Finite Group Databasebeta

← #14331659

Subgroups — #14331659

Order 1920.

1888 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6769C211yesmaximal, characteristic, complemented
2C2×#91446C211yesmaximal, characteristic, complemented
3C2×#91428C212yesmaximal, complemented
4#11750772C211yesmaximal, characteristic, complemented
5C5×#4666C211yesmaximal, characteristic, complemented
6C3×#64945C211yesmaximal, characteristic, complemented
7#11748932C212yesmaximal, complemented
8#11748924C212yesmaximal, complemented
9#11748881C212yesmaximal, complemented
10#11748769C211yesmaximal, characteristic, complemented
11#11748753C211yesmaximal, characteristic, complemented
12#10605311—31nomaximal, Hall
13C22×D60C2212yes—
14C22×D60C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C22×C3×Dic10C2211yescharacteristic
17C22×#1203C2211yescharacteristic
18C22×#1203C2212yes—
19C22×#1200C2211yescharacteristic
20C22×#1200C2212yes—
21C2×#6769—24no—
22C2×#6769—28no—
23C2×#6714C2212yes—
24C2×#6714C2211yescharacteristic
25C2×C5×(C2×D3)⋊C4C2212yes—
26C2×C4×C5×Dic3C2212yes—
27C2×C3×C4⋊Dic5C2212yes—
28C2×C3×#683C2211yescharacteristic
29C2×#6667C2212yes—
30C2×#6667C2212yes—
31C2×#6667C2212yes—
32C2×(C2×D3)⋊Dic5C2211yescharacteristic
33C2×Dic3×Dic5C2211yescharacteristic
34#91446—24no—
35#91428—28no—
36C3×C5×#95C2211yescharacteristic
37C5×C3⋊#95C2211yescharacteristic
38C3×#3963C2212yes—
39#90994C2212yes—
40#77169—51nomaximal, Hall
41C22×#709—31no—
42C2×C4×C22⋊D5—31no—
43C2×C4×D20—32no—
44C4×C5×C22⋊C4—31no—
45#65250—32no—
46#65249—32no—
47C4×#685—32no—
48#64962—31no—
49#64961—31no—
50#64960—31no—
51#64945D311yescharacteristic, complemented
52C23×D15C2312yes—
53C23×D15C2311yescharacteristic
54C23×C5×D3C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2312yes—
57C22×Dic15C2311yescharacteristic
58C2×D60—24no—
59C2×D60—24no—
60C2×D60—24no—
61C2×D60—22no—
62C2×D60—24no—
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2311yescharacteristic
65C2×C4×C5×D3—24no—
66C2×C4×C5×D3D414yescomplemented
67C22×C3×Dic5C2311yescharacteristic
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2311yescharacteristic
70C2×C3×Dic10—22no—
71C2×C3×Dic10—24no—
72C2×#1203—24no—
73C2×#1203—22no—
74C2×#1203—22no—
75C2×#1203—24no—
76C2×#1203—24no—
77C2×#1203—22no—
78C2×#1200—24no—
79C2×#1200—24no—
80C2×#1200—24no—
81C2×#1200—22no—
82C2×#1200D418yescomplemented
83#6769—232no—
84#6714—22no—
85#6714—24no—
86C5×(C2×D3)⋊C4—24no—
87C4×C5×Dic3—24no—
88C3×C4⋊Dic5—24no—
89C3×#683—22no—
90#6667—24no—
91#6667—24no—
92#6667—24no—
93(C2×D3)⋊Dic5—22no—
94Dic3×Dic5—22no—
95C22×#239—51no—
96C2×#893—51no—
97C2×#893—52no—
98C3×#395—51no—
99#5231—51no—
100#4991—52no—
101#4991—51no—
102#4671—52no—
103#4671—51no—
104#4666—52no—
105#4666D511yescharacteristic, complemented
106C23×C4×C5—31no—
107C22×C22⋊D5—31no—
108C22×C22⋊D5—32no—
109C2×#709—68no—
110C2×#709—64no—
111C22×D20—32no—
112C22×D20—31no—
