Finite Group Databasebeta

← #14297239

Subgroups — #14297239

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4150C211yesmaximal, characteristic
2C2×#91121C211yesmaximal, characteristic, complemented
3C5×#5232C211yesmaximal, characteristic, complemented
4#11748610C211yesmaximal, characteristic, complemented
5C2×#90976C211yesmaximal, characteristic, complemented
6#11748368C211yesmaximal, characteristic, complemented
7C2×#90961C211yesmaximal, characteristic, complemented
8#10601101—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C3×#4150—22no—
11C3×#4150—22no—
12C3×#4150—22no—
13C3×#4150C414yescomplemented
14C2×C3×Q8×D5—21no—
15C2×C3×#711—21no—
16C2×C3×#711—22no—
17C2×C3×#709—21no—
18C2×C3×#709C2211yescharacteristic
19C22×C3×Dic10—21no—
20C22×C3×Dic10C2211yescharacteristic
21C2×C4×Dic15C2211yescharacteristic
22C2×#6710C2211yescharacteristic
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C2×C5×#208C2211yescharacteristic
25#91121—22no—
26C5×#835—21no—
27C5×#832—21no—
28#90994—22no—
29#90976—22no—
30#90970—21no—
31#90964—21no—
32#90961—22no—
33#72143—51nomaximal, Hall
34C2×#4150D311yescharacteristic
35C5×#417—31no—
36C2×#3969—31no—
37C2×#3957—31no—
38C2×#3956—31no—
39#65263—31no—
40#65255—31no—
41C3×C5×#41—21no—
42C3×C5×#41—21no—
43C3×C5×#41C2×C412yes—
44C3×C5×#41D412yes—
45C2×C3×C5×Q8D411yescharacteristic
46C2×C3×C5×D4—21no—
47C2×C3×C5×D4D411yescharacteristic
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15—21no—
51C22×C5×Dic3—21no—
52C2×C3×C22⋊D5—22no—
53C2×C3×C22⋊D5—21no—
54C22×C3×Dic5—22no—
55C22×C3×Dic5D412yes—
56C3×Q8×D5—24no—
57C3×Q8×D5—24no—
58C3×#711—28no—
59C3×#711—24no—
60C3×#711—24no—
61C3×#711—28no—
62C3×#709—24no—
63C3×#709—21no—
64C3×#709—21no—
65C3×#709—24no—
66C3×#709C2×C412yes—
67C3×#709D412yes—
68C2×C3×D20D411yescharacteristic
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5—21no—
71C2×C3×Dic10—22no—
72C2×C3×Dic10—24no—
73C2×C3×Dic10—21no—
74C2×C3×Dic10—21no—
75C2×C3×Dic10—21no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10—24no—
78C2×C3×Dic10C2×C412yes—
79C2×C3×Dic10D412yes—
80C2×C3×Dic10D411yescharacteristic
81C4×Dic15—21no—
82C4×Dic15—21no—
83#6710—21no—
84#6710—21no—
85C2×C3⋊#168—21no—
86C5×C4⋊Dic3—21no—
87C5×C4⋊Dic3—21no—
88C5×#208—21no—
89C5×#208—21no—
90C2×C5×C3⋊C8—21no—
91C2×C3×2−1+4—51no—
92C2×#837—51no—
93C2×#837—51no—
94#5232—51no—
95#5232D511yescharacteristic, complemented
96#5229—51no—
97C2×#836—51no—
98C2×C5×#41C2×D311yescharacteristic
99#4150—22no—
100#4150—22no—
101#4150—22no—
102#4150Dic314yescomplemented
103C2×Q8×D5—21no—
104C2×#711—21no—
105C2×#711—22no—
106C2×#709—21no—
107C2×#709C2×D311yescharacteristic
108C22×Dic10—21no—
109C22×Dic10C2×D311yescharacteristic
