Finite Group Databasebeta

← #14331671

Subgroups — #14331671

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×#6765C211yesmaximal, characteristic, complemented
2C2×#91446C211yesmaximal, characteristic, complemented
3C2×#91395C212yesmaximal, complemented
4#11750774C211yesmaximal, characteristic, complemented
5C5×#4666C211yesmaximal, characteristic, complemented
6C3×#64961C211yesmaximal, characteristic, complemented
7#11748925C212yesmaximal, complemented
8#11748923C211yesmaximal, characteristic, complemented
9#11748922C212yesmaximal, complemented
10Dic3×#685C212yesmaximal, complemented
11#11748846C211yesmaximal, characteristic, complemented
12#10605311—31nomaximal, Hall
13C22×Dic30C2211yescharacteristic
14C22×C4×C5×D3C2211yescharacteristic
15C22×C3×D20C2211yescharacteristic
16C22×#1203C2211yescharacteristic
17C22×#1202C2212yes—
18C22×#1201C2212yes—
19C22×#1200C2211yescharacteristic
20C22×D5×Dic3C2212yes—
21C2×#6765—24no—
22C2×#6765—28no—
23C2×#6714C2211yescharacteristic
24C2×#6714C2212yes—
25C2×C5×(C2×D3)⋊C4C2212yes—
26C2×C4×C5×Dic3C2212yes—
27C2×C3×#685C2212yes—
28C2×C3×#685C2212yes—
29C2×C3×#683C2211yescharacteristic
30C2×Dic3⋊Dic5C2212yes—
31C2×(C2×D3)⋊Dic5C2211yescharacteristic
32C2×#6665C2212yes—
33C2×Dic3×Dic5C2211yescharacteristic
34#91446—24no—
35#91395—28no—
36C3×C5×#95C2211yescharacteristic
37#91115C2212yes—
38C5×C3⋊#95C2211yescharacteristic
39#90994C2212yes—
40#76889—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#64961D311yescharacteristic, complemented
50#64960—31no—
51#64945—31no—
52C23×D15C2311yescharacteristic
53C23×C5×D3C2311yescharacteristic
54C23×C3×D5C2312yes—
55C22×C3×C4×C5C2312yes—
56C22×C3×C4×C5C2311yescharacteristic
57C22×Dic15C2311yescharacteristic
58C22×Dic15C2312yes—
59C2×Dic30—22no—
60C2×Dic30—24no—
61C22×C5×Dic3C2312yes—
62C22×C5×Dic3C2311yescharacteristic
63C2×C4×C5×D3—24no—
64C2×C4×C5×D3D414yescomplemented
65C22×C3×Dic5C2311yescharacteristic
66C22×C3×Dic5C2311yescharacteristic
67C2×C3×D20—24no—
68C2×C3×D20—22no—
69C2×#1203—22no—
70C2×#1203—22no—
71C2×#1203—22no—
72C2×#1202—24no—
73C2×#1202—24no—
74C2×#1202—24no—
75C2×#1201—24no—
76C2×#1201—24no—
77C2×#1201—24no—
78C2×#1200—24no—
79C2×#1200—22no—
80C2×D5×Dic3—24no—
81C2×D5×Dic3—24no—
82C2×D5×Dic3D418yescomplemented
83#6765—232no—
84#6714—22no—
85#6714—24no—
86C5×(C2×D3)⋊C4—24no—
87C4×C5×Dic3—24no—
88C3×#685—24no—
89C3×#685—24no—
90C3×#683—22no—
91Dic3⋊Dic5—24no—
92(C2×D3)⋊Dic5—22no—
93#6665—24no—
94Dic3×Dic5—22no—
95C22×#237—51no—
96C2×#893—51no—
97C2×#67⋊C4—52no—
98C3×#394—51no—
99#5223—51no—
100#4979—51no—
101#4960—52no—
102#4959—52no—
103Dic3×C22⋊C4—52no—
104#4673—51no—
105#4666D511yescharacteristic, complemented
106C23×C4×C5—31no—
107C22×C22⋊D5—32no—
108C22×C22⋊D5—31no—
