Finite Group Databasebeta

← #14330654

Subgroups — #14330654

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#937C211yesmaximal, characteristic
2#11751321C211yesmaximal, characteristic, complemented
3C3×#65510C211yesmaximal, characteristic, complemented
4#11749501C212yesmaximal, complemented
5#11749496C212yesmaximal, complemented
6#11749482C212yesmaximal, complemented
7#11749478C212yesmaximal, complemented
8#11748747C212yesmaximal, complemented
9#11748675C212yesmaximal, complemented
10#10614311—31nomaximal, Hall
11C24×C5×D3C2211yescharacteristic
12C22×C3×C5×D4C2211yescharacteristic
13C23×Dic15C2211yescharacteristic, complemented
14C22×C5×#67C2212yes—
15C2×#6719C2212yes—
16C2×#6719C2211yescharacteristic, complemented
17C2×C5×#217C2211yescharacteristic
18C5×#937C418yescomplemented
19C2×C5×(C2×D3)⋊C4C2212yes—
20C2×C3×C22⋊Dic5C2212yes—
21C2×C3×C22⋊Dic5C2212yescomplemented
22C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
23C2×C3×C4×Dic5C2211yescharacteristic, complemented
24C2×Dic3⋊Dic5C2212yescomplemented
25C2×(C2×D3)⋊Dic5C2212yes—
26C2×(C2×D3)⋊Dic5C2212yes—
27C2×(C2×D3)⋊Dic5C2212yes—
28C2×(C2×D3)⋊Dic5C2212yes—
29C2×Dic3×Dic5C2212yescomplemented
30#91115C2212yescomplemented
31#90994C2212yescomplemented
32#90994C2212yescomplemented
33#76434—51nomaximal, Hall
34C2×C5×#120—31no—
35#65536—32no—
36#65510—32no—
37#65510D311yescharacteristic, complemented
38#65509—31no—
39#65509—32no—
40#65240—32no—
41#65240—32no—
42#65240—32no—
43C24×C3×C5C2311yescharacteristic
44C24×C3×C5C2311yescharacteristic
45C23×C5×D3—41no—
46C23×C5×D3—41no—
47C23×C5×D3—42no—
48C23×C5×D3—42no—
49C23×C5×D3C2×C414yescomplemented
50C23×C5×D3C2312yes—
51C2×C3×C5×D4—41no—
52C2×C3×C5×D4—41no—
53C2×C3×C5×D4C2×C414yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15—41no—
56C22×Dic15—42no—
57C22×Dic15C2312yes—
58C22×Dic15C2312yes—
59C2×C5×#67—42no—
60C2×C5×#67—42no—
61C2×C5×#67C2×C418yes—
62C22×C5×Dic3C2312yes—
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2312yes—
65#6719—42no—
66#6719—41no—
67C5×#217C2×C414yescomplemented
68C5×(C2×D3)⋊C4C2×C418yescomplemented
69C3×C22⋊Dic5—42no—
70C3×C22⋊Dic5—42no—
71C3×C4⋊Dic5—41no—
72C3×C4×Dic5—41no—
73Dic3⋊Dic5—42no—
74(C2×D3)⋊Dic5—42no—
75(C2×D3)⋊Dic5—42no—
76(C2×D3)⋊Dic5—42no—
77(C2×D3)⋊Dic5—42no—
78Dic3×Dic5—42no—
79C2×#937D511yescharacteristic
80C3×#390—51no—
81#5220—51no—
82#4990—52no—
83#4958—52no—
84#4957—52no—
85#4955—52no—
86#4944—52no—
87#4940—52no—
88C25×C5—31no—
89C22×C5×D4—32no—
90C22×C5×D4C2×D311yescharacteristic
91C23×Dic5—31no—
92C5×#120—38no—
93C2×C5×C22⋊C4—31no—
94C2×C5×C22⋊C4—32no—
95C2×C22⋊Dic5—32no—
96C2×C22⋊Dic5—31no—
97C2×C22⋊Dic5—32no—
