Subgroups — #11986976

Order 1280.

86 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#1371	C₂	1	1	yes	maximal, characteristic
2	C₄×#3926	C₂	1	1	yes	maximal, characteristic
3	#10597991	C₂	1	1	yes	maximal, characteristic
4	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
5	C₅×#335	—	2	1	no	—
6	C₂×#3926	C₄	1	1	yes	characteristic
7	C₂×#3926	C₄	1	1	yes	characteristic
8	#64678	—	2	1	no	—
9	#7460	—	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	C₄⋊#168	—	4	1	no	—
15	#3926	—	2	1	no	—
16	#3926	C₈	1	2	yes	complemented
17	C₄×C₃₂	—	5	1	no	—
18	#1371	—	5	1	no	—
19	#1371	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	Q₁₆	1	1	yes	characteristic
23	C₄²×C₅	D₈	1	1	yes	characteristic
24	C₂×#168	—	8	1	no	—
25	C₅×C₁₆	—	2	1	no	—
26	C₅×C₁₆	C₂×C₈	1	1	yes	characteristic
27	C₅×C₁₆	M₁₆	1	1	yes	characteristic
28	C₂×C₃₂	—	5	1	no	—
29	C₂×C₃₂	—	5	1	no	—
30	C₄×C₁₆	C₂×D₅	1	1	yes	characteristic
31	#335	—	2	1	no	—
32	#335	—	10	1	no	—
33	C₂×C₄×C₅	#107	1	1	yes	characteristic
34	C₂×C₄×C₅	D₁₆	1	1	yes	characteristic
35	C₂×C₄×C₅	Q₃₂	1	1	yes	characteristic
36	C₅×C₈	—	2	1	no	—
37	C₅×C₈	—	16	1	no	—
38	C₅×C₈	C₄⋊C₈	1	1	yes	characteristic
39	C₅×C₈	#108	1	1	yes	characteristic
40	#168	—	16	1	no	—
41	C₂×C₁₆	Dic₁₀	1	1	yes	characteristic
42	C₂×C₁₆	C₄×D₅	1	1	yes	characteristic
43	C₄⋊C₈	—	4	1	no	—
44	C₄⋊C₈	—	20	1	no	—
45	C₄×C₈	C₂²⋊D₅	1	1	yes	characteristic
46	C₃₂	—	5	2	no	—
47	C₃₂	—	10	1	no	—
48	C₂²×C₅	#366	1	1	yes	characteristic
49	C₄×C₅	—	2	1	no	—
50	C₄×C₅	#335	1	1	yes	characteristic
51	C₄×C₅	#368	1	1	yes	characteristic
52	C₄×C₅	D₃₂	1	1	yes	characteristic
53	C₄×C₅	Q₆₄	1	1	yes	characteristic
54	C₂×C₈	—	8	1	no	—
55	C₂×C₈	—	40	1	no	—
56	C₂×C₈	#683	1	1	yes	characteristic
57	C₂×C₈	#689	1	1	yes	characteristic
58	C₄²	#686	1	1	yes	characteristic
59	C₁₆	—	2	1	no	—
60	C₁₆	C₈×D₅	1	1	yes	characteristic
61	C₁₆	#676	1	1	yes	characteristic
62	C₂×C₅	#1371	1	1	yes	characteristic
63	C₂×C₅	#1423	1	1	yes	characteristic
64	C₂×C₅	#1425	1	1	yes	characteristic
65	C₂×C₄	#3939	1	1	yes	characteristic
66	C₂×C₄	#3958	1	1	yes	characteristic
67	C₂×C₄	#3961	1	1	yes	characteristic
68	C₈	—	2	1	no	—
69	C₈	—	16	1	no	—
70	C₈	—	80	1	no	—
71	C₈	#3946	1	1	yes	characteristic
72	C₈	#3954	1	1	yes	characteristic
73	C₅	#7460	1	1	yes	characteristic, complemented, Sylow
74	C₂²	#64709	1	1	yes	characteristic
75	C₄	—	2	1	no	—
76	C₄	#64699	1	1	yes	characteristic
77	C₄	#64713	1	1	yes	characteristic
78	C₄	#64739	1	1	yes	characteristic
79	C₄	#64742	1	1	yes	characteristic
80	C₂	#10597960	1	1	yes	characteristic
81	C₂	#10598066	1	1	yes	characteristic
82	C₂	#10598072	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#3958
commutator	C₅×C₁₆	C₂×C₈
Frattini	C₄×C₁₆	C₂×D₅
Fitting	C₅×#1371	C₂
socle, prime radical	C₂²×C₅	#366
cosocle	C₄×C₅×C₁₆	C₂²
hypercenter	#1371	D₅
hypocenter	C₅	#7460
LCS	G ▷ C₅×C₁₆ ▷ C₅×C₈ ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆ ◁ #1371

Complements

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

N	H ≅ G/N	type
16. #3926	C₈	semidirect
73. C₅	#7460	semidirect

Maximal subgroups

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

subgroup	index
C₅×#1371	2
C₄×#3926	2
#10597991	2
#7460	5