Finite Group Databasebeta

← #14471928

Subgroups — #14471928

Order 1920.

784 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752680C211yesmaximal, characteristic
2#11752472C211yesmaximal, characteristic, complemented
3#11750931C211yesmaximal, characteristic, complemented
4C5×#4848C211yesmaximal, characteristic, complemented
5C3×#65131C211yesmaximal, characteristic, complemented
6#11748011C212yesmaximal, complemented
7#11748001C212yesmaximal, complemented
8#11747808C212yesmaximal, complemented
9#11747807C212yesmaximal, complemented
10C4×#6655C211yesmaximal, characteristic, complemented
11#11746901C211yesmaximal, characteristic, complemented
12#10612100—31nomaximal, Hall
13C2×#6772—21no—
14C4×Dic30C2211yescharacteristic
15C2×C5×#204C2212yes—
16C5×#874C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20#91470C2212yes—
21#91469—21no—
22#91463C2212yes—
23#91453—22no—
24#91449—21no—
25#91435C2212yes—
26#91344C2212yes—
27#91340—21no—
28#91327—22no—
29C2×#6655C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4×C3⋊#168C2211yescharacteristic
34C5×#821C2212yes—
35C3×#3953C2212yes—
36C3×#3949C2212yes—
37#90986C2211yescharacteristic
38#90972C2211yescharacteristic
39#90966C2212yes—
40#90966C2212yes—
41#90964C2211yescharacteristic
42#81090—51nomaximal, Hall
43#66052—31no—
44Q8×Dic10—31no—
45C5×#460—31no—
46#65452—32no—
47SD16×Dic5—32no—
48#65359—31no—
49C4×#688—31no—
50#65131D311yescharacteristic, complemented
51#65119—31no—
52#65050—32no—
53#65049—32no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12—21no—
56C2×C5×D12—21no—
57C2×C5×D12C2312yes—
58C2×C5×Dic6C2311yescharacteristic
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10—21no—
62C2×#1204—22no—
63C2×#1201—22no—
64C2×#1201—22no—
65C2×D3×Dic5—22no—
66#6772—44no—
67C2×C3×C5×C8C2312yes—
68C3×C42×C5C2311yescharacteristic
69C4⋊Dic15D411yescharacteristic
70#6712D412yes—
71C4×Dic15C2312yes—
72C2×C3⋊#168C2311yescharacteristic
73C2×C3⋊#168C2311yescharacteristic
74C5×C4⋊Dic3C2311yescharacteristic
75C5×Dic3⋊C4—21no—
76C4×C5×Dic3—21no—
77C5×#204—24no—
78C3×#685—21no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4⋊Dic5C2312yes—
82Dic3⋊Dic5—22no—
83#6669—22no—
84(C2×D3)⋊Dic5—22no—
85Dic3×Dic5—22no—
86#6655—22no—
87#5722—51no—
88#5553—51no—
89C3×#476—51no—
90#5088—51no—
91C4×#214—51no—
92#4870—52no—
93#4852—52no—
94#4848D511yescharacteristic, complemented
95#4830—51no—
96#4762—52no—
97#4760—52no—
98C2×#711—61no—
99C2×C5×SD16—32no—
100C5×#127—31no—
101C4×C5×Q8—31no—
102Q8×Dic5—32no—
103C2×#688—31no—
104#4086—32no—
105#4085—62no—
106#4084—61no—
107D4×Dic5—32no—
108#4034—32no—
109#4034—62no—
110C4×D20C2×D311yescharacteristic
111#4015—61no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#102—32no—
117#3967—31no—
118#3964—32no—
119#3964—32no—
120#3953C2×D312yes—
121#3949C2×D312yes—
122#3946—32no—
123C8×Dic5—32no—
124#3941—31no—
125#3940—31no—
126C4×#168—31no—
127#3362—151noSylow
128C22×C5×D3—22no—
129C22×C3×D5—21no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15C2×D412yes—
134C2×Dic15C2×D412yes—
135Dic30SD1614yescomplemented
136C2×C5×Dic3—21no—
137C2×C5×Dic3—21no—
138C5×D12—22no—
139C5×D12—22no—
140C5×D12—42no—
141C5×D12—81no—
142C5×Dic6—21no—
143C5×Dic6#4112yescomplemented
144C2×C3×Dic5—22no—
145C2×C3×Dic5—21no—
146C3×D20—21no—
147C3×D20—21no—
148C3×C4×D5—42no—
149C3×Dic10—81no—
150#1204—82no—
151#1201—44no—
152#1201—82no—
153D3×Dic5—44no—
154C3×C5×C8—22no—
155C3⋊#168—21no—
156C3⋊#168—21no—
157C2×#235—101no—
158C3×C4⋊Q8—51no—
159C3×C4×D4—51no—