109C2×#709—68no—
110C2×#709—64no—
111C22×D20—32no—
112C22×D20C2×D311yescharacteristic
113C22×C4×D5—32no—
114C22×C4×D5—31no—
115C22×Dic10—31no—
116C2×C5×C22⋊C4—32no—
117C2×C42×C5—32no—
118C2×C22⋊Dic5—31no—
119C4×C22⋊D5—64no—
120C2×#685—32no—
121C2×#685—32no—
122C2×#685—31no—
123C2×#685C2×D312yes—
124C2×#685C2×D312yes—
125C2×C4⋊Dic5—32no—
126C2×#683C2×D311yescharacteristic
127C2×C4×Dic5—31no—
128C4×D20—68no—
129C5×#95—31no—
130C5×#95C2×D311yescharacteristic
131#3963—32no—
132#3963—32no—
133#2388—151noSylow
134C23×C3×C5C2411yescharacteristic
135C22×D15—22no—
136C22×D15—21no—
137C22×D15—22no—
138C22×D15—21no—
139C22×D15#4112yescomplemented
140C22×C5×D3—22no—
141C22×C5×D3—22no—
142C22×C5×D3—21no—
143C22×C5×D3—21no—
144C22×C5×D3C2×D412yes—
145C22×C3×D5—22no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5C2×D414yes—
152C2×C3×C4×C5—22no—
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—22no—
155C2×C3×C4×C5—22no—
156C2×C3×C4×C5C2×D412yes—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—21no—
160C2×Dic15—22no—
161C2×Dic15C2×D414yes—
162Dic30—28no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—22no—
165C2×C5×Dic3C2×D412yes—
166C2×C5×Dic3C2×D414yes—
167C2×C5×Dic3#4114yescomplemented
168C4×C5×D3—28no—
169C2×C3×Dic5—21no—
170C2×C3×Dic5—21no—
171C2×C3×Dic5—21no—
172C2×C3×Dic5—22no—
173C2×C3×Dic5#4112yescomplemented
174C3×D20—28no—
175#1203—28no—
176#1202—216no—
177#1201—216no—
178#1200—44no—
179D5×Dic3—216no—
180C22×C3×D4—51no—
181C22×#67—52no—
182C22×#67—52no—
183C23×Dic3—52no—
184C2×#237—108no—
185C2×#237—104no—
186C22×D12—51no—
187C22×C4×D3—51no—
188C22×C4×D3C2×D511yescharacteristic
189C22×Dic6—51no—
190C2×C3×C4⋊C4—51no—
191C2×C3×C22⋊C4—52no—
192C2×C3×C22⋊C4—52no—
193C2×#217—52no—
194C2×(C2×D3)⋊C4—51no—
195C2×(C2×D3)⋊C4—52no—
196C2×(C2×D3)⋊C4—51no—
197C2×(C2×D3)⋊C4C2×D512yes—
198C2×Dic3⋊C4—52no—
199C2×C4×Dic3—51no—
200C2×C4×Dic3C2×D512yes—
201#893—104no—
202#67⋊C4—108no—
203C3×#95C2×D511yescharacteristic
204C3⋊#95—52no—
205C3⋊#95—52no—
206C3⋊#95C2×D511yescharacteristic
207C24×C5—31no—
208C23×D5—31no—
209C23×D5C22×D312yes—
210C22×C4×C5—31no—
211C22×C4×C5—32no—
212C22×C4×C5—34no—
213C22×C4×C5—64no—
214C22×C4×C5C22×D312yes—
215C22×C4×C5C22×D311yescharacteristic
216C2×C22⋊D5—62no—
217C2×C22⋊D5—62no—
218C2×C22⋊D5—64no—
219C2×C22⋊D5—64no—
220C2×C22⋊D5—64no—
221C2×C22⋊D5—62no—
222C22×Dic5—32no—
223C22×Dic5—31no—
224C22×Dic5C22×D311yescharacteristic
225C22×Dic5C22×D311yescharacteristic
226#709—632no—
227C2×D20—24no—
228C2×D20—22no—
229C2×D20—64no—
230C2×D20—64no—
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—64no—
238C2×Dic10—62no—
239C5×C22⋊C4—64no—
240C42×C5—64no—
241C22⋊Dic5—62no—
242#685—24no—
243#685—24no—
244#685—64no—
245#685—64no—
246#685—62no—
247C4⋊Dic5—64no—
