Finite Group Databasebeta

← #14300548

Subgroups — #14300548

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#11754577C211yesmaximal, characteristic
2C2×D3×#681C211yesmaximal, characteristic, complemented
3C4×C5×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×#3937C211yesmaximal, characteristic, complemented
5C2×#90977C211yesmaximal, characteristic, complemented
6#11746344C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10600246—31nomaximal, Hall
9C22×C4×C5×D3C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C2×C5×(C2×D3)⋊C4—21no—
15C2×C4×C5×Dic3C2211yescharacteristic
16C2×C3×#681C2211yescharacteristic
17#91568—21no—
18#91536—21no—
19#91456C411yescharacteristic, complemented
20#91456C411yescharacteristic, complemented
21C4×#1201—21no—
22C4×#1201—21no—
23#91369C411yescharacteristic, complemented
24#91369C411yescharacteristic, complemented
25C2×#6650—21no—
26D3×#681—22no—
27D3×#681—22no—
28C2×D3×#168—21no—
29C5×C3⋊#95—21no—
30C3×#3937—22no—
31#90977—22no—
32#70381—51nomaximal, Hall
33#66125—31no—
34C22×#681—31no—
35C4×C5×C22⋊C4—31no—
36C2×#3937—31no—
37C2×#3937D311yescharacteristic, complemented
38#64743—31no—
39#64743—31no—
40C23×C5×D3D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×C5×Dic3—21no—
44C22×C5×Dic3D411yescharacteristic
45C2×C4×C5×D3—21no—
46C2×C4×C5×D3—21no—
47C2×C4×C5×D3—21no—
48C2×C4×C5×D3—21no—
49C2×C4×C5×D3C2×C411yescharacteristic
50C2×C4×C5×D3C2×C411yescharacteristic
51C2×C4×C5×D3D411yescharacteristic
52C2×C4×C5×D3D411yescharacteristic
53C2×C3×C22⋊D5—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×C42×C5—21no—
64C3×C42×C5—21no—
65#6719—21no—
66C4⋊Dic15C2×C411yescharacteristic
67C4⋊Dic15C2×C411yescharacteristic
68C4×Dic15—21no—
69#6710—21no—
70#6710D412yescomplemented
71C2×C3⋊#168—21no—
72C5×(C2×D3)⋊C4—24no—
73C4×C5×Dic3—21no—
74C4×C5×Dic3—21no—
75C3×#681—21no—
76C3×#681D412yescomplemented
77C2×C3×#168—21no—
78#6669—21no—
79#6669—21no—
80(C2×D3)⋊Dic5—21no—
81(C2×D3)⋊Dic5—21no—
82#6665—21no—
83#6665—21no—
84#6650—24no—
85D3×#168—24no—
86#5828—51no—
87C2×D3×M16—51no—
88C2×C3×#104—51no—
89C2×#837—51no—
90C4×(C2×D3)⋊C4D511yescharacteristic, complemented
91#4555—51no—
92#4523—51no—
93C23×C4×C5—31no—
94C2×#709C2×D311yescharacteristic
95C2×C5×C22⋊C4—61no—
96C2×C42×C5—31no—
97C2×C42×C5C2×D311yescharacteristic
98#4099—61no—
99#4076—31no—
100#4076—31no—
101#4075—61no—
102C4×C22⋊D5—61no—
103C4×C22⋊D5—61no—
104#4072—31no—
105#4070—31no—
106#4070—31no—
107C2×#681—31no—
108C2×#681—61no—
109C2×#681—62no—
110C2×#681—62no—
111C2×#681C2×D311yescharacteristic
112C22×#168—61no—
113C5×#95—61no—
114#3937—22no—
115#3937—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×C5—22no—
126C2×C3×C4×C5—41no—
127C2×C3×C4×C5—41no—
128C2×C3×C4×C5C22×C411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5#4111yescharacteristic
133C2×C3×C4×C5#4111yescharacteristic
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—21no—
138C2×C5×Dic3—22no—
139C2×C5×Dic3—41no—
140C2×C5×Dic3—41no—
141C2×C5×Dic3C22⋊C411yescharacteristic
142C2×C5×Dic3C22⋊C411yescharacteristic
143C4×C5×D3—21no—
144C4×C5×D3—21no—
145C4×C5×D3—21no—
146C4×C5×D3—21no—
147C4×C5×D3—21no—
148C4×C5×D3—21no—
149C4×C5×D3—21no—
150C4×C5×D3—21no—
151C3×C22⋊D5—41no—
152C3×C22⋊D5—41no—
153C2×C3×Dic5—21no—
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⋊#168—22no—
163C3×#168—22no—
164C2×C3×#41—51no—
165C22×C4×D3C2×D511yescharacteristic
166C2×C3×M16—51no—
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—21no—
177#926—51no—
178C2×C4×Dic3C2×D511yescharacteristic
179C2×#208—51no—
180D3×M16—102no—
181D3×M16—102no—
182C2×ΓL(1,𝔽25)—101no—
183C2×D3×C8—101no—
184C3×#104—102no—
185#837—102no—
186C3⋊#95—21no—
187C24×C5—31no—
188C22×C4×C5—21no—
