Finite Group Databasebeta

← #14411994

Subgroups — #14411994

Order 1920.

1600 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92019C211yesmaximal, characteristic
2#11756280C211yesmaximal, characteristic, complemented
3#11754515C211yesmaximal, characteristic, complemented
4C5×#5006C211yesmaximal, characteristic, complemented
5C3×#65295C211yesmaximal, characteristic, complemented
6#11748625C211yesmaximal, characteristic, complemented
7#11748624C211yesmaximal, characteristic, complemented
8#11747128C218yesmaximal, complemented
9#10610425—31nomaximal, Hall
10C22×D60C2211yescharacteristic
11C2×C5×#235C2211yescharacteristic
12C2×C3×#709C2211yescharacteristic
13C2×#6790C2214yes—
14#92019—22no—
15#92019—22no—
16#92019—22no—
17#92019—22no—
18C2×D3×D20C412yescomplemented
19C2×D5×D12C412yescomplemented
20C2×#6773C412yescomplemented
21C2×#6769C412yescomplemented
22C3×C5×#117C2211yescharacteristic, complemented
23#91815C2211yescharacteristic, complemented
24#91782—22no—
25C22⋊C4×D15C2214yescomplemented
26C4×D60—22no—
27C5×#926C2211yescharacteristic, complemented
28C3×#4072C2211yescharacteristic, complemented
29#91561C2214yescomplemented
30#91428—22no—
31#91418—22no—
32C5×#806C2214yescomplemented
33C3×#3938C2214yescomplemented
34#90996C2214yescomplemented
35#90995C2214yescomplemented
36#78694—51nomaximal, Hall
37C2×#4149—31no—
38#65855—31no—
39#65855—31no—
40C5×#410—31no—
41#65529—31no—
42#65295—31no—
43#65295D311yescharacteristic, complemented
44D5×#99—38no—
45C23×D15C2312yes—
46C22×D3×D5C2×C414yescomplemented
47C22×C3×C4×C5C2311yescharacteristic
48C2×D60C2×C412yes—
49C2×D60C2×C412yes—
50C2×D60D412yes—
51C2×D60D412yes—
52C2×D60D412yes—
53C2×D60D412yes—
54C2×C4×D15—24no—
55C2×C5×#67C2312yes—
56C5×#235—21no—
57C5×#235—21no—
58C5×#235—21no—
59C5×#235—21no—
60C2×C5×D12C2×C411yescharacteristic, complemented
61C2×C4×C5×D3C2×C412yescomplemented
62C2×C5×Dic6C2×C411yescharacteristic, complemented
63C2×C3×C22⋊D5C2312yes—
64C3×#709—21no—
65C3×#709—21no—
66C3×#709—21no—
67C3×#709—21no—
68C2×C3×D20C2×C411yescharacteristic, complemented
69C2×C3×C4×D5C2×C412yescomplemented
70C2×C3×Dic10C2×C411yescharacteristic, complemented
71#6790—28no—
72#6790—28no—
73C2×#1203C2×C414yescomplemented
74C2×#1202C2×C414yescomplemented
75C2×#1200—24no—
76C2×#1200C2×C414yescomplemented
77D3×D20—24no—
78D3×D20—24no—
79D5×D12—24no—
80D5×D12—24no—
81#6773—24no—
82#6773—24no—
83#6769—24no—
84#6769—24no—
85C3×C5×C4⋊C4—21no—
86C3×C5×C22⋊C4C2312yes—
87C3×C42×C5—21no—
88#6719C2312yes—
89#6714—24no—
90C4⋊Dic15—21no—
91C4×Dic15—21no—
92C5×#217C2312yes—
