Finite Group Databasebeta

← #14329026

Subgroups — #14329026

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C5×D4C211yesmaximal, characteristic, complemented
2C2×#91827C211yesmaximal, characteristic
3C2×#91781C211yesmaximal, characteristic, complemented
4#11751322C211yesmaximal, characteristic, complemented
5#11751314C212yesmaximal, complemented
6C4×#6719C212yesmaximal, complemented
7C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
8#11751058C212yesmaximal, complemented
9#11751045C212yesmaximal, complemented
10C4×#6714C211yesmaximal, characteristic, complemented
11#11751029C211yesmaximal, characteristic, complemented
12#10614072—31nomaximal, Hall
13C22×C3×C5×D4C2211yescharacteristic
14C23×C3×C4×C5C2212yes—
15C22×#1220C2212yes—
16C22×C4×D15C2211yescharacteristic
17C3×C4×C5×D4—24no—
18C2×C3×C5×C4⋊C4C2211yescharacteristic
19C2×C3×C5×C22⋊C4C2212yes—
20C2×C3×C42×C5C2211yescharacteristic
21C2×#6719C2212yes—
22C2×#6719C2212yes—
23C2×#6719C2212yes—
24#91827C418yescomplemented
25C2×#6714C2211yescharacteristic
26C2×#6714C2211yescharacteristic
27C2×#6714C2212yes—
28C2×C4⋊Dic15C2211yescharacteristic
29C2×C4⋊Dic15C2211yescharacteristic
30C2×#6712C2212yes—
31C2×C4×Dic15C2211yescharacteristic
32C2×C4×Dic15C2212yes—
33C2×C4×Dic15C2212yes—
34#91781—24no—
35#91115C2212yes—
36#91115C2211yescharacteristic
37#91115C2211yescharacteristic
38#91115C2212yes—
39#82341—51nomaximal, Hall
40C2×C4×C5×D4D311yescharacteristic, complemented
41C2×#4084—31no—
42C2×#4038—31no—
43#65510—31no—
44#65502—32no—
45C4×C22⋊Dic5—32no—
46C4⋊C4×Dic5—31no—
47#65246—32no—
48#65233—32no—
49C4×#685—31no—
50#65217—31no—
51C24×C3×C5C2312yes—
52C23×D15C2311yescharacteristic
53C2×C3×C5×D4—22no—
54C2×C3×C5×D4—22no—
55C2×C3×C5×D4C2×C414yes—
56C22×C3×C4×C5—24no—
57C22×C3×C4×C5—24no—
58C22×C3×C4×C5—42no—
59C22×C3×C4×C5C2311yescharacteristic
60C22×C3×C4×C5C2312yes—
61C22×C3×C4×C5C2311yescharacteristic
62C22×C3×C4×C5C2311yescharacteristic
63C2×#1220—42no—
64C2×#1220—42no—
65C2×#1220C2×C418yescomplemented
66C22×Dic15C2312yes—
67C22×Dic15C2311yescharacteristic
68C22×Dic15C2311yescharacteristic
69C22×Dic15C2312yes—
70C22×Dic15C2311yescharacteristic
71C2×C4×D15—22no—
72C2×C4×D15—22no—
73C2×C4×D15C2×C414yescomplemented
74C3×C5×C4⋊C4D414yescomplemented
75C3×C5×C22⋊C4—24no—
76C3×C42×C5—22no—
77#6719—24no—
78#6719—42no—
79#6719C2×C418yescomplemented
80#6714—24no—
81#6714—22no—
82#6714—22no—
83C4⋊Dic15—22no—
84C4⋊Dic15C2×C414yescomplemented
85#6712—42no—
86C4×Dic15—24no—
87C4×Dic15—22no—
88C4×Dic15—42no—
89C2×C3×C4×D4D511yescharacteristic, complemented
90C2×#938—51no—
91C2×#892—51no—
92#5221—51no—
93#5213—52no—
94C4×#217—52no—
95Dic3×C4⋊C4—51no—
96#4957—52no—
97#4944—52no—
98C4×(C2×D3)⋊C4—51no—
99#4928—51no—
100C22×C5×D4C2×D311yescharacteristic
101C23×C4×C5C2×D312yes—
102C22×C22⋊D5—32no—
103C22×C4×D5—31no—
104C4×C5×D4—24no—
105C2×C5×C4⋊C4C2×D311yescharacteristic
106C2×C5×C22⋊C4C2×D312yes—
107C2×C42×C5C2×D311yescharacteristic
108C2×C22⋊Dic5—32no—
109C2×C22⋊Dic5—32no—
