Finite Group Databasebeta

← #14301023

Subgroups — #14301023

Order 1920.

876 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6715C211yesmaximal, characteristic
2C2×C4×D60C211yesmaximal, characteristic, complemented
3C3×C5×#390C211yesmaximal, characteristic, complemented
4C2×#91116C211yesmaximal, characteristic, complemented
5C2×#91093C211yesmaximal, characteristic, complemented
6#11746350C211yesmaximal, characteristic, complemented
7#11746345C211yesmaximal, characteristic, complemented
8#10600450—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C22×C4×D15—21no—
12C2×C3×C5×C4⋊C4C2211yescharacteristic
13C2×C3×C5×C22⋊C4—21no—
14C2×C3×C5×C22⋊C4—21no—
15C2×C3×C42×C5C2211yescharacteristic
16C2×#6715—22no—
17C2×#6715—22no—
18C2×#6715C414yescomplemented
19C2×#6714—21no—
20C2×C4⋊Dic15C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C4×D60—22no—
24C4×D60—22no—
25#91116—22no—
26#91093—22no—
27#69657—51nomaximal, Hall
28C22×#686—31no—
29C2×C4×D20—31no—
30C5×#390D311yescharacteristic, complemented
31C2×#3964—31no—
32C2×#3941—31no—
33#64749—31no—
34#64744—31no—
35C24×C3×C5—21no—
36C23×D15—21no—
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4—21no—
42C2×C3×C5×D4C2×C412yescomplemented
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5D411yescharacteristic
45C22×C3×C4×C5D411yescharacteristic
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15—21no—
48C2×D60—21no—
49C2×D60—21no—
50C2×D60—21no—
51C2×D60C2×C412yes—
52C2×D60D412yes—
53C2×D60D412yes—
54C2×C4×D15—24no—
55C2×C4×D15—42no—
56C2×C4×D15—42no—
57C3×C5×C4⋊C4—21no—
58C3×C5×C4⋊C4—21no—
59C3×C5×C22⋊C4—42no—
60C3×C5×C22⋊C4—42no—
61C3×C42×C5—21no—
62C3×C42×C5—21no—
63#6715—28no—
64#6714—24no—
65C4⋊Dic15—21no—
66C4⋊Dic15D412yes—
67C2×C3⋊#168—21no—
68C2×C3⋊#168—21no—
69C2×C3⋊#168—21no—
70C2×C3⋊#168—21no—
71C2×C3⋊#168—21no—
72C2×C3⋊#168C2×C412yescomplemented
73C22×#213—51no—
74C2×C4×D12—51no—
75C3×#390D511yescharacteristic, complemented
76C2×#832—51no—
77C2×#809—51no—
78#4529—51no—
79#4524—51no—
80C22×C5×D4C2×D311yescharacteristic
81C22×D20—31no—
82C22×C4×D5—61no—
83C2×C5×C4⋊C4C2×D311yescharacteristic
84C2×C5×C22⋊C4—21no—
85C2×C5×C22⋊C4—21no—
86C2×C42×C5C2×D311yescharacteristic
87C2×#686—34no—
88C2×#686—62no—
89C2×#686—62no—
90C2×#685—61no—
91C2×C4⋊Dic5—31no—
92C22×#168—31no—
93C22×#168—31no—
94C4×D20—62no—
95C4×D20—62no—
96#3964—62no—
97#3941—62no—
98#1879—151noSylow
99C23×C3×C5—22no—
100C23×C3×C5—41no—
101C23×C3×C5—41no—
102C23×C3×C5—41no—
103C23×C3×C5—41no—
104C23×C3×C5—41no—
105C23×C3×C5—41no—
106C23×C3×C5C2×D411yescharacteristic
107C22×D15—22no—
108C22×D15—22no—
109C22×D15—22no—
110C22×D15—41no—
111C22×D15—41no—
112C22×D15—41no—
113C22×D15—41no—
114C3×C5×D4—22no—
115C3×C5×D4—22no—
116C3×C5×D4—41no—
117C3×C5×D4—41no—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5D812yescomplemented
127C2×C3×C4×C5C22×C411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5#4111yescharacteristic
132C2×C3×C4×C5#4111yescharacteristic
133C2×Dic15—22no—
134C2×Dic15—41no—
135C2×Dic15—41no—
136D60—22no—
137D60—22no—
138D60—22no—
139D60C22⋊C414yescomplemented
140C4×D15—48no—
141C3⋊#168—22no—
142C3⋊#168—41no—
143C22×C3×D4C2×D511yescharacteristic
144C22×D12—51no—
145C22×C4×D3—101no—
146C2×C3×C4⋊C4C2×D511yescharacteristic
147C2×C3×C22⋊C4—21no—
148C2×C3×C22⋊C4—21no—
149C2×C3×C42C2×D511yescharacteristic
150C2×#213—54no—
