Finite Group Databasebeta

← #14471961

Subgroups — #14471961

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
1C3×#66056C211yesmaximal, characteristic, complemented
2#11752538C211yesmaximal, characteristic
3#11751189C211yesmaximal, characteristic, complemented
4C5×#5084C211yesmaximal, characteristic, complemented
5#11747400C212yesmaximal, complemented
6#11747240C212yesmaximal, complemented
7#11747225C212yesmaximal, complemented
8#11747138C212yesmaximal, complemented
9#11747064C211yesmaximal, characteristic, complemented
10C4×#6656C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612821—31nomaximal, Hall
13C2×#6769—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15#91763C2211yescharacteristic
16C4×C5×D12C2211yescharacteristic
17C3×#4090—22no—
18C3×#4034—21no—
19C3×#4034C2212yes—
20C3×#4033—21no—
21C3×#4033C2212yes—
22C3×C4×Dic10C2211yescharacteristic
23C3×C4×Dic10C2211yescharacteristic
24#91460—21no—
25#91451C2212yes—
26#91420—22no—
27#91418C2212yes—
28C2×#6658C2212yes—
29C2×#6656C2211yescharacteristic
30#91093C2212yes—
31#91093C2212yes—
32C4×C3⋊#168C2211yescharacteristic
33C5×#809C2212yes—
34C5×#808C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36#90986C2211yescharacteristic
37#90982C2212yes—
38#90970C2211yescharacteristic
39#90968C2212yes—
40#90966C2211yescharacteristic
41Dic5×C3⋊C8C2212yes—
42#83703—51nomaximal, Hall
43#66056D311yescharacteristic, complemented
44#65887—31no—
45C5×#476—31no—
46#65377—31no—
47C4×#687—31no—
48#65159—32no—
49#65141—32no—
50#65137—31no—
51#65119—31no—
52#65051—32no—
53#65049—32no—
54C2×C3×C5×Q8—21no—
55C2×D60—21no—
56C2×D60—21no—
57C2×D60C2312yes—
58C2×C5×D12C2311yescharacteristic
59C2×C4×C5×D3—21no—
60C2×C3×Dic10—22no—
61C2×C3×Dic10D411yescharacteristic
62C2×C3×Dic10C2311yescharacteristic
63C2×#1203—22no—
64C2×#1203—22no—
65C2×#1200—22no—
66#6769—44no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2312yes—
69C3×C42×C5C2311yescharacteristic
70C2×C3⋊#168C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72C5×(C2×D3)⋊C4—21no—
73C5×C4⋊Dic3C2311yescharacteristic
74C2×C5×C3⋊C8C2312yes—
75C3×C4⋊Dic5D411yescharacteristic
76C3×C4⋊Dic5C2311yescharacteristic
77C3×#683—21no—
78C3×#683—22no—
79C3×#683—22no—
80C3×#683D412yes—
81C3×C4×Dic5—21no—
82C3×C4×Dic5—22no—
83C3×C4×Dic5C2312yes—
84#6667—22no—
85#6658—24no—
86#6656—22no—
87C3×Q82—51no—
88#5577—51no—
89#5088—51no—
90#5088—52no—
91#5084—52no—
92#5084D511yescharacteristic, complemented
93#5027—52no—
94#5027—51no—
95C4×#215—51no—
96C4×#215—52no—
97Q8×C3⋊C8—51no—
98C2×#709—61no—
99C5×C4⋊Q8C2×D311yescharacteristic
100C4×C5×D4—31no—
101#4090—22no—
102#4086—32no—
103C2×#687—31no—
104#4076—61no—
105C2×#677—32no—
106#4039—32no—
107#4034—21no—
108#4034C2×D312yes—
109#4033—21no—
110#4033C2×D312yes—
111#4030—62no—
112#4020—31no—
113C4×Dic10C2×D311yescharacteristic
114C4×Dic10C2×D311yescharacteristic
115C5×#106—32no—
116C5×C4⋊C8—31no—
117C5×#102—32no—
118#3964—31no—
119#3953—32no—
120#3946—32no—
121C8×Dic5—32no—
122#3942—31no—
123#3941—32no—
124#3941—32no—
125#3940—31no—
126C4×#168—31no—
127#3362—151noSylow
128C22×D15—22no—
129C22×C5×D3—21no—
130C3×C5×Q8—81no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135D60—22no—
136D60—22no—
137D60—42no—
138D60—81no—
139C2×C5×Dic3—21no—
140C5×D12—21no—
141C5×D12—21no—
142C4×C5×D3—42no—
143C2×C3×Dic5—21no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5C2×D412yes—
146C2×C3×Dic5C2×D412yes—
147C3×Dic10—21no—
148C3×Dic10—82no—
149C3×Dic10SD1614yescomplemented
150C3×Dic10#4112yescomplemented
151#1203—44no—
152#1203—82no—
153#1200—44no—
154C3⋊#168—21no—
155C3⋊#168—21no—
