Finite Group Databasebeta

← #14471611

Subgroups — #14471611

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756491C211yesmaximal, characteristic, complemented
2#11756302C211yesmaximal, characteristic, complemented
3C3×C5×#461C211yesmaximal, characteristic, complemented
4#11751266C212yesmaximal
5SD16×Dic15C212yesmaximal, complemented
6#11751180C211yesmaximal, characteristic, complemented
7C4×#6715C211yesmaximal, characteristic
8#11750943C211yesmaximal, characteristic, complemented
9#11750931C211yesmaximal, characteristic, complemented
10#11750901C212yesmaximal, complemented
11#11750900C212yesmaximal, complemented
12#10612146—31nomaximal, Hall
13C2×C3×C5×SD16C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16#91836C2212yes—
17Q8×Dic15C2212yes—
18D4×Dic15C2212yes—
19C2×#6715C2211yescharacteristic
20C2×C4⋊Dic15—21no—
21#91813—21no—
22#91787—22no—
23#91786—21no—
24#91781—21no—
25#91779C2212yes—
26#91767—22no—
27C4×D60C2211yescharacteristic
28#91758C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31C3×C5×#103C2212yes—
32#91119C2212yes—
33#91119C2212yes—
34#91116C2211yescharacteristic
35#91105C2212yes—
36#91101C2212yes—
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91093C2211yescharacteristic
40#91091C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#80415—51nomaximal, Hall
43#66066—31no—
44#65877—31no—
45C5×#461D311yescharacteristic, complemented
46#65454—32no—
47SD16×Dic5—32no—
48#65370—31no—
49C4×#686—31no—
50#65131—31no—
51#65119—31no—
52#65089—32no—
53#65088—32no—
54C2×C3×C5×Q8C2312yes—
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C22×Dic15—22no—
58C2×D60C2311yescharacteristic
59C2×C4×D15—21no—
60C2×Dic30—21no—
61C2×Dic30D411yescharacteristic
62C3×C5×SD16—24no—
63C2×C3×C5×C8C2312yes—
64C3×C5×C4⋊C4—21no—
65C3×C5×C4⋊C4—21no—
66C3×C5×C4⋊C4C2311yescharacteristic
67C3×C5×C22⋊C4—21no—
68C3×C42×C5C2311yescharacteristic
69#6719—22no—
70#6715—22no—
71#6714—21no—
72#6714—22no—
73#6714—22no—
74C4⋊Dic15—21no—
75C4⋊Dic15—22no—
76C4⋊Dic15—22no—
77C4⋊Dic15D411yescharacteristic
78C4⋊Dic15C2312yes—
79C4⋊Dic15C2311yescharacteristic
80#6712—22no—
81#6712D412yes—
82C4×Dic15—22no—
83C4×Dic15C2312yes—
84C2×C3⋊#168C2311yescharacteristic
85C2×C3⋊#168C2311yescharacteristic
86#5732—51no—
87#5543—51no—
88C3×#461D511yescharacteristic, complemented
89#5165—52no—
90Dic3×SD16—52no—
91#5079—51no—
92C4×#213—51no—
93#4842—51no—
94#4830—51no—
95#4800—52no—
96#4799—52no—
97C2×C5×SD16C2×D312yes—
98C5×C4⋊Q8C2×D311yescharacteristic
99C4×C5×D4C2×D311yescharacteristic
100#4093—32no—
101Q8×Dic5—32no—
102D4×Dic5—32no—
103C2×#686—31no—
104C2×C4⋊Dic5—61no—
105#4070—61no—
106#4044—62no—
107#4043—61no—