93C5×C4⋊Dic3—21no—
94C4×C5×Dic3—21no—
95C3×C22⋊Dic5C2312yes—
96C3×C4⋊Dic5—21no—
97C3×C4×Dic5—21no—
98#6667—24no—
99C2×#1009—51no—
100#5521—51no—
101#5521—51no—
102C3×#410—51no—
103#5240—51no—
104#5006—51no—
105#5006D511yescharacteristic, complemented
106D3×#99—58no—
107C2×C5×#41—31no—
108#4149—62no—
109#4149—62no—
110#4149—62no—
111#4149—62no—
112C2×#713—32no—
113C2×D4×D5—34no—
114C2×D4×D5—32no—
115C2×#709—32no—
116C2×#709C2×D311yescharacteristic
117C22×D20—31no—
118C22×D20—32no—
119C5×#117—31no—
120C5×#117C2×D311yescharacteristic, complemented
121#4072—31no—
122#4072C2×D311yescharacteristic, complemented
123#4039—62no—
124#4039—62no—
125D5×C22⋊C4—34no—
126D5×C22⋊C4—34no—
127C4×D20—62no—
128C4×D20—62no—
129C5×#99—34no—
130#3966—34no—
131#3938—34no—
132#3938C2×D314yescomplemented
133#2883—151noSylow
134C23×C3×C5C2411yescharacteristic
135C22×D15—82no—
136C22×D15C22×C414yes—
137C22×D15C2×D414yes—
138C22×D15C2×D414yes—
139C22×C5×D3C22×C412yes—
140C22×C3×D5C22×C412yes—
141C2×D3×D5—28no—
142C2×D3×D5—84no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C22×C411yescharacteristic
145C2×C3×C4×C5C22×C411yescharacteristic
146C2×C3×C4×C5C2×D411yescharacteristic
147C2×C3×C4×C5C2×D411yescharacteristic
148C2×C3×C4×C5C2×D411yescharacteristic
149C2×C3×C4×C5C2×D411yescharacteristic
150C2×Dic15—22no—
151D60C22⋊C414yes—
152D60C22⋊C414yes—
153D60C22⋊C414yes—
154D60C22⋊C414yes—
155C4×D15—84no—
156C5×#67—22no—
157C5×#67—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3C22×C412yes—
160C5×D12—21no—
161C5×D12—21no—
162C4×C5×D3—22no—
163C4×C5×D3—22no—
164C5×Dic6—21no—
165C5×Dic6—21no—
166C3×C22⋊D5—22no—
167C3×C22⋊D5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5C22×C412yes—
170C3×D20—21no—
171C3×D20—21no—
172C3×C4×D5—22no—
173C3×C4×D5—22no—
174C3×Dic10—21no—
175C3×Dic10—21no—
176#1203—28no—
177#1202—28no—
178#1200—28no—
179#1200—84no—
180C2×C3×#41—51no—
181#1009—102no—
182#1009—102no—
183#1009—102no—
184#1009—102no—
185C2×#239—52no—
186C2×D3×D4—54no—
187C2×D3×D4—52no—
188C2×#235—52no—
189C2×#235C2×D511yescharacteristic
190C22×D12—51no—
191C22×D12—52no—
192C3×#117—51no—
193C3×#117C2×D511yescharacteristic, complemented
194#926—51no—
195#926C2×D511yescharacteristic, complemented
196#893—102no—
197#893—102no—
198D3×C22⋊C4—54no—
199D3×C22⋊C4—54no—
200C4×D12—102no—
201C4×D12—102no—
202C3×#99—54no—
203#834—54no—
204#806—54no—
205#806C2×D514yescomplemented
206C23×D5—32no—
207C23×D5—34no—
208C5×#41—61no—
209C5×#41—61no—
210C5×#41—61no—
211C5×#41—61no—
212C2×C5×Q8—31no—
213C2×C5×D4—32no—
214C2×C5×D4—31no—
215C22×C4×C5—32no—
