Finite Group Databasebeta

← #14471948

Subgroups — #14471948

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×Q8×Dic10C211yesmaximal, characteristic, complemented
2#11752536C211yesmaximal, characteristic
3C4×#6717C211yesmaximal, characteristic, complemented
4C5×#5027C211yesmaximal, characteristic, complemented
5#11749338C212yesmaximal, complemented
6Dic5×#215C212yesmaximal, complemented
7#11747239C212yesmaximal, complemented
8#11747138C212yesmaximal, complemented
9#11746942C211yesmaximal, characteristic, complemented
10#11746901C211yesmaximal, characteristic, complemented
11#11746846C211yesmaximal, characteristic, complemented
12#10612100—31nomaximal, Hall
13C2×#6768—21no—
14C3×C4×C5×Q8C2211yescharacteristic
15C2×#6717C2211yescharacteristic
16C4×D60C2211yescharacteristic
17C2×C5×#215C2212yes—
18C5×#874C2211yescharacteristic
19C3×Q8×Dic5C2212yes—
20C3×#4034—22no—
21C3×#4034C2212yes—
22C3×#4015—21no—
23C3×#4015C2211yescharacteristic
24C3×C4×Dic10—21no—
25C3×C4×Dic10C2211yescharacteristic
26#91466—21no—
27#91451C2212yes—
28#91416—22no—
29Dic5×D12C2212yes—
30#91119C2211yescharacteristic
31#91093C2211yescharacteristic
32#91092C2211yescharacteristic
33C4×C3⋊#168C2211yescharacteristic
34C5×#809C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36#90987C2212yes—
37#90982C2212yes—
38#90968C2212yes—
39#90966C2212yes—
40#90966C2212yes—
41Dic5×C3⋊C8C2212yes—
42#83703—51nomaximal, Hall
43#66052—31no—
44Q8×Dic10D311yescharacteristic, complemented
45C5×#460—31no—
46#65452—32no—
47SD16×Dic5—32no—
48#65359—31no—
49C4×#688—31no—
50#65131—31no—
51#65119—31no—
52#65050—32no—
53#65049—32no—
54C2×C3×C5×Q8C2311yescharacteristic
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×C5×D12—21no—
58C2×C5×D12—21no—
59C2×C5×D12C2312yes—
60C2×C3×Dic10—21no—
61C2×C3×Dic10—22no—
62C2×C3×Dic10D411yescharacteristic
63C2×#1203—22no—
64C2×#1203—22no—
65C2×D3×Dic5—22no—
66#6768—44no—
67C3×C5×C4⋊C4—21no—
68C3×C5×C4⋊C4C2311yescharacteristic
69C3×C42×C5—21no—
70C3×C42×C5C2311yescharacteristic
71#6717—22no—
72#6714—21no—
73C4⋊Dic15C2311yescharacteristic
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76C5×#215—24no—
77C2×C5×C3⋊C8C2312yes—
78C3×C4⋊Dic5—21no—
79C3×C4⋊Dic5—22no—
80C3×C4⋊Dic5D411yescharacteristic
81C3×C4⋊Dic5C2312yes—
82C3×#683—22no—
83C3×#683D412yes—
84C3×C4×Dic5—22no—
85C3×C4×Dic5C2312yes—
86(C2×D3)⋊Dic5—22no—
87C3×Q82—51no—
88#5577—51no—
89#5088—51no—
90#5088—52no—
91#5084—52no—
92#5084—51no—
93#5027—52no—
94#5027D511yescharacteristic, complemented
95C4×#215—51no—
96C4×#215—52no—
97Q8×C3⋊C8—51no—
98C2×#711—61no—
99C2×C5×SD16—32no—
100C5×#127—31no—
101C4×C5×Q8C2×D311yescharacteristic
102Q8×Dic5C2×D312yes—
103C2×#688—31no—
104#4086—32no—
105#4085—62no—
106#4084—61no—
107D4×Dic5—32no—
108#4034—22no—
109#4034C2×D312yes—
110C4×D20—31no—
