Subgroups — C₂₉⋊((C₅⋊D₅)⋊ΓL(1,𝔽₈)) #44478583

Order 30450.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₇⋊(C₅²⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₅⋊D₁₄₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₅²×C₇×C₂₉	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	C₂₉⋊((C₅⋊D₅)⋊C₃)	—	7	1	no	maximal, Hall
5	C₂₉×C₅²⋊C₃	—	7	1	no	Hall
6	C₇×D₁₄₅	—	15	2	no	—
7	C₅⋊D₁₄₅	ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
8	ΓL(1,𝔽₈)×D₂₉	—	25	1	no	maximal, Hall
9	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	—	29	1	no	maximal, Hall
10	C₅×C₇×C₂₉	—	3	2	no	—
11	C₅²×C₂₉	C₂×ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Hall
12	ΓL(1,𝔽₈)×C₂₉	—	25	1	no	Hall
13	C₇⋊(C₅²⋊C₃)	D₂₉	1	1	yes	characteristic, complemented, Hall
14	C₇×D₂₉	—	75	1	no	Hall
15	C₇×C₅⋊D₅	—	29	1	no	Hall
16	D₁₄₅	—	15	2	no	—
17	C₇×C₂₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₅²×C₇	C₃×D₂₉	1	1	yes	characteristic, complemented, Hall
19	C₃×D₂₉	—	175	1	no	Hall
20	(C₅⋊D₅)⋊C₃	—	203	1	no	Hall
21	C₅×C₂₉	—	3	2	no	—
22	C₃×C₂₉	—	175	1	no	Hall
23	C₅²⋊C₃	—	7	1	no	Hall
24	C₇×D₅	—	435	2	no	—
25	D₂₉	—	75	1	no	Hall
26	C₅⋊D₅	—	29	1	no	Hall
27	C₂×ΓL(1,𝔽₈)	—	725	1	no	Hall
28	C₅×C₇	—	3	2	no	—
29	C₂₉	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	1	1	yes	characteristic, complemented, Sylow
30	C₅²	ΓL(1,𝔽₈)×D₂₉	1	1	yes	characteristic, complemented, Sylow
31	ΓL(1,𝔽₈)	—	25	1	no	Hall
32	C₂×C₇	—	2175	1	no	Hall
33	D₅	—	435	2	no	—
34	C₇	C₂₉⋊((C₅⋊D₅)⋊C₃)	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	5075	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	175	1	no	Sylow
38	C₂	—	2175	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₅²×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₅²×C₇×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₇⋊(C₅²⋊C₃)	C₂	semidirect
2. C₇×C₅⋊D₁₄₅	C₃	semidirect
3. C₅²×C₇×C₂₉	C₂×C₃	semidirect
7. C₅⋊D₁₄₅	ΓL(1,𝔽₈)	semidirect
11. C₅²×C₂₉	C₂×ΓL(1,𝔽₈)	semidirect
13. C₇⋊(C₅²⋊C₃)	D₂₉	semidirect
17. C₇×C₂₉	(C₅⋊D₅)⋊C₃	semidirect
18. C₅²×C₇	C₃×D₂₉	semidirect
29. C₂₉	(C₅⋊D₅)⋊ΓL(1,𝔽₈)	semidirect
30. C₅²	ΓL(1,𝔽₈)×D₂₉	semidirect
34. C₇	C₂₉⋊((C₅⋊D₅)⋊C₃)	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×C₇⋊(C₅²⋊C₃)	2
C₇×C₅⋊D₁₄₅	3
C₂₉⋊((C₅⋊D₅)⋊C₃)	7
ΓL(1,𝔽₈)×D₂₉	25
(C₅⋊D₅)⋊ΓL(1,𝔽₈)	29

Subgroups — C29⋊((C5⋊D5)⋊ΓL(1,𝔽8)) #44478583

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉⋊((C₅⋊D₅)⋊ΓL(1,𝔽₈)) #44478583