Finite Group Databasebeta

← #14471941

Subgroups — #14471941

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
2Dic6×Dic10C211yesmaximal, characteristic, complemented
3#11750795C211yesmaximal, characteristic, complemented
4C5×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×C4×#677C211yesmaximal, characteristic, complemented
6#11748003C212yesmaximal, complemented
7#11747839C212yesmaximal, complemented
8#11747830C212yesmaximal, complemented
9#11747790C212yesmaximal, complemented
10#11747064C211yesmaximal, characteristic, complemented
11#11746881C211yesmaximal, characteristic, complemented
12#10611663—31nomaximal, Hall
13C2×#6773—21no—
14#91763C2211yescharacteristic
15#91758C2211yescharacteristic
16C4×C5×Dic6C2211yescharacteristic
17C2×C3×#677C2211yescharacteristic
18C3×C4×D20C2211yescharacteristic
19C3×C4×Dic10C2211yescharacteristic
20#91469C2212yes—
21#91468—21no—
22#91459—22no—
23#91458C2212yes—
24#91450—21no—
25#91428C2212yes—
26Dic5×Dic6—21no—
27Dic3×Dic10C2212yes—
28#91328—22no—
29C2×#6658C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2212yes—
32#91105C2212yes—
33C5×Dic3⋊C8C2212yes—
34C5×C8×Dic3C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×#3953C2211yescharacteristic
37C3×#3949C2211yescharacteristic
38C3×#3948C2211yescharacteristic
39#90987C2212yes—
40#90968C2212yes—
41#90965C2212yes—
42#79622—51nomaximal, Hall
43#65911—31no—
44Q8×Dic10—31no—
45C5×C8×Q8—31no—
46#65137—32no—
47#65137—31no—
48#65131—31no—
49#65131—32no—
50#64983—31no—
51#64983—32no—
52C4×#677—32no—
53C4×#677D311yescharacteristic, complemented
54C2×D60—21no—
55C2×D60—21no—
56C2×D60C2312yes—
57C2×Dic30—21no—
58C2×C5×Dic6D411yescharacteristic
59C2×C3×D20C2311yescharacteristic
60C2×C3×C4×D5—21no—
61C2×C3×Dic10C2311yescharacteristic
62C2×#1204—22no—
63C2×#1202—22no—
64C2×#1202—22no—
65C2×#1200—22no—
66#6773—44no—
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C42×C5C2311yescharacteristic
70C4⋊Dic15—21no—
71C4⋊Dic15C2312yes—
72C5×C4⋊Dic3D411yescharacteristic
73C5×Dic3⋊C4D412yes—
74C4×C5×Dic3C2312yes—
75C2×C5×C3⋊C8C2312yes—
76C3×#685—21no—
77C3×C4⋊Dic5C2311yescharacteristic
78C3×C4⋊Dic5C2311yescharacteristic
79C3×#683—21no—
80C3×C4×Dic5—21no—
81C3×#677—22no—
82Dic3⋊Dic5—22no—
83#6668—22no—
84#6667—22no—
85Dic3×Dic5—22no—
86#6658—24no—
87Q8×Dic6—51no—
88#5553—51no—
89C3×C4×SD16—51no—
90#5163—52no—
91#5027—51no—
92#5008—51no—
93#4870—52no—
94#4788—52no—
95#4760—52no—
96#4694—51no—
97C8×Dic6D511yescharacteristic, complemented
98C2×#713—61no—
99C4×C5×Q8—31no—
100Q8×Dic5—61no—
101C2×#677—32no—
102C2×#677C2×D311yescharacteristic
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—31no—
112#4015—32no—
113C4×Dic10—32no—
114C4×Dic10C2×D311yescharacteristic
115C5×C4⋊C8—32no—
116C5×C4⋊C8—31no—
117C4×C5×C8—32no—
118C4×C5×C8C2×D311yescharacteristic
119#3953—32no—
120#3953—32no—
121#3953—32no—
122#3953—32no—
123#3953C2×D311yescharacteristic
124#3949—32no—
125#3949C2×D311yescharacteristic
126#3948C2×D311yescharacteristic
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—22no—
134D60—22no—
135D60—22no—
136D60—42no—
137D60—81no—
138Dic30—81no—
139C2×C5×Dic3C2×D412yes—
140C2×C5×Dic3C2×D412yes—
141C5×Dic6SD1614yescomplemented
142C2×C3×Dic5—21no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C3×D20—21no—