216C22×C4×C5C22×D311yescharacteristic
217C2×C22⋊D5—34no—
218C2×C22⋊D5C22×D312yes—
219#713—64no—
220#713—64no—
221D4×D5—64no—
222D4×D5—64no—
223D4×D5—68no—
224D4×D5—68no—
225#709—21no—
226#709—21no—
227#709—21no—
228#709—21no—
229#709—64no—
230#709—64no—
231C2×D20—32no—
232C2×D20—32no—
233C2×D20—32no—
234C2×D20—32no—
235C2×D20—32no—
236C2×D20—32no—
237C2×D20—34no—
238C2×D20—64no—
239C2×D20—64no—
240C2×D20C4×D311yescharacteristic, complemented
241C2×C4×D5—34no—
242C2×C4×D5—64no—
243C2×C4×D5—64no—
244C2×C4×D5C4×D312yescomplemented
245C2×Dic10C4×D311yescharacteristic, complemented
246C5×C4⋊C4—21no—
247C5×C4⋊C4—61no—
248C5×C22⋊C4—32no—
249C5×C22⋊C4C22×D312yes—
250C42×C5—21no—
251C42×C5—61no—
252C22⋊Dic5—32no—
253C22⋊Dic5C22×D312yes—
254#685—64no—
255#685—64no—
256C4⋊Dic5—21no—
257C4⋊Dic5—61no—
258C4×Dic5—21no—
259C4×Dic5—61no—
260C2×H(5,𝔽2)—151no—
261#518—151no—
262#518—151no—
263#410—31no—
264#410—51no—
265#410—151no—
266#410—151no—
267C2×#99—158no—
268C22×C3×C5—41no—
269C22×C3×C5C23×C411yescharacteristic
270C22×C3×C5C22×D411yescharacteristic
271C22×C3×C5C22×D411yescharacteristic
272C2×D15—44no—
273C2×D15—44no—
274C2×D15—44no—
275C2×D15C2×C22⋊C418yes—
276C2×C5×D3—22no—
277C2×C5×D3—42no—
278C2×C3×D5—22no—
279C2×C3×D5—42no—
280D3×D5—88no—
281C3×C4×C5—42no—
282C3×C4×C5C2×C22⋊C411yescharacteristic
283C3×C4×C5C2×C22⋊C411yescharacteristic
284C3×C4×C5C2×C22⋊C411yescharacteristic
285C3×C4×C5C2×C22⋊C411yescharacteristic
286Dic15—42no—
287C3×Dic5—22no—
288C3×Dic5—42no—
289C5×Dic3—22no—
290C5×Dic3—42no—
291C23×D3—52no—
292C23×D3—54no—
293C3×#41—101no—
294C3×#41—101no—
295C3×#41—101no—
296C3×#41—101no—
297C2×C3×Q8—51no—
298C2×C3×D4—52no—
299C2×C3×D4—51no—
300C22×C3×C4—52no—
301C22×C3×C4C22×D511yescharacteristic
302C2×#67—54no—
303C2×#67C22×D512yes—
304#239—104no—
305#239—104no—
306D3×D4—104no—
307D3×D4—104no—
308D3×D4—108no—
309D3×D4—108no—
310#235—21no—
311#235—21no—
312#235—21no—
313#235—21no—
314#235—104no—
315#235—104no—
316C2×D12—52no—
317C2×D12—52no—
318C2×D12—52no—
319C2×D12—52no—
320C2×D12—52no—
321C2×D12—52no—
322C2×D12—54no—
323C2×D12—104no—
324C2×D12—104no—
325C2×D12C4×D511yescharacteristic, complemented
326C2×C4×D3—54no—
327C2×C4×D3—104no—
328C2×C4×D3—104no—
329C2×C4×D3C4×D512yescomplemented
330C2×Dic6C4×D511yescharacteristic, complemented
331C3×C4⋊C4—21no—
332C3×C4⋊C4—101no—
333C3×C22⋊C4—52no—
334C3×C22⋊C4C22×D512yes—
335C3×C42—21no—
336C3×C42—101no—
337#217—52no—
338#217C22×D512yes—
339(C2×D3)⋊C4—104no—
340(C2×D3)⋊C4—104no—
341C4⋊Dic3—21no—
342C4⋊Dic3—101no—
343C4×Dic3—21no—
344C4×Dic3—101no—
345C23×C5—32no—
346C23×C5C23×D311yescharacteristic
