Subgroups — C₂×C₅×C₂₃×C₃⋊D₂₁ #44394679

Order 28980.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₂₃×C₃⋊D₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₃²×C₅×C₇×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×C₂₃×D₂₁	—	3	4	no	maximal
4	C₃²×C₅×C₇×C₂₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	C₂×C₂₃×C₃⋊D₂₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₅×C₂₃×D₂₁	—	3	8	no	—
7	C₂×C₃×C₅×C₇×C₂₃	D₃	1	4	yes	complemented
8	C₂×C₅×C₃⋊D₃×C₂₃	—	7	1	no	maximal, Hall
9	C₂×C₅×D₇×C₂₃	—	9	1	no	Hall
10	C₂₃×C₃⋊D₂₁	C₂×C₅	1	2	yes	direct product factor
11	C₂×C₃²×C₇×C₂₃	C₂×C₅	1	1	yes	characteristic, complemented
12	C₃×C₅×C₇×C₂₃	C₂×D₃	1	4	yes	complemented
13	C₅×C₃⋊D₃×C₂₃	—	7	2	no	—
14	C₂×C₃²×C₅×C₂₃	D₇	1	1	yes	characteristic, complemented
15	C₂×C₂₃×D₂₁	—	3	4	no	—
16	C₂×C₅×C₇×C₂₃	C₃⋊D₃	1	1	yes	characteristic, complemented
17	C₅×D₇×C₂₃	—	9	2	no	—
18	C₃²×C₇×C₂₃	C₂²×C₅	1	1	yes	characteristic, complemented, Hall
19	C₂×C₅×D₃×C₂₃	—	21	4	no	—
20	C₂×C₅×C₃⋊D₂₁	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₃²×C₅×C₂₃	C₂×D₇	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃×C₇×C₂₃	C₅×D₃	1	4	yes	complemented
23	C₂₃×D₂₁	—	3	8	no	—
24	C₂×C₃⋊D₃×C₂₃	—	7	1	no	Hall
25	C₅×C₇×C₂₃	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
26	C₂×C₃×C₅×C₂₃	D₂₁	1	4	yes	complemented
27	C₅×D₃×C₂₃	—	21	8	no	—
28	C₂×D₇×C₂₃	—	9	1	no	Hall
29	C₂×C₃²×C₅×C₇	C₂×C₂₃	1	1	yes	characteristic, complemented
30	C₅×C₃⋊D₂₁	C₂×C₂₃	1	2	yes	direct product factor
31	C₃×C₇×C₂₃	C₂×C₅×D₃	1	4	yes	complemented
32	C₂²×C₅×C₂₃	—	63	1	no	Hall
33	C₂×C₅×D₂₁	—	3	4	no	—
34	C₂×C₃²×C₂₃	C₅×D₇	1	1	yes	characteristic, complemented
35	C₃⋊D₃×C₂₃	—	7	2	no	—
36	C₃×C₅×C₂₃	C₂×D₂₁	1	4	yes	complemented
37	C₂×C₇×C₂₃	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
38	D₇×C₂₃	—	9	2	no	—
39	C₃²×C₅×C₇	C₂²×C₂₃	1	1	yes	characteristic, complemented, Hall
40	C₂×D₃×C₂₃	—	21	4	no	—
41	C₂×C₃⋊D₂₁	C₅×C₂₃	1	1	yes	characteristic, direct product factor, Hall
42	C₂×C₅×C₂₃	—	63	2	no	—
43	C₂×C₅×C₂₃	C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
44	C₂×C₃×C₅×C₇	D₃×C₂₃	1	4	yes	complemented
45	C₅×D₂₁	—	3	8	no	—
46	C₃²×C₂₃	C₂×C₅×D₇	1	1	yes	characteristic, complemented, Hall
47	C₂×C₅×C₃⋊D₃	—	7	1	no	Hall
