Finite Group Databasebeta

← #14319953

Subgroups — #14319953

Order 1920.

2176 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
1C22×C4×D3×D5C211yesmaximal, characteristic
2C2×#91400C212yesmaximal, complemented
3#11750767C211yesmaximal, characteristic, complemented
4C5×#4664C211yesmaximal, characteristic, complemented
5C3×#64956C211yesmaximal, characteristic, complemented
6#11748940C212yesmaximal
7#11748884C212yesmaximal, complemented
8#11748876C212yesmaximal, complemented
9#11748777C211yesmaximal, characteristic, complemented
10#11748738C211yesmaximal, characteristic, complemented
11#11748670C211yesmaximal, characteristic, complemented
12#10605781—31nomaximal, Hall
13C23×D3×D5C2211yescharacteristic
14C22×C4×D15C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C22×#1200C2211yescharacteristic
18C22×D3×Dic5C2211yescharacteristic
19C22×D5×Dic3C2211yescharacteristic
20C2×C4×D3×D5—28no—
21C2×C4×D3×D5C418yescomplemented
22C2×#6714C2212yes—
23C2×C4×Dic15C2212yescomplemented
24C2×C5×(C2×D3)⋊C4C2212yes—
25C2×C3×#685C2212yes—
26C2×C3×#683C2212yescomplemented
27C2×#6668C2212yescomplemented
28C2×#6667C2212yes—
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×#6665C2212yes—
31C2×Dic3×Dic5C2212yescomplemented
32#91400—28no—
33C3×C5×#95C2211yescharacteristic, complemented
34#91115C2211yescharacteristic, complemented
35C5×C3⋊#95C2212yescomplemented
36C5×C3⋊#95C2211yescharacteristic, complemented
37C3×#3963C2211yescharacteristic, complemented
38#90994C2212yescomplemented
39#73862—51nomaximal, Hall
40C23×C4×D5—31no—
41C2×#4023—32no—
42C5×#381—31no—
43#65500—31no—
44#65244—32no—
45#64956—32no—
46#64956—31no—
47#64956D311yescharacteristic, complemented
48#64955—32no—
49#64955—31no—
50#64955—31no—
51C23×D15C2311yescharacteristic
52C23×C5×D3C2311yescharacteristic
53C23×C3×D5C2311yescharacteristic
54C22×D3×D5—24no—
55C22×D3×D5—24no—
56C22×D3×D5—22no—
57C22×D3×D5—22no—
58C22×D3×D5C2×C414yes—
59C22×C3×C4×C5C2312yes—
60C22×C3×C4×C5C2311yescharacteristic
61C22×Dic15C2312yes—
62C22×Dic15C2311yescharacteristic
63C2×C4×D15—24no—
64C2×C4×D15C2×C414yes—
65C22×C5×Dic3C2312yes—
66C22×C5×Dic3C2311yescharacteristic
67C2×C4×C5×D3—24no—
68C2×C4×C5×D3C2×C414yes—
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2311yescharacteristic
71C2×C3×C4×D5—24no—
72C2×C3×C4×D5C2×C414yes—
73C2×#1200—24no—
74C2×#1200C2×C414yes—
75C2×D3×Dic5C2×C414yes—
76C2×D3×Dic5D418yes—
77C2×D5×Dic3—24no—
78C2×D5×Dic3C2×C414yes—
79C4×D3×D5—232no—
80#6714—24no—
81C4×Dic15—24no—
82C5×(C2×D3)⋊C4—24no—
83C3×#685—24no—
84C3×#683—24no—
85#6668—24no—
86#6667—24no—
87(C2×D3)⋊Dic5—24no—
88#6665—24no—
89Dic3×Dic5—24no—
90C23×C4×D3—51no—
91C2×#892—52no—
92C3×#380—51no—
93#5212—51no—
94#4987—52no—
95#4955—52no—
96Dic3×C22⋊C4—52no—
97#4666—51no—
98#4666—51no—
99#4664—51no—
100#4664D511yescharacteristic, complemented
101C24×D5—31no—
102C23×C4×C5—31no—
103C23×Dic5—31no—
104C22×C4×D5—31no—
105C22×C4×D5—31no—
