Finite Group Databasebeta

← #14300554

Subgroups — #14300554

Order 1920.

752 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×D3×M16C211yesmaximal, characteristic, complemented
2#11754577C211yesmaximal, characteristic
3C2×C3×#3957C211yesmaximal, characteristic, complemented
4C4×(C2×D3)⋊Dic5C211yesmaximal, characteristic, complemented
5C2×#90976C211yesmaximal, characteristic, complemented
6#11746376C211yesmaximal, characteristic, complemented
7#11745978C211yesmaximal, characteristic, complemented
8#10602777—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C4×Dic15C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C5×D3×M16—22no—
16C5×D3×M16—22no—
17C2×C5×ΓL(1,𝔽25)—21no—
18C2×C5×D3×C8—21no—
19C2×C3×C4×Dic5C2211yescharacteristic
20#91568—21no—
21C2×(C2×D3)⋊Dic5—21no—
22#91536—21no—
23#91456C411yescharacteristic, complemented
24#91456C411yescharacteristic, complemented
25C4×#1201—21no—
26C4×#1201—21no—
27#91369C411yescharacteristic, complemented
28#91369C411yescharacteristic, complemented
29C3×#3957—22no—
30#90994—21no—
31#90976—22no—
32#70381—51nomaximal, Hall
33C22×C5×M16—31no—
34#66125—31no—
35C4×C22⋊Dic5—31no—
36C2×#3957—31no—
37C2×#3957D311yescharacteristic, complemented
38#64775—31no—
39#64775—31no—
40C23×C5×D3D411yescharacteristic
41C22×C3×C4×C5C2311yescharacteristic
42C22×Dic15—21no—
43C22×C5×Dic3D411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C4×C5×D3—21no—
46C2×C4×C5×D3—21no—
47C2×C4×C5×D3—21no—
48C2×C4×C5×D3C2×C411yescharacteristic
49C2×C4×C5×D3C2×C411yescharacteristic
50C2×C4×C5×D3D411yescharacteristic
51C2×C4×C5×D3D411yescharacteristic
52C2×C3×C22⋊D5—21no—
53C22×C3×Dic5—21no—
54C3×#709—21no—
55C3×#709—21no—
56C3×#709—21no—
57C3×#709—21no—
58C2×C3×D20C2×C411yescharacteristic
59C2×C3×C4×D5—21no—
60C2×C3×Dic10C2×C411yescharacteristic
61C2×#1201—21no—
62C2×#1201—21no—
63C3×C5×M16—21no—
64C3×C5×M16D412yescomplemented
65C2×C3×C5×C8—21no—
66#6719—21no—
67C4⋊Dic15C2×C411yescharacteristic
68C4⋊Dic15C2×C411yescharacteristic
69C4×Dic15—21no—
70C4×Dic15—21no—
71C4×Dic15—21no—
72C5×#208—21no—
73C5×#208D412yescomplemented
74C2×C5×C3⋊C8—21no—
75C5×ΓL(1,𝔽25)—24no—
76C5×D3×C8—24no—
77C3×C4×Dic5—21no—
78C3×C4×Dic5—21no—
79#6669—21no—
80#6669—21no—
81(C2×D3)⋊Dic5—24no—
82(C2×D3)⋊Dic5—21no—
83(C2×D3)⋊Dic5—21no—
84#6665—21no—
85#6665—21no—
86#5828—51no—
87C2×D3×M16D511yescharacteristic, complemented
88C2×C3×#104—51no—
89C2×#837—51no—
90C4×(C2×D3)⋊C4—51no—
91#4555—51no—
92#4523—51no—
93C23×C4×C5—31no—
94C2×#709C2×D311yescharacteristic
95C2×C5×M16—31no—
96C2×C5×M16—61no—
97C2×C5×M16—62no—
98C2×C5×M16—62no—
99C2×C5×M16C2×D311yescharacteristic
100C22×C5×C8—61no—
101#4099—61no—
102C2×C22⋊Dic5—61no—
103#4076—31no—
104#4076—31no—
105#4075—61no—
106C4×C22⋊D5—61no—
107C4×C22⋊D5—61no—
108#4072—31no—
109#4070—31no—
110#4070—31no—
111C2×C4×Dic5—31no—
