Finite Group Databasebeta

← #14307128

Subgroups — #14307128

Order 1920.

520 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
1#11756229C211yesmaximal, characteristic
2C3×C4×C5×M16C211yesmaximal, characteristic
3C4×C4⋊Dic15C211yesmaximal, characteristic
4#11746376C214yesmaximal
5#10600661—31nomaximal, Hall
6C2×C3×C5×M16C2212yes—
7C2×C3×C42×C5C2211yescharacteristic
8#91815C2212yes—
9C2×C4⋊Dic15—21no—
10#91813—21no—
11#91813—21no—
12C2×C4×Dic15C2212yes—
13#91759C412yescomplemented
14#91758C411yescharacteristic, complemented
15#91758C411yescharacteristic, complemented
16C4×Dic30—21no—
17C4×Dic30—21no—
18C3×C5×#97—21no—
19C3×C4×C5×C8—21no—
20#91115—21no—
21#69868—51nomaximal, Hall
22#65804—31no—
23C4×C5×M16D311yescharacteristic
24C4×C4⋊Dic5—31no—
25#64775—34no—
26C22×C3×C4×C5D411yescharacteristic
27C22×C3×C4×C5D411yescharacteristic
28C22×C3×C4×C5C2311yescharacteristic
29C22×Dic15—22no—
30C2×Dic30—21no—
31C2×Dic30—21no—
32C3×C5×M16—22no—
33C3×C5×M16Q814yescomplemented
34C2×C3×C5×C8—22no—
35C3×C42×C5C2×C411yescharacteristic
36C3×C42×C5C2×C411yescharacteristic
37C3×C42×C5D411yescharacteristic
38C3×C42×C5D411yescharacteristic
39#6719—22no—
40C4⋊Dic15—24no—
41C4⋊Dic15—21no—
42C4⋊Dic15—21no—
43C4⋊Dic15C2×C412yes—
44C4⋊Dic15C2×C412yes—
45#6712—22no—
46#6712—22no—
47C4×Dic15—22no—
48C4×Dic15—24no—
49#5470—51no—
50C3×C4×M16D511yescharacteristic
51C4×C4⋊Dic3—51no—
52#4555—54no—
53C2×C5×M16C2×D312yes—
54C2×C42×C5C2×D311yescharacteristic
55#4072—32no—
56C2×C4⋊Dic5—61no—
57#4070—61no—
58#4070—61no—
59C2×C4×Dic5—32no—
60#4016—32no—
61#4015—31no—
62#4015—31no—
63C4×Dic10—61no—
64C4×Dic10—61no—
65C5×#97—21no—
66C4×C5×C8—21no—
67#3963—61no—
68#1986—151noSylow
69C23×C3×C5C2×D411yescharacteristic
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—41no—
72C2×C3×C4×C5C22⋊C411yescharacteristic
73C2×C3×C4×C5C22⋊C411yescharacteristic
74C2×C3×C4×C5C22⋊C411yescharacteristic
75C2×C3×C4×C5C22⋊C411yescharacteristic
76C2×C3×C4×C5C22×C411yescharacteristic
77C2×C3×C4×C5C2×D411yescharacteristic
78C2×C3×C4×C5C2×Q812yes—
79C2×C3×C4×C5#4112yes—
80C2×Dic15—24no—
81C2×Dic15—22no—
82C2×Dic15—22no—
83C2×Dic15—42no—
84C2×Dic15—42no—
85Dic30—42no—
86Dic30—42no—
87C3×C5×C8—24no—
88C2×C3×M16C2×D512yes—
89C2×C3×C42C2×D511yescharacteristic
90#926—52no—
91C2×C4⋊Dic3—101no—
92#924—101no—
93#924—101no—
94C2×C4×Dic3—52no—
95#870—52no—
96#869—51no—
97#869—51no—
98C4×Dic6—101no—
99C4×Dic6—101no—
100C3×#97—21no—
101C3×C4×C8—21no—
102C3⋊#95—101no—
103C22×C4×C5D1211yescharacteristic
104C22×C4×C5D1211yescharacteristic
105C22×C4×C5C22×D311yescharacteristic
106C22×Dic5—62no—
107C2×Dic10—61no—
108C2×Dic10—61no—
109C5×M16—22no—
110C5×M16Dic614yescomplemented
111C2×C5×C8—22no—
112C42×C5C4×D311yescharacteristic
113C42×C5C4×D311yescharacteristic
