Finite Group Databasebeta

← #14416717

Subgroups — #14416717

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
1C3×#65856C211yesmaximal, characteristic, complemented
2C2×Dic5×D12C211yesmaximal, characteristic, complemented
3C2×#91299C211yesmaximal, characteristic
4#11751096C211yesmaximal, characteristic, complemented
5C5×#5001C211yesmaximal, characteristic, complemented
6#11748369C211yesmaximal, characteristic, complemented
7Dic5×#208C211yesmaximal, characteristic, complemented
8#11747468C212yesmaximal, complemented
9#11747218C212yesmaximal, complemented
10#11747217C212yesmaximal, complemented
11#11747216C212yesmaximal, complemented
12#10610645—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C2×C3×#709C2211yescharacteristic
15C22×D3×Dic5—21no—
16C3×C5×#117C2211yescharacteristic
17C2×C4⋊Dic15C2211yescharacteristic
18C2×#6710C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C2×C3×C4×Dic5C2211yescharacteristic
21C3×#4039C2211yescharacteristic, complemented
22C3×#4039C2211yescharacteristic, complemented
23C3×#4033C2211yescharacteristic, complemented
24C3×#4033C2211yescharacteristic, complemented
25C3×#4027—21no—
26C3×#4027—21no—
27C3×#4018—21no—
28C3×C42×D5—21no—
29C2×(C2×D3)⋊Dic5—21no—
30Dic5×D12—21no—
31Dic5×D12—21no—
32Dic5×D12C2212yes—
33Dic5×D12C2212yes—
34C2×#6656C2212yes—
35#91299C418yescomplemented
36C2×#6652C2212yes—
37#91092C2212yescomplemented
38#91091C2212yescomplemented
39C5×#809C2212yes—
40C5×#809C2212yes—
41#90971C2212yescomplemented
42#90965C2212yescomplemented
43#90952C2212yescomplemented
44Dic5×C3⋊C8C2212yescomplemented
45C4×#949—51nomaximal, Hall
46C2×D4×Dic5—31no—
47C2×#4078—31no—
48#65856D311yescharacteristic, complemented
49C5×#418—31no—
50#65422—31no—
51M16×Dic5—31no—
52#65284—31no—
53#65074—32no—
54#65047—32no—
55#65046—32no—
56#65045—32no—
57C23×C5×D3—21no—
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—21no—
60C2×C5×D12—21no—
61C2×C5×D12—22no—
62C2×C5×D12C2×C414yescomplemented
63C2×C5×D12C2312yes—
64C2×C3×C22⋊D5—21no—
65C22×C3×Dic5D411yescharacteristic
66C22×C3×Dic5D411yescharacteristic
67C3×#709—22no—
68C3×#709C2×C414yescomplemented
69C2×C3×D20C2311yescharacteristic
70C2×C3×C4×D5—21no—
71C2×C3×C4×D5—21no—
72C2×C3×C4×D5—21no—
73C2×C3×Dic10C2311yescharacteristic
74C2×D3×Dic5—22no—
75C2×D3×Dic5—22no—
76C2×D3×Dic5—44no—
77C3×C5×C4⋊C4C2311yescharacteristic
78C3×C5×C4⋊C4C2311yescharacteristic
79C3×C5×C22⋊C4—21no—
80C3×C42×C5—21no—
81C4⋊Dic15—21no—
82C4⋊Dic15C2312yes—
83#6710C2×C414yescomplemented
84C2×C3⋊#168C2312yes—
85C5×#208—22no—
86C2×C5×C3⋊C8C2312yes—
87C3×#685—21no—
88C3×#685—21no—
89C3×#683—21no—
90C3×#683—21no—
91C3×C4×Dic5—21no—
92C3×C4×Dic5—21no—
93C3×C4×Dic5D411yescharacteristic
94C3×C4×Dic5D411yescharacteristic
95C3×C4×Dic5C2311yescharacteristic
96C3×C4×Dic5C2311yescharacteristic
97(C2×D3)⋊Dic5—22no—
98(C2×D3)⋊Dic5—22no—