156C5×C3⋊C8—22no—
157C2×#239—101no—
158C3×C4⋊Q8—52no—
159C3×C4⋊Q8—101no—
160C3×C4⋊Q8—102no—
161C3×C4⋊Q8C2×D511yescharacteristic
162C3×C4×Q8—51no—
163C3×C4×Q8—52no—
164C3×C4×Q8—51no—
165C3×C4×Q8—101no—
166C2×#215—51no—
167C2×#215—52no—
168#895—102no—
169#895—101no—
170#874—52no—
171#874—51no—
172C4×D12—52no—
173C4×D12C2×D511yescharacteristic
174#835—51no—
175#809—51no—
176#809—52no—
177#809—52no—
178#809—52no—
179#809C2×D512yes—
180#808—51no—
181#808C2×D512yes—
182C4⋊(C3⋊C8)—52no—
183C4⋊(C3⋊C8)C2×D511yescharacteristic
184C4×C3⋊C8—51no—
185C4×C3⋊C8—52no—
186C2×C5×Q8—21no—
187C2×C5×D4—31no—
188C22×C4×C5—61no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191#709—124no—
192C2×D20—32no—
193C2×D20—61no—
194C2×D20—61no—
195C2×C4×D5—62no—
196C2×Dic10—22no—
197C2×Dic10#6711yescharacteristic
198C2×Dic10C22×D311yescharacteristic
199C2×C5×C8—32no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—31no—
202C5×C4⋊C4C22×D312yes—
203C5×C22⋊C4—61no—
204C42×C5C22×D311yescharacteristic
205#687—62no—
206#685—62no—
207C4⋊Dic5#6711yescharacteristic
208C4⋊Dic5C22×D311yescharacteristic
209#683—21no—
210#683—22no—
211#683—22no—
212#683#6712yes—
213C4×Dic5—21no—
214C4×Dic5—22no—
215C4×Dic5C22×D312yes—
216C2×#168—31no—
217C2×#168—31no—
218#677—64no—
219Q82—51no—
220#550—151no—
221#486—152no—
222#486—151no—
223#476—31no—
224#476—152no—
225#460—152no—
226#460—151no—
227C8×Q8—151no—
228C4×SD16—152no—
229C4×SD16—151no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—42no—
232C2×D15—42no—
233C2×D15—42no—
234C2×C5×D3—41no—
235C2×C5×D3—41no—
236C2×C5×D3—41no—
237C3×C4×C5—21no—
238C3×C4×C5—42no—
239C3×C4×C5C2×SD1612yes—
240C3×C4×C5C2×#4111yescharacteristic
241C3×C4×C52−1+411yescharacteristic
242C3×Dic5—22no—
243C3×Dic5—22no—
244C3×Dic5—41no—
245C3×Dic5C2×SD1614yes—
246C5×Dic3—41no—
247C2×C3×Q8—21no—
248C2×C3×Q8—51no—
249C2×C3×Q8—51no—
250C2×C3×Q8—102no—
251#239—204no—
252C2×D12—52no—
253C2×D12—102no—
254C2×D12—101no—
255C2×D12—102no—
256C2×D12—101no—
257C2×D12C22×D511yescharacteristic
258C2×C4×D3—21no—
259C2×C4×D3—102no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—52no—
262C3×C4⋊C4—51no—
263C3×C4⋊C4—51no—
264C3×C4⋊C4—102no—
265C3×C4⋊C4—102no—
266C3×C4⋊C4—101no—
267C3×C4⋊C4C22×D512yes—
268C3×C42—52no—
269C3×C42—102no—
270C3×C42—101no—
271C3×C42C22×D511yescharacteristic
272#215—104no—
273#215—102no—
274(C2×D3)⋊C4—21no—
275(C2×D3)⋊C4—102no—
276C4⋊Dic3C22×D511yescharacteristic
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—61no—
281C22×D5—62no—
282C5×Q8—81no—
283C5×D4—61no—
284C5×D4—61no—
285C2×C4×C5—22no—
286C2×C4×C5—61no—
287C2×C4×C5—122no—
288C2×C4×C5C2×#6711yescharacteristic
289C2×C4×C5C2×#6711yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—21no—
294C2×Dic5—21no—
295C2×Dic5C2×#6712yes—
296C2×Dic5C2×#6712yes—
297D20—62no—
298D20—62no—
299D20—122no—
300D20—241no—
301C4×D5—124no—
302Dic10—21no—
303Dic10—82no—
304Dic10#21514yescomplemented
305Dic10#23912yescomplemented
306C5×C8—62no—
307#168—61no—
308#168—61no—
309C2×#41—301no—
310C2×SD16—152no—
311C2×SD16—151no—
312C4⋊Q8—52no—
313C4⋊Q8—101no—
314C4⋊Q8—102no—
315C4⋊Q8D3×D511yescharacteristic
316#127—152no—
317#127—151no—
318#121—302no—
319#121—301no—
320C4×Q8—51no—
321C4×Q8—52no—
322C4×Q8—51no—
323C4×Q8—101no—
324C4×D4—31no—
325C4×D4—152no—
326#106—32no—
327#106—151no—
328C4⋊C8—31no—
329C4⋊C8—152no—
330#103—151no—
331#102—32no—
332#102—152no—
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
341D15—82no—
342C5×D3—81no—
343C22×D3—21no—
344C22×D3—102no—
345C3×Q8—54no—
346C3×Q8—52no—
347C3×Q8—81no—
348C3×Q8—101no—
349C3×Q8—402no—
350C2×C3×C4—22no—
351C2×C3×C4—52no—
352C2×C3×C4—52no—
