Finite Group Databasebeta

← #14417005

Subgroups — #14417005

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×C5×#518C211yesmaximal, characteristic, complemented
2C2×#91821C211yesmaximal, characteristic
3#11756282C211yesmaximal, characteristic, complemented
4C2×#91116C211yesmaximal, characteristic, complemented
5#11751119C212yesmaximal, complemented
6C4×#6716C212yesmaximal, complemented
7#11751115C212yesmaximal, complemented
8C4×#6715C212yesmaximal, complemented
9#11751103C211yesmaximal, characteristic, complemented
10#11751098C211yesmaximal, characteristic, complemented
11#11751096C211yesmaximal, characteristic, complemented
12#10614268—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C2×#6817C2211yescharacteristic
15C3×C4×C5×D4—21no—
16C3×C4×C5×D4—21no—
17C3×C4×C5×D4C2212yes—
18C3×C4×C5×D4C2212yes—
19C3×C5×#117C2211yescharacteristic
20C3×C5×#117C2211yescharacteristic
21C2×C3×C5×C22⋊C4—22no—
22C2×#6716C2212yes—
23#91821C418yescomplemented
24C2×#6715C2212yes—
25C2×C4⋊Dic15C2211yescharacteristic
26C2×#6710C2211yescharacteristic
27C22×C3⋊#168C2211yescharacteristic
28#91781—21no—
29C4⋊C4×D15—21no—
30#91770—22no—
31C4×D60C2212yescomplemented
32C4×Dic30C2212yescomplemented
33#91116C2212yes—
34#91116C2212yes—
35#91094C2211yescharacteristic, complemented
36#91094C2211yescharacteristic, complemented
37#91093C2211yescharacteristic, complemented
38#91093C2211yescharacteristic, complemented
39#91092C2212yescomplemented
40#91091C2212yescomplemented
41#91087C2212yescomplemented
42C4×C3⋊#168C2212yescomplemented
43#82537—51nomaximal, Hall
44C5×#518D311yescharacteristic, complemented
45C2×#4078—31no—
46#65857—31no—
47C2×#3964—31no—
48#65307—32no—
49C4×#687—32no—
50#65303—32no—
51C4×#686—32no—
52#65291—31no—
53#65286—31no—
54#65284—31no—
55C24×C3×C5—21no—
56C2×C3×C5×D4—21no—
57C2×C3×C5×D4—22no—
58C2×C3×C5×D4C2×C414yescomplemented
59C2×C3×C5×D4C2312yes—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—21no—
64C22×Dic15—21no—
65#6817—22no—
66#6817C2×C414yescomplemented
67C2×D60C2311yescharacteristic
68C2×C4×D15—21no—
69C2×C4×D15—22no—
70C2×Dic30C2311yescharacteristic
71C3×C5×C4⋊C4D411yescharacteristic
72C3×C5×C4⋊C4D411yescharacteristic
73C3×C5×C4⋊C4C2311yescharacteristic
74C3×C5×C4⋊C4C2311yescharacteristic
75C3×C5×C22⋊C4—21no—
76C3×C5×C22⋊C4—22no—
77C3×C5×C22⋊C4—22no—
78C3×C5×C22⋊C4D412yes—
79C3×C42×C5—21no—
80C3×C42×C5C2312yes—
81#6716C2×C418yescomplemented
82#6715C2×C418yescomplemented
83#6714—22no—
84C4⋊Dic15—21no—
85C4⋊Dic15C2312yes—
86#6712—22no—
87C4×Dic15—22no—
88#6710C2×C414yescomplemented
89C2×C3⋊#168—22no—
90C2×C3⋊#168C2311yescharacteristic
