Subgroups — (C₁₉⋊C₃)⋊Dic₆₇ #29504136

Order 15276.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉⋊C₃×C₆₇	C₂	1	1	yes	maximal, characteristic
2	Dic₁₂₇₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₉⋊C₃×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₉×C₆₇	C₂×C₃	1	1	yes	characteristic
5	C₁₉×C₆₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
6	C₃×Dic₆₇	—	19	1	no	maximal, Hall
7	C₂×C₃×C₆₇	—	38	1	no	—
8	Dic₆₇	—	19	1	no	Hall
9	(C₁₉⋊C₃)⋊C₄	—	67	1	no	maximal, Hall
10	C₃×C₆₇	—	38	1	no	Hall
11	C₂×C₆₇	D₁₉⋊C₃	1	1	yes	characteristic
12	C₂×C₁₉⋊C₃	D₆₇	1	1	yes	characteristic
13	Dic₁₉	—	67	1	no	Hall
14	C₆₇	(C₁₉⋊C₃)⋊C₄	1	1	yes	characteristic, complemented, Sylow
15	C₁₉⋊C₃	Dic₆₇	1	1	yes	characteristic, complemented, Hall
16	C₂×C₁₉	C₃×D₆₇	1	1	yes	characteristic
17	C₁₉	C₃×Dic₆₇	1	1	yes	characteristic, complemented, Sylow
18	C₃×C₄	—	1273	1	no	Hall
19	C₂×C₃	—	38	1	no	—
20	C₄	—	1273	1	no	Sylow
21	C₃	—	38	1	no	Sylow
22	C₂	(C₁₉⋊C₃)⋊D₆₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	(C₁₉⋊C₃)⋊D₆₇
commutator, hypocenter	C₁₉×C₆₇	C₃×C₄
Fitting, socle, cosocle	C₂×C₁₉×C₆₇	C₂×C₃
prime radical	C₂×C₁₉⋊C₃×C₆₇	C₂
LCS	G ▷ C₁₉×C₆₇
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.