Finite Group Databasebeta

← #14300531

Subgroups — #14300531

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×M16×D15C211yesmaximal, characteristic, complemented
2#11756283C211yesmaximal, characteristic
3C2×#91109C211yesmaximal, characteristic, complemented
4C4×#6714C211yesmaximal, characteristic, complemented
5C2×#91089C211yesmaximal, characteristic, complemented
6C3×C5×#339C211yesmaximal, characteristic, complemented
7#11746353C211yesmaximal, characteristic, complemented
8#10599548—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C4×D15C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C2×C3×C42×C5C2211yescharacteristic
14C2×#6714—21no—
15C2×C4×Dic15C2211yescharacteristic
16C2×#6710C2211yescharacteristic
17M16×D15—22no—
18M16×D15—22no—
19C2×#6705—21no—
20C2×C8×D15—21no—
21#91786C411yescharacteristic, complemented
22#91786C411yescharacteristic, complemented
23#91784C411yescharacteristic, complemented
24#91784C411yescharacteristic, complemented
25#91775—21no—
26#91771—21no—
27C4×D60—21no—
28C4×D60—21no—
29#91115—21no—
30#91109—22no—
31#91089—22no—
32#68755—51nomaximal, Hall
33C2×D5×M16—31no—
34#65858—31no—
35C2×#3957—31no—
36C4×#685—31no—
37C2×#3937—31no—
38C5×#339D311yescharacteristic, complemented
39#64752—31no—
40C23×D15D411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C2×#1220—21no—
44C22×Dic15—21no—
45C22×Dic15D411yescharacteristic
46#6817—21no—
47#6817—21no—
48#6817—21no—
49#6817—21no—
50C2×D60—21no—
51C2×D60—21no—
52C2×D60C2×C411yescharacteristic
53C2×C4×D15—21no—
54C2×C4×D15—21no—
55C2×C4×D15—21no—
56C2×C4×D15—21no—
57C2×C4×D15—21no—
58C2×C4×D15C2×C411yescharacteristic
59C2×C4×D15C2×C411yescharacteristic
60C2×C4×D15D411yescharacteristic
61C2×C4×D15D411yescharacteristic
62C2×Dic30C2×C411yescharacteristic
63C3×C5×M16—21no—
64C3×C5×M16D412yescomplemented
65C2×C3×C5×C8—21no—
66C3×C5×C4⋊C4C2×C411yescharacteristic
67C3×C5×C4⋊C4C2×C411yescharacteristic
68C3×C5×C22⋊C4—21no—
69C3×C42×C5—21no—
70C3×C42×C5—21no—
71C3×C42×C5—21no—
72#6714—24no—
73#6714—21no—
74#6714—21no—
75#6714—21no—
76#6714—21no—
77C4⋊Dic15—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—
86C2×D3×M16—51no—
87#5524—51no—
88C2×#825—51no—
89C4×(C2×D3)⋊C4—51no—
90C2×#805—51no—
91C3×#339D511yescharacteristic, complemented
92#4532—51no—
93C2×#709—31no—
94C22×C4×D5—31no—
95C2×C5×M16C2×D311yescharacteristic
96C5×#117C2×D311yescharacteristic
97C2×C42×C5C2×D311yescharacteristic
98C2×#685—61no—
99C2×C4×Dic5—31no—
100C2×#681—31no—
101D5×M16—62no—
102D5×M16—62no—
103C2×#676—61no—
104C2×C8×D5—61no—
105#4043—31no—
106#4043—31no—
107#4041—31no—
108#4041—31no—
109#4032—61no—
110#4028—61no—
111C4×D20—61no—
112C4×D20—61no—
113#3963—61no—
114#3957—62no—
115#3937—62no—
116#1871—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×D15—21no—
119C22×D15—21no—
120C22×D15—22no—
121C22×D15—21no—
122C22×D15—41no—
123C22×D15C22⋊C411yescharacteristic
124C22×D15C22⋊C411yescharacteristic
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5—41no—
129C2×C3×C4×C5—41no—
130C2×C3×C4×C5C22×C411yescharacteristic
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5#4111yescharacteristic
135C2×C3×C4×C5#4111yescharacteristic
136#1220—41no—
137#1220—41no—
138C2×Dic15—21no—
139C2×Dic15—21no—
140C2×Dic15—22no—
141C2×Dic15—21no—