160#944—102no—
161#940—52no—
162C2×#214—51no—
163#930—101no—
164C2×#204C2×D512yes—
165#893—52no—
166#888—52no—
167#888—101no—
168#887—52no—
169#887—101no—
170#884—102no—
171#874C2×D511yescharacteristic
172C4×Dic6—51no—
173C4×Dic6C2×D511yescharacteristic
174C3×#106—52no—
175C3×C4⋊C8C2×D511yescharacteristic
176C3×#102—52no—
177#832—51no—
178#821C2×D512yes—
179Dic3⋊C8—52no—
180C8×Dic3—52no—
181#810—51no—
182#809—52no—
183#809—52no—
184#808—51no—
185C4×C3⋊C8—51no—
186C2×C5×Q8—31no—
187C2×C5×D4—32no—
188C2×C5×D4—61no—
189C2×C5×D4—61no—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—124no—
194C2×D20C22×D311yescharacteristic
195C2×C4×D5—21no—
196C2×Dic10—21no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C5×SD16—64no—
200C2×C5×C8C22×D312yes—
201C5×C4⋊C4—31no—
202C5×C4⋊C4—61no—
203C42×C5—61no—
204C42×C5C22×D311yescharacteristic
205C22⋊Dic5—62no—
206#688—62no—
207#685—21no—
208C4⋊Dic5—21no—
209C4⋊Dic5—31no—
210C4⋊Dic5—62no—
211C4⋊Dic5C22×D311yescharacteristic
212C4⋊Dic5C22×D312yes—
213#683—32no—
214#683—62no—
215C4×Dic5—32no—
216C4×Dic5—62no—
217C2×#168—31no—
218C2×#168—31no—
219Q82—151no—
220#550—151no—
221#486—152no—
222#486—151no—
223#476—51no—
224#476—152no—
225#460—31no—
226#460—152no—
227C8×Q8—151no—
228C4×SD16—152no—
229C4×SD16—151no—
230C22×C3×C5C22×D411yescharacteristic
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C2×C5×D3—42no—
234C2×C3×D5—41no—
235C2×C3×D5—41no—
236C2×C3×D5—41no—
237C3×C4×C5—21no—
238C3×C4×C5C2×SD1612yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—22no—
242Dic15C2×SD1614yes—
243C3×Dic5—41no—
244C3×Dic5—42no—
245C5×Dic3—22no—
246C5×Dic3—41no—
247C2×C3×Q8—101no—
248C2×C3×D4—51no—
249C22×C3×C4—101no—
250C2×#67—102no—
251C2×#67—102no—
252#235—204no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12C22×D512yes—
256C2×C4×D3—102no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6C22×D511yescharacteristic
260C2×C3×C8C22×D512yes—
261C3×C4⋊C4—51no—
262C3×C4⋊C4—52no—
263C3×C4⋊C4—101no—
264C3×C22⋊C4—101no—
265C3×C42C22×D511yescharacteristic
266#214—102no—
267(C2×D3)⋊C4—102no—
268C4⋊Dic3—51no—
269C4⋊Dic3C22×D511yescharacteristic
270Dic3⋊C4—21no—
271Dic3⋊C4—52no—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274C4×Dic3—21no—
275C4×Dic3—52no—
276C4×Dic3—102no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279#204—24no—
280C23×C5—62no—
281C22×D5—21no—
282C5×Q8—32no—
283C5×Q8—61no—
284C5×D4—62no—
285C5×D4—62no—
286C5×D4—122no—
287C5×D4—241no—
288C2×C4×C5—61no—
289C2×C4×C5—61no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—22no—
296C2×Dic5—21no—
297C2×Dic5—32no—
298C2×Dic5—32no—
299C2×Dic5—124no—
300D20—21no—
301D20—21no—
302C4×D5—42no—
303Dic10—34no—
304Dic10—81no—
305Dic10—242no—
306C5×C8—22no—
307#168—61no—
308#168—61no—
309C2×#41—301no—
310C2×SD16—32no—
311C2×SD16—151no—
312C4⋊Q8—51no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—31no—
317#127—152no—
318#121—302no—
319#121—301no—
320C4×Q8—31no—
321C4×Q8—151no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—51no—
325C4×D4—152no—
326#106—52no—
327#106—151no—
328C4⋊C8—152no—
329C4⋊C8D3×D511yescharacteristic
330#103—151no—
331#102—32no—
332#102—52no—
333#102—151no—
334#102—152no—
335#102—152no—
336C4×C8—152no—
337C4×C8—151no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341C3×D5—81no—
342C5×D3—82no—
343C23×C3—101no—
344C22×D3—22no—
345C3×Q8—401no—
346C3×D4—101no—
347C3×D4—101no—
348C2×C3×C4—102no—
349C2×C3×C4—101no—
350C2×C3×C4—202no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—21no—
