Finite Group Databasebeta

← #14327162

Subgroups — #14327162

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic15C211yesmaximal, characteristic
2C2×C5×D4×Dic3C211yesmaximal, characteristic
3C2×C3×D4×Dic5C211yesmaximal, characteristic
4#11749515C212yesmaximal, complemented
5#11749511C212yesmaximal, complemented
6#11749506C212yesmaximal, complemented
7C2×#90994C212yesmaximal, complemented
8#11748865C211yesmaximal, characteristic, complemented
9#11748857C211yesmaximal, characteristic, complemented
10C4×#6668C211yesmaximal, characteristic, complemented
11#11748613C211yesmaximal, characteristic, complemented
12#10614065—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×Dic15C2212yes—
15C23×C5×Dic3C2212yes—
16C23×C3×Dic5C2212yes—
17C2×#6719C2212yes—
18D4×Dic15—24no—
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C4×Dic15C2211yescharacteristic
21C2×C5×#217C2212yes—
22C5×D4×Dic3—24no—
23C2×C5×C4⋊Dic3C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×C22⋊Dic5C2212yes—
26C3×D4×Dic5C418yescomplemented
27C2×C3×C4⋊Dic5C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C2×#6668C2211yescharacteristic
30C2×#6668C2211yescharacteristic
31C2×#6668C2212yes—
32C2×#6668C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2211yescharacteristic
37#90994C2212yes—
38#90994C2211yescharacteristic
39#82333—51nomaximal, Hall
40C2×C4×C5×D4—31no—
41C2×D4×Dic5—31no—
42C2×D4×Dic5D311yescharacteristic
43#65499—32no—
44C2×#3963—32no—
45#65266—31no—
46#65262—31no—
47#65235—32no—
48#65231—32no—
49C4×#683—31no—
50#65217—31no—
51C24×C3×C5C2312yes—
52C2×C3×C5×D4C2×C414yes—
53C2×C3×C5×D4D414yes—
54C2×C3×C5×D4Q814yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—24no—
57C22×Dic15—24no—
58C22×Dic15—42no—
59C22×Dic15C2312yes—
60C22×Dic15C2311yescharacteristic
61C22×Dic15C2311yescharacteristic
62C22×C5×Dic3—24no—
63C22×C5×Dic3—24no—
64C22×C5×Dic3—42no—
65C22×C5×Dic3C2311yescharacteristic
66C22×C5×Dic3C2312yes—
67C22×C5×Dic3C2311yescharacteristic
68C22×C3×Dic5—42no—
69C22×C3×Dic5—42no—
70C22×C3×Dic5C2×C418yescomplemented
71C22×C3×Dic5C2311yescharacteristic
72C22×C3×Dic5C2312yes—
73C22×C3×Dic5C2311yescharacteristic
74#6719—24no—
75C4⋊Dic15—22no—
76C4×Dic15—22no—
77C5×#217—24no—
78C5×C4⋊Dic3—22no—
79C4×C5×Dic3—22no—
80C3×C22⋊Dic5C2×C418yescomplemented
81C3×C4⋊Dic5C2×C414yescomplemented
82C3×C4×Dic5C2×C414yescomplemented
83#6668—22no—
84#6668—22no—
85#6668—42no—
86#6668—42no—
87C2×C3×C4×D4—51no—
88C2×D4×Dic3—51no—
89C2×D4×Dic3D511yescharacteristic
90#5212—52no—
91C2×C3⋊#95—52no—
92#4984—51no—
93#4984—51no—
94#4950—52no—
95#4950—52no—
96#4936—51no—
97C4×C4⋊Dic3—51no—
98C22×C5×D4C2×D311yescharacteristic
99C23×C4×C5—32no—
100C23×Dic5—32no—
101C23×Dic5C2×D312yes—
102C4×C5×D4—64no—
103C2×C5×C4⋊C4—31no—
104C2×C5×C22⋊C4—32no—
105C2×C42×C5—31no—
106C2×C22⋊Dic5—32no—
