Finite Group Databasebeta

← #14322621

Subgroups — #14322621

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6665C211yesmaximal, characteristic
2C22⋊C4×Dic15C211yesmaximal, characteristic, complemented
3C5×#4942C211yesmaximal, characteristic, complemented
4C3×#65244C211yesmaximal, characteristic
5#11749513C211yesmaximal, characteristic, complemented
6#11749488C211yesmaximal, characteristic
7#11749487C211yesmaximal, characteristic, complemented
8#11748712C212yesmaximal, complemented
9#11748711C212yesmaximal, complemented
10#11748710C212yesmaximal, complemented
11#11748709C212yesmaximal, complemented
12#10605735—31nomaximal, Hall
13C24×C3×D5C2211yescharacteristic
14C23×Dic15C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C2×C3×C5×C22⋊C4C2211yescharacteristic
17C2×#6719C2211yescharacteristic
18C2×C4×Dic15C2212yescomplemented
19C2×C5×#217C2211yescharacteristic
20C2×C5×Dic3⋊C4C2212yescomplemented
21C2×C3×C22⋊Dic5C2211yescharacteristic
22C2×C3×#685C2212yes—
23C2×C3×#685C2212yes—
24C2×Dic3⋊Dic5C2212yescomplemented
25C2×#6665C418yescomplemented
26C2×#6665C2212yes—
27C2×#6665C2212yes—
28C2×#6665C2211yescharacteristic
29C2×#6665C2211yescharacteristic
30C2×#6665C2211yescharacteristic
31C2×#6665C2211yescharacteristic
32C2×Dic3×Dic5C2212yescomplemented
33#91115C2212yescomplemented
34C5×C3⋊#95C2212yescomplemented
35#90994C2212yescomplemented
36#90994C2212yescomplemented
37#73820—51nomaximal, Hall
38C22×#685—31no—
39C5×#380—31no—
40#65501—31no—
41#65279—32no—
42#65279—32no—
43#65244—31no—
44#65244D311yescharacteristic
45C22⋊C4×Dic5—31no—
46C22⋊C4×Dic5—31no—
47#64959—32no—
48#64959—32no—
49C24×C3×C5C2311yescharacteristic
50C23×C3×D5—22no—
51C23×C3×D5—22no—
52C23×C3×D5—42no—
53C23×C3×D5—42no—
54C23×C3×D5C2×C414yes—
55C23×C3×D5C2311yescharacteristic
56C23×C3×D5C2311yescharacteristic
57C22×C3×C4×C5C2312yes—
58C22×Dic15—42no—
59C22×Dic15C2×C414yes—
60C22×Dic15C2312yes—
61C22×Dic15C2311yescharacteristic
62C22×Dic15C2311yescharacteristic
63C22×C5×Dic3—42no—
64C22×C5×Dic3C2×C414yes—
65C22×C5×Dic3C2312yes—
66C22×C5×Dic3C2311yescharacteristic
67C22×C5×Dic3C2311yescharacteristic
68C22×C3×Dic5C2312yes—
69C3×C5×C22⋊C4—22no—
70#6719—22no—
71C4×Dic15—42no—
72C5×#217—22no—
73C5×Dic3⋊C4—42no—
74C3×C22⋊Dic5—22no—
75C3×#685—42no—
76C3×#685—42no—
77Dic3⋊Dic5—42no—
78#6665—42no—
79#6665—42no—
80#6665C2×C414yes—
81#6665C2×C414yes—
82#6665C2×C414yes—
83#6665C2×C414yes—
84Dic3×Dic5—42no—
85C22×#217—51no—
86C3×#379—51no—
87#5247—51no—
88#4945—52no—
89#4945—52no—
90#4944—52no—
91#4944—52no—
92#4942—51no—
93#4942D511yescharacteristic, complemented
94Dic3×C22⋊C4—51no—
95Dic3×C22⋊C4—51no—
96C24×D5C2×D311yescharacteristic
97C23×C4×C5—31no—
98C23×Dic5—31no—
