Subgroups — #13014355

Order 1280.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10598644	C₂	1	2	yes	maximal
2	Dic₅×C₃₂	C₂	1	1	yes	maximal, characteristic
3	#64882	—	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	#7460	—	5	1	no	maximal, Sylow
8	C₄⋊#170	—	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	complemented
13	#3926	—	2	1	no	—
14	C₄×C₃₂	—	5	1	no	—
15	#1371	—	5	2	no	—
16	C₂×#170	—	8	2	no	—
17	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
18	C₄×Dic₅	D₈	1	1	yes	characteristic
19	C₂×#168	Q₁₆	1	1	yes	characteristic
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	C₄×C₁₆	—	5	1	no	—
26	#335	—	10	2	no	—
27	C₂×C₄×C₅	#107	1	1	yes	characteristic
28	C₂×Dic₅	D₁₆	1	1	yes	characteristic
29	C₂×Dic₅	Q₃₂	1	1	yes	characteristic
30	#170	—	16	2	no	—
31	C₅×C₈	C₄⋊C₈	1	1	yes	characteristic
32	C₅×C₈	#108	1	1	yes	characteristic
33	#168	—	2	1	no	—
34	C₂×C₁₆	—	5	1	no	—
35	C₂×C₁₆	C₂×AGL(1,𝔽₅)	1	1	yes	characteristic
36	C₄⋊C₈	—	20	2	no	—
37	C₄×C₈	—	5	1	no	—
38	C₃₂	—	10	1	no	—
39	C₃₂	#170	1	2	yes	complemented
40	C₂²×C₅	#366	1	1	yes	characteristic
41	C₄×C₅	#335	1	1	yes	characteristic
42	C₄×C₅	#368	1	1	yes	characteristic
43	Dic₅	—	2	1	no	—
44	Dic₅	D₃₂	1	1	yes	characteristic
45	Dic₅	Q₆₄	1	1	yes	characteristic
46	C₂×C₈	—	5	1	no	—
47	C₂×C₈	—	40	2	no	—
48	C₂×C₈	C₄⋊AGL(1,𝔽₅)	1	1	yes	characteristic
49	C₄²	—	5	1	no	—
50	C₁₆	—	10	1	no	—
51	C₁₆	#700	1	1	yes	characteristic
52	C₁₆	C₂×#170	1	1	yes	characteristic
53	C₂×C₅	#1371	1	1	yes	characteristic
54	C₂×C₅	#1423	1	1	yes	characteristic
55	C₂×C₅	#1425	1	1	yes	characteristic
56	C₂×C₄	—	5	1	no	—
57	C₂×C₄	—	5	1	no	—
58	C₂×C₄	#3994	1	1	yes	characteristic
59	C₈	—	10	1	no	—
60	C₈	—	80	2	no	—
61	C₈	#3996	1	1	yes	characteristic
62	C₈	C₄⋊#170	1	1	yes	characteristic
63	C₅	#7460	1	1	yes	characteristic, complemented, Sylow
64	C₂²	#64849	1	1	yes	characteristic
65	C₄	—	5	1	no	—
66	C₄	—	5	1	no	—
67	C₄	—	10	1	no	—
68	C₄	#64851	1	1	yes	characteristic
69	C₄	#64882	1	1	yes	characteristic
70	C₂	#10598489	1	1	yes	characteristic
71	C₂	#10598493	1	1	yes	characteristic
72	C₂	#10598644	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#64849
commutator	C₅×C₁₆	C₂×C₈
Frattini	C₂×C₁₆	C₂×AGL(1,𝔽₅)
Fitting	C₂×C₅×C₃₂	C₄
socle, prime radical	C₂²×C₅	#366
cosocle	C₁₆×Dic₅	C₂²
hypercenter	C₂×C₃₂	AGL(1,𝔽₅)
hypocenter	C₅	#7460
LCS	G ▷ C₅×C₁₆ ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
12. C₅×C₃₂	C₈	semidirect
39. C₃₂	#170	semidirect
63. C₅	#7460	semidirect

Maximal subgroups

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

subgroup	index
#10598644	2
Dic₅×C₃₂	2
#7460	5