112C2×C4×Dic5C2×D311yescharacteristic
113#3963—61no—
114#3957—22no—
115#3957—62no—
116#1871—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×C5×D3—21no—
119C22×C5×D3—21no—
120C22×C5×D3—22no—
121C22×C5×D3—41no—
122C22×C5×D3C22⋊C411yescharacteristic
123C22×C5×D3C22⋊C411yescharacteristic
124C22×C3×D5—21no—
125C2×C3×C4×C5C22×C411yescharacteristic
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5#4111yescharacteristic
130C2×C3×C4×C5#4111yescharacteristic
131C2×Dic15—22no—
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15—41no—
135C2×Dic15—41no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3C22⋊C411yescharacteristic
139C2×C5×Dic3C22⋊C411yescharacteristic
140C4×C5×D3—21no—
141C4×C5×D3—21no—
142C4×C5×D3—21no—
143C4×C5×D3—21no—
144C4×C5×D3—21no—
145C4×C5×D3—21no—
146C4×C5×D3—21no—
147C4×C5×D3—21no—
148C3×C22⋊D5—41no—
149C3×C22⋊D5—41no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—41no—
153C2×C3×Dic5—41no—
154C3×D20—21no—
155C3×D20—21no—
156C3×C4×D5—41no—
157C3×C4×D5—41no—
158C3×Dic10—21no—
159C3×Dic10—21no—
160#1201—42no—
161#1201—42no—
162C3×C5×C8—22no—
163C5×C3⋊C8—22no—
164C2×C3×#41—51no—
165C22×C4×D3C2×D511yescharacteristic
166C2×C3×M16C2×D511yescharacteristic
167C2×C3×C42—51no—
168#946—51no—
169#946—51no—
170#938—51no—
171#938—51no—
172#937—101no—
173#935—101no—
174C4×#67—101no—
175C4×#67—101no—
176C2×(C2×D3)⋊C4—101no—
177#926—51no—
178C2×C4×Dic3—51no—
179C2×#208C2×D511yescharacteristic
180D3×M16—22no—
181D3×M16—22no—
182C2×ΓL(1,𝔽25)—21no—
183C2×D3×C8—21no—
184C3×#104—102no—
185#837—102no—
186C3⋊#95—101no—
187C24×C5—31no—
188C22×C4×C5—31no—
189C22×C4×C5—31no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—31no—
193C22×C4×C5—61no—
194C22×C4×C5—61no—
195C22×C4×C5—61no—
196C22×C4×C5—61no—
197C22×C4×C5C22×D311yescharacteristic
198C2×C22⋊D5—21no—
199C2×C22⋊D5—61no—
200C2×C22⋊D5—61no—
201C22×Dic5—21no—
202C22×Dic5—61no—
203#709—21no—
204#709—21no—
205#709—21no—
206#709—21no—
207C2×D20C4×D311yescharacteristic
208C2×C4×D5—21no—
209C2×Dic10C4×D311yescharacteristic
210C5×M16—21no—
211C5×M16—32no—
212C5×M16—64no—
213C5×M16—61no—
214C5×M16#6712yescomplemented
215C2×C5×C8—21no—
216C2×C5×C8—64no—
217C2×C5×C8—61no—
218C22⋊Dic5—61no—
219C22⋊Dic5—61no—
220C22⋊Dic5—64no—
221C22⋊Dic5—61no—
222#685—61no—
223#685—61no—
224C4⋊Dic5—31no—
225C4⋊Dic5—31no—
226#683—61no—
227#683—61no—
228C4×Dic5—21no—
229C4×Dic5—21no—
230C4×Dic5—61no—
231C4×Dic5—61no—
232C4×Dic5—61no—
233C22×M16—31no—
234#525—151no—
235C2×#104—51no—
236C2×#104—151no—
237C4×C22⋊C4—151no—
238#339—151no—
239#339—151no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5C2×C22⋊C411yescharacteristic
243C22×C3×C5#12111yescharacteristic
244C22×C3×C5#12111yescharacteristic
245C2×C5×D3—21no—
246C2×C5×D3—21no—
247C2×C5×D3—21no—
248C2×C5×D3—21no—
249C2×C5×D3—21no—
250C2×C5×D3—42no—
251C2×C5×D3—42no—
252C2×C5×D3#10412yescomplemented
