Finite Group Databasebeta

← #14431350

Subgroups — #14431350

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754619C211yesmaximal, characteristic, complemented
2#11754492C211yesmaximal, characteristic
3#11751220C211yesmaximal, characteristic, complemented
4C5×#5133C211yesmaximal, characteristic
5C3×#65410C211yesmaximal, characteristic, complemented
6C2×#90986C211yesmaximal, characteristic, complemented
7#11748382C211yesmaximal, characteristic
8#11747887C212yesmaximal, complemented
9#11747881C212yesmaximal, complemented
10#11747817C212yesmaximal, complemented
11#11747808C212yesmaximal, complemented
12#10610604—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15#91815C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C2×C5×C4⋊Dic3C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×C3×C4⋊Dic5C2211yescharacteristic
20#91575—22no—
21Dic5×#67—22no—
22#91470C2212yes—
23#91468—21no—
24#91435C2212yes—
25D3×C4⋊Dic5—21no—
26#91388—21no—
27#91384C2212yes—
28#91344C2212yes—
29#91338—21no—
30#91098C2212yes—
31#91098C2212yes—
32C5×#821C2212yes—
33C5×#816C2212yes—
34C3×#3950C2212yes—
35C3×#3949C2212yes—
36#90986C2212yes—
37#90986C2212yes—
38#90972C2211yescharacteristic
39#90972C2211yescharacteristic
40#90966C2211yescharacteristic
41#90966C2211yescharacteristic
42#79244—51nomaximal, Hall
43#66161—31no—
44#65834—31no—
45C5×#417—31no—
46#65522—31no—
47#65410D311yescharacteristic, complemented
48#65408—31no—
49C2×#3940—31no—
50#65085—32no—
51#65080—32no—
52#65055—32no—
53#65050—32no—
54C22×C3×C4×C5C2311yescharacteristic
55C2×C5×#67—21no—
56C22×C5×Dic3—21no—
57C5×#235—22no—
58C5×#235Q814yescomplemented
59C2×C5×D12C2311yescharacteristic
60C2×C4×C5×D3—21no—
61C2×C5×Dic6C2311yescharacteristic
62C22×C3×Dic5—21no—
63C2×#1204—22no—
64C2×D3×Dic5—22no—
65C3×C5×M16—22no—
66C2×C3×C5×C8C2312yes—
67#6719D412yes—
68C4⋊Dic15D411yescharacteristic
69C4⋊Dic15D411yescharacteristic
70C4×Dic15C2312yes—
71C2×C3⋊#168—22no—
72C2×C3⋊#168C2311yescharacteristic
73C2×C3⋊#168C2311yescharacteristic
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C3×C22⋊Dic5—21no—
77C3×C4⋊Dic5—21no—
78C3×C4⋊Dic5C2312yes—
79C3×C4⋊Dic5C2311yescharacteristic
80C3×C4⋊Dic5C2311yescharacteristic
81C3×C4×Dic5—21no—
82Dic3⋊Dic5—22no—
83Dic3⋊Dic5—22no—
84#6669—22no—
85#6668—22no—
86(C2×D3)⋊Dic5—22no—
87Dic3×Dic5—22no—
88#5519—51no—
89#5504—51no—
90C3×#428—51no—
91#5133D511yescharacteristic
92#5119—51no—
93#5002—51no—
94C2×#808—51no—
95#4891—52no—
96#4877—52no—
97#4870—52no—
98#4854—52no—
99C2×C5×#41—31no—
100C2×C5×M16C2×D311yescharacteristic
101C2×C5×C4⋊C4—31no—
102Q8×Dic5—32no—
103D4×Dic5—32no—
104D4×Dic5—62no—
105#4072—31no—
106#4072—61no—
107#4072C2×D311yescharacteristic
108C2×C4⋊Dic5—61no—
109C2×C4⋊Dic5C2×D311yescharacteristic
