Subgroups — D₁₅⋊D₁₃₃ #22547739

Order 7980.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₁₉×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×D₃₉₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₆₆₅	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₁₃₃	—	3	1	no	maximal, Hall
5	C₃×C₅×C₇×C₁₉	C₂²	1	1	yes	characteristic, complemented, Hall
6	D₃×D₁₃₃	—	5	1	no	maximal, Hall
7	D₆₆₅	D₃	1	1	yes	characteristic, complemented
8	C₇×D₅×C₁₉	—	3	1	no	—
9	C₅×D₁₃₃	—	3	1	no	—
10	D₁₅⋊D₁₉	—	7	1	no	maximal, Hall
11	D₃₉₉	D₅	1	1	yes	characteristic, complemented
12	D₃×C₇×C₁₉	—	5	1	no	—
13	C₃×D₁₃₃	—	5	1	no	—
14	C₅×C₇×C₁₉	C₂×D₃	1	1	yes	characteristic, complemented, Hall
15	C₁₉×D₁₅	D₇	1	1	yes	characteristic, complemented
16	C₅×D₅₇	—	7	1	no	—
17	C₃×D₉₅	—	7	1	no	—
18	C₂×D₁₃₃	—	15	1	no	Hall
19	D₁₅⋊D₇	—	19	1	no	maximal, Hall
20	C₃×C₇×C₁₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
21	D₅×D₁₉	—	21	1	no	Hall
22	C₃×C₅×C₁₉	C₂×D₇	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇×C₁₉	—	15	1	no	—
24	D₁₃₃	—	3	1	no	—
25	D₁₃₃	—	5	1	no	—
26	D₃×D₁₉	—	35	1	no	Hall
27	C₇×D₁₅	D₁₉	1	1	yes	characteristic, complemented
28	C₅×D₂₁	—	19	1	no	—
29	C₃×D₃₅	—	19	1	no	—
30	D₉₅	—	7	1	no	—
31	C₅×D₁₉	—	21	1	no	—
32	D₅×C₁₉	—	3	1	no	—
33	D₅×D₇	—	57	1	no	Hall
34	C₇×C₁₉	D₃×D₅	1	1	yes	characteristic, complemented, Hall
35	D₅₇	—	7	1	no	—
36	C₃×D₁₉	—	35	1	no	—
37	D₃×C₁₉	—	5	1	no	—
38	C₃×C₅×C₇	C₂×D₁₉	1	1	yes	characteristic, complemented, Hall
39	C₅×C₁₉	D₃×D₇	1	1	yes	characteristic, complemented, Hall
40	D₃×D₇	—	95	1	no	Hall
41	C₂×D₁₉	—	105	1	no	Hall
42	D₃₅	—	19	1	no	—
43	C₅×D₇	—	57	1	no	—
44	C₇×D₅	—	3	1	no	—
45	D₃×D₅	—	133	1	no	Hall
46	C₃×C₁₉	D₅×D₇	1	1	yes	characteristic, complemented, Hall
47	D₂₁	—	19	1	no	—
48	C₃×D₇	—	95	1	no	—
49	D₃×C₇	—	5	1	no	—
50	C₂×C₁₉	—	15	1	no	—
51	D₁₉	—	21	1	no	—
52	D₁₉	—	35	1	no	—
53	C₅×C₇	D₃×D₁₉	1	1	yes	characteristic, complemented, Hall
54	D₁₅	D₁₃₃	1	1	yes	characteristic, complemented
55	C₃×D₅	—	133	1	no	—
56	C₅×D₃	—	133	1	no	—
57	C₂×D₇	—	285	1	no	Hall
58	C₃×C₇	D₅×D₁₉	1	1	yes	characteristic, complemented, Hall
59	C₂×D₅	—	399	1	no	Hall
60	C₁₉	D₁₅⋊D₇	1	1	yes	characteristic, complemented, Sylow
61	C₃×C₅	C₂×D₁₃₃	1	1	yes	characteristic, complemented, Hall
62	C₂×C₇	—	15	1	no	—
63	D₇	—	57	1	no	—
64	D₇	—	95	1	no	—
65	C₂×D₃	—	665	1	no	Hall
66	C₂×C₅	—	399	1	no	—
67	D₅	—	3	1	no	—
68	D₅	—	133	1	no	—
69	C₇	D₁₅⋊D₁₉	1	1	yes	characteristic, complemented, Sylow
70	C₂×C₃	—	665	1	no	—
71	D₃	—	5	1	no	—
72	D₃	—	133	1	no	—
73	C₅	D₃×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
74	C₂²	—	1995	1	no	Sylow
75	C₃	D₅×D₁₃₃	1	1	yes	characteristic, complemented, Sylow
76	C₂	—	15	1	no	—
77	C₂	—	399	1	no	—
78	C₂	—	665	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃×C₅×C₇×C₁₉	C₂²
LCS	G ▷ C₃×C₅×C₇×C₁₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₇×C₁₉×D₁₅	C₂	semidirect
2. C₅×D₃₉₉	C₂	semidirect
3. C₃×D₆₆₅	C₂	semidirect
5. C₃×C₅×C₇×C₁₉	C₂²	semidirect
7. D₆₆₅	D₃	semidirect
11. D₃₉₉	D₅	semidirect
14. C₅×C₇×C₁₉	C₂×D₃	semidirect
15. C₁₉×D₁₅	D₇	semidirect
20. C₃×C₇×C₁₉	C₂×D₅	semidirect
22. C₃×C₅×C₁₉	C₂×D₇	semidirect
27. C₇×D₁₅	D₁₉	semidirect
34. C₇×C₁₉	D₃×D₅	semidirect
38. C₃×C₅×C₇	C₂×D₁₉	semidirect
39. C₅×C₁₉	D₃×D₇	semidirect
46. C₃×C₁₉	D₅×D₇	semidirect
53. C₅×C₇	D₃×D₁₉	semidirect
54. D₁₅	D₁₃₃	semidirect
58. C₃×C₇	D₅×D₁₉	semidirect
60. C₁₉	D₁₅⋊D₇	semidirect
61. C₃×C₅	C₂×D₁₃₃	semidirect
69. C₇	D₁₅⋊D₁₉	semidirect
73. C₅	D₃×D₁₃₃	semidirect
75. C₃	D₅×D₁₃₃	semidirect

Subgroups — D15⋊D133 #22547739

Conjugacy classes of subgroups

Complements

Subgroups — D₁₅⋊D₁₃₃ #22547739