Finite Group Databasebeta

← #14413423

Subgroups — #14413423

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×M16C211yesmaximal, characteristic
2D3×#4072C211yesmaximal, characteristic
3C2×#91338C211yesmaximal, characteristic
4#11751222C211yesmaximal, characteristic, complemented
5C3×#65410C211yesmaximal, characteristic, complemented
6#11748455C211yesmaximal, characteristic, complemented
7#11748453C211yesmaximal, characteristic, complemented
8#11747682C212yesmaximal, complemented
9#11747679C212yesmaximal, complemented
10#11747630C212yesmaximal, complemented
11#11747628C212yesmaximal, complemented
12#10615483—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C2×C3×C5×M16C2211yescharacteristic
15#91815C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C5×D3×M16C418yescomplemented
19C2×C5×ΓL(1,𝔽25)C2212yes—
20C2×C5×D3×C8C2212yes—
21C3×#4072C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23D3×C22⋊Dic5—21no—
24C2×(C2×D3)⋊Dic5—21no—
25#91529—21no—
26C2×Dic3×Dic5—21no—
27D3×C4⋊Dic5C2211yescharacteristic
28D3×C4⋊Dic5C2211yescharacteristic
29C4×D3×Dic5—21no—
30#91371—21no—
31#91338—21no—
32#91338—21no—
33#91338C2212yes—
34#91338C2211yescharacteristic
35#91338C2212yes—
36#91338C2211yescharacteristic
37#91102C2212yescomplemented
38#91101C2212yescomplemented
39C3×#3950C2212yescomplemented
40C3×#3949C2212yescomplemented
41#90990C2212yescomplemented
42#90990C2212yescomplemented
43#90987C2212yescomplemented
44#90987C2212yescomplemented
45#79208—51nomaximal, Hall
46C22×C5×M16—31no—
47C2×#4072—31no—
48C2×#4072—31no—
49#65410—31no—
50#65410—31no—
51#65410—32no—
52#65410—32no—
53#65410—31no—
54#65410D311yescharacteristic, complemented
55#65395—32no—
56#65395—32no—
57C23×C5×D3D411yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15—21no—
60C22×C5×Dic3D411yescharacteristic
61C2×C4×C5×D3C2×C414yes—
62C2×C4×C5×D3D411yescharacteristic
63C2×C4×C5×D3D411yescharacteristic
64C2×C4×C5×D3Q814yes—
65C2×C4×C5×D3C2311yescharacteristic
66C2×C4×C5×D3C2311yescharacteristic
67C22×C3×Dic5—21no—
68C2×D3×Dic5—21no—
69C2×D3×Dic5—21no—
70C3×C5×M16C2×C414yescomplemented
71C2×C3×C5×C8C2312yes—
72#6719—21no—
73C4⋊Dic15—21no—
74C4⋊Dic15C2311yescharacteristic
75C4⋊Dic15C2311yescharacteristic
76C4⋊Dic15C2312yes—
77C4×Dic15—21no—
78C5×#208C2×C414yescomplemented
79C2×C5×C3⋊C8C2312yes—
80C5×ΓL(1,𝔽25)C2×C418yescomplemented
81C5×D3×C8C2×C418yescomplemented
82C3×C22⋊Dic5—21no—
83C3×C4⋊Dic5—21no—
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4⋊Dic5C2311yescharacteristic
86C3×C4⋊Dic5C2312yes—
87C3×C4×Dic5—21no—
88Dic3⋊Dic5—21no—
89Dic3⋊Dic5—21no—
90(C2×D3)⋊Dic5—22no—
91(C2×D3)⋊Dic5—22no—
92(C2×D3)⋊Dic5—21no—
93(C2×D3)⋊Dic5—21no—
94Dic3×Dic5—21no—
95Dic3×Dic5—21no—
96Dic3×Dic5—22no—
97Dic3×Dic5—22no—
98C2×D3×M16D511yescharacteristic