146C3×D20—21no—
147C3×C4×D5—42no—
148C3×Dic10—21no—
149C3×Dic10#4112yescomplemented
150#1204—82no—
151#1202—44no—
152#1202—82no—
153#1200—44no—
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C5×C3⋊C8—22no—
157C2×#235—101no—
158C2×C3×SD16—51no—
159C3×C4×Q8—51no—
160C3×C4×D4—51no—
161Q8×Dic3—52no—
162C2×#215—52no—
163#940—52no—
164#930—101no—
165#893—52no—
166#888—52no—
167#888—102no—
168#884—102no—
169#874—51no—
170#869—51no—
171#869—101no—
172C4×Dic6—101no—
173C4×Dic6C2×D511yescharacteristic
174C3×#106—51no—
175C3×#103—51no—
176C3×#102—51no—
177C3×C4×C8C2×D511yescharacteristic
178#832—52no—
179#821—52no—
180#821—52no—
181Dic3⋊C8C2×D512yes—
182C8×Dic3C2×D512yes—
183#809—52no—
184#808—52no—
185C4⋊(C3⋊C8)C2×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—62no—
197C2×Dic10—61no—
198C2×Dic10C22×D311yescharacteristic
199C2×C5×C8—32no—
200C2×C5×C8C22×D311yescharacteristic
201C2×C5×C8C22×D311yescharacteristic
202C5×C4⋊C4—32no—
203C5×C4⋊C4—31no—
204C42×C5—32no—
205C42×C5C22×D311yescharacteristic
206#685—21no—
207#685—62no—
208C4⋊Dic5—32no—
209C4⋊Dic5—62no—
210C4⋊Dic5—61no—
211C4⋊Dic5C22×D311yescharacteristic
212C4⋊Dic5C22×D311yescharacteristic
213#683—21no—
214#683—62no—
215C4×Dic5—21no—
216C4×Dic5—62no—
217#677—22no—
218#677—64no—
219Q82—151no—
220#550—151no—
221#486—152no—
222#486—151no—
223#476—152no—
224#476—151no—
225#460—151no—
226#460—152no—
227C8×Q8—31no—
228C4×SD16—51no—
229C4×SD16—152no—
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—42no—
242C3×Dic5—22no—
243C3×Dic5—41no—
244C3×Dic5—41no—
245C5×Dic3—22no—
246C5×Dic3C2×SD1614yes—
247C2×C3×Q8—51no—
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—101no—
258C2×Dic6—102no—
259C2×Dic6D2011yescharacteristic
260C3×SD16—102no—
261C2×C3×C8C22×D511yescharacteristic
262C2×C3×C8C22×D511yescharacteristic
263C3×C4⋊C4—51no—
264C3×C4⋊C4—51no—
265C3×C4⋊C4—101no—
266C3×C22⋊C4—101no—
267C3×C42—101no—
268C3×C42C22×D511yescharacteristic
269#215—104no—
270(C2×D3)⋊C4—102no—
271C4⋊Dic3—52no—
272C4⋊Dic3—101no—
273C4⋊Dic3—102no—
274C4⋊Dic3D2011yescharacteristic
275Dic3⋊C4—102no—
276Dic3⋊C4D2012yes—
277C4×Dic3—102no—
278C4×Dic3C22×D512yes—
279C2×C3⋊C8C22×D512yes—
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—21no—
289C2×Dic5—21no—
290C2×Dic5—21no—
291C2×Dic5—62no—
292D20—21no—
293D20—21no—
294D20—62no—
295D20—62no—
296D20—124no—
297D20—122no—
298D20—241no—
299D20—242no—
300C4×D5—42no—
301C4×D5—124no—
302Dic10—21no—
303Dic10—242no—
304Dic10—241no—
305Dic10#23512yescomplemented
306C5×C8—21no—
307C5×C8—21no—
308C5×C8—62no—
309C2×#41—301no—
310C2×SD16—51no—
311C2×SD16—152no—
312C4⋊Q8—152no—
313C4⋊Q8—151no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—152no—
317#127—151no—
318#121—302no—
319#121—301no—
320C4×Q8—31no—
321C4×Q8—51no—
322C4×Q8—152no—
323C4×Q8—301no—
324C4×D4—51no—
325C4×D4—152no—
326#106—51no—
327#106—152no—
328C4⋊C8—32no—
329C4⋊C8—31no—
330#103—51no—
331#102—51no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—152no—
336C4×C8—32no—
337C4×C8D3×D511yescharacteristic
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—52no—
346C3×Q8—101no—
347C3×D4—101no—
348C3×D4—101no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4—101no—
