Finite Group Databasebeta

← #14300525

Subgroups — #14300525

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
1#11756587C211yesmaximal, characteristic
2C2×M16×D15C211yesmaximal, characteristic, complemented
3C2×C3×C5×#104C211yesmaximal, characteristic, complemented
4C2×#91121C211yesmaximal, characteristic, complemented
5C4×#6714C211yesmaximal, characteristic, complemented
6#11746376C211yesmaximal, characteristic, complemented
7#11746344C211yesmaximal, characteristic, complemented
8#10601174—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C4×D15C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C2×C3×C42×C5C2211yescharacteristic
13#91835C411yescharacteristic, complemented
14#91835C411yescharacteristic, complemented
15#91827C411yescharacteristic, complemented
16#91827C411yescharacteristic, complemented
17#91826—21no—
18#91824—21no—
19C4×#1220—21no—
20C4×#1220—21no—
21C2×#6714—21no—
22#91815C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C2×#6710C2211yescharacteristic
25M16×D15—22no—
26M16×D15—22no—
27C2×#6705—21no—
28C2×C8×D15—21no—
29C3×C5×#104—22no—
30#91121—22no—
31#91115—21no—
32#70381—51nomaximal, Hall
33#66162—31no—
34C2×D5×M16—31no—
35C2×C5×#104D311yescharacteristic, complemented
36C2×#3969—31no—
37C4×#685—31no—
38#64775—31no—
39#64743—31no—
40C23×D15D411yescharacteristic
41C3×C5×#41—21no—
42C3×C5×#41—21no—
43C3×C5×#41—21no—
44C3×C5×#41—21no—
45C2×C3×C5×Q8C2×C411yescharacteristic
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4C2×C411yescharacteristic
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2311yescharacteristic
51C2×#1220—21no—
52C2×#1220—21no—
53C22×Dic15—21no—
54C22×Dic15D411yescharacteristic
55C2×C4×D15—21no—
56C2×C4×D15—21no—
57C2×C4×D15—21no—
58C2×C4×D15—21no—
59C2×C4×D15C2×C411yescharacteristic
60C2×C4×D15C2×C411yescharacteristic
61C2×C4×D15D411yescharacteristic
62C2×C4×D15D411yescharacteristic
63C3×C5×M16—21no—
64C3×C5×M16D412yescomplemented
65C2×C3×C5×C8—21no—
66C3×C42×C5—21no—
67C3×C42×C5—21no—
68#6719—21no—
69#6719—21no—
70#6719—21no—
71#6714—24no—
72#6714—21no—
73#6714—21no—
74C4⋊Dic15C2×C411yescharacteristic
75C4⋊Dic15C2×C411yescharacteristic
76#6712—21no—
77#6712—21no—
78C4×Dic15—21no—
79C4×Dic15—21no—
80C4×Dic15—21no—
81#6710—21no—
82#6710D412yescomplemented
83C2×C3⋊#168—21no—
84#6705—24no—
85C8×D15—24no—
86#5828—51no—
87C2×D3×M16—51no—
88C2×C3×#104D511yescharacteristic, complemented
89C2×#837—51no—
90C4×(C2×D3)⋊C4—51no—
91#4555—51no—
92#4523—51no—
93C2×C5×#41C2×D311yescharacteristic
94C22×C4×D5—31no—
95C2×C5×M16C2×D311yescharacteristic
96C2×C42×C5C2×D311yescharacteristic
97#4092—31no—
98#4092—31no—
99#4084—31no—
100#4084—31no—
101#4083—61no—
102#4081—61no—
103C4×C22⋊D5—61no—
104C4×C22⋊D5—61no—
105C2×#685—61no—
106#4072—31no—
107C2×C4×Dic5—31no—
108C2×#681—31no—
109D5×M16—62no—
110D5×M16—62no—
111C2×#676—61no—
112C2×C8×D5—61no—
113C5×#104—22no—
114#3969—62no—
115#3963—61no—
116#1871—151noSylow
117C23×C3×C5—21no—
118C23×C3×C5C2×D411yescharacteristic
119C22×D15—21no—
120C22×D15—21no—
121C22×D15—22no—
122C22×D15—41no—
123C22×D15C22⋊C411yescharacteristic
124C22×D15C22⋊C411yescharacteristic
125C3×C5×Q8—21no—
126C3×C5×Q8—21no—
127C3×C5×D4—21no—
128C3×C5×D4—21no—
129C3×C5×D4—41no—
130C3×C5×D4—41no—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5—41no—
135C2×C3×C4×C5—41no—
136C2×C3×C4×C5—41no—
