Finite Group Databasebeta

← #14460266

Subgroups — #14460266

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756491C211yesmaximal, characteristic, complemented
2#11756477C211yesmaximal, characteristic
3C3×C5×#486C211yesmaximal, characteristic, complemented
4#11751195C211yesmaximal, characteristic, complemented
5#11751176C211yesmaximal, characteristic, complemented
6#11750885C212yesmaximal, complemented
7#11750884C212yesmaximal, complemented
8#11750879C212yesmaximal, complemented
9#11750873C212yesmaximal, complemented
10C4×Dic60C211yesmaximal, characteristic, complemented
11C8×D60C211yesmaximal, characteristic, complemented
12#10613309—31nomaximal, Hall
13C2×#6819C2212yes—
14C3×C5×C4⋊Q8C2211yescharacteristic
15C3×C5×#127C2211yescharacteristic
16#91836—21no—
17Q8×Dic15—21no—
18#91829—21no—
19#91828—22no—
20#91827C2212yes—
21D4×Dic15—21no—
22C2×#6716C2212yes—
23C2×Dic60C2211yescharacteristic
24C2×C8×D15C2212yes—
25#91787—22no—
26#91786C2212yes—
27#91781C2212yes—
28C4×D60C2211yescharacteristic
29C4×Dic30C2211yescharacteristic
30C4×Dic30C2211yescharacteristic
31C3×C5×#102C2212yes—
32C3×C5×#102C2212yes—
33C3×C4×C5×C8C2211yescharacteristic
34#91116C2212yes—
35#91104C2212yes—
36#91102C2211yescharacteristic
37#91100C2211yescharacteristic
38#91100C2211yescharacteristic
39#91094C2212yes—
40#91092C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#81578—51nomaximal, Hall
43#66066—31no—
44#66052—31no—
45C5×#486D311yescharacteristic, complemented
46#65383—31no—
47#65364—31no—
48#65073—32no—
49#65072—32no—
50#65067—32no—
51#65061—32no—
52C4×Dic20—31no—
53C8×D20—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—24no—
62#6819—42no—
63C2×D60D411yescharacteristic
64C2×C4×D15C2312yes—
65C2×Dic30C2311yescharacteristic
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—42no—
74#6714—22no—
75#6714—22no—
76#6714D412yes—
77C4⋊Dic15—22no—
78C4⋊Dic15D411yescharacteristic
79C4⋊Dic15C2311yescharacteristic
80C4⋊Dic15C2311yescharacteristic
81#6712—21no—
82#6712—21no—
83C4×Dic15—21no—
84C4×Dic15—21no—
85C4×Dic15—22no—
86C2×C3⋊#168C2312yes—
87Dic60—22no—
88C8×D15—42no—
89#5732—51no—
90#5718—51no—
91C3×#486D511yescharacteristic, complemented
92#5094—51no—
93#5075—51no—
94#4784—52no—
95#4783—52no—
96#4778—52no—
97#4772—52no—
98C4×Dic12—51no—
99C8×D12—51no—
100C2×#711—32no—
101C5×C4⋊Q8C2×D311yescharacteristic
102C5×#127C2×D311yescharacteristic
103#4093—61no—
104Q8×Dic5—61no—
105#4086—61no—
106#4085—62no—
107#4084—32no—
108D4×Dic5—61no—
109C2×#687—32no—
110C2×Dic20—31no—
111C2×C8×D5—32no—
112#4044—62no—
113#4043—32no—
114#4038—32no—
115C4×D20—31no—
116C4×Dic10—31no—
117C4×Dic10—31no—
118C5×#102C2×D312yes—
119C5×#102C2×D312yes—
120C4×C5×C8C2×D311yescharacteristic
