Finite Group Databasebeta

← #14430701

Subgroups — #14430701

Order 1920.

768 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
1D3×#4016C211yesmaximal, characteristic, complemented
2C4×#6765C211yesmaximal, characteristic
3#11750930C211yesmaximal, characteristic, complemented
4C5×#4837C211yesmaximal, characteristic, complemented
5C3×#65136C211yesmaximal, characteristic, complemented
6#11748138C211yesmaximal, characteristic
7#11748138C211yesmaximal, characteristic
8#11747874C211yesmaximal, characteristic, complemented
9#11747871C211yesmaximal, characteristic, complemented
10#11747784C211yesmaximal, characteristic, complemented
11#11747783C211yesmaximal, characteristic, complemented
12#11747630C211yesmaximal, characteristic, complemented
13#11747628C211yesmaximal, characteristic, complemented
14#11746934C211yesmaximal, characteristic, complemented
15#11746888C211yesmaximal, characteristic, complemented
16#10610792—31nomaximal, Hall
17C2×#6765C2211yescharacteristic
18#91759C2211yescharacteristic
19C4×Dic30C2211yescharacteristic
20C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
21C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
22C42×C5×D3C2211yescharacteristic
23C3×C4×D20C2211yescharacteristic
24C3×#4016C2211yescharacteristic
25#91441—21no—
26C4×#1201—21no—
27D3×C4⋊Dic5C2211yescharacteristic
28D3×C4⋊Dic5C2211yescharacteristic
29Dic3×D20C2211yescharacteristic
30D3×#683—21no—
31D3×#683—21no—
32#91393—21no—
33C4×D5×Dic3—21no—
34#91381C2211yescharacteristic
35#91381C2211yescharacteristic
36#91379—21no—
37#91379—21no—
38#91340C2211yescharacteristic
39#91338C2211yescharacteristic
40C3×C5×C4⋊C8C2211yescharacteristic
41#91102C2211yescharacteristic
42#91101C2211yescharacteristic
43#91100C2211yescharacteristic
44#91100C2211yescharacteristic
45C5×Dic3⋊C8C2211yescharacteristic
46C5×Dic3⋊C8C2211yescharacteristic
47C5×C4⋊(C3⋊C8)C2211yescharacteristic
48C3×#3953C2211yescharacteristic
49C3×#3953C2211yescharacteristic
50C3×#3950C2211yescharacteristic
51C3×#3949C2211yescharacteristic
52#90990C2211yescharacteristic
53#90990C2211yescharacteristic
54#90987C2211yescharacteristic
55#90987C2211yescharacteristic
56#90974C2211yescharacteristic
57#90974C2211yescharacteristic
58#90965C2211yescharacteristic
59#90965C2211yescharacteristic
60#81167—51nomaximal, Hall
61C4×#709—31no—
62C2×#4016—31no—
63C5×#423—31no—
64#65422—31no—
65#65422—31no—
66#65410—31no—
67#65410—31no—
68#65136—31no—
69#65136—31no—
70#65136—31no—
71#65136D311yescharacteristic, complemented
72#65118—31no—
73#65118—31no—
74#65118—31no—
75#65118—31no—
76C2×Dic30C2311yescharacteristic
77C2×C4×C5×D3D411yescharacteristic
78C2×C4×C5×D3D411yescharacteristic
79C2×C4×C5×D3C2311yescharacteristic
80C2×C3×D20C2311yescharacteristic
81C2×C3×C4×D5—21no—
82C2×#1201—21no—
83C2×D3×Dic5—21no—
84C2×D3×Dic5—21no—
85C2×D5×Dic3—21no—
86C2×D5×Dic3—21no—
87#6765—22no—
88#6765Q814yes—
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C3×C42×C5C2311yescharacteristic