111#4015—21no—
112#4015C2×D311yescharacteristic
113C4×Dic10—21no—
114C4×Dic10C2×D311yescharacteristic
115C5×C4⋊C8—31no—
116C5×#102—32no—
117#3967—31no—
118#3964—32no—
119#3964—32no—
120#3953—32no—
121#3949—32no—
122#3946—32no—
123C8×Dic5—32no—
124#3941—31no—
125#3940—31no—
126C4×#168—31no—
127#3362—151noSylow
128C22×D15—21no—
129C22×C5×D3—22no—
130C3×C5×Q8—21no—
131C3×C5×Q8#4112yescomplemented
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5C2×D411yescharacteristic
135C2×C3×C4×C5C2×D411yescharacteristic
136C2×C3×C4×C5C2411yescharacteristic
137C2×Dic15—21no—
138D60—21no—
139D60—21no—
140C4×D15—42no—
141C5×D12—22no—
142C5×D12—22no—
143C5×D12—42no—
144C5×D12—81no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5C2×D412yes—
147C2×C3×Dic5C2×D412yes—
148C3×Dic10—82no—
149C3×Dic10—81no—
150C3×Dic10SD1614yescomplemented
151#1203—44no—
152#1203—82no—
153D3×Dic5—44no—
154C3⋊#168—21no—
155C3⋊#168—21no—
156C5×C3⋊C8—22no—
157C2×#239—101no—
158C3×C4⋊Q8—52no—
159C3×C4⋊Q8—51no—
160C3×C4⋊Q8—101no—
161C3×C4⋊Q8—102no—
162C3×C4×Q8—51no—
163C3×C4×Q8—52no—
164C3×C4×Q8—101no—
165C3×C4×Q8C2×D511yescharacteristic
166C2×#215—51no—
167C2×#215C2×D512yes—
168#895—102no—
169#895—101no—
170#874—52no—
171#874C2×D511yescharacteristic
172C4×D12—52no—
173C4×D12—51no—
174#835—51no—
175#809—52no—
176#809—52no—
177#809—51no—
178#809—52no—
179#809C2×D512yes—
180#808—51no—
181#808—52no—
182C4⋊(C3⋊C8)—52no—
183C4⋊(C3⋊C8)C2×D511yescharacteristic
184C4×C3⋊C8—51no—
185C4×C3⋊C8—52no—
186C2×C5×Q8C22×D311yescharacteristic
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×D20—31no—
195C2×C4×D5—61no—
196C2×Dic10—21no—
197C2×Dic10—22no—
198C2×Dic10#6711yescharacteristic
199C5×SD16—64no—
200C2×C5×C8—32no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4C22×D311yescharacteristic
203C42×C5—21no—
204C42×C5C22×D311yescharacteristic
205C22⋊Dic5—62no—
206#688—62no—
207#685—61no—
208C4⋊Dic5—21no—
209C4⋊Dic5—22no—
210C4⋊Dic5—31no—
211C4⋊Dic5#6711yescharacteristic
212C4⋊Dic5C22×D312yes—
213#683—22no—
214#683#6712yes—
215C4×Dic5—22no—
216C4×Dic5C22×D312yes—
217C2×#168—31no—
218C2×#168—31no—
219Q82—51no—
220#550—151no—
221#486—152no—
222#486—151no—
223#476—152no—
224#476—151no—
225#460—31no—
226#460—152no—
227C8×Q8—151no—
228C4×SD16—152no—
229C4×SD16—151no—
230C22×C3×C5C22×D411yescharacteristic
231C2×D15—41no—
232C2×D15—41no—
233C2×D15—41no—
234C2×C5×D3—42no—
235C2×C5×D3—42no—
236C2×C5×D3—42no—
237C3×C4×C5—22no—
238C3×C4×C5—21no—
239C3×C4×C5—41no—
240C3×C4×C5C2×SD1612yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C52−1+411yescharacteristic
243Dic15—41no—
244C3×Dic5—22no—
245C3×Dic5—42no—
246C3×Dic5C2×SD1614yes—
247C2×C3×Q8—51no—
248C2×C3×Q8—102no—
249C2×C3×Q8—101no—
250C2×C3×Q8C22×D511yescharacteristic
251#239—204no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—51no—