137C2×C3×C4×C5C22×C411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5#4111yescharacteristic
142C2×C3×C4×C5#4111yescharacteristic
143#1220—42no—
144#1220—42no—
145C2×Dic15—21no—
146C2×Dic15—21no—
147C2×Dic15—22no—
148C2×Dic15—21no—
149C2×Dic15—21no—
150C2×Dic15—41no—
151C2×Dic15—41no—
152C2×Dic15C22⋊C411yescharacteristic
153C2×Dic15C22⋊C411yescharacteristic
154C4×D15—21no—
155C4×D15—21no—
156C4×D15—21no—
157C4×D15—21no—
158C4×D15—21no—
159C4×D15—21no—
160C4×D15—21no—
161C4×D15—21no—
162C3×C5×C8—22no—
163C3⋊#168—22no—
164C2×C3×#41C2×D511yescharacteristic
165C22×C4×D3—51no—
166C2×C3×M16C2×D511yescharacteristic
167C2×C3×C42C2×D511yescharacteristic
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×#208—51no—
180D3×M16—102no—
181D3×M16—102no—
182C2×ΓL(1,𝔽25)—101no—
183C2×D3×C8—101no—
184C3×#104—22no—
185#837—102no—
186C3⋊#95—101no—
187C23×D5—31no—
188C5×#41—21no—
189C5×#41—21no—
190C5×#41—21no—
191C5×#41—21no—
192C2×C5×Q8C4×D311yescharacteristic
193C2×C5×D4—21no—
194C2×C5×D4C4×D311yescharacteristic
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5C22×D311yescharacteristic
198C2×C22⋊D5—61no—
199C2×C22⋊D5—61no—
200C22×Dic5—31no—
201C22×Dic5—61no—
202C2×C4×D5—31no—
203C2×C4×D5—31no—
204C2×C4×D5—31no—
205C2×C4×D5—31no—
206C2×C4×D5—61no—
207C2×C4×D5—61no—
208C2×C4×D5—61no—
209C2×C4×D5—61no—
210C5×M16—21no—
211C5×M16#6712yescomplemented
212C2×C5×C8—21no—
213C42×C5—21no—
214C42×C5—21no—
215C22⋊Dic5—61no—
216C22⋊Dic5—61no—
217C22⋊Dic5—61no—
218#685—61no—
219#685—61no—
220#685—64no—
221C4⋊Dic5—31no—
222C4⋊Dic5—31no—
223#683—61no—
224#683—61no—
225C4×Dic5—61no—
226C4×Dic5—61no—
227C4×Dic5—61no—
228#681—32no—
229#681—61no—
230C2×#168—61no—
231#676—64no—
232C8×D5—64no—
233C22×M16—151no—
234#525—151no—
235C2×#104—151no—
236C2×#104D1511yescharacteristic, complemented
237C4×C22⋊C4—151no—
238#339—151no—
239#339—151no—
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5—41no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5C2×C22⋊C411yescharacteristic
246C22×C3×C5#12111yescharacteristic
247C22×C3×C5#12111yescharacteristic
248C2×D15—21no—
249C2×D15—21no—
250C2×D15—21no—
251C2×D15—21no—
252C2×D15—21no—
253C2×D15—42no—
254C2×D15—42no—
255C2×D15#10412yescomplemented
256C3×C4×C5—42no—
257C3×C4×C5—41no—
258C3×C4×C5C4×D411yescharacteristic
259C3×C4×C5C4×D411yescharacteristic
260C3×C4×C5#12011yescharacteristic
261C3×C4×C5#12311yescharacteristic
262Dic15—21no—
263Dic15—21no—
264Dic15—42no—
265Dic15—41no—
266Dic15—41no—
267C23×D3—51no—
268C3×#41—21no—
269C3×#41—21no—
270C3×#41—21no—
271C3×#41—21no—
272C2×C3×Q8C4×D511yescharacteristic
273C2×C3×D4—21no—
274C2×C3×D4C4×D511yescharacteristic
275C22×C3×C4—21no—
276C22×C3×C4—21no—
277C22×C3×C4C22×D511yescharacteristic
278C2×#67—101no—
279C2×#67—101no—
280C22×Dic3—51no—
281C22×Dic3—101no—
282C2×C4×D3—51no—
283C2×C4×D3—51no—
284C2×C4×D3—51no—
285C2×C4×D3—51no—
286C2×C4×D3—101no—
287C2×C4×D3—101no—
288C2×C4×D3—101no—
289C2×C4×D3—101no—
290C3×M16—21no—
291C3×M16C22⋊D512yescomplemented
292C2×C3×C8—21no—
293C3×C42—21no—
294C3×C42—21no—
295#217—101no—
296#217—101no—
297#217—101no—
298(C2×D3)⋊C4—101no—
299(C2×D3)⋊C4—101no—
300(C2×D3)⋊C4—104no—
301C4⋊Dic3—51no—
302C4⋊Dic3—51no—
303Dic3⋊C4—101no—
304Dic3⋊C4—101no—
305C4×Dic3—101no—
306C4×Dic3—101no—
307C4×Dic3—101no—
308#208—52no—
309#208—101no—
310C2×C3⋊C8—101no—
311ΓL(1,𝔽25)—104no—
312D3×C8—104no—
313C23×C5—21no—
314C23×C5D3×D411yescharacteristic
315C22×D5—31no—
