Finite Group Databasebeta

← #14412664

Subgroups — #14412664

Order 1920.

1556 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×#92019C211yesmaximal, characteristic
2C2×C5×#901C211yesmaximal, characteristic, complemented
3#11754513C211yesmaximal, characteristic, complemented
4C2×#91105C211yesmaximal, characteristic, complemented
5C3×#65402C211yesmaximal, characteristic, complemented
6#11748392C211yesmaximal, characteristic, complemented
7#11748369C211yesmaximal, characteristic, complemented
8#11748107C212yesmaximal, complemented
9D3×#3953C212yesmaximal, complemented
10#11747643C212yesmaximal, complemented
11#11747608C212yesmaximal, complemented
12#10615528—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C2×C5×#235C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C2×#6790—22no—
17#92019—24no—
18#92019C418yescomplemented
19C2×D3×D20C2212yes—
20C2×D5×D12—21no—
21C2×#6773—21no—
22C2×#6769C2212yes—
23C22×C3×C5×C8C2211yescharacteristic, complemented
24C2×C4⋊Dic15C2211yescharacteristic, complemented
25C2×C5×#208C2211yescharacteristic, complemented
26C5×#901—24no—
27C2×C5×ΓL(1,𝔽25)C2212yescomplemented
28C2×C5×D3×C8C2212yescomplemented
29C3×#4072C2211yescharacteristic, complemented
30#67⋊Dic5—22no—
31D3×C4⋊Dic5C2212yescomplemented
32Dic5×D12—21no—
33#91338C2212yescomplemented
34Dic5×Dic6—21no—
35#91105C2212yescomplemented
36#91105C2212yescomplemented
37C3×#3953C2211yescharacteristic, complemented
38C3×#3953C2211yescharacteristic, complemented
39C3×#3948C2211yescharacteristic, complemented
40C3×#3948C2211yescharacteristic, complemented
41#90971C2212yescomplemented
42#90968C2212yescomplemented
43#90968C2212yescomplemented
44#90965C2212yescomplemented
45#78831—51nomaximal, Hall
46C2×#4149—31no—
47C2×C5×#131—31no—
48#66161—31no—
49#65422—32no—
50#65422—31no—
51#65420—31no—
52#65420—32no—
53#65402—32no—
54#65402D311yescharacteristic, complemented
55C2×#3953—32no—
56C2×#3953—31no—
57C23×D15—21no—
58C22×D3×D5—22no—
59C22×C3×C4×C5C2311yescharacteristic
60C22×Dic15—21no—
61C2×D60—21no—
62C2×D60—22no—
63C2×D60C2×C414yescomplemented
64C2×D60C2312yes—
65C2×C5×#67D412yes—
66C5×#235C2×C414yes—
67C5×#235D414yes—
68C2×C5×D12D411yescharacteristic
69C2×C4×C5×D3C2312yes—
70C2×C5×Dic6D411yescharacteristic
71C2×C3×C22⋊D5—21no—
72C3×#709—22no—
73C3×#709C2×C414yescomplemented
74C2×C3×D20C2311yescharacteristic
75C2×C3×C4×D5—21no—
76C2×C3×Dic10C2311yescharacteristic
77#6790—216no—
78C2×#1203—22no—
79C2×#1202—22no—
80C2×#1200—22no—
81C2×D3×Dic5—22no—
82D3×D20—24no—
83D3×D20C2×C418yescomplemented
84D5×D12—28no—
