Subgroups — #13014359

Order 1280.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10598650	C₂	1	2	yes	maximal
2	Dic₅×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#64889	—	2	2	no	—
4	C₂×C₅×C₃₂	C₄	1	1	yes	characteristic
5	C₁₆×Dic₅	C₂²	1	1	yes	characteristic
6	C₂×#3926	C₄	1	1	yes	characteristic
7	#7462	—	5	1	no	maximal, Sylow
8	#3998	—	4	2	no	—
9	C₂×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
10	C₈×Dic₅	D₄	1	1	yes	characteristic
11	C₂×#672	Q₈	1	1	yes	characteristic
12	C₅×C₃₂	C₈	1	2	yes	—
13	#3926	—	2	1	no	—
14	C₄×C₃₂	—	5	1	no	—
15	#1373	—	5	2	no	—
16	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
17	C₄×Dic₅	Q₁₆	1	1	yes	characteristic
18	C₂×#168	D₈	1	1	yes	characteristic
19	#674	—	8	2	no	—
20	C₅×C₁₆	C₂×C₈	1	1	yes	characteristic
21	C₅×C₁₆	M₁₆	1	1	yes	characteristic
22	#672	—	2	1	no	—
23	C₂×C₃₂	—	5	1	no	—
24	C₂×C₃₂	AGL(1,𝔽₅)	1	1	yes	characteristic
25	#364	—	10	2	no	—
26	C₄×C₁₆	—	5	1	no	—
27	C₂×C₄×C₅	#107	1	1	yes	characteristic
28	C₂×Dic₅	—	2	1	no	—
29	C₅×C₈	C₄⋊C₈	1	1	yes	characteristic
30	C₅×C₈	#108	1	1	yes	characteristic
31	#168	D₁₆	1	1	yes	characteristic
32	#168	Q₃₂	1	1	yes	characteristic
33	M₃₂	—	20	2	no	—
34	C₂×C₁₆	—	5	1	no	—
35	C₂×C₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
36	C₄×C₈	—	5	1	no	—
37	C₃₂	—	10	1	no	—
38	C₃₂	#170	1	2	yes	—
39	C₂²×C₅	#368	1	1	yes	characteristic
40	C₄×C₅	#335	1	1	yes	characteristic
41	C₄×C₅	#366	1	1	yes	characteristic
42	Dic₅	—	2	2	no	—
43	C₂×C₈	—	5	1	no	—
44	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
45	C₄²	—	5	1	no	—
46	C₁₆	—	10	1	no	—
47	C₁₆	—	40	2	no	—
48	C₁₆	#700	1	1	yes	characteristic
49	C₁₆	C₂×#170	1	1	yes	characteristic
50	C₂×C₅	—	2	1	no	—
51	C₂×C₅	#1371	1	1	yes	characteristic
52	C₂×C₄	—	10	1	no	—
53	C₂×C₄	#3994	1	1	yes	characteristic
54	C₈	—	5	1	no	—
55	C₈	—	5	1	no	—
56	C₈	#3996	1	1	yes	characteristic
57	C₈	C₄⋊#170	1	1	yes	characteristic
58	C₅	#7462	1	1	yes	characteristic, complemented, Sylow
59	C₂²	#64851	1	1	yes	characteristic
60	C₄	—	10	2	no	—
61	C₄	#64849	1	1	yes	characteristic
62	C₄	#64882	1	1	yes	characteristic
63	C₂	—	2	1	no	—
64	C₂	#10598644	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#64849
commutator	C₅×C₁₆	C₂×C₈
Frattini	C₂×C₁₆	C₂×AGL(1,𝔽₅)
Fitting	C₂×C₅×C₃₂	C₄
socle	C₂×C₅	#1371
prime radical	C₂²×C₅	#368
cosocle	C₁₆×Dic₅	C₂²
hypercenter	C₂×C₃₂	AGL(1,𝔽₅)
hypocenter	C₅	#7462
LCS	G ▷ C₅×C₁₆ ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
58. C₅	#7462	semidirect

Maximal subgroups

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

subgroup	index
#10598650	2
Dic₅×C₃₂	2
#7462	5