48	C₇×C₂₃	C₂×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented, Hall
49	C₂×C₅×D₇	—	9	1	no	Hall
50	C₂×C₃×C₂₃	C₅×D₂₁	1	4	yes	complemented
51	D₃×C₂₃	—	21	8	no	—
52	C₂×C₃²×C₇	C₂×C₅×C₂₃	1	1	yes	characteristic, complemented
53	C₃⋊D₂₁	C₂×C₅×C₂₃	1	2	yes	direct product factor
54	C₅×C₂₃	C₂×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Hall
55	C₃×C₅×C₇	C₂×D₃×C₂₃	1	4	yes	complemented
56	C₂²×C₂₃	—	63	1	no	Hall
57	C₂×C₃²×C₅	D₇×C₂₃	1	1	yes	characteristic, complemented
58	C₅×C₃⋊D₃	—	7	2	no	—
59	C₂×D₂₁	—	3	4	no	—
60	C₂×C₅×C₇	C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented
61	C₅×D₇	—	9	2	no	—
62	C₃×C₂₃	C₂×C₅×D₂₁	1	4	yes	complemented
63	C₃²×C₇	C₂²×C₅×C₂₃	1	1	yes	characteristic, complemented, Hall
64	C₂×C₅×D₃	—	21	4	no	—
65	C₂×C₂₃	—	63	2	no	—
66	C₂×C₂₃	C₅×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
67	C₃²×C₅	C₂×D₇×C₂₃	1	1	yes	characteristic, complemented, Hall
68	C₂×C₃×C₇	C₅×D₃×C₂₃	1	4	yes	complemented
69	D₂₁	—	3	8	no	—
70	C₂×C₃⋊D₃	—	7	1	no	Hall
71	C₅×C₇	C₂×C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented, Hall
72	C₂×C₃×C₅	C₂₃×D₂₁	1	4	yes	complemented
73	C₅×D₃	—	21	8	no	—
74	C₂×D₇	—	9	1	no	Hall
75	C₂₃	C₂×C₅×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
76	C₃×C₇	C₂×C₅×D₃×C₂₃	1	4	yes	complemented
77	C₂²×C₅	—	63	1	no	Hall
78	C₂×C₃²	C₅×D₇×C₂₃	1	1	yes	characteristic, complemented
79	C₃⋊D₃	—	7	2	no	—
80	C₃×C₅	C₂×C₂₃×D₂₁	1	4	yes	complemented
81	C₂×C₇	C₅×C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented
82	D₇	—	9	2	no	—
83	C₂×D₃	—	21	4	no	—
84	C₂×C₅	—	63	2	no	—
85	C₂×C₅	C₂₃×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor
86	C₃²	C₂×C₅×D₇×C₂₃	1	1	yes	characteristic, complemented, Sylow
87	C₇	C₂×C₅×C₃⋊D₃×C₂₃	1	1	yes	characteristic, complemented, Sylow
88	C₂×C₃	C₅×C₂₃×D₂₁	1	4	yes	complemented
89	D₃	—	21	8	no	—
90	C₅	C₂×C₂₃×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor, Sylow
91	C₂²	—	63	1	no	Sylow
92	C₃	C₂×C₅×C₂₃×D₂₁	1	4	yes	complemented
93	C₂	—	63	2	no	—
94	C₂	C₅×C₂₃×C₃⋊D₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₅×C₂₃	C₃⋊D₂₁
commutator, cosocle, hypocenter	C₃²×C₇	C₂²×C₅×C₂₃
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅×C₇×C₂₃	C₂
LCS	G ▷ C₃²×C₇
UCS	C₁ ◁ C₂×C₅×C₂₃

