Finite Group Databasebeta

← #11756459

Subgroups — #11756459

Order 960.

440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#125C211yesmaximal, characteristic, complemented
2#91785C214yesmaximal, complemented
3#91784C214yesmaximal, complemented
4#91783C214yesmaximal, complemented
5#91764C212yesmaximal, complemented
6#66034—31nomaximal, Hall
7C2×D60C2212yes—
8C2×D60C2214yes—
9C2×C4×D15C2214yes—
10C2×Dic30C2212yes—
11C3×C5×C4⋊C4C2212yes—
12C3×C5×C4⋊C4C2214yes—
13C3×C42×C5C2211yescharacteristic
14#6714C2214yes—
15#6714C2214yes—
16#6714C2214yes—
17#6712C2214yes—
18#5700—51nomaximal, Hall
19C5×#125D311yescharacteristic, complemented
20#4042—34no—
21#4041—34no—
22#4040—34no—
23#4021—32no—
24C22×D15C2314yes—
25C2×C3×C4×C5C2314yes—
26C2×C3×C4×C5C2311yescharacteristic
27C2×C3×C4×C5C2312yes—
28C2×Dic15C2314yes—
29D60—42no—
30D60—44no—
31C4×D15—44no—
32Dic30—42no—
33C3×#125D511yescharacteristic, complemented
34#896—54no—
35#895—54no—
36#894—54no—
37#875—52no—
38C2×D20—32no—
39C2×D20—34no—
40C2×C4×D5—34no—
41C2×Dic10—32no—
42C5×C4⋊C4C2×D312yes—
43C5×C4⋊C4C2×D314yes—
44C42×C5C2×D311yescharacteristic
45#685—34no—
46#685—34no—
47#685—34no—
48#683—34no—
49#562—151noSylow
50C22×C3×C5C2411yescharacteristic
51C2×D15—24no—
52C2×D15—24no—
53C2×D15—24no—
54C3×C4×C5—22no—
55C3×C4×C5—24no—
56C3×C4×C5—21no—
57Dic15—24no—
58C2×D12—52no—
59C2×D12—54no—
60C2×C4×D3—54no—
61C2×Dic6—52no—
62C3×C4⋊C4C2×D512yes—
63C3×C4⋊C4C2×D514yes—
64C3×C42C2×D511yescharacteristic
65(C2×D3)⋊C4—54no—
66(C2×D3)⋊C4—54no—
67(C2×D3)⋊C4—54no—
68Dic3⋊C4—54no—
69C22×D5—34no—
70C2×C4×C5C22×D314yes—
71C2×C4×C5C22×D311yescharacteristic
72C2×C4×C5C22×D312yes—
73C2×Dic5—34no—
74D20—122no—
75D20—124no—
76C4×D5—124no—
77Dic10—122no—
78#125D1511yescharacteristic, complemented
79#124—152no—
80#123—154no—
81C22⋊Q8—154no—
82#121—154no—
83C2×C3×C5H(5,𝔽2)12yes—
84C2×C3×C52−1+411yescharacteristic
85D15—44no—
86C22×D3—54no—
87C2×C3×C4C22×D514yes—
88C2×C3×C4C22×D511yescharacteristic
89C2×C3×C4C22×D512yes—
90C2×Dic3—54no—
91D12—202no—
92D12—204no—
93C4×D3—204no—
94Dic6—202no—
95C22×C5C23×D311yescharacteristic
96C2×D5—64no—
97C2×D5—64no—
98C2×D5—64no—
99C4×C5—21no—
100C4×C5—22no—
101C4×C5—24no—
102Dic5—64no—
103C2×Q8—152no—
104C2×D4—154no—
105C2×D4—152no—
106C22×C4—154no—
107C4⋊C4—154no—
108C4⋊C4C2×D1514yes—
109C4⋊C4C2×D1512yes—
110C22⋊C4—154no—
111C22⋊C4—154no—
112C22⋊C4—154no—
113C42C2×D1511yescharacteristic
114C3×C5#56211yescharacteristic, complemented, Hall
115C22×C3C23×D511yescharacteristic
116C2×D3—104no—
117C2×D3—104no—
118C2×D3—104no—
119C3×C4—21no—
120C3×C4—22no—
121C3×C4—24no—
122Dic3—104no—
123C2×C5#100711yescharacteristic
124C2×C5#100912yes—
125D5—124no—
126C23—154no—
127Q8—602no—
128D4—604no—
129D4—602no—
130C2×C4—154no—
131C2×C4—604no—
132C2×C4C22×D1511yescharacteristic
133C2×C4C22×D1512yes—
134C2×C4C22×D1514yes—
135C2×C3#414711yescharacteristic
136C2×C3#414912yes—
137D3—204no—
138C5#570011yescharacteristic, complemented, Sylow
139C22—304no—
140C22—304no—
141C22—304no—
142C22C23×D1511yescharacteristic
143C4—21no—
144C4—24no—
145C4—22no—
146C4—304no—
147C3#6603411yescharacteristic, complemented, Sylow
148C2—604no—
149C2#9209811yescharacteristic
150C2#9210012yes—
subgroupG/H
center, FrattiniC22C23×D15
commutator, socle, cosocleC22×C3×C5C24
FittingC3×C5×#125C2
hypercenter#125D15
hypocenterC3×C5#562
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #125

Complements

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

NH ≅ G/Ntype
1. C3×C5×#125C2semidirect
2. #91785C2semidirect
3. #91784C2semidirect
4. #91783C2semidirect
5. #91764C2semidirect
19. C5×#125D3semidirect
33. C3×#125D5semidirect
78. #125D15semidirect
114. C3×C5#562semidirect
138. C5#5700semidirect
147. C3#66034semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#1252
#917852
#917842
#917832
#917642
#660343
#57005