99#6656C2×C418yescomplemented
100#6652C2×C418yescomplemented
101C3×C4×#41—51no—
102C2×#949—51no—
103C2×C4×D12—51no—
104#5232—51no—
105#5026—52no—
106C4×#215—52no—
107#5014—52no—
108C4×#213—52no—
109#5001D511yescharacteristic, complemented
110#4995—51no—
111C4×#208—51no—
112C22×C5×D4—31no—
113C23×Dic5—61no—
114C2×#709C2×D311yescharacteristic
115C2×C5×M16—31no—
116C5×#117C2×D311yescharacteristic
117C2×C22⋊Dic5—61no—
118D4×Dic5—32no—
119D4×Dic5—32no—
120D4×Dic5—61no—
121D4×Dic5—61no—
122C2×#687—32no—
123#4078—38no—
124C2×#686—32no—
125C2×C4⋊Dic5—31no—
126C2×C4×Dic5C2×D311yescharacteristic
127C2×#681—31no—
128#4039C2×D311yescharacteristic, complemented
129#4039C2×D311yescharacteristic, complemented
130#4033C2×D311yescharacteristic, complemented
131#4033C2×D311yescharacteristic, complemented
132#4027—21no—
133#4027—21no—
134#4018—21no—
135C42×D5—21no—
136C5×#102—32no—
137C5×#102—32no—
138#3953—32no—
139#3948—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—24no—
147C22×C5×D3—22no—
148C22×C5×D3—42no—
149C22×C5×D3—42no—
150C22×C3×D5—21no—
151C2×C3×C4×C5—21no—
152C2×C3×C4×C5—21no—
153C2×C3×C4×C5C22×C412yes—
154C2×C3×C4×C5C2×D411yescharacteristic
155C2×C3×C4×C5#4112yes—
156C2×C3×C4×C5C2411yescharacteristic
157C2×Dic15—22no—
158C2×Dic15—42no—
159C5×D12—24no—
160C5×D12—22no—
161C5×D12C22×C414yes—
162C3×C22⋊D5—24no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—22no—
165C2×C3×Dic5—41no—
166C2×C3×Dic5C2×D411yescharacteristic
167C2×C3×Dic5C2×D411yescharacteristic
168C2×C3×Dic5C2×D411yescharacteristic
169C2×C3×Dic5C2×D411yescharacteristic
170C3×D20—21no—
171C3×D20C22×C412yescomplemented
172C3×C4×D5—24no—
173C3×C4×D5—42no—
174C3×C4×D5—42no—
175C3×Dic10—21no—
176C3×Dic10C22×C412yescomplemented
177D3×Dic5—44no—
178D3×Dic5—44no—
179C3⋊#168C22×C414yescomplemented
180C5×C3⋊C8—22no—
181C2×C3×#41—51no—
182C22×D12C2×D511yescharacteristic
183C22×C4×D3—101no—
184C3×C4×Q8—51no—
185C3×C4×Q8—51no—
186C3×C4×D4—51no—
187C3×C4×D4—51no—
188C3×C4×D4—101no—
189C3×C4×D4—101no—
190C3×#117—101no—
191C3×#117C2×D511yescharacteristic
192C2×C3×C42—51no—
193C2×C3×C42—101no—
194#949—58no—
195C2×#215—52no—
196C2×#213—52no—
197C2×(C2×D3)⋊C4—101no—
198C2×C4⋊Dic3—51no—
199C2×#208—51no—
200C2×#208C2×D511yescharacteristic
201C4×D12—52no—
202C4×D12—52no—
203C4×D12—101no—
204C4×D12—101no—
205#835—52no—
206#832—52no—
207#809C2×D512yes—
208#809C2×D512yes—
209#808—52no—
210#807—52no—
211#803—52no—
212C4×C3⋊C8—52no—
213C24×C5—61no—
214C2×C5×D4—34no—
215C2×C5×D4—32no—
216C2×C5×D4—62no—
217C2×C5×D4—61no—
218C22×C4×C5C22×D311yescharacteristic
219C2×C22⋊D5—21no—
220C22×Dic5—61no—
221C22×Dic5—62no—
222C22×Dic5—62no—
223C22×Dic5—124no—
224C22×Dic5#6711yescharacteristic
225C22×Dic5#6711yescharacteristic
226#709—22no—
227#709C4×D314yescomplemented
228C2×D20C22×D311yescharacteristic
229C2×C4×D5—21no—
230C2×C4×D5—21no—
231C2×C4×D5—21no—