91C2×C3⋊#168C2311yescharacteristic
92C2×C3⋊#168C2312yes—
93C3×#518D511yescharacteristic, complemented
94C2×#932—51no—
95#5523—51no—
96C2×#832—51no—
97#5018—52no—
98C4×#214—52no—
99#5014—52no—
100C4×#213—52no—
101#5002—51no—
102#4997—51no—
103#4995—51no—
104C22×C5×D4C2×D311yescharacteristic
105C2×#709—31no—
106C4×C5×D4—21no—
107C4×C5×D4—21no—
108C4×C5×D4C2×D312yes—
109C4×C5×D4C2×D312yes—
110C5×#117C2×D311yescharacteristic
111C5×#117C2×D311yescharacteristic
112C2×C5×C22⋊C4—22no—
113C2×#687—32no—
114#4078—38no—
115C2×#686—32no—
116C2×C4⋊Dic5—31no—
117C2×#681—31no—
118C22×#168—31no—
119#4038—61no—
120D5×C4⋊C4—61no—
121#4027—62no—
122C4×D20—32no—
123C4×Dic10—32no—
124#3964—32no—
125#3964—32no—
126#3942—31no—
127#3942—31no—
128#3941—31no—
129#3941—31no—
130#3940—32no—
131#3939—32no—
132#3935—32no—
133C4×#168—32no—
134#2946—151noSylow
135C23×C3×C5—22no—
136C23×C3×C5—24no—
137C23×C3×C5—81no—
138C23×C3×C5—81no—
139C23×C3×C5C2×D411yescharacteristic
140C22×D15—21no—
141C3×C5×D4—24no—
142C3×C5×D4—22no—
143C3×C5×D4C22×C414yes—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—82no—
147C2×C3×C4×C5—82no—
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5C2×D411yescharacteristic
152C2×C3×C4×C5#4112yes—
153C2×C3×C4×C5C2411yescharacteristic
154#1220—24no—
155C2×Dic15—21no—
156C2×Dic15—22no—
157C2×Dic15—81no—
158D60—21no—
159D60C22×C412yes—
160C4×D15—24no—
161C4×D15—82no—
162Dic30—21no—
163Dic30C22×C412yes—
164C3⋊#168—21no—
165C3⋊#168—21no—
166C3⋊#168C22×C414yes—
167C22×C3×D4C2×D511yescharacteristic
168C2×#235—51no—
169C3×C4×D4—21no—
170C3×C4×D4—21no—
171C3×C4×D4C2×D512yes—
172C3×C4×D4C2×D512yes—
173C3×#117C2×D511yescharacteristic
174C3×#117C2×D511yescharacteristic
175C2×C3×C22⋊C4—22no—
176C2×#214—52no—
177#932—58no—
178C2×#213—52no—
179C2×C4⋊Dic3—51no—
180C2×#208—51no—
181C22×C3⋊C8—51no—
182#892—101no—
183D3×C4⋊C4—101no—
184#67⋊C4—102no—
185C4×D12—52no—
186C4×Dic6—52no—
187#832—52no—
188#832—52no—
189#810—51no—
190#810—51no—
191#809—51no—
192#809—51no—
193#808—52no—
194#807—52no—
195#803—52no—
196C4×C3⋊C8—52no—
197C24×C5—21no—
198C2×C5×D4—22no—
199C2×C5×D4—21no—
200C2×C5×D4C4×D314yescomplemented
201C2×C5×D4C22×D312yes—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5C22×D311yescharacteristic
205C2×C22⋊D5—61no—
206C22×Dic5—61no—
207#709—34no—
208#709—62no—
209C2×D20—31no—
210C2×C4×D5—61no—
211C2×C4×D5—62no—
212C2×Dic10—31no—
213C5×C4⋊C4#6711yescharacteristic
214C5×C4⋊C4#6711yescharacteristic
215C5×C4⋊C4C22×D311yescharacteristic
216C5×C4⋊C4C22×D311yescharacteristic
217C5×C22⋊C4—21no—
218C5×C22⋊C4—22no—
219C5×C22⋊C4—22no—
220C5×C22⋊C4#6712yes—
221C42×C5—21no—
222C42×C5C22×D312yes—