107C2×C22⋊Dic5C2×D312yes—
108D4×Dic5—64no—
109D4×Dic5Dic318yescomplemented
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5C2×D311yescharacteristic
112C2×#683—31no—
113C2×#683—31no—
114C2×#683—32no—
115C2×#683—32no—
116C2×C4×Dic5—31no—
117C2×C4×Dic5C2×D311yescharacteristic
118#3963—32no—
119#3963—31no—
120#3963—31no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2349—151noSylow
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—22no—
129C23×C3×C5C22×C414yes—
130C23×C3×C5C2×D414yes—
131C23×C3×C5C2×Q814yes—
132C23×C3×C5C2411yescharacteristic
133C3×C5×D4C4⋊C4116yescomplemented
134C2×C3×C4×C5C22×C412yes—
135C2×C3×C4×C5C2×D412yes—
136C2×C3×C4×C5C2×Q812yes—
137C2×Dic15—21no—
138C2×Dic15—21no—
139C2×Dic15—21no—
140C2×Dic15—22no—
141C2×Dic15—21no—
142C2×Dic15—22no—
143C2×Dic15—21no—
144C2×Dic15—22no—
145C2×Dic15—48no—
146C2×Dic15#4112yes—
147C2×C5×Dic3—21no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—22no—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—22no—
155C2×C5×Dic3—48no—
156C2×C5×Dic3#4112yes—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—21no—
162C2×C3×Dic5—21no—
163C2×C3×Dic5—48no—
164C2×C3×Dic5C22×C412yes—
165C2×C3×Dic5C22×C412yes—
166C2×C3×Dic5C22×C414yes—
167C22×C3×D4C2×D511yescharacteristic
168C23×C3×C4—52no—
169C23×Dic3—52no—
170C23×Dic3C2×D512yes—
171C3×C4×D4—58no—
172C2×C3×C4⋊C4—51no—
173C2×C3×C22⋊C4—52no—
174C2×C3×C42—51no—
175C2×#217—52no—
176C2×#217C2×D512yes—
177D4×Dic3—24no—
178D4×Dic3—104no—
179C2×C4⋊Dic3—51no—
180C2×C4⋊Dic3—51no—
181C2×C4⋊Dic3—51no—
182C2×C4⋊Dic3—52no—
183C2×C4⋊Dic3—52no—
184C2×C4⋊Dic3C2×D511yescharacteristic
185C2×C4×Dic3—51no—
186C2×C4×Dic3C2×D511yescharacteristic
187C3⋊#95—51no—
188C3⋊#95—51no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C3⋊#95—52no—
192C3⋊#95—52no—
193C24×C5C22×D312yes—
194C2×C5×D4Dic614yes—
195C2×C5×D4D1214yes—
196C2×C5×D4C2×Dic314yes—
197C22×C4×C5—31no—
198C22×C4×C5—31no—
199C22×C4×C5—32no—
200C22×C4×C5—64no—
201C22×C4×C5—64no—
202C22×C4×C5—122no—
203C22×C4×C5C22×D311yescharacteristic
204C22×Dic5—31no—
205C22×Dic5—31no—
206C22×Dic5—32no—
207C22×Dic5—42no—
208C22×Dic5—42no—
209C22×Dic5—64no—
210C22×Dic5—64no—
211C22×Dic5—122no—
212C22×Dic5C2×Dic318yescomplemented
213C22×Dic5C22×D311yescharacteristic
214C22×Dic5C22×D312yes—
215C22×Dic5C22×D311yescharacteristic
216C5×C4⋊C4—62no—
217C5×C22⋊C4—64no—
218C42×C5—62no—
219C22⋊Dic5—64no—
220C22⋊Dic5C2×Dic318yescomplemented
221C4⋊Dic5—62no—
222C4⋊Dic5C2×Dic314yescomplemented
223#683—62no—
224#683—62no—
225#683—122no—
226#683—122no—
227C4×Dic5—62no—
228C4×Dic5C2×Dic314yescomplemented
229C2×C4×D4—31no—
230C2×C4×D4—51no—
231C2×C4×D4—151no—
232#389—151no—
233#389—151no—
234#385—152no—
235#385—152no—
236#382—151no—
237#380—152no—
238C4×C4⋊C4—151no—
239C2×#95—152no—
240C22×C3×C5—24no—
241C22×C3×C5—24no—
