Subgroups — (#13094089⋊C₃)⋊C₇ #44539769

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊C₃×C₂₉⋊C₇	C₂	1	1	yes	maximal, characteristic
2	#13094089⋊C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃⋊C₃×C₂₉⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
4	D₁₃×C₂₉⋊C₇	C₂×C₃	1	1	yes	characteristic
5	#13094089⋊C₃	C₇	1	1	yes	maximal, characteristic, complemented, Hall
6	C₁₃×C₂₉⋊C₇	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₃×Dic₂₉⋊C₇	—	13	1	no	maximal, Hall
8	C₂₉×D₁₃⋊C₃	C₂×C₇	1	1	yes	characteristic
9	#13094089	C₃×C₇	1	1	yes	characteristic, complemented, Hall
10	C₂×C₃×C₂₉⋊C₇	—	13	1	no	—
11	C₂₉×C₁₃⋊C₃	C₄×C₇	1	1	yes	characteristic, complemented, Hall
12	C₇×AGL(1,𝔽₁₃)	—	29	1	no	maximal, Hall
13	Dic₂₉⋊C₇	—	13	1	no	Hall
14	D₁₃×C₂₉	C₂×C₃×C₇	1	1	yes	characteristic
15	C₃×C₂₉⋊C₇	—	13	1	no	Hall
16	C₇×D₁₃⋊C₃	—	29	1	no	—
17	C₂×C₂₉⋊C₇	—	13	1	no	—
18	C₁₃×C₂₉	C₃×C₄×C₇	1	1	yes	characteristic, complemented, Hall
19	C₇×#261	—	29	1	no	Hall
20	C₃×Dic₂₉	—	13	1	no	Hall
21	C₇×C₁₃⋊C₃	—	29	1	no	Hall
22	C₂₉⋊C₇	AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Hall
23	C₇×D₁₃	—	29	1	no	—
24	C₂×C₃×C₂₉	—	13	1	no	—
25	AGL(1,𝔽₁₃)	—	29	1	no	Hall
26	Dic₂₉	—	13	1	no	Hall
27	C₇×C₁₃	—	29	1	no	Hall
28	C₃×C₂₉	—	13	1	no	Hall
29	C₃×C₄×C₇	—	377	1	no	Hall
30	D₁₃⋊C₃	D₂₉⋊C₇	1	1	yes	characteristic
31	C₂×C₂₉	—	13	1	no	—
32	#261	—	29	1	no	Hall
33	C₂×C₃×C₇	—	377	1	no	—
34	C₁₃⋊C₃	Dic₂₉⋊C₇	1	1	yes	characteristic, complemented, Hall
35	C₂₉	C₇×AGL(1,𝔽₁₃)	1	1	yes	characteristic, complemented, Sylow
36	C₄×C₇	—	377	1	no	Hall
37	D₁₃	C₃×D₂₉⋊C₇	1	1	yes	characteristic
38	C₃×C₇	—	377	1	no	Hall
39	C₂×C₇	—	377	1	no	—
40	C₁₃	C₃×Dic₂₉⋊C₇	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	377	1	no	Hall
42	C₇	—	29	1	no	Sylow
43	C₂×C₃	—	13	1	no	—
44	C₄	—	377	1	no	Sylow
45	C₃	—	13	1	no	Sylow
46	C₂	—	13	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₃×C₂₉	C₃×C₄×C₇
prime radical	D₁₃⋊C₃×C₂₉⋊C₇	C₂
cosocle	D₁₃×C₂₉	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. #13094089⋊C₇	C₃	semidirect
3. C₁₃⋊C₃×C₂₉⋊C₇	C₄	semidirect
5. #13094089⋊C₃	C₇	semidirect
6. C₁₃×C₂₉⋊C₇	C₃×C₄	semidirect
9. #13094089	C₃×C₇	semidirect
11. C₂₉×C₁₃⋊C₃	C₄×C₇	semidirect
18. C₁₃×C₂₉	C₃×C₄×C₇	semidirect
22. C₂₉⋊C₇	AGL(1,𝔽₁₃)	semidirect
34. C₁₃⋊C₃	Dic₂₉⋊C₇	semidirect
35. C₂₉	C₇×AGL(1,𝔽₁₃)	semidirect
40. C₁₃	C₃×Dic₂₉⋊C₇	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊C₃×C₂₉⋊C₇	2
#13094089⋊C₇	3
#13094089⋊C₃	7
C₃×Dic₂₉⋊C₇	13
C₇×AGL(1,𝔽₁₃)	29

Subgroups — (#13094089⋊C3)⋊C7 #44539769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (#13094089⋊C₃)⋊C₇ #44539769