Finite Group Databasebeta

← #14430668

Subgroups — #14430668

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4034C211yesmaximal, characteristic, complemented
2#11753398C211yesmaximal, characteristic
3#11750955C211yesmaximal, characteristic, complemented
4C5×#4861C211yesmaximal, characteristic, complemented
5C3×#65159C211yesmaximal, characteristic, complemented
6#11748138C211yesmaximal, characteristic
7#11747849C211yesmaximal, characteristic, complemented
8#11747803C211yesmaximal, characteristic, complemented
9#11747590C211yesmaximal, characteristic, complemented
10#11747503C211yesmaximal, characteristic
11#11747415C211yesmaximal, characteristic, complemented
12#11747285C211yesmaximal, characteristic, complemented
13#11747253C211yesmaximal, characteristic, complemented
14#11747191C211yesmaximal, characteristic, complemented
15#11747181C211yesmaximal, characteristic, complemented
16#10610971—31nomaximal, Hall
17C2×D3×Dic10—21no—
18C2×#6765C2211yescharacteristic
19#91777C2211yescharacteristic
20#91776C2211yescharacteristic
21C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
22C5×#892C2211yescharacteristic
23C5×D3×C4⋊C4C2211yescharacteristic
24C3×#4039C2211yescharacteristic
25C3×#4034C2211yescharacteristic
26#91470C2211yescharacteristic
27#91468C2211yescharacteristic
28#91442—21no—
29#91440—21no—
30#91434C2211yescharacteristic
31D3×C4⋊Dic5C2211yescharacteristic
32D3×#683—21no—
33C4×D3×Dic5C2211yescharacteristic
34#91393—21no—
35C4×D5×Dic3—21no—
36#91333C2211yescharacteristic
37#91328—21no—
38#91327—21no—
39C2×#6650C2211yescharacteristic
40C3×C5×#106C2211yescharacteristic
41#91100C2211yescharacteristic
42#91098C2211yescharacteristic
43#91094C2211yescharacteristic
44#91092C2211yescharacteristic
45C5×#818C2211yescharacteristic
46C5×#808C2211yescharacteristic
47C5×#807C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3946C2211yescharacteristic
50C3×#3941C2211yescharacteristic
51C3×#3940C2211yescharacteristic
52#90989C2211yescharacteristic
53#90988C2211yescharacteristic
54#90983C2211yescharacteristic
55#90982C2211yescharacteristic
56#90975C2211yescharacteristic
57#90974C2211yescharacteristic
58#90965C2211yescharacteristic
59#90964C2211yescharacteristic
60#81061—51nomaximal, Hall
61#65856—31no—
62C2×#4034—31no—
63C5×#428—31no—
64#65422—31no—
65#65407—31no—
66#65284—31no—
67#65255—31no—
68#65179—31no—
69#65179—31no—
70#65164—31no—
71#65164—31no—
72#65159—31no—
73#65159D311yescharacteristic, complemented
74#65143—31no—
75#65143—31no—
76C2×Dic30—21no—
77C2×Dic30C2311yescharacteristic
78C2×C4×C5×D3—21no—
79C2×C4×C5×D3C2311yescharacteristic
80C2×C3×D20C2311yescharacteristic
81C2×C3×C4×D5—21no—
82C2×C3×Dic10—21no—
83C2×#1204—21no—
84C2×#1204—21no—
85C2×#1201—21no—
86C2×D3×Dic5—21no—
87C2×D3×Dic5D411yescharacteristic
88C2×D3×Dic5D411yescharacteristic
89C2×D5×Dic3—21no—
90C2×D5×Dic3—21no—
91D3×Dic10—44no—
92#6765—22no—
93#6765Q814yescomplemented
94C2×C3×C5×C8C2311yescharacteristic
95C3×C5×C4⋊C4C2311yescharacteristic
96C3×C5×C4⋊C4C2311yescharacteristic
97C4⋊Dic15C2311yescharacteristic
98#6712—21no—