110#4070—62no—
111C22×#168—31no—
112#4036—32no—
113#4036—61no—
114#4034—32no—
115#4034—61no—
116C5×#103—32no—
117C5×#102—32no—
118#3967—31no—
119#3967—31no—
120#3964—31no—
121#3964—31no—
122#3950C2×D312yes—
123#3949C2×D312yes—
124#3946—32no—
125#3946—32no—
126#3940—32no—
127#3940—32no—
128#3084—151noSylow
129C23×C3×C5C2×D411yescharacteristic
130C22×C5×D3—21no—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×Q812yes—
133C2×C3×C4×C5#4112yes—
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15C2×D412yes—
136C2×Dic15C2×D412yes—
137C5×#67—24no—
138C2×C5×Dic3—21no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—81no—
141C5×D12—21no—
142C5×D12C2×Q812yes—
143C4×C5×D3—24no—
144C5×Dic6—21no—
145C5×Dic6C2×Q812yes—
146C2×C3×Dic5—22no—
147C2×C3×Dic5—21no—
148C2×C3×Dic5—21no—
149C2×C3×Dic5—81no—
150#1204—82no—
151D3×Dic5—82no—
152C3×C5×C8—22no—
153C3⋊#168—21no—
154C3⋊#168—21no—
155C2×#235C2×D511yescharacteristic
156C2×C3×M16C2×D511yescharacteristic
157C3×#117—51no—
158C2×C3×C4⋊C4—51no—
159C4×#67—102no—
160#926—51no—
161C2×C4⋊Dic3C2×D511yescharacteristic
162C22×C3⋊C8—51no—
163#893—52no—
164#892—101no—
165D3×C4⋊C4—101no—
166#890—52no—
167#888—52no—
168#887—52no—
169#878—102no—
170#870—101no—
171#869—101no—
172C3×#107—52no—
173C3×#106—52no—
174#821C2×D512yes—
175#816C2×D512yes—
176Dic3⋊C8—52no—
177Dic3⋊C8—52no—
178#810—51no—
179#810—51no—
180#809—51no—
181#809—51no—
182#808—52no—
183#808—52no—
184C5×#41—34no—
185C5×#41—62no—
186C2×C5×Q8—31no—
187C2×C5×D4—31no—
188C2×C5×D4—61no—
189C22×C4×C5—61no—
190C22×C4×C5—61no—
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—21no—
193C22×Dic5—62no—
194C2×Dic10—62no—
195C5×M16—22no—
196C2×C5×C8C22×D312yes—
197C5×C4⋊C4—32no—
198C5×C4⋊C4—61no—
199C22⋊Dic5—21no—
200C22⋊Dic5—32no—
201C22⋊Dic5—62no—
202C4⋊Dic5—21no—
203C4⋊Dic5—31no—
204C4⋊Dic5—31no—
205C4⋊Dic5—62no—
206C4⋊Dic5—62no—
207C4⋊Dic5C22×D312yes—
208C4⋊Dic5C22×D311yescharacteristic
209C4⋊Dic5C22×D311yescharacteristic
210#683—62no—
211#683—62no—
212C4×Dic5—21no—
213C4×Dic5—32no—
214C4×Dic5—62no—
215C2×#168—31no—
216C2×#168—31no—
217C2×#168—62no—
218#544—151no—
219#520—151no—
220#479—152no—
221#478—152no—
222#476—152no—
223#475—152no—
224#428—51no—
225C2×#106—151no—
226#424—151no—
227#417—31no—
228#416—151no—
229C22×C3×C5—21no—
230C22×C3×C5—21no—
231C22×C3×C5C22⋊Q812yes—
232C22×C3×C5C22×D411yescharacteristic
233C2×C5×D3—22no—
234C2×C5×D3—41no—
235C2×C5×D3—41no—
236C3×C4×C5C22⋊Q812yes—
237C3×C4×C5C22×Q811yescharacteristic
238C3×C4×C5C2×#4111yescharacteristic
239Dic15—22no—
240Dic15—22no—
241C3×Dic5—42no—
242C3×Dic5—41no—
243C3×Dic5—41no—
244C5×Dic3—22no—
245C5×Dic3—42no—
246C22×C3×C4—101no—
247C22×C3×C4C22×D511yescharacteristic
248C2×#67—21no—
249C22×Dic3—21no—
250#235—22no—
251#235Dic1014yescomplemented