114C42×C5#6711yescharacteristic
115C42×C5#6711yescharacteristic
116C22⋊Dic5—62no—
117C4⋊Dic5—32no—
118C4⋊Dic5—32no—
119C4⋊Dic5—64no—
120C4⋊Dic5—61no—
121C4⋊Dic5—61no—
122#683—62no—
123#683—62no—
124C4×Dic5—62no—
125C4×Dic5—64no—
126#533—151no—
127C4×M16D1511yescharacteristic
128C4×C4⋊C4—151no—
129#339—154no—
130C22×C3×C5—21no—
131C22×C3×C5—21no—
132C22×C3×C5C2×C22⋊C411yescharacteristic
133C22×C3×C5#12411yescharacteristic
134C22×C3×C5C4⋊Q811yescharacteristic
135C3×C4×C5—21no—
136C3×C4×C5—21no—
137C3×C4×C5—21no—
138C3×C4×C5#10412yes—
139C3×C4×C5C4×Q812yes—
140C3×C4×C5C22⋊Q812yes—
141Dic15—44no—
142Dic15—42no—
143Dic15—42no—
144C22×C3×C4D2011yescharacteristic
145C22×C3×C4D2011yescharacteristic
146C22×C3×C4C22×D511yescharacteristic
147C22×Dic3—102no—
148C2×Dic6—101no—
149C2×Dic6—101no—
150C3×M16—22no—
151C3×M16Dic1014yescomplemented
152C2×C3×C8—22no—
153C3×C42C4×D511yescharacteristic
154C3×C42C4×D511yescharacteristic
155C3×C42C22⋊D511yescharacteristic
156C3×C42C22⋊D511yescharacteristic
157#217—102no—
158C4⋊Dic3—52no—
159C4⋊Dic3—52no—
160C4⋊Dic3—104no—
161C4⋊Dic3—101no—
162C4⋊Dic3—101no—
163Dic3⋊C4—102no—
164Dic3⋊C4—102no—
165C4×Dic3—102no—
166C4×Dic3—104no—
167C23×C5C2×D1211yescharacteristic
168C2×C4×C5—22no—
169C2×C4×C5—41no—
170C2×C4×C5(C2×D3)⋊C411yescharacteristic
171C2×C4×C5(C2×D3)⋊C411yescharacteristic
172C2×C4×C5(C2×D3)⋊C411yescharacteristic
173C2×C4×C5(C2×D3)⋊C411yescharacteristic
174C2×C4×C5C2×Dic612yes—
175C2×C4×C5C2×C4×D311yescharacteristic
176C2×C4×C5#23512yes—
177C2×C4×C5C2×#6711yescharacteristic
178C2×Dic5—64no—
179C2×Dic5—62no—
180C2×Dic5—62no—
181C2×Dic5—122no—
182C2×Dic5—122no—
183Dic10—122no—
184Dic10—122no—
185C5×C8—24no—
186C2×M16C2×D1512yes—
187C4⋊Q8—151no—
188C4⋊Q8—151no—
189#125—152no—
190C22⋊Q8—301no—
191C22⋊Q8—301no—
192C4×Q8—301no—
193C4×Q8—301no—
194#117—152no—
195C2×C4⋊C4—301no—
196C2×C42—152no—
197C2×C42C2×D1511yescharacteristic
198#97—21no—
199C4×C8—21no—
200#95—301no—
201C2×C3×C5—21no—
202C2×C3×C5—21no—
203C2×C3×C5#39111yescharacteristic
204C2×C3×C5C2×#10411yescharacteristic
205C2×C3×C5#42111yescharacteristic
206C23×C3C2×D2011yescharacteristic
207C2×C3×C4—22no—
208C2×C3×C4—41no—
209C2×C3×C4#68511yescharacteristic
210C2×C3×C4#68511yescharacteristic
211C2×C3×C4#68511yescharacteristic
212C2×C3×C4#68511yescharacteristic
213C2×C3×C4C2×Dic1012yes—
214C2×C3×C4C2×C4×D511yescharacteristic
215C2×C3×C4#70912yes—
216C2×C3×C4C2×C22⋊D511yescharacteristic
217C2×Dic3—104no—
218C2×Dic3—102no—
219C2×Dic3—102no—
220C2×Dic3—202no—
221C2×Dic3—202no—
222Dic6—202no—
223Dic6—202no—
224C3×C8—24no—
225C22×C5—21no—
226C22×C5—21no—
227C22×C5#86911yescharacteristic
228C22×C5#87511yescharacteristic
229C22×C5C2×(C2×D3)⋊C411yescharacteristic
230C4×C5—21no—
231C4×C5—21no—
232C4×C5—21no—
233C4×C5#82512yes—