253C2×C3×D5—41no—
254C2×C3×D5—41no—
255C2×C3×D5—41no—
256C3×C4×C5C4×D411yescharacteristic
257C3×C4×C5C4×D411yescharacteristic
258C3×C4×C5#12011yescharacteristic
259C3×C4×C5#12311yescharacteristic
260Dic15—42no—
261Dic15—41no—
262Dic15—41no—
263C3×Dic5—42no—
264C3×Dic5—41no—
265C5×Dic3—21no—
266C5×Dic3—21no—
267C23×D3D2011yescharacteristic
268C3×#41—101no—
269C3×#41—101no—
270C3×#41—101no—
271C3×#41—101no—
272C2×C3×Q8—51no—
273C2×C3×D4—51no—
274C2×C3×D4—101no—
275C22×C3×C4—101no—
276C22×C3×C4—101no—
277C22×C3×C4C22×D511yescharacteristic
278C2×#67—101no—
279C2×#67—101no—
280C22×Dic3—101no—
281C22×Dic3D2011yescharacteristic
282C2×C4×D3—21no—
283C2×C4×D3—21no—
284C2×C4×D3—21no—
285C2×C4×D3—21no—
286C2×C4×D3C4×D511yescharacteristic
287C2×C4×D3C4×D511yescharacteristic
288C2×C4×D3C22⋊D511yescharacteristic
289C2×C4×D3C22⋊D511yescharacteristic
290C3×M16—21no—
291C3×M16C22⋊D512yescomplemented
292C2×C3×C8—21no—
293C3×C42—101no—
294C3×C42—101no—
295#217—101no—
296#217—101no—
297#217—101no—
298(C2×D3)⋊C4—104no—
299(C2×D3)⋊C4—101no—
300(C2×D3)⋊C4—101no—
301C4⋊Dic3—51no—
302C4⋊Dic3—51no—
303Dic3⋊C4—101no—
304Dic3⋊C4—101no—
305C4×Dic3—101no—
306C4×Dic3—101no—
307C4×Dic3—101no—
308#208—21no—
309#208C22⋊D512yescomplemented
310C2×C3⋊C8—21no—
311ΓL(1,𝔽25)—24no—
312D3×C8—24no—
313C23×C5—31no—
314C23×C5—31no—
315C23×C5—62no—
316C23×C5—61no—
317C23×C5—61no—
318C23×C5—121no—
319C23×C5D3×D411yescharacteristic
320C22×D5—21no—
321C2×C4×C5—31no—
322C2×C4×C5—31no—
323C2×C4×C5—61no—
324C2×C4×C5—61no—
325C2×C4×C5—61no—
326C2×C4×C5—61no—
327C2×C4×C5—61no—
328C2×C4×C5—61no—
329C2×C4×C5—61no—
330C2×C4×C5—61no—
331C2×C4×C5—61no—
332C2×C4×C5—61no—
333C2×C4×C5C2×C4×D311yescharacteristic
334C2×C4×C5#23511yescharacteristic
335C2×C4×C5D3×D411yescharacteristic
336C2×C4×C5D3×D411yescharacteristic
337C2×C4×C5#23711yescharacteristic
338C2×C4×C5C2×#6711yescharacteristic
339C22⋊D5—41no—
340C22⋊D5—41no—
341C22⋊D5—122no—
342C22⋊D5—122no—
343C2×Dic5—22no—
344C2×Dic5—21no—
345C2×Dic5—41no—
346C2×Dic5—41no—
347C2×Dic5—62no—
348C2×Dic5—61no—
349C2×Dic5—61no—
350C2×Dic5—121no—
351C2×Dic5—121no—
352D20—21no—
353D20—21no—
354C4×D5—41no—
355C4×D5—41no—
356Dic10—21no—
357Dic10—21no—
358C5×C8—22no—
359C5×C8—62no—
360C2×#41—51no—
361C23×C4—31no—
362C2×M16—31no—
363C2×M16—61no—
364C2×M16—62no—
365C2×M16—62no—
366C2×M16D3×D511yescharacteristic
367C22×C8—61no—
368#123—301no—
369C22⋊Q8—151no—
370C22⋊Q8—151no—
371#121—151no—
372#121—151no—
373#120—301no—
374C4×D4—301no—
375C4×D4—301no—
376#117—151no—
377C2×C22⋊C4—301no—
378C2×C42—51no—
379C2×C42—151no—
380#104—102no—
381#104—302no—
382#95—301no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5#38611yescharacteristic
386C2×C3×C5C2×#10411yescharacteristic
387C2×C3×C5#42111yescharacteristic
388C3×D5—81no—
389C5×D3—22no—
390C5×D3—41no—
391C23×C3—101no—