110C2×C5×M16—31no—
111C2×C5×C4⋊C4—31no—
112C2×C4×Dic5—31no—
113C2×#681—31no—
114C5×#103—61no—
115C5×#102—61no—
116#3969—62no—
117#3963—62no—
118#3957—62no—
119#3956—62no—
120#3942—61no—
121#3941—61no—
122#1793—151noSylow
123C23×C3×C5—21no—
124C23×C3×C5C2×D411yescharacteristic
125C22×C3×D5—21no—
126C3×C5×Q8—21no—
127C3×C5×Q8C22⋊C412yes—
128C3×C5×D4—22no—
129C3×C5×D4—22no—
130C3×C5×D4—21no—
131C3×C5×D4C22⋊C412yes—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5C22×C411yescharacteristic
136C2×C3×C4×C5C2×D411yescharacteristic
137C2×C3×C4×C5C2×D411yescharacteristic
138C2×C3×C4×C5C2×D411yescharacteristic
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×Dic15—22no—
142C2×Dic15—41no—
143C2×Dic15—41no—
144C2×C5×Dic3—42no—
145C2×C5×Dic3—41no—
146C3×C22⋊D5—28no—
147C3×C22⋊D5—22no—
148C3×C22⋊D5—22no—
149C2×C3×Dic5—28no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—21no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5C22⋊C414yes—
154C3×D20—21no—
155C3×D20C22⋊C412yes—
156C3×C4×D5—28no—
157C3×C4×D5—22no—
158C3×C4×D5—22no—
159C3×Dic10—28no—
160C3×Dic10—22no—
161C3×Dic10—22no—
162C3×Dic10—22no—
163C3×Dic10—21no—
164C3×Dic10—22no—
165C3×Dic10C22⋊C412yes—
166C3⋊#168—41no—
167C5×C3⋊C8—41no—
168C3×2−1+4—54no—
169C3×2−1+4—102no—
170C3×2−1+4—102no—
171C3×2−1+4—102no—
172C2×C3×#41—51no—
173C2×C3×#41—101no—
174C2×C3×#41—102no—
175C2×C3×#41—101no—
176C2×C3×#41C2×D511yescharacteristic
177C22×C3×Q8—51no—
178C22×C3×Q8—101no—
179C22×C3×Q8—101no—
180C2×C4⋊Dic3C2×D511yescharacteristic
181C2×C4×Dic3—51no—
182C2×#208—51no—
183C2×#208C2×D511yescharacteristic
184#837—102no—
185#837—102no—
186#836—102no—
187#835—21no—
188#835—101no—
189#832—21no—
190#832—101no—
191C3⋊#95—102no—
192C5×#41—21no—
193C5×#41—21no—
194C5×#41C2×Dic312yes—
195C5×#41#6712yes—
196C2×C5×Q8#6711yescharacteristic
197C2×C5×D4—21no—
198C2×C5×D4#6711yescharacteristic
199C22×C4×C5—21no—
200C22×C4×C5—61no—
201C22×C4×C5C22×D311yescharacteristic
202C2×C22⋊D5—22no—
203C2×C22⋊D5—21no—
204C22×Dic5—22no—
205C22×Dic5—61no—
206C22×Dic5#6712yes—
207Q8×D5—24no—
208Q8×D5—24no—
209#711—28no—
210#711—24no—
211#711—24no—
212#711—28no—
213#709—24no—
214#709—21no—
215#709—21no—
216#709—24no—
217#709C2×Dic312yes—
218#709#6712yes—
219C2×D20#6711yescharacteristic
220C2×C4×D5—22no—
221C2×C4×D5—21no—
222C2×Dic10—22no—
223C2×Dic10—24no—
224C2×Dic10—21no—
225C2×Dic10—21no—
226C2×Dic10—21no—
227C2×Dic10—21no—
228C2×Dic10—24no—
229C2×Dic10C2×Dic312yes—
230C2×Dic10#6712yes—
231C2×Dic10#6711yescharacteristic
232C5×M16—61no—
233C5×M16—61no—
234C2×C5×C8—61no—
235C5×C4⋊C4—61no—
236C5×C4⋊C4—61no—
237C4×Dic5—61no—
238C4×Dic5—61no—
239#681—61no—
240#681—61no—
241C2×#168—61no—
242C2×2−1+4—51no—
243C2×#104—151no—
