Finite Group Databasebeta

← #14298489

Subgroups — #14298489

Order 1920.

600 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91815C211yesmaximal, characteristic
2C3×C5×#380C211yesmaximal, characteristic
3C2×#91114C211yesmaximal, characteristic
4#11746350C212yesmaximal, complemented
5#11746350C212yesmaximal, complemented
6#10600296—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C3×C5×C4⋊C4C2212yes—
9C2×C3×C5×C22⋊C4—21no—
10C2×#6719—21no—
11#91815—22no—
12#91815C414yescomplemented
13C2×C4⋊Dic15C2211yescharacteristic
14C2×C4⋊Dic15C2211yescharacteristic
15C2×C4×Dic15—21no—
16C22×C3⋊#168C2212yes—
17C3×C5×#95—21no—
18#91114—22no—
19#69503—51nomaximal, Hall
20C2×#4072—31no—
21C5×#380D311yescharacteristic
22C2×C22⋊#168—31no—
23#64749—32no—
24#64749—32no—
25C24×C3×C5D411yescharacteristic
26C22×C3×C4×C5—24no—
27C22×C3×C4×C5—22no—
28C22×C3×C4×C5C2×C412yes—
29C22×C3×C4×C5D411yescharacteristic
30C22×C3×C4×C5D412yes—
31C22×C3×C4×C5C2311yescharacteristic
32C22×Dic15—21no—
33C22×Dic15—21no—
34C3×C5×C4⋊C4—24no—
35C3×C5×C22⋊C4—42no—
36#6719—24no—
37C4⋊Dic15—21no—
38C4⋊Dic15—21no—
39C4⋊Dic15C2×C412yes—
40C4⋊Dic15C2×C412yes—
41C4×Dic15—24no—
42C2×C3⋊#168—22no—
43C2×C3⋊#168—24no—
44C2×#926—51no—
45C3×#380D511yescharacteristic
46C2×#830—51no—
47#4529—52no—
48#4529—52no—
49C23×C4×C5C2×D311yescharacteristic
50C2×C5×C4⋊C4C2×D312yes—
51C2×C5×C22⋊C4—21no—
52C2×C22⋊Dic5—61no—
53#4072—34no—
54#4072—62no—
55C2×C4⋊Dic5—31no—
56C2×C4⋊Dic5—31no—
57C2×C4×Dic5—61no—
58C22×#168—32no—
59C5×#95—21no—
60C22⋊#168—62no—
61#1825—151noSylow
62C23×C3×C5—22no—
63C23×C3×C5—22no—
64C23×C3×C5—21no—
65C23×C3×C5—21no—
66C23×C3×C5C22⋊C412yes—
67C23×C3×C5C2×D411yescharacteristic
68C2×C3×C4×C5—22no—
69C2×C3×C4×C5—24no—
70C2×C3×C4×C5—24no—
71C2×C3×C4×C5—42no—
72C2×C3×C4×C5—42no—
73C2×C3×C4×C5—42no—
74C2×C3×C4×C5C22⋊C412yes—
75C2×C3×C4×C5C22×C411yescharacteristic
76C2×C3×C4×C5C2×D411yescharacteristic
77C2×C3×C4×C5#4114yes—
78C2×Dic15—22no—
79C2×Dic15—22no—
80C2×Dic15—42no—
81C2×Dic15—41no—
82C2×Dic15—41no—
83C3⋊#168—42no—
84C23×C3×C4C2×D511yescharacteristic
85C2×C3×C4⋊C4C2×D512yes—
86C2×C3×C22⋊C4—21no—
87C2×#217—101no—
88#926—54no—
89#926—102no—
90C2×C4⋊Dic3—51no—
91C2×C4⋊Dic3—51no—
92C2×C4×Dic3—101no—
93C22×C3⋊C8—52no—
94C3×#95—21no—
95#830—102no—
96C24×C5#6711yescharacteristic
97C22×C4×C5—24no—
98C22×C4×C5—22no—
99C22×C4×C5C4×D312yes—
100C22×C4×C5D1212yes—
101C22×C4×C5#6711yescharacteristic
102C22×C4×C5C22×D311yescharacteristic
103C22×Dic5—61no—
104C22×Dic5—61no—
105C5×C4⋊C4—24no—
106C5×C22⋊C4—42no—
107C22⋊Dic5—64no—
108C4⋊Dic5—32no—
109C4⋊Dic5—32no—
