Subgroups — C₂×#1201 #6784

Order 240.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Dic₁₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#1201	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₂²⋊D₅	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
7	C₂×C₅×D₃	—	2	2	no	—
8	C₂×C₅×D₃	C₂²	1	2	yes	complemented
9	C₂×C₃×D₅	—	2	2	no	—
10	C₂×C₃×D₅	C₂²	1	2	yes	complemented
11	Dic₁₅	C₂²	1	2	yes	complemented
12	C₂×#67	—	5	1	no	maximal, Hall
13	C₂³×C₅	—	3	1	no	—
14	C₂²×D₅	D₃	1	1	yes	characteristic, complemented
15	C₂²⋊D₅	—	3	4	no	—
16	C₂×Dic₅	—	3	1	no	—
17	C₂×C₃×C₅	D₄	1	2	yes	complemented
18	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
19	C₃×D₅	—	2	2	no	—
20	C₅×D₃	—	2	2	no	—
21	C₂³×C₃	—	5	1	no	—
22	C₂²×D₃	D₅	1	1	yes	characteristic, complemented
23	#67	—	5	4	no	—
24	C₂×Dic₃	—	5	1	no	—
25	C₂²×C₅	—	3	2	no	—
26	C₂²×C₅	—	6	2	no	—
27	C₂²×C₅	C₂×D₃	1	1	yes	characteristic
28	C₂×D₅	—	2	2	no	—
29	C₂×D₅	C₂×D₃	1	2	yes	complemented
30	Dic₅	—	3	2	no	—
31	C₂×D₄	—	15	1	no	Sylow
32	C₃×C₅	C₂×D₄	1	1	yes	characteristic, complemented, Hall
33	C₂²×C₃	—	5	2	no	—
34	C₂²×C₃	—	10	2	no	—
35	C₂²×C₃	C₂×D₅	1	1	yes	characteristic
36	C₂×D₃	—	2	2	no	—
37	C₂×D₃	C₂×D₅	1	2	yes	complemented
38	Dic₃	—	5	2	no	—
39	C₂×C₅	—	6	2	no	—
40	C₂×C₅	#67	1	2	yes	complemented
41	C₂×C₅	C₂²×D₃	1	1	yes	characteristic
42	D₅	—	2	2	no	—
43	C₂³	—	3	1	no	—
44	C₂³	—	5	1	no	—
45	D₄	—	15	4	no	—
46	C₂×C₄	—	15	1	no	—
47	C₂×C₃	—	10	2	no	—
48	C₂×C₃	C₂²⋊D₅	1	2	yes	complemented
49	C₂×C₃	C₂²×D₅	1	1	yes	characteristic
50	D₃	—	2	2	no	—
51	C₅	C₂×#67	1	1	yes	characteristic, complemented, Sylow
52	C₂²	—	3	2	no	—
53	C₂²	—	5	2	no	—
54	C₂²	—	6	2	no	—
55	C₂²	—	10	2	no	—
56	C₂²	D₃×D₅	1	1	yes	characteristic
57	C₄	—	15	2	no	—
58	C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic, complemented, Sylow
59	C₂	—	6	2	no	—
60	C₂	—	10	2	no	—
61	C₂	#1201	1	2	yes	direct product factor
62	C₂	C₂×D₃×D₅	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²	D₃×D₅
commutator, cosocle	C₂×C₃×C₅	C₂³
Frattini	C₂	C₂×D₃×D₅
Fitting, socle	C₂²×C₃×C₅	C₂²
hypocenter	C₃×C₅	C₂×D₄
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×D₃	C₂	semidirect
2. C₂²×C₃×D₅	C₂	semidirect
3. C₂×Dic₁₅	C₂	semidirect
4. #1201	C₂	direct (N × H)
8. C₂×C₅×D₃	C₂²	semidirect
10. C₂×C₃×D₅	C₂²	semidirect
11. Dic₁₅	C₂²	semidirect
14. C₂²×D₅	D₃	semidirect
17. C₂×C₃×C₅	D₄	semidirect
22. C₂²×D₃	D₅	semidirect
29. C₂×D₅	C₂×D₃	semidirect
32. C₃×C₅	C₂×D₄	semidirect
37. C₂×D₃	C₂×D₅	semidirect
40. C₂×C₅	#67	semidirect
48. C₂×C₃	C₂²⋊D₅	semidirect
51. C₅	C₂×#67	semidirect
58. C₃	C₂×C₂²⋊D₅	semidirect
61. C₂	#1201	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×C₅×D₃	2
C₂²×C₃×D₅	2
C₂×Dic₁₅	2
#1201	2
C₂×C₂²⋊D₅	3
C₂×#67	5

Subgroups — C2×#1201 #6784

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1201 #6784