Finite Group Databasebeta

← #14301020

Subgroups — #14301020

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×C3×C5×D8C211yesmaximal, characteristic
2C2×D4×Dic15C211yesmaximal, characteristic, complemented
3#11751322C211yesmaximal, characteristic, complemented
4C2×#91116C211yesmaximal, characteristic, complemented
5C2×#91116C211yesmaximal, characteristic, complemented
6#11746372C211yesmaximal, characteristic, complemented
7#11746371C211yesmaximal, characteristic, complemented
8#10602830—31nomaximal, Hall
9C22×C3×C5×D4C2211yescharacteristic
10C22×C3×C5×D4C2211yescharacteristic
11C23×Dic15—21no—
12C2×C3×C5×D8—22no—
13C2×C3×C5×D8—22no—
14C2×C3×C5×D8C414yescomplemented
15C22×C3×C5×C8C2211yescharacteristic
16C2×#6719—21no—
17C2×#6719—21no—
18C2×#6719—21no—
19D4×Dic15—22no—
20D4×Dic15—22no—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×C4×Dic15C2211yescharacteristic
24C22×C3⋊#168C2211yescharacteristic
25#91116—22no—
26#91116—22no—
27#72037—51nomaximal, Hall
28C22×C5×D8D311yescharacteristic
29C2×D4×Dic5—31no—
30#65510—31no—
31C2×#3964—31no—
32C2×#3964—31no—
33#64771—31no—
34#64770—31no—
35C24×C3×C5—21no—
36C24×C3×C5—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×D4—21no—
43C2×C3×C5×D4—21no—
44C2×C3×C5×D4—21no—
45C2×C3×C5×D4C2×C412yes—
46C2×C3×C5×D4C2×C412yescomplemented
47C2×C3×C5×D4D412yes—
48C2×C3×C5×D4D412yes—
49C22×C3×C4×C5C2311yescharacteristic
50C22×Dic15—24no—
51C22×Dic15—21no—
52C22×Dic15—21no—
53C22×Dic15—42no—
54C22×Dic15—42no—
55C22×Dic15D411yescharacteristic
56C22×Dic15D411yescharacteristic
57C3×C5×D8—28no—
58C2×C3×C5×C8—21no—
59C2×C3×C5×C8—21no—
60C2×C3×C5×C8C2×C412yescomplemented
61#6719—24no—
62#6719—42no—
63#6719—42no—
64C4⋊Dic15—21no—
65C4⋊Dic15—21no—
66C4⋊Dic15—21no—
67C4⋊Dic15D412yes—
68C4×Dic15—21no—
69C4×Dic15—21no—
70C2×C3⋊#168—21no—
71C2×C3⋊#168—21no—
72C2×C3⋊#168—21no—
73C22×C3×D8D511yescharacteristic
74C2×D4×Dic3—51no—
75#5221—51no—
76C2×#832—51no—
77C2×#832—51no—
78#4551—51no—
79#4550—51no—
80C22×C5×D4C2×D311yescharacteristic
81C22×C5×D4C2×D311yescharacteristic
82C23×Dic5—61no—
83C2×C5×D8—22no—
84C2×C5×D8—22no—
85C2×C5×D8Dic314yescomplemented
86C22×C5×C8C2×D311yescharacteristic
87C2×C22⋊Dic5—61no—
88C2×C22⋊Dic5—61no—
89C2×C22⋊Dic5—61no—
90D4×Dic5—62no—
91D4×Dic5—62no—
92C2×C4⋊Dic5—31no—
93C2×C4⋊Dic5—31no—
94C2×C4×Dic5—31no—
95C22×#168—31no—
96#3964—62no—
97#3964—62no—
98#1879—151noSylow
99C23×C3×C5—22no—
100C23×C3×C5—22no—
101C23×C3×C5—22no—
102C23×C3×C5—22no—
103C23×C3×C5—41no—
104C23×C3×C5—41no—
105C23×C3×C5—41no—
106C23×C3×C5—41no—
107C23×C3×C5—41no—
108C23×C3×C5—41no—
109C23×C3×C5—41no—
110C23×C3×C5—41no—
111C23×C3×C5—41no—
112C23×C3×C5—41no—
113C23×C3×C5C2×D411yescharacteristic
114C3×C5×D4—22no—
115C3×C5×D4—22no—
