Subgroups — C₂×C₄₇⋊(D₁₉⋊C₃) #24924273

Order 10716.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇⋊(D₁₉⋊C₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₄₇×C₁₉⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₈₉₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₄₇×C₁₉⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₉×C₄₇	C₂×C₃	1	1	yes	characteristic, complemented
6	D₈₉₃	C₂×C₃	1	2	yes	complemented
7	C₁₉×C₄₇	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₄₇	—	19	1	no	maximal, Hall
9	C₂×C₃×C₄₇	—	19	1	no	—
10	C₃×D₄₇	—	19	2	no	—
11	C₂×D₁₉⋊C₃	—	47	1	no	maximal, Hall
12	C₂×D₄₇	—	19	1	no	Hall
13	C₃×C₄₇	—	19	1	no	Hall
14	C₂×C₁₉⋊C₃	D₄₇	1	1	yes	characteristic, complemented
15	D₁₉⋊C₃	—	47	2	no	—
16	C₂×C₄₇	D₁₉⋊C₃	1	1	yes	characteristic, complemented
17	D₄₇	—	19	2	no	—
18	C₂×D₁₉	—	47	1	no	Hall
19	C₁₉⋊C₃	C₂×D₄₇	1	1	yes	characteristic, complemented, Hall
20	C₄₇	C₂×D₁₉⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₂×C₁₉	C₃×D₄₇	1	1	yes	characteristic, complemented
22	D₁₉	—	47	2	no	—
23	C₁₉	C₂×C₃×D₄₇	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	893	1	no	Hall
25	C₂×C₃	—	19	1	no	—
26	C₂×C₃	—	893	2	no	—
27	C₂²	—	893	1	no	Sylow
28	C₃	—	19	1	no	Sylow
29	C₂	—	893	2	no	—
30	C₂	C₄₇⋊(D₁₉⋊C₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₄₇⋊(D₁₉⋊C₃)
commutator, cosocle, hypocenter	C₁₉×C₄₇	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₉×C₄₇	C₂×C₃
LCS	G ▷ C₁₉×C₄₇
UCS	C₁ ◁ C₂

Splittings G = N ⋊ H with N normal; H ≅ G/N.