Finite Group Databasebeta

← #14308930

Subgroups — #14308930

Order 1920.

564 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#11754619C211yesmaximal, characteristic, complemented
2#11751232C211yesmaximal, characteristic
3#11748768C211yesmaximal, characteristic
4#11748392C211yesmaximal, characteristic
5C5×#4554C211yesmaximal, characteristic, complemented
6C3×#64775C211yesmaximal, characteristic, complemented
7#11745978C211yesmaximal, characteristic, complemented
8#10599788—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×C5×M16C2211yescharacteristic
11#91815C2211yescharacteristic
12C2×C5×C4⋊Dic3C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4072C2211yescharacteristic
15C2×C3×C4×Dic5C2211yescharacteristic
16#91575—22no—
17C2×#6667—22no—
18#91470—21no—
19#91468—21no—
20#91388—21no—
21#91384—21no—
22#91105—21no—
23#91105—21no—
24#90968—21no—
25#90968—21no—
26#68763—51nomaximal, Hall
27#65834—31no—
28#65420—31no—
29#65420—31no—
30#65277—31no—
31C5×#343—31no—
32#64775—31no—
33#64775D311yescharacteristic, complemented
34C23×D15—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60—21no—
40C2×D60—21no—
41C2×D60Q812yescomplemented
42C22×C5×Dic3D412yes—
43C22×C3×Dic5—21no—
44C2×#1204—22no—
45C3×C5×M16—21no—
46C3×C5×M16—21no—
47C2×C3×C5×C8—21no—
48#6719—21no—
49C4⋊Dic15D411yescharacteristic
50C4⋊Dic15D411yescharacteristic
51C4×Dic15—21no—
52C5×C4⋊Dic3—21no—
53C5×C4⋊Dic3—21no—
54C5×#208—21no—
55C5×#208—21no—
56C2×C5×C3⋊C8—21no—
57C3×C22⋊Dic5—21no—
58C3×C4⋊Dic5D411yescharacteristic
59C3×C4⋊Dic5D411yescharacteristic
60C3×C4×Dic5—21no—
61C3×C4×Dic5—21no—
62C3×C4×Dic5—21no—
63Dic3⋊Dic5—22no—
64#6669—22no—
65#6668—22no—
66#6667—44no—
67#5519—51no—
68#5131—51no—
69#5001—51no—
70#4939—51no—
71C3×#339—51no—
72#4554D511yescharacteristic, complemented
73#4523—51no—
74C22×D20—31no—
75C2×C5×M16—31no—
76C2×C5×M16C2×D311yescharacteristic
77C2×C5×C4⋊C4—31no—
78C2×#685—62no—
79#4072—31no—
80#4072C2×D311yescharacteristic
81#4070—62no—
82C2×C4×Dic5C2×D311yescharacteristic
83#4036—61no—
84#4036—61no—
85#4034—61no—
86#4034—61no—
87#3953—61no—
88#3953—61no—
89#3953—61no—
90#3953—61no—
91#2027—151noSylow
92C23×C3×C5C2×D411yescharacteristic
93C22×D15—22no—
94C22×D15—42no—
95C22×D15—42no—
96C22×D15—41no—
97C22×D15—41no—
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×Q811yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×C3×C4×C5#4111yescharacteristic
104C2×Dic15—21no—
105C2×Dic15—21no—
106D60—22no—
107D60—22no—
108D60—41no—
109D60—41no—
110C2×C5×Dic3—22no—
111C2×C5×Dic3—42no—
112C2×C3×Dic5—22no—
113C2×C3×Dic5—21no—
114C2×C3×Dic5—21no—
115C2×C3×Dic5—41no—
116C2×C3×Dic5—41no—
117#1204—82no—
118C3×C5×C8—41no—
119C5×C3⋊C8—41no—
120C22×D12—51no—
121C2×C3×M16C2×D511yescharacteristic
122C3×#117—51no—
123C2×C3×C42—51no—
124C2×(C2×D3)⋊C4—102no—
125#926—51no—
126C2×C4⋊Dic3C2×D511yescharacteristic
127C2×#208C2×D511yescharacteristic
128#890—101no—
129#888—101no—
130#878—102no—
131#870—101no—
132#869—101no—
133#821—101no—
134#821—101no—
135#809—101no—
136#809—101no—
137C23×D5—61no—
138C22×C4×C5—32no—
139C22×C4×C5C22×D311yescharacteristic
140C22×Dic5—21no—
141C2×D20—32no—
142C2×D20—61no—
143C2×D20—61no—
144C2×D20—61no—
145C2×D20—61no—
146C2×D20—61no—
147C2×Dic10—62no—
148C5×M16—21no—
149C5×M16—21no—
150C5×M16—61no—
151C5×M16—61no—
152C2×C5×C8—21no—
153C2×C5×C8—61no—
154C5×C4⋊C4—61no—
155C5×C4⋊C4—61no—
