Subgroups — C₂×C₅×#16809809 #46776513

Order 33540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#16809809	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#13131976	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₁₃×D₄₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#13131976	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#16809809	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₁₃×D₄₃	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
8	#16809809	C₂×C₅	1	2	yes	direct product factor
9	C₂×#13131976	C₂×C₅	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×C₁₃×D₄₃	C₃×C₅	1	1	yes	characteristic, complemented, Hall
13	#13131976	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₄₃⋊C₃	—	13	1	no	—
15	C₅×D₄₃⋊C₃	—	13	2	no	—
16	C₂×C₁₃×C₄₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
17	C₁₃×D₄₃	C₂×C₃×C₅	1	2	yes	complemented
18	C₂×C₅×D₄₃	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
19	C₂²×C₅×C₁₃⋊C₃	—	43	1	no	maximal, Hall
20	C₅×C₄₃⋊C₃	—	13	1	no	Hall
21	C₁₃×C₄₃	C₂²×C₃×C₅	1	1	yes	characteristic, complemented, Hall
22	C₂×D₄₃⋊C₃	—	13	1	no	Hall
23	C₂×C₅×C₄₃	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented
24	C₅×D₄₃	C₂×C₁₃⋊C₃	1	2	yes	complemented
25	C₂×C₅×C₁₃⋊C₃	—	43	2	no	—
26	C₂×C₅×C₁₃⋊C₃	—	43	1	no	—
27	C₂²×C₅×C₁₃	—	43	1	no	Hall
28	C₂×C₄₃⋊C₃	—	13	1	no	—
29	D₄₃⋊C₃	—	13	2	no	—
30	C₅×C₄₃	C₂²×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₅×C₁₃⋊C₃	—	43	1	no	Hall
32	C₂×D₄₃	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₁₃⋊C₃	—	43	1	no	Hall
34	C₂×C₅×C₁₃	—	43	2	no	—
35	C₂×C₅×C₁₃	D₄₃⋊C₃	1	1	yes	characteristic, complemented
36	C₄₃⋊C₃	—	13	1	no	Hall
37	C₂×C₄₃	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented
38	D₄₃	C₂×C₅×C₁₃⋊C₃	1	2	yes	complemented
39	C₂×C₁₃⋊C₃	—	43	2	no	—
40	C₂×C₁₃⋊C₃	—	43	1	no	—
41	C₅×C₁₃	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
42	C₂²×C₃×C₅	—	559	1	no	Hall
43	C₂²×C₁₃	—	43	1	no	Hall
44	C₄₃	C₂²×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
45	C₁₃⋊C₃	—	43	1	no	Hall
46	C₂×C₃×C₅	—	559	2	no	—
47	C₂×C₃×C₅	—	559	1	no	—
48	C₂×C₁₃	—	43	2	no	—
49	C₂×C₁₃	C₅×D₄₃⋊C₃	1	1	yes	characteristic, complemented
50	C₂²×C₅	—	43	1	no	Hall
51	C₃×C₅	—	559	1	no	Hall
52	C₁₃	C₂×C₅×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₃	—	559	1	no	Hall
54	C₂×C₅	—	43	2	no	—
55	C₂×C₅	#16809809	1	1	yes	characteristic, direct product factor
56	C₂×C₃	—	559	2	no	—
57	C₂×C₃	—	559	1	no	—
58	C₅	C₂×#16809809	1	1	yes	characteristic, direct product factor, Sylow
59	C₂²	—	43	1	no	Sylow
60	C₃	—	559	1	no	Sylow
61	C₂	—	43	2	no	—
62	C₂	C₅×#16809809	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅	#16809809
commutator, cosocle, hypocenter	C₁₃×C₄₃	C₂²×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃×C₄₃	C₂×C₃
LCS	G ▷ C₁₃×C₄₃
UCS	C₁ ◁ C₂×C₅

Complements

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

N	H ≅ G/N	type
1. C₅×#16809809	C₂	direct (N × H)
2. C₂×C₅×#13131976	C₂	semidirect
3. C₂×C₅×C₁₃×D₄₃	C₃	semidirect
4. C₅×#13131976	C₂²	semidirect
5. C₂×#16809809	C₅	direct (N × H)
6. C₅×C₁₃×D₄₃	C₂×C₃	semidirect
7. C₂×C₅×C₁₃×C₄₃	C₂×C₃	semidirect
8. #16809809	C₂×C₅	direct (N × H)
9. C₂×#13131976	C₂×C₅	semidirect
10. C₅×C₁₃×C₄₃	C₂²×C₃	semidirect
12. C₂×C₁₃×D₄₃	C₃×C₅	semidirect
13. #13131976	C₂²×C₅	semidirect
16. C₂×C₁₃×C₄₃	C₂×C₃×C₅	semidirect
17. C₁₃×D₄₃	C₂×C₃×C₅	semidirect
18. C₂×C₅×D₄₃	C₁₃⋊C₃	semidirect
21. C₁₃×C₄₃	C₂²×C₃×C₅	semidirect
23. C₂×C₅×C₄₃	C₂×C₁₃⋊C₃	semidirect
24. C₅×D₄₃	C₂×C₁₃⋊C₃	semidirect
30. C₅×C₄₃	C₂²×C₁₃⋊C₃	semidirect
32. C₂×D₄₃	C₅×C₁₃⋊C₃	semidirect
35. C₂×C₅×C₁₃	D₄₃⋊C₃	semidirect
37. C₂×C₄₃	C₂×C₅×C₁₃⋊C₃	semidirect
38. D₄₃	C₂×C₅×C₁₃⋊C₃	semidirect
41. C₅×C₁₃	C₂×D₄₃⋊C₃	semidirect
44. C₄₃	C₂²×C₅×C₁₃⋊C₃	semidirect
49. C₂×C₁₃	C₅×D₄₃⋊C₃	semidirect
52. C₁₃	C₂×C₅×D₄₃⋊C₃	semidirect
55. C₂×C₅	#16809809	direct (N × H)
58. C₅	C₂×#16809809	direct (N × H)
62. C₂	C₅×#16809809	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×#16809809	2
C₂×C₅×#13131976	2
C₂×C₅×C₁₃×D₄₃	3
C₂×#16809809	5
C₂×C₅×D₄₃⋊C₃	13
C₂²×C₅×C₁₃⋊C₃	43

Subgroups — C2×C5×#16809809 #46776513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#16809809 #46776513