Subgroups — C₃×D₁₃×D₅₅ #22575134

Order 8580.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₇₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₁₃×D₅₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×C₁₁×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₁₃×D₅₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₃×C₅×C₁₁×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
6	C₃×D₁₁×D₁₃	—	5	1	no	maximal, Hall
7	D₇₁₅	C₂×C₃	1	1	yes	characteristic, complemented
8	C₁₃×D₅₅	C₂×C₃	1	1	yes	characteristic, complemented
9	C₅×C₁₁×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
10	C₃×D₁₄₃	—	5	1	no	—
11	C₃×C₁₃×D₁₁	—	5	1	no	—
12	C₃×C₁₁×D₁₃	D₅	1	1	yes	characteristic, complemented
13	C₃×D₅×D₁₃	—	11	1	no	maximal, Hall
14	C₅×C₁₁×C₁₃	C₂²×C₃	1	1	yes	characteristic, complemented, Hall
15	C₂×C₃×D₅₅	—	13	1	no	maximal, Hall
16	D₁₁×D₁₃	—	5	1	no	Hall
17	C₃×C₁₁×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
18	C₃×D₆₅	—	11	1	no	—
19	C₃×D₅×C₁₃	—	11	1	no	—
20	C₃×C₅×D₁₃	D₁₁	1	1	yes	characteristic, complemented
21	C₂×C₃×C₅×C₁₁	—	13	1	no	—
22	C₃×D₅₅	—	13	1	no	—
23	C₃×D₅₅	D₁₃	1	1	yes	characteristic, direct product factor
24	D₁₄₃	—	5	1	no	—
25	C₁₁×D₁₃	C₃×D₅	1	1	yes	characteristic, complemented
26	C₁₃×D₁₁	—	5	1	no	—
27	D₅×D₁₃	—	11	1	no	Hall
28	C₂×D₅₅	—	13	1	no	Hall
29	C₃×C₅×C₁₃	C₂×D₁₁	1	1	yes	characteristic, complemented, Hall
30	C₃×C₅×C₁₁	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
31	C₂×C₃×D₁₃	—	55	1	no	Hall
32	C₁₁×C₁₃	C₂×C₃×D₅	1	1	yes	characteristic, complemented, Hall
33	C₂×C₃×D₁₁	—	65	1	no	Hall
34	D₆₅	—	11	1	no	—
35	C₅×D₁₃	C₃×D₁₁	1	1	yes	characteristic, complemented
36	D₅×C₁₃	—	11	1	no	—
37	C₂×C₅×C₁₁	—	13	1	no	—
38	D₅₅	—	13	1	no	—
39	D₅₅	C₃×D₁₃	1	1	yes	characteristic, direct product factor
40	C₂×C₃×C₁₃	—	55	1	no	—
41	C₃×D₁₃	—	55	1	no	—
42	C₃×D₁₃	D₅₅	1	1	yes	characteristic, direct product factor
43	C₂×C₃×C₁₁	—	13	1	no	—
44	C₃×D₁₁	—	5	1	no	—
45	C₃×D₁₁	—	65	1	no	—
46	C₅×C₁₃	C₂×C₃×D₁₁	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃×D₅	—	143	1	no	Hall
48	C₅×C₁₁	C₂×C₃×D₁₃	1	1	yes	characteristic, complemented, Hall
49	C₂×D₁₃	—	55	1	no	Hall
50	C₂×D₁₁	—	65	1	no	Hall
51	C₃×C₁₃	C₂×D₅₅	1	1	yes	characteristic, complemented, Hall
52	C₃×C₁₁	D₅×D₁₃	1	1	yes	characteristic, complemented, Hall
53	C₂×C₃×C₅	—	13	1	no	—
54	C₃×D₅	—	11	1	no	—
55	C₃×D₅	—	143	1	no	—
56	C₂×C₁₃	—	55	1	no	—
57	D₁₃	—	55	1	no	—
58	D₁₃	C₃×D₅₅	1	1	yes	characteristic, direct product factor
59	C₂×C₁₁	—	13	1	no	—
60	D₁₁	—	5	1	no	—
61	D₁₁	—	65	1	no	—
62	C₂×D₅	—	143	1	no	Hall
63	C₃×C₅	D₁₁×D₁₃	1	1	yes	characteristic, complemented, Hall
64	C₁₃	C₂×C₃×D₅₅	1	1	yes	characteristic, complemented, Sylow
65	C₂²×C₃	—	715	1	no	Hall
66	C₁₁	C₃×D₅×D₁₃	1	1	yes	characteristic, complemented, Sylow
67	C₂×C₅	—	13	1	no	—
68	D₅	—	11	1	no	—
69	D₅	—	143	1	no	—
70	C₂×C₃	—	13	1	no	—
71	C₂×C₃	—	55	1	no	—
72	C₂×C₃	—	715	1	no	—
73	C₅	C₃×D₁₁×D₁₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	715	1	no	Sylow
75	C₃	D₁₃×D₅₅	1	1	yes	characteristic, direct product factor, Sylow
76	C₂	—	13	1	no	—
77	C₂	—	55	1	no	—
78	C₂	—	715	1	no	—