234C4×C5C4×Dic612yes—
235C4×C5#92412yes—
236Dic5—124no—
237Dic5—122no—
238Dic5—122no—
239C2×Q8—301no—
240C2×Q8—301no—
241C22×C4—302no—
242C22×C4D6011yescharacteristic
243C22×C4D6011yescharacteristic
244C22×C4C22×D1511yescharacteristic
245M16—22no—
246M16Dic3014yescomplemented
247C2×C8—22no—
248C4⋊C4—152no—
249C4⋊C4—152no—
250C4⋊C4—304no—
251C4⋊C4—302no—
252C4⋊C4—302no—
253C4⋊C4—301no—
254C4⋊C4—301no—
255C22⋊C4—302no—
256C42—302no—
257C42—304no—
258C42C4×D1511yescharacteristic
259C42C4×D1511yescharacteristic
260C42#122011yescharacteristic
261C42#122011yescharacteristic
262C3×C5#198611yescharacteristic, complemented, Hall
263C22×C3—21no—
264C22×C3—21no—
265C22×C3#401511yescharacteristic
266C22×C3#402111yescharacteristic
267C22×C3C2×#68511yescharacteristic
268C3×C4—21no—
269C3×C4—21no—
270C3×C4—21no—
271C3×C4#395712yes—
272C3×C4C4×Dic1012yes—
273C3×C4#407012yes—
274Dic3—204no—
275Dic3—202no—
276Dic3—202no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5#492911yescharacteristic
280C2×C5C2×#82511yescharacteristic
281C2×C5#513911yescharacteristic
282C23C2×D6011yescharacteristic
283Q8—602no—
284Q8—602no—
285C2×C4—22no—
286C2×C4—41no—
287C2×C4—304no—
288C2×C4—302no—
289C2×C4—302no—
290C2×C4—602no—
291C2×C4—602no—
292C2×C4#671411yescharacteristic
293C2×C4#671411yescharacteristic
294C2×C4#671411yescharacteristic
295C2×C4#671411yescharacteristic
296C2×C4C2×Dic3012yes—
297C2×C4C2×C4×D1511yescharacteristic
298C2×C4#681712yes—
299C2×C4C2×#122011yescharacteristic
300C8—24no—
301C2×C3—21no—
302C2×C3—21no—
303C2×C3#6521811yescharacteristic
304C2×C3C2×#395711yescharacteristic
305C2×C3#6542811yescharacteristic
306C5#6986811yescharacteristic, complemented, Sylow
307C22—21no—
308C22—21no—
309C22#9175811yescharacteristic
310C22#9176411yescharacteristic
311C22C2×#671411yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—604no—
316C4—602no—
317C4—602no—
318C4#9110912yes—
319C4C4×Dic3012yes—
320C4#9181312yes—
321C3#1060066111yescharacteristic, complemented, Sylow
322C2—21no—
323C2—21no—
324C2#1175103011yescharacteristic
325C2C2×#9110911yescharacteristic
326C2#1175124011yescharacteristic
subgroupG/H
centerC2×C4C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C4×C5×M16C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC4×M16D15
hypocenterC3×C5#1986
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
13. #91759C4semidirect
14. #91758C4semidirect
15. #91758C4semidirect
33. C3×C5×M16Q8semidirect
110. C5×M16Dic6semidirect
151. C3×M16Dic10semidirect
246. M16Dic30semidirect
262. C3×C5#1986semidirect
306. C5#69868semidirect
321. C3#10600661semidirect

Maximal subgroups

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

subgroupindex
#117562292
C3×C4×C5×M162
C4×C4⋊Dic152
#117463762
#106006613
#698685