99#6712—21no—
100C4×Dic15—21no—
101C4×Dic15C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×(C2×D3)⋊C4—21no—
104C5×C4⋊Dic3C2311yescharacteristic
105C5×C4⋊Dic3C2311yescharacteristic
106C5×Dic3⋊C4—21no—
107C4×C5×Dic3—21no—
108C2×C5×C3⋊C8C2311yescharacteristic
109C5×ΓL(1,𝔽25)—22no—
110C3×#685—21no—
111C3×C4⋊Dic5C2311yescharacteristic
112C3×#683—21no—
113C3×C4×Dic5C2311yescharacteristic
114C2×C3×#168C2311yescharacteristic
115Dic3⋊Dic5—21no—
116#6669—21no—
117#6669—21no—
118#6668—21no—
119#6665—21no—
120Dic3×Dic5—21no—
121Dic3×Dic5D411yescharacteristic
122Dic3×Dic5D411yescharacteristic
123#6650—22no—
124D3×C4⋊Q8—51no—
125C4×#237—51no—
126C3×#476—51no—
127#5091—51no—
128#5008—51no—
129#4861—51no—
130#4861D511yescharacteristic, complemented
131#4854—51no—
132#4854—51no—
133#4850—51no—
134#4837—51no—
135#4771—51no—
136#4771—51no—
137#4759—51no—
138#4759—51no—
139C2×#709—31no—
140C22×Dic10—61no—
141C2×C5×M16—31no—
142C5×#117—31no—
143C2×C5×C4⋊C4—31no—
144C2×C4⋊Dic5—31no—
145C2×#683—61no—
146C2×C4×Dic5—31no—
147C2×#681—31no—
148#4039—31no—
149#4039C2×D311yescharacteristic
150#4034—31no—
151#4034—31no—
152#4034—31no—
153#4034—61no—
154#4034—61no—
155#4034C2×D311yescharacteristic
156#4033—31no—
157#4033—31no—
158#4027—61no—
159#4027—61no—
160#4018—61no—
161C42×D5—61no—
162C5×#107—31no—
163C5×#107—31no—
164C5×#106—31no—
165C5×#106C2×D311yescharacteristic
166#3953—31no—
167#3953C2×D311yescharacteristic
168#3948—31no—
169#3948—31no—
170#3946—31no—
171#3946—31no—
172#3946—31no—
173#3946C2×D311yescharacteristic
174#3942—31no—
175#3942—31no—
176#3941—31no—
177#3941C2×D311yescharacteristic
178#3940—31no—
179#3940C2×D311yescharacteristic
180#3939—31no—
181#3939—31no—
182#3079—151noSylow
183C22×C5×D3C2×D411yescharacteristic
184C22×C3×D5—21no—
185C2×C3×C4×C5—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5C2411yescharacteristic
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15C2×D411yescharacteristic
191C2×Dic15C2×D411yescharacteristic
192Dic30—21no—
193Dic30—42no—
194Dic30C2×Q812yescomplemented
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3C2×D411yescharacteristic
198C4×C5×D3—42no—
199C4×C5×D3C2×Q812yes—
200C4×C5×D3#4112yes—
201C2×C3×Dic5—21no—
202C2×C3×Dic5C2×D411yescharacteristic
203C2×C3×Dic5C2×D411yescharacteristic
204C3×D20—21no—
205C3×D20C2×Q812yescomplemented
206C3×C4×D5—42no—
207C3×Dic10—42no—
208#1204—42no—
209#1204—42no—
210#1201—24no—
211D3×Dic5—22no—
212D3×Dic5—22no—
213D3×Dic5—42no—
214D5×Dic3—24no—
215D5×Dic3—42no—
216C3×C5×C8—21no—
217C3⋊#168—21no—
218C3×#168—21no—
219C5×C3⋊C8—21no—
220C2×D3×Q8—101no—
221C2×#237—51no—
222C3×C4⋊Q8—51no—
223C3×C4×D4—51no—
224#944—101no—
225D4×Dic3—51no—
226C4×#67—101no—
227C2×C4×Dic3—101no—
228C2×ΓL(1,𝔽25)—51no—
229C2×ΓL(1,𝔽25)C2×D511yescharacteristic
230#892C2×D511yescharacteristic
231D3×C4⋊C4—51no—
232D3×C4⋊C4—101no—
233D3×C4⋊C4C2×D511yescharacteristic
234#888—51no—
235#888—51no—
236#888—101no—
237#887—51no—
238#67⋊C4—101no—
239#877—101no—
240C42×D3—51no—
241#869—51no—
242C4×Dic6—51no—
243C3×#106—51no—
244C3×#106C2×D511yescharacteristic