223#687—38no—
224#686—38no—
225#685—62no—
226C4⋊Dic5—32no—
227C4⋊Dic5—61no—
228#683—62no—
229C4×Dic5—62no—
230#681—34no—
231C2×#168—32no—
232C2×#168—31no—
233C2×#168—31no—
234C2×#168—62no—
235C2×AGL(1,ℤ/8)—151no—
236#520—151no—
237#518D1511yescharacteristic, complemented
238#442—152no—
239#440—152no—
240C4×SD16—152no—
241C4×D8—152no—
242#428—151no—
243#416—151no—
244C2×#102—151no—
245#405—151no—
246C22×C3×C5—21no—
247C22×C3×C5—21no—
248C22×C3×C5—24no—
249C22×C3×C5—42no—
250C22×C3×C5—42no—
251C22×C3×C5—84no—
252C22×C3×C5C4×D412yes—
253C22×C3×C5C22×D411yescharacteristic
254C2×D15—22no—
255C2×D15—41no—
256C2×D15—41no—
257C3×C4×C5—22no—
258C3×C4×C5—22no—
259C3×C4×C5—41no—
260C3×C4×C5—41no—
261C3×C4×C5C4×D412yes—
262C3×C4×C5C23×C411yescharacteristic
263C3×C4×C5C2×#4111yescharacteristic
264Dic15—22no—
265Dic15—42no—
266C24×C3—21no—
267C2×C3×D4—22no—
268C2×C3×D4—21no—
269C2×C3×D4C4×D514yescomplemented
270C2×C3×D4C22×D512yes—
271C22×C3×C4—22no—
272C22×C3×C4—22no—
273C22×C3×C4C22×D511yescharacteristic
274C2×#67—101no—
275C22×Dic3—101no—
276#235—54no—
277#235—102no—
278C2×D12—51no—
279C2×C4×D3—101no—
280C2×C4×D3—102no—
281C2×Dic6—51no—
282C3×C4⋊C4C22⋊D511yescharacteristic
283C3×C4⋊C4C22⋊D511yescharacteristic
284C3×C4⋊C4C22×D511yescharacteristic
285C3×C4⋊C4C22×D511yescharacteristic
286C3×C22⋊C4—21no—
287C3×C22⋊C4—22no—
288C3×C22⋊C4—22no—
289C3×C22⋊C4C22⋊D512yes—
290C3×C42—21no—
291C3×C42C22×D512yes—
292#214—58no—
293#213—58no—
294(C2×D3)⋊C4—102no—
295C4⋊Dic3—52no—
296C4⋊Dic3—101no—
297Dic3⋊C4—102no—
298C4×Dic3—102no—
299#208—54no—
300C2×C3⋊C8—52no—
301C2×C3⋊C8—51no—
302C2×C3⋊C8—51no—
303C2×C3⋊C8—102no—
304C23×C5—22no—
305C23×C5—24no—
306C23×C5—81no—
307C23×C5—81no—
308C23×C5C2×#6711yescharacteristic
309C22×D5—61no—
310C5×D4—24no—
311C5×D4—22no—
312C5×D4C2×C4×D314yes—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—82no—
316C2×C4×C5—82no—
317C2×C4×C5C2×C4×D312yes—
318C2×C4×C5#23512yes—
319C2×C4×C5C2×#6712yes—
320C2×C4×C5C2×#6712yes—
321C2×C4×C5C2×#6711yescharacteristic
322C2×C4×C5C23×D311yescharacteristic
323C22⋊D5—64no—
324C2×Dic5—61no—
325C2×Dic5—62no—
326C2×Dic5—241no—
327D20—32no—
328D20—61no—
329C4×D5—64no—
330C4×D5—242no—
331Dic10—32no—
332Dic10—61no—
333#168—34no—
334#168—61no—
335#168—61no—
336C2×#41—151no—
337C22×D4C2×D1511yescharacteristic
338AGL(1,ℤ/8)—158no—
339C2×SD16—152no—
340C2×D8—152no—
341C2×M16—151no—
342C22×C8—151no—
343C4×Q8—152no—
344C4×D4—21no—
345C4×D4—21no—
346C4×D4—152no—
347C4×D4—302no—
348C4×D4C2×D1512yes—
349C4×D4C2×D1512yes—
350#117—301no—
351#117C2×D1511yescharacteristic
352#117C2×D1511yescharacteristic
353C2×C4⋊C4—151no—
354C2×C4⋊C4—301no—