99C2×C5×C4⋊C4—32no—
100C2×C5×C22⋊C4—31no—
101C2×C5×C22⋊C4C2×D311yescharacteristic
102C2×C22⋊Dic5—31no—
103C2×C22⋊Dic5C2×D311yescharacteristic
104C2×#685—38no—
105C2×#685—31no—
106C2×#685—31no—
107C2×#685—31no—
108C2×#685—31no—
109C2×#685—32no—
110C2×#685—32no—
111C2×#685C2×D312yes—
112C2×#685C2×D312yes—
113C2×C4⋊Dic5—32no—
114C2×C4×Dic5—32no—
115C2×C4×Dic5—32no—
116C5×#95—32no—
117#3963—32no—
118#3963—32no—
119#3963—32no—
120#2312—151noSylow
121C23×C3×C5—22no—
122C23×C3×C5—22no—
123C23×C3×C5C22×C412yes—
124C23×C3×C5#4112yes—
125C23×C3×C5#4112yes—
126C23×C3×C5C2411yescharacteristic
127C22×C3×D5—28no—
128C22×C3×D5—21no—
129C22×C3×D5—21no—
130C22×C3×D5—21no—
131C22×C3×D5—21no—
132C22×C3×D5—22no—
133C22×C3×D5—22no—
134C22×C3×D5—22no—
135C22×C3×D5—22no—
136C22×C3×D5—44no—
137C22×C3×D5—44no—
138C22×C3×D5—48no—
139C22×C3×D5—48no—
140C22×C3×D5C22×C412yes—
141C22×C3×D5C22×C412yes—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15—22no—
149C2×Dic15—22no—
150C2×Dic15—44no—
151C2×Dic15C22×C412yes—
152C2×Dic15C22×C412yes—
153C2×C5×Dic3—22no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—22no—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—44no—
159C2×C5×Dic3C22×C412yes—
160C2×C5×Dic3C22×C412yes—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C2×C3×Dic5—22no—
164C25×C3—51no—
165C23×Dic3—51no—
166C23×Dic3C2×D511yescharacteristic
167C2×C3×C22⋊C4—51no—
168C2×C3×C22⋊C4—52no—
169C2×C3×C22⋊C4—52no—
170C2×C3×C22⋊C4C2×D511yescharacteristic
171C2×#217—58no—
172C2×#217—51no—
173C2×#217—51no—
174C2×#217—51no—
175C2×#217—51no—
176C2×#217—51no—
177C2×#217—52no—
178C2×#217—52no—
179C2×#217C2×D511yescharacteristic
180C2×Dic3⋊C4—52no—
181C2×Dic3⋊C4C2×D512yescomplemented
182C2×C4×Dic3—52no—
183C2×C4×Dic3—52no—
184C3⋊#95—52no—
185C3⋊#95—52no—
186C3⋊#95—52no—
187C3⋊#95C2×D512yescomplemented
188C24×C5C22×D311yescharacteristic
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—42no—
192C23×D5—42no—
193C23×D5C4×D314yes—
194C23×D5C22×D311yescharacteristic
195C23×D5C22×D311yescharacteristic
196C22×C4×C5—31no—
197C22×C4×C5—31no—
198C22×C4×C5—34no—
199C22×C4×C5—32no—
200C22×C4×C5—122no—
201C22×C4×C5C22×D312yes—
202C22×Dic5—31no—
203C22×Dic5—31no—
204C22×Dic5—34no—
205C22×Dic5—32no—
206C22×Dic5—122no—
207C22×Dic5C22×D312yes—
208C5×C4⋊C4—122no—
209C5×C22⋊C4—22no—
210C5×C22⋊C4—62no—
211C22⋊Dic5—22no—
212C22⋊Dic5—62no—
213#685—34no—
214#685—34no—
215#685—34no—
216#685—34no—
217#685—42no—
218#685—42no—
219#685—122no—
220#685—122no—
221C4⋊Dic5—122no—
222C4×Dic5—122no—
223C4×Dic5—122no—
224C22×C22⋊C4—151no—
225#388—152no—
226#388—152no—
227#388—152no—
228#388—152no—
229#380—31no—
230#380—151no—
231#379—51no—
232#379—151no—
233C4×C22⋊C4—151no—
234C4×C22⋊C4—151no—
