Finite Group Databasebeta

← #14416752

Subgroups — #14416752

Order 1920.

1096 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4039C211yesmaximal, characteristic, complemented
2Dic5×#235C211yesmaximal, characteristic, complemented
3C2×#91298C211yesmaximal, characteristic
4#11751065C211yesmaximal, characteristic, complemented
5C5×#4966C211yesmaximal, characteristic, complemented
6#11748367C211yesmaximal, characteristic, complemented
7Dic5×#208C211yesmaximal, characteristic, complemented
8#11747471C212yesmaximal, complemented
9#11747468C212yesmaximal, complemented
10#11747261C212yesmaximal, complemented
11#11747216C212yesmaximal, complemented
12#10610597—31nomaximal, Hall
13C2×C5×#235C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×C3×C4×D5—21no—
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17#91815C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C2×C3×#685—21no—
21C2×C3×C4×Dic5C2211yescharacteristic
22C3×#4039—21no—
23C3×#4039—21no—
24C3×#4039C2212yes—
25C3×#4039C2212yes—
26Dic5×#67—21no—
27Dic5×#67—21no—
28Dic5×D12C2211yescharacteristic, complemented
29Dic5×D12C2211yescharacteristic, complemented
30C4×D3×Dic5—21no—
31#91371—21no—
32Dic5×Dic6C2211yescharacteristic, complemented
33Dic5×Dic6C2211yescharacteristic, complemented
34C2×#6655C2212yes—
35#91298C418yescomplemented
36C2×#6652C2212yes—
37#91092C2212yescomplemented
38#91091C2212yescomplemented
39C5×#810C2212yescomplemented
40C5×#809C2212yescomplemented
41#90965C2212yes—
42#90965C2212yes—
43#90952C2212yescomplemented
44Dic5×C3⋊C8C2212yescomplemented
45C4×#932—51nomaximal, Hall
46#41×Dic5—31no—
47C2×#4095—31no—
48C2×#4039D311yescharacteristic, complemented
49C5×#417—31no—
50#65420—31no—
51M16×Dic5—31no—
52#65253—31no—
53#65106—32no—
54#65077—32no—
55#65074—32no—
56#65045—32no—
57C23×C3×D5—21no—
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5C2311yescharacteristic
60C2×C5×#67—21no—
61C5×#235—22no—
62C5×#235C2×C414yescomplemented
63C2×C5×D12C2311yescharacteristic
64C2×C4×C5×D3—21no—
65C2×C5×Dic6C2311yescharacteristic
66C22×C3×Dic5D411yescharacteristic
67C22×C3×Dic5D411yescharacteristic
68C2×C3×D20—21no—
69C2×C3×D20—22no—
70C2×C3×D20C2×C414yescomplemented
71C2×C3×D20C2312yes—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5—22no—
74C2×C3×C4×D5—44no—
75C2×D3×Dic5—21no—
76C2×D3×Dic5—21no—
77C3×C5×C4⋊C4—21no—
78C3×C5×C4⋊C4C2312yes—
79#6719—21no—
80C4⋊Dic15C2311yescharacteristic
81C4⋊Dic15C2311yescharacteristic
82C4×Dic15—21no—
83#6710C2×C414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×#208—22no—
86C2×C5×C3⋊C8C2312yes—
87C3×#685—22no—
88C3×#685—22no—
89C3×C4×Dic5D411yescharacteristic
90C3×C4×Dic5D411yescharacteristic
91C3×C4×Dic5C2311yescharacteristic
92C3×C4×Dic5C2311yescharacteristic
93Dic3⋊Dic5—21no—
94Dic3⋊Dic5—21no—
95(C2×D3)⋊Dic5—21no—
96(C2×D3)⋊Dic5—21no—
97Dic3×Dic5—21no—
98Dic3×Dic5—21no—