85#6773—28no—
86#6769—24no—
87#6769C2×C418yescomplemented
88C2×C3×C5×C8—22no—
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C4⋊Dic15—21no—
92C4⋊Dic15C2312yes—
93C5×#208—22no—
94C2×C5×C3⋊C8C2312yes—
95C5×ΓL(1,𝔽25)—24no—
96C5×D3×C8—24no—
97C3×C22⋊Dic5—21no—
98C3×C4⋊Dic5C2311yescharacteristic
99C3×C4⋊Dic5C2311yescharacteristic
100C3×C4×Dic5—21no—
101Dic3⋊Dic5—22no—
102(C2×D3)⋊Dic5—22no—
103Dic3×Dic5—22no—
104C2×#1009—51no—
105C2×#901D511yescharacteristic, complemented
106#5523—51no—
107C3×#416—51no—
108#5232—51no—
109C2×#821—51no—
110#5001—51no—
111#4804—52no—
112#4803—52no—
113#4770—52no—
114D3×#102—52no—
115C2×C5×#41—31no—
116#4149—38no—
117#4149—64no—
118C2×#713—61no—
119C2×D4×D5—61no—
120C2×D4×D5—62no—
121C2×#709—32no—
122C2×#709C2×D311yescharacteristic
123C22×D20—31no—
124C22×D20—32no—
125C5×#131—64no—
126C2×C5×M16—31no—
127C2×C5×M16—32no—
128C22×C5×C8—32no—
129C22×C5×C8C2×D311yescharacteristic, complemented
130Q8×Dic5—61no—
131D4×Dic5—61no—
132D4×Dic5—62no—
133#4072—32no—
134#4072C2×D311yescharacteristic, complemented
135C2×C4⋊Dic5—31no—
136C2×C4⋊Dic5—32no—
137#3953—32no—
138#3953—32no—
139#3953—32no—
140#3953—32no—
141#3953—32no—
142#3953C2×D311yescharacteristic, complemented
143#3953C2×D311yescharacteristic, complemented
144#3948—32no—
145#3948C2×D311yescharacteristic, complemented
146#3948C2×D311yescharacteristic, complemented
147#2897—151noSylow
148C23×C3×C5C2×D411yescharacteristic
149C22×D15—22no—
150C22×D15—24no—
151C22×D15—81no—
152C22×D15—81no—
153C22×C5×D3C2×D412yes—
154C22×C3×D5—21no—
155C2×D3×D5—28no—
156C2×D3×D5—82no—
157C2×D3×D5—82no—
158C2×C3×C4×C5C22×C412yes—
159C2×C3×C4×C5C2×D411yescharacteristic
160C2×C3×C4×C5C2×D412yes—
161C2×C3×C4×C5C2411yescharacteristic
162C2×Dic15—22no—
163C2×Dic15—81no—
164D60—24no—
165D60—22no—
166D60C22×C414yes—
167C5×#67C22⋊C418yes—
168C2×C5×Dic3C2×D412yes—
169C5×D12C22⋊C414yes—
170C4×C5×D3C22×C414yes—
171C4×C5×D3C2×D414yes—
172C5×Dic6C22⋊C414yes—
173C3×C22⋊D5—24no—
174C2×C3×Dic5—21no—
175C2×C3×Dic5—21no—
176C2×C3×Dic5—21no—
177C3×D20—21no—
178C3×D20C22×C412yes—
179C3×C4×D5—24no—
180C3×Dic10—21no—
181C3×Dic10C22×C412yes—
182#1203—28no—
183#1202—28no—
184#1200—28no—
185D3×Dic5—82no—
186C3×C5×C8—21no—
187C3×C5×C8—21no—
188C5×C3⋊C8—22no—
189C2×C3×#41—51no—
190#1009—58no—
191#1009—104no—
192C2×#239—52no—
193C2×D3×D4—52no—
194C2×D3×D4—102no—
195C2×#235—101no—
196C2×#235C2×D511yescharacteristic
197C22×D12—51no—
198C22×D12—101no—
199C22×C3×C8C2×D511yescharacteristic, complemented
200C3×#117—51no—
201C2×C4⋊Dic3—51no—
202C2×#208C2×D511yescharacteristic, complemented
