Finite Group Databasebeta

← #14294922

Subgroups — #14294922

Order 1920.

480 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×#91099C211yesmaximal, characteristic
2C2×C8×Dic15C211yesmaximal, characteristic
3#11751033C211yesmaximal, characteristic
4C3×C5×#336C211yesmaximal, characteristic
5#11746371C211yesmaximal, characteristic
6#11746371C211yesmaximal, characteristic
7#11746345C211yesmaximal, characteristic
8#10599391—31nomaximal, Hall
9C22×C3×C5×C8C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×C4×Dic15C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C22×C3⋊#168C2211yescharacteristic
15C22×C3⋊#168C2211yescharacteristic
16#91115C412yes—
17#91115C412yes—
18#91099C414yescomplemented
19C8×Dic15C414yescomplemented
20#68598—51nomaximal, Hall
21C2×#3947—31no—
22C2×C8×Dic5—31no—
23#65221—31no—
24C5×#336D311yescharacteristic
25#64770—31no—
26#64770—31no—
27#64744—31no—
28C22×C3×C4×C5C2×C412yes—
29C22×C3×C4×C5C2311yescharacteristic
30C22×Dic15C2×C412yes—
31C22×Dic15C2×C411yescharacteristic
32C22×Dic15C2×C411yescharacteristic
33C2×C3×C5×C8—21no—
34C2×C3×C5×C8—21no—
35C2×C3×C5×C8—21no—
36C2×C3×C5×C8—21no—
37C2×C3×C5×C8C2×C412yes—
38C2×C3×C5×C8C2×C412yes—
39C3×C42×C5—21no—
40C3×C42×C5—21no—
41C4×Dic15—21no—
42C4×Dic15—21no—
43C4×Dic15C2×C412yes—
44C4×Dic15C2×C412yes—
45C2×C3⋊#168—21no—
46C2×C3⋊#168—21no—
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C2×C3⋊#168C2×C412yes—
50C2×C3⋊#168C2×C412yes—
51C2×#815—51no—
52C2×C8×Dic3—51no—
53#4932—51no—
54C3×#336D511yescharacteristic
55#4550—51no—
56#4550—51no—
57#4524—51no—
58C22×C5×C8C2×D311yescharacteristic
59C22×C5×C8C2×D311yescharacteristic
60C2×C42×C5C2×D311yescharacteristic
61C2×C4×Dic5—31no—
62C2×C4×Dic5—31no—
63C22×#168—31no—
64C22×#168—31no—
65#3963—32no—
66#3963—32no—
67#3947—34no—
68C8×Dic5—34no—
69#1746—151noSylow
70C23×C3×C5C22×C411yescharacteristic
71C2×C3×C4×C5—22no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—22no—
74C2×C3×C4×C5C22×C411yescharacteristic
75C2×C3×C4×C5C22×C411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×C3×C4×C5#4111yescharacteristic
78C2×C3×C4×C5#4111yescharacteristic
79C2×C3×C4×C5#4111yescharacteristic
80C2×Dic15—22no—
81C2×Dic15—22no—
82C2×Dic15—22no—
83C2×Dic15—22no—
84C2×Dic15—22no—
85C2×Dic15C4212yes—
86C2×Dic15C4212yes—
87C3×C5×C8—22no—
88C3×C5×C8—22no—
89C3⋊#168—22no—
90C3⋊#168—22no—
91C22×C3×C8C2×D511yescharacteristic
92C22×C3×C8C2×D511yescharacteristic
93C2×C3×C42C2×D511yescharacteristic
94C2×C4×Dic3—51no—
95C2×C4×Dic3—51no—
96C22×C3⋊C8—51no—
97C22×C3⋊C8—51no—
98C3⋊#95—52no—
99C3⋊#95—52no—
100#815—54no—
101C8×Dic3—54no—
102C22×C4×C5C4×D312yes—
103C22×C4×C5C22×D311yescharacteristic
104C22×Dic5—31no—
105C22×Dic5—31no—
106C22×Dic5—32no—
107C2×C5×C8—21no—
108C2×C5×C8—21no—
109C2×C5×C8—21no—
110C2×C5×C8—21no—
111C2×C5×C8C4×D312yes—