110C4⋊Dic5—61no—
111C4⋊Dic5—61no—
112C4×Dic5—64no—
113C2×#168—62no—
114C2×#168—64no—
115C2×#117—151no—
116C2×C22⋊C8—151no—
117#380D1511yescharacteristic
118#340—152no—
119#340—152no—
120C22×C3×C5—22no—
121C22×C3×C5—22no—
122C22×C3×C5—22no—
123C22×C3×C5—42no—
124C22×C3×C5—42no—
125C22×C3×C5C2×C22⋊C411yescharacteristic
126C22×C3×C5#12312yes—
127C22×C3×C5#13512yes—
128C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
129C22×C3×C5#13711yescharacteristic
130C3×C4×C5—22no—
131C3×C4×C5—82no—
132C3×C4×C5#11712yes—
133C3×C4×C5#12312yes—
134Dic15—42no—
135Dic15—42no—
136C24×C3C22⋊D511yescharacteristic
137C22×C3×C4—24no—
138C22×C3×C4—22no—
139C22×C3×C4C4×D512yes—
140C22×C3×C4D2012yes—
141C22×C3×C4C22⋊D511yescharacteristic
142C22×C3×C4C22×D511yescharacteristic
143C22×Dic3—101no—
144C22×Dic3—101no—
145C3×C4⋊C4—24no—
146C3×C22⋊C4—42no—
147#217—104no—
148C4⋊Dic3—52no—
149C4⋊Dic3—52no—
150C4⋊Dic3—101no—
151C4⋊Dic3—101no—
152C4×Dic3—104no—
153C2×C3⋊C8—102no—
154C2×C3⋊C8—104no—
155C23×C5—21no—
156C23×C5—22no—
157C23×C5—21no—
158C23×C5—22no—
159C23×C5(C2×D3)⋊C412yes—
160C23×C5C2×#6711yescharacteristic
161C2×C4×C5—22no—
162C2×C4×C5—24no—
163C2×C4×C5—24no—
164C2×C4×C5—42no—
165C2×C4×C5—42no—
166C2×C4×C5—42no—
167C2×C4×C5(C2×D3)⋊C412yes—
168C2×C4×C5C2×C4×D311yescharacteristic
169C2×C4×C5C2×D1211yescharacteristic
170C2×C4×C5#23714yes—
171C2×Dic5—62no—
172C2×Dic5—62no—
173C2×Dic5—121no—
174C2×Dic5—121no—
175C2×Dic5—122no—
176#168—122no—
177C23×C4C2×D1511yescharacteristic
178C22×C8—152no—
179#117—154no—
180#117—302no—
181C2×C4⋊C4—151no—
182C2×C4⋊C4—151no—
183C2×C4⋊C4C2×D1512yes—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—301no—
186C2×C42—301no—
187C22⋊C8—302no—
188#95—21no—
189C2×C3×C5—42no—
190C2×C3×C5#38111yescharacteristic
191C2×C3×C5#41611yescharacteristic
192C2×C3×C5#41711yescharacteristic
193C2×C3×C5#48212yes—
194C2×C3×C5#48512yes—
195C23×C3—22no—
196C23×C3—21no—
197C23×C3—22no—
198C23×C3—21no—
199C23×C3#68512yes—
200C23×C3C2×C22⋊D511yescharacteristic
201C2×C3×C4—22no—
202C2×C3×C4—24no—
203C2×C3×C4—24no—
204C2×C3×C4—42no—
205C2×C3×C4—42no—
206C2×C3×C4—42no—
207C2×C3×C4#68512yes—
208C2×C3×C4C2×C4×D511yescharacteristic
209C2×C3×C4C2×D2011yescharacteristic
210C2×C3×C4#71114yes—
211C2×Dic3—102no—
212C2×Dic3—102no—
213C2×Dic3—202no—
214C2×Dic3—201no—
215C2×Dic3—201no—
216C3⋊C8—202no—
217C22×C5—22no—
218C22×C5—22no—
219C22×C5—22no—
220C22×C5—42no—
221C22×C5—42no—
222C22×C5C2×(C2×D3)⋊C411yescharacteristic
223C22×C5#93211yescharacteristic
224C22×C5#93512yes—
225C22×C5#94211yescharacteristic
226C22×C5#95012yes—
227C4×C5—22no—
228C4×C5—82no—
