Finite Group Databasebeta

← #14417082

Subgroups — #14417082

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
1C3×#65838C211yesmaximal, characteristic, complemented
2#11754515C211yesmaximal, characteristic, complemented
3C2×#91301C211yesmaximal, characteristic
4C2×#91093C211yesmaximal, characteristic, complemented
5C5×#4964C211yesmaximal, characteristic, complemented
6#11748364C211yesmaximal, characteristic, complemented
7#11748320C211yesmaximal, characteristic, complemented
8#11747469C212yesmaximal, complemented
9#11747225C212yesmaximal, complemented
10#11747224C212yesmaximal, complemented
11#11747223C212yesmaximal, complemented
12#10610932—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C22×C3⋊#168C2211yescharacteristic
17C5×#926C2211yescharacteristic
18C2×C5×#208C2211yescharacteristic
19C3×C4×C22⋊D5—22no—
20C3×#4072C2211yescharacteristic
21C3×#4039C2212yescomplemented
22C3×#4038—21no—
23C3×D5×C4⋊C4—21no—
24C3×#4033C2212yescomplemented
25#91561—22no—
26#91428—21no—
27#91428—21no—
28#91418C2212yes—
29#91418C2212yes—
30C2×#6658C2212yes—
31#91301C418yescomplemented
32C2×#6653C2212yes—
33#91093C2212yes—
34#91093C2212yes—
35C5×#808C2212yescomplemented
36C5×#807C2212yescomplemented
37#90970C2211yescharacteristic, complemented
38#90970C2211yescharacteristic, complemented
39#90964C2211yescharacteristic, complemented
40#90964C2211yescharacteristic, complemented
41#90952C2212yescomplemented
42Dic5×C3⋊C8C2212yescomplemented
43#82564—51nomaximal, Hall
44C2×#4054—31no—
45#65855—31no—
46#65838D311yescharacteristic, complemented
47C5×#428—31no—
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×D60—21no—
59C2×D60—22no—
60C2×D60C2×C414yescomplemented
61C2×D60C2312yes—
62C2×C3×C22⋊D5—21no—
63C3×#709—22no—
64C3×#709C2×C414yescomplemented
65C2×C3×D20C2311yescharacteristic
66C2×C3×C4×D5—21no—
67C2×C3×C4×D5—22no—
68C2×C3×Dic10C2311yescharacteristic
69C2×#1200—22no—
70C2×#1200—22no—
71C3×C5×C4⋊C4—21no—
72C3×C5×C4⋊C4C2312yes—
73C2×C3⋊#168—22no—
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2311yescharacteristic
76C5×#217—21no—
77C5×C4⋊Dic3C2311yescharacteristic
78C5×C4⋊Dic3C2311yescharacteristic
79C4×C5×Dic3—21no—
80C5×#208C2×C414yescomplemented
81C2×C5×C3⋊C8C2312yes—
82C3×C22⋊Dic5D412yes—
83C3×#685—22no—
84C3×C4⋊Dic5D411yescharacteristic
85C3×C4⋊Dic5D411yescharacteristic
86C3×#683—22no—
87C3×C4×Dic5—22no—
88C3×C4×Dic5C2312yes—
89#6667—22no—
90#6667—22no—
91#6658C2×C418yescomplemented
92#6653C2×C418yescomplemented
93C3×#520—51no—
94C2×#949—51no—
95#5521—51no—
96#5233—51no—
97#5026—52no—
98C4×#215—52no—
99#5014—52no—
100C4×#213—52no—
101#4997—51no—
102C2×#809—51no—
103#4964D511yescharacteristic, complemented
104C2×#709C2×D311yescharacteristic
105C22×D20—31no—
106C2×C5×M16—31no—
107C5×#117—31no—
108C2×C5×C4⋊C4C2×D311yescharacteristic
109C4×C22⋊D5—22no—
110#4072C2×D311yescharacteristic
111C22×#168—31no—
112#4054—38no—
113C2×D40—32no—
114C2×#677—32no—
115#4039—32no—
116#4039—32no—
117#4039C2×D312yescomplemented
118#4038—21no—
119D5×C4⋊C4—21no—
120#4033C2×D312yescomplemented
121D5×C22⋊C4—62no—
122C4×D20—61no—