121#3964—32no—
122#3952—32no—
123#3950—31no—
124#3948—31no—
125#3948—31no—
126#3942—32no—
127#3940—32no—
128C4⋊#168—31no—
129#3304—151noSylow
130C23×C3×C5—22no—
131C22×D15C2×D412yes—
132C3×C5×Q8—42no—
133C3×C5×D4—22no—
134C3×C5×D4—22no—
135C3×C5×D4—42no—
136C3×C5×D4—81no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2411yescharacteristic
141#1220—44no—
142#1220—82no—
143C2×Dic15—21no—
144C2×Dic15—21no—
145C2×Dic15—21no—
146C2×Dic15—21no—
147C2×Dic15—44no—
148C2×Dic15C2×D412yes—
149D60—22no—
150C4×D15—22no—
151C4×D15—22no—
152Dic30—21no—
153Dic30—21no—
154Dic30—21no—
155Dic30#4112yes—
156C3×C5×C8—21no—
157C3×C5×C8—21no—
158C3⋊#168—22no—
159C2×#237—52no—
160C3×C4⋊Q8C2×D511yescharacteristic
161C3×#127C2×D511yescharacteristic
162#947—101no—
163Q8×Dic3—101no—
164#940—101no—
165#939—102no—
166#938—52no—
167D4×Dic3—101no—
168C2×#214—52no—
169C2×Dic12—51no—
170C2×D3×C8—52no—
171#898—102no—
172#897—52no—
173#892—52no—
174C4×D12—51no—
175C4×Dic6—51no—
176C4×Dic6—51no—
177C3×#102C2×D512yes—
178C3×#102C2×D512yes—
179C3×C4×C8C2×D511yescharacteristic
180#832—52no—
181(C2×D3)⋊C8—52no—
182#818—51no—
183#816—51no—
184#816—51no—
185#810—52no—
186#808—52no—
187C4⋊(C3⋊C8)—51no—
188C2×C5×Q8—21no—
189C2×C5×D4—21no—
190C2×C5×D4—21no—
191C2×C5×D4C22×D312yes—
192C2×C22⋊D5—62no—
193C2×C22⋊D5—62no—
194C22×Dic5—62no—
195#711—64no—
196#711—122no—
197C2×D20—31no—
198C2×C4×D5—32no—
199C2×Dic10—31no—
200C2×Dic10—31no—
201C2×C5×C8C22×D311yescharacteristic
202C2×C5×C8C22×D311yescharacteristic
203C5×C4⋊C4—21no—
204C5×C4⋊C4C22×D312yes—
205C42×C5C22×D311yescharacteristic
206C22⋊Dic5—62no—
207#687—122no—
208#685—32no—
209#685—62no—
210#685—62no—
211C4⋊Dic5—31no—
212C4⋊Dic5—31no—
213C4⋊Dic5—31no—
214C4⋊Dic5—62no—
215#683—61no—
216#683—61no—
217C4×Dic5—62no—
218C4×Dic5—61no—
219C4×Dic5—61no—
220C2×#168—32no—
221Dic20—62no—
222C8×D5—122no—
223#556—151no—
224#550—151no—
225#486D1511yescharacteristic, complemented
226#482—152no—
227#475—151no—
228#465—152no—
229#460—151no—
230#452—152no—
231C4×Q16—151no—
232C8×D4—151no—
233#416—152no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5—42no—
237C22×C3×C5C22×D411yescharacteristic
238C2×D15—22no—
239C2×D15—22no—
240C2×D15—22no—
241C3×C4×C5—21no—
242C3×C4×C5—42no—
243C3×C4×C5#13512yes—
244C3×C4×C5C2×#4111yescharacteristic
245C3×C4×C5H(5,𝔽2)11yescharacteristic
246Dic15—22no—
247Dic15—22no—
248Dic15—41no—
249Dic15—41no—
250Dic15—41no—
251C2×C3×Q8—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4C22×D512yes—
255C2×#67—102no—
256C2×#67—102no—
257C22×Dic3—102no—
258#237—104no—
259#237—202no—
260C2×D12—51no—
261C2×C4×D3—52no—
262C2×Dic6—51no—
263C2×Dic6—51no—
264C2×C3×C8C22×D511yescharacteristic
265C2×C3×C8C22×D511yescharacteristic