99#6655C2×C418yescomplemented
100#6652C2×C418yescomplemented
101C2×C3×C4×D4—51no—
102C2×#932—51no—
103C4×#235—51no—
104#5215—51no—
105#5018—52no—
106C4×#214—52no—
107#5014—52no—
108C4×#213—52no—
109#4966D511yescharacteristic, complemented
110#4964—51no—
111C4×#208—51no—
112C2×C5×#41—31no—
113C22×D20C2×D311yescharacteristic
114C22×C4×D5—21no—
115C2×C5×M16—31no—
116C2×C5×C4⋊C4C2×D311yescharacteristic
117#4095—38no—
118Q8×Dic5—31no—
119Q8×Dic5—31no—
120C2×#688—32no—
121D4×Dic5—31no—
122D4×Dic5—31no—
123D4×Dic5—61no—
124D4×Dic5—61no—
125C2×#686—32no—
126C2×#685—21no—
127#4072—31no—
128#4072—61no—
129C2×C4×Dic5—61no—
130C2×C4×Dic5C2×D311yescharacteristic
131C2×#681—31no—
132#4039—21no—
133#4039—21no—
134#4039C2×D312yes—
135#4039C2×D312yes—
136C5×#103—32no—
137C5×#102—32no—
138#3953—32no—
139#3953—32no—
140#3947—32no—
141C8×Dic5—32no—
142#3940—32no—
143#3939—32no—
144C4×AGL(1,ℤ/8)—151noSylow
145C23×C3×C5C2×D411yescharacteristic
146C22×C5×D3—21no—
147C22×C3×D5—24no—
148C22×C3×D5—22no—
149C22×C3×D5—42no—
150C22×C3×D5—42no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—42no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5#4112yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×Dic15—21no—
158C2×Dic15—21no—
159C5×#67—24no—
160C2×C5×Dic3—21no—
161C5×D12—21no—
162C5×D12C22×C412yescomplemented
163C4×C5×D3—24no—
164C5×Dic6—21no—
165C5×Dic6C22×C412yescomplemented
166C2×C3×Dic5—22no—
167C2×C3×Dic5—41no—
168C2×C3×Dic5C2×D411yescharacteristic
169C2×C3×Dic5C2×D411yescharacteristic
170C2×C3×Dic5C2×D411yescharacteristic
171C2×C3×Dic5C2×D411yescharacteristic
172C3×D20—24no—
173C3×D20—22no—
174C3×D20C22×C414yes—
175C3×C4×D5—44no—
176C3×C4×D5—44no—
177D3×Dic5—42no—
178D3×Dic5—42no—
179C3⋊#168C22×C414yescomplemented
180C5×C3⋊C8—22no—
181C22×C3×D4—51no—
182C23×C3×C4—101no—
183C2×#235C2×D511yescharacteristic
184C3×C4×D4—52no—
185C3×C4×D4—52no—
186C3×C4×D4—101no—
187C3×C4×D4—101no—
188C2×C3×C4⋊C4C2×D511yescharacteristic
189C2×C3×C22⋊C4—101no—
190C2×C3×C42—51no—
191C2×#214—52no—
192#932—58no—
193C2×#213—52no—
194C4×#67—101no—
195C4×#67—101no—
196#926—51no—
197C2×#208—51no—
198C2×#208C2×D511yescharacteristic
199C4×D12—51no—
200C4×D12—51no—
201#872—101no—
202C42×D3—101no—
203C4×Dic6—51no—
204C4×Dic6—51no—
205#832—52no—
206#832—52no—
207#810C2×D512yescomplemented
208#809C2×D512yescomplemented
209#808—52no—
210#807—52no—
211#803—52no—
212C4×C3⋊C8—52no—
213C23×D5—21no—
214C5×#41—34no—
215C5×#41—62no—
216C2×C5×Q8—31no—
217C2×C5×D4—31no—
218C2×C5×D4—61no—
219C22×C4×C5—21no—
220C22×C4×C5—61no—
221C22×C4×C5C22×D311yescharacteristic
222C22×Dic5—61no—
223C22×Dic5—61no—
224C22×Dic5#6711yescharacteristic
225C22×Dic5#6711yescharacteristic
226C2×D20—22no—
227C2×D20—21no—
228C2×D20C4×D314yescomplemented
229C2×D20C22×D312yes—
230C2×C4×D5—22no—
231C2×C4×D5—22no—
232C2×C4×D5—44no—
233C5×M16—62no—
234C2×C5×C8—32no—
235C5×C4⋊C4—21no—
236C5×C4⋊C4C22×D312yes—
