Finite Group Databasebeta

← #14471930

Subgroups — #14471930

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#11752677C211yesmaximal, characteristic
2#11752472C211yesmaximal, characteristic, complemented
3#11750949C211yesmaximal, characteristic, complemented
4C5×#4830C211yesmaximal, characteristic, complemented
5C3×#65131C211yesmaximal, characteristic, complemented
6#11748004C212yesmaximal, complemented
7#11748003C212yesmaximal, complemented
8#11747790C212yesmaximal, complemented
9#11747789C212yesmaximal, complemented
10C4×#6657C211yesmaximal, characteristic, complemented
11#11746910C211yesmaximal, characteristic, complemented
12#10611663—31nomaximal, Hall
13C2×#6773—21no—
14C2×#6706C2212yes—
15#91763C2211yescharacteristic
16C4×Dic30C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19C3×#4015C2211yescharacteristic
20#91470—21no—
21#91469C2212yes—
22#91459—22no—
23#91458C2212yes—
24#91450—21no—
25#91428C2212yes—
26#91344—21no—
27#91340C2212yes—
28#91327—22no—
29C2×#6657C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91105C2212yes—
32C5×Dic3⋊C8C2212yes—
33C5×C8×Dic3C2212yes—
34C4×C5×C3⋊C8C2211yescharacteristic
35C3×#3953C2212yes—
36C3×#3949C2212yes—
37#90987C2211yescharacteristic
38#90974C2211yescharacteristic
39#90968C2212yes—
40#90968C2212yes—
41#90965C2211yescharacteristic
42#81090—51nomaximal, Hall
43#65911—31no—
44Q8×Dic10—31no—
45C5×C8×Q8—31no—
46#65137—31no—
47#65137—32no—
48#65131—32no—
49#65131D311yescharacteristic, complemented
50#64983—31no—
51#64983—32no—
52C4×#677—31no—
53C4×#677—32no—
54C2×D60—21no—
55C2×D60—21no—
56C2×D60C2312yes—
57C2×Dic30C2311yescharacteristic
58C2×C5×Dic6D411yescharacteristic
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10—21no—
62C2×#1204—22no—
63C2×#1202—22no—
64C2×#1202—22no—
65C2×#1200—22no—
66#6773—44no—
67C2×C3×C5×C8C2312yes—
68C3×C42×C5C2311yescharacteristic
69C4⋊Dic15C2311yescharacteristic
70#6712—21no—
71C4×Dic15—21no—
72#6706—24no—
73C5×C4⋊Dic3D411yescharacteristic
74C5×Dic3⋊C4D412yes—
75C4×C5×Dic3C2312yes—
76C2×C5×C3⋊C8C2311yescharacteristic
77C2×C5×C3⋊C8C2311yescharacteristic
78C3×#685—21no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4⋊Dic5C2312yes—
82Dic3⋊Dic5—22no—
83#6669—22no—
84#6667—22no—
85Dic3×Dic5—22no—
86#6657—22no—
87#5722—51no—
88#5553—51no—
89C3×#476—51no—
90#5088—51no—
91C4×#214—51no—
92#4870—52no—
93#4852—52no—
94#4848—51no—
95#4830D511yescharacteristic, complemented
96#4762—52no—
97#4760—52no—
98C2×#713—61no—
99C4×C5×Q8—31no—
100Q8×Dic5—61no—
101C2×#677—31no—
102C2×#677—32no—
103#4041—62no—
104#4041—61no—
105#4034—61no—
106#4034—62no—
107#4020—32no—
108#4020—31no—
109C4×D20—32no—
110C4×D20C2×D311yescharacteristic
111#4015—32no—
112#4015C2×D311yescharacteristic
113C4×Dic10—31no—
114C4×Dic10—32no—
115C5×C4⋊C8—32no—
116C5×C4⋊C8C2×D311yescharacteristic
117C4×C5×C8—32no—
118C4×C5×C8—31no—
119#3953—31no—
120#3953—32no—
121#3953—32no—
122#3953—32no—
123#3953C2×D312yes—
124#3949—31no—
125#3949C2×D312yes—
126#3948—31no—
127#3362—151noSylow
128C22×D15—22no—
129C22×C3×D5—21no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15—21no—
134C2×Dic15—21no—
135D60—22no—
136D60—22no—
137D60—42no—
138D60—81no—
139Dic30—21no—
140Dic30#4112yescomplemented
141C2×C5×Dic3C2×D412yes—
142C2×C5×Dic3C2×D412yes—
143C5×Dic6SD1614yescomplemented
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#1202—44no—
152#1202—82no—
153#1200—44no—