156C22⋊Dic5—21no—
157C22⋊Dic5—61no—
158#685—124no—
159C4⋊Dic5—31no—
160C4⋊Dic5—31no—
161C4⋊Dic5—62no—
162C4⋊Dic5D1211yescharacteristic
163C4⋊Dic5D1211yescharacteristic
164#683—62no—
165#683—62no—
166C4×Dic5—21no—
167C4×Dic5—21no—
168C4×Dic5—21no—
169C4×Dic5—61no—
170#544—151no—
171#418—151no—
172#418—151no—
173#390—151no—
174#343—31no—
175#339—51no—
176#339—151no—
177C22×C3×C5—21no—
178C22×C3×C5—21no—
179C22×C3×C5#12011yescharacteristic
180C22×C3×C5C22⋊Q811yescharacteristic
181C22×C3×C5#12411yescharacteristic
182C2×D15—44no—
183C2×D15—42no—
184C2×D15—82no—
185C2×D15—81no—
186C2×D15—81no—
187C3×C4×C5C22⋊Q811yescharacteristic
188C3×C4×C5C22⋊Q811yescharacteristic
189C3×C4×C5#12411yescharacteristic
190C3×C4×C5#12411yescharacteristic
191Dic15—41no—
192Dic15—41no—
193C3×Dic5—42no—
194C3×Dic5—41no—
195C3×Dic5—41no—
196C5×Dic3—42no—
197C23×D3—101no—
198C22×C3×C4—101no—
199C22×C3×C4C22×D511yescharacteristic
200C22×Dic3D2012yes—
201C2×D12—52no—
202C2×D12—101no—
203C2×D12—101no—
204C2×D12—101no—
205C2×D12—101no—
206C2×D12—101no—
207C2×Dic6—102no—
208C3×M16—21no—
209C3×M16—21no—
210C2×C3×C8—21no—
211C3×C4⋊C4—51no—
212C3×C4⋊C4—51no—
213C3×C22⋊C4—101no—
214C3×C42—101no—
215C3×C42—101no—
216C3×C42—101no—
217#217—101no—
218(C2×D3)⋊C4—204no—
219C4⋊Dic3—21no—
220C4⋊Dic3—21no—
221C4⋊Dic3—51no—
222C4⋊Dic3—51no—
223C4⋊Dic3—102no—
224Dic3⋊C4—102no—
225Dic3⋊C4—102no—
226C4×Dic3—101no—
227#208—21no—
228#208—21no—
229C2×C3⋊C8—21no—
230C23×C5D3×D411yescharacteristic
231C22×D5—62no—
232C22×D5—122no—
233C22×D5—122no—
234C22×D5—121no—
235C22×D5—121no—
236C2×C4×C5—62no—
237C2×C4×C5—122no—
238C2×C4×C5C2×D1211yescharacteristic
239C2×C4×C5#23511yescharacteristic
240C2×C4×C5#23511yescharacteristic
241C2×C4×C5D3×D411yescharacteristic
242C2×C4×C5#23711yescharacteristic
243C2×C4×C5D3×Q811yescharacteristic
244C2×Dic5—22no—
245C2×Dic5—21no—
246C2×Dic5—21no—
247C2×Dic5—41no—
248C2×Dic5—41no—
249C2×Dic5—61no—
250C2×Dic5—61no—
251D20—62no—
252D20—62no—
253D20—121no—
254D20—121no—
255Dic10—242no—
256C5×C8—41no—
257C5×C8—121no—
258C22×D4—151no—
259C2×M16—31no—
260C2×M16D3×D511yescharacteristic
261C4⋊Q8—301no—
262C4⋊Q8—301no—
263#125—301no—
264#125—301no—
265C22⋊Q8—302no—
266#117—51no—
267#117—151no—
268C2×C4⋊C4—31no—
269C2×C22⋊C4—302no—
270C2×C42—51no—
271#102—301no—
272#102—301no—
273#102—301no—
274#102—301no—
275C2×C3×C5—21no—
276C2×C3×C5—21no—
277C2×C3×C5#39311yescharacteristic
278C2×C3×C5#45311yescharacteristic
279C2×C3×C5#45411yescharacteristic
280D15—82no—
281C23×C3C2×D2011yescharacteristic
282C22×D3—102no—
283C22×D3—202no—
284C22×D3—202no—
285C22×D3—201no—
286C22×D3—201no—
287C2×C3×C4—102no—
288C2×C3×C4—101no—
289C2×C3×C4—101no—
290C2×C3×C4—201no—
291C2×C3×C4—201no—
292C2×C3×C4#70911yescharacteristic
293C2×C3×C4#70911yescharacteristic
294C2×C3×C4D4×D511yescharacteristic
295C2×C3×C4D4×D511yescharacteristic
296C2×C3×C4#71111yescharacteristic
297C2×C3×C4Q8×D511yescharacteristic
298C2×Dic3—22no—
299C2×Dic3—42no—
300C2×Dic3—101no—
301C2×Dic3—101no—
302D12—102no—
303D12—102no—
304D12—201no—
305D12—201no—
306Dic6—402no—
307C3×C8—41no—
308C3⋊C8—41no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5#88211yescharacteristic
312C22×C5#88511yescharacteristic
313C22×C5#89611yescharacteristic
314C2×D5—124no—
315C2×D5—122no—
316C2×D5—242no—
317C2×D5—241no—
318C2×D5—241no—
319C4×C5—122no—
320C4×C5#87511yescharacteristic
321C4×C5#88511yescharacteristic