203#901—24no—
204C2×ΓL(1,𝔽25)C2×D512yescomplemented
205C2×D3×C8C2×D512yescomplemented
206#892—52no—
207D3×C4⋊C4—52no—
208#67⋊C4—102no—
209C4×D12—101no—
210C4×Dic6—101no—
211C3×#103—51no—
212C3×#103—51no—
213C3×#102—51no—
214C3×#102—51no—
215#835—52no—
216#832—52no—
217#821—52no—
218#821—52no—
219#809—52no—
220#809—52no—
221C23×D5—62no—
222C23×D5—61no—
223C5×#41—34no—
224C5×#41—34no—
225C2×C5×Q8—31no—
226C2×C5×D4—32no—
227C2×C5×D4—31no—
228C22×C4×C5—32no—
229C22×C4×C5C22×D311yescharacteristic
230C2×C22⋊D5—21no—
231C2×C22⋊D5—62no—
232C22×Dic5—62no—
233C22×Dic5—61no—
234#713—68no—
235D4×D5—68no—
236D4×D5—616no—
237#709—22no—
238#709—38no—
239#709—64no—
240#709C4×D314yescomplemented
241C2×D20—34no—
242C2×D20—32no—
243C2×D20—38no—
244C2×D20—64no—
245C2×D20—62no—
246C2×D20—61no—
247C2×D20—62no—
248C2×D20C22×D311yescharacteristic
249C2×C4×D5—21no—
250C2×C4×D5—62no—
251C2×Dic10C22×D311yescharacteristic
252C5×M16—64no—
253C5×M16—62no—
254C2×C5×C8—22no—
255C2×C5×C8—32no—
256C2×C5×C8—64no—
257C2×C5×C8C22×D311yescharacteristic
258C2×C5×C8C22×D311yescharacteristic
259C22⋊Dic5—21no—
260C22⋊Dic5—62no—
261C4⋊Dic5—32no—
262C4⋊Dic5—62no—
263C4⋊Dic5—61no—
264C4⋊Dic5C22×D311yescharacteristic
265C4⋊Dic5C22×D311yescharacteristic
266C4×Dic5—21no—
267C4×Dic5—62no—
268C2×H(5,𝔽2)—151no—
269C2×#131—31no—
270#520—151no—
271#418—152no—
272#418—151no—
273#417—152no—
274#417—151no—
275#416—51no—
276#416—152no—
277C2×#102—152no—
278C2×#102—151no—
279C22×C3×C5—21no—
280C22×C3×C5—21no—
281C22×C3×C5C2×C22⋊C412yes—
282C22×C3×C5C22×D411yescharacteristic
283C2×D15—24no—
284C2×D15—42no—
285C2×D15—42no—
286C2×D15—84no—
287C2×C5×D3—22no—
288C2×C5×D3—22no—
289C2×C5×D3C2×C22⋊C414yes—
290C2×C3×D5—22no—
291C2×C3×D5—41no—
292C2×C3×D5—41no—
293D3×D5—88no—
294C3×C4×C5C2×C22⋊C412yes—
295C3×C4×C5C23×C411yescharacteristic
296C3×C4×C5C22×D411yescharacteristic
297Dic15—42no—
298C3×Dic5—22no—
299C3×Dic5—41no—
300C3×Dic5—41no—
301C5×Dic3C2×C22⋊C414yes—
302C23×D3—101no—
303C23×D3—102no—
304C3×#41—54no—
305C3×#41—102no—
306C2×C3×Q8—51no—
307C2×C3×D4—51no—
308C2×C3×D4—101no—
309C22×C3×C4—101no—
310C22×C3×C4C22×D511yescharacteristic
311C2×#67—102no—
312C2×#67D2012yes—
313C22×Dic3—101no—
314#239—58no—
315#239—104no—
316D3×D4—58no—
317D3×D4—1016no—
318D3×D4—104no—
319#235—108no—
320#235C4×D514yes—
321#235C22⋊D514yes—
322C2×D12—54no—
323C2×D12—52no—
324C2×D12—102no—
325C2×D12—101no—
326C2×D12—102no—
327C2×D12—108no—
328C2×D12D2011yescharacteristic
329C2×C4×D3—102no—
330C2×C4×D3—102no—
331C2×C4×D3C22×D512yes—
332C2×Dic6D2011yescharacteristic
