Subgroups — C₂×C₅⋊((C₄₃⋊C₃)⋊D₁₃) #46776532

Order 33540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊((C₄₃⋊C₃)⋊D₁₃)	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₁₃×C₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₂₇₉₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×C₁₃×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×(C₄₃⋊C₃)⋊D₁₃	—	5	1	no	maximal, Hall
6	D₂₇₉₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
8	(C₄₃⋊C₃)⋊D₁₃	—	5	2	no	—
9	C₂×C₁₃×C₄₃⋊C₃	D₅	1	1	yes	characteristic, complemented
10	C₅×C₁₃×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅⋊(D₄₃⋊C₃)	—	13	1	no	maximal, Hall
12	C₂×D₅₅₉	—	5	1	no	Hall
13	C₁₃×C₄₃⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₄₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
15	C₅⋊(D₄₃⋊C₃)	—	13	2	no	—
16	C₂×C₁₃×C₄₃	C₃×D₅	1	1	yes	characteristic, complemented
17	D₅₅₉	—	5	2	no	—
18	C₂×D₂₁₅	—	13	1	no	Hall
19	C₂×C₃×D₆₅	—	43	1	no	maximal, Hall
20	C₅×C₄₃⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
21	C₁₃×C₄₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
22	C₂×D₄₃⋊C₃	—	65	1	no	Hall
23	C₂×C₅×C₄₃	C₃×D₁₃	1	1	yes	characteristic, complemented
24	D₂₁₅	—	13	2	no	—
25	C₂×C₃×C₅×C₁₃	—	43	1	no	—
26	C₃×D₆₅	—	43	2	no	—
27	C₂×D₆₅	—	43	1	no	Hall
28	C₂×C₄₃⋊C₃	D₆₅	1	1	yes	characteristic, complemented
29	D₄₃⋊C₃	—	65	2	no	—
30	C₅×C₄₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
31	C₃×C₅×C₁₃	—	43	1	no	Hall
32	C₂×D₄₃	—	65	1	no	Hall
33	C₂×C₃×D₁₃	—	215	1	no	Hall
34	C₂×C₅×C₁₃	D₄₃⋊C₃	1	1	yes	characteristic, complemented
35	D₆₅	—	43	2	no	—
36	C₄₃⋊C₃	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
37	C₂×C₄₃	C₃×D₆₅	1	1	yes	characteristic, complemented
38	D₄₃	—	65	2	no	—
39	C₂×C₃×C₁₃	—	43	1	no	—
40	C₃×D₁₃	—	215	2	no	—
41	C₅×C₁₃	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×D₅	—	559	1	no	Hall
43	C₂×D₁₃	—	215	1	no	Hall
44	C₄₃	C₂×C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
45	C₃×C₁₃	—	43	1	no	Hall
46	C₂×C₃×C₅	—	43	1	no	—
47	C₃×D₅	—	559	2	no	—
48	C₂×C₁₃	C₅⋊(D₄₃⋊C₃)	1	1	yes	characteristic, complemented
49	D₁₃	—	215	2	no	—
50	C₂×D₅	—	559	1	no	Hall
51	C₃×C₅	—	43	1	no	Hall
52	C₁₃	C₂×C₅⋊(D₄₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₃	—	2795	1	no	Hall
54	C₂×C₅	(C₄₃⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented
55	D₅	—	559	2	no	—
56	C₂×C₃	—	43	1	no	—
57	C₂×C₃	—	2795	2	no	—
58	C₅	C₂×(C₄₃⋊C₃)⋊D₁₃	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	2795	1	no	Sylow
60	C₃	—	43	1	no	Sylow
61	C₂	—	2795	2	no	—
62	C₂	C₅⋊((C₄₃⋊C₃)⋊D₁₃)	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊((C₄₃⋊C₃)⋊D₁₃)
commutator, cosocle, hypocenter	C₅×C₁₃×C₄₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₄₃
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₅⋊((C₄₃⋊C₃)⋊D₁₃)	C₂	direct (N × H)
2. C₂×C₅×C₁₃×C₄₃⋊C₃	C₂	semidirect
3. C₂×D₂₇₉₅	C₃	semidirect
4. C₅×C₁₃×C₄₃⋊C₃	C₂²	semidirect
6. D₂₇₉₅	C₂×C₃	semidirect
7. C₂×C₅×C₁₃×C₄₃	C₂×C₃	semidirect
9. C₂×C₁₃×C₄₃⋊C₃	D₅	semidirect
10. C₅×C₁₃×C₄₃	C₂²×C₃	semidirect
13. C₁₃×C₄₃⋊C₃	C₂×D₅	semidirect
14. C₂×C₅×C₄₃⋊C₃	D₁₃	semidirect
16. C₂×C₁₃×C₄₃	C₃×D₅	semidirect
20. C₅×C₄₃⋊C₃	C₂×D₁₃	semidirect
21. C₁₃×C₄₃	C₂×C₃×D₅	semidirect
23. C₂×C₅×C₄₃	C₃×D₁₃	semidirect
28. C₂×C₄₃⋊C₃	D₆₅	semidirect
30. C₅×C₄₃	C₂×C₃×D₁₃	semidirect
34. C₂×C₅×C₁₃	D₄₃⋊C₃	semidirect
36. C₄₃⋊C₃	C₂×D₆₅	semidirect
37. C₂×C₄₃	C₃×D₆₅	semidirect
41. C₅×C₁₃	C₂×D₄₃⋊C₃	semidirect
44. C₄₃	C₂×C₃×D₆₅	semidirect
48. C₂×C₁₃	C₅⋊(D₄₃⋊C₃)	semidirect
52. C₁₃	C₂×C₅⋊(D₄₃⋊C₃)	semidirect
54. C₂×C₅	(C₄₃⋊C₃)⋊D₁₃	semidirect
58. C₅	C₂×(C₄₃⋊C₃)⋊D₁₃	semidirect
62. C₂	C₅⋊((C₄₃⋊C₃)⋊D₁₃)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅⋊((C₄₃⋊C₃)⋊D₁₃)	2
C₂×C₅×C₁₃×C₄₃⋊C₃	2
C₂×D₂₇₉₅	3
C₂×(C₄₃⋊C₃)⋊D₁₃	5
C₂×C₅⋊(D₄₃⋊C₃)	13
C₂×C₃×D₆₅	43

Subgroups — C2×C5⋊((C43⋊C3)⋊D13) #46776532

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊((C₄₃⋊C₃)⋊D₁₃) #46776532