Finite Group Databasebeta

← #14303017

Subgroups — #14303017

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#65827C211yesmaximal, characteristic
2#11755406C211yesmaximal, characteristic, complemented
3C2×#90995C211yesmaximal, characteristic, complemented
4C2×#90995C211yesmaximal, characteristic, complemented
5C2×#90995C211yesmaximal, characteristic, complemented
6#11746348C211yesmaximal, characteristic, complemented
7C5×#4527C211yesmaximal, characteristic, complemented
8#10599757—31nomaximal, Hall
9C22×C3×C22⋊D5C2211yescharacteristic
10C22×C3×C22⋊D5C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C2×C5×#217C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C3×#4076—22no—
17C3×#4032—21no—
18C3×#4032C412yescomplemented
19C3×#4028—21no—
20C3×#4028C412yescomplemented
21#91559—22no—
22Dic3×C22⋊D5—22no—
23D5×#217—21no—
24#91528—21no—
25#90995—22no—
26#90995—22no—
27#90995—22no—
28#71848—51nomaximal, Hall
29#65827D311yescharacteristic
30#65820—31no—
31C2×#3938—31no—
32C2×#3938—31no—
33C2×#3938—31no—
34C5×#342—31no—
35#64747—31no—
36C24×C3×C5C2311yescharacteristic
37C23×C3×D5C2×C411yescharacteristic, complemented
38C23×C3×D5D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×Dic15—21no—
41C22×Dic15—21no—
42C22×C5×Dic3—21no—
43C22×C5×Dic3—21no—
44C2×C3×C22⋊D5—21no—
45C2×C3×C22⋊D5—21no—
46C2×C3×C22⋊D5—21no—
47C2×C3×C22⋊D5—21no—
48C2×C3×C22⋊D5—21no—
49C2×C3×C22⋊D5—21no—
50C2×C3×C22⋊D5—21no—
51C2×C3×C22⋊D5—21no—
52C2×C3×C22⋊D5—21no—
53C2×C3×C22⋊D5—21no—
54C2×C3×C22⋊D5C2×C412yes—
55C2×C3×C22⋊D5D412yes—
56C22×C3×Dic5C2×C411yescharacteristic, complemented
57C22×C3×Dic5D411yescharacteristic
58C2×C3×D20—22no—
59C2×D5×Dic3—22no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4C2×C412yescomplemented
62#6719—21no—
63#6719—21no—
64#6719—21no—
65#6719D412yescomplemented
66C5×#217—21no—
67C5×#217—21no—
68C5×#217—21no—
69C5×#217D412yescomplemented
70C3×#685—22no—
71C3×#685—22no—
72C3×C4⋊Dic5—22no—
73#6668—22no—
74#6665—22no—
75Dic3×Dic5—22no—
76C3×#534—51no—
77#5798—51no—
78C2×#834—51no—
79C2×#834—51no—
80C2×#834—51no—
81#4527—51no—
82#4527D511yescharacteristic, complemented
83C22×C22⋊D5C2×D311yescharacteristic
84C22×C22⋊D5C2×D311yescharacteristic
85C2×C5×C22⋊C4—31no—
86C2×C5×C22⋊C4—31no—
87C2×C5×C22⋊C4C2×D311yescharacteristic
88C2×C22⋊Dic5—31no—
89C2×C22⋊Dic5—31no—
90#4076—22no—
91C4×C22⋊D5—62no—
92#4032—21no—
93#4032Dic312yescomplemented
94#4028—21no—
95#4028Dic312yescomplemented
96#4027—62no—
97D5×C22⋊C4—61no—
98#4023—61no—
99#3938—62no—
100#3938—62no—
101#3938—62no—
102#1913—151noSylow
103C23×C3×C5—81no—
104C23×C3×C5C22×C411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×D411yescharacteristic
