Finite Group Databasebeta

← #14301434

Subgroups — #14301434

Order 1920.

720 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 155 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
1#11756557C211yesmaximal, characteristic
2C2×#91825C211yesmaximal, characteristic
3C2×C3×C5×#100C211yesmaximal, characteristic
4#11751221C212yesmaximal, complemented
5#11746376C212yesmaximal, complemented
6#10600862—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×Dic30C2211yescharacteristic
9C2×C3×C5×M16C2212yes—
10C2×#6719—22no—
11C2×#6719—22no—
12#91825—22no—
13#91825C414yescomplemented
14D4×Dic15—24no—
15#91815C2212yes—
16C2×C4×Dic15C2211yescharacteristic
17C3×C5×#100—22no—
18#91100—24no—
19#70069—51nomaximal, Hall
20#66132—31no—
21C2×#4082—31no—
22C2×C5×#100D311yescharacteristic
23#65409—32no—
24#64775—32no—
25C24×C3×C5D412yes—
26C2×C3×C5×D4—22no—
27C2×C3×C5×D4—22no—
28C2×C3×C5×D4C2×C412yes—
29C2×C3×C5×D4D412yes—
30C22×C3×C4×C5C2311yescharacteristic
31C22×Dic15—21no—
32C22×Dic15—21no—
33C22×Dic15—24no—
34C2×Dic30—22no—
35C2×Dic30—22no—
36C2×Dic30—21no—
37C2×Dic30C2×C412yescomplemented
38C3×C5×M16—22no—
39C3×C5×M16—22no—
40C2×C3×C5×C8—22no—
41#6719—24no—
42#6719—28no—
43#6719—22no—
44C4⋊Dic15D414yes—
45C4×Dic15—21no—
46C4×Dic15—22no—
47C4×Dic15C2×C412yescomplemented
48#5798—51no—
49C2×#936—51no—
50C2×C3×#100D511yescharacteristic
51#5120—52no—
52#4555—52no—
53C22×C5×D4C2×D311yescharacteristic
54C22×Dic10—31no—
55C2×C5×M16C2×D312yes—
56C2×C22⋊Dic5—62no—
57C2×C22⋊Dic5—62no—
58#4082—34no—
59#4082—62no—
60D4×Dic5—64no—
61#4072—32no—
62C2×C4×Dic5—31no—
63C5×#100—22no—
64#3948—64no—
65#1885—151noSylow
66C23×C3×C5—22no—
67C23×C3×C5—22no—
68C23×C3×C5—44no—
69C23×C3×C5C22⋊C414yes—
70C23×C3×C5C2×D411yescharacteristic
71C3×C5×D4—24no—
72C3×C5×D4—24no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4112yes—
77C2×Dic15—22no—
78C2×Dic15—22no—
79C2×Dic15—24no—
80C2×Dic15—42no—
81C2×Dic15—41no—
82C2×Dic15—41no—
83C2×Dic15—84no—
84Dic30—24no—
85Dic30—42no—
86C3×C5×C8—42no—
87C22×C3×D4C2×D511yescharacteristic
88C22×Dic6—51no—
89C2×C3×M16C2×D512yes—
90C2×#217—102no—
91C2×#217—102no—
92#936—54no—
93#936—102no—
94D4×Dic3—104no—
95#926—52no—
96C2×C4×Dic3—51no—
97C3×#100—22no—
98#816—104no—
99C24×C5D1212yes—
100C2×C5×D4—22no—
101C2×C5×D4—22no—
102C2×C5×D4C4×D312yes—
103C2×C5×D4#6712yes—
104C22×C4×C5C22×D311yescharacteristic
105C22×Dic5—61no—
106C22×Dic5—61no—
107C22×Dic5—64no—
108C2×Dic10—32no—
109C2×Dic10—62no—
110C2×Dic10—62no—
111C2×Dic10—61no—
112C5×M16—22no—
113C5×M16—22no—
114C2×C5×C8—22no—
115C22⋊Dic5—64no—
116C22⋊Dic5—68no—
117C22⋊Dic5—62no—
118C4⋊Dic5—34no—
119C4×Dic5—32no—
120C4×Dic5—62no—
121C4×Dic5—61no—
122C2×#124—151no—
123#518—151no—
124#419—152no—
125C2×#100D1511yescharacteristic
126#339—152no—
127C22×C3×C5—22no—
128C22×C3×C5—24no—
129C22×C3×C5—44no—
130C22×C3×C5—44no—
131C22×C3×C5—82no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5#12011yescharacteristic
134C22×C3×C5#12311yescharacteristic
135C3×C4×C5C4×D412yes—
136C3×C4×C5#12112yes—
137Dic15—42no—
138Dic15—42no—
139Dic15—44no—
140C24×C3D2012yes—
141C2×C3×D4—22no—
142C2×C3×D4—22no—
143C2×C3×D4C4×D512yes—
144C2×C3×D4C22⋊D512yes—
145C22×C3×C4C22×D511yescharacteristic
146C22×Dic3—101no—
147C22×Dic3—101no—
148C22×Dic3—104no—
149C2×Dic6—52no—
150C2×Dic6—102no—
151C2×Dic6—102no—
152C2×Dic6—101no—
153C3×M16—22no—
154C3×M16—22no—
155C2×C3×C8—22no—
156#217—104no—
157#217—108no—
158#217—102no—
159C4⋊Dic3—54no—
160C4×Dic3—52no—
161C4×Dic3—102no—
162C4×Dic3—101no—
163C23×C5—22no—
164C23×C5—22no—
165C23×C5—44no—
166C23×C5(C2×D3)⋊C414yes—
167C23×C5C2×D1211yescharacteristic
168C5×D4—24no—
169C5×D4—24no—
170C2×C4×C5C2×C4×D311yescharacteristic