353C2×C3×C4—101no—
354C2×C3×C4—101no—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4C23×D511yescharacteristic
358C2×Dic3—21no—
359D12—21no—
360D12—21no—
361D12—102no—
362D12—102no—
363D12—204no—
364D12—202no—
365D12—401no—
366D12—402no—
367C4×D3—42no—
368C4×D3—204no—
369C3⋊C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5—121no—
373C22×C5—121no—
374C22×C5—121no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—122no—
377C2×D5—122no—
378C2×D5—122no—
379C4×C5—21no—
380C4×C5—42no—
381C4×C5—121no—
382C4×C5C2×#21512yes—
383C4×C5C2×#23911yescharacteristic
384C4×C5#100711yescharacteristic
385Dic5—22no—
386Dic5—22no—
387Dic5—41no—
388Dic5C2×#21514yes—
389#41—604no—
390C2×Q8—21no—
391C2×Q8—51no—
392C2×Q8—51no—
393C2×Q8—102no—
394C2×D4—31no—
395C2×D4—152no—
396C2×D4—302no—
397C2×D4—302no—
398C2×D4—301no—
399C2×D4—301no—
400C22×C4—61no—
401C22×C4—302no—
402SD16—304no—
403SD16—302no—
404C2×C8—32no—
405C2×C8—151no—
406C2×C8—151no—
407C4⋊C4—21no—
408C4⋊C4—31no—
409C4⋊C4—52no—
410C4⋊C4—51no—
411C4⋊C4—51no—
412C4⋊C4—102no—
413C4⋊C4—102no—
414C4⋊C4—101no—
415C4⋊C4C2×D3×D512yes—
416C22⋊C4—61no—
417C22⋊C4—302no—
418C42—52no—
419C42—102no—
420C42—101no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3C2×D4×D511yescharacteristic
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—41no—
427C2×D3—202no—
428C2×D3—202no—
429C2×D3—202no—
430C3×C4—21no—
431C3×C4—42no—
432C3×C4—54no—
433C3×C4—102no—
434C3×C4—102no—
435C3×C4—201no—
436C3×C4D5×SD1612yes—
437C3×C4#414711yescharacteristic
438C3×C4D5×#4111yescharacteristic
439Dic3—41no—
440C2×C5—241no—
441C2×C5C22×#21511yescharacteristic
442C2×C5#581711yescharacteristic
443C2×C5#583511yescharacteristic
444D5—242no—
445C23—61no—
446C23—302no—
447Q8—54no—
448Q8—52no—
449Q8—81no—
450Q8—101no—
451Q8—402no—
452D4—61no—
453D4—61no—
454D4—302no—
455D4—302no—
456D4—604no—
457D4—602no—
458D4—1201no—
459D4—1202no—
460C2×C4—22no—
461C2×C4—52no—
462C2×C4—52no—
463C2×C4—61no—
464C2×C4—101no—
465C2×C4—101no—
466C2×C4—122no—
467C2×C4—604no—
468C2×C4D5×#6711yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—301no—
473C8—301no—
474C2×C3#6596711yescharacteristic
475C2×C3C2×D5×SD1611yescharacteristic
476C2×C3#6610811yescharacteristic
477D3—81no—
478D3—402no—
479C5#8370311yescharacteristic, complemented, Sylow
480C22—121no—
481C22—121no—
482C22—121no—
483C22—602no—
484C22—602no—
485C22—602no—
486C22C2×D5×#6711yescharacteristic
487C4—21no—
488C4—42no—
489C4—54no—
490C4—102no—
491C4—102no—
492C4—121no—
493C4—201no—
494C4D5×#21512yes—
495C4#9202911yescharacteristic
496C4D5×#23911yescharacteristic
497C3#1061282111yescharacteristic, complemented, Sylow
498C2—241no—
499C2—1202no—
500C2#1175469211yescharacteristic
501C2C2×D5×#21511yescharacteristic
502C2#1175522711yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C22×D4
prime radical#11752538C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. C3×#66056C2semidirect
3. #11751189C2semidirect
4. C5×#5084C2semidirect
5. #11747400C2semidirect
6. #11747240C2semidirect
7. #11747225C2semidirect
8. #11747138C2semidirect
9. #11747064C2semidirect
10. C4×#6656C2semidirect
11. #11746846C2semidirect
43. #66056D3semidirect
92. #5084D5semidirect
149. C3×Dic10SD16semidirect
150. C3×Dic10#41semidirect
304. Dic10#215semidirect
305. Dic10#239semidirect
422. C3×C5#3362semidirect
479. C5#83703semidirect
497. C3#10612821semidirect

Maximal subgroups

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

subgroupindex
C3×#660562
#117525382
#117511892
C5×#50842
#117474002
#117472402
#117472252
#117471382
#117470642
C4×#66562
#117468462
#106128213
#837035