352C2×C3×C4—202no—
353C2×C3×C4C2×D2011yescharacteristic
354C2×C3×C4C2×D2011yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357#67—402no—
358C2×Dic3—102no—
359C2×Dic3C2×D2012yes—
360C2×Dic3C2×D2012yes—
361D12—102no—
362D12—102no—
363D12—202no—
364D12—401no—
365C4×D3—204no—
366Dic6—402no—
367Dic6—401no—
368Dic6#67714yescomplemented
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—22no—
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×C5C2×#23511yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—22no—
386Dic5—41no—
387Dic5—41no—
388Dic5—122no—
389#41—604no—
390C2×Q8—31no—
391C2×Q8—51no—
392C2×Q8—302no—
393C2×Q8—301no—
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—102no—
403SD16—304no—
404C2×C8—32no—
405C2×C8C2×D3×D511yescharacteristic
406C2×C8C2×D3×D511yescharacteristic
407C4⋊C4—32no—
408C4⋊C4—31no—
409C4⋊C4—51no—
410C4⋊C4—51no—
411C4⋊C4—101no—
412C4⋊C4—152no—
413C4⋊C4—302no—
414C4⋊C4—302no—
415C4⋊C4—301no—
416C22⋊C4—101no—
417C22⋊C4—302no—
418C42—32no—
419C42—101no—
420C42—302no—
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—102no—
432C3×C4—201no—
433C3×C4—201no—
434C3×C4C2×#67712yes—
435C3×C4#414711yescharacteristic
436C3×C4D5×#4111yescharacteristic
437Dic3—22no—
438Dic3—202no—
439Dic3C2×#67714yes—
440C2×C5#555211yescharacteristic
441C2×C5C2×D3×SD1611yescharacteristic
442C2×C5#576911yescharacteristic
443D5—81no—
444D5—242no—
445C23—101no—
446C23—302no—
447Q8—34no—
448Q8—52no—
449Q8—101no—
450Q8—1201no—
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—101no—
463C2×C4—101no—
464C2×C4—101no—
465C2×C4—202no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4D3×D2011yescharacteristic
469C2×C4D3×D2011yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—21no—
472C8—21no—
473C8—62no—
474C2×C3—401no—
475C2×C3#6591011yescharacteristic
476C2×C3C22×#67711yescharacteristic
477C2×C3#6608611yescharacteristic
478D3—402no—
479C5#7962211yescharacteristic, complemented, Sylow
480C22—201no—
481C22—201no—
482C22—201no—
483C22—602no—
484C22—602no—
485C22—602no—
486C22C2×D3×D2011yescharacteristic
487C4—21no—
488C4—34no—
489C4—62no—
490C4—102no—
491C4—201no—
492C4—201no—
493C4—602no—
494C4D3×#67712yes—
495C4#9200011yescharacteristic
496C4D5×#23511yescharacteristic
497C3#1061166311yescharacteristic, complemented, Sylow
498C2—401no—
499C2—1202no—
500C2#1175254111yescharacteristic
501C2C2×D3×#67711yescharacteristic
502C2#1175397311yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×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. Dic6×Dic10C2semidirect
3. #11750795C2semidirect
4. C5×C8×Dic6C2semidirect
5. C3×C4×#677C2semidirect
6. #11748003C2semidirect
7. #11747839C2semidirect
8. #11747830C2semidirect
9. #11747790C2semidirect
10. #11747064C2semidirect
11. #11746881C2semidirect
53. C4×#677D3semidirect
97. C8×Dic6D5semidirect
141. C5×Dic6SD16semidirect
149. C3×Dic10#41semidirect
305. Dic10#235semidirect
368. Dic6#677semidirect
422. C3×C5#3362semidirect
479. C5#79622semidirect
497. C3#10611663semidirect

Maximal subgroups

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

subgroupindex
#117526772
Dic6×Dic102
#117507952
C5×C8×Dic62
C3×C4×#6772
#117480032
#117478392
#117478302
#117477902
#117470642
#117468812
#106116633
#796225