Finite Group Databasebeta

← #14329534

Subgroups — #14329534

Order 1920.

1264 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
1C2×C3×C5×#124C211yesmaximal, characteristic
2C2×Q8×Dic15C211yesmaximal, characteristic, complemented
3C2×D4×Dic15C211yesmaximal, characteristic
4#11751330C211yesmaximal, characteristic, complemented
5#11751322C211yesmaximal, characteristic
6#11751052C212yesmaximal, complemented
7#11751052C212yesmaximal, complemented
8#11751051C212yesmaximal, complemented
9C22⋊C4×Dic15C212yesmaximal, complemented
10C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
11C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
12#10614686—31nomaximal, Hall
13C22×C3×C5×Q8C2211yescharacteristic
14C22×C3×C5×D4C2211yescharacteristic
15C23×Dic15C2212yes—
16C3×C5×#124C418yescomplemented
17C2×C3×C5×C22⋊C4C2212yes—
18C2×C3×C5×C22⋊C4C2212yes—
19C2×C3×C42×C5C2211yescharacteristic
20C2×#6719C2212yes—
21C2×#6719C2212yes—
22C2×#6719C2212yes—
23Q8×Dic15—24no—
24D4×Dic15—24no—
25C2×C4⋊Dic15C2212yes—
26C2×C4⋊Dic15C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2211yescharacteristic
30C2×C4×Dic15C2211yescharacteristic
31C2×C4×Dic15C2211yescharacteristic
32C2×C4×Dic15C2212yes—
33C2×C4×Dic15C2212yes—
34#91115C2211yescharacteristic
35#91115C2212yes—
36#91115C2211yescharacteristic
37#91115C2212yes—
38#91115C2212yes—
39#82955—51nomaximal, Hall
40C2×C5×#124D311yescharacteristic
41C2×Q8×Dic5—31no—
42C2×D4×Dic5—31no—
43#65519—31no—
44#65510—31no—
45#65240—32no—
46#65240—32no—
47#65239—32no—
48C22⋊C4×Dic5—32no—
49C4×C4⋊Dic5—31no—
50C4×C4⋊Dic5—31no—
51C24×C3×C5C2312yes—
52C2×C3×C5×Q8—22no—
53C2×C3×C5×Q8—22no—
54C2×C3×C5×Q8C2×C414yescomplemented
55C2×C3×C5×D4—22no—
56C2×C3×C5×D4—22no—
57C2×C3×C5×D4C2×C414yes—
58C22×C3×C4×C5C2311yescharacteristic
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C22×C3×C4×C5C2311yescharacteristic
62C22×Dic15—24no—
63C22×Dic15—24no—
64C22×Dic15—42no—
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2312yes—
68C22×Dic15C2312yes—
69C22×Dic15C2311yescharacteristic
70C22×Dic15C2311yescharacteristic
71C3×C5×C22⋊C4C2×C418yescomplemented
72C3×C5×C22⋊C4C2×C418yescomplemented
73C3×C42×C5C2×C414yescomplemented
74#6719—24no—
75#6719—24no—
76#6719—42no—
77C4⋊Dic15—22no—
78C4⋊Dic15—24no—
79C4⋊Dic15—22no—
80C4⋊Dic15—22no—
81C4⋊Dic15D414yes—
82C4×Dic15—22no—
83C4×Dic15—22no—
84C4×Dic15—24no—
85C4×Dic15—42no—
86C2×C3×#124D511yescharacteristic
87C2×Q8×Dic3—51no—
88C2×D4×Dic3—51no—
89#5229—51no—
90#5221—51no—
91#4951—52no—
92#4951—52no—
93#4950—52no—
94Dic3×C22⋊C4—52no—
95C4×C4⋊Dic3—51no—
96C4×C4⋊Dic3—51no—
97C22×C5×Q8C2×D311yescharacteristic
98C22×C5×D4C2×D311yescharacteristic
99C23×Dic5—32no—
100C5×#124Dic318yescomplemented
101C2×C5×C22⋊C4C2×D312yes—
102C2×C5×C22⋊C4C2×D312yes—
103C2×C42×C5C2×D311yescharacteristic
104C2×C22⋊Dic5—32no—