347C22×D5—34no—
348C22×D5—34no—
349C22×D5—34no—
350C22×D5—68no—
351C22×D5—244no—
352C22×D5—242no—
353C22×D5C2×C4×D312yes—
354C5×Q8—61no—
355C5×Q8—61no—
356C5×D4—62no—
357C5×D4—62no—
358C5×D4—61no—
359C5×D4—61no—
360C2×C4×C5—22no—
361C2×C4×C5—32no—
362C2×C4×C5—62no—
363C2×C4×C5—62no—
364C2×C4×C5—62no—
365C2×C4×C5C2×C4×D311yescharacteristic
366C2×C4×C5C2×C4×D311yescharacteristic
367C2×C4×C5D3×D411yescharacteristic
368C2×C4×C5D3×D411yescharacteristic
369C2×C4×C5D3×D411yescharacteristic
370C2×C4×C5D3×D411yescharacteristic
371C22⋊D5—22no—
372C22⋊D5—22no—
373C22⋊D5—68no—
374C2×Dic5—22no—
375C2×Dic5—62no—
376C2×Dic5C2×C4×D312yes—
377D20—21no—
378D20—21no—
379D20—34no—
380D20—34no—
381D20—34no—
382D20—34no—
383D20—68no—
384C4×D5—22no—
385C4×D5—22no—
386C4×D5—68no—
387C4×D5—244no—
388C4×D5—244no—
389Dic10—21no—
390Dic10—21no—
391H(5,𝔽2)—302no—
392H(5,𝔽2)—302no—
393H(5,𝔽2)—302no—
394H(5,𝔽2)—302no—
395C2×#41—31no—
396C2×#41—51no—
397C2×#41—152no—
398C2×#41—152no—
399C22×D4—152no—
400C22×D4—152no—
401C22×D4—154no—
402C22×D4—151no—
403C4×D4—302no—
404C4×D4—302no—
405C4×D4—302no—
406C4×D4—302no—
407#117—31no—
408#117—51no—
409#117—151no—
410#117D3×D511yescharacteristic, complemented
411C2×C22⋊C4—154no—
412C2×C22⋊C4—154no—
413#99—34no—
414#99—54no—
415#99—154no—
416#99—154no—
417C2×C3×C5—21no—
418C2×C3×C5—21no—
419C2×C3×C5—21no—
420C2×C3×C5C22×C22⋊C411yescharacteristic
421D15—28no—
422C3×D5—42no—
423C5×D3—42no—
424C23×C3—52no—
425C23×C3C23×D511yescharacteristic
426C22×D3—54no—
427C22×D3—54no—
428C22×D3—54no—
429C22×D3—108no—
430C22×D3—404no—
431C22×D3—402no—
432C22×D3C2×C4×D512yes—
433C3×Q8—101no—
434C3×Q8—101no—
435C3×D4—102no—
436C3×D4—102no—
437C3×D4—101no—
438C3×D4—101no—
439C2×C3×C4—22no—
440C2×C3×C4—52no—
441C2×C3×C4—102no—
442C2×C3×C4—102no—
443C2×C3×C4—102no—
444C2×C3×C4C2×C4×D511yescharacteristic
445C2×C3×C4C2×C4×D511yescharacteristic
446C2×C3×C4D4×D511yescharacteristic
447C2×C3×C4D4×D511yescharacteristic
448C2×C3×C4D4×D511yescharacteristic
449C2×C3×C4D4×D511yescharacteristic
450#67—22no—
451#67—22no—
452#67—108no—
453C2×Dic3—22no—
454C2×Dic3—102no—
455C2×Dic3C2×C4×D512yes—
456D12—21no—
457D12—21no—
458D12—54no—
459D12—54no—
460D12—54no—
461D12—54no—
462D12—108no—
463C4×D3—22no—
464C4×D3—22no—
465C4×D3—108no—
466C4×D3—404no—
467C4×D3—404no—
468Dic6—21no—
469Dic6—21no—
470C22×C5—41no—
471C22×C5—62no—
472C22×C5—122no—
473C22×C5C22×C4×D311yescharacteristic
474C22×C5C2×D3×D411yescharacteristic
475C22×C5C2×D3×D411yescharacteristic
476C2×D5—22no—
477C2×D5—38no—
478C2×D5—42no—
479C2×D5—124no—
480C2×D5—124no—
