Finite Group Databasebeta

← #14416999

Subgroups — #14416999

Order 1920.

1012 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91797C211yesmaximal, characteristic
2#11756280C211yesmaximal, characteristic, complemented
3#11756263C211yesmaximal, characteristic, complemented
4C3×C5×#428C211yesmaximal, characteristic, complemented
5#11751223C211yesmaximal, characteristic, complemented
6#11751103C211yesmaximal, characteristic, complemented
7C2×#91093C211yesmaximal, characteristic, complemented
8#11750990C212yesmaximal, complemented
9#11750973C212yesmaximal, complemented
10#11750970C212yesmaximal, complemented
11#11750953C212yesmaximal, complemented
12#10610932—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×D60C2211yescharacteristic
15C2×C3×C5×M16C2211yescharacteristic
16C3×C5×#117C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C4×#1220—22no—
19#91815C2211yescharacteristic
20C22×C3⋊#168C2211yescharacteristic
21#91797C418yescomplemented
22C2×D120C2212yes—
23C2×#6706C2212yes—
24#91782C2212yes—
25#91782C2212yes—
26#91782C2212yescomplemented
27#91781—21no—
28C4⋊C4×D15—21no—
29#91776C2212yescomplemented
30C22⋊C4×D15—22no—
31C4×D60—21no—
32C4×D60—21no—
33C3×C5×#107C2212yescomplemented
34C3×C5×#106C2212yescomplemented
35#91099C2212yescomplemented
36C8×Dic15C2212yescomplemented
37#91094C2211yescharacteristic, complemented
38#91094C2211yescharacteristic, complemented
39#91093C2212yes—
40#91093C2212yes—
41#91093C2211yescharacteristic, complemented
42#91093C2211yescharacteristic, complemented
43#79201—51nomaximal, Hall
44C2×#4054—31no—
45#65855—31no—
46#65838—31no—
47C5×#428D311yescharacteristic, complemented
48#65411—31no—
49#65291—31no—
50C2×#3941—31no—
51#65178—32no—
52#65161—32no—
53#65158—32no—
54#65141—32no—
55C23×D15—21no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5C2311yescharacteristic
58C2×#1220—21no—
59#6817—22no—
60#6817C2×C414yescomplemented
61C2×D60—21no—
62C2×D60—22no—
63C2×D60C2×C414yescomplemented
64C2×D60C2312yes—
65C2×D60C2311yescharacteristic
66C2×C4×D15—21no—
67C2×C4×D15—22no—
68C2×C4×D15—22no—
69C2×C4×D15—22no—
70C2×Dic30C2311yescharacteristic
71C3×C5×M16C2×C414yescomplemented
72C2×C3×C5×C8C2312yes—
73C3×C5×C4⋊C4—21no—
74C3×C5×C4⋊C4C2312yes—
75C3×C5×C4⋊C4C2311yescharacteristic
76C3×C5×C4⋊C4C2311yescharacteristic
77C3×C5×C22⋊C4—21no—
78C3×C42×C5—21no—
79#6719D412yes—
80#6714—22no—
81#6714—22no—
82#6714—22no—
83C4⋊Dic15D411yescharacteristic
84C4⋊Dic15D411yescharacteristic
85#6712—22no—
86C4×Dic15—22no—
87C4×Dic15C2312yes—
88C2×C3⋊#168—22no—
89C2×C3⋊#168C2311yescharacteristic
90C2×C3⋊#168C2311yescharacteristic
91D120C2×C418yescomplemented
92#6706C2×C418yescomplemented
93C2×#908—51no—
94#5521—51no—
95#5504—51no—
96C3×#428D511yescharacteristic, complemented
97#5122—51no—
98#5002—51no—
99C2×#809—51no—
100#4889—52no—
101#4872—52no—
102#4869—52no—
103#4852—52no—
104C2×#709—31no—
105C22×D20—31no—
106C2×C5×M16C2×D311yescharacteristic
107C5×#117C2×D311yescharacteristic
108C2×C5×C4⋊C4C2×D311yescharacteristic
109C4×C22⋊D5—62no—
110#4072—31no—
111C22×#168—31no—
112#4054—38no—
113C2×D40—32no—
114C2×#677—32no—
115#4039—32no—
116#4039—32no—
117#4039—32no—
118#4038—61no—
119D5×C4⋊C4—61no—
120#4033—32no—
121D5×C22⋊C4—62no—
122C4×D20—61no—