108C23×C3×C5C2×D411yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C22×C3×D5—21no—
112C22×C3×D5—21no—
113C22×C3×D5—21no—
114C22×C3×D5—21no—
115C22×C3×D5—21no—
116C22×C3×D5—81no—
117C22×C3×D5—81no—
118C22×C3×D5C22⋊C412yes—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—81no—
121C2×Dic15—22no—
122C2×Dic15—41no—
123C2×Dic15—81no—
124C2×Dic15—81no—
125C2×C5×Dic3—22no—
126C2×C5×Dic3—41no—
127C2×C5×Dic3—81no—
128C2×C5×Dic3—81no—
129C3×C22⋊D5—22no—
130C3×C22⋊D5—22no—
131C3×C22⋊D5—22no—
132C3×C22⋊D5—22no—
133C3×C22⋊D5—41no—
134C3×C22⋊D5—41no—
135C3×C22⋊D5—41no—
136C3×C22⋊D5—41no—
137C2×C3×Dic5—21no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5—21no—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5C22⋊C412yes—
143C3×D20—82no—
144D5×Dic3—82no—
145C22×C3×D4—51no—
146C22×C3×D4—51no—
147C3×#123—52no—
148C3×#123—101no—
149C3×#121—102no—
150C3×#120—52no—
151C3×#120—101no—
152C2×C3×C22⋊C4C2×D511yescharacteristic
153C2×#217—51no—
154C2×#217—51no—
155C2×#217—101no—
156C2×#217C2×D511yescharacteristic
157C2×#217C2×D511yescharacteristic
158D4×Dic3—102no—
159D4×Dic3—102no—
160#926—101no—
161#834—102no—
162#834—102no—
163#834—102no—
164C24×C5C22×D311yescharacteristic
165C23×D5C2×Dic311yescharacteristic, complemented
166C23×D5#6711yescharacteristic
167C22×C4×C5—21no—
168C22×C4×C5—61no—
169C22×C4×C5—61no—
170C2×C22⋊D5—21no—
171C2×C22⋊D5—21no—
172C2×C22⋊D5—21no—
173C2×C22⋊D5—21no—
174C2×C22⋊D5—21no—
175C2×C22⋊D5—21no—
176C2×C22⋊D5—21no—
177C2×C22⋊D5—21no—
178C2×C22⋊D5—21no—
179C2×C22⋊D5—21no—
180C2×C22⋊D5C2×Dic312yes—
181C2×C22⋊D5#6712yes—
182C22×Dic5—61no—
183C22×Dic5—61no—
184C22×Dic5C2×Dic311yescharacteristic, complemented
185C22×Dic5#6711yescharacteristic
186C2×D20—22no—
187C2×C4×D5—62no—
188C5×C22⋊C4—21no—
189C5×C22⋊C4—32no—
190C5×C22⋊C4—61no—
191C5×C22⋊C4—61no—
192C5×C22⋊C4—61no—
193C5×C22⋊C4C2×Dic312yescomplemented
194C22⋊Dic5—32no—
195C22⋊Dic5—61no—
196C22⋊Dic5—61no—
197C22⋊Dic5—61no—
198#685—22no—
199#685—22no—
200#685—62no—
201C4⋊Dic5—22no—
202#683—62no—
203C4×Dic5—62no—
204#534—51no—
205#518—151no—
206C2×#99—151no—
207C2×#99—151no—
208C2×#99—151no—
209#342—31no—
210#342—151no—
211C22×C3×C5—41no—
212C22×C3×C5—41no—
213C22×C3×C5—41no—
214C22×C3×C5—41no—
215C22×C3×C5—41no—
216C22×C3×C5—41no—
217C22×C3×C5—41no—
218C22×C3×C5C2×C22⋊C411yescharacteristic
219C22×C3×C5C4×D411yescharacteristic
220C22×C3×C5C4×D411yescharacteristic
221C22×C3×C5#12011yescharacteristic
222C22×C3×C5#12111yescharacteristic
223C22×C3×C5#12111yescharacteristic
224C22×C3×C5#12311yescharacteristic
225C2×C3×D5—22no—
226C2×C3×D5—42no—
227C2×C3×D5—42no—
228C2×C3×D5—42no—
229C2×C3×D5—41no—
