Subgroups — C₂²×C₅×C₃⋊D₁₅ #14268548

Order 1800.

444 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×C₃⋊D₁₅	C₂	1	6	yes	maximal, direct product factor
3	C₂²×C₅×D₁₅	—	3	4	no	maximal
4	C₂×C₃²×C₅²	C₂²	1	3	yes	complemented
5	C₅×C₃⋊D₁₅	C₂²	1	4	yes	direct product factor
6	C₂²×C₃⋊D₁₅	C₅	1	1	yes	maximal, characteristic, direct product factor
7	C₂²×C₅×C₃⋊D₃	—	5	1	no	maximal
8	C₂²×C₃×C₅²	D₃	1	4	yes	complemented
9	C₂×C₅×D₁₅	—	3	24	no	—
10	C₃²×C₅²	C₂³	1	1	yes	characteristic, complemented, Hall
11	C₂²×C₅×D₅	—	9	1	no	Hall
12	C₂²×C₃²×C₅	—	2	2	no	—
13	C₂²×C₃²×C₅	D₅	1	1	yes	characteristic, complemented
14	C₂²×C₃²×C₅	C₂×C₅	1	1	yes	characteristic, complemented
15	C₂×C₃⋊D₁₅	C₂×C₅	1	6	yes	direct product factor
16	C₂×C₅×C₃⋊D₃	—	5	6	no	—
17	C₂×C₃×C₅²	C₂×D₃	1	12	yes	complemented
18	C₅×D₁₅	—	3	16	no	—
19	C₂²×D₁₅	—	3	4	no	—
20	C₂²×C₅×D₃	—	15	4	no	—
21	C₂²×C₅²	C₃⋊D₃	1	1	yes	characteristic, complemented
22	C₂×C₅×D₅	—	9	6	no	—
23	C₂×C₃²×C₅	—	2	6	no	—
24	C₂×C₃²×C₅	C₂×D₅	1	3	yes	complemented
25	C₂×C₃²×C₅	C₂²×C₅	1	3	yes	complemented
26	C₃⋊D₁₅	C₂²×C₅	1	4	yes	direct product factor
27	C₅×C₃⋊D₃	—	5	4	no	—
28	C₃×C₅²	C₂²×D₃	1	4	yes	complemented
29	C₂²×C₃⋊D₃	—	5	1	no	Hall
30	C₂²×C₃×C₅	—	2	8	no	—
31	C₂²×C₃×C₅	C₅×D₃	1	4	yes	complemented
32	C₂²×C₃×C₅	D₁₅	1	4	yes	complemented
33	C₂×D₁₅	—	3	24	no	—
34	C₂×C₅×D₃	—	15	24	no	—
35	C₂×C₅²	C₂×C₃⋊D₃	1	3	yes	complemented
36	C₅×D₅	—	9	4	no	—
37	C₃²×C₅	—	2	2	no	—
38	C₃²×C₅	C₂²×D₅	1	1	yes	characteristic, complemented
39	C₃²×C₅	C₂³×C₅	1	1	yes	characteristic, complemented
40	C₂³×C₅	—	45	1	no	—
41	C₂²×D₅	—	9	1	no	—
42	C₂²×C₃²	C₅×D₅	1	1	yes	characteristic, complemented
43	C₂×C₃⋊D₃	—	5	6	no	—
44	C₂×C₃×C₅	—	2	24	no	—
45	C₂×C₃×C₅	C₂×C₅×D₃	1	12	yes	complemented
46	C₂×C₃×C₅	C₂×D₁₅	1	12	yes	complemented
47	D₁₅	—	3	16	no	—
48	C₅×D₃	—	15	16	no	—
49	C₅²	C₂²×C₃⋊D₃	1	1	yes	characteristic, complemented, Sylow
50	C₂²×D₃	—	15	4	no	—
51	C₂²×C₅	—	2	2	no	—
52	C₂²×C₅	—	45	6	no	—
53	C₂²×C₅	C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
54	C₂²×C₅	C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
55	C₂×D₅	—	9	6	no	—
56	C₂×C₃²	C₂×C₅×D₅	1	3	yes	complemented
57	C₃⋊D₃	—	5	4	no	—
58	C₃×C₅	—	2	8	no	—
59	C₃×C₅	C₂²×C₅×D₃	1	4	yes	complemented
60	C₃×C₅	C₂²×D₁₅	1	4	yes	complemented
61	C₂²×C₃	C₅×D₁₅	1	4	yes	complemented
62	C₂×D₃	—	15	24	no	—
63	C₂×C₅	—	2	6	no	—
