Finite Group Databasebeta

← #14323929

Subgroups — #14323929

Order 1920.

1336 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×D12C211yesmaximal, characteristic, complemented
2C2×C3×#4018C211yesmaximal, characteristic, complemented
3C2×#91449C211yesmaximal, characteristic
4C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
5#11748915C212yesmaximal, complemented
6#11748910C212yesmaximal, complemented
7#11748841C211yesmaximal, characteristic, complemented
8#11748764C211yesmaximal, characteristic, complemented
9#11748759C211yesmaximal, characteristic, complemented
10#11748717C212yesmaximal, complemented
11#11748716C212yesmaximal, complemented
12#10614127—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×C4×C5×D3C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1201C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C4×Dic15C2212yes—
21C2×C5×(C2×D3)⋊C4C2212yes—
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C4×C5×D12—24no—
24C2×C3×#685C2211yescharacteristic
25C2×C3×#685C2211yescharacteristic
26C2×C3×#683C2211yescharacteristic
27C2×C3×#683C2211yescharacteristic
28C2×C3×C4×Dic5C2211yescharacteristic
29C3×#4018—24no—
30C2×#6669C2212yes—
31C2×(C2×D3)⋊Dic5C2212yes—
32C2×(C2×D3)⋊Dic5C2212yes—
33C2×(C2×D3)⋊Dic5C2212yes—
34C2×#6665C2212yes—
35#91449C418yescomplemented
36#91115C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82236—51nomaximal, Hall
40C2×C4×C5×D4—31no—
41C2×#4084—31no—
42C2×#4018D311yescharacteristic, complemented
43#65510—31no—
44#65502—32no—
45#65499—32no—
46#65276—31no—
47#65262—31no—
48#65246—32no—
49#65234—32no—
50C4×C4⋊Dic5—31no—
51C23×C5×D3C2312yes—
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15C2312yes—
57C22×Dic15C2312yes—
58C22×C5×Dic3C2312yes—
59C2×C5×D12—22no—
60C2×C5×D12—22no—
61C2×C5×D12C2×C414yes—
62C2×C4×C5×D3—24no—
63C2×C4×C5×D3—42no—
64C2×C4×C5×D3—42no—
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C22×C3×Dic5C2311yescharacteristic
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5C2×C414yescomplemented
71C2×#1201—42no—
72C2×#1201—42no—
73C2×#1201C2×C418yescomplemented
74C3×C42×C5D414yescomplemented
75C4⋊Dic15—22no—
76C4⋊Dic15C2×C414yescomplemented
77C4×Dic15—42no—
78C5×(C2×D3)⋊C4—24no—
79C5×C4⋊Dic3—22no—
80C3×#685—22no—
81C3×#685—22no—
82C3×#683—22no—
83C3×#683—22no—
84C3×C4×Dic5—22no—
85#6669—42no—
86(C2×D3)⋊Dic5—42no—
87(C2×D3)⋊Dic5—42no—
88(C2×D3)⋊Dic5C2×C418yescomplemented
89#6665—42no—
90C2×C3×#117—51no—
91C2×#930—51no—
92C2×C4×D12D511yescharacteristic, complemented
93#5212—51no—
94#4990—52no—
95#4989—52no—
96#4957—52no—
97#4956—52no—
98#4939—51no—
99C4×C4⋊Dic3—51no—
100#4928—51no—
101C22×C5×D4—31no—
102C23×C4×C5—32no—
103C22×C22⋊D5—32no—
104C22×C4×D5C2×D311yescharacteristic
105C4×C5×D4—64no—
106C2×C5×C4⋊C4—31no—
107C2×C5×C22⋊C4—32no—
108C2×C42×C5C2×D311yescharacteristic
109C2×C22⋊Dic5—32no—
110C2×C22⋊Dic5—32no—
111C2×C22⋊Dic5—32no—
112#4084—38no—
113C2×#685—32no—
114C2×#685C2×D311yescharacteristic
