Subgroups — C₂×#4022 #65812

Order 320.

246 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#685	C₂	1	3	yes	maximal
3	C₂×#683	C₂	1	3	yes	maximal, complemented
4	#4022	C₂	1	8	yes	maximal, direct product factor
5	C₂³×D₅	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₅	C₂²	1	3	yes	—
7	C₂²×Dic₅	C₂²	1	3	yes	—
8	C₄²×C₅	C₂²	1	4	yes	complemented
9	#685	C₂²	1	12	yes	—
10	#683	C₂²	1	12	yes	complemented
11	C₂×#126	—	5	1	no	maximal, Sylow
12	C₂³×C₅	C₂³	1	1	yes	characteristic
13	C₂²×D₅	—	2	6	no	—
14	C₂²×D₅	C₂³	1	2	yes	—
15	C₂×C₄×C₅	—	2	6	no	—
16	C₂×C₄×C₅	C₂³	1	6	yes	—
17	C₂×Dic₅	—	2	6	no	—
18	C₂×Dic₅	C₂³	1	6	yes	—
19	#126	—	5	8	no	—
20	C₂×C₄⋊C₄	—	5	3	no	—
21	C₂×C₂²⋊C₄	—	5	3	no	—
22	C₂×C₄²	D₅	1	1	yes	characteristic, complemented
23	C₂²×C₅	#41	1	6	yes	—
24	C₂²×C₅	C₂⁴	1	1	yes	characteristic
25	C₂×D₅	—	2	6	no	—
26	C₂×D₅	—	4	4	no	—
27	C₄×C₅	—	2	6	no	—
28	Dic₅	—	2	6	no	—
29	C₂⁴	—	5	1	no	—
30	C₂²×C₄	—	5	3	no	—
31	C₂²×C₄	C₂×D₅	1	3	yes	—
32	C₄⋊C₄	—	5	12	no	—
33	C₂²⋊C₄	—	5	12	no	—
34	C₄²	C₂×D₅	1	4	yes	complemented
35	C₂×C₅	#126	1	4	yes	complemented
36	C₂×C₅	C₂×#41	1	3	yes	—
37	D₅	—	4	2	no	—
38	C₂³	—	5	2	no	—
39	C₂³	—	10	6	no	—
40	C₂³	C₂²×D₅	1	1	yes	characteristic
41	C₂×C₄	—	2	6	no	—
42	C₂×C₄	—	5	6	no	—
43	C₂×C₄	—	10	6	no	—
44	C₂×C₄	C₂²×D₅	1	6	yes	—
45	C₅	C₂×#126	1	1	yes	characteristic, complemented, Sylow
46	C₂²	—	10	6	no	—
47	C₂²	—	20	4	no	—
48	C₂²	#709	1	6	yes	—
49	C₂²	C₂³×D₅	1	1	yes	characteristic
50	C₄	—	2	6	no	—
51	C₄	—	10	6	no	—
52	C₂	—	20	2	no	—
53	C₂	#4022	1	4	yes	direct product factor
54	C₂	C₂×#709	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₅
commutator, cosocle	C₂²×C₅	C₂⁴
Frattini	C₂²	C₂³×D₅
Fitting	C₂×C₄²×C₅	C₂
socle	C₂³×C₅	C₂³
prime radical	C₂³×D₅	C₂²
hypercenter	C₂×C₄²	D₅
hypocenter	C₅	C₂×#126
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₄²×C₅	C₂	semidirect
3. C₂×#683	C₂	semidirect
4. #4022	C₂	direct (N × H)
8. C₄²×C₅	C₂²	semidirect
10. #683	C₂²	semidirect
22. C₂×C₄²	D₅	semidirect
34. C₄²	C₂×D₅	semidirect
35. C₂×C₅	#126	semidirect
45. C₅	C₂×#126	semidirect
53. C₂	#4022	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×C₄²×C₅	2
C₂×#685	2
C₂×#683	2
#4022	2
C₂×#126	5

Subgroups — C2×#4022 #65812

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#4022 #65812