Subgroups — C₂×#4094 #66152

Order 320.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	#4094	C₂	1	8	yes	maximal, direct product factor
3	C₂×#681	C₂	1	3	yes	maximal, complemented
4	C₂²×#168	C₂	1	3	yes	maximal, complemented
5	C₅×#41	C₄	1	4	yes	—
6	C₅×#41	C₂²	1	4	yes	—
7	C₂×C₅×Q₈	C₄	1	1	yes	characteristic
8	C₂×C₅×D₄	C₄	1	3	yes	—
9	C₂²×C₄×C₅	C₂²	1	3	yes	—
10	#681	C₂²	1	12	yes	complemented
11	C₂×#168	C₂²	1	1	yes	characteristic
12	C₂×#168	C₂²	1	3	yes	—
13	C₂×#168	C₂²	1	12	yes	complemented
14	C₂×#131	—	5	1	no	maximal, Sylow
15	C₂³×C₅	C₂×C₄	1	3	yes	—
16	C₅×Q₈	C₂×C₄	1	4	yes	—
17	C₅×D₄	C₂×C₄	1	12	yes	—
18	C₂×C₄×C₅	C₂×C₄	1	3	yes	—
19	C₂×C₄×C₅	C₂×C₄	1	6	yes	—
20	C₂×C₄×C₅	C₂³	1	6	yes	—
21	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
22	#168	C₂³	1	2	yes	—
23	#168	C₂³	1	6	yes	—
24	C₂×#41	D₅	1	1	yes	characteristic
25	#131	—	5	8	no	—
26	C₂×M₁₆	—	5	3	no	—
27	C₂²×C₈	—	5	3	no	—
28	C₂²×C₅	—	2	6	no	—
29	C₂²×C₅	C₂²×C₄	1	6	yes	—
30	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
31	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₅	C₂²×C₄	1	6	yes	—
33	C₄×C₅	C₂⁴	1	1	yes	characteristic
34	#41	Dic₅	1	4	yes	—
35	#41	C₂×D₅	1	4	yes	—
36	C₂×Q₈	Dic₅	1	1	yes	characteristic
37	C₂×D₄	Dic₅	1	3	yes	—
38	C₂²×C₄	C₂×D₅	1	3	yes	—
39	M₁₆	—	5	12	no	—
40	C₂×C₈	—	5	12	no	—
41	C₂×C₈	—	5	1	no	—
42	C₂×C₈	—	5	3	no	—
43	C₂×C₅	—	2	6	no	—
44	C₂×C₅	#131	1	2	yes	complemented
45	C₂×C₅	C₂³×C₄	1	1	yes	characteristic
46	C₂³	C₂×Dic₅	1	3	yes	—
47	Q₈	C₂×Dic₅	1	4	yes	—
48	D₄	C₂×Dic₅	1	12	yes	—
49	C₂×C₄	C₂×Dic₅	1	3	yes	—
50	C₂×C₄	C₂×Dic₅	1	6	yes	—
51	C₂×C₄	C₂²×D₅	1	6	yes	—
52	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
53	C₈	—	5	2	no	—
54	C₈	—	5	6	no	—
55	C₅	C₂×#131	1	1	yes	characteristic, complemented, Sylow
56	C₂²	—	2	6	no	—
57	C₂²	C₂²×Dic₅	1	6	yes	—
58	C₂²	C₂²×Dic₅	1	1	yes	characteristic
59	C₄	C₂²×Dic₅	1	1	yes	characteristic
60	C₄	C₂²×Dic₅	1	6	yes	—
61	C₄	C₂³×D₅	1	1	yes	characteristic
62	C₂	—	2	6	no	—
63	C₂	#4094	1	2	yes	direct product factor
64	C₂	C₂³×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₅
commutator	C₂×C₅	C₂³×C₄
Frattini	C₄	C₂³×D₅
Fitting, prime radical	C₂×C₅×#41	C₂
socle	C₂²×C₅	C₂²×C₄
cosocle	C₄×C₅	C₂⁴
hypercenter	C₂×#41	D₅
hypocenter	C₅	C₂×#131
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
2. #4094	C₂	direct (N × H)
3. C₂×#681	C₂	semidirect
4. C₂²×#168	C₂	semidirect
10. #681	C₂²	semidirect
13. C₂×#168	C₂²	semidirect
44. C₂×C₅	#131	semidirect
55. C₅	C₂×#131	semidirect
63. C₂	#4094	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×C₅×#41	2
#4094	2
C₂×#681	2
C₂²×#168	2
C₂×#131	5

Subgroups — C2×#4094 #66152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4094 #66152