333C2×C3×C8—22no—
334C2×C3×C8C22×D511yescharacteristic
335C2×C3×C8C22×D511yescharacteristic
336C3×C4⋊C4—51no—
337C3×C4⋊C4—51no—
338C3×C22⋊C4—101no—
339C3×C42—101no—
340(C2×D3)⋊C4—102no—
341C4⋊Dic3—52no—
342C4⋊Dic3—101no—
343Dic3⋊C4—102no—
344C4×Dic3—102no—
345#208—22no—
346C2×C3⋊C8C22×D512yes—
347ΓL(1,𝔽25)—24no—
348D3×C8—24no—
349C23×C5—32no—
350C23×C5D3×D411yescharacteristic
351C22×D5—21no—
352C22×D5—68no—
353C22×D5—62no—
354C22×D5—64no—
355C22×D5—242no—
356C22×D5—242no—
357C22×D5—241no—
358C22×D5—241no—
359C5×Q8—34no—
360C5×D4—38no—
361C5×D4—34no—
362C2×C4×C5—32no—
363C2×C4×C5—34no—
364C2×C4×C5—34no—
365C2×C4×C5C2×C4×D312yes—
366C2×C4×C5D3×D411yescharacteristic
367C2×C4×C5D3×D412yes—
368C2×C4×C5C23×D311yescharacteristic
369C22⋊D5—24no—
370C22⋊D5—68no—
371C2×Dic5—21no—
372C2×Dic5—21no—
373C2×Dic5—21no—
374C2×Dic5—62no—
375C2×Dic5—242no—
376C2×Dic5—241no—
377D20—21no—
378D20—34no—
379D20—68no—
380D20—64no—
381D20—62no—
382D20C2×C4×D312yes—
383C4×D5—24no—
384C4×D5—68no—
385Dic10—21no—
386Dic10C2×C4×D312yes—
387C5×C8—21no—
388C5×C8—21no—
389C5×C8—62no—
390H(5,𝔽2)—158no—
391H(5,𝔽2)—304no—
392C2×#41—31no—
393C2×#41—51no—
394C2×#41—152no—
395C2×#41—301no—
396C22×D4—152no—
397C22×D4—151no—
398C22×D4—301no—
399C22×D4—302no—
400#131—64no—
401C2×M16—31no—
402C2×M16—32no—
403C22×C8—32no—
404C22×C8D3×D511yescharacteristic, complemented
405C4×Q8—301no—
406C4×D4—301no—
407C4×D4—302no—
408#117—51no—
409#117—152no—
410C2×C4⋊C4—152no—
411C2×C4⋊C4—151no—
412#103—51no—
413#103—51no—
414#103—152no—
415#102—51no—
416#102—51no—
417#102—152no—
418#102—152no—
419#102—152no—
420#102—152no—
421#102—152no—
422C2×C3×C5—22no—
423C2×C3×C5C22×C22⋊C411yescharacteristic
424C2×C3×C5#57611yescharacteristic
425C2×C3×C5#57711yescharacteristic
426D15—44no—
427C3×D5—42no—
428C5×D3—24no—
429C23×C3—101no—
430C23×C3C2×D2011yescharacteristic
431C22×D3—102no—
432C22×D3—104no—
433C22×D3—108no—
434C22×D3—402no—
435C22×D3—402no—
436C22×D3—401no—
437C22×D3—401no—
438C22×D3C2×D2012yes—
439C3×Q8—52no—
440C3×Q8—101no—
441C3×D4—52no—
442C3×D4—104no—
443C3×D4—101no—
444C2×C3×C4—101no—
445C2×C3×C4—104no—
446C2×C3×C4—101no—
447C2×C3×C4—101no—
448C2×C3×C4C2×C4×D512yes—
449C2×C3×C4C2×D2011yescharacteristic
450C2×C3×C4C2×C22⋊D512yes—
451C2×C3×C4C23×D511yescharacteristic
452#67—108no—
453#67#68518yes—
454C2×Dic3—102no—
455C2×Dic3—401no—
456C2×Dic3C2×D2012yes—
457D12—54no—
458D12—108no—
459D12—102no—
460D12—104no—
461D12#68514yes—
462C4×D3—108no—
463C4×D3—402no—
464C4×D3C2×C4×D514yes—
465C4×D3C2×C22⋊D514yes—
466Dic6#68514yes—
467C3×C8—21no—