230C2×C3×D5—81no—
231C2×C3×D5—81no—
232C2×C3×D5—81no—
233C3×C4×C5—42no—
234Dic15—42no—
235Dic15—81no—
236C3×Dic5—22no—
237C3×Dic5—41no—
238C5×Dic3—42no—
239C5×Dic3—81no—
240C24×C3—51no—
241C24×C3—51no—
242C24×C3C22×D511yescharacteristic
243C2×C3×D4—52no—
244C2×C3×D4—52no—
245C2×C3×D4—102no—
246C2×C3×D4—101no—
247C2×C3×D4—101no—
248C2×C3×D4—101no—
249C2×C3×D4—101no—
250C2×C3×D4—101no—
251C2×C3×D4—101no—
252C2×C3×D4—101no—
253C2×C3×D4—101no—
254C2×C3×D4—101no—
255C2×C3×D4—101no—
256C22×C3×C4—21no—
257C22×C3×C4—51no—
258C22×C3×C4—51no—
259C22×Dic3—21no—
260C22×Dic3—21no—
261C22×Dic3—102no—
262C22×Dic3—101no—
263C22×Dic3—101no—
264C3×C4⋊C4—102no—
265C3×C22⋊C4—21no—
266C3×C22⋊C4—102no—
267C3×C22⋊C4—102no—
268C3×C22⋊C4C4×D512yescomplemented
269#217—21no—
270#217—21no—
271#217—21no—
272#217—52no—
273#217—102no—
274#217—101no—
275#217—101no—
276#217—101no—
277#217D2012yescomplemented
278C4⋊Dic3—102no—
279C4×Dic3—102no—
280C23×C5—81no—
281C23×C5D3×D411yescharacteristic
282C23×C5D3×D411yescharacteristic
283C23×C5#23711yescharacteristic
284C23×C5#23711yescharacteristic
285C23×C5C22×Dic311yescharacteristic
286C23×C5C2×#6711yescharacteristic
287C23×C5C2×#6711yescharacteristic
288C22×D5—21no—
289C22×D5—21no—
290C22×D5—21no—
291C22×D5—21no—
292C22×D5—21no—
293C22×D5—81no—
294C22×D5—81no—
295C22×D5#21712yes—
296C2×C4×C5—22no—
297C2×C4×C5—62no—
298C2×C4×C5—81no—
299C2×C4×C5—121no—
300C2×C4×C5—241no—
301C2×C4×C5—241no—
302C22⋊D5—22no—
303C22⋊D5—22no—
304C22⋊D5—22no—
305C22⋊D5—22no—
306C22⋊D5—41no—
307C22⋊D5—41no—
308C22⋊D5—41no—
309C22⋊D5—41no—
310C2×Dic5—21no—
311C2×Dic5—21no—
312C2×Dic5—21no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—62no—
316C2×Dic5—121no—
317C2×Dic5—241no—
318C2×Dic5—241no—
319C2×Dic5#21712yes—
320D20—82no—
321C4×D5—242no—
322C22×D4—51no—
323C22×D4—51no—
324#123—52no—
325#123—101no—
326#121—102no—
327#120—52no—
328#120—101no—
329C4×D4—302no—
330C4×D4—302no—
331#117—301no—
332C2×C22⋊C4—31no—
333C2×C22⋊C4—31no—
334C2×C22⋊C4—151no—
335C2×C22⋊C4—151no—
336C2×C22⋊C4—301no—
337C2×C22⋊C4D3×D511yescharacteristic
338#99—302no—
339#99—302no—
340#99—302no—
341C2×C3×C5—21no—
342C2×C3×C5—21no—
343C2×C3×C5—21no—
344C2×C3×C5—21no—
345C2×C3×C5—21no—
346C2×C3×C5—21no—
347C2×C3×C5—21no—
348C2×C3×C5#38611yescharacteristic
349C3×D5—42no—
350C3×D5—81no—
351C23×C3—52no—
352C23×C3—81no—
353C23×C3—101no—
354C23×C3—101no—
355C23×C3—101no—
356C23×C3—101no—
357C23×C3—101no—
358C23×C3—401no—
359C23×C3—401no—
360C23×C3C2×C4×D511yescharacteristic
361C23×C3C2×D2011yescharacteristic
362C23×C3#70911yescharacteristic
363C23×C3D4×D511yescharacteristic
364C23×C3D4×D511yescharacteristic
365C23×C3D4×D511yescharacteristic