151C2×#213—102no—
152C2×#213—102no—
153C2×(C2×D3)⋊C4—101no—
154C2×C4⋊Dic3—51no—
155C22×C3⋊C8—51no—
156C22×C3⋊C8—51no—
157C4×D12—102no—
158C4×D12—102no—
159#832—102no—
160#809—102no—
161C24×C5—21no—
162C23×D5—61no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4C4×D312yescomplemented
169C22×C4×C5—21no—
170C22×C4×C5#6711yescharacteristic
171C22×C4×C5#6711yescharacteristic
172C22×C4×C5C22×D311yescharacteristic
173C22×Dic5—61no—
174C2×D20—32no—
175C2×D20—32no—
176C2×D20—32no—
177C2×D20—61no—
178C2×D20—61no—
179C2×D20—61no—
180C2×C4×D5—64no—
181C2×C4×D5—122no—
182C2×C4×D5—122no—
183C5×C4⋊C4—21no—
184C5×C4⋊C4—21no—
185C5×C22⋊C4—42no—
186C5×C22⋊C4—42no—
187C42×C5—21no—
188C42×C5—21no—
189#686—68no—
190#685—64no—
191C4⋊Dic5—32no—
192C4⋊Dic5—61no—
193C2×#168—32no—
194C2×#168—61no—
195C2×#168—61no—
196C2×#168—61no—
197C2×#168—61no—
198C2×#168—61no—
199C22×D8—151no—
200C2×C4×D4—151no—
201C2×#102—151no—
202C2×#102—151no—
203#390D1511yescharacteristic, complemented
204#340—151no—
205#336—151no—
206C22×C3×C5—42no—
207C22×C3×C5—42no—
208C22×C3×C5—42no—
209C22×C3×C5—81no—
210C22×C3×C5—81no—
211C22×C3×C5—81no—
212C22×C3×C5—81no—
213C22×C3×C5C4×D411yescharacteristic
214C22×C3×C5#12011yescharacteristic
215C22×C3×C5#12111yescharacteristic
216C22×C3×C5C2×D811yescharacteristic
217C22×C3×C5#13511yescharacteristic
218C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
219C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
220C2×D15—24no—
221C2×D15—42no—
222C2×D15—42no—
223C2×D15—42no—
224C2×D15—42no—
225C2×D15—42no—
226C2×D15—42no—
227C3×C4×C5—22no—
228C3×C4×C5—41no—
229C3×C4×C5—81no—
230C3×C4×C5C2×C22⋊C411yescharacteristic
231C3×C4×C5C4×D411yescharacteristic
232C3×C4×C5#12111yescharacteristic
233C3×C4×C5#12311yescharacteristic
234Dic15—42no—
235C24×C3—21no—
236C23×D3—101no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4C4×D512yescomplemented
243C22×C3×C4—21no—
244C22×C3×C4C22⋊D511yescharacteristic
245C22×C3×C4C22⋊D511yescharacteristic
246C22×C3×C4C22×D511yescharacteristic
247C22×Dic3—101no—
248C2×D12—52no—
249C2×D12—52no—
250C2×D12—52no—
251C2×D12—101no—
252C2×D12—101no—
253C2×D12—101no—
254C2×C4×D3—104no—
255C2×C4×D3—202no—
256C2×C4×D3—202no—
257C3×C4⋊C4—21no—
258C3×C4⋊C4—21no—
259C3×C22⋊C4—42no—
260C3×C22⋊C4—42no—
261C3×C42—21no—
262C3×C42—21no—
263#213—108no—
264(C2×D3)⋊C4—104no—
265C4⋊Dic3—52no—
266C4⋊Dic3—101no—
267C2×C3⋊C8—52no—
268C2×C3⋊C8—101no—
269C2×C3⋊C8—101no—
270C2×C3⋊C8—101no—
271C2×C3⋊C8—101no—
272C2×C3⋊C8—101no—
273C23×C5—22no—
274C23×C5—41no—
275C23×C5—41no—
276C23×C5—41no—
277C23×C5—41no—
278C23×C5—41no—
279C23×C5—41no—
280C23×C5C2×#6711yescharacteristic
281C22×D5—62no—
282C22×D5—62no—
283C22×D5—62no—
284C22×D5—121no—
285C22×D5—121no—
286C22×D5—121no—
287C22×D5—121no—
288C5×D4—22no—
289C5×D4—22no—
290C5×D4—41no—
291C5×D4—41no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—41no—
298C2×C4×C5—41no—
299C2×C4×C5—41no—
300C2×C4×C5#21312yescomplemented
301C2×C4×C5C2×C4×D311yescharacteristic
302C2×C4×C5#23511yescharacteristic
303C2×C4×C5D3×D411yescharacteristic
304C2×C4×C5D3×D411yescharacteristic
305C2×C4×C5D3×D411yescharacteristic
306C2×C4×C5#23711yescharacteristic
307C2×Dic5—62no—
308C2×Dic5—121no—
309C2×Dic5—121no—
310D20—34no—
311D20—62no—
312D20—62no—
313D20—62no—
314C4×D5—128no—
315#168—62no—
316#168—121no—
317C22×D4—151no—
318C22×D4C2×D1511yescharacteristic
