Subgroups — C₂³×C₂²⋊Dic₅ #10619201

Order 640.

4632 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₅	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×Dic₅	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂²⋊Dic₅	C₂	1	28	yes	maximal, direct product factor
4	C₂⁵×C₅	—	2	16	no	—
5	C₂⁵×C₅	C₄	1	16	yes	complemented
6	C₂⁵×C₅	C₂²	1	14	yes	—
7	C₂⁵×C₅	C₂²	1	1	yes	characteristic
8	C₂³×Dic₅	—	2	16	no	—
9	C₂³×Dic₅	C₂²	1	28	yes	complemented
10	C₂×C₂²⋊Dic₅	C₂²	1	112	yes	direct product factor
11	C₂³×C₂²⋊C₄	—	5	1	no	maximal, Sylow
12	C₂⁴×C₅	—	2	128	no	—
13	C₂⁴×C₅	—	2	112	no	—
14	C₂⁴×C₅	C₂×C₄	1	8	yes	—
15	C₂⁴×C₅	C₂×C₄	1	112	yes	complemented
16	C₂⁴×C₅	D₄	1	16	yes	—
17	C₂⁴×C₅	C₂³	1	28	yes	—
18	C₂⁴×C₅	C₂³	1	7	yes	—
19	C₂²×Dic₅	—	2	112	no	—
20	C₂²×Dic₅	C₂³	1	56	yes	complemented
21	C₂²⋊Dic₅	C₂³	1	64	yes	direct product factor
22	C₂⁶	D₅	1	1	yes	characteristic
23	C₂⁴×C₄	—	5	2	no	—
24	C₂²×C₂²⋊C₄	—	5	28	no	—
25	C₂³×C₅	—	2	448	no	—
26	C₂³×C₅	—	2	112	no	—
27	C₂³×C₅	C₂²⋊C₄	1	64	yes	complemented
28	C₂³×C₅	C₂²×C₄	1	28	yes	—
29	C₂³×C₅	C₂²×C₄	1	112	yes	complemented
30	C₂³×C₅	C₂×D₄	1	56	yes	—
31	C₂³×C₅	C₂⁴	1	8	yes	—
32	C₂³×C₅	C₂⁴	1	7	yes	—
33	C₂×Dic₅	—	2	112	no	—
34	C₂×Dic₅	C₂⁴	1	16	yes	complemented
35	C₂⁵	—	2	16	no	—
36	C₂⁵	Dic₅	1	16	yes	complemented
37	C₂⁵	C₂×D₅	1	14	yes	—
38	C₂⁵	C₂×D₅	1	1	yes	characteristic
39	C₂³×C₄	—	5	28	no	—
40	C₂³×C₄	—	10	16	no	—
41	C₂×C₂²⋊C₄	—	5	112	no	—
42	C₂²×C₅	—	2	224	no	—
43	C₂²×C₅	—	2	16	no	—
44	C₂²×C₅	C₂×C₂²⋊C₄	1	112	yes	complemented
45	C₂²×C₅	C₂³×C₄	1	14	yes	—
46	C₂²×C₅	C₂³×C₄	1	16	yes	complemented
47	C₂²×C₅	C₂²×D₄	1	28	yes	—
48	C₂²×C₅	C₂⁵	1	1	yes	characteristic
49	Dic₅	—	2	16	no	—
50	C₂⁴	—	2	128	no	—
51	C₂⁴	—	2	112	no	—
52	C₂⁴	C₂×Dic₅	1	8	yes	—
53	C₂⁴	C₂×Dic₅	1	112	yes	complemented
54	C₂⁴	C₂²⋊D₅	1	16	yes	—
55	C₂⁴	C₂²×D₅	1	28	yes	—
56	C₂⁴	C₂²×D₅	1	7	yes	—
57	C₂²×C₄	—	5	56	no	—
58	C₂²×C₄	—	10	112	no	—
59	C₂²⋊C₄	—	5	64	no	—
60	C₂×C₅	—	2	16	no	—
61	C₂×C₅	C₂²×C₂²⋊C₄	1	28	yes	complemented
62	C₂×C₅	C₂⁴×C₄	1	1	yes	characteristic
63	C₂×C₅	C₂³×D₄	1	2	yes	—
64	C₂³	—	2	448	no	—
65	C₂³	—	2	112	no	—
66	C₂³	C₂²⋊Dic₅	1	64	yes	direct product factor
67	C₂³	C₂²×Dic₅	1	28	yes	—
68	C₂³	C₂²×Dic₅	1	112	yes	complemented
69	C₂³	C₂×C₂²⋊D₅	1	56	yes	—
70	C₂³	C₂³×D₅	1	8	yes	—
71	C₂³	C₂³×D₅	1	7	yes	—
72	C₂×C₄	—	5	16	no	—
73	C₂×C₄	—	10	112	no	—
74	C₅	C₂³×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
75	C₂²	—	2	224	no	—
76	C₂²	—	2	16	no	—
77	C₂²	C₂×C₂²⋊Dic₅	1	112	yes	direct product factor
78	C₂²	C₂³×Dic₅	1	14	yes	—
79	C₂²	C₂³×Dic₅	1	16	yes	complemented
80	C₂²	C₂²×C₂²⋊D₅	1	28	yes	—
81	C₂²	C₂⁴×D₅	1	1	yes	characteristic
82	C₄	—	10	16	no	—
83	C₂	—	2	16	no	—
84	C₂	C₂²×C₂²⋊Dic₅	1	28	yes	direct product factor
85	C₂	C₂⁴×Dic₅	1	1	yes	characteristic
86	C₂	C₂³×C₂²⋊D₅	1	2	yes	—

