Subgroups — C₄×D₃×D₅ #6774

Order 240.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃×D₅	C₂	1	1	yes	maximal, characteristic
2	C₄×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
5	#1200	C₂	1	1	yes	maximal, characteristic, complemented
6	D₃×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
7	D₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₅	—	3	1	no	maximal, Hall
9	C₂×D₁₅	C₂²	1	1	yes	characteristic
10	C₂×C₅×D₃	C₂²	1	1	yes	characteristic
11	C₂×C₃×D₅	C₂²	1	1	yes	characteristic
12	D₃×D₅	C₄	1	4	yes	direct product factor
13	C₃×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
14	Dic₁₅	C₂²	1	1	yes	characteristic, complemented
15	C₃×Dic₅	C₂²	1	1	yes	characteristic, complemented
16	C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₄×D₃	—	5	1	no	maximal, Hall
18	C₂²×D₅	—	3	1	no	—
19	C₂×C₄×C₅	—	3	1	no	—
20	C₂×Dic₅	—	3	1	no	—
21	C₄×D₅	—	3	1	no	—
22	C₄×D₅	—	3	1	no	—
23	C₄×D₅	—	3	1	no	—
24	C₄×D₅	D₃	1	1	yes	characteristic, direct product factor
25	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
26	D₁₅	C₂×C₄	1	2	yes	complemented
27	C₃×D₅	C₂×C₄	1	2	yes	complemented
28	C₅×D₃	C₂×C₄	1	2	yes	complemented
29	C₂²×D₃	—	5	1	no	—
30	C₂×C₃×C₄	—	5	1	no	—
31	C₂×Dic₃	—	5	1	no	—
32	C₄×D₃	—	5	1	no	—
33	C₄×D₃	—	5	1	no	—
34	C₄×D₃	—	5	1	no	—
35	C₄×D₃	D₅	1	1	yes	characteristic, direct product factor
36	C₂²×C₅	—	3	1	no	—
37	C₂×D₅	—	3	1	no	—
38	C₂×D₅	—	3	4	no	—
39	C₂×D₅	C₂×D₃	1	1	yes	characteristic
40	C₄×C₅	—	3	1	no	—
41	C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
42	Dic₅	—	3	1	no	—
43	Dic₅	C₂×D₃	1	1	yes	characteristic, complemented
44	C₂²×C₄	—	15	1	no	Sylow
45	C₃×C₅	C₂²×C₄	1	1	yes	characteristic, complemented, Hall
46	C₂²×C₃	—	5	1	no	—
47	C₂×D₃	—	5	1	no	—
48	C₂×D₃	—	5	4	no	—
49	C₂×D₃	C₂×D₅	1	1	yes	characteristic
50	C₃×C₄	—	5	1	no	—
51	C₃×C₄	C₂×D₅	1	1	yes	characteristic, complemented
52	Dic₃	—	5	1	no	—
53	Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
54	C₂×C₅	—	3	2	no	—
55	C₂×C₅	C₂²×D₃	1	1	yes	characteristic
56	D₅	—	3	2	no	—
57	D₅	C₄×D₃	1	2	yes	direct product factor
58	C₂³	—	15	1	no	—
59	C₂×C₄	—	3	1	no	—
60	C₂×C₄	—	5	1	no	—
61	C₂×C₄	—	15	1	no	—
62	C₂×C₄	—	15	1	no	—
63	C₂×C₄	—	15	1	no	—
64	C₂×C₄	—	15	1	no	—
65	C₂×C₃	—	5	2	no	—
66	C₂×C₃	C₂²×D₅	1	1	yes	characteristic
67	D₃	—	5	2	no	—
68	D₃	C₄×D₅	1	2	yes	direct product factor
69	C₅	C₂×C₄×D₃	1	1	yes	characteristic, complemented, Sylow
70	C₂²	—	3	1	no	—
71	C₂²	—	5	1	no	—
72	C₂²	—	15	4	no	—
73	C₂²	—	15	1	no	—
74	C₄	—	3	1	no	—
75	C₄	—	5	1	no	—
76	C₄	—	15	1	no	—
77	C₄	D₃×D₅	1	1	yes	characteristic, direct product factor
78	C₃	C₂×C₄×D₅	1	1	yes	characteristic, complemented, Sylow
79	C₂	—	3	2	no	—
80	C₂	—	5	2	no	—
81	C₂	—	15	2	no	—
82	C₂	C₂×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₄	D₃×D₅
commutator, hypocenter	C₃×C₅	C₂²×C₄
Frattini	C₂	C₂×D₃×D₅
Fitting	C₃×C₄×C₅	C₂²
socle, cosocle	C₂×C₃×C₅	C₂³
prime radical	C₂×D₃×D₅	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₄×D₁₅	C₂	semidirect
3. C₄×C₅×D₃	C₂	semidirect
4. C₃×C₄×D₅	C₂	semidirect
5. #1200	C₂	semidirect
6. D₃×Dic₅	C₂	semidirect
7. D₅×Dic₃	C₂	semidirect
12. D₃×D₅	C₄	direct (N × H)
13. C₃×C₄×C₅	C₂²	semidirect
14. Dic₁₅	C₂²	semidirect
15. C₃×Dic₅	C₂²	semidirect
16. C₅×Dic₃	C₂²	semidirect
24. C₄×D₅	D₃	direct (N × H)
26. D₁₅	C₂×C₄	semidirect
27. C₃×D₅	C₂×C₄	semidirect
28. C₅×D₃	C₂×C₄	semidirect
35. C₄×D₃	D₅	direct (N × H)
41. C₄×C₅	C₂×D₃	semidirect
43. Dic₅	C₂×D₃	semidirect
45. C₃×C₅	C₂²×C₄	semidirect
51. C₃×C₄	C₂×D₅	semidirect
53. Dic₃	C₂×D₅	semidirect
57. D₅	C₄×D₃	direct (N × H)
68. D₃	C₄×D₅	direct (N × H)
69. C₅	C₂×C₄×D₃	semidirect
77. C₄	D₃×D₅	direct (N × H)
78. C₃	C₂×C₄×D₅	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃×D₅	2
C₄×D₁₅	2
C₄×C₅×D₃	2
C₃×C₄×D₅	2
#1200	2
D₃×Dic₅	2
D₅×Dic₃	2
C₂×C₄×D₅	3
C₂×C₄×D₃	5

Subgroups — C4×D3×D5 #6774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×D₃×D₅ #6774