Subgroups — D₃×D₂₆₈₅ #44567376

Order 32220.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×D₃×C₁₇₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₆₈₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊D₂₆₈₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₆₈₅	—	3	1	no	maximal
5	D₃×D₈₉₅	—	3	1	no	maximal
6	C₃²×C₅×C₁₇₉	C₂²	1	1	yes	characteristic, complemented, Hall
7	D₃×D₅₃₇	—	5	1	no	maximal, Hall
8	D₂₆₈₅	—	3	1	no	—
9	D₂₆₈₅	—	3	1	no	—
10	D₂₆₈₅	—	6	1	no	—
11	D₂₆₈₅	D₃	1	1	yes	characteristic, direct product factor
12	C₅×D₃×C₁₇₉	D₃	1	1	yes	characteristic, complemented
13	C₃×D₈₉₅	—	3	1	no	—
14	C₂×C₃×C₅×C₁₇₉	—	3	1	no	—
15	C₂×D₈₉₅	—	9	1	no	Hall
16	C₃⋊D₅₃₇	—	5	1	no	—
17	C₃×D₅₃₇	—	5	1	no	—
18	C₃×D₃×C₁₇₉	D₅	1	1	yes	characteristic, complemented
19	C₃×C₅×C₁₇₉	—	2	1	no	—
20	C₃×C₅×C₁₇₉	C₂×D₃	1	1	yes	characteristic, complemented
21	C₃×C₅×C₁₇₉	C₂×D₃	1	1	yes	characteristic, complemented
22	C₂×D₅₃₇	—	15	1	no	—
23	D₃×D₁₇₉	—	15	1	no	—
24	C₂×C₅×C₁₇₉	—	3	1	no	—
25	D₈₉₅	—	3	1	no	—
26	D₈₉₅	—	9	1	no	—
27	C₃²×C₁₇₉	C₂×D₅	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×C₁₇₉	—	3	1	no	—
29	D₅₃₇	—	5	1	no	—
30	D₅₃₇	—	15	1	no	—
31	D₅₃₇	—	15	1	no	—
32	D₅₃₇	—	30	1	no	—
33	C₃×D₁₇₉	—	15	1	no	—
34	D₃×C₁₇₉	D₁₅	1	1	yes	characteristic, complemented
35	C₅×C₁₇₉	D₃²	1	1	yes	characteristic, complemented, Hall
36	C₂×D₁₇₉	—	45	1	no	Hall
37	C₃×C₁₇₉	—	2	1	no	—
38	C₃×C₁₇₉	D₃×D₅	1	1	yes	characteristic, complemented
39	C₃×C₁₇₉	C₂×D₁₅	1	1	yes	characteristic, complemented
40	C₂×C₁₇₉	—	3	1	no	—
41	D₁₇₉	—	15	1	no	—
42	D₁₇₉	—	45	1	no	—
43	D₃×D₁₅	—	179	1	no	maximal, Hall
44	C₁₇₉	D₃×D₁₅	1	1	yes	characteristic, complemented, Sylow
45	C₃⋊D₁₅	—	179	1	no	—
46	C₃×D₁₅	—	179	1	no	—
47	C₃×C₅×D₃	D₁₇₉	1	1	yes	characteristic, complemented
48	C₂×D₁₅	—	537	1	no	—
49	D₃×D₅	—	537	1	no	—
50	C₃²×C₅	C₂×D₁₇₉	1	1	yes	characteristic, complemented, Hall
51	D₃²	—	895	1	no	Hall
52	C₂×C₃×C₅	—	3	1	no	—
53	D₁₅	—	537	1	no	—
54	D₁₅	—	537	1	no	—
55	D₁₅	—	1074	1	no	—
56	D₁₅	—	179	1	no	—
57	C₃×D₅	—	537	1	no	—
58	C₅×D₃	D₅₃₇	1	1	yes	characteristic, complemented
59	C₂×D₅	—	1611	1	no	Hall
60	C₃⋊D₃	—	895	1	no	—
61	C₃×D₃	—	895	1	no	—
62	C₃×D₃	D₈₉₅	1	1	yes	characteristic, complemented
63	C₃×C₅	—	2	1	no	—
64	C₃×C₅	D₃×D₁₇₉	1	1	yes	characteristic, complemented
65	C₃×C₅	C₂×D₅₃₇	1	1	yes	characteristic, complemented
66	C₂×D₃	—	2685	1	no	—
67	C₂×D₃	—	2685	1	no	—
68	C₂×C₅	—	3	1	no	—
69	D₅	—	537	1	no	—
70	D₅	—	1611	1	no	—
71	C₃²	C₂×D₈₉₅	1	1	yes	characteristic, complemented, Sylow
72	C₂×C₃	—	3	1	no	—
73	C₂×C₃	—	2685	1	no	—
74	D₃	—	2685	1	no	—
75	D₃	—	2685	1	no	—
76	D₃	—	895	1	no	—
77	D₃	—	5370	1	no	—
78	D₃	D₂₆₈₅	1	1	yes	characteristic, direct product factor
79	C₅	D₃×D₅₃₇	1	1	yes	characteristic, complemented, Sylow
80	C₂²	—	8055	1	no	Sylow
81	C₃	—	2	1	no	—
82	C₃	D₃×D₈₉₅	1	1	yes	characteristic, complemented
83	C₃	C₂×D₂₆₈₅	1	1	yes	characteristic, complemented
84	C₂	—	3	1	no	—
85	C₂	—	8055	1	no	—
86	C₂	—	2685	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₅×C₁₇₉	C₂²
LCS	G ▷ C₃²×C₅×C₁₇₉
UCS	C₁

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×D₃×C₁₇₉	C₂	semidirect
2. C₃×D₂₆₈₅	C₂	semidirect
3. C₃⋊D₂₆₈₅	C₂	semidirect
6. C₃²×C₅×C₁₇₉	C₂²	semidirect
11. D₂₆₈₅	D₃	direct (N × H)
12. C₅×D₃×C₁₇₉	D₃	semidirect
18. C₃×D₃×C₁₇₉	D₅	semidirect
20. C₃×C₅×C₁₇₉	C₂×D₃	semidirect
21. C₃×C₅×C₁₇₉	C₂×D₃	semidirect
27. C₃²×C₁₇₉	C₂×D₅	semidirect
34. D₃×C₁₇₉	D₁₅	semidirect
35. C₅×C₁₇₉	D₃²	semidirect
38. C₃×C₁₇₉	D₃×D₅	semidirect
39. C₃×C₁₇₉	C₂×D₁₅	semidirect
44. C₁₇₉	D₃×D₁₅	semidirect
47. C₃×C₅×D₃	D₁₇₉	semidirect
50. C₃²×C₅	C₂×D₁₇₉	semidirect
58. C₅×D₃	D₅₃₇	semidirect
62. C₃×D₃	D₈₉₅	semidirect
64. C₃×C₅	D₃×D₁₇₉	semidirect
65. C₃×C₅	C₂×D₅₃₇	semidirect
71. C₃²	C₂×D₈₉₅	semidirect
78. D₃	D₂₆₈₅	direct (N × H)
79. C₅	D₃×D₅₃₇	semidirect
82. C₃	D₃×D₈₉₅	semidirect
83. C₃	C₂×D₂₆₈₅	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×D₃×C₁₇₉	2
C₃×D₂₆₈₅	2
C₃⋊D₂₆₈₅	2
C₂×D₂₆₈₅	3
D₃×D₈₉₅	3
D₃×D₅₃₇	5
D₃×D₁₅	179

Subgroups — D3×D2685 #44567376

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×D₂₆₈₅ #44567376