113C22×C4×D5—32no—
114C22×C4×D5—31no—
115C22×Dic10C2×D311yescharacteristic
116C2×C5×C22⋊C4—32no—
117C2×C42×C5—32no—
118C2×C22⋊Dic5—31no—
119C4×C22⋊D5—64no—
120C2×#685—31no—
121C2×#685—32no—
122C2×#685—32no—
123C2×#685—32no—
124C2×#685—32no—
125C2×C4⋊Dic5C2×D312yes—
126C2×#683C2×D311yescharacteristic
127C2×C4×Dic5—31no—
128C4×D20—68no—
129C5×#95—31no—
130C5×#95C2×D311yescharacteristic
131#3963—32no—
132#3963C2×D312yes—
133#2388—151noSylow
134C23×C3×C5C2411yescharacteristic
135C22×D15—22no—
136C22×D15—21no—
137C22×D15—22no—
138C22×D15—22no—
139C22×D15—22no—
140C22×D15—22no—
141C22×D15—21no—
142C22×D15—22no—
143C22×D15—22no—
144C22×D15—22no—
145C22×D15C2×D414yes—
146C22×D15#4112yescomplemented
147C22×C5×D3—22no—
148C22×C5×D3—22no—
149C22×C5×D3—21no—
150C22×C5×D3—21no—
151C22×C5×D3C2×D412yes—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5C2×D412yes—
156C2×C3×C4×C5#4114yescomplemented
157C2×Dic15—21no—
158C2×Dic15—22no—
159D60—28no—
160D60—216no—
161C2×C5×Dic3—22no—
162C2×C5×Dic3—22no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3C2×D412yes—
165C2×C5×Dic3C2×D414yes—
166C4×C5×D3—28no—
167C2×C3×Dic5—21no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5C2×D414yes—
174C2×C3×Dic5#4112yescomplemented
175C3×Dic10—28no—
176#1203—216no—
177#1203—28no—
178#1200—216no—
179#1200—44no—
180C22×C3×Q8—51no—
181C2×#239—108no—
182C2×#239—104no—
183C22×D12—51no—
184C22×D12—52no—
185C22×D12—52no—
186C22×D12—51no—
187C22×C4×D3—52no—
188C22×C4×D3—51no—
189C22×C4×D3C2×D511yescharacteristic
190C2×C3×C4⋊C4—51no—
191C2×C3×C4⋊C4—52no—
192C2×(C2×D3)⋊C4—51no—
193C2×(C2×D3)⋊C4—52no—
194C2×(C2×D3)⋊C4—51no—
195C2×(C2×D3)⋊C4—52no—
196C2×(C2×D3)⋊C4—52no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4C2×D512yes—
199C2×C4×Dic3—51no—
200C2×C4×Dic3C2×D512yes—
201#893—108no—
202#893—104no—
203C3×#95—52no—
204C3×#95C2×D511yescharacteristic
205C3⋊#95—52no—
206C3⋊#95C2×D511yescharacteristic
207C24×C5—31no—
208C23×D5—32no—
209C23×D5—31no—
210C22×C4×C5—31no—
211C22×C4×C5—34no—
212C22×C4×C5—32no—
213C22×C4×C5—64no—
214C22×C4×C5C22×D311yescharacteristic
215C22×C4×C5C22×D312yes—
216C2×C22⋊D5—64no—
217C2×C22⋊D5—62no—
218C2×C22⋊D5—64no—
219C2×C22⋊D5—62no—
220C2×C22⋊D5—64no—
221C2×C22⋊D5—62no—
222C22×Dic5—31no—
223C22×Dic5C22×D311yescharacteristic
224C22×Dic5C22×D312yes—
225C22×Dic5C22×D311yescharacteristic
226#709—632no—
227C2×D20—64no—
228C2×D20—64no—
229C2×D20—64no—
230C2×D20—62no—
231C2×D20—64no—
232C2×C4×D5—38no—
233C2×C4×D5—64no—
234C2×C4×D5—64no—
235C2×C4×D5—64no—
236C2×C4×D5—62no—
237C2×Dic10—22no—
238C2×Dic10—24no—
239C5×C22⋊C4—64no—
240C42×C5—64no—
241C22⋊Dic5—62no—
242#685—64no—
243#685—62no—
244#685—64no—
245#685—64no—
246#685—64no—
247C4⋊Dic5—24no—
248#683—22no—
249C4×Dic5—62no—
250C22×#41—151no—
251C2×C4×D4—152no—
252C2×C4×D4—151no—
253#395—51no—
254#394—151no—
255#394—152no—
256#393—151no—
257#392—152no—
258#392—151no—