112C2×C5×C8C4×D312yes—
113C42×C5—21no—
114C42×C5—21no—
115C4×Dic5—32no—
116C4×Dic5—32no—
117C4×Dic5—61no—
118C4×Dic5—61no—
119C2×#168—32no—
120C2×#168—32no—
121C2×#168—61no—
122C2×#168—61no—
123C2×#168—61no—
124C2×#168—61no—
125C2×#97—151no—
126C2×C4×C8—151no—
127#376—151no—
128#336—151no—
129#336—151no—
130#336—151no—
131#336D1511yescharacteristic
132C22×C3×C5C2×C4211yescharacteristic
133C22×C3×C5#11711yescharacteristic
134C22×C3×C5#11711yescharacteristic
135C22×C3×C5#13112yes—
136C22×C3×C5#13112yes—
137C3×C4×C5—42no—
138C3×C4×C5#11711yescharacteristic
139C3×C4×C5#11711yescharacteristic
140C3×C4×C5#11711yescharacteristic
141C3×C4×C5#11711yescharacteristic
142Dic15—22no—
143Dic15—22no—
144Dic15—42no—
145C22×C3×C4C4×D512yes—
146C22×C3×C4C22×D511yescharacteristic
147C22×Dic3—51no—
148C22×Dic3—51no—
149C22×Dic3—52no—
150C2×C3×C8—21no—
151C2×C3×C8—21no—
152C2×C3×C8—21no—
153C2×C3×C8—21no—
154C2×C3×C8C4×D512yes—
155C2×C3×C8C4×D512yes—
156C3×C42—21no—
157C3×C42—21no—
158C4×Dic3—52no—
159C4×Dic3—52no—
160C4×Dic3—101no—
161C4×Dic3—101no—
162C2×C3⋊C8—52no—
163C2×C3⋊C8—52no—
164C2×C3⋊C8—101no—
165C2×C3⋊C8—101no—
166C2×C3⋊C8—101no—
167C2×C3⋊C8—101no—
168C23×C5C2×C4×D311yescharacteristic
169C2×C4×C5—22no—
170C2×C4×C5—22no—
171C2×C4×C5—22no—
172C2×C4×C5C2×C4×D311yescharacteristic
173C2×C4×C5C2×C4×D311yescharacteristic
174C2×C4×C5#23711yescharacteristic
175C2×C4×C5#23711yescharacteristic
176C2×C4×C5#23711yescharacteristic
177C2×C4×C5#23911yescharacteristic
178C2×Dic5—32no—
179C2×Dic5—32no—
180C2×Dic5—62no—
181C2×Dic5—62no—
182C2×Dic5—62no—
183C2×Dic5—62no—
184C2×Dic5—62no—
185C5×C8—22no—
186C5×C8—22no—
187#168—62no—
188#168—62no—
189C22×C8—151no—
190C22×C8—151no—
191C22×C8C2×D1511yescharacteristic
192C22×C8C2×D1511yescharacteristic
193C2×C42—151no—
194C2×C42—151no—
195C2×C42C2×D1511yescharacteristic
196#97—154no—
197C4×C8—154no—
198#95—152no—
199#95—152no—
200C2×C3×C5#37611yescharacteristic
201C2×C3×C5#40511yescharacteristic
202C2×C3×C5#40511yescharacteristic
203C2×C3×C5#43312yes—
204C2×C3×C5#43312yes—
205C23×C3C2×C4×D511yescharacteristic
206C2×C3×C4—22no—
207C2×C3×C4—22no—
208C2×C3×C4—22no—
209C2×C3×C4C2×C4×D511yescharacteristic
210C2×C3×C4C2×C4×D511yescharacteristic
211C2×C3×C4#71111yescharacteristic
212C2×C3×C4#71111yescharacteristic
213C2×C3×C4#71111yescharacteristic
214C2×C3×C4#71311yescharacteristic
215C2×Dic3—52no—
216C2×Dic3—52no—
217C2×Dic3—102no—
218C2×Dic3—102no—
219C2×Dic3—102no—
220C2×Dic3—102no—
221C2×Dic3—102no—
222C3×C8—22no—
223C3×C8—22no—
224C3⋊C8—102no—
225C3⋊C8—102no—
226C22×C5C42×D311yescharacteristic
227C22×C5#87711yescharacteristic
228C22×C5#89211yescharacteristic
229C22×C5#90112yes—
230C22×C5#90712yes—
231C4×C5—42no—
232C4×C5#87711yescharacteristic
233C4×C5#87711yescharacteristic
234C4×C5#89211yescharacteristic
