Finite Group Databasebeta

← #14471774

Subgroups — #14471774

Order 1920.

724 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66015C211yesmaximal, characteristic, complemented
2#11752583C211yesmaximal, characteristic, complemented
3#11751157C211yesmaximal, characteristic, complemented
4C5×#5057C211yesmaximal, characteristic, complemented
5#11749351C211yesmaximal, characteristic, complemented
6#11749331C211yesmaximal, characteristic, complemented
7#11749224C211yesmaximal, characteristic, complemented
8Dic5×#215C211yesmaximal, characteristic, complemented
9#11749102C211yesmaximal, characteristic, complemented
10#11749083C211yesmaximal, characteristic, complemented
11#11748974C211yesmaximal, characteristic
12Dic5×#213C211yesmaximal, characteristic, complemented
13C4×#6652C211yesmaximal, characteristic, complemented
14#11746888C211yesmaximal, characteristic, complemented
15#11746846C211yesmaximal, characteristic, complemented
16#10612248—31nomaximal, Hall
17C3×C5×#124C2211yescharacteristic
18#91759C2211yescharacteristic
19C2×C5×#215C2211yescharacteristic
20C2×C5×#213C2211yescharacteristic
21C4×C5×D12C2211yescharacteristic
22C3×#4093C2211yescharacteristic
23C3×Q8×Dic5C2211yescharacteristic
24C3×#4086C2211yescharacteristic
25C3×D4×Dic5C2211yescharacteristic
26C3×#4032—21no—
27C3×#4031—21no—
28C3×#4029—21no—
29C3×#4027—21no—
30C3×C4×D20C2211yescharacteristic
31C3×C4×Dic10C2211yescharacteristic
32#91468C2211yescharacteristic
33#91436—21no—
34Dic5×D12C2211yescharacteristic
35Dic5×D12C2211yescharacteristic
36#91410—21no—
37D3×#683—21no—
38#91388C2211yescharacteristic
39#91352—21no—
40C2×#6652C2211yescharacteristic
41#91119C2211yescharacteristic
42#91119C2211yescharacteristic
43#91116C2211yescharacteristic
44#91116C2211yescharacteristic
45C4×C3⋊#168C2211yescharacteristic
46C5×#835C2211yescharacteristic
47C5×#832C2211yescharacteristic
48C5×C4⋊(C3⋊C8)C2211yescharacteristic
49#90990C2211yescharacteristic
50#90989C2211yescharacteristic
51#90987C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90966C2211yescharacteristic
55#90965C2211yescharacteristic
56#90965C2211yescharacteristic
57#90964C2211yescharacteristic
58Dic5×C3⋊C8C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#83713—51nomaximal, Hall
61#66015D311yescharacteristic, complemented
62#65873—31no—
63C5×#463—31no—
64#65454—31no—
65SD16×Dic5—31no—
66#65439—31no—
67D8×Dic5—31no—
68#65345—31no—
69C4×#686—31no—
70#65136—31no—
71#65119—31no—
72#65089—31no—
73#65083—31no—
74#65052—31no—
75#65049—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C2×C5×D12C2311yescharacteristic
79C2×C4×C5×D3—21no—
80C2×C3×C22⋊D5—21no—
81C2×C3×C22⋊D5—21no—
82C22×C3×Dic5—21no—
83C2×C3×D20C2311yescharacteristic
84C2×C3×C4×D5—21no—
85C2×C3×Dic10D411yescharacteristic
86C2×#1204—21no—
87C2×D3×Dic5—21no—
88C2×D3×Dic5—21no—
89C3×C5×C22⋊C4—21no—
90C3×C5×C22⋊C4—21no—
91C3×C42×C5C2311yescharacteristic
92C4⋊Dic15C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94#6712—21no—
95#6712—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#215—22no—