115C2×#685C2×D311yescharacteristic
116C2×C4⋊Dic5—31no—
117C2×C4⋊Dic5—31no—
118C2×#683—32no—
119C2×#683C2×D311yescharacteristic
120C2×#683C2×D311yescharacteristic
121C2×C4×Dic5—32no—
122C2×C4×Dic5C2×D311yescharacteristic
123#4018—24no—
124#3963—32no—
125#3963—32no—
126#3963—32no—
127#2324—151noSylow
128C23×C3×C5C2411yescharacteristic
129C22×C5×D3—22no—
130C22×C5×D3—22no—
131C22×C5×D3—22no—
132C22×C5×D3—22no—
133C22×C5×D3—22no—
134C22×C5×D3—22no—
135C22×C5×D3C22×C414yes—
136C22×C3×D5—21no—
137C22×C3×D5—21no—
138C22×C3×D5—21no—
139C22×C3×D5—21no—
140C22×C3×D5—21no—
141C22×C3×D5—21no—
142C22×C3×D5C22×C412yes—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5—21no—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5C2×D412yes—
151C2×C3×C4×C5#4112yes—
152C2×Dic15—22no—
153C2×Dic15—22no—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15C22×C414yes—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C5×D12—28no—
162C4×C5×D3—48no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—21no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5C22×C412yes—
172C3×C4×D5—28no—
173#1201—48no—
174C23×C3×C4—51no—
175C22×#67—52no—
176C22×D12C2×D511yescharacteristic
177C22×C4×D3C2×D512yes—
178C3×#117—104no—
179C2×C3×C4⋊C4—51no—
180C2×C3×C4⋊C4—51no—
181C2×C3×C22⋊C4—51no—
182C2×C3×C22⋊C4—51no—
183C2×C3×C42—51no—
184C2×C3×C42C2×D511yescharacteristic
185C2×#217—52no—
186#930—58no—
187C2×(C2×D3)⋊C4—52no—
188C2×(C2×D3)⋊C4—52no—
189C2×(C2×D3)⋊C4—52no—
190C2×(C2×D3)⋊C4C2×D512yes—
191C2×C4⋊Dic3—51no—
192C2×C4⋊Dic3—51no—
193C2×C4⋊Dic3C2×D511yescharacteristic
194C2×Dic3⋊C4—52no—
195C2×C4×Dic3—52no—
196C4×D12—24no—
197C3⋊#95—52no—
198C3⋊#95—52no—
199C3⋊#95—52no—
200C24×C5—32no—
201C23×D5C22×D311yescharacteristic
202C2×C5×D4—34no—
203C2×C5×D4—62no—
204C2×C5×D4—62no—
205C22×C4×C5—32no—
206C22×C4×C5—64no—
207C22×C4×C5—122no—
208C22×C4×C5—122no—
209C22×C4×C5C22×D311yescharacteristic
210C22×C4×C5C22×D311yescharacteristic
211C22×C4×C5C22×D311yescharacteristic
212C2×C22⋊D5—38no—
213C2×C22⋊D5—122no—
214C2×C22⋊D5—122no—
215C22×Dic5—32no—
216C22×Dic5—32no—
217C22×Dic5C22×D311yescharacteristic
218C22×Dic5C22×D311yescharacteristic
219C22×Dic5C22×D311yescharacteristic
220C2×C4×D5—22no—
221C2×C4×D5—22no—
222C2×C4×D5C4×D314yescomplemented
223C5×C4⋊C4—62no—
224C5×C22⋊C4—64no—
225C42×C5#6714yescomplemented
226C22⋊Dic5—38no—
227C22⋊Dic5—122no—
228C22⋊Dic5—122no—
229#685—22no—
230#685—22no—
231#685—122no—
232C4⋊Dic5—34no—
233C4⋊Dic5—62no—
234#683—22no—
235#683—22no—
236#683—122no—
237C4×Dic5—22no—
238C4×Dic5—122no—
239C2×#121—151no—
240C2×C4×D4—31no—
241C2×#117—51no—
242#390—151no—
243#390—152no—
244#389—151no—
245#388—152no—
246#386—152no—
247#385—152no—
248#380—151no—
249C4×C4⋊C4—151no—
250C22×C3×C5C23×C411yescharacteristic
251C22×C3×C5C22×D411yescharacteristic
252C22×C3×C5C2×#4111yescharacteristic
253C22×C3×C5H(5,𝔽2)11yescharacteristic
254C22×C3×C5H(5,𝔽2)11yescharacteristic
255C22×C3×C5H(5,𝔽2)11yescharacteristic
