Subgroups — C₂×#3947 #65389

Order 320.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×#168	C₂	1	1	yes	maximal, characteristic
4	#3947	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
6	C₂²×Dic₅	C₄	1	2	yes	—
7	C₂×C₅×C₈	C₄	1	4	yes	complemented
8	C₂×C₅×C₈	C₂²	1	2	yes	—
9	C₄×Dic₅	C₄	1	2	yes	—
10	C₄×Dic₅	C₂²	1	2	yes	—
11	C₂×#168	C₄	1	4	yes	complemented
12	C₂×#168	C₂²	1	2	yes	—
13	C₂×#97	—	5	1	no	maximal, Sylow
14	C₂³×C₅	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₅	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
18	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
19	C₂×Dic₅	—	2	4	no	—
20	C₂×Dic₅	C₂×C₄	1	4	yes	—
21	C₅×C₈	C₂×C₄	1	4	yes	complemented
22	#168	C₂×C₄	1	4	yes	complemented
23	C₂²×C₈	—	5	1	no	—
24	C₂²×C₈	D₅	1	1	yes	characteristic
25	C₂×C₄²	—	5	1	no	—
26	#97	—	5	4	no	—
27	C₂²×C₅	C₄²	1	2	yes	—
28	C₂²×C₅	M₁₆	1	4	yes	—
29	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₅	C₄²	1	2	yes	—
31	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
32	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
33	Dic₅	—	2	4	no	—
34	C₂²×C₄	—	5	2	no	—
35	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
36	C₂×C₈	—	5	4	no	—
37	C₂×C₈	—	5	2	no	—
38	C₂×C₈	Dic₅	1	4	yes	complemented
39	C₂×C₈	C₂×D₅	1	2	yes	—
40	C₄²	—	5	2	no	—
41	C₄²	—	5	2	no	—
42	C₂×C₅	#97	1	4	yes	complemented
43	C₂×C₅	C₂×C₄²	1	1	yes	characteristic
44	C₂×C₅	C₂×M₁₆	1	2	yes	—
45	C₂³	C₄×D₅	1	1	yes	characteristic
46	C₂×C₄	—	5	4	no	—
47	C₂×C₄	—	10	4	no	—
48	C₂×C₄	C₄×D₅	1	1	yes	characteristic
49	C₂×C₄	C₄×D₅	1	2	yes	—
50	C₂×C₄	C₂×Dic₅	1	2	yes	—
51	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
52	C₈	—	5	4	no	—
53	C₈	C₂×Dic₅	1	4	yes	complemented
54	C₅	C₂×#97	1	1	yes	characteristic, complemented, Sylow
55	C₂²	#676	1	4	yes	—
56	C₂²	C₄×Dic₅	1	2	yes	—
57	C₂²	C₂×C₄×D₅	1	1	yes	characteristic
58	C₄	—	10	4	no	—
59	C₄	C₄×Dic₅	1	2	yes	—
60	C₄	C₂×C₄×D₅	1	1	yes	characteristic
61	C₄	C₂²×Dic₅	1	1	yes	characteristic
62	C₂	#3947	1	4	yes	direct product factor
63	C₂	C₂×#676	1	2	yes	—
64	C₂	C₂×C₄×Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₅
commutator	C₂×C₅	C₂×C₄²
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₂²×C₅×C₈	C₂
socle, prime radical	C₂³×C₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	C₂²×C₈	D₅
hypocenter	C₅	C₂×#97
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #3947	C₂	direct (N × H)
7. C₂×C₅×C₈	C₄	semidirect
11. C₂×#168	C₄	semidirect
21. C₅×C₈	C₂×C₄	semidirect
22. #168	C₂×C₄	semidirect
38. C₂×C₈	Dic₅	semidirect
42. C₂×C₅	#97	semidirect
53. C₈	C₂×Dic₅	semidirect
54. C₅	C₂×#97	semidirect
62. C₂	#3947	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×C₈	2
C₂×C₄×Dic₅	2
C₂²×#168	2
#3947	2
C₂×#97	5

Subgroups — C2×#3947 #65389

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3947 #65389