99C5×#213—22no—
100C5×(C2×D3)⋊C4—21no—
101C5×C4⋊Dic3C2311yescharacteristic
102C2×C5×C3⋊C8C2311yescharacteristic
103C2×C5×C3⋊C8C2311yescharacteristic
104C3×C22⋊Dic5—21no—
105C3×#685—21no—
106C3×#685—21no—
107C3×#685—21no—
108C3×C4⋊Dic5—21no—
109C3×C4⋊Dic5D411yescharacteristic
110C3×C4⋊Dic5C2311yescharacteristic
111C3×#683D411yescharacteristic
112C3×#683D411yescharacteristic
113C3×C4×Dic5—21no—
114C3×C4×Dic5C2311yescharacteristic
115C3×C4×Dic5C2311yescharacteristic
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6668—21no—
119(C2×D3)⋊Dic5—21no—
120(C2×D3)⋊Dic5—21no—
121#6652—22no—
122C3×#559—51no—
123#5579—51no—
124#5072—51no—
125#5070—51no—
126#5057—51no—
127#5057D511yescharacteristic, complemented
128#5056—51no—
129#5056—51no—
130C4×#215—51no—
131Q8×C3⋊C8—51no—
132#5021—51no—
133C4×#213—51no—
134C4×#213—51no—
135#5009—51no—
136#5009—51no—
137C2×C5×SD16—31no—
138C2×C5×D8—31no—
139C5×#124C2×D311yescharacteristic
140C4×C5×D4—31no—
141#4093C2×D311yescharacteristic
142Q8×Dic5C2×D311yescharacteristic
143#4086C2×D311yescharacteristic
144D4×Dic5—31no—
145D4×Dic5—31no—
146D4×Dic5C2×D311yescharacteristic
147C2×#686—31no—
148#4070—61no—
149C2×#683—61no—
150#4036—31no—
151#4034—31no—
152#4032—21no—
153#4031—21no—
154#4029—21no—
155#4027—21no—
156#4024—61no—
157#4024—61no—
158C4×D20C2×D311yescharacteristic
159#4016—31no—
160C4×Dic10C2×D311yescharacteristic
161C5×C4⋊C8—31no—
162C5×#103—31no—
163C5×#102—31no—
164#3967—31no—
165#3967—31no—
166#3964—31no—
167#3964—31no—
168#3964—31no—
169#3953—31no—
170#3953—31no—
171#3950—31no—
172#3949—31no—
173#3946—31no—
174#3946—31no—
175C8×Dic5—31no—
176C8×Dic5—31no—
177#3941—31no—
178#3939—31no—
179C4×#168—31no—
180#3361—151noSylow
181C23×C3×C5—21no—
182C22×C5×D3—21no—
183C22×C3×D5—21no—
184C3×C5×Q8—21no—
185C3×C5×Q8—21no—
186C3×C5×D4—21no—
187C3×C5×D4—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2411yescharacteristic
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×C5×Dic3—21no—
195C5×D12—21no—
196C5×D12#4112yes—
197C4×C5×D3—81no—
198C3×C22⋊D5—42no—
199C3×C22⋊D5—81no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—81no—
202C2×C3×Dic5C2×D411yescharacteristic
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C2×C3×Dic5C2×D411yescharacteristic
206C3×D20—21no—
207C3×D20—21no—
208C3×C4×D5—81no—
209C3×Dic10—22no—
210#1204—81no—
211D3×Dic5—42no—
212D3×Dic5—81no—
213C3⋊#168—21no—
214C3⋊#168—21no—
215C5×C3⋊C8—21no—
216C5×C3⋊C8—21no—
217C3×#127—51no—
218C3×#124—51no—
219C3×#124—101no—
220C3×#124C2×D511yescharacteristic
221C3×#123—101no—
222C3×#123—101no—
223C3×C4×Q8—51no—
224C3×C4×Q8—51no—
225C3×C4×D4—51no—
226C3×C4×D4—51no—
227C3×C4×D4—101no—
228#946—101no—
229C2×#215C2×D511yescharacteristic
230C2×#213—51no—
231C2×#213C2×D511yescharacteristic
232#896—101no—
233#896—101no—
234D3×C4⋊C4—101no—
235C4×D12—51no—
236C4×D12—51no—
237C4×D12C2×D511yescharacteristic
238#870—51no—
239#870—51no—
240#869—51no—
241#835—51no—
242#835—51no—
243#835C2×D511yescharacteristic
244#832—51no—
245#832—51no—
246#832—51no—
247#832—51no—
248#832—51no—