244C2×#104—151no—
245#417—31no—
246#417—151no—
247C2×#101—151no—
248#391—151no—
249C22×C3×C5—21no—
250C22×C3×C5—21no—
251C22×C3×C5—22no—
252C22×C3×C5—41no—
253C22×C3×C5—41no—
254C22×C3×C5C2×C22⋊C411yescharacteristic
255C22×C3×C5#12011yescharacteristic
256C22×C3×C5#12011yescharacteristic
257C2×C3×D5—22no—
258C2×C3×D5—41no—
259C2×C3×D5—41no—
260C3×C4×C5—22no—
261C3×C4×C5C2×C22⋊C411yescharacteristic
262C3×C4×C5C2×C22⋊C411yescharacteristic
263C3×C4×C5#12011yescharacteristic
264C3×C4×C5#12011yescharacteristic
265Dic15—42no—
266C3×Dic5—24no—
267C3×Dic5—22no—
268C5×Dic3—81no—
269C3×#41—21no—
270C3×#41—21no—
271C3×#41—52no—
272C3×#41—52no—
273C3×#41—104no—
274C3×#41—104no—
275C3×#41—108no—
276C3×#41—108no—
277C3×#41—104no—
278C3×#41—104no—
279C3×#41—101no—
280C3×#41—101no—
281C3×#41C4×D512yes—
282C3×#41D2012yes—
283C2×C3×Q8—52no—
284C2×C3×Q8—52no—
285C2×C3×Q8—51no—
286C2×C3×Q8—104no—
287C2×C3×Q8—102no—
288C2×C3×Q8—104no—
289C2×C3×Q8—104no—
290C2×C3×Q8—104no—
291C2×C3×Q8—101no—
292C2×C3×Q8—101no—
293C2×C3×Q8—101no—
294C2×C3×Q8—101no—
295C2×C3×Q8C22⋊D511yescharacteristic
296C2×C3×D4—21no—
297C2×C3×D4—51no—
298C2×C3×D4—102no—
299C2×C3×D4—101no—
300C2×C3×D4C22⋊D511yescharacteristic
301C22×C3×C4—21no—
302C22×C3×C4—52no—
303C22×C3×C4—102no—
304C22×C3×C4—102no—
305C22×C3×C4—101no—
306C22×C3×C4C22×D511yescharacteristic
307C22×Dic3—21no—
308C22×Dic3—101no—
309C4⋊Dic3—21no—
310C4⋊Dic3—21no—
311C4×Dic3—101no—
312C4×Dic3—101no—
313#208—21no—
314#208—21no—
315#208—101no—
316#208—101no—
317C2×C3⋊C8—21no—
318C2×C3⋊C8—101no—
319C23×C5—21no—
320C23×C5C2×#6711yescharacteristic
321C22×D5—21no—
322C5×Q8—21no—
323C5×Q8#21712yes—
324C5×D4—22no—
325C5×D4—22no—
326C5×D4—21no—
327C5×D4#21712yes—
328C2×C4×C5—21no—
329C2×C4×C5—22no—
330C2×C4×C5—22no—
331C2×C4×C5—122no—
332C2×C4×C5—121no—
333C2×C4×C5C22×Dic311yescharacteristic
334C2×C4×C5C2×#6711yescharacteristic
335C2×C4×C5C2×#6711yescharacteristic
336C2×C4×C5C2×#6711yescharacteristic
337C2×C4×C5C2×#6711yescharacteristic
338C2×C4×C5C2×#6711yescharacteristic
339C22⋊D5—28no—
340C22⋊D5—22no—
341C22⋊D5—22no—
342C2×Dic5—28no—
343C2×Dic5—22no—
344C2×Dic5—21no—
345C2×Dic5—22no—
346C2×Dic5—62no—
347C2×Dic5—121no—
348C2×Dic5—121no—
349C2×Dic5#21714yes—
350D20—21no—
351D20#21712yes—
352C4×D5—28no—
353C4×D5—22no—
354C4×D5—22no—
355Dic10—28no—
356Dic10—22no—
357Dic10—22no—
358Dic10—22no—
359Dic10—21no—
360Dic10—22no—
361Dic10#21712yes—
362C5×C8—121no—
363#168—121no—
3642−1+4—54no—
3652−1+4—102no—
3662−1+4—102no—
3672−1+4—102no—
368C2×#41—51no—
369C2×#41—101no—
370C2×#41—102no—
371C2×#41—101no—
372C2×#41D3×D511yescharacteristic
373C22×Q8—51no—
374C22×Q8—101no—
375C22×Q8—101no—
376C2×M16—31no—
377C2×M16—151no—
378C2×C4⋊C4—31no—
