Subgroups — #13104157

Order 1600.

204 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11717386	C₂	1	2	yes	maximal
2	#11717380	C₂	1	2	yes	maximal
3	#11716920	C₂	1	2	yes	maximal
4	C₈×#1044	C₂	1	1	yes	maximal, characteristic
5	#87872	C₂²	1	4	yes	—
6	C₄×#1044	C₂²	1	1	yes	characteristic
7	#87862	C₂²	1	1	yes	characteristic
8	#87839	—	2	4	no	—
9	#87836	—	2	4	no	—
10	C₈×C₅⋊D₅	C₂²	1	1	yes	characteristic
11	C₅×Dic₂₀	—	2	2	no	—
12	#87775	—	2	2	no	—
13	C₂×#1044	D₄	1	2	yes	—
14	C₄×C₅⋊D₅	C₂³	1	1	yes	characteristic
15	C₅×Dic₁₀	—	2	4	no	—
16	#6039	—	2	4	no	—
17	#6036	—	2	4	no	—
18	#6034	D₄	1	2	yes	—
19	C₅²×C₈	D₄	1	1	yes	characteristic
20	#6029	D₄	1	1	yes	characteristic
21	D₅×Q₁₆	—	10	2	no	—
22	C₈×AGL(1,𝔽₅)	—	10	1	no	—
23	C₂×C₅⋊D₅	C₂×D₄	1	1	yes	characteristic
24	#1044	Q₁₆	1	4	yes	complemented
25	C₄×C₅²	C₂×D₄	1	1	yes	characteristic
26	#1039	C₂×D₄	1	1	yes	characteristic
27	C₅×Dic₅	—	4	4	no	—
28	Q₈×D₅	—	10	4	no	—
29	C₄×AGL(1,𝔽₅)	—	10	1	no	—
30	D₅⋊C₈	—	10	1	no	—
31	C₅×Q₁₆	—	10	2	no	—
32	#689	—	10	4	no	—
33	Dic₂₀	—	2	2	no	—
34	C₈×D₅	—	10	1	no	—
35	C₈×D₅	—	10	2	no	—
36	#494	—	25	1	no	maximal, Sylow
37	C₂×C₅²	#127	1	1	yes	characteristic
38	C₅⋊D₅	C₂×Q₁₆	1	2	yes	—
39	C₂×AGL(1,𝔽₅)	—	10	2	no	—
40	C₅×Q₈	—	10	4	no	—
41	C₄×D₅	—	10	1	no	—
42	C₄×D₅	—	10	2	no	—
43	C₄×D₅	—	20	4	no	—
44	Dic₁₀	—	2	4	no	—
45	Dic₁₀	—	20	4	no	—
46	#170	—	10	2	no	—
47	C₅×C₈	—	2	1	no	—
48	C₅×C₈	—	2	2	no	—
49	#168	—	10	1	no	—
50	#168	—	10	2	no	—
51	C₂×Q₁₆	—	25	2	no	—
52	C₂×Q₁₆	—	25	2	no	—
53	C₄⋊Q₈	—	25	2	no	—
54	C₄×C₈	—	25	1	no	—
55	C₅²	#494	1	1	yes	characteristic, complemented, Sylow
56	C₂×D₅	—	10	2	no	—
57	C₂×D₅	—	10	1	no	—
58	AGL(1,𝔽₅)	—	10	4	no	—
59	C₄×C₅	—	2	2	no	—
60	C₄×C₅	—	2	1	no	—
61	C₄×C₅	—	20	4	no	—
62	Dic₅	—	4	4	no	—
63	Dic₅	—	10	1	no	—
64	Dic₅	—	10	2	no	—
65	C₂×Q₈	—	25	4	no	—
66	Q₁₆	—	10	2	no	—
67	Q₁₆	—	50	2	no	—
68	Q₁₆	—	50	4	no	—
69	C₂×C₈	—	25	1	no	—
70	C₂×C₈	—	25	1	no	—
71	C₄⋊C₄	—	50	4	no	—
72	C₄²	—	25	1	no	—
73	C₂×C₅	—	2	2	no	—
74	C₂×C₅	—	2	1	no	—
75	D₅	—	10	2	no	—
76	D₅	—	10	4	no	—
77	Q₈	—	10	4	no	—
78	Q₈	—	50	4	no	—
79	C₂×C₄	—	25	2	no	—
80	C₂×C₄	—	25	1	no	—
81	C₂×C₄	—	50	4	no	—
82	C₈	—	25	2	no	—
83	C₈	—	25	1	no	—
84	C₈	D₅²⋊C₂	1	1	yes	characteristic
85	C₅	—	2	1	no	—
86	C₅	—	2	2	no	—
87	C₂²	—	25	1	no	—
88	C₄	—	20	4	no	—
89	C₄	—	25	4	no	—
90	C₄	—	25	1	no	—
91	C₄	C₂×D₅²⋊C₂	1	1	yes	characteristic
92	C₂	—	25	2	no	—
93	C₂	#11717389	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11717389
commutator, cosocle	C₄×C₅⋊D₅	C₂³
Frattini	C₄	C₂×D₅²⋊C₂
Fitting	C₅²×C₈	D₄
socle	C₂×C₅²	#127
prime radical	C₂×C₅⋊D₅	C₂×D₄
hypercenter	C₈	D₅²⋊C₂
hypocenter	C₅²	#494
LCS	G ▷ C₄×C₅⋊D₅ ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂ ◁ C₄ ◁ C₈

Complements

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

N	H ≅ G/N	type
24. #1044	Q₁₆	semidirect
55. C₅²	#494	semidirect

Maximal subgroups

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

subgroup	index
#11717386	2
#11717380	2
#11716920	2
C₈×#1044	2
#494	25