Finite Group Databasebeta

← #14431394

Subgroups — #14431394

Order 1920.

752 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
1#11755220C211yesmaximal, characteristic
2#11753665C211yesmaximal, characteristic, complemented
3#11750900C211yesmaximal, characteristic, complemented
4C5×#4804C211yesmaximal, characteristic
5C3×#65088C211yesmaximal, characteristic, complemented
6#11749361C211yesmaximal, characteristic, complemented
7#11749348C211yesmaximal, characteristic, complemented
8#11749201C211yesmaximal, characteristic
9#11747808C211yesmaximal, characteristic, complemented
10#11747758C211yesmaximal, characteristic, complemented
11#11747655C211yesmaximal, characteristic, complemented
12D3×#3949C211yesmaximal, characteristic, complemented
13#11747258C211yesmaximal, characteristic, complemented
14#11747241C211yesmaximal, characteristic, complemented
15#11747190C211yesmaximal, characteristic, complemented
16#10610555—31nomaximal, Hall
17C2×C5×#239C2211yescharacteristic
18Q8×Dic15C2211yescharacteristic
19#91779C2211yescharacteristic
20C2×C5×D3×C8C2211yescharacteristic
21C5×#892C2211yescharacteristic
22C3×Q8×Dic5C2211yescharacteristic
23C3×#4036C2211yescharacteristic
24#91470C2211yescharacteristic
25#91469—21no—
26#91468C2211yescharacteristic
27#91436—21no—
28#91435—21no—
29#91435C2211yescharacteristic
30D3×C4⋊Dic5—21no—
31D3×C4⋊Dic5C2211yescharacteristic
32D3×C4⋊Dic5C2211yescharacteristic
33#91417—21no—
34Dic5×D12—21no—
35Dic5×D12C2211yescharacteristic
36#91379—21no—
37#91371—21no—
38#91371C2211yescharacteristic
39C2×#6650C2211yescharacteristic
40C3×C5×#103C2211yescharacteristic
41#91119C2211yescharacteristic
42#91101C2211yescharacteristic
43#91098C2211yescharacteristic
44#91091C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#821C2211yescharacteristic
47C5×#809C2211yescharacteristic
48C3×#3967C2211yescharacteristic
49C3×#3949C2211yescharacteristic
50C3×#3946C2211yescharacteristic
51C3×#3939C2211yescharacteristic
52#90987C2211yescharacteristic
53#90987C2211yescharacteristic
54#90986C2211yescharacteristic
55#90985C2211yescharacteristic
56#90983C2211yescharacteristic
57#90982C2211yescharacteristic
58#90967C2211yescharacteristic
59#90966C2211yescharacteristic
60#81235—51nomaximal, Hall
61#66161—31no—
62#65853—31no—
63C5×#416—31no—
64#65521—31no—
65C2×#3949—31no—
66#65391—31no—
67#65284—31no—
68#65088—31no—
69#65088D311yescharacteristic, complemented
70#65080—31no—
71#65080—31no—
72#65052—31no—
73#65052—31no—
74#65050—31no—
75#65050—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C5×#239—22no—
78C5×#239Q814yescomplemented
79C2×C5×D12—21no—
80C2×C5×D12C2311yescharacteristic
81C2×C4×C5×D3—21no—
82C2×C4×C5×D3C2311yescharacteristic
83C2×#1204—21no—
84C2×#1204—21no—
85C2×D3×Dic5—21no—
86C2×D3×Dic5—21no—
87C2×D3×Dic5—21no—
88C2×D3×Dic5—21no—
89C2×C3×C5×C8C2311yescharacteristic
90C3×C5×C4⋊C4C2311yescharacteristic
91C4⋊Dic15—21no—
92C4⋊Dic15—21no—
93C4⋊Dic15C2311yescharacteristic
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96C4×Dic15—21no—
97C4×Dic15C2311yescharacteristic
98C2×C3⋊#168C2311yescharacteristic
99C5×(C2×D3)⋊C4—21no—
100C5×C4⋊Dic3C2311yescharacteristic
101C4×C5×Dic3—21no—
102C2×C5×C3⋊C8C2311yescharacteristic
103C5×D3×C8—22no—
104C3×C4⋊Dic5—21no—
105C3×C4⋊Dic5—21no—
106C3×C4⋊Dic5C2311yescharacteristic
107C3×C4⋊Dic5C2311yescharacteristic
108C3×#683—21no—
109C3×C4×Dic5—21no—
110C3×C4×Dic5C2311yescharacteristic
111C2×C3×#168C2311yescharacteristic
112Dic3⋊Dic5—21no—
113Dic3⋊Dic5—21no—
114Dic3⋊Dic5D411yescharacteristic
115Dic3⋊Dic5D411yescharacteristic
116#6669—21no—
117#6668—21no—
118(C2×D3)⋊Dic5—21no—
119(C2×D3)⋊Dic5—21no—
120(C2×D3)⋊Dic5D411yescharacteristic
121(C2×D3)⋊Dic5D411yescharacteristic
122#6650—22no—
123#5689—51no—
124#5574—51no—