98C2×C22⋊Dic5—32no—
99C2×C22⋊Dic5—32no—
100C2×C22⋊Dic5—32no—
101C2×C22⋊Dic5C2×D312yes—
102C2×C22⋊Dic5C2×D312yescomplemented
103C2×C4⋊Dic5—32no—
104C2×C4⋊Dic5C2×D311yescharacteristic, complemented
105C2×C4×Dic5—32no—
106C2×C4×Dic5C2×D311yescharacteristic, complemented
107#3963—32no—
108#3963—32no—
109#3963—32no—
110#2375—151noSylow
111C23×C3×C5—22no—
112C23×C3×C5—22no—
113C23×C3×C5—21no—
114C23×C3×C5—22no—
115C23×C3×C5—22no—
116C23×C3×C5—21no—
117C23×C3×C5—21no—
118C23×C3×C5—21no—
119C23×C3×C5C22×C412yes—
120C23×C3×C5C22×C412yes—
121C23×C3×C5C2411yescharacteristic
122C22×C5×D3—22no—
123C22×C5×D3—22no—
124C22×C5×D3—22no—
125C22×C5×D3—22no—
126C22×C5×D3—22no—
127C22×C5×D3—22no—
128C22×C5×D3—48no—
129C22×C5×D3—44no—
130C22×C5×D3—44no—
131C22×C5×D3—48no—
132C22×C5×D3—44no—
133C22×C5×D3C22×C414yes—
134C3×C5×D4—44no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5C22×C412yes—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—44no—
145C5×#67—48no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3C22×C414yes—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—22no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C24×D3C2×D511yescharacteristic
156C22×C3×D4C2×D511yescharacteristic
157C22×#67C2×D512yes—
158C23×Dic3—51no—
159C2×C3×C4⋊C4—51no—
160C2×C3×C22⋊C4—52no—
161C2×C3×C22⋊C4—52no—
162C2×C3×C42—51no—
163C2×#217—52no—
164C2×#217—51no—
165C2×#217C2×D511yescharacteristic
166#937Dic518yescomplemented
167C2×(C2×D3)⋊C4—52no—
168C2×(C2×D3)⋊C4—52no—
169C2×(C2×D3)⋊C4—52no—
170C2×(C2×D3)⋊C4—52no—
171C2×(C2×D3)⋊C4C2×D512yes—
172C2×Dic3⋊C4—52no—
173C2×C4×Dic3—52no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95—52no—
177C24×C5—32no—
178C24×C5—34no—
179C24×C5—122no—
180C24×C5—121no—
181C24×C5—121no—
182C24×C5—122no—
183C24×C5C22×D311yescharacteristic
184C24×C5C22×D311yescharacteristic
185C2×C5×D4—38no—
186C2×C5×D4—41no—
187C2×C5×D4—41no—
188C2×C5×D4—122no—
189C2×C5×D4—122no—
190C2×C5×D4C4×D314yes—
191C22×C4×C5—32no—
192C22×C4×C5C22×D311yescharacteristic
193C22×Dic5—32no—
194C22×Dic5—32no—
195C22×Dic5—121no—
196C22×Dic5—122no—
197C22×Dic5C22×D312yes—
198C22×Dic5C22×D312yes—
199C5×C22⋊C4—34no—
200C5×C22⋊C4—38no—
201C22⋊Dic5—42no—
202C22⋊Dic5—42no—
203C22⋊Dic5—122no—
204C22⋊Dic5—122no—
205C22⋊Dic5—122no—
206C22⋊Dic5—122no—
207C22⋊Dic5—121no—
208C22⋊Dic5—122no—
209C4⋊Dic5—41no—
210C4⋊Dic5—122no—
211C4×Dic5—41no—
212C4×Dic5—122no—
213C2×#120—31no—
214#390—51no—
215#390—152no—
216#388—152no—
217#388—152no—
218#388—152no—
219#386—152no—
220#386—151no—
221#379—152no—
222C22×C3×C5—24no—
223C22×C3×C5—22no—
224C22×C3×C5—22no—
225C22×C3×C5—24no—
226C22×C3×C5—41no—
227C22×C3×C5—42no—
228C22×C3×C5—41no—