355C2×C22⋊C4—22no—
356#107—152no—
357#106—152no—
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×C5—44no—
368C2×C3×C5C2×C4×D411yescharacteristic
369C2×C3×C5#57611yescharacteristic
370C2×C3×C5#57711yescharacteristic
371D15—42no—
372C23×C3—22no—
373C23×C3—24no—
374C23×C3—81no—
375C23×C3—81no—
376C23×C3C2×C22⋊D511yescharacteristic
377C22×D3—101no—
378C3×D4—22no—
379C3×D4—24no—
380C3×D4C2×C4×D514yes—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—82no—
384C2×C3×C4—82no—
385C2×C3×C4C2×C4×D512yes—
386C2×C3×C4#70912yes—
387C2×C3×C4C2×C22⋊D512yes—
388C2×C3×C4C2×C22⋊D512yes—
389C2×C3×C4C2×C22⋊D511yescharacteristic
390C2×C3×C4C23×D511yescharacteristic
391#67—104no—
392C2×Dic3—101no—
393C2×Dic3—102no—
394C2×Dic3—401no—
395D12—52no—
396D12—101no—
397C4×D3—104no—
398C4×D3—402no—
399Dic6—52no—
400Dic6—101no—
401C3⋊C8—54no—
402C3⋊C8—101no—
403C3⋊C8—101no—
404C22×C5—21no—
405C22×C5—21no—
406C22×C5—24no—
407C22×C5—42no—
408C22×C5—42no—
409C22×C5—84no—
410C22×C5C4×#6712yes—
411C22×C5C22×#6711yescharacteristic
412C2×D5—62no—
413C2×D5—121no—
414C2×D5—121no—
415C4×C5—22no—
416C4×C5—22no—
417C4×C5—41no—
418C4×C5—41no—
419C4×C5C4×#6712yes—
420C4×C5C22×C4×D311yescharacteristic
421C4×C5C2×#23511yescharacteristic
422Dic5—62no—
423Dic5—122no—
424C24—21no—
425#41—154no—
426#41—302no—
427C2×Q8—151no—
428C2×D4—22no—
429C2×D4—21no—
430C2×D4—151no—
431C2×D4—301no—
432C2×D4C4×D1514yescomplemented
433C2×D4C22×D1512yes—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—301no—
437C22×C4—301no—
438C22×C4—302no—
439C22×C4C22×D1511yescharacteristic
440SD16—158no—
441D8—158no—
442M16—154no—
443C2×C8—152no—
444C2×C8—151no—
445C2×C8—151no—
446C2×C8—302no—
447C4⋊C4—152no—
448C4⋊C4—301no—
449C4⋊C4—302no—
450C4⋊C4#122011yescharacteristic
451C4⋊C4#122011yescharacteristic
452C4⋊C4C22×D1511yescharacteristic
453C4⋊C4C22×D1511yescharacteristic
454C22⋊C4—21no—
455C22⋊C4—22no—
456C22⋊C4—22no—
457C22⋊C4—302no—
458C22⋊C4#122012yes—
459C42—21no—
460C42—302no—
461C42C22×D1512yes—
462C3×C5#294611yescharacteristic, complemented, Hall
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—24no—
466C22×C3—42no—
467C22×C3—42no—
468C22×C3—84no—
469C22×C3C4×C22⋊D512yes—
470C22×C3C22×C22⋊D511yescharacteristic
471C2×D3—102no—
472C2×D3—201no—
473C2×D3—201no—
474C3×C4—22no—
475C3×C4—22no—
476C3×C4—41no—
477C3×C4—41no—
478C3×C4C4×C22⋊D512yes—
479C3×C4C22×C4×D511yescharacteristic
480C3×C4C2×#70911yescharacteristic
481Dic3—102no—
482Dic3—202no—
483C2×C5—22no—
484C2×C5—44no—
485C2×C5C2×C4×#6711yescharacteristic
486C2×C5#583511yescharacteristic
487C2×C5#583611yescharacteristic
488D5—122no—
489C23—22no—
490C23—24no—