237C22⋊Dic5—61no—
238C22⋊Dic5—61no—
239C22⋊Dic5—61no—
240#688—38no—
241#686—38no—
242#685—22no—
243#685—22no—
244C4⋊Dic5—31no—
245C4⋊Dic5—31no—
246C4⋊Dic5—61no—
247C4⋊Dic5—61no—
248C4×Dic5—61no—
249C4×Dic5—61no—
250C4×Dic5—61no—
251C4×Dic5#6711yescharacteristic
252C4×Dic5#6711yescharacteristic
253C4×Dic5C22×D311yescharacteristic
254C4×Dic5C22×D311yescharacteristic
255#681—34no—
256C2×#168—32no—
257C2×AGL(1,ℤ/8)—151no—
258C4×#41—151no—
259C2×C4×D4—51no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—151no—
266#417—31no—
267C4×M16—151no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5C4×D412yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×C5×D3—22no—
273C2×C5×D3—41no—
274C2×C5×D3—41no—
275C2×C3×D5—24no—
276C2×C3×D5—48no—
277C2×C3×D5—42no—
278C2×C3×D5—42no—
279C3×C4×C5—42no—
280C3×C4×C5C4×D412yes—
281C3×C4×C5C23×C411yescharacteristic
282C3×C4×C5C2×#4111yescharacteristic
283Dic15—41no—
284Dic15—41no—
285C3×Dic5—21no—
286C3×Dic5—21no—
287C3×Dic5—21no—
288C3×Dic5AGL(1,ℤ/8)12yescomplemented
289C5×Dic3—22no—
290C24×C3—101no—
291C2×C3×D4—54no—
292C2×C3×D4—52no—
293C2×C3×D4—101no—
294C2×C3×D4—102no—
295C22×C3×C4—21no—
296C22×C3×C4—51no—
297C22×C3×C4—51no—
298C22×C3×C4—102no—
299C22×C3×C4—102no—
300C22×C3×C4—204no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—21no—
303#235—22no—
304#235C4×D514yescomplemented
305C2×D12C22×D511yescharacteristic
306C2×C4×D3—21no—
307C2×C4×D3—101no—
308C2×C4×D3—101no—
309C2×Dic6C22×D511yescharacteristic
310C3×C4⋊C4—21no—
311C3×C4⋊C4C22×D512yes—
312C3×C22⋊C4—102no—
313C3×C22⋊C4—102no—
314C3×C42—51no—
315C3×C42—51no—
316C3×C42—51no—
317C3×C42—51no—
318#217—101no—
319#214—58no—
320#213—58no—
321(C2×D3)⋊C4—101no—
322(C2×D3)⋊C4—101no—
323C4⋊Dic3—51no—
324C4⋊Dic3—51no—
325Dic3⋊C4—101no—
326Dic3⋊C4—101no—
327C4×Dic3—101no—
328C4×Dic3—101no—
329C4×Dic3—101no—
330#208—22no—
331#208—54no—
332C2×C3⋊C8—52no—
333C2×C3⋊C8C22×D512yes—
334C23×C5—61no—
335C23×C5C2×#6711yescharacteristic
336C22×D5—24no—
337C22×D5—22no—
338C22×D5—42no—
339C22×D5—42no—
340C5×Q8—32no—
341C5×Q8—61no—
342C5×D4—32no—
343C5×D4—64no—
344C5×D4—61no—
345C2×C4×C5—22no—
346C2×C4×C5—42no—
347C2×C4×C5—61no—
348C2×C4×C5—64no—
349C2×C4×C5C2×C4×D312yes—
350C2×C4×C5#23512yes—
351C2×C4×C5C2×#6711yescharacteristic
352C2×C4×C5C23×D311yescharacteristic
353C2×Dic5—22no—
354C2×Dic5—41no—
355C2×Dic5—61no—
356C2×Dic5—61no—
357C2×Dic5—122no—
358C2×Dic5—122no—
359C2×Dic5C2×#6711yescharacteristic
360C2×Dic5C2×#6711yescharacteristic
361C2×Dic5C2×#6711yescharacteristic
362C2×Dic5C2×#6711yescharacteristic
363D20—24no—
364D20—22no—
365D20C2×C4×D314yes—
366C4×D5—44no—
367C4×D5—44no—
368C5×C8—62no—
369#168—34no—
370C2×#41—31no—
371C22×D4—51no—
372C23×C4—101no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—31no—
377C2×M16—151no—
378C4×Q8—151no—
379C4×Q8—151no—
380C4×D4—52no—
381C4×D4—52no—
382C4×D4—101no—
383C4×D4—101no—