235C4×C5#89211yescharacteristic
236Dic5—62no—
237Dic5—62no—
238Dic5—122no—
239C22×C4—151no—
240C22×C4—151no—
241C22×C4—152no—
242C22×C4C4×D1512yes—
243C22×C4C22×D1511yescharacteristic
244C2×C8—21no—
245C2×C8—21no—
246C2×C8—21no—
247C2×C8—21no—
248C2×C8—152no—
249C2×C8—152no—
250C2×C8—301no—
251C2×C8—301no—
252C2×C8—301no—
253C2×C8—301no—
254C2×C8C4×D1512yes—
255C2×C8C4×D1512yes—
256C42—21no—
257C42—21no—
258C42—152no—
259C42—152no—
260C42—301no—
261C42—301no—
262C3×C5#174611yescharacteristic, complemented, Hall
263C22×C3C42×D511yescharacteristic
264C22×C3#402311yescharacteristic
265C22×C3#403811yescharacteristic
266C22×C3#404712yes—
267C22×C3#405312yes—
268C3×C4—42no—
269C3×C4#402311yescharacteristic
270C3×C4#402311yescharacteristic
271C3×C4#403811yescharacteristic
272C3×C4#403811yescharacteristic
273Dic3—102no—
274Dic3—102no—
275Dic3—202no—
276C2×C5#464811yescharacteristic
277C2×C5#468911yescharacteristic
278C2×C5#470811yescharacteristic
279C2×C5#472012yes—
280C2×C5#484012yes—
281C23C2×C4×D1511yescharacteristic
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—22no—
285C2×C4—152no—
286C2×C4—152no—
287C2×C4—302no—
288C2×C4—302no—
289C2×C4—302no—
290C2×C4—302no—
291C2×C4—302no—
292C2×C4C2×C4×D1511yescharacteristic
293C2×C4C2×C4×D1511yescharacteristic
294C2×C4#681911yescharacteristic
295C2×C4#681911yescharacteristic
296C2×C4#681911yescharacteristic
297C2×C4#682111yescharacteristic
298C8—22no—
299C8—22no—
300C8—302no—
301C8—302no—
302C2×C3#6493711yescharacteristic
303C2×C3#6497811yescharacteristic
304C2×C3#6499711yescharacteristic
305C2×C3#6500912yes—
306C2×C3#6512912yes—
307C5#6859811yescharacteristic, complemented, Sylow
308C22C42×D1511yescharacteristic
309C22#9176611yescharacteristic
310C22#9178111yescharacteristic
311C22#9179012yes—
312C22#9179612yes—
313C4—42no—
314C4—302no—
315C4—302no—
316C4—602no—
317C4#9176611yescharacteristic
318C4#9176611yescharacteristic
319C4#9178111yescharacteristic
320C4#9178111yescharacteristic
321C3#1059939111yescharacteristic, complemented, Sylow
322C2#1175074911yescharacteristic
323C2#1175079011yescharacteristic
324C2#1175080911yescharacteristic
325C2#1175082112yes—
326C2#1175094112yes—
subgroupG/H
center, FrattiniC22×C4C22×D15
commutatorC22×C3×C5C2×C42
FittingC3×C5×#336C2
socle, prime radicalC23×C3×C5C22×C4
cosocleC22×C3×C4×C5C23
hypercenter#336D15
hypocenterC3×C5#1746
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ #336

Complements

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

NH ≅ G/Ntype
18. #91099C4semidirect
19. C8×Dic15C4semidirect
262. C3×C5#1746semidirect
307. C5#68598semidirect
321. C3#10599391semidirect

Maximal subgroups

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

subgroupindex
C2×#910992
C2×C8×Dic152
#117510332
C3×C5×#3362
#117463712
#117463452
#105993913
#685985