106C22×C4×D5—31no—
107C22×C4×D5—38no—
108C22×C4×D5—68no—
109C22×C4×D5C2×D311yescharacteristic
110C2×C5×C22⋊C4—32no—
111C2×C22⋊Dic5—32no—
112C2×#685—32no—
113C2×#685—32no—
114C2×#685—32no—
115C2×#685C2×D312yes—
116C2×#683—32no—
117C2×#683C2×D312yescomplemented
118C2×C4×Dic5—32no—
119C2×C4×Dic5—32no—
120#4023—68no—
121C5×#95—32no—
122C5×#95—31no—
123C5×#95C2×D311yescharacteristic, complemented
124#3963—31no—
125#3963—32no—
126#3963C2×D311yescharacteristic, complemented
127#2280—151noSylow
128C23×C3×C5C2411yescharacteristic
129C22×D15—22no—
130C22×D15—21no—
131C22×D15—21no—
132C22×D15C22×C412yes—
133C22×D15#4114yes—
134C22×C5×D3—21no—
135C22×C5×D3—21no—
136C22×C5×D3—22no—
137C22×C5×D3C22×C412yes—
138C22×C5×D3C2×D414yes—
139C22×C3×D5—22no—
140C22×C3×D5—22no—
141C22×C3×D5C22×C412yes—
142C22×C3×D5#4112yes—
143C22×C3×D5#4112yes—
144C2×D3×D5—216no—
145C2×D3×D5—216no—
146C2×D3×D5—28no—
147C2×D3×D5—28no—
148C2×D3×D5—28no—
149C2×C3×C4×C5—22no—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5C22×C412yes—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15C22×C412yes—
158C2×Dic15C2×D414yes—
159C4×D15—28no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3C22×C412yes—
165C4×C5×D3—28no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5C22×C412yes—
170C2×C3×Dic5C2×D414yes—
171C3×C4×D5—28no—
172#1200—28no—
173D3×Dic5C22⋊C4116yescomplemented
174D5×Dic3—28no—
175C24×D3—51no—
176C23×C3×C4—51no—
177C23×Dic3—51no—
178C22×C4×D3—51no—
179C22×C4×D3—51no—
180C22×C4×D3—51no—
181C22×C4×D3—58no—
182C22×C4×D3—108no—
183C22×C4×D3C2×D511yescharacteristic
184C2×C3×C4⋊C4—52no—
185C2×C3×C22⋊C4—52no—
186C2×#217—52no—
187C2×(C2×D3)⋊C4—52no—
188C2×(C2×D3)⋊C4—52no—
189C2×(C2×D3)⋊C4—52no—
190C2×(C2×D3)⋊C4C2×D512yes—
191C2×C4⋊Dic3—52no—
192C2×C4×Dic3—52no—
193C2×C4×Dic3—52no—
194#892—108no—
195C3×#95—51no—
196C3×#95C2×D511yescharacteristic, complemented
197C3⋊#95—51no—
198C3⋊#95—52no—
199C3⋊#95C2×D511yescharacteristic, complemented
200C3⋊#95C2×D512yescomplemented
201C24×C5—31no—
202C23×D5—31no—
203C23×D5—34no—
204C23×D5—64no—
205C23×D5—64no—
206C23×D5—62no—
207C23×D5—62no—
208C23×D5C22×D311yescharacteristic
209C22×C4×C5—31no—
210C22×C4×C5—34no—
211C22×C4×C5—32no—
212C22×C4×C5—64no—
213C22×C4×C5C22×D312yes—
214C22×C4×C5C22×D311yescharacteristic
215C22×Dic5—31no—
216C22×Dic5—34no—
217C22×Dic5—38no—
218C22×Dic5—32no—
219C22×Dic5C22×D312yes—
220C22×Dic5C22×D311yescharacteristic
221C2×C4×D5—24no—
222C2×C4×D5—34no—
223C2×C4×D5—34no—
224C2×C4×D5—34no—
225C2×C4×D5—632no—
226C2×C4×D5—64no—
227C2×C4×D5—64no—
228C2×C4×D5—64no—
229C2×C4×D5C4×D314yes—
230C5×C22⋊C4—64no—
231C22⋊Dic5—64no—
232#685—24no—
233#685—64no—
234#685—64no—
235#685—64no—
236#683—24no—
237#683—64no—
238C4×Dic5—64no—
239C4×Dic5—64no—
240C24×C4—151no—
241C2×#117—152no—
242#381—31no—
243#381—151no—
244#380—51no—
245#380—152no—
246#380—151no—
247#379—152no—
248C4×C22⋊C4—151no—
249C4×C22⋊C4—152no—
250C4×C22⋊C4—151no—