108#4038—61no—
109#4036—32no—
110#4024—62no—
111C4×D20—31no—
112#4015—31no—
113C4×Dic10—31no—
114C5×C4⋊C8C2×D311yescharacteristic
115C5×#103C2×D312yes—
116#3967—32no—
117#3967—32no—
118#3964—31no—
119#3953—32no—
120#3949—32no—
121#3946—32no—
122C8×Dic5—32no—
123#3941—31no—
124#3939—31no—
125C4×#168—31no—
126#3360—151noSylow
127C23×C3×C5—21no—
128C22×D15—21no—
129C3×C5×Q8—22no—
130C3×C5×Q8—22no—
131C3×C5×D4—21no—
132C3×C5×D4#4112yes—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—42no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139C2×Dic15—21no—
140C2×Dic15—22no—
141C2×Dic15—82no—
142C2×Dic15C2×D412yes—
143C2×Dic15C2×D412yes—
144D60—21no—
145D60—21no—
146C4×D15—42no—
147Dic30—22no—
148Dic30—81no—
149C3×C5×C8—22no—
150C3⋊#168—21no—
151C3⋊#168—21no—
152C2×C3×SD16C2×D512yes—
153C3×C4⋊Q8C2×D511yescharacteristic
154C3×C4×D4C2×D511yescharacteristic
155#947—52no—
156Q8×Dic3—52no—
157D4×Dic3—52no—
158C2×#213—51no—
159C2×C4⋊Dic3—101no—
160#924—101no—
161#898—102no—
162#897—101no—
163#892—101no—
164#890—52no—
165#878—102no—
166C4×D12—51no—
167#869—51no—
168C4×Dic6—51no—
169C3×C4⋊C8C2×D511yescharacteristic
170C3×#103C2×D512yes—
171#835—52no—
172#835—52no—
173#832—51no—
174#821—52no—
175#817—52no—
176Dic3⋊C8—52no—
177C8×Dic3—52no—
178#809—51no—
179#807—51no—
180C4×C3⋊C8—51no—
181C2×C5×Q8C22×D312yes—
182C2×C5×D4C22×D311yescharacteristic
183C22×C4×C5—21no—
184C22×Dic5—62no—
185C2×D20—31no—
186C2×C4×D5—61no—
187C2×Dic10—31no—
188C2×Dic10—61no—
189C5×SD16—24no—
190C2×C5×C8C22×D312yes—
191C5×C4⋊C4—21no—
192C5×C4⋊C4—21no—
193C5×C4⋊C4C22×D311yescharacteristic
194C5×C22⋊C4—21no—
195C42×C5C22×D311yescharacteristic
196C22⋊Dic5—62no—
197#686—62no—
198#685—62no—
199#685—62no—
200#685—61no—
201C4⋊Dic5—31no—
202C4⋊Dic5—31no—
203C4⋊Dic5—32no—
204C4⋊Dic5—62no—
205C4⋊Dic5—62no—
206C4⋊Dic5—61no—
207#683—32no—
208#683—62no—
209C4×Dic5—32no—
210C4×Dic5—62no—
211C2×#168—31no—
212C2×#168—31no—
213#556—151no—
214#554—151no—
215#488—152no—
216#487—151no—
217#479—152no—
218#476—151no—
219#463—152no—
220#461D1511yescharacteristic, complemented
221C8×Q8—151no—
222C4×SD16—152no—
223C4×D8—151no—
224C22×C3×C5—22no—
225C22×C3×C5—41no—
226C22×C3×C5—41no—
227C22×C3×C5C22×D411yescharacteristic
228C2×D15—41no—
229C2×D15—41no—
230C2×D15—41no—
231C3×C4×C5—21no—
232C3×C4×C5—42no—
233C3×C4×C5—41no—
234C3×C4×C5#13512yes—
235C3×C4×C5C2×#4111yescharacteristic
236C3×C4×C52−1+411yescharacteristic
237Dic15—22no—
238Dic15—22no—
239Dic15—41no—
240Dic15—42no—
241C2×C3×Q8C22×D512yes—
242C2×C3×D4C22×D511yescharacteristic
243C22×C3×C4—21no—
244C22×Dic3—102no—
245C2×D12—51no—
246C2×C4×D3—101no—
247C2×Dic6—51no—
248C2×Dic6—101no—
249C3×SD16—24no—
