Subgroups — #13100352

Order 1600.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#6034	C₂	1	2	yes	maximal
2	C₈×#1039	C₂	1	1	yes	maximal, characteristic
3	C₂×#6034	—	2	2	no	—
4	C₂×C₅²×C₈	C₄	1	1	yes	characteristic
5	C₄×#1039	C₂²	1	1	yes	characteristic
6	C₂×#6029	C₄	1	1	yes	characteristic
7	#64883	—	5	2	no	maximal
8	C₂×C₄×C₅²	C₂×C₄	1	1	yes	characteristic
9	C₂×#1039	D₄	1	1	yes	characteristic
10	C₂×#1039	Q₈	1	1	yes	characteristic
11	#6034	—	4	2	no	—
12	C₅²×C₈	—	2	1	no	—
13	#6029	C₈	1	2	yes	complemented
14	C₄⋊#170	—	5	4	no	—
15	C₈×Dic₅	—	5	2	no	—
16	C₈×Dic₅	—	10	2	no	—
17	C₂²×C₅²	C₄⋊C₄	1	1	yes	characteristic
18	C₄×C₅²	C₂×C₈	1	1	yes	characteristic
19	C₄×C₅²	M₁₆	1	1	yes	characteristic
20	#1039	—	2	1	no	—
21	#1039	SD₁₆	1	2	yes	—
22	C₂×#170	—	10	4	no	—
23	C₂×C₅×C₈	—	2	2	no	—
24	C₂×C₅×C₈	AGL(1,𝔽₅)	1	2	yes	—
25	C₄×Dic₅	—	5	2	no	—
26	C₄×Dic₅	—	10	2	no	—
27	C₂×#168	—	5	2	no	—
28	C₂×#168	—	10	2	no	—
29	#334	—	25	1	no	Sylow
30	C₂×C₅²	C₄⋊C₈	1	1	yes	characteristic
31	C₂×C₅²	#106	1	1	yes	characteristic
32	C₂×C₅²	#108	1	1	yes	characteristic
33	C₂×C₄×C₅	—	2	2	no	—
34	C₂×C₄×C₅	C₂×AGL(1,𝔽₅)	1	2	yes	—
35	C₂×Dic₅	—	5	2	no	—
36	C₂×Dic₅	—	5	2	no	—
37	C₂×Dic₅	—	10	2	no	—
38	C₂×Dic₅	—	10	2	no	—
39	#170	—	20	4	no	—
40	C₅×C₈	—	2	4	no	—
41	C₅×C₈	—	2	2	no	—
42	#168	—	5	4	no	—
43	#168	—	10	4	no	—
44	C₄⋊C₈	—	25	2	no	—
45	C₄×C₈	—	25	1	no	—
46	C₅²	#334	1	1	yes	characteristic, complemented, Sylow
47	C₂²×C₅	—	2	2	no	—
48	C₂²×C₅	C₄⋊AGL(1,𝔽₅)	1	2	yes	—
49	C₄×C₅	—	2	2	no	—
50	C₄×C₅	—	2	2	no	—
51	C₄×C₅	D₅⋊C₈	1	2	yes	—
52	C₄×C₅	#704	1	2	yes	—
53	Dic₅	—	5	4	no	—
54	Dic₅	—	10	4	no	—
55	Dic₅	—	10	4	no	—
56	Dic₅	—	10	2	no	—
57	C₂×C₈	—	25	1	no	—
58	C₂×C₈	—	50	2	no	—
59	C₂×C₈	#1044	1	1	yes	characteristic
60	C₄²	—	25	1	no	—
61	C₂×C₅	—	2	2	no	—
62	C₂×C₅	—	2	2	no	—
63	C₂×C₅	—	2	2	no	—
64	C₂×C₅	#3993	1	2	yes	—
65	C₂×C₅	#3996	1	2	yes	—
66	C₂×C₅	#4004	1	2	yes	—
67	C₂×C₄	—	25	1	no	—
68	C₂×C₄	—	25	1	no	—
69	C₂×C₄	C₂×#1044	1	1	yes	characteristic
70	C₈	—	2	1	no	—
71	C₈	—	25	2	no	—
72	C₈	—	100	2	no	—
73	C₅	—	2	2	no	—
74	C₅	#64883	1	2	yes	complemented
75	C₂²	C₄⋊#1044	1	1	yes	characteristic
76	C₄	—	25	2	no	—
77	C₄	—	50	1	no	—
78	C₄	#87862	1	1	yes	characteristic
79	C₄	#87867	1	1	yes	characteristic
80	C₂	#11716886	1	1	yes	characteristic
81	C₂	#11716889	1	1	yes	characteristic
82	C₂	#11716897	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#1044
commutator	C₄×C₅²	C₂×C₈
Frattini	C₂×C₄	C₂×#1044
Fitting	C₂×C₅²×C₈	C₄
socle, prime radical	C₂²×C₅²	C₄⋊C₄
cosocle	C₄×#1039	C₂²
hypercenter	C₂×C₈	#1044
hypocenter	C₅²	#334
LCS	G ▷ C₄×C₅² ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
13. #6029	C₈	semidirect
46. C₅²	#334	semidirect
74. C₅	#64883	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊#6034	2
C₈×#1039	2
#64883	5