123C4×D20—61no—
124C5×#107C2×D312yescomplemented
125C5×#106C2×D312yescomplemented
126#3947—32no—
127C8×Dic5—32no—
128#3942—31no—
129#3942—31no—
130#3941—31no—
131#3941—31no—
132#3941—32no—
133#3941—32no—
134#2946—151noSylow
135C23×C3×C5C2×D411yescharacteristic
136C22×D15—21no—
137C22×D15—22no—
138C22×D15—24no—
139C22×D15—81no—
140C22×D15—81no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—81no—
145C2×C3×C4×C5C22×C412yes—
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5#4112yes—
148C2×C3×C4×C5C2411yescharacteristic
149#1220—24no—
150C2×Dic15—21no—
151C2×Dic15C2×D412yes—
152C2×Dic15C2×D412yes—
153D60—24no—
154D60—22no—
155D60—21no—
156D60C22×C414yes—
157D60C22×C412yes—
158C4×D15—24no—
159C4×D15—82no—
160C4×D15—82no—
161C4×D15—82no—
162Dic30—21no—
163Dic30C22×C412yes—
164C3×C5×C8C22×C414yes—
165C3⋊#168—21no—
166C3⋊#168—21no—
167C2×#235—51no—
168C22×D12—51no—
169C2×C3×M16C2×D511yescharacteristic
170C3×#117C2×D511yescharacteristic
171C2×C3×C4⋊C4C2×D511yescharacteristic
172C4×#67—102no—
173#926—51no—
174C22×C3⋊C8—51no—
175#908—58no—
176C2×D24—52no—
177C2×#204—52no—
178#893—52no—
179#893—52no—
180#893—52no—
181#892—101no—
182D3×C4⋊C4—101no—
183#887—52no—
184D3×C22⋊C4—102no—
185C4×D12—101no—
186C4×D12—101no—
187C3×#107C2×D512yescomplemented
188C3×#106C2×D512yescomplemented
189#815—52no—
190C8×Dic3—52no—
191#810—51no—
192#810—51no—
193#809—51no—
194#809—52no—
195#809—51no—
196#809—52no—
197C23×D5—61no—
198C22×C4×C5—21no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—61no—
201#709—34no—
202#709—62no—
203C2×D20—34no—
204C2×D20—32no—
205C2×D20—31no—
206C2×D20—61no—
207C2×D20—62no—
208C2×C4×D5—61no—
209C2×C4×D5—62no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×Dic10—31no—
213C5×M16C4×D314yescomplemented
214C2×C5×C8C22×D312yes—
215C5×C4⋊C4—21no—
216C5×C4⋊C4C22×D312yes—
217C5×C4⋊C4C22×D311yescharacteristic
218C5×C4⋊C4C22×D311yescharacteristic
219C5×C22⋊C4—21no—
220C42×C5—21no—
221C22⋊Dic5—32no—
222#685—62no—
223#685—62no—
224#685—62no—
225C4⋊Dic5—31no—
226C4⋊Dic5—31no—
227#683—62no—
228C4×Dic5—32no—
229C4×Dic5—62no—
230C2×#168—31no—
231C2×#168—31no—
232C2×#168—62no—
233D40—38no—
234#677—38no—
235C2×AGL(1,ℤ/8)—151no—
236#520—151no—
237#518—151no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428D1511yescharacteristic, complemented
243#416—151no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5C4×D412yes—
249C22×C3×C5C22×D411yescharacteristic
250C2×D15—22no—
251C2×D15—24no—
252C2×D15—41no—
253C2×D15—42no—
254C2×D15—42no—
255C2×D15—41no—
256C2×D15—84no—
257C3×C4×C5—41no—
258C3×C4×C5—42no—
259C3×C4×C5—41no—
260C3×C4×C5C4×D412yes—
261C3×C4×C5C23×C411yescharacteristic
262C3×C4×C5C2×#4111yescharacteristic
263Dic15—22no—
264Dic15—22no—
265Dic15—22no—
266C23×D3—101no—
267C22×C3×C4—21no—
268C22×C3×C4C22×D511yescharacteristic
269C2×#67—101no—
270#235—54no—
271#235—102no—
272C2×D12—54no—
273C2×D12—52no—
274C2×D12—51no—
275C2×D12—101no—
276C2×D12—102no—
277C2×C4×D3—101no—
278C2×C4×D3—102no—
279C2×C4×D3—102no—
280C2×C4×D3—102no—
281C2×Dic6—51no—
282C3×M16C4×D514yescomplemented
283C2×C3×C8C22×D512yes—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C22×D512yes—
286C3×C4⋊C4C22×D511yescharacteristic
287C3×C4⋊C4C22×D511yescharacteristic
