Finite Group Databasebeta

← #14302012

Subgroups — #14302012

Order 1920.

716 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756550C211yesmaximal, characteristic
2C2×C3×#4072C211yesmaximal, characteristic, complemented
3C5×#5207C211yesmaximal, characteristic, complemented
4C2×#90981C212yesmaximal, complemented
5#11745978C212yesmaximal, complemented
6#10600759—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×#6817C2211yescharacteristic
9#91842—21no—
10#91819C412yescomplemented
11#91818—21no—
12C4×#1220—22no—
13#91815C2211yescharacteristic
14#91813C412yescomplemented
15C2×C5×#208C2212yes—
16C2×C3×C22⋊Dic5—21no—
17C3×#4072—24no—
18C2×C3×C4⋊Dic5—21no—
19C2×C3×C4×Dic5C2212yes—
20C5×#830—22no—
21#90981—24no—
22#71591—51nomaximal, Hall
23#66125—31no—
24C2×#4072D311yescharacteristic, complemented
25C5×#407—31no—
26C2×#3957—32no—
27#64775—32no—
28C24×C3×C5D411yescharacteristic
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5—22no—
31C22×C3×C4×C5C2×C412yes—
32C22×C3×C4×C5D411yescharacteristic
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C2×#1220—22no—
36C2×#1220—21no—
37#6817—22no—
38#6817—22no—
39C2×D60C2×C411yescharacteristic
40C2×C4×D15—21no—
41C2×Dic30C2×C411yescharacteristic
42C22×C3×Dic5—22no—
43#6719—22no—
44#6719—21no—
45#6714—22no—
46C4⋊Dic15C2×C412yes—
47#6712—22no—
48C4×Dic15—21no—
49C5×#208—22no—
50C5×#208—22no—
51C2×C5×C3⋊C8—22no—
52C3×C22⋊Dic5—24no—
53C3×C4⋊Dic5—24no—
54C3×C4×Dic5—22no—
55C3×C4×Dic5D414yescomplemented
56C2×C3×#117—51no—
57#5791—51no—
58#5207D511yescharacteristic, complemented
59C2×#805—52no—
60#4523—52no—
61C23×C4×C5C2×D311yescharacteristic
62C2×#709—31no—
63C2×C5×M16—32no—
64#4099—61no—
65C2×C22⋊Dic5—21no—
66#4076—32no—
67#4075—61no—
68C4×C22⋊D5—62no—
69#4072—24no—
70#4072—31no—
71C2×C4⋊Dic5—21no—
72#4070—32no—
73C2×C4×Dic5C2×D312yes—
74C5×C22⋊C8—62no—
75#3957—64no—
76#1897—151noSylow
77C23×C3×C5—21no—
78C23×C3×C5—21no—
79C23×C3×C5—42no—
80C23×C3×C5C22⋊C412yes—
81C23×C3×C5C2×D411yescharacteristic
82C22×D15—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—24no—
86C2×C3×C4×C5—24no—
87C2×C3×C4×C5C22⋊C412yes—
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D412yes—
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4112yes—
92#1220—44no—
93#1220—41no—
94#1220—41no—
95C2×Dic15—22no—
96C2×Dic15—21no—
97D60—22no—
98C4×D15—42no—
99Dic30—22no—
100C2×C3×Dic5—24no—
101C2×C3×Dic5—44no—
102C5×C3⋊C8—42no—
103C23×C3×C4C2×D511yescharacteristic
104C2×#235—51no—
105C3×#117—104no—
106C2×C3×C4⋊C4—101no—
107C2×C3×C22⋊C4—101no—
108C2×C3×C42—52no—
109#953—101no—
110#930—52no—
111#929—101no—
112C4×#67—102no—
113#926—51no—
114#924—52no—
115C2×#208C2×D512yes—
116#830—22no—
117#805—104no—
118C24×C5#6711yescharacteristic
119C22×C4×C5—22no—
120C22×C4×C5—22no—
121C22×C4×C5C4×D312yes—
122C22×C4×C5D1212yes—
123C22×C4×C5#6711yescharacteristic
124C22×C4×C5C22×D311yescharacteristic
125C2×C22⋊D5—62no—
126C2×C22⋊D5—61no—
127C22×Dic5—22no—
128#709—62no—