255C2×D12—102no—
256C2×D12—102no—
257C2×D12C22×D512yes—
258C2×C4×D3—102no—
259C2×C4×D3—101no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—52no—
262C3×C4⋊C4—51no—
263C3×C4⋊C4—52no—
264C3×C4⋊C4—102no—
265C3×C4⋊C4—102no—
266C3×C4⋊C4—101no—
267C3×C4⋊C4C22×D511yescharacteristic
268C3×C42—21no—
269C3×C42—52no—
270C3×C42—102no—
271C3×C42C22×D511yescharacteristic
272#215—24no—
273#215—102no—
274(C2×D3)⋊C4—102no—
275(C2×D3)⋊C4—101no—
276C4⋊Dic3—51no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8C22×D512yes—
280C23×C5—62no—
281C22×D5—61no—
282C5×Q8—21no—
283C5×Q8#23912yescomplemented
284C5×D4—62no—
285C5×D4—62no—
286C5×D4—122no—
287C5×D4—241no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5C2×#6711yescharacteristic
291C2×C4×C5C2×#6711yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—22no—
296C2×Dic5—61no—
297C2×Dic5—124no—
298C2×Dic5C2×#6712yes—
299C2×Dic5C2×#6712yes—
300D20—61no—
301D20—61no—
302C4×D5—122no—
303Dic10—82no—
304Dic10—81no—
305Dic10#21514yescomplemented
306C5×C8—62no—
307#168—61no—
308#168—61no—
309C2×#41—301no—
310C2×SD16—32no—
311C2×SD16—151no—
312C4⋊Q8—52no—
313C4⋊Q8—51no—
314C4⋊Q8—101no—
315C4⋊Q8—102no—
316#127—31no—
317#127—152no—
318#121—301no—
319#121—302no—
320C4×Q8—51no—
321C4×Q8—52no—
322C4×Q8—101no—
323C4×Q8D3×D511yescharacteristic
324C4×D4—152no—
325C4×D4—151no—
326#106—152no—
327#106—151no—
328C4⋊C8—31no—
329C4⋊C8—152no—
330#103—151no—
331#102—32no—
332#102—152no—
333#102—152no—
334#102—152no—
335#102—151no—
336C4×C8—152no—
337C4×C8—151no—
338C2×C3×C5#54811yescharacteristic
339C2×C3×C5C22×SD1611yescharacteristic
340C2×C3×C5#57611yescharacteristic
341D15—81no—
342C5×D3—82no—
343C22×D3—22no—
344C22×D3—101no—
345C3×Q8—21no—
346C3×Q8—54no—
347C3×Q8—401no—
348C3×Q8—402no—
349C3×Q8#71112yescomplemented
350C2×C3×C4—21no—
351C2×C3×C4—21no—
352C2×C3×C4—52no—
353C2×C3×C4—52no—
354C2×C3×C4—102no—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4C23×D511yescharacteristic
358C2×Dic3—101no—
359D12—22no—
360D12—22no—
361D12—42no—
362D12—81no—
363D12—101no—
364D12—101no—
365D12—204no—
366D12—402no—
367C4×D3—204no—
368C4×D3—202no—
369C3⋊C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5—122no—
373C22×C5—122no—
374C22×C5—122no—
375C22×C5C22×#6711yescharacteristic
376C2×D5—121no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—22no—
380C4×C5—21no—
381C4×C5—41no—
382C4×C5C2×#21512yes—
383C4×C5C2×#23911yescharacteristic
384C4×C5#100711yescharacteristic
385Dic5—22no—
386Dic5—42no—
387Dic5—121no—
388Dic5C2×#21514yes—
389#41—604no—
390C2×Q8—51no—
391C2×Q8—102no—
392C2×Q8—101no—
393C2×Q8C2×D3×D511yescharacteristic
394C2×D4—32no—
395C2×D4—61no—
396C2×D4—61no—
397C2×D4—151no—
398C2×D4—302no—
399C2×D4—302no—
400C22×C4—302no—
401C22×C4—301no—
402SD16—64no—