384C4×D4—151no—
385C4×D4—151no—
386C4×D4—301no—
387C4×D4—301no—
388#117—151no—
389#117—301no—
390C2×C4⋊C4D3×D511yescharacteristic
391C2×C22⋊C4—101no—
392C2×C42—51no—
393C2×C42—301no—
394#107—152no—
395#106—152no—
396#103—32no—
397#102—32no—
398#102—152no—
399#102—152no—
400#97—152no—
401C4×C8—152no—
402C2×C3×C5—22no—
403C2×C3×C5C2×C4×D411yescharacteristic
404C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
405C2×C3×C5#57511yescharacteristic
406C3×D5—44no—
407C5×D3—42no—
408C23×C3—102no—
409C23×C3—104no—
410C23×C3—202no—
411C23×C3—202no—
412C23×C3D4×D511yescharacteristic
413C22×D3—21no—
414C3×D4—54no—
415C3×D4—102no—
416C3×D4—104no—
417C2×C3×C4—22no—
418C2×C3×C4—42no—
419C2×C3×C4—51no—
420C2×C3×C4—51no—
421C2×C3×C4—51no—
422C2×C3×C4—51no—
423C2×C3×C4—102no—
424C2×C3×C4—204no—
425C2×C3×C4—204no—
426C2×C3×C4—201no—
427C2×C3×C4C2×C4×D512yes—
428C2×C3×C4D4×D511yescharacteristic
429C2×C3×C4#71112yes—
430C2×C3×C4C23×D511yescharacteristic
431#67—24no—
432C2×Dic3—21no—
433C2×Dic3—101no—
434C2×Dic3—101no—
435D12—21no—
436D12C2×C4×D512yescomplemented
437C4×D3—24no—
438C4×D3—202no—
439C4×D3—202no—
440Dic6—21no—
441Dic6C2×C4×D512yescomplemented
442C3⋊C8—22no—
443C3⋊C8—54no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—62no—
447C22×C5—121no—
448C22×C5—121no—
449C22×C5C4×#6712yes—
450C22×C5C22×#6711yescharacteristic
451C2×D5—24no—
452C2×D5—48no—
453C2×D5—42no—
454C2×D5—42no—
455C4×C5—42no—
456C4×C5—62no—
457C4×C5C4×#6712yes—
458C4×C5C22×C4×D311yescharacteristic
459C4×C5C2×#23511yescharacteristic
460Dic5—21no—
461Dic5—21no—
462Dic5—21no—
463Dic5—121no—
464Dic5—121no—
465Dic5#93212yescomplemented
466C24—101no—
467#41—34no—
468#41—62no—
469C2×Q8—31no—
470C2×D4—31no—
471C2×D4—54no—
472C2×D4—52no—
473C2×D4—61no—
474C2×D4—102no—
475C2×D4—101no—
476C22×C4—21no—
477C22×C4—51no—
478C22×C4—51no—
479C22×C4—61no—
480C22×C4—102no—
481C22×C4—102no—
482C22×C4—204no—
483C22×C4—301no—
484C22×C4—301no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—62no—
489M16—154no—
490C2×C8—32no—
491C2×C8—152no—
492C4⋊C4—21no—
493C4⋊C4—151no—
494C4⋊C4—151no—
495C4⋊C4—301no—
496C4⋊C4—301no—
497C4⋊C4C2×D3×D512yes—
498C22⋊C4—102no—
499C22⋊C4—102no—
500C22⋊C4—301no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C42—51no—
504C42—51no—
505C42—51no—
506C42—51no—
507C42—301no—
508C42—301no—
509C42—301no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—104no—
514C22×C3—208no—
515C22×C3—202no—
516C22×C3—202no—
517C22×C3#402712yes—
518C22×C3C2×D4×D511yescharacteristic
519C2×D3—22no—
520C2×D3—41no—
521C2×D3—41no—
522C3×C4—42no—
523C3×C4—52no—
524C3×C4—101no—
525C3×C4—101no—
526C3×C4—101no—
527C3×C4#402712yes—
528C3×C4C22×C4×D511yescharacteristic
529C3×C4C2×#71111yescharacteristic
530Dic3—22no—
531Dic3—201no—
532Dic3—201no—
533C2×C5—22no—
534C2×C5—122no—
535C2×C5C2×C4×#6711yescharacteristic
536C2×C5C2×#93211yescharacteristic