	subgroup	G/H
center, hypercenter	C₃	D₁₃×D₅₅
commutator, hypocenter	C₅×C₁₁×C₁₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₁₁×C₁₃	C₂²
LCS	G ▷ C₅×C₁₁×C₁₃
UCS	C₁ ◁ C₃

Complements

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

N	H ≅ G/N	type
1. C₃×D₇₁₅	C₂	semidirect
2. C₃×C₁₃×D₅₅	C₂	semidirect
3. C₃×C₅×C₁₁×D₁₃	C₂	semidirect
4. D₁₃×D₅₅	C₃	direct (N × H)
5. C₃×C₅×C₁₁×C₁₃	C₂²	semidirect
7. D₇₁₅	C₂×C₃	semidirect
8. C₁₃×D₅₅	C₂×C₃	semidirect
9. C₅×C₁₁×D₁₃	C₂×C₃	semidirect
12. C₃×C₁₁×D₁₃	D₅	semidirect
14. C₅×C₁₁×C₁₃	C₂²×C₃	semidirect
17. C₃×C₁₁×C₁₃	C₂×D₅	semidirect
20. C₃×C₅×D₁₃	D₁₁	semidirect
23. C₃×D₅₅	D₁₃	direct (N × H)
25. C₁₁×D₁₃	C₃×D₅	semidirect
29. C₃×C₅×C₁₃	C₂×D₁₁	semidirect
30. C₃×C₅×C₁₁	C₂×D₁₃	semidirect
32. C₁₁×C₁₃	C₂×C₃×D₅	semidirect
35. C₅×D₁₃	C₃×D₁₁	semidirect
39. D₅₅	C₃×D₁₃	direct (N × H)
42. C₃×D₁₃	D₅₅	direct (N × H)
46. C₅×C₁₃	C₂×C₃×D₁₁	semidirect
48. C₅×C₁₁	C₂×C₃×D₁₃	semidirect
51. C₃×C₁₃	C₂×D₅₅	semidirect
52. C₃×C₁₁	D₅×D₁₃	semidirect
58. D₁₃	C₃×D₅₅	direct (N × H)
63. C₃×C₅	D₁₁×D₁₃	semidirect
64. C₁₃	C₂×C₃×D₅₅	semidirect
66. C₁₁	C₃×D₅×D₁₃	semidirect
73. C₅	C₃×D₁₁×D₁₃	semidirect
75. C₃	D₁₃×D₅₅	direct (N × H)

Subgroups — C3×D13×D55 #22575134

Conjugacy classes of subgroups

Complements

Subgroups — C₃×D₁₃×D₅₅ #22575134