392C23×C3C2×D2011yescharacteristic
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—22no—
396C22×D3—41no—
397C22×D3#68511yescharacteristic
398C22×D3#68511yescharacteristic
399C3×Q8—101no—
400C3×Q8—101no—
401C3×D4—101no—
402C3×D4—101no—
403C3×D4—201no—
404C3×D4—201no—
405C2×C3×C4—102no—
406C2×C3×C4—101no—
407C2×C3×C4—201no—
408C2×C3×C4—201no—
409C2×C3×C4—201no—
410C2×C3×C4—201no—
411C2×C3×C4C2×C4×D511yescharacteristic
412C2×C3×C4#70911yescharacteristic
413C2×C3×C4#70911yescharacteristic
414C2×C3×C4C2×C22⋊D511yescharacteristic
415C2×C3×C4C2×C22⋊D511yescharacteristic
416C2×C3×C4C2×C22⋊D511yescharacteristic
417#67—202no—
418#67—202no—
419C2×Dic3—21no—
420C2×Dic3—21no—
421C2×Dic3—102no—
422C2×Dic3—101no—
423C2×Dic3—101no—
424C2×Dic3—201no—
425C2×Dic3—201no—
426C2×Dic3#68511yescharacteristic
427C2×Dic3#68511yescharacteristic
428C4×D3—21no—
429C4×D3—21no—
430C4×D3—21no—
431C4×D3—21no—
432C4×D3—21no—
433C4×D3—21no—
434C4×D3—21no—
435C4×D3—21no—
436C3×C8—22no—
437C3⋊C8—22no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5—32no—
441C22×C5—61no—
442C22×C5—61no—
443C22×C5—61no—
444C22×C5—61no—
445C22×C5—61no—
446C22×C5—122no—
447C22×C5—122no—
448C22×C5D3×C22⋊C411yescharacteristic
449C22×C5#88411yescharacteristic
450C22×C5#93811yescharacteristic
451C2×D5—41no—
452C2×D5—41no—
453C2×D5—41no—
454C4×C5—61no—
455C4×C5—61no—
456C4×C5#67⋊C411yescharacteristic
457C4×C5#88311yescharacteristic
458C4×C5C4×#6711yescharacteristic
459C4×C5#93711yescharacteristic
460Dic5—42no—
461Dic5—41no—
462Dic5—122no—
463Dic5—121no—
464Dic5—121no—
465C24—31no—
466#41—101no—
467#41—101no—
468#41—101no—
469#41—101no—
470C2×Q8—51no—
471C2×D4—51no—
472C2×D4—101no—
473C2×D4—301no—
474C2×D4—301no—
475C22×C4—31no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—101no—
485C22×C4—101no—
486C22×C4—301no—
487C22×C4C2×D3×D511yescharacteristic
488M16—21no—
489M16—32no—
490M16—64no—
491M16—61no—
492M16#120112yescomplemented
493C2×C8—21no—
494C2×C8—64no—
495C2×C8—61no—
496C4⋊C4—151no—
497C4⋊C4—151no—
498C4⋊C4—301no—
499C4⋊C4—301no—
500C22⋊C4—301no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C22⋊C4—301no—
504C22⋊C4—304no—
505C22⋊C4—301no—
506C42—101no—
507C42—101no—
508C42—301no—
509C42—301no—
510C42—301no—
511C3×C5#187111yescharacteristic, complemented, Hall
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—201no—
515C22×C3—201no—
516C22×C3—201no—
517C22×C3C2×#68511yescharacteristic
518C22×C3#407611yescharacteristic
519C22×C3#407611yescharacteristic
520C2×D3—21no—
521C2×D3—21no—
522C2×D3—21no—
523C2×D3—21no—
524C2×D3—21no—
525C2×D3—42no—
526C2×D3—42no—
527C2×D3#395712yescomplemented
528C3×C4—202no—
529C3×C4—201no—
530C3×C4C4×C22⋊D511yescharacteristic
531C3×C4C4×C22⋊D511yescharacteristic
532C3×C4#407511yescharacteristic
533C3×C4#409911yescharacteristic
534Dic3—21no—
535Dic3—21no—
536Dic3—202no—
537Dic3—201no—
