Subgroups — C₂×D₅×C₃⋊D₃ #67222

Order 360.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, hypercenter	C₂	D₅×C₃⋊D₃
commutator, cosocle, hypocenter	C₃²×C₅	C₂³
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅	C₂²
LCS	G ▷ C₃²×C₅
UCS	C₁ ◁ C₂

Complements

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

N	H ≅ G/N	type
1. C₂×C₃⋊D₁₅	C₂	semidirect
2. C₂×C₅×C₃⋊D₃	C₂	semidirect
3. C₂×C₃²×D₅	C₂	semidirect
4. D₅×C₃⋊D₃	C₂	direct (N × H)
6. C₂×C₃²×C₅	C₂²	semidirect
7. C₃⋊D₁₅	C₂²	semidirect
8. C₅×C₃⋊D₃	C₂²	semidirect
9. C₃²×D₅	C₂²	semidirect
13. C₂×C₃×D₅	D₃	semidirect
15. C₃²×C₅	C₂³	semidirect
20. C₂×C₃⋊D₃	D₅	direct (N × H)
21. C₂×C₃×C₅	C₂×D₃	semidirect
23. C₃×D₅	C₂×D₃	semidirect
29. C₂×D₅	C₃⋊D₃	direct (N × H)
31. C₂×C₃²	C₂×D₅	semidirect
33. C₃⋊D₃	C₂×D₅	direct (N × H)
34. C₃×C₅	C₂²×D₃	semidirect
40. C₂×C₅	C₂×C₃⋊D₃	semidirect
42. D₅	C₂×C₃⋊D₃	direct (N × H)
43. C₃²	C₂²×D₅	semidirect
46. C₂×C₃	D₃×D₅	semidirect
49. C₅	C₂²×C₃⋊D₃	semidirect
54. C₃	C₂×D₃×D₅	semidirect
58. C₂	D₅×C₃⋊D₃	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃⋊D₁₅	2
C₂×C₅×C₃⋊D₃	2
C₂×C₃²×D₅	2
D₅×C₃⋊D₃	2
C₂×D₃×D₅	3
C₂²×C₃⋊D₃	5

Subgroups — C2×D5×C3⋊D3 #67222

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×D₅×C₃⋊D₃ #67222