Subgroups — #13102524

Order 1600.

744 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#87808	C₂	1	3	yes	maximal
2	C₂×#87806	C₂	1	3	yes	maximal, complemented
3	C₅²×#95	C₂	1	1	yes	maximal, characteristic, 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	#87808	—	2	6	no	—
8	#87806	—	2	6	no	—
9	#64965	—	5	6	no	maximal
10	C₂³×C₅²	C₂³	1	1	yes	characteristic
11	C₂²×C₅⋊D₅	—	2	3	no	—
12	C₂²×C₅⋊D₅	—	2	3	no	—
13	C₂²×C₅⋊D₅	Q₈	1	2	yes	—
14	C₂×C₄×C₅²	—	2	3	no	—
15	C₂×C₄×C₅²	—	2	3	no	—
16	C₂×C₄×C₅²	—	2	3	no	—
17	C₂×#1039	—	2	3	no	—
18	C₂×#1039	—	2	3	no	—
19	C₂×#1039	D₄	1	6	yes	—
20	C₂×#685	—	5	18	no	—
21	C₂×#683	—	5	18	no	—
22	C₅×#95	D₅	1	6	yes	complemented
23	C₂²×C₅²	C₂×D₄	1	3	yes	—
24	C₂²×C₅²	C₂×Q₈	1	1	yes	characteristic
25	C₂²×C₅²	#41	1	3	yes	—
26	C₂×C₅⋊D₅	—	2	6	no	—
27	C₂×C₅⋊D₅	—	4	3	no	—
28	C₂×C₅⋊D₅	—	4	1	no	—
29	C₄×C₅²	—	4	3	no	—
30	#1039	—	2	6	no	—
31	C₂³×D₅	—	5	6	no	—
32	C₂²×C₄×C₅	C₂×D₅	1	18	yes	—
33	C₂²×Dic₅	—	5	18	no	—
34	#685	—	10	36	no	—
35	#683	—	10	36	no	—
36	#396	—	25	1	no	Sylow
37	C₂×C₅²	#121	1	3	yes	—
38	C₂×C₅²	C₂²⋊Q₈	1	3	yes	—
39	C₂×C₅²	#126	1	1	yes	characteristic
40	C₅⋊D₅	—	4	2	no	—
41	C₂³×C₅	C₂²×D₅	1	6	yes	—
42	C₂²×D₅	—	5	12	no	—
43	C₂²×D₅	—	10	18	no	—
44	C₂²×D₅	—	10	18	no	—
45	C₂×C₄×C₅	—	2	18	no	—
46	C₂×C₄×C₅	—	2	18	no	—
47	C₂×C₄×C₅	—	2	18	no	—
48	C₂×Dic₅	—	5	36	no	—
49	C₂×Dic₅	—	10	18	no	—
50	C₂×Dic₅	—	10	18	no	—
51	C₂×C₄⋊C₄	—	25	3	no	—
52	C₂×C₂²⋊C₄	—	25	3	no	—
53	#95	C₅⋊D₅	1	1	yes	characteristic, complemented
54	C₅²	#396	1	1	yes	characteristic, complemented, Sylow
55	C₂²×C₅	#709	1	18	yes	—
56	C₂²×C₅	D₄×D₅	1	18	yes	—
57	C₂²×C₅	Q₈×D₅	1	6	yes	—
58	C₂×D₅	—	10	36	no	—
59	C₂×D₅	—	20	6	no	—
60	C₂×D₅	—	20	18	no	—
61	C₄×C₅	—	4	18	no	—
62	Dic₅	—	10	36	no	—
63	C₂⁴	—	25	1	no	—
64	C₂²×C₄	—	25	3	no	—
65	C₂²×C₄	C₂×C₅⋊D₅	1	3	yes	—
66	C₄⋊C₄	—	50	6	no	—
67	C₂²⋊C₄	—	50	6	no	—
68	C₂×C₅	#4022	1	6	yes	—
69	C₂×C₅	#4030	1	18	yes	—
70	C₂×C₅	#4042	1	18	yes	—
71	D₅	—	20	12	no	—
72	C₂³	—	25	2	no	—
73	C₂³	—	50	3	no	—
74	C₂³	—	50	3	no	—
75	C₂³	C₂²×C₅⋊D₅	1	1	yes	characteristic
76	C₂×C₄	—	2	3	no	—
77	C₂×C₄	—	2	3	no	—
78	C₂×C₄	—	2	3	no	—
79	C₂×C₄	—	25	6	no	—
80	C₂×C₄	—	50	3	no	—
81	C₂×C₄	—	50	3	no	—
82	C₅	#64965	1	6	yes	complemented
83	C₂²	—	50	6	no	—
84	C₂²	—	100	1	no	—
85	C₂²	—	100	3	no	—
86	C₂²	#87900	1	3	yes	—
87	C₂²	D₄×C₅⋊D₅	1	3	yes	—
88	C₂²	Q₈×C₅⋊D₅	1	1	yes	characteristic
89	C₄	—	4	3	no	—
90	C₄	—	50	6	no	—
91	C₂	—	100	2	no	—
92	C₂	#11717196	1	1	yes	characteristic
93	C₂	#11717204	1	3	yes	—
94	C₂	#11717216	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×C₅⋊D₅
commutator, socle, cosocle	C₂³×C₅²	C₂³
Fitting	C₅²×#95	C₂
prime radical	C₂³×C₅⋊D₅	C₂²
hypercenter	#95	C₅⋊D₅
hypocenter	C₅²	#396
LCS	G ▷ C₂³×C₅² ▷ C₅²
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
2. C₂×#87806	C₂	semidirect
3. C₅²×#95	C₂	semidirect
22. C₅×#95	D₅	semidirect
53. #95	C₅⋊D₅	semidirect
54. C₅²	#396	semidirect
82. C₅	#64965	semidirect

Maximal subgroups

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

subgroup	index
C₂×#87808	2
C₂×#87806	2
C₅²×#95	2
#64965	5