Complements

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

N	H ≅ G/N	type
1. C₅×C₂₃×C₃⋊D₂₁	C₂	direct (N × H)
2. C₂×C₃²×C₅×C₇×C₂₃	C₂	semidirect
4. C₃²×C₅×C₇×C₂₃	C₂²	semidirect
5. C₂×C₂₃×C₃⋊D₂₁	C₅	direct (N × H)
7. C₂×C₃×C₅×C₇×C₂₃	D₃	semidirect
10. C₂₃×C₃⋊D₂₁	C₂×C₅	direct (N × H)
11. C₂×C₃²×C₇×C₂₃	C₂×C₅	semidirect
12. C₃×C₅×C₇×C₂₃	C₂×D₃	semidirect
14. C₂×C₃²×C₅×C₂₃	D₇	semidirect
16. C₂×C₅×C₇×C₂₃	C₃⋊D₃	semidirect
18. C₃²×C₇×C₂₃	C₂²×C₅	semidirect
20. C₂×C₅×C₃⋊D₂₁	C₂₃	direct (N × H)
21. C₃²×C₅×C₂₃	C₂×D₇	semidirect
22. C₂×C₃×C₇×C₂₃	C₅×D₃	semidirect
25. C₅×C₇×C₂₃	C₂×C₃⋊D₃	semidirect
26. C₂×C₃×C₅×C₂₃	D₂₁	semidirect
29. C₂×C₃²×C₅×C₇	C₂×C₂₃	semidirect
30. C₅×C₃⋊D₂₁	C₂×C₂₃	direct (N × H)
31. C₃×C₇×C₂₃	C₂×C₅×D₃	semidirect
34. C₂×C₃²×C₂₃	C₅×D₇	semidirect
36. C₃×C₅×C₂₃	C₂×D₂₁	semidirect
37. C₂×C₇×C₂₃	C₅×C₃⋊D₃	semidirect
39. C₃²×C₅×C₇	C₂²×C₂₃	semidirect
41. C₂×C₃⋊D₂₁	C₅×C₂₃	direct (N × H)
43. C₂×C₅×C₂₃	C₃⋊D₂₁	direct (N × H)
44. C₂×C₃×C₅×C₇	D₃×C₂₃	semidirect
46. C₃²×C₂₃	C₂×C₅×D₇	semidirect
48. C₇×C₂₃	C₂×C₅×C₃⋊D₃	semidirect
50. C₂×C₃×C₂₃	C₅×D₂₁	semidirect
52. C₂×C₃²×C₇	C₂×C₅×C₂₃	semidirect
53. C₃⋊D₂₁	C₂×C₅×C₂₃	direct (N × H)
54. C₅×C₂₃	C₂×C₃⋊D₂₁	direct (N × H)
55. C₃×C₅×C₇	C₂×D₃×C₂₃	semidirect
57. C₂×C₃²×C₅	D₇×C₂₃	semidirect
60. C₂×C₅×C₇	C₃⋊D₃×C₂₃	semidirect
62. C₃×C₂₃	C₂×C₅×D₂₁	semidirect
63. C₃²×C₇	C₂²×C₅×C₂₃	semidirect
66. C₂×C₂₃	C₅×C₃⋊D₂₁	direct (N × H)
67. C₃²×C₅	C₂×D₇×C₂₃	semidirect
68. C₂×C₃×C₇	C₅×D₃×C₂₃	semidirect
71. C₅×C₇	C₂×C₃⋊D₃×C₂₃	semidirect
72. C₂×C₃×C₅	C₂₃×D₂₁	semidirect
75. C₂₃	C₂×C₅×C₃⋊D₂₁	direct (N × H)
76. C₃×C₇	C₂×C₅×D₃×C₂₃	semidirect
78. C₂×C₃²	C₅×D₇×C₂₃	semidirect
80. C₃×C₅	C₂×C₂₃×D₂₁	semidirect
81. C₂×C₇	C₅×C₃⋊D₃×C₂₃	semidirect
85. C₂×C₅	C₂₃×C₃⋊D₂₁	direct (N × H)
86. C₃²	C₂×C₅×D₇×C₂₃	semidirect
87. C₇	C₂×C₅×C₃⋊D₃×C₂₃	semidirect
88. C₂×C₃	C₅×C₂₃×D₂₁	semidirect
90. C₅	C₂×C₂₃×C₃⋊D₂₁	direct (N × H)
92. C₃	C₂×C₅×C₂₃×D₂₁	semidirect
94. C₂	C₅×C₂₃×C₃⋊D₂₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×C₂₃×C₃⋊D₂₁	2
C₂×C₃²×C₅×C₇×C₂₃	2
C₂×C₅×C₂₃×D₂₁	3
C₂×C₂₃×C₃⋊D₂₁	5
C₂×C₅×C₃⋊D₃×C₂₃	7
C₂×C₅×C₃⋊D₂₁	23

Subgroups — C2×C5×C23×C3⋊D21 #44394679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×C₂₃×C₃⋊D₂₁ #44394679