Subgroups — C₁₃×Dic₁₃⋊C₉ #20258751

Order 6084.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×C₁₃⋊C₉	C₂	1	1	yes	maximal, characteristic
2	C₃×C₁₃×Dic₁₃	C₃	1	1	yes	maximal, characteristic
3	C₁₃×C₁₃⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₂×C₃×C₁₃²	C₂×C₃	1	1	yes	characteristic
5	C₁₃×Dic₁₃	C₉	1	1	yes	characteristic, complemented, Hall
6	C₃×C₁₃²	C₃×C₄	1	1	yes	characteristic
7	C₄×C₉×C₁₃	—	13	1	no	maximal
8	Dic₁₃⋊C₉	C₁₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₁₃²	C₂×C₉	1	1	yes	characteristic
10	C₂×C₉×C₁₃	—	13	1	no	—
11	C₂×C₁₃⋊C₉	C₂×C₁₃	1	1	yes	characteristic
12	C₁₃²	C₄×C₉	1	1	yes	characteristic, complemented, Sylow
13	C₃×C₄×C₁₃	—	13	1	no	—
14	C₃×Dic₁₃	C₃×C₁₃	1	1	yes	characteristic
15	C₉×C₁₃	—	13	1	no	—
16	C₁₃⋊C₉	C₄×C₁₃	1	1	yes	characteristic, complemented
17	C₂×C₃×C₁₃	—	6	2	no	—
18	C₂×C₃×C₁₃	D₁₃⋊C₃	1	1	yes	characteristic
19	C₂×C₃×C₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic
20	C₄×C₁₃	—	13	1	no	—
21	Dic₁₃	C₉×C₁₃	1	1	yes	characteristic, complemented
22	C₃×C₁₃	—	6	2	no	—
23	C₃×C₁₃	Dic₁₃⋊C₃	1	1	yes	characteristic
24	C₃×C₁₃	C₃×C₄×C₁₃	1	1	yes	characteristic
25	C₄×C₉	—	13	1	no	Hall
26	C₂×C₁₃	—	6	2	no	—
27	C₂×C₁₃	D₁₃⋊C₉	1	1	yes	characteristic
28	C₂×C₁₃	C₂×C₉×C₁₃	1	1	yes	characteristic
29	C₂×C₉	—	13	1	no	—
30	C₁₃	—	6	2	no	—
31	C₁₃	Dic₁₃⋊C₉	1	1	yes	characteristic, direct product factor
32	C₁₃	C₄×C₉×C₁₃	1	1	yes	characteristic, complemented
33	C₃×C₄	—	13	1	no	—
34	C₉	—	13	1	no	Sylow
35	C₂×C₃	C₁₃×D₁₃⋊C₃	1	1	yes	characteristic
36	C₄	—	13	1	no	Sylow
37	C₃	C₁₃×Dic₁₃⋊C₃	1	1	yes	characteristic
38	C₂	C₁₃×D₁₃⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₃	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₁₃
Frattini	C₂×C₃	C₁₃×D₁₃⋊C₃
Fitting, socle	C₂×C₃×C₁₃²	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₁₃

Complements

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

N	H ≅ G/N	type
3. C₁₃×C₁₃⋊C₉	C₄	semidirect
5. C₁₃×Dic₁₃	C₉	semidirect
8. Dic₁₃⋊C₉	C₁₃	direct (N × H)
12. C₁₃²	C₄×C₉	semidirect
16. C₁₃⋊C₉	C₄×C₁₃	semidirect
21. Dic₁₃	C₉×C₁₃	semidirect
31. C₁₃	Dic₁₃⋊C₉	direct (N × H)
32. C₁₃	C₄×C₉×C₁₃	semidirect

Subgroups — C13×Dic13⋊C9 #20258751

Conjugacy classes of subgroups

Complements

Subgroups — C₁₃×Dic₁₃⋊C₉ #20258751