116C3×C5×D4—22no—
117C3×C5×D4—22no—
118C3×C5×D4—22no—
119C3×C5×D4—41no—
120C3×C5×D4—41no—
121C3×C5×D4C22⋊C414yescomplemented
122C2×C3×C4×C5C22×C411yescharacteristic
123C2×C3×C4×C5C2×D411yescharacteristic
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5#4111yescharacteristic
127C2×C3×C4×C5#4111yescharacteristic
128C2×Dic15—21no—
129C2×Dic15—21no—
130C2×Dic15—21no—
131C2×Dic15—22no—
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15—48no—
135C2×Dic15—41no—
136C2×Dic15—41no—
137C2×Dic15—41no—
138C2×Dic15—41no—
139C2×Dic15—41no—
140C2×Dic15D812yescomplemented
141C3×C5×C8—22no—
142C3⋊#168—41no—
143C22×C3×D4C2×D511yescharacteristic
144C22×C3×D4C2×D511yescharacteristic
145C23×Dic3—101no—
146C2×C3×D8—22no—
147C2×C3×D8—22no—
148C2×C3×D8Dic514yescomplemented
149C22×C3×C8C2×D511yescharacteristic
150C2×#217—101no—
151C2×#217—101no—
152C2×#217—101no—
153D4×Dic3—102no—
154D4×Dic3—102no—
155C2×C4⋊Dic3—51no—
156C2×C4⋊Dic3—51no—
157C2×C4×Dic3—51no—
158C22×C3⋊C8—51no—
159#832—102no—
160#832—102no—
161C24×C5—21no—
162C24×C5—21no—
163C2×C5×D4—21no—
164C2×C5×D4—21no—
165C2×C5×D4—21no—
166C2×C5×D4—21no—
167C2×C5×D4—21no—
168C2×C5×D4—21no—
169C2×C5×D4—21no—
170C2×C5×D4—21no—
171C2×C5×D4C2×Dic312yes—
172C2×C5×D4C2×Dic312yescomplemented
173C2×C5×D4#6712yes—
174C2×C5×D4#6712yes—
175C22×C4×C5C22×D311yescharacteristic
176C22×Dic5—31no—
177C22×Dic5—31no—
178C22×Dic5—64no—
179C22×Dic5—61no—
180C22×Dic5—61no—
181C22×Dic5—122no—
182C22×Dic5—122no—
183C5×D8—28no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8C2×Dic312yescomplemented
187C22⋊Dic5—64no—
188C22⋊Dic5—122no—
189C22⋊Dic5—122no—
190C4⋊Dic5—32no—
191C4⋊Dic5—61no—
192C4⋊Dic5—61no—
193C4⋊Dic5—61no—
194C4×Dic5—61no—
195C4×Dic5—61no—
196C2×#168—61no—
197C2×#168—61no—
198C2×#168—61no—
199C22×D8D1511yescharacteristic
200C2×C4×D4—151no—
201C2×#102—151no—
202C2×#102—151no—
203#390—151no—
204#340—151no—
205#336—151no—
206C22×C3×C5—24no—
207C22×C3×C5—42no—
208C22×C3×C5—42no—
209C22×C3×C5—42no—
210C22×C3×C5—42no—
211C22×C3×C5—42no—
212C22×C3×C5—42no—
213C22×C3×C5—42no—
214C22×C3×C5—42no—
215C22×C3×C5—42no—
216C22×C3×C5—81no—
217C22×C3×C5—81no—
218C22×C3×C5—81no—
219C22×C3×C5—81no—
220C22×C3×C5C4×D411yescharacteristic
221C22×C3×C5#12011yescharacteristic
222C22×C3×C5#12111yescharacteristic
223C22×C3×C5C2×D811yescharacteristic
224C22×C3×C5#13511yescharacteristic
225C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
226C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
227C3×C4×C5C2×C22⋊C411yescharacteristic
228C3×C4×C5C4×D411yescharacteristic
229C3×C4×C5#12111yescharacteristic
230C3×C4×C5#12311yescharacteristic
231Dic15—22no—
232Dic15—42no—
233Dic15—41no—
234Dic15—81no—
235C24×C3—21no—
236C24×C3—21no—
237C2×C3×D4—21no—