259C4×C22⋊C4—31no—
260C4×C22⋊C4—152no—
261C22×C3×C5C22×D411yescharacteristic
262C22×C3×C5C22×D412yes—
263C22×C3×C5C2×#4112yes—
264C22×C3×C5C2×#4111yescharacteristic
265C22×C3×C5C2×#4111yescharacteristic
266C2×D15—24no—
267C2×D15—22no—
268C2×D15—24no—
269C2×D15—24no—
270C2×D15—24no—
271C2×D15—41no—
272C2×D15—42no—
273C2×D15—42no—
274C2×D15—41no—
275C2×D15—42no—
276C2×D15—42no—
277C2×D15—42no—
278C2×C5×D3—22no—
279C2×C5×D3—22no—
280C2×C5×D3—22no—
281C2×C5×D3—42no—
282C2×C5×D3—42no—
283C3×C4×C5—22no—
284C3×C4×C5—24no—
285Dic15—41no—
286C3×Dic5—24no—
287C3×Dic5—22no—
288C3×Dic5—41no—
289C5×Dic3—42no—
290C5×Dic3#12014yes—
291C23×D3—52no—
292C23×D3—51no—
293C23×D3C22×D511yescharacteristic
294C2×C3×Q8—104no—
295C2×C3×Q8—102no—
296C22×C3×C4—52no—
297C22×C3×C4—51no—
298C22×C3×C4—51no—
299C22×C3×C4C22×D511yescharacteristic
300C22×C3×C4C22×D512yes—
301C22×Dic3—51no—
302C22×Dic3C22×D512yes—
303C22×Dic3C22×D511yescharacteristic
304#239—1032no—
305C2×D12—104no—
306C2×D12—104no—
307C2×D12—104no—
308C2×D12—102no—
309C2×D12—104no—
310C2×D12—102no—
311C2×D12—104no—
312C2×D12—102no—
313C2×D12—104no—
314C2×D12—102no—
315C2×D12—104no—
316C2×C4×D3—24no—
317C2×C4×D3—58no—
318C2×C4×D3—104no—
319C2×C4×D3—104no—
320C2×C4×D3—102no—
321C2×C4×D3—104no—
322C2×C4×D3D2014yescomplemented
323C3×C4⋊C4—104no—
324C3×C4⋊C4—102no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—104no—
327(C2×D3)⋊C4—104no—
328(C2×D3)⋊C4—104no—
329(C2×D3)⋊C4—102no—
330(C2×D3)⋊C4—102no—
331(C2×D3)⋊C4—104no—
332C4×Dic3—24no—
333C4×Dic3—102no—
334C23×C5—32no—
335C23×C5—62no—
336C23×C5—62no—
337C23×C5—61no—
338C23×C5—61no—
339C23×C5C23×D311yescharacteristic
340C22×D5—34no—
341C22×D5—32no—
342C22×D5—62no—
343C22×D5—61no—
344C22×D5—62no—
345C22×D5—62no—
346C22×D5—62no—
347C22×D5—62no—
348C22×D5—62no—
349C22×D5—62no—
350C22×D5—61no—
351C22×D5—62no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—32no—
356C2×C4×C5—34no—
357C2×C4×C5—68no—
358C2×C4×C5—62no—
359C2×C4×C5—62no—
360C2×C4×C5—62no—
361C2×C4×C5D3×D412yes—
362C2×C4×C5#23914yescomplemented
363C22⋊D5—616no—
364C22⋊D5—68no—
365C2×Dic5—21no—
366C2×Dic5—22no—
367C2×Dic5—22no—
368C2×Dic5—21no—
369C2×Dic5—21no—
370C2×Dic5—22no—
371C2×Dic5—61no—
372C2×Dic5—62no—
373C2×Dic5D3×D414yes—
374C2×Dic5#23912yescomplemented
375D20—616no—
376D20—68no—
377C4×D5—616no—
378C4×D5—124no—
379Dic10—28no—
380C2×#41—304no—
381C2×#41—308no—
382C22×Q8—51no—
383C22×D4—151no—
384C22×D4—152no—
385C22×D4—152no—
386C22×D4—151no—
387C23×C4—31no—
388C23×C4—152no—
389C23×C4—151no—
390C4×D4—308no—
391C4×D4—304no—
392C2×C4⋊C4—51no—
393C2×C4⋊C4—52no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—152no—
396C2×C22⋊C4—152no—
397C2×C22⋊C4—152no—
398C2×C22⋊C4—151no—
399C2×C22⋊C4—151no—
400C2×C22⋊C4—152no—
401C2×C42—32no—
402C2×C42—151no—
403#95—31no—
404#95—52no—
405#95—152no—
406#95D3×D511yescharacteristic
407C2×C3×C5C2×#12011yescharacteristic
408C2×C3×C5#52511yescharacteristic
