Finite Group Databasebeta

← #14327389

Subgroups — #14327389

Order 1920.

1320 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D20C211yesmaximal, characteristic
2C2×D5×C4⋊Dic3C211yesmaximal, characteristic, complemented
3C2×#91358C211yesmaximal, characteristic, complemented
4C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
5C5×#4936C211yesmaximal, characteristic, complemented
6#11748896C212yesmaximal
7#11748884C212yesmaximal, complemented
8#11748791C212yesmaximal, complemented
9#11748759C211yesmaximal, characteristic, complemented
10#11748759C211yesmaximal, characteristic, complemented
11#11748698C212yesmaximal, complemented
12#10605960—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×C3×C4×D5C2211yescharacteristic
16C22×D5×Dic3C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×C4×Dic15C2212yes—
21C2×C5×C4⋊Dic3C2211yescharacteristic
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C3×#685C2211yescharacteristic
24C2×C3×#685C2211yescharacteristic
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C3×C4×D20C418yescomplemented
27C2×#6668C2212yes—
28C2×#6665C2212yes—
29C2×#6665C2212yes—
30C2×#6665C2212yes—
31C2×Dic3×Dic5C2212yes—
32D5×C4⋊Dic3—24no—
33#91358—24no—
34#91115C2212yes—
35C5×C3⋊#95C2212yes—
36C5×C3⋊#95C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82335—51nomaximal, Hall
40C2×#4038—31no—
41C2×D5×C4⋊C4—31no—
42C2×C4×D20D311yescharacteristic
43C5×#382—31no—
44#65276—31no—
45#65276—31no—
46C4×C4⋊Dic5—31no—
47#64958—32no—
48#64955—32no—
49#64954—32no—
50#64943—32no—
51C23×C3×D5C2311yescharacteristic
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15C2312yes—
57C22×Dic15C2312yes—
58C22×C5×Dic3C2312yes—
59C22×C5×Dic3C2312yes—
60C22×C3×Dic5C2311yescharacteristic
61C22×C3×Dic5C2311yescharacteristic
62C2×C3×D20—22no—
63C2×C3×D20—22no—
64C2×C3×D20C2×C414yes—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5—22no—
67C2×C3×C4×D5—22no—
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5C2×C414yes—
70C2×C3×C4×D5C2×C414yescomplemented
71C2×D5×Dic3—24no—
72C2×D5×Dic3—24no—
73C2×D5×Dic3—42no—
74C3×C42×C5C2×C414yescomplemented
75C4⋊Dic15—22no—
76C4⋊Dic15D414yescomplemented
77C4×Dic15—42no—
78C5×C4⋊Dic3—22no—
79C5×C4⋊Dic3—22no—
80C3×#685C2×C414yes—
81C3×#685C2×C414yescomplemented
82C3×C4⋊Dic5C2×C414yescomplemented
83#6668—24no—
84#6665—24no—
85#6665—24no—
86#6665—42no—
87Dic3×Dic5—24no—
88C2×C3×C4×D4—51no—
89C2×#926—51no—
90C22×C4⋊Dic3—51no—
91#5220—52no—
92#5212—51no—
93#5212—51no—
94#4980—52no—
95#4951—52no—
96Dic3×C22⋊C4—52no—
97#4936D511yescharacteristic, complemented
98C4×C4⋊Dic3—51no—
99C22×D20C2×D311yescharacteristic
100C22×C4×D5—32no—
101C22×C4×D5C2×D311yescharacteristic
102C22×C4×D5C2×D311yescharacteristic
103C2×C5×C4⋊C4—31no—
104C2×C5×C4⋊C4—31no—
105C2×C42×C5C2×D311yescharacteristic
106C2×#685—32no—
107C2×#685—32no—
108C2×#685—32no—
109C2×#685C2×D311yescharacteristic
110C2×#685C2×D311yescharacteristic
111C2×C4⋊Dic5—31no—
112C2×C4⋊Dic5—31no—