238C2×C3×D4—21no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—21no—
242C2×C3×D4—21no—
243C2×C3×D4—21no—
244C2×C3×D4—21no—
245C2×C3×D4C2×Dic512yes—
246C2×C3×D4C2×Dic512yescomplemented
247C2×C3×D4C22⋊D512yes—
248C2×C3×D4C22⋊D512yes—
249C22×C3×C4C22×D511yescharacteristic
250C22×Dic3—51no—
251C22×Dic3—51no—
252C22×Dic3—104no—
253C22×Dic3—101no—
254C22×Dic3—101no—
255C22×Dic3—202no—
256C22×Dic3—202no—
257C3×D8—28no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8C2×Dic512yescomplemented
261#217—104no—
262#217—202no—
263#217—202no—
264C4⋊Dic3—52no—
265C4⋊Dic3—101no—
266C4⋊Dic3—101no—
267C4⋊Dic3—101no—
268C4×Dic3—101no—
269C4×Dic3—101no—
270C2×C3⋊C8—101no—
271C2×C3⋊C8—101no—
272C2×C3⋊C8—101no—
273C23×C5—22no—
274C23×C5—22no—
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—41no—
278C23×C5—41no—
279C23×C5—41no—
280C23×C5—41no—
281C23×C5—41no—
282C23×C5—41no—
283C23×C5—41no—
284C23×C5—41no—
285C23×C5—41no—
286C23×C5—41no—
287C23×C5D3×D411yescharacteristic
288C5×D4—22no—
289C5×D4—22no—
290C5×D4—22no—
291C5×D4—22no—
292C5×D4—22no—
293C5×D4—41no—
294C5×D4—41no—
295C5×D4#21714yescomplemented
296C2×C4×C5D3×D411yescharacteristic
297C2×C4×C5#23711yescharacteristic
298C2×C4×C5#23711yescharacteristic
299C2×C4×C5C22×Dic311yescharacteristic
300C2×C4×C5C2×#6711yescharacteristic
301C2×C4×C5C2×#6711yescharacteristic
302C2×Dic5—32no—
303C2×Dic5—61no—
304C2×Dic5—61no—
305C2×Dic5—61no—
306C2×Dic5—61no—
307C2×Dic5—61no—
308C2×Dic5—62no—
309C2×Dic5—128no—
310C2×Dic5—121no—
311C2×Dic5—121no—
312C2×Dic5—121no—
313C2×Dic5—121no—
314C2×Dic5—121no—
315C5×C8—22no—
316#168—121no—
317C22×D4C2×D1511yescharacteristic
318C22×D4C2×D1511yescharacteristic
319C23×C4—301no—
320C2×D8—22no—
321C2×D8—22no—
322C2×D8Dic1514yescomplemented
323C22×C8—151no—
324C22×C8C2×D1511yescharacteristic
325C4×D4—302no—
326C4×D4—302no—
327C2×C4⋊C4—151no—
328C2×C4⋊C4—151no—
329C2×C22⋊C4—301no—
330C2×C22⋊C4—301no—
331C2×C22⋊C4—301no—
332C2×C42—151no—
333#102—302no—
334#102—302no—
335C2×C3×C5—44no—
336C2×C3×C5—82no—
337C2×C3×C5#38611yescharacteristic
338C2×C3×C5C4×D811yescharacteristic
339C2×C3×C5#44211yescharacteristic
340C2×C3×C5#44711yescharacteristic
341C2×C3×C5#44911yescharacteristic
342C2×C3×C5#45911yescharacteristic
343C2×C3×C5#46311yescharacteristic
344C23×C3—22no—
345C23×C3—22no—
346C23×C3—22no—
347C23×C3—22no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3D4×D511yescharacteristic
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—22no—
362C3×D4—22no—
363C3×D4—22no—
364C3×D4—41no—
365C3×D4—41no—
366C3×D4C22⋊Dic514yescomplemented
367C2×C3×C4D4×D511yescharacteristic
368C2×C3×C4#71111yescharacteristic
369C2×C3×C4#71111yescharacteristic
370C2×C3×C4C22×Dic511yescharacteristic
371C2×C3×C4C2×C22⋊D511yescharacteristic