105C2×C22⋊Dic5—32no—
106C2×C22⋊Dic5—32no—
107Q8×Dic5—64no—
108D4×Dic5—64no—
109C2×C4⋊Dic5—31no—
110C2×C4⋊Dic5—32no—
111C2×C4⋊Dic5—31no—
112C2×C4⋊Dic5—31no—
113C2×C4⋊Dic5—31no—
114C2×C4×Dic5—31no—
115C2×C4×Dic5—31no—
116C2×C4×Dic5—32no—
117C2×C4×Dic5—32no—
118#3963—31no—
119#3963—32no—
120#3963—31no—
121#3963—32no—
122#3963—32no—
123#2367—151noSylow
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5C22×C414yes—
131C23×C3×C5C2411yescharacteristic
132C3×C5×Q8—28no—
133C3×C5×D4—28no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—22no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×C4×C5C22×C414yes—
143C2×C3×C4×C5C22×C412yes—
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5#4112yes—
146C2×Dic15—21no—
147C2×Dic15—21no—
148C2×Dic15—22no—
149C2×Dic15—22no—
150C2×Dic15—21no—
151C2×Dic15—21no—
152C2×Dic15—21no—
153C2×Dic15—21no—
154C2×Dic15—21no—
155C2×Dic15—21no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—21no—
160C2×Dic15—21no—
161C2×Dic15—48no—
162C2×Dic15C2×D414yes—
163C2×Dic15#4112yes—
164C2×Dic15#4112yes—
165C22×C3×Q8C2×D511yescharacteristic
166C22×C3×D4C2×D511yescharacteristic
167C23×Dic3—52no—
168C3×#124Dic518yescomplemented
169C2×C3×C22⋊C4C2×D512yes—
170C2×C3×C22⋊C4C2×D512yes—
171C2×C3×C42C2×D511yescharacteristic
172C2×#217—52no—
173C2×#217—52no—
174C2×#217—52no—
175Q8×Dic3—104no—
176D4×Dic3—104no—
177C2×C4⋊Dic3—51no—
178C2×C4⋊Dic3—51no—
179C2×C4⋊Dic3—51no—
180C2×C4⋊Dic3—51no—
181C2×C4⋊Dic3—52no—
182C2×C4×Dic3—51no—
183C2×C4×Dic3—51no—
184C2×C4×Dic3—52no—
185C2×C4×Dic3—52no—
186C3⋊#95—51no—
187C3⋊#95—52no—
188C3⋊#95—51no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C24×C5C22×D312yes—
192C2×C5×Q8—22no—
193C2×C5×Q8—22no—
194C2×C5×Q8C2×Dic314yescomplemented
195C2×C5×D4—22no—
196C2×C5×D4—22no—
197C2×C5×D4C2×Dic314yes—
198C22×C4×C5C22×D311yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C22×C4×C5C22×D312yes—
201C22×C4×C5C22×D311yescharacteristic
202C22×Dic5—31no—
203C22×Dic5—32no—
204C22×Dic5—31no—
205C22×Dic5—31no—
206C22×Dic5—32no—
207C22×Dic5—31no—
208C22×Dic5—64no—
209C22×Dic5—64no—
210C22×Dic5—122no—
211C5×C22⋊C4C2×Dic318yescomplemented
212C5×C22⋊C4C2×Dic318yescomplemented
213C42×C5C2×Dic314yescomplemented
214C22⋊Dic5—64no—
215C22⋊Dic5—64no—
216C22⋊Dic5—122no—
217C4⋊Dic5—34no—
218C4⋊Dic5—62no—
219C4⋊Dic5—62no—
220C4⋊Dic5—64no—
221C4⋊Dic5—62no—
222C4×Dic5—64no—
223C4×Dic5—62no—
224C4×Dic5—62no—
225C4×Dic5—122no—
226C2×#124D1511yescharacteristic
227C2×C4×Q8—151no—
228C2×C4×D4—151no—
229#391—151no—
230#390—151no—
231#388—152no—
232#388—152no—
233#385—152no—
234C4×C4⋊C4—151no—
235C4×C4⋊C4—151no—
236C4×C22⋊C4—152no—
237C22×C3×C5—24no—
238C22×C3×C5—24no—
239C22×C3×C5—24no—
240C22×C3×C5—42no—
241C22×C3×C5—42no—
242C22×C3×C5—42no—
243C22×C3×C5—42no—
244C22×C3×C5C23×C411yescharacteristic
245C22×C3×C5C22×D411yescharacteristic