64	C₂×C₅	—	45	4	no	—
65	C₂×C₅	C₂×C₅×C₃⋊D₃	1	3	yes	complemented
66	C₂×C₅	C₂×C₃⋊D₁₅	1	3	yes	direct product factor
67	D₅	—	9	4	no	—
68	C₃²	C₂²×C₅×D₅	1	1	yes	characteristic, complemented, Sylow
69	C₂³	—	45	1	no	Sylow
70	C₂×C₃	C₂×C₅×D₁₅	1	12	yes	complemented
71	D₃	—	15	16	no	—
72	C₅	—	2	2	no	—
73	C₅	C₂²×C₅×C₃⋊D₃	1	1	yes	characteristic, complemented
74	C₅	C₂²×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
75	C₂²	—	45	6	no	—
76	C₂²	C₅×C₃⋊D₁₅	1	1	yes	characteristic, direct product factor
77	C₃	C₂²×C₅×D₁₅	1	4	yes	complemented
78	C₂	—	45	4	no	—
79	C₂	C₂×C₅×C₃⋊D₁₅	1	3	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂²×C₅	C₃⋊D₁₅
commutator, cosocle, hypocenter	C₃²×C₅	C₂³×C₅
Frattini	C₁	G
Fitting, socle	C₂²×C₃²×C₅²	C₂
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂²×C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×C₅²	C₂	semidirect
2. C₂×C₅×C₃⋊D₁₅	C₂	direct (N × H)
4. C₂×C₃²×C₅²	C₂²	semidirect
5. C₅×C₃⋊D₁₅	C₂²	direct (N × H)
6. C₂²×C₃⋊D₁₅	C₅	direct (N × H)
8. C₂²×C₃×C₅²	D₃	semidirect
10. C₃²×C₅²	C₂³	semidirect
13. C₂²×C₃²×C₅	D₅	semidirect
14. C₂²×C₃²×C₅	C₂×C₅	semidirect
15. C₂×C₃⋊D₁₅	C₂×C₅	direct (N × H)
17. C₂×C₃×C₅²	C₂×D₃	semidirect
21. C₂²×C₅²	C₃⋊D₃	semidirect
24. C₂×C₃²×C₅	C₂×D₅	semidirect
25. C₂×C₃²×C₅	C₂²×C₅	semidirect
26. C₃⋊D₁₅	C₂²×C₅	direct (N × H)
28. C₃×C₅²	C₂²×D₃	semidirect
31. C₂²×C₃×C₅	C₅×D₃	semidirect
32. C₂²×C₃×C₅	D₁₅	semidirect
35. C₂×C₅²	C₂×C₃⋊D₃	semidirect
38. C₃²×C₅	C₂²×D₅	semidirect
39. C₃²×C₅	C₂³×C₅	semidirect
42. C₂²×C₃²	C₅×D₅	semidirect
45. C₂×C₃×C₅	C₂×C₅×D₃	semidirect
46. C₂×C₃×C₅	C₂×D₁₅	semidirect
49. C₅²	C₂²×C₃⋊D₃	semidirect
53. C₂²×C₅	C₅×C₃⋊D₃	semidirect
54. C₂²×C₅	C₃⋊D₁₅	direct (N × H)
56. C₂×C₃²	C₂×C₅×D₅	semidirect
59. C₃×C₅	C₂²×C₅×D₃	semidirect
60. C₃×C₅	C₂²×D₁₅	semidirect
61. C₂²×C₃	C₅×D₁₅	semidirect
65. C₂×C₅	C₂×C₅×C₃⋊D₃	semidirect
66. C₂×C₅	C₂×C₃⋊D₁₅	direct (N × H)
68. C₃²	C₂²×C₅×D₅	semidirect
70. C₂×C₃	C₂×C₅×D₁₅	semidirect
73. C₅	C₂²×C₅×C₃⋊D₃	semidirect
74. C₅	C₂²×C₃⋊D₁₅	direct (N × H)
76. C₂²	C₅×C₃⋊D₁₅	direct (N × H)
77. C₃	C₂²×C₅×D₁₅	semidirect
79. C₂	C₂×C₅×C₃⋊D₁₅	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×C₅²	2
C₂×C₅×C₃⋊D₁₅	2
C₂²×C₅×D₁₅	3
C₂²×C₃⋊D₁₅	5
C₂²×C₅×C₃⋊D₃	5

Subgroups — C22×C5×C3⋊D15 #14268548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×C₃⋊D₁₅ #14268548