372C2×C3×C4C2×C22⋊D511yescharacteristic
373C2×Dic3—52no—
374C2×Dic3—101no—
375C2×Dic3—101no—
376C2×Dic3—101no—
377C2×Dic3—101no—
378C2×Dic3—101no—
379C2×Dic3—102no—
380C2×Dic3—208no—
381C2×Dic3—201no—
382C2×Dic3—201no—
383C2×Dic3—201no—
384C2×Dic3—201no—
385C2×Dic3—201no—
386C3×C8—22no—
387C3⋊C8—201no—
388C22×C5—24no—
389C22×C5—42no—
390C22×C5—42no—
391C22×C5—42no—
392C22×C5—42no—
393C22×C5—42no—
394C22×C5—42no—
395C22×C5—42no—
396C22×C5—42no—
397C22×C5—42no—
398C22×C5—81no—
399C22×C5—81no—
400C22×C5—81no—
401C22×C5—81no—
402C22×C5D3×D811yescharacteristic
403C22×C5#91111yescharacteristic
404C22×C5#91111yescharacteristic
405C22×C5#91211yescharacteristic
406C22×C5D4×Dic311yescharacteristic
407C22×C5#93711yescharacteristic
408C22×C5#93911yescharacteristic
409C4×C5D4×Dic311yescharacteristic
410C4×C5#93511yescharacteristic
411C4×C5#93911yescharacteristic
412C4×C5C2×#21711yescharacteristic
413Dic5—62no—
414Dic5—122no—
415Dic5—121no—
416Dic5—241no—
417C24—21no—
418C24—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4C2×Dic1512yes—
428C2×D4C2×Dic1512yescomplemented
429C2×D4#122012yes—
430C2×D4#122012yes—
431C22×C4—151no—
432C22×C4—151no—
433C22×C4—304no—
434C22×C4—301no—
435C22×C4—301no—
436C22×C4—602no—
437C22×C4—602no—
438C22×C4C22×D1511yescharacteristic
439D8—28no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—301no—
443C2×C8—301no—
444C2×C8—301no—
445C2×C8C2×Dic1512yescomplemented
446C4⋊C4—152no—
447C4⋊C4—301no—
448C4⋊C4—301no—
449C4⋊C4—301no—
450C22⋊C4—304no—
451C22⋊C4—602no—
452C22⋊C4—602no—
453C42—301no—
454C42—301no—
455C3×C5#187911yescharacteristic, complemented, Hall
456C22×C3—24no—
457C22×C3—42no—
458C22×C3—42no—
459C22×C3—42no—
460C22×C3—42no—
461C22×C3—42no—
462C22×C3—42no—
463C22×C3—42no—
464C22×C3—42no—
465C22×C3—42no—
466C22×C3—81no—
467C22×C3—81no—
468C22×C3—81no—
469C22×C3—81no—
470C22×C3D5×D811yescharacteristic
471C22×C3#405711yescharacteristic
472C22×C3#405711yescharacteristic
473C22×C3#405811yescharacteristic
474C22×C3D4×Dic511yescharacteristic
475C22×C3#408311yescharacteristic
476C22×C3#408511yescharacteristic
477C3×C4D4×Dic511yescharacteristic
478C3×C4#408111yescharacteristic
479C3×C4#408511yescharacteristic
480C3×C4C2×C22⋊Dic511yescharacteristic
481Dic3—102no—
482Dic3—202no—
483Dic3—201no—
484Dic3—401no—
485C2×C5—44no—
486C2×C5—82no—
487C2×C5Dic3×D811yescharacteristic
488C2×C5#515011yescharacteristic
489C2×C5#515211yescharacteristic
490C2×C5#515311yescharacteristic
491C2×C5#515611yescharacteristic
492C2×C5#515811yescharacteristic
493C2×C5#522011yescharacteristic
494C23—22no—
495C23—22no—
496C23—22no—
497C23—22no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23D4×D1511yescharacteristic
509D4—22no—
510D4—22no—