266C3×C4⋊C4—21no—
267C3×C4⋊C4C22×D512yes—
268C3×C42C22×D511yescharacteristic
269#217—102no—
270#214—202no—
271(C2×D3)⋊C4—52no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274C4⋊Dic3—51no—
275C4⋊Dic3—51no—
276C4⋊Dic3—51no—
277C4⋊Dic3—102no—
278Dic3⋊C4—101no—
279Dic3⋊C4—101no—
280C4×Dic3—102no—
281C4×Dic3—101no—
282C4×Dic3—101no—
283C2×C3⋊C8—52no—
284Dic12—102no—
285D3×C8—202no—
286C23×C5—22no—
287C22×D5—32no—
288C5×Q8—42no—
289C5×D4—22no—
290C5×D4—22no—
291C5×D4—42no—
292C5×D4—81no—
293C2×C4×C5—22no—
294C2×C4×C5D3×D411yescharacteristic
295C2×C4×C5D3×D411yescharacteristic
296C2×C4×C5C23×D311yescharacteristic
297C22⋊D5—124no—
298C22⋊D5—242no—
299C2×Dic5—32no—
300C2×Dic5—61no—
301C2×Dic5—61no—
302C2×Dic5—61no—
303C2×Dic5—61no—
304C2×Dic5—124no—
305D20—62no—
306C4×D5—62no—
307C4×D5—62no—
308Dic10—32no—
309Dic10—61no—
310Dic10—61no—
311Dic10—61no—
312C5×C8—21no—
313C5×C8—21no—
314#168—62no—
315C2×#41—152no—
316C2×Q16—151no—
317C2×SD16—152no—
318C22×C8—152no—
319C4⋊Q8C2×D1511yescharacteristic
320#127—301no—
321#127C2×D1511yescharacteristic
322#126—302no—
323#124—301no—
324C22⋊Q8—152no—
325#121—152no—
326#121—302no—
327C4×Q8—151no—
328C4×Q8—151no—
329C4×Q8—301no—
330C4×D4—151no—
331C4×D4—301no—
332#117—152no—
333#107—151no—
334#106—152no—
335C4⋊C8—151no—
336#103—151no—
337#103—151no—
338#103—152no—
339#102—152no—
340#102C2×D1512yes—
341#102C2×D1512yes—
342C22⋊C8—152no—
343C4×C8C2×D1511yescharacteristic
344C2×C3×C5—82no—
345C2×C3×C5#54611yescharacteristic
346C2×C3×C5C2×#13511yescharacteristic
347C2×C3×C5#57711yescharacteristic
348D15—42no—
349C23×C3—22no—
350C22×D3—52no—
351C3×Q8—42no—
352C3×D4—22no—
353C3×D4—22no—
354C3×D4—42no—
355C3×D4—81no—
356C2×C3×C4—22no—
357C2×C3×C4D4×D511yescharacteristic
358C2×C3×C4D4×D511yescharacteristic
359C2×C3×C4C23×D511yescharacteristic
360#67—204no—
361#67—402no—
362C2×Dic3—52no—
363C2×Dic3—101no—
364C2×Dic3—101no—
365C2×Dic3—101no—
366C2×Dic3—101no—
367C2×Dic3—204no—
368D12—102no—
369C4×D3—102no—
370C4×D3—102no—
371Dic6—52no—
372Dic6—101no—
373Dic6—101no—
374Dic6—101no—
375C3×C8—21no—
376C3×C8—21no—
377C3⋊C8—102no—
378C22×C5—42no—
379C22×C5—42no—
380C22×C5—42no—
381C22×C5C2×D3×D411yescharacteristic
382C2×D5—62no—
383C2×D5—62no—
384C2×D5—62no—
385C4×C5—21no—
386C4×C5—42no—
387C4×C5#91212yes—
388C4×C5D3×#4111yescharacteristic
389C4×C5#100911yescharacteristic
390Dic5—62no—
391Dic5—62no—
392Dic5—121no—
393Dic5—121no—
394Dic5—121no—
395#41—304no—
396#41—602no—
397C2×Q8—21no—
398C2×Q8—151no—
399C2×Q8—151no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—151no—
403C2×D4—302no—
404C2×D4—302no—
405C2×D4C22×D1512yes—
406C22×C4—152no—
407C22×C4—302no—
408Q16—302no—
409SD16—602no—
410C2×C8—152no—
411C2×C8—602no—