248#683—22no—
249C4×Dic5—62no—
250C22×#41—151no—
251C2×C4×D4—152no—
252C2×C4×D4—151no—
253#395—151no—
254#394—51no—
255#394—152no—
256#393—151no—
257#392—151no—
258#392—152no—
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—41no—
269C2×D15—41no—
270C2×D15—42no—
271C2×C5×D3—22no—
272C2×C5×D3—22no—
273C2×C5×D3—22no—
274C2×C5×D3—42no—
275C2×C5×D3—42no—
276C2×C3×D5—24no—
277C2×C3×D5—24no—
278C2×C3×D5—24no—
279C2×C3×D5—42no—
280C2×C3×D5—42no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C3×C4×C5—22no—
284C3×C4×C5—42no—
285Dic15—24no—
286Dic15—41no—
287C3×Dic5—22no—
288C3×Dic5—41no—
289C5×Dic3—24no—
290C5×Dic3#12014yes—
291C24×C3—52no—
292C23×D3—51no—
293C23×D3C22×D511yescharacteristic
294C2×C3×D4—104no—
295C2×C3×D4—102no—
296C22×C3×C4—51no—
297C22×C3×C4—51no—
298C22×C3×C4C22×D512yes—
299C22×C3×C4C22×D511yescharacteristic
300C2×#67—104no—
301C2×#67—104no—
302C2×#67—104no—
303C2×#67—104no—
304C2×#67—104no—
305C2×#67—104no—
306C22×Dic3—52no—
307C22×Dic3—58no—
308C22×Dic3—51no—
309C22×Dic3—104no—
310C22×Dic3—104no—
311C22×Dic3C22×D512yes—
312C22×Dic3C22×D511yescharacteristic
313#237—1032no—
314C2×D12—102no—
315C2×D12—102no—
316C2×D12—102no—
317C2×C4×D3—24no—
318C2×C4×D3—102no—
319C2×C4×D3—104no—
320C2×C4×D3D2014yescomplemented
321C2×Dic6—104no—
322C2×Dic6—102no—
323C3×C4⋊C4—102no—
324C3×C22⋊C4—104no—
325C3×C22⋊C4—104no—
326#217—104no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—104no—
329(C2×D3)⋊C4—102no—
330(C2×D3)⋊C4—102no—
331Dic3⋊C4—104no—
332C4×Dic3—24no—
333C4×Dic3—102no—
334C23×C5—32no—
335C23×C5—62no—
336C23×C5—61no—
337C23×C5—62no—
338C23×C5—61no—
339C23×C5C23×D311yescharacteristic
340C22×D5—22no—
341C22×D5—22no—
342C22×D5—22no—
343C22×D5—22no—
344C22×D5—22no—
345C22×D5—22no—
346C22×D5—32no—
347C22×D5—62no—
348C22×D5—61no—
349C22×D5—61no—
350C22×D5—62no—
351C22×D5D3×D414yes—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—22no—
355C2×C4×C5—22no—
356C2×C4×C5—32no—
357C2×C4×C5—34no—
358C2×C4×C5—34no—
359C2×C4×C5—68no—
360C2×C4×C5—62no—
361C2×C4×C5—62no—
362C2×C4×C5D3×D412yes—
363C22⋊D5—68no—
364C22⋊D5—616no—
365C2×Dic5—21no—
366C2×Dic5—21no—
367C2×Dic5—21no—
368C2×Dic5—22no—
369C2×Dic5—34no—
370C2×Dic5—62no—
371C2×Dic5—62no—
372C2×Dic5—61no—
373C2×Dic5—62no—
374C2×Dic5#23712yescomplemented
375D20—28no—
376D20—616no—
377C4×D5—616no—
378C4×D5—124no—
379Dic10—68no—
380C2×#41—304no—
381C2×#41—308no—
382C22×Q8—151no—
383C22×D4—51no—
384C22×D4—152no—
385C22×D4—151no—
386C22×D4—152no—
387C23×C4—31no—
388C23×C4—151no—
389C23×C4—152no—
390C4×D4—308no—
391C4×D4—304no—
392C2×C4⋊C4—51no—
393C2×C4⋊C4—152no—
394C2×C22⋊C4—32no—
395C2×C22⋊C4—52no—
396C2×C22⋊C4—52no—
397C2×C22⋊C4—152no—
398C2×C22⋊C4—151no—
399C2×C22⋊C4—152no—
400C2×C22⋊C4—151no—
401C2×C42—32no—
