Subgroups — C₂×C₅⋊((C₁₃⋊C₃)⋊D₁₃) #23778533

Order 10140.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₁₃×C₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅⋊((C₁₃⋊C₃)⋊D₁₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₅⋊(C₁₃⋊D₁₃)	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₁₃×C₁₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×(C₁₃⋊C₃)⋊D₁₃	—	5	1	no	maximal, Hall
6	C₂×C₅×C₁₃²	C₂×C₃	1	1	yes	characteristic, complemented
7	C₅⋊(C₁₃⋊D₁₃)	C₂×C₃	1	2	yes	complemented
8	C₂×C₁₃×C₁₃⋊C₃	D₅	1	1	yes	characteristic, complemented
9	(C₁₃⋊C₃)⋊D₁₃	—	5	2	no	—
10	C₅×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₃×D₆₅	—	13	1	no	maximal
12	C₂×C₅⋊(D₁₃⋊C₃)	—	13	1	no	maximal
13	C₂×C₁₃⋊D₁₃	—	5	1	no	Hall
14	C₁₃×C₁₃⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×C₅×C₁₃	—	13	1	no	—
16	C₃×D₆₅	—	13	2	no	—
17	C₂×C₅×C₁₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
18	C₅⋊(D₁₃⋊C₃)	—	13	2	no	—
19	C₂×C₁₃²	C₃×D₅	1	1	yes	characteristic, complemented
20	C₁₃⋊D₁₃	—	5	2	no	—
21	C₂×D₆₅	—	13	1	no	—
22	C₂×D₆₅	—	13	1	no	—
23	C₂×D₆₅	—	39	4	no	—
24	C₃×C₅×C₁₃	—	13	1	no	—
25	C₅×C₁₃⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented
26	C₁₃²	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃×D₁₃	—	65	1	no	—
28	C₂×D₁₃⋊C₃	—	65	1	no	—
29	C₂×C₅×C₁₃	—	3	4	no	—
30	C₂×C₅×C₁₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
31	C₂×C₅×C₁₃	C₃×D₁₃	1	1	yes	characteristic, complemented
32	D₆₅	—	13	2	no	—
33	D₆₅	—	13	2	no	—
34	D₆₅	—	39	8	no	—
35	C₂×C₃×C₁₃	—	13	1	no	—
36	C₃×D₁₃	—	65	2	no	—
37	C₂×C₁₃⋊C₃	D₆₅	1	1	yes	characteristic, complemented
38	D₁₃⋊C₃	—	65	2	no	—
39	C₅×C₁₃	—	3	4	no	—
40	C₅×C₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
41	C₅×C₁₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented
42	C₂×C₃×D₅	—	169	1	no	Hall
43	C₂×D₁₃	—	65	1	no	—
44	C₂×D₁₃	—	65	1	no	—
45	C₂×D₁₃	—	195	4	no	—
46	C₃×C₁₃	—	13	1	no	—
47	C₁₃⋊C₃	C₂×D₆₅	1	1	yes	characteristic, complemented
48	C₂×C₃×C₅	—	13	1	no	—
49	C₃×D₅	—	169	2	no	—
50	C₂×C₁₃	—	3	4	no	—
51	C₂×C₁₃	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
52	C₂×C₁₃	C₃×D₆₅	1	1	yes	characteristic, complemented
53	D₁₃	—	65	2	no	—
54	D₁₃	—	65	2	no	—
55	D₁₃	—	195	8	no	—
56	C₂×D₅	—	169	1	no	Hall
57	C₃×C₅	—	13	1	no	Hall
58	C₁₃	—	3	4	no	—
59	C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
60	C₁₃	C₂×C₃×D₆₅	1	1	yes	characteristic, complemented
61	C₂²×C₃	—	845	1	no	Hall
62	C₂×C₅	(C₁₃⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented
63	D₅	—	169	2	no	—
64	C₂×C₃	—	13	1	no	—
65	C₂×C₃	—	845	2	no	—
66	C₅	C₂×(C₁₃⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
67	C₂²	—	845	1	no	Sylow
68	C₃	—	13	1	no	Sylow
69	C₂	—	845	2	no	—
70	C₂	C₅⋊((C₁₃⋊C₃)⋊D₁₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊((C₁₃⋊C₃)⋊D₁₃)
commutator, cosocle, hypocenter	C₅×C₁₃²	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃²	C₂×C₃
LCS	G ▷ C₅×C₁₃²
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×C₁₃×C₁₃⋊C₃	C₂	semidirect
2. C₅⋊((C₁₃⋊C₃)⋊D₁₃)	C₂	direct (N × H)
3. C₂×C₅⋊(C₁₃⋊D₁₃)	C₃	semidirect
4. C₅×C₁₃×C₁₃⋊C₃	C₂²	semidirect
6. C₂×C₅×C₁₃²	C₂×C₃	semidirect
7. C₅⋊(C₁₃⋊D₁₃)	C₂×C₃	semidirect
8. C₂×C₁₃×C₁₃⋊C₃	D₅	semidirect
10. C₅×C₁₃²	C₂²×C₃	semidirect
14. C₁₃×C₁₃⋊C₃	C₂×D₅	semidirect
17. C₂×C₅×C₁₃⋊C₃	D₁₃	semidirect
19. C₂×C₁₃²	C₃×D₅	semidirect
25. C₅×C₁₃⋊C₃	C₂×D₁₃	semidirect
26. C₁₃²	C₂×C₃×D₅	semidirect
30. C₂×C₅×C₁₃	D₁₃⋊C₃	semidirect
31. C₂×C₅×C₁₃	C₃×D₁₃	semidirect
37. C₂×C₁₃⋊C₃	D₆₅	semidirect
40. C₅×C₁₃	C₂×D₁₃⋊C₃	semidirect
41. C₅×C₁₃	C₂×C₃×D₁₃	semidirect
47. C₁₃⋊C₃	C₂×D₆₅	semidirect
51. C₂×C₁₃	C₅⋊(D₁₃⋊C₃)	semidirect
52. C₂×C₁₃	C₃×D₆₅	semidirect
59. C₁₃	C₂×C₅⋊(D₁₃⋊C₃)	semidirect
60. C₁₃	C₂×C₃×D₆₅	semidirect
62. C₂×C₅	(C₁₃⋊C₃)⋊D₁₃	semidirect
66. C₅	C₂×(C₁₃⋊C₃)⋊D₁₃	semidirect
70. C₂	C₅⋊((C₁₃⋊C₃)⋊D₁₃)	direct (N × H)

Subgroups — C2×C5⋊((C13⋊C3)⋊D13) #23778533

Conjugacy classes of subgroups

Complements

Subgroups — C₂×C₅⋊((C₁₃⋊C₃)⋊D₁₃) #23778533