Finite Group Databasebeta

← #14430704

Subgroups — #14430704

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
1C4×#6773C211yesmaximal, characteristic
2D5×#870C211yesmaximal, characteristic, complemented
3#11750948C211yesmaximal, characteristic, complemented
4C5×#4829C211yesmaximal, characteristic, complemented
5C3×#65126C211yesmaximal, characteristic, complemented
6#11747860C211yesmaximal, characteristic, complemented
7#11747855C211yesmaximal, characteristic, complemented
8#11747780C211yesmaximal, characteristic, complemented
9#11747773C211yesmaximal, characteristic, complemented
10#11747619C211yesmaximal, characteristic, complemented
11#11747618C211yesmaximal, characteristic, complemented
12#11747606C211yesmaximal, characteristic
13#11747606C211yesmaximal, characteristic
14#11746965C211yesmaximal, characteristic, complemented
15#11746899C211yesmaximal, characteristic, complemented
16#10612962—31nomaximal, Hall
17C2×#6773C2211yescharacteristic
18C4×D60C2211yescharacteristic
19#91759C2211yescharacteristic
20C5×#870C2211yescharacteristic
21C4×C5×Dic6C2211yescharacteristic
22C2×C3×#676C2211yescharacteristic
23C2×C3×#676C2211yescharacteristic
24C3×C42×D5C2211yescharacteristic
25#91444—21no—
26C4×#1202—21no—
27#91418C2211yescharacteristic
28D5×C4⋊Dic3C2211yescharacteristic
29D5×C4⋊Dic3C2211yescharacteristic
30#91402—21no—
31C4×#1200—21no—
32D5×Dic3⋊C4—21no—
33D5×Dic3⋊C4—21no—
34#91388C2211yescharacteristic
35#91388C2211yescharacteristic
36#91378—21no—
37#91378—21no—
38#91358C2211yescharacteristic
39Dic5×Dic6C2211yescharacteristic
40C3×C5×C4⋊C8C2211yescharacteristic
41#91105C2211yescharacteristic
42#91105C2211yescharacteristic
43#91102C2211yescharacteristic
44#91101C2211yescharacteristic
45C5×#818C2211yescharacteristic
46C5×#817C2211yescharacteristic
47C5×#816C2211yescharacteristic
48C5×#816C2211yescharacteristic
49C3×#3946C2211yescharacteristic
50C3×#3946C2211yescharacteristic
51C3×C4⋊#168C2211yescharacteristic
52#90988C2211yescharacteristic
53#90988C2211yescharacteristic
54#90985C2211yescharacteristic
55#90985C2211yescharacteristic
56#90973C2211yescharacteristic
57#90973C2211yescharacteristic
58#90969C2211yescharacteristic
59#90969C2211yescharacteristic
60#79061—51nomaximal, Hall
61D5×#125—31no—
62C4×#713—31no—
63C5×#479—31no—
64#65355—31no—
65#65311—31no—
66#65180—31no—
67#65170—31no—
68#65160—31no—
69#65150—31no—
70#65136—31no—
71#65126D311yescharacteristic, complemented
72#65092—31no—
73#65092—31no—
74#65088—31no—
75#65085—31no—
76C2×D60C2311yescharacteristic
77C2×C4×D15—21no—
78C2×C5×Dic6C2311yescharacteristic
79C2×C3×C4×D5D411yescharacteristic
80C2×C3×C4×D5D411yescharacteristic
81C2×C3×C4×D5C2311yescharacteristic
82C2×#1202—21no—
83C2×#1200—21no—
84C2×#1200—21no—
85C2×D5×Dic3—21no—
86C2×D5×Dic3—21no—
87#6773—22no—
88#6773Q814yes—
89C2×C3×C5×C8C2311yescharacteristic
90C2×C3×C5×C8C2311yescharacteristic
91C3×C42×C5C2311yescharacteristic
