Finite Group Databasebeta

← #14298422

Subgroups — #14298422

Order 1920.

544 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 110 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×#91528C211yesmaximal, characteristic
2#11752457C211yesmaximal, characteristic
3C3×#65798C211yesmaximal, characteristic
4#11746574C214yesmaximal, complemented
5#10604247—31nomaximal, Hall
6C23×C3×Dic5C2211yescharacteristic
7C2×#6762C2212yes—
8C2×C3×#704C2212yes—
9C2×#6719C411yescharacteristic
10C2×C5×#217C411yescharacteristic
11C2×#6668C2212yes—
12#91528—22no—
13#91528—22no—
14C2×Dic3×Dic5C412yes—
15#91241—22no—
16C3×C22⋊#170—22no—
17#69974—51nomaximal, Hall
18C2×#4023—31no—
19#65798—31no—
20#65798D311yescharacteristic
21#64919—34no—
22C24×C3×C5C2×C411yescharacteristic
23C22×Dic15C2×C412yes—
24C22×C5×Dic3C2×C412yes—
25C22×C3×Dic5—24no—
26C22×C3×Dic5C2×C411yescharacteristic
27C22×C3×Dic5D412yes—
28C22×C3×Dic5D412yes—
29C22×C3×Dic5C2311yescharacteristic
30#6762—24no—
31C2×C3⋊#170—22no—
32C3×#704—24no—
33C2×C3×#170—22no—
34#6719—22no—
35C5×#217—22no—
36#6668—22no—
37#6668—22no—
38Dic3×Dic5—24no—
39C2×#926—51no—
40C3×#407—51no—
41#5207—51no—
42#4554—54no—
43C23×Dic5C2×D311yescharacteristic
44C2×#704—32no—
45C2×#704C2×D312yes—
46C2×C5×C22⋊C4—31no—
47C2×C22⋊Dic5—31no—
48C2×#683—32no—
49C2×C4×Dic5—32no—
50#4023—62no—
51#4023—62no—
52C22⋊#170—22no—
53C22⋊#170—62no—
54#1822—151noSylow
55C23×C3×C5—22no—
56C23×C3×C5—42no—
57C23×C3×C5C22⋊C412yes—
58C23×C3×C5C22×C411yescharacteristic
59C2×Dic15—22no—
60C2×Dic15—42no—
61C2×C5×Dic3—22no—
62C2×C5×Dic3—42no—
63C2×C3×Dic5—22no—
64C2×C3×Dic5—24no—
65C2×C3×Dic5—24no—
66C2×C3×Dic5C22⋊C412yes—
67C2×C3×Dic5C2×D411yescharacteristic
68C2×C3×Dic5C2×D411yescharacteristic
69C2×C3×Dic5#4114yes—
70C3⋊#170—42no—
71C3×#170—42no—
72C23×C3×C4—51no—
73C2×C3×M16—52no—
74C2×#217—51no—
75C2×#217AGL(1,𝔽5)11yescharacteristic
76#926—102no—
77#926—102no—
78C2×C4⋊Dic3—52no—
79C2×C4×Dic3—52no—
80C2×#208—52no—
81C3×C22⋊C8—102no—
82#830—102no—
83C24×C5C4×D311yescharacteristic
84C22×C4×C5—32no—
85C22×Dic5—24no—
86C22×Dic5—32no—
87C22×Dic5C4×D311yescharacteristic
88C22×Dic5D1212yes—
89C22×Dic5#6712yes—
90C22×Dic5C22×D311yescharacteristic
91#704—24no—
92#704—64no—
93C2×#170—22no—
94C2×#170—62no—
95C5×C22⋊C4—62no—
96C22⋊Dic5—62no—
97#683—62no—
98#683—62no—
99C4×Dic5—64no—
100C2×#117—151no—
101#407—51no—
102#407—151no—
103#343—154no—
104C22×C3×C5—22no—
105C22×C3×C5—22no—
106C22×C3×C5—24no—
107C22×C3×C5—44no—
108C22×C3×C5C2×C22⋊C411yescharacteristic
109C22×C3×C5#11712yes—
110Dic15—42no—
111C3×Dic5—22no—
112C3×Dic5#12312yes—
113C3×Dic5#12312yes—
114C5×Dic3—42no—
115C24×C3C2×AGL(1,𝔽5)11yescharacteristic
116C22×C3×C4—51no—
117C22×C3×C4—52no—
118C22×C3×C4—52no—
119C22×C3×C4—51no—
120C22×C3×C4—104no—
121C22×Dic3—52no—
122C22×Dic3C2×AGL(1,𝔽5)12yes—
123C3×M16—104no—
124C2×C3×C8—102no—
125#217—22no—
126#217—102no—
127C4⋊Dic3—102no—
128C4⋊Dic3—102no—
129C4×Dic3—104no—
130#208—104no—
131C2×C3⋊C8—102no—
132C23×C5—22no—
133C23×C5—42no—
134C23×C5(C2×D3)⋊C412yes—
135C23×C5C2×C4×D311yescharacteristic
136C2×C4×C5—62no—
137C2×C4×C5—122no—
138C2×Dic5—22no—