229C22×C3×C5—42no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5C23×C411yescharacteristic
233C22×C3×C5H(5,𝔽2)12yes—
234C22×C3×C5H(5,𝔽2)11yescharacteristic
235C22×C3×C5H(5,𝔽2)11yescharacteristic
236C22×C3×C5H(5,𝔽2)12yes—
237C2×C5×D3—24no—
238C2×C5×D3—24no—
239C2×C5×D3—24no—
240C2×C5×D3—416no—
241C2×C5×D3—42no—
242C2×C5×D3—42no—
243C2×C5×D3—42no—
244C2×C5×D3—42no—
245C3×C4×C5—22no—
246Dic15—42no—
247Dic15—42no—
248C3×Dic5—42no—
249C3×Dic5—42no—
250C5×Dic3—24no—
251C24×C3C22×D511yescharacteristic
252C24×C3C22×D511yescharacteristic
253C23×D3—41no—
254C23×D3—41no—
255C23×D3—42no—
256C23×D3—42no—
257C23×D3C2×Dic514yescomplemented
258C23×D3C22×D512yes—
259C2×C3×D4—41no—
260C2×C3×D4—41no—
261C2×C3×D4C2×Dic514yes—
262C22×C3×C4—52no—
263C22×C3×C4—52no—
264C22×C3×C4C22×D511yescharacteristic
265C2×#67—42no—
266C2×#67—42no—
267C2×#67C2×Dic518yes—
268C22×Dic3—52no—
269C22×Dic3—52no—
270C22×Dic3—201no—
271C22×Dic3—202no—
272C22×Dic3C22×D512yes—
273C3×C4⋊C4—201no—
274C3×C22⋊C4—202no—
275C3×C22⋊C4—202no—
276C3×C42—201no—
277#217—202no—
278#217—201no—
279#217C2×Dic514yescomplemented
280(C2×D3)⋊C4—202no—
281(C2×D3)⋊C4—202no—
282(C2×D3)⋊C4—202no—
283(C2×D3)⋊C4—202no—
284(C2×D3)⋊C4C2×Dic518yescomplemented
285Dic3⋊C4—202no—
286C4×Dic3—202no—
287C23×C5—22no—
288C23×C5—22no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5—22no—
294C23×C5—22no—
295C23×C5—34no—
296C23×C5—62no—
297C23×C5—62no—
298C23×C5—62no—
299C23×C5—62no—
300C23×C5—62no—
301C23×C5—62no—
302C23×C5—124no—
303C23×C5—128no—
304C23×C5—124no—
305C23×C5—124no—
306C23×C5—128no—
307C23×C5C2×C4×D312yes—
308C23×C5C2×C4×D312yes—
309C23×C5C23×D311yescharacteristic
310C5×D4—44no—
311C5×D4—128no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—34no—
315C2×C4×C5—62no—
316C2×C4×C5—62no—
317C2×C4×C5C2×C4×D312yes—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—22no—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—124no—
331C25—31no—
332C22×D4—32no—
333C22×D4D3×D511yescharacteristic
334C23×C4—151no—
335#120—38no—
336C2×C4⋊C4—51no—
337C2×C4⋊C4—152no—
338C2×C22⋊C4—31no—
339C2×C22⋊C4—32no—
340C2×C22⋊C4—52no—
341C2×C22⋊C4—52no—
342C2×C22⋊C4—152no—
343C2×C22⋊C4—152no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4—152no—
346C2×C22⋊C4—152no—
347C2×C22⋊C4—151no—
348C2×C42—51no—
349C2×C42—152no—
350#95—152no—
351#95—152no—
352#95—152no—
353C2×C3×C5—42no—
354C2×C3×C5—42no—
355C2×C3×C5#51811yescharacteristic
356C2×C3×C5#51812yes—
357C2×C3×C5#56011yescharacteristic
358C2×C3×C5#56012yes—
359C2×C3×C5H(3,𝔽4)11yescharacteristic
360C5×D3—44no—
361C23×C3—21no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—22no—
366C23×C3—21no—
