Subgroups — C₂×#11717196 #13107006

Order 1600.

984 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄²×C₅²	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#87808	C₂	1	3	yes	maximal
3	C₂×#87806	C₂	1	3	yes	maximal, complemented
4	#11717196	C₂	1	8	yes	maximal, direct product factor
5	C₂³×C₅⋊D₅	C₂²	1	1	yes	characteristic
6	C₂²×C₄×C₅²	C₂²	1	3	yes	—
7	C₂²×#1039	C₂²	1	3	yes	—
8	C₄²×C₅²	C₂²	1	4	yes	complemented
9	#87808	C₂²	1	12	yes	—
10	#87806	C₂²	1	12	yes	complemented
11	C₂×#4022	—	5	6	no	maximal
12	C₂³×C₅²	C₂³	1	1	yes	characteristic
13	C₂²×C₅⋊D₅	—	2	6	no	—
14	C₂²×C₅⋊D₅	C₂³	1	2	yes	—
15	C₂×C₄×C₅²	—	2	6	no	—
16	C₂×C₄×C₅²	C₂³	1	6	yes	—
17	C₂×#1039	—	2	6	no	—
18	C₂×#1039	C₂³	1	6	yes	—
19	C₂×C₄²×C₅	D₅	1	6	yes	complemented
20	C₂×#685	—	5	18	no	—
21	C₂×#683	—	5	18	no	—
22	#4022	—	5	48	no	—
23	C₂²×C₅²	#41	1	6	yes	—
24	C₂²×C₅²	C₂⁴	1	1	yes	characteristic
25	C₂×C₅⋊D₅	—	2	6	no	—
26	C₂×C₅⋊D₅	—	4	4	no	—
27	C₄×C₅²	—	2	6	no	—
28	#1039	—	2	6	no	—
29	C₂³×D₅	—	5	6	no	—
30	C₂²×C₄×C₅	C₂×D₅	1	18	yes	—
31	C₂²×Dic₅	—	5	18	no	—
32	C₄²×C₅	C₂×D₅	1	24	yes	complemented
33	#685	—	5	72	no	—
34	#683	—	5	72	no	—
35	C₂×#126	—	25	1	no	Sylow
36	C₂×C₅²	#126	1	4	yes	complemented
37	C₂×C₅²	C₂×#41	1	3	yes	—
38	C₅⋊D₅	—	4	2	no	—
39	C₂³×C₅	C₂²×D₅	1	6	yes	—
40	C₂²×D₅	—	5	12	no	—
41	C₂²×D₅	—	10	36	no	—
42	C₂×C₄×C₅	—	2	36	no	—
43	C₂×C₄×C₅	C₂²×D₅	1	36	yes	—
44	C₂×Dic₅	—	5	36	no	—
45	C₂×Dic₅	—	10	36	no	—
46	#126	—	25	8	no	—
47	C₂×C₄⋊C₄	—	25	3	no	—
48	C₂×C₂²⋊C₄	—	25	3	no	—
49	C₂×C₄²	C₅⋊D₅	1	1	yes	characteristic, complemented
50	C₅²	C₂×#126	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	#709	1	36	yes	—
52	C₂²×C₅	C₂³×D₅	1	6	yes	—
53	C₂×D₅	—	10	36	no	—
54	C₂×D₅	—	20	24	no	—
55	C₄×C₅	—	2	36	no	—
56	Dic₅	—	10	36	no	—
57	C₂⁴	—	25	1	no	—
58	C₂²×C₄	—	25	3	no	—
59	C₂²×C₄	C₂×C₅⋊D₅	1	3	yes	—
60	C₄⋊C₄	—	25	12	no	—
61	C₂²⋊C₄	—	25	12	no	—
62	C₄²	C₂×C₅⋊D₅	1	4	yes	complemented
63	C₂×C₅	#4022	1	24	yes	complemented
64	C₂×C₅	C₂×#709	1	18	yes	—
65	D₅	—	20	12	no	—
66	C₂³	—	25	2	no	—
67	C₂³	—	50	6	no	—
68	C₂³	C₂²×C₅⋊D₅	1	1	yes	characteristic
69	C₂×C₄	—	2	6	no	—
70	C₂×C₄	—	25	6	no	—
71	C₂×C₄	—	50	6	no	—
72	C₂×C₄	C₂²×C₅⋊D₅	1	6	yes	—
73	C₅	C₂×#4022	1	6	yes	complemented
74	C₂²	—	50	6	no	—
75	C₂²	—	100	4	no	—
76	C₂²	#87900	1	6	yes	—
77	C₂²	C₂³×C₅⋊D₅	1	1	yes	characteristic
78	C₄	—	2	6	no	—
79	C₄	—	50	6	no	—
80	C₂	—	100	2	no	—
81	C₂	#11717196	1	4	yes	direct product factor
82	C₂	C₂×#87900	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂²×C₅⋊D₅
commutator, cosocle	C₂²×C₅²	C₂⁴
Frattini	C₂²	C₂³×C₅⋊D₅
Fitting	C₂×C₄²×C₅²	C₂
socle	C₂³×C₅²	C₂³
prime radical	C₂³×C₅⋊D₅	C₂²
hypercenter	C₂×C₄²	C₅⋊D₅
hypocenter	C₅²	C₂×#126
LCS	G ▷ C₂²×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. C₂×C₄²×C₅²	C₂	semidirect
3. C₂×#87806	C₂	semidirect
4. #11717196	C₂	direct (N × H)
8. C₄²×C₅²	C₂²	semidirect
10. #87806	C₂²	semidirect
19. C₂×C₄²×C₅	D₅	semidirect
32. C₄²×C₅	C₂×D₅	semidirect
36. C₂×C₅²	#126	semidirect
49. C₂×C₄²	C₅⋊D₅	semidirect
50. C₅²	C₂×#126	semidirect
62. C₄²	C₂×C₅⋊D₅	semidirect
63. C₂×C₅	#4022	semidirect
73. C₅	C₂×#4022	semidirect
81. C₂	#11717196	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×C₅²	2
C₂×#87808	2
C₂×#87806	2
#11717196	2
C₂×#4022	5

Subgroups — C2×#11717196 #13107006

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11717196 #13107006