189C22×C4×C5—31no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—31no—
193C22×C4×C5—31no—
194C22×C4×C5—61no—
195C22×C4×C5—61no—
196C22×C4×C5—61no—
197C22×C4×C5—61no—
198C22×C4×C5—61no—
199C22×C4×C5C22×D311yescharacteristic
200C2×C22⋊D5—21no—
201C2×C22⋊D5—61no—
202C2×C22⋊D5—61no—
203#709—21no—
204#709—21no—
205#709—21no—
206#709—21no—
207C2×D20C4×D311yescharacteristic
208C2×C4×D5—21no—
209C2×Dic10C4×D311yescharacteristic
210C5×C22⋊C4—64no—
211C42×C5—21no—
212C42×C5—21no—
213C42×C5—61no—
214C42×C5—61no—
215C22⋊Dic5—61no—
216C22⋊Dic5—61no—
217C22⋊Dic5—61no—
218#685—61no—
219#685—61no—
220C4⋊Dic5—31no—
221C4⋊Dic5—31no—
222#683—61no—
223#683—61no—
224C4×Dic5—61no—
225#681—21no—
226#681—32no—
227#681—64no—
228#681—61no—
229#681#6712yescomplemented
230C2×#168—21no—
231C2×#168—64no—
232C2×#168—61no—
233C22×M16—151no—
234#525—151no—
235C2×#104—51no—
236C2×#104—151no—
237C4×C22⋊C4—31no—
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×C5—42no—
257C3×C4×C5C4×D411yescharacteristic
258C3×C4×C5C4×D411yescharacteristic
259C3×C4×C5#12011yescharacteristic
260C3×C4×C5#12311yescharacteristic
261Dic15—41no—
262Dic15—41no—
263C3×Dic5—41no—
264C5×Dic3—21no—
265C5×Dic3—21no—
266C5×Dic3—42no—
267C23×D3C22⋊D511yescharacteristic
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—21no—
276C22×C3×C4—101no—
277C22×C3×C4C22×D511yescharacteristic
278C2×#67—101no—
279C2×#67—101no—
280C22×Dic3—21no—
281C22×Dic3C22⋊D511yescharacteristic
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×D3D2011yescharacteristic
289C2×C4×D3D2011yescharacteristic
290C3×M16—52no—
291C3×M16—101no—
292C2×C3×C8—101no—
293C3×C42—21no—
294C3×C42—21no—
295#217—101no—
296#217—101no—
297#217—101no—
298(C2×D3)⋊C4—24no—
299(C2×D3)⋊C4—101no—
300(C2×D3)⋊C4—101no—
301C4⋊Dic3—51no—
302C4⋊Dic3—51no—
303Dic3⋊C4—101no—
304Dic3⋊C4—101no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307C4×Dic3—101no—
308#208—52no—
309#208—101no—
310C2×C3⋊C8—101no—
311ΓL(1,𝔽25)—104no—
312D3×C8—104no—
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—22no—
322C2×C4×C5—31no—
323C2×C4×C5—31no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
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×C5—61no—
334C2×C4×C5—61no—
335C2×C4×C5—61no—
336C2×C4×C5—62no—
337C2×C4×C5—121no—
338C2×C4×C5—121no—
339C2×C4×C5C2×C4×D311yescharacteristic
340C2×C4×C5#23511yescharacteristic
341C2×C4×C5D3×D411yescharacteristic
342C2×C4×C5D3×D411yescharacteristic
343C2×C4×C5#23711yescharacteristic
344C2×C4×C5C2×#6711yescharacteristic
345C22⋊D5—41no—
346C22⋊D5—41no—
347C22⋊D5—122no—
348C22⋊D5—122no—
349C2×Dic5—21no—
350C2×Dic5—61no—
351C2×Dic5—61no—
352D20—21no—
353D20—21no—
354C4×D5—41no—
355C4×D5—41no—
356Dic10—21no—
357Dic10—21no—
358#168—22no—
359#168—62no—
360C2×#41—51no—
361C23×C4—31no—
362C2×M16—51no—
363C2×M16—151no—
364C2×M16—301no—
365C2×M16—302no—
366C2×M16—302no—
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—61no—
378C2×C42—31no—
379C2×C42D3×D511yescharacteristic
380#104—102no—
381#104—302no—
382#95—61no—
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×C22⋊D511yescharacteristic
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—22no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—101no—
409C2×C3×C4—201no—
410C2×C3×C4—201no—
411C2×C3×C4C2×C4×D511yescharacteristic
412C2×C3×C4C2×D2011yescharacteristic
413C2×C3×C4D4×D511yescharacteristic
414C2×C3×C4D4×D511yescharacteristic
415C2×C3×C4#71111yescharacteristic
416C2×C3×C4#71111yescharacteristic
417#67—202no—
418#67—202no—
419C2×Dic3—21no—
420C2×Dic3—21no—
421C2×Dic3—22no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3—101no—
425C2×Dic3—101no—
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—102no—
437C3⋊C8—102no—
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—42no—
