Subgroups — C₇×C₂₉×ΓL(1,𝔽₁₆) #27131780

Order 12180.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×D₅×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₇×AGL(1,𝔽₅)×C₂₉	—	3	1	no	maximal, Hall
3	C₃×C₅×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×Dic₃×C₂₉	—	5	1	no	maximal, Hall
5	C₇×D₅×C₂₉	D₃	1	1	yes	characteristic
6	C₂₉×ΓL(1,𝔽₁₆)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₇×C₂₉	—	5	1	no	—
8	C₅×C₇×C₂₉	Dic₃	1	1	yes	characteristic, complemented, Hall
9	C₃×D₅×C₂₉	C₂×C₇	1	1	yes	characteristic
10	C₄×C₇×C₂₉	—	15	1	no	Hall
11	C₃×C₇×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
12	AGL(1,𝔽₅)×C₂₉	—	3	1	no	Hall
13	C₃×C₅×C₂₉	C₄×C₇	1	1	yes	characteristic, complemented, Hall
14	C₇×ΓL(1,𝔽₁₆)	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
15	C₂×C₇×C₂₉	—	5	1	no	—
16	Dic₃×C₂₉	—	5	1	no	Hall
17	D₅×C₂₉	D₃×C₇	1	1	yes	characteristic
18	C₃×C₇×D₅	C₂×C₂₉	1	1	yes	characteristic
19	C₇×C₂₉	ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Hall
20	C₂×C₃×C₂₉	—	5	1	no	—
21	C₅×C₂₉	C₇×Dic₃	1	1	yes	characteristic, complemented, Hall
22	C₇×AGL(1,𝔽₅)	—	3	1	no	Hall
23	C₄×C₂₉	—	15	1	no	Hall
24	C₃×C₅×C₇	C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
25	C₃×C₂₉	C₇×AGL(1,𝔽₅)	1	1	yes	characteristic, complemented, Hall
26	C₇×Dic₃	—	5	1	no	Hall
27	C₇×D₅	D₃×C₂₉	1	1	yes	characteristic
28	ΓL(1,𝔽₁₆)	C₇×C₂₉	1	1	yes	characteristic, direct product factor, Hall
29	C₂×C₂₉	—	5	1	no	—
30	C₂×C₃×C₇	—	5	1	no	—
31	C₅×C₇	Dic₃×C₂₉	1	1	yes	characteristic, complemented, Hall
32	C₃×D₅	C₂×C₇×C₂₉	1	1	yes	characteristic
33	C₂₉	C₇×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
34	C₄×C₇	—	15	1	no	Hall
35	C₃×C₇	AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented, Hall
36	AGL(1,𝔽₅)	—	3	1	no	Hall
37	C₃×C₅	C₄×C₇×C₂₉	1	1	yes	characteristic, complemented, Hall
38	C₂×C₇	—	5	1	no	—
39	Dic₃	—	5	1	no	Hall
40	D₅	D₃×C₇×C₂₉	1	1	yes	characteristic
41	C₇	C₂₉×ΓL(1,𝔽₁₆)	1	1	yes	characteristic, direct product factor, Sylow
42	C₂×C₃	—	5	1	no	—
43	C₅	C₇×Dic₃×C₂₉	1	1	yes	characteristic, complemented, Sylow
44	C₄	—	15	1	no	Sylow
45	C₃	C₇×AGL(1,𝔽₅)×C₂₉	1	1	yes	characteristic, complemented, Sylow
46	C₂	—	5	1	no	—

	subgroup	G/H
center, hypercenter	C₇×C₂₉	ΓL(1,𝔽₁₆)
commutator, hypocenter	C₃×C₅	C₄×C₇×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₂₉	C₄
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇×C₂₉

Complements

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

N	H ≅ G/N	type
3. C₃×C₅×C₇×C₂₉	C₄	semidirect
6. C₂₉×ΓL(1,𝔽₁₆)	C₇	direct (N × H)
8. C₅×C₇×C₂₉	Dic₃	semidirect
11. C₃×C₇×C₂₉	AGL(1,𝔽₅)	semidirect
13. C₃×C₅×C₂₉	C₄×C₇	semidirect
14. C₇×ΓL(1,𝔽₁₆)	C₂₉	direct (N × H)
19. C₇×C₂₉	ΓL(1,𝔽₁₆)	direct (N × H)
21. C₅×C₂₉	C₇×Dic₃	semidirect
24. C₃×C₅×C₇	C₄×C₂₉	semidirect
25. C₃×C₂₉	C₇×AGL(1,𝔽₅)	semidirect
28. ΓL(1,𝔽₁₆)	C₇×C₂₉	direct (N × H)
31. C₅×C₇	Dic₃×C₂₉	semidirect
33. C₂₉	C₇×ΓL(1,𝔽₁₆)	direct (N × H)
35. C₃×C₇	AGL(1,𝔽₅)×C₂₉	semidirect
37. C₃×C₅	C₄×C₇×C₂₉	semidirect
41. C₇	C₂₉×ΓL(1,𝔽₁₆)	direct (N × H)
43. C₅	C₇×Dic₃×C₂₉	semidirect
45. C₃	C₇×AGL(1,𝔽₅)×C₂₉	semidirect

Subgroups — C7×C29×ΓL(1,𝔽16) #27131780

Conjugacy classes of subgroups

Complements

Subgroups — C₇×C₂₉×ΓL(1,𝔽₁₆) #27131780