Finite Group Databasebeta

← #14471902

Subgroups — #14471902

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#11756477C211yesmaximal, characteristic
2Q8×Dic30C211yesmaximal, characteristic, complemented
3C3×C5×#460C211yesmaximal, characteristic, complemented
4#11751264C212yesmaximal, complemented
5SD16×Dic15C212yesmaximal, complemented
6#11751171C211yesmaximal, characteristic, complemented
7C4×#6717C211yesmaximal, characteristic, complemented
8#11750943C211yesmaximal, characteristic, complemented
9#11750931C211yesmaximal, characteristic, complemented
10#11750862C212yesmaximal, complemented
11#11750861C212yesmaximal, complemented
12#10612100—31nomaximal, Hall
13C2×#6819—21no—
14C2×C3×C5×SD16C2212yes—
15C3×C5×#127C2211yescharacteristic
16C3×C4×C5×Q8C2211yescharacteristic
17Q8×Dic15C2212yes—
18C2×#6717C2211yescharacteristic
19#91829C2212yes—
20#91828—22no—
21#91827—21no—
22D4×Dic15C2212yes—
23#91777—22no—
24#91777C2212yes—
25C4×D60C2211yescharacteristic
26#91758—21no—
27#91758C2211yescharacteristic
28C4×Dic30—21no—
29C4×Dic30C2211yescharacteristic
30C3×C5×C4⋊C8C2211yescharacteristic
31C3×C5×#102C2212yes—
32#91119C2211yescharacteristic
33#91116C2212yes—
34#91116C2212yes—
35#91105C2212yes—
36#91101C2212yes—
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91093C2211yescharacteristic
40#91092C2211yescharacteristic
41C4×C3⋊#168C2211yescharacteristic
42#80369—51nomaximal, Hall
43#66052—31no—
44Q8×Dic10—31no—
45C5×#460D311yescharacteristic, complemented
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×C3×C5×D4—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4C2312yes—
58C2×#1220—22no—
59C2×#1220—22no—
60C22×Dic15—22no—
61#6819—44no—
62C2×D60C2311yescharacteristic
63C2×C4×D15—21no—
64C2×Dic30—21no—
65C2×Dic30—22no—
66C2×Dic30D411yescharacteristic
67C3×C5×SD16—24no—
68C2×C3×C5×C8C2312yes—
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C42×C5—21no—
72C3×C42×C5C2311yescharacteristic
73#6719—22no—
74#6717—22no—
75#6714—21no—
76C4⋊Dic15—21no—
77C4⋊Dic15—22no—
78C4⋊Dic15D411yescharacteristic
79C4⋊Dic15C2312yes—
80C4⋊Dic15C2311yescharacteristic
81#6712—22no—
82#6712D412yes—
83C4×Dic15—22no—
84C4×Dic15C2312yes—
85C2×C3⋊#168C2311yescharacteristic
86C2×C3⋊#168C2311yescharacteristic
87#5718—51no—
88Q8×Dic6—51no—
89C3×#460D511yescharacteristic, complemented
90#5163—52no—
91Dic3×SD16—52no—
92#5070—51no—
93C4×#215—51no—
94#4842—51no—
95#4830—51no—
96#4761—52no—
97#4760—52no—
98C2×#711—61no—
99C2×C5×SD16C2×D312yes—
100C5×#127C2×D311yescharacteristic
101C4×C5×Q8C2×D311yescharacteristic
102Q8×Dic5—32no—
103C2×#688—31no—
104#4086—32no—
105#4085—62no—
106#4084—61no—
107D4×Dic5—32no—
108#4034—32no—
109#4034—62no—
110C4×D20—31no—
111#4015—31no—
112#4015—61no—
113C4×Dic10—31no—
114C4×Dic10—61no—
115C5×C4⋊C8C2×D311yescharacteristic
116C5×#102C2×D312yes—
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
128C23×C3×C5—22no—
129C22×D15—21no—
130C3×C5×Q8—21no—
131C3×C5×Q8#4112yescomplemented
132C3×C5×D4—22no—
133C3×C5×D4—22no—
134C3×C5×D4—42no—
135C3×C5×D4—81no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2411yescharacteristic
141#1220—44no—
142#1220—82no—
143C2×Dic15—22no—
144C2×Dic15—21no—
145C2×Dic15—44no—
146C2×Dic15C2×D412yes—
147C2×Dic15C2×D412yes—
148D60—21no—
149D60—21no—
150C4×D15—42no—
151Dic30—82no—
152Dic30—81no—
153Dic30SD1614yescomplemented
154C3×C5×C8—22no—
155C3⋊#168—21no—
156C3⋊#168—21no—
157C2×#237—101no—
158C2×C3×SD16C2×D512yes—
159C3×#127C2×D511yescharacteristic
160C3×C4×Q8C2×D511yescharacteristic
161Q8×Dic3—52no—
162C2×#215—51no—
163#940—52no—
164#939—102no—
165#938—101no—
166D4×Dic3—52no—
167#888—52no—