110C2×C22⋊Dic5—32no—
111#4084—38no—
112C2×#685—32no—
113C2×#685—31no—
114C2×#685—31no—
115C2×C4⋊Dic5—31no—
116C2×C4⋊Dic5—31no—
117C2×#683—32no—
118C2×C4×Dic5—32no—
119C2×C4×Dic5—31no—
120C2×C4×Dic5—32no—
121#4038—64no—
122#3963—32no—
123#3963—31no—
124#3963—31no—
125#3963—32no—
126#2363—151noSylow
127C23×C3×C5—22no—
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5—22no—
131C23×C3×C5—22no—
132C23×C3×C5—22no—
133C23×C3×C5C22×C414yes—
134C23×C3×C5C2411yescharacteristic
135C22×D15—21no—
136C22×D15—21no—
137C22×D15—21no—
138C22×D15—21no—
139C22×D15—21no—
140C22×D15—21no—
141C22×D15C22×C412yes—
142C3×C5×D4—28no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—22no—
145C2×C3×C4×C5—22no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5—21no—
148C2×C3×C4×C5—21no—
149C2×C3×C4×C5—21no—
150C2×C3×C4×C5—48no—
151C2×C3×C4×C5C22×C412yes—
152C2×C3×C4×C5C2×D414yes—
153C2×C3×C4×C5C2×D412yes—
154C2×C3×C4×C5#4112yes—
155C2×C3×C4×C5#4112yes—
156#1220—48no—
157C2×Dic15—21no—
158C2×Dic15—21no—
159C2×Dic15—21no—
160C2×Dic15—21no—
161C2×Dic15—22no—
162C2×Dic15—22no—
163C2×Dic15—22no—
164C2×Dic15—21no—
165C2×Dic15—21no—
166C2×Dic15—22no—
167C2×Dic15—22no—
168C2×Dic15—21no—
169C2×Dic15C22×C414yes—
170C2×Dic15C22×C412yes—
171C2×Dic15#4112yes—
172C4×D15—28no—
173C22×C3×D4C2×D511yescharacteristic
174C23×C3×C4C2×D512yes—
175C22×#67—52no—
176C22×C4×D3—51no—
177C3×C4×D4—24no—
178C2×C3×C4⋊C4C2×D511yescharacteristic
179C2×C3×C22⋊C4C2×D512yes—
180C2×C3×C42C2×D511yescharacteristic
181C2×#217—52no—
182C2×#217—52no—
183C2×#217—52no—
184#938—58no—
185C2×(C2×D3)⋊C4—51no—
186C2×(C2×D3)⋊C4—51no—
187C2×(C2×D3)⋊C4—52no—
188C2×C4⋊Dic3—51no—
189C2×C4⋊Dic3—51no—
190C2×Dic3⋊C4—52no—
191C2×C4×Dic3—51no—
192C2×C4×Dic3—52no—
193C2×C4×Dic3—52no—
194#892—104no—
195C3⋊#95—52no—
196C3⋊#95—51no—
197C3⋊#95—51no—
198C3⋊#95—52no—
199C24×C5C22×D312yes—
200C23×D5—31no—
201C2×C5×D4—22no—
202C2×C5×D4—22no—
203C2×C5×D4C4×D314yes—
204C22×C4×C5—24no—
205C22×C4×C5—24no—
206C22×C4×C5—42no—
207C22×C4×C5C22×D311yescharacteristic
208C22×C4×C5C22×D311yescharacteristic
209C22×C4×C5C22×D312yes—
210C22×C4×C5C22×D311yescharacteristic
211C2×C22⋊D5—38no—
212C2×C22⋊D5—122no—
213C2×C22⋊D5—122no—
214C22×Dic5—31no—
215C22×Dic5—31no—
216C22×Dic5—32no—
217C22×Dic5—31no—
218C22×Dic5—32no—
219C2×C4×D5—34no—
220C2×C4×D5—62no—
221C2×C4×D5—62no—
222C5×C4⋊C4#6714yescomplemented
223C5×C22⋊C4—24no—
224C42×C5—22no—
225C22⋊Dic5—38no—
226C22⋊Dic5—64no—
227C22⋊Dic5—122no—
228#685—62no—
229#685—62no—
230#685—64no—
231C4⋊Dic5—34no—
232C4⋊Dic5—62no—
233#683—122no—
234C4×Dic5—62no—
235C4×Dic5—64no—
236C4×Dic5—122no—
237C2×#121—151no—
238C2×C4×D4D1511yescharacteristic, complemented
239C2×#117—151no—
240#390—151no—
241#390—152no—
242#389—151no—
243#388—152no—
244#386—152no—
245C4×C4⋊C4—151no—
246C4×C22⋊C4—152no—
247C4×C22⋊C4—151no—
248C22×C3×C5—24no—
249C22×C3×C5—24no—
250C22×C3×C5—24no—
251C22×C3×C5—42no—
252C22×C3×C5—42no—
253C22×C3×C5—42no—
254C22×C3×C5—42no—
255C22×C3×C5C23×C411yescharacteristic