403SD16—302no—
404C2×C8—32no—
405C2×C8—151no—
406C2×C8—151no—
407C4⋊C4—21no—
408C4⋊C4—52no—
409C4⋊C4—51no—
410C4⋊C4—52no—
411C4⋊C4—102no—
412C4⋊C4—102no—
413C4⋊C4—101no—
414C4⋊C4—151no—
415C4⋊C4C2×D3×D511yescharacteristic
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—21no—
419C42—52no—
420C42—102no—
421C42C2×D3×D511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3C2×D4×D511yescharacteristic
424C2×D3—42no—
425C2×D3—42no—
426C2×D3—42no—
427C2×D3—201no—
428C2×D3—201no—
429C2×D3—201no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4—54no—
434C3×C4—102no—
435C3×C4—202no—
436C3×C4D5×SD1612yes—
437C3×C4C2×#71111yescharacteristic
438C3×C4#415011yescharacteristic
439Dic3—201no—
440C2×C5—242no—
441C2×C5C22×#21511yescharacteristic
442C2×C5#581711yescharacteristic
443C2×C5#583511yescharacteristic
444D5—241no—
445C23—62no—
446C23—301no—
447Q8—21no—
448Q8—54no—
449Q8—401no—
450Q8—402no—
451Q8#676812yescomplemented
452D4—62no—
453D4—62no—
454D4—122no—
455D4—241no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—1202no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—52no—
463C2×C4—52no—
464C2×C4—102no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D5×#6711yescharacteristic
469C2×C4D5×#6711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—62no—
472C8—301no—
473C8—301no—
474C2×C3#6593211yescharacteristic
475C2×C3C2×D5×SD1611yescharacteristic
476C2×C3#6610811yescharacteristic
477D3—82no—
478D3—401no—
479C5#8370311yescharacteristic, complemented, Sylow
480C22—122no—
481C22—122no—
482C22—122no—
483C22—601no—
484C22—601no—
485C22—601no—
486C22C2×D5×#6711yescharacteristic
487C4—21no—
488C4—22no—
489C4—41no—
490C4—54no—
491C4—102no—
492C4—202no—
493C4—601no—
494C4D5×#21512yes—
495C4C2×#676811yescharacteristic
496C4#9200411yescharacteristic
497C3#1061210011yescharacteristic, complemented, Sylow
498C2—242no—
499C2—1201no—
500C2#1175431911yescharacteristic
501C2C2×D5×#21511yescharacteristic
502C2#1175531611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#11752536C2
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×Q8×Dic10C2semidirect
3. C4×#6717C2semidirect
4. C5×#5027C2semidirect
5. #11749338C2semidirect
6. Dic5×#215C2semidirect
7. #11747239C2semidirect
8. #11747138C2semidirect
9. #11746942C2semidirect
10. #11746901C2semidirect
11. #11746846C2semidirect
44. Q8×Dic10D3semidirect
94. #5027D5semidirect
131. C3×C5×Q8#41semidirect
150. C3×Dic10SD16semidirect
283. C5×Q8#239semidirect
305. Dic10#215semidirect
349. C3×Q8#711semidirect
422. C3×C5#3362semidirect
451. Q8#6768semidirect
479. C5#83703semidirect
497. C3#10612100semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic102
#117525362
C4×#67172
C5×#50272
#117493382
Dic5×#2152
#117472392
#117471382
#117469422
#117469012
#117468462
#106121003
#837035