Subgroups — C₁₃⋊C₃×AGL(1,𝔽₂₉) #44539773

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃⋊C₃×D₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₁₃×AGL(1,𝔽₂₉)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₂₉⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	C₁₃×D₂₉⋊C₇	C₂×C₃	1	1	yes	characteristic
5	C₁₃⋊C₃×#1181	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₃×C₂₉⋊C₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×AGL(1,𝔽₂₉)	—	13	1	no	maximal, Hall
8	C₁₃⋊C₃×D₂₉	C₂×C₇	1	1	yes	characteristic
9	C₁₃×#1181	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₃×D₂₉⋊C₇	—	13	1	no	—
11	C₂₉×C₁₃⋊C₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₄×C₇×C₁₃⋊C₃	—	29	1	no	maximal, Hall
13	AGL(1,𝔽₂₉)	C₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Hall
14	C₁₃×D₂₉	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₂₉⋊C₇	—	13	1	no	Hall
16	C₂×C₇×C₁₃⋊C₃	—	29	1	no	—
17	D₂₉⋊C₇	C₂×C₁₃⋊C₃	1	1	yes	characteristic
18	C₁₃×C₂₉	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
19	C₄×C₇×C₁₃	—	29	1	no	Hall
20	C₃×#1181	—	13	1	no	Hall
21	C₇×C₁₃⋊C₃	—	29	1	no	Hall
22	C₂₉⋊C₇	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	—	29	1	no	—
24	C₃×D₂₉	—	13	1	no	—
25	C₄×C₁₃⋊C₃	—	29	1	no	Hall
26	#1181	C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
27	C₇×C₁₃	—	29	1	no	Hall
28	C₃×C₂₉	—	13	1	no	Hall
29	C₃×C₄×C₇	—	377	1	no	Hall
30	C₂×C₁₃⋊C₃	—	29	1	no	—
31	D₂₉	C₂×C₇×C₁₃⋊C₃	1	1	yes	characteristic
32	C₄×C₁₃	—	29	1	no	Hall
33	C₂×C₃×C₇	—	377	1	no	—
34	C₁₃⋊C₃	AGL(1,𝔽₂₉)	1	1	yes	characteristic, direct product factor, Hall
35	C₂₉	C₄×C₇×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₇	—	29	1	no	Hall
37	C₂×C₁₃	—	29	1	no	—
38	C₃×C₇	—	377	1	no	Hall
39	C₂×C₇	—	29	1	no	—
40	C₁₃	C₃×AGL(1,𝔽₂₉)	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	377	1	no	Hall
42	C₇	—	29	1	no	Sylow
43	C₂×C₃	—	377	1	no	—
44	C₄	—	29	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	29	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₂₉	C₃×C₄×C₇
prime radical	C₁₃⋊C₃×D₂₉⋊C₇	C₂
cosocle	C₁₃×D₂₉	C₂×C₃×C₇
LCS	G ▷ C₁₃×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₁₃×AGL(1,𝔽₂₉)	C₃	semidirect
3. C₁₃⋊C₃×C₂₉⋊C₇	C₄	semidirect
5. C₁₃⋊C₃×#1181	C₇	semidirect
6. C₁₃×C₂₉⋊C₇	C₃×C₄	semidirect
9. C₁₃×#1181	C₃×C₇	semidirect
11. C₂₉×C₁₃⋊C₃	C₄×C₇	semidirect
13. AGL(1,𝔽₂₉)	C₁₃⋊C₃	direct (N × H)
18. C₁₃×C₂₉	C₃×C₄×C₇	semidirect
22. C₂₉⋊C₇	C₄×C₁₃⋊C₃	semidirect
26. #1181	C₇×C₁₃⋊C₃	semidirect
34. C₁₃⋊C₃	AGL(1,𝔽₂₉)	direct (N × H)
35. C₂₉	C₄×C₇×C₁₃⋊C₃	semidirect
40. C₁₃	C₃×AGL(1,𝔽₂₉)	semidirect

Maximal subgroups

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

subgroup	index
C₁₃⋊C₃×D₂₉⋊C₇	2
C₁₃×AGL(1,𝔽₂₉)	3
C₁₃⋊C₃×#1181	7
C₃×AGL(1,𝔽₂₉)	13
C₄×C₇×C₁₃⋊C₃	29

Subgroups — C13⋊C3×AGL(1,𝔽29) #44539773

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₃⋊C₃×AGL(1,𝔽₂₉) #44539773