409C2×C3×C5#52512yes—
410C2×C3×C5#53211yescharacteristic
411C2×C3×C5#53212yes—
412D15—44no—
413D15—42no—
414C5×D3—42no—
415C23×C3C23×D511yescharacteristic
416C22×D3—22no—
417C22×D3—22no—
418C22×D3—21no—
419C22×D3—21no—
420C22×D3—54no—
421C22×D3—52no—
422C22×D3—101no—
423C22×D3—102no—
424C22×D3—102no—
425C22×D3—102no—
426C22×D3—102no—
427C22×D3—102no—
428C22×D3—102no—
429C22×D3—102no—
430C22×D3—102no—
431C22×D3—101no—
432C22×D3C2×D2012yes—
433C3×Q8—108no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—54no—
438C2×C3×C4—52no—
439C2×C3×C4—101no—
440C2×C3×C4—102no—
441C2×C3×C4—102no—
442C2×C3×C4—101no—
443C2×C3×C4—101no—
444C2×C3×C4—102no—
445C2×C3×C4C2×D2012yes—
446C2×C3×C4#70914yescomplemented
447C2×Dic3—22no—
448C2×Dic3—22no—
449C2×Dic3—22no—
450C2×Dic3—101no—
451C2×Dic3—102no—
452C2×Dic3C2×D2012yes—
453C2×Dic3D4×D514yes—
454D12—1016no—
455D12—108no—
456D12—108no—
457D12—1016no—
458C4×D3—28no—
459C4×D3—1016no—
460C4×D3—204no—
461C22×C5—62no—
462C22×C5—62no—
463C22×C5—62no—
464C22×C5—122no—
465C22×C5—122no—
466C22×C5C2×D3×D411yescharacteristic
467C22×C5C2×D3×D412yes—
468C22×C5C2×#23912yes—
469C22×C5C2×#23911yescharacteristic
470C22×C5D3×#4111yescharacteristic
471C2×D5—64no—
472C2×D5—64no—
473C2×D5—64no—
474C2×D5—64no—
475C2×D5—62no—
476C2×D5—121no—
477C2×D5—122no—
478C2×D5—122no—
479C2×D5—122no—
480C2×D5—121no—
481C2×D5—122no—
482C2×D5—122no—
483C4×C5—22no—
484C4×C5—24no—
485C4×C5—34no—
486C4×C5—122no—
487Dic5—24no—
488Dic5—22no—
489Dic5—41no—
490Dic5—121no—
491C24—31no—
492C24—152no—
493C24—151no—
494#41—3032no—
495C2×Q8—104no—
496C2×Q8—102no—
497C2×D4—304no—
498C2×D4—304no—
499C2×D4—304no—
500C2×D4—304no—
501C2×D4—302no—
502C2×D4—302no—
503C2×D4—304no—
504C2×D4—304no—
505C2×D4—302no—
506C2×D4—304no—
507C2×D4—302no—
508C22×C4—31no—
509C22×C4—34no—
510C22×C4—32no—
511C22×C4—51no—
512C22×C4—52no—
513C22×C4—51no—
514C22×C4—64no—
515C22×C4—158no—
516C22×C4—151no—
517C22×C4—304no—
518C22×C4—304no—
519C22×C4—302no—
520C22×C4—304no—
521C22×C4C2×D3×D512yes—
522C22×C4C2×D3×D511yescharacteristic
523C4⋊C4—104no—
524C4⋊C4—102no—
525C22⋊C4—64no—
526C22⋊C4—304no—
527C22⋊C4—304no—
528C22⋊C4—304no—
529C22⋊C4—302no—
530C22⋊C4—304no—
531C22⋊C4—302no—
532C42—64no—
533C42—302no—
534C3×C5#238811yescharacteristic, complemented, Hall
535C22×C3C22×D2011yescharacteristic
536C22×C3C2×#70912yes—
537C22×C3C2×D4×D512yes—
538C22×C3D5×#4111yescharacteristic
539C22×C3D5×#4111yescharacteristic
540C2×D3—22no—
541C2×D3—22no—
542C2×D3—22no—
543C2×D3—42no—
544C2×D3—42no—
545C2×D3—104no—
546C2×D3—102no—
547C2×D3—104no—
548C2×D3—104no—
549C2×D3—104no—
550C2×D3—201no—
551C2×D3—202no—
552C2×D3—201no—
553C2×D3—202no—
554C2×D3—202no—
555C2×D3—202no—
556C2×D3—202no—
557C3×C4—22no—
558C3×C4—24no—
559C3×C4—104no—
560C3×C4—102no—
561C3×C4—201no—
562Dic3—42no—
563Dic3—201no—
564Dic3#402814yes—
565C2×C5—122no—
566C2×C5D3×#12011yescharacteristic