288C3×C22⋊C4—21no—
289C3×C42—21no—
290#217—52no—
291(C2×D3)⋊C4—102no—
292(C2×D3)⋊C4—102no—
293(C2×D3)⋊C4—102no—
294C4⋊Dic3—51no—
295C4⋊Dic3—51no—
296Dic3⋊C4—102no—
297C4×Dic3—52no—
298C4×Dic3—102no—
299C2×C3⋊C8—51no—
300C2×C3⋊C8—51no—
301C2×C3⋊C8—102no—
302D24—58no—
303#204—58no—
304C23×C5D3×D411yescharacteristic
305C22×D5—61no—
306C22×D5—62no—
307C22×D5—64no—
308C22×D5—241no—
309C22×D5—241no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—81no—
314C2×C4×C5C2×C4×D312yes—
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5#23912yes—
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—64no—
319C2×Dic5—32no—
320C2×Dic5—32no—
321C2×Dic5—61no—
322D20—34no—
323D20—32no—
324D20—64no—
325D20—62no—
326D20—61no—
327C4×D5—64no—
328C4×D5—242no—
329C4×D5—242no—
330C4×D5—242no—
331Dic10—32no—
332Dic10—61no—
333C5×C8C2×C4×D314yes—
334#168—61no—
335#168—61no—
336C2×#41—151no—
337C22×D4—151no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16C2×D1511yescharacteristic
342C22×C8—151no—
343C4×Q8—152no—
344C4×D4—152no—
345C4×D4—152no—
346C4×D4—152no—
347C4×D4—301no—
348C4×D4—301no—
349C4×D4—302no—
350#117—151no—
351#117—301no—
352#117C2×D1511yescharacteristic
353C2×C4⋊C4—301no—
354C2×C4⋊C4C2×D1511yescharacteristic
355C2×C22⋊C4—302no—
356#107C2×D1512yescomplemented
357#106C2×D1512yescomplemented
358#103—151no—
359#103—151no—
360#102—152no—
361#102—152no—
362#102—151no—
363#102—151no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5#57611yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—42no—
371D15—44no—
372C23×C3D4×D511yescharacteristic
373C22×D3—101no—
374C22×D3—102no—
375C22×D3—104no—
376C22×D3—401no—
377C22×D3—401no—
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—81no—
382C2×C3×C4C2×C4×D512yes—
383C2×C3×C4D4×D511yescharacteristic
384C2×C3×C4#71312yes—
385C2×C3×C4C23×D511yescharacteristic
386#67—104no—
387C2×Dic3—52no—
388C2×Dic3—52no—
389C2×Dic3—101no—
390D12—54no—
391D12—52no—
392D12—102no—
393D12—101no—
394D12—104no—
395C4×D3—104no—
396C4×D3—402no—
397C4×D3—402no—
398C4×D3—402no—
399Dic6—52no—
400Dic6—101no—
401C3×C8C2×C4×D514yes—
402C3⋊C8—101no—
403C3⋊C8—101no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5#89312yes—
407C22×C5C2×D3×D411yescharacteristic
408C2×D5—62no—
409C2×D5—64no—
410C2×D5—121no—
411C2×D5—122no—
412C2×D5—122no—
413C2×D5—121no—
414C2×D5—244no—
415C4×C5—41no—
416C4×C5—42no—
417C4×C5—41no—
418C4×C5#89312yes—
419C4×C5C22×C4×D311yescharacteristic
420C4×C5C2×#23911yescharacteristic
421Dic5—62no—
422Dic5—62no—
423Dic5—62no—
424C24—301no—
425#41—154no—
426#41—302no—
427C2×Q8—151no—
428C2×D4—154no—
429C2×D4—151no—
430C2×D4—152no—
431C2×D4—301no—
432C2×D4—301no—
433C2×D4—302no—
434C22×C4—21no—
435C22×C4—302no—
436C22×C4—302no—
437C22×C4—302no—
438C22×C4—301no—
439C22×C4C22×D1511yescharacteristic
440SD16—158no—
441D8—158no—
442M16C4×D1514yescomplemented
443C2×C8—151no—
444C2×C8—151no—
445C2×C8—302no—
446C2×C8C22×D1512yes—
447C4⋊C4—21no—
448C4⋊C4—151no—
449C4⋊C4—151no—
450C4⋊C4—302no—
451C4⋊C4C22×D1512yes—
452C4⋊C4C22×D1511yescharacteristic
453C4⋊C4C22×D1511yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—152no—
456C22⋊C4—302no—
457C22⋊C4—302no—
458C22⋊C4—302no—
459C42—21no—
460C42—152no—
