Finite Group Databasebeta

← #14309001

Subgroups — #14309001

Order 1920.

580 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 580 conjugacy classes of subgroups — too many to draw. Only its 123 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#11756242C211yesmaximal, characteristic
2C3×C5×#381C211yesmaximal, characteristic
3#11751312C212yesmaximal
4#11746348C212yesmaximal
5#11746347C211yesmaximal, characteristic
6#10600329—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×C3×C5×C22⋊C4C2211yescharacteristic
10C2×#6719C2212yes—
11C2×#6719C2212yes—
12#91813—22no—
13#91767—24no—
14C3×C5×#95—22no—
15#91115—24no—
16#69536—51nomaximal, Hall
17#65817—31no—
18C5×#381D311yescharacteristic
19#65500—32no—
20#64747—32no—
21#64746—31no—
22C24×C3×C5C2311yescharacteristic
23C22×C3×C4×C5—22no—
24C22×C3×C4×C5—21no—
25C22×C3×C4×C5—21no—
26C22×C3×C4×C5—22no—
27C22×C3×C4×C5—21no—
28C22×C3×C4×C5D412yes—
29C22×C3×C4×C5Q812yescomplemented
30C22×Dic15—22no—
31C22×Dic15D414yes—
32C2×Dic30—22no—
33C3×C5×C22⋊C4—22no—
34C3×C5×C22⋊C4—22no—
35#6719—22no—
36#6719—22no—
37#6719—22no—
38#6719—22no—
39C4⋊Dic15—22no—
40#6712—24no—
41#5483—51no—
42C3×#381D511yescharacteristic
43#5211—52no—
44#4527—52no—
45#4526—51no—
46C23×C4×C5C2×D311yescharacteristic
47C2×C5×C22⋊C4C2×D311yescharacteristic
48C2×C5×C22⋊C4C2×D311yescharacteristic
49C2×C22⋊Dic5—32no—
50C2×C22⋊Dic5—32no—
51#4070—62no—
52#4024—64no—
53C5×#95—22no—
54#3963—64no—
55#2030—151noSylow
56C23×C3×C5—42no—
57C23×C3×C5C2×D412yes—
58C23×C3×C5C2×D411yescharacteristic
59C23×C3×C5C2×Q811yescharacteristic
60C23×C3×C5#4111yescharacteristic
61C23×C3×C5#4112yes—
62C2×C3×C4×C5—22no—
63C2×C3×C4×C5—24no—
64C2×C3×C4×C5—22no—
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5—42no—
67C2×C3×C4×C5—41no—
68C2×C3×C4×C5—42no—
69C2×C3×C4×C5—42no—
70C2×C3×C4×C5—41no—
71C2×Dic15—24no—
72C2×Dic15—44no—
73C2×Dic15—44no—
74C2×Dic15—42no—
75Dic30—82no—
76C23×C3×C4C2×D511yescharacteristic
77C2×C3×C22⋊C4C2×D511yescharacteristic
78C2×C3×C22⋊C4C2×D511yescharacteristic
79C2×#217—52no—
80C2×#217—52no—
81#924—102no—
82#878—104no—
83C3×#95—22no—
84C3⋊#95—104no—
85C24×C5C22×D311yescharacteristic
86C22×C4×C5—21no—
87C22×C4×C5—22no—
88C22×C4×C5—22no—
89C22×C4×C5—21no—
90C22×C4×C5—21no—
91C22×C4×C5Dic612yescomplemented
92C22×C4×C5#6712yes—
93C22×Dic5—34no—
94C22×Dic5—62no—
95C2×Dic10—62no—
96C5×C22⋊C4—22no—
97C5×C22⋊C4—22no—
98C22⋊Dic5—62no—
99C22⋊Dic5—62no—
100C22⋊Dic5—62no—
101C22⋊Dic5—62no—
102C4⋊Dic5—62no—
103#683—64no—
104#543—151no—
105#381—152no—
106#381D1511yescharacteristic
107#342—151no—
108#342—152no—
109C22×C3×C5—24no—
110C22×C3×C5—22no—
111C22×C3×C5—41no—
112C22×C3×C5—41no—
113C22×C3×C5—42no—
114C22×C3×C5#12011yescharacteristic
115C22×C3×C5C22⋊Q812yes—
116C22×C3×C5C22⋊Q811yescharacteristic
117C22×C3×C5#12412yes—
118C22×C3×C5#12411yescharacteristic
119C3×C4×C5—42no—
120C3×C4×C5—42no—
121C3×C4×C5—81no—
122Dic15—44no—
123Dic15—82no—
124C24×C3C22×D511yescharacteristic
125C22×C3×C4—21no—
126C22×C3×C4—22no—
127C22×C3×C4—22no—
128C22×C3×C4—21no—
129C22×C3×C4—21no—
130C22×C3×C4Dic1012yescomplemented
131C22×C3×C4C22⋊D512yes—
132C22×Dic3—54no—
133C22×Dic3—102no—
134C2×Dic6—102no—
135C3×C22⋊C4—22no—
136C3×C22⋊C4—22no—
137#217—102no—
138#217—102no—
139#217—102no—
140#217—102no—
141C4⋊Dic3—102no—
142Dic3⋊C4—104no—
143C23×C5—42no—
144C23×C5C2×Dic611yescharacteristic
145C23×C5#23511yescharacteristic
146C23×C5D3×D412yes—
147C23×C5#23712yes—
148C23×C5C2×#6711yescharacteristic
149C2×C4×C5—24no—
150C2×C4×C5—22no—
151C2×C4×C5—22no—
152C2×C4×C5—42no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—42no—
