Subgroups — #11986972

Order 1280.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×C₄⋊C₃₂	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#3926	C₂	1	1	yes	maximal, characteristic
3	C₁₆×#168	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×C₃₂	—	2	1	no	—
5	C₄×C₅×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×#3926	—	2	1	no	—
7	C₄×#672	C₄	1	1	yes	characteristic
8	C₈×#168	C₄	1	1	yes	characteristic
9	#7458	—	5	1	no	maximal, Sylow
10	C₂×C₅×C₁₆	D₄	1	1	yes	characteristic
11	C₂×C₅×C₁₆	Q₈	1	1	yes	characteristic
12	C₄×C₅×C₈	C₂×C₄	1	1	yes	characteristic
13	C₂×#672	—	2	1	no	—
14	C₄×#168	C₈	1	1	yes	characteristic
15	C₄×#168	C₈	1	1	yes	characteristic
16	C₅×C₃₂	—	4	1	no	—
17	#3926	—	4	1	no	—
18	C₄⋊C₃₂	—	5	1	no	—
19	C₄⋊C₃₂	D₅	1	1	yes	characteristic
20	C₈×C₁₆	—	5	1	no	—
21	C₂×C₅×C₈	C₄⋊C₄	1	1	yes	characteristic
22	C₂×C₅×C₈	M₁₆	1	1	yes	characteristic
23	C₄²×C₅	C₂×C₈	1	1	yes	characteristic
24	C₂×#168	—	2	1	no	—
25	C₂×#168	C₁₆	1	1	yes	characteristic
26	C₂×#168	C₁₆	1	1	yes	characteristic
27	C₅×C₁₆	—	2	1	no	—
28	C₅×C₁₆	D₈	1	1	yes	characteristic
29	C₅×C₁₆	Q₁₆	1	1	yes	characteristic
30	#672	—	2	2	no	—
31	C₂×C₃₂	—	2	1	no	—
32	C₂×C₃₂	—	10	1	no	—
33	C₄×C₁₆	—	5	1	no	—
34	C₄×C₁₆	C₂×D₅	1	1	yes	characteristic
35	C₈²	—	5	1	no	—
36	C₂×C₄×C₅	C₄⋊C₈	1	1	yes	characteristic
37	C₂×C₄×C₅	C₂×C₁₆	1	1	yes	characteristic
38	C₂×C₄×C₅	M₃₂	1	1	yes	characteristic
39	C₅×C₈	—	2	1	no	—
40	C₅×C₈	#107	1	1	yes	characteristic
41	C₅×C₈	#108	1	1	yes	characteristic
42	#168	—	2	2	no	—
43	#168	—	2	1	no	—
44	#168	C₃₂	1	2	yes	complemented
45	C₂×C₁₆	—	10	1	no	—
46	C₂×C₁₆	Dic₁₀	1	1	yes	characteristic
47	C₂×C₁₆	C₂²⋊D₅	1	1	yes	characteristic
48	C₄×C₈	—	5	1	no	—
49	C₄×C₈	—	5	1	no	—
50	C₄×C₈	C₄×D₅	1	1	yes	characteristic
51	C₃₂	—	4	1	no	—
52	C₃₂	—	20	1	no	—
53	C₂²×C₅	C₄⋊C₁₆	1	1	yes	characteristic
54	C₄×C₅	—	2	1	no	—
55	C₄×C₅	#335	1	1	yes	characteristic
56	C₄×C₅	#364	1	1	yes	characteristic
57	C₄×C₅	C₂×C₃₂	1	1	yes	characteristic
58	C₄×C₅	M₆₄	1	1	yes	characteristic
59	C₂×C₈	—	5	1	no	—
60	C₂×C₈	—	5	1	no	—
61	C₂×C₈	—	10	1	no	—
62	C₂×C₈	#676	1	1	yes	characteristic
63	C₂×C₈	#683	1	1	yes	characteristic
64	C₄²	C₈×D₅	1	1	yes	characteristic
65	C₁₆	—	2	1	no	—
66	C₁₆	—	10	2	no	—
67	C₁₆	#686	1	1	yes	characteristic
68	C₁₆	#689	1	1	yes	characteristic
69	C₂×C₅	#1370	1	1	yes	characteristic
70	C₂×C₅	C₄⋊C₃₂	1	1	yes	characteristic
71	C₂×C₅	#1422	1	1	yes	characteristic
72	C₂×C₄	D₅×C₁₆	1	1	yes	characteristic
73	C₂×C₄	#3930	1	1	yes	characteristic
74	C₂×C₄	#3946	1	1	yes	characteristic
75	C₈	—	2	1	no	—
76	C₈	—	5	2	no	—
77	C₈	—	10	2	no	—
78	C₈	—	10	1	no	—
79	C₈	#3939	1	1	yes	characteristic
80	C₈	#3954	1	1	yes	characteristic
81	C₅	#7458	1	1	yes	characteristic, complemented, Sylow
82	C₂²	#64721	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	D₅×C₃₂	1	1	yes	characteristic
85	C₄	#64667	1	1	yes	characteristic
86	C₄	#64699	1	1	yes	characteristic
87	C₄	#64731	1	1	yes	characteristic
88	C₂	#10598046	1	1	yes	characteristic
89	C₂	#10598081	1	1	yes	characteristic
90	C₂	#10598090	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²⋊D₅
commutator	C₄×C₅	C₂×C₃₂
Frattini	C₄×C₁₆	C₂×D₅
Fitting	C₅×C₄⋊C₃₂	C₂
socle, prime radical	C₂²×C₅	C₄⋊C₁₆
cosocle	C₄×C₅×C₁₆	C₂²
hypercenter	C₄⋊C₃₂	D₅
hypocenter	C₅	#7458
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₁₆ ◁ C₄×C₁₆ ◁ C₄⋊C₃₂

Complements

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

N	H ≅ G/N	type
44. #168	C₃₂	semidirect
81. C₅	#7458	semidirect

Maximal subgroups

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

subgroup	index
C₅×C₄⋊C₃₂	2
C₄⋊#3926	2
C₁₆×#168	2
#7458	5