412C2×C8C22×D1511yescharacteristic
413C2×C8C22×D1511yescharacteristic
414C4⋊C4—21no—
415C4⋊C4—151no—
416C4⋊C4—151no—
417C4⋊C4—151no—
418C4⋊C4—302no—
419C4⋊C4—301no—
420C4⋊C4—301no—
421C4⋊C4C22×D1512yes—
422C22⋊C4—152no—
423C22⋊C4—302no—
424C22⋊C4—302no—
425C22⋊C4—302no—
426C42—302no—
427C42—301no—
428C42—301no—
429C42C22×D1511yescharacteristic
430C3×C5#330411yescharacteristic, complemented, Hall
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3C2×D4×D511yescharacteristic
435C2×D3—102no—
436C2×D3—102no—
437C2×D3—102no—
438C3×C4—21no—
439C3×C4—42no—
440C3×C4#405812yes—
441C3×C4D5×#4111yescharacteristic
442C3×C4#414911yescharacteristic
443Dic3—102no—
444Dic3—102no—
445Dic3—201no—
446Dic3—201no—
447Dic3—201no—
448C2×C5—82no—
449C2×C5#567611yescharacteristic
450C2×C5C2×#91211yescharacteristic
451C2×C5#576211yescharacteristic
452D5—122no—
453C23—22no—
454C23—152no—
455Q8—42no—
456Q8—152no—
457Q8—301no—
458Q8—301no—
459Q8—301no—
460D4—22no—
461D4—22no—
462D4—42no—
463D4—81no—
464D4—302no—
465D4—604no—
466D4—1202no—
467C2×C4—22no—
468C2×C4—152no—
469C2×C4—301no—
470C2×C4—302no—
471C2×C4—302no—
472C2×C4—301no—
473C2×C4—301no—
474C2×C4—301no—
475C2×C4—604no—
476C2×C4D4×D1511yescharacteristic
477C2×C4D4×D1511yescharacteristic
478C2×C4C23×D1511yescharacteristic
479C8—21no—
480C8—21no—
481C8—302no—
482C2×C3—82no—
483C2×C3#6601011yescharacteristic
484C2×C3C2×#405811yescharacteristic
485C2×C3#6609611yescharacteristic
486D3—202no—
487C5#8157811yescharacteristic, complemented, Sylow
488C22—42no—
489C22—42no—
490C22—42no—
491C22—302no—
492C22—302no—
493C22—302no—
494C22C2×D4×D1511yescharacteristic
495C4—21no—
496C4—42no—
497C4—302no—
498C4—302no—
499C4—601no—
500C4—601no—
501C4—601no—
502C4#9180112yes—
503C4#41×D1511yescharacteristic
504C4#9210011yescharacteristic
505C3#1061330911yescharacteristic, complemented, Sylow
506C2—82no—
507C2—602no—
508C2#1175643511yescharacteristic
509C2C2×#9180111yescharacteristic
510C2#1175652111yescharacteristic
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#3304
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. #11756491C2semidirect
3. C3×C5×#486C2semidirect
4. #11751195C2semidirect
5. #11751176C2semidirect
6. #11750885C2semidirect
7. #11750884C2semidirect
8. #11750879C2semidirect
9. #11750873C2semidirect
10. C4×Dic60C2semidirect
11. C8×D60C2semidirect
45. C5×#486D3semidirect
91. C3×#486D5semidirect
225. #486D15semidirect
430. C3×C5#3304semidirect
487. C5#81578semidirect
505. C3#10613309semidirect

Maximal subgroups

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

subgroupindex
#117564912
#117564772
C3×C5×#4862
#117511952
#117511762
#117508852
#117508842
#117508792
#117508732
C4×Dic602
C8×D602
#106133093
#815785