Subgroups — D₁₅×D₁₂₉ #21440938

Order 7740.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₆₄₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₁₅×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₁₂₉	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅×D₁₂₉	—	3	1	no	maximal
5	D₁₅×D₄₃	—	3	1	no	maximal
6	C₃²×C₅×C₄₃	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×D₁₂₉	—	5	1	no	maximal, Hall
8	D₆₄₅	—	3	1	no	—
9	D₆₄₅	—	3	1	no	—
10	D₆₄₅	—	6	1	no	—
11	D₁₅×C₄₃	D₃	1	1	yes	characteristic, complemented
12	C₅×D₁₂₉	D₃	1	1	yes	characteristic, complemented
13	C₃×D₅×C₄₃	—	3	1	no	—
14	C₃×C₅×D₄₃	—	3	1	no	—
15	D₅×D₄₃	—	9	1	no	Hall
16	C₃⋊D₁₂₉	—	5	1	no	—
17	C₃×D₁₂₉	D₅	1	1	yes	characteristic, complemented
18	C₃×D₃×C₄₃	—	5	1	no	—
19	C₃×C₅×C₄₃	—	2	1	no	—
20	C₃×C₅×C₄₃	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₄₃	C₂×D₃	1	1	yes	characteristic, complemented
22	C₂×D₁₂₉	—	15	1	no	—
23	D₃×D₄₃	—	15	1	no	—
24	D₂₁₅	—	9	1	no	—
25	C₅×D₄₃	—	3	1	no	—
26	D₅×C₄₃	—	3	1	no	—
27	C₃²×C₄₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₄₃	—	15	1	no	—
29	D₁₂₉	—	15	1	no	—
30	D₁₂₉	—	15	1	no	—
31	D₁₂₉	—	30	1	no	—
32	D₁₂₉	D₁₅	1	1	yes	characteristic, direct product factor
33	C₃×D₄₃	—	3	1	no	—
34	D₃×C₄₃	—	5	1	no	—
35	C₅×C₄₃	D₃²	1	1	yes	characteristic, complemented, Hall
36	D₃×D₁₅	—	43	1	no	maximal, Hall
37	C₂×D₄₃	—	45	1	no	Hall
38	C₃×C₄₃	—	2	1	no	—
39	C₃×C₄₃	D₃×D₅	1	1	yes	characteristic, complemented
40	C₃×C₄₃	C₂×D₁₅	1	1	yes	characteristic, complemented
41	C₃⋊D₁₅	—	43	1	no	—
42	C₃×D₁₅	D₄₃	1	1	yes	characteristic, complemented
43	C₃×C₅×D₃	—	43	1	no	—
44	C₂×C₄₃	—	15	1	no	—
45	D₄₃	—	3	1	no	—
46	D₄₃	—	45	1	no	—
47	C₂×D₁₅	—	129	1	no	—
48	D₃×D₅	—	129	1	no	—
49	C₃²×C₅	C₂×D₄₃	1	1	yes	characteristic, complemented, Hall
50	C₄₃	D₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
51	D₃²	—	215	1	no	Hall
52	C₂×C₃×C₅	—	129	1	no	—
53	D₁₅	—	258	1	no	—
54	D₁₅	—	129	1	no	—
55	D₁₅	—	129	1	no	—
56	D₁₅	D₁₂₉	1	1	yes	characteristic, direct product factor
57	C₃×D₅	—	3	1	no	—
58	C₅×D₃	—	43	1	no	—
59	C₂×D₅	—	387	1	no	Hall
60	C₃⋊D₃	—	215	1	no	—
61	C₃×D₃	—	5	1	no	—
62	C₃×D₃	—	43	1	no	—
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	D₃×D₄₃	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×D₁₂₉	1	1	yes	characteristic, complemented
66	C₂×D₃	—	645	1	no	—
67	C₂×D₃	—	645	1	no	—
68	C₂×C₅	—	129	1	no	—
69	D₅	—	3	1	no	—
70	D₅	—	387	1	no	—
71	C₃²	D₅×D₄₃	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	15	1	no	—
73	C₂×C₃	—	129	1	no	—
74	D₃	—	5	1	no	—
75	D₃	—	1290	1	no	—
76	D₃	—	43	1	no	—
77	D₃	—	645	1	no	—
78	D₃	—	645	1	no	—
79	C₅	D₃×D₁₂₉	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	1935	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₁₅×D₄₃	1	1	yes	characteristic, complemented
83	C₃	D₅×D₁₂₉	1	1	yes	characteristic, complemented
84	C₂	—	15	1	no	—
85	C₂	—	129	1	no	—
86	C₂	—	1935	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₅×C₄₃	C₂²
LCS	G ▷ C₃²×C₅×C₄₃
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃⋊D₆₄₅	C₂	semidirect
2. C₃×D₁₅×C₄₃	C₂	semidirect
3. C₃×C₅×D₁₂₉	C₂	semidirect
6. C₃²×C₅×C₄₃	C₂²	semidirect
11. D₁₅×C₄₃	D₃	semidirect
12. C₅×D₁₂₉	D₃	semidirect
17. C₃×D₁₂₉	D₅	semidirect
20. C₃×C₅×C₄₃	C₂×D₃	semidirect
21. C₃×C₅×C₄₃	C₂×D₃	semidirect
27. C₃²×C₄₃	C₂×D₅	semidirect
32. D₁₂₉	D₁₅	direct (N × H)
35. C₅×C₄₃	D₃²	semidirect
39. C₃×C₄₃	D₃×D₅	semidirect
40. C₃×C₄₃	C₂×D₁₅	semidirect
42. C₃×D₁₅	D₄₃	semidirect
49. C₃²×C₅	C₂×D₄₃	semidirect
50. C₄₃	D₃×D₁₅	semidirect
56. D₁₅	D₁₂₉	direct (N × H)
64. C₃×C₅	D₃×D₄₃	semidirect
65. C₃×C₅	C₂×D₁₂₉	semidirect
71. C₃²	D₅×D₄₃	semidirect
79. C₅	D₃×D₁₂₉	semidirect
82. C₃	D₁₅×D₄₃	semidirect
83. C₃	D₅×D₁₂₉	semidirect

Subgroups — D15×D129 #21440938

Conjugacy classes of subgroups

Complements

Subgroups — D₁₅×D₁₂₉ #21440938