235C22×C3×C5—22no—
236C22×C3×C5—22no—
237C22×C3×C5—24no—
238C22×C3×C5—24no—
239C22×C3×C5#11714yes—
240C22×C3×C5C23×C411yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5C2×#4111yescharacteristic
243C22×C3×C5H(5,𝔽2)12yes—
244C22×C3×C5H(5,𝔽2)12yes—
245C2×C3×D5—22no—
246C2×C3×D5—22no—
247C2×C3×D5—22no—
248C2×C3×D5—22no—
249C2×C3×D5—22no—
250C2×C3×D5—22no—
251C2×C3×D5—416no—
252C2×C3×D5—42no—
253C2×C3×D5—42no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C3×C4×C5—42no—
257Dic15—22no—
258Dic15—22no—
259Dic15—42no—
260C3×Dic5—42no—
261C5×Dic3—22no—
262C5×Dic3—22no—
263C5×Dic3—42no—
264C24×C3—51no—
265C24×C3—51no—
266C24×C3—54no—
267C24×C3—102no—
268C24×C3—102no—
269C24×C3—202no—
270C24×C3—202no—
271C24×C3C22×D511yescharacteristic
272C22×C3×C4—52no—
273C22×C3×C4C22×D512yes—
274C22×Dic3—42no—
275C22×Dic3—51no—
276C22×Dic3—51no—
277C22×Dic3—54no—
278C22×Dic3—52no—
279C22×Dic3—202no—
280C22×Dic3C4×D514yes—
281C22×Dic3C22×D512yes—
282C22×Dic3C22×D511yescharacteristic
283C22×Dic3C22×D511yescharacteristic
284C3×C22⋊C4—22no—
285C3×C22⋊C4—102no—
286C3×C22⋊C4—202no—
287C3×C22⋊C4—202no—
288#217—22no—
289#217—54no—
290#217—54no—
291#217—54no—
292#217—54no—
293#217—102no—
294#217—202no—
295#217—202no—
296Dic3⋊C4—42no—
297Dic3⋊C4—202no—
298C4×Dic3—202no—
299C4×Dic3—202no—
300C23×C5—22no—
301C23×C5—22no—
302C23×C5C2×C4×D312yes—
303C23×C5#23712yes—
304C23×C5#23712yes—
305C23×C5C23×D311yescharacteristic
306C22×D5—28no—
307C22×D5—21no—
308C22×D5—21no—
309C22×D5—21no—
310C22×D5—21no—
311C22×D5—22no—
312C22×D5—22no—
313C22×D5—22no—
314C22×D5—22no—
315C22×D5—44no—
316C22×D5—44no—
317C22×D5—48no—
318C22×D5—48no—
319C22×D5C2×C4×D312yes—
320C22×D5C2×C4×D312yes—
321C2×C4×C5—22no—
322C2×C4×C5—22no—
323C2×C4×C5—22no—
324C2×C4×C5—32no—
325C2×C4×C5—32no—
326C2×C4×C5—62no—
327C2×C4×C5—62no—
328C2×C4×C5—62no—
329C2×C4×C5—62no—
330C2×C4×C5—62no—
331C2×C4×C5—124no—
332C2×Dic5—22no—
333C2×Dic5—22no—
334C2×Dic5—22no—
335C2×Dic5—32no—
336C2×Dic5—32no—
337C2×Dic5—62no—
338C2×Dic5—62no—
339C2×Dic5—62no—
340C2×Dic5—62no—
341C2×Dic5—62no—
342C2×Dic5—124no—
343C25—51no—
344C23×C4—31no—
345C23×C4—151no—
346C2×C4⋊C4—32no—
347C2×C4⋊C4—152no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—51no—
350C2×C22⋊C4—52no—
351C2×C22⋊C4—52no—
352C2×C22⋊C4—151no—
353C2×C22⋊C4—151no—
354C2×C22⋊C4—151no—
355C2×C22⋊C4—151no—
356C2×C22⋊C4—158no—
357C2×C22⋊C4—151no—
358C2×C22⋊C4—152no—
359C2×C22⋊C4—152no—
360C2×C22⋊C4D3×D511yescharacteristic
361C2×C42—152no—
362C2×C42—152no—
363#95—32no—
364#95—152no—
365#95—152no—
366#95—152no—
367C2×C3×C5—24no—
368C2×C3×C5C2×#11711yescharacteristic
369C2×C3×C5#51811yescharacteristic
370C2×C3×C5#51811yescharacteristic
371C2×C3×C5#53812yes—
372C2×C3×C5#53812yes—
