Subgroups — #39908099

Order 26100.

128 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	1	no	maximal
4	#19104885	—	5	1	no	maximal
5	C₃⋊(C₅⋊D₁₄₅)	—	6	2	no	—
6	#15668529	—	9	1	no	maximal, Hall
7	C₃⋊D₄₃₅	—	5	1	no	—
8	C₃⋊D₄₃₅	—	5	1	no	—
9	C₃⋊D₄₃₅	—	10	2	no	—
10	C₃×C₅²×C₂₉	—	2	2	no	—
11	C₅⋊D₁₄₅	—	9	1	no	—
12	C₃²×C₅×C₂₉	—	2	2	no	—
13	C₃²×C₅×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
14	C₃²×C₅×C₂₉	AGL(1,𝔽₅)	1	1	yes	characteristic, complemented
15	#11760329	—	25	1	no	Hall
16	#11744708	—	29	1	no	maximal, Hall
17	D₄₃₅	—	30	2	no	—
18	D₄₃₅	—	30	2	no	—
19	D₄₃₅	—	30	8	no	—
20	C₅²×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
21	#10596815	—	45	1	no	—
22	#10596814	—	45	1	no	—
23	C₃⋊D₈₇	—	25	1	no	—
24	C₃⋊(C₃⋊(C₅⋊D₅))	—	29	1	no	—
25	C₃×C₅×C₂₉	—	2	8	no	—
26	C₃×C₅×C₂₉	—	2	2	no	—
27	C₃×C₅×C₂₉	—	2	2	no	—
28	D₁₄₅	—	45	1	no	—
29	D₁₄₅	—	45	1	no	—
30	D₁₄₅	—	90	2	no	—
31	C₃²×C₂₉	#1044	1	1	yes	characteristic, complemented, Hall
32	C₃²×C₅²	#1181	1	1	yes	characteristic, complemented, Hall
33	#4380	—	145	1	no	—
34	#4380	—	145	1	no	—
35	D₈₇	—	150	2	no	—
36	C₃⋊(C₅⋊D₅)	—	174	2	no	—
37	C₅×C₂₉	—	2	2	no	—
38	C₅×C₂₉	#4380	1	1	yes	characteristic, complemented
39	C₅×C₂₉	#4380	1	1	yes	characteristic, complemented
40	#1181	—	225	1	no	Hall
41	#1044	—	261	1	no	Hall
42	C₃⋊D₁₅	—	290	2	no	—
43	C₃⋊D₁₅	—	145	1	no	—
44	C₃⋊D₁₅	—	145	1	no	—
45	C₃×C₂₉	—	2	2	no	—
46	C₃×C₅²	—	2	2	no	—
47	D₂₉	—	225	1	no	—
48	C₅⋊D₅	—	261	1	no	—
49	C₃²×C₅	—	2	2	no	—
50	C₃²×C₅	#10596814	1	1	yes	characteristic, complemented
51	C₃²×C₅	#10596815	1	1	yes	characteristic, complemented
52	#157	—	725	1	no	Hall
53	D₁₅	—	870	2	no	—
54	D₁₅	—	870	2	no	—
55	D₁₅	—	870	8	no	—
56	C₂₉	#11744708	1	1	yes	characteristic, complemented, Sylow
57	C₅²	#11760329	1	1	yes	characteristic, complemented, Sylow
58	AGL(1,𝔽₅)	—	1305	1	no	—
59	AGL(1,𝔽₅)	—	1305	1	no	—
60	C₃⋊D₃	—	725	1	no	—
61	C₃×C₅	—	2	8	no	—
62	C₃×C₅	—	2	2	no	—
63	C₃×C₅	—	2	2	no	—
64	D₅	—	1305	1	no	—
65	D₅	—	1305	1	no	—
66	D₅	—	2610	2	no	—
67	C₃²	#15668529	1	1	yes	characteristic, complemented, Sylow
68	D₃	—	4350	2	no	—
69	C₅	—	2	2	no	—
70	C₅	#19104885	1	1	yes	characteristic, complemented
71	C₅	#19104886	1	1	yes	characteristic, complemented
72	C₄	—	6525	1	no	Sylow
73	C₃	—	2	2	no	—
74	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
13. C₃²×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
14. C₃²×C₅×C₂₉	AGL(1,𝔽₅)	semidirect
20. C₅²×C₂₉	#157	semidirect
31. C₃²×C₂₉	#1044	semidirect
32. C₃²×C₅²	#1181	semidirect
38. C₅×C₂₉	#4380	semidirect
39. C₅×C₂₉	#4380	semidirect
50. C₃²×C₅	#10596814	semidirect
51. C₃²×C₅	#10596815	semidirect
56. C₂₉	#11744708	semidirect
57. C₅²	#11760329	semidirect
67. C₃²	#15668529	semidirect
70. C₅	#19104885	semidirect
71. 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
#19104885	5
#15668529	9
#11744708	29