Subgroups — C₅×C₉⋊#10596817 #39907947

Order 26100.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅²×C₉×D₂₉	C₂	1	1	yes	maximal, characteristic
2	C₅×C₃⋊#10596817	—	3	1	no	maximal
3	C₅²×C₉×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
4	C₉⋊#10596817	C₅	1	1	yes	maximal, characteristic, direct product factor
5	C₅×C₉⋊#1181	—	5	1	no	maximal
6	C₃×C₅²×D₂₉	D₃	1	1	yes	characteristic
7	C₅×#10596817	—	9	1	no	Hall
8	C₅×C₉×D₂₉	—	2	2	no	—
9	C₅×C₉×D₂₉	D₅	1	1	yes	characteristic
10	C₅×C₉×D₂₉	C₂×C₅	1	1	yes	characteristic
11	C₃×C₅²×C₂₉	Dic₃	1	1	yes	characteristic
12	C₃⋊#10596817	—	3	1	no	—
13	C₅×C₃⋊#1181	—	15	1	no	—
14	C₅²×D₂₉	D₉	1	1	yes	characteristic
15	C₅×C₉×C₂₉	—	2	2	no	—
16	C₅×C₉×C₂₉	Dic₅	1	1	yes	characteristic, complemented
17	C₅×C₉×C₂₉	C₄×C₅	1	1	yes	characteristic, complemented
18	C₉⋊#1181	—	5	1	no	Hall
19	C₅×Dic₄₅	—	29	1	no	maximal, Hall
20	C₃×C₅×D₂₉	—	2	2	no	—
21	C₃×C₅×D₂₉	C₅×D₃	1	1	yes	characteristic
22	C₃×C₅×D₂₉	D₁₅	1	1	yes	characteristic
23	C₅²×C₂₉	Dic₉	1	1	yes	characteristic, complemented, Hall
24	#10596817	—	9	1	no	—
25	C₅×#1181	—	45	1	no	—
26	C₉×D₂₉	C₅×D₅	1	1	yes	characteristic
27	C₂×C₅²×C₉	—	29	1	no	—
28	C₃×C₅×C₂₉	—	2	2	no	—
29	C₃×C₅×C₂₉	C₅×Dic₃	1	1	yes	characteristic
30	C₃×C₅×C₂₉	Dic₁₅	1	1	yes	characteristic
31	C₃⋊#1181	—	15	1	no	—
32	C₅×Dic₁₅	—	87	1	no	—
33	C₅×D₂₉	—	2	2	no	—
34	C₅×D₂₉	C₅×D₉	1	1	yes	characteristic
35	C₅×D₂₉	D₄₅	1	1	yes	characteristic
36	C₉×C₂₉	C₅×Dic₅	1	1	yes	characteristic, complemented, Hall
37	C₅²×C₉	#1181	1	1	yes	characteristic, complemented, Hall
38	Dic₄₅	—	29	1	no	—
39	C₅×Dic₉	—	145	1	no	—
40	C₃×D₂₉	C₅×D₁₅	1	1	yes	characteristic
41	C₂×C₃×C₅²	—	29	1	no	—
42	C₅×C₂₉	—	2	2	no	—
43	C₅×C₂₉	C₅×Dic₉	1	1	yes	characteristic, complemented
44	C₅×C₂₉	Dic₄₅	1	1	yes	characteristic, complemented
45	#1181	—	45	1	no	Hall
46	C₅×Dic₅	—	261	1	no	Hall
47	C₂×C₅×C₉	—	29	1	no	—
48	C₂×C₅×C₉	—	29	1	no	—
49	C₂×C₅×C₉	—	58	2	no	—
50	C₃×C₂₉	C₅×Dic₁₅	1	1	yes	characteristic
51	C₃×C₅²	C₃⋊#1181	1	1	yes	characteristic
52	Dic₁₅	—	87	1	no	—
53	C₅×Dic₃	—	435	1	no	—
54	D₂₉	C₅×D₄₅	1	1	yes	characteristic
55	C₂×C₅²	—	29	1	no	—
56	C₅×C₉	—	2	2	no	—
57	C₅×C₉	C₅×#1181	1	1	yes	characteristic, complemented
58	C₅×C₉	#10596817	1	1	yes	characteristic, complemented
59	Dic₉	—	145	1	no	Hall
60	C₂×C₃×C₅	—	29	1	no	—
61	C₂×C₃×C₅	—	29	1	no	—
62	C₂×C₃×C₅	—	58	2	no	—
63	C₂₉	C₅×Dic₄₅	1	1	yes	characteristic, complemented, Sylow
64	C₅²	C₉⋊#1181	1	1	yes	characteristic, complemented, Sylow
65	C₄×C₅	—	1305	1	no	—
66	Dic₅	—	261	1	no	—
67	C₂×C₉	—	29	1	no	—
68	C₃×C₅	—	2	2	no	—
69	C₃×C₅	C₅×C₃⋊#1181	1	1	yes	characteristic
70	C₃×C₅	C₃⋊#10596817	1	1	yes	characteristic
71	Dic₃	—	435	1	no	—
72	C₂×C₅	—	29	1	no	—
73	C₂×C₅	—	29	1	no	—
74	C₂×C₅	—	58	2	no	—
75	C₉	C₅×#10596817	1	1	yes	characteristic, complemented, Sylow
76	C₂×C₃	—	29	1	no	—
77	C₅	—	2	2	no	—
78	C₅	C₅×C₉⋊#1181	1	1	yes	characteristic, complemented
79	C₅	C₉⋊#10596817	1	1	yes	characteristic, direct product factor
80	C₄	—	1305	1	no	Sylow
81	C₃	C₅×C₃⋊#10596817	1	1	yes	characteristic
82	C₂	—	29	1	no	—

	subgroup	G/H
center, hypercenter	C₅	C₉⋊#10596817
commutator, hypocenter	C₅×C₉×C₂₉	C₄×C₅
Frattini	C₃	C₅×C₃⋊#10596817
Fitting	C₅²×C₉×C₂₉	C₄
socle	C₃×C₅²×C₂₉	Dic₃
prime radical	C₃×C₅²×D₂₉	D₃
cosocle	C₅×C₉×D₂₉	C₂×C₅
LCS	G ▷ C₅×C₉×C₂₉
UCS	C₁ ◁ C₅

Complements

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

N	H ≅ G/N	type
3. C₅²×C₉×C₂₉	C₄	semidirect
4. C₉⋊#10596817	C₅	direct (N × H)
16. C₅×C₉×C₂₉	Dic₅	semidirect
17. C₅×C₉×C₂₉	C₄×C₅	semidirect
23. C₅²×C₂₉	Dic₉	semidirect
36. C₉×C₂₉	C₅×Dic₅	semidirect
37. C₅²×C₉	#1181	semidirect
43. C₅×C₂₉	C₅×Dic₉	semidirect
44. C₅×C₂₉	Dic₄₅	semidirect
57. C₅×C₉	C₅×#1181	semidirect
58. C₅×C₉	#10596817	semidirect
63. C₂₉	C₅×Dic₄₅	semidirect
64. C₅²	C₉⋊#1181	semidirect
75. C₉	C₅×#10596817	semidirect
78. C₅	C₅×C₉⋊#1181	semidirect
79. C₅	C₉⋊#10596817	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅²×C₉×D₂₉	2
C₅×C₃⋊#10596817	3
C₉⋊#10596817	5
C₅×C₉⋊#1181	5
C₅×Dic₄₅	29

Subgroups — C5×C9⋊#10596817 #39907947

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×C₉⋊#10596817 #39907947