92#6714—21no—
93C4⋊Dic15C2311yescharacteristic
94C4⋊Dic15C2311yescharacteristic
95C4⋊Dic15C2311yescharacteristic
96#6712—21no—
97#6712—21no—
98C5×C4⋊Dic3C2311yescharacteristic
99C5×C4⋊Dic3C2311yescharacteristic
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C4×C5×Dic3—21no—
105C3×C4×Dic5D411yescharacteristic
106C3×C4×Dic5D411yescharacteristic
107C3×C4×Dic5C2311yescharacteristic
108C2×C3×#168C2311yescharacteristic
109C2×C3×#168C2311yescharacteristic
110C3×#676—22no—
111C3×#676—22no—
112Dic3⋊Dic5—21no—
113Dic3⋊Dic5—21no—
114Dic3⋊Dic5—21no—
115#6669—21no—
116#6669—21no—
117#6668—21no—
118#6668—21no—
119#6667—21no—
120#6665—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123C4×#235—51no—
124C2×#870—51no—
125C3×#423—51no—
126#5133—51no—
127#5133—51no—
128#5121—51no—
129#5121—51no—
130#4847—51no—
131#4847—51no—
132#4847—51no—
133#4847—51no—
134#4829—51no—
135#4829—51no—
136#4829—51no—
137#4829D511yescharacteristic, complemented
138C2×#713—31no—
139C5×#125—31no—
140C4×C5×Q8—31no—
141Q8×Dic5—31no—
142C2×#676C2×D311yescharacteristic
143C2×#676C2×D311yescharacteristic
144#4039—31no—
145#4039—61no—
146#4038—31no—
147#4038—61no—
148D5×C4⋊C4—31no—
149D5×C4⋊C4—31no—
150D5×C4⋊C4—61no—
151D5×C4⋊C4—61no—
152#4036—31no—
153#4036—31no—
154#4035—61no—
155#4035—61no—
156C4×D20—31no—
157C4×D20—61no—
158C42×D5—61no—
159C42×D5C2×D311yescharacteristic
160#4016—31no—
161C5×#107—31no—
162C5×#106—31no—
163C5×C4⋊C8C2×D311yescharacteristic
164C5×#103—31no—
165C5×#103—31no—
166#3967—31no—
167#3967—31no—
168#3953—31no—
169#3953—31no—
170#3950—31no—
171#3949—31no—
172#3946C2×D311yescharacteristic
173#3946C2×D311yescharacteristic
174#3941—31no—
175#3941—31no—
176#3940—31no—
177#3940—31no—
178#3939—31no—
179#3939—31no—
180C4⋊#168C2×D311yescharacteristic
181#3080—151noSylow
182C22×D15—21no—
183C22×C3×D5C2×D411yescharacteristic
184C2×C3×C4×C5C2×D411yescharacteristic
185C2×C3×C4×C5C2×D411yescharacteristic
186C2×C3×C4×C5C2411yescharacteristic
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—21no—
190D60—21no—
191D60C2×Q812yes—
192C4×D15—42no—
193C2×C5×Dic3—21no—
194C2×C5×Dic3—21no—
195C2×C5×Dic3—21no—
196C2×C5×Dic3—21no—
197C5×Dic6—21no—
198C5×Dic6C2×Q812yes—
199C2×C3×Dic5C2×D411yescharacteristic
200C2×C3×Dic5C2×D411yescharacteristic
201C2×C3×Dic5C2×D411yescharacteristic
202C3×C4×D5—41no—
203C3×C4×D5—41no—
204C3×C4×D5C2×Q812yes—
205C3×C4×D5#4112yes—
206#1202—24no—
207#1200—24no—
208#1200—42no—
209D5×Dic3—42no—
210D5×Dic3—42no—
211C3×C5×C8—21no—
212C3×C5×C8—21no—
213C3×#168—21no—
214C3×#168—21no—
215C2×#235—51no—
216C2×C3×M16—51no—
217C2×C3×M16—51no—
218C2×C3×C42—51no—
219C4×#67—101no—
220C4×#67—101no—
221#926—51no—
222C2×C4⋊Dic3—51no—
223C2×C4⋊Dic3—51no—
224C2×Dic3⋊C4—101no—
225C2×Dic3⋊C4—101no—
226C4×D12—51no—
227C4×D12—51no—
228#872—101no—
229C42×D3—101no—
230#870—51no—
231#870—51no—
232#870—51no—
233#870—101no—
234#870—101no—
235#870C2×D511yescharacteristic
