Subgroups — C₂×D₁₃×C₅²⋊C₉ #26043405

Order 11700.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂×C₃	D₁₃×C₅²⋊C₃
commutator, hypocenter	C₅²×C₁₃	C₂²×C₉
Frattini	C₃	C₂×D₁₃×C₅²⋊C₃
Fitting, socle	C₂×C₃×C₅²×C₁₃	C₂×C₃
prime radical	C₂×C₃×C₅²×D₁₃	C₃
cosocle	C₃×C₅²×C₁₃	C₂²×C₃
LCS	G ▷ C₅²×C₁₃
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×C₅²⋊C₉	C₂	semidirect
2. D₁₃×C₅²⋊C₉	C₂	direct (N × H)
4. C₁₃×C₅²⋊C₉	C₂²	semidirect
7. C₂×C₅²×D₁₃	C₉	semidirect
11. C₂×C₅²×C₁₃	C₂×C₉	semidirect
12. C₅²×D₁₃	C₂×C₉	semidirect
15. C₂×C₅²⋊C₉	D₁₃	direct (N × H)
18. C₅²×C₁₃	C₂²×C₉	semidirect
23. C₅²⋊C₉	C₂×D₁₃	direct (N × H)
37. C₂×D₁₃	C₅²⋊C₉	direct (N × H)
39. C₂×C₅²	C₉×D₁₃	semidirect
44. C₂×C₁₃	C₂×C₅²⋊C₉	semidirect
45. D₁₃	C₂×C₅²⋊C₉	direct (N × H)
46. C₅²	C₂×C₉×D₁₃	semidirect
51. C₁₃	C₂²×C₅²⋊C₉	semidirect
62. C₂	D₁₃×C₅²⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₃×C₅²⋊C₉	2
D₁₃×C₅²⋊C₉	2
C₂×C₃×C₅²×D₁₃	3
C₂²×C₅²⋊C₉	13
C₂×C₉×D₁₃	25

Subgroups — C2×D13×C52⋊C9 #26043405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₁₃×C₅²⋊C₉ #26043405