Finite Group Databasebeta

← D₅₉×D₁₁₃ #40998662

Subgroups — D₅₉×D₁₁₃ #40998662

Order 26668.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₆₆₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅₉×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁₃×D₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅₉×C₁₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×D₁₁₃	—	59	1	no	maximal, Hall
6	C₂×D₅₉	—	113	1	no	maximal, Hall
7	C₂×C₁₁₃	—	59	1	no	—
8	D₁₁₃	—	59	1	no	—
9	D₁₁₃	D₅₉	1	1	yes	characteristic, direct product factor
10	C₂×C₅₉	—	113	1	no	—
11	D₅₉	—	113	1	no	—
12	D₅₉	D₁₁₃	1	1	yes	characteristic, direct product factor
13	C₁₁₃	C₂×D₅₉	1	1	yes	characteristic, complemented, Sylow
14	C₅₉	C₂×D₁₁₃	1	1	yes	characteristic, complemented, Sylow
15	C₂²	—	6667	1	no	Sylow
16	C₂	—	6667	1	no	—
17	C₂	—	59	1	no	—
18	C₂	—	113	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅₉×C₁₁₃	C₂²
LCS	G ▷ C₅₉×C₁₁₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. D₆₆₆₇	C₂	semidirect
2. C₅₉×D₁₁₃	C₂	semidirect
3. C₁₁₃×D₅₉	C₂	semidirect
4. C₅₉×C₁₁₃	C₂²	semidirect
9. D₁₁₃	D₅₉	direct (N × H)
12. D₅₉	D₁₁₃	direct (N × H)
13. C₁₁₃	C₂×D₅₉	semidirect
14. C₅₉	C₂×D₁₁₃	semidirect

Maximal subgroups

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

subgroup	index
D₆₆₆₇	2
C₅₉×D₁₁₃	2
C₁₁₃×D₅₉	2
C₂×D₁₁₃	59
C₂×D₅₉	113