Subgroups — D₅×C₄₁×D₁₃⋊C₃ #44544371

Order 31980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₁×C₅⋊(D₁₃⋊C₃)	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅×C₁₃⋊C₃×C₄₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₄₁×D₁₃⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₁₃×C₄₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₅×C₁₃⋊C₃×C₄₁	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₂×C₄₁×D₁₃⋊C₃	—	5	1	no	maximal, Hall
7	C₄₁×D₆₅	C₂×C₃	1	1	yes	characteristic, complemented
8	D₅×C₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×D₁₃×C₄₁	C₂×C₃	1	1	yes	characteristic, complemented
10	C₄₁×D₁₃⋊C₃	—	5	1	no	—
11	C₄₁×D₁₃⋊C₃	D₅	1	1	yes	characteristic, direct product factor
12	C₂×C₁₃⋊C₃×C₄₁	—	5	1	no	—
13	C₅×C₁₃×C₄₁	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
14	C₂×C₃×D₅×C₄₁	—	13	1	no	maximal, Hall
15	C₂×D₁₃×C₄₁	—	5	1	no	Hall
16	C₁₃⋊C₃×C₄₁	C₂×D₅	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃×C₅×C₄₁	—	13	1	no	—
18	C₃×D₅×C₄₁	—	13	1	no	—
19	C₃×D₅×C₄₁	—	13	1	no	—
20	C₂×C₁₃×C₄₁	—	5	1	no	—
21	D₁₃×C₄₁	—	5	1	no	—
22	D₁₃×C₄₁	C₃×D₅	1	1	yes	characteristic, complemented
23	C₂×D₅×C₄₁	—	13	1	no	Hall
24	D₅×D₁₃⋊C₃	C₄₁	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₃×C₅×C₄₁	—	13	1	no	Hall
26	C₁₃×C₄₁	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃×C₄₁	—	65	1	no	Hall
28	C₂×C₅×C₄₁	—	13	1	no	—
29	D₅×C₄₁	—	13	1	no	—
30	D₅×C₄₁	D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
31	C₅⋊(D₁₃⋊C₃)	C₂×C₄₁	1	1	yes	characteristic, complemented
32	D₅×C₁₃⋊C₃	C₂×C₄₁	1	1	yes	characteristic, complemented
33	C₅×D₁₃⋊C₃	C₂×C₄₁	1	1	yes	characteristic, complemented
34	D₅×D₁₃	C₃×C₄₁	1	1	yes	characteristic, complemented, Hall
35	C₂×C₃×C₄₁	—	13	1	no	—
36	C₂×C₃×C₄₁	—	65	1	no	—
37	C₂×C₃×C₄₁	—	65	1	no	—
38	C₅×C₄₁	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₃⋊C₃	C₂²×C₄₁	1	1	yes	characteristic, complemented, Hall
40	C₂²×C₄₁	—	65	1	no	Hall
41	C₂×D₁₃⋊C₃	—	5	1	no	Hall
42	D₆₅	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented
43	C₅×D₁₃	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented
44	D₅×C₁₃	C₂×C₃×C₄₁	1	1	yes	characteristic, complemented
45	C₃×C₄₁	—	13	1	no	Hall
46	C₂×C₄₁	—	5	1	no	—
47	C₂×C₄₁	—	13	1	no	—
48	C₂×C₄₁	—	65	1	no	—
49	C₂×C₁₃⋊C₃	—	5	1	no	—
50	D₁₃⋊C₃	—	5	1	no	—
51	D₁₃⋊C₃	D₅×C₄₁	1	1	yes	characteristic, direct product factor
52	C₅×C₁₃	C₂²×C₃×C₄₁	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×D₅	—	13	1	no	Hall
54	C₂×D₁₃	—	5	1	no	Hall
55	C₄₁	D₅×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor, Sylow
56	C₁₃⋊C₃	C₂×D₅×C₄₁	1	1	yes	characteristic, complemented, Hall
57	C₂×C₃×C₅	—	13	1	no	—
58	C₃×D₅	—	13	1	no	—
59	C₃×D₅	—	13	1	no	—
60	C₂×C₁₃	—	5	1	no	—
61	D₁₃	—	5	1	no	—
62	D₁₃	C₃×D₅×C₄₁	1	1	yes	characteristic, complemented
63	C₂×D₅	—	13	1	no	Hall
64	C₃×C₅	—	13	1	no	Hall
65	C₁₃	C₂×C₃×D₅×C₄₁	1	1	yes	characteristic, complemented, Sylow
66	C₂²×C₃	—	65	1	no	Hall
67	C₂×C₅	—	13	1	no	—
68	D₅	—	13	1	no	—
69	D₅	C₄₁×D₁₃⋊C₃	1	1	yes	characteristic, direct product factor
70	C₂×C₃	—	13	1	no	—
71	C₂×C₃	—	65	1	no	—
72	C₂×C₃	—	65	1	no	—
73	C₅	C₂×C₄₁×D₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	65	1	no	Sylow
75	C₃	—	13	1	no	Sylow
76	C₂	—	5	1	no	—
77	C₂	—	13	1	no	—
78	C₂	—	65	1	no	—