252C2×D12C22×D511yescharacteristic
253C2×C4×D3—21no—
254C2×C4×D3—102no—
255C2×Dic6—102no—
256C2×Dic6C22×D511yescharacteristic
257C3×M16—22no—
258C2×C3×C8C22×D512yes—
259C3×C4⋊C4—52no—
260C3×C4⋊C4—51no—
261C3×C4⋊C4—51no—
262C3×C4⋊C4—101no—
263C3×C22⋊C4—101no—
264C3×C42—101no—
265#217—52no—
266(C2×D3)⋊C4—102no—
267C4⋊Dic3—21no—
268C4⋊Dic3—51no—
269C4⋊Dic3—51no—
270C4⋊Dic3—102no—
271C4⋊Dic3C22×D512yes—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274Dic3⋊C4—102no—
275C4×Dic3—52no—
276C4×Dic3—102no—
277C2×C3⋊C8—51no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8—102no—
280C23×C5—61no—
281C23×C5D3×D411yescharacteristic
282C5×Q8—32no—
283C5×Q8—61no—
284C5×D4—32no—
285C5×D4—64no—
286C5×D4—61no—
287C2×C4×C5—61no—
288C2×C4×C5—64no—
289C2×C4×C5—62no—
290C2×C4×C5—241no—
291C2×C4×C5#23512yes—
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5D3×Q812yes—
294C2×C4×C5C23×D311yescharacteristic
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—22no—
298C2×Dic5—32no—
299C2×Dic5—32no—
300C2×Dic5—81no—
301C2×Dic5—242no—
302Dic10—242no—
303C5×C8—22no—
304#168—61no—
305#168—61no—
306C2×#41—31no—
307C2×M16D3×D511yescharacteristic
308C22×C8—151no—
309C4⋊Q8—152no—
310C4⋊Q8—301no—
311#125—152no—
312#125—301no—
313C22⋊Q8—302no—
314C4×Q8—152no—
315C4×D4—152no—
316C4×D4—302no—
317#117—51no—
318#117—151no—
319#117—301no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—51no—
322C2×C4⋊C4—301no—
323#107—52no—
324#106—52no—
325#106—152no—
326#106—152no—
327C4⋊C8—152no—
328C4⋊C8—152no—
329#103—32no—
330#103—151no—
331#103—151no—
332#102—32no—
333#102—151no—
334#102—151no—
335C2×C3×C5—22no—
336C2×C3×C5C2×C22⋊Q811yescharacteristic
337C2×C3×C5#57711yescharacteristic
338C2×C3×C5#57711yescharacteristic
339C5×D3—42no—
340C23×C3D4×D511yescharacteristic
341C22×D3—21no—
342C2×C3×C4—102no—
343C2×C3×C4—101no—
344C2×C3×C4—101no—
345C2×C3×C4—401no—
346C2×C3×C4C2×Dic1012yes—
347C2×C3×C4D4×D511yescharacteristic
348C2×C3×C4#71112yes—
349C2×C3×C4C23×D511yescharacteristic
350#67—24no—
351C2×Dic3—21no—
352C2×Dic3—22no—
353C2×Dic3—52no—
354C2×Dic3—52no—
355C2×Dic3—81no—
356D12—21no—
357D12C2×Dic1012yes—
358C4×D3—24no—
359C4×D3—402no—
360Dic6—21no—
361Dic6—402no—
362Dic6C2×Dic1012yes—
363C3×C8—22no—
364C3⋊C8—101no—
365C3⋊C8—101no—
366C22×C5—21no—
367C22×C5—21no—
368C22×C5—62no—
369C22×C5—121no—
370C22×C5—121no—
371C22×C5#89612yes—
372C22×C5C2×D3×D411yescharacteristic
373C4×C5—62no—
374C4×C5—122no—
375C4×C5#89612yes—
376C4×C5C2×#23511yescharacteristic
377C4×C5C2×D3×Q811yescharacteristic
378Dic5—41no—
379Dic5—42no—
380Dic5—41no—
381Dic5—62no—
382Dic5—62no—
383#41—34no—
384#41—62no—
385C2×Q8—31no—
386C2×Q8—302no—
387C2×D4—31no—
388C2×D4—61no—
389C22×C4—61no—
390C22×C4—61no—
391C22×C4—101no—
392C22×C4—302no—