99D3×#117—51no—
100C2×#892—51no—
101C3×#428—51no—
102#5121—51no—
103#4995—51no—
104#4964—51no—
105#4881—52no—
106#4880—52no—
107#4861—52no—
108#4860—52no—
109C23×C4×C5—31no—
110C2×C5×M16—31no—
111C2×C5×M16—38no—
112C2×C5×M16—32no—
113C2×C5×M16C2×D311yescharacteristic
114C22×C5×C8—32no—
115C2×C22⋊Dic5—61no—
116C2×C22⋊Dic5—61no—
117#4072—31no—
118#4072—31no—
119#4072—32no—
120#4072—31no—
121#4072—32no—
122#4072—61no—
123#4072—61no—
124#4072—61no—
125#4072—61no—
126#4072C2×D311yescharacteristic
127C2×C4⋊Dic5—31no—
128C2×C4⋊Dic5—31no—
129C2×C4⋊Dic5—31no—
130C2×C4⋊Dic5C2×D311yescharacteristic
131C2×C4×Dic5—61no—
132C2×C4×Dic5—61no—
133#3950—32no—
134#3950—32no—
135#3950—32no—
136#3950C2×D312yescomplemented
137#3949—32no—
138#3949—32no—
139#3949—32no—
140#3949C2×D312yescomplemented
141#2911—151noSylow
142C23×C3×C5C2×D411yescharacteristic
143C22×C5×D3—41no—
144C22×C5×D3—41no—
145C22×C5×D3C4⋊C414yes—
146C22×C5×D3C2×D411yescharacteristic
147C22×C5×D3C2×D411yescharacteristic
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×C3×C4×C5C2×Q812yes—
151C2×C3×C4×C5C2411yescharacteristic
152C2×Dic15—22no—
153C2×Dic15—21no—
154C2×Dic15—21no—
155C2×Dic15—42no—
156C2×C5×Dic3C4⋊C414yes—
157C2×C5×Dic3C2×D411yescharacteristic
158C2×C5×Dic3C2×D411yescharacteristic
159C4×C5×D3C4⋊C414yes—
160C4×C5×D3C4⋊C414yes—
161C4×C5×D3C22×C412yes—
162C4×C5×D3C22×C412yes—
163C4×C5×D3C2×Q812yes—
164C4×C5×D3C2×Q812yes—
165C2×C3×Dic5—22no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—42no—
169D3×Dic5—42no—
170D3×Dic5—42no—
171C3×C5×C8C22×C414yes—
172C5×C3⋊C8C22×C414yes—
173C22×C4×D3C2×D511yescharacteristic
174C2×C3×M16C2×D511yescharacteristic
175C3×#117—51no—
176C2×C3×C4⋊C4—51no—
177C2×(C2×D3)⋊C4—101no—
178#926—51no—
179C2×C4⋊Dic3—51no—
180C2×C4×Dic3—101no—
181C2×#208C2×D511yescharacteristic
182D3×M16Dic518yescomplemented
183C2×ΓL(1,𝔽25)C2×D512yes—
184C2×D3×C8C2×D512yes—
185#892—51no—
186#892—52no—
187#892—52no—
188#892—51no—
189#892—101no—
190#892—101no—
191D3×C4⋊C4—51no—
192D3×C4⋊C4—51no—
193D3×C22⋊C4—101no—
194#877—101no—
195#872—101no—
196C42×D3—101no—
197C3×#107—52no—
198C3×#106—52no—
199#818—52no—
200#817—52no—
201#808—52no—
202#808—52no—
203#807—52no—
204#807—52no—
205C24×C5—31no—
206C22×C4×C5—31no—
207C22×C4×C5—34no—
208C22×C4×C5—31no—
209C22×C4×C5—31no—
210C22×C4×C5—34no—
211C22×C4×C5—31no—
212C22×C4×C5—31no—
213C22×C4×C5C22×D311yescharacteristic
214C22×Dic5—21no—
215C22×Dic5—61no—
216C22×Dic5—61no—
217C22×Dic5—61no—
218C5×M16—34no—
219C5×M16—38no—
220C5×M16C4×D314yescomplemented
221C2×C5×C8—32no—
222C2×C5×C8—38no—
223C2×C5×C8C22×D312yes—
224C22⋊Dic5—21no—
225C22⋊Dic5—61no—
226C22⋊Dic5—61no—
227C22⋊Dic5—62no—
228C22⋊Dic5—62no—
229C22⋊Dic5—61no—
230C4⋊Dic5—21no—
231C4⋊Dic5—31no—
232C4⋊Dic5—31no—
233C4⋊Dic5—32no—
234C4⋊Dic5—61no—