373C3×D5—42no—
374C3×D5—42no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—52no—
378C23×C3—52no—
379C23×C3—101no—
380C23×C3—101no—
381C23×C3—102no—
382C23×C3—102no—
383C23×C3—101no—
384C23×C3—101no—
385C23×C3—102no—
386C23×C3—102no—
387C23×C3—108no—
388C23×C3—204no—
389C23×C3—204no—
390C23×C3—208no—
391C23×C3—208no—
392C23×C3C2×C4×D512yes—
393C23×C3#71112yes—
394C23×C3#71312yes—
395C23×C3C23×D511yescharacteristic
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—102no—
400C2×C3×C4—102no—
401C2×C3×C4—102no—
402C2×Dic3—22no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—44no—
408C2×Dic3—52no—
409C2×Dic3—52no—
410C2×Dic3—102no—
411C2×Dic3—102no—
412C2×Dic3—102no—
413C2×Dic3—102no—
414C2×Dic3—102no—
415C2×Dic3—204no—
416C2×Dic3C2×C4×D512yes—
417C2×Dic3C2×C4×D512yes—
418C22×C5—22no—
419C22×C5—22no—
420C22×C5—24no—
421C22×C5—24no—
422C22×C5#87714yes—
423C22×C5C22×C4×D311yescharacteristic
424C22×C5C2×#23711yescharacteristic
425C22×C5C2×#23711yescharacteristic
426C22×C5#100412yes—
427C22×C5#100412yes—
428C2×D5—22no—
429C2×D5—22no—
430C2×D5—22no—
431C2×D5—22no—
432C2×D5—22no—
433C2×D5—22no—
434C2×D5—416no—
435C2×D5—42no—
436C2×D5—42no—
437C2×D5—42no—
438C2×D5—42no—
439C4×C5—42no—
440C4×C5—62no—
441C4×C5—62no—
442C4×C5—122no—
443Dic5—42no—
444Dic5—62no—
445Dic5—62no—
446Dic5—122no—
447C24—51no—
448C24—51no—
449C24—54no—
450C24—102no—
451C24—102no—
452C24—202no—
453C24—202no—
454C24C2×D3×D511yescharacteristic
455C22×C4—31no—
456C22×C4—31no—
457C22×C4—34no—
458C22×C4—32no—
459C22×C4—52no—
460C22×C4—122no—
461C22×C4—151no—
462C22×C4—151no—
463C22×C4—154no—
464C22×C4—152no—
465C22×C4—602no—
466C22×C4C2×D3×D512yes—
467C4⋊C4—122no—
468C4⋊C4—602no—
469C22⋊C4—22no—
470C22⋊C4—62no—
471C22⋊C4—102no—
472C22⋊C4—154no—
473C22⋊C4—154no—
474C22⋊C4—154no—
475C22⋊C4—154no—
476C22⋊C4—202no—
477C22⋊C4—202no—
478C22⋊C4—302no—
479C22⋊C4—602no—
480C22⋊C4—602no—
481C42—602no—
482C42—602no—
483C3×C5#231211yescharacteristic, complemented, Hall
484C22×C3—22no—
485C22×C3—22no—
486C22×C3—24no—
487C22×C3—24no—
488C22×C3—102no—
489C22×C3—102no—
490C22×C3—102no—
491C22×C3—102no—
492C22×C3—102no—
493C22×C3—102no—
494C22×C3—2016no—
495C22×C3—202no—
496C22×C3—202no—
497C22×C3—202no—
498C22×C3—202no—
499C22×C3#403814yes—
500C22×C3C22×C4×D511yescharacteristic
501C22×C3C2×#71111yescharacteristic
502C22×C3#414412yes—
503C22×C3C2×#71311yescharacteristic
504C22×C3#414912yes—
505C3×C4—42no—
506C3×C4—202no—
507Dic3—22no—
508Dic3—22no—
509Dic3—42no—
510Dic3—102no—
511Dic3—102no—
512Dic3—202no—
513C2×C5—24no—
514C2×C5C2×#87711yescharacteristic
515C2×C5#548611yescharacteristic
516C2×C5#548611yescharacteristic
517C2×C5#559312yes—
518C2×C5#559312yes—
519D5—42no—