156C2×C4×C5—42no—
157C2×C4×C5—41no—
158C2×Dic5—64no—
159C2×Dic5—124no—
160C2×Dic5—124no—
161C2×Dic5—122no—
162Dic10—242no—
163C23×C4C2×D1511yescharacteristic
164C22⋊Q8—304no—
165C22⋊Q8—302no—
166C2×C22⋊C4—152no—
167C2×C22⋊C4—152no—
168C2×C22⋊C4C2×D1511yescharacteristic
169C2×C22⋊C4C2×D1511yescharacteristic
170#95—22no—
171#95—304no—
172C2×C3×C5—22no—
173C2×C3×C5—21no—
174C2×C3×C5—22no—
175C2×C3×C5—21no—
176C2×C3×C5#39311yescharacteristic
177C2×C3×C5#45812yes—
178C23×C3—42no—
179C23×C3C2×Dic1011yescharacteristic
180C23×C3#70911yescharacteristic
181C23×C3D4×D512yes—
182C23×C3#71112yes—
183C23×C3C2×C22⋊D511yescharacteristic
184C2×C3×C4—24no—
185C2×C3×C4—22no—
186C2×C3×C4—22no—
187C2×C3×C4—42no—
188C2×C3×C4—41no—
189C2×C3×C4—41no—
190C2×C3×C4—42no—
191C2×C3×C4—42no—
192C2×C3×C4—41no—
193C2×Dic3—104no—
194C2×Dic3—204no—
195C2×Dic3—204no—
196C2×Dic3—202no—
197Dic6—402no—
198C22×C5—24no—
199C22×C5—22no—
200C22×C5—41no—
201C22×C5—41no—
202C22×C5—42no—
203C22×C5#87812yes—
204C22×C5#88512yes—
205C22×C5#92411yescharacteristic
206C22×C5#93611yescharacteristic
207C22×C5#93711yescharacteristic
208C4×C5—42no—
209C4×C5—42no—
210C4×C5—81no—
211Dic5—124no—
212Dic5—242no—
213C24C22×D1511yescharacteristic
214C2×Q8—302no—
215C22×C4—21no—
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—21no—
219C22×C4—21no—
220C22×C4—154no—
221C22×C4—302no—
222C22×C4Dic3012yescomplemented
223C22×C4#122012yes—
224C4⋊C4—304no—
225C4⋊C4—302no—
226C22⋊C4—22no—
227C22⋊C4—22no—
228C22⋊C4—302no—
229C22⋊C4—302no—
230C22⋊C4—302no—
231C22⋊C4—302no—
232C3×C5#203011yescharacteristic, complemented, Hall
233C22×C3—24no—
234C22×C3—22no—
235C22×C3—41no—
236C22×C3—41no—
237C22×C3—42no—
238C22×C3#402412yes—
239C22×C3#403112yes—
240C22×C3#407011yescharacteristic
241C22×C3#408211yescharacteristic
242C22×C3#408311yescharacteristic
243C3×C4—42no—
244C3×C4—42no—
245C3×C4—81no—
246Dic3—204no—
247Dic3—402no—
248C2×C5—22no—
249C2×C5—21no—
250C2×C5—22no—
251C2×C5—21no—
252C2×C5#494711yescharacteristic
253C2×C5#505312yes—
254C23—42no—
255C23C2×Dic3011yescharacteristic
256C23#681711yescharacteristic
257C23D4×D1512yes—
258C23#681912yes—
259C23C2×#122011yescharacteristic
260Q8—1202no—
261C2×C4—24no—
262C2×C4—22no—
263C2×C4—22no—
264C2×C4—42no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—304no—
271C2×C4—604no—
272C2×C4—604no—
273C2×C4—602no—
274C2×C3—22no—
275C2×C3—21no—
276C2×C3—22no—
277C2×C3—21no—
278C2×C3#6523611yescharacteristic
279C2×C3#6534212yes—
280C5#6953611yescharacteristic, complemented, Sylow
281C22—22no—
282C22—24no—
283C22—41no—
284C22—41no—
285C22—42no—
286C22#9176712yes—
287C22#9177412yes—
288C22#9181311yescharacteristic
289C22#9182511yescharacteristic
290C22#9182611yescharacteristic
291C4—42no—
292C4—42no—
293C4—81no—
294C4—604no—
295C4—1202no—
296C3#1060032911yescharacteristic, complemented, Sylow
297C2—21no—
298C2—22no—
299C2—22no—
300C2—21no—
301C2#1175104811yescharacteristic
302C2#1175115412yes—
subgroupG/H
centerC22#91826
commutator, prime radical, cosocleC24×C3×C5C23
FrattiniC24C22×D15
FittingC3×C5×#381C2
socleC22×C3×C5#120
hypercenter#381D15
hypocenterC3×C5#2030
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
29. C22×C3×C4×C5Q8semidirect
91. C22×C4×C5Dic6semidirect
130. C22×C3×C4Dic10semidirect
222. C22×C4Dic30semidirect
232. C3×C5#2030semidirect
280. C5#69536semidirect
296. C3#10600329semidirect

Maximal subgroups

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

subgroupindex
#117562422
C3×C5×#3812
#117513122
#117463482
#117463472
#106003293
#695365