256C22×C3×C5C22×D411yescharacteristic
257C22×C3×C5C2×#4111yescharacteristic
258C22×C3×C5C2×#4111yescharacteristic
259C22×C3×C5C2×#4111yescharacteristic
260C22×C3×C5H(5,𝔽2)11yescharacteristic
261C22×C3×C5H(5,𝔽2)11yescharacteristic
262C2×D15—22no—
263C2×D15—22no—
264C2×D15—22no—
265C2×D15—41no—
266C2×D15—41no—
267C2×D15—41no—
268C2×D15—41no—
269C3×C4×C5—22no—
270C3×C4×C5—24no—
271C3×C4×C5—41no—
272C3×C4×C5C4×D414yes—
273Dic15—22no—
274Dic15—24no—
275Dic15—22no—
276Dic15—42no—
277Dic15—41no—
278C24×C3C22×D512yes—
279C23×D3—51no—
280C2×C3×D4—22no—
281C2×C3×D4—22no—
282C2×C3×D4C4×D514yes—
283C22×C3×C4—24no—
284C22×C3×C4—24no—
285C22×C3×C4—42no—
286C22×C3×C4C22×D511yescharacteristic
287C22×C3×C4C22×D511yescharacteristic
288C22×C3×C4C22×D512yes—
289C22×C3×C4C22×D511yescharacteristic
290C2×#67—58no—
291C2×#67—202no—
292C2×#67—202no—
293C22×Dic3—51no—
294C22×Dic3—52no—
295C22×Dic3—51no—
296C22×Dic3—51no—
297C22×Dic3—52no—
298C2×C4×D3—54no—
299C2×C4×D3—102no—
300C2×C4×D3—102no—
301C3×C4⋊C4C22⋊D514yescomplemented
302C3×C22⋊C4—24no—
303C3×C42—22no—
304#217—58no—
305#217—104no—
306#217—202no—
307(C2×D3)⋊C4—102no—
308(C2×D3)⋊C4—102no—
309(C2×D3)⋊C4—104no—
310C4⋊Dic3—54no—
311C4⋊Dic3—102no—
312Dic3⋊C4—202no—
313C4×Dic3—102no—
314C4×Dic3—104no—
315C4×Dic3—202no—
316C23×C5—22no—
317C23×C5—22no—
318C23×C5—22no—
319C23×C5—22no—
320C23×C5—22no—
321C23×C5—22no—
322C23×C5C2×C4×D314yes—
323C23×C5C23×D311yescharacteristic
324C22×D5—32no—
325C22×D5—61no—
326C22×D5—61no—
327C22×D5—61no—
328C22×D5—61no—
329C22×D5—61no—
330C22×D5—61no—
331C5×D4—28no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—21no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—48no—
340C2×C4×C5C2×C4×D312yes—
341C2×C4×C5#23512yes—
342C2×C4×C5#23712yes—
343C2×C4×C5C2×#6714yes—
344C2×C4×C5C2×#6712yes—
345C22⋊D5—128no—
346C2×Dic5—34no—
347C2×Dic5—32no—
348C2×Dic5—32no—
349C2×Dic5—61no—
350C2×Dic5—61no—
351C2×Dic5—61no—
352C2×Dic5—62no—
353C2×Dic5—62no—
354C2×Dic5—61no—
355C2×Dic5—61no—
356C2×Dic5—61no—
357C2×Dic5—62no—
358C2×Dic5—62no—
359C2×Dic5—61no—
360C2×Dic5—62no—
361C4×D5—68no—
362C22×D4—152no—
363C22×D4C2×D1511yescharacteristic
364C23×C4—151no—
365C23×C4C2×D1512yes—
366#121—158no—
367C4×D4—24no—
368#117—304no—
369C2×C4⋊C4—151no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—152no—
372C2×C4⋊C4C2×D1511yescharacteristic
373C2×C22⋊C4—152no—
374C2×C22⋊C4—152no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4—151no—
377C2×C22⋊C4—151no—
378C2×C22⋊C4—152no—
379C2×C22⋊C4C2×D1512yes—
380C2×C42—152no—
381C2×C42—151no—
382C2×C42—152no—
383C2×C42C2×D1511yescharacteristic
384#95—151no—
385#95—152no—
386#95—151no—
387#95—152no—
388C2×C3×C5—44no—
389C2×C3×C5C2×C4×D411yescharacteristic
390C2×C3×C5C4×#4111yescharacteristic
391C2×C3×C5#51811yescharacteristic
392C2×C3×C5#54611yescharacteristic
393C2×C3×C5#55011yescharacteristic
394C2×C3×C5#55311yescharacteristic
395C2×C3×C5#55511yescharacteristic
396D15—42no—
397C23×C3—22no—
398C23×C3—22no—
399C23×C3—22no—