520D5—42no—
521C23—22no—
522C23—22no—
523C23—52no—
524C23—52no—
525C23—108no—
526C23—101no—
527C23—101no—
528C23—102no—
529C23—102no—
530C23—102no—
531C23—102no—
532C23—101no—
533C23—101no—
534C23—204no—
535C23—204no—
536C23—208no—
537C23—208no—
538C23#676612yes—
539C23C4×D3×D512yes—
540C23#678012yes—
541C23C22×D3×D511yescharacteristic
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—32no—
546C2×C4—32no—
547C2×C4—62no—
548C2×C4—62no—
549C2×C4—62no—
550C2×C4—62no—
551C2×C4—62no—
552C2×C4—102no—
553C2×C4—102no—
554C2×C4—102no—
555C2×C4—124no—
556C2×C4—152no—
557C2×C4—152no—
558C2×C4—302no—
559C2×C4—302no—
560C2×C4—302no—
561C2×C4—302no—
562C2×C4—302no—
563C2×C4—604no—
564C2×C3—24no—
565C2×C3—202no—
566C2×C3—202no—
567C2×C3#6582011yescharacteristic
568C2×C3C2×#403811yescharacteristic
569C2×C3#6585511yescharacteristic
570C2×C3#6595112yes—
571C2×C3#6597812yes—
572C5#7382011yescharacteristic, complemented, Sylow
573C22—24no—
574C22—22no—
575C22—22no—
576C22—24no—
577C22—102no—
578C22—102no—
579C22—102no—
580C22—102no—
581C22—102no—
582C22—102no—
583C22—2016no—
584C22—202no—
585C22—202no—
586C22—202no—
587C22—202no—
588C22#9139414yes—
589C22C2×#676611yescharacteristic
590C22C2×C4×D3×D511yescharacteristic
591C22#9202512yes—
592C22#9202612yes—
593C22C2×#678011yescharacteristic
594C4—42no—
595C4—62no—
596C4—62no—
597C4—122no—
598C4—202no—
599C4—302no—
600C4—302no—
601C4—602no—
602C3#1060573511yescharacteristic, complemented, Sylow
603C2—24no—
604C2—202no—
605C2—202no—
606C2#1175304712yes—
607C2#1175306511yescharacteristic
608C2#1175306611yescharacteristic
609C2C2×#9139411yescharacteristic
610C2#1175474512yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C22⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC24×C3×D5C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2312
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×Dic15C2semidirect
3. C5×#4942C2semidirect
5. #11749513C2semidirect
7. #11749487C2semidirect
8. #11748712C2semidirect
9. #11748711C2semidirect
10. #11748710C2semidirect
11. #11748709C2semidirect
18. C2×C4×Dic15C22semidirect
20. C2×C5×Dic3⋊C4C22semidirect
24. C2×Dic3⋊Dic5C22semidirect
25. C2×#6665C4semidirect
32. C2×Dic3×Dic5C22semidirect
33. #91115C22semidirect
34. C5×C3⋊#95C22semidirect
35. #90994C22semidirect
36. #90994C22semidirect
93. #4942D5semidirect
181. C2×Dic3⋊C4C2×D5semidirect
187. C3⋊#95C2×D5semidirect
483. C3×C5#2312semidirect
572. C5#73820semidirect
602. C3#10605735semidirect

Maximal subgroups

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

subgroupindex
C22×#66652
C22⋊C4×Dic152
C5×#49422
C3×#652442
#117495132
#117494882
#117494872
#117487122
#117487112
#117487102
#117487092
#106057353
#738205