402C2×C42—151no—
403#95—31no—
404#95—152no—
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—42no—
413C3×D5—44no—
414C5×D3—42no—
415C23×C3—54no—
416C23×C3—102no—
417C23×C3—102no—
418C23×C3—102no—
419C23×C3—102no—
420C23×C3—102no—
421C23×C3—102no—
422C23×C3C23×D511yescharacteristic
423C22×D3—22no—
424C22×D3—22no—
425C22×D3—21no—
426C22×D3—21no—
427C22×D3—52no—
428C22×D3—101no—
429C22×D3—102no—
430C22×D3—102no—
431C22×D3—101no—
432C22×D3C2×D2012yes—
433C3×D4—108no—
434C2×C3×C4—22no—
435C2×C3×C4—22no—
436C2×C3×C4—22no—
437C2×C3×C4—22no—
438C2×C3×C4—52no—
439C2×C3×C4—101no—
440C2×C3×C4—101no—
441C2×C3×C4—101no—
442C2×C3×C4—102no—
443C2×C3×C4C2×D2012yes—
444#67—1016no—
445#67—1016no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—54no—
449C2×Dic3—102no—
450C2×Dic3—102no—
451C2×Dic3—1016no—
452C2×Dic3—101no—
453C2×Dic3—102no—
454C2×Dic3C2×D2012yes—
455C2×Dic3#70914yescomplemented
456C2×Dic3D4×D514yes—
457D12—108no—
458C4×D3—28no—
459C4×D3—204no—
460Dic6—108no—
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×#23711yescharacteristic
469C22×C5D3×#4112yes—
470C22×C5D3×#4111yescharacteristic
471C2×D5—24no—
472C2×D5—24no—
473C2×D5—24no—
474C2×D5—42no—
475C2×D5—42no—
476C2×D5—42no—
477C2×D5—42no—
478C2×D5—64no—
479C2×D5—62no—
480C2×D5—121no—
481C2×D5—121no—
482C2×D5—122no—
483C4×C5—22no—
484C4×C5—34no—
485C4×C5—42no—
486C4×C5—64no—
487Dic5—22no—
488Dic5—41no—
489Dic5—64no—
490Dic5—121no—
491C24—31no—
492C24—52no—
493C24—151no—
494#41—3032no—
495C2×Q8—304no—
496C2×Q8—302no—
497C2×D4—104no—
498C2×D4—102no—
499C2×D4—304no—
500C2×D4—302no—
501C2×D4—304no—
502C2×D4—304no—
503C2×D4—302no—
504C2×D4—302no—
505C2×D4—304no—
506C2×D4—304no—
507C2×D4—304no—
508C22×C4—31no—
509C22×C4—32no—
510C22×C4—34no—
511C22×C4—51no—
512C22×C4—51no—
513C22×C4—64no—
514C22×C4—158no—
515C22×C4—152no—
516C22×C4—151no—
517C22×C4—302no—
518C22×C4—304no—
519C22×C4—304no—
520C22×C4—304no—
521C22×C4C2×D3×D512yes—
522C22×C4C2×D3×D511yescharacteristic
523C4⋊C4—102no—
524C4⋊C4—304no—
525C22⋊C4—64no—
526C22⋊C4—104no—
527C22⋊C4—104no—
528C22⋊C4—304no—
529C22⋊C4—304no—
530C22⋊C4—302no—
531C22⋊C4—302no—
532C42—64no—
533C42—302no—
534C3×C5#238811yescharacteristic, complemented, Hall
535C22×C3—104no—
536C22×C3—104no—
537C22×C3—104no—
538C22×C3—202no—
539C22×C3—202no—
540C22×C3—202no—
541C22×C3—202no—
542C22×C3C22×D2011yescharacteristic
543C22×C3C2×#70912yes—
544C22×C3C2×D4×D512yes—
545C22×C3D5×#4111yescharacteristic
546C22×C3D5×#4111yescharacteristic
547C2×D3—22no—
548C2×D3—22no—
549C2×D3—22no—
550C2×D3—42no—
551C2×D3—42no—
552C2×D3—102no—
553C2×D3—104no—
554C2×D3—201no—
555C2×D3—201no—
556C2×D3—202no—
557C3×C4—22no—
558C3×C4—42no—
559C3×C4—102no—
560C3×C4—201no—
561Dic3—24no—
562Dic3—104no—
563Dic3—201no—