232C2×Dic10C22×D311yescharacteristic
233C5×M16—62no—
234C2×C5×C8—32no—
235C5×C4⋊C4C22×D311yescharacteristic
236C5×C4⋊C4C22×D311yescharacteristic
237C5×C22⋊C4—21no—
238C42×C5—21no—
239C22⋊Dic5—62no—
240C22⋊Dic5—62no—
241#687—38no—
242#686—38no—
243#685—21no—
244#685—21no—
245C4⋊Dic5—32no—
246C4⋊Dic5—61no—
247#683—21no—
248#683—21no—
249C4×Dic5—21no—
250C4×Dic5—21no—
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—51no—
259C2×C4×D4—151no—
260#442—152no—
261#440—152no—
262C4×SD16—152no—
263C4×D8—152no—
264#428—151no—
265#418—31no—
266#417—151no—
267C4×M16—151no—
268C22×C3×C5—21no—
269C22×C3×C5—21no—
270C22×C3×C5C4×D412yes—
271C22×C3×C5C22×D411yescharacteristic
272C2×C5×D3—24no—
273C2×C5×D3—48no—
274C2×C5×D3—42no—
275C2×C5×D3—42no—
276C2×C3×D5—22no—
277C2×C3×D5—41no—
278C2×C3×D5—41no—
279C3×C4×C5—41no—
280C3×C4×C5—41no—
281C3×C4×C5C4×D412yes—
282C3×C4×C5C23×C411yescharacteristic
283C3×C4×C5C2×#4111yescharacteristic
284Dic15—42no—
285C3×Dic5—22no—
286C3×Dic5—21no—
287C3×Dic5—21no—
288C3×Dic5—21no—
289C3×Dic5AGL(1,ℤ/8)12yescomplemented
290C23×D3—21no—
291C3×#41—54no—
292C3×#41—102no—
293C2×C3×Q8—51no—
294C2×C3×D4—51no—
295C2×C3×D4—101no—
296C22×C3×C4—51no—
297C22×C3×C4—51no—
298C22×C3×C4—101no—
299C22×C3×C4—101no—
300C22×C3×C4—101no—
301C22×C3×C4C22×D511yescharacteristic
302C22×Dic3—101no—
303C2×D12—21no—
304C2×D12—22no—
305C2×D12C4×D514yescomplemented
306C2×D12C22×D512yes—
307C2×C4×D3—102no—
308C2×C4×D3—102no—
309C2×C4×D3—204no—
310C3×C4⋊C4—101no—
311C3×C4⋊C4—101no—
312C3×C4⋊C4C22×D511yescharacteristic
313C3×C4⋊C4C22×D511yescharacteristic
314C3×C22⋊C4—21no—
315C3×C22⋊C4—101no—
316C3×C22⋊C4—101no—
317C3×C42—21no—
318C3×C42—51no—
319C3×C42—51no—
320C3×C42—51no—
321C3×C42—51no—
322C3×C42—101no—
323C3×C42—101no—
324#215—58no—
325#213—58no—
326(C2×D3)⋊C4—102no—
327(C2×D3)⋊C4—102no—
328C4⋊Dic3—52no—
329C4⋊Dic3—101no—
330#208—22no—
331#208—54no—
332C2×C3⋊C8—52no—
333C2×C3⋊C8C22×D512yes—
334C23×C5—64no—
335C23×C5—62no—
336C23×C5—122no—
337C23×C5—122no—
338C23×C5C2×#6711yescharacteristic
339C22×D5—21no—
340C5×D4—34no—
341C5×D4—64no—
342C5×D4—62no—
343C2×C4×C5—21no—
344C2×C4×C5—21no—
345C2×C4×C5C2×C4×D312yes—
346C2×C4×C5#23512yes—
347C2×C4×C5C2×#6711yescharacteristic
348C2×C4×C5C23×D311yescharacteristic
349C22⋊D5—24no—
350C2×Dic5—21no—
351C2×Dic5—22no—
352C2×Dic5—41no—
353C2×Dic5—62no—
354C2×Dic5—124no—
355C2×Dic5—122no—
356C2×Dic5—124no—
357C2×Dic5C2×#6711yescharacteristic
358C2×Dic5C2×#6711yescharacteristic
359C2×Dic5C2×#6711yescharacteristic
360C2×Dic5C2×#6711yescharacteristic
361D20—21no—
362D20C2×C4×D312yescomplemented
363C4×D5—24no—
364C4×D5—42no—
365C4×D5—42no—
366Dic10—21no—
367Dic10C2×C4×D312yescomplemented
368C5×C8—62no—
369#168—34no—
370C2×#41—51no—
371C22×D4—31no—
372C23×C4—301no—
373AGL(1,ℤ/8)—158no—
374C2×SD16—152no—
375C2×D8—152no—
376C2×M16—31no—
377C2×M16—151no—
378C4×Q8—51no—