92C4⋊Dic15C2311yescharacteristic
93C4⋊Dic15C2311yescharacteristic
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96#6712—21no—
97#6712—21no—
98C4×Dic15—21no—
99C4×C5×Dic3D411yescharacteristic
100C4×C5×Dic3D411yescharacteristic
101C4×C5×Dic3C2311yescharacteristic
102C2×C5×C3⋊C8C2311yescharacteristic
103C2×C5×C3⋊C8C2311yescharacteristic
104C5×ΓL(1,𝔽25)—22no—
105C5×ΓL(1,𝔽25)—22no—
106C3×#685—21no—
107C3×C4⋊Dic5C2311yescharacteristic
108C3×C4⋊Dic5C2311yescharacteristic
109C3×C4⋊Dic5C2311yescharacteristic
110C3×#683—21no—
111C3×#683—21no—
112Dic3⋊Dic5—21no—
113Dic3⋊Dic5—21no—
114#6669—21no—
115#6669—21no—
116#6669—21no—
117#6668—21no—
118#6668—21no—
119(C2×D3)⋊Dic5—21no—
120#6665—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123D3×#125—51no—
124C4×#237—51no—
125C3×#478—51no—
126#5063—51no—
127#5009—51no—
128#4881—51no—
129#4877—51no—
130#4861—51no—
131#4857—51no—
132#4837D511yescharacteristic, complemented
133#4829—51no—
134#4771—51no—
135#4771—51no—
136#4766—51no—
137#4763—51no—
138C2×#709—31no—
139C2×C5×M16—31no—
140C2×C5×M16—31no—
141C2×C42×C5—31no—
142C4×C22⋊D5—61no—
143C4×C22⋊D5—61no—
144#4072—31no—
145C2×C4⋊Dic5—31no—
146C2×C4⋊Dic5—31no—
147C2×#683—61no—
148C2×#683—61no—
149C4×D20—31no—
150C4×D20C2×D311yescharacteristic
151#4018—61no—
152C42×D5—61no—
153#4016—31no—
154#4016—31no—
155#4016—31no—
156#4016—61no—
157#4016—61no—
158#4016C2×D311yescharacteristic
159C4×Dic10—31no—
160C4×Dic10—31no—
161C5×C4⋊C8—31no—
162C5×C4⋊C8—31no—
163C5×C4⋊C8—31no—
164C5×C4⋊C8C2×D311yescharacteristic
165#3953—31no—
166#3953—31no—
167#3953C2×D311yescharacteristic
168#3953C2×D311yescharacteristic
169#3950—31no—
170#3950—31no—
171#3950—31no—
172#3950C2×D311yescharacteristic
173#3949—31no—
174#3949—31no—
175#3949—31no—
176#3949C2×D311yescharacteristic
177#3948—31no—
178#3948—31no—
179#3948—31no—
180#3948—31no—
181#3080—151noSylow
182C22×C5×D3C2×D411yescharacteristic
183C22×C3×D5—21no—
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2411yescharacteristic
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190C2×Dic15—21no—
191Dic30—21no—
192Dic30C2×Q812yes—
193C2×C5×Dic3C2×D411yescharacteristic
194C2×C5×Dic3C2×D411yescharacteristic
195C2×C5×Dic3C2×D411yescharacteristic
196C4×C5×D3—41no—
197C4×C5×D3—41no—
198C4×C5×D3C2×Q812yes—
199C4×C5×D3#4112yes—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C3×D20—21no—
204C3×D20C2×Q812yes—
205C3×C4×D5—42no—
206#1201—24no—
207D3×Dic5—42no—
208D3×Dic5—42no—
209D5×Dic3—24no—
210D5×Dic3—42no—
211C3×C5×C8—21no—
212C3×C5×C8—21no—
213C5×C3⋊C8—21no—
214C5×C3⋊C8—21no—
215C2×#237—51no—
216C3×#125—51no—
217C3×C4×D4—51no—
218D4×Dic3—51no—
219C4×#67—101no—
220C2×C4×Dic3—101no—
221C2×ΓL(1,𝔽25)C2×D511yescharacteristic
222C2×ΓL(1,𝔽25)C2×D511yescharacteristic
223#892—51no—
224D3×C4⋊C4—51no—
225D3×C4⋊C4—51no—
226D3×C4⋊C4—101no—
227D3×C4⋊C4—101no—
228#890—51no—
229#890—51no—
230#889—101no—
231#889—101no—
232#887—51no—
233#67⋊C4—101no—
234#877—101no—
235C42×D3C2×D511yescharacteristic
236#870—51no—
237C4×Dic6—51no—