400C23×C3—22no—
401C23×C3—22no—
402C23×C3—22no—
403C23×C3C2×C4×D514yes—
404C23×C3C23×D511yescharacteristic
405C22×D3—52no—
406C22×D3—101no—
407C22×D3—101no—
408C22×D3—101no—
409C22×D3—101no—
410C22×D3—101no—
411C22×D3—101no—
412C3×D4—28no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—48no—
421C2×C3×C4C2×C4×D512yes—
422C2×C3×C4#70912yes—
423C2×C3×C4#71112yes—
424C2×C3×C4C2×C22⋊D514yes—
425C2×C3×C4C2×C22⋊D512yes—
426#67—208no—
427C2×Dic3—54no—
428C2×Dic3—52no—
429C2×Dic3—52no—
430C2×Dic3—101no—
431C2×Dic3—101no—
432C2×Dic3—101no—
433C2×Dic3—102no—
434C2×Dic3—102no—
435C2×Dic3—101no—
436C2×Dic3—101no—
437C2×Dic3—101no—
438C2×Dic3—102no—
439C2×Dic3—102no—
440C2×Dic3—101no—
441C2×Dic3—102no—
442C4×D3—108no—
443C22×C5—24no—
444C22×C5—24no—
445C22×C5—24no—
446C22×C5—42no—
447C22×C5—42no—
448C22×C5—42no—
449C22×C5—42no—
450C22×C5C22×C4×D311yescharacteristic
451C22×C5C2×#23511yescharacteristic
452C22×C5C2×#23711yescharacteristic
453C22×C5#100411yescharacteristic
454C22×C5D3×#4111yescharacteristic
455C22×C5#100911yescharacteristic
456C22×C5C22×#6711yescharacteristic
457C2×D5—62no—
458C2×D5—62no—
459C2×D5—62no—
460C2×D5—121no—
461C2×D5—121no—
462C2×D5—121no—
463C2×D5—121no—
464C4×C5—22no—
465C4×C5—24no—
466C4×C5—41no—
467C4×C5C4×#6714yes—
468Dic5—62no—
469Dic5—64no—
470Dic5—62no—
471Dic5—121no—
472Dic5—122no—
473C24—151no—
474C24C22×D1512yes—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—158no—
478C2×D4—602no—
479C2×D4—602no—
480C2×D4C4×D1514yes—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—42no—
484C22×C4—151no—
485C22×C4—152no—
486C22×C4—151no—
487C22×C4—154no—
488C22×C4—151no—
489C22×C4—152no—
490C22×C4—302no—
491C22×C4—302no—
492C22×C4C22×D1511yescharacteristic
493C22×C4C22×D1511yescharacteristic
494C22×C4C22×D1512yes—
495C22×C4C22×D1511yescharacteristic
496C4⋊C4—154no—
497C4⋊C4—302no—
498C4⋊C4—602no—
499C4⋊C4#122014yescomplemented
500C22⋊C4—24no—
501C22⋊C4—158no—
502C22⋊C4—302no—
503C22⋊C4—304no—
504C22⋊C4—302no—
505C22⋊C4—304no—
506C22⋊C4—602no—
507C42—22no—
508C42—302no—
509C42—304no—
510C42—602no—
511C3×C5#236311yescharacteristic, complemented, Hall
512C22×C3—24no—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—42no—
516C22×C3—42no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3C22×C4×D511yescharacteristic
520C22×C3C2×#70911yescharacteristic
521C22×C3C2×#71111yescharacteristic
522C22×C3#414411yescharacteristic
523C22×C3D5×#4111yescharacteristic
524C22×C3#414911yescharacteristic
525C22×C3C22×C22⋊D511yescharacteristic
526C2×D3—102no—
527C2×D3—102no—
528C2×D3—102no—
529C2×D3—201no—
530C2×D3—201no—
531C2×D3—201no—
532C2×D3—201no—
533C3×C4—22no—
534C3×C4—24no—
535C3×C4—41no—
536C3×C4C4×C22⋊D514yes—
537Dic3—102no—
538Dic3—104no—
539Dic3—102no—
540Dic3—201no—
541Dic3—202no—
542C2×C5—44no—
543C2×C5C4×#23711yescharacteristic
544C2×C5#554511yescharacteristic
545C2×C5#555811yescharacteristic
546C2×C5#556311yescharacteristic
547C2×C5C2×C4×#6711yescharacteristic
548C2×C5#580611yescharacteristic