379C4×Q8—51no—
380C4×D4—51no—
381C4×D4—51no—
382C4×D4—101no—
383C4×D4—101no—
384C4×D4—152no—
385C4×D4—152no—
386C4×D4—301no—
387C4×D4—301no—
388#117—101no—
389#117D3×D511yescharacteristic
390C2×C4⋊C4—151no—
391C2×C22⋊C4—301no—
392C2×C42—51no—
393C2×C42—101no—
394#107—152no—
395#106—152no—
396#103—152no—
397#102—32no—
398#102—32no—
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—42no—
407C5×D3—44no—
408C23×C3—101no—
409C23×C3D4×D511yescharacteristic
410C22×D3—22no—
411C22×D3—24no—
412C22×D3—42no—
413C22×D3—42no—
414C3×Q8—52no—
415C3×Q8—101no—
416C3×D4—52no—
417C3×D4—104no—
418C3×D4—101no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—51no—
422C2×C3×C4—51no—
423C2×C3×C4—51no—
424C2×C3×C4—51no—
425C2×C3×C4—102no—
426C2×C3×C4—101no—
427C2×C3×C4—104no—
428C2×C3×C4—202no—
429C2×C3×C4—202no—
430C2×C3×C4—201no—
431C2×C3×C4C2×C4×D512yes—
432C2×C3×C4D4×D511yescharacteristic
433C2×C3×C4#71112yes—
434C2×C3×C4C23×D511yescharacteristic
435C2×Dic3—102no—
436C2×Dic3—202no—
437D12—22no—
438D12—24no—
439D12C2×C4×D514yes—
440C4×D3—204no—
441C4×D3—204no—
442C3⋊C8—22no—
443C3⋊C8—54no—
444C22×C5—21no—
445C22×C5—21no—
446C22×C5—64no—
447C22×C5—128no—
448C22×C5—122no—
449C22×C5—122no—
450C22×C5C4×#6712yes—
451C22×C5C22×#6711yescharacteristic
452C2×D5—22no—
453C2×D5—41no—
454C2×D5—41no—
455C4×C5—41no—
456C4×C5—41no—
457C4×C5C4×#6712yes—
458C4×C5C22×C4×D311yescharacteristic
459C4×C5C2×#23511yescharacteristic
460Dic5—22no—
461Dic5—21no—
462Dic5—21no—
463Dic5—21no—
464Dic5—122no—
465Dic5#94912yescomplemented
466C24—61no—
467#41—54no—
468#41—102no—
469C2×Q8—51no—
470C2×D4—34no—
471C2×D4—32no—
472C2×D4—51no—
473C2×D4—62no—
474C2×D4—61no—
475C2×D4—101no—
476C22×C4—51no—
477C22×C4—51no—
478C22×C4—101no—
479C22×C4—101no—
480C22×C4—101no—
481C22×C4—302no—
482C22×C4—302no—
483C22×C4—301no—
484C22×C4—604no—
485C22×C4C2×D3×D511yescharacteristic
486SD16—158no—
487D8—158no—
488M16—62no—
489M16—154no—
490C2×C8—32no—
491C2×C8—152no—
492C4⋊C4—101no—
493C4⋊C4—101no—
494C4⋊C4—152no—
495C4⋊C4—301no—
496C4⋊C4C2×D3×D511yescharacteristic
497C4⋊C4C2×D3×D511yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—101no—
500C22⋊C4—101no—
501C22⋊C4—302no—
502C22⋊C4—302no—
503C42—21no—
504C42—51no—
505C42—51no—
506C42—51no—
507C42—51no—
508C42—101no—
509C42—101no—
510C3×C5C4×AGL(1,ℤ/8)11yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—102no—
514C22×C3—201no—
515C22×C3—201no—
516C22×C3#402712yes—
517C22×C3C2×D4×D511yescharacteristic
518C2×D3—24no—
519C2×D3—48no—
520C2×D3—42no—
521C2×D3—42no—
522C3×C4—41no—
523C3×C4—41no—
524C3×C4—52no—
525C3×C4—102no—
526C3×C4—101no—
527C3×C4—101no—
528C3×C4—101no—
529C3×C4#402712yes—
530C3×C4C22×C4×D511yescharacteristic
531C3×C4C2×#71111yescharacteristic
532Dic3—202no—
533C2×C5—22no—
534C2×C5—124no—
535C2×C5C2×C4×#6711yescharacteristic
536C2×C5C2×#94911yescharacteristic