229C4×C5#87712yes—
230C4×C5#88612yes—
231Dic5—122no—
232Dic5—122no—
233C24#122011yescharacteristic
234C22×C4—24no—
235C22×C4—22no—
236C22×C4—301no—
237C22×C4—301no—
238C22×C4C4×D1512yes—
239C22×C4D6012yes—
240C22×C4#122011yescharacteristic
241C22×C4C22×D1511yescharacteristic
242C2×C8—302no—
243C2×C8—304no—
244C4⋊C4—24no—
245C4⋊C4—152no—
246C4⋊C4—152no—
247C4⋊C4—301no—
248C4⋊C4—301no—
249C22⋊C4—42no—
250C22⋊C4—304no—
251C42—304no—
252C3×C5#182511yescharacteristic, complemented, Hall
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—42no—
257C22×C3—42no—
258C22×C3C2×#68511yescharacteristic
259C22×C3#407811yescharacteristic
260C22×C3#408112yes—
261C22×C3#408811yescharacteristic
262C22×C3#409612yes—
263C3×C4—22no—
264C3×C4—82no—
265C3×C4#402312yes—
266C3×C4#403212yes—
267Dic3—202no—
268Dic3—202no—
269C2×C5—42no—
270C2×C5#494311yescharacteristic
271C2×C5#496611yescharacteristic
272C2×C5#500211yescharacteristic
273C2×C5#503512yes—
274C2×C5#504512yes—
275C23—21no—
276C23—22no—
277C23—21no—
278C23—22no—
279C23#671412yes—
280C23C2×#122011yescharacteristic
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—302no—
288C2×C4—302no—
289C2×C4—601no—
290C2×C4—601no—
291C2×C4—602no—
292C2×C4#671412yes—
293C2×C4C2×C4×D1511yescharacteristic
294C2×C4C2×D6011yescharacteristic
295C2×C4#681914yes—
296C8—602no—
297C2×C3—42no—
298C2×C3#6523211yescharacteristic
299C2×C3#6525511yescharacteristic
300C2×C3#6529111yescharacteristic
301C2×C3#6532412yes—
302C2×C3#6533412yes—
303C5#6950311yescharacteristic, complemented, Sylow
304C22—22no—
305C22—22no—
306C22—22no—
307C22—42no—
308C22—42no—
309C22C2×#671411yescharacteristic
310C22#9182111yescharacteristic
311C22#9182412yes—
312C22#9183111yescharacteristic
313C22#9183912yes—
314C4—22no—
315C4—82no—
316C4—602no—
317C4—602no—
318C4#9176612yes—
319C4#9177512yes—
320C3#1060029611yescharacteristic, complemented, Sylow
321C2—42no—
322C2#1175104411yescharacteristic
323C2#1175106711yescharacteristic
324C2#1175110311yescharacteristic
325C2#1175113612yes—
326C2#1175114612yes—
subgroupG/H
centerC23C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#380C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4×C5C23
hypercenter#380D15
hypocenterC3×C5#1825
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
4. #11746350C2semidirect
5. #11746350C2semidirect
12. #91815C4semidirect
252. C3×C5#1825semidirect
303. C5#69503semidirect
320. C3#10600296semidirect

Maximal subgroups

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

subgroupindex
C2×#918152
C3×C5×#3802
C2×#911142
#117463502
#106002963
#695035