142C2×Dic15—41no—
143C2×Dic15—41no—
144C2×Dic15C22⋊C411yescharacteristic
145C2×Dic15C22⋊C411yescharacteristic
146D60—21no—
147D60—21no—
148D60—42no—
149D60—42no—
150C4×D15—21no—
151C4×D15—21no—
152C4×D15—21no—
153C4×D15—21no—
154C4×D15—21no—
155C4×D15—21no—
156C4×D15—21no—
157C4×D15—21no—
158C4×D15—41no—
159C4×D15—41no—
160Dic30—21no—
161Dic30—21no—
162C3×C5×C8—22no—
163C3⋊#168—22no—
164C2×#235—51no—
165C22×C4×D3—51no—
166C2×C3×M16C2×D511yescharacteristic
167C3×#117C2×D511yescharacteristic
168C2×C3×C42C2×D511yescharacteristic
169C2×(C2×D3)⋊C4—101no—
170C2×C4×Dic3—51no—
171C2×#208—51no—
172D3×M16—102no—
173D3×M16—102no—
174C2×ΓL(1,𝔽25)—101no—
175C2×D3×C8—101no—
176#897—51no—
177#897—51no—
178#895—51no—
179#895—51no—
180#886—101no—
181#882—101no—
182C4×D12—101no—
183C4×D12—101no—
184C3⋊#95—101no—
185#825—102no—
186#805—102no—
187C23×D5—31no—
188C22×C4×C5—21no—
189C22×C4×C5C22×D311yescharacteristic
190C2×C22⋊D5—61no—
191C22×Dic5—31no—
192C22×Dic5—61no—
193#709—61no—
194#709—61no—
195#709—61no—
196#709—61no—
197C2×D20—31no—
198C2×D20—61no—
199C2×D20—61no—
200C2×C4×D5—31no—
201C2×C4×D5—31no—
202C2×C4×D5—31no—
203C2×C4×D5—31no—
204C2×C4×D5—61no—
205C2×C4×D5—61no—
206C2×C4×D5—61no—
207C2×C4×D5—61no—
208C2×C4×D5—61no—
209C2×Dic10—31no—
210C5×M16—21no—
211C5×M16D1212yescomplemented
212C2×C5×C8—21no—
213C5×C4⋊C4C4×D311yescharacteristic
214C5×C4⋊C4C4×D311yescharacteristic
215C5×C22⋊C4—21no—
216C42×C5—21no—
217C42×C5—21no—
218C42×C5—21no—
219#685—61no—
220#685—61no—
221#685—61no—
222#685—61no—
223#685—64no—
224C4⋊Dic5—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×#104—151no—
237C4×C22⋊C4—151no—
238#339—151no—
239#339D1511yescharacteristic, complemented
240C22×C3×C5—21no—
241C22×C3×C5—21no—
242C22×C3×C5C2×C22⋊C411yescharacteristic
243C22×C3×C5#12111yescharacteristic
244C22×C3×C5#12111yescharacteristic
245C2×D15—21no—
246C2×D15—21no—
247C2×D15—21no—
248C2×D15—21no—
249C2×D15—21no—
250C2×D15—42no—
251C2×D15—42no—
252C2×D15—41no—
253C2×D15—41no—
254C2×D15—41no—
255C2×D15#10412yescomplemented
256C3×C4×C5—42no—
257C3×C4×C5—41no—
258C3×C4×C5—41no—
259C3×C4×C5C4×D411yescharacteristic
260C3×C4×C5C4×D411yescharacteristic
261C3×C4×C5#12011yescharacteristic
262C3×C4×C5#12311yescharacteristic
263Dic15—21no—
264Dic15—21no—
265Dic15—42no—
266Dic15—41no—
267C23×D3—51no—
268C22×C3×C4—21no—
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—101no—
271C22×Dic3—51no—
272C22×Dic3—101no—
273#235—101no—
274#235—101no—
275#235—101no—
276#235—101no—
277C2×D12—51no—
278C2×D12—101no—
279C2×D12—101no—
280C2×C4×D3—51no—
281C2×C4×D3—51no—
282C2×C4×D3—51no—
283C2×C4×D3—51no—
284C2×C4×D3—101no—
285C2×C4×D3—101no—
286C2×C4×D3—101no—
287C2×C4×D3—101no—
288C2×C4×D3—101no—
289C2×Dic6—51no—
290C3×M16—21no—
291C3×M16D2012yescomplemented
292C2×C3×C8—21no—
293C3×C4⋊C4C4×D511yescharacteristic
294C3×C4⋊C4C4×D511yescharacteristic
295C3×C22⋊C4—21no—
296C3×C42—21no—
297C3×C42—21no—
298C3×C42—21no—
299(C2×D3)⋊C4—101no—
300(C2×D3)⋊C4—101no—
301(C2×D3)⋊C4—101no—
302(C2×D3)⋊C4—101no—
303(C2×D3)⋊C4—104no—
304C4⋊Dic3—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×C5D3×D411yescharacteristic
314C22×D5—31no—
315C22×D5—31no—
316C22×D5—62no—
317C22×D5—61no—
318C22×D5—61no—
319C22×D5—61no—
320C22×D5—121no—
321C2×C4×C5—22no—
322C2×C4×C5—21no—