245C3×C4⋊C8—51no—
246C3×#102—51no—
247C3×#102—51no—
248#832—51no—
249#832—51no—
250#818—51no—
251#818C2×D511yescharacteristic
252#816—51no—
253#816—51no—
254Dic3⋊C8—51no—
255Dic3⋊C8—51no—
256#810—51no—
257#810—51no—
258#808—51no—
259#808C2×D511yescharacteristic
260#807—51no—
261#807C2×D511yescharacteristic
262C4⋊(C3⋊C8)—51no—
263C22×C4×C5—31no—
264C22×C4×C5—61no—
265C2×C22⋊D5—61no—
266C22×Dic5—31no—
267C22×Dic5—31no—
268C22×Dic5—61no—
269#709—34no—
270#709—62no—
271C2×D20C22×D311yescharacteristic
272C2×C4×D5—21no—
273C2×C4×D5—61no—
274C2×C4×D5—61no—
275C2×Dic10—21no—
276C2×Dic10—31no—
277C2×Dic10—61no—
278C2×Dic10—61no—
279C2×Dic10—61no—
280C2×Dic10—124no—
281C5×M16—62no—
282C2×C5×C8—31no—
283C2×C5×C8C22×D311yescharacteristic
284C5×C4⋊C4—31no—
285C5×C4⋊C4—31no—
286C5×C4⋊C4—61no—
287C5×C4⋊C4C22×D311yescharacteristic
288C5×C4⋊C4C22×D311yescharacteristic
289C5×C22⋊C4—61no—
290C42×C5—61no—
291#685—21no—
292#685—61no—
293C4⋊Dic5—31no—
294C4⋊Dic5—61no—
295C4⋊Dic5C22×D311yescharacteristic
296#683—21no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302C4×Dic5—31no—
303C4×Dic5—31no—
304C4×Dic5—31no—
305C4×Dic5—61no—
306C4×Dic5—61no—
307C4×Dic5C22×D311yescharacteristic
308#681—62no—
309C2×#168—31no—
310C2×#168C22×D311yescharacteristic
311C2×C4⋊Q8—151no—
312C4×#41—151no—
313#477—151no—
314#477—151no—
315#476—51no—
316#476—151no—
317#475—151no—
318#475—151no—
319#474—151no—
320#474—151no—
321#428—31no—
322#428—151no—
323#423—151no—
324#417—151no—
325#417—151no—
326C22×C3×C5C22×D411yescharacteristic
327C2×C5×D3—21no—
328C2×C5×D3—21no—
329C2×C5×D3C22⋊Q812yes—
330C2×C3×D5—22no—
331C2×C3×D5—41no—
332C2×C3×D5—41no—
333C3×C4×C5—41no—
334C3×C4×C5—41no—
335C3×C4×C5C22×Q811yescharacteristic
336C3×C4×C5C2×#4111yescharacteristic
337Dic15—22no—
338Dic15—21no—
339Dic15—41no—
340Dic15AGL(1,ℤ/8)12yes—
341C3×Dic5—21no—
342C3×Dic5—41no—
343C3×Dic5#13712yes—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C5×Dic3C22⋊Q812yes—
347C2×C3×Q8—101no—
348C2×C3×D4—51no—
349C22×C3×C4—101no—
350C2×#67—101no—
351C22×Dic3—101no—
352C22×Dic3—101no—
353D3×Q8—204no—
354#237—54no—
355#237—102no—
356C2×C4×D3—21no—
357C2×C4×D3—51no—
358C2×C4×D3—51no—
359C2×C4×D3—101no—
360C2×C4×D3C22×D511yescharacteristic
361C2×Dic6—51no—
362C2×Dic6—101no—
363C2×Dic6—101no—
364C2×Dic6—101no—
365C2×C3×C8—51no—
366C2×C3×C8C22×D511yescharacteristic
367C3×C4⋊C4—51no—
368C3×C4⋊C4—101no—
369C3×C4⋊C4C22×D511yescharacteristic
370C3×C4⋊C4C22×D511yescharacteristic
371C3×C22⋊C4—101no—
372C3×C42—51no—
373#217—101no—
374(C2×D3)⋊C4—21no—
375C4⋊Dic3—51no—
376C4⋊Dic3—101no—
377C4⋊Dic3C22×D511yescharacteristic
378C4⋊Dic3C22×D511yescharacteristic
379Dic3⋊C4—21no—
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385C4×Dic3—21no—
386C4×Dic3—51no—
387C4×Dic3—51no—
388C4×Dic3—51no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C2×C3⋊C8—51no—
392C2×C3⋊C8C22×D511yescharacteristic
393ΓL(1,𝔽25)—22no—
394ΓL(1,𝔽25)—102no—
395C23×C5—31no—
396C22×D5—21no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5—31no—
400C2×C4×C5—32no—
401C2×C4×C5—32no—
402C2×C4×C5—61no—
403C2×C4×C5—61no—