235C4⋊Dic5—61no—
236C4⋊Dic5—61no—
237C4⋊Dic5C22×D311yescharacteristic
238C4⋊Dic5C22×D312yes—
239C4⋊Dic5C22×D311yescharacteristic
240C4×Dic5—21no—
241C4×Dic5—61no—
242C4×Dic5—61no—
243C4×Dic5—62no—
244C4×Dic5—62no—
245C4×Dic5—61no—
246C22×M16—31no—
247C2×#117—151no—
248C2×#117—151no—
249#428—51no—
250#428—152no—
251#428—152no—
252#428—151no—
253#428—151no—
254#428—151no—
255#427—152no—
256#427—152no—
257C22×C3×C5—21no—
258C22×C3×C5—21no—
259C22×C3×C5C2×C4⋊C412yes—
260C22×C3×C5C22×D411yescharacteristic
261C2×C5×D3—21no—
262C2×C5×D3—21no—
263C2×C5×D3—21no—
264C2×C5×D3—21no—
265C2×C5×D3—44no—
266C2×C5×D3C2×C4⋊C412yes—
267C2×C5×D3C2×C4⋊C412yes—
268C3×C4×C5C2×C4⋊C412yes—
269C3×C4×C5C23×C411yescharacteristic
270C3×C4×C5C22×Q811yescharacteristic
271Dic15—41no—
272Dic15—41no—
273Dic15—42no—
274C3×Dic5—41no—
275C3×Dic5—41no—
276C3×Dic5—42no—
277C5×Dic3C2×C4⋊C412yes—
278C5×Dic3C2×C4⋊C412yes—
279C23×D3D2011yescharacteristic
280C22×C3×C4—101no—
281C22×C3×C4C22×D511yescharacteristic
282C22×Dic3—101no—
283C22×Dic3D2011yescharacteristic
284C2×C4×D3—101no—
285C2×C4×D3—101no—
286C2×C4×D3Dic1014yes—
287C2×C4×D3D2011yescharacteristic
288C2×C4×D3D2011yescharacteristic
289C2×C4×D3C2×Dic514yes—
290C2×C4×D3C22×D511yescharacteristic
291C2×C4×D3C22×D511yescharacteristic
292C3×M16C2×Dic514yescomplemented
293C2×C3×C8C22×D512yes—
294C3×C4⋊C4—51no—
295C3×C4⋊C4—52no—
296C3×C4⋊C4—51no—
297C3×C4⋊C4—101no—
298C3×C22⋊C4—101no—
299C3×C42—101no—
300#217—101no—
301(C2×D3)⋊C4—101no—
302(C2×D3)⋊C4—101no—
303(C2×D3)⋊C4—102no—
304(C2×D3)⋊C4—102no—
305C4⋊Dic3—51no—
306C4⋊Dic3—52no—
307C4⋊Dic3—51no—
308C4⋊Dic3—101no—
309Dic3⋊C4—101no—
310Dic3⋊C4—101no—
311C4×Dic3—101no—
312C4×Dic3—101no—
313C4×Dic3—101no—
314C4×Dic3—102no—
315C4×Dic3—102no—
316#208C2×Dic514yescomplemented
317C2×C3⋊C8C22×D512yes—
318ΓL(1,𝔽25)C2×Dic518yescomplemented
319D3×C8C2×Dic518yescomplemented
320C23×C5—31no—
321C23×C5—31no—
322C23×C5—34no—
323C23×C5—121no—
324C23×C5—121no—
325C23×C5D3×D411yescharacteristic
326C2×C4×C5—34no—
327C2×C4×C5—31no—
328C2×C4×C5—31no—
329C2×C4×C5—34no—
330C2×C4×C5—34no—
331C2×C4×C5—32no—
332C2×C4×C5—32no—
333C2×C4×C5—32no—
334C2×C4×C5—32no—
335C2×C4×C5C2×C4×D312yes—
336C2×C4×C5D3×D411yescharacteristic
337C2×C4×C5D3×Q812yes—
338C2×C4×C5C23×D311yescharacteristic
339C2×Dic5—21no—
340C2×Dic5—21no—
341C2×Dic5—22no—
342C2×Dic5—42no—
343C2×Dic5—61no—
344C2×Dic5—62no—
345C2×Dic5—61no—
346C2×Dic5—122no—
347C2×Dic5—122no—
348C2×Dic5—122no—
349C5×C8—34no—
350C5×C8C2×C4×D314yes—
351C23×C4—31no—
352C2×M16—31no—
353C2×M16—38no—
354C2×M16—32no—
355C2×M16D3×D511yescharacteristic
356C22×C8—32no—
357#117—51no—
358#117—151no—
359#117—152no—
360#117—151no—
361#117—152no—
362#117—151no—
363#117—301no—
364#117—301no—
365#117—301no—
366#117—301no—
367C2×C4⋊C4—51no—