323C2×C4×C5—21no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5C2×C4×D311yescharacteristic
327C2×C4×C5C2×D1211yescharacteristic
328C2×C4×C5#23511yescharacteristic
329C2×C4×C5D3×D411yescharacteristic
330C2×C4×C5D3×D411yescharacteristic
331C2×C4×C5#23911yescharacteristic
332C22⋊D5—121no—
333C22⋊D5—121no—
334C2×Dic5—31no—
335C2×Dic5—31no—
336C2×Dic5—61no—
337C2×Dic5—61no—
338C2×Dic5—62no—
339C2×Dic5—61no—
340C2×Dic5—121no—
341C2×Dic5—121no—
342D20—61no—
343D20—61no—
344D20—122no—
345D20—122no—
346C4×D5—61no—
347C4×D5—61no—
348C4×D5—61no—
349C4×D5—61no—
350C4×D5—61no—
351C4×D5—61no—
352C4×D5—61no—
353C4×D5—61no—
354C4×D5—121no—
355C4×D5—121no—
356Dic10—61no—
357Dic10—61no—
358C5×C8—22no—
359#168—62no—
360C2×#41—151no—
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#117C2×D1511yescharacteristic
377C2×C22⋊C4—301no—
378C2×C42—151no—
379C2×C42C2×D1511yescharacteristic
380#104—302no—
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
388D15—22no—
389D15—41no—
390D15—81no—
391C23×C3D4×D511yescharacteristic
392C22×D3—51no—
393C22×D3—51no—
394C22×D3—102no—
395C22×D3—101no—
396C22×D3—101no—
397C22×D3—101no—
398C22×D3—201no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4C2×C4×D511yescharacteristic
405C2×C3×C4C2×D2011yescharacteristic
406C2×C3×C4#70911yescharacteristic
407C2×C3×C4D4×D511yescharacteristic
408C2×C3×C4D4×D511yescharacteristic
409C2×C3×C4#71311yescharacteristic
410#67—201no—
411#67—201no—
412C2×Dic3—51no—
413C2×Dic3—51no—
414C2×Dic3—101no—
415C2×Dic3—101no—
416C2×Dic3—102no—
417C2×Dic3—101no—
418C2×Dic3—201no—
419C2×Dic3—201no—
420D12—101no—
421D12—101no—
422D12—202no—
423D12—202no—
424C4×D3—101no—
425C4×D3—101no—
426C4×D3—101no—
427C4×D3—101no—
428C4×D3—101no—
429C4×D3—101no—
430C4×D3—101no—
431C4×D3—101no—
432C4×D3—201no—
433C4×D3—201no—
434Dic6—101no—
435Dic6—101no—
436C3×C8—22no—
437C3⋊C8—102no—
438C22×C5—21no—
439C22×C5—21no—
440C22×C5D3×C22⋊C411yescharacteristic
441C22×C5#88411yescharacteristic
442C22×C5#89511yescharacteristic
443C2×D5—32no—
444C2×D5—61no—
445C2×D5—61no—
446C2×D5—61no—
447C2×D5—61no—
448C2×D5—61no—
449C2×D5—122no—
450C2×D5—122no—
451C2×D5—121no—
452C2×D5—121no—
453C2×D5—121no—
454C4×C5—42no—
455C4×C5—41no—
456C4×C5—41no—
457C4×C5C4×D1211yescharacteristic
458C4×C5#88211yescharacteristic
459C4×C5#89311yescharacteristic
460C4×C5#89411yescharacteristic
461Dic5—61no—
462Dic5—61no—
463Dic5—122no—
464Dic5—121no—
465C24—151no—
466#41—301no—
467#41—301no—
468#41—301no—
469#41—301no—
470C2×Q8—151no—
471C2×D4—151no—
472C2×D4—301no—
473C2×D4—301no—
474C2×D4—301no—
475C22×C4—21no—
476C22×C4—151no—
477C22×C4—151no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—151no—
481C22×C4—301no—
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—
492M16D6012yescomplemented
493C2×C8—21no—
494C2×C8—304no—
495C2×C8—301no—
496C4⋊C4—301no—
497C4⋊C4—301no—
498C4⋊C4C4×D1511yescharacteristic
499C4⋊C4C4×D1511yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—301no—
502C22⋊C4—301no—
503C22⋊C4—301no—
504C22⋊C4—301no—
505C22⋊C4—304no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—301no—
510C42—301no—
511C3×C5#187111yescharacteristic, complemented, Hall
512C22×C3—21no—
513C22×C3—21no—
514C22×C3D5×C22⋊C411yescharacteristic
515C22×C3#403011yescharacteristic
