Finite Group Databasebeta

← #14298413

Subgroups — #14298413

Order 1920.

544 conjugacy classes of subgroups; only the 156 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 156 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×#4072C211yesmaximal, characteristic
2#11751308C211yesmaximal, characteristic
3C5×#5207C211yesmaximal, characteristic
4#11745985C214yesmaximal, complemented
5#10600767—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C2×#6710C2212yes—
8C2×C5×#208C2212yes—
9C2×C3×C22⋊Dic5C412yes—
10C3×#4072—22no—
11C3×#4072—22no—
12C2×C3×C4⋊Dic5C2212yes—
13C2×C3×C4×Dic5C412yes—
14#91114—22no—
15C5×#830—22no—
16#71589—51nomaximal, Hall
17C2×#4072D311yescharacteristic
18C5×#407—31no—
19#65496—31no—
20#64774—34no—
21C24×C3×C5C2×C411yescharacteristic
22C22×C3×C4×C5—24no—
23C22×C3×C4×C5C2×C411yescharacteristic
24C22×C3×C4×C5D412yes—
25C22×C3×C4×C5D412yes—
26C22×C3×C4×C5C2311yescharacteristic
27C22×C3×Dic5C2×C414yes—
28#6710—24no—
29C2×C3⋊#168—22no—
30C5×#208—24no—
31C2×C5×C3⋊C8—22no—
32C3×C22⋊Dic5—24no—
33C3×C4⋊Dic5—22no—
34C3×C4⋊Dic5—22no—
35C3×C4×Dic5—24no—
36C2×C3×#117—51no—
37#5207—51no—
38#5207D511yescharacteristic
39#4530—54no—
40C23×C4×C5C2×D311yescharacteristic
41C2×C5×M16—32no—
42C2×C22⋊Dic5Dic312yes—
43#4072—22no—
44#4072—22no—
45C2×C4⋊Dic5C2×D312yes—
46C2×C4×Dic5Dic312yes—
47C2×#681—32no—
48C5×C22⋊C8—62no—
49C22⋊#168—62no—
50#1822—151noSylow
51C23×C3×C5—22no—
52C23×C3×C5—42no—
53C23×C3×C5C22⋊C412yes—
54C23×C3×C5C22×C411yescharacteristic
55C2×C3×C4×C5—22no—
56C2×C3×C4×C5—24no—
57C2×C3×C4×C5—24no—
58C2×C3×C4×C5C22⋊C412yes—
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5#4114yes—
62C2×C3×Dic5—24no—
63C2×C3×Dic5—44no—
64C3⋊#168—42no—
65C5×C3⋊C8—42no—
66C23×C3×C4C2×D511yescharacteristic
67C3×#117—102no—
68C3×#117—102no—
69C2×C3×C4⋊C4—52no—
70C2×C3×C22⋊C4—52no—
71C2×C3×C42—52no—
72C2×#208—52no—
73C2×#208C2×D512yes—
74#830—22no—
75#830—102no—
76C24×C5C2×Dic311yescharacteristic
77C22×C4×C5—24no—
78C22×C4×C5C2×Dic311yescharacteristic
79C22×C4×C5#6712yes—
80C22×C4×C5#6712yes—
81C22×C4×C5C22×D311yescharacteristic
82C22×Dic5C2×Dic314yes—
83C5×M16—64no—
84C2×C5×C8—62no—
85C22⋊Dic5—24no—
86C4⋊Dic5—22no—
87C4⋊Dic5—22no—
88C4×Dic5—24no—
89#681—64no—
90C2×#168—62no—
91C2×#117—51no—
92#407—31no—
93#407—151no—
94#343—154no—
95C22×C3×C5—22no—
96C22×C3×C5—22no—
97C22×C3×C5—24no—
98C22×C3×C5—44no—
99C22×C3×C5C2×C22⋊C411yescharacteristic
100C22×C3×C5#11712yes—
101C3×C4×C5—22no—
102C3×C4×C5#12312yes—
103C3×C4×C5#12312yes—
104C3×Dic5—44no—
105C24×C3C4×D511yescharacteristic
106C22×C3×C4—24no—
107C22×C3×C4—54no—
108C22×C3×C4C4×D511yescharacteristic
109C22×C3×C4D2012yes—
110C22×C3×C4C22⋊D512yes—
111C22×C3×C4C22×D511yescharacteristic
112C3×C4⋊C4—102no—
113C3×C4⋊C4—102no—
114C3×C22⋊C4—104no—
115C3×C42—104no—
116#208—24no—
117#208—104no—
118C2×C3⋊C8—22no—
119C2×C3⋊C8—102no—
120C23×C5—22no—