461C42—302no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3#403912yes—
466C22×C3C2×D4×D511yescharacteristic
467C2×D3—102no—
468C2×D3—104no—
469C2×D3—201no—
470C2×D3—202no—
471C2×D3—202no—
472C2×D3—201no—
473C2×D3—404no—
474C3×C4—41no—
475C3×C4—42no—
476C3×C4—41no—
477C3×C4#403912yes—
478C3×C4C22×C4×D511yescharacteristic
479C3×C4C2×#71311yescharacteristic
480Dic3—102no—
481Dic3—102no—
482Dic3—102no—
483C2×C5—22no—
484C2×C5C2×#89311yescharacteristic
485C2×C5#577411yescharacteristic
486C2×C5#577811yescharacteristic
487D5—124no—
488D5—122no—
489C23—301no—
490C23—302no—
491C23—304no—
492C23—1201no—
493C23—1201no—
494C23D4×D1511yescharacteristic
495Q8—152no—
496Q8—301no—
497D4—152no—
498D4—154no—
499D4—304no—
500D4—304no—
501D4—302no—
502D4—301no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—22no—
506C2×C4—81no—
507C2×C4—152no—
508C2×C4—152no—
509C2×C4—301no—
510C2×C4—304no—
511C2×C4—1202no—
512C2×C4—1202no—
513C2×C4—1202no—
514C2×C4C2×C4×D1512yes—
515C2×C4D4×D1511yescharacteristic
516C2×C4#682112yes—
517C2×C4C23×D1511yescharacteristic
518C8—301no—
519C8—301no—
520C8C2×C4×D1514yes—
521C2×C3—22no—
522C2×C3C2×#403911yescharacteristic
523C2×C3#6610811yescharacteristic
524C2×C3#6611211yescharacteristic
525D3—204no—
526D3—202no—
527C5#7920111yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—302no—
531C22—304no—
532C22—601no—
533C22—602no—
534C22—602no—
535C22—601no—
536C22—1204no—
537C22#9178212yes—
538C22C2×D4×D1511yescharacteristic
539C4—42no—
540C4—41no—
541C4—41no—
542C4—302no—
543C4—302no—
544C4—302no—
545C4#9178212yes—
546C4C22×C4×D1511yescharacteristic
547C4C2×#682111yescharacteristic
548C3#1061093211yescharacteristic, complemented, Sylow
549C2—22no—
550C2—604no—
551C2—602no—
552C2C2×#9178211yescharacteristic
553C2#1175653311yescharacteristic
554C2#1175653711yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#428C2
socleC22×C3×C5C22×D4
prime radicalC2×#91797C2
cosocleC2×C3×C4×C5C24
hypercenter#428D15
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. #11756280C2semidirect
3. #11756263C2semidirect
4. C3×C5×#428C2semidirect
5. #11751223C2semidirect
6. #11751103C2semidirect
7. C2×#91093C2semidirect
8. #11750990C2semidirect
9. #11750973C2semidirect
10. #11750970C2semidirect
11. #11750953C2semidirect
21. #91797C4semidirect
26. #91782C22semidirect
29. #91776C22semidirect
33. C3×C5×#107C22semidirect
34. C3×C5×#106C22semidirect
35. #91099C22semidirect
36. C8×Dic15C22semidirect
37. #91094C22semidirect
38. #91094C22semidirect
41. #91093C22semidirect
42. #91093C22semidirect
47. C5×#428D3semidirect
60. #6817C2×C4semidirect
63. C2×D60C2×C4semidirect
71. C3×C5×M16C2×C4semidirect
91. D120C2×C4semidirect
92. #6706C2×C4semidirect
96. C3×#428D5semidirect
124. C5×#107C2×D3semidirect
125. C5×#106C2×D3semidirect
187. C3×#107C2×D5semidirect
188. C3×#106C2×D5semidirect
213. C5×M16C4×D3semidirect
242. #428D15semidirect
282. C3×M16C4×D5semidirect
356. #107C2×D15semidirect
357. #106C2×D15semidirect
442. M16C4×D15semidirect
462. C3×C5#2946semidirect
527. C5#79201semidirect
548. C3#10610932semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
#117562802
#117562632
C3×C5×#4282
#117512232
#117511032
C2×#910932
#117509902
#117509732
#117509702
#117509532
#106109323
#792015