Subgroups — C₂×C₉×D₄₅₅ #30655178

Order 16380.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×D₄₅₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₅×C₇×C₉×C₁₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₄₅₅	C₃	1	1	yes	maximal, characteristic
4	C₅×C₇×C₉×C₁₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₉×D₉₁	—	5	1	no	maximal, Hall
6	C₃×D₄₅₅	C₂×C₃	1	2	yes	—
7	C₂×C₃×C₅×C₇×C₁₃	C₂×C₃	1	1	yes	characteristic
8	C₂×C₉×D₆₅	—	7	1	no	maximal, Hall
9	C₂×D₄₅₅	C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₇×C₉×C₁₃	D₅	1	1	yes	characteristic, complemented
11	C₉×D₉₁	—	5	2	no	—
12	C₃×C₅×C₇×C₁₃	C₂²×C₃	1	1	yes	characteristic
13	C₂×C₉×D₃₅	—	13	1	no	maximal, Hall
14	C₂×C₅×C₉×C₁₃	D₇	1	1	yes	characteristic, complemented
15	C₉×D₆₅	—	7	2	no	—
16	C₂×C₃×D₉₁	—	5	1	no	—
17	C₂×C₅×C₇×C₁₃	C₂×C₉	1	1	yes	characteristic, complemented
18	D₄₅₅	C₂×C₉	1	2	yes	direct product factor
19	C₇×C₉×C₁₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
20	C₂×C₃×D₆₅	—	7	1	no	—
21	C₂×C₅×C₇×C₉	D₁₃	1	1	yes	characteristic, complemented
22	C₉×D₃₅	—	13	2	no	—
23	C₅×C₉×C₁₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
24	C₂×C₃×C₇×C₁₃	C₃×D₅	1	1	yes	characteristic
25	C₃×D₉₁	—	5	2	no	—
26	C₂×C₉×D₁₃	—	35	1	no	Hall
27	C₅×C₇×C₁₃	C₂²×C₉	1	1	yes	characteristic, complemented, Hall
28	C₂×C₃×D₃₅	—	13	1	no	—
29	C₂×C₃×C₅×C₁₃	C₃×D₇	1	1	yes	characteristic
30	C₃×D₆₅	—	7	2	no	—
31	C₂×D₉₁	—	5	1	no	Hall
32	C₅×C₇×C₉	C₂×D₁₃	1	1	yes	characteristic, complemented, Hall
33	C₃×C₇×C₁₃	C₂×C₃×D₅	1	1	yes	characteristic
34	C₂×D₆₅	—	7	1	no	Hall
35	C₂×C₉×D₇	—	65	1	no	Hall
36	C₂×C₉×C₁₃	D₃₅	1	1	yes	characteristic, complemented
37	C₉×D₁₃	—	35	2	no	—
38	C₂×C₃×C₅×C₇	C₃×D₁₃	1	1	yes	characteristic
39	C₃×D₃₅	—	13	2	no	—
40	C₃×C₅×C₁₃	C₂×C₃×D₇	1	1	yes	characteristic
41	C₂×C₇×C₁₃	C₉×D₅	1	1	yes	characteristic, complemented
42	D₉₁	—	5	2	no	—
43	C₂×C₉×D₅	—	91	1	no	Hall
44	C₂×C₃×D₁₃	—	35	1	no	—
45	C₂×D₃₅	—	13	1	no	Hall
46	C₂×C₅×C₁₃	C₉×D₇	1	1	yes	characteristic, complemented
47	D₆₅	—	7	2	no	—
48	C₂×C₇×C₉	D₆₅	1	1	yes	characteristic, complemented
49	C₉×D₇	—	65	2	no	—
50	C₉×C₁₃	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
51	C₃×C₅×C₇	C₂×C₃×D₁₃	1	1	yes	characteristic
52	C₇×C₁₃	C₂×C₉×D₅	1	1	yes	characteristic, complemented, Hall
53	C₂×C₅×C₉	D₉₁	1	1	yes	characteristic, complemented
54	C₉×D₅	—	91	2	no	—
55	C₂×C₃×D₇	—	65	1	no	—
56	C₂×C₃×C₁₃	C₃×D₃₅	1	1	yes	characteristic
57	C₃×D₁₃	—	35	2	no	—
58	C₂×C₅×C₇	C₉×D₁₃	1	1	yes	characteristic, complemented
59	D₃₅	—	13	2	no	—
60	C₅×C₁₃	C₂×C₉×D₇	1	1	yes	characteristic, complemented, Hall
61	C₇×C₉	C₂×D₆₅	1	1	yes	characteristic, complemented, Hall
62	C₂×C₃×D₅	—	91	1	no	—
63	C₂×D₁₃	—	35	1	no	Hall
64	C₅×C₉	C₂×D₉₁	1	1	yes	characteristic, complemented, Hall
65	C₂×C₃×C₇	C₃×D₆₅	1	1	yes	characteristic
66	C₃×D₇	—	65	2	no	—
67	C₃×C₁₃	C₂×C₃×D₃₅	1	1	yes	characteristic
68	C₂²×C₉	—	455	1	no	Hall
69	C₅×C₇	C₂×C₉×D₁₃	1	1	yes	characteristic, complemented, Hall
70	C₂×C₃×C₅	C₃×D₉₁	1	1	yes	characteristic
71	C₃×D₅	—	91	2	no	—
72	C₂×D₇	—	65	1	no	Hall
73	C₂×C₁₃	C₉×D₃₅	1	1	yes	characteristic, complemented
74	D₁₃	—	35	2	no	—
75	C₃×C₇	C₂×C₃×D₆₅	1	1	yes	characteristic
76	C₂×D₅	—	91	1	no	Hall
77	C₂×C₉	—	455	2	no	—
78	C₂×C₉	D₄₅₅	1	1	yes	characteristic, direct product factor
79	C₃×C₅	C₂×C₃×D₉₁	1	1	yes	characteristic
80	C₂×C₇	C₉×D₆₅	1	1	yes	characteristic, complemented
81	D₇	—	65	2	no	—
82	C₁₃	C₂×C₉×D₃₅	1	1	yes	characteristic, complemented, Sylow
83	C₂²×C₃	—	455	1	no	—
84	C₂×C₅	C₉×D₉₁	1	1	yes	characteristic, complemented
85	D₅	—	91	2	no	—
86	C₉	C₂×D₄₅₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₇	C₂×C₉×D₆₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	455	2	no	—
89	C₂×C₃	C₃×D₄₅₅	1	1	yes	characteristic
90	C₅	C₂×C₉×D₉₁	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	455	1	no	Sylow
92	C₃	C₂×C₃×D₄₅₅	1	1	yes	characteristic
93	C₂	—	455	2	no	—
94	C₂	C₉×D₄₅₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₉	D₄₅₅
commutator, hypocenter	C₅×C₇×C₁₃	C₂²×C₉
Frattini	C₃	C₂×C₃×D₄₅₅
Fitting	C₂×C₅×C₇×C₉×C₁₃	C₂
socle	C₂×C₃×C₅×C₇×C₁₃	C₂×C₃
prime radical	C₂×C₃×D₄₅₅	C₃
cosocle	C₃×C₅×C₇×C₁₃	C₂²×C₃
LCS	G ▷ C₅×C₇×C₁₃
UCS	C₁ ◁ C₂×C₉

