Subgroups — C₂²×#6037 #11717490

Order 800.

526 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₅×D₅	C₂	1	2	yes	maximal, complemented
2	C₂²×#1039	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#6037	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₅²	C₂²	1	1	yes	characteristic
5	C₂²×C₅×D₅	—	2	8	no	—
6	C₂²×C₅×D₅	C₂²	1	12	yes	complemented
7	C₂×#1039	C₂²	1	6	yes	complemented
8	#6037	C₂²	1	16	yes	direct product factor
9	C₂²×C₂²⋊D₅	—	5	2	no	maximal
10	C₂²×C₅²	D₄	1	4	yes	complemented
11	C₂²×C₅²	C₂³	1	3	yes	—
12	C₂×C₅×D₅	—	2	24	no	—
13	C₂×C₅×D₅	C₂³	1	8	yes	complemented
14	#1039	C₂³	1	4	yes	complemented
15	C₂⁴×C₅	—	5	2	no	—
16	C₂³×D₅	D₅	1	2	yes	complemented
17	C₂×C₂²⋊D₅	—	5	24	no	—
18	C₂²×Dic₅	—	5	2	no	—
19	C₂²×Dic₅	—	10	2	no	—
20	C₂×C₅²	C₂×D₄	1	6	yes	complemented
21	C₂×C₅²	C₂⁴	1	1	yes	characteristic
22	C₅×D₅	—	2	8	no	—
23	C₂³×C₅	—	2	2	no	—
24	C₂³×C₅	—	5	12	no	—
25	C₂³×C₅	—	10	8	no	—
26	C₂³×C₅	C₂×D₅	1	2	yes	—
27	C₂²×D₅	—	2	8	no	—
28	C₂²×D₅	C₂×D₅	1	12	yes	complemented
29	C₂²⋊D₅	—	5	32	no	—
30	C₂×Dic₅	—	5	12	no	—
31	C₂×Dic₅	—	10	12	no	—
32	C₂²×D₄	—	25	1	no	Sylow
33	C₅²	C₂²×D₄	1	1	yes	characteristic, complemented, Sylow
34	C₂²×C₅	—	2	8	no	—
35	C₂²×C₅	—	2	6	no	—
36	C₂²×C₅	—	5	8	no	—
37	C₂²×C₅	—	10	24	no	—
38	C₂²×C₅	C₂²⋊D₅	1	8	yes	complemented
39	C₂²×C₅	C₂²×D₅	1	6	yes	—
40	C₂×D₅	—	2	24	no	—
41	C₂×D₅	C₂²×D₅	1	8	yes	complemented
42	Dic₅	—	5	8	no	—
43	Dic₅	—	10	8	no	—
44	C₂⁴	—	5	2	no	—
45	C₂×D₄	—	25	12	no	—
46	C₂²×C₄	—	25	1	no	—
47	C₂×C₅	—	2	12	no	—
48	C₂×C₅	—	2	2	no	—
49	C₂×C₅	—	10	8	no	—
50	C₂×C₅	C₂×C₂²⋊D₅	1	12	yes	complemented
51	C₂×C₅	C₂³×D₅	1	2	yes	—
52	D₅	—	2	8	no	—
53	C₂³	—	5	12	no	—
54	C₂³	—	10	8	no	—
55	C₂³	D₅²	1	1	yes	characteristic
56	D₄	—	25	16	no	—
57	C₂×C₄	—	25	6	no	—
58	C₅	—	2	2	no	—
59	C₅	C₂²×C₂²⋊D₅	1	2	yes	complemented
60	C₂²	—	5	8	no	—
61	C₂²	—	10	24	no	—
62	C₂²	#6037	1	4	yes	direct product factor
63	C₂²	C₂×D₅²	1	3	yes	—
64	C₄	—	25	4	no	—
65	C₂	—	10	8	no	—
66	C₂	C₂×#6037	1	6	yes	direct product factor
67	C₂	C₂²×D₅²	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂³	D₅²
commutator, cosocle	C₂×C₅²	C₂⁴
Frattini	C₂	C₂²×D₅²
Fitting, socle	C₂³×C₅²	C₂²
hypocenter	C₅²	C₂²×D₄
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³

Complements

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

N	H ≅ G/N	type
1. C₂³×C₅×D₅	C₂	semidirect
2. C₂²×#1039	C₂	semidirect
3. C₂×#6037	C₂	direct (N × H)
6. C₂²×C₅×D₅	C₂²	semidirect
7. C₂×#1039	C₂²	semidirect
8. #6037	C₂²	direct (N × H)
10. C₂²×C₅²	D₄	semidirect
13. C₂×C₅×D₅	C₂³	semidirect
14. #1039	C₂³	semidirect
16. C₂³×D₅	D₅	semidirect
20. C₂×C₅²	C₂×D₄	semidirect
28. C₂²×D₅	C₂×D₅	semidirect
33. C₅²	C₂²×D₄	semidirect
38. C₂²×C₅	C₂²⋊D₅	semidirect
41. C₂×D₅	C₂²×D₅	semidirect
50. C₂×C₅	C₂×C₂²⋊D₅	semidirect
59. C₅	C₂²×C₂²⋊D₅	semidirect
62. C₂²	#6037	direct (N × H)
66. C₂	C₂×#6037	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₅×D₅	2
C₂²×#1039	2
C₂×#6037	2
C₂²×C₂²⋊D₅	5

Subgroups — C22×#6037 #11717490

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#6037 #11717490