Subgroups — C₂×(C₁₃⋊C₃)⋊D₁₉ #15688317

Order 2964.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	(C₁₃⋊C₃)⋊D₁₉	C₂	1	2	yes	maximal, direct product factor
3	C₂×D₂₄₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₁₉×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₁₃×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented
6	D₂₄₇	C₂×C₃	1	2	yes	complemented
7	C₁₃×C₁₉	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
8	C₂×C₃×D₁₉	—	13	1	no	maximal, Hall
9	C₂×D₁₃⋊C₃	—	19	1	no	maximal, Hall
10	C₂×C₃×C₁₉	—	13	1	no	—
11	C₃×D₁₉	—	13	2	no	—
12	C₂×C₁₃⋊C₃	D₁₉	1	1	yes	characteristic, complemented
13	D₁₃⋊C₃	—	19	2	no	—
14	C₂×D₁₉	—	13	1	no	Hall
15	C₃×C₁₉	—	13	1	no	Hall
16	C₂×D₁₃	—	19	1	no	Hall
17	C₁₃⋊C₃	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
19	D₁₉	—	13	2	no	—
20	C₂×C₁₃	C₃×D₁₉	1	1	yes	characteristic, complemented
21	D₁₃	—	19	2	no	—
22	C₁₉	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
23	C₁₃	C₂×C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
24	C₂²×C₃	—	247	1	no	Hall
25	C₂×C₃	—	13	1	no	—
26	C₂×C₃	—	247	2	no	—
27	C₂²	—	247	1	no	Sylow
28	C₃	—	13	1	no	Sylow
29	C₂	—	247	2	no	—
30	C₂	(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	(C₁₃⋊C₃)⋊D₁₉
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
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.