Finite Group Databasebeta

← #14298498

Subgroups — #14298498

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×C3×C5×#117C211yesmaximal, characteristic
2#11751313C211yesmaximal, characteristic
3C2×#91114C211yesmaximal, characteristic
4#11746350C212yesmaximal, complemented
5#11746350C212yesmaximal, complemented
6#10602368—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C3×C5×#117—22no—
9C3×C5×#117C414yescomplemented
10C2×C3×C5×C4⋊C4C2211yescharacteristic
11C2×C3×C5×C4⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4—21no—
13C2×C3×C42×C5—21no—
14C2×#6719—21no—
15C2×C4⋊Dic15C2212yes—
16C22×C3⋊#168C2212yes—
17#91115—21no—
18#91114—22no—
19#71575—51nomaximal, Hall
20C2×C5×#117D311yescharacteristic
21#65501—31no—
22C2×C22⋊#168—31no—
23#64749—32no—
24#64749—32no—
25C24×C3×C5D411yescharacteristic
26C22×C3×C4×C5—24no—
27C22×C3×C4×C5—21no—
28C22×C3×C4×C5—21no—
29C22×C3×C4×C5C2×C412yes—
30C22×C3×C4×C5D411yescharacteristic
31C22×C3×C4×C5D412yes—
32C22×C3×C4×C5C2311yescharacteristic
33C22×Dic15—22no—
34C3×C5×C4⋊C4—21no—
35C3×C5×C4⋊C4—21no—
36C3×C5×C4⋊C4C2×C412yes—
37C3×C5×C4⋊C4C2×C412yes—
38C3×C5×C22⋊C4—24no—
39C3×C42×C5—24no—
40#6719—42no—
41C4⋊Dic15—24no—
42C2×C3⋊#168—22no—
43C2×C3⋊#168—24no—
44C2×C3×#117D511yescharacteristic
45#5212—51no—
46C2×#830—51no—
47#4529—52no—
48#4529—52no—
49C23×C4×C5C2×D311yescharacteristic
50C5×#117—22no—
51C5×#117Dic314yescomplemented
52C2×C5×C4⋊C4C2×D311yescharacteristic
53C2×C5×C4⋊C4C2×D311yescharacteristic
54C2×C5×C22⋊C4—21no—
55C2×C42×C5—21no—
56C2×C22⋊Dic5—61no—
57C2×C4⋊Dic5—32no—
58C22×#168—32no—
59#3963—61no—
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—22no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—42no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C22⋊C412yes—
77C2×C3×C4×C5C22×C411yescharacteristic
78C2×C3×C4×C5C2×D411yescharacteristic
79C2×C3×C4×C5#4114yes—
80C2×Dic15—42no—
81C2×Dic15—42no—
82C2×Dic15—42no—
83C3⋊#168—42no—
84C23×C3×C4C2×D511yescharacteristic
85C3×#117—22no—
86C3×#117Dic514yescomplemented
87C2×C3×C4⋊C4C2×D511yescharacteristic
88C2×C3×C4⋊C4C2×D511yescharacteristic
89C2×C3×C22⋊C4—21no—
90C2×C3×C42—21no—
91C2×#217—101no—
92C2×C4⋊Dic3—52no—
93C22×C3⋊C8—52no—
94C3⋊#95—101no—
95#830—102no—
96C24×C5#6711yescharacteristic
97C22×C4×C5—24no—
98C22×C4×C5—21no—
99C22×C4×C5—21no—
100C22×C4×C5C2×Dic312yes—
101C22×C4×C5#6711yescharacteristic
102C22×C4×C5#6712yes—
103C22×C4×C5C22×D311yescharacteristic
104C22×Dic5—62no—
105C5×C4⋊C4—21no—
106C5×C4⋊C4—21no—
107C5×C4⋊C4C2×Dic312yes—
108C5×C4⋊C4C2×Dic312yes—
109C5×C22⋊C4—24no—
110C42×C5—24no—
111C22⋊Dic5—122no—
112C4⋊Dic5—64no—
113C2×#168—64no—
114C2×#168—62no—
115C2×#117D1511yescharacteristic
116C2×C22⋊C8—151no—
117#380—151no—
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—42no—
132C3×C4×C5—42no—
133C3×C4×C5#11712yes—
134C3×C4×C5#12312yes—
135Dic15—82no—
136C24×C3C22⋊D511yescharacteristic
137C22×C3×C4—24no—
138C22×C3×C4—21no—
139C22×C3×C4—21no—
140C22×C3×C4C2×Dic512yes—
141C22×C3×C4C22⋊D511yescharacteristic
142C22×C3×C4C22⋊D512yes—
143C22×C3×C4C22×D511yescharacteristic
144C22×Dic3—102no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4C2×Dic512yes—
148C3×C4⋊C4C2×Dic512yes—
149C3×C22⋊C4—24no—
150C3×C42—24no—
151#217—202no—
152C4⋊Dic3—104no—
153C2×C3⋊C8—104no—
154C2×C3⋊C8—102no—
155C23×C5—22no—
156C23×C5—21no—
157C23×C5—22no—
158C23×C5—21no—
159C23×C5#21712yes—
160C23×C5C2×#6711yescharacteristic
161C2×C4×C5—22no—
162C2×C4×C5—24no—
163C2×C4×C5—24no—
164C2×C4×C5—22no—
165C2×C4×C5—22no—
166C2×C4×C5—41no—
167C2×C4×C5—42no—
168C2×C4×C5—41no—
169C2×C4×C5#21712yes—
170C2×C4×C5#23514yes—
171C2×C4×C5C22×Dic311yescharacteristic
172C2×C4×C5C2×#6711yescharacteristic
173C2×Dic5—122no—
174C2×Dic5—122no—
175C2×Dic5—122no—