129#709—62no—
130C2×D20—31no—
131C2×C4×D5—61no—
132C2×Dic10—31no—
133C5×M16—62no—
134C5×M16—62no—
135C2×C5×C8—62no—
136C22⋊Dic5—24no—
137C22⋊Dic5—62no—
138C22⋊Dic5—61no—
139#685—62no—
140C4⋊Dic5—24no—
141C4⋊Dic5—32no—
142#683—62no—
143C4×Dic5—22no—
144C4×Dic5—61no—
145C4×Dic5#6714yescomplemented
146#525—151no—
147C2×#117—51no—
148C2×#104—152no—
149#407—31no—
150#339—152no—
151C22×C3×C5—22no—
152C22×C3×C5—22no—
153C22×C3×C5—22no—
154C22×C3×C5—22no—
155C22×C3×C5—42no—
156C22×C3×C5—42no—
157C22×C3×C5C2×C22⋊C411yescharacteristic
158C22×C3×C5#12011yescharacteristic
159C22×C3×C5#12311yescharacteristic
160C2×D15—41no—
161C2×D15—42no—
162C3×C4×C5—22no—
163C3×C4×C5C4×D412yes—
164C3×C4×C5#12112yes—
165Dic15—41no—
166Dic15—42no—
167C3×Dic5—44no—
168C24×C3D2011yescharacteristic
169C22×C3×C4—22no—
170C22×C3×C4—22no—
171C22×C3×C4—102no—
172C22×C3×C4C4×D512yes—
173C22×C3×C4D2011yescharacteristic
174C22×C3×C4C22⋊D512yes—
175C22×C3×C4C22×D511yescharacteristic
176C2×#67—102no—
177C2×#67—101no—
178#235—102no—
179#235—102no—
180C2×D12—51no—
181C2×C4×D3—101no—
182C2×Dic6—51no—
183C3×C4⋊C4—104no—
184C3×C22⋊C4—104no—
185C3×C42—54no—
186C3×C42—102no—
187#217—102no—
188#217—101no—
189(C2×D3)⋊C4—102no—
190C4⋊Dic3—52no—
191Dic3⋊C4—102no—
192C4×Dic3—101no—
193#208—22no—
194#208—22no—
195C2×C3⋊C8—22no—
196C23×C5—21no—
197C23×C5—21no—
198C23×C5—42no—
199C23×C5(C2×D3)⋊C412yes—
200C23×C5C2×#6711yescharacteristic
201C22×D5—61no—
202C2×C4×C5—21no—
203C2×C4×C5—21no—
204C2×C4×C5—24no—
205C2×C4×C5—24no—
206C2×C4×C5(C2×D3)⋊C412yes—
207C2×C4×C5C2×C4×D311yescharacteristic
208C2×C4×C5C2×D1211yescharacteristic
209C2×C4×C5#23512yes—
210C2×C4×C5C2×#6712yes—
211C22⋊D5—124no—
212C22⋊D5—121no—
213C22⋊D5—121no—
214C2×Dic5—24no—
215C2×Dic5—44no—
216C2×Dic5—62no—
217C2×Dic5—61no—
218D20—62no—
219C4×D5—122no—
220Dic10—62no—
221C5×C8—122no—
222C2×#41—151no—
223C23×C4D3×D511yescharacteristic
224C2×M16—32no—
225#123—301no—
226C22⋊Q8—152no—
227#121—152no—
228#120—301no—
229C4×D4—302no—
230#117—104no—
231#117—151no—
232C2×C4⋊C4—101no—
233C2×C22⋊C4—101no—
234C2×C42—52no—
235#104—304no—
236C22⋊C8—62no—
237C2×C3×C5—21no—
238C2×C3×C5—21no—
239C2×C3×C5—42no—
240C2×C3×C5#38611yescharacteristic
241C2×C3×C5#42112yes—
242D15—81no—
243C23×C3—21no—
244C23×C3—21no—
245C23×C3—42no—
246C23×C3#68512yes—
247C23×C3C2×D2011yescharacteristic
248C22×D3—101no—
249C2×C3×C4—21no—
250C2×C3×C4—21no—
251C2×C3×C4—24no—
252C2×C3×C4—24no—
253C2×C3×C4—104no—
254C2×C3×C4—204no—
255C2×C3×C4#68512yes—
256C2×C3×C4C2×C4×D511yescharacteristic
257C2×C3×C4D4×D512yes—
258C2×C3×C4#71112yes—
259C2×C3×C4C2×C22⋊D511yescharacteristic
260#67—204no—
261#67—201no—
262#67—201no—
263C2×Dic3—102no—
264C2×Dic3—101no—
265D12—102no—
266C4×D3—202no—
267Dic6—102no—
268C3⋊C8—42no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—22no—
272C22×C5—22no—
273C22×C5—42no—
274C22×C5—42no—
275C22×C5C2×(C2×D3)⋊C411yescharacteristic
276C22×C5#92911yescharacteristic
277C22×C5#95311yescharacteristic