481C2×D5—124no—
482C2×D5—248no—
483C4×C5—42no—
484C4×C5—62no—
485C4×C5—122no—
486C4×C5D3×C22⋊C411yescharacteristic
487C4×C5D3×C22⋊C411yescharacteristic
488C4×C5D3×C22⋊C411yescharacteristic
489C4×C5D3×C22⋊C411yescharacteristic
490Dic5—22no—
491Dic5—42no—
492Dic5—122no—
493C24—154no—
494C24—152no—
495#41—61no—
496#41—61no—
497#41—61no—
498#41—61no—
499#41—101no—
500#41—101no—
501#41—101no—
502#41—101no—
503#41—304no—
504#41—304no—
505#41—304no—
506#41—304no—
507C2×Q8—31no—
508C2×Q8—51no—
509C2×D4—32no—
510C2×D4—31no—
511C2×D4—52no—
512C2×D4—51no—
513C2×D4—154no—
514C2×D4—154no—
515C2×D4—152no—
516C2×D4—152no—
517C2×D4—152no—
518C2×D4—152no—
519C2×D4—152no—
520C2×D4—152no—
521C2×D4—304no—
522C2×D4—304no—
523C2×D4—304no—
524C2×D4—304no—
525C2×D4—308no—
526C2×D4—308no—
527C22×C4—32no—
528C22×C4—52no—
529C22×C4—154no—
530C22×C4—304no—
531C22×C4—304no—
532C22×C4C2×D3×D511yescharacteristic
533C4⋊C4—21no—
534C4⋊C4—61no—
535C4⋊C4—101no—
536C4⋊C4—301no—
537C22⋊C4—32no—
538C22⋊C4—52no—
539C22⋊C4—152no—
540C22⋊C4—304no—
541C22⋊C4—304no—
542C22⋊C4C2×D3×D512yes—
543C42—21no—
544C42—61no—
545C42—101no—
546C42—301no—
547C3×C5#288311yescharacteristic, complemented, Hall
548C22×C3—41no—
549C22×C3—102no—
550C22×C3—202no—
551C22×C3C22×C4×D511yescharacteristic
552C22×C3C2×D4×D511yescharacteristic
553C22×C3C2×D4×D511yescharacteristic
554C2×D3—22no—
555C2×D3—42no—
556C2×D3—58no—
557C2×D3—204no—
558C2×D3—204no—
559C2×D3—204no—
560C2×D3—408no—
561C3×C4—42no—
562C3×C4—102no—
563C3×C4—202no—
564C3×C4D5×C22⋊C411yescharacteristic
565C3×C4D5×C22⋊C411yescharacteristic
566C3×C4D5×C22⋊C411yescharacteristic
567C3×C4D5×C22⋊C411yescharacteristic
568Dic3—22no—
569Dic3—42no—
570Dic3—202no—
571C2×C5—21no—
572C2×C5—21no—
573C2×C5—21no—
574C2×C5—122no—
575C2×C5C2×D3×C22⋊C411yescharacteristic
576D5—42no—
577D5—68no—
578C23—32no—
579C23—52no—
580C23—154no—
581C23—154no—
582C23—154no—
583C23—308no—
584C23—1202no—
585C23—1204no—
586C23C22×D3×D511yescharacteristic
587Q8—61no—
588Q8—61no—
589Q8—101no—
590Q8—101no—
591D4—62no—
592D4—62no—
593D4—61no—
594D4—61no—
595D4—102no—
596D4—102no—
597D4—101no—
598D4—101no—
599D4—154no—
600D4—154no—
601D4—154no—
602D4—154no—
603D4—308no—
604D4—308no—
605C2×C4—22no—
606C2×C4—32no—
607C2×C4—52no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—62no—
611C2×C4—102no—
612C2×C4—102no—
613C2×C4—102no—
614C2×C4—308no—
615C2×C4—302no—
616C2×C4—1204no—
617C2×C4—1204no—
618C2×C4C4×D3×D511yescharacteristic
619C2×C4C4×D3×D511yescharacteristic
620C2×C4#677711yescharacteristic
621C2×C4#677711yescharacteristic
622C2×C4#679011yescharacteristic