316C22×D5—31no—
317C22×D5—62no—
318C22×D5—61no—
319C22×D5—61no—
320C22×D5—121no—
321C5×Q8—21no—
322C5×Q8—21no—
323C5×D4—21no—
324C5×D4—21no—
325C5×D4—41no—
326C5×D4—41no—
327C2×C4×C5—22no—
328C2×C4×C5—21no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
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—122no—
340C22⋊D5—122no—
341C2×Dic5—31no—
342C2×Dic5—31no—
343C2×Dic5—61no—
344C2×Dic5—61no—
345C2×Dic5—62no—
346C2×Dic5—61no—
347C2×Dic5—61no—
348C2×Dic5—121no—
349C2×Dic5—121no—
350C4×D5—61no—
351C4×D5—61no—
352C4×D5—61no—
353C4×D5—61no—
354C4×D5—61no—
355C4×D5—61no—
356C4×D5—61no—
357C4×D5—61no—
358C5×C8—22no—
359#168—62no—
360C2×#41C2×D1511yescharacteristic
361C23×C4—151no—
362C2×M16—151no—
363C2×M16—301no—
364C2×M16—302no—
365C2×M16—302no—
366C2×M16C2×D1511yescharacteristic
367C22×C8—301no—
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—151no—
379C2×C42C2×D1511yescharacteristic
380#104—22no—
381#104—302no—
382#95—301no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5—81no—
386C2×C3×C5#38611yescharacteristic
387C2×C3×C5C2×#10411yescharacteristic
388C2×C3×C5#42111yescharacteristic
389D15—22no—
390D15—41no—
391C23×C3—21no—
392C23×C3D4×D511yescharacteristic
393C22×D3—51no—
394C22×D3—51no—
395C22×D3—102no—
396C22×D3—101no—
397C22×D3—101no—
398C22×D3—201no—
399C3×Q8—21no—
400C3×Q8—21no—
401C3×D4—21no—
402C3×D4—21no—
403C3×D4—41no—
404C3×D4—41no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4C2×C4×D511yescharacteristic
412C2×C3×C4#70911yescharacteristic
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4D4×D511yescharacteristic
415C2×C3×C4#71111yescharacteristic
416C2×C3×C4C2×C22⋊D511yescharacteristic
417#67—202no—
418#67—202no—
419C2×Dic3—51no—
420C2×Dic3—51no—
421C2×Dic3—101no—
422C2×Dic3—101no—
423C2×Dic3—102no—
424C2×Dic3—101no—
425C2×Dic3—101no—
426C2×Dic3—201no—
427C2×Dic3—201no—
428C4×D3—101no—
429C4×D3—101no—
430C4×D3—101no—
431C4×D3—101no—
432C4×D3—101no—
433C4×D3—101no—
434C4×D3—101no—
435C4×D3—101no—
436C3×C8—22no—
437C3⋊C8—102no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5D3×C22⋊C411yescharacteristic
444C22×C5#88411yescharacteristic
445C22×C5#93811yescharacteristic
446C2×D5—32no—
447C2×D5—61no—
448C2×D5—61no—
449C2×D5—61no—
450C2×D5—61no—
451C2×D5—61no—
452C2×D5—122no—
453C2×D5—122no—
454C4×C5—42no—
455C4×C5—41no—
456C4×C5#67⋊C411yescharacteristic
457C4×C5#88311yescharacteristic
458C4×C5C4×#6711yescharacteristic
459C4×C5#93711yescharacteristic
460Dic5—61no—
461Dic5—61no—
462Dic5—122no—
463Dic5—121no—
464Dic5—121no—
465C24—151no—
466#41—21no—
467#41—21no—
468#41—21no—
469#41—21no—
470C2×Q8C4×D1511yescharacteristic
471C2×D4—21no—
472C2×D4—301no—
473C2×D4—301no—
474C2×D4C4×D1511yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—151no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—151no—
481C22×C4—151no—
482C22×C4—301no—
483C22×C4—301no—
484C22×C4—301no—
485C22×C4—301no—
486C22×C4—301no—
487C22×C4C22×D1511yescharacteristic
488M16—21no—
489M16—152no—
490M16—304no—
491M16—301no—
492M16#122012yescomplemented
493C2×C8—21no—
494C2×C8—304no—
495C2×C8—301no—
496C4⋊C4—151no—
497C4⋊C4—151no—
498C4⋊C4—301no—
499C4⋊C4—301no—
500C22⋊C4—301no—
501C22⋊C4—301no—
502C22⋊C4—304no—
503C22⋊C4—301no—
504C22⋊C4—301no—
505C22⋊C4—301no—
506C42—21no—
507C42—21no—
508C42—301no—
509C42—301no—
510C42—301no—
511C3×C5#187111yescharacteristic, complemented, Hall
