Finite Group Databasebeta

← #14471929

Subgroups — #14471929

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#11752545C211yesmaximal, characteristic
2Dic6×Dic10C211yesmaximal, characteristic, complemented
3#11750943C211yesmaximal, characteristic, complemented
4C5×#4830C211yesmaximal, characteristic, complemented
5C3×#65137C211yesmaximal, characteristic, complemented
6#11748003C212yesmaximal, complemented
7#11747839C212yesmaximal, complemented
8Dic3×#677C212yesmaximal, complemented
9#11747781C212yesmaximal, complemented
10C4×#6658C211yesmaximal, characteristic, complemented
11#11746890C211yesmaximal, characteristic, complemented
12#10611663—31nomaximal, Hall
13C2×#6766—21no—
14C4×D60C2211yescharacteristic
15#91758C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C2×C3×#677C2212yes—
18C3×#4020C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20#91469C2212yes—
21#91468—21no—
22#91465—21no—
23#91458C2212yes—
24Dic3×D20C2212yes—
25#91409—22no—
26Dic5×Dic6—21no—
27Dic3×Dic10C2212yes—
28#91328—22no—
29C2×#6658C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31#91105C2212yes—
32#91101C2212yes—
33C5×Dic3⋊C8C2212yes—
34C5×C8×Dic3C2212yes—
35C4×C5×C3⋊C8C2211yescharacteristic
36C3×#3953C2212yes—
37#90987C2211yescharacteristic
38#90971C2211yescharacteristic
39#90968C2211yescharacteristic
40#90965C2212yes—
41#90965C2212yes—
42#80369—51nomaximal, Hall
43#65911—31no—
44Q8×Dic10—31no—
45C5×C8×Q8—31no—
46#65137—32no—
47#65137D311yescharacteristic, complemented
48#65131—31no—
49#65131—32no—
50#64983—31no—
51#64983—32no—
52C4×#677—32no—
53C4×#677—31no—
54C2×D60C2311yescharacteristic
55C2×C4×D15—21no—
56C2×Dic30—21no—
57C2×C5×Dic6D411yescharacteristic
58C2×C3×D20—21no—
59C2×C3×D20—21no—
60C2×C3×D20C2312yes—
61C2×C3×Dic10C2311yescharacteristic
62C2×#1204—22no—
63C2×#1202—22no—
64C2×#1202—22no—
65C2×D5×Dic3—22no—
66#6766—44no—
67C2×C3×C5×C8C2312yes—
68C3×C42×C5C2311yescharacteristic
69#6714—21no—
70C4⋊Dic15—21no—
71C4⋊Dic15C2311yescharacteristic
72C4⋊Dic15C2312yes—
73C5×C4⋊Dic3D411yescharacteristic
74C5×Dic3⋊C4D412yes—
75C4×C5×Dic3C2312yes—
76C2×C5×C3⋊C8C2311yescharacteristic
77C2×C5×C3⋊C8C2311yescharacteristic
78C3×C4⋊Dic5C2311yescharacteristic
79C3×#683—21no—
80C3×C4×Dic5—21no—
81C3×#677—24no—
82Dic3⋊Dic5—22no—
83#6668—22no—
84#6665—22no—
85Dic3×Dic5—22no—
86#6658—22no—
87#5718—51no—
88Q8×Dic6—51no—
89C3×#460—51no—
90#5163—52no—
91Dic3×SD16—52no—
92#5070—51no—
93C4×#215—51no—
94#4842—51no—
95#4830D511yescharacteristic, complemented
96#4761—52no—
97#4760—52no—
98C2×#713—61no—
99C4×C5×Q8—31no—
100Q8×Dic5—61no—
101C2×#677—31no—
102C2×#677C2×D312yes—
103#4041—62no—
104#4041—61no—
105#4034—61no—
106#4034—62no—
107#4020—32no—
108#4020C2×D311yescharacteristic
109C4×D20—32no—
110C4×D20—31no—
111#4015—31no—
112#4015—32no—
113C4×Dic10—32no—
114C4×Dic10C2×D311yescharacteristic
115C5×C4⋊C8—32no—
116C5×C4⋊C8C2×D311yescharacteristic
117C4×C5×C8—32no—
118C4×C5×C8—31no—
119#3953—32no—
120#3953—32no—
121#3953—32no—
122#3953—31no—
123#3953C2×D312yes—
124#3949—32no—
125#3949—31no—
126#3948—31no—
127#3362—151noSylow
128C22×D15—21no—
129C22×C3×D5—22no—
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15—22no—
134C2×Dic15—21no—
135D60—21no—
136D60—21no—
137C4×D15—42no—
138Dic30—81no—
139C2×C5×Dic3C2×D412yes—
140C2×C5×Dic3C2×D412yes—
141C5×Dic6SD1614yescomplemented
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C3×D20—22no—
145C3×D20—22no—
146C3×D20—42no—
147C3×D20—81no—
148C3×Dic10—21no—
149C3×Dic10#4112yescomplemented
150#1204—82no—
151#1202—44no—