238C3×#107—51no—
239C3×#106—51no—
240C3×C4⋊C8C2×D511yescharacteristic
241C3×#102—51no—
242C3×#102—51no—
243#832—51no—
244#832—51no—
245#818—51no—
246#817—51no—
247#816—51no—
248#816—51no—
249Dic3⋊C8C2×D511yescharacteristic
250Dic3⋊C8C2×D511yescharacteristic
251#810—51no—
252#810—51no—
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)C2×D511yescharacteristic
258C22×C4×C5—31no—
259C22×C4×C5—31no—
260C22×C4×C5—31no—
261C2×C22⋊D5—61no—
262C22×Dic5—61no—
263C22×Dic5—61no—
264#709—34no—
265#709—62no—
266C2×D20C22×D311yescharacteristic
267C2×C4×D5—21no—
268C2×C4×D5—61no—
269C2×C4×D5—61no—
270C2×Dic10—31no—
271C5×M16—62no—
272C5×M16—62no—
273C2×C5×C8—31no—
274C2×C5×C8—31no—
275C2×C5×C8C22×D311yescharacteristic
276C2×C5×C8C22×D311yescharacteristic
277C42×C5—31no—
278C42×C5—31no—
279C42×C5—31no—
280C42×C5C22×D311yescharacteristic
281C22⋊Dic5—61no—
282#685—21no—
283#685—61no—
284C4⋊Dic5—31no—
285C4⋊Dic5—31no—
286C4⋊Dic5—31no—
287C4⋊Dic5—61no—
288C4⋊Dic5—61no—
289C4⋊Dic5C22×D311yescharacteristic
290C4⋊Dic5C22×D311yescharacteristic
291C4⋊Dic5C22×D311yescharacteristic
292#683—21no—
293#683—21no—
294#683—61no—
295#683—61no—
296#683—61no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302C4×Dic5—61no—
303C4×Dic5—61no—
304C4×Dic5—61no—
305C2×#125—151no—
306C4×#41—151no—
307#479—151no—
308#479—151no—
309#479—151no—
310#479—151no—
311#478—51no—
312#478—151no—
313#478—151no—
314#478—151no—
315#428—151no—
316#428—151no—
317#423—31no—
318#417—151no—
319#417—151no—
320C22×C3×C5C22×D411yescharacteristic
321C2×C5×D3—21no—
322C2×C5×D3—21no—
323C2×C5×D3C22⋊Q812yes—
324C2×C3×D5—22no—
325C2×C3×D5—41no—
326C2×C3×D5—41no—
327C3×C4×C5—21no—
328C3×C4×C5—21no—
329C3×C4×C5C22×Q811yescharacteristic
330C3×C4×C5C2×#4111yescharacteristic
331Dic15—22no—
332Dic15—41no—
333Dic15—41no—
334Dic15—41no—
335C3×Dic5—41no—
336C3×Dic5—41no—
337C3×Dic5—41no—
338C5×Dic3—21no—
339C5×Dic3—21no—
340C5×Dic3C22⋊Q812yes—
341C2×C3×D4—51no—
342C22×C3×C4—101no—
343C2×#67—101no—
344C22×Dic3—101no—
345C22×Dic3—101no—
346#237—54no—
347#237—102no—
348C2×C4×D3—101no—
349C2×C4×D3—101no—
350C2×C4×D3D2011yescharacteristic
351C2×C4×D3D2011yescharacteristic
352C2×C4×D3C22×D511yescharacteristic
353C2×Dic6—51no—
354C2×C3×C8C22×D511yescharacteristic
355C2×C3×C8C22×D511yescharacteristic
356C3×C4⋊C4—51no—
357C3×C4⋊C4—51no—
358C3×C4⋊C4—51no—
359C3×C4⋊C4—101no—
360C3×C4⋊C4—101no—
361C3×C22⋊C4—101no—
362C3×C42C22×D511yescharacteristic
363#217—101no—
364(C2×D3)⋊C4—101no—
365C4⋊Dic3—51no—
366C4⋊Dic3—51no—
367C4⋊Dic3—51no—
368C4⋊Dic3—101no—
369C4⋊Dic3—101no—
370Dic3⋊C4—101no—
371Dic3⋊C4—101no—
372Dic3⋊C4—101no—
373Dic3⋊C4—101no—
374Dic3⋊C4—101no—
375Dic3⋊C4—101no—
376Dic3⋊C4—101no—
377Dic3⋊C4—101no—
378C4×Dic3—101no—
379C4×Dic3—101no—
380C4×Dic3—101no—
381C4×Dic3D2011yescharacteristic
382C4×Dic3D2011yescharacteristic
383C4×Dic3C22×D511yescharacteristic
384C2×C3⋊C8C22×D511yescharacteristic
385C2×C3⋊C8C22×D511yescharacteristic
386ΓL(1,𝔽25)—22no—
387ΓL(1,𝔽25)—22no—
388C23×C5—31no—
