Subgroups — C₂×#1204 #6787

Order 240.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×Dic₅	C₂	1	1	yes	maximal, characteristic
4	#1204	C₂	1	4	yes	maximal, direct product factor
5	C₂×Dic₁₀	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅	C₂²	1	1	yes	characteristic
7	Dic₁₅	C₂²	1	2	yes	—
8	C₃×Dic₅	C₂²	1	2	yes	—
9	C₅×Dic₃	C₂²	1	2	yes	—
10	C₂×Dic₆	—	5	1	no	maximal, Hall
11	C₂×C₄×C₅	—	3	1	no	—
12	C₂×Dic₅	—	3	1	no	—
13	C₂×Dic₅	D₃	1	1	yes	characteristic
14	Dic₁₀	—	3	4	no	—
15	C₂×C₃×C₅	Q₈	1	2	yes	complemented
16	C₂×C₃×C₅	C₂³	1	1	yes	characteristic
17	C₂×C₃×C₄	—	5	1	no	—
18	C₂×Dic₃	—	5	1	no	—
19	C₂×Dic₃	D₅	1	1	yes	characteristic
20	Dic₆	—	5	4	no	—
21	C₂²×C₅	C₂×D₃	1	1	yes	characteristic
22	C₄×C₅	—	3	2	no	—
23	Dic₅	—	3	2	no	—
24	Dic₅	C₂×D₃	1	2	yes	—
25	C₂×Q₈	—	15	1	no	Sylow
26	C₃×C₅	C₂×Q₈	1	1	yes	characteristic, complemented, Hall
27	C₂²×C₃	C₂×D₅	1	1	yes	characteristic
28	C₃×C₄	—	5	2	no	—
29	Dic₃	—	5	2	no	—
30	Dic₃	C₂×D₅	1	2	yes	—
31	C₂×C₅	Dic₆	1	2	yes	complemented
32	C₂×C₅	C₂²×D₃	1	1	yes	characteristic
33	Q₈	—	15	4	no	—
34	C₂×C₄	—	3	1	no	—
35	C₂×C₄	—	5	1	no	—
36	C₂×C₄	—	15	1	no	—
37	C₂×C₃	Dic₁₀	1	2	yes	complemented
38	C₂×C₃	C₂²×D₅	1	1	yes	characteristic
39	C₅	C₂×Dic₆	1	1	yes	characteristic, complemented, Sylow
40	C₂²	D₃×D₅	1	1	yes	characteristic
41	C₄	—	3	2	no	—
42	C₄	—	5	2	no	—
43	C₄	—	15	2	no	—
44	C₃	C₂×Dic₁₀	1	1	yes	characteristic, complemented, Sylow
45	C₂	#1204	1	2	yes	direct product factor
46	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, prime radical	C₂²×C₃×C₅	C₂²
hypocenter	C₃×C₅	C₂×Q₈
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
4. #1204	C₂	direct (N × H)
15. C₂×C₃×C₅	Q₈	semidirect
26. C₃×C₅	C₂×Q₈	semidirect
31. C₂×C₅	Dic₆	semidirect
37. C₂×C₃	Dic₁₀	semidirect
39. C₅	C₂×Dic₆	semidirect
44. C₃	C₂×Dic₁₀	semidirect
45. C₂	#1204	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×Dic₁₅	2
C₂×C₅×Dic₃	2
C₂×C₃×Dic₅	2
#1204	2
C₂×Dic₁₀	3
C₂×Dic₆	5

Subgroups — C2×#1204 #6787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1204 #6787