246C22×C3×C5C2×#4111yescharacteristic
247C22×C3×C5C2×#4111yescharacteristic
248C22×C3×C5C2×#4111yescharacteristic
249C22×C3×C5H(5,𝔽2)11yescharacteristic
250C22×C3×C52−1+411yescharacteristic
251C3×C4×C5—24no—
252C3×C4×C5—22no—
253C3×C4×C5—22no—
254C3×C4×C5C4×D414yes—
255Dic15—22no—
256Dic15—24no—
257Dic15—22no—
258Dic15—41no—
259Dic15—41no—
260Dic15—42no—
261C24×C3C22×D512yes—
262C2×C3×Q8—22no—
263C2×C3×Q8—22no—
264C2×C3×Q8C2×Dic514yescomplemented
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4C2×Dic514yes—
268C22×C3×C4C22×D511yescharacteristic
269C22×C3×C4C22×D512yes—
270C22×C3×C4C22×D511yescharacteristic
271C22×C3×C4C22×D511yescharacteristic
272C22×Dic3—51no—
273C22×Dic3—51no—
274C22×Dic3—52no—
275C22×Dic3—51no—
276C22×Dic3—52no—
277C22×Dic3—51no—
278C22×Dic3—104no—
279C22×Dic3—104no—
280C22×Dic3—202no—
281C3×C22⋊C4C2×Dic518yescomplemented
282C3×C22⋊C4C2×Dic518yescomplemented
283C3×C42C2×Dic514yescomplemented
284#217—104no—
285#217—104no—
286#217—202no—
287C4⋊Dic3—54no—
288C4⋊Dic3—102no—
289C4⋊Dic3—102no—
290C4⋊Dic3—104no—
291C4⋊Dic3—102no—
292C4×Dic3—104no—
293C4×Dic3—102no—
294C4×Dic3—102no—
295C4×Dic3—202no—
296C23×C5—22no—
297C23×C5—22no—
298C23×C5—22no—
299C23×C5—22no—
300C23×C5—22no—
301C23×C5—22no—
302C23×C5C22×Dic314yes—
303C23×C5C23×D311yescharacteristic
304C5×Q8—28no—
305C5×D4—28no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5D3×D412yes—
313C2×C4×C5#23712yes—
314C2×C4×C5C22×Dic312yes—
315C2×C4×C5C22×Dic312yes—
316C2×C4×C5C22×Dic314yes—
317C2×C4×C5C22×Dic312yes—
318C2×Dic5—34no—
319C2×Dic5—32no—
320C2×Dic5—32no—
321C2×Dic5—61no—
322C2×Dic5—61no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—61no—
326C2×Dic5—61no—
327C2×Dic5—61no—
328C2×Dic5—61no—
329C2×Dic5—62no—
330C2×Dic5—61no—
331C2×Dic5—61no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334C2×Dic5—61no—
335C2×Dic5—61no—
336C2×Dic5—128no—
337C22×Q8C2×D1511yescharacteristic
338C22×D4C2×D1511yescharacteristic
339C23×C4—152no—
340#124Dic1518yescomplemented
341C4×Q8—304no—
342C4×D4—304no—
343C2×C4⋊C4—151no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—151no—
346C2×C4⋊C4—151no—
347C2×C4⋊C4—151no—
348C2×C22⋊C4—152no—
349C2×C22⋊C4—152no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4C2×D1512yes—
352C2×C22⋊C4C2×D1512yes—
353C2×C42—151no—
354C2×C42—152no—
355C2×C42—151no—
356C2×C42—152no—
357C2×C42C2×D1511yescharacteristic
358#95—151no—
359#95—152no—
360#95—152no—
361#95—151no—
362#95—152no—
363C2×C3×C5—44no—
364C2×C3×C5C2×C4×D411yescharacteristic
365C2×C3×C5C4×#4111yescharacteristic
366C2×C3×C5#52011yescharacteristic
367C2×C3×C5#54611yescharacteristic
368C2×C3×C5#54811yescharacteristic
369C2×C3×C5#55611yescharacteristic
370C2×C3×C5#55911yescharacteristic
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3C22×Dic514yes—