236C4×Dic6—51no—
237C4×Dic6C2×D511yescharacteristic
238C3×C4⋊C8—51no—
239C3×C4⋊C8—51no—
240C3×C4⋊C8—51no—
241C3×C4⋊C8C2×D511yescharacteristic
242#821—51no—
243#821—51no—
244#821—51no—
245#821—51no—
246#818—51no—
247#818—51no—
248#818—51no—
249#818C2×D511yescharacteristic
250#817—51no—
251#817—51no—
252#817—51no—
253#817C2×D511yescharacteristic
254#816—51no—
255#816—51no—
256#816C2×D511yescharacteristic
257#816C2×D511yescharacteristic
258C2×C5×Q8—31no—
259#713—34no—
260#713—62no—
261C2×D20—31no—
262C2×D20—61no—
263C2×C4×D5—61no—
264C2×C4×D5—61no—
265C2×C4×D5—61no—
266C2×C4×D5—61no—
267C2×C4×D5—61no—
268C2×C4×D5D1211yescharacteristic
269C2×C4×D5D1211yescharacteristic
270C2×C4×D5C22×D311yescharacteristic
271C2×C5×C8C22×D311yescharacteristic
272C2×C5×C8C22×D311yescharacteristic
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—61no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4—61no—
279C42×C5—61no—
280C42×C5C22×D311yescharacteristic
281#685—61no—
282#685—61no—
283#685—61no—
284C4⋊Dic5—31no—
285C4⋊Dic5—31no—
286C4⋊Dic5—31no—
287C4⋊Dic5—61no—
288C4⋊Dic5—61no—
289C4⋊Dic5—61no—
290#683—61no—
291#683—61no—
292#683—61no—
293#683—61no—
294#683—61no—
295#683—61no—
296C4×Dic5—61no—
297C4×Dic5—61no—
298C4×Dic5D1211yescharacteristic
299C4×Dic5D1211yescharacteristic
300C4×Dic5C22×D311yescharacteristic
301C2×#168C22×D311yescharacteristic
302C2×#168C22×D311yescharacteristic
303#676—22no—
304#676—22no—
305C2×#125—151no—
306C4×#41—151no—
307#479—31no—
308#479—151no—
309#479—151no—
310#479—151no—
311#478—151no—
312#478—151no—
313#478—151no—
314#478—151no—
315#428—151no—
316#428—151no—
317#423—51no—
318#417—151no—
319#417—151no—
320C22×C3×C5C22×D411yescharacteristic
321C2×D15—22no—
322C2×D15—41no—
323C2×D15—41no—
324C2×C3×D5—21no—
325C2×C3×D5—21no—
326C2×C3×D5C22⋊Q812yes—
327C3×C4×C5—21no—
328C3×C4×C5—21no—
329C3×C4×C5C22×Q811yescharacteristic
330C3×C4×C5C2×#4111yescharacteristic
331Dic15—41no—
332Dic15—41no—
333Dic15—41no—
334C3×Dic5—21no—
335C3×Dic5—21no—
336C3×Dic5C22⋊Q812yes—
337C5×Dic3—22no—
338C5×Dic3—41no—
339C5×Dic3—41no—
340C5×Dic3—41no—
341C22×C3×C4—51no—
342C22×C3×C4—51no—
343C22×C3×C4—51no—
344C2×#67—101no—
345C22×Dic3—101no—
346C22×Dic3—101no—
347#235—54no—
348#235—102no—
349C2×D12—51no—
350C2×C4×D3—101no—
351C2×C4×D3—101no—
352C2×C4×D3—101no—
353C2×Dic6C22×D511yescharacteristic
354C3×M16—102no—
355C3×M16—102no—
356C2×C3×C8—51no—
357C2×C3×C8—51no—
358C2×C3×C8C22×D511yescharacteristic
359C2×C3×C8C22×D511yescharacteristic
360C3×C42—51no—
361C3×C42—51no—
362C3×C42—51no—
363C3×C42C22×D511yescharacteristic
364#217—101no—
365(C2×D3)⋊C4—101no—
366(C2×D3)⋊C4—101no—
367C4⋊Dic3—51no—
368C4⋊Dic3—51no—
369C4⋊Dic3—51no—
370C4⋊Dic3—101no—
371C4⋊Dic3—101no—
372C4⋊Dic3C22×D511yescharacteristic
373C4⋊Dic3C22×D511yescharacteristic
374C4⋊Dic3C22×D511yescharacteristic
375Dic3⋊C4—21no—
376Dic3⋊C4—21no—
377Dic3⋊C4—21no—