152#1202—82no—
153D5×Dic3—44no—
154C3×C5×C8—22no—
155C5×C3⋊C8—21no—
156C5×C3⋊C8—21no—
157C2×#237—101no—
158C2×C3×SD16—52no—
159C3×#127—51no—
160C3×C4×Q8—51no—
161Q8×Dic3—52no—
162C2×#215—51no—
163#940—52no—
164#939—102no—
165#938—101no—
166D4×Dic3—52no—
167#888—52no—
168#888—102no—
169C4×D12—51no—
170#869—51no—
171#869—101no—
172C4×Dic6—101no—
173C4×Dic6C2×D511yescharacteristic
174C3×C4⋊C8C2×D511yescharacteristic
175C3×#102—52no—
176#835—51no—
177#832—52no—
178#832—52no—
179#821—52no—
180#817—52no—
181Dic3⋊C8C2×D512yes—
182C8×Dic3C2×D512yes—
183#809—51no—
184#808—51no—
185C4×C3⋊C8C2×D511yescharacteristic
186C2×C5×Q8—31no—
187#713—124no—
188C2×D20—21no—
189C2×D20—21no—
190C2×D20—31no—
191C2×D20—62no—
192C2×D20—62no—
193C2×D20C22×D312yes—
194C2×C4×D5—62no—
195C2×C4×D5—61no—
196C2×Dic10—62no—
197C2×Dic10—61no—
198C2×Dic10C22×D311yescharacteristic
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—62no—
207#685—61no—
208C4⋊Dic5—31no—
209C4⋊Dic5—32no—
210C4⋊Dic5—62no—
211C4⋊Dic5—61no—
212C4⋊Dic5C22×D311yescharacteristic
213#683—21no—
214#683—62no—
215C4×Dic5—21no—
216C4×Dic5—62no—
217#677—24no—
218#677—62no—
219Q82—151no—
220#550—151no—
221#486—152no—
222#486—151no—
223#476—152no—
224#476—151no—
225#460—51no—
226#460—152no—
227C8×Q8—31no—
228C4×SD16—151no—
229C4×SD16—152no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—41no—
232C2×D15—41no—
233C2×D15—41no—
234C2×C3×D5—42no—
235C2×C3×D5—42no—
236C2×C3×D5—42no—
237C3×C4×C5—21no—
238C3×C4×C5C2×SD1612yes—
239C3×C4×C5C2×#4111yescharacteristic
240C3×C4×C52−1+411yescharacteristic
241Dic15—41no—
242Dic15—42no—
243C3×Dic5—22no—
244C3×Dic5—41no—
245C5×Dic3—22no—
246C5×Dic3C2×SD1614yes—
247C2×C3×Q8—51no—
248C2×C3×D4—52no—
249C2×C3×D4—101no—
250C2×C3×D4—101no—
251C2×#67—102no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—204no—
255C2×D12—51no—
256C2×C4×D3—101no—
257C2×Dic6—101no—
258C2×Dic6—102no—
259C2×Dic6D2011yescharacteristic
260C3×SD16—104no—
261C2×C3×C8C22×D512yes—
262C3×C4⋊C4—51no—
263C3×C4⋊C4—101no—
264C3×C42—101no—
265C3×C42C22×D511yescharacteristic
266#217—102no—
267#215—102no—
268(C2×D3)⋊C4—101no—
269C4⋊Dic3—51no—
270C4⋊Dic3—52no—
271C4⋊Dic3—101no—
272C4⋊Dic3—102no—
273C4⋊Dic3D2011yescharacteristic
274Dic3⋊C4—102no—
275Dic3⋊C4D2012yes—
276C4×Dic3—102no—
277C4×Dic3C22×D512yes—
278C2×C3⋊C8C22×D511yescharacteristic
279C2×C3⋊C8C22×D511yescharacteristic
280C22×D5—22no—
281C22×D5—61no—
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—21no—
289C2×Dic5—21no—
290C2×Dic5—62no—
291C2×Dic5—61no—
292D20—22no—
293D20—22no—
294D20—42no—
295D20—61no—
296D20—61no—
297D20—81no—
298D20—124no—
299D20—242no—
300C4×D5—124no—
301C4×D5—122no—
302Dic10—21no—
303Dic10—242no—
304Dic10—241no—
305Dic10#23712yescomplemented
306C5×C8—22no—
307C5×C8—61no—
308C5×C8—61no—
309C2×#41—301no—
310C2×SD16—52no—
311C2×SD16—151no—
312C4⋊Q8—152no—
313C4⋊Q8—151no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—51no—
317#127—152no—
318#121—301no—
319#121—302no—
320C4×Q8—31no—
321C4×Q8—51no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—152no—
325C4×D4—151no—
326#106—151no—
327#106—152no—
328C4⋊C8—32no—
329C4⋊C8D3×D511yescharacteristic
330#103—151no—
331#102—52no—
332#102—151no—
333#102—152no—
334#102—152no—
335#102—152no—
336C4×C8—32no—
337C4×C8—31no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341D15—81no—
342C3×D5—82no—
343C23×C3—102no—
344C22×D3—101no—
345C3×Q8—52no—
346C3×Q8—101no—
347C3×D4—102no—
348C3×D4—102no—
349C3×D4—202no—
350C3×D4—401no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4C2×D2011yescharacteristic