366C23×C3#71311yescharacteristic
367C3×D4—102no—
368C3×D4—102no—
369C3×D4—102no—
370C3×D4—102no—
371C3×D4—201no—
372C3×D4—201no—
373C3×D4—201no—
374C3×D4—201no—
375C3×D4—402no—
376C2×C3×C4—22no—
377C2×C3×C4—52no—
378C2×C3×C4—81no—
379C2×C3×C4—101no—
380C2×C3×C4—101no—
381C2×C3×C4—101no—
382C2×C3×C4—101no—
383C2×C3×C4—101no—
384C2×Dic3—22no—
385C2×Dic3—41no—
386C2×Dic3—81no—
387C2×Dic3—81no—
388C2×Dic3—102no—
389C2×Dic3—201no—
390C2×Dic3—402no—
391C2×Dic3—401no—
392C2×Dic3—401no—
393C22×C5—41no—
394C22×C5—41no—
395C22×C5—41no—
396C22×C5—41no—
397C22×C5—41no—
398C22×C5—41no—
399C22×C5—41no—
400C22×C5D4×Dic311yescharacteristic
401C22×C5D4×Dic311yescharacteristic
402C22×C5#93511yescharacteristic
403C22×C5#93711yescharacteristic
404C22×C5#93911yescharacteristic
405C22×C5#93911yescharacteristic
406C22×C5C2×#21711yescharacteristic
407C2×D5—22no—
408C2×D5—42no—
409C2×D5—42no—
410C2×D5—42no—
411C2×D5—41no—
412C2×D5—81no—
413C2×D5—81no—
414C2×D5—81no—
415C4×C5—42no—
416C4×C5—122no—
417C4×C5—241no—
418Dic5—22no—
419Dic5—41no—
420Dic5—122no—
421Dic5—241no—
422C24—51no—
423C24—51no—
424C24C2×D3×D511yescharacteristic
425C2×D4—52no—
426C2×D4—52no—
427C2×D4—102no—
428C2×D4—101no—
429C2×D4—101no—
430C2×D4—101no—
431C2×D4—101no—
432C2×D4—101no—
433C2×D4—101no—
434C2×D4—101no—
435C2×D4—101no—
436C2×D4—101no—
437C2×D4—101no—
438C22×C4—21no—
439C22×C4—51no—
440C22×C4—51no—
441C22×C4—61no—
442C22×C4—61no—
443C22×C4—302no—
444C22×C4—301no—
445C22×C4—301no—
446C4⋊C4—102no—
447C4⋊C4—302no—
448C22⋊C4—21no—
449C22⋊C4—32no—
450C22⋊C4—61no—
451C22⋊C4—61no—
452C22⋊C4—61no—
453C22⋊C4—102no—
454C22⋊C4—102no—
455C22⋊C4—152no—
456C22⋊C4—302no—
457C22⋊C4—301no—
458C22⋊C4—301no—
459C22⋊C4—301no—
460C22⋊C4D5×Dic312yescomplemented
461C42—302no—
462C3×C5#191311yescharacteristic, complemented, Hall
463C22×C3—41no—
464C22×C3—41no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—41no—
468C22×C3—41no—
469C22×C3—41no—
470C22×C3—102no—
471C22×C3—202no—
472C22×C3—202no—
473C22×C3—202no—
474C22×C3—201no—
475C22×C3—401no—
476C22×C3—401no—
477C22×C3—401no—
478C22×C3C4×D2011yescharacteristic
479C22×C3D5×C22⋊C411yescharacteristic
480C22×C3#402811yescharacteristic
481C22×C3#403011yescharacteristic
482C22×C3#403911yescharacteristic
483C22×C3#404011yescharacteristic
484C22×C3#404111yescharacteristic
485C3×C4—42no—
486C3×C4—102no—
487C3×C4—201no—
488Dic3—42no—
489Dic3—81no—
490Dic3—202no—
491Dic3—401no—
492C2×C5—21no—
493C2×C5—21no—
494C2×C5—21no—
495C2×C5—21no—
496C2×C5—21no—
497C2×C5—21no—
498C2×C5—21no—
499C2×C5#522011yescharacteristic
500D5—42no—
501D5—81no—
502C23—52no—
503C23—81no—
504C23—101no—
505C23—101no—
506C23—101no—
