Subgroups — #11986969

Order 1280.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1368	C₂	1	1	yes	maximal, characteristic
2	#10598010	C₂	1	1	yes	maximal, characteristic
3	#10598005	C₂	1	1	yes	maximal, characteristic
4	C₅×#346	C₂²	1	1	yes	characteristic
5	C₅×#334	—	2	1	no	—
6	#64719	C₄	1	1	yes	characteristic
7	#64719	C₄	1	1	yes	characteristic
8	#64683	—	2	1	no	—
9	#7457	—	5	1	no	maximal, Sylow
10	C₂×C₅×C₁₆	C₂×C₄	1	1	yes	characteristic
11	C₂×C₅×C₁₆	Q₈	1	1	yes	characteristic
12	C₅×C₄⋊C₈	—	4	1	no	—
13	C₄×C₅×C₈	D₄	1	1	yes	characteristic
14	#3944	—	4	1	no	—
15	#3926	—	2	1	no	—
16	#3926	C₈	1	2	yes	complemented
17	#1398	—	5	1	no	—
18	#1369	—	5	1	no	—
19	#1368	D₅	1	1	yes	characteristic
20	C₂×C₅×C₈	—	8	1	no	—
21	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₅×C₈	SD₁₆	1	1	yes	characteristic
23	C₄²×C₅	SD₁₆	1	1	yes	characteristic
24	C₅×C₁₆	—	2	1	no	—
25	C₅×C₁₆	C₂×C₈	1	1	yes	characteristic
26	C₅×C₁₆	M₁₆	1	1	yes	characteristic
27	#672	—	8	1	no	—
28	M₆₄	—	5	1	no	—
29	M₆₄	—	5	1	no	—
30	#364	—	10	1	no	—
31	#346	C₂×D₅	1	1	yes	characteristic
32	#334	—	2	1	no	—
33	C₂×C₄×C₅	—	2	1	no	—
34	C₂×C₄×C₅	#106	1	1	yes	characteristic
35	C₅×C₈	—	2	1	no	—
36	C₅×C₈	—	16	1	no	—
37	C₅×C₈	C₄⋊C₈	1	1	yes	characteristic
38	C₅×C₈	#108	1	1	yes	characteristic
39	M₃₂	—	20	1	no	—
40	C₂×C₁₆	Dic₁₀	1	1	yes	characteristic
41	C₂×C₁₆	C₄×D₅	1	1	yes	characteristic
42	C₄⋊C₈	—	4	1	no	—
43	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
44	C₃₂	—	5	2	no	—
45	C₃₂	—	10	1	no	—
46	C₂²×C₅	#365	1	1	yes	characteristic
47	C₄×C₅	—	4	1	no	—
48	C₄×C₅	#334	1	1	yes	characteristic
49	C₄×C₅	#365	1	1	yes	characteristic
50	C₂×C₈	—	8	1	no	—
51	C₂×C₈	#683	1	1	yes	characteristic
52	C₂×C₈	#688	1	1	yes	characteristic
53	C₄²	#687	1	1	yes	characteristic
54	C₁₆	—	2	1	no	—
55	C₁₆	—	40	1	no	—
56	C₁₆	C₈×D₅	1	1	yes	characteristic
57	C₁₆	#676	1	1	yes	characteristic
58	C₂×C₅	—	2	1	no	—
59	C₂×C₅	#1368	1	1	yes	characteristic
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	#3940	1	1	yes	characteristic
62	C₈	—	2	1	no	—
63	C₈	—	16	1	no	—
64	C₈	#3946	1	1	yes	characteristic
65	C₈	#3954	1	1	yes	characteristic
66	C₅	#7457	1	1	yes	characteristic, complemented, Sylow
67	C₂²	#64707	1	1	yes	characteristic
68	C₄	—	4	1	no	—
69	C₄	#64700	1	1	yes	characteristic
70	C₄	#64714	1	1	yes	characteristic
71	C₂	—	2	1	no	—
72	C₂	#10597955	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10597955
commutator	C₅×C₁₆	C₂×C₈
Frattini	#346	C₂×D₅
Fitting	C₅×#1368	C₂
socle	C₂×C₅	#1368
prime radical	C₂²×C₅	#365
cosocle	C₅×#346	C₂²
hypercenter	#1368	D₅
hypocenter	C₅	#7457
LCS	G ▷ C₅×C₁₆ ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #346 ◁ #1368

Complements

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

N	H ≅ G/N	type
16. #3926	C₈	semidirect
66. C₅	#7457	semidirect

Maximal subgroups

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

subgroup	index
C₅×#1368	2
#10598010	2
#10598005	2
#7457	5