256C22×C3×C52−1+411yescharacteristic
257C2×C5×D3—24no—
258C2×C5×D3—24no—
259C2×C5×D3—24no—
260C2×C5×D3—42no—
261C2×C5×D3—42no—
262C2×C5×D3—42no—
263C2×C5×D3—42no—
264C2×C3×D5—22no—
265C2×C3×D5—22no—
266C2×C3×D5—22no—
267C2×C3×D5—41no—
268C2×C3×D5—41no—
269C2×C3×D5—41no—
270C2×C3×D5—41no—
271C3×C4×C5—22no—
272C3×C4×C5—22no—
273C3×C4×C5C4×D414yes—
274Dic15—24no—
275Dic15—42no—
276C3×Dic5—22no—
277C3×Dic5—41no—
278C3×Dic5—41no—
279C5×Dic3—42no—
280C24×C3—51no—
281C23×D3C22×D512yes—
282C22×C3×C4—51no—
283C22×C3×C4—54no—
284C22×C3×C4—51no—
285C22×C3×C4—51no—
286C22×C3×C4—102no—
287C22×C3×C4—102no—
288C22×C3×C4C22×D511yescharacteristic
289C22×C3×C4C22×D511yescharacteristic
290C22×C3×C4C22×D511yescharacteristic
291C2×#67—58no—
292C2×#67—202no—
293C2×#67—202no—
294C22×Dic3—52no—
295C22×Dic3—52no—
296C22×Dic3C22×D512yes—
297C2×D12—22no—
298C2×D12—22no—
299C2×D12C4×D514yes—
300C2×C4×D3—24no—
301C2×C4×D3—42no—
302C2×C4×D3—42no—
303C3×C4⋊C4—102no—
304C3×C4⋊C4—102no—
305C3×C22⋊C4—102no—
306C3×C22⋊C4—102no—
307C3×C42—102no—
308C3×C42C22⋊D514yescomplemented
309#217—202no—
310(C2×D3)⋊C4—24no—
311(C2×D3)⋊C4—58no—
312(C2×D3)⋊C4—202no—
313(C2×D3)⋊C4—202no—
314C4⋊Dic3—22no—
315C4⋊Dic3—54no—
316C4⋊Dic3—102no—
317Dic3⋊C4—202no—
318C4×Dic3—202no—
319C23×C5—34no—
320C23×C5—62no—
321C23×C5—62no—
322C23×C5—62no—
323C23×C5—62no—
324C23×C5—62no—
325C23×C5—62no—
326C23×C5C23×D311yescharacteristic
327C22×D5—21no—
328C22×D5—21no—
329C22×D5—21no—
330C22×D5—21no—
331C22×D5—21no—
332C22×D5—21no—
333C22×D5C2×C4×D312yes—
334C5×D4—68no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—21no—
338C2×C4×C5—21no—
339C2×C4×C5—62no—
340C2×C4×C5—62no—
341C2×C4×C5—62no—
342C2×C4×C5—128no—
343C2×C4×C5C2×C4×D312yes—
344C2×C4×C5#23512yes—
345C2×C4×C5C2×#6712yes—
346C2×C4×C5C2×#6712yes—
347C2×C4×C5C2×#6712yes—
348C22⋊D5—128no—
349C2×Dic5—21no—
350C2×Dic5—21no—
351C2×Dic5—21no—
352C2×Dic5—21no—
353C2×Dic5—21no—
354C2×Dic5—21no—
355C2×Dic5—21no—
356C2×Dic5—21no—
357C2×Dic5—34no—
358C2×Dic5—62no—
359C2×Dic5—62no—
360C2×Dic5—62no—
361C2×Dic5—62no—
362C2×Dic5—62no—
363C2×Dic5C2×C4×D312yes—
364C4×D5—28no—
365C22×D4—31no—
366C22×D4—152no—
367C23×C4—32no—
368C23×C4—51no—
369#121—158no—
370C4×D4—64no—
371#117—104no—
372C2×C4⋊C4—31no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—51no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4—152no—
378C2×C22⋊C4—32no—
379C2×C22⋊C4—51no—
380C2×C22⋊C4—51no—
381C2×C22⋊C4—152no—
382C2×C22⋊C4—152no—
383C2×C22⋊C4—152no—
384C2×C22⋊C4—152no—
385C2×C42—51no—
386C2×C42—152no—
387C2×C42D3×D511yescharacteristic
388#95—152no—
389#95—152no—
390#95—152no—
391C2×C3×C5C2×C4×D411yescharacteristic
392C2×C3×C5#51811yescharacteristic
393C2×C3×C5#52011yescharacteristic
394C2×C3×C5#53511yescharacteristic
395C2×C3×C5#53711yescharacteristic
396C2×C3×C5#54011yescharacteristic
397C2×C3×C5#54211yescharacteristic
398C3×D5—42no—
399C5×D3—44no—
400C23×C3—52no—
401C23×C3—101no—
402C23×C3—101no—
403C23×C3—101no—
404C23×C3—101no—