242C22×C3×C5—24no—
243C22×C3×C5—24no—
244C22×C3×C5—24no—
245C22×C3×C5—24no—
246C22×C3×C5C2×C4⋊C418yes—
247C22×C3×C5C23×C411yescharacteristic
248C22×C3×C5C22×D411yescharacteristic
249C22×C3×C5C22×Q811yescharacteristic
250C22×C3×C5C2×#4111yescharacteristic
251C22×C3×C5C2×#4111yescharacteristic
252C22×C3×C5H(5,𝔽2)11yescharacteristic
253C22×C3×C5H(5,𝔽2)11yescharacteristic
254C3×C4×C5C2×C4⋊C414yes—
255Dic15—22no—
256Dic15—41no—
257Dic15—42no—
258C3×Dic5—22no—
259C3×Dic5—22no—
260C3×Dic5—24no—
261C5×Dic3—22no—
262C5×Dic3—41no—
263C5×Dic3—42no—
264C24×C3C22×D512yes—
265C2×C3×D4Dic1014yes—
266C2×C3×D4C4×D514yes—
267C2×C3×D4C22⋊D514yes—
268C22×C3×C4—51no—
269C22×C3×C4—51no—
270C22×C3×C4—52no—
271C22×C3×C4—58no—
272C22×C3×C4—202no—
273C22×C3×C4—202no—
274C22×C3×C4C22×D511yescharacteristic
275C22×Dic3—24no—
276C22×Dic3—24no—
277C22×Dic3—42no—
278C22×Dic3—51no—
279C22×Dic3—52no—
280C22×Dic3—51no—
281C22×Dic3—104no—
282C22×Dic3—104no—
283C22×Dic3—202no—
284C22×Dic3C22×D512yes—
285C22×Dic3C22×D511yescharacteristic
286C22×Dic3C22×D511yescharacteristic
287C3×C4⋊C4—54no—
288C3×C22⋊C4—58no—
289C3×C42—54no—
290#217—24no—
291#217—104no—
292C4⋊Dic3—22no—
293C4⋊Dic3—102no—
294C4⋊Dic3—102no—
295C4⋊Dic3—102no—
296C4⋊Dic3—202no—
297C4⋊Dic3—202no—
298C4×Dic3—22no—
299C4×Dic3—102no—
300C23×C5—22no—
301C23×C5—22no—
302C23×C5—22no—
303C23×C5—22no—
304C23×C5C2×Dic614yes—
305C23×C5C2×D1214yes—
306C23×C5C22×Dic314yes—
307C23×C5C23×D311yescharacteristic
308C5×D4C4⋊Dic3116yescomplemented
309C2×C4×C5—32no—
310C2×C4×C5—61no—
311C2×C4×C5—61no—
312C2×C4×C5—61no—
313C2×C4×C5—62no—
314C2×C4×C5—61no—
315C2×C4×C5—62no—
316C2×C4×C5—61no—
317C2×C4×C5—62no—
318C2×C4×C5—128no—
319C2×C4×C5C2×Dic612yes—
320C2×C4×C5C2×D1212yes—
321C2×C4×C5C22×Dic312yes—
322C2×Dic5—22no—
323C2×Dic5—22no—
324C2×Dic5—21no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—21no—
328C2×Dic5—32no—
329C2×Dic5—48no—
330C2×Dic5—61no—
331C2×Dic5—61no—
332C2×Dic5—61no—
333C2×Dic5—62no—
334C2×Dic5—61no—
335C2×Dic5—62no—
336C2×Dic5—61no—
337C2×Dic5—62no—
338C2×Dic5—128no—
339C2×Dic5C22×Dic312yes—
340C2×Dic5C22×Dic312yes—
341C2×Dic5C22×Dic314yes—
342C22×D4D3×D511yescharacteristic
343C23×C4—32no—
344C23×C4—52no—
345C23×C4—152no—
346C4×D4—58no—
347C4×D4—64no—
348C4×D4—304no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—51no—
351C2×C4⋊C4—151no—
352C2×C4⋊C4—151no—
353C2×C4⋊C4—151no—
354C2×C4⋊C4—152no—
355C2×C4⋊C4—152no—
356C2×C22⋊C4—32no—
357C2×C22⋊C4—52no—
358C2×C22⋊C4—152no—
359C2×C42—31no—
360C2×C42—51no—
361C2×C42—151no—
362#95—151no—
363#95—152no—
364#95—152no—
365#95—152no—
366#95—151no—
367#95—152no—
368C2×C3×C5—28no—
369C2×C3×C5C22×C4⋊C411yescharacteristic
370C2×C3×C5C4×#4111yescharacteristic
371C2×C3×C5#51811yescharacteristic
372C2×C3×C5#54611yescharacteristic
373C2×C3×C5#54611yescharacteristic