378C23×C3C23×D511yescharacteristic
379C3×Q8—28no—
380C3×D4—28no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4D4×D512yes—
388C2×C3×C4#71112yes—
389C2×C3×C4C22×Dic512yes—
390C2×C3×C4C22×Dic512yes—
391C2×C3×C4C22×Dic514yes—
392C2×C3×C4C22×Dic512yes—
393C2×Dic3—54no—
394C2×Dic3—52no—
395C2×Dic3—52no—
396C2×Dic3—101no—
397C2×Dic3—101no—
398C2×Dic3—102no—
399C2×Dic3—102no—
400C2×Dic3—101no—
401C2×Dic3—101no—
402C2×Dic3—101no—
403C2×Dic3—101no—
404C2×Dic3—102no—
405C2×Dic3—101no—
406C2×Dic3—101no—
407C2×Dic3—102no—
408C2×Dic3—102no—
409C2×Dic3—101no—
410C2×Dic3—101no—
411C2×Dic3—208no—
412C22×C5—24no—
413C22×C5—24no—
414C22×C5—24no—
415C22×C5—42no—
416C22×C5—42no—
417C22×C5—42no—
418C22×C5—42no—
419C22×C5C2×D3×D411yescharacteristic
420C22×C5C2×#23711yescharacteristic
421C22×C5D3×#4111yescharacteristic
422C22×C5D3×#4111yescharacteristic
423C22×C5#100911yescharacteristic
424C22×C5#101011yescharacteristic
425C22×C5C23×Dic311yescharacteristic
426C4×C5—24no—
427C4×C5—22no—
428C4×C5—22no—
429C4×C5D4×Dic314yes—
430Dic5—64no—
431Dic5—62no—
432Dic5—62no—
433Dic5—121no—
434Dic5—121no—
435Dic5—122no—
436C24C22×D1512yes—
437C2×Q8—22no—
438C2×Q8—22no—
439C2×Q8C2×Dic1514yescomplemented
440C2×D4—22no—
441C2×D4—22no—
442C2×D4C2×Dic1514yes—
443C22×C4—151no—
444C22×C4—151no—
445C22×C4—152no—
446C22×C4—151no—
447C22×C4—152no—
448C22×C4—151no—
449C22×C4—304no—
450C22×C4—304no—
451C22×C4—602no—
452C22×C4C22×D1511yescharacteristic
453C22×C4C22×D1512yes—
454C22×C4C22×D1511yescharacteristic
455C22×C4C22×D1511yescharacteristic
456C4⋊C4—154no—
457C4⋊C4—304no—
458C4⋊C4—302no—
459C4⋊C4—302no—
460C4⋊C4—302no—
461C22⋊C4—304no—
462C22⋊C4—304no—
463C22⋊C4—602no—
464C22⋊C4C2×Dic1518yescomplemented
465C22⋊C4C2×Dic1518yescomplemented
466C42—304no—
467C42—302no—
468C42—302no—
469C42—602no—
470C42C2×Dic1514yescomplemented
471C3×C5#236711yescharacteristic, complemented, Hall
472C22×C3—24no—
473C22×C3—24no—
474C22×C3—24no—
475C22×C3—42no—
476C22×C3—42no—
477C22×C3—42no—
478C22×C3—42no—
479C22×C3C2×D4×D511yescharacteristic
480C22×C3C2×#71111yescharacteristic
481C22×C3D5×#4111yescharacteristic
482C22×C3D5×#4111yescharacteristic
483C22×C3#414911yescharacteristic
484C22×C3#415011yescharacteristic
485C22×C3C23×Dic511yescharacteristic
486C3×C4—24no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4D4×Dic514yes—
490Dic3—104no—
491Dic3—102no—
492Dic3—102no—
493Dic3—201no—
494Dic3—201no—
495Dic3—202no—
496C2×C5—44no—
497C2×C5#567111yescharacteristic
498C2×C5#567611yescharacteristic
499C2×C5#567711yescharacteristic
500C2×C5#568111yescharacteristic
501C2×C5C2×D4×Dic311yescharacteristic
502C2×C5Dic3×#4111yescharacteristic
503C2×C5#582711yescharacteristic
504C23—22no—
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23C22×Dic1514yes—
511C23C23×D1511yescharacteristic
512Q8—28no—