405C23×C3—101no—
406C23×C3—101no—
407C23×C3C23×D511yescharacteristic
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3—22no—
412C22×D3—22no—
413C22×D3—22no—
414C22×D3C2×C4×D514yes—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—52no—
420C2×C3×C4—101no—
421C2×C3×C4—101no—
422C2×C3×C4—108no—
423C2×C3×C4—101no—
424C2×C3×C4—101no—
425C2×C3×C4—101no—
426C2×C3×C4—101no—
427C2×C3×C4—101no—
428C2×C3×C4—101no—
429C2×C3×C4C2×C4×D512yes—
430C2×C3×C4#70912yes—
431C2×C3×C4C2×C22⋊D512yes—
432C2×C3×C4C2×C22⋊D512yes—
433C2×C3×C4C2×C22⋊D512yes—
434#67—208no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—54no—
439C2×Dic3—102no—
440C2×Dic3—102no—
441C2×Dic3—102no—
442C2×Dic3—102no—
443C2×Dic3—102no—
444D12—28no—
445C4×D3—48no—
446C22×C5—64no—
447C22×C5—64no—
448C22×C5—64no—
449C22×C5—122no—
450C22×C5—122no—
451C22×C5—122no—
452C22×C5—122no—
453C22×C5C22×C4×D311yescharacteristic
454C22×C5C2×#23511yescharacteristic
455C22×C5#100911yescharacteristic
456C22×C5#100911yescharacteristic
457C22×C5#100911yescharacteristic
458C22×C5#101011yescharacteristic
459C22×C5C22×#6711yescharacteristic
460C2×D5—22no—
461C2×D5—22no—
462C2×D5—22no—
463C2×D5—41no—
464C2×D5—41no—
465C2×D5—41no—
466C2×D5—41no—
467C4×C5—22no—
468C4×C5—22no—
469C4×C5—122no—
470C4×C5C4×#6714yes—
471Dic5—22no—
472Dic5—41no—
473Dic5—41no—
474Dic5—64no—
475Dic5—122no—
476C24—32no—
477C24—51no—
478C2×D4—34no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—158no—
482C2×D4—602no—
483C2×D4—602no—
484C22×C4—32no—
485C22×C4—51no—
486C22×C4—54no—
487C22×C4—51no—
488C22×C4—51no—
489C22×C4—64no—
490C22×C4—102no—
491C22×C4—102no—
492C22×C4—122no—
493C22×C4—122no—
494C22×C4—152no—
495C22×C4—152no—
496C22×C4C2×D3×D511yescharacteristic
497C22×C4C2×D3×D511yescharacteristic
498C22×C4C2×D3×D511yescharacteristic
499C4⋊C4—62no—
500C4⋊C4—102no—
501C4⋊C4—102no—
502C4⋊C4—154no—
503C4⋊C4—302no—
504C4⋊C4—602no—
505C22⋊C4—64no—
506C22⋊C4—102no—
507C22⋊C4—102no—
508C22⋊C4—158no—
509C22⋊C4—602no—
510C22⋊C4—602no—
511C22⋊C4—602no—
512C42—102no—
513C42—602no—
514C42#120114yescomplemented
515C3×C5#232411yescharacteristic, complemented, Hall
516C22×C3—102no—
517C22×C3—102no—
518C22×C3—102no—
519C22×C3—201no—
520C22×C3—201no—
521C22×C3—201no—
522C22×C3—201no—
523C22×C3C22×C4×D511yescharacteristic
524C22×C3C2×#70911yescharacteristic
525C22×C3#414411yescharacteristic
526C22×C3#414411yescharacteristic
527C22×C3#414911yescharacteristic
528C22×C3#415011yescharacteristic
529C22×C3C22×C22⋊D511yescharacteristic
530C2×D3—24no—
531C2×D3—24no—
532C2×D3—24no—
533C2×D3—42no—
534C2×D3—42no—
535C2×D3—42no—
536C2×D3—42no—
537C3×C4—22no—
538C3×C4—22no—
539C3×C4—102no—
540C3×C4—201no—
541C3×C4—201no—
542C3×C4C4×C22⋊D514yes—
543Dic3—42no—
544Dic3—104no—
545Dic3—202no—
546C2×C5—124no—
547C2×C5#552111yescharacteristic
548C2×C5#552311yescharacteristic
549C2×C5#553411yescharacteristic
550C2×C5#553511yescharacteristic
551C2×C5C2×C4×#6711yescharacteristic
552C2×C5#583011yescharacteristic
