Finite Group Databasebeta

← #14277115

Subgroups — #14277115

Order 1920.

368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 115 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
1C2×C3×C5×C22⋊C8C211yesmaximal, characteristic
2#11751308C212yesmaximal
3#10598170—31nomaximal, Hall
4C23×C3×C4×C5C2211yescharacteristic
5C22×C3×C5×C8C412yes—
6C2×#6710—22no—
7C3×C5×C22⋊C8—22no—
8#91114—22no—
9#91114C414yes—
10#67679—51nomaximal, Hall
11C2×C5×C22⋊C8D311yescharacteristic
12#65496—32no—
13C24×C3×C5Q811yescharacteristic
14C22×C3×C4×C5—42no—
15C22×C3×C4×C5C2×C411yescharacteristic
16C22×C3×C4×C5C2×C412yes—
17C22×C3×C4×C5D412yes—
18C22×C3×C4×C5D411yescharacteristic
19C2×C3×C5×C8—22no—
20C2×C3×C5×C8—42no—
21#6710—44no—
22C2×C3⋊#168—24no—
23C2×C3×C22⋊C8D511yescharacteristic
24#5207—52no—
25C23×C4×C5C2×D311yescharacteristic
26C22×C5×C8Dic312yes—
27C2×#681—62no—
28C5×C22⋊C8—22no—
29C22⋊#168—34no—
30C22⋊#168—62no—
31#1293—151noSylow
32C23×C3×C5—22no—
33C23×C3×C5—41no—
34C23×C3×C5—41no—
35C23×C3×C5C4⋊C412yes—
36C23×C3×C5C4⋊C411yescharacteristic
37C2×C3×C4×C5—24no—
38C2×C3×C4×C5—22no—
39C2×C3×C4×C5—42no—
40C2×C3×C4×C5—41no—
41C2×C3×C4×C5C4211yescharacteristic
42C2×C3×C4×C5C22⋊C412yes—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C3×C5×C8—42no—
45C3⋊#168—44no—
46C23×C3×C4C2×D511yescharacteristic
47C22×C3×C8Dic512yes—
48C2×#208—102no—
49C3×C22⋊C8—22no—
50#830—54no—
51#830—102no—
52C24×C5Dic611yescharacteristic
53C22×C4×C5—42no—
54C22×C4×C5C4×D312yes—
55C22×C4×C5D1211yescharacteristic
56C22×C4×C5C2×Dic311yescharacteristic
57C22×C4×C5#6712yes—
58C2×C5×C8—22no—
59C2×C5×C8—42no—
60#681—124no—
61C2×#168—64no—
62#407—152no—
63C2×C22⋊C8D1511yescharacteristic
64C22×C3×C5—21no—
65C22×C3×C5—21no—
66C22×C3×C5—22no—
67C22×C3×C5—22no—
68C22×C3×C5—22no—
69C22×C3×C5—44no—
70C22×C3×C5#9511yescharacteristic
71C22×C3×C5#10812yes—
72C3×C4×C5—22no—
73C3×C4×C5—21no—
74C3×C4×C5#9912yes—
75C24×C3Dic1011yescharacteristic
76C22×C3×C4—42no—
77C22×C3×C4C4×D512yes—
78C22×C3×C4D2011yescharacteristic
79C22×C3×C4C2×Dic511yescharacteristic
80C22×C3×C4C22⋊D512yes—
81C2×C3×C8—22no—
82C2×C3×C8—42no—
83#208—204no—
84C2×C3⋊C8—104no—
85C23×C5—22no—
86C23×C5—41no—
87C23×C5—41no—
88C23×C5Dic3⋊C412yes—
89C23×C5C4⋊Dic311yescharacteristic
90C2×C4×C5—24no—
91C2×C4×C5—22no—
92C2×C4×C5—42no—
93C2×C4×C5—41no—
94C2×C4×C5C4×Dic311yescharacteristic
95C2×C4×C5(C2×D3)⋊C412yes—
96C2×C4×C5#21711yescharacteristic
97C5×C8—42no—
98#168—124no—
99C23×C4C2×D1511yescharacteristic
100C2×M16—302no—
101C22×C8Dic1512yes—
102C22⋊C8—22no—