249#832C2×D511yescharacteristic
250#809—51no—
251#808—51no—
252#807—51no—
253#807—51no—
254C4⋊(C3⋊C8)—51no—
255C4⋊(C3⋊C8)—51no—
256C4⋊(C3⋊C8)C2×D511yescharacteristic
257C4×C3⋊C8—51no—
258C4×C3⋊C8—51no—
259C4×C3⋊C8—51no—
260C2×C5×Q8C22×D311yescharacteristic
261C2×C5×D4—31no—
262C2×C5×D4C22×D311yescharacteristic
263C22×C4×C5—61no—
264C2×C22⋊D5—21no—
265C2×C22⋊D5—21no—
266C22×Dic5—21no—
267C22×Dic5—61no—
268C22×Dic5—61no—
269C2×D20C22×D311yescharacteristic
270C2×C4×D5—21no—
271C2×Dic10—61no—
272C2×Dic10#6711yescharacteristic
273C5×SD16—62no—
274C5×D8—62no—
275C2×C5×C8—31no—
276C2×C5×C8—31no—
277C5×C4⋊C4—31no—
278C5×C22⋊C4—21no—
279C5×C22⋊C4—21no—
280C5×C22⋊C4—61no—
281C42×C5C22×D311yescharacteristic
282C22⋊Dic5—21no—
283C22⋊Dic5—61no—
284C22⋊Dic5—61no—
285#686—62no—
286#685—21no—
287#685—21no—
288#685—21no—
289C4⋊Dic5—21no—
290C4⋊Dic5—31no—
291C4⋊Dic5—31no—
292C4⋊Dic5—61no—
293C4⋊Dic5#6711yescharacteristic
294C4⋊Dic5C22×D311yescharacteristic
295#683—61no—
296#683—61no—
297#683—61no—
298#683—61no—
299#683#6711yescharacteristic
300#683#6711yescharacteristic
301C4×Dic5—21no—
302C4×Dic5C22×D311yescharacteristic
303C4×Dic5C22×D311yescharacteristic
304C2×#168—31no—
305C2×#168—31no—
306#559—51no—
307#554—151no—
308#488—151no—
309#488—151no—
310#486—151no—
311#478—151no—
312#478—151no—
313#477—151no—
314#463—31no—
315#463—151no—
316#459—151no—
317C8×Q8—151no—
318C4×SD16—151no—
319C4×D8—151no—
320C4×D8—151no—
321C22×C3×C5—41no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5C22×D411yescharacteristic
325C2×C5×D3—22no—
326C2×C5×D3—41no—
327C2×C5×D3—41no—
328C2×C3×D5—41no—
329C2×C3×D5—41no—
330C2×C3×D5—41no—
331C3×C4×C5—21no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5C2×#4111yescharacteristic
335C3×C4×C52−1+411yescharacteristic
336Dic15—41no—
337Dic15—41no—
338C3×Dic5—21no—
339C3×Dic5—21no—
340C3×Dic5—21no—
341C3×Dic5—41no—
342C3×Dic5#13512yes—
343C5×Dic3—41no—
344C2×C3×Q8—51no—
345C2×C3×Q8C22×D511yescharacteristic
346C2×C3×D4—51no—
347C2×C3×D4—101no—
348C2×C3×D4—101no—
349C2×C3×D4C22×D511yescharacteristic
350C22×C3×C4—101no—
351C22×C3×C4—101no—
352C2×D12C22×D511yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—101no—
355C2×C4×D3—101no—
356C2×Dic6—101no—
357C3×C4⋊C4—51no—
358C3×C4⋊C4—51no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4—101no—
362C3×C22⋊C4—21no—
363C3×C22⋊C4—21no—
364C3×C22⋊C4—101no—
365C3×C22⋊C4—101no—
366C3×C22⋊C4—101no—
367C3×C22⋊C4—101no—
368C3×C42—51no—
369C3×C42—51no—
370C3×C42—101no—
371C3×C42C22×D511yescharacteristic
372#215—22no—
373#213—22no—
374#213—102no—
375(C2×D3)⋊C4—21no—
376(C2×D3)⋊C4—101no—
377(C2×D3)⋊C4—101no—
378C4⋊Dic3—51no—
379C4⋊Dic3—51no—
380C4⋊Dic3—101no—
381C4⋊Dic3C22×D511yescharacteristic
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386C2×C3⋊C8—51no—
387C2×C3⋊C8—51no—
388C2×C3⋊C8C22×D511yescharacteristic
389C2×C3⋊C8C22×D511yescharacteristic
390C23×C5—21no—
391C23×C5—61no—
392C22×D5—21no—
393C5×Q8—21no—
394C5×Q8—21no—
395C5×D4—21no—
396C5×D4—21no—
397C5×D4—32no—
398C5×D4—61no—
399C2×C4×C5—21no—
400C2×C4×C5—61no—