549C2×C5#583411yescharacteristic
550D5—122no—
551C23—22no—
552C23—22no—
553C23—22no—
554C23—22no—
555C23—22no—
556C23—22no—
557C23—152no—
558C23—301no—
559C23—301no—
560C23—301no—
561C23—301no—
562C23—301no—
563C23—301no—
564C23C2×C4×D1514yes—
565C23C23×D1511yescharacteristic
566D4—28no—
567D4—608no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—48no—
576C2×C4—152no—
577C2×C4—154no—
578C2×C4—152no—
579C2×C4—301no—
580C2×C4—301no—
581C2×C4—301no—
582C2×C4—302no—
583C2×C4—302no—
584C2×C4—301no—
585C2×C4—308no—
586C2×C4—301no—
587C2×C4—301no—
588C2×C4—302no—
589C2×C4—301no—
590C2×C4—302no—
591C2×C4—302no—
592C2×C4C2×C4×D1512yes—
593C2×C4#681712yes—
594C2×C4#681912yes—
595C2×C4C2×#122014yes—
596C2×C4C2×#122012yes—
597C2×C3—44no—
598C2×C3C4×#71111yescharacteristic
599C2×C3#6587911yescharacteristic
600C2×C3#6589211yescharacteristic
601C2×C3#6589711yescharacteristic
602C2×C3C2×C4×C22⋊D511yescharacteristic
603C2×C3#6614011yescharacteristic
604C2×C3#6616811yescharacteristic
605D3—202no—
606C5#8234111yescharacteristic, complemented, Sylow
607C22—24no—
608C22—24no—
609C22—24no—
610C22—42no—
611C22—42no—
612C22—42no—
613C22—42no—
614C22—302no—
615C22—302no—
616C22—302no—
617C22—601no—
618C22—601no—
619C22—601no—
620C22—601no—
621C22C22×C4×D1511yescharacteristic
622C22C2×#681711yescharacteristic
623C22C2×#681911yescharacteristic
624C22#9209511yescharacteristic
625C22#41×D1511yescharacteristic
626C22#9210011yescharacteristic
627C22C22×#122011yescharacteristic
628C4—22no—
629C4—24no—
630C4—41no—
631C4—302no—
632C4—304no—
633C4—302no—
634C4—601no—
635C4—602no—
636C4C4×#122014yes—
637C3#1061407211yescharacteristic, complemented, Sylow
638C2—44no—
639C2—602no—
640C2C4×#681911yescharacteristic
641C2#1175630411yescharacteristic
642C2#1175631711yescharacteristic
643C2#1175632211yescharacteristic
644C2C2×C4×#122011yescharacteristic
645C2#1175656511yescharacteristic
646C2#1175659311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC2×C3×C4×C5×D4C2
socle, cosocleC23×C3×C5C24
prime radicalC2×#91827C2
hypercenterC2×C4×D4D15
hypocenterC3×C5#2363
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×C5×D4C2semidirect
3. C2×#91781C2semidirect
4. #11751322C2semidirect
5. #11751314C2semidirect
6. C4×#6719C2semidirect
7. C4⋊C4×Dic15C2semidirect
8. #11751058C2semidirect
9. #11751045C2semidirect
10. C4×#6714C2semidirect
11. #11751029C2semidirect
24. #91827C4semidirect
40. C2×C4×C5×D4D3semidirect
65. C2×#1220C2×C4semidirect
73. C2×C4×D15C2×C4semidirect
74. C3×C5×C4⋊C4D4semidirect
79. #6719C2×C4semidirect
84. C4⋊Dic15C2×C4semidirect
89. C2×C3×C4×D4D5semidirect
222. C5×C4⋊C4#67semidirect
238. C2×C4×D4D15semidirect
301. C3×C4⋊C4C22⋊D5semidirect
499. C4⋊C4#1220semidirect
511. C3×C5#2363semidirect
606. C5#82341semidirect
637. C3#10614072semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C5×D42
C2×#918272
C2×#917812
#117513222
#117513142
C4×#67192
C4⋊C4×Dic152
#117510582
#117510452
C4×#67142
#117510292
#106140723
#823415