319C23×C4—301no—
320C2×D8—154no—
321C2×D8—302no—
322C2×D8—302no—
323C22×C8—151no—
324C22×C8—151no—
325C4×D4—302no—
326C4×D4—302no—
327C2×C4⋊C4—151no—
328C2×C4⋊C4C2×D1511yescharacteristic
329C2×C22⋊C4—21no—
330C2×C22⋊C4—21no—
331C2×C22⋊C4—301no—
332C2×C42C2×D1511yescharacteristic
333#102—302no—
334#102—302no—
335C2×C3×C5—82no—
336C2×C3×C5#38611yescharacteristic
337C2×C3×C5C4×D811yescharacteristic
338C2×C3×C5#44211yescharacteristic
339C2×C3×C5#44711yescharacteristic
340C2×C3×C5#44911yescharacteristic
341C2×C3×C5#45911yescharacteristic
342C2×C3×C5#46311yescharacteristic
343D15—44no—
344C23×C3—22no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3—41no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3C2×C22⋊D511yescharacteristic
352C22×D3—102no—
353C22×D3—102no—
354C22×D3—102no—
355C22×D3—201no—
356C22×D3—201no—
357C22×D3—201no—
358C22×D3—201no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—41no—
362C3×D4—41no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4#68612yescomplemented
372C2×C3×C4C2×C4×D511yescharacteristic
373C2×C3×C4#70911yescharacteristic
374C2×C3×C4D4×D511yescharacteristic
375C2×C3×C4D4×D511yescharacteristic
376C2×C3×C4D4×D511yescharacteristic
377C2×C3×C4#71111yescharacteristic
378C2×Dic3—102no—
379C2×Dic3—201no—
380C2×Dic3—201no—
381D12—54no—
382D12—102no—
383D12—102no—
384D12—102no—
385C4×D3—208no—
386C3⋊C8—102no—
387C3⋊C8—201no—
388C22×C5—42no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—81no—
392C22×C5—81no—
393C22×C5—81no—
394C22×C5—81no—
395C22×C5C4×#6711yescharacteristic
396C22×C5C2×#21311yescharacteristic
397C22×C5#93211yescharacteristic
398C22×C5#93711yescharacteristic
399C22×C5#93811yescharacteristic
400C22×C5#94911yescharacteristic
401C22×C5#95011yescharacteristic
402C2×D5—64no—
403C2×D5—122no—
404C2×D5—122no—
405C2×D5—122no—
406C2×D5—122no—
407C2×D5—122no—
408C2×D5—122no—
409C4×C5—22no—
410C4×C5—41no—
411C4×C5—81no—
412C4×C5D3×C22⋊C411yescharacteristic
413C4×C5#67⋊C411yescharacteristic
414C4×C5#88311yescharacteristic
415C4×C5#88411yescharacteristic
416Dic5—122no—
417C24—21no—
418C24—301no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—152no—
425C2×D4—152no—
426C2×D4—152no—
427C2×D4—301no—
428C2×D4—301no—
429C2×D4—301no—
430C2×D4C4×D1512yescomplemented
431C22×C4—21no—
432C22×C4—304no—
433C22×C4—301no—
434C22×C4—602no—
435C22×C4—602no—
436C22×C4#122011yescharacteristic
437C22×C4#122011yescharacteristic
438C22×C4C22×D1511yescharacteristic
439D8—308no—
440C2×C8—152no—
441C2×C8—301no—
442C2×C8—301no—
443C2×C8—301no—
444C2×C8—301no—
445C2×C8—301no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—152no—
449C4⋊C4—301no—
450C22⋊C4—42no—
451C22⋊C4—42no—
452C22⋊C4—304no—
453C42—21no—
454C42—21no—
455C3×C5#187911yescharacteristic, complemented, Hall
456C22×C3—42no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—81no—
460C22×C3—81no—
461C22×C3—81no—
462C22×C3—81no—
463C22×C3C4×C22⋊D511yescharacteristic
464C22×C3C2×#68611yescharacteristic
465C22×C3#407811yescharacteristic
466C22×C3#408311yescharacteristic
467C22×C3#408411yescharacteristic
468C22×C3#409511yescharacteristic
469C22×C3#409611yescharacteristic
470C2×D3—104no—
471C2×D3—202no—
472C2×D3—202no—
473C2×D3—202no—
474C2×D3—202no—
475C2×D3—202no—
476C2×D3—202no—
477C3×C4—22no—
478C3×C4—41no—
479C3×C4—81no—
480C3×C4D5×C22⋊C411yescharacteristic
