Subgroups — #11716471

Order 800.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#87744	C₂	1	1	yes	maximal, characteristic
2	C₂×Dic₅₀	C₂	1	1	yes	maximal, characteristic, complemented
3	M₁₆×C₂₅	C₂	1	1	yes	maximal, characteristic, complemented
4	#87713	C₂	1	2	yes	maximal, complemented
5	Dic₁₀₀	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₂₅	C₂²	1	1	yes	characteristic
7	C₂²⋊D₂₅	—	2	1	no	—
8	C₂×Dic₂₅	—	2	1	no	—
9	D₁₀₀	C₂²	1	1	yes	characteristic
10	C₄×D₂₅	—	2	1	no	—
11	Dic₅₀	—	2	1	no	—
12	Dic₅₀	C₂²	1	1	yes	characteristic
13	Dic₅₀	C₂²	1	2	yes	—
14	C₈×C₂₅	C₂²	1	2	yes	—
15	#4055	—	5	1	no	maximal
16	C₂²×C₂₅	D₄	1	1	yes	characteristic
17	C₂×D₂₅	—	2	1	no	—
18	C₄×C₂₅	D₄	1	1	yes	characteristic
19	C₄×C₂₅	C₂³	1	1	yes	characteristic
20	Dic₂₅	—	2	2	no	—
21	Dic₂₅	—	2	1	no	—
22	#709	—	5	1	no	—
23	C₂×Dic₁₀	—	5	1	no	—
24	C₅×M₁₆	D₅	1	1	yes	characteristic
25	Dic₂₀	—	5	2	no	—
26	#677	—	5	2	no	—
27	C₂×C₂₅	—	2	1	no	—
28	C₂×C₂₅	C₂×D₄	1	1	yes	characteristic
29	D₂₅	—	4	1	no	—
30	C₂×C₄×C₅	C₂×D₅	1	1	yes	characteristic
31	C₂²⋊D₅	—	10	1	no	—
32	C₂×Dic₅	—	10	1	no	—
33	D₂₀	—	5	1	no	—
34	C₄×D₅	—	10	1	no	—
35	Dic₁₀	—	5	2	no	—
36	Dic₁₀	—	5	1	no	—
37	Dic₁₀	—	10	1	no	—
38	C₅×C₈	C₂×D₅	1	2	yes	—
39	#137	—	25	1	no	Sylow
40	C₂₅	#137	1	1	yes	characteristic, complemented, Sylow
41	C₂²×C₅	D₂₀	1	1	yes	characteristic
42	C₂×D₅	—	10	1	no	—
43	C₄×C₅	D₂₀	1	1	yes	characteristic
44	C₄×C₅	C₂²×D₅	1	1	yes	characteristic
45	Dic₅	—	10	2	no	—
46	Dic₅	—	10	1	no	—
47	#41	—	25	1	no	—
48	C₂×Q₈	—	25	1	no	—
49	Q₁₆	—	25	2	no	—
50	SD₁₆	—	25	2	no	—
51	M₁₆	D₂₅	1	1	yes	characteristic, complemented
52	C₂×C₅	—	2	1	no	—
53	C₂×C₅	C₂×D₂₀	1	1	yes	characteristic
54	D₅	—	20	1	no	—
55	Q₈	—	25	2	no	—
56	Q₈	—	25	1	no	—
57	Q₈	—	50	1	no	—
58	D₄	—	25	1	no	—
59	D₄	—	50	1	no	—
60	C₂×C₄	—	50	1	no	—
61	C₂×C₄	—	50	1	no	—
62	C₂×C₄	C₂×D₂₅	1	1	yes	characteristic
63	C₈	C₂×D₂₅	1	2	yes	—
64	C₅	#4055	1	1	yes	characteristic
65	C₂²	—	50	1	no	—
66	C₂²	D₁₀₀	1	1	yes	characteristic
67	C₄	—	50	1	no	—
68	C₄	—	50	2	no	—
69	C₄	D₁₀₀	1	1	yes	characteristic
70	C₄	C₂²×D₂₅	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	—	100	1	no	—
73	C₂	C₂×D₁₀₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₁₀₀
commutator, cosocle	C₄×C₂₅	C₂³
Frattini	C₄×C₅	C₂²×D₅
Fitting	M₁₆×C₂₅	C₂
socle	C₂×C₅	C₂×D₂₀
prime radical	#87744	C₂
hypercenter	M₁₆	D₂₅
hypocenter	C₂₅	#137
LCS	G ▷ C₄×C₂₅ ▷ C₂×C₂₅ ▷ C₂₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₅₀	C₂	semidirect
3. M₁₆×C₂₅	C₂	semidirect
4. #87713	C₂	semidirect
5. Dic₁₀₀	C₂	semidirect
40. C₂₅	#137	semidirect
51. M₁₆	D₂₅	semidirect

Maximal subgroups

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

subgroup	index
#87744	2
C₂×Dic₅₀	2
M₁₆×C₂₅	2
#87713	2
Dic₁₀₀	2
#4055	5