507C23—101no—
508C23—101no—
509C23—401no—
510C23—401no—
511C23#676511yescharacteristic
512C23#676611yescharacteristic
513C23D3×D2011yescharacteristic
514C23#677711yescharacteristic
515C23C2×D5×Dic311yescharacteristic
516C23D5×#6711yescharacteristic
517C23D5×#6711yescharacteristic
518D4—102no—
519D4—102no—
520D4—102no—
521D4—102no—
522D4—201no—
523D4—201no—
524D4—201no—
525D4—201no—
526D4—402no—
527C2×C4—22no—
528C2×C4—52no—
529C2×C4—62no—
530C2×C4—81no—
531C2×C4—101no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—101no—
535C2×C4—101no—
536C2×C4—121no—
537C2×C4—241no—
538C2×C4—241no—
539C2×C4—302no—
540C2×C4—601no—
541C2×C4—1202no—
542C2×C4—1201no—
543C2×C4—1201no—
544C2×C3—21no—
545C2×C3—21no—
546C2×C3—21no—
547C2×C3—21no—
548C2×C3—21no—
549C2×C3—21no—
550C2×C3—21no—
551C2×C3—202no—
552C2×C3—401no—
553C2×C3#6495411yescharacteristic
554C5#7184811yescharacteristic, complemented, Sylow
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—102no—
563C22—202no—
564C22—202no—
565C22—202no—
566C22—201no—
567C22—401no—
568C22—401no—
569C22—401no—
570C22#9140711yescharacteristic
571C22#9140811yescharacteristic
572C22#9140911yescharacteristic
573C22Dic3×D2011yescharacteristic
574C22#9143411yescharacteristic
575C22#9147411yescharacteristic
576C22D5×#21711yescharacteristic
577C4—42no—
578C4—102no—
579C4—122no—
580C4—201no—
581C4—241no—
582C4—602no—
583C4—1201no—
584C3#1059975711yescharacteristic, complemented, Sylow
585C2—21no—
586C2—21no—
587C2—21no—
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—202no—
593C2—401no—
594C2#1174889611yescharacteristic
subgroupG/H
centerC2#11748896
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC2×C3×C5#386
prime radicalC3×#65827C2
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1913
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #11755406C2semidirect
3. C2×#90995C2semidirect
4. C2×#90995C2semidirect
5. C2×#90995C2semidirect
6. #11746348C2semidirect
7. C5×#4527C2semidirect
18. C3×#4032C4semidirect
20. C3×#4028C4semidirect
37. C23×C3×D5C2×C4semidirect
56. C22×C3×Dic5C2×C4semidirect
61. C3×C5×C22⋊C4C2×C4semidirect
65. #6719D4semidirect
69. C5×#217D4semidirect
82. #4527D5semidirect
93. #4032Dic3semidirect
95. #4028Dic3semidirect
165. C23×D5C2×Dic3semidirect
184. C22×Dic5C2×Dic3semidirect
193. C5×C22⋊C4C2×Dic3semidirect
268. C3×C22⋊C4C4×D5semidirect
277. #217D20semidirect
460. C22⋊C4D5×Dic3semidirect
462. C3×C5#1913semidirect
554. C5#71848semidirect
584. C3#10599757semidirect

Maximal subgroups

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

subgroupindex
C3×#658272
#117554062
C2×#909952
#117463482
C5×#45272
#105997573
#718485