Subgroups — #11987194

Order 1280.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₈₀	C₂	1	1	yes	maximal, characteristic
2	C₅×M₁₂₈	C₂	1	1	yes	maximal, characteristic
3	#10598084	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₄₀	—	2	1	no	—
5	C₂×C₅×C₃₂	C₂²	1	1	yes	characteristic
6	#64726	—	2	1	no	—
7	Dic₈₀	—	2	1	no	—
8	Dic₈₀	C₄	1	2	yes	—
9	C₅×C₆₄	—	2	1	no	—
10	#7542	—	5	1	no	maximal, Sylow
11	C₂×Dic₂₀	—	4	1	no	—
12	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
13	#3951	—	4	1	no	—
14	Dic₄₀	—	2	2	no	—
15	Dic₄₀	—	4	1	no	—
16	C₅×C₃₂	C₂×C₄	1	1	yes	characteristic
17	C₅×C₃₂	D₄	1	1	yes	characteristic
18	C₂×Q₆₄	—	5	1	no	—
19	M₁₂₈	D₅	1	1	yes	characteristic
20	#1425	—	5	1	no	—
21	C₂×Dic₁₀	—	8	1	no	—
22	C₂×C₅×C₈	D₈	1	1	yes	characteristic
23	#681	—	8	1	no	—
24	Dic₂₀	—	4	2	no	—
25	Dic₂₀	—	8	1	no	—
26	C₅×C₁₆	C₂²⋊C₄	1	1	yes	characteristic
27	C₅×C₁₆	SD₁₆	1	1	yes	characteristic
28	C₂×Q₃₂	—	10	1	no	—
29	Q₆₄	—	5	2	no	—
30	Q₆₄	—	10	1	no	—
31	C₂×C₃₂	C₂×D₅	1	1	yes	characteristic
32	#368	—	10	1	no	—
33	C₆₄	—	2	1	no	—
34	C₂×C₄×C₅	D₁₆	1	1	yes	characteristic
35	C₂×Dic₅	—	16	1	no	—
36	Dic₁₀	—	8	2	no	—
37	Dic₁₀	—	16	1	no	—
38	C₅×C₈	#102	1	1	yes	characteristic
39	C₅×C₈	SD₃₂	1	1	yes	characteristic
40	#168	—	16	1	no	—
41	C₂×Q₁₆	—	20	1	no	—
42	Q₃₂	—	10	2	no	—
43	Q₃₂	—	20	1	no	—
44	C₂×C₁₆	D₂₀	1	1	yes	characteristic
45	#108	—	20	1	no	—
46	C₃₂	C₄×D₅	1	1	yes	characteristic
47	C₃₂	C₂²⋊D₅	1	1	yes	characteristic
48	C₂²×C₅	SD₆₄	1	1	yes	characteristic
49	C₄×C₅	#357	1	1	yes	characteristic
50	C₄×C₅	D₃₂	1	1	yes	characteristic
51	Dic₅	—	16	2	no	—
52	C₂×Q₈	—	40	1	no	—
53	Q₁₆	—	20	2	no	—
54	Q₁₆	—	40	1	no	—
55	M₁₆	—	40	1	no	—
56	C₂×C₈	D₄₀	1	1	yes	characteristic
57	C₁₆	#677	1	1	yes	characteristic
58	C₁₆	#685	1	1	yes	characteristic
59	C₂×C₅	—	2	1	no	—
60	C₂×C₅	#1415	1	1	yes	characteristic
61	Q₈	—	40	2	no	—
62	Q₈	—	80	1	no	—
63	C₂×C₄	—	80	1	no	—
64	C₂×C₄	D₈₀	1	1	yes	characteristic
65	C₈	—	80	1	no	—
66	C₈	#3932	1	1	yes	characteristic
67	C₈	#3953	1	1	yes	characteristic
68	C₅	#7542	1	1	yes	characteristic, complemented, Sylow
69	C₂²	#64669	1	1	yes	characteristic
70	C₄	—	80	2	no	—
71	C₄	D₁₆₀	1	1	yes	characteristic
72	C₄	#64729	1	1	yes	characteristic
73	C₂	—	2	1	no	—
74	C₂	#10598087	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10598087
commutator	C₅×C₃₂	C₂×C₄
Frattini	C₂×C₃₂	C₂×D₅
Fitting	C₅×M₁₂₈	C₂
socle	C₂×C₅	#1415
prime radical	C₂²×C₅	SD₆₄
cosocle	C₂×C₅×C₃₂	C₂²
hypercenter	M₁₂₈	D₅
hypocenter	C₅	#7542
LCS	G ▷ C₅×C₃₂ ▷ C₅×C₁₆ ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂ ◁ M₁₂₈

Complements

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

N	H ≅ G/N	type
68. C₅	#7542	semidirect

Maximal subgroups

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

subgroup	index
C₂×Dic₈₀	2
C₅×M₁₂₈	2
#10598084	2
#7542	5