Subgroups — C₂×C₃²×D₈₀₅ #44394668

Order 28980.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₈₀₅	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×D₈₀₅	C₃	1	4	yes	maximal, direct product factor
4	C₃²×C₅×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₃²×D₁₆₁	—	5	1	no	maximal, Hall
6	C₃×D₈₀₅	C₂×C₃	1	8	yes	direct product factor
7	C₂×C₃×C₅×C₇×C₂₃	C₂×C₃	1	4	yes	complemented
8	C₂×C₃²×D₁₁₅	—	7	1	no	maximal, Hall
9	C₂×D₈₀₅	C₃²	1	1	yes	characteristic, direct product factor, Hall
10	C₃²×D₁₆₁	—	5	2	no	—
11	C₂×C₃²×C₇×C₂₃	D₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₂₃	C₂²×C₃	1	4	yes	complemented
13	C₃²×D₁₁₅	—	7	2	no	—
14	C₂×C₃²×C₅×C₂₃	D₇	1	1	yes	characteristic, complemented
15	C₂×C₃×D₁₆₁	—	5	4	no	—
16	C₂×C₅×C₇×C₂₃	C₂×C₃²	1	1	yes	characteristic, complemented
17	D₈₀₅	C₂×C₃²	1	2	yes	direct product factor
18	C₃²×C₇×C₂₃	C₂×D₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₃×D₁₁₅	—	7	4	no	—
20	C₂×C₃²×D₃₅	—	23	1	no	maximal, Hall
21	C₃²×C₅×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₂₃	C₃×D₅	1	4	yes	complemented
23	C₃×D₁₆₁	—	5	8	no	—
24	C₂×C₃²×D₂₃	—	35	1	no	Hall
25	C₅×C₇×C₂₃	C₂²×C₃²	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅×C₂₃	C₃×D₇	1	4	yes	complemented
27	C₃×D₁₁₅	—	7	8	no	—
28	C₂×D₁₆₁	—	5	1	no	Hall
29	C₂×C₃²×C₅×C₇	D₂₃	1	1	yes	characteristic, complemented
30	C₃²×D₃₅	—	23	2	no	—
31	C₃×C₇×C₂₃	C₂×C₃×D₅	1	4	yes	complemented
32	C₂×D₁₁₅	—	7	1	no	Hall
33	C₂×C₃×D₃₅	—	23	4	no	—
34	C₂×C₃²×C₂₃	D₃₅	1	1	yes	characteristic, complemented
35	C₃²×D₂₃	—	35	2	no	—
36	C₃×C₅×C₂₃	C₂×C₃×D₇	1	4	yes	complemented
37	C₂×C₇×C₂₃	C₃²×D₅	1	1	yes	characteristic, complemented
38	D₁₆₁	—	5	2	no	—
39	C₃²×C₅×C₇	C₂×D₂₃	1	1	yes	characteristic, complemented, Hall
40	C₂×C₃×D₂₃	—	35	4	no	—
41	C₂×C₃²×D₇	—	115	1	no	Hall
42	C₂×C₅×C₂₃	C₃²×D₇	1	1	yes	characteristic, complemented
43	D₁₁₅	—	7	2	no	—
44	C₂×C₃×C₅×C₇	C₃×D₂₃	1	4	yes	complemented
45	C₃×D₃₅	—	23	8	no	—
46	C₃²×C₂₃	C₂×D₃₅	1	1	yes	characteristic, complemented, Hall
47	C₂×C₃²×D₅	—	161	1	no	Hall
48	C₇×C₂₃	C₂×C₃²×D₅	1	1	yes	characteristic, complemented, Hall
49	C₂×D₃₅	—	23	1	no	Hall
50	C₂×C₃×C₂₃	C₃×D₃₅	1	4	yes	complemented
51	C₃×D₂₃	—	35	8	no	—
52	C₂×C₃²×C₇	D₁₁₅	1	1	yes	characteristic, complemented
53	C₃²×D₇	—	115	2	no	—
54	C₅×C₂₃	C₂×C₃²×D₇	1	1	yes	characteristic, complemented, Hall
55	C₃×C₅×C₇	C₂×C₃×D₂₃	1	4	yes	complemented
56	C₂×D₂₃	—	35	1	no	Hall
57	C₂×C₃²×C₅	D₁₆₁	1	1	yes	characteristic, complemented
58	C₃²×D₅	—	161	2	no	—
59	C₂×C₃×D₇	—	115	4	no	—
60	C₂×C₅×C₇	C₃²×D₂₃	1	1	yes	characteristic, complemented
61	D₃₅	—	23	2	no	—
62	C₃×C₂₃	C₂×C₃×D₃₅	1	4	yes	complemented
63	C₃²×C₇	C₂×D₁₁₅	1	1	yes	characteristic, complemented, Hall
64	C₂×C₃×D₅	—	161	4	no	—
65	C₂×C₂₃	C₃²×D₃₅	1	1	yes	characteristic, complemented
66	D₂₃	—	35	2	no	—
67	C₃²×C₅	C₂×D₁₆₁	1	1	yes	characteristic, complemented, Hall
68	C₂×C₃×C₇	C₃×D₁₁₅	1	4	yes	complemented
69	C₃×D₇	—	115	8	no	—
70	C₂²×C₃²	—	805	1	no	Hall
71	C₅×C₇	C₂×C₃²×D₂₃	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	C₃×D₁₆₁	1	4	yes	complemented
73	C₃×D₅	—	161	8	no	—
74	C₂×D₇	—	115	1	no	Hall
75	C₂₃	C₂×C₃²×D₃₅	1	1	yes	characteristic, complemented, Sylow
76	C₃×C₇	C₂×C₃×D₁₁₅	1	4	yes	complemented
77	C₂×D₅	—	161	1	no	Hall
78	C₂×C₃²	—	805	2	no	—
79	C₂×C₃²	D₈₀₅	1	1	yes	characteristic, direct product factor
80	C₃×C₅	C₂×C₃×D₁₆₁	1	4	yes	complemented
81	C₂×C₇	C₃²×D₁₁₅	1	1	yes	characteristic, complemented
82	D₇	—	115	2	no	—
83	C₂²×C₃	—	805	4	no	—
84	C₂×C₅	C₃²×D₁₆₁	1	1	yes	characteristic, complemented
85	D₅	—	161	2	no	—
86	C₃²	C₂×D₈₀₅	1	1	yes	characteristic, direct product factor, Sylow
87	C₇	C₂×C₃²×D₁₁₅	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	—	805	8	no	—
89	C₂×C₃	C₃×D₈₀₅	1	4	yes	direct product factor
90	C₅	C₂×C₃²×D₁₆₁	1	1	yes	characteristic, complemented, Sylow
91	C₂²	—	805	1	no	Sylow
92	C₃	C₂×C₃×D₈₀₅	1	4	yes	direct product factor
93	C₂	—	805	2	no	—
94	C₂	C₃²×D₈₀₅	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₃²	D₈₀₅
commutator, cosocle, hypocenter	C₅×C₇×C₂₃	C₂²×C₃²
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₂₃	C₂
LCS	G ▷ C₅×C₇×C₂₃
UCS	C₁ ◁ C₂×C₃²