113C2×C4⋊Dic5C2×D311yescharacteristic
114C2×#683—32no—
115C2×C4×Dic5—32no—
116C2×C4×Dic5—32no—
117#4038—64no—
118D5×C4⋊C4—64no—
119C4×D20Dic318yescomplemented
120C5×#95—32no—
121C5×#95—32no—
122#3963—32no—
123#3963—32no—
124#3963—32no—
125#2352—151noSylow
126C23×C3×C5C2411yescharacteristic
127C22×C3×D5—21no—
128C22×C3×D5—21no—
129C22×C3×D5—21no—
130C22×C3×D5—21no—
131C22×C3×D5—21no—
132C22×C3×D5—21no—
133C22×C3×D5—21no—
134C22×C3×D5—21no—
135C22×C3×D5—21no—
136C22×C3×D5—21no—
137C22×C3×D5C22×C412yes—
138C22×C3×D5C22×C412yes—
139C22×C3×D5#4112yes—
140C22×C3×D5#4112yes—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5C22×C412yes—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C2×D412yes—
149C2×C3×C4×C5#4112yes—
150C2×Dic15—22no—
151C2×Dic15—22no—
152C2×Dic15—22no—
153C2×Dic15—22no—
154C2×Dic15—22no—
155C2×Dic15C2×D414yes—
156C2×C5×Dic3—22no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—22no—
160C2×C5×Dic3—22no—
161C2×C5×Dic3—22no—
162C2×C3×Dic5—21no—
163C2×C3×Dic5—21no—
164C2×C3×Dic5—21no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5C22×C412yes—
167C2×C3×Dic5C22×C412yes—
168C3×D20—28no—
169C3×C4×D5—28no—
170C3×C4×D5—28no—
171D5×Dic3—48no—
172C22×C3×D4—51no—
173C23×C3×C4—51no—
174C23×C3×C4—51no—
175C23×Dic3—52no—
176C3×C4×D4—58no—
177C2×C3×C4⋊C4—51no—
178C2×C3×C22⋊C4—51no—
179C2×C3×C22⋊C4—51no—
180C2×C3×C42C2×D511yescharacteristic
181C2×#217—52no—
182C2×#217—52no—
183C2×#217—52no—
184#926—104no—
185C2×C4⋊Dic3—51no—
186C2×C4⋊Dic3—51no—
187C2×C4⋊Dic3—52no—
188C2×C4⋊Dic3—104no—
189C2×C4⋊Dic3C2×D511yescharacteristic
190C2×C4⋊Dic3C2×D511yescharacteristic
191C2×C4×Dic3—52no—
192C2×C4×Dic3—52no—
193C3⋊#95—52no—
194C3⋊#95—52no—
195C3⋊#95—52no—
196C3⋊#95C2×D512yes—
197C3⋊#95C2×D512yes—
198C23×D5C22×D311yescharacteristic
199C23×D5C22×D311yescharacteristic
200C22×C4×C5—32no—
201C22×C4×C5—32no—
202C22×C4×C5C22×D311yescharacteristic
203C22×C4×C5C22×D311yescharacteristic
204C22×C4×C5C22×D311yescharacteristic
205C22×Dic5—32no—
206C22×Dic5—32no—
207C22×Dic5C22×D311yescharacteristic
208C22×Dic5C22×D311yescharacteristic
209C2×D20—22no—
210C2×D20—22no—
211C2×D20C2×Dic314yes—
212C2×C4×D5—22no—
213C2×C4×D5—22no—
214C2×C4×D5—22no—
215C2×C4×D5—22no—
216C2×C4×D5—64no—
217C2×C4×D5—64no—
218C2×C4×D5—122no—
219C2×C4×D5C2×Dic314yes—
220C2×C4×D5C2×Dic314yescomplemented
221C5×C4⋊C4—62no—
222C5×C4⋊C4—62no—
223C42×C5C2×Dic314yescomplemented
224#685—64no—
225#685—64no—
226#685—122no—
227#685C2×Dic314yes—
228#685C2×Dic314yescomplemented
229C4⋊Dic5—34no—
230C4⋊Dic5—62no—
231C4⋊Dic5C2×Dic314yescomplemented
232#683—64no—
233C4×Dic5—64no—
234C4×Dic5—122no—
235C2×C4×D4—51no—
236C2×#117—151no—
237C22×C4⋊C4—151no—
238#388—152no—
239#387—152no—
240#386—152no—
241#382—31no—
242#380—151no—
243#380—151no—
244C4×C4⋊C4—151no—
245C4×C22⋊C4—152no—
246C22×C3×C5C23×C411yescharacteristic
247C22×C3×C5C22×D411yescharacteristic
248C22×C3×C5C2×#4111yescharacteristic
249C22×C3×C5C2×#4111yescharacteristic
250C22×C3×C5C2×#4111yescharacteristic