537C2×C5#582211yescharacteristic
538D5—42no—
539C23—64no—
540C23—62no—
541C23—101no—
542C23—122no—
543C23—122no—
544C23D5×#6711yescharacteristic
545Q8—52no—
546Q8—101no—
547D4—34no—
548D4—52no—
549D4—64no—
550D4—62no—
551D4—104no—
552D4—101no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—51no—
556C2×C4—51no—
557C2×C4—51no—
558C2×C4—51no—
559C2×C4—102no—
560C2×C4—101no—
561C2×C4—104no—
562C2×C4—202no—
563C2×C4—202no—
564C2×C4—201no—
565C2×C4—302no—
566C2×C4—604no—
567C2×C4—604no—
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—202no—
577C2×C3C2×#402711yescharacteristic
578C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
579C2×C3#6610711yescharacteristic
580D3—44no—
581C5C4×#94911yescharacteristic, complemented, Sylow
582C22—21no—
583C22—21no—
584C22—64no—
585C22—102no—
586C22—128no—
587C22—122no—
588C22—122no—
589C22—201no—
590C22—201no—
591C22#9144012yes—
592C22C2×D5×#6711yescharacteristic
593C4—41no—
594C4—41no—
595C4—52no—
596C4—102no—
597C4—101no—
598C4—101no—
599C4—101no—
600C4—602no—
601C4#9144012yes—
602C4C2×#677211yescharacteristic
603C4C2×C4×D3×D511yescharacteristic
604C3#1061064511yescharacteristic, complemented, Sylow
605C2—22no—
606C2—124no—
607C2—202no—
608C2C2×#9144011yescharacteristic
609C2D5×#94911yescharacteristic
610C2#1175534311yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#91299C2
cosocleC2×C3×C4×C5C24
hypercenter#117D3×D5
hypocenterC3×C5C4×AGL(1,ℤ/8)
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#65856C2semidirect
2. C2×Dic5×D12C2semidirect
4. #11751096C2semidirect
5. C5×#5001C2semidirect
6. #11748369C2semidirect
7. Dic5×#208C2semidirect
8. #11747468C2semidirect
9. #11747218C2semidirect
10. #11747217C2semidirect
11. #11747216C2semidirect
21. C3×#4039C22semidirect
22. C3×#4039C22semidirect
23. C3×#4033C22semidirect
24. C3×#4033C22semidirect
35. #91299C4semidirect
37. #91092C22semidirect
38. #91091C22semidirect
41. #90971C22semidirect
42. #90965C22semidirect
43. #90952C22semidirect
44. Dic5×C3⋊C8C22semidirect
48. #65856D3semidirect
62. C2×C5×D12C2×C4semidirect
68. C3×#709C2×C4semidirect
83. #6710C2×C4semidirect
99. #6656C2×C4semidirect
100. #6652C2×C4semidirect
109. #5001D5semidirect
128. #4039C2×D3semidirect
129. #4039C2×D3semidirect
130. #4033C2×D3semidirect
131. #4033C2×D3semidirect
171. C3×D20C22×C4semidirect
176. C3×Dic10C22×C4semidirect
179. C3⋊#168C22×C4semidirect
227. #709C4×D3semidirect
289. C3×Dic5AGL(1,ℤ/8)semidirect
305. C2×D12C4×D5semidirect
362. D20C2×C4×D3semidirect
367. Dic10C2×C4×D3semidirect
465. Dic5#949semidirect
510. C3×C5C4×AGL(1,ℤ/8)semidirect
581. C5C4×#949semidirect
604. C3#10610645semidirect

Maximal subgroups

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

subgroupindex
C3×#658562
C2×Dic5×D122
C2×#912992
#117510962
C5×#50012
#117483692
Dic5×#2082
#117474682
#117472182
#117472172
#117472162
#106106453
C4×#9495