516C22×C3#404111yescharacteristic
517C2×D3—52no—
518C2×D3—101no—
519C2×D3—101no—
520C2×D3—101no—
521C2×D3—101no—
522C2×D3—101no—
523C2×D3—202no—
524C2×D3—202no—
525C2×D3—201no—
526C2×D3—201no—
527C2×D3—201no—
528C3×C4—42no—
529C3×C4—41no—
530C3×C4—41no—
531C3×C4C4×D2011yescharacteristic
532C3×C4#402811yescharacteristic
533C3×C4#403911yescharacteristic
534C3×C4#404011yescharacteristic
535Dic3—101no—
536Dic3—101no—
537Dic3—202no—
538Dic3—201no—
539C2×C5—21no—
540C2×C5—21no—
541C2×C5#466511yescharacteristic
542C2×C5D3×#10411yescharacteristic
543C2×C5#482111yescharacteristic
544D5—62no—
545D5—121no—
546D5—241no—
547C23—151no—
548C23—151no—
549C23—302no—
550C23—301no—
551C23—301no—
552C23—301no—
553C23—601no—
554C23D4×D1511yescharacteristic
555Q8—301no—
556Q8—301no—
557D4—301no—
558D4—301no—
559D4—602no—
560D4—602no—
561D4—601no—
562D4—601no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—151no—
569C2×C4—151no—
570C2×C4—301no—
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—302no—
581C2×C4—301no—
582C2×C4—601no—
583C2×C4—601no—
584C2×C4—601no—
585C2×C4—601no—
586C2×C4C2×C4×D1511yescharacteristic
587C2×C4C2×D6011yescharacteristic
588C2×C4#681711yescharacteristic
589C2×C4D4×D1511yescharacteristic
590C2×C4D4×D1511yescharacteristic
591C2×C4#682111yescharacteristic
592C8—22no—
593C8—302no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3#6495411yescharacteristic
597C2×C3D5×#10411yescharacteristic
598C2×C3#6511011yescharacteristic
599D3—102no—
600D3—201no—
601D3—401no—
602C5#6875511yescharacteristic, complemented, Sylow
603C22—21no—
604C22—21no—
605C22—152no—
606C22—301no—
607C22—301no—
608C22—301no—
609C22—301no—
610C22—301no—
611C22—602no—
612C22—602no—
613C22—601no—
614C22—601no—
615C22—601no—
616C22C22⋊C4×D1511yescharacteristic
617C22#9177311yescharacteristic
618C22#9178411yescharacteristic
619C4—42no—
620C4—41no—
621C4—41no—
622C4—301no—
623C4—301no—
624C4—602no—
625C4—601no—
626C4C4×D6011yescharacteristic
627C4#9177111yescharacteristic
628C4#9178211yescharacteristic
629C4#9178311yescharacteristic
630C3#1059954811yescharacteristic, complemented, Sylow
631C2—21no—
632C2—21no—
633C2—302no—
634C2—601no—
635C2—1201no—
636C2#1175076611yescharacteristic
637C2D15×#10411yescharacteristic
638C2#1175092211yescharacteristic
subgroupG/H
centerC2×C4D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#339C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756283C2
cosocleC22×C3×C4×C5C23
hypercenter#339D15
hypocenterC3×C5#1871
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×M16×D15C2semidirect
3. C2×#91109C2semidirect
4. C4×#6714C2semidirect
5. C2×#91089C2semidirect
6. C3×C5×#339C2semidirect
7. #11746353C2semidirect
21. #91786C4semidirect
22. #91786C4semidirect
23. #91784C4semidirect
24. #91784C4semidirect
38. C5×#339D3semidirect
64. C3×C5×M16D4semidirect
82. #6710D4semidirect
91. C3×#339D5semidirect
211. C5×M16D12semidirect
239. #339D15semidirect
255. C2×D15#104semidirect
291. C3×M16D20semidirect
492. M16D60semidirect
511. C3×C5#1871semidirect
602. C5#68755semidirect
630. C3#10599548semidirect

Maximal subgroups

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

subgroupindex
C2×M16×D152
#117562832
C2×#911092
C4×#67142
C2×#910892
C3×C5×#3392
#117463532
#105995483
#687555