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3D5×C22⋊C411yescharacteristic
518C22×C3#403011yescharacteristic
519C22×C3#408411yescharacteristic
520C2×D3—52no—
521C2×D3—101no—
522C2×D3—101no—
523C2×D3—101no—
524C2×D3—101no—
525C2×D3—101no—
526C2×D3—202no—
527C2×D3—202no—
528C3×C4—42no—
529C3×C4—41no—
530C3×C4#402711yescharacteristic
531C3×C4#402911yescharacteristic
532C3×C4C4×C22⋊D511yescharacteristic
533C3×C4#408311yescharacteristic
534Dic3—101no—
535Dic3—101no—
536Dic3—202no—
537Dic3—201no—
538Dic3—201no—
539C2×C5—21no—
540C2×C5—21no—
541C2×C5—81no—
542C2×C5D3×#10411yescharacteristic
543C2×C5#482111yescharacteristic
544C2×C5#495611yescharacteristic
545D5—62no—
546D5—121no—
547C23—21no—
548C23—151no—
549C23—151no—
550C23—302no—
551C23—301no—
552C23—301no—
553C23—601no—
554C23D4×D1511yescharacteristic
555Q8—21no—
556Q8—21no—
557D4—21no—
558D4—21no—
559D4—41no—
560D4—41no—
561D4—602no—
562D4—602no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—151no—
570C2×C4—151no—
571C2×C4—301no—
572C2×C4—301no—
573C2×C4—301no—
574C2×C4—301no—
575C2×C4—301no—
576C2×C4—301no—
577C2×C4—301no—
578C2×C4—301no—
579C2×C4—301no—
580C2×C4—301no—
581C2×C4—302no—
582C2×C4—301no—
583C2×C4—301no—
584C2×C4—601no—
585C2×C4—601no—
586C2×C4C2×C4×D1511yescharacteristic
587C2×C4#681711yescharacteristic
588C2×C4D4×D1511yescharacteristic
589C2×C4D4×D1511yescharacteristic
590C2×C4#681911yescharacteristic
591C2×C4C2×#122011yescharacteristic
592C8—22no—
593C8—302no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—81no—
597C2×C3D5×#10411yescharacteristic
598C2×C3#6511011yescharacteristic
599C2×C3#6524511yescharacteristic
600D3—102no—
601D3—201no—
602C5#7038111yescharacteristic, complemented, Sylow
603C22—21no—
604C22—21no—
605C22—41no—
606C22—41no—
607C22—41no—
608C22—152no—
609C22—301no—
610C22—301no—
611C22—301no—
612C22—301no—
613C22—301no—
614C22—602no—
615C22—602no—
616C22C22⋊C4×D1511yescharacteristic
617C22#9177311yescharacteristic
618C22#9182711yescharacteristic
619C4—42no—
620C4—41no—
621C4—301no—
622C4—301no—
623C4—602no—
624C4—601no—
625C4—601no—
626C4#9177011yescharacteristic
627C4#9177211yescharacteristic
628C4C4×#122011yescharacteristic
629C4#9182611yescharacteristic
630C3#1060117411yescharacteristic, complemented, Sylow
631C2—21no—
632C2—21no—
633C2—81no—
634C2—302no—
635C2—601no—
636C2D15×#10411yescharacteristic
637C2#1175092211yescharacteristic
638C2#1175105711yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC2×C3×C5×#104C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756587C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#104D15
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×M16×D15C2semidirect
3. C2×C3×C5×#104C2semidirect
4. C2×#91121C2semidirect
5. C4×#6714C2semidirect
6. #11746376C2semidirect
7. #11746344C2semidirect
13. #91835C4semidirect
14. #91835C4semidirect
15. #91827C4semidirect
16. #91827C4semidirect
35. C2×C5×#104D3semidirect
64. C3×C5×M16D4semidirect
82. #6710D4semidirect
88. C2×C3×#104D5semidirect
211. C5×M16#67semidirect
236. C2×#104D15semidirect
255. C2×D15#104semidirect
291. C3×M16C22⋊D5semidirect
492. M16#1220semidirect
511. C3×C5#1871semidirect
602. C5#70381semidirect
630. C3#10601174semidirect

Maximal subgroups

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

subgroupindex
#117565872
C2×M16×D152
C2×C3×C5×#1042
C2×#911212
C4×#67142
#117463762
#117463442
#106011743
#703815