564Dic3#402814yes—
565C2×C5—122no—
566C2×C5D3×#12011yescharacteristic
567C2×C5#559612yes—
568C2×C5#560611yescharacteristic
569C2×C5#565612yes—
570C2×C5#566811yescharacteristic
571D5—44no—
572D5—122no—
573C23—32no—
574C23—54no—
575C23—62no—
576C23—62no—
577C23—61no—
578C23—61no—
579C23—102no—
580C23—102no—
581C23—102no—
582C23—102no—
583C23—102no—
584C23—102no—
585C23—152no—
586C23—301no—
587C23—302no—
588C23—302no—
589C23—301no—
590C23C22×D3×D511yescharacteristic
591Q8—308no—
592D4—108no—
593D4—3016no—
594D4—308no—
595D4—3016no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—32no—
601C2×C4—34no—
602C2×C4—34no—
603C2×C4—52no—
604C2×C4—68no—
605C2×C4—62no—
606C2×C4—62no—
607C2×C4—101no—
608C2×C4—101no—
609C2×C4—101no—
610C2×C4—102no—
611C2×C4—154no—
612C2×C4—3016no—
613C2×C4—302no—
614C2×C4—302no—
615C2×C4—301no—
616C2×C4—302no—
617C2×C4—604no—
618C2×C4D3×D2012yes—
619C2×C3—204no—
620C2×C3#6581111yescharacteristic
621C2×C3C2×#402811yescharacteristic
622C2×C3#6585811yescharacteristic
623C2×C3#6588112yes—
624C2×C3#6588212yes—
625D3—42no—
626D3—202no—
627C5#7688911yescharacteristic, complemented, Sylow
628C22—62no—
629C22—62no—
630C22—62no—
631C22—104no—
632C22—104no—
633C22—104no—
634C22—122no—
635C22—122no—
636C22—202no—
637C22—202no—
638C22—202no—
639C22—202no—
640C22—304no—
641C22—302no—
642C22—601no—
643C22—602no—
644C22—601no—
645C22C2×D3×D2011yescharacteristic
646C22D3×#70912yes—
647C22D3×D4×D512yes—
648C22D5×#23711yescharacteristic
649C22#9203411yescharacteristic
650C4—22no—
651C4—34no—
652C4—42no—
653C4—64no—
654C4—102no—
655C4—201no—
656C4—304no—
657C4—601no—
658C3#1060531111yescharacteristic, complemented, Sylow
659C2—122no—
660C2—204no—
661C2—602no—
662C2#1175254311yescharacteristic
663C2#1175283112yes—
664C2D3×#402811yescharacteristic
665C2#1175385212yes—
666C2#1175387911yescharacteristic
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×#6765C2semidirect
2. C2×#91446C2semidirect
3. C2×#91395C2semidirect
4. #11750774C2semidirect
5. C5×#4666C2semidirect
6. C3×#64961C2semidirect
7. #11748925C2semidirect
8. #11748923C2semidirect
9. #11748922C2semidirect
10. Dic3×#685C2semidirect
11. #11748846C2semidirect
49. #64961D3semidirect
64. C2×C4×C5×D3D4semidirect
82. C2×D5×Dic3D4semidirect
105. #4666D5semidirect
139. C22×D15#41semidirect
167. C2×C5×Dic3#41semidirect
173. C2×C3×Dic5#41semidirect
320. C2×C4×D3D20semidirect
374. C2×Dic5#237semidirect
455. C2×Dic3#709semidirect
534. C3×C5#2388semidirect
627. C5#76889semidirect
658. C3#10605311semidirect

Maximal subgroups

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

subgroupindex
C22×#67652
C2×#914462
C2×#913952
#117507742
C5×#46662
C3×#649612
#117489252
#117489232
#117489222
Dic3×#6852
#117488462
#106053113
#768895