378Dic3⋊C4—101no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381Dic3⋊C4—101no—
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385C4×Dic3—21no—
386C4×Dic3—101no—
387C4×Dic3—101no—
388C22×D5—61no—
389C22×D5C2×D1211yescharacteristic
390C5×Q8—32no—
391C5×Q8—61no—
392C2×C4×C5—61no—
393C2×C4×C5—61no—
394C2×C4×C5—61no—
395C2×C4×C5—61no—
396C2×C4×C5C2×D1211yescharacteristic
397C2×C4×C5C2×D1211yescharacteristic
398C2×C4×C5C23×D311yescharacteristic
399C2×Dic5—61no—
400C2×Dic5—61no—
401C2×Dic5—61no—
402C2×Dic5C2×D1211yescharacteristic
403C2×Dic5C2×D1211yescharacteristic
404C2×Dic5C2×D1211yescharacteristic
405D20—32no—
406D20—64no—
407D20—61no—
408C4×D5—41no—
409C4×D5—41no—
410C4×D5—64no—
411C4×D5—122no—
412C4×D5—122no—
413C4×D5—122no—
414C4×D5—122no—
415C4×D5#23712yes—
416C4×D5D3×Q812yes—
417C5×C8—21no—
418C5×C8—21no—
419#168—21no—
420#168—21no—
421C2×#41—151no—
422C2×M16—51no—
423C2×M16—51no—
424#125—31no—
425#125—151no—
426#125—151no—
427#125—151no—
428#125—301no—
429#125—301no—
430C4×Q8—31no—
431C4×Q8—151no—
432C4×D4—151no—
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—51no—
443C2×C42—301no—
444#107—31no—
445#107—151no—
446#107—151no—
447#107—151no—
448#106—31no—
449#106—151no—
450#106—151no—
451#106—151no—
452C4⋊C8—51no—
453C4⋊C8—51no—
454C4⋊C8—51no—
455C4⋊C8D3×D511yescharacteristic
456#103—31no—
457#103—31no—
458#103—151no—
459#103—151no—
460#102—151no—
461#102—151no—
462#102—151no—
463#102—151no—
464C2×C3×C5C2×C22⋊Q811yescharacteristic
465C2×C3×C5#57511yescharacteristic
466C2×C3×C5#57511yescharacteristic
467D15—42no—
468C3×D5—22no—
469C23×C3—51no—
470C22×D3—101no—
471C2×C3×C4—51no—
472C2×C3×C4—52no—
473C2×C3×C4—52no—
474C2×C3×C4—51no—
475C2×C3×C4—51no—
476C2×C3×C4—201no—
477C2×C3×C4—201no—
478C2×C3×C4D4×D511yescharacteristic
479C2×C3×C4D4×D511yescharacteristic
480C2×C3×C4C23×D511yescharacteristic
481#67—104no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—101no—
487C2×Dic3—101no—
488C2×Dic3—101no—
489C2×Dic3—202no—
490C2×Dic3—202no—
491D12—52no—
492D12—101no—
493C4×D3—104no—
494C4×D3—202no—
495C4×D3—202no—
496Dic6—21no—
497Dic6Q8×D512yes—
498C3×C8—21no—
499C3×C8—21no—
500C3×C8—101no—
501C3×C8—101no—
502C22×C5C22×D1211yescharacteristic
503C2×D5—21no—
504C2×D5—21no—
505C2×D5—62no—
506C2×D5—121no—
507C2×D5—121no—
508C2×D5#89712yes—
509C4×C5—21no—
510C4×C5—21no—
511C4×C5—62no—
512C4×C5—121no—
513C4×C5—121no—
514C4×C5—121no—
515C4×C5C2×#23711yescharacteristic
516C4×C5C2×D3×Q811yescharacteristic
517Dic5—21no—
518Dic5—21no—
519Dic5—121no—
520Dic5—121no—
521Dic5—121no—
522Dic5#89712yes—
523#41—154no—
524#41—302no—
525C2×Q8—31no—
526C2×D4—151no—
527C2×D4—301no—
528C22×C4—51no—
529C22×C4—51no—
530C22×C4—51no—
531C22×C4—301no—
532C22×C4—301no—
533C22×C4—301no—
534C22×C4—301no—
535C22×C4—301no—
536M16—102no—
537M16—102no—
538C2×C8—51no—
539C2×C8—51no—
540C2×C8C2×D3×D511yescharacteristic
541C2×C8C2×D3×D511yescharacteristic
542C4⋊C4—31no—
543C4⋊C4—31no—
