Subgroups — #39908100

Order 26100.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉×C₃⋊(C₃⋊(C₅⋊D₅))	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₅²×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	#19104887	—	5	2	no	maximal
4	C₂₉×C₃⋊(C₅⋊D₅)	—	6	2	no	—
5	#15668530	—	9	1	no	maximal, Hall
6	C₂₉×C₃⋊D₁₅	—	5	2	no	—
7	C₂₉×C₃⋊D₁₅	—	10	2	no	—
8	C₃×C₅²×C₂₉	—	2	2	no	—
9	C₂₉×C₅⋊D₅	—	9	1	no	—
10	C₃²×C₅×C₂₉	—	2	2	no	—
11	C₃²×C₅×C₂₉	AGL(1,𝔽₅)	1	2	yes	complemented
12	#11760330	—	25	1	no	Hall
13	#11744708	—	29	1	no	maximal, Hall
14	C₂₉×D₁₅	—	30	4	no	—
15	C₂₉×D₁₅	—	30	8	no	—
16	C₅²×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
17	#10596816	—	45	2	no	—
18	C₃⋊D₃×C₂₉	—	25	1	no	—
19	C₃⋊(C₃⋊(C₅⋊D₅))	D₂₉	1	1	yes	characteristic
20	C₃×C₅×C₂₉	—	2	8	no	—
21	C₃×C₅×C₂₉	—	2	4	no	—
22	D₅×C₂₉	—	45	2	no	—
23	D₅×C₂₉	—	90	2	no	—
24	C₃²×C₂₉	#1044	1	1	yes	characteristic, complemented, Hall
25	C₃²×C₅²	Dic₂₉	1	1	yes	characteristic, complemented, Hall
26	#4380	—	145	2	no	—
27	D₃×C₂₉	—	150	2	no	—
28	C₃⋊(C₅⋊D₅)	—	6	2	no	—
29	C₅×C₂₉	—	2	2	no	—
30	C₅×C₂₉	#4380	1	2	yes	complemented
31	Dic₂₉	—	225	1	no	Hall
32	#1044	—	261	1	no	Hall
33	C₃⋊D₁₅	—	5	2	no	—
34	C₃⋊D₁₅	—	10	2	no	—
35	C₃×C₂₉	—	2	2	no	—
36	C₃×C₅²	—	2	2	no	—
37	C₂×C₂₉	—	225	1	no	—
38	C₅⋊D₅	—	9	1	no	—
39	C₃²×C₅	—	2	2	no	—
40	C₃²×C₅	#10596816	1	2	yes	complemented
41	#157	—	725	1	no	Hall
42	D₁₅	—	30	4	no	—
43	D₁₅	—	30	8	no	—
44	C₂₉	#11744708	1	1	yes	characteristic, complemented, Sylow
45	C₅²	#11760330	1	1	yes	characteristic, complemented, Sylow
46	AGL(1,𝔽₅)	—	1305	2	no	—
47	C₃⋊D₃	—	25	1	no	—
48	C₃×C₅	—	2	8	no	—
49	C₃×C₅	—	2	4	no	—
50	D₅	—	45	2	no	—
51	D₅	—	90	2	no	—
52	C₃²	#15668530	1	1	yes	characteristic, complemented, Sylow
53	D₃	—	150	2	no	—
54	C₅	—	2	2	no	—
55	C₅	#19104887	1	2	yes	complemented
56	C₄	—	6525	1	no	Sylow
57	C₃	—	2	2	no	—
58	C₂	—	225	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅²×C₂₉	C₄
prime radical, cosocle	C₂₉×C₃⋊(C₃⋊(C₅⋊D₅))	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
11. C₃²×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
16. C₅²×C₂₉	#157	semidirect
24. C₃²×C₂₉	#1044	semidirect
25. C₃²×C₅²	Dic₂₉	semidirect
30. C₅×C₂₉	#4380	semidirect
40. C₃²×C₅	#10596816	semidirect
44. C₂₉	#11744708	semidirect
45. C₅²	#11760330	semidirect
52. C₃²	#15668530	semidirect
55. C₅	#19104887	semidirect

Maximal subgroups

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

subgroup	index
C₂₉×C₃⋊(C₃⋊(C₅⋊D₅))	2
#19104887	5
#15668530	9
#11744708	29