Subgroups — C₄×#683 #65220

Order 320.

194 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
2	C₂×#683	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic
5	#3963	C₂	1	2	yes	maximal
6	C₂²×C₄×C₅	C₂²	1	2	yes	—
7	C₂²×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×Dic₅	C₂²	1	1	yes	characteristic
9	C₂²×Dic₅	C₂²	1	2	yes	—
10	C₂²×Dic₅	C₂²	1	1	yes	characteristic
11	C₄²×C₅	—	2	2	no	—
12	#683	C₄	1	8	yes	direct product factor
13	C₄×Dic₅	—	2	2	no	—
14	C₄×Dic₅	C₄	1	4	yes	complemented
15	C₄×C₄⋊C₄	—	5	1	no	maximal, Sylow
16	C₂³×C₅	C₂³	1	1	yes	characteristic
17	C₂×C₄×C₅	—	2	2	no	—
18	C₂×C₄×C₅	—	2	2	no	—
19	C₂×C₄×C₅	C₂×C₄	1	4	yes	—
20	C₂×C₄×C₅	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₅	D₄	1	2	yes	—
22	C₂×C₄×C₅	Q₈	1	2	yes	—
23	C₂×Dic₅	—	2	2	no	—
24	C₂×Dic₅	—	2	2	no	—
25	C₂×Dic₅	—	2	2	no	—
26	C₂×Dic₅	C₂×C₄	1	2	yes	—
27	C₂×Dic₅	C₂×C₄	1	4	yes	—
28	C₂×Dic₅	C₂×C₄	1	2	yes	—
29	C₂×Dic₅	C₂×C₄	1	4	yes	—
30	C₂×C₄⋊C₄	—	5	2	no	—
31	C₂×C₄²	—	5	1	no	—
32	C₂×C₄²	—	5	1	no	—
33	C₂×C₄²	D₅	1	1	yes	characteristic
34	#95	—	5	2	no	—
35	C₂²×C₅	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₅	C₂²×C₄	1	2	yes	—
37	C₂²×C₅	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₅	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₅	#41	1	2	yes	—
40	C₄×C₅	—	2	4	no	—
41	C₄×C₅	C₄⋊C₄	1	4	yes	complemented
42	Dic₅	—	2	2	no	—
43	Dic₅	—	2	4	no	—
44	Dic₅	C₄²	1	4	yes	complemented
45	C₂²×C₄	—	5	1	no	—
46	C₂²×C₄	—	5	1	no	—
47	C₂²×C₄	—	5	2	no	—
48	C₂²×C₄	C₂×D₅	1	2	yes	—
49	C₂²×C₄	C₂×D₅	1	1	yes	characteristic
50	C₄⋊C₄	—	5	8	no	—
51	C₄²	—	2	2	no	—
52	C₄²	—	5	4	no	—
53	C₄²	—	10	2	no	—
54	C₂×C₅	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₅	#117	1	1	yes	characteristic
57	C₂×C₅	C₄×D₄	1	2	yes	—
58	C₂×C₅	C₄×Q₈	1	2	yes	—
59	C₂³	C₂²×D₅	1	1	yes	characteristic
60	C₂×C₄	—	2	2	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	5	2	no	—
63	C₂×C₄	—	5	4	no	—
64	C₂×C₄	—	5	2	no	—
65	C₂×C₄	—	5	4	no	—
66	C₂×C₄	—	10	2	no	—
67	C₂×C₄	—	10	2	no	—
68	C₂×C₄	—	10	2	no	—
69	C₂×C₄	Dic₁₀	1	2	yes	—
70	C₂×C₄	C₄×D₅	1	4	yes	—
71	C₂×C₄	C₄×D₅	1	2	yes	—
72	C₂×C₄	C₂²⋊D₅	1	2	yes	—
73	C₅	C₄×C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
74	C₂²	C₂×Dic₁₀	1	1	yes	characteristic
75	C₂²	C₂×C₄×D₅	1	2	yes	—
76	C₂²	C₂×C₄×D₅	1	1	yes	characteristic
77	C₂²	#709	1	2	yes	—
78	C₂²	C₂×C₂²⋊D₅	1	1	yes	characteristic
79	C₄	—	2	4	no	—
80	C₄	—	5	4	no	—
81	C₄	—	10	2	no	—
82	C₄	—	10	4	no	—
83	C₄	#683	1	4	yes	direct product factor
84	C₂	C₄×Dic₁₀	1	2	yes	—
85	C₂	C₄²×D₅	1	1	yes	characteristic
86	C₂	#4018	1	1	yes	characteristic
87	C₂	C₂×#683	1	1	yes	characteristic
88	C₂	C₄×C₂²⋊D₅	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
12. #683	C₄	direct (N × H)
14. C₄×Dic₅	C₄	semidirect
41. C₄×C₅	C₄⋊C₄	semidirect
44. Dic₅	C₄²	semidirect
73. C₅	C₄×C₄⋊C₄	semidirect
83. C₄	#683	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×#683	2
C₂×C₄×Dic₅	2
#3963	2
C₄×C₄⋊C₄	5

Subgroups — C4×#683 #65220

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#683 #65220