Finite Group Databasebeta

← #14299753

Subgroups — #14299753

Order 1920.

604 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754499C211yesmaximal, characteristic
2#11751222C211yesmaximal, characteristic, complemented
3C2×C3×#3957C211yesmaximal, characteristic
4#11748834C211yesmaximal, characteristic, complemented
5#11748369C211yesmaximal, characteristic
6C5×#4554C211yesmaximal, characteristic, complemented
7#11745978C211yesmaximal, characteristic, complemented
8#10599795—31nomaximal, Hall
9C2×C3×#709C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C4⋊Dic15C2211yescharacteristic
13C2×C5×C4⋊Dic3C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16Dic3×C22⋊D5—22no—
17C2×#6668—22no—
18#91434—21no—
19D5×C4⋊Dic3—21no—
20#91358—21no—
21#91331—21no—
22#91102—21no—
23#91101—21no—
24C3×#3957C414yescomplemented
25#90971—21no—
26#90965—21no—
27#70363—51nomaximal, Hall
28#65838—31no—
29C2×#3957D311yescharacteristic
30#65422—31no—
31#65410—31no—
32#65265—31no—
33C5×#343—31no—
34#64775—31no—
35C22×C3×C4×C5C2311yescharacteristic
36C22×Dic15—21no—
37C22×C5×Dic3D412yes—
38C2×C3×C22⋊D5—21no—
39C22×C3×Dic5—21no—
40C3×#709—21no—
41C3×#709—21no—
42C3×#709C2×C412yes—
43C3×#709Q812yes—
44C2×C3×D20D411yescharacteristic
45C2×C3×C4×D5—21no—
46C2×C3×Dic10D411yescharacteristic
47C2×D5×Dic3—22no—
48C3×C5×M16—21no—
49C3×C5×M16C2×C412yescomplemented
50C2×C3×C5×C8—21no—
51#6719—21no—
52C4⋊Dic15—21no—
53C4⋊Dic15—21no—
54C4⋊Dic15D411yescharacteristic
55C4⋊Dic15D411yescharacteristic
56C4×Dic15—21no—
57C5×C4⋊Dic3—21no—
58C5×C4⋊Dic3—21no—
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8—21no—
62C3×C4×Dic5—21no—
63C3×C4×Dic5C2×C412yescomplemented
64#6668—22no—
65#6668—44no—
66#6665—22no—
67Dic3×Dic5—22no—
68#5827—51no—
69C2×C3×#104—51no—
70#5232—51no—
71#5121—51no—
72#4935—51no—
73#4554D511yescharacteristic, complemented
74#4523—51no—
75C2×#709C2×D311yescharacteristic
76C2×C5×M16—31no—
77C2×C5×M16C2×D311yescharacteristic
78C2×C5×C4⋊C4—31no—
79C4×C22⋊D5—62no—
80#4072—31no—
81C2×C4⋊Dic5—31no—
82C2×#683—62no—
83C2×C4×Dic5C2×D311yescharacteristic
84#4039—61no—
85#4038—61no—
86D5×C4⋊C4—61no—
87#4033—61no—
88#3957Dic314yescomplemented
89#3953—61no—
90#3950—61no—
91#3949—61no—
92#3948—61no—
93#1859—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C2×C3×C4×C5C22×C411yescharacteristic
97C2×C3×C4×C5C2×D411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×Q811yescharacteristic
100C2×C3×C4×C5#4111yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×Dic15—21no—
103C2×Dic15—21no—
104C2×Dic15—42no—
105C2×Dic15—41no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3—42no—
108C3×C22⋊D5—22no—
109C3×C22⋊D5—22no—
110C2×C3×Dic5—22no—
111C2×C3×Dic5—22no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—21no—
114C3×D20—21no—
115C3×D20C4⋊C412yescomplemented
116C3×C4×D5—22no—
117C3×C4×D5—22no—
118C3×Dic10—21no—
119C3×Dic10C4⋊C412yescomplemented
120D5×Dic3—82no—
121C3×C5×C8—22no—
122C5×C3⋊C8—41no—
123C2×C3×#41—51no—
124C2×C3×M16C2×D511yescharacteristic
125C2×C3×C42—51no—
126Q8×Dic3—101no—
127D4×Dic3—101no—
128D4×Dic3—102no—
129#926—51no—
130#926—101no—
131C2×C4⋊Dic3—51no—
132C2×C4⋊Dic3—101no—
133C2×C4⋊Dic3—102no—
134C2×C4⋊Dic3C2×D511yescharacteristic
135C2×#208C2×D511yescharacteristic
136C3×#104—54no—
137#835—101no—
138#832—101no—
139#818—101no—
140#817—101no—
141C22×C4×C5—32no—
142C22×C4×C5C22×D311yescharacteristic
143C2×C22⋊D5—21no—
144C22×Dic5—21no—
145C22×Dic5—61no—
146#709—21no—
147#709—21no—
148#709Dic612yes—
149#709C2×Dic312yes—
150C2×D20D1211yescharacteristic