154C3×C5×C8—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—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×#204—52no—
165#893—52no—
166#888—52no—
167#888—101no—
168#887—52no—
169#887—101no—
170#884—102no—
171#874—51no—
172C4×Dic6—51no—
173C4×Dic6C2×D511yescharacteristic
174C3×#106—52no—
175C3×C4⋊C8C2×D511yescharacteristic
176C3×#102—52no—
177#832—51no—
178#821—52no—
179Dic3⋊C8C2×D512yes—
180C8×Dic3C2×D512yes—
181#810—51no—
182#809—52no—
183#809—52no—
184#808—51no—
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×Q8—31no—
187#713—124no—
188C2×D20—32no—
189C2×D20—62no—
190C2×D20—61no—
191C2×D20—62no—
192C2×D20—61no—
193C2×D20C22×D311yescharacteristic
194C2×C4×D5—21no—
195C2×C4×D5—62no—
196C2×Dic10—21no—
197C2×Dic10—31no—
198C2×Dic10—62no—
199C2×C5×C8—31no—
200C2×C5×C8—31no—
201C2×C5×C8C22×D312yes—
202C5×C4⋊C4—32no—
203C5×C4⋊C4—31no—
204C42×C5—32no—
205C42×C5C22×D311yescharacteristic
206#685—21no—
207#685—62no—
208C4⋊Dic5—21no—
209C4⋊Dic5—31no—
210C4⋊Dic5—62no—
211C4⋊Dic5C22×D311yescharacteristic
212C4⋊Dic5C22×D312yes—
213#683—62no—
214#683—61no—
215C4×Dic5—62no—
216C4×Dic5—61no—
217#677—64no—
218#677—62no—
219Q82—151no—
220#550—151no—
221#486—152no—
222#486—151no—
223#476—51no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—31no—
228C4×SD16—152no—
229C4×SD16—151no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—42no—
232C2×D15—42no—
233C2×D15—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—
242Dic15—41no—
243C3×Dic5—41no—
244C3×Dic5—42no—
245C5×Dic3—22no—
246C5×Dic3C2×SD1614yes—
247C2×C3×Q8—101no—
248C2×C3×D4—51no—
249C22×C3×C4—101no—
250C2×#67—102no—
251C2×#67—102no—
252#235—204no—
253C2×D12—52no—
254C2×D12—101no—
255C2×D12—101no—
256C2×C4×D3—102no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6D2011yescharacteristic
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⋊Dic3D2011yescharacteristic
270Dic3⋊C4—101no—
271Dic3⋊C4—102no—
272Dic3⋊C4—102no—
273Dic3⋊C4D2012yes—
274C4×Dic3—101no—
275C4×Dic3—102no—
276C4×Dic3C22×D512yes—
277C2×C3⋊C8C22×D511yescharacteristic
278C2×C3⋊C8C22×D511yescharacteristic
279#204—104no—
280C22×D5—21no—
281C22×D5—62no—
282C5×Q8—34no—
283C2×C4×C5—32no—
284C2×C4×C5—32no—
285C2×C4×C5D3×D411yescharacteristic
286C2×C4×C5D3×D411yescharacteristic
287C2×C4×C5C23×D311yescharacteristic
288C2×Dic5—22no—
289C2×Dic5—21no—
290C2×Dic5—61no—
291C2×Dic5—61no—
292D20—21no—
293D20—21no—
294D20—62no—
295D20—62no—
296D20—124no—
297D20—122no—
298D20—241no—
299D20—242no—
300C4×D5—42no—
301C4×D5—124no—
302Dic10—32no—
303Dic10—61no—
304Dic10—81no—
305Dic10—242no—
306C5×C8—22no—
307C5×C8—61no—
308C5×C8—61no—
309C2×#41—301no—
310C2×SD16—151no—
311C2×SD16—152no—
312C4⋊Q8—51no—
313C4⋊Q8—152no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—152no—
317#127—151no—
318#121—302no—
319#121—301no—
320C4×Q8—31no—
321C4×Q8—152no—
322C4×Q8—151no—
323C4×Q8—301no—
324C4×D4—51no—
325C4×D4—152no—
326#106—52no—
327#106—151no—
328C4⋊C8—32no—
329C4⋊C8D3×D511yescharacteristic
330#103—151no—
331#102—52no—
332#102—152no—
333#102—152no—
334#102—151no—
335#102—152no—
336C4×C8—32no—
337C4×C8—31no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341D15—82no—
342C3×D5—81no—
343C23×C3—101no—
344C22×D3—102no—
345C3×Q8—401no—
346C3×D4—101no—
347C3×D4—101no—
348C2×C3×C4—102no—
349C2×C3×C4—101no—
350C2×C3×C4—202no—
351C2×C3×C4C2×D2011yescharacteristic
352C2×C3×C4C2×D2011yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—101no—
357C2×Dic3—101no—
358C2×Dic3C2×D2012yes—
359C2×Dic3C2×D2012yes—