Complements

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

N	H ≅ G/N	type
1. C₃²×D₈₀₅	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₂₃	C₂	semidirect
3. C₂×C₃×D₈₀₅	C₃	direct (N × H)
4. C₃²×C₅×C₇×C₂₃	C₂²	semidirect
6. C₃×D₈₀₅	C₂×C₃	direct (N × H)
7. C₂×C₃×C₅×C₇×C₂₃	C₂×C₃	semidirect
9. C₂×D₈₀₅	C₃²	direct (N × H)
11. C₂×C₃²×C₇×C₂₃	D₅	semidirect
12. C₃×C₅×C₇×C₂₃	C₂²×C₃	semidirect
14. C₂×C₃²×C₅×C₂₃	D₇	semidirect
16. C₂×C₅×C₇×C₂₃	C₂×C₃²	semidirect
17. D₈₀₅	C₂×C₃²	direct (N × H)
18. C₃²×C₇×C₂₃	C₂×D₅	semidirect
21. C₃²×C₅×C₂₃	C₂×D₇	semidirect
22. C₂×C₃×C₇×C₂₃	C₃×D₅	semidirect
25. C₅×C₇×C₂₃	C₂²×C₃²	semidirect
26. C₂×C₃×C₅×C₂₃	C₃×D₇	semidirect
29. C₂×C₃²×C₅×C₇	D₂₃	semidirect
31. C₃×C₇×C₂₃	C₂×C₃×D₅	semidirect
34. C₂×C₃²×C₂₃	D₃₅	semidirect
36. C₃×C₅×C₂₃	C₂×C₃×D₇	semidirect
37. C₂×C₇×C₂₃	C₃²×D₅	semidirect
39. C₃²×C₅×C₇	C₂×D₂₃	semidirect
42. C₂×C₅×C₂₃	C₃²×D₇	semidirect
44. C₂×C₃×C₅×C₇	C₃×D₂₃	semidirect
46. C₃²×C₂₃	C₂×D₃₅	semidirect
48. C₇×C₂₃	C₂×C₃²×D₅	semidirect
50. C₂×C₃×C₂₃	C₃×D₃₅	semidirect
52. C₂×C₃²×C₇	D₁₁₅	semidirect
54. C₅×C₂₃	C₂×C₃²×D₇	semidirect
55. C₃×C₅×C₇	C₂×C₃×D₂₃	semidirect
57. C₂×C₃²×C₅	D₁₆₁	semidirect
60. C₂×C₅×C₇	C₃²×D₂₃	semidirect
62. C₃×C₂₃	C₂×C₃×D₃₅	semidirect
63. C₃²×C₇	C₂×D₁₁₅	semidirect
65. C₂×C₂₃	C₃²×D₃₅	semidirect
67. C₃²×C₅	C₂×D₁₆₁	semidirect
68. C₂×C₃×C₇	C₃×D₁₁₅	semidirect
71. C₅×C₇	C₂×C₃²×D₂₃	semidirect
72. C₂×C₃×C₅	C₃×D₁₆₁	semidirect
75. C₂₃	C₂×C₃²×D₃₅	semidirect
76. C₃×C₇	C₂×C₃×D₁₁₅	semidirect
79. C₂×C₃²	D₈₀₅	direct (N × H)
80. C₃×C₅	C₂×C₃×D₁₆₁	semidirect
81. C₂×C₇	C₃²×D₁₁₅	semidirect
84. C₂×C₅	C₃²×D₁₆₁	semidirect
86. C₃²	C₂×D₈₀₅	direct (N × H)
87. C₇	C₂×C₃²×D₁₁₅	semidirect
89. C₂×C₃	C₃×D₈₀₅	direct (N × H)
90. C₅	C₂×C₃²×D₁₆₁	semidirect
92. C₃	C₂×C₃×D₈₀₅	direct (N × H)
94. C₂	C₃²×D₈₀₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×D₈₀₅	2
C₂×C₃²×C₅×C₇×C₂₃	2
C₂×C₃×D₈₀₅	3
C₂×C₃²×D₁₆₁	5
C₂×C₃²×D₁₁₅	7
C₂×C₃²×D₃₅	23

Subgroups — C2×C32×D805 #44394668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃²×D₈₀₅ #44394668