121C23×C5—42no—
122C23×C5#21712yes—
123C23×C5C22×Dic311yescharacteristic
124C2×C4×C5—22no—
125C2×C4×C5—24no—
126C2×C4×C5—24no—
127C2×C4×C5#21712yes—
128C2×C4×C5#23514yes—
129C2×C4×C5C2×#6711yescharacteristic
130C2×C4×C5C2×#6711yescharacteristic
131C2×Dic5—24no—
132C2×Dic5—44no—
133C5×C8—122no—
134#168—122no—
135C23×C4D3×D511yescharacteristic
136C2×M16—32no—
137C2×M16—152no—
138#117—102no—
139#117—102no—
140C2×C4⋊C4—52no—
141C2×C22⋊C4—52no—
142C2×C42—52no—
143C22⋊C8—62no—
144C22⋊C8—302no—
145C2×C3×C5—22no—
146C2×C3×C5—42no—
147C2×C3×C5#38111yescharacteristic
148C2×C3×C5#41312yes—
149C23×C3—22no—
150C23×C3—42no—
151C23×C3#68512yes—
152C23×C3C2×C4×D511yescharacteristic
153C2×C3×C4—22no—
154C2×C3×C4—24no—
155C2×C3×C4—24no—
156C2×C3×C4—104no—
157C2×C3×C4—204no—
158C2×C3×C4#68512yes—
159C2×C3×C4C2×D2011yescharacteristic
160C2×C3×C4#71114yes—
161C2×C3×C4C2×C22⋊D511yescharacteristic
162C3⋊C8—42no—
163C3⋊C8—202no—
164C22×C5—22no—
165C22×C5—22no—
166C22×C5—24no—
167C22×C5—44no—
168C22×C5#92612yes—
169C22×C5C2×#21711yescharacteristic
170C4×C5—22no—
171C4×C5#92912yes—
172C4×C5#92912yes—
173Dic5—44no—
174C24D5×Dic311yescharacteristic
175C22×C4—24no—
176C22×C4—54no—
177C22×C4D5×Dic311yescharacteristic
178C22×C4#120112yes—
179C22×C4#120212yes—
180C22×C4C2×D3×D511yescharacteristic
181M16—64no—
182M16—304no—
183C2×C8—62no—
184C2×C8—302no—
185C4⋊C4—102no—
186C4⋊C4—102no—
187C22⋊C4—104no—
188C42—104no—
189C3×C5#182211yescharacteristic, complemented, Hall
190C22×C3—22no—
191C22×C3—24no—
192C22×C3—22no—
193C22×C3—44no—
194C22×C3#402312yes—
195C22×C3C2×#68511yescharacteristic
196C3×C4—22no—
197C3×C4—204no—
198C3×C4#403212yes—
199C3×C4#408112yes—
200C2×C5—22no—
201C2×C5—42no—
202C2×C5#521111yescharacteristic
203C2×C5#523712yes—
204C23—22no—
205C23—42no—
206C23#666512yes—
207C23C2×D5×Dic311yescharacteristic
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—24no—
211C2×C4—104no—
212C2×C4—204no—
213C2×C4#666512yes—
214C2×C4#678214yes—
215C2×C4C2×#120111yescharacteristic
216C2×C4C2×#120211yescharacteristic
217C8—122no—
218C8—602no—
219C2×C3—22no—
220C2×C3—42no—
221C2×C3#6523211yescharacteristic
222C2×C3#6542112yes—
223C5#7158911yescharacteristic, complemented, Sylow
224C22—22no—
225C22—24no—
226C22—22no—
227C22—44no—
228C22#9152812yes—
229C22C2×#666511yescharacteristic
230C4—22no—
231C4—204no—
232C4#9153912yes—
233C4#9154612yes—
234C3#1060076711yescharacteristic, complemented, Sylow
235C2—22no—
236C2—42no—
237C2#1174835312yes—
238C2#1174947111yescharacteristic
subgroupG/H
centerC22C2×#6665
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC24×C3×C5C2×C4
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #11745985C2semidirect
189. C3×C5#1822semidirect
223. C5#71589semidirect
234. C3#10600767semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40722
#117513082
C5×#52072
#117459852
#106007673
#715895