251C22×C3×C5C23×C411yescharacteristic
252C22×C3×C5C22×D412yes—
253C22×C3×C5C2×#4111yescharacteristic
254C22×C3×C5C2×#4111yescharacteristic
255C22×C3×C5C2×#4112yes—
256C2×D15—22no—
257C2×D15—22no—
258C2×D15—24no—
259C2×D15—24no—
260C2×D15#11714yescomplemented
261C2×C5×D3—22no—
262C2×C5×D3—22no—
263C2×C5×D3—24no—
264C2×C5×D3—24no—
265C2×C5×D3C2×C22⋊C414yes—
266C2×C3×D5—22no—
267C2×C3×D5—22no—
268C2×C3×D5—24no—
269C2×C3×D5—24no—
270C2×C3×D5#11714yescomplemented
271D3×D5—232no—
272C3×C4×C5—22no—
273C3×C4×C5—42no—
274Dic15—42no—
275Dic15C2×C22⋊C414yes—
276C3×Dic5—42no—
277C3×Dic5C2×C22⋊C414yes—
278C5×Dic3—22no—
279C5×Dic3—42no—
280C24×C3—51no—
281C23×D3—51no—
282C23×D3—54no—
283C23×D3—104no—
284C23×D3—102no—
285C23×D3—102no—
286C23×D3—104no—
287C23×D3C22×D511yescharacteristic
288C22×C3×C4—51no—
289C22×C3×C4—54no—
290C22×C3×C4—52no—
291C22×C3×C4—104no—
292C22×C3×C4C22×D512yes—
293C22×C3×C4C22×D511yescharacteristic
294C22×Dic3—51no—
295C22×Dic3—54no—
296C22×Dic3—52no—
297C22×Dic3—104no—
298C22×Dic3C22×D512yes—
299C22×Dic3C22×D511yescharacteristic
300C2×C4×D3—24no—
301C2×C4×D3—54no—
302C2×C4×D3—58no—
303C2×C4×D3—54no—
304C2×C4×D3—54no—
305C2×C4×D3—1032no—
306C2×C4×D3—104no—
307C2×C4×D3—104no—
308C2×C4×D3C4×D514yes—
309C3×C4⋊C4—104no—
310C3×C22⋊C4—104no—
311#217—104no—
312(C2×D3)⋊C4—24no—
313(C2×D3)⋊C4—104no—
314(C2×D3)⋊C4—104no—
315(C2×D3)⋊C4—104no—
316C4⋊Dic3—104no—
317C4×Dic3—104no—
318C4×Dic3—104no—
319C23×C5—32no—
320C23×C5—34no—
321C23×C5—61no—
322C23×C5—61no—
323C23×C5—62no—
324C23×C5C23×D311yescharacteristic
325C22×D5—22no—
326C22×D5—22no—
327C22×D5—32no—
328C22×D5—34no—
329C22×D5—68no—
330C22×D5—68no—
331C22×D5—616no—
332C22×D5—616no—
333C22×D5—62no—
334C22×D5—61no—
335C22×D5—61no—
336C22×D5—68no—
337C22×D5C2×C4×D312yes—
338C22×D5#23712yes—
339C22×D5#23912yes—
340C2×C4×C5—22no—
341C2×C4×C5—22no—
342C2×C4×C5—22no—
343C2×C4×C5—22no—
344C2×C4×C5—32no—
345C2×C4×C5—68no—
346C2×C4×C5—62no—
347C2×C4×C5—62no—
348C2×C4×C5—62no—
349C2×C4×C5—62no—
350C2×C4×C5C2×C4×D312yes—
351C2×Dic5—22no—
352C2×Dic5—22no—
353C2×Dic5—22no—
354C2×Dic5—32no—
355C2×Dic5—34no—
356C2×Dic5—316no—
357C2×Dic5—62no—
358C2×Dic5—62no—
359C2×Dic5—62no—
360C2×Dic5C2×C4×D312yes—
361C2×Dic5D3×D414yes—
362C4×D5—28no—
363C4×D5—68no—
364C4×D5—68no—
365C4×D5—68no—
366C25—151no—
367C23×C4—31no—
368C23×C4—51no—
369C23×C4—151no—
370C23×C4—158no—
371C23×C4—151no—
372C23×C4—151no—
373C23×C4—151no—
374C23×C4—308no—
375#117—308no—
376C2×C4⋊C4—52no—
377C2×C4⋊C4—152no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—52no—
380C2×C22⋊C4—152no—
381C2×C22⋊C4—152no—
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C42—152no—
385C2×C42—152no—
386#95—32no—
387#95—31no—
388#95—51no—
389#95—152no—
390#95—151no—
391#95D3×D511yescharacteristic, complemented
392C2×C3×C5C22×C22⋊C411yescharacteristic
393C2×C3×C5C2×#11711yescharacteristic
394C2×C3×C5C2×#11711yescharacteristic
395C2×C3×C5#52512yes—
396C2×C3×C5#52512yes—