	subgroup	G/H
center, hypercenter	C₄₁	D₅×D₁₃⋊C₃
commutator, cosocle, hypocenter	C₅×C₁₃	C₂²×C₃×C₄₁
Frattini	C₁	G
Fitting, socle	C₅×C₁₃×C₄₁	C₂²×C₃
LCS	G ▷ C₅×C₁₃
UCS	C₁ ◁ C₄₁

Complements

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

N	H ≅ G/N	type
1. C₄₁×C₅⋊(D₁₃⋊C₃)	C₂	semidirect
2. D₅×C₁₃⋊C₃×C₄₁	C₂	semidirect
3. C₅×C₄₁×D₁₃⋊C₃	C₂	semidirect
4. D₅×D₁₃×C₄₁	C₃	semidirect
5. C₅×C₁₃⋊C₃×C₄₁	C₂²	semidirect
7. C₄₁×D₆₅	C₂×C₃	semidirect
8. D₅×C₁₃×C₄₁	C₂×C₃	semidirect
9. C₅×D₁₃×C₄₁	C₂×C₃	semidirect
11. C₄₁×D₁₃⋊C₃	D₅	direct (N × H)
13. C₅×C₁₃×C₄₁	C₂²×C₃	semidirect
16. C₁₃⋊C₃×C₄₁	C₂×D₅	semidirect
22. D₁₃×C₄₁	C₃×D₅	semidirect
24. D₅×D₁₃⋊C₃	C₄₁	direct (N × H)
26. C₁₃×C₄₁	C₂×C₃×D₅	semidirect
30. D₅×C₄₁	D₁₃⋊C₃	direct (N × H)
31. C₅⋊(D₁₃⋊C₃)	C₂×C₄₁	semidirect
32. D₅×C₁₃⋊C₃	C₂×C₄₁	semidirect
33. C₅×D₁₃⋊C₃	C₂×C₄₁	semidirect
34. D₅×D₁₃	C₃×C₄₁	semidirect
38. C₅×C₄₁	C₂×D₁₃⋊C₃	semidirect
39. C₅×C₁₃⋊C₃	C₂²×C₄₁	semidirect
42. D₆₅	C₂×C₃×C₄₁	semidirect
43. C₅×D₁₃	C₂×C₃×C₄₁	semidirect
44. D₅×C₁₃	C₂×C₃×C₄₁	semidirect
51. D₁₃⋊C₃	D₅×C₄₁	direct (N × H)
52. C₅×C₁₃	C₂²×C₃×C₄₁	semidirect
55. C₄₁	D₅×D₁₃⋊C₃	direct (N × H)
56. C₁₃⋊C₃	C₂×D₅×C₄₁	semidirect
62. D₁₃	C₃×D₅×C₄₁	semidirect
65. C₁₃	C₂×C₃×D₅×C₄₁	semidirect
69. D₅	C₄₁×D₁₃⋊C₃	direct (N × H)
73. C₅	C₂×C₄₁×D₁₃⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₄₁×C₅⋊(D₁₃⋊C₃)	2
D₅×C₁₃⋊C₃×C₄₁	2
C₅×C₄₁×D₁₃⋊C₃	2
D₅×D₁₃×C₄₁	3
C₂×C₄₁×D₁₃⋊C₃	5
C₂×C₃×D₅×C₄₁	13
D₅×D₁₃⋊C₃	41

Subgroups — D5×C41×D13⋊C3 #44544371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₅×C₄₁×D₁₃⋊C₃ #44544371