278C2×D5—121no—
279C2×D5—122no—
280C4×C5—22no—
281C4×C5C4×#6712yes—
282C4×C5#93012yes—
283Dic5—44no—
284Dic5—121no—
285Dic5—122no—
286C24#120211yescharacteristic
287#41—302no—
288#41—302no—
289C2×Q8—151no—
290C2×D4—151no—
291C2×D4—302no—
292C2×D4—301no—
293C22×C4—22no—
294C22×C4—22no—
295C22×C4—102no—
296C22×C4—301no—
297C22×C4#120012yes—
298C22×C4#120211yescharacteristic
299C22×C4#120312yes—
300C22×C4C2×D3×D511yescharacteristic
301M16—62no—
302M16—62no—
303C2×C8—62no—
304C4⋊C4—104no—
305C4⋊C4—152no—
306C4⋊C4—302no—
307C22⋊C4—104no—
308C22⋊C4—302no—
309C22⋊C4—301no—
310C22⋊C4—302no—
311C42—54no—
312C42—102no—
313C42—301no—
314C3×C5#189711yescharacteristic, complemented, Hall
315C22×C3—22no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—22no—
319C22×C3—42no—
320C22×C3—42no—
321C22×C3#402811yescharacteristic
322C22×C3#403211yescharacteristic
323C22×C3C2×#68511yescharacteristic
324C2×D3—202no—
325C2×D3—201no—
326C3×C4—22no—
327C3×C4—204no—
328C3×C4#402712yes—
329C3×C4#408512yes—
330Dic3—202no—
331Dic3—201no—
332C2×C5—21no—
333C2×C5—21no—
334C2×C5—42no—
335C2×C5#500512yes—
336C2×C5#521311yescharacteristic
337D5—241no—
338C23—21no—
339C23—21no—
340C23—42no—
341C23—301no—
342C23#666712yes—
343C23C2×#120211yescharacteristic
344Q8—302no—
345D4—302no—
346D4—604no—
347D4—601no—
348D4—601no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—24no—
352C2×C4—24no—
353C2×C4—104no—
354C2×C4—204no—
355C2×C4—302no—
356C2×C4—301no—
357C2×C4—602no—
358C2×C4#666712yes—
359C2×C4#678212yes—
360C2×C4C2×#120011yescharacteristic
361C2×C4C2×#120311yescharacteristic
362C2×C4D5×#6712yes—
363C8—122no—
364C2×C3—21no—
365C2×C3—21no—
366C2×C3—42no—
367C2×C3#6524711yescharacteristic
368C2×C3#6542812yes—
369D3—401no—
370C5#7159111yescharacteristic, complemented, Sylow
371C22—22no—
372C22—22no—
373C22—22no—
374C22—22no—
375C22—42no—
376C22—42no—
377C22—602no—
378C22—601no—
379C22C2×#666711yescharacteristic
380C22#9154611yescharacteristic
381C22#9156411yescharacteristic
382C4—22no—
383C4—204no—
384C4—602no—
385C4—601no—
386C4#9155212yes—
387C4#9156612yes—
388C3#1060075911yescharacteristic, complemented, Sylow
389C2—21no—
390C2—21no—
391C2—42no—
392C2—1201no—
393C2#1174842912yes—
394C2#1174949411yescharacteristic
subgroupG/H
centerC2×C4C2×#1203
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756550C2
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1897
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×#4072C2semidirect
3. C5×#5207C2semidirect
4. C2×#90981C2semidirect
5. #11745978C2semidirect
10. #91819C4semidirect
14. #91813C4semidirect
24. C2×#4072D3semidirect
55. C3×C4×Dic5D4semidirect
58. #5207D5semidirect
145. C4×Dic5#67semidirect
314. C3×C5#1897semidirect
370. C5#71591semidirect
388. C3#10600759semidirect

Maximal subgroups

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

subgroupindex
#117565502
C2×C3×#40722
C5×#52072
C2×#909812
#117459782
#106007593
#715915