481C3×C4#402711yescharacteristic
482C3×C4#402911yescharacteristic
483C3×C4#403011yescharacteristic
484Dic3—202no—
485C2×C5—82no—
486C2×C5#495611yescharacteristic
487C2×C5C4×#21311yescharacteristic
488C2×C5#501411yescharacteristic
489C2×C5#503611yescharacteristic
490C2×C5#503711yescharacteristic
491C2×C5#505711yescharacteristic
492C2×C5#507211yescharacteristic
493D5—124no—
494C23—22no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—302no—
502C23—302no—
503C23—302no—
504C23—601no—
505C23—601no—
506C23—601no—
507C23—601no—
508C23C2×#122011yescharacteristic
509D4—22no—
510D4—22no—
511D4—41no—
512D4—41no—
513D4—154no—
514D4—302no—
515D4—302no—
516D4—302no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—302no—
526C2×C4—608no—
527C2×C4—601no—
528C2×C4—601no—
529C2×C4#671512yescomplemented
530C2×C4C2×C4×D1511yescharacteristic
531C2×C4#681711yescharacteristic
532C2×C4D4×D1511yescharacteristic
533C2×C4D4×D1511yescharacteristic
534C2×C4D4×D1511yescharacteristic
535C2×C4#681911yescharacteristic
536C8—302no—
537C8—601no—
538C2×C3—82no—
539C2×C3#6524511yescharacteristic
540C2×C3C4×#68611yescharacteristic
541C2×C3#6530311yescharacteristic
542C2×C3#6532511yescharacteristic
543C2×C3#6532611yescharacteristic
544C2×C3#6534611yescharacteristic
545C2×C3#6536111yescharacteristic
546D3—204no—
547C5#6965711yescharacteristic, complemented, Sylow
548C22—42no—
549C22—42no—
550C22—42no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22—81no—
555C22—304no—
556C22—602no—
557C22—602no—
558C22—602no—
559C22—602no—
560C22—602no—
561C22—602no—
562C22C4×#122011yescharacteristic
563C22C2×#671511yescharacteristic
564C22#9182111yescharacteristic
565C22#9182611yescharacteristic
566C22#9182711yescharacteristic
567C22#9183811yescharacteristic
568C22#9183911yescharacteristic
569C4—22no—
570C4—41no—
571C4—81no—
572C4—602no—
573C4C22⋊C4×D1511yescharacteristic
574C4#9177011yescharacteristic
575C4#9177211yescharacteristic
576C4#9177311yescharacteristic
577C3#1060045011yescharacteristic, complemented, Sylow
578C2—82no—
579C2—604no—
580C2#1175105711yescharacteristic
581C2C4×#671511yescharacteristic
582C2#1175111511yescharacteristic
583C2#1175113711yescharacteristic
584C2#1175113811yescharacteristic
585C2#1175115811yescharacteristic
586C2#1175117311yescharacteristic
subgroupG/H
centerC23C2×#1220
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
FittingC3×C5×#390C2
socleC23×C3×C5C2×D4
prime radicalC22×#6715C2
cosocleC22×C3×C4×C5C23
hypercenter#390D15
hypocenterC3×C5#1879
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×C4×D60C2semidirect
3. C3×C5×#390C2semidirect
4. C2×#91116C2semidirect
5. C2×#91093C2semidirect
6. #11746350C2semidirect
7. #11746345C2semidirect
18. C2×#6715C4semidirect
30. C5×#390D3semidirect
42. C2×C3×C5×D4C2×C4semidirect
72. C2×C3⋊#168C2×C4semidirect
75. C3×#390D5semidirect
126. C2×C3×C4×C5D8semidirect
139. D60C22⋊C4semidirect
168. C2×C5×D4C4×D3semidirect
203. #390D15semidirect
242. C2×C3×D4C4×D5semidirect
300. C2×C4×C5#213semidirect
371. C2×C3×C4#686semidirect
430. C2×D4C4×D15semidirect
455. C3×C5#1879semidirect
529. C2×C4#6715semidirect
547. C5#69657semidirect
577. C3#10600450semidirect

Maximal subgroups

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

subgroupindex
C22×#67152
C2×C4×D602
C3×C5×#3902
C2×#911162
C2×#910932
#117463502
#117463452
#106004503
#696575