Subgroups — C₂×#3940 #65252

Order 320.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×C₄⋊C₄	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	#3940	C₂	1	4	yes	maximal, direct product factor
5	C₂²×C₄×C₅	—	2	1	no	—
6	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
7	C₂²×Dic₅	—	2	1	no	—
8	C₅×C₄⋊C₄	—	2	1	no	—
9	C₅×C₄⋊C₄	C₂²	1	2	yes	—
10	C₄⋊Dic₅	—	2	1	no	—
11	C₄⋊Dic₅	C₂²	1	2	yes	—
12	C₂×#168	C₄	1	4	yes	complemented
13	C₂×#168	C₂²	1	2	yes	—
14	C₂×#106	—	5	1	no	maximal, Sylow
15	C₂³×C₅	D₄	1	1	yes	characteristic
16	C₂×C₄×C₅	—	2	2	no	—
17	C₂×C₄×C₅	—	4	2	no	—
18	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
19	C₂×C₄×C₅	D₄	1	1	yes	characteristic
20	C₂×C₄×C₅	Q₈	1	2	yes	—
21	C₂×C₄×C₅	C₂³	1	1	yes	characteristic
22	C₂×Dic₅	—	2	2	no	—
23	C₂×Dic₅	—	4	2	no	—
24	#168	C₂×C₄	1	4	yes	complemented
25	C₂²×C₈	—	5	1	no	—
26	C₂×C₄⋊C₄	—	5	1	no	—
27	C₂×C₄⋊C₄	D₅	1	1	yes	characteristic
28	#106	—	5	4	no	—
29	C₂²×C₅	C₄⋊C₄	1	2	yes	—
30	C₂²×C₅	SD₁₆	1	2	yes	—
31	C₂²×C₅	SD₁₆	1	2	yes	—
32	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
33	C₄×C₅	—	4	2	no	—
34	C₄×C₅	C₄⋊C₄	1	2	yes	—
35	C₄×C₅	C₂²×C₄	1	1	yes	characteristic
36	C₄×C₅	C₂×Q₈	1	1	yes	characteristic
37	Dic₅	—	4	2	no	—
38	C₂²×C₄	—	2	1	no	—
39	C₂²×C₄	—	10	1	no	—
40	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
41	C₂×C₈	—	5	4	no	—
42	C₂×C₈	—	5	2	no	—
43	C₄⋊C₄	—	2	1	no	—
44	C₄⋊C₄	—	5	2	no	—
45	C₄⋊C₄	—	10	1	no	—
46	C₄⋊C₄	C₂×D₅	1	2	yes	—
47	C₂×C₅	#106	1	4	yes	complemented
48	C₂×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
49	C₂×C₅	C₂×SD₁₆	1	1	yes	characteristic
50	C₂×C₅	C₂×SD₁₆	1	1	yes	characteristic
51	C₂³	C₂²⋊D₅	1	1	yes	characteristic
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	4	2	no	—
54	C₂×C₄	—	10	2	no	—
55	C₂×C₄	—	20	2	no	—
56	C₂×C₄	Dic₁₀	1	2	yes	—
57	C₂×C₄	C₄×D₅	1	2	yes	—
58	C₂×C₄	C₂²⋊D₅	1	1	yes	characteristic
59	C₂×C₄	C₂²×D₅	1	1	yes	characteristic
60	C₈	—	5	4	no	—
61	C₅	C₂×#106	1	1	yes	characteristic, complemented, Sylow
62	C₂²	#683	1	2	yes	—
63	C₂²	#687	1	2	yes	—
64	C₂²	#688	1	2	yes	—
65	C₂²	C₂×C₂²⋊D₅	1	1	yes	characteristic
66	C₄	—	4	2	no	—
67	C₄	—	20	2	no	—
68	C₄	#683	1	2	yes	—
69	C₄	C₂×Dic₁₀	1	1	yes	characteristic
70	C₄	C₂×C₄×D₅	1	1	yes	characteristic
71	C₂	#3940	1	4	yes	direct product factor
72	C₂	C₂×#683	1	1	yes	characteristic
73	C₂	C₂×#687	1	1	yes	characteristic
74	C₂	C₂×#688	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊D₅
commutator	C₄×C₅	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₅
Fitting	C₂×C₅×C₄⋊C₄	C₂
socle, prime radical	C₂³×C₅	D₄
cosocle	C₂×C₄×C₅	C₂³
hypercenter	C₂×C₄⋊C₄	D₅
hypocenter	C₅	C₂×#106
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #3940	C₂	direct (N × H)
12. C₂×#168	C₄	semidirect
24. #168	C₂×C₄	semidirect
47. C₂×C₅	#106	semidirect
61. C₅	C₂×#106	semidirect
71. C₂	#3940	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×C₄⋊C₄	2
C₂×C₄⋊Dic₅	2
C₂²×#168	2
#3940	2
C₂×#106	5

Subgroups — C2×#3940 #65252

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3940 #65252