360D12—102no—
361D12—102no—
362D12—202no—
363D12—401no—
364C4×D3—204no—
365Dic6—52no—
366Dic6—101no—
367Dic6—402no—
368Dic6#67714yescomplemented
369C3×C8—22no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C22×C5C2×D3×D411yescharacteristic
373C2×D5—41no—
374C2×D5—41no—
375C2×D5—41no—
376C2×D5—122no—
377C2×D5—122no—
378C2×D5—122no—
379C4×C5—21no—
380C4×C5—34no—
381C4×C5—62no—
382C4×C5D3×SD1612yes—
383C4×C5#100711yescharacteristic
384C4×C5D3×#4111yescharacteristic
385Dic5—41no—
386Dic5—42no—
387Dic5—62no—
388Dic5—121no—
389#41—604no—
390C2×Q8—31no—
391C2×Q8—101no—
392C2×Q8—151no—
393C2×Q8—302no—
394C2×D4—51no—
395C2×D4—152no—
396C2×D4—302no—
397C2×D4—302no—
398C2×D4—301no—
399C2×D4—301no—
400C22×C4—101no—
401C22×C4—302no—
402SD16—304no—
403SD16—302no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8C2×D3×D512yes—
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—52no—
410C4⋊C4—51no—
411C4⋊C4—101no—
412C4⋊C4—151no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C22⋊C4—101no—
417C22⋊C4—302no—
418C42—32no—
419C42—302no—
420C42—301no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—201no—
424C22×C3—201no—
425C22×C3—201no—
426C22×C3C22×D2011yescharacteristic
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C3×C4—21no—
431C3×C4—201no—
432C3×C4—202no—
433C3×C4C2×#67712yes—
434C3×C4#414711yescharacteristic
435C3×C4D5×#4111yescharacteristic
436Dic3—22no—
437Dic3—102no—
438Dic3—201no—
439Dic3C2×#67714yes—
440C2×C5#563311yescharacteristic
441C2×C5C2×D3×SD1611yescharacteristic
442C2×C5#577411yescharacteristic
443D5—81no—
444D5—242no—
445C23—101no—
446C23—302no—
447Q8—34no—
448Q8—152no—
449Q8—301no—
450Q8—401no—
451Q8—1202no—
452D4—101no—
453D4—101no—
454D4—302no—
455D4—302no—
456D4—604no—
457D4—602no—
458D4—1201no—
459D4—1202no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—102no—
463C2×C4—101no—
464C2×C4—202no—
465C2×C4—301no—
466C2×C4—301no—
467C2×C4—604no—
468C2×C4D3×D2011yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—22no—
472C8—61no—
473C8—61no—
474C2×C3—401no—
475C2×C3#6591011yescharacteristic
476C2×C3C22×#67711yescharacteristic
477C2×C3#6608611yescharacteristic
478D3—402no—
479C5#8109011yescharacteristic, complemented, Sylow
480C22—201no—
481C22—201no—
482C22—201no—
483C22—602no—
484C22—602no—
485C22—602no—
486C22C2×D3×D2011yescharacteristic
487C4—21no—
488C4—34no—
489C4—62no—
490C4—202no—
491C4—201no—
492C4—302no—
493C4—601no—
494C4D3×#67712yes—
495C4#9202411yescharacteristic
496C4#9202911yescharacteristic
497C3#1061166311yescharacteristic, complemented, Sylow
498C2—401no—
499C2—1202no—
500C2#1175334211yescharacteristic
501C2C2×D3×#67711yescharacteristic
502C2#1175403111yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radical#11752677C2
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. #11750949C2semidirect
4. C5×#4830C2semidirect
5. C3×#65131C2semidirect
6. #11748004C2semidirect
7. #11748003C2semidirect
8. #11747790C2semidirect
9. #11747789C2semidirect
10. C4×#6657C2semidirect
11. #11746910C2semidirect
49. #65131D3semidirect
95. #4830D5semidirect
140. Dic30#41semidirect
143. C5×Dic6SD16semidirect
368. Dic6#677semidirect
422. C3×C5#3362semidirect
479. C5#81090semidirect
497. C3#10611663semidirect

Maximal subgroups

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

subgroupindex
#117526772
#117524722
#117509492
C5×#48302
C3×#651312
#117480042
#117480032
#117477902
#117477892
C4×#66572
#117469102
#106116633
#810905