401C2×C4×C5—241no—
402C2×C4×C5C2×#6711yescharacteristic
403C2×C4×C5C2×#6711yescharacteristic
404C2×C4×C5C23×D311yescharacteristic
405C22⋊D5—42no—
406C22⋊D5—81no—
407C2×Dic5—21no—
408C2×Dic5—61no—
409C2×Dic5—61no—
410C2×Dic5—81no—
411C2×Dic5—122no—
412C2×Dic5—241no—
413C2×Dic5C2×#6711yescharacteristic
414C2×Dic5C2×#6711yescharacteristic
415C2×Dic5C2×#6711yescharacteristic
416C2×Dic5C2×#6711yescharacteristic
417D20—21no—
418D20—21no—
419C4×D5—81no—
420Dic10—22no—
421Dic10—241no—
422C5×C8—61no—
423C5×C8—61no—
424#168—61no—
425#168—61no—
426C2×SD16—31no—
427C2×D8—31no—
428C2×D8—151no—
429C4⋊Q8—151no—
430#127—51no—
431#125—151no—
432#125—151no—
433#124—51no—
434#124—101no—
435#124D3×D511yescharacteristic
436#123—101no—
437#123—101no—
438C22⋊Q8—301no—
439C22⋊Q8—301no—
440C22⋊Q8—301no—
441C4×Q8—51no—
442C4×Q8—51no—
443C4×D4—31no—
444C4×D4—51no—
445C4×D4—51no—
446C4×D4—101no—
447C4×D4—151no—
448C4×D4—151no—
449C2×C4⋊C4—301no—
450#107—151no—
451#107—151no—
452#106—151no—
453C4⋊C8—31no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—31no—
457#103—151no—
458#103—151no—
459#102—31no—
460#102—151no—
461#102—151no—
462#102—151no—
463#102—151no—
464#102—151no—
465#102—151no—
466C4×C8—151no—
467C4×C8—151no—
468C4×C8—151no—
469C2×C3×C5—81no—
470C2×C3×C5#54811yescharacteristic
471C2×C3×C5C2×#13511yescharacteristic
472C2×C3×C5#57611yescharacteristic
473C3×D5—81no—
474C5×D3—42no—
475C23×C3—21no—
476C23×C3—101no—
477C22×D3—21no—
478C3×Q8—21no—
479C3×Q8—21no—
480C3×Q8—102no—
481C3×D4—21no—
482C3×D4—21no—
483C3×D4—101no—
484C3×D4—101no—
485C3×D4—202no—
486C3×D4—401no—
487C2×C3×C4—21no—
488C2×C3×C4—51no—
489C2×C3×C4—51no—
490C2×C3×C4—51no—
491C2×C3×C4—51no—
492C2×C3×C4—101no—
493C2×C3×C4—401no—
494C2×C3×C4—401no—
495C2×C3×C4D4×D511yescharacteristic
496C2×C3×C4D4×D511yescharacteristic
497C2×C3×C4C23×D511yescharacteristic
498C2×Dic3—21no—
499C2×Dic3—101no—
500C2×Dic3—101no—
501D12—21no—
502D12#71112yes—
503C4×D3—81no—
504C4×D3—202no—
505C4×D3—401no—
506Dic6—401no—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—41no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5—62no—
515C22×C5—121no—
516C22×C5—121no—
517C22×C5C22×#6711yescharacteristic
518C2×D5—41no—
519C2×D5—41no—
520C2×D5—41no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—41no—
524C4×C5—121no—
525C4×C5D3×#4111yescharacteristic
526C4×C5#101011yescharacteristic
527Dic5—21no—
528Dic5—21no—
529Dic5—21no—
530Dic5—41no—
531Dic5—121no—
532Dic5—121no—
533Dic5#95012yes—
534C2×Q8—51no—
535C2×Q8—301no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—31no—
538C2×D4—51no—
539C2×D4—101no—
540C2×D4—101no—
541C2×D4C2×D3×D511yescharacteristic
542C22×C4—61no—
543C22×C4—101no—
544C22×C4—101no—
545C22×C4—301no—
546C22×C4—301no—
547SD16—62no—
548D8—62no—
549D8—302no—
550C2×C8—31no—
551C2×C8—31no—
552C2×C8—151no—
553C2×C8—151no—
554C4⋊C4—31no—
555C4⋊C4—51no—
556C4⋊C4—51no—
557C4⋊C4—51no—
558C4⋊C4—51no—
559C4⋊C4—101no—
560C4⋊C4—151no—
561C4⋊C4—151no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C22⋊C4—21no—
568C22⋊C4—21no—
569C22⋊C4—61no—