468C3×C8—21no—
469C3⋊C8—22no—
470C22×C5—21no—
471C22×C5—21no—
472C22×C5—34no—
473C22×C5—62no—
474C22×C5—62no—
475C22×C5D3×C22⋊C412yes—
476C22×C5C2×D3×D411yescharacteristic
477C2×D5—22no—
478C2×D5—41no—
479C2×D5—41no—
480C2×D5—64no—
481C2×D5—122no—
482C2×D5—122no—
483C2×D5—248no—
484C2×D5—244no—
485C4×C5—34no—
486C4×C5D3×C22⋊C412yes—
487C4×C5C22×C4×D311yescharacteristic
488C4×C5C2×D3×D411yescharacteristic
489Dic5—22no—
490Dic5—41no—
491Dic5—41no—
492Dic5—122no—
493C24—302no—
494C24—301no—
495#41—34no—
496#41—34no—
497#41—54no—
498#41—102no—
499#41—158no—
500#41—304no—
501#41—308no—
502C2×Q8—31no—
503C2×Q8—51no—
504C2×D4—32no—
505C2×D4—31no—
506C2×D4—51no—
507C2×D4—101no—
508C2×D4—158no—
509C2×D4—154no—
510C2×D4—152no—
511C2×D4—304no—
512C2×D4—302no—
513C2×D4—308no—
514C2×D4—302no—
515C2×D4—3016no—
516C2×D4—301no—
517C2×D4—302no—
518C22×C4—32no—
519C22×C4—101no—
520C22×C4—302no—
521C22×C4—302no—
522C22×C4—301no—
523C22×C4C2×D3×D511yescharacteristic
524M16—64no—
525M16—62no—
526C2×C8—22no—
527C2×C8—32no—
528C2×C8—64no—
529C2×C8C2×D3×D511yescharacteristic
530C2×C8C2×D3×D511yescharacteristic
531C4⋊C4—51no—
532C4⋊C4—51no—
533C4⋊C4—152no—
534C4⋊C4—302no—
535C4⋊C4—301no—
536C22⋊C4—101no—
537C22⋊C4—302no—
538C42—101no—
539C42—302no—
540C3×C5#289711yescharacteristic, complemented, Hall
541C22×C3—21no—
542C22×C3—21no—
543C22×C3—102no—
544C22×C3—201no—
545C22×C3—201no—
546C22×C3C2×#68512yes—
547C22×C3C22×D2011yescharacteristic
548C2×D3—22no—
549C2×D3—22no—
550C2×D3—104no—
551C2×D3—202no—
552C2×D3—202no—
553C2×D3—408no—
554C2×D3—404no—
555C2×D3C2×#68514yes—
556C3×C4—102no—
557C3×C4—201no—
558C3×C4—201no—
559C3×C4C2×#68512yes—
560C3×C4C22×C4×D511yescharacteristic
561C3×C4C22×C22⋊D511yescharacteristic
562Dic3—202no—
563Dic3C2×#68514yes—
564C2×C5—22no—
565C2×C5—64no—
566C2×C5C2×D3×C22⋊C411yescharacteristic
567C2×C5#576911yescharacteristic
568C2×C5#577011yescharacteristic
569D5—42no—
570D5—124no—
571C23—32no—
572C23—101no—
573C23—308no—
574C23—302no—
575C23—304no—
576C23—1201no—
577C23—1201no—
578C23—1202no—
579C23—1202no—
580C23D3×D2011yescharacteristic
581Q8—34no—
582Q8—52no—
583Q8—101no—
584D4—38no—
585D4—34no—
586D4—52no—
587D4—104no—
588D4—101no—
589D4—154no—
590D4—308no—
591D4—308no—
592D4—304no—
593D4—302no—
594C2×C4—32no—
595C2×C4—34no—
596C2×C4—34no—
597C2×C4—101no—
598C2×C4—104no—
599C2×C4—101no—
600C2×C4—101no—
601C2×C4—308no—
602C2×C4—302no—
603C2×C4—1202no—
604C2×C4—1201no—
605C2×C4C4×D3×D512yes—
606C2×C4D3×D2011yescharacteristic
607C2×C4D3×C22⋊D512yes—
608C2×C4C22×D3×D511yescharacteristic