176#168—122no—
177C23×C4C2×D1511yescharacteristic
178C22×C8—152no—
179#117—22no—
180#117Dic1514yescomplemented
181C2×C4⋊C4—152no—
182C2×C4⋊C4C2×D1511yescharacteristic
183C2×C4⋊C4C2×D1511yescharacteristic
184C2×C22⋊C4—21no—
185C2×C22⋊C4—301no—
186C2×C42—21no—
187C22⋊C8—302no—
188#95—301no—
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×C3C22⋊Dic512yes—
200C23×C3C2×C22⋊D511yescharacteristic
201C2×C3×C4—22no—
202C2×C3×C4—24no—
203C2×C3×C4—24no—
204C2×C3×C4—22no—
205C2×C3×C4—22no—
206C2×C3×C4—42no—
207C2×C3×C4—41no—
208C2×C3×C4—41no—
209C2×C3×C4C22⋊Dic512yes—
210C2×C3×C4#70914yes—
211C2×C3×C4C22×Dic511yescharacteristic
212C2×C3×C4C2×C22⋊D511yescharacteristic
213C2×Dic3—202no—
214C2×Dic3—202no—
215C2×Dic3—202no—
216C3⋊C8—202no—
217C22×C5—22no—
218C22×C5—22no—
219C22×C5—22no—
220C22×C5—42no—
221C22×C5—42no—
222C22×C5#92912yes—
223C22×C5#94911yescharacteristic
224C22×C5#95012yes—
225C22×C5#95111yescharacteristic
226C22×C5C2×#21711yescharacteristic
227C4×C5—22no—
228C4×C5—42no—
229C4×C5—42no—
230C4×C5#92612yes—
231C4×C5#92912yes—
232Dic5—242no—
233C24#122011yescharacteristic
234C22×C4—24no—
235C22×C4—21no—
236C22×C4—21no—
237C22×C4—302no—
238C22×C4C2×Dic1512yes—
239C22×C4#122011yescharacteristic
240C22×C4#122012yes—
241C22×C4C22×D1511yescharacteristic
242C2×C8—304no—
243C2×C8—302no—
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—304no—
247C4⋊C4C2×Dic1512yes—
248C4⋊C4C2×Dic1512yes—
249C22⋊C4—24no—
250C22⋊C4—602no—
251C42—24no—
252C3×C5#182511yescharacteristic, complemented, Hall
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—42no—
257C22×C3—42no—
258C22×C3#407512yes—
259C22×C3#409511yescharacteristic
260C22×C3#409612yes—
261C22×C3#409711yescharacteristic
262C22×C3C2×C22⋊Dic511yescharacteristic
263C3×C4—22no—
264C3×C4—42no—
265C3×C4—42no—
266C3×C4#407212yes—
267C3×C4#407512yes—
268Dic3—402no—
269C2×C5—42no—
270C2×C5#499612yes—
271C2×C5#500312yes—
272C2×C5#521111yescharacteristic
273C2×C5#523211yescharacteristic
274C2×C5#523311yescharacteristic
275C23—22no—
276C23—21no—
277C23—22no—
278C23—21no—
279C23#671912yes—
280C23C2×#122011yescharacteristic
281C2×C4—22no—
282C2×C4—24no—
283C2×C4—24no—
284C2×C4—22no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—42no—
288C2×C4—41no—
289C2×C4—602no—
290C2×C4—602no—
291C2×C4—602no—
292C2×C4#671912yes—
293C2×C4#681714yes—
294C2×C4C22×Dic1511yescharacteristic
295C2×C4C2×#122011yescharacteristic
296C8—602no—
297C2×C3—42no—
298C2×C3#6528512yes—
299C2×C3#6529212yes—
300C2×C3#6550011yescharacteristic
301C2×C3#6552111yescharacteristic
302C2×C3#6552211yescharacteristic
303C5#7157511yescharacteristic, complemented, Sylow
304C22—22no—
305C22—22no—
306C22—22no—
307C22—42no—
308C22—42no—
309C22#9181812yes—
310C22#9183811yescharacteristic
311C22#9183912yes—
312C22#9184011yescharacteristic
313C22C2×#671911yescharacteristic
314C4—22no—
315C4—42no—
316C4—42no—
317C4—1202no—
318C4#9181512yes—
319C4#9181812yes—
320C3#1060236811yescharacteristic, complemented, Sylow
321C2—42no—
322C2#1175109712yes—
323C2#1175110412yes—
324C2#1175131211yescharacteristic
325C2#1175133311yescharacteristic
326C2#1175133411yescharacteristic
subgroupG/H
centerC23C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#117C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
cosocleC22×C3×C4×C5C23
hypercenterC2×#117D15
hypocenterC3×C5#1825
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
4. #11746350C2semidirect
5. #11746350C2semidirect
9. C3×C5×#117C4semidirect
51. C5×#117Dic3semidirect
86. C3×#117Dic5semidirect
180. #117Dic15semidirect
252. C3×C5#1825semidirect
303. C5#71575semidirect
320. C3#10602368semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1172
#117513132
C2×#911142
#117463502
#106023683
#715755