389C22×D5—21no—
390C2×C4×C5—31no—
391C2×C4×C5—32no—
392C2×C4×C5—32no—
393C2×C4×C5—31no—
394C2×C4×C5—31no—
395C2×C4×C5—121no—
396C2×C4×C5—121no—
397C2×C4×C5D3×D411yescharacteristic
398C2×C4×C5D3×D411yescharacteristic
399C2×C4×C5C23×D311yescharacteristic
400C22⋊D5—64no—
401C2×Dic5—21no—
402C2×Dic5—21no—
403C2×Dic5—21no—
404C2×Dic5—61no—
405C2×Dic5—61no—
406C2×Dic5—61no—
407C2×Dic5—61no—
408C2×Dic5—122no—
409C2×Dic5—122no—
410D20—21no—
411D20D3×Q812yes—
412C4×D5—42no—
413C4×D5—64no—
414C4×D5—122no—
415Dic10—32no—
416Dic10—61no—
417C5×C8—21no—
418C5×C8—21no—
419C5×C8—61no—
420C5×C8—61no—
421C2×#41—151no—
422C2×M16—31no—
423C2×M16—31no—
424#125—51no—
425#125—151no—
426#125—151no—
427#125—151no—
428#125—301no—
429#125—301no—
430C4×Q8—151no—
431C4×Q8—151no—
432C4×D4—51no—
433C4×D4—151no—
434C4×D4—301no—
435C4×D4—301no—
436#117—151no—
437#117—301no—
438C2×C4⋊C4—151no—
439C2×C4⋊C4—151no—
440C2×C4⋊C4—301no—
441C2×C4⋊C4—301no—
442C2×C42—31no—
443C2×C42—301no—
444#107—51no—
445#107—151no—
446#107—151no—
447#107—151no—
448#106—51no—
449#106—151no—
450#106—151no—
451#106—151no—
452C4⋊C8—31no—
453C4⋊C8—31no—
454C4⋊C8—31no—
455C4⋊C8D3×D511yescharacteristic
456#103—151no—
457#103—151no—
458#103—151no—
459#103—151no—
460#102—51no—
461#102—51no—
462#102—151no—
463#102—151no—
464C2×C3×C5C2×C22⋊Q811yescharacteristic
465C2×C3×C5#57511yescharacteristic
466C2×C3×C5#57511yescharacteristic
467C3×D5—42no—
468C5×D3—22no—
469C23×C3—101no—
470C22×D3C2×D2011yescharacteristic
471C3×D4—52no—
472C3×D4—101no—
473C2×C3×C4—101no—
474C2×C3×C4—101no—
475C2×C3×C4—101no—
476C2×C3×C4—202no—
477C2×C3×C4C2×D2011yescharacteristic
478C2×C3×C4C2×D2011yescharacteristic
479C2×C3×C4C23×D511yescharacteristic
480#67—104no—
481C2×Dic3—101no—
482C2×Dic3—104no—
483C2×Dic3—101no—
484C2×Dic3—101no—
485C2×Dic3—101no—
486C2×Dic3—202no—
487C2×Dic3C2×D2011yescharacteristic
488C2×Dic3C2×D2011yescharacteristic
489C2×Dic3C2×D2011yescharacteristic
490C4×D3—41no—
491C4×D3—41no—
492C4×D3—202no—
493C4×D3—202no—
494C4×D3#71112yes—
495C4×D3Q8×D512yes—
496Dic6—52no—
497Dic6—101no—
498C3×C8—21no—
499C3×C8—21no—
500C3⋊C8—21no—
501C3⋊C8—21no—
502C22×C5—32no—
503C22×C5—61no—
504C22×C5—61no—
505C22×C5C2×D3×D411yescharacteristic
506C2×D5—22no—
507C2×D5—41no—
508C2×D5—41no—
509C4×C5—21no—
510C4×C5—21no—
511C4×C5—32no—
512C4×C5—61no—
513C4×C5—61no—
514C4×C5C2×D3×Q811yescharacteristic
515C4×C5D3×#4111yescharacteristic
516Dic5—41no—
517Dic5—41no—
518Dic5—41no—
519Dic5—62no—
520Dic5—121no—
521Dic5—121no—
522Dic5—121no—
523#41—154no—
524#41—302no—
525C2×Q8—151no—
526C2×D4—51no—
527C2×D4—301no—
528C22×C4—31no—
529C22×C4—31no—
530C22×C4—31no—
531C22×C4—101no—
532C22×C4—301no—
533C22×C4—301no—
534C22×C4—301no—
535C22×C4—301no—
536M16—62no—
537M16—62no—
538C2×C8—31no—
539C2×C8—31no—
540C2×C8C2×D3×D511yescharacteristic
541C2×C8C2×D3×D511yescharacteristic
542C4⋊C4—51no—
543C4⋊C4—51no—
544C4⋊C4—51no—
545C4⋊C4—101no—
546C4⋊C4—101no—
547C4⋊C4—151no—
548C4⋊C4—151no—
549C4⋊C4—151no—
550C4⋊C4—301no—
551C4⋊C4—301no—