367C23×C3—21no—
368C23×C3—21no—
369C23×C3C22×Dic512yes—
370C23×C3C22×Dic512yes—
371C23×C3C23×D511yescharacteristic
372C22×D3—22no—
373C22×D3—22no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—22no—
377C22×D3—22no—
378C22×D3—48no—
379C22×D3—44no—
380C22×D3—44no—
381C22×D3—48no—
382C22×D3—44no—
383C22×D3C22×Dic514yes—
384C3×D4—44no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4—102no—
393C2×C3×C4C22×Dic512yes—
394#67—48no—
395C2×Dic3—22no—
396C2×Dic3—22no—
397C2×Dic3—102no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—204no—
404C2×Dic3C22×Dic514yes—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—24no—
408C22×C5—24no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5—41no—
412C22×C5—41no—
413C22×C5—42no—
414C22×C5—42no—
415C22×C5—64no—
416C22×C5—64no—
417C22×C5—64no—
418C22×C5—1216no—
419C22×C5—122no—
420C22×C5—122no—
421C22×C5—122no—
422C22×C5—122no—
423C22×C5C22×C4×D311yescharacteristic
424C22×C5#100412yes—
425C22×C5#100411yescharacteristic
426C22×C5#100411yescharacteristic
427C22×C5#100912yes—
428C4×C5—22no—
429C4×C5—64no—
430Dic5—42no—
431Dic5—42no—
432Dic5—122no—
433Dic5—122no—
434C24—32no—
435C24—34no—
436C24—122no—
437C24—122no—
438C24—121no—
439C24—121no—
440C24C2×D3×D511yescharacteristic
441C24C2×D3×D511yescharacteristic
442C2×D4—38no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—122no—
446C2×D4—122no—
447C2×D4D3×Dic514yes—
448C22×C4—32no—
449C22×C4—52no—
450C22×C4—52no—
451C22×C4—152no—
452C22×C4—152no—
453C22×C4—602no—
454C22×C4—601no—
455C22×C4C2×D3×D511yescharacteristic
456C4⋊C4—201no—
457C4⋊C4—602no—
458C22⋊C4—34no—
459C22⋊C4—38no—
460C22⋊C4—202no—
461C22⋊C4—202no—
462C22⋊C4—602no—
463C22⋊C4—602no—
464C22⋊C4—602no—
465C22⋊C4—602no—
466C22⋊C4—602no—
467C22⋊C4—601no—
468C42—201no—
469C42—602no—
470C3×C5#237511yescharacteristic, complemented, Hall
471C22×C3—24no—
472C22×C3—22no—
473C22×C3—22no—
474C22×C3—24no—
475C22×C3—41no—
476C22×C3—41no—
477C22×C3—42no—
478C22×C3—41no—
479C22×C3—42no—
480C22×C3—41no—
481C22×C3#414412yes—
482C22×C3#414412yes—
483C22×C3#414411yescharacteristic
484C22×C3#414411yescharacteristic
485C22×C3C23×Dic511yescharacteristic
486C2×D3—24no—
487C2×D3—24no—
488C2×D3—24no—
489C2×D3—416no—
490C2×D3—42no—
491C2×D3—42no—
492C2×D3—42no—
493C2×D3—42no—
494C3×C4—22no—
495C3×C4—202no—
496C3×C4—202no—
497Dic3—24no—
498Dic3—202no—
499Dic3—202no—
500C2×C5—42no—
501C2×C5—42no—
502C2×C5—124no—
503C2×C5#548611yescharacteristic
504C2×C5#554512yes—
505C2×C5#562012yes—
506C2×C5#568311yescharacteristic
507C2×C5#572011yescharacteristic
508C23—22no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—34no—
517C23—62no—
518C23—62no—