168#888—102no—
169C4×D12—51no—
170#869—51no—
171#869—101no—
172C4×Dic6—51no—
173C4×Dic6—101no—
174C3×C4⋊C8C2×D511yescharacteristic
175C3×#102C2×D512yes—
176#835—51no—
177#832—52no—
178#832—52no—
179#821—52no—
180#817—52no—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809—51no—
184#808—51no—
185C4×C3⋊C8—51no—
186C2×C5×Q8C22×D311yescharacteristic
187C2×C5×D4—21no—
188C2×C5×D4—21no—
189C2×C5×D4C22×D312yes—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192C22×Dic5—62no—
193#711—124no—
194C2×D20—31no—
195C2×C4×D5—61no—
196C2×Dic10—31no—
197C2×Dic10—62no—
198C2×Dic10—61no—
199C5×SD16—24no—
200C2×C5×C8C22×D312yes—
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—31no—
209C4⋊Dic5—31no—
210C4⋊Dic5—32no—
211C4⋊Dic5—62no—
212C4⋊Dic5—61no—
213#683—32no—
214#683—62no—
215C4×Dic5—32no—
216C4×Dic5—62no—
217C2×#168—31no—
218C2×#168—31no—
219Q82—151no—
220#550—151no—
221#486—151no—
222#486—152no—
223#476—151no—
224#476—152no—
225#460—152no—
226#460D1511yescharacteristic, complemented
227C8×Q8—151no—
228C4×SD16—152no—
229C4×SD16—151no—
230C22×C3×C5—42no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5C22×D411yescharacteristic
234C2×D15—41no—
235C2×D15—41no—
236C2×D15—41no—
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—22no—
244Dic15—41no—
245Dic15—42no—
246Dic15C2×SD1614yes—
247C2×C3×Q8C22×D511yescharacteristic
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4C22×D512yes—
251C2×#67—102no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—204no—
255C2×D12—51no—
256C2×C4×D3—101no—
257C2×Dic6—51no—
258C2×Dic6—102no—
259C2×Dic6—101no—
260C3×SD16—24no—
261C2×C3×C8C22×D512yes—
262C3×C4⋊C4—21no—
263C3×C4⋊C4C22×D511yescharacteristic
264C3×C42—21no—
265C3×C42C22×D511yescharacteristic
266#217—102no—
267#215—102no—
268(C2×D3)⋊C4—101no—
269C4⋊Dic3—51no—
270C4⋊Dic3—51no—
271C4⋊Dic3—52no—
272C4⋊Dic3—102no—
273C4⋊Dic3—101no—
274Dic3⋊C4—52no—
275Dic3⋊C4—102no—
276C4×Dic3—52no—
277C4×Dic3—102no—
278C2×C3⋊C8—51no—
279C2×C3⋊C8—51no—
280C23×C5—22no—
281C22×D5—61no—
282C5×Q8—21no—
283C5×Q8#23712yescomplemented
284C5×D4—22no—
285C5×D4—22no—
286C5×D4—42no—
287C5×D4—81no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5D3×D411yescharacteristic
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C22⋊D5—124no—
294C22⋊D5—242no—
295C2×Dic5—32no—
296C2×Dic5—32no—
297C2×Dic5—62no—
298C2×Dic5—61no—
299C2×Dic5—124no—
300D20—61no—
301D20—61no—
302C4×D5—122no—
303Dic10—34no—
304Dic10—242no—
305Dic10—241no—
306C5×C8—22no—
307#168—61no—
308#168—61no—
309C2×#41—301no—
310C2×SD16—151no—
311C2×SD16C2×D1512yes—
312C4⋊Q8—152no—
313C4⋊Q8—151no—
314C4⋊Q8—301no—
315C4⋊Q8—302no—
316#127—152no—
317#127C2×D1511yescharacteristic
318#121—301no—
319#121—302no—
320C4×Q8—151no—
321C4×Q8—152no—
322C4×Q8—301no—
323C4×Q8C2×D1511yescharacteristic
324C4×D4—152no—
325C4×D4—151no—
326#106—152no—
327#106—151no—
328C4⋊C8—152no—
329C4⋊C8C2×D1511yescharacteristic
330#103—151no—
331#102—152no—
332#102—152no—
333#102—152no—
334#102—151no—
335#102C2×D1512yes—
336C4×C8—152no—
337C4×C8—151no—
338C2×C3×C5—82no—
339C2×C3×C5#54811yescharacteristic
340C2×C3×C5C22×SD1611yescharacteristic
341C2×C3×C5#57611yescharacteristic
342D15—81no—
343C23×C3—22no—
344C22×D3—101no—
345C3×Q8—21no—
346C3×Q8#71112yescomplemented
347C3×D4—22no—
348C3×D4—22no—
349C3×D4—42no—
350C3×D4—81no—
351C2×C3×C4—21no—
352C2×C3×C4—21no—
353C2×C3×C4D4×D511yescharacteristic
354C2×C3×C4D4×D511yescharacteristic
355C2×C3×C4C23×D511yescharacteristic
356#67—204no—
357#67—402no—
358C2×Dic3—52no—
359C2×Dic3—52no—
360C2×Dic3—102no—
361C2×Dic3—101no—
362C2×Dic3—204no—
363D12—101no—
364D12—101no—
365C4×D3—202no—
366Dic6—54no—