	subgroup	G/H
center	C₂⁵	C₂×D₅
commutator	C₂×C₅	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₅
Fitting, prime radical	C₂⁶×C₅	C₂
socle	C₂⁵×C₅	C₂²
cosocle	C₂²×C₅	C₂⁵
hypercenter	C₂⁶	D₅
hypocenter	C₅	C₂³×C₂²⋊C₄
LCS	G ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁵ ◁ C₂⁶

Complements

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

N	H ≅ G/N	type
2. C₂⁴×Dic₅	C₂	semidirect
3. C₂²×C₂²⋊Dic₅	C₂	direct (N × H)
5. C₂⁵×C₅	C₄	semidirect
9. C₂³×Dic₅	C₂²	semidirect
10. C₂×C₂²⋊Dic₅	C₂²	direct (N × H)
15. C₂⁴×C₅	C₂×C₄	semidirect
20. C₂²×Dic₅	C₂³	semidirect
21. C₂²⋊Dic₅	C₂³	direct (N × H)
27. C₂³×C₅	C₂²⋊C₄	semidirect
29. C₂³×C₅	C₂²×C₄	semidirect
34. C₂×Dic₅	C₂⁴	semidirect
36. C₂⁵	Dic₅	semidirect
44. C₂²×C₅	C₂×C₂²⋊C₄	semidirect
46. C₂²×C₅	C₂³×C₄	semidirect
53. C₂⁴	C₂×Dic₅	semidirect
61. C₂×C₅	C₂²×C₂²⋊C₄	semidirect
66. C₂³	C₂²⋊Dic₅	direct (N × H)
68. C₂³	C₂²×Dic₅	semidirect
74. C₅	C₂³×C₂²⋊C₄	semidirect
77. C₂²	C₂×C₂²⋊Dic₅	direct (N × H)
79. C₂²	C₂³×Dic₅	semidirect
84. C₂	C₂²×C₂²⋊Dic₅	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁶×C₅	2
C₂⁴×Dic₅	2
C₂²×C₂²⋊Dic₅	2
C₂³×C₂²⋊C₄	5

Subgroups — C23×C22⋊Dic5 #10619201

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₂²⋊Dic₅ #10619201