544C4⋊C4—31no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—151no—
549C4⋊C4—151no—
550C4⋊C4—151no—
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—301no—
561C22⋊C4—301no—
562C22⋊C4—301no—
563C42—51no—
564C42—51no—
565C42—51no—
566C42—61no—
567C42—301no—
568C42—301no—
569C42C2×D3×D511yescharacteristic
570C3×C5#308011yescharacteristic, complemented, Hall
571C22×C3—52no—
572C22×C3—101no—
573C22×C3—101no—
574C22×C3C2×D4×D511yescharacteristic
575C2×D3—102no—
576C2×D3—201no—
577C2×D3—201no—
578C3×C4—21no—
579C3×C4—21no—
580C3×C4—52no—
581C3×C4—101no—
582C3×C4—101no—
583C3×C4C2×Q8×D511yescharacteristic
584C3×C4D5×#4111yescharacteristic
585Dic3—22no—
586Dic3—41no—
587Dic3—41no—
588Dic3—41no—
589Dic3—201no—
590Dic3—201no—
591Dic3—201no—
592C2×C5C2×#89711yescharacteristic
593C2×C5#574811yescharacteristic
594C2×C5#574811yescharacteristic
595D5—22no—
596D5—122no—
597C23—51no—
598C23—301no—
599Q8—32no—
600Q8—61no—
601D4—152no—
602D4—304no—
603D4—301no—
604C2×C4—51no—
605C2×C4—52no—
606C2×C4—52no—
607C2×C4—51no—
608C2×C4—51no—
609C2×C4—61no—
610C2×C4—61no—
611C2×C4—61no—
612C2×C4—61no—
613C2×C4—201no—
614C2×C4—201no—
615C2×C4—304no—
616C2×C4—301no—
617C2×C4—301no—
618C2×C4—301no—
619C2×C4—602no—
620C2×C4—602no—
621C2×C4—602no—
622C2×C4—602no—
623C2×C4D5×D1211yescharacteristic
624C2×C4D5×D1211yescharacteristic
625C2×C4C22×D3×D511yescharacteristic
626C8—21no—
627C8—21no—
628C8—101no—
629C8—101no—
630C2×C3—102no—
631C2×C3D5×C22⋊Q811yescharacteristic
632C2×C3#6610211yescharacteristic
633C2×C3#6611111yescharacteristic
634D3—202no—
635C5#7906111yescharacteristic, complemented, Sylow
636C22—52no—
637C22—101no—
638C22—101no—
639C22—302no—
640C22—601no—
641C22—601no—
642C22C2×D5×D1211yescharacteristic
643C4—21no—
644C4—21no—
645C4—52no—
646C4—62no—
647C4—101no—
648C4—101no—
649C4—121no—
650C4—121no—
651C4—121no—
652C4—601no—
653C4—601no—
654C4—601no—
655C4D5×#23711yescharacteristic
656C4D3×Q8×D511yescharacteristic
657C3#1061296211yescharacteristic, complemented, Sylow
658C2—102no—
659C2—602no—
660C2D5×#89711yescharacteristic
661C2#1175395911yescharacteristic
662C2#1175402111yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#6773C22
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
2. D5×#870C2semidirect
3. #11750948C2semidirect
4. C5×#4829C2semidirect
5. C3×#65126C2semidirect
6. #11747860C2semidirect
7. #11747855C2semidirect
8. #11747780C2semidirect
9. #11747773C2semidirect
10. #11747619C2semidirect
11. #11747618C2semidirect
14. #11746965C2semidirect
15. #11746899C2semidirect
71. #65126D3semidirect
137. #4829D5semidirect
570. C3×C5#3080semidirect
635. C5#79061semidirect
657. C3#10612962semidirect

Maximal subgroups

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

subgroupindex
C4×#67732
D5×#8702
#117509482
C5×#48292
C3×#651262
#117478602
#117478552
#117477802
#117477732
#117476192
#117476182
#117476062
#117469652
#117468992
#106129623
#790615