Subgroups — C₂²×C₃×C₂²⋊D₅ #92073

Order 480.

472 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₃×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₃×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₂²⋊D₅	C₂	1	12	yes	maximal, direct product factor
4	C₂²×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊D₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₅	—	2	4	no	—
7	C₂³×C₃×C₅	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₅	C₂²	1	6	yes	complemented
9	C₂²×C₃×D₅	—	2	4	no	—
10	C₂²×C₃×D₅	C₂²	1	6	yes	complemented
11	C₃×C₂²⋊D₅	C₂²	1	16	yes	direct product factor
12	C₂×C₃×Dic₅	C₂²	1	6	yes	complemented
13	C₂²×C₃×D₄	—	5	1	no	maximal, Hall
14	C₂⁴×C₅	C₂×C₃	1	1	yes	characteristic, complemented
15	C₂³×D₅	C₂×C₃	1	1	yes	characteristic, complemented
16	C₂×C₂²⋊D₅	C₂×C₃	1	12	yes	direct product factor
17	C₂²×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂²×C₃×C₅	—	2	12	no	—
19	C₂²×C₃×C₅	D₄	1	4	yes	complemented
20	C₂²×C₃×C₅	C₂³	1	3	yes	—
21	C₂²×C₃×C₅	C₂³	1	4	yes	complemented
22	C₂×C₃×D₅	—	2	12	no	—
23	C₂×C₃×D₅	C₂³	1	4	yes	complemented
24	C₃×Dic₅	C₂³	1	4	yes	complemented
25	C₂⁴×C₃	—	5	1	no	—
26	C₂⁴×C₃	D₅	1	1	yes	characteristic, complemented
27	C₂×C₃×D₄	—	5	12	no	—
28	C₂²×C₃×C₄	—	5	1	no	—
29	C₂³×C₅	—	2	4	no	—
30	C₂³×C₅	C₂²×C₃	1	1	yes	characteristic
31	C₂³×C₅	C₂²×C₃	1	6	yes	complemented
32	C₂²×D₅	—	2	4	no	—
33	C₂²×D₅	C₂²×C₃	1	6	yes	complemented
34	C₂²⋊D₅	C₂²×C₃	1	16	yes	direct product factor
35	C₂×Dic₅	C₂²×C₃	1	6	yes	complemented
36	C₂²×D₄	—	5	1	no	Sylow
37	C₂×C₃×C₅	—	2	4	no	—
38	C₂×C₃×C₅	C₂×D₄	1	6	yes	complemented
39	C₂×C₃×C₅	C₂⁴	1	1	yes	characteristic
40	C₃×D₅	—	2	4	no	—
41	C₂³×C₃	—	2	4	no	—
42	C₂³×C₃	—	5	6	no	—
43	C₂³×C₃	—	10	4	no	—
44	C₂³×C₃	C₂×D₅	1	1	yes	characteristic
45	C₂³×C₃	C₂×D₅	1	6	yes	complemented
46	C₃×D₄	—	5	16	no	—
47	C₂×C₃×C₄	—	5	6	no	—
48	C₂²×C₅	—	2	12	no	—
49	C₂²×C₅	C₃×D₄	1	4	yes	complemented
50	C₂²×C₅	C₂³×C₃	1	3	yes	—
51	C₂²×C₅	C₂³×C₃	1	4	yes	complemented
52	C₂×D₅	—	2	12	no	—
53	C₂×D₅	C₂³×C₃	1	4	yes	complemented
54	Dic₅	C₂³×C₃	1	4	yes	complemented
55	C₂⁴	—	5	1	no	—
56	C₂⁴	C₃×D₅	1	1	yes	characteristic, complemented
57	C₂×D₄	—	5	12	no	—
58	C₂²×C₄	—	5	1	no	—
59	C₃×C₅	C₂²×D₄	1	1	yes	characteristic, complemented, Hall
60	C₂²×C₃	—	2	12	no	—
61	C₂²×C₃	—	5	4	no	—
62	C₂²×C₃	—	10	12	no	—
63	C₂²×C₃	C₂²⋊D₅	1	4	yes	direct product factor
64	C₂²×C₃	C₂²×D₅	1	3	yes	—
65	C₂²×C₃	C₂²×D₅	1	4	yes	complemented
66	C₃×C₄	—	5	4	no	—
67	C₂×C₅	—	2	4	no	—
68	C₂×C₅	C₂×C₃×D₄	1	6	yes	complemented
69	C₂×C₅	C₂⁴×C₃	1	1	yes	characteristic
70	D₅	—	2	4	no	—
71	C₂³	—	2	4	no	—
72	C₂³	—	5	6	no	—
73	C₂³	—	10	4	no	—
74	C₂³	C₂×C₃×D₅	1	1	yes	characteristic
75	C₂³	C₂×C₃×D₅	1	6	yes	complemented
76	D₄	—	5	16	no	—
77	C₂×C₄	—	5	6	no	—
78	C₂×C₃	—	2	4	no	—
79	C₂×C₃	—	10	4	no	—
80	C₂×C₃	C₂×C₂²⋊D₅	1	6	yes	direct product factor
81	C₂×C₃	C₂³×D₅	1	1	yes	characteristic
82	C₅	C₂²×C₃×D₄	1	1	yes	characteristic, complemented, Sylow
83	C₂²	—	2	12	no	—
84	C₂²	—	5	4	no	—
85	C₂²	—	10	12	no	—
86	C₂²	C₃×C₂²⋊D₅	1	4	yes	direct product factor
87	C₂²	C₂²×C₃×D₅	1	3	yes	—
88	C₂²	C₂²×C₃×D₅	1	4	yes	complemented
89	C₄	—	5	4	no	—
90	C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic, direct product factor, Sylow
91	C₂	—	2	4	no	—
92	C₂	—	10	4	no	—
93	C₂	C₂×C₃×C₂²⋊D₅	1	6	yes	direct product factor
94	C₂	C₂³×C₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂×D₅
commutator, cosocle	C₂×C₅	C₂⁴×C₃
Frattini	C₂	C₂³×C₃×D₅
Fitting	C₂⁴×C₃×C₅	C₂
socle	C₂³×C₃×C₅	C₂²
hypercenter	C₂⁴×C₃	D₅
hypocenter	C₅	C₂²×C₃×D₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂⁴×C₃

