Subgroups — D₆₅×D₄₃⋊C₃ #46776501

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	1	yes	maximal, characteristic, complemented
2	C₄₃⋊C₃×D₆₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₁₃×D₄₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄₃×D₆₅	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×C₁₃×C₄₃⋊C₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₁₃×D₄₃⋊C₃	—	5	1	no	maximal, Hall
7	D₂₇₉₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₄₃×D₆₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₃×D₄₃	C₂×C₃	1	1	yes	characteristic, complemented
10	(C₄₃⋊C₃)⋊D₁₃	—	5	1	no	—
11	D₁₃×C₄₃⋊C₃	—	5	1	no	—
12	C₁₃×D₄₃⋊C₃	D₅	1	1	yes	characteristic, complemented
13	C₅×C₁₃×C₄₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	D₅×D₄₃⋊C₃	—	13	1	no	maximal, Hall
15	D₁₃×D₄₃	—	5	1	no	Hall
16	C₁₃×C₄₃⋊C₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₅⋊(D₄₃⋊C₃)	—	13	1	no	—
18	D₅×C₄₃⋊C₃	—	13	1	no	—
19	C₅×D₄₃⋊C₃	D₁₃	1	1	yes	characteristic, complemented
20	D₅₅₉	—	5	1	no	—
21	C₁₃×D₄₃	C₃×D₅	1	1	yes	characteristic, complemented
22	D₁₃×C₄₃	—	5	1	no	—
23	D₅×D₄₃	—	13	1	no	Hall
24	C₂×C₃×D₆₅	—	43	1	no	maximal, Hall
25	C₅×C₄₃⋊C₃	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
26	C₁₃×C₄₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
27	C₂×D₄₃⋊C₃	—	65	1	no	Hall
28	D₂₁₅	—	13	1	no	—
29	C₅×D₄₃	C₃×D₁₃	1	1	yes	characteristic, complemented
30	D₅×C₄₃	—	13	1	no	—
31	C₂×C₃×C₅×C₁₃	—	43	1	no	—
32	C₃×D₆₅	—	43	1	no	—
33	C₃×D₆₅	—	43	1	no	—
34	C₂×D₆₅	—	43	1	no	Hall
35	C₂×C₄₃⋊C₃	—	65	1	no	—
36	D₄₃⋊C₃	—	65	1	no	—
37	D₄₃⋊C₃	D₆₅	1	1	yes	characteristic, direct product factor
38	C₅×C₄₃	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
39	C₃×C₅×C₁₃	—	43	1	no	Hall
40	C₂×D₄₃	—	65	1	no	Hall
41	C₂×C₃×D₁₃	—	215	1	no	Hall
42	C₂×C₅×C₁₃	—	43	1	no	—
43	D₆₅	—	43	1	no	—
44	D₆₅	D₄₃⋊C₃	1	1	yes	characteristic, direct product factor
45	C₄₃⋊C₃	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
46	C₂×C₄₃	—	65	1	no	—
47	D₄₃	—	65	1	no	—
48	D₄₃	C₃×D₆₅	1	1	yes	characteristic, complemented
49	C₂×C₃×C₁₃	—	43	1	no	—
50	C₃×D₁₃	—	215	1	no	—
51	C₃×D₁₃	—	215	1	no	—
52	C₅×C₁₃	C₂×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×D₅	—	559	1	no	Hall
54	C₂×D₁₃	—	215	1	no	Hall
55	C₄₃	C₂×C₃×D₆₅	1	1	yes	characteristic, complemented, Sylow
56	C₃×C₁₃	—	43	1	no	Hall
57	C₂×C₃×C₅	—	43	1	no	—
58	C₃×D₅	—	559	1	no	—
59	C₃×D₅	—	559	1	no	—
60	C₂×C₁₃	—	43	1	no	—
61	D₁₃	—	5	1	no	—
62	D₁₃	—	215	1	no	—
63	C₂×D₅	—	559	1	no	Hall
64	C₃×C₅	—	43	1	no	Hall
65	C₁₃	D₅×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	2795	1	no	Hall
67	C₂×C₅	—	43	1	no	—
68	D₅	—	13	1	no	—
69	D₅	—	559	1	no	—
70	C₂×C₃	—	43	1	no	—
71	C₂×C₃	—	2795	1	no	—
72	C₂×C₃	—	2795	1	no	—
73	C₅	D₁₃×D₄₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	2795	1	no	Sylow
75	C₃	—	43	1	no	Sylow
76	C₂	—	43	1	no	—
77	C₂	—	65	1	no	—
78	C₂	—	2795	1	no	—

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

Complements

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

N	H ≅ G/N	type
1. C₅⋊((C₄₃⋊C₃)⋊D₁₃)	C₂	semidirect
2. C₄₃⋊C₃×D₆₅	C₂	semidirect
3. C₅×C₁₃×D₄₃⋊C₃	C₂	semidirect
4. D₄₃×D₆₅	C₃	semidirect
5. C₅×C₁₃×C₄₃⋊C₃	C₂²	semidirect
7. D₂₇₉₅	C₂×C₃	semidirect
8. C₄₃×D₆₅	C₂×C₃	semidirect
9. C₅×C₁₃×D₄₃	C₂×C₃	semidirect
12. C₁₃×D₄₃⋊C₃	D₅	semidirect
13. C₅×C₁₃×C₄₃	C₂²×C₃	semidirect
16. C₁₃×C₄₃⋊C₃	C₂×D₅	semidirect
19. C₅×D₄₃⋊C₃	D₁₃	semidirect
21. C₁₃×D₄₃	C₃×D₅	semidirect
25. C₅×C₄₃⋊C₃	C₂×D₁₃	semidirect
26. C₁₃×C₄₃	C₂×C₃×D₅	semidirect
29. C₅×D₄₃	C₃×D₁₃	semidirect
37. D₄₃⋊C₃	D₆₅	direct (N × H)
38. C₅×C₄₃	C₂×C₃×D₁₃	semidirect
44. D₆₅	D₄₃⋊C₃	direct (N × H)
45. C₄₃⋊C₃	C₂×D₆₅	semidirect
48. D₄₃	C₃×D₆₅	semidirect
52. C₅×C₁₃	C₂×D₄₃⋊C₃	semidirect
55. C₄₃	C₂×C₃×D₆₅	semidirect
65. C₁₃	D₅×D₄₃⋊C₃	semidirect
73. C₅	D₁₃×D₄₃⋊C₃	semidirect

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
C₄₃⋊C₃×D₆₅	2
C₅×C₁₃×D₄₃⋊C₃	2
D₄₃×D₆₅	3
D₁₃×D₄₃⋊C₃	5
D₅×D₄₃⋊C₃	13
C₂×C₃×D₆₅	43

Subgroups — D65×D43⋊C3 #46776501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₆₅×D₄₃⋊C₃ #46776501