139C2×Dic5—24no—
140C2×Dic5—24no—
141C2×Dic5—62no—
142C2×Dic5—122no—
143C2×Dic5(C2×D3)⋊C412yes—
144C2×Dic5C2×D1211yescharacteristic
145C2×Dic5#23714yes—
146C2×Dic5C2×#6711yescharacteristic
147#170—42no—
148#170—122no—
149C23×C4—51no—
150C2×M16—52no—
151C2×M16—152no—
152#117—302no—
153#117—302no—
154C2×C4⋊C4—152no—
155C2×C22⋊C4—31no—
156C2×C22⋊C4—151no—
157C2×C42—152no—
158C22⋊C8—102no—
159C22⋊C8—302no—
160C2×C3×C5—22no—
161C2×C3×C5—42no—
162C2×C3×C5#38111yescharacteristic
163C2×C3×C5#41312yes—
164C23×C3—22no—
165C23×C3—42no—
166C23×C3C22⋊AGL(1,𝔽5)12yes—
167C23×C3C22×AGL(1,𝔽5)11yescharacteristic
168C2×C3×C4—54no—
169C2×C3×C4—51no—
170C2×C3×C4—51no—
171C2×C3×C4—52no—
172C2×C3×C4—104no—
173C2×C3×C4—104no—
174C2×C3×C4—102no—
175C2×Dic3—22no—
176C2×Dic3—42no—
177C2×Dic3—102no—
178C2×Dic3—202no—
179C3×C8—202no—
180C3⋊C8—202no—
181C22×C5—22no—
182C22×C5—24no—
183C22×C5—22no—
184C22×C5—44no—
185C22×C5#87712yes—
186C22×C5C2×(C2×D3)⋊C411yescharacteristic
187C4×C5—122no—
188Dic5—22no—
189Dic5—122no—
190Dic5#88612yes—
191Dic5#93512yes—
192C24D3×AGL(1,𝔽5)11yescharacteristic
193C22×C4—32no—
194C22×C4—51no—
195C22×C4—52no—
196C22×C4—52no—
197C22×C4—51no—
198C22×C4—104no—
199C22×C4—152no—
200M16—104no—
201M16—304no—
202C2×C8—102no—
203C2×C8—302no—
204C4⋊C4—302no—
205C4⋊C4—302no—
206C22⋊C4—62no—
207C22⋊C4—302no—
208C42—304no—
209C3×C5#182211yescharacteristic, complemented, Hall
210C22×C3—22no—
211C22×C3—22no—
212C22×C3—24no—
213C22×C3—44no—
214C22×C3#413012yes—
215C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
216C3×C4—52no—
217C3×C4—52no—
218C3×C4—102no—
219Dic3—42no—
220Dic3—202no—
221C2×C5—22no—
222C2×C5—42no—
223C2×C5#494311yescharacteristic
224C2×C5#513212yes—
225C23—22no—
226C23—42no—
227C23(C2×D3)⋊AGL(1,𝔽5)12yes—
228C23C2×D3×AGL(1,𝔽5)11yescharacteristic
229C2×C4—54no—
230C2×C4—51no—
231C2×C4—51no—
232C2×C4—52no—
233C2×C4—62no—
234C2×C4—104no—
235C2×C4—104no—
236C2×C4—102no—
237C2×C4—122no—
238C2×C4—302no—
239C2×C4—602no—
240C8—202no—
241C8—602no—
242C2×C3—22no—
243C2×C3—42no—
244C2×C3#6576411yescharacteristic
245C2×C3#6577712yes—
246C5#6997411yescharacteristic, complemented, Sylow
247C22—22no—
248C22—22no—
249C22—24no—
250C22—44no—
251C22#9192312yes—
252C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
253C4—52no—
254C4—52no—
255C4—102no—
256C4—122no—
257C4—602no—
258C3#1060424711yescharacteristic, complemented, Sylow
259C2—22no—
260C2—42no—
261C2#1175198411yescharacteristic
262C2#1175200812yes—
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC23×C3×C5C22×C4
FrattiniC23C2×D3×AGL(1,𝔽5)
Fitting, prime radicalC24×C3×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
cosocleC22×C3×Dic5C23
hypercenterC24D3×AGL(1,𝔽5)
hypocenterC3×C5#1822
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24

Complements

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

NH ≅ G/Ntype
4. #11746574C2semidirect
209. C3×C5#1822semidirect
246. C5#69974semidirect
258. C3#10604247semidirect

Maximal subgroups

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

subgroupindex
C2×#915282
#117524572
C3×#657982
#117465742
#106042473
#699745