357C2×Dic3—21no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360D12—22no—
361D12—22no—
362D12—42no—
363D12—81no—
364C4×D3—204no—
365Dic6—21no—
366Dic6—54no—
367Dic6—402no—
368Dic6#71112yescomplemented
369C3×C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5—122no—
373C22×C5—122no—
374C22×C5—122no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—41no—
377C2×D5—41no—
378C2×D5—41no—
379C4×C5—21no—
380C4×C5—62no—
381C4×C5—121no—
382C4×C5D3×SD1612yes—
383C4×C5#100711yescharacteristic
384C4×C5D3×#4111yescharacteristic
385Dic5—34no—
386Dic5—41no—
387Dic5—42no—
388Dic5—62no—
389#41—604no—
390C2×Q8—31no—
391C2×Q8—101no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—32no—
395C2×D4—51no—
396C2×D4—61no—
397C2×D4—61no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—101no—
401C22×C4—302no—
402SD16—64no—
403SD16—302no—
404C2×C8—151no—
405C2×C8—151no—
406C2×C8C2×D3×D512yes—
407C4⋊C4—31no—
408C4⋊C4—52no—
409C4⋊C4—51no—
410C4⋊C4—61no—
411C4⋊C4—101no—
412C4⋊C4—152no—
413C4⋊C4—151no—
414C4⋊C4—302no—
415C4⋊C4—302no—
416C22⋊C4—101no—
417C22⋊C4—302no—
418C42—61no—
419C42—152no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—201no—
424C22×C3—201no—
425C22×C3—201no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—42no—
428C2×D3—42no—
429C2×D3—42no—
430C3×C4—21no—
431C3×C4—201no—
432C3×C4—202no—
433C3×C4D5×SD1612yes—
434C3×C4C2×#71111yescharacteristic
435C3×C4#415011yescharacteristic
436Dic3—22no—
437Dic3—41no—
438Dic3—54no—
439Dic3—102no—
440C2×C5—242no—
441C2×C5#563311yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#577411yescharacteristic
444D5—81no—
445C23—62no—
446C23—101no—
447Q8—32no—
448Q8—61no—
449Q8—154no—
450Q8—401no—
451Q8—1202no—
452D4—62no—
453D4—62no—
454D4—101no—
455D4—101no—
456D4—122no—
457D4—241no—
458D4—604no—
459D4—1202no—
460C2×C4—61no—
461C2×C4—61no—
462C2×C4—102no—
463C2×C4—101no—
464C2×C4—152no—
465C2×C4—152no—
466C2×C4—202no—
467C2×C4—604no—
468C2×C4#677711yescharacteristic
469C2×C4#677711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—22no—
472C8—301no—
473C8—301no—
474C2×C3—401no—
475C2×C3#6593211yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610811yescharacteristic
478D3—82no—
479C5#8109011yescharacteristic, complemented, Sylow
480C22—122no—
481C22—122no—
482C22—122no—
483C22—201no—
484C22—201no—
485C22—201no—
486C22C2×#677711yescharacteristic
487C4—21no—
488C4—62no—
489C4—121no—
490C4—154no—
491C4—202no—
492C4—201no—
493C4—302no—
494C4#9125512yes—
495C4D3×#71111yescharacteristic
496C4#9203011yescharacteristic
497C3#1061210011yescharacteristic, complemented, Sylow
498C2—242no—
499C2—401no—
500C2#1175370311yescharacteristic
501C2C2×#9125511yescharacteristic
502C2#1175403811yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11752680C2
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
2. #11752472C2semidirect
3. #11750931C2semidirect
4. C5×#4848C2semidirect
5. C3×#65131C2semidirect
6. #11748011C2semidirect
7. #11748001C2semidirect
8. #11747808C2semidirect
9. #11747807C2semidirect
10. C4×#6655C2semidirect
11. #11746901C2semidirect
50. #65131D3semidirect
94. #4848D5semidirect
135. Dic30SD16semidirect
143. C5×Dic6#41semidirect
368. Dic6#711semidirect
422. C3×C5#3362semidirect
479. C5#81090semidirect
497. C3#10612100semidirect

Maximal subgroups

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

subgroupindex
#117526802
#117524722
#117509312
C5×#48482
C3×#651312
#117480112
#117480012
#117478082
#117478072
C4×#66552
#117469012
#106121003
#810905