123C4×D20—61no—
124C5×#107—32no—
125C5×#106—32no—
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—22no—
137C22×D15—24no—
138C22×D15—81no—
139C22×D15—81no—
140C22×C3×D5—21no—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—81no—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5#4112yes—
146C2×C3×C4×C5C2411yescharacteristic
147D60—24no—
148D60—22no—
149D60C22×C414yes—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C3×C22⋊D5—24no—
153C2×C3×Dic5—21no—
154C2×C3×Dic5C2×D412yes—
155C2×C3×Dic5C2×D412yes—
156C3×D20—21no—
157C3×D20C22×C412yes—
158C3×C4×D5—24no—
159C3×C4×D5—82no—
160C3×Dic10—21no—
161C3×Dic10C22×C412yes—
162#1200—82no—
163#1200—82no—
164C3⋊#168—21no—
165C3⋊#168—21no—
166C5×C3⋊C8C22×C414yes—
167C2×C3×#41—51no—
168C22×D12—51no—
169C3×C4×Q8—52no—
170C3×C4×D4—52no—
171C3×C4×D4—102no—
172C3×#117—51no—
173C3×#117—101no—
174C2×C3×C4⋊C4—101no—
175C2×C3×C4⋊C4C2×D511yescharacteristic
176#949—58no—
177C2×#215—52no—
178C2×#213—52no—
179#926C2×D511yescharacteristic
180C2×#208C2×D511yescharacteristic
181C22×C3⋊C8—51no—
182#893—101no—
183#893—101no—
184D3×C22⋊C4—102no—
185C4×D12—52no—
186C4×D12—52no—
187#835—51no—
188#835—51no—
189#832—51no—
190#832—51no—
191#809—52no—
192#809—52no—
193#808C2×D512yescomplemented
194#807C2×D512yescomplemented
195#803—52no—
196C4×C3⋊C8—52no—
197C23×D5—61no—
198C22×C4×C5—21no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—21no—
201#709—22no—
202#709C4×D314yescomplemented
203C2×D20—34no—
204C2×D20—32no—
205C2×D20—62no—
206C2×D20—61no—
207C2×D20C22×D311yescharacteristic
208C2×C4×D5—21no—
209C2×C4×D5—22no—
210C2×C4×D5—62no—
211C2×C4×D5—62no—
212C2×Dic10C22×D311yescharacteristic
213C5×M16—34no—
214C2×C5×C8—32no—
215C5×C4⋊C4—21no—
216C5×C4⋊C4—31no—
217C5×C4⋊C4—31no—
218C5×C4⋊C4C22×D312yes—
219C5×C22⋊C4—61no—
220C42×C5—61no—
221C22⋊Dic5#6712yes—
222#685—22no—
223#685—62no—
224#685—62no—
225C4⋊Dic5#6711yescharacteristic
226C4⋊Dic5#6711yescharacteristic
227#683—22no—
228C4×Dic5—22no—
229C4×Dic5C22×D312yes—
230C2×#168—31no—
231C2×#168—31no—
232C2×#168—62no—
233D40—38no—
234#677—38no—
235C2×AGL(1,ℤ/8)—151no—
236#520—51no—
237#518—151no—
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—31no—
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—24no—
251C2×D15—42no—
252C2×D15—42no—
253C2×D15—84no—
254C2×C3×D5—22no—
255C2×C3×D5—41no—
256C2×C3×D5—41no—
257C3×C4×C5—42no—
258C3×C4×C5C4×D412yes—
259C3×C4×C5C23×C411yescharacteristic
260C3×C4×C5C2×#4111yescharacteristic
261C3×Dic5—22no—
262C3×Dic5—22no—
263C3×Dic5—22no—
264C5×Dic3—41no—
265C5×Dic3—41no—
266C23×D3—101no—
267C3×#41—54no—
268C3×#41—102no—
269C2×C3×Q8—51no—
270C2×C3×D4—51no—
271C2×C3×D4—101no—
272C22×C3×C4—21no—
273C22×C3×C4—102no—
274C22×C3×C4—101no—
275C22×C3×C4C22×D511yescharacteristic
276C2×D12—54no—
277C2×D12—52no—
278C2×D12—101no—
279C2×D12—102no—
280C2×C4×D3—102no—
281C2×C4×D3—102no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—51no—
284C3×C4⋊C4—51no—
285C3×C4⋊C4—102no—
286C3×C4⋊C4C22×D512yes—
287C3×C22⋊C4—52no—
288C3×C22⋊C4—102no—
289C3×C42—52no—
290C3×C42—102no—
291#217—21no—
292#215—58no—
293#213—58no—