609C8—21no—
610C8—21no—
611C8—62no—
612C2×C3—22no—
613C2×C3—202no—
614C2×C3#6608511yescharacteristic
615C2×C3#6608611yescharacteristic
616C2×C3C22×#68511yescharacteristic
617D3—24no—
618D3—204no—
619C5#7883111yescharacteristic, complemented, Sylow
620C22—21no—
621C22—21no—
622C22—34no—
623C22—62no—
624C22—62no—
625C22—102no—
626C22—201no—
627C22—201no—
628C22—304no—
629C22—602no—
630C22—602no—
631C22—1204no—
632C22—1208no—
633C22D3×#68512yes—
634C22C2×D3×D2011yescharacteristic
635C4—34no—
636C4—102no—
637C4—201no—
638C4—201no—
639C4—602no—
640C4D3×#68512yes—
641C4C2×C4×D3×D511yescharacteristic
642C4C2×D3×C22⋊D511yescharacteristic
643C3#1061552811yescharacteristic, complemented, Sylow
644C2—22no—
645C2—64no—
646C2—202no—
647C2—604no—
648C2#1175397211yescharacteristic
649C2#1175397311yescharacteristic
650C2C2×D3×#68511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#92019C2
cosocleC2×C3×C4×C5C24
hypercenterC22×C8D3×D5
hypocenterC3×C5#2897
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C5×#901C2semidirect
3. #11754513C2semidirect
4. C2×#91105C2semidirect
5. C3×#65402C2semidirect
6. #11748392C2semidirect
7. #11748369C2semidirect
8. #11748107C2semidirect
9. D3×#3953C2semidirect
10. #11747643C2semidirect
11. #11747608C2semidirect
18. #92019C4semidirect
23. C22×C3×C5×C8C22semidirect
24. C2×C4⋊Dic15C22semidirect
25. C2×C5×#208C22semidirect
27. C2×C5×ΓL(1,𝔽25)C22semidirect
28. C2×C5×D3×C8C22semidirect
29. C3×#4072C22semidirect
31. D3×C4⋊Dic5C22semidirect
33. #91338C22semidirect
35. #91105C22semidirect
36. #91105C22semidirect
37. C3×#3953C22semidirect
38. C3×#3953C22semidirect
39. C3×#3948C22semidirect
40. C3×#3948C22semidirect
41. #90971C22semidirect
42. #90968C22semidirect
43. #90968C22semidirect
44. #90965C22semidirect
54. #65402D3semidirect
63. C2×D60C2×C4semidirect
73. C3×#709C2×C4semidirect
83. D3×D20C2×C4semidirect
87. #6769C2×C4semidirect
105. C2×#901D5semidirect
129. C22×C5×C8C2×D3semidirect
134. #4072C2×D3semidirect
142. #3953C2×D3semidirect
143. #3953C2×D3semidirect
145. #3948C2×D3semidirect
146. #3948C2×D3semidirect
199. C22×C3×C8C2×D5semidirect
202. C2×#208C2×D5semidirect
204. C2×ΓL(1,𝔽25)C2×D5semidirect
205. C2×D3×C8C2×D5semidirect
240. #709C4×D3semidirect
404. C22×C8D3×D5semidirect
540. C3×C5#2897semidirect
619. C5#78831semidirect
643. C3#10615528semidirect

Maximal subgroups

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

subgroupindex
C2×#920192
C2×C5×#9012
#117545132
C2×#911052
C3×#654022
#117483922
#117483692
#117481072
D3×#39532
#117476432
#117476082
#106155283
#788315