455C4×C5—61no—
456C4×C5—61no—
457C4×C5—122no—
458C4×C5#67⋊C411yescharacteristic
459C4×C5#88311yescharacteristic
460C4×C5C4×#6711yescharacteristic
461C4×C5#93711yescharacteristic
462Dic5—41no—
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—21no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—31no—
479C22×C4—31no—
480C22×C4—31no—
481C22×C4—61no—
482C22×C4—61no—
483C22×C4—61no—
484C22×C4—61no—
485C22×C4—61no—
486C22×C4—101no—
487C22×C4C2×D3×D511yescharacteristic
488M16—52no—
489M16—101no—
490M16—152no—
491M16—304no—
492M16—301no—
493C2×C8—101no—
494C2×C8—304no—
495C2×C8—301no—
496C4⋊C4—151no—
497C4⋊C4—151no—
498C4⋊C4—301no—
499C4⋊C4—301no—
500C22⋊C4—64no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C22⋊C4—301no—
504C22⋊C4—301no—
505C22⋊C4—301no—
506C42—21no—
507C42—21no—
508C42—61no—
509C42—61no—
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#408511yescharacteristic
519C22×C3#408511yescharacteristic
520C2×D3—21no—
521C2×D3—21no—
522C2×D3—21no—
523C2×D3—21no—
524C2×D3—21no—
525C2×D3—42no—
526C2×D3—42no—
527C2×D3#393712yescomplemented
528C3×C4—42no—
529C3×C4—201no—
530C3×C4#402711yescharacteristic
531C3×C4#402711yescharacteristic
532C3×C4#402811yescharacteristic
533C3×C4#403211yescharacteristic
534Dic3—21no—
535Dic3—21no—
536Dic3—42no—
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×C22⋊D511yescharacteristic
555Q8—101no—
556Q8—101no—
557D4—101no—
558D4—101no—
559D4—201no—
560D4—201no—
561D4—602no—
562D4—602no—
563C2×C4—22no—
564C2×C4—31no—
565C2×C4—31no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—61no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—61no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—61no—
578C2×C4—62no—
579C2×C4—101no—
580C2×C4—121no—
581C2×C4—121no—
582C2×C4—201no—
583C2×C4—201no—
584C2×C4—301no—
585C2×C4—301no—
586C2×C4#677211yescharacteristic
587C2×C4C4×D3×D511yescharacteristic
588C2×C4D3×D2011yescharacteristic
589C2×C4#677711yescharacteristic
590C2×C4#678011yescharacteristic
591C2×C4D5×#6711yescharacteristic
592C8—102no—
593C8—302no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—401no—
597C2×C3C2×#393711yescharacteristic
598C2×C3#6524711yescharacteristic
599C2×C3#6529411yescharacteristic
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#9145311yescharacteristic
617C22D3×#68511yescharacteristic
618C22#9156511yescharacteristic
619C4—42no—
620C4—61no—
621C4—61no—
622C4—122no—
623C4—201no—
624C4—601no—
625C4—601no—
626C4#9144011yescharacteristic
627C4#9144211yescharacteristic
628C4#9145711yescharacteristic
629C4#9147411yescharacteristic
630C3#1060024611yescharacteristic, complemented, Sylow
631C2—21no—
632C2—21no—
633C2—62no—
634C2—121no—
635C2—401no—
636C2D3×#393711yescharacteristic
637C2#1174711111yescharacteristic
638C2#1174891111yescharacteristic
subgroupG/H
centerC2×C4D3×D20
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C42×C5C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11754577C2
cosocleC22×C3×C4×C5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×D3×#681C2semidirect
3. C4×C5×(C2×D3)⋊C4C2semidirect
4. C2×C3×#3937C2semidirect
5. C2×#90977C2semidirect
6. #11746344C2semidirect
7. #11745976C2semidirect
19. #91456C4semidirect
20. #91456C4semidirect
23. #91369C4semidirect
24. #91369C4semidirect
37. C2×#3937D3semidirect
70. #6710D4semidirect
76. C3×#681D4semidirect
90. C4×(C2×D3)⋊C4D5semidirect
229. #681#67semidirect
252. C2×C5×D3#104semidirect
511. C3×C5#1871semidirect
527. C2×D3#3937semidirect
602. C5#70381semidirect
630. C3#10600246semidirect

Maximal subgroups

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

subgroupindex
#117545772
C2×D3×#6812
C4×C5×(C2×D3)⋊C42
C2×C3×#39372
C2×#909772
#117463442
#117459762
#106002463
#703815