Subgroups — C₂²×C₃×C₅×Dic₅ #11925683

Order 1200.

280 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×Dic₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₅×Dic₅	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₂²×C₃×C₅²	C₄	1	4	yes	complemented
5	C₂²×C₃×C₅²	C₂²	1	3	yes	—
6	C₃×C₅×Dic₅	C₂²	1	4	yes	direct product factor
7	C₂²×C₃×C₄×C₅	—	5	1	no	maximal
8	C₂²×C₃×Dic₅	C₅	1	1	yes	maximal, characteristic, direct product factor
9	C₂³×C₅²	C₂×C₃	1	1	yes	characteristic
10	C₂×C₅×Dic₅	C₂×C₃	1	6	yes	direct product factor
11	C₂×C₃×C₅²	C₂×C₄	1	6	yes	complemented
12	C₂×C₃×C₅²	C₂³	1	1	yes	characteristic
13	C₂³×C₃×C₅	—	2	2	no	—
14	C₂³×C₃×C₅	D₅	1	1	yes	characteristic
15	C₂³×C₃×C₅	C₂×C₅	1	1	yes	characteristic
16	C₂×C₃×C₄×C₅	—	5	6	no	—
17	C₂×C₃×Dic₅	C₂×C₅	1	6	yes	direct product factor
18	C₂²×C₅²	C₃×C₄	1	4	yes	complemented
19	C₂²×C₅²	C₂²×C₃	1	3	yes	—
20	C₅×Dic₅	C₂²×C₃	1	4	yes	direct product factor
21	C₂²×C₄×C₅	—	5	1	no	—
22	C₂²×Dic₅	C₃×C₅	1	1	yes	characteristic, direct product factor
23	C₃×C₅²	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
24	C₂²×C₃×C₅	—	2	8	no	—
25	C₂²×C₃×C₅	—	2	6	no	—
26	C₂²×C₃×C₅	Dic₅	1	4	yes	direct product factor
27	C₂²×C₃×C₅	C₄×C₅	1	4	yes	complemented
28	C₂²×C₃×C₅	C₂×D₅	1	3	yes	—
29	C₂²×C₃×C₅	C₂²×C₅	1	3	yes	—
30	C₃×C₄×C₅	—	5	4	no	—
31	C₃×Dic₅	C₂²×C₅	1	4	yes	direct product factor
32	C₂×C₅²	C₂×C₃×C₄	1	6	yes	complemented
33	C₂×C₅²	C₂³×C₃	1	1	yes	characteristic
34	C₂²×C₃×C₄	—	5	1	no	Hall
35	C₂³×C₅	—	2	2	no	—
36	C₂³×C₅	C₃×D₅	1	1	yes	characteristic
37	C₂³×C₅	C₂×C₃×C₅	1	1	yes	characteristic
38	C₂×C₄×C₅	—	5	6	no	—
39	C₂×Dic₅	C₂×C₃×C₅	1	6	yes	direct product factor
40	C₂×C₃×C₅	—	2	12	no	—
41	C₂×C₃×C₅	—	2	2	no	—
42	C₂×C₃×C₅	C₂×Dic₅	1	6	yes	direct product factor
43	C₂×C₃×C₅	C₂×C₄×C₅	1	6	yes	complemented
44	C₂×C₃×C₅	C₂²×D₅	1	1	yes	characteristic
45	C₂×C₃×C₅	C₂³×C₅	1	1	yes	characteristic
46	C₅²	C₂²×C₃×C₄	1	1	yes	characteristic, complemented, Sylow
47	C₂³×C₃	C₅×D₅	1	1	yes	characteristic
48	C₂×C₃×C₄	—	5	6	no	—
49	C₂²×C₅	—	2	8	no	—
50	C₂²×C₅	—	2	6	no	—
51	C₂²×C₅	C₃×Dic₅	1	4	yes	direct product factor
52	C₂²×C₅	C₃×C₄×C₅	1	4	yes	complemented
53	C₂²×C₅	C₂×C₃×D₅	1	3	yes	—
54	C₂²×C₅	C₂²×C₃×C₅	1	3	yes	—
55	C₄×C₅	—	5	4	no	—
56	Dic₅	C₂²×C₃×C₅	1	4	yes	direct product factor
57	C₂²×C₄	—	5	1	no	Sylow
58	C₃×C₅	—	2	2	no	—
59	C₃×C₅	C₂²×Dic₅	1	1	yes	characteristic, direct product factor
60	C₃×C₅	C₂²×C₄×C₅	1	1	yes	characteristic, complemented
61	C₂²×C₃	C₅×Dic₅	1	4	yes	direct product factor
62	C₂²×C₃	C₂×C₅×D₅	1	3	yes	—
63	C₃×C₄	—	5	4	no	—
64	C₂×C₅	—	2	12	no	—
65	C₂×C₅	—	2	2	no	—
66	C₂×C₅	C₂×C₃×Dic₅	1	6	yes	direct product factor
67	C₂×C₅	C₂×C₃×C₄×C₅	1	6	yes	complemented
68	C₂×C₅	C₂²×C₃×D₅	1	1	yes	characteristic
69	C₂×C₅	C₂³×C₃×C₅	1	1	yes	characteristic
70	C₂³	C₃×C₅×D₅	1	1	yes	characteristic
71	C₂×C₄	—	5	6	no	—
72	C₂×C₃	C₂×C₅×Dic₅	1	6	yes	direct product factor
73	C₂×C₃	C₂²×C₅×D₅	1	1	yes	characteristic
74	C₅	—	2	2	no	—
75	C₅	C₂²×C₃×Dic₅	1	1	yes	characteristic, direct product factor
76	C₅	C₂²×C₃×C₄×C₅	1	1	yes	characteristic, complemented
77	C₂²	C₃×C₅×Dic₅	1	4	yes	direct product factor
78	C₂²	C₂×C₃×C₅×D₅	1	3	yes	—
79	C₄	—	5	4	no	—
80	C₃	C₂²×C₅×Dic₅	1	1	yes	characteristic, direct product factor, Sylow
81	C₂	C₂×C₃×C₅×Dic₅	1	6	yes	direct product factor
82	C₂	C₂²×C₃×C₅×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³×C₃×C₅	D₅
commutator, hypocenter	C₅	C₂²×C₃×C₄×C₅
Frattini	C₂	C₂²×C₃×C₅×D₅
Fitting, socle, prime radical	C₂³×C₃×C₅²	C₂
cosocle	C₂×C₅	C₂³×C₃×C₅
LCS	G ▷ C₅
UCS	C₁ ◁ C₂³×C₃×C₅