103C22⋊C8—154no—
104C22⋊C8—302no—
105C2×C3×C5—22no—
106C2×C3×C5—42no—
107C2×C3×C5#33811yescharacteristic
108C2×C3×C5#34111yescharacteristic
109C2×C3×C5#34211yescharacteristic
110C23×C3—22no—
111C23×C3—41no—
112C23×C3—41no—
113C23×C3#68312yes—
114C23×C3C4⋊Dic511yescharacteristic
115C2×C3×C4—24no—
116C2×C3×C4—22no—
117C2×C3×C4—42no—
118C2×C3×C4—41no—
119C2×C3×C4C4×Dic511yescharacteristic
120C2×C3×C4#68512yes—
121C2×C3×C4C22⋊Dic511yescharacteristic
122C3×C8—42no—
123C3⋊C8—204no—
124C22×C5—21no—
125C22×C5—21no—
126C22×C5—22no—
127C22×C5—22no—
128C22×C5—22no—
129C22×C5—44no—
130C22×C5#81912yes—
131C22×C5C3⋊#9511yescharacteristic
132C4×C5—22no—
133C4×C5—21no—
134C4×C5#83412yes—
135C24Dic3011yescharacteristic
136C22×C4—42no—
137C22×C4C4×D1512yes—
138C22×C4D6011yescharacteristic
139C22×C4C2×Dic1511yescharacteristic
140C22×C4#122012yes—
141M16—604no—
142C2×C8—22no—
143C2×C8—42no—
144C2×C8—304no—
145C3×C5#129311yescharacteristic, complemented, Hall
146C22×C3—21no—
147C22×C3—21no—
148C22×C3—22no—
149C22×C3—22no—
150C22×C3—22no—
151C22×C3—44no—
152C22×C3#395112yes—
153C22×C3#396311yescharacteristic
154C3×C4—22no—
155C3×C4—21no—
156C3×C4#396612yes—
157C2×C5—22no—
158C2×C5—42no—
159C2×C5#452611yescharacteristic
160C2×C5#455211yescharacteristic
161C2×C5C3⋊#33811yescharacteristic
162C23—22no—
163C23—41no—
164C23—41no—
165C23#671212yes—
166C23C4⋊Dic1511yescharacteristic
167C2×C4—22no—
168C2×C4—24no—
169C2×C4—42no—
170C2×C4—41no—
171C2×C4C4×Dic1511yescharacteristic
172C2×C4#671412yes—
173C2×C4#671911yescharacteristic
174C8—42no—
175C8—604no—
176C2×C3—22no—
177C2×C3—42no—
178C2×C3#6474611yescharacteristic
179C2×C3#6477211yescharacteristic
180C2×C3#6478011yescharacteristic
181C5#6767911yescharacteristic, complemented, Sylow
182C22—21no—
183C22—21no—
184C22—22no—
185C22—22no—
186C22—22no—
187C22—44no—
188C22#9110312yes—
189C22#9111511yescharacteristic
190C4—22no—
191C4—21no—
192C4#9111812yes—
193C3#1059817011yescharacteristic, complemented, Sylow
194C2—22no—
195C2—42no—
196C2#1174634711yescharacteristic
197C2#1174637311yescharacteristic
198C2#1174638111yescharacteristic
subgroupG/H
centerC22#91115
commutatorC2×C3×C4×C5C42
FrattiniC23×C4C2×D15
FittingC2×C3×C5×C22⋊C8C2
socleC22×C3×C5#95
prime radicalC24×C3×C5Q8
cosocleC23×C3×C4×C5C22
hypercenterC2×C22⋊C8D15
hypocenterC3×C5#1293
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
145. C3×C5#1293semidirect
181. C5#67679semidirect
193. C3#10598170semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×C22⋊C82
#117513082
#105981703
#676795