570C22⋊C4—101no—
571C22⋊C4—101no—
572C22⋊C4—101no—
573C22⋊C4—101no—
574C22⋊C4—301no—
575C22⋊C4—301no—
576C42—51no—
577C42—51no—
578C42—101no—
579C42C2×D3×D511yescharacteristic
580C3×C5#336111yescharacteristic, complemented, Hall
581C22×C3—41no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—201no—
585C22×C3—201no—
586C22×C3—201no—
587C22×C3C2×D4×D511yescharacteristic
588C2×D3—22no—
589C2×D3—41no—
590C2×D3—41no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—41no—
594C3×C4—52no—
595C3×C4—101no—
596C3×C4—101no—
597C3×C4—101no—
598C3×C4—201no—
599C3×C4C2×#71111yescharacteristic
600C3×C4#415011yescharacteristic
601Dic3—41no—
602Dic3—201no—
603Dic3—201no—
604C2×C5—81no—
605C2×C5—122no—
606C2×C5C2×#95011yescharacteristic
607C2×C5#583111yescharacteristic
608C2×C5#583511yescharacteristic
609D5—81no—
610C23—21no—
611C23—61no—
612C23—101no—
613Q8—21no—
614Q8—21no—
615Q8—102no—
616Q8—1201no—
617D4—21no—
618D4—21no—
619D4—32no—
620D4—61no—
621D4—101no—
622D4—101no—
623D4—202no—
624D4—401no—
625C2×C4—21no—
626C2×C4—51no—
627C2×C4—51no—
628C2×C4—51no—
629C2×C4—51no—
630C2×C4—61no—
631C2×C4—101no—
632C2×C4—241no—
633C2×C4—301no—
634C2×C4—301no—
635C2×C4—401no—
636C2×C4—401no—
637C2×C4—602no—
638C2×C4—1201no—
639C2×C4D5×#6711yescharacteristic
640C2×C4D5×#6711yescharacteristic
641C2×C4C22×D3×D511yescharacteristic
642C8—61no—
643C8—61no—
644C8—301no—
645C8—301no—
646C2×C3—81no—
647C2×C3—401no—
648C2×C3#6593211yescharacteristic
649C2×C3D5×#13511yescharacteristic
650C2×C3#6610811yescharacteristic
651D3—42no—
652C5#8371311yescharacteristic, complemented, Sylow
653C22—41no—
654C22—41no—
655C22—41no—
656C22—62no—
657C22—121no—
658C22—121no—
659C22—201no—
660C22—201no—
661C22—201no—
662C22C2×D5×#6711yescharacteristic
663C4—21no—
664C4—21no—
665C4—41no—
666C4—52no—
667C4—101no—
668C4—101no—
669C4—101no—
670C4—121no—
671C4—201no—
672C4—601no—
673C4—601no—
674C4#9202011yescharacteristic
675C4D3×#71111yescharacteristic
676C3#1061224811yescharacteristic, complemented, Sylow
677C2—81no—
678C2—122no—
679C2—401no—
680C2#1175479811yescharacteristic
681C2D5×#95011yescharacteristic
682C2#1175531611yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radical#11748974C2
hypercenter#124D3×D5
hypocenterC3×C5#3361
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#66015C2semidirect
2. #11752583C2semidirect
3. #11751157C2semidirect
4. C5×#5057C2semidirect
5. #11749351C2semidirect
6. #11749331C2semidirect
7. #11749224C2semidirect
8. Dic5×#215C2semidirect
9. #11749102C2semidirect
10. #11749083C2semidirect
12. Dic5×#213C2semidirect
13. C4×#6652C2semidirect
14. #11746888C2semidirect
15. #11746846C2semidirect
61. #66015D3semidirect
127. #5057D5semidirect
580. C3×C5#3361semidirect
652. C5#83713semidirect
676. C3#10612248semidirect

Maximal subgroups

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

subgroupindex
C3×#660152
#117525832
#117511572
C5×#50572
#117493512
#117493312
#117492242
Dic5×#2152
#117491022
#117490832
#117489742
Dic5×#2132
C4×#66522
#117468882
#117468462
#106122483
#837135