294(C2×D3)⋊C4—102no—
295(C2×D3)⋊C4—102no—
296C4⋊Dic3C22×D511yescharacteristic
297C4⋊Dic3C22×D511yescharacteristic
298C4×Dic3—21no—
299#208C4×D514yescomplemented
300C2×C3⋊C8—51no—
301C2×C3⋊C8—51no—
302C2×C3⋊C8—102no—
303C2×C3⋊C8C22×D512yes—
304C23×C5C2×#6711yescharacteristic
305C22×D5—21no—
306C22×D5—62no—
307C22×D5—64no—
308C22×D5—241no—
309C22×D5—241no—
310C2×C4×C5—22no—
311C2×C4×C5—61no—
312C2×C4×C5—61no—
313C2×C4×C5—81no—
314C2×C4×C5C2×C4×D312yes—
315C2×C4×C5#23512yes—
316C2×C4×C5C2×#6711yescharacteristic
317C2×C4×C5C23×D311yescharacteristic
318C22⋊D5—24no—
319C2×Dic5—21no—
320C2×Dic5C2×#6712yes—
321C2×Dic5C2×#6712yes—
322D20—21no—
323D20—34no—
324D20—64no—
325D20—62no—
326D20C2×C4×D312yes—
327C4×D5—24no—
328C4×D5—82no—
329C4×D5—242no—
330C4×D5—242no—
331Dic10—21no—
332Dic10C2×C4×D312yes—
333C5×C8—34no—
334#168—61no—
335#168—61no—
336C2×#41—51no—
337C22×D4—151no—
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—31no—
342C22×C8—151no—
343C4×Q8—52no—
344C4×D4—52no—
345C4×D4—102no—
346C4×D4—152no—
347C4×D4—152no—
348C4×D4—301no—
349C4×D4—301no—
350#117—31no—
351#117—51no—
352#117—101no—
353C2×C4⋊C4—101no—
354C2×C4⋊C4D3×D511yescharacteristic
355C2×C22⋊C4—302no—
356#107—32no—
357#106—32no—
358#103—151no—
359#103—151no—
360#102—151no—
361#102—151no—
362#102—152no—
363#102—152no—
364#97—152no—
365C4×C8—152no—
366C2×C3×C5—22no—
367C2×C3×C5C2×C4×D411yescharacteristic
368C2×C3×C5#57611yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—44no—
371C3×D5—42no—
372C23×C3—101no—
373C23×C3D4×D511yescharacteristic
374C22×D3—102no—
375C22×D3—104no—
376C22×D3—401no—
377C22×D3—401no—
378C3×Q8—52no—
379C3×Q8—101no—
380C3×D4—52no—
381C3×D4—104no—
382C3×D4—101no—
383C2×C3×C4—22no—
384C2×C3×C4—52no—
385C2×C3×C4—52no—
386C2×C3×C4—81no—
387C2×C3×C4—101no—
388C2×C3×C4—104no—
389C2×C3×C4—402no—
390C2×C3×C4C2×C4×D512yes—
391C2×C3×C4D4×D511yescharacteristic
392C2×C3×C4#71312yes—
393C2×C3×C4C23×D511yescharacteristic
394C2×Dic3—21no—
395C2×Dic3—21no—
396D12—54no—
397D12—102no—
398D12—104no—
399C4×D3—402no—
400C4×D3—402no—
401C3⋊C8—101no—
402C3⋊C8—101no—
403C3⋊C8C2×C4×D514yes—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5C4×#6712yes—
407C22×C5C22×#6711yescharacteristic
408C2×D5—22no—
409C2×D5—41no—
410C2×D5—41no—
411C2×D5—64no—
412C2×D5—122no—
413C2×D5—122no—
414C2×D5—244no—
415C4×C5—42no—
416C4×C5—121no—
417C4×C5—121no—
418C4×C5C4×#6712yes—
419C4×C5C22×C4×D311yescharacteristic
420C4×C5C2×#23511yescharacteristic
421Dic5—22no—
422Dic5—22no—
423Dic5—22no—
424C24—301no—
425#41—54no—
426#41—102no—
427C2×Q8—51no—
428C2×D4—51no—
429C2×D4—101no—
430C2×D4—154no—
431C2×D4—152no—
432C2×D4—302no—
433C2×D4—301no—
434C22×C4—21no—
435C22×C4—102no—
436C22×C4—101no—
437C22×C4—302no—
438C22×C4—302no—
439C22×C4C2×D3×D511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—34no—
443C2×C8—32no—
444C2×C8—151no—
445C2×C8—151no—
446C2×C8—302no—
447C4⋊C4—21no—
448C4⋊C4—31no—
449C4⋊C4—31no—
450C4⋊C4—51no—
451C4⋊C4—51no—
452C4⋊C4—102no—
453C4⋊C4C2×D3×D512yes—
454C22⋊C4—52no—
455C22⋊C4—61no—
456C22⋊C4—102no—
457C22⋊C4—302no—
458C22⋊C4—302no—
459C42—52no—
