Finite Group Databasebeta

← #14471908

Subgroups — #14471908

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#11756481C211yesmaximal, characteristic, complemented
2#11756477C211yesmaximal, characteristic
3C3×C5×#486C211yesmaximal, characteristic, complemented
4#11751185C211yesmaximal, characteristic, complemented
5#11751176C211yesmaximal, characteristic, complemented
6#11750863C212yesmaximal, complemented
7#11750862C212yesmaximal, complemented
8#11750861C212yesmaximal, complemented
9#11750859C212yesmaximal, complemented
10C4×#6706C211yesmaximal, characteristic, complemented
11C8×Dic30C211yesmaximal, characteristic, complemented
12#10613319—31nomaximal, Hall
13C2×#6819—21no—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C5×#127C2211yescharacteristic
16#91833—22no—
17#91829C2212yes—
18#91828—22no—
19#91827—21no—
20D4×Dic15C2212yes—
21C2×#6716C2212yes—
22C2×#6706C2211yescharacteristic
23#91777—21no—
24#91777C2212yes—
25#91776—21no—
26#91776C2212yes—
27C4×D60C2211yescharacteristic
28C4×Dic30C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C3×C5×#102C2212yes—
31C3×C5×#102C2212yes—
32C3×C4×C5×C8C2211yescharacteristic
33#91116C2212yes—
34#91105C2211yescharacteristic
35#91101C2211yescharacteristic
36#91100C2211yescharacteristic
37#91098C2212yes—
38C8×Dic15C2212yes—
39#91093C2212yes—
40#91092C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#81588—51nomaximal, Hall
43#66056—31no—
44#66052—31no—
45C5×#486D311yescharacteristic, complemented
46#65373—31no—
47#65364—31no—
48#65051—32no—
49#65050—32no—
50#65049—32no—
51#65047—32no—
52C4×#677—31no—
53C8×Dic10—31no—
54C2×C3×C5×Q8—21no—
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—22no—
65C2×Dic30D411yescharacteristic
66C2×Dic30C2311yescharacteristic
67C2×C3×C5×C8C2311yescharacteristic
68C2×C3×C5×C8C2311yescharacteristic
69C3×C5×C4⋊C4—21no—
70C3×C5×C4⋊C4C2312yes—
71C3×C42×C5C2311yescharacteristic
72#6719—22no—
73#6716—24no—
74#6714—21no—
75C4⋊Dic15D411yescharacteristic
76C4⋊Dic15C2311yescharacteristic
77C4⋊Dic15C2311yescharacteristic
78#6712—21no—
79#6712—22no—
80#6712—22no—
81#6712D412yes—
82C4×Dic15—21no—
83C4×Dic15—22no—
84C4×Dic15C2312yes—
85C2×C3⋊#168C2312yes—
86#6706—22no—
87#5722—51no—
88#5718—51no—
89C3×#486D511yescharacteristic, complemented
90#5084—51no—
91#5075—51no—
92#4762—52no—
93#4761—52no—
94#4760—52no—
95#4758—52no—
96C4×#204—51no—
97C8×Dic6—51no—
98C2×#711—61no—
99C5×C4⋊Q8C2×D311yescharacteristic
100C5×#127C2×D311yescharacteristic
101#4090—62no—
102#4086—32no—
103#4085—62no—
104#4084—61no—
105D4×Dic5—32no—
106C2×#687—32no—
107C2×#677—31no—
108#4034—32no—
109#4034—61no—
110#4033—32no—
111#4033—61no—
112C4×D20—31no—
113C4×Dic10—31no—
114C4×Dic10—31no—
115C5×#102C2×D312yes—
116C5×#102C2×D312yes—
117C4×C5×C8C2×D311yescharacteristic
118#3964—32no—
119#3953—31no—
120#3949—31no—
121#3948—31no—
122#3946—32no—
123C8×Dic5—32no—
124#3941—32no—
125#3940—32no—
126C4⋊#168—31no—
127#3362—151noSylow
128C23×C3×C5—22no—
129C22×D15—21no—
130C3×C5×Q8—81no—
131C3×C5×D4—22no—
132C3×C5×D4—22no—
133C3×C5×D4—42no—
134C3×C5×D4—81no—
135C2×C3×C4×C5—22no—
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2411yescharacteristic
139#1220—44no—
140#1220—82no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15—21no—
144C2×Dic15—44no—
145C2×Dic15C2×D412yes—
146C2×Dic15C2×D412yes—
147D60—21no—
148D60—21no—
149C4×D15—42no—