553C2×C5#583311yescharacteristic
554D5—42no—
555C23—34no—
556C23—52no—
557C23—62no—
558C23—62no—
559C23—62no—
560C23—62no—
561C23—62no—
562C23—62no—
563C23—101no—
564C23—101no—
565C23—101no—
566C23—101no—
567C23—101no—
568C23—101no—
569C23C22×D3×D511yescharacteristic
570D4—68no—
571D4—608no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—52no—
577C2×C4—62no—
578C2×C4—62no—
579C2×C4—62no—
580C2×C4—101no—
581C2×C4—101no—
582C2×C4—108no—
583C2×C4—101no—
584C2×C4—101no—
585C2×C4—101no—
586C2×C4—101no—
587C2×C4—101no—
588C2×C4—101no—
589C2×C4—128no—
590C2×C4—154no—
591C2×C4—302no—
592C2×C4—302no—
593C2×C4—302no—
594C2×C4—302no—
595C2×C4—302no—
596C2×C4#677112yes—
597C2×C4C4×D3×D512yes—
598C2×C4C2×#120112yes—
599C2×C4C2×#120112yes—
600C2×C4C2×#120112yes—
601C2×C3—202no—
602C2×C3#6587911yescharacteristic
603C2×C3#6588011yescharacteristic
604C2×C3#6589511yescharacteristic
605C2×C3#6589611yescharacteristic
606C2×C3C2×C4×C22⋊D511yescharacteristic
607C2×C3#6613911yescharacteristic
608C2×C3#6616711yescharacteristic
609D3—44no—
610C5#8223611yescharacteristic, complemented, Sylow
611C22—64no—
612C22—64no—
613C22—64no—
614C22—102no—
615C22—102no—
616C22—102no—
617C22—122no—
618C22—122no—
619C22—122no—
620C22—122no—
621C22—201no—
622C22—201no—
623C22—201no—
624C22—201no—
625C22#9200111yescharacteristic
626C22C2×#677111yescharacteristic
627C22C2×C4×D3×D511yescharacteristic
628C22#9201811yescharacteristic
629C22#9201811yescharacteristic
630C22#9201911yescharacteristic
631C22C22×#120111yescharacteristic
632C4—22no—
633C4—22no—
634C4—102no—
635C4—122no—
636C4—201no—
637C4—201no—
638C4—304no—
639C4—602no—
640C4C4×#120114yes—
641C3#1061412711yescharacteristic, complemented, Sylow
642C2—124no—
643C2—202no—
644C2#1175266911yescharacteristic
645C2#1175271111yescharacteristic
646C2#1175271311yescharacteristic
647C2#1175272511yescharacteristic
648C2C2×C4×#120111yescharacteristic
649C2#1175460411yescharacteristic
650C2#1175460711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91449C2
hypercenterC2×C42D3×D5
hypocenterC3×C5#2324
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×C4×C5×D12C2semidirect
2. C2×C3×#4018C2semidirect
4. C4×C4⋊Dic15C2semidirect
5. #11748915C2semidirect
6. #11748910C2semidirect
7. #11748841C2semidirect
8. #11748764C2semidirect
9. #11748759C2semidirect
10. #11748717C2semidirect
11. #11748716C2semidirect
35. #91449C4semidirect
42. C2×#4018D3semidirect
70. C2×C3×C4×D5C2×C4semidirect
73. C2×#1201C2×C4semidirect
74. C3×C42×C5D4semidirect
76. C4⋊Dic15C2×C4semidirect
88. (C2×D3)⋊Dic5C2×C4semidirect
92. C2×C4×D12D5semidirect
222. C2×C4×D5C4×D3semidirect
225. C42×C5#67semidirect
308. C3×C42C22⋊D5semidirect
514. C42#1201semidirect
515. C3×C5#2324semidirect
610. C5#82236semidirect
641. C3#10614127semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×D122
C2×C3×#40182
C2×#914492
C4×C4⋊Dic152
#117489152
#117489102
#117488412
#117487642
#117487592
#117487172
#117487162
#106141273
#822365