367Dic6—402no—
368Dic6—401no—
369C3×C8—22no—
370C3⋊C8—101no—
371C3⋊C8—101no—
372C22×C5—42no—
373C22×C5—42no—
374C22×C5—42no—
375C22×C5C2×D3×D411yescharacteristic
376C2×D5—121no—
377C2×D5—121no—
378C2×D5—121no—
379C4×C5—21no—
380C4×C5—22no—
381C4×C5—41no—
382C4×C5D3×SD1612yes—
383C4×C5C2×#23711yescharacteristic
384C4×C5#101011yescharacteristic
385Dic5—34no—
386Dic5—62no—
387Dic5—121no—
388Dic5—122no—
389#41—604no—
390C2×Q8—151no—
391C2×Q8—302no—
392C2×Q8—301no—
393C2×Q8C22×D1511yescharacteristic
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—151no—
397C2×D4—302no—
398C2×D4—302no—
399C2×D4C22×D1512yes—
400C22×C4—302no—
401C22×C4—301no—
402SD16—24no—
403SD16—302no—
404C2×C8—151no—
405C2×C8—151no—
406C2×C8C22×D1512yes—
407C4⋊C4—21no—
408C4⋊C4—152no—
409C4⋊C4—151no—
410C4⋊C4—152no—
411C4⋊C4—151no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C22×D1511yescharacteristic
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—21no—
419C42—152no—
420C42—302no—
421C42C22×D1511yescharacteristic
422C3×C5#336211yescharacteristic, complemented, Hall
423C22×C3—42no—
424C22×C3—42no—
425C22×C3—42no—
426C22×C3C2×D4×D511yescharacteristic
427C2×D3—201no—
428C2×D3—201no—
429C2×D3—201no—
430C3×C4—21no—
431C3×C4—22no—
432C3×C4—41no—
433C3×C4D5×SD1612yes—
434C3×C4C2×#71111yescharacteristic
435C3×C4#415011yescharacteristic
436Dic3—54no—
437Dic3—102no—
438Dic3—201no—
439Dic3—202no—
440C2×C5—82no—
441C2×C5#559811yescharacteristic
442C2×C5C2×D3×SD1611yescharacteristic
443C2×C5#577411yescharacteristic
444D5—241no—
445C23—22no—
446C23—301no—
447Q8—21no—
448Q8—154no—
449Q8—1201no—
450Q8—1202no—
451Q8#681912yescomplemented
452D4—22no—
453D4—22no—
454D4—42no—
455D4—81no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—1202no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—152no—
463C2×C4—152no—
464C2×C4—302no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D4×D1511yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C2×C4C23×D1511yescharacteristic
471C8—22no—
472C8—301no—
473C8—301no—
474C2×C3—82no—
475C2×C3#6593211yescharacteristic
476C2×C3C2×D5×SD1611yescharacteristic
477C2×C3#6610811yescharacteristic
478D3—401no—
479C5#8036911yescharacteristic, complemented, Sylow
480C22—42no—
481C22—42no—
482C22—42no—
483C22—601no—
484C22—601no—
485C22—601no—
486C22C2×D4×D1511yescharacteristic
487C4—22no—
488C4—21no—
489C4—41no—
490C4—154no—
491C4—302no—
492C4—601no—
493C4—602no—
494C4SD16×D1512yes—
495C4C2×#681911yescharacteristic
496C4#9210111yescharacteristic
497C3#1061210011yescharacteristic, complemented, Sylow
498C2—82no—
499C2—1201no—
500C2#1175635711yescharacteristic
501C2C2×SD16×D1511yescharacteristic
502C2#1175653311yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#460C2
socleC22×C3×C5C22×D4
prime radical#11756477C2
hypercenter#460D15
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
2. Q8×Dic30C2semidirect
3. C3×C5×#460C2semidirect
4. #11751264C2semidirect
5. SD16×Dic15C2semidirect
6. #11751171C2semidirect
7. C4×#6717C2semidirect
8. #11750943C2semidirect
9. #11750931C2semidirect
10. #11750862C2semidirect
11. #11750861C2semidirect
45. C5×#460D3semidirect
89. C3×#460D5semidirect
131. C3×C5×Q8#41semidirect
153. Dic30SD16semidirect
226. #460D15semidirect
283. C5×Q8#237semidirect
346. C3×Q8#711semidirect
422. C3×C5#3362semidirect
451. Q8#6819semidirect
479. C5#80369semidirect
497. C3#10612100semidirect

Maximal subgroups

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

subgroupindex
#117564772
Q8×Dic302
C3×C5×#4602
#117512642
SD16×Dic152
#117511712
C4×#67172
#117509432
#117509312
#117508622
#117508612
#106121003
#803695