537C2×C5#582211yescharacteristic
538D5—44no—
539C23—61no—
540C23—104no—
541C23—102no—
542C23—202no—
543C23—202no—
544C23D5×#6711yescharacteristic
545Q8—32no—
546Q8—61no—
547D4—32no—
548D4—54no—
549D4—64no—
550D4—61no—
551D4—104no—
552D4—102no—
553C2×C4—22no—
554C2×C4—42no—
555C2×C4—51no—
556C2×C4—51no—
557C2×C4—51no—
558C2×C4—51no—
559C2×C4—61no—
560C2×C4—64no—
561C2×C4—102no—
562C2×C4—204no—
563C2×C4—204no—
564C2×C4—201no—
565C2×C4—301no—
566C2×C4—301no—
567C2×C4—602no—
568C2×C4—602no—
569C2×C4#677212yes—
570C2×C4C4×D3×D512yes—
571C2×C4D5×#6711yescharacteristic
572C2×C4C22×D3×D511yescharacteristic
573C8—62no—
574C8—154no—
575C2×C3—22no—
576C2×C3—204no—
577C2×C3C2×#402711yescharacteristic
578C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
579C2×C3#6611111yescharacteristic
580D3—42no—
581C5C4×#93211yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—62no—
585C22—104no—
586C22—121no—
587C22—121no—
588C22—208no—
589C22—202no—
590C22—202no—
591C22#9144012yes—
592C22C2×D5×#6711yescharacteristic
593C4—42no—
594C4—52no—
595C4—62no—
596C4—101no—
597C4—101no—
598C4—101no—
599C4—601no—
600C4—601no—
601C4#9144012yes—
602C4C2×#677211yescharacteristic
603C4C2×C4×D3×D511yescharacteristic
604C3#1061059711yescharacteristic, complemented, Sylow
605C2—22no—
606C2—122no—
607C2—204no—
608C2C2×#9144011yescharacteristic
609C2D5×#93211yescharacteristic
610C2#1175508411yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC22×C3×C5C22×D4
prime radicalC2×#91298C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
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. C2×C3×#4039C2semidirect
2. Dic5×#235C2semidirect
4. #11751065C2semidirect
5. C5×#4966C2semidirect
6. #11748367C2semidirect
7. Dic5×#208C2semidirect
8. #11747471C2semidirect
9. #11747468C2semidirect
10. #11747261C2semidirect
11. #11747216C2semidirect
28. Dic5×D12C22semidirect
29. Dic5×D12C22semidirect
32. Dic5×Dic6C22semidirect
33. Dic5×Dic6C22semidirect
35. #91298C4semidirect
37. #91092C22semidirect
38. #91091C22semidirect
39. C5×#810C22semidirect
40. C5×#809C22semidirect
43. #90952C22semidirect
44. Dic5×C3⋊C8C22semidirect
48. C2×#4039D3semidirect
62. C5×#235C2×C4semidirect
70. C2×C3×D20C2×C4semidirect
83. #6710C2×C4semidirect
99. #6655C2×C4semidirect
100. #6652C2×C4semidirect
109. #4966D5semidirect
162. C5×D12C22×C4semidirect
165. C5×Dic6C22×C4semidirect
179. C3⋊#168C22×C4semidirect
207. #810C2×D5semidirect
208. #809C2×D5semidirect
228. C2×D20C4×D3semidirect
288. C3×Dic5AGL(1,ℤ/8)semidirect
304. #235C4×D5semidirect
436. D12C2×C4×D5semidirect
441. Dic6C2×C4×D5semidirect
465. Dic5#932semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
581. C5C4×#932semidirect
604. C3#10610597semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40392
Dic5×#2352
C2×#912982
#117510652
C5×#49662
#117483672
Dic5×#2082
#117474712
#117474682
#117472612
#117472162
#106105973
C4×#9325