519C23—62no—
520C23—62no—
521C23—62no—
522C23—62no—
523C23—124no—
524C23—128no—
525C23—128no—
526C23—124no—
527C23—124no—
528C23C2×D3×Dic512yes—
529C23C2×D3×Dic512yes—
530C23C22×D3×D511yescharacteristic
531D4—44no—
532D4—128no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—34no—
536C2×C4—62no—
537C2×C4—62no—
538C2×C4—102no—
539C2×C4—102no—
540C2×C4—102no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4—302no—
547C2×C4—302no—
548C2×C4—302no—
549C2×C4—302no—
550C2×C4—604no—
551C2×C4C2×D3×Dic512yes—
552C2×C3—42no—
553C2×C3—42no—
554C2×C3#6592811yescharacteristic
555C2×C3#6592912yes—
556C2×C3#6592911yescharacteristic
557C2×C3#6613211yescharacteristic
558C2×C3#6613212yes—
559D3—44no—
560C5#7643411yescharacteristic, complemented, Sylow
561C22—22no—
562C22—22no—
563C22—24no—
564C22—24no—
565C22—42no—
566C22—42no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—64no—
572C22—64no—
573C22—64no—
574C22—1216no—
575C22—122no—
576C22—122no—
577C22—122no—
578C22—122no—
579C22#9202512yes—
580C22#9202712yes—
581C22C22×D3×Dic511yescharacteristic
582C22#9204911yescharacteristic
583C22#9204911yescharacteristic
584C4—22no—
585C4—64no—
586C4—202no—
587C4—202no—
588C4—602no—
589C4—602no—
590C3#1061431111yescharacteristic, complemented, Sylow
591C2—42no—
592C2—42no—
593C2—124no—
594C2#1175491412yes—
595C2#1175498712yes—
596C2#1175499111yescharacteristic
597C2#1175500311yescharacteristic
598C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×C5×#937C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2375
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. #11751321C2semidirect
3. C3×#65510C2semidirect
4. #11749501C2semidirect
5. #11749496C2semidirect
6. #11749482C2semidirect
7. #11749478C2semidirect
8. #11748747C2semidirect
9. #11748675C2semidirect
13. C23×Dic15C22semidirect
16. C2×#6719C22semidirect
18. C5×#937C4semidirect
21. C2×C3×C22⋊Dic5C22semidirect
22. C2×C3×C4⋊Dic5C22semidirect
23. C2×C3×C4×Dic5C22semidirect
24. C2×Dic3⋊Dic5C22semidirect
29. C2×Dic3×Dic5C22semidirect
30. #91115C22semidirect
31. #90994C22semidirect
32. #90994C22semidirect
37. #65510D3semidirect
49. C23×C5×D3C2×C4semidirect
67. C5×#217C2×C4semidirect
68. C5×(C2×D3)⋊C4C2×C4semidirect
102. C2×C22⋊Dic5C2×D3semidirect
104. C2×C4⋊Dic5C2×D3semidirect
106. C2×C4×Dic5C2×D3semidirect
166. #937Dic5semidirect
257. C23×D3C2×Dic5semidirect
279. #217C2×Dic5semidirect
284. (C2×D3)⋊C4C2×Dic5semidirect
470. C3×C5#2375semidirect
560. C5#76434semidirect
590. C3#10614311semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9372
#117513212
C3×#655102
#117495012
#117494962
#117494822
#117494782
#117487472
#117486752
#106143113
#764345