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×Dic₅	C₂	direct (N × H)
3. C₂²×C₅×Dic₅	C₃	direct (N × H)
4. C₂²×C₃×C₅²	C₄	semidirect
6. C₃×C₅×Dic₅	C₂²	direct (N × H)
8. C₂²×C₃×Dic₅	C₅	direct (N × H)
10. C₂×C₅×Dic₅	C₂×C₃	direct (N × H)
11. C₂×C₃×C₅²	C₂×C₄	semidirect
17. C₂×C₃×Dic₅	C₂×C₅	direct (N × H)
18. C₂²×C₅²	C₃×C₄	semidirect
20. C₅×Dic₅	C₂²×C₃	direct (N × H)
22. C₂²×Dic₅	C₃×C₅	direct (N × H)
23. C₃×C₅²	C₂²×C₄	semidirect
26. C₂²×C₃×C₅	Dic₅	direct (N × H)
27. C₂²×C₃×C₅	C₄×C₅	semidirect
31. C₃×Dic₅	C₂²×C₅	direct (N × H)
32. C₂×C₅²	C₂×C₃×C₄	semidirect
39. C₂×Dic₅	C₂×C₃×C₅	direct (N × H)
42. C₂×C₃×C₅	C₂×Dic₅	direct (N × H)
43. C₂×C₃×C₅	C₂×C₄×C₅	semidirect
46. C₅²	C₂²×C₃×C₄	semidirect
51. C₂²×C₅	C₃×Dic₅	direct (N × H)
52. C₂²×C₅	C₃×C₄×C₅	semidirect
56. Dic₅	C₂²×C₃×C₅	direct (N × H)
59. C₃×C₅	C₂²×Dic₅	direct (N × H)
60. C₃×C₅	C₂²×C₄×C₅	semidirect
61. C₂²×C₃	C₅×Dic₅	direct (N × H)
66. C₂×C₅	C₂×C₃×Dic₅	direct (N × H)
67. C₂×C₅	C₂×C₃×C₄×C₅	semidirect
72. C₂×C₃	C₂×C₅×Dic₅	direct (N × H)
75. C₅	C₂²×C₃×Dic₅	direct (N × H)
76. C₅	C₂²×C₃×C₄×C₅	semidirect
77. C₂²	C₃×C₅×Dic₅	direct (N × H)
80. C₃	C₂²×C₅×Dic₅	direct (N × H)
81. C₂	C₂×C₃×C₅×Dic₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₅²	2
C₂×C₃×C₅×Dic₅	2
C₂²×C₅×Dic₅	3
C₂²×C₃×C₄×C₅	5
C₂²×C₃×Dic₅	5

Subgroups — C22×C3×C5×Dic5 #11925683

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×C₅×Dic₅ #11925683