151C2×C4×D5—21no—
152C2×C4×D5—62no—
153C2×Dic10D1211yescharacteristic
154C5×M16—21no—
155C5×M16—61no—
156C5×M16—61no—
157C5×M16C2×Dic312yescomplemented
158C2×C5×C8—21no—
159C2×C5×C8—61no—
160C5×C4⋊C4—61no—
161C5×C4⋊C4—61no—
162C22⋊Dic5—61no—
163#685—62no—
164C4⋊Dic5—31no—
165C4⋊Dic5—31no—
166C4⋊Dic5—61no—
167C4⋊Dic5—61no—
168#683—62no—
169#683—124no—
170C4×Dic5—21no—
171C4×Dic5—62no—
172C4×Dic5—61no—
173C4×Dic5C2×Dic312yescomplemented
174#520—151no—
175#428—151no—
176C2×#104—51no—
177#417—151no—
178#384—151no—
179#343—31no—
180#339—151no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5C4×D411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5C22⋊Q811yescharacteristic
186C2×C3×D5—22no—
187C2×C3×D5—41no—
188C2×C3×D5—41no—
189C3×C4×C5C2×C4⋊C411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5C22⋊Q811yescharacteristic
192C3×C4×C5#12311yescharacteristic
193Dic15—41no—
194Dic15—41no—
195Dic15—81no—
196C3×Dic5—24no—
197C3×Dic5—22no—
198C5×Dic3—42no—
199C3×#41—52no—
200C3×#41—52no—
201C3×#41—101no—
202C3×#41—101no—
203C2×C3×Q8—51no—
204C2×C3×D4—51no—
205C2×C3×D4—101no—
206C22×C3×C4—101no—
207C22×C3×C4—101no—
208C22×C3×C4C22×D511yescharacteristic
209C22×Dic3—102no—
210C22×Dic3—101no—
211C22×Dic3D2012yes—
212C3×M16—21no—
213C3×M16C4×D512yescomplemented
214C2×C3×C8—21no—
215C3×C42—52no—
216C3×C42—101no—
217#217—102no—
218#217—101no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—51no—
222C4⋊Dic3—51no—
223C4⋊Dic3—102no—
224C4⋊Dic3—101no—
225C4⋊Dic3—101no—
226C4⋊Dic3—204no—
227C4×Dic3—102no—
228C4×Dic3—101no—
229#208—21no—
230#208—21no—
231C2×C3⋊C8—21no—
232C23×C5D3×D411yescharacteristic
233C22×D5—21no—
234C2×C4×C5—62no—
235C2×C4×C5—122no—
236C2×C4×C5C2×Dic611yescharacteristic
237C2×C4×C5C2×D1211yescharacteristic
238C2×C4×C5D3×D411yescharacteristic
239C2×C4×C5#23711yescharacteristic
240C2×C4×C5#23711yescharacteristic
241C2×C4×C5C22×Dic311yescharacteristic
242C22⋊D5—22no—
243C22⋊D5—22no—
244C2×Dic5—22no—
245C2×Dic5—22no—
246C2×Dic5—21no—
247C2×Dic5—22no—
248C2×Dic5—61no—
249C2×Dic5—61no—
250C2×Dic5—122no—
251C2×Dic5—121no—
252D20—21no—
253D20C4⋊Dic312yescomplemented
254C4×D5—22no—
255C4×D5—22no—
256C4×D5—242no—
257Dic10—21no—
258Dic10C4⋊Dic312yescomplemented
259C5×C8—22no—
260C5×C8—121no—
261C2×#41—51no—
262C2×M16—31no—
263C2×M16D3×D511yescharacteristic
264C4×Q8—301no—
265C4×D4—301no—
266C4×D4—302no—
267#117—151no—
268#117—301no—
269C2×C4⋊C4—31no—
270C2×C4⋊C4—151no—
271C2×C4⋊C4—301no—
272C2×C4⋊C4—302no—
273C2×C42—51no—
274#107—301no—
275#106—301no—
276#104—54no—
277#103—301no—
278#102—301no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38511yescharacteristic
282C2×C3×C5#45311yescharacteristic
283C2×C3×C5#45611yescharacteristic
284C3×D5—42no—
285C23×C3—101no—
286C23×C3C2×D2011yescharacteristic
287C3×Q8—52no—
288C3×Q8—101no—
289C3×D4—52no—
290C3×D4—102no—
291C3×D4—102no—
292C3×D4—101no—
293C2×C3×C4—102no—
294C2×C3×C4—102no—
295C2×C3×C4—102no—
296C2×C3×C4—101no—
297C2×C3×C4—102no—
298C2×C3×C4—102no—
299C2×C3×C4C2×C4×D511yescharacteristic
300C2×C3×C4#70911yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4#71111yescharacteristic
304C2×C3×C4Q8×D511yescharacteristic
305C2×Dic3—22no—
306C2×Dic3—42no—
307C2×Dic3—101no—
308C2×Dic3—101no—
309C2×Dic3—202no—
310C2×Dic3—201no—
311C2×Dic3—402no—
312C3×C8—22no—
313C3⋊C8—41no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5#87811yescharacteristic
317C22×C5#88211yescharacteristic
318C22×C5D4×Dic311yescharacteristic
319C2×D5—22no—
320C2×D5—41no—
321C2×D5—41no—
322C4×C5—122no—
323C4×C5#87811yescharacteristic