251C22×C3×C5H(5,𝔽2)11yescharacteristic
252C22×C3×C52−1+411yescharacteristic
253C2×C3×D5—22no—
254C2×C3×D5—22no—
255C2×C3×D5—22no—
256C2×C3×D5—22no—
257C2×C3×D5—22no—
258C2×C3×D5—22no—
259C2×C3×D5—22no—
260C2×C3×D5—22no—
261C2×C3×D5—22no—
262C2×C3×D5—41no—
263C2×C3×D5—41no—
264C2×C3×D5—41no—
265C2×C3×D5—41no—
266C2×C3×D5#11714yescomplemented
267C3×C4×C5—22no—
268C3×C4×C5—22no—
269C3×C4×C5C4×D414yes—
270Dic15—24no—
271Dic15—42no—
272C3×Dic5—22no—
273C3×Dic5—22no—
274C5×Dic3—42no—
275C5×Dic3—42no—
276C24×C3—51no—
277C24×C3—51no—
278C2×C3×D4—54no—
279C2×C3×D4—102no—
280C2×C3×D4—102no—
281C22×C3×C4—51no—
282C22×C3×C4—51no—
283C22×C3×C4—54no—
284C22×C3×C4—54no—
285C22×C3×C4—102no—
286C22×C3×C4—102no—
287C22×C3×C4—102no—
288C22×C3×C4—102no—
289C22×C3×C4C22×D511yescharacteristic
290C22×C3×C4C22×D511yescharacteristic
291C22×C3×C4C22×D511yescharacteristic
292C22×Dic3—52no—
293C22×Dic3—52no—
294C22×Dic3—104no—
295C22×Dic3—104no—
296C22×Dic3—202no—
297C22×Dic3C22×D512yes—
298C22×Dic3C22×D512yes—
299C3×C4⋊C4—54no—
300C3×C22⋊C4—54no—
301C3×C22⋊C4—54no—
302C3×C42C4×D514yescomplemented
303#217—104no—
304#217—104no—
305#217—202no—
306C4⋊Dic3—22no—
307C4⋊Dic3—22no—
308C4⋊Dic3—54no—
309C4⋊Dic3—104no—
310C4⋊Dic3—102no—
311C4×Dic3—104no—
312C4×Dic3—202no—
313C23×C5C23×D311yescharacteristic
314C22×D5—21no—
315C22×D5—21no—
316C22×D5—21no—
317C22×D5—21no—
318C22×D5—21no—
319C22×D5—21no—
320C22×D5—21no—
321C22×D5—21no—
322C22×D5—21no—
323C22×D5—21no—
324C22×D5#23512yes—
325C22×D5#23512yes—
326C22×D5C22×Dic312yes—
327C22×D5C22×Dic312yes—
328C2×C4×C5—21no—
329C2×C4×C5—21no—
330C2×C4×C5—21no—
331C2×C4×C5—21no—
332C2×C4×C5—62no—
333C2×C4×C5—62no—
334C2×C4×C5—62no—
335C2×C4×C5—62no—
336C2×C4×C5—62no—
337C2×C4×C5—62no—
338C2×C4×C5D3×D412yes—
339C2×C4×C5#23712yes—
340C2×C4×C5C22×Dic312yes—
341C2×C4×C5C22×Dic312yes—
342C2×C4×C5C22×Dic312yes—
343C2×Dic5—21no—
344C2×Dic5—21no—
345C2×Dic5—21no—
346C2×Dic5—21no—
347C2×Dic5—34no—
348C2×Dic5—62no—
349C2×Dic5—62no—
350C2×Dic5—62no—
351C2×Dic5—62no—
352C2×Dic5—62no—
353C2×Dic5C22×Dic312yes—
354C2×Dic5C22×Dic312yes—
355D20—28no—
356C4×D5—28no—
357C4×D5—28no—
358C4×D5—128no—
359C22×D4—51no—
360C23×C4—51no—
361C23×C4—51no—
362C23×C4—152no—
363C4×D4—58no—
364#117—304no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—51no—
368C2×C4⋊C4—151no—
369C2×C4⋊C4—152no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—304no—
372C2×C22⋊C4—51no—
373C2×C22⋊C4—51no—
374C2×C22⋊C4—152no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4—152no—
377C2×C42—152no—
378C2×C42—152no—
379C2×C42D3×D511yescharacteristic
380#95—32no—
381#95—32no—
382#95—152no—
383#95—152no—
384#95—152no—
385C2×C3×C5C2×#11711yescharacteristic
386C2×C3×C5C2×C4×D411yescharacteristic
387C2×C3×C5#52011yescharacteristic
388C2×C3×C5#54611yescharacteristic
389C2×C3×C5#54811yescharacteristic
390C2×C3×C5#55211yescharacteristic
391C2×C3×C5#55311yescharacteristic
392C3×D5—24no—
393C3×D5—42no—
394C23×C3—52no—
395C23×C3—52no—
396C23×C3—52no—