150Dic30—21no—
151Dic30—82no—
152Dic30SD1614yescomplemented
153Dic30#4112yescomplemented
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C3⋊#168—22no—
157C2×#237—101no—
158C3×C4⋊Q8C2×D511yescharacteristic
159C3×#127C2×D511yescharacteristic
160#944—102no—
161#940—52no—
162#939—102no—
163#938—101no—
164D4×Dic3—52no—
165C2×#214—52no—
166C2×#204—51no—
167#888—52no—
168#888—101no—
169#887—52no—
170#887—101no—
171C4×D12—51no—
172C4×Dic6—51no—
173C4×Dic6—51no—
174C3×#102C2×D512yes—
175C3×#102C2×D512yes—
176C3×C4×C8C2×D511yescharacteristic
177#832—52no—
178#821—51no—
179#817—51no—
180#816—51no—
181Dic3⋊C8—52no—
182C8×Dic3—52no—
183#809—52no—
184#808—52no—
185C4⋊(C3⋊C8)—51no—
186C2×C5×Q8—21no—
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—31no—
198C2×Dic10—62no—
199C2×C5×C8C22×D311yescharacteristic
200C2×C5×C8C22×D311yescharacteristic
201C5×C4⋊C4—21no—
202C5×C4⋊C4C22×D312yes—
203C42×C5C22×D311yescharacteristic
204C22⋊Dic5—62no—
205#687—64no—
206#685—61no—
207C4⋊Dic5—31no—
208C4⋊Dic5—31no—
209C4⋊Dic5—31no—
210#683—32no—
211#683—62no—
212#683—62no—
213#683—61no—
214C4×Dic5—32no—
215C4×Dic5—62no—
216C4×Dic5—61no—
217C2×#168—32no—
218#677—62no—
219Q82—151no—
220#550—151no—
221#486—152no—
222#486D1511yescharacteristic, complemented
223#476—151no—
224#476—152no—
225#460—151no—
226#460—152no—
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—21no—
238C3×C4×C5—42no—
239C3×C4×C5C2×SD1612yes—
240C3×C4×C5C2×#4111yescharacteristic
241C3×C4×C52−1+411yescharacteristic
242Dic15—22no—
243Dic15—22no—
244Dic15—41no—
245Dic15—41no—
246Dic15C2×SD1614yes—
247C2×C3×Q8—21no—
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—51no—
259C2×Dic6—102no—
260C2×C3×C8C22×D511yescharacteristic
261C2×C3×C8C22×D511yescharacteristic
262C3×C4⋊C4—21no—
263C3×C4⋊C4C22×D512yes—
264C3×C42C22×D511yescharacteristic
265#217—102no—
266#214—104no—
267(C2×D3)⋊C4—101no—
268C4⋊Dic3—51no—
269C4⋊Dic3—51no—
270C4⋊Dic3—51no—
271Dic3⋊C4—52no—
272Dic3⋊C4—102no—
273Dic3⋊C4—102no—
274Dic3⋊C4—101no—
275C4×Dic3—52no—
276C4×Dic3—102no—
277C4×Dic3—101no—
278C2×C3⋊C8—52no—
279#204—102no—
280C23×C5—22no—
281C22×D5—61no—
282C5×Q8—81no—
283C5×D4—22no—
284C5×D4—22no—
285C5×D4—42no—
286C5×D4—81no—
287C2×C4×C5—22no—
288C2×C4×C5D3×D411yescharacteristic
289C2×C4×C5D3×D411yescharacteristic
290C2×C4×C5C23×D311yescharacteristic
291C22⋊D5—124no—
292C22⋊D5—242no—
293C2×Dic5—32no—
294C2×Dic5—32no—
295C2×Dic5—61no—
296C2×Dic5—61no—
297C2×Dic5—61no—
298C2×Dic5—124no—
299D20—61no—
300D20—61no—
301C4×D5—122no—
302Dic10—34no—
303Dic10—32no—
304Dic10—61no—
305Dic10—242no—
306C5×C8—21no—
307C5×C8—21no—
308#168—62no—
309C2×#41—301no—
310C2×SD16—152no—
311C2×SD16—151no—
312C4⋊Q8—152no—
313C4⋊Q8—301no—
314C4⋊Q8—302no—
315C4⋊Q8C2×D1511yescharacteristic
316#127—152no—
317#127C2×D1511yescharacteristic
318#121—301no—
319#121—302no—
320C4×Q8—151no—
321C4×Q8—152no—
322C4×Q8—151no—
323C4×Q8—301no—
324C4×D4—152no—
325C4×D4—151no—
326#106—151no—
327#106—152no—
328C4⋊C8—152no—
329C4⋊C8—151no—
330#103—151no—
331#102—152no—
332#102—151no—
333#102—152no—
334#102C2×D1512yes—
335#102C2×D1512yes—
336C4×C8—152no—
337C4×C8C2×D1511yescharacteristic
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—81no—
346C3×D4—22no—
347C3×D4—22no—
348C3×D4—42no—
349C3×D4—81no—
350C2×C3×C4—22no—
351C2×C3×C4D4×D511yescharacteristic
352C2×C3×C4D4×D511yescharacteristic
