Subgroups — C₄×C₂₉×#63270 #44539710

Order 31668.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₉×#63270	C₂	1	1	yes	maximal, characteristic
2	C₄×C₇×C₁₃×C₂₉	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂₉×#63270	C₄	1	1	yes	characteristic, direct product factor, Hall
4	C₂×C₇×C₁₃×C₂₉	C₂×C₃	1	1	yes	characteristic
5	C₄×C₂₉×C₁₃⋊C₃	—	7	1	no	maximal, Hall
6	C₇×C₁₃×C₂₉	C₃×C₄	1	1	yes	characteristic, complemented, Hall
7	C₄×ΓL(1,𝔽₈)×C₂₉	—	13	1	no	maximal, Hall
8	C₂×C₂₉×C₁₃⋊C₃	—	7	1	no	—
9	C₄×C₁₃×C₂₉	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
10	C₂×ΓL(1,𝔽₈)×C₂₉	—	13	1	no	—
11	C₂₉×C₁₃⋊C₃	—	7	1	no	Hall
12	C₄×#63270	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₄×C₇×C₂₉	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₁₃×C₂₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic
15	ΓL(1,𝔽₈)×C₂₉	—	13	1	no	Hall
16	C₂×#63270	C₂×C₂₉	1	1	yes	characteristic
17	C₂×C₇×C₂₉	C₂×C₁₃⋊C₃	1	1	yes	characteristic
18	C₁₃×C₂₉	C₄×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
19	C₄×C₇×C₁₃	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
20	C₃×C₄×C₂₉	—	91	1	no	Hall
21	#63270	C₄×C₂₉	1	1	yes	characteristic, direct product factor, Hall
22	C₇×C₂₉	C₄×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₃	C₂×C₃×C₂₉	1	1	yes	characteristic
24	C₂×C₃×C₂₉	—	91	1	no	—
25	C₄×C₁₃⋊C₃	—	7	1	no	Hall
26	C₄×C₂₉	#63270	1	1	yes	characteristic, direct product factor, Hall
27	C₇×C₁₃	C₃×C₄×C₂₉	1	1	yes	characteristic, complemented, Hall
28	C₃×C₂₉	—	91	1	no	Hall
29	C₄×ΓL(1,𝔽₈)	—	13	1	no	Hall
30	C₂×C₁₃⋊C₃	—	7	1	no	—
31	C₂×C₂₉	C₂×#63270	1	1	yes	characteristic
32	C₄×C₁₃	ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic, complemented, Hall
33	C₂×ΓL(1,𝔽₈)	—	13	1	no	—
34	C₁₃⋊C₃	—	7	1	no	Hall
35	C₂₉	C₄×#63270	1	1	yes	characteristic, direct product factor, Sylow
36	C₄×C₇	C₂₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
37	C₂×C₁₃	C₂×ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic
38	ΓL(1,𝔽₈)	—	13	1	no	Hall
39	C₂×C₇	C₂×C₂₉×C₁₃⋊C₃	1	1	yes	characteristic
40	C₁₃	C₄×ΓL(1,𝔽₈)×C₂₉	1	1	yes	characteristic, complemented, Sylow
41	C₃×C₄	—	91	1	no	Hall
42	C₇	C₄×C₂₉×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
43	C₂×C₃	—	91	1	no	—
44	C₄	C₂₉×#63270	1	1	yes	characteristic, direct product factor, Sylow
45	C₃	—	91	1	no	Sylow
46	C₂	C₂×C₂₉×#63270	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄×C₂₉	#63270
commutator, hypocenter	C₇×C₁₃	C₃×C₄×C₂₉
Frattini	C₂	C₂×C₂₉×#63270
Fitting	C₄×C₇×C₁₃×C₂₉	C₃
socle	C₂×C₇×C₁₃×C₂₉	C₂×C₃
prime radical	C₂×C₂₉×#63270	C₂
cosocle	C₂×C₇×C₁₃	C₂×C₃×C₂₉
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₄×C₂₉

Complements

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

N	H ≅ G/N	type
2. C₄×C₇×C₁₃×C₂₉	C₃	semidirect
3. C₂₉×#63270	C₄	direct (N × H)
6. C₇×C₁₃×C₂₉	C₃×C₄	semidirect
9. C₄×C₁₃×C₂₉	ΓL(1,𝔽₈)	semidirect
12. C₄×#63270	C₂₉	direct (N × H)
13. C₄×C₇×C₂₉	C₁₃⋊C₃	semidirect
18. C₁₃×C₂₉	C₄×ΓL(1,𝔽₈)	semidirect
19. C₄×C₇×C₁₃	C₃×C₂₉	semidirect
21. #63270	C₄×C₂₉	direct (N × H)
22. C₇×C₂₉	C₄×C₁₃⋊C₃	semidirect
26. C₄×C₂₉	#63270	direct (N × H)
27. C₇×C₁₃	C₃×C₄×C₂₉	semidirect
32. C₄×C₁₃	ΓL(1,𝔽₈)×C₂₉	semidirect
35. C₂₉	C₄×#63270	direct (N × H)
36. C₄×C₇	C₂₉×C₁₃⋊C₃	semidirect
40. C₁₃	C₄×ΓL(1,𝔽₈)×C₂₉	semidirect
42. C₇	C₄×C₂₉×C₁₃⋊C₃	semidirect
44. C₄	C₂₉×#63270	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₉×#63270	2
C₄×C₇×C₁₃×C₂₉	3
C₄×C₂₉×C₁₃⋊C₃	7
C₄×ΓL(1,𝔽₈)×C₂₉	13
C₄×#63270	29

Subgroups — C4×C29×#63270 #44539710

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂₉×#63270 #44539710