Subgroups — C₂₉×#11760386 #44478580

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	C₂₉×C₅⋊D₃₅	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	C₂₉×D₃₅	—	15	2	no	—
7	C₂₉×C₅⋊D₅	—	7	1	no	Hall
8	C₂₉×AGL(1,𝔽₇)	—	25	1	no	maximal, Hall
9	#11760386	C₂₉	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₅×C₇×C₂₉	—	3	2	no	—
11	C₅²×C₂₉	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Hall
12	ΓL(1,𝔽₈)×C₂₉	—	25	1	no	Hall
13	C₇⋊(C₅²⋊C₃)	C₂×C₂₉	1	1	yes	characteristic, complemented, Hall
14	D₇×C₂₉	—	25	1	no	Hall
15	C₅⋊D₃₅	C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
16	D₅×C₂₉	—	105	2	no	—
17	C₇×C₂₉	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₅²×C₇	C₂×C₃×C₂₉	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×C₂₉	—	175	1	no	Hall
20	(C₅⋊D₅)⋊C₃	—	7	1	no	Hall
21	C₅×C₂₉	—	3	2	no	—
22	C₃×C₂₉	—	175	1	no	Hall
23	C₅²⋊C₃	—	7	1	no	Hall
24	D₃₅	—	15	2	no	—
25	C₂×C₂₉	—	175	1	no	Hall
26	C₅⋊D₅	—	7	1	no	Hall
27	AGL(1,𝔽₇)	—	25	1	no	Hall
28	C₅×C₇	—	3	2	no	—
29	C₂₉	#11760386	1	1	yes	characteristic, direct product factor, Sylow
30	C₅²	C₂₉×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented, Sylow
31	ΓL(1,𝔽₈)	—	25	1	no	Hall
32	D₇	—	25	1	no	Hall
33	D₅	—	105	2	no	—
34	C₇	C₂₉×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic, complemented, Sylow
35	C₂×C₃	—	175	1	no	Hall
36	C₅	—	3	2	no	—
37	C₃	—	175	1	no	Sylow
38	C₂	—	175	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₂₉	#11760386
commutator, cosocle, hypocenter	C₅²×C₇	C₂×C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₅²×C₇×C₂₉	C₂×C₃
LCS	G ▷ C₅²×C₇
UCS	C₁ ◁ C₂₉

Complements

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

N	H ≅ G/N	type
1. C₂₉×C₇⋊(C₅²⋊C₃)	C₂	semidirect
2. C₂₉×C₅⋊D₃₅	C₃	semidirect
3. C₅²×C₇×C₂₉	C₂×C₃	semidirect
9. #11760386	C₂₉	direct (N × H)
11. C₅²×C₂₉	AGL(1,𝔽₇)	semidirect
13. C₇⋊(C₅²⋊C₃)	C₂×C₂₉	semidirect
15. C₅⋊D₃₅	C₃×C₂₉	semidirect
17. C₇×C₂₉	(C₅⋊D₅)⋊C₃	semidirect
18. C₅²×C₇	C₂×C₃×C₂₉	semidirect
29. C₂₉	#11760386	direct (N × H)
30. C₅²	C₂₉×AGL(1,𝔽₇)	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
C₂₉×C₅⋊D₃₅	3
C₂₉×(C₅⋊D₅)⋊C₃	7
C₂₉×AGL(1,𝔽₇)	25
#11760386	29

Subgroups — C29×#11760386 #44478580

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₉×#11760386 #44478580