250C2×C3×C8C22×D512yes—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4C22×D511yescharacteristic
254C3×C22⋊C4—21no—
255C3×C42C22×D511yescharacteristic
256#217—102no—
257#213—102no—
258(C2×D3)⋊C4—102no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—101no—
261C4⋊Dic3—51no—
262C4⋊Dic3—51no—
263C4⋊Dic3—52no—
264C4⋊Dic3—102no—
265C4⋊Dic3—102no—
266C4⋊Dic3—101no—
267Dic3⋊C4—52no—
268Dic3⋊C4—102no—
269C4×Dic3—52no—
270C4×Dic3—102no—
271C2×C3⋊C8—51no—
272C2×C3⋊C8—51no—
273C23×C5—21no—
274C22×D5—61no—
275C5×Q8—22no—
276C5×Q8—22no—
277C5×D4—21no—
278C5×D4#23712yes—
279C2×C4×C5—22no—
280C2×C4×C5—21no—
281C2×C4×C5—42no—
282C2×C4×C5D3×D411yescharacteristic
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5C23×D311yescharacteristic
285C2×Dic5—32no—
286C2×Dic5—32no—
287C2×Dic5—61no—
288C2×Dic5—62no—
289C2×Dic5—242no—
290D20—61no—
291D20—61no—
292C4×D5—122no—
293Dic10—62no—
294Dic10—241no—
295C5×C8—22no—
296#168—61no—
297#168—61no—
298C2×SD16C2×D1512yes—
299C2×D8—151no—
300C4⋊Q8—151no—
301C4⋊Q8C2×D1511yescharacteristic
302#126—302no—
303#125—152no—
304#124—152no—
305C22⋊Q8—302no—
306C22⋊Q8—301no—
307C22⋊Q8—301no—
308C4×Q8—151no—
309C4×Q8—152no—
310C4×D4—152no—
311C4×D4—151no—
312C4×D4C2×D1511yescharacteristic
313#117—301no—
314C2×C4⋊C4—301no—
315#107—151no—
316#106—152no—
317C4⋊C8—152no—
318C4⋊C8C2×D1511yescharacteristic
319#103—152no—
320#103—152no—
321#103C2×D1512yes—
322#102—151no—
323#102—152no—
324#102—151no—
325C4×C8—152no—
326C4×C8—151no—
327C2×C3×C5—42no—
328C2×C3×C5#54811yescharacteristic
329C2×C3×C5C2×#13511yescharacteristic
330C2×C3×C5#57711yescharacteristic
331D15—81no—
332C23×C3—21no—
333C22×D3—101no—
334C3×Q8—22no—
335C3×Q8—22no—
336C3×D4—21no—
337C3×D4#71112yes—
338C2×C3×C4—22no—
339C2×C3×C4—21no—
340C2×C3×C4—42no—
341C2×C3×C4D4×D511yescharacteristic
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4C23×D511yescharacteristic
344C2×Dic3—52no—
345C2×Dic3—52no—
346C2×Dic3—101no—
347C2×Dic3—102no—
348C2×Dic3—402no—
349D12—101no—
350D12—101no—
351C4×D3—202no—
352Dic6—102no—
353Dic6—401no—
354C3×C8—22no—
355C3⋊C8—101no—
356C3⋊C8—101no—
357C22×C5—22no—
358C22×C5—41no—
359C22×C5—41no—
360C22×C5C2×D3×D411yescharacteristic
361C2×D5—121no—
362C2×D5—121no—
363C2×D5—121no—
364C4×C5—21no—
365C4×C5—41no—
366C4×C5—42no—
367C4×C5#91612yes—
368C4×C5C2×#23711yescharacteristic
369C4×C5#101011yescharacteristic
370Dic5—62no—
371Dic5—62no—
372Dic5—121no—
373Dic5—122no—
374C2×Q8—151no—
375C2×Q8—301no—
376C2×Q8C22×D1512yes—
377C2×D4—151no—
378C2×D4C22×D1511yescharacteristic
379C22×C4—21no—
380C22×C4—302no—
381C22×C4—301no—
382SD16—24no—
383D8—302no—
384C2×C8—151no—
385C2×C8—151no—
