Finite Group Databasebeta

← #14298415

Subgroups — #14298415

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×C5×#926C211yesmaximal, characteristic
2#11751308C211yesmaximal, characteristic
3C3×#65496C211yesmaximal, characteristic
4#11745986C214yesmaximal, complemented
5#10602382—31nomaximal, Hall
6C23×C3×C4×C5C2211yescharacteristic
7C2×#6710C2212yes—
8C2×C5×#217C412yes—
9C5×#926—22no—
10C5×#926—22no—
11C2×C5×C4⋊Dic3C2212yes—
12C2×C4×C5×Dic3C412yes—
13C2×C3×#681C2212yes—
14#91114—22no—
15C3×C22⋊#168—22no—
16#69974—51nomaximal, Hall
17C2×C5×#117—31no—
18#65496—31no—
19#65496D311yescharacteristic
20#64750—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×C5×Dic3C2×C414yes—
28#6710—24no—
29C2×C3⋊#168—22no—
30C5×#217—24no—
31C5×C4⋊Dic3—22no—
32C5×C4⋊Dic3—22no—
33C4×C5×Dic3—24no—
34C3×#681—24no—
35C2×C3×#168—22no—
36C2×#926D511yescharacteristic
37C3×#407—51no—
38#5207—51no—
39#4554—54no—
40C23×C4×C5C2×D311yescharacteristic
41C5×#117—62no—
42C5×#117—62no—
43C2×C5×C4⋊C4—32no—
44C2×C5×C22⋊C4—32no—
45C2×C42×C5—32no—
46C2×#681—32no—
47C2×#681C2×D312yes—
48C22⋊#168—22no—
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×C5×Dic3—24no—
63C2×C5×Dic3—44no—
64C3⋊#168—42no—
65C3×#168—42no—
66C23×C3×C4C2×D511yescharacteristic
67C2×C3×M16—52no—
68C2×#217Dic512yes—
69#926—22no—
70#926—22no—
71C2×C4⋊Dic3C2×D512yes—
72C2×C4×Dic3Dic512yes—
73C2×#208—52no—
74C3×C22⋊C8—102no—
75#830—102no—
76C24×C5C4×D311yescharacteristic
77C22×C4×C5—24no—
78C22×C4×C5—34no—
79C22×C4×C5C4×D311yescharacteristic
80C22×C4×C5D1212yes—
81C22×C4×C5#6712yes—
82C22×C4×C5C22×D311yescharacteristic
83C5×C4⋊C4—62no—
84C5×C4⋊C4—62no—
85C5×C22⋊C4—64no—
86C42×C5—64no—
87#681—24no—
88#681—64no—
89C2×#168—22no—
90C2×#168—62no—
91C2×#117—31no—
92#407—51no—
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—
104C5×Dic3—44no—
105C24×C3C2×Dic511yescharacteristic
106C22×C3×C4—24no—
107C22×C3×C4C2×Dic511yescharacteristic
108C22×C3×C4C22⋊D512yes—
109C22×C3×C4C22⋊D512yes—
110C22×C3×C4C22×D511yescharacteristic
111C22×Dic3C2×Dic514yes—
112C3×M16—104no—
113C2×C3×C8—102no—
114#217—24no—
115C4⋊Dic3—22no—
116C4⋊Dic3—22no—
117C4×Dic3—24no—
118#208—104no—
119C2×C3⋊C8—102no—
120C23×C5—22no—
121C23×C5—42no—
122C23×C5(C2×D3)⋊C412yes—
123C23×C5C2×C4×D311yescharacteristic
124C2×C4×C5—22no—
125C2×C4×C5—24no—
126C2×C4×C5—24no—
127C2×C4×C5—64no—
128C2×C4×C5—124no—
129C2×C4×C5(C2×D3)⋊C412yes—
130C2×C4×C5C2×D1211yescharacteristic
131C2×C4×C5#23714yes—
132C2×C4×C5C2×#6711yescharacteristic
133#168—42no—
134#168—122no—
135C23×C4D3×D511yescharacteristic
136C2×M16—52no—
137C2×M16—152no—
138#117—62no—
139#117—62no—
140C2×C4⋊C4—32no—
141C2×C22⋊C4—32no—
142C2×C42—32no—
143C22⋊C8—102no—
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×C3C22⋊Dic512yes—
152C23×C3C22×Dic511yescharacteristic
153C2×C3×C4—22no—
154C2×C3×C4—24no—
155C2×C3×C4—24no—
156C2×C3×C4C22⋊Dic512yes—
157C2×C3×C4#70914yes—
158C2×C3×C4C2×C22⋊D511yescharacteristic
159C2×C3×C4C2×C22⋊D511yescharacteristic
160C2×Dic3—24no—
161C2×Dic3—44no—
162C3×C8—202no—
163C3⋊C8—202no—
164C22×C5—22no—
165C22×C5—24no—
166C22×C5—22no—
167C22×C5—44no—
168C22×C5#87712yes—
169C22×C5C2×(C2×D3)⋊C411yescharacteristic
170C4×C5—22no—
171C4×C5—124no—
172C4×C5#88612yes—
173C4×C5#93512yes—
174C24D3×Dic511yescharacteristic
175C22×C4—24no—
176C22×C4—34no—
177C22×C4D3×Dic511yescharacteristic
178C22×C4#120112yes—
179C22×C4#120312yes—
180C22×C4C2×D3×D511yescharacteristic
181M16—104no—
182M16—304no—
183C2×C8—102no—
184C2×C8—302no—
185C4⋊C4—62no—
186C4⋊C4—62no—
187C22⋊C4—64no—
188C42—64no—
189C3×C5#182211yescharacteristic, complemented, Hall
190C22×C3—22no—
191C22×C3—22no—
192C22×C3—24no—
193C22×C3—44no—
194C22×C3#407212yes—
195C22×C3C2×C22⋊Dic511yescharacteristic
196C3×C4—22no—
197C3×C4#407512yes—
198C3×C4#407512yes—
199Dic3—44no—
200C2×C5—22no—
201C2×C5—42no—
202C2×C5#494311yescharacteristic
203C2×C5#513212yes—
204C23—22no—
205C23—42no—
206C23(C2×D3)⋊Dic512yes—
207C23C2×D3×Dic511yescharacteristic
208C2×C4—22no—
209C2×C4—24no—
210C2×C4—24no—
211C2×C4—64no—
212C2×C4—124no—
213C2×C4(C2×D3)⋊Dic512yes—
214C2×C4#677914yes—
215C2×C4C2×#120111yescharacteristic
216C2×C4C2×#120311yescharacteristic
217C8—202no—
218C8—602no—
219C2×C3—22no—
220C2×C3—42no—
221C2×C3#6550011yescharacteristic
222C2×C3#6552612yes—
223C5#6997411yescharacteristic, complemented, Sylow
224C22—22no—
225C22—24no—
226C22—22no—
227C22—44no—
228C22#9152912yes—
229C22C2×(C2×D3)⋊Dic511yescharacteristic
230C4—22no—
231C4—124no—
232C4#9153612yes—
233C4#9154212yes—
234C3#1060238211yescharacteristic, complemented, Sylow
235C2—22no—
236C2—42no—
237C2#1174835512yes—
238C2#1174947211yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊Dic5
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. #11745986C2semidirect
189. C3×C5#1822semidirect
223. C5#69974semidirect
234. C3#10602382semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9262
#117513082
C3×#654962
#117459862
#106023823
#699745