374C2×C3×C5#55411yescharacteristic
375C2×C3×C5#55411yescharacteristic
376C23×C3—22no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3C2×Dic1014yes—
381C23×C3C2×C4×D514yes—
382C23×C3C2×C22⋊D514yes—
383C23×C3C23×D511yescharacteristic
384C3×D4#683116yescomplemented
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—54no—
388C2×C3×C4—101no—
389C2×C3×C4—102no—
390C2×C3×C4—101no—
391C2×C3×C4—101no—
392C2×C3×C4—102no—
393C2×C3×C4—101no—
394C2×C3×C4—208no—
395C2×C3×C4C2×Dic1012yes—
396C2×C3×C4C2×C4×D512yes—
397C2×C3×C4C2×C22⋊D512yes—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—22no—
406C2×Dic3—48no—
407C2×Dic3—52no—
408C2×Dic3—101no—
409C2×Dic3—101no—
410C2×Dic3—101no—
411C2×Dic3—101no—
412C2×Dic3—102no—
413C2×Dic3—102no—
414C2×Dic3—101no—
415C2×Dic3—102no—
416C2×Dic3—208no—
417C2×Dic3#71112yes—
418C22×C5—24no—
419C22×C5—24no—
420C22×C5—24no—
421C22×C5—24no—
422C22×C5—24no—
423C22×C5—24no—
424C22×C5C2×C4⋊Dic318yes—
425C22×C5C22×Dic611yescharacteristic
426C22×C5C22×D1211yescharacteristic
427C22×C5#100411yescharacteristic
428C22×C5#100411yescharacteristic
429C22×C5D3×#4111yescharacteristic
430C22×C5D3×#4111yescharacteristic
431C22×C5C23×Dic311yescharacteristic
432C4×C5—62no—
433C4×C5—121no—
434C4×C5—122no—
435C4×C5C2×C4⋊Dic314yes—
436Dic5—22no—
437Dic5—24no—
438Dic5—22no—
439Dic5—62no—
440Dic5—121no—
441Dic5—122no—
442C24C2×D3×D512yes—
443C2×D4D5×Dic314yes—
444C2×D4#120314yes—
445C2×D4#120414yes—
446C22×C4—31no—
447C22×C4—32no—
448C22×C4—31no—
449C22×C4—51no—
450C22×C4—51no—
451C22×C4—52no—
452C22×C4—58no—
453C22×C4—64no—
454C22×C4—64no—
455C22×C4—122no—
456C22×C4—151no—
457C22×C4—152no—
458C22×C4—151no—
459C22×C4—202no—
460C22×C4—202no—
461C22×C4—304no—
462C22×C4—304no—
463C22×C4—602no—
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—54no—
466C4⋊C4—62no—
467C4⋊C4—302no—
468C4⋊C4—302no—
469C4⋊C4—302no—
470C4⋊C4—602no—
471C4⋊C4—602no—
472C22⋊C4—58no—
473C22⋊C4—64no—
474C22⋊C4—304no—
475C42—54no—
476C42—62no—
477C42—302no—
478C3×C5#234911yescharacteristic, complemented, Hall
479C22×C3—24no—
480C22×C3—24no—
481C22×C3—24no—
482C22×C3—24no—
483C22×C3—24no—
484C22×C3—24no—
485C22×C3C2×#68318yes—
486C22×C3C22×Dic1011yescharacteristic
487C22×C3C22×C4×D511yescharacteristic
488C22×C3C2×#71111yescharacteristic
489C22×C3#414411yescharacteristic
490C22×C3D5×#4111yescharacteristic
491C22×C3#414911yescharacteristic
492C22×C3C22×C22⋊D511yescharacteristic
493C3×C4—102no—
494C3×C4—104no—
495C3×C4—102no—
496C3×C4C2×#68314yes—
497Dic3—22no—
498Dic3—42no—
499Dic3—41no—
500Dic3—102no—
501Dic3—201no—
502Dic3—202no—
503C2×C5—28no—
504C2×C5#553911yescharacteristic
505C2×C5#553911yescharacteristic
506C2×C5#555411yescharacteristic
507C2×C5#555411yescharacteristic
508C2×C5C22×C4⋊Dic311yescharacteristic
509C2×C5#579811yescharacteristic
510C2×C5Dic3×#4111yescharacteristic