567C2×C5#562712yes—
568C2×C5#562711yescharacteristic
569C2×C5#572511yescharacteristic
570C2×C5#572512yes—
571D5—124no—
572D5—122no—
573C23—32no—
574C23—62no—
575C23—62no—
576C23—61no—
577C23—61no—
578C23—154no—
579C23—152no—
580C23—302no—
581C23—302no—
582C23—302no—
583C23—301no—
584C23—302no—
585C23—302no—
586C23—302no—
587C23—302no—
588C23—302no—
589C23—301no—
590C23C22×D3×D511yescharacteristic
591Q8—108no—
592D4—308no—
593D4—3016no—
594D4—3016no—
595D4—308no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—32no—
600C2×C4—34no—
601C2×C4—54no—
602C2×C4—52no—
603C2×C4—68no—
604C2×C4—62no—
605C2×C4—62no—
606C2×C4—62no—
607C2×C4—101no—
608C2×C4—102no—
609C2×C4—102no—
610C2×C4—101no—
611C2×C4—101no—
612C2×C4—102no—
613C2×C4—3016no—
614C2×C4—302no—
615C2×C4—301no—
616C2×C4—604no—
617C2×C4#676914yescomplemented
618C2×C4D3×D2012yes—
619C2×C3#6581111yescharacteristic
620C2×C3C2×#402811yescharacteristic
621C2×C3#6585811yescharacteristic
622C2×C3#6588112yes—
623C2×C3#6588212yes—
624D3—42no—
625D3—204no—
626D3—202no—
627C5#7716911yescharacteristic, complemented, Sylow
628C22—62no—
629C22—62no—
630C22—62no—
631C22—122no—
632C22—122no—
633C22—304no—
634C22—304no—
635C22—302no—
636C22—304no—
637C22—304no—
638C22—602no—
639C22—601no—
640C22—602no—
641C22—602no—
642C22—602no—
643C22—602no—
644C22—601no—
645C22C2×#676912yes—
646C22C2×D3×D2011yescharacteristic
647C22D3×D4×D512yes—
648C22#9202411yescharacteristic
649C22D5×#23911yescharacteristic
650C4—24no—
651C4—22no—
652C4—34no—
653C4—102no—
654C4—104no—
655C4—122no—
656C4—201no—
657C4—601no—
658C3#1060531111yescharacteristic, complemented, Sylow
659C2—122no—
660C2—602no—
661C2—604no—
662C2#1175255011yescharacteristic
663C2#1175284912yes—
664C2D3×#402811yescharacteristic
665C2#1175342412yes—
666C2#1175388011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutator, socle, cosocleC23×C3×C5C24
FittingC3×C5×#95C22
hypercenter#95D3×D5
hypocenterC3×C5#2388
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C22×#6769C2semidirect
2. C2×#91446C2semidirect
3. C2×#91428C2semidirect
4. #11750772C2semidirect
5. C5×#4666C2semidirect
6. C3×#64945C2semidirect
7. #11748932C2semidirect
8. #11748924C2semidirect
9. #11748881C2semidirect
10. #11748769C2semidirect
11. #11748753C2semidirect
51. #64945D3semidirect
66. C2×C4×C5×D3D4semidirect
82. C2×#1200D4semidirect
105. #4666D5semidirect
146. C22×D15#41semidirect
156. C2×C3×C4×C5#41semidirect
174. C2×C3×Dic5#41semidirect
322. C2×C4×D3D20semidirect
362. C2×C4×C5#239semidirect
374. C2×Dic5#239semidirect
446. C2×C3×C4#709semidirect
534. C3×C5#2388semidirect
617. C2×C4#6769semidirect
627. C5#77169semidirect
658. C3#10605311semidirect

Maximal subgroups

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

subgroupindex
C22×#67692
C2×#914462
C2×#914282
#117507722
C5×#46662
C3×#649452
#117489322
#117489242
#117488812
#117487692
#117487532
#106053113
#771695