404C2×C4×C5—122no—
405C2×C4×C5C23×D311yescharacteristic
406C22⋊D5—64no—
407C2×Dic5—21no—
408C2×Dic5—31no—
409C2×Dic5—31no—
410C2×Dic5—62no—
411C2×Dic5—61no—
412C2×Dic5—62no—
413C2×Dic5—61no—
414C2×Dic5—122no—
415C2×Dic5D3×D411yescharacteristic
416C2×Dic5D3×D411yescharacteristic
417D20—21no—
418D20D3×Q812yescomplemented
419C4×D5—42no—
420C4×D5—64no—
421C4×D5—122no—
422Dic10—32no—
423Dic10—42no—
424Dic10—61no—
425Dic10—122no—
426Dic10—122no—
427Dic10—122no—
428C5×C8—21no—
429C5×C8—61no—
430#168—21no—
431#168—61no—
432C2×#41—151no—
433C22×Q8—301no—
434C2×M16—31no—
435C2×M16—151no—
436C4⋊Q8—51no—
437C4⋊Q8—151no—
438C4⋊Q8—151no—
439C4⋊Q8—151no—
440C4⋊Q8—301no—
441C4⋊Q8—301no—
442C4×Q8—151no—
443C4×Q8—151no—
444C4×D4—51no—
445C4×D4—151no—
446C4×D4—301no—
447C4×D4—301no—
448#117—31no—
449#117—301no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—151no—
452C2×C4⋊C4—301no—
453C2×C42—151no—
454C2×C42—301no—
455#107—31no—
456#107—31no—
457#107—151no—
458#107—151no—
459#106—31no—
460#106—51no—
461#106—151no—
462#106D3×D511yescharacteristic
463C4⋊C8—51no—
464C4⋊C8—151no—
465C4⋊C8—151no—
466C4⋊C8—151no—
467#103—151no—
468#103—151no—
469#103—151no—
470#103—151no—
471#102—51no—
472#102—51no—
473#102—151no—
474#102—151no—
475C2×C3×C5C2×C22⋊Q811yescharacteristic
476C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
477C2×C3×C5C2×#13711yescharacteristic
478C3×D5—42no—
479C5×D3—22no—
480C23×C3—101no—
481C22×D3D4×D511yescharacteristic
482C3×Q8—202no—
483C3×D4—52no—
484C3×D4—101no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—51no—
488C2×C3×C4—51no—
489C2×C3×C4—101no—
490C2×C3×C4—202no—
491C2×C3×C4C23×D511yescharacteristic
492#67—104no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—51no—
496C2×Dic3—51no—
497C2×Dic3—101no—
498C2×Dic3—104no—
499C2×Dic3—101no—
500C2×Dic3—202no—
501C2×Dic3D4×D511yescharacteristic
502C4×D3—42no—
503C4×D3—102no—
504C4×D3—102no—
505C4×D3—202no—
506C4×D3#70912yes—
507C4×D3Q8×D512yes—
508Dic6—52no—
509Dic6—101no—
510Dic6—202no—
511Dic6—202no—
512Dic6—202no—
513C3×C8—21no—
514C3×C8—101no—
515C3⋊C8—21no—
516C3⋊C8—101no—
517C22×C5—32no—
518C22×C5—61no—
519C22×C5—61no—
520C22×C5C2×D3×D411yescharacteristic
521C2×D5—22no—
522C2×D5—41no—
523C2×D5—41no—
524C4×C5—32no—
525C4×C5—41no—
526C4×C5—41no—
527C4×C5—121no—
528C4×C5—121no—
529C4×C5C2×D3×Q811yescharacteristic
530C4×C5D3×#4111yescharacteristic
531Dic5—21no—
532Dic5—32no—
533Dic5—41no—
534Dic5—61no—
535Dic5—62no—
536Dic5—121no—
537Dic5#91512yes—
538#41—154no—
539#41—302no—
540C2×Q8—101no—
541C2×Q8—151no—
542C2×Q8—301no—
543C2×Q8—301no—
544C2×Q8—301no—
545C2×Q8—604no—
546C2×D4—51no—
547C2×D4—301no—
548C22×C4—31no—
549C22×C4—61no—
550C22×C4—101no—
551C22×C4—151no—
552C22×C4—151no—
553C22×C4—301no—
554C22×C4—301no—
555C22×C4—301no—
556M16—62no—
557M16—302no—
558C2×C8—31no—
559C2×C8—51no—
560C2×C8—151no—
561C2×C8C2×D3×D511yescharacteristic
562C4⋊C4—31no—
563C4⋊C4—31no—
564C4⋊C4—51no—
565C4⋊C4—61no—
566C4⋊C4—101no—
567C4⋊C4—151no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4—301no—
573C4⋊C4—301no—
574C4⋊C4C2×D3×D511yescharacteristic