397D15—24no—
398C3×D5—24no—
399C5×D3—24no—
400C23×C3—52no—
401C23×C3—52no—
402C23×C3—52no—
403C23×C3—102no—
404C23×C3—102no—
405C23×C3C23×D511yescharacteristic
406C22×D3—22no—
407C22×D3—21no—
408C22×D3—21no—
409C22×D3—52no—
410C22×D3—54no—
411C22×D3—108no—
412C22×D3—108no—
413C22×D3—1016no—
414C22×D3—1016no—
415C22×D3—102no—
416C22×D3—101no—
417C22×D3—101no—
418C22×D3—108no—
419C22×D3C2×C4×D512yes—
420C22×D3D4×D514yes—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—52no—
426C2×C3×C4—54no—
427C2×C3×C4—108no—
428C2×C3×C4—102no—
429C2×C3×C4—102no—
430C2×C3×C4—102no—
431C2×C3×C4C2×C4×D512yes—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—52no—
437C2×Dic3—54no—
438C2×Dic3—108no—
439C2×Dic3—102no—
440C2×Dic3—102no—
441C2×Dic3—102no—
442C2×Dic3C2×C4×D512yes—
443C4×D3—28no—
444C4×D3—516no—
445C4×D3—108no—
446C4×D3—108no—
447C22×C5—34no—
448C22×C5—62no—
449C22×C5—62no—
450C22×C5—64no—
451C22×C5—64no—
452C22×C5C22×C4×D311yescharacteristic
453C22×C5C2×D3×D412yes—
454C22×C5C2×#23711yescharacteristic
455C22×C5C2×#23911yescharacteristic
456C22×C5D3×#4112yes—
457C2×D5—22no—
458C2×D5—22no—
459C2×D5—24no—
460C2×D5—24no—
461C2×D5—34no—
462C2×D5—632no—
463C2×D5—62no—
464C2×D5—62no—
465C2×D5—64no—
466C2×D5—64no—
467C2×D5#89214yescomplemented
468C4×C5—22no—
469C4×C5—42no—
470C4×C5—62no—
471C4×C5—122no—
472Dic5—34no—
473Dic5—42no—
474Dic5—122no—
475Dic5D3×C22⋊C414yes—
476C24—31no—
477C24—51no—
478C24—154no—
479C24—151no—
480C24—304no—
481C24—302no—
482C24—302no—
483C24—304no—
484C22×C4—31no—
485C22×C4—34no—
486C22×C4—32no—
487C22×C4—51no—
488C22×C4—54no—
489C22×C4—52no—
490C22×C4—64no—
491C22×C4—104no—
492C22×C4—154no—
493C22×C4—154no—
494C22×C4—158no—
495C22×C4—154no—
496C22×C4—151no—
497C22×C4—154no—
498C22×C4—152no—
499C22×C4—304no—
500C22×C4—304no—
501C22×C4—3032no—
502C22×C4—304no—
503C22×C4C2×D3×D512yes—
504C22×C4C2×D3×D511yescharacteristic
505C4⋊C4—104no—
506C4⋊C4—304no—
507C22⋊C4—64no—
508C22⋊C4—104no—
509C22⋊C4—304no—
510C22⋊C4—304no—
511C22⋊C4—304no—
512C22⋊C4—304no—
513C42—304no—
514C42—304no—
515C3×C5#228011yescharacteristic, complemented, Hall
516C22×C3—54no—
517C22×C3—102no—
518C22×C3—102no—
519C22×C3—104no—
520C22×C3—104no—
521C22×C3C22×C4×D511yescharacteristic
522C22×C3C2×D4×D512yes—
523C22×C3D5×#4112yes—
524C22×C3D5×#4111yescharacteristic
525C22×C3D5×#4111yescharacteristic
526C2×D3—22no—
527C2×D3—22no—
528C2×D3—24no—
529C2×D3—24no—
530C2×D3—54no—
531C2×D3—1032no—
532C2×D3—102no—
533C2×D3—102no—
534C2×D3—104no—
535C2×D3—104no—
536C2×D3D5×C22⋊C414yes—
537C3×C4—22no—
538C3×C4—42no—
539C3×C4—54no—
540C3×C4—202no—
541Dic3—22no—
542Dic3—42no—
543Dic3—54no—
544Dic3—202no—
545C2×C5—64no—
546C2×C5C2×D3×C22⋊C411yescharacteristic
547C2×C5C2×#89211yescharacteristic
548C2×C5D3×#11711yescharacteristic
549C2×C5#560612yes—
550C2×C5#562712yes—
551D5—24no—
552D5—64no—
553C23—32no—
554C23—34no—
555C23—52no—
556C23—52no—
557C23—52no—
558C23—62no—
