1	1	yes	characteristic, direct product factor, Hall
15	C₃×C₁₃	—	109	1	no	Hall
16	C₂×C₁₃	C₂×C₁₀₉⋊C₃	1	1	yes	characteristic
17	C₁₃	C₄×C₁₀₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1417	1	no	Hall
19	C₂×C₃	—	109	1	no	—
20	C₄	—	13	1	no	Sylow
21	C₃	—	109	1	no	Sylow
22	C₂	D₁₃×C₁₀₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₃×C₁₀₉⋊C₃
commutator, hypocenter	C₁₃×C₁₀₉	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₃×C₁₀₉	C₂×C₃
prime radical	C₂×C₁₃×C₁₀₉⋊C₃	C₂
LCS	G ▷ C₁₃×C₁₀₉
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.