Complements

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

N	H ≅ G/N	type
1. C₉×D₄₅₅	C₂	direct (N × H)
2. C₂×C₅×C₇×C₉×C₁₃	C₂	semidirect
4. C₅×C₇×C₉×C₁₃	C₂²	semidirect
9. C₂×D₄₅₅	C₉	direct (N × H)
10. C₂×C₇×C₉×C₁₃	D₅	semidirect
14. C₂×C₅×C₉×C₁₃	D₇	semidirect
17. C₂×C₅×C₇×C₁₃	C₂×C₉	semidirect
18. D₄₅₅	C₂×C₉	direct (N × H)
19. C₇×C₉×C₁₃	C₂×D₅	semidirect
21. C₂×C₅×C₇×C₉	D₁₃	semidirect
23. C₅×C₉×C₁₃	C₂×D₇	semidirect
27. C₅×C₇×C₁₃	C₂²×C₉	semidirect
32. C₅×C₇×C₉	C₂×D₁₃	semidirect
36. C₂×C₉×C₁₃	D₃₅	semidirect
41. C₂×C₇×C₁₃	C₉×D₅	semidirect
46. C₂×C₅×C₁₃	C₉×D₇	semidirect
48. C₂×C₇×C₉	D₆₅	semidirect
50. C₉×C₁₃	C₂×D₃₅	semidirect
52. C₇×C₁₃	C₂×C₉×D₅	semidirect
53. C₂×C₅×C₉	D₉₁	semidirect
58. C₂×C₅×C₇	C₉×D₁₃	semidirect
60. C₅×C₁₃	C₂×C₉×D₇	semidirect
61. C₇×C₉	C₂×D₆₅	semidirect
64. C₅×C₉	C₂×D₉₁	semidirect
69. C₅×C₇	C₂×C₉×D₁₃	semidirect
73. C₂×C₁₃	C₉×D₃₅	semidirect
78. C₂×C₉	D₄₅₅	direct (N × H)
80. C₂×C₇	C₉×D₆₅	semidirect
82. C₁₃	C₂×C₉×D₃₅	semidirect
84. C₂×C₅	C₉×D₉₁	semidirect
86. C₉	C₂×D₄₅₅	direct (N × H)
87. C₇	C₂×C₉×D₆₅	semidirect
90. C₅	C₂×C₉×D₉₁	semidirect
94. C₂	C₉×D₄₅₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×D₄₅₅	2
C₂×C₅×C₇×C₉×C₁₃	2
C₂×C₃×D₄₅₅	3
C₂×C₉×D₉₁	5
C₂×C₉×D₆₅	7
C₂×C₉×D₃₅	13

Subgroups — C2×C9×D455 #30655178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×D₄₅₅ #30655178