559C23—61no—
560C23—61no—
561C23—102no—
562C23—102no—
563C23—152no—
564C23—154no—
565C23—308no—
566C23—308no—
567C23—308no—
568C23—3016no—
569C23—3016no—
570C23—302no—
571C23—301no—
572C23—301no—
573C23C22×D3×D511yescharacteristic
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—32no—
579C2×C4—52no—
580C2×C4—54no—
581C2×C4—68no—
582C2×C4—62no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—108no—
587C2×C4—102no—
588C2×C4—102no—
589C2×C4—102no—
590C2×C4—1516no—
591C2×C4—152no—
592C2×C4—154no—
593C2×C4—308no—
594C2×C4—308no—
595C2×C4—308no—
596C2×C4—302no—
597C2×C4—302no—
598C2×C4—302no—
599C2×C4C4×D3×D512yes—
600C2×C3—104no—
601C2×C3C2×D5×C22⋊C411yescharacteristic
602C2×C3D5×#11711yescharacteristic
603C2×C3D5×#11711yescharacteristic
604C2×C3#6599012yes—
605C2×C3#6599012yes—
606D3—24no—
607D3—104no—
608C5#7386211yescharacteristic, complemented, Sylow
609C22—34no—
610C22—54no—
611C22—62no—
612C22—64no—
613C22—62no—
614C22—64no—
615C22—102no—
616C22—104no—
617C22—104no—
618C22—102no—
619C22—154no—
620C22—3032no—
621C22—304no—
622C22—302no—
623C22—304no—
624C22—302no—
625C22C2×C4×D3×D511yescharacteristic
626C22#9201612yes—
627C22D3×D4×D512yes—
628C22D5×#23711yescharacteristic
629C22D5×#23911yescharacteristic
630C4—22no—
631C4—42no—
632C4—54no—
633C4—62no—
634C4—122no—
635C4—154no—
636C4—202no—
637C4—602no—
638C3#1060578111yescharacteristic, complemented, Sylow
639C2—64no—
640C2—104no—
641C2—304no—
642C2#1175272311yescharacteristic
643C2D3×D5×C22⋊C411yescharacteristic
644C2#1175324512yes—
645C2D5×#89211yescharacteristic
646C2#1175386412yes—
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC3×C5×#95C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D3×D5C22
hypercenter#95D3×D5
hypocenterC3×C5#2280
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#91400C2semidirect
3. #11750767C2semidirect
4. C5×#4664C2semidirect
5. C3×#64956C2semidirect
7. #11748884C2semidirect
8. #11748876C2semidirect
9. #11748777C2semidirect
10. #11748738C2semidirect
11. #11748670C2semidirect
21. C2×C4×D3×D5C4semidirect
23. C2×C4×Dic15C22semidirect
26. C2×C3×#683C22semidirect
27. C2×#6668C22semidirect
31. C2×Dic3×Dic5C22semidirect
33. C3×C5×#95C22semidirect
34. #91115C22semidirect
35. C5×C3⋊#95C22semidirect
36. C5×C3⋊#95C22semidirect
37. C3×#3963C22semidirect
38. #90994C22semidirect
47. #64956D3semidirect
100. #4664D5semidirect
117. C2×#683C2×D3semidirect
123. C5×#95C2×D3semidirect
126. #3963C2×D3semidirect
173. D3×Dic5C22⋊C4semidirect
196. C3×#95C2×D5semidirect
199. C3⋊#95C2×D5semidirect
200. C3⋊#95C2×D5semidirect
260. C2×D15#117semidirect
270. C2×C3×D5#117semidirect
391. #95D3×D5semidirect
467. C2×D5#892semidirect
515. C3×C5#2280semidirect
608. C5#73862semidirect
638. C3#10605781semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D3×D52
C2×#914002
#117507672
C5×#46642
C3×#649562
#117489402
#117488842
#117488762
#117487772
#117487382
#117486702
#106057813
#738625