Complements

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

N	H ≅ G/N	type
1. C₂⁴×C₃×C₅	C₂	semidirect
2. C₂³×C₃×D₅	C₂	semidirect
3. C₂×C₃×C₂²⋊D₅	C₂	direct (N × H)
4. C₂²×C₃×Dic₅	C₂	semidirect
5. C₂²×C₂²⋊D₅	C₃	direct (N × H)
8. C₂³×C₃×C₅	C₂²	semidirect
10. C₂²×C₃×D₅	C₂²	semidirect
11. C₃×C₂²⋊D₅	C₂²	direct (N × H)
12. C₂×C₃×Dic₅	C₂²	semidirect
14. C₂⁴×C₅	C₂×C₃	semidirect
15. C₂³×D₅	C₂×C₃	semidirect
16. C₂×C₂²⋊D₅	C₂×C₃	direct (N × H)
17. C₂²×Dic₅	C₂×C₃	semidirect
19. C₂²×C₃×C₅	D₄	semidirect
21. C₂²×C₃×C₅	C₂³	semidirect
23. C₂×C₃×D₅	C₂³	semidirect
24. C₃×Dic₅	C₂³	semidirect
26. C₂⁴×C₃	D₅	semidirect
31. C₂³×C₅	C₂²×C₃	semidirect
33. C₂²×D₅	C₂²×C₃	semidirect
34. C₂²⋊D₅	C₂²×C₃	direct (N × H)
35. C₂×Dic₅	C₂²×C₃	semidirect
38. C₂×C₃×C₅	C₂×D₄	semidirect
45. C₂³×C₃	C₂×D₅	semidirect
49. C₂²×C₅	C₃×D₄	semidirect
51. C₂²×C₅	C₂³×C₃	semidirect
53. C₂×D₅	C₂³×C₃	semidirect
54. Dic₅	C₂³×C₃	semidirect
56. C₂⁴	C₃×D₅	semidirect
59. C₃×C₅	C₂²×D₄	semidirect
63. C₂²×C₃	C₂²⋊D₅	direct (N × H)
65. C₂²×C₃	C₂²×D₅	semidirect
68. C₂×C₅	C₂×C₃×D₄	semidirect
75. C₂³	C₂×C₃×D₅	semidirect
80. C₂×C₃	C₂×C₂²⋊D₅	direct (N × H)
82. C₅	C₂²×C₃×D₄	semidirect
86. C₂²	C₃×C₂²⋊D₅	direct (N × H)
88. C₂²	C₂²×C₃×D₅	semidirect
90. C₃	C₂²×C₂²⋊D₅	direct (N × H)
93. C₂	C₂×C₃×C₂²⋊D₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₃×C₅	2
C₂³×C₃×D₅	2
C₂×C₃×C₂²⋊D₅	2
C₂²×C₃×Dic₅	2
C₂²×C₂²⋊D₅	3
C₂²×C₃×D₄	5

Subgroups — C22×C3×C22⋊D5 #92073

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₂²⋊D₅ #92073