Subgroups — #11717385

Order 800.

125 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#87877	C₂	1	1	yes	maximal, characteristic
2	#87872	C₂	1	1	yes	maximal, characteristic, complemented
3	#87862	C₂	1	1	yes	maximal, characteristic, complemented
4	#87838	C₂	1	4	yes	maximal, complemented
5	C₂×D₅²	—	2	1	no	—
6	C₄×C₅⋊D₅	C₂²	1	1	yes	characteristic
7	C₅×D₂₀	—	2	1	no	—
8	C₅×Dic₁₀	—	2	1	no	—
9	#6039	C₂²	1	2	yes	complemented
10	#6037	C₂²	1	2	yes	—
11	#6036	—	2	1	no	—
12	#6034	C₂²	1	2	yes	complemented
13	C₂×C₅⋊D₅	D₄	1	1	yes	characteristic
14	C₂×C₅×D₅	—	2	2	no	—
15	D₅²	—	4	2	no	—
16	C₄×C₅²	D₄	1	1	yes	characteristic
17	#1039	C₂³	1	1	yes	characteristic
18	C₅×Dic₅	—	2	2	no	—
19	Q₈×D₅	—	10	1	no	—
20	D₄×D₅	—	10	1	no	—
21	D₅⋊C₈	—	10	1	no	—
22	C₂×C₅²	C₂×D₄	1	1	yes	characteristic
23	C₅⋊D₅	SD₁₆	1	2	yes	complemented
24	C₅×D₅	—	4	2	no	—
25	C₂²×D₅	—	10	2	no	—
26	C₅×Q₈	—	10	1	no	—
27	C₅×D₄	—	10	1	no	—
28	C₂²⋊D₅	—	10	2	no	—
29	D₂₀	—	2	1	no	—
30	C₄×D₅	—	10	1	no	—
31	C₄×D₅	—	10	1	no	—
32	C₄×D₅	—	10	1	no	—
33	C₄×D₅	—	10	2	no	—
34	Dic₁₀	—	2	1	no	—
35	Dic₁₀	—	10	2	no	—
36	#170	—	10	2	no	—
37	C₂×SD₁₆	—	25	1	no	maximal, Sylow
38	C₅²	C₂×SD₁₆	1	1	yes	characteristic, complemented, Sylow
39	C₂²×C₅	—	10	2	no	—
40	C₂×D₅	—	2	2	no	—
41	C₂×D₅	—	10	1	no	—
42	C₂×D₅	—	10	1	no	—
43	C₂×D₅	—	10	1	no	—
44	C₂×D₅	—	20	4	no	—
45	C₄×C₅	—	2	1	no	—
46	C₄×C₅	—	2	1	no	—
47	C₄×C₅	—	2	1	no	—
48	C₄×C₅	—	10	2	no	—
49	Dic₅	—	2	2	no	—
50	Dic₅	—	10	1	no	—
51	Dic₅	—	10	1	no	—
52	Dic₅	—	10	1	no	—
53	C₂×Q₈	—	25	1	no	—
54	C₂×D₄	—	25	1	no	—
55	SD₁₆	—	25	4	no	—
56	C₂×C₈	—	25	1	no	—
57	C₂×C₅	—	2	1	no	—
58	C₂×C₅	—	2	1	no	—
59	C₂×C₅	—	2	1	no	—
60	C₂×C₅	—	20	2	no	—
61	D₅	—	4	2	no	—
62	D₅	—	10	2	no	—
63	D₅	—	10	2	no	—
64	D₅	—	10	2	no	—
65	C₂³	—	50	1	no	—
66	Q₈	—	10	1	no	—
67	Q₈	—	25	2	no	—
68	D₄	—	10	1	no	—
69	D₄	—	25	2	no	—
70	C₂×C₄	—	25	1	no	—
71	C₂×C₄	—	50	1	no	—
72	C₈	—	25	2	no	—
73	C₅	—	2	1	no	—
74	C₅	—	2	1	no	—
75	C₅	—	2	1	no	—
76	C₂²	—	10	2	no	—
77	C₂²	—	25	1	no	—
78	C₂²	—	100	2	no	—
79	C₄	—	10	2	no	—
80	C₄	—	25	1	no	—
81	C₄	D₅²⋊C₂	1	1	yes	characteristic
82	C₂	—	20	2	no	—
83	C₂	—	25	2	no	—
84	C₂	C₂×D₅²⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×D₅²⋊C₂
commutator, cosocle	#1039	C₂³
Fitting	C₄×C₅²	D₄
socle	C₂×C₅²	C₂×D₄
prime radical	#87877	C₂
hypercenter	C₄	D₅²⋊C₂
hypocenter	C₅²	C₂×SD₁₆
LCS	G ▷ #1039 ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. #87872	C₂	semidirect
3. #87862	C₂	semidirect
4. #87838	C₂	semidirect
9. #6039	C₂²	semidirect
12. #6034	C₂²	semidirect
23. C₅⋊D₅	SD₁₆	semidirect
38. C₅²	C₂×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
#87877	2
#87872	2
#87862	2
#87838	2
C₂×SD₁₆	25