368C2×C4⋊C4—151no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4—151no—
371C2×C22⋊C4—301no—
372C2×C22⋊C4—301no—
373C2×C42—301no—
374C2×C42—301no—
375#107—52no—
376#107—152no—
377#107—152no—
378#107—152no—
379#106—52no—
380#106—152no—
381#106—152no—
382#106—152no—
383C2×C3×C5—22no—
384C2×C3×C5C22×C4⋊C411yescharacteristic
385C2×C3×C5#57511yescharacteristic
386C2×C3×C5#57511yescharacteristic
387C5×D3—22no—
388C5×D3—22no—
389C23×C3C2×D2011yescharacteristic
390C22×D3—41no—
391C22×D3—41no—
392C22×D3C4⋊Dic514yes—
393C22×D3C2×D2011yescharacteristic
394C22×D3C2×D2011yescharacteristic
395C2×C3×C4—102no—
396C2×C3×C4—101no—
397C2×C3×C4—101no—
398C2×C3×C4—202no—
399C2×C3×C4C2×Dic1012yes—
400C2×C3×C4C2×D2011yescharacteristic
401C2×C3×C4C22×Dic512yes—
402C2×C3×C4C23×D511yescharacteristic
403C2×Dic3—101no—
404C2×Dic3—101no—
405C2×Dic3—102no—
406C2×Dic3—202no—
407C2×Dic3C4⋊Dic514yes—
408C2×Dic3C2×D2011yescharacteristic
409C2×Dic3C2×D2011yescharacteristic
410C4×D3—202no—
411C4×D3—202no—
412C4×D3C4⋊Dic514yes—
413C4×D3C4⋊Dic514yes—
414C4×D3C2×Dic1012yes—
415C4×D3C2×Dic1012yes—
416C4×D3C22×Dic512yes—
417C4×D3C22×Dic512yes—
418C3×C8C22×Dic514yes—
419C3⋊C8C22×Dic514yes—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—32no—
423C22×C5—32no—
424C22×C5—61no—
425C22×C5—61no—
426C22×C5—61no—
427C22×C5—61no—
428C22×C5—124no—
429C22×C5D3×C4⋊C412yes—
430C22×C5C2×D3×D411yescharacteristic
431C4×C5—32no—
432C4×C5—32no—
433C4×C5D3×C4⋊C412yes—
434C4×C5C22×C4×D311yescharacteristic
435C4×C5C2×D3×Q811yescharacteristic
436Dic5—42no—
437Dic5—41no—
438Dic5—41no—
439Dic5—121no—
440Dic5—121no—
441Dic5—122no—
442C24—31no—
443C22×C4—31no—
444C22×C4—34no—
445C22×C4—31no—
446C22×C4—31no—
447C22×C4—34no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—101no—
451C22×C4—301no—
452C22×C4—301no—
453C22×C4—301no—
454C22×C4C2×D3×D511yescharacteristic
455M16—34no—
456M16—38no—
457M16D3×Dic514yescomplemented
458C2×C8—32no—
459C2×C8—38no—
460C2×C8C2×D3×D512yes—
461C4⋊C4—51no—
462C4⋊C4—52no—
463C4⋊C4—51no—
464C4⋊C4—101no—
465C4⋊C4—151no—
466C4⋊C4—152no—
467C4⋊C4—151no—
468C4⋊C4—301no—
469C4⋊C4—301no—
470C4⋊C4—301no—
471C22⋊C4—101no—
472C22⋊C4—301no—
473C22⋊C4—301no—
474C22⋊C4—302no—
475C22⋊C4—302no—
476C22⋊C4—301no—
477C42—101no—
478C42—301no—
479C42—301no—
480C42—302no—
481C42—302no—
482C42—301no—
483C3×C5#291111yescharacteristic, complemented, Hall
484C22×C3—21no—
485C22×C3—21no—
486C22×C3C2×C4⋊Dic512yes—
487C22×C3C22×D2011yescharacteristic
488C2×D3—21no—
489C2×D3—21no—
490C2×D3—21no—
491C2×D3—21no—
492C2×D3—44no—
493C2×D3C2×C4⋊Dic512yes—
494C2×D3C2×C4⋊Dic512yes—
495C3×C4—201no—
496C3×C4—201no—
497C3×C4—202no—
498C3×C4C2×C4⋊Dic512yes—
499C3×C4C22×Dic1011yescharacteristic
500C3×C4C23×Dic511yescharacteristic
501Dic3—201no—
502Dic3—201no—
503Dic3—202no—
504Dic3C2×C4⋊Dic512yes—
