Subgroups — #39908096

Order 26100.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊(C₃⋊(C₅⋊D₁₄₅))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#19104886	—	5	6	no	maximal
4	C₃⋊(C₅⋊D₁₄₅)	—	6	2	no	—
5	#15668526	—	9	1	no	maximal, Hall
6	C₃⋊D₄₃₅	—	5	6	no	—
7	C₃×C₅²×C₂₉	—	2	2	no	—
8	C₅⋊D₁₄₅	—	9	1	no	—
9	C₃²×C₅×C₂₉	AGL(1,𝔽₅)	1	6	yes	complemented
10	#11760329	—	25	1	no	Hall
11	#11744707	—	29	1	no	maximal, Hall
12	D₄₃₅	—	30	12	no	—
13	C₅²×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
14	#10596815	—	45	6	no	—
15	C₃⋊D₈₇	—	25	1	no	—
16	C₃⋊(C₃⋊(C₅⋊D₅))	—	29	1	no	—
17	C₃×C₅×C₂₉	—	2	12	no	—
18	D₁₄₅	—	45	6	no	—
19	C₃²×C₂₉	#1043	1	1	yes	characteristic, complemented, Hall
20	C₃²×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
21	#4380	—	145	6	no	—
22	D₈₇	—	150	2	no	—
23	C₃⋊(C₅⋊D₅)	—	174	2	no	—
24	C₅×C₂₉	#4380	1	6	yes	complemented
25	#1181	—	225	1	no	Hall
26	#1043	—	261	1	no	Hall
27	C₃⋊D₁₅	—	145	6	no	—
28	C₃×C₂₉	—	2	2	no	—
29	C₃×C₅²	—	2	2	no	—
30	D₂₉	—	225	1	no	—
31	C₅⋊D₅	—	261	1	no	—
32	C₃²×C₅	#10596815	1	6	yes	complemented
33	#157	—	725	1	no	Hall
34	D₁₅	—	870	12	no	—
35	C₂₉	#11744707	1	1	yes	characteristic, complemented, Sylow
36	C₅²	#11760329	1	1	yes	characteristic, complemented, Sylow
37	AGL(1,𝔽₅)	—	1305	6	no	—
38	C₃⋊D₃	—	725	1	no	—
39	C₃×C₅	—	2	12	no	—
40	D₅	—	1305	6	no	—
41	C₃²	#15668526	1	1	yes	characteristic, complemented, Sylow
42	D₃	—	4350	2	no	—
43	C₅	#19104886	1	6	yes	complemented
44	C₄	—	6525	1	no	Sylow
45	C₃	—	2	2	no	—
46	C₂	—	6525	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₂₉	C₄
prime radical, cosocle	C₃⋊(C₃⋊(C₅⋊D₁₄₅))	C₂
LCS	G ▷ C₃²×C₅²×C₂₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
2. C₃²×C₅²×C₂₉	C₄	semidirect
9. C₃²×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
13. C₅²×C₂₉	#157	semidirect
19. C₃²×C₂₉	#1043	semidirect
20. C₃²×C₅²	#1181	semidirect
24. C₅×C₂₉	#4380	semidirect
32. C₃²×C₅	#10596815	semidirect
35. C₂₉	#11744707	semidirect
36. C₅²	#11760329	semidirect
41. C₃²	#15668526	semidirect
43. C₅	#19104886	semidirect

Maximal subgroups

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

subgroup	index
C₃⋊(C₃⋊(C₅⋊D₁₄₅))	2
#19104886	5
#15668526	9
#11744707	29