379C2×C42—151no—
380#104—302no—
381#104—302no—
382#103—61no—
383#103—301no—
384#102—61no—
385#102—301no—
386#101—302no—
387#95—302no—
388C2×C3×C5—21no—
389C2×C3×C5—21no—
390C2×C3×C5—42no—
391C2×C3×C5#37911yescharacteristic
392C2×C3×C5#45411yescharacteristic
393C2×C3×C5#45611yescharacteristic
394C3×D5—42no—
395C23×C3—21no—
396C23×C3—101no—
397C23×C3D4×D511yescharacteristic
398C3×Q8—21no—
399C3×Q8—52no—
400C3×Q8—108no—
401C3×Q8—102no—
402C3×Q8—102no—
403C3×Q8—101no—
404C3×Q8—102no—
405C3×Q8—102no—
406C3×Q8#68512yes—
407C3×D4—22no—
408C3×D4—22no—
409C3×D4—21no—
410C3×D4—52no—
411C3×D4—108no—
412C3×D4—102no—
413C3×D4—102no—
414C3×D4—101no—
415C3×D4#68512yes—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—54no—
420C2×C3×C4—108no—
421C2×C3×C4—108no—
422C2×C3×C4—102no—
423C2×C3×C4—102no—
424C2×C3×C4—101no—
425C2×C3×C4—102no—
426C2×C3×C4—102no—
427C2×C3×C4C2×C4×D511yescharacteristic
428C2×C3×C4C2×D2011yescharacteristic
429C2×C3×C4D4×D511yescharacteristic
430C2×C3×C4D4×D511yescharacteristic
431C2×C3×C4D4×D511yescharacteristic
432C2×C3×C4C2×C22⋊D511yescharacteristic
433C2×Dic3—42no—
434C2×Dic3—41no—
435C2×Dic3—102no—
436C2×Dic3—201no—
437C2×Dic3—201no—
438C3⋊C8—41no—
439C3⋊C8—201no—
440C22×C5—21no—
441C22×C5—21no—
442C22×C5—22no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5C2×#21711yescharacteristic
446C22×C5#95311yescharacteristic
447C22×C5#95311yescharacteristic
448C2×D5—22no—
449C2×D5—41no—
450C2×D5—41no—
451C4×C5—22no—
452C4×C5—241no—
453C4×C5C2×#21711yescharacteristic
454C4×C5C2×#21711yescharacteristic
455C4×C5#95311yescharacteristic
456C4×C5#95311yescharacteristic
457Dic5—24no—
458Dic5—22no—
459Dic5—122no—
460#41—21no—
461#41—21no—
462#41—52no—
463#41—52no—
464#41—104no—
465#41—104no—
466#41—108no—
467#41—108no—
468#41—104no—
469#41—104no—
470#41—101no—
471#41—101no—
472#41D5×Dic312yes—
473#41#120212yes—
474C2×Q8—52no—
475C2×Q8—52no—
476C2×Q8—51no—
477C2×Q8—104no—
478C2×Q8—102no—
479C2×Q8—104no—
480C2×Q8—104no—
481C2×Q8—104no—
482C2×Q8—101no—
483C2×Q8—101no—
484C2×Q8—101no—
485C2×Q8—101no—
486C2×Q8#120111yescharacteristic
487C2×D4—21no—
488C2×D4—51no—
489C2×D4—102no—
490C2×D4—101no—
491C2×D4#120111yescharacteristic
492C22×C4—21no—
493C22×C4—52no—
494C22×C4—61no—
495C22×C4—102no—
496C22×C4—102no—
497C22×C4—101no—
498C22×C4—301no—
499C22×C4C2×D3×D511yescharacteristic
500M16—61no—
501M16—61no—
502M16—301no—
503M16—301no—
504C2×C8—61no—
505C2×C8—301no—
506C4⋊C4—61no—
507C4⋊C4—61no—
508C42—301no—
509C42—301no—
510C3×C5#179311yescharacteristic, complemented, Hall
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—102no—
517C22×C3—201no—
518C22×C3—201no—
519C22×C3D5×C22⋊C411yescharacteristic
520C22×C3#402811yescharacteristic