397C23×C3—52no—
398C23×C3—101no—
399C23×C3—101no—
400C23×C3—101no—
401C23×C3—101no—
402C23×C3—101no—
403C23×C3—101no—
404C23×C3—101no—
405C23×C3—101no—
406C23×C3—101no—
407C23×C3—101no—
408C23×C3C23×D511yescharacteristic
409C3×D4—108no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—52no—
415C2×C3×C4—52no—
416C2×C3×C4—101no—
417C2×C3×C4—101no—
418C2×C3×C4—101no—
419C2×C3×C4—101no—
420C2×C3×C4—108no—
421C2×C3×C4—108no—
422C2×C3×C4C2×C4×D512yes—
423C2×C3×C4C2×C4×D512yes—
424C2×C3×C4C2×C4×D512yes—
425C2×C3×C4D4×D512yes—
426C2×C3×C4#71312yes—
427C2×Dic3—22no—
428C2×Dic3—22no—
429C2×Dic3—22no—
430C2×Dic3—22no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—54no—
434C2×Dic3—102no—
435C2×Dic3—102no—
436C2×Dic3—102no—
437C2×Dic3—102no—
438C2×Dic3—102no—
439C2×Dic3—208no—
440C22×C5C2×#23511yescharacteristic
441C22×C5C2×#23511yescharacteristic
442C22×C5C2×D3×D411yescharacteristic
443C22×C5C2×#23711yescharacteristic
444C22×C5#100911yescharacteristic
445C22×C5#101011yescharacteristic
446C22×C5C23×Dic311yescharacteristic
447C2×D5—22no—
448C2×D5—22no—
449C2×D5—22no—
450C2×D5—22no—
451C2×D5—22no—
452C2×D5—22no—
453C2×D5—22no—
454C2×D5—22no—
455C2×D5—22no—
456C2×D5—41no—
457C2×D5—41no—
458C2×D5—41no—
459C2×D5—41no—
460C2×D5#92614yescomplemented
461C4×C5—22no—
462C4×C5—22no—
463C4×C5—122no—
464C4×C5—122no—
465C4×C5D4×Dic314yes—
466Dic5—22no—
467Dic5—22no—
468Dic5—64no—
469Dic5—122no—
470C24—51no—
471C24—51no—
472C2×D4—54no—
473C2×D4—102no—
474C2×D4—102no—
475C22×C4—32no—
476C22×C4—32no—
477C22×C4—51no—
478C22×C4—51no—
479C22×C4—54no—
480C22×C4—54no—
481C22×C4—102no—
482C22×C4—102no—
483C22×C4—102no—
484C22×C4—102no—
485C22×C4—152no—
486C22×C4—152no—
487C22×C4—304no—
488C22×C4—304no—
489C22×C4—602no—
490C22×C4C2×D3×D511yescharacteristic
491C22×C4C2×D3×D511yescharacteristic
492C22×C4C2×D3×D511yescharacteristic
493C4⋊C4—54no—
494C4⋊C4—62no—
495C4⋊C4—62no—
496C4⋊C4—154no—
497C4⋊C4—304no—
498C4⋊C4—302no—
499C22⋊C4—54no—
500C22⋊C4—54no—
501C22⋊C4—304no—
502C22⋊C4—304no—
503C22⋊C4—602no—
504C42—304no—
505C42—602no—
506C42D5×Dic314yescomplemented
507C3×C5#235211yescharacteristic, complemented, Hall
508C22×C3—54no—
509C22×C3—102no—
510C22×C3—102no—
511C22×C3—102no—
512C22×C3—102no—
513C22×C3—102no—
514C22×C3—102no—
515C22×C3—102no—
516C22×C3—102no—
517C22×C3—102no—
518C22×C3—201no—
519C22×C3—201no—
520C22×C3—201no—
521C22×C3—201no—
522C22×C3C22×C4×D511yescharacteristic
523C22×C3C2×D4×D511yescharacteristic
524C22×C3C2×#71311yescharacteristic
525C22×C3D5×#4111yescharacteristic
526C22×C3D5×#4111yescharacteristic
527C22×C3#414911yescharacteristic
528C22×C3#415011yescharacteristic
529C3×C4—22no—
530C3×C4—22no—
531C3×C4—102no—
532C3×C4—102no—
533C3×C4#403914yes—
534Dic3—42no—
535Dic3—42no—
536Dic3—104no—
537Dic3—202no—
538C2×C5#554111yescharacteristic
539C2×C5#555011yescharacteristic
540C2×C5#555211yescharacteristic
541C2×C5#556511yescharacteristic
542C2×C5C2×#92611yescharacteristic
543C2×C5C2×D4×Dic311yescharacteristic
