Subgroups — #13097990

Order 1600.

165 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11716436	C₂	1	1	yes	maximal, characteristic
2	#11716432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
4	#11716369	C₂	1	4	yes	maximal, complemented
5	C₂×D₁₀₀	—	2	2	no	—
6	C₂×D₁₀₀	C₂²	1	2	yes	—
7	C₂×C₈×C₂₅	C₂²	1	2	yes	—
8	C₄²×C₂₅	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₂₅	C₂²	1	2	yes	—
10	#87718	—	2	2	no	—
11	#65002	—	5	1	no	maximal
12	C₂²×D₂₅	—	2	2	no	—
13	C₂×C₄×C₂₅	D₄	1	2	yes	—
14	C₂×C₄×C₂₅	C₂³	1	1	yes	characteristic
15	C₂×Dic₂₅	—	2	2	no	—
16	D₁₀₀	—	2	4	no	—
17	D₁₀₀	—	4	4	no	—
18	C₈×C₂₅	—	2	2	no	—
19	#4020	—	5	1	no	—
20	#4016	—	5	1	no	—
21	C₅×#97	D₅	1	1	yes	characteristic
22	#3953	—	5	4	no	—
23	C₂²×C₂₅	C₂×D₄	1	1	yes	characteristic
24	C₂×D₂₅	—	4	2	no	—
25	C₂×D₂₅	—	4	4	no	—
26	C₄×C₂₅	—	2	2	no	—
27	C₄×C₂₅	#41	1	2	yes	—
28	Dic₂₅	—	4	2	no	—
29	C₂×D₂₀	—	5	2	no	—
30	C₂×D₂₀	—	10	2	no	—
31	C₂×C₅×C₈	C₂×D₅	1	2	yes	—
32	C₄²×C₅	C₂×D₅	1	1	yes	characteristic
33	C₄⋊Dic₅	—	5	2	no	—
34	#683	—	10	2	no	—
35	#490	—	25	1	no	Sylow
36	C₂×C₂₅	#124	1	1	yes	characteristic
37	C₂×C₂₅	AGL(1,ℤ/8)	1	2	yes	—
38	D₂₅	—	8	2	no	—
39	C₂²×D₅	—	10	2	no	—
40	C₂×C₄×C₅	D₂₀	1	2	yes	—
41	C₂×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
42	C₂×Dic₅	—	10	2	no	—
43	D₂₀	—	10	4	no	—
44	D₂₀	—	20	4	no	—
45	C₅×C₈	—	2	2	no	—
46	#127	—	25	1	no	—
47	#125	—	25	1	no	—
48	#102	—	25	4	no	—
49	#97	D₂₅	1	1	yes	characteristic, complemented
50	C₂₅	#490	1	1	yes	characteristic, complemented, Sylow
51	C₂²×C₅	C₂×D₂₀	1	1	yes	characteristic
52	C₂×D₅	—	20	2	no	—
53	C₂×D₅	—	20	4	no	—
54	C₄×C₅	—	2	2	no	—
55	C₄×C₅	#709	1	2	yes	—
56	Dic₅	—	20	2	no	—
57	C₂×D₄	—	25	2	no	—
58	C₂×D₄	—	50	2	no	—
59	C₂×C₈	C₂×D₂₅	1	2	yes	—
60	C₄⋊C₄	—	25	2	no	—
61	C₄⋊C₄	—	50	2	no	—
62	C₄²	C₂×D₂₅	1	1	yes	characteristic
63	C₂×C₅	#4021	1	1	yes	characteristic
64	C₂×C₅	#4054	1	2	yes	—
65	D₅	—	40	2	no	—
66	C₂³	—	50	2	no	—
67	D₄	—	50	4	no	—
68	D₄	—	100	4	no	—
69	C₂×C₄	—	50	2	no	—
70	C₂×C₄	D₁₀₀	1	2	yes	—
71	C₂×C₄	C₂²×D₂₅	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₅	#65002	1	1	yes	characteristic
74	C₂²	—	100	2	no	—
75	C₂²	—	100	4	no	—
76	C₂²	C₂×D₁₀₀	1	1	yes	characteristic
77	C₄	—	2	2	no	—
78	C₄	—	100	2	no	—
79	C₄	#87744	1	2	yes	—
80	C₂	—	200	2	no	—
81	C₂	#11716437	1	1	yes	characteristic
82	C₂	#11716470	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₁₀₀
commutator, cosocle	C₂×C₄×C₂₅	C₂³
Frattini	C₂×C₄×C₅	C₂²×D₅
Fitting	C₂₅×#97	C₂
socle	C₂²×C₅	C₂×D₂₀
prime radical	#11716436	C₂
hypercenter	#97	D₂₅
hypocenter	C₂₅	#490
LCS	G ▷ C₂×C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. #11716432	C₂	semidirect
3. C₂₅×#97	C₂	semidirect
4. #11716369	C₂	semidirect
49. #97	D₂₅	semidirect
50. C₂₅	#490	semidirect

Maximal subgroups

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

subgroup	index
#11716436	2
#11716432	2
C₂₅×#97	2
#11716369	2
#65002	5