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23C2×D5×Dic314yes—
516C23C2×#120314yes—
517C23C2×#120414yes—
518C23C22×D3×D511yescharacteristic
519D4#6668116yescomplemented
520C2×C4—32no—
521C2×C4—52no—
522C2×C4—52no—
523C2×C4—54no—
524C2×C4—61no—
525C2×C4—61no—
526C2×C4—62no—
527C2×C4—61no—
528C2×C4—62no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—62no—
532C2×C4—101no—
533C2×C4—101no—
534C2×C4—102no—
535C2×C4—101no—
536C2×C4—102no—
537C2×C4—101no—
538C2×C4—128no—
539C2×C4—152no—
540C2×C4—208no—
541C2×C4—301no—
542C2×C4—301no—
543C2×C4—301no—
544C2×C4—302no—
545C2×C4—301no—
546C2×C4—302no—
547C2×C4—301no—
548C2×C4—302no—
549C2×C4—608no—
550C2×C4C2×D5×Dic312yes—
551C2×C4C2×#120312yes—
552C2×C4C2×#120412yes—
553C2×C3—28no—
554C2×C3C4×#71111yescharacteristic
555C2×C3#6587311yescharacteristic
556C2×C3#6587711yescharacteristic
557C2×C3#6587911yescharacteristic
558C2×C3C22×#68311yescharacteristic
559C2×C3#6614011yescharacteristic
560C2×C3#6616311yescharacteristic
561C5#8233311yescharacteristic, complemented, Sylow
562C22—24no—
563C22—24no—
564C22—24no—
565C22—24no—
566C22—24no—
567C22—24no—
568C22C2×#666818yes—
569C22D3×#71111yescharacteristic
570C22#9202411yescharacteristic
571C22#9202511yescharacteristic
572C22#9202611yescharacteristic
573C22C22×D5×Dic311yescharacteristic
574C22C22×#120311yescharacteristic
575C22C22×#120411yescharacteristic
576C4—62no—
577C4—102no—
578C4—102no—
579C4—104no—
580C4—122no—
581C4—121no—
582C4—302no—
583C4—601no—
584C4—602no—
585C4C2×#666814yes—
586C3#1061406511yescharacteristic, complemented, Sylow
587C2—28no—
588C2Dic3×#71111yescharacteristic
589C2#1175491011yescharacteristic
590C2#1175497511yescharacteristic
591C2#1175498211yescharacteristic
592C2#1175501211yescharacteristic
593C2#1175501411yescharacteristic
594C2C22×#666811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
Fitting, prime radicalC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11749515C2semidirect
5. #11749511C2semidirect
6. #11749506C2semidirect
7. C2×#90994C2semidirect
8. #11748865C2semidirect
9. #11748857C2semidirect
10. C4×#6668C2semidirect
11. #11748613C2semidirect
26. C3×D4×Dic5C4semidirect
70. C22×C3×Dic5C2×C4semidirect
80. C3×C22⋊Dic5C2×C4semidirect
81. C3×C4⋊Dic5C2×C4semidirect
82. C3×C4×Dic5C2×C4semidirect
109. D4×Dic5Dic3semidirect
133. C3×C5×D4C4⋊C4semidirect
212. C22×Dic5C2×Dic3semidirect
220. C22⋊Dic5C2×Dic3semidirect
222. C4⋊Dic5C2×Dic3semidirect
228. C4×Dic5C2×Dic3semidirect
308. C5×D4C4⋊Dic3semidirect
384. C3×D4#683semidirect
478. C3×C5#2349semidirect
519. D4#6668semidirect
561. C5#82333semidirect
586. C3#10614065semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic152
C2×C5×D4×Dic32
C2×C3×D4×Dic52
#117495152
#117495112
#117495062
C2×#909942
#117488652
#117488572
C4×#66682
#117486132
#106140653
#823335