538Dic3—201no—
539C2×C5—21no—
540C2×C5—21no—
541C2×C5—62no—
542C2×C5—121no—
543C2×C5D3×#10411yescharacteristic
544C2×C5#482111yescharacteristic
545C2×C5#495611yescharacteristic
546D5—81no—
547C23—31no—
548C23—31no—
549C23—62no—
550C23—61no—
551C23—61no—
552C23—101no—
553C23—121no—
554C23D3×D2011yescharacteristic
555Q8—101no—
556Q8—101no—
557D4—101no—
558D4—101no—
559D4—201no—
560D4—201no—
561D4—602no—
562D4—602no—
563C2×C4—31no—
564C2×C4—31no—
565C2×C4—61no—
566C2×C4—61no—
567C2×C4—61no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—102no—
576C2×C4—101no—
577C2×C4—201no—
578C2×C4—201no—
579C2×C4—201no—
580C2×C4—201no—
581C2×C4—302no—
582C2×C4—301no—
583C2×C4—301no—
584C2×C4—601no—
585C2×C4—601no—
586C2×C4#676511yescharacteristic
587C2×C4#677111yescharacteristic
588C2×C4C4×D3×D511yescharacteristic
589C2×C4C2×#120111yescharacteristic
590C2×C4D3×C22⋊D511yescharacteristic
591C2×C4D3×C22⋊D511yescharacteristic
592C8—22no—
593C8—62no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—401no—
597C2×C3C2×#395711yescharacteristic
598C2×C3#6542811yescharacteristic
599C2×C3#6550211yescharacteristic
600D3—22no—
601D3—41no—
602C5#7038111yescharacteristic, complemented, Sylow
603C22—21no—
604C22—21no—
605C22—32no—
606C22—61no—
607C22—61no—
608C22—61no—
609C22—61no—
610C22—61no—
611C22—122no—
612C22—122no—
613C22—201no—
614C22—201no—
615C22—201no—
616C22#9145411yescharacteristic
617C22#9145611yescharacteristic
618C22D3×#68511yescharacteristic
619C4—61no—
620C4—61no—
621C4—202no—
622C4—201no—
623C4—602no—
624C4—601no—
625C4—601no—
626C4C4×#120111yescharacteristic
627C4#9144111yescharacteristic
628C4#9145211yescharacteristic
629C4#9156811yescharacteristic
630C3#1060277711yescharacteristic, complemented, Sylow
631C2—21no—
632C2—21no—
633C2—62no—
634C2—121no—
635C2—401no—
636C2D3×#395711yescharacteristic
637C2#1174823311yescharacteristic
638C2#1174891011yescharacteristic
subgroupG/H
centerC2×C4D3×C22⋊D5
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754577C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C5×D3×M16C2semidirect
3. C2×C3×#3957C2semidirect
4. C4×(C2×D3)⋊Dic5C2semidirect
5. C2×#90976C2semidirect
6. #11746376C2semidirect
7. #11745978C2semidirect
23. #91456C4semidirect
24. #91456C4semidirect
27. #91369C4semidirect
28. #91369C4semidirect
37. C2×#3957D3semidirect
64. C3×C5×M16D4semidirect
73. C5×#208D4semidirect
87. C2×D3×M16D5semidirect
214. C5×M16#67semidirect
252. C2×C5×D3#104semidirect
291. C3×M16C22⋊D5semidirect
309. #208C22⋊D5semidirect
492. M16#1201semidirect
511. C3×C5#1871semidirect
527. C2×D3#3957semidirect
602. C5#70381semidirect
630. C3#10602777semidirect

Maximal subgroups

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

subgroupindex
C2×C5×D3×M162
#117545772
C2×C3×#39572
C4×(C2×D3)⋊Dic52
C2×#909762
#117463762
#117459782
#106027773
#703815