511D4—22no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
516D4#671914yescomplemented
517C2×C4—152no—
518C2×C4—301no—
519C2×C4—301no—
520C2×C4—301no—
521C2×C4—301no—
522C2×C4—301no—
523C2×C4—302no—
524C2×C4—608no—
525C2×C4—601no—
526C2×C4—601no—
527C2×C4—601no—
528C2×C4—601no—
529C2×C4—601no—
530C2×C4D4×D1511yescharacteristic
531C2×C4#681911yescharacteristic
532C2×C4#681911yescharacteristic
533C2×C4C22×Dic1511yescharacteristic
534C2×C4C2×#122011yescharacteristic
535C2×C4C2×#122011yescharacteristic
536C8—22no—
537C8—601no—
538C2×C3—44no—
539C2×C3—82no—
540C2×C3D8×Dic511yescharacteristic
541C2×C3#6543911yescharacteristic
542C2×C3#6544111yescharacteristic
543C2×C3#6544211yescharacteristic
544C2×C3#6544511yescharacteristic
545C2×C3#6544711yescharacteristic
546C2×C3#6550911yescharacteristic
547C5#7203711yescharacteristic, complemented, Sylow
548C22—24no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22D8×D1511yescharacteristic
563C22#9180011yescharacteristic
564C22#9180011yescharacteristic
565C22#9180111yescharacteristic
566C22D4×Dic1511yescharacteristic
567C22#9182611yescharacteristic
568C22#9182811yescharacteristic
569C4—302no—
570C4—602no—
571C4—601no—
572C4—1201no—
573C4D4×Dic1511yescharacteristic
574C4#9182411yescharacteristic
575C4#9182811yescharacteristic
576C4C2×#671911yescharacteristic
577C3#1060283011yescharacteristic, complemented, Sylow
578C2—44no—
579C2—82no—
580C2D8×Dic1511yescharacteristic
581C2#1175125111yescharacteristic
582C2#1175125311yescharacteristic
583C2#1175125411yescharacteristic
584C2#1175125711yescharacteristic
585C2#1175125911yescharacteristic
586C2#1175132111yescharacteristic
subgroupG/H
centerC23D4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C22×D15
Fitting, prime radicalC22×C3×C5×D8C2
socleC23×C3×C5C2×D4
cosocleC22×C3×C4×C5C23
hypercenterC22×D8D15
hypocenterC3×C5#1879
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic15C2semidirect
3. #11751322C2semidirect
4. C2×#91116C2semidirect
5. C2×#91116C2semidirect
6. #11746372C2semidirect
7. #11746371C2semidirect
14. C2×C3×C5×D8C4semidirect
46. C2×C3×C5×D4C2×C4semidirect
60. C2×C3×C5×C8C2×C4semidirect
85. C2×C5×D8Dic3semidirect
121. C3×C5×D4C22⋊C4semidirect
140. C2×Dic15D8semidirect
148. C2×C3×D8Dic5semidirect
172. C2×C5×D4C2×Dic3semidirect
186. C2×C5×C8C2×Dic3semidirect
246. C2×C3×D4C2×Dic5semidirect
260. C2×C3×C8C2×Dic5semidirect
295. C5×D4#217semidirect
322. C2×D8Dic15semidirect
366. C3×D4C22⋊Dic5semidirect
428. C2×D4C2×Dic15semidirect
445. C2×C8C2×Dic15semidirect
455. C3×C5#1879semidirect
516. D4#6719semidirect
547. C5#72037semidirect
577. C3#10602830semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C5×D82
C2×D4×Dic152
#117513222
C2×#911162
#117463722
#117463712
#106028303
#720375