Finite Group Databasebeta

← C₂×D₆₃₈₃ #38784309

Subgroups — C₂×D₆₃₈₃ #38784309

Order 25532.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₄₉₁	C₂	1	1	yes	maximal, characteristic, complemented
2	D₆₃₈₃	C₂	1	2	yes	maximal, direct product factor
3	C₁₃×C₄₉₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₄₉₁	—	13	1	no	maximal, Hall
5	C₂×C₄₉₁	D₁₃	1	1	yes	characteristic, complemented
6	D₄₉₁	—	13	2	no	—
7	C₄₉₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Sylow
8	C₂×D₁₃	—	491	1	no	maximal, Hall
9	C₂×C₁₃	D₄₉₁	1	1	yes	characteristic, complemented
10	D₁₃	—	491	2	no	—
11	C₁₃	C₂×D₄₉₁	1	1	yes	characteristic, complemented, Sylow
12	C₂²	—	6383	1	no	Sylow
13	C₂	—	6383	2	no	—
14	C₂	D₆₃₈₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	D₆₃₈₃
commutator, cosocle, hypocenter	C₁₃×C₄₉₁	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₄₉₁	C₂
LCS	G ▷ C₁₃×C₄₉₁
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×C₄₉₁	C₂	semidirect
2. D₆₃₈₃	C₂	direct (N × H)
3. C₁₃×C₄₉₁	C₂²	semidirect
5. C₂×C₄₉₁	D₁₃	semidirect
7. C₄₉₁	C₂×D₁₃	semidirect
9. C₂×C₁₃	D₄₉₁	semidirect
11. C₁₃	C₂×D₄₉₁	semidirect
14. C₂	D₆₃₈₃	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₃×C₄₉₁	2
D₆₃₈₃	2
C₂×D₄₉₁	13
C₂×D₁₃	491