Subgroups — #13098675

Order 1600.

267 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#1035	C₂	1	2	yes	maximal
2	C₄²×D₂₅	C₂	1	1	yes	maximal, characteristic
3	(C₂×#1035)⋊C₄	C₂	1	4	yes	maximal
4	C₂²×#1035	C₂²	1	4	yes	—
5	C₂×C₄×D₂₅	C₂²	1	2	yes	—
6	C₂×C₄×D₂₅	C₂²	1	1	yes	characteristic
7	C₄×#1035	C₄	1	8	yes	complemented
8	C₄²×C₂₅	C₄	1	1	yes	characteristic, complemented
9	C₄×Dic₂₅	C₄	1	1	yes	characteristic, complemented
10	C₄×Dic₂₅	C₄	1	2	yes	complemented
11	#65686	—	5	1	no	maximal
12	C₂²×D₂₅	C₂³	1	1	yes	characteristic
13	C₂×#1035	—	2	8	no	—
14	C₂×#1035	C₂×C₄	1	8	yes	—
15	C₂×C₄×C₂₅	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₂₅	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₂₅	C₂×C₄	1	2	yes	—
18	C₂×Dic₂₅	C₂×C₄	1	1	yes	characteristic
19	C₄×D₂₅	—	2	4	no	—
20	C₄×D₂₅	C₂×C₄	1	4	yes	—
21	C₂×C₄×AGL(1,𝔽₅)	—	5	2	no	—
22	C₄²×D₅	—	5	1	no	—
23	(C₂×AGL(1,𝔽₅))⋊C₄	—	5	4	no	—
24	C₂²×C₂₅	C₂²×C₄	1	1	yes	characteristic
25	C₂×D₂₅	C₂²×C₄	1	2	yes	—
26	C₂×D₂₅	#41	1	4	yes	—
27	#1035	—	2	8	no	—
28	C₄×C₂₅	—	2	2	no	—
29	C₄×C₂₅	C₄²	1	2	yes	—
30	Dic₂₅	—	2	2	no	—
31	Dic₂₅	C₄²	1	2	yes	—
32	C₂²×AGL(1,𝔽₅)	—	5	4	no	—
33	C₂×C₄×D₅	—	5	1	no	—
34	C₂×C₄×D₅	—	5	2	no	—
35	C₄×AGL(1,𝔽₅)	—	5	8	no	—
36	C₄²×C₅	AGL(1,𝔽₅)	1	1	yes	characteristic
37	C₄×Dic₅	—	5	2	no	—
38	C₄×Dic₅	—	5	1	no	—
39	#376	—	25	1	no	Sylow
40	C₂×C₂₅	C₂×C₄²	1	1	yes	characteristic
41	C₂×C₂₅	#117	1	2	yes	—
42	D₂₅	#117	1	4	yes	—
43	C₂²×D₅	—	5	1	no	—
44	C₂×AGL(1,𝔽₅)	—	5	8	no	—
45	C₂×AGL(1,𝔽₅)	—	10	8	no	—
46	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	2	yes	—
47	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
48	C₂×Dic₅	—	5	1	no	—
49	C₂×Dic₅	—	5	2	no	—
50	C₄×D₅	—	5	4	no	—
51	C₄×D₅	—	10	4	no	—
52	C₂×C₄²	—	25	2	no	—
53	C₂×C₄²	—	25	1	no	—
54	#95	—	25	4	no	—
55	C₂₅	#376	1	1	yes	characteristic, complemented, Sylow
56	C₂²×C₅	C₂²×AGL(1,𝔽₅)	1	1	yes	characteristic
57	C₂×D₅	—	5	2	no	—
58	C₂×D₅	—	5	4	no	—
59	AGL(1,𝔽₅)	—	10	8	no	—
60	C₄×C₅	—	2	2	no	—
61	C₄×C₅	C₄×AGL(1,𝔽₅)	1	2	yes	—
62	Dic₅	—	5	2	no	—
63	Dic₅	—	10	2	no	—
64	C₂²×C₄	—	25	1	no	—
65	C₂²×C₄	—	25	4	no	—
66	C₂²×C₄	—	25	2	no	—
67	C₄²	—	25	8	no	—
68	C₄²	—	25	2	no	—
69	C₄²	—	25	1	no	—
70	C₄²	#1035	1	1	yes	characteristic, complemented
71	C₂×C₅	C₂×C₄×AGL(1,𝔽₅)	1	1	yes	characteristic
72	C₂×C₅	#4130	1	2	yes	—
73	D₅	—	5	4	no	—
74	C₂³	—	25	1	no	—
75	C₂×C₄	—	25	1	no	—
76	C₂×C₄	—	25	4	no	—
77	C₂×C₄	—	25	8	no	—
78	C₂×C₄	—	25	2	no	—
79	C₂×C₄	—	50	4	no	—
80	C₂×C₄	—	50	8	no	—
81	C₂×C₄	C₂×#1035	1	2	yes	—
82	C₂×C₄	C₂×#1035	1	1	yes	characteristic
83	C₅	#65686	1	1	yes	characteristic
84	C₂²	—	25	2	no	—
85	C₂²	—	25	4	no	—
86	C₂²	C₂²×#1035	1	1	yes	characteristic
87	C₄	—	2	2	no	—
88	C₄	—	25	2	no	—
89	C₄	—	50	8	no	—
90	C₄	—	50	2	no	—
91	C₄	C₄×#1035	1	2	yes	—
92	C₂	—	25	4	no	—
93	C₂	C₂×C₄×#1035	1	1	yes	characteristic
94	C₂	#11716549	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×#1035
commutator	C₂×C₂₅	C₂×C₄²
Frattini, socle	C₂²×C₅	C₂²×AGL(1,𝔽₅)
Fitting	C₄²×C₂₅	C₄
prime radical, cosocle	C₂²×D₂₅	C₂³
hypercenter	C₄²	#1035
hypocenter	C₂₅	#376
LCS	G ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

Complements

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

N	H ≅ G/N	type
7. C₄×#1035	C₄	semidirect
8. C₄²×C₂₅	C₄	semidirect
9. C₄×Dic₂₅	C₄	semidirect
10. C₄×Dic₂₅	C₄	semidirect
55. C₂₅	#376	semidirect
70. C₄²	#1035	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×#1035	2
C₄²×D₂₅	2
(C₂×#1035)⋊C₄	2
#65686	5