513D4—28no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—154no—
521C2×C4—152no—
522C2×C4—152no—
523C2×C4—301no—
524C2×C4—301no—
525C2×C4—302no—
526C2×C4—302no—
527C2×C4—301no—
528C2×C4—301no—
529C2×C4—301no—
530C2×C4—301no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—301no—
534C2×C4—301no—
535C2×C4—302no—
536C2×C4—301no—
537C2×C4—301no—
538C2×C4—608no—
539C2×C4D4×D1512yes—
540C2×C4#681912yes—
541C2×C4C22×Dic1512yes—
542C2×C4C22×Dic1512yes—
543C2×C4C22×Dic1514yes—
544C2×C4C22×Dic1512yes—
545C2×C3—44no—
546C2×C3#6600511yescharacteristic
547C2×C3#6601011yescharacteristic
548C2×C3#6601111yescharacteristic
549C2×C3#6601511yescharacteristic
550C2×C3C2×D4×Dic511yescharacteristic
551C2×C3#41×Dic511yescharacteristic
552C2×C3#6616111yescharacteristic
553C5#8295511yescharacteristic, complemented, Sylow
554C22—24no—
555C22—24no—
556C22—24no—
557C22—42no—
558C22—42no—
559C22—42no—
560C22—42no—
561C22C2×D4×D1511yescharacteristic
562C22C2×#681911yescharacteristic
563C22#41×D1511yescharacteristic
564C22#41×D1511yescharacteristic
565C22#9210011yescharacteristic
566C22#9210111yescharacteristic
567C22C23×Dic1511yescharacteristic
568C4—24no—
569C4—22no—
570C4—22no—
571C4—302no—
572C4—304no—
573C4—302no—
574C4—601no—
575C4—601no—
576C4—602no—
577C4D4×Dic1514yes—
578C3#1061468611yescharacteristic, complemented, Sylow
579C2—44no—
580C2#1175643011yescharacteristic
581C2#1175643511yescharacteristic
582C2#1175643611yescharacteristic
583C2#1175644011yescharacteristic
584C2C2×D4×Dic1511yescharacteristic
585C2#41×Dic1511yescharacteristic
586C2#1175658611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×#124C2
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×C5×D4C22
hypercenterC2×#124D15
hypocenterC3×C5#2367
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic15C2semidirect
4. #11751330C2semidirect
6. #11751052C2semidirect
7. #11751052C2semidirect
8. #11751051C2semidirect
9. C22⋊C4×Dic15C2semidirect
10. C4×C4⋊Dic15C2semidirect
11. C4×C4⋊Dic15C2semidirect
16. C3×C5×#124C4semidirect
54. C2×C3×C5×Q8C2×C4semidirect
71. C3×C5×C22⋊C4C2×C4semidirect
72. C3×C5×C22⋊C4C2×C4semidirect
73. C3×C42×C5C2×C4semidirect
100. C5×#124Dic3semidirect
168. C3×#124Dic5semidirect
194. C2×C5×Q8C2×Dic3semidirect
211. C5×C22⋊C4C2×Dic3semidirect
212. C5×C22⋊C4C2×Dic3semidirect
213. C42×C5C2×Dic3semidirect
264. C2×C3×Q8C2×Dic5semidirect
281. C3×C22⋊C4C2×Dic5semidirect
282. C3×C22⋊C4C2×Dic5semidirect
283. C3×C42C2×Dic5semidirect
340. #124Dic15semidirect
439. C2×Q8C2×Dic15semidirect
464. C22⋊C4C2×Dic15semidirect
465. C22⋊C4C2×Dic15semidirect
470. C42C2×Dic15semidirect
471. C3×C5#2367semidirect
553. C5#82955semidirect
578. C3#10614686semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#1242
C2×Q8×Dic152
C2×D4×Dic152
#117513302
#117513222
#117510522
#117510512
C22⋊C4×Dic152
C4×C4⋊Dic152
#106146863
#829555