Subgroups — C₁₃×C₁₁⋊AGL(1,𝔽₁₃) #36373313

Order 22308.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×C₁₃×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic
2	C₁₃×C₁₁⋊#261	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₁×C₁₃×C₁₃⋊C₃	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₁×C₁₃×D₁₃	C₂×C₃	1	1	yes	characteristic
5	C₁₃×AGL(1,𝔽₁₃)	—	11	1	no	maximal, Hall
6	C₁₁×C₁₃²	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₁₁⋊AGL(1,𝔽₁₃)	C₁₃	1	1	yes	maximal, characteristic, direct product factor
8	C₃×C₁₃×Dic₁₁	—	13	1	no	maximal
9	C₁₃×D₁₃⋊C₃	D₁₁	1	1	yes	characteristic
10	C₂×C₃×C₁₁×C₁₃	—	13	1	no	—
11	C₁₁×D₁₃⋊C₃	C₂×C₁₃	1	1	yes	characteristic
12	C₁₃×#261	—	11	1	no	Hall
13	C₁₁⋊#261	C₃×C₁₃	1	1	yes	characteristic, complemented
14	C₁₃×Dic₁₁	—	13	1	no	—
15	C₁₃×C₁₃⋊C₃	Dic₁₁	1	1	yes	characteristic, complemented, Hall
16	C₃×C₁₁×C₁₃	—	52	1	no	—
17	C₁₁×C₁₃⋊C₃	C₄×C₁₃	1	1	yes	characteristic, complemented
18	C₁₃×D₁₃	C₃×D₁₁	1	1	yes	characteristic
19	C₂×C₁₁×C₁₃	—	13	1	no	—
20	C₁₁×D₁₃	C₂×C₃×C₁₃	1	1	yes	characteristic
21	C₁₃²	C₃×Dic₁₁	1	1	yes	characteristic, complemented, Sylow
22	AGL(1,𝔽₁₃)	—	11	1	no	—
23	C₃×C₄×C₁₃	—	143	1	no	—
24	C₁₁×C₁₃	—	12	1	no	—
25	C₁₁×C₁₃	C₃×C₄×C₁₃	1	1	yes	characteristic, complemented
26	C₁₁×C₁₃	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented
27	C₃×Dic₁₁	—	13	1	no	Hall
28	C₂×C₃×C₁₃	—	13	1	no	—
29	D₁₃⋊C₃	C₁₃×D₁₁	1	1	yes	characteristic
30	C₂×C₃×C₁₁	—	13	1	no	—
31	#261	—	11	1	no	—
32	C₄×C₁₃	—	143	1	no	—
33	Dic₁₁	—	13	1	no	Hall
34	C₃×C₁₃	—	52	1	no	—
35	C₁₃⋊C₃	C₁₃×Dic₁₁	1	1	yes	characteristic, complemented
36	C₃×C₁₁	—	52	1	no	Hall
37	C₂×C₁₃	—	13	1	no	—
38	D₁₃	C₃×C₁₃×D₁₁	1	1	yes	characteristic
39	C₂×C₁₁	—	13	1	no	—
40	C₁₃	—	12	1	no	—
41	C₁₃	C₃×C₁₃×Dic₁₁	1	1	yes	characteristic, complemented
42	C₁₃	C₁₁⋊AGL(1,𝔽₁₃)	1	1	yes	characteristic, direct product factor
43	C₃×C₄	—	143	1	no	Hall
44	C₁₁	C₁₃×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
45	C₂×C₃	—	13	1	no	—
46	C₄	—	143	1	no	Sylow
47	C₃	—	52	1	no	Sylow
48	C₂	—	13	1	no	—

	subgroup	G/H
center, hypercenter	C₁₃	C₁₁⋊AGL(1,𝔽₁₃)
commutator, hypocenter	C₁₁×C₁₃	C₃×C₄×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₁×C₁₃²	C₃×C₄
prime radical	C₁₁×C₁₃×D₁₃⋊C₃	C₂
cosocle	C₁₁×D₁₃	C₂×C₃×C₁₃
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₁₃

Complements

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

N	H ≅ G/N	type
2. C₁₃×C₁₁⋊#261	C₃	semidirect
3. C₁₁×C₁₃×C₁₃⋊C₃	C₄	semidirect
6. C₁₁×C₁₃²	C₃×C₄	semidirect
7. C₁₁⋊AGL(1,𝔽₁₃)	C₁₃	direct (N × H)
13. C₁₁⋊#261	C₃×C₁₃	semidirect
15. C₁₃×C₁₃⋊C₃	Dic₁₁	semidirect
17. C₁₁×C₁₃⋊C₃	C₄×C₁₃	semidirect
21. C₁₃²	C₃×Dic₁₁	semidirect
25. C₁₁×C₁₃	C₃×C₄×C₁₃	semidirect
26. C₁₁×C₁₃	AGL(1,𝔽₁₃)	semidirect
35. C₁₃⋊C₃	C₁₃×Dic₁₁	semidirect
41. C₁₃	C₃×C₁₃×Dic₁₁	semidirect
42. C₁₃	C₁₁⋊AGL(1,𝔽₁₃)	direct (N × H)
44. C₁₁	C₁₃×AGL(1,𝔽₁₃)	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×C₁₃×D₁₃⋊C₃	2
C₁₃×C₁₁⋊#261	3
C₁₃×AGL(1,𝔽₁₃)	11
C₁₁⋊AGL(1,𝔽₁₃)	13
C₃×C₁₃×Dic₁₁	13

Subgroups — C13×C11⋊AGL(1,𝔽13) #36373313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃×C₁₁⋊AGL(1,𝔽₁₃) #36373313