521C22×C3#408311yescharacteristic
522C3×C4—22no—
523C3×C4—104no—
524C3×C4—102no—
525C3×C4D5×C22⋊C411yescharacteristic
526C3×C4#402811yescharacteristic
527C3×C4C2×#68511yescharacteristic
528C3×C4#408311yescharacteristic
529Dic3—81no—
530Dic3—202no—
531C2×C5—21no—
532C2×C5—21no—
533C2×C5—42no—
534C2×C5#524511yescharacteristic
535C2×C5#524611yescharacteristic
536C2×C5#524711yescharacteristic
537D5—42no—
538C23—21no—
539C23—101no—
540C23D5×#6711yescharacteristic
541Q8—21no—
542Q8—52no—
543Q8—108no—
544Q8—102no—
545Q8—102no—
546Q8—102no—
547Q8—102no—
548Q8—101no—
549Q8#666512yes—
550D4—22no—
551D4—22no—
552D4—21no—
553D4—52no—
554D4—108no—
555D4—102no—
556D4—102no—
557D4—101no—
558D4#666512yes—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—54no—
563C2×C4—108no—
564C2×C4—108no—
565C2×C4—102no—
566C2×C4—101no—
567C2×C4—102no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—122no—
571C2×C4—121no—
572C2×C4—302no—
573C2×C4—601no—
574C2×C4—601no—
575C2×C4C2×D5×Dic311yescharacteristic
576C2×C4C2×#120111yescharacteristic
577C2×C4C2×#120211yescharacteristic
578C2×C4D5×#6711yescharacteristic
579C2×C4D5×#6711yescharacteristic
580C2×C4D5×#6711yescharacteristic
581C8—121no—
582C8—601no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—42no—
586C2×C3—202no—
587C2×C3#6524411yescharacteristic
588C2×C3#6549011yescharacteristic
589C2×C3#6549411yescharacteristic
590C5#7214311yescharacteristic, complemented, Sylow
591C22—21no—
592C22—21no—
593C22—22no—
594C22—41no—
595C22—41no—
596C22—102no—
597C22—201no—
598C22—201no—
599C22D5×#21711yescharacteristic
600C22#9156311yescharacteristic
601C22#9156411yescharacteristic
602C4—22no—
603C4—104no—
604C4—102no—
605C4—241no—
606C4—602no—
607C4C2×#666511yescharacteristic
608C4D5×#21711yescharacteristic
609C4#9156311yescharacteristic
610C4#9156411yescharacteristic
611C3#1060110111yescharacteristic, complemented, Sylow
612C2—21no—
613C2—21no—
614C2—42no—
615C2—202no—
616C2#1174945611yescharacteristic
617C2#1174946211yescharacteristic
618C2#1174948811yescharacteristic
subgroupG/H
centerC22#91563
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5#120
prime radicalC2×C3×#4150C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1793
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#91121C2semidirect
3. C5×#5232C2semidirect
4. #11748610C2semidirect
5. C2×#90976C2semidirect
6. #11748368C2semidirect
7. C2×#90961C2semidirect
13. C3×#4150C4semidirect
95. #5232D5semidirect
102. #4150Dic3semidirect
510. C3×C5#1793semidirect
590. C5#72143semidirect
611. C3#10601101semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#41502
C2×#911212
C5×#52322
#117486102
C2×#909762
#117483682
C2×#909612
#106011013
#721435