491C23—81no—
492C23—81no—
493C23—301no—
494C23C2×#122011yescharacteristic
495Q8—152no—
496Q8—301no—
497D4—24no—
498D4—22no—
499D4—152no—
500D4—304no—
501D4—301no—
502D4C2×C4×D1514yes—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—82no—
506C2×C4—82no—
507C2×C4—301no—
508C2×C4—304no—
509C2×C4—302no—
510C2×C4—1202no—
511C2×C4—1201no—
512C2×C4C2×C4×D1512yes—
513C2×C4#681712yes—
514C2×C4C2×#122012yes—
515C2×C4C2×#122012yes—
516C2×C4C2×#122011yescharacteristic
517C2×C4C23×D1511yescharacteristic
518C8—154no—
519C8—301no—
520C8—301no—
521C2×C3—22no—
522C2×C3—44no—
523C2×C3C2×C4×C22⋊D511yescharacteristic
524C2×C3#6616911yescharacteristic
525C2×C3#6617011yescharacteristic
526D3—202no—
527C5#8253711yescharacteristic, complemented, Sylow
528C22—21no—
529C22—21no—
530C22—24no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22—302no—
535C22—601no—
536C22—601no—
537C22C4×#122012yes—
538C22C22×#122011yescharacteristic
539C4—22no—
540C4—22no—
541C4—41no—
542C4—41no—
543C4—302no—
544C4—602no—
545C4C4×#122012yes—
546C4C22×C4×D1511yescharacteristic
547C4C2×#681711yescharacteristic
548C3#1061426811yescharacteristic, complemented, Sylow
549C2—22no—
550C2—44no—
551C2—602no—
552C2C2×C4×#122011yescharacteristic
553C2#1175659411yescharacteristic
554C2#1175659511yescharacteristic
subgroupG/H
centerC22C22×#1220
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC3×C5×#518C2
socleC22×C3×C5C22×D4
prime radicalC2×#91821C2
cosocleC2×C3×C4×C5C24
hypercenter#518D15
hypocenterC3×C5#2946
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. C3×C5×#518C2semidirect
3. #11756282C2semidirect
4. C2×#91116C2semidirect
5. #11751119C2semidirect
6. C4×#6716C2semidirect
7. #11751115C2semidirect
8. C4×#6715C2semidirect
9. #11751103C2semidirect
10. #11751098C2semidirect
11. #11751096C2semidirect
23. #91821C4semidirect
31. C4×D60C22semidirect
32. C4×Dic30C22semidirect
35. #91094C22semidirect
36. #91094C22semidirect
37. #91093C22semidirect
38. #91093C22semidirect
39. #91092C22semidirect
40. #91091C22semidirect
41. #91087C22semidirect
42. C4×C3⋊#168C22semidirect
44. C5×#518D3semidirect
58. C2×C3×C5×D4C2×C4semidirect
66. #6817C2×C4semidirect
81. #6716C2×C4semidirect
82. #6715C2×C4semidirect
88. #6710C2×C4semidirect
93. C3×#518D5semidirect
200. C2×C5×D4C4×D3semidirect
237. #518D15semidirect
269. C2×C3×D4C4×D5semidirect
432. C2×D4C4×D15semidirect
462. C3×C5#2946semidirect
527. C5#82537semidirect
548. C3#10614268semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5182
C2×#918212
#117562822
C2×#911162
#117511192
C4×#67162
#117511152
C4×#67152
#117511032
#117510982
#117510962
#106142683
#825375