Subgroups — C₂×C₅⋊#16809814 #46776524

Order 33540.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅⋊#16809814	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×#13131975	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₃×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
4	C₅×#13131975	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×#16809814	—	5	1	no	maximal, Hall
6	C₄₃×D₆₅	C₂×C₃	1	2	yes	complemented
7	C₂×C₅×C₁₃×C₄₃	C₂×C₃	1	1	yes	characteristic, complemented
8	#16809814	—	5	2	no	—
9	C₂×#13131975	D₅	1	1	yes	characteristic, complemented
10	C₅×C₁₃×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×D₅×C₄₃⋊C₃	—	13	1	no	maximal, Hall
12	C₂×D₁₃×C₄₃	—	5	1	no	Hall
13	#13131975	C₂×D₅	1	1	yes	characteristic, complemented, Hall
14	C₂×C₅×C₄₃⋊C₃	—	13	1	no	—
15	D₅×C₄₃⋊C₃	—	13	2	no	—
16	C₂×C₁₃×C₄₃	C₃×D₅	1	1	yes	characteristic, complemented
17	D₁₃×C₄₃	—	5	2	no	—
18	C₂×D₅×C₄₃	—	13	1	no	Hall
19	C₂×C₅⋊(D₁₃⋊C₃)	—	43	1	no	maximal, Hall
20	C₅×C₄₃⋊C₃	—	13	1	no	Hall
21	C₁₃×C₄₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
22	C₂²×C₄₃⋊C₃	—	65	1	no	Hall
23	C₂×C₅×C₄₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
24	D₅×C₄₃	—	13	2	no	—
25	C₂×C₅×C₁₃⋊C₃	—	43	1	no	—
26	C₅⋊(D₁₃⋊C₃)	—	43	2	no	—
27	C₂×D₆₅	C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
28	C₂×C₄₃⋊C₃	—	13	1	no	—
29	C₂×C₄₃⋊C₃	—	65	2	no	—
30	C₅×C₄₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
31	C₅×C₁₃⋊C₃	—	43	1	no	Hall
32	C₂²×C₄₃	—	65	1	no	Hall
33	C₂×D₁₃⋊C₃	—	215	1	no	Hall
34	C₂×C₅×C₁₃	C₂×C₄₃⋊C₃	1	1	yes	characteristic, complemented
35	D₆₅	C₂×C₄₃⋊C₃	1	2	yes	complemented
36	C₄₃⋊C₃	—	13	1	no	Hall
37	C₂×C₄₃	—	65	2	no	—
38	C₂×C₄₃	C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented
39	C₂×C₁₃⋊C₃	—	43	1	no	—
40	D₁₃⋊C₃	—	215	2	no	—
41	C₅×C₁₃	C₂²×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
42	C₂×C₃×D₅	—	559	1	no	Hall
43	C₂×D₁₃	—	5	1	no	Hall
44	C₄₃	C₂×C₅⋊(D₁₃⋊C₃)	1	1	yes	characteristic, complemented, Sylow
45	C₁₃⋊C₃	—	43	1	no	Hall
46	C₂×C₃×C₅	—	559	1	no	—
47	C₃×D₅	—	559	2	no	—
48	C₂×C₁₃	D₅×C₄₃⋊C₃	1	1	yes	characteristic, complemented
49	D₁₃	—	5	2	no	—
50	C₂×D₅	—	13	1	no	Hall
51	C₃×C₅	—	559	1	no	Hall
52	C₁₃	C₂×D₅×C₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₃	—	2795	1	no	Hall
54	C₂×C₅	#16809814	1	1	yes	characteristic, complemented
55	D₅	—	13	2	no	—
56	C₂×C₃	—	559	1	no	—
57	C₂×C₃	—	2795	2	no	—
58	C₅	C₂×#16809814	1	1	yes	characteristic, complemented, Sylow
59	C₂²	—	65	1	no	Sylow
60	C₃	—	559	1	no	Sylow
61	C₂	—	65	2	no	—
62	C₂	C₅⋊#16809814	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂	C₅⋊#16809814
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⋊#16809814	C₂	direct (N × H)
2. C₂×C₅×#13131975	C₂	semidirect
3. C₂×C₄₃×D₆₅	C₃	semidirect
4. C₅×#13131975	C₂²	semidirect
6. C₄₃×D₆₅	C₂×C₃	semidirect
7. C₂×C₅×C₁₃×C₄₃	C₂×C₃	semidirect
9. C₂×#13131975	D₅	semidirect
10. C₅×C₁₃×C₄₃	C₂²×C₃	semidirect
13. #13131975	C₂×D₅	semidirect
16. C₂×C₁₃×C₄₃	C₃×D₅	semidirect
21. C₁₃×C₄₃	C₂×C₃×D₅	semidirect
23. C₂×C₅×C₄₃	D₁₃⋊C₃	semidirect
27. C₂×D₆₅	C₄₃⋊C₃	semidirect
30. C₅×C₄₃	C₂×D₁₃⋊C₃	semidirect
34. C₂×C₅×C₁₃	C₂×C₄₃⋊C₃	semidirect
35. D₆₅	C₂×C₄₃⋊C₃	semidirect
38. C₂×C₄₃	C₅⋊(D₁₃⋊C₃)	semidirect
41. C₅×C₁₃	C₂²×C₄₃⋊C₃	semidirect
44. C₄₃	C₂×C₅⋊(D₁₃⋊C₃)	semidirect
48. C₂×C₁₃	D₅×C₄₃⋊C₃	semidirect
52. C₁₃	C₂×D₅×C₄₃⋊C₃	semidirect
54. C₂×C₅	#16809814	semidirect
58. C₅	C₂×#16809814	semidirect
62. C₂	C₅⋊#16809814	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⋊#16809814	2
C₂×C₅×#13131975	2
C₂×C₄₃×D₆₅	3
C₂×#16809814	5
C₂×D₅×C₄₃⋊C₃	13
C₂×C₅⋊(D₁₃⋊C₃)	43

Subgroups — C2×C5⋊#16809814 #46776524

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅⋊#16809814 #46776524