Subgroups — C₁₃×(C₁₃⋊C₃)⋊D₁₉ #34064197

Order 19266.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×C₁₉×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₃×D₂₄₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₁₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₃×C₁₃×D₁₉	—	13	1	no	maximal
5	(C₁₃⋊C₃)⋊D₁₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor
6	C₁₃×D₁₃⋊C₃	—	19	1	no	maximal, Hall
7	C₃×C₁₃×C₁₉	—	13	1	no	—
8	C₁₉×C₁₃⋊C₃	C₂×C₁₃	1	1	yes	characteristic, complemented
9	C₁₃×C₁₃⋊C₃	D₁₉	1	1	yes	characteristic, complemented, Hall
10	D₂₄₇	C₃×C₁₃	1	1	yes	characteristic, complemented
11	C₁₃×D₁₉	—	39	1	no	—
12	C₁₃×D₁₃	—	19	1	no	Hall
13	C₁₃×C₁₉	—	6	2	no	—
14	C₁₃×C₁₉	D₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₁₉	C₂×C₃×C₁₃	1	1	yes	characteristic, complemented
16	C₁₃²	C₃×D₁₉	1	1	yes	characteristic, complemented, Sylow
17	C₃×D₁₉	—	13	1	no	Hall
18	C₂×C₃×C₁₃	—	247	1	no	—
19	D₁₃⋊C₃	—	19	1	no	—
20	C₃×C₁₉	—	13	1	no	Hall
21	C₃×C₁₃	—	13	1	no	—
22	C₁₃⋊C₃	C₁₃×D₁₉	1	1	yes	characteristic, complemented
23	D₁₉	—	13	1	no	Hall
24	C₂×C₁₃	—	741	1	no	—
25	D₁₃	—	19	1	no	—
26	C₁₉	C₁₃×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
27	C₁₃	—	6	2	no	—
28	C₁₃	(C₁₃⋊C₃)⋊D₁₉	1	1	yes	characteristic, direct product factor
29	C₁₃	C₃×C₁₃×D₁₉	1	1	yes	characteristic, complemented
30	C₂×C₃	—	247	1	no	Hall
31	C₃	—	13	1	no	Sylow
32	C₂	—	247	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₁₃	(C₁₃⋊C₃)⋊D₁₉
commutator, cosocle, hypocenter	C₁₃×C₁₉	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃²×C₁₉	C₂×C₃
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
1. C₁₃×C₁₉×C₁₃⋊C₃	C₂	semidirect
2. C₁₃×D₂₄₇	C₃	semidirect
3. C₁₃²×C₁₉	C₂×C₃	semidirect
5. (C₁₃⋊C₃)⋊D₁₉	C₁₃	direct (N × H)
8. C₁₉×C₁₃⋊C₃	C₂×C₁₃	semidirect
9. C₁₃×C₁₃⋊C₃	D₁₉	semidirect
10. D₂₄₇	C₃×C₁₃	semidirect
14. C₁₃×C₁₉	D₁₃⋊C₃	semidirect
15. C₁₃×C₁₉	C₂×C₃×C₁₃	semidirect
16. C₁₃²	C₃×D₁₉	semidirect
22. C₁₃⋊C₃	C₁₃×D₁₉	semidirect
26. C₁₉	C₁₃×D₁₃⋊C₃	semidirect
28. C₁₃	(C₁₃⋊C₃)⋊D₁₉	direct (N × H)
29. C₁₃	C₃×C₁₃×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×C₁₉×C₁₃⋊C₃	2
C₁₃×D₂₄₇	3
C₃×C₁₃×D₁₉	13
(C₁₃⋊C₃)⋊D₁₉	13
C₁₃×D₁₃⋊C₃	19

Subgroups — C13×(C13⋊C3)⋊D19 #34064197

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×(C₁₃⋊C₃)⋊D₁₉ #34064197