623C2×C4#679011yescharacteristic
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—202no—
628C2×C3C2×D5×C22⋊C411yescharacteristic
629D3—42no—
630D3—108no—
631C5#7869411yescharacteristic, complemented, Sylow
632C22—41no—
633C22—62no—
634C22—102no—
635C22—122no—
636C22—158no—
637C22—202no—
638C22—604no—
639C22—604no—
640C22—604no—
641C22—1208no—
642C22C2×C4×D3×D511yescharacteristic
643C22C2×#677711yescharacteristic
644C22C2×#679011yescharacteristic
645C4—42no—
646C4—62no—
647C4—102no—
648C4—122no—
649C4—202no—
650C4—602no—
651C4#9147311yescharacteristic
652C4#9147311yescharacteristic
653C4#9147311yescharacteristic
654C4#9147311yescharacteristic
655C3#1061042511yescharacteristic, complemented, Sylow
656C2—21no—
657C2—21no—
658C2—21no—
659C2—122no—
660C2—202no—
661C2—308no—
662C2C2×#9147311yescharacteristic
subgroupG/H
centerC2C2×#91473
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5C22×C22⋊C4
prime radicalC2×#92019C2
cosocleC23×C3×C5C24
hypercenter#117D3×D5
hypocenterC3×C5#2883
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #11756280C2semidirect
3. #11754515C2semidirect
4. C5×#5006C2semidirect
5. C3×#65295C2semidirect
6. #11748625C2semidirect
7. #11748624C2semidirect
8. #11747128C2semidirect
18. C2×D3×D20C4semidirect
19. C2×D5×D12C4semidirect
20. C2×#6773C4semidirect
21. C2×#6769C4semidirect
22. C3×C5×#117C22semidirect
23. #91815C22semidirect
25. C22⋊C4×D15C22semidirect
27. C5×#926C22semidirect
28. C3×#4072C22semidirect
29. #91561C22semidirect
32. C5×#806C22semidirect
33. C3×#3938C22semidirect
34. #90996C22semidirect
35. #90995C22semidirect
43. #65295D3semidirect
46. C22×D3×D5C2×C4semidirect
60. C2×C5×D12C2×C4semidirect
61. C2×C4×C5×D3C2×C4semidirect
62. C2×C5×Dic6C2×C4semidirect
68. C2×C3×D20C2×C4semidirect
69. C2×C3×C4×D5C2×C4semidirect
70. C2×C3×Dic10C2×C4semidirect
73. C2×#1203C2×C4semidirect
74. C2×#1202C2×C4semidirect
76. C2×#1200C2×C4semidirect
105. #5006D5semidirect
120. C5×#117C2×D3semidirect
122. #4072C2×D3semidirect
132. #3938C2×D3semidirect
193. C3×#117C2×D5semidirect
195. #926C2×D5semidirect
205. #806C2×D5semidirect
240. C2×D20C4×D3semidirect
244. C2×C4×D5C4×D3semidirect
245. C2×Dic10C4×D3semidirect
325. C2×D12C4×D5semidirect
329. C2×C4×D3C4×D5semidirect
330. C2×Dic6C4×D5semidirect
410. #117D3×D5semidirect
547. C3×C5#2883semidirect
631. C5#78694semidirect
655. C3#10610425semidirect

Maximal subgroups

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

subgroupindex
C2×#920192
#117562802
#117545152
C5×#50062
C3×#652952
#117486252
#117486242
#117471282
#106104253
#786945