354C2×C3×C4C2×D2011yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357#67—402no—
358C2×Dic3—102no—
359C2×Dic3—101no—
360C2×Dic3—204no—
361C2×Dic3C2×D2012yes—
362C2×Dic3C2×D2012yes—
363D12—101no—
364D12—101no—
365C4×D3—202no—
366Dic6—402no—
367Dic6—401no—
368Dic6#67714yescomplemented
369C3×C8—22no—
370C3⋊C8—21no—
371C3⋊C8—21no—
372C22×C5C2×D3×D411yescharacteristic
373C2×D5—42no—
374C2×D5—42no—
375C2×D5—42no—
376C2×D5—121no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—34no—
381C4×C5—62no—
382C4×C5D3×SD1612yes—
383C4×C5C2×#23711yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—22no—
386Dic5—41no—
387Dic5—121no—
388Dic5—122no—
389#41—604no—
390C2×Q8—31no—
391C2×Q8—51no—
392C2×Q8—302no—
393C2×Q8—301no—
394C2×D4—52no—
395C2×D4—101no—
396C2×D4—101no—
397C2×D4—151no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—302no—
401C22×C4—301no—
402SD16—104no—
403SD16—302no—
404C2×C8—31no—
405C2×C8—31no—
406C2×C8C2×D3×D512yes—
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—51no—
410C4⋊C4—101no—
411C4⋊C4—152no—
412C4⋊C4—151no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—32no—
419C42—101no—
420C42—302no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—202no—
424C22×C3—202no—
425C22×C3—202no—
426C22×C3C22×D2011yescharacteristic
427C2×D3—201no—
428C2×D3—201no—
429C2×D3—201no—
430C3×C4—21no—
431C3×C4—102no—
432C3×C4—201no—
433C3×C4C2×#67712yes—
434C3×C4#414711yescharacteristic
435C3×C4D5×#4111yescharacteristic
436Dic3—22no—
437Dic3—201no—
438Dic3—202no—
439Dic3C2×#67714yes—
440C2×C5#559811yescharacteristic
441C2×C5C2×D3×SD1611yescharacteristic
442C2×C5#577411yescharacteristic
443D5—82no—
444D5—241no—
445C23—102no—
446C23—301no—
447Q8—34no—
448Q8—52no—
449Q8—101no—
450Q8—1201no—
451Q8—1202no—
452D4—102no—
453D4—102no—
454D4—202no—
455D4—301no—
456D4—301no—
457D4—401no—
458D4—604no—
459D4—1202no—
460C2×C4—32no—
461C2×C4—32no—
462C2×C4—101no—
463C2×C4—101no—
464C2×C4—302no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D3×D2011yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—22no—
472C8—61no—
473C8—61no—
474C2×C3—402no—
475C2×C3#6591011yescharacteristic
476C2×C3C22×#67711yescharacteristic
477C2×C3#6608611yescharacteristic
478D3—401no—
479C5#8036911yescharacteristic, complemented, Sylow
480C22—202no—
481C22—202no—
482C22—202no—
483C22—601no—
484C22—601no—
485C22—601no—
486C22C2×D3×D2011yescharacteristic
487C4—21no—
488C4—34no—
489C4—62no—
490C4—102no—
491C4—201no—
492C4—602no—
493C4—601no—
494C4D3×#67712yes—
495C4D5×#23711yescharacteristic
496C4#9202811yescharacteristic
497C3#1061166311yescharacteristic, complemented, Sylow
498C2—402no—
499C2—1201no—
500C2#1175343911yescharacteristic
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#11752545C2
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. Dic6×Dic10C2semidirect
3. #11750943C2semidirect
4. C5×#4830C2semidirect
5. C3×#65137C2semidirect
6. #11748003C2semidirect
7. #11747839C2semidirect
8. Dic3×#677C2semidirect
9. #11747781C2semidirect
10. C4×#6658C2semidirect
11. #11746890C2semidirect
47. #65137D3semidirect
95. #4830D5semidirect
141. C5×Dic6SD16semidirect
149. C3×Dic10#41semidirect
305. Dic10#237semidirect
368. Dic6#677semidirect
422. C3×C5#3362semidirect
479. C5#80369semidirect
497. C3#10611663semidirect

Maximal subgroups

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

subgroupindex
#117525452
Dic6×Dic102
#117509432
C5×#48302
C3×#651372
#117480032
#117478392
Dic3×#6772
#117477812
C4×#66582
#117468902
#106116633
#803695