386C2×C8C22×D1512yes—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—151no—
390C4⋊C4—152no—
391C4⋊C4—152no—
392C4⋊C4—151no—
393C4⋊C4—302no—
394C4⋊C4—302no—
395C4⋊C4—302no—
396C4⋊C4—301no—
397C4⋊C4C22×D1511yescharacteristic
398C22⋊C4—21no—
399C22⋊C4—302no—
400C22⋊C4—302no—
401C22⋊C4—302no—
402C22⋊C4—301no—
403C42—152no—
404C42—302no—
405C42C22×D1511yescharacteristic
406C3×C5#336011yescharacteristic, complemented, Hall
407C22×C3—22no—
408C22×C3—41no—
409C22×C3—41no—
410C22×C3C2×D4×D511yescharacteristic
411C2×D3—201no—
412C2×D3—201no—
413C2×D3—201no—
414C3×C4—21no—
415C3×C4—41no—
416C3×C4—42no—
417C3×C4#406212yes—
418C3×C4C2×#71111yescharacteristic
419C3×C4#415011yescharacteristic
420Dic3—102no—
421Dic3—102no—
422Dic3—201no—
423Dic3—202no—
424C2×C5—42no—
425C2×C5#559811yescharacteristic
426C2×C5C2×#91611yescharacteristic
427C2×C5#577811yescharacteristic
428D5—241no—
429C23—21no—
430C23—301no—
431Q8—22no—
432Q8—22no—
433Q8—302no—
434Q8—1201no—
435D4—21no—
436D4—301no—
437D4—301no—
438D4#681912yes—
439C2×C4—22no—
440C2×C4—21no—
441C2×C4—42no—
442C2×C4—152no—
443C2×C4—152no—
444C2×C4—301no—
445C2×C4—302no—
446C2×C4—602no—
447C2×C4—1202no—
448C2×C4D4×D1511yescharacteristic
449C2×C4D4×D1511yescharacteristic
450C2×C4C23×D1511yescharacteristic
451C8—22no—
452C8—301no—
453C8—301no—
454C2×C3—42no—
455C2×C3#6593211yescharacteristic
456C2×C3C2×#406211yescharacteristic
457C2×C3#6611211yescharacteristic
458D3—401no—
459C5#8041511yescharacteristic, complemented, Sylow
460C22—22no—
461C22—41no—
462C22—41no—
463C22—601no—
464C22—601no—
465C22—601no—
466C22C2×D4×D1511yescharacteristic
467C4—21no—
468C4—42no—
469C4—41no—
470C4—302no—
471C4—302no—
472C4—601no—
473C4—602no—
474C4#9180512yes—
475C4C2×#681911yescharacteristic
476C4#9210111yescharacteristic
477C3#1061214611yescharacteristic, complemented, Sylow
478C2—42no—
479C2—1201no—
480C2#1175635711yescharacteristic
481C2C2×#9180511yescharacteristic
482C2#1175653711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#461C2
socleC22×C3×C5C22×D4
prime radicalC2×#6715C22
hypercenter#461D15
hypocenterC3×C5#3360
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #11756491C2semidirect
2. #11756302C2semidirect
3. C3×C5×#461C2semidirect
5. SD16×Dic15C2semidirect
6. #11751180C2semidirect
8. #11750943C2semidirect
9. #11750931C2semidirect
10. #11750901C2semidirect
11. #11750900C2semidirect
45. C5×#461D3semidirect
88. C3×#461D5semidirect
220. #461D15semidirect
406. C3×C5#3360semidirect
459. C5#80415semidirect
477. C3#10612146semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117563022
C3×C5×#4612
#117512662
SD16×Dic152
#117511802
C4×#67152
#117509432
#117509312
#117509012
#117509002
#106121463
#804155