460C42—61no—
461C42—102no—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—102no—
466C22×C3—201no—
467C22×C3—201no—
468C22×C3#403912yes—
469C22×C3C2×D4×D511yescharacteristic
470C2×D3—104no—
471C2×D3—202no—
472C2×D3—202no—
473C2×D3—404no—
474C3×C4—42no—
475C3×C4—102no—
476C3×C4—102no—
477C3×C4—102no—
478C3×C4#403912yes—
479C3×C4C22×C4×D511yescharacteristic
480C3×C4C2×#71311yescharacteristic
481Dic3—41no—
482Dic3—41no—
483C2×C5—22no—
484C2×C5C2×C4×#6711yescharacteristic
485C2×C5#583511yescharacteristic
486C2×C5#583711yescharacteristic
487D5—42no—
488D5—124no—
489C23—101no—
490C23—302no—
491C23—304no—
492C23—1201no—
493C23—1201no—
494C23D5×#6711yescharacteristic
495Q8—52no—
496Q8—101no—
497D4—52no—
498D4—104no—
499D4—101no—
500D4—154no—
501D4—304no—
502D4—302no—
503C2×C4—22no—
504C2×C4—52no—
505C2×C4—52no—
506C2×C4—61no—
507C2×C4—61no—
508C2×C4—81no—
509C2×C4—101no—
510C2×C4—104no—
511C2×C4—402no—
512C2×C4—1202no—
513C2×C4—1202no—
514C2×C4#677312yes—
515C2×C4C4×D3×D512yes—
516C2×C4D5×#6711yescharacteristic
517C2×C4C22×D3×D511yescharacteristic
518C8—34no—
519C8—301no—
520C8—301no—
521C2×C3—22no—
522C2×C3—202no—
523C2×C3C2×#403911yescharacteristic
524C2×C3#6610811yescharacteristic
525C2×C3#6611211yescharacteristic
526D3—204no—
527C5#8256411yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—102no—
531C22—201no—
532C22—201no—
533C22—304no—
534C22—602no—
535C22—602no—
536C22—1204no—
537C22#9144412yes—
538C22C2×D5×#6711yescharacteristic
539C4—42no—
540C4—102no—
541C4—102no—
542C4—102no—
543C4—121no—
544C4—121no—
545C4#9144412yes—
546C4C2×#677311yescharacteristic
547C4C2×C4×D3×D511yescharacteristic
548C3#1061093211yescharacteristic, complemented, Sylow
549C2—22no—
550C2—202no—
551C2—604no—
552C2C2×#9144411yescharacteristic
553C2#1175469211yescharacteristic
554C2#1175508611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91301C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65838C2semidirect
2. #11754515C2semidirect
4. C2×#91093C2semidirect
5. C5×#4964C2semidirect
6. #11748364C2semidirect
7. #11748320C2semidirect
8. #11747469C2semidirect
9. #11747225C2semidirect
10. #11747224C2semidirect
11. #11747223C2semidirect
21. C3×#4039C22semidirect
24. C3×#4033C22semidirect
31. #91301C4semidirect
35. C5×#808C22semidirect
36. C5×#807C22semidirect
37. #90970C22semidirect
38. #90970C22semidirect
39. #90964C22semidirect
40. #90964C22semidirect
41. #90952C22semidirect
42. Dic5×C3⋊C8C22semidirect
46. #65838D3semidirect
60. C2×D60C2×C4semidirect
64. C3×#709C2×C4semidirect
80. C5×#208C2×C4semidirect
91. #6658C2×C4semidirect
92. #6653C2×C4semidirect
103. #4964D5semidirect
117. #4039C2×D3semidirect
120. #4033C2×D3semidirect
193. #808C2×D5semidirect
194. #807C2×D5semidirect
202. #709C4×D3semidirect
299. #208C4×D5semidirect
462. C3×C5#2946semidirect
527. C5#82564semidirect
548. C3#10610932semidirect

Maximal subgroups

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

subgroupindex
C3×#658382
#117545152
C2×#913012
C2×#910932
C5×#49642
#117483642
#117483202
#117474692
#117472252
#117472242
#117472232
#106109323
#825645