322C4×C5#89611yescharacteristic
323C4×C5#89711yescharacteristic
324Dic5—42no—
325Dic5—41no—
326Dic5—41no—
327Dic5—121no—
328Dic5—121no—
329C24—301no—
330C2×Q8—302no—
331C2×D4—152no—
332C2×D4—301no—
333C2×D4—301no—
334C2×D4—301no—
335C2×D4—301no—
336C2×D4—301no—
337C22×C4—32no—
338C22×C4—101no—
339C22×C4C2×D3×D511yescharacteristic
340M16—21no—
341M16—21no—
342M16—61no—
343M16—61no—
344C2×C8—21no—
345C2×C8—61no—
346C4⋊C4—51no—
347C4⋊C4—51no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C4⋊C4—151no—
351C4⋊C4—151no—
352C4⋊C4—302no—
353C4⋊C4—302no—
354C4⋊C4—302no—
355C22⋊C4—101no—
356C22⋊C4—301no—
357C22⋊C4—604no—
358C42—101no—
359C42—101no—
360C42—101no—
361C42—301no—
362C3×C5#202711yescharacteristic, complemented, Hall
363C22×C3—21no—
364C22×C3—21no—
365C22×C3#402111yescharacteristic
366C22×C3#402811yescharacteristic
367C22×C3#404311yescharacteristic
368C2×D3—204no—
369C2×D3—202no—
370C2×D3—402no—
371C2×D3—401no—
372C2×D3—401no—
373C3×C4—202no—
374C3×C4—201no—
375C3×C4—201no—
376C3×C4#403111yescharacteristic
377C3×C4#403111yescharacteristic
378C3×C4#404211yescharacteristic
379C3×C4#404211yescharacteristic
380Dic3—42no—
381Dic3—201no—
382Dic3—201no—
383C2×C5—21no—
384C2×C5—21no—
385C2×C5#467311yescharacteristic
386C2×C5#482211yescharacteristic
387C2×C5#482711yescharacteristic
388D5—242no—
389C23—302no—
390C23—602no—
391C23—602no—
392C23—601no—
393C23—601no—
394C23D3×D2011yescharacteristic
395Q8—1202no—
396D4—302no—
397D4—302no—
398D4—601no—
399D4—601no—
400C2×C4—62no—
401C2×C4—102no—
402C2×C4—101no—
403C2×C4—101no—
404C2×C4—122no—
405C2×C4—201no—
406C2×C4—201no—
407C2×C4—301no—
408C2×C4—301no—
409C2×C4D15⋊Q811yescharacteristic
410C2×C4#677111yescharacteristic
411C2×C4D5×D1211yescharacteristic
412C2×C4#677911yescharacteristic
413C2×C4#678211yescharacteristic
414C2×C4#679011yescharacteristic
415C8—41no—
416C8—121no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3#6496211yescharacteristic
420C2×C3#6503611yescharacteristic
421C2×C3#6504211yescharacteristic
422D3—402no—
423C5#6876311yescharacteristic, complemented, Sylow
424C22—21no—
425C22—21no—
426C22—604no—
427C22—602no—
428C22—1202no—
429C22—1201no—
430C22—1201no—
431C22#9135311yescharacteristic
432C22#9142911yescharacteristic
433C22#9147611yescharacteristic
434C4—122no—
435C4—202no—
436C4—201no—
437C4—201no—
438C4—601no—
439C4—601no—
440C4#9135011yescharacteristic
441C4#9137711yescharacteristic
442C4#9141911yescharacteristic
443C4#9152611yescharacteristic
444C3#1059978811yescharacteristic, complemented, Sylow
445C2—21no—
446C2—21no—
447C2—1202no—
448C2#1174824911yescharacteristic
449C2#1174826111yescharacteristic
450C2#1174857911yescharacteristic
subgroupG/H
centerC22#91476
commutator, cosocleC22×C3×C4×C5C23
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5#120
prime radicalC22×D60C22
hypercenterC2×M16D3×D5
hypocenterC3×C5#2027
LCSG ▷ C22×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
1. #11754619C2semidirect
5. C5×#4554C2semidirect
6. C3×#64775C2semidirect
7. #11745978C2semidirect
33. #64775D3semidirect
41. C2×D60Q8semidirect
72. #4554D5semidirect
362. C3×C5#2027semidirect
423. C5#68763semidirect
444. C3#10599788semidirect

Maximal subgroups

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

subgroupindex
#117546192
#117512322
#117487682
#117483922
C5×#45542
C3×#647752
#117459782
#105997883
#687635