505Dic3C2×C4⋊Dic512yes—
506C2×C5—22no—
507C2×C5—62no—
508C2×C5—62no—
509C2×C5C2×D3×C4⋊C411yescharacteristic
510C2×C5#577311yescharacteristic
511C2×C5#577711yescharacteristic
512C23—31no—
513C23—31no—
514C23—34no—
515C23—121no—
516C23—121no—
517C23D3×D2011yescharacteristic
518C2×C4—34no—
519C2×C4—31no—
520C2×C4—31no—
521C2×C4—34no—
522C2×C4—34no—
523C2×C4—32no—
524C2×C4—32no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—101no—
528C2×C4—101no—
529C2×C4—102no—
530C2×C4—202no—
531C2×C4—302no—
532C2×C4—301no—
533C2×C4—301no—
534C2×C4—602no—
535C2×C4—602no—
536C2×C4—602no—
537C2×C4D3×Dic1012yes—
538C2×C4D3×D2011yescharacteristic
539C2×C4C2×D3×Dic512yes—
540C2×C4C22×D3×D511yescharacteristic
541C8—34no—
542C8C2×D3×Dic514yes—
543C2×C3—22no—
544C2×C3#6608211yescharacteristic
545C2×C3#6608211yescharacteristic
546C2×C3C22×C4⋊Dic511yescharacteristic
547D3—22no—
548D3—22no—
549C5#7920811yescharacteristic, complemented, Sylow
550C22—21no—
551C22—21no—
552C22—32no—
553C22—32no—
554C22—61no—
555C22—61no—
556C22—61no—
557C22—61no—
558C22—124no—
559C22D3×C4⋊Dic512yes—
560C22C2×D3×D2011yescharacteristic
561C4—32no—
562C4—32no—
563C4—201no—
564C4—202no—
565C4—201no—
566C4—601no—
567C4—602no—
568C4—601no—
569C4D3×C4⋊Dic512yes—
570C4C2×D3×Dic1011yescharacteristic
571C4C22×D3×Dic511yescharacteristic
572C3#1061548311yescharacteristic, complemented, Sylow
573C2—22no—
574C2—62no—
575C2—62no—
576C2#1175402811yescharacteristic
577C2#1175402911yescharacteristic
578C2C2×D3×C4⋊Dic511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C22×D4
prime radicalC23×C5×D3D4
cosocleC2×C3×C4×C5C24
hypercenterC2×M16D3×D5
hypocenterC3×C5#2911
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
4. #11751222C2semidirect
5. C3×#65410C2semidirect
6. #11748455C2semidirect
7. #11748453C2semidirect
8. #11747682C2semidirect
9. #11747679C2semidirect
10. #11747630C2semidirect
11. #11747628C2semidirect
18. C5×D3×M16C4semidirect
37. #91102C22semidirect
38. #91101C22semidirect
39. C3×#3950C22semidirect
40. C3×#3949C22semidirect
41. #90990C22semidirect
42. #90990C22semidirect
43. #90987C22semidirect
44. #90987C22semidirect
54. #65410D3semidirect
70. C3×C5×M16C2×C4semidirect
78. C5×#208C2×C4semidirect
80. C5×ΓL(1,𝔽25)C2×C4semidirect
81. C5×D3×C8C2×C4semidirect
136. #3950C2×D3semidirect
140. #3949C2×D3semidirect
182. D3×M16Dic5semidirect
220. C5×M16C4×D3semidirect
292. C3×M16C2×Dic5semidirect
316. #208C2×Dic5semidirect
318. ΓL(1,𝔽25)C2×Dic5semidirect
319. D3×C8C2×Dic5semidirect
457. M16D3×Dic5semidirect
483. C3×C5#2911semidirect
549. C5#79208semidirect
572. C3#10615483semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×M162
D3×#40722
C2×#913382
#117512222
C3×#654102
#117484552
#117484532
#117476822
#117476792
#117476302
#117476282
#106154833
#792085