552C4⋊C4—301no—
553C4⋊C4—301no—
554C4⋊C4—301no—
555C4⋊C4—301no—
556C4⋊C4—301no—
557C4⋊C4—301no—
558C4⋊C4—301no—
559C4⋊C4—301no—
560C22⋊C4—101no—
561C22⋊C4—301no—
562C22⋊C4—301no—
563C42—31no—
564C42—31no—
565C42—31no—
566C42—301no—
567C42—301no—
568C42—301no—
569C42C2×D3×D511yescharacteristic
570C3×C5#308011yescharacteristic, complemented, Hall
571C22×C3—102no—
572C22×C3—201no—
573C22×C3—201no—
574C22×C3C22×D2011yescharacteristic
575C2×D3—21no—
576C2×D3—21no—
577C2×D3#404312yes—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—201no—
581C3×C4—201no—
582C3×C4—201no—
583C3×C4C2×#71111yescharacteristic
584C3×C4C2×Q8×D511yescharacteristic
585Dic3—21no—
586Dic3—21no—
587Dic3—102no—
588Dic3—201no—
589Dic3—201no—
590Dic3—201no—
591Dic3#404312yes—
592C2×C5—62no—
593C2×C5D3×C22⋊Q811yescharacteristic
594C2×C5#576811yescharacteristic
595C2×C5#577311yescharacteristic
596D5—42no—
597C23—31no—
598C23—101no—
599Q8—152no—
600Q8—301no—
601D4—52no—
602D4—101no—
603D4—304no—
604C2×C4—31no—
605C2×C4—32no—
606C2×C4—32no—
607C2×C4—31no—
608C2×C4—31no—
609C2×C4—101no—
610C2×C4—101no—
611C2×C4—101no—
612C2×C4—121no—
613C2×C4—121no—
614C2×C4—202no—
615C2×C4—304no—
616C2×C4—301no—
617C2×C4—301no—
618C2×C4—301no—
619C2×C4—301no—
620C2×C4—602no—
621C2×C4—602no—
622C2×C4—602no—
623C2×C4D3×D2011yescharacteristic
624C2×C4D3×D2011yescharacteristic
625C2×C4C22×D3×D511yescharacteristic
626C8—21no—
627C8—21no—
628C8—61no—
629C8—61no—
630C2×C3—202no—
631C2×C3C2×#404311yescharacteristic
632C2×C3#6608211yescharacteristic
633C2×C3#6608211yescharacteristic
634D3—22no—
635C5#8116711yescharacteristic, complemented, Sylow
636C22—32no—
637C22—61no—
638C22—61no—
639C22—102no—
640C22—201no—
641C22—201no—
642C22C2×D3×D2011yescharacteristic
643C4—21no—
644C4—21no—
645C4—32no—
646C4—61no—
647C4—61no—
648C4—201no—
649C4—201no—
650C4—201no—
651C4—302no—
652C4—601no—
653C4—601no—
654C4—601no—
655C4D3×#71111yescharacteristic
656C4D3×Q8×D511yescharacteristic
657C3#1061079211yescharacteristic, complemented, Sylow
658C2—62no—
659C2—202no—
660C2D3×#404311yescharacteristic
661C2#1175396911yescharacteristic
662C2#1175402911yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6765C22
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3080
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. D3×#4016C2semidirect
3. #11750930C2semidirect
4. C5×#4837C2semidirect
5. C3×#65136C2semidirect
8. #11747874C2semidirect
9. #11747871C2semidirect
10. #11747784C2semidirect
11. #11747783C2semidirect
12. #11747630C2semidirect
13. #11747628C2semidirect
14. #11746934C2semidirect
15. #11746888C2semidirect
71. #65136D3semidirect
132. #4837D5semidirect
570. C3×C5#3080semidirect
635. C5#81167semidirect
657. C3#10610792semidirect

Maximal subgroups

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

subgroupindex
D3×#40162
C4×#67652
#117509302
C5×#48372
C3×#651362
#117481382
#117478742
#117478712
#117477842
#117477832
#117476302
#117476282
#117469342
#117468882
#106107923
#811675