171C2×C4×C5D3×D412yes—
172C2×C4×C5#23712yes—
173C2×C4×C5C2×#6711yescharacteristic
174C2×Dic5—64no—
175C2×Dic5—62no—
176C2×Dic5—62no—
177C2×Dic5—122no—
178C2×Dic5—121no—
179C2×Dic5—121no—
180C2×Dic5—244no—
181Dic10—64no—
182Dic10—122no—
183C5×C8—42no—
184C22×Q8—151no—
185C22×D4C2×D1511yescharacteristic
186C2×M16C2×D1512yes—
187#124—154no—
188#124—302no—
189C4×D4—304no—
190#117—152no—
191C2×C22⋊C4—302no—
192C2×C22⋊C4—302no—
193C2×C42—151no—
194#103—304no—
195#100—22no—
196C2×C3×C5—21no—
197C2×C3×C5—21no—
198C2×C3×C5—44no—
199C2×C3×C5#38611yescharacteristic
200C2×C3×C5#45512yes—
201C23×C3—22no—
202C23×C3—22no—
203C23×C3—44no—
204C23×C3#68514yes—
205C23×C3C2×D2011yescharacteristic
206C3×D4—24no—
207C3×D4—24no—
208C2×C3×C4C2×C4×D511yescharacteristic
209C2×C3×C4D4×D512yes—
210C2×C3×C4#71112yes—
211C2×C3×C4C2×C22⋊D511yescharacteristic
212C2×Dic3—104no—
213C2×Dic3—102no—
214C2×Dic3—102no—
215C2×Dic3—202no—
216C2×Dic3—201no—
217C2×Dic3—201no—
218C2×Dic3—404no—
219Dic6—104no—
220Dic6—202no—
221C3×C8—42no—
222C22×C5—22no—
223C22×C5—24no—
224C22×C5—44no—
225C22×C5—44no—
226C22×C5—82no—
227C22×C5#88211yescharacteristic
228C22×C5#88611yescharacteristic
229C22×C5C2×(C2×D3)⋊C411yescharacteristic
230C4×C5#67⋊C412yes—
231C4×C5#93912yes—
232Dic5—122no—
233Dic5—122no—
234Dic5—124no—
235C24D6012yes—
236C2×Q8—152no—
237C2×Q8—301no—
238C2×Q8—302no—
239C2×Q8—302no—
240C2×D4—22no—
241C2×D4—22no—
242C2×D4C4×D1512yes—
243C2×D4#122012yes—
244C22×C4—301no—
245C22×C4—301no—
246C22×C4—304no—
247C22×C4C22×D1511yescharacteristic
248M16—22no—
249M16—22no—
250C2×C8—22no—
251C4⋊C4—154no—
252C22⋊C4—304no—
253C22⋊C4—308no—
254C22⋊C4—302no—
255C42—152no—
256C42—302no—
257C42—301no—
258C3×C5#188511yescharacteristic, complemented, Hall
259C22×C3—22no—
260C22×C3—24no—
261C22×C3—44no—
262C22×C3—44no—
263C22×C3—82no—
264C22×C3#402811yescharacteristic
265C22×C3#403211yescharacteristic
266C22×C3C2×#68511yescharacteristic
267C3×C4#402712yes—
268C3×C4#408512yes—
269Dic3—202no—
270Dic3—204no—
271Dic3—202no—
272C2×C5—21no—
273C2×C5—21no—
274C2×C5—44no—
275C2×C5#474612yes—
276C2×C5#495811yescharacteristic
277C23—22no—
278C23—22no—
279C23—44no—
280C23#671414yes—
281C23C2×D6011yescharacteristic
282Q8—304no—
283Q8—602no—
284D4—24no—
285D4—24no—
286C2×C4—304no—
287C2×C4—302no—
288C2×C4—302no—
289C2×C4—602no—
290C2×C4—601no—
291C2×C4—601no—
292C2×C4—1204no—
293C2×C4C2×C4×D1511yescharacteristic
294C2×C4D4×D1512yes—
295C2×C4#681912yes—
296C2×C4C2×#122011yescharacteristic
297C8—42no—
298C2×C3—21no—
299C2×C3—21no—
300C2×C3—44no—
301C2×C3#6503512yes—
302C2×C3#6524711yescharacteristic
303C5#7006911yescharacteristic, complemented, Sylow
304C22—22no—
305C22—24no—
306C22—44no—
307C22—44no—
308C22—82no—
309C22#9177111yescharacteristic
310C22#9177511yescharacteristic
311C22C2×#671411yescharacteristic
312C4—602no—
313C4—602no—
314C4—604no—
315C4#9177012yes—
316C4#9182812yes—
317C3#1060086211yescharacteristic, complemented, Sylow
318C2—21no—
319C2—21no—
320C2—44no—
321C2#1175084712yes—
322C2#1175105911yescharacteristic
subgroupG/H
centerC22#91771
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#100C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
cosocleC22×C3×C4×C5C23
hypercenterC2×#100D15
hypocenterC3×C5#1885
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
4. #11751221C2semidirect
5. #11746376C2semidirect
13. #91825C4semidirect
37. C2×Dic30C2×C4semidirect
47. C4×Dic15C2×C4semidirect
258. C3×C5#1885semidirect
303. C5#70069semidirect
317. C3#10600862semidirect

Maximal subgroups

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

subgroupindex
#117565572
C2×#918252
C2×C3×C5×#1002
#117512212
#117463762
#106008623
#700695