575C4⋊C4C2×D3×D511yescharacteristic
576C22⋊C4—61no—
577C22⋊C4—101no—
578C22⋊C4—301no—
579C42—51no—
580C42—61no—
581C42—151no—
582C42—151no—
583C42—151no—
584C42—301no—
585C42—301no—
586C3×C5#307911yescharacteristic, complemented, Hall
587C22×C3—102no—
588C22×C3—201no—
589C22×C3—201no—
590C22×C3C2×D4×D511yescharacteristic
591C2×D3—21no—
592C2×D3—21no—
593C2×D3#404212yes—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—52no—
597C3×C4—101no—
598C3×C4—201no—
599C3×C4C2×#70911yescharacteristic
600C3×C4C2×Q8×D511yescharacteristic
601Dic3—41no—
602Dic3—41no—
603Dic3—52no—
604Dic3—102no—
605Dic3—101no—
606Dic3—201no—
607Dic3#404212yes—
608C2×C5—62no—
609C2×C5D3×C22⋊Q811yescharacteristic
610C2×C5C2×#91511yescharacteristic
611C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
612D5—42no—
613C23—31no—
614C23—101no—
615Q8—152no—
616Q8—202no—
617Q8—301no—
618Q8—602no—
619Q8—602no—
620Q8—602no—
621D4—52no—
622D4—101no—
623D4—304no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—31no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—51no—
630C2×C4—51no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—101no—
634C2×C4—122no—
635C2×C4—151no—
636C2×C4—151no—
637C2×C4—202no—
638C2×C4—304no—
639C2×C4—302no—
640C2×C4—302no—
641C2×C4—301no—
642C2×C4—301no—
643C2×C4—602no—
644C2×C4—602no—
645C2×C4C22×D3×D511yescharacteristic
646C8—21no—
647C8—61no—
648C8—101no—
649C8—301no—
650C2×C3—202no—
651C2×C3C2×#404211yescharacteristic
652C2×C3D5×AGL(1,ℤ/8)11yescharacteristic
653C2×C3D5×#13711yescharacteristic
654D3—22no—
655C5#8106111yescharacteristic, complemented, Sylow
656C22—32no—
657C22—61no—
658C22—61no—
659C22—102no—
660C22—201no—
661C22—201no—
662C22D3×D4×D511yescharacteristic
663C4—32no—
664C4—41no—
665C4—41no—
666C4—52no—
667C4—101no—
668C4—121no—
669C4—121no—
670C4—152no—
671C4—201no—
672C4—301no—
673C4—302no—
674C4—601no—
675C4D3×#70911yescharacteristic
676C4D3×Q8×D511yescharacteristic
677C3#1061097111yescharacteristic, complemented, Sylow
678C2—62no—
679C2—202no—
680C2D3×#404211yescharacteristic
681C2#1175406711yescharacteristic
682C2D5×#91511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC2×#6765C22
hypercenter#106D3×D5
hypocenterC3×C5#3079
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
1. D3×#4034C2semidirect
3. #11750955C2semidirect
4. C5×#4861C2semidirect
5. C3×#65159C2semidirect
7. #11747849C2semidirect
8. #11747803C2semidirect
9. #11747590C2semidirect
11. #11747415C2semidirect
12. #11747285C2semidirect
13. #11747253C2semidirect
14. #11747191C2semidirect
15. #11747181C2semidirect
73. #65159D3semidirect
93. #6765Q8semidirect
130. #4861D5semidirect
194. Dic30C2×Q8semidirect
205. C3×D20C2×Q8semidirect
418. D20D3×Q8semidirect
586. C3×C5#3079semidirect
655. C5#81061semidirect
677. C3#10610971semidirect

Maximal subgroups

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

subgroupindex
D3×#40342
#117533982
#117509552
C5×#48612
C3×#651592
#117481382
#117478492
#117478032
#117475902
#117475032
#117474152
#117472852
#117472532
#117471912
#117471812
#106109713
#810615