Subgroups — #14520342

Order 1976.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₂₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₃×C₁₉	C₂²	1	1	yes	characteristic
5	D₂₄₇	—	2	1	no	—
6	C₁₉×D₁₃	—	2	1	no	—
7	C₁₃×C₁₉	D₄	1	1	yes	characteristic, complemented, Hall
8	C₂²⋊D₁₉	—	13	1	no	maximal, Hall
9	D₅₂	—	19	1	no	maximal, Hall
10	C₂²×C₁₉	—	13	1	no	—
11	C₂×D₁₉	—	13	1	no	—
12	Dic₁₉	D₁₃	1	1	yes	characteristic, complemented
13	C₂×D₁₃	—	19	1	no	—
14	C₂×D₁₃	D₁₉	1	1	yes	characteristic, complemented
15	C₄×C₁₃	—	19	1	no	—
16	C₂×C₁₉	—	26	1	no	—
17	C₂×C₁₉	C₂×D₁₃	1	1	yes	characteristic
18	D₁₉	—	26	1	no	—
19	C₂×C₁₃	C₂×D₁₉	1	1	yes	characteristic
20	D₁₃	—	2	1	no	—
21	D₁₃	—	38	1	no	—
22	C₁₉	D₅₂	1	1	yes	characteristic, complemented, Sylow
23	C₁₃	C₂²⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
24	D₄	—	247	1	no	Sylow
25	C₂²	—	13	1	no	—
26	C₂²	—	247	1	no	—
27	C₄	—	19	1	no	—
28	C₂	—	26	1	no	—
29	C₂	—	494	1	no	—
30	C₂	D₁₃×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₁₃×D₁₉
commutator, Fitting, socle, cosocle	C₂×C₁₃×C₁₉	C₂²
hypocenter	C₁₃×C₁₉	D₄
LCS	G ▷ C₂×C₁₃×C₁₉ ▷ 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.