Subgroups — #95×C₅⋊D₅ #13102530

Order 1600.

1320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅⋊D₅	C₂	1	3	yes	maximal
2	C₅²×#95	C₂	1	1	yes	maximal, characteristic, complemented
3	#11716698	C₂	1	3	yes	maximal, complemented
4	C₂³×C₅⋊D₅	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₅²	C₂²	1	3	yes	—
6	C₂²×#1039	C₂²	1	3	yes	—
7	C₂×C₄×C₅⋊D₅	—	2	12	no	—
8	C₂×C₄×C₅⋊D₅	C₄	1	12	yes	complemented
9	D₅×#95	—	5	6	no	maximal
10	C₂³×C₅²	C₂³	1	1	yes	characteristic
11	C₂²×C₅⋊D₅	C₂×C₄	1	6	yes	—
12	C₂²×C₅⋊D₅	D₄	1	6	yes	—
13	C₂²×C₅⋊D₅	Q₈	1	2	yes	—
14	C₂×C₄×C₅²	—	2	6	no	—
15	C₂×C₄×C₅²	C₂×C₄	1	6	yes	complemented
16	C₂×#1039	—	2	6	no	—
17	C₂×#1039	C₂×C₄	1	6	yes	complemented
18	C₄×C₅⋊D₅	—	2	24	no	—
19	C₂²×C₄×D₅	—	5	18	no	—
20	C₅×#95	D₅	1	6	yes	complemented
21	#3963	—	5	18	no	—
22	C₂²×C₅²	C₂²×C₄	1	3	yes	—
23	C₂²×C₅²	C₂×D₄	1	3	yes	—
24	C₂²×C₅²	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₅⋊D₅	C₄²	1	4	yes	—
26	C₂×C₅⋊D₅	C₂²⋊C₄	1	12	yes	—
27	C₂×C₅⋊D₅	C₄⋊C₄	1	12	yes	—
28	C₄×C₅²	—	2	6	no	—
29	#1039	—	2	6	no	—
30	C₂³×D₅	—	5	6	no	—
31	C₂²×C₄×C₅	C₂×D₅	1	18	yes	—
32	C₂²×Dic₅	—	5	18	no	—
33	C₂×C₄×D₅	—	5	72	no	—
34	C₂×C₄×D₅	—	10	72	no	—
35	C₂×#95	—	25	1	no	Sylow
36	C₂×C₅²	C₂×C₄²	1	1	yes	characteristic
37	C₂×C₅²	C₂×C₂²⋊C₄	1	3	yes	—
38	C₂×C₅²	C₂×C₄⋊C₄	1	3	yes	—
39	C₅⋊D₅	#95	1	8	yes	direct product factor
40	C₂³×C₅	C₂²×D₅	1	6	yes	—
41	C₂²×D₅	—	5	36	no	—
42	C₂²×D₅	—	5	36	no	—
43	C₂²×D₅	—	5	12	no	—
44	C₂×C₄×C₅	—	2	36	no	—
45	C₂×C₄×C₅	C₄×D₅	1	36	yes	complemented
46	C₂×Dic₅	—	5	36	no	—
47	C₂×Dic₅	—	10	36	no	—
48	C₄×D₅	—	10	144	no	—
49	C₂³×C₄	—	25	3	no	—
50	#95	—	25	3	no	—
51	#95	C₅⋊D₅	1	1	yes	characteristic, direct product factor
52	C₅²	C₂×#95	1	1	yes	characteristic, complemented, Sylow
53	C₂²×C₅	C₂×C₄×D₅	1	18	yes	—
54	C₂²×C₅	D₄×D₅	1	18	yes	—
55	C₂²×C₅	Q₈×D₅	1	6	yes	—
56	C₂×D₅	—	5	24	no	—
57	C₂×D₅	—	5	72	no	—
58	C₂×D₅	—	5	72	no	—
59	C₄×C₅	—	2	36	no	—
60	Dic₅	—	10	36	no	—
61	C₂⁴	—	25	1	no	—
62	C₂²×C₄	—	25	3	no	—
63	C₂²×C₄	—	25	12	no	—
64	C₂²×C₄	—	50	12	no	—
65	C₂²×C₄	C₂×C₅⋊D₅	1	3	yes	—
66	C₂×C₅	C₄²×D₅	1	6	yes	—
67	C₂×C₅	D₅×C₂²⋊C₄	1	18	yes	—
68	C₂×C₅	D₅×C₄⋊C₄	1	18	yes	—
69	D₅	—	5	48	no	—
70	C₂³	—	25	6	no	—
71	C₂³	—	25	6	no	—
72	C₂³	—	25	2	no	—
73	C₂³	C₂²×C₅⋊D₅	1	1	yes	characteristic
74	C₂×C₄	—	2	6	no	—
75	C₂×C₄	—	25	6	no	—
76	C₂×C₄	—	50	24	no	—
77	C₂×C₄	—	50	6	no	—
78	C₂×C₄	C₄×C₅⋊D₅	1	6	yes	complemented
79	C₅	D₅×#95	1	6	yes	complemented
80	C₂²	—	25	4	no	—
81	C₂²	—	25	12	no	—
82	C₂²	—	25	12	no	—
83	C₂²	C₂×C₄×C₅⋊D₅	1	3	yes	—
84	C₂²	D₄×C₅⋊D₅	1	3	yes	—
85	C₂²	Q₈×C₅⋊D₅	1	1	yes	characteristic
86	C₄	—	2	6	no	—
87	C₄	—	50	6	no	—
88	C₂	—	25	8	no	—
89	C₂	C₄²×C₅⋊D₅	1	1	yes	characteristic
90	C₂	C₂²⋊C₄×C₅⋊D₅	1	3	yes	—
91	C₂	C₄⋊C₄×C₅⋊D₅	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×C₅⋊D₅
commutator	C₂×C₅²	C₂×C₄²
Fitting	C₅²×#95	C₂
socle, cosocle	C₂³×C₅²	C₂³
prime radical	C₂³×C₅⋊D₅	C₂²
hypercenter	#95	C₅⋊D₅
hypocenter	C₅²	C₂×#95
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₅²×#95	C₂	semidirect
3. #11716698	C₂	semidirect
8. C₂×C₄×C₅⋊D₅	C₄	semidirect
15. C₂×C₄×C₅²	C₂×C₄	semidirect
17. C₂×#1039	C₂×C₄	semidirect
20. C₅×#95	D₅	semidirect
39. C₅⋊D₅	#95	direct (N × H)
45. C₂×C₄×C₅	C₄×D₅	semidirect
51. #95	C₅⋊D₅	direct (N × H)
52. C₅²	C₂×#95	semidirect
78. C₂×C₄	C₄×C₅⋊D₅	semidirect
79. C₅	D₅×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₅⋊D₅	2
C₅²×#95	2
#11716698	2
D₅×#95	5

Subgroups — #95×C5⋊D5 #13102530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #95×C₅⋊D₅ #13102530