Subgroups — C₂³×C₂²⋊(C₅⋊D₅) #13107894

Order 1600.

5448 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁴×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊(C₅⋊D₅)	C₂	1	28	yes	maximal, direct product factor
4	C₂³×#1039	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂⁴×C₅²	—	2	8	no	—
6	C₂⁴×C₅²	C₂²	1	1	yes	characteristic
7	C₂⁴×C₅²	C₂²	1	14	yes	complemented
8	C₂³×C₅⋊D₅	—	2	8	no	—
9	C₂³×C₅⋊D₅	C₂²	1	14	yes	complemented
10	C₂×C₂²⋊(C₅⋊D₅)	C₂²	1	112	yes	direct product factor
11	C₂²×#1039	C₂²	1	14	yes	complemented
12	C₂³×C₂²⋊D₅	—	5	6	no	maximal
13	C₂³×C₅²	—	2	56	no	—
14	C₂³×C₅²	D₄	1	8	yes	complemented
15	C₂³×C₅²	C₂³	1	7	yes	—
16	C₂³×C₅²	C₂³	1	28	yes	complemented
17	C₂²×C₅⋊D₅	—	2	56	no	—
18	C₂²×C₅⋊D₅	C₂³	1	28	yes	complemented
19	C₂²⋊(C₅⋊D₅)	C₂³	1	64	yes	direct product factor
20	C₂×#1039	C₂³	1	28	yes	complemented
21	C₂⁵×C₅	D₅	1	6	yes	complemented
22	C₂⁴×D₅	—	5	6	no	—
23	C₂²×C₂²⋊D₅	—	5	168	no	—
24	C₂³×Dic₅	—	5	6	no	—
25	C₂²×C₅²	—	2	56	no	—
26	C₂²×C₅²	C₂×D₄	1	28	yes	complemented
27	C₂²×C₅²	C₂⁴	1	7	yes	—
28	C₂²×C₅²	C₂⁴	1	8	yes	complemented
29	C₂×C₅⋊D₅	—	2	56	no	—
30	C₂×C₅⋊D₅	C₂⁴	1	8	yes	complemented
31	#1039	C₂⁴	1	8	yes	complemented
32	C₂⁴×C₅	—	2	48	no	—
33	C₂⁴×C₅	C₂×D₅	1	6	yes	—
34	C₂⁴×C₅	C₂×D₅	1	84	yes	complemented
35	C₂³×D₅	—	5	84	no	—
36	C₂³×D₅	—	10	48	no	—
37	C₂×C₂²⋊D₅	—	5	672	no	—
38	C₂²×Dic₅	—	5	84	no	—
39	C₂³×D₄	—	25	1	no	Sylow
40	C₂×C₅²	—	2	8	no	—
41	C₂×C₅²	C₂²×D₄	1	14	yes	complemented
42	C₂×C₅²	C₂⁵	1	1	yes	characteristic
43	C₅⋊D₅	—	2	8	no	—
44	C₂³×C₅	—	2	336	no	—
45	C₂³×C₅	C₂²⋊D₅	1	48	yes	complemented
46	C₂³×C₅	C₂²×D₅	1	42	yes	—
47	C₂³×C₅	C₂²×D₅	1	168	yes	complemented
48	C₂²×D₅	—	5	168	no	—
49	C₂²×D₅	—	10	336	no	—
50	C₂²⋊D₅	—	5	384	no	—
51	C₂×Dic₅	—	5	168	no	—
52	C₂⁵	—	25	1	no	—
53	C₂⁵	C₅⋊D₅	1	1	yes	characteristic, complemented
54	C₂²×D₄	—	25	28	no	—
55	C₂³×C₄	—	25	1	no	—
56	C₅²	C₂³×D₄	1	1	yes	characteristic, complemented, Sylow
57	C₂²×C₅	—	2	336	no	—
58	C₂²×C₅	C₂×C₂²⋊D₅	1	168	yes	complemented
59	C₂²×C₅	C₂³×D₅	1	42	yes	—
60	C₂²×C₅	C₂³×D₅	1	48	yes	complemented
61	C₂×D₅	—	5	48	no	—
62	C₂×D₅	—	10	336	no	—
63	Dic₅	—	5	48	no	—
64	C₂⁴	—	2	8	no	—
65	C₂⁴	—	25	14	no	—
66	C₂⁴	—	50	8	no	—
67	C₂⁴	C₂×C₅⋊D₅	1	1	yes	characteristic
68	C₂⁴	C₂×C₅⋊D₅	1	14	yes	complemented
69	C₂×D₄	—	25	112	no	—
70	C₂²×C₄	—	25	14	no	—
71	C₂×C₅	—	2	48	no	—
72	C₂×C₅	C₂²×C₂²⋊D₅	1	84	yes	complemented
73	C₂×C₅	C₂⁴×D₅	1	6	yes	—
74	D₅	—	10	48	no	—
75	C₂³	—	2	56	no	—
76	C₂³	—	25	28	no	—
77	C₂³	—	50	56	no	—
78	C₂³	C₂²⋊(C₅⋊D₅)	1	8	yes	direct product factor
79	C₂³	C₂²×C₅⋊D₅	1	7	yes	—
80	C₂³	C₂²×C₅⋊D₅	1	28	yes	complemented
81	D₄	—	25	64	no	—
82	C₂×C₄	—	25	28	no	—
83	C₅	C₂³×C₂²⋊D₅	1	6	yes	complemented
84	C₂²	—	2	56	no	—
85	C₂²	—	25	8	no	—
86	C₂²	—	50	56	no	—
87	C₂²	C₂×C₂²⋊(C₅⋊D₅)	1	28	yes	direct product factor
88	C₂²	C₂³×C₅⋊D₅	1	7	yes	—
89	C₂²	C₂³×C₅⋊D₅	1	8	yes	complemented
90	C₄	—	25	8	no	—
91	C₂	—	2	8	no	—
92	C₂	—	50	8	no	—
93	C₂	C₂²×C₂²⋊(C₅⋊D₅)	1	14	yes	direct product factor
94	C₂	C₂⁴×C₅⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₅⋊D₅
commutator, cosocle	C₂×C₅²	C₂⁵
Frattini	C₂	C₂⁴×C₅⋊D₅
Fitting	C₂⁵×C₅²	C₂
socle	C₂⁴×C₅²	C₂²
hypercenter	C₂⁵	C₅⋊D₅
hypocenter	C₅²	C₂³×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂⁴ ◁ C₂⁵