393C22×C4C2×D3×D511yescharacteristic
394M16—22no—
395C2×C8—151no—
396C2×C8—151no—
397C2×C8—302no—
398C2×C8C2×D3×D512yes—
399C4⋊C4—32no—
400C4⋊C4—51no—
401C4⋊C4—51no—
402C4⋊C4—52no—
403C4⋊C4—61no—
404C4⋊C4—101no—
405C4⋊C4—151no—
406C4⋊C4—151no—
407C4⋊C4—302no—
408C4⋊C4—302no—
409C4⋊C4—302no—
410C4⋊C4—302no—
411C22⋊C4—101no—
412C22⋊C4—152no—
413C22⋊C4—302no—
414C42—101no—
415C42—152no—
416C42—302no—
417C3×C5#308411yescharacteristic, complemented, Hall
418C22×C3—21no—
419C22×C3—21no—
420C22×C3#402412yes—
421C22×C3C2×D4×D511yescharacteristic
422C2×D3—22no—
423C2×D3—41no—
424C2×D3—41no—
425C3×C4—201no—
426C3×C4—202no—
427C3×C4—201no—
428C3×C4#402412yes—
429C3×C4C22×Dic1011yescharacteristic
430C3×C4C2×#71111yescharacteristic
431Dic3—22no—
432Dic3—42no—
433Dic3—102no—
434Dic3—102no—
435C2×C5—22no—
436C2×C5—122no—
437C2×C5C2×#89611yescharacteristic
438C2×C5#577511yescharacteristic
439C2×C5#577811yescharacteristic
440C23—61no—
441C23#677711yescharacteristic
442Q8—32no—
443Q8—61no—
444Q8—1202no—
445D4—32no—
446D4—64no—
447D4—61no—
448C2×C4—61no—
449C2×C4—64no—
450C2×C4—62no—
451C2×C4—101no—
452C2×C4—101no—
453C2×C4—102no—
454C2×C4—152no—
455C2×C4—152no—
456C2×C4—241no—
457C2×C4—401no—
458C2×C4—1202no—
459C2×C4D3×Dic1012yes—
460C2×C4#677711yescharacteristic
461C2×C4#678212yes—
462C2×C4C22×D3×D511yescharacteristic
463C8—22no—
464C8—301no—
465C8—301no—
466C2×C3—22no—
467C2×C3C2×#402411yescharacteristic
468C2×C3#6610911yescharacteristic
469C2×C3#6611211yescharacteristic
470D3—42no—
471C5#7924411yescharacteristic, complemented, Sylow
472C22—21no—
473C22—21no—
474C22—62no—
475C22—121no—
476C22—121no—
477C22#9143612yes—
478C22C2×#677711yescharacteristic
479C4—62no—
480C4—122no—
481C4—202no—
482C4—201no—
483C4—201no—
484C4—302no—
485C4—302no—
486C4#9143612yes—
487C4C2×D3×Dic1011yescharacteristic
488C4C2×#678211yescharacteristic
489C3#1061060411yescharacteristic, complemented, Sylow
490C2—22no—
491C2—122no—
492C2#1175403711yescharacteristic
493C2#1175403911yescharacteristic
494C2C2×#9143611yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
hypercenterC2×M16D3×D5
hypocenterC3×C5#3084
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #11754619C2semidirect
3. #11751220C2semidirect
5. C3×#65410C2semidirect
6. C2×#90986C2semidirect
8. #11747887C2semidirect
9. #11747881C2semidirect
10. #11747817C2semidirect
11. #11747808C2semidirect
47. #65410D3semidirect
58. C5×#235Q8semidirect
251. #235Dic10semidirect
417. C3×C5#3084semidirect
471. C5#79244semidirect
489. C3#10610604semidirect

Maximal subgroups

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

subgroupindex
#117546192
#117544922
#117512202
C5×#51332
C3×#654102
C2×#909862
#117483822
#117478872
#117478812
#117478172
#117478082
#106106043
#792445