Subgroups — #39907908

Order 26100.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₉⋊((C₅⋊D₅)⋊C₉)	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#15668529	—	3	1	no	maximal
3	C₂₉×C₅²⋊C₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₃×C₅⋊D₁₄₅	D₃	1	1	yes	characteristic
5	#15668529	—	9	1	no	Hall
6	C₃×C₅²×C₂₉	Dic₃	1	1	yes	characteristic
7	C₃⋊#10596814	—	15	1	no	—
8	C₃⋊#10596815	—	15	1	no	—
9	C₅⋊D₁₄₅	D₉	1	1	yes	characteristic
10	C₉⋊#1181	—	25	1	no	maximal, Hall
11	#11744634	—	29	1	no	maximal, Hall
12	C₃×D₁₄₅	—	30	1	no	—
13	C₃×D₁₄₅	—	30	1	no	—
14	C₅²×C₂₉	Dic₉	1	1	yes	characteristic, complemented, Hall
15	#10596815	—	45	1	no	—
16	#10596814	—	45	1	no	—
17	C₉×D₂₉	—	25	1	no	—
18	(C₅⋊D₅)⋊C₉	—	29	1	no	—
19	C₃×C₅×C₂₉	—	6	1	no	—
20	C₃×C₅×C₂₉	—	6	1	no	—
21	C₃⋊#1181	—	75	1	no	—
22	C₃⋊#1044	—	87	1	no	—
23	D₁₄₅	—	30	1	no	—
24	D₁₄₅	—	30	1	no	—
25	C₉×C₂₉	—	100	1	no	Hall
26	C₅²⋊C₉	#1181	1	1	yes	characteristic, complemented, Hall
27	C₃×D₂₉	—	25	1	no	—
28	C₃×C₅⋊D₅	—	29	1	no	—
29	C₅×C₂₉	—	6	1	no	—
30	C₅×C₂₉	—	6	1	no	—
31	#1181	—	225	1	no	Hall
32	#1044	—	261	1	no	Hall
33	C₃×C₂₉	#64480	1	1	yes	characteristic
34	C₃×C₅²	C₃⋊#1181	1	1	yes	characteristic
35	ΓL(1,𝔽₁₆)	—	435	1	no	—
36	ΓL(1,𝔽₁₆)	—	435	1	no	—
37	D₂₉	—	25	1	no	—
38	C₅⋊D₅	—	29	1	no	—
39	Dic₉	—	725	1	no	Hall
40	C₃×D₅	—	870	1	no	—
41	C₃×D₅	—	870	1	no	—
42	C₂₉	#11744634	1	1	yes	characteristic, complemented, Sylow
43	C₅²	C₉⋊#1181	1	1	yes	characteristic, complemented, Sylow
44	AGL(1,𝔽₅)	—	1305	1	no	—
45	AGL(1,𝔽₅)	—	1305	1	no	—
46	C₂×C₉	—	725	1	no	—
47	C₃×C₅	—	6	1	no	—
48	C₃×C₅	—	6	1	no	—
49	Dic₃	—	2175	1	no	—
50	D₅	—	870	1	no	—
51	D₅	—	435	1	no	—
52	C₉	—	100	1	no	Sylow
53	C₂×C₃	—	725	1	no	—
54	C₅	—	3	1	no	—
55	C₅	—	6	1	no	—
56	C₄	—	6525	1	no	Sylow
57	C₃	#22576424	1	1	yes	characteristic
58	C₂	—	725	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, hypocenter	C₂₉×C₅²⋊C₉	C₄
Frattini	C₃	#22576424
Fitting, socle	C₃×C₅²×C₂₉	Dic₃
prime radical	C₃×C₅⋊D₁₄₅	D₃
cosocle	C₂₉⋊((C₅⋊D₅)⋊C₉)	C₂
LCS	G ▷ C₂₉×C₅²⋊C₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
3. C₂₉×C₅²⋊C₉	C₄	semidirect
14. C₅²×C₂₉	Dic₉	semidirect
26. C₅²⋊C₉	#1181	semidirect
42. C₂₉	#11744634	semidirect
43. C₅²	C₉⋊#1181	semidirect

Maximal subgroups

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

subgroup	index
C₂₉⋊((C₅⋊D₅)⋊C₉)	2
C₃⋊#15668529	3
C₉⋊#1181	25
#11744634	29