544C2×C5#582711yescharacteristic
545D5—24no—
546D5—42no—
547C23—52no—
548C23—52no—
549C23—52no—
550C23—52no—
551C23—101no—
552C23—101no—
553C23—101no—
554C23—101no—
555C23—101no—
556C23—101no—
557C23—101no—
558C23—101no—
559C23—101no—
560C23—101no—
561C23C22×D3×D511yescharacteristic
562D4—108no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—52no—
568C2×C4—52no—
569C2×C4—62no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—101no—
576C2×C4—101no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—108no—
580C2×C4—108no—
581C2×C4—154no—
582C2×C4—302no—
583C2×C4—302no—
584C2×C4—302no—
585C2×C4—302no—
586C2×C4—302no—
587C2×C4—608no—
588C2×C4#676612yes—
589C2×C4#677712yes—
590C2×C4C2×D5×Dic312yes—
591C2×C4C2×D5×Dic312yes—
592C2×C4C2×D5×Dic312yes—
593C2×C3—104no—
594C2×C3—202no—
595C2×C3C2×#403911yescharacteristic
596C2×C3D5×#11711yescharacteristic
597C2×C3#6585711yescharacteristic
598C2×C3#6601011yescharacteristic
599C2×C3#6601111yescharacteristic
600C2×C3#6602811yescharacteristic
601C2×C3#6602911yescharacteristic
602C5#8233511yescharacteristic, complemented, Sylow
603C22—54no—
604C22—102no—
605C22—102no—
606C22—102no—
607C22—102no—
608C22—102no—
609C22—102no—
610C22—102no—
611C22—102no—
612C22—102no—
613C22—201no—
614C22—201no—
615C22—201no—
616C22—201no—
617C22C2×#676611yescharacteristic
618C22#9200111yescharacteristic
619C22C2×#677711yescharacteristic
620C22D5×#23511yescharacteristic
621C22D5×#23511yescharacteristic
622C22#9201911yescharacteristic
623C22C22×D5×Dic311yescharacteristic
624C4—22no—
625C4—22no—
626C4—102no—
627C4—102no—
628C4—122no—
629C4—122no—
630C4—304no—
631C4—602no—
632C4#9143414yes—
633C3#1060596011yescharacteristic, complemented, Sylow
634C2—104no—
635C2—202no—
636C2#1175255311yescharacteristic
637C2#1175257311yescharacteristic
638C2#1175257711yescharacteristic
639C2#1175274811yescharacteristic
640C2C2×#9143411yescharacteristic
641C2D5×#92611yescharacteristic
642C2#1175450911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2352
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×D5×C4⋊Dic3C2semidirect
3. C2×#91358C2semidirect
4. C4×C4⋊Dic15C2semidirect
5. C5×#4936C2semidirect
7. #11748884C2semidirect
8. #11748791C2semidirect
9. #11748759C2semidirect
10. #11748759C2semidirect
11. #11748698C2semidirect
26. C3×C4×D20C4semidirect
70. C2×C3×C4×D5C2×C4semidirect
74. C3×C42×C5C2×C4semidirect
76. C4⋊Dic15D4semidirect
81. C3×#685C2×C4semidirect
82. C3×C4⋊Dic5C2×C4semidirect
97. #4936D5semidirect
119. C4×D20Dic3semidirect
220. C2×C4×D5C2×Dic3semidirect
223. C42×C5C2×Dic3semidirect
228. #685C2×Dic3semidirect
231. C4⋊Dic5C2×Dic3semidirect
266. C2×C3×D5#117semidirect
302. C3×C42C4×D5semidirect
460. C2×D5#926semidirect
506. C42D5×Dic3semidirect
507. C3×C5#2352semidirect
602. C5#82335semidirect
633. C3#10605960semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
C2×D5×C4⋊Dic32
C2×#913582
C4×C4⋊Dic152
C5×#49362
#117488962
#117488842
#117487912
#117487592
#117486982
#106059603
#823355