Subgroups — (C₁₂₇⋊C₃)⋊Dic₁₉ #44394162

Order 28956.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₁₂₇⋊C₃	C₂	1	1	yes	maximal, characteristic
2	Dic₂₄₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉×C₁₂₇⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₁₂₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₁₂₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	(C₁₂₇⋊C₃)⋊C₄	—	19	1	no	maximal, Hall
7	C₂×C₁₂₇⋊C₃	D₁₉	1	1	yes	characteristic
8	Dic₁₂₇	—	19	1	no	Hall
9	C₁₂₇⋊C₃	Dic₁₉	1	1	yes	characteristic, complemented, Hall
10	C₂×C₁₂₇	C₃×D₁₉	1	1	yes	characteristic
11	C₃×Dic₁₉	—	127	1	no	maximal, Hall
12	C₁₂₇	C₃×Dic₁₉	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₁₉	—	254	1	no	—
14	Dic₁₉	—	127	1	no	Hall
15	C₃×C₁₉	—	254	1	no	Hall
16	C₂×C₁₉	D₁₂₇⋊C₃	1	1	yes	characteristic
17	C₁₉	(C₁₂₇⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	2413	1	no	Hall
19	C₂×C₃	—	254	1	no	—
20	C₄	—	2413	1	no	Sylow
21	C₃	—	254	1	no	Sylow
22	C₂	(C₁₂₇⋊C₃)⋊D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₁₂₇⋊C₃)⋊D₁₉
commutator, hypocenter	C₁₉×C₁₂₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₉×C₁₂₇	C₂×C₃
prime radical	C₂×C₁₉×C₁₂₇⋊C₃	C₂
LCS	G ▷ C₁₉×C₁₂₇
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.