324C4×C5#88611yescharacteristic
325C4×C5C2×C4⋊Dic311yescharacteristic
326C4×C5D4×Dic311yescharacteristic
327Dic5—24no—
328Dic5—22no—
329Dic5—121no—
330Dic5—121no—
331Dic5—241no—
332#41—52no—
333#41—52no—
334#41—101no—
335#41—101no—
336C2×Q8—51no—
337C2×D4—51no—
338C2×D4—101no—
339C22×C4—32no—
340C22×C4—101no—
341C22×C4—101no—
342C22×C4—302no—
343C22×C4—301no—
344C22×C4C2×D3×D511yescharacteristic
345M16—21no—
346M16—61no—
347M16—61no—
348M16D5×Dic312yescomplemented
349C2×C8—21no—
350C2×C8—61no—
351C4⋊C4—61no—
352C4⋊C4—61no—
353C4⋊C4—151no—
354C4⋊C4—151no—
355C4⋊C4—302no—
356C4⋊C4—301no—
357C4⋊C4—301no—
358C4⋊C4—604no—
359C22⋊C4—302no—
360C22⋊C4—301no—
361C42—52no—
362C42—101no—
363C42—302no—
364C42—301no—
365C3×C5#185911yescharacteristic, complemented, Hall
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—102no—
369C22×C3—201no—
370C22×C3—201no—
371C22×C3C4×D2011yescharacteristic
372C22×C3#402811yescharacteristic
373C22×C3#404311yescharacteristic
374C3×C4—104no—
375C3×C4—102no—
376C3×C4#402711yescharacteristic
377C3×C4#402911yescharacteristic
378C3×C4D5×C4⋊C411yescharacteristic
379C3×C4#404211yescharacteristic
380Dic3—42no—
381Dic3—201no—
382Dic3—201no—
383Dic3—401no—
384C2×C5—21no—
385C2×C5—21no—
386C2×C5#482211yescharacteristic
387C2×C5#482611yescharacteristic
388C2×C5#495011yescharacteristic
389D5—42no—
390C23—101no—
391C23D3×D2011yescharacteristic
392Q8—52no—
393Q8—101no—
394D4—52no—
395D4—102no—
396D4—102no—
397D4—101no—
398C2×C4—62no—
399C2×C4—102no—
400C2×C4—102no—
401C2×C4—102no—
402C2×C4—101no—
403C2×C4—102no—
404C2×C4—102no—
405C2×C4—122no—
406C2×C4—301no—
407C2×C4—301no—
408C2×C4—602no—
409C2×C4—601no—
410C2×C4—1202no—
411C2×C4D5×Dic611yescharacteristic
412C2×C4#676511yescharacteristic
413C2×C4D5×D1211yescharacteristic
414C2×C4C2×D5×Dic311yescharacteristic
415C2×C4#678011yescharacteristic
416C2×C4#679011yescharacteristic
417C8—22no—
418C8—121no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—202no—
422C2×C3#6495711yescharacteristic
423C2×C3#6503611yescharacteristic
424C2×C3#6504111yescharacteristic
425C5#7036311yescharacteristic, complemented, Sylow
426C22—21no—
427C22—21no—
428C22—102no—
429C22—201no—
430C22—201no—
431C22#9142211yescharacteristic
432C22Dic3×D2011yescharacteristic
433C22#9147611yescharacteristic
434C4—104no—
435C4—102no—
436C4—122no—
437C4—601no—
438C4—601no—
439C4—1201no—
440C4D5×C4⋊Dic311yescharacteristic
441C4#9141411yescharacteristic
442C4#9143111yescharacteristic
443C4#9155911yescharacteristic
444C3#1059979511yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—202no—
448C2#1174824911yescharacteristic
449C2#1174826011yescharacteristic
450C2#1174890011yescharacteristic
subgroupG/H
centerC22#91476
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1859
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11751222C2semidirect
4. #11748834C2semidirect
6. C5×#4554C2semidirect
7. #11745978C2semidirect
24. C3×#3957C4semidirect
49. C3×C5×M16C2×C4semidirect
63. C3×C4×Dic5C2×C4semidirect
73. #4554D5semidirect
88. #3957Dic3semidirect
115. C3×D20C4⋊C4semidirect
119. C3×Dic10C4⋊C4semidirect
157. C5×M16C2×Dic3semidirect
173. C4×Dic5C2×Dic3semidirect
213. C3×M16C4×D5semidirect
253. D20C4⋊Dic3semidirect
258. Dic10C4⋊Dic3semidirect
348. M16D5×Dic3semidirect
365. C3×C5#1859semidirect
425. C5#70363semidirect
444. C3#10599795semidirect

Maximal subgroups

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

subgroupindex
#117544992
#117512222
C2×C3×#39572
#117488342
#117483692
C5×#45542
#117459782
#105997953
#703635