353C2×C3×C4C23×D511yescharacteristic
354#67—204no—
355#67—402no—
356C2×Dic3—52no—
357C2×Dic3—52no—
358C2×Dic3—101no—
359C2×Dic3—101no—
360C2×Dic3—101no—
361C2×Dic3—204no—
362D12—101no—
363D12—101no—
364C4×D3—202no—
365Dic6—54no—
366Dic6—52no—
367Dic6—101no—
368Dic6—402no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—102no—
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—42no—
381C4×C5D3×SD1612yes—
382C4×C5D3×#4111yescharacteristic
383C4×C5#101011yescharacteristic
384Dic5—34no—
385Dic5—62no—
386Dic5—62no—
387Dic5—121no—
388Dic5—121no—
389#41—604no—
390C2×Q8—21no—
391C2×Q8—151no—
392C2×Q8—151no—
393C2×Q8—302no—
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—302no—
403SD16—304no—
404C2×C8—152no—
405C2×C8C22×D1511yescharacteristic
406C2×C8C22×D1511yescharacteristic
407C4⋊C4—21no—
408C4⋊C4—152no—
409C4⋊C4—151no—
410C4⋊C4—151no—
411C4⋊C4—151no—
412C4⋊C4—302no—
413C4⋊C4—302no—
414C4⋊C4—301no—
415C4⋊C4C22×D1512yes—
416C22⋊C4—302no—
417C22⋊C4—301no—
418C42—152no—
419C42—302no—
420C42—301no—
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—42no—
432C3×C4D5×SD1612yes—
433C3×C4D5×#4111yescharacteristic
434C3×C4#415011yescharacteristic
435Dic3—54no—
436Dic3—102no—
437Dic3—102no—
438Dic3—201no—
439Dic3—201no—
440C2×C5—82no—
441C2×C5#567711yescharacteristic
442C2×C5#575711yescharacteristic
443C2×C5C2×D3×SD1611yescharacteristic
444D5—241no—
445C23—22no—
446C23—301no—
447Q8—81no—
448Q8—154no—
449Q8—152no—
450Q8—301no—
451Q8—1202no—
452D4—22no—
453D4—22no—
454D4—42no—
455D4—81no—
456D4—301no—
457D4—301no—
458D4—604no—
459D4—1202no—
460C2×C4—22no—
461C2×C4—152no—
462C2×C4—152no—
463C2×C4—301no—
464C2×C4—301no—
465C2×C4—301no—
466C2×C4—604no—
467C2×C4—602no—
468C2×C4D4×D1511yescharacteristic
469C2×C4D4×D1511yescharacteristic
470C2×C4C23×D1511yescharacteristic
471C8—21no—
472C8—21no—
473C8—302no—
474C2×C3—82no—
475C2×C3#6601111yescharacteristic
476C2×C3#6609111yescharacteristic
477C2×C3C2×D5×SD1611yescharacteristic
478D3—401no—
479C5#8158811yescharacteristic, complemented, Sylow
480C22—42no—
481C22—42no—
482C22—42no—
483C22—601no—
484C22—601no—
485C22—601no—
486C22C2×D4×D1511yescharacteristic
487C4—21no—
488C4—42no—
489C4—154no—
490C4—302no—
491C4—302no—
492C4—601no—
493C4—601no—
494C4SD16×D1512yes—
495C4#41×D1511yescharacteristic
496C4#9210111yescharacteristic
497C3#1061331911yescharacteristic, complemented, Sylow
498C2—82no—
499C2—1201no—
500C2#1175643611yescharacteristic
501C2#1175651611yescharacteristic
502C2C2×SD16×D1511yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×#486C2
socleC22×C3×C5C22×D4
prime radical#11756477C2
hypercenter#486D15
hypocenterC3×C5#3362
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11756481C2semidirect
3. C3×C5×#486C2semidirect
4. #11751185C2semidirect
5. #11751176C2semidirect
6. #11750863C2semidirect
7. #11750862C2semidirect
8. #11750861C2semidirect
9. #11750859C2semidirect
10. C4×#6706C2semidirect
11. C8×Dic30C2semidirect
45. C5×#486D3semidirect
89. C3×#486D5semidirect
152. Dic30SD16semidirect
153. Dic30#41semidirect
222. #486D15semidirect
422. C3×C5#3362semidirect
479. C5#81588semidirect
497. C3#10613319semidirect

Maximal subgroups

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

subgroupindex
#117564812
#117564772
C3×C5×#4862
#117511852
#117511762
#117508632
#117508622
#117508612
#117508592
C4×#67062
C8×Dic302
#106133193
#815885