Complements

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

N	H ≅ G/N	type
1. C₂⁵×C₅²	C₂	semidirect
2. C₂⁴×C₅⋊D₅	C₂	semidirect
3. C₂²×C₂²⋊(C₅⋊D₅)	C₂	direct (N × H)
4. C₂³×#1039	C₂	semidirect
7. C₂⁴×C₅²	C₂²	semidirect
9. C₂³×C₅⋊D₅	C₂²	semidirect
10. C₂×C₂²⋊(C₅⋊D₅)	C₂²	direct (N × H)
11. C₂²×#1039	C₂²	semidirect
14. C₂³×C₅²	D₄	semidirect
16. C₂³×C₅²	C₂³	semidirect
18. C₂²×C₅⋊D₅	C₂³	semidirect
19. C₂²⋊(C₅⋊D₅)	C₂³	direct (N × H)
20. C₂×#1039	C₂³	semidirect
21. C₂⁵×C₅	D₅	semidirect
26. C₂²×C₅²	C₂×D₄	semidirect
28. C₂²×C₅²	C₂⁴	semidirect
30. C₂×C₅⋊D₅	C₂⁴	semidirect
31. #1039	C₂⁴	semidirect
34. C₂⁴×C₅	C₂×D₅	semidirect
41. C₂×C₅²	C₂²×D₄	semidirect
45. C₂³×C₅	C₂²⋊D₅	semidirect
47. C₂³×C₅	C₂²×D₅	semidirect
53. C₂⁵	C₅⋊D₅	semidirect
56. C₅²	C₂³×D₄	semidirect
58. C₂²×C₅	C₂×C₂²⋊D₅	semidirect
60. C₂²×C₅	C₂³×D₅	semidirect
68. C₂⁴	C₂×C₅⋊D₅	semidirect
72. C₂×C₅	C₂²×C₂²⋊D₅	semidirect
78. C₂³	C₂²⋊(C₅⋊D₅)	direct (N × H)
80. C₂³	C₂²×C₅⋊D₅	semidirect
83. C₅	C₂³×C₂²⋊D₅	semidirect
87. C₂²	C₂×C₂²⋊(C₅⋊D₅)	direct (N × H)
89. C₂²	C₂³×C₅⋊D₅	semidirect
93. C₂	C₂²×C₂²⋊(C₅⋊D₅)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁵×C₅²	2
C₂⁴×C₅⋊D₅	2
C₂²×C₂²⋊(C₅⋊D₅)	2
C₂³×#1039	2
C₂³×C₂²⋊D₅	5

Subgroups — C23×C22⋊(C5⋊D5) #13107894

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₂²⋊(C₅⋊D₅) #13107894