Subgroups — D₁₃×(C₅⋊D₅)⋊C₉ #26043390

Order 11700.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19154328	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₃×(C₅⋊D₅)⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₃×C₅²⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₁₃×C₅⋊D₅	C₃	1	1	yes	maximal, characteristic
5	C₁₃×C₅²⋊C₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×C₅⋊D₆₅	C₂×C₃	1	1	yes	characteristic
7	C₃×C₁₃×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic
8	C₃×C₅²×D₁₃	C₂×C₃	1	1	yes	characteristic
9	D₁₃×C₅⋊D₅	C₉	1	1	yes	characteristic, complemented, Hall
10	C₃×C₅²×C₁₃	C₂²×C₃	1	1	yes	characteristic
11	C₂×(C₅⋊D₅)⋊C₉	—	13	1	no	maximal, Hall
12	C₃×D₅×D₁₃	—	15	2	no	—
13	C₅⋊D₆₅	C₂×C₉	1	1	yes	characteristic, complemented
14	C₁₃×C₅⋊D₅	C₂×C₉	1	1	yes	characteristic, complemented
15	C₅²×D₁₃	C₂×C₉	1	1	yes	characteristic, complemented
16	C₂×C₉×D₁₃	—	25	1	no	maximal, Hall
17	C₂×C₅²⋊C₉	—	13	1	no	—
18	(C₅⋊D₅)⋊C₉	—	13	1	no	—
19	(C₅⋊D₅)⋊C₉	D₁₃	1	1	yes	characteristic, direct product factor
20	C₃×D₆₅	—	15	2	no	—
21	C₃×D₅×C₁₃	—	15	2	no	—
22	C₃×C₅×D₁₃	—	3	2	no	—
23	C₅²×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₅⋊D₅	—	13	1	no	—
25	D₅×D₁₃	—	15	2	no	—
26	C₂×C₉×C₁₃	—	25	1	no	—
27	C₉×D₁₃	—	25	1	no	—
28	C₉×D₁₃	—	25	1	no	—
29	C₅²⋊C₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅×C₁₃	—	3	2	no	—
31	C₂×C₃×D₁₃	—	25	1	no	—
32	C₂×C₃×C₅²	—	13	1	no	—
33	C₃×C₅⋊D₅	—	13	1	no	—
34	C₃×C₅⋊D₅	C₃×D₁₃	1	1	yes	characteristic
35	D₆₅	—	15	2	no	—
36	C₅×D₁₃	—	3	2	no	—
37	D₅×C₁₃	—	15	2	no	—
38	C₉×C₁₃	—	25	1	no	Hall
39	C₂×C₅⋊D₅	—	13	1	no	Hall
40	C₂×C₃×C₁₃	—	25	1	no	—
41	C₃×D₁₃	—	25	1	no	—
42	C₃×D₁₃	(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
43	C₃×C₅²	C₂×C₃×D₁₃	1	1	yes	characteristic
44	C₅×C₁₃	—	3	2	no	—
45	C₂×C₃×D₅	—	195	2	no	—
46	C₂×D₁₃	—	25	1	no	Hall
47	C₂×C₅²	—	13	1	no	—
48	C₅⋊D₅	—	13	1	no	—
49	C₅⋊D₅	C₉×D₁₃	1	1	yes	characteristic, complemented
50	C₃×C₁₃	C₂×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
51	C₂²×C₉	—	325	1	no	Hall
52	C₂×C₃×C₅	—	39	2	no	—
53	C₃×D₅	—	15	2	no	—
54	C₃×D₅	—	195	2	no	—
55	C₂×C₁₃	—	25	1	no	—
56	D₁₃	—	25	1	no	—
57	D₁₃	(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, direct product factor
58	C₅²	C₂×C₉×D₁₃	1	1	yes	characteristic, complemented, Sylow
59	C₂×D₅	—	195	2	no	—
60	C₂×C₉	—	25	1	no	—
61	C₂×C₉	—	325	1	no	—
62	C₂×C₉	—	325	1	no	—
63	C₃×C₅	—	3	2	no	—
64	C₁₃	C₂×(C₅⋊D₅)⋊C₉	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₃	—	325	1	no	—
66	C₂×C₅	—	39	2	no	—
67	D₅	—	15	2	no	—
68	D₅	—	195	2	no	—
69	C₉	—	25	1	no	Sylow
70	C₂×C₃	—	13	1	no	—
71	C₂×C₃	—	25	1	no	—
72	C₂×C₃	—	325	1	no	—
73	C₅	—	3	2	no	—
74	C₂²	—	325	1	no	Sylow
75	C₃	D₁₃×(C₅⋊D₅)⋊C₃	1	1	yes	characteristic
76	C₂	—	13	1	no	—
77	C₂	—	25	1	no	—
78	C₂	—	325	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₃	D₁₃×(C₅⋊D₅)⋊C₃
commutator, hypocenter	C₅²×C₁₃	C₂²×C₉
Fitting, socle, cosocle	C₃×C₅²×C₁₃	C₂²×C₃
prime radical	C₃×D₁₃×C₅⋊D₅	C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. #19154328	C₂	semidirect
2. C₁₃×(C₅⋊D₅)⋊C₉	C₂	semidirect
3. D₁₃×C₅²⋊C₉	C₂	semidirect
5. C₁₃×C₅²⋊C₉	C₂²	semidirect
9. D₁₃×C₅⋊D₅	C₉	semidirect
13. C₅⋊D₆₅	C₂×C₉	semidirect
14. C₁₃×C₅⋊D₅	C₂×C₉	semidirect
15. C₅²×D₁₃	C₂×C₉	semidirect
19. (C₅⋊D₅)⋊C₉	D₁₃	direct (N × H)
23. C₅²×C₁₃	C₂²×C₉	semidirect
29. C₅²⋊C₉	C₂×D₁₃	semidirect
49. C₅⋊D₅	C₉×D₁₃	semidirect
57. D₁₃	(C₅⋊D₅)⋊C₉	direct (N × H)
58. C₅²	C₂×C₉×D₁₃	semidirect
64. C₁₃	C₂×(C₅⋊D₅)⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
#19154328	2
C₁₃×(C₅⋊D₅)⋊C₉	2
D₁₃×C₅²⋊C₉	2
C₃×D₁₃×C₅⋊D₅	3
C₂×(C₅⋊D₅)⋊C₉	13
C₂×C₉×D₁₃	25

Subgroups — D13×(C5⋊D5)⋊C9 #26043390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×(C₅⋊D₅)⋊C₉ #26043390