125C3×#479—51no—
126#5066—51no—
127#5020—51no—
128#4891—51no—
129#4881—51no—
130#4870—51no—
131D3×#106—51no—
132#4842—51no—
133#4839—51no—
134#4804D511yescharacteristic
135#4803—51no—
136#4799—51no—
137#4791—51no—
138C2×C5×#41—31no—
139C22×C5×C8—31no—
140C5×#117—31no—
141Q8×Dic5—31no—
142Q8×Dic5C2×D311yescharacteristic
143D4×Dic5—31no—
144D4×Dic5—31no—
145D4×Dic5—61no—
146D4×Dic5—61no—
147#4072—31no—
148#4072—61no—
149C2×C4⋊Dic5—31no—
150C2×C4⋊Dic5—31no—
151C2×C4⋊Dic5—61no—
152C2×#681—31no—
153#4036—31no—
154#4036C2×D311yescharacteristic
155#4034—31no—
156#4034—31no—
157#4024—61no—
158#4024—61no—
159#4016—61no—
160#4015—61no—
161C5×#103—31no—
162C5×#103C2×D311yescharacteristic
163C5×#102—31no—
164C5×#102—31no—
165#3967—31no—
166#3967C2×D311yescharacteristic
167#3964—31no—
168#3964—31no—
169#3949—31no—
170#3949—31no—
171#3949—31no—
172#3949C2×D311yescharacteristic
173#3946—31no—
174#3946—31no—
175#3946—31no—
176#3946C2×D311yescharacteristic
177#3940—31no—
178#3940—31no—
179#3939—31no—
180#3939C2×D311yescharacteristic
181#3084—151noSylow
182C22×C5×D3—21no—
183C22×C5×D3C2×D411yescharacteristic
184C3×C5×Q8—21no—
185C3×C5×Q8C2×Q812yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5C2411yescharacteristic
189C2×Dic15—21no—
190C2×Dic15—21no—
191C2×Dic15C2×D411yescharacteristic
192C2×Dic15C2×D411yescharacteristic
193C2×C5×Dic3—21no—
194C2×C5×Dic3C2×D411yescharacteristic
195C5×D12—24no—
196C5×D12—21no—
197C5×D12C2×Q812yes—
198C4×C5×D3—24no—
199C4×C5×D3C2×Q812yes—
200C4×C5×D3#4112yes—
201C2×C3×Dic5—21no—
202C2×C3×Dic5—21no—
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205#1204—81no—
206#1204—81no—
207D3×Dic5—81no—
208D3×Dic5—81no—
209D3×Dic5—81no—
210D3×Dic5—81no—
211C3×C5×C8—21no—
212C3⋊#168—21no—
213C3×#168—21no—
214C5×C3⋊C8—21no—
215C2×#239C2×D511yescharacteristic
216C3×#125—51no—
217C3×C4×Q8—51no—
218Q8×Dic3—51no—
219C2×ΓL(1,𝔽25)—51no—
220C2×D3×C8C2×D511yescharacteristic
221#897—101no—
222#896—101no—
223#893—51no—
224#893—101no—
225#892C2×D511yescharacteristic
226D3×C4⋊C4—51no—
227D3×C4⋊C4—51no—
228D3×C4⋊C4—101no—
229#890—51no—
230#889—101no—
231#888—51no—
232#888—101no—
233C4×D12—51no—
234C4×D12—101no—
235#872—51no—
236#872—101no—
237#869—51no—
238C3×#107—51no—
239C3×#106—51no—
240C3×C4⋊C8—51no—
241C3×#103—51no—
242C3×#103C2×D511yescharacteristic
243#835—51no—
244#835C2×D511yescharacteristic
245#821—51no—
246#821C2×D511yescharacteristic
247#817—51no—
248#817—51no—
249Dic3⋊C8—51no—
250Dic3⋊C8—51no—
251#809—51no—
252#809C2×D511yescharacteristic
253#808—51no—
254#808—51no—
255#808—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C5×#41—34no—
259C5×#41—62no—
260C2×C5×Q8C22×D311yescharacteristic
261C2×C5×D4—31no—
262C2×C5×D4—61no—
263C22×C4×C5—31no—
264C22×C4×C5—61no—
265C22×Dic5—61no—
266C22×Dic5—61no—
267C22×Dic5—61no—
268C22×Dic5—61no—
269C2×Dic10—61no—
270C2×Dic10—61no—
271C2×C5×C8—31no—
272C2×C5×C8—62no—
273C2×C5×C8C22×D311yescharacteristic
274C5×C4⋊C4—31no—
275C5×C4⋊C4C22×D311yescharacteristic
276C5×C22⋊C4—61no—
277C42×C5—61no—
278C22⋊Dic5—31no—
279C22⋊Dic5—31no—
280C22⋊Dic5—61no—
281C22⋊Dic5—61no—
282C4⋊Dic5—21no—
283C4⋊Dic5—21no—
284C4⋊Dic5—31no—
285C4⋊Dic5—31no—
286C4⋊Dic5—31no—
287C4⋊Dic5—31no—
288C4⋊Dic5—61no—
289C4⋊Dic5—61no—
290C4⋊Dic5—61no—
291C4⋊Dic5—61no—
292C4⋊Dic5C22×D311yescharacteristic
293C4⋊Dic5C22×D311yescharacteristic
294#683—21no—
295#683—61no—
296#683—61no—
297#683—61no—
298C4×Dic5—21no—
299C4×Dic5—31no—
300C4×Dic5—61no—
301C4×Dic5C22×D311yescharacteristic
302#681—62no—
303C2×#168—31no—
304C2×#168C22×D311yescharacteristic
305#544—151no—
306#520—151no—
307#479—51no—
308#479—151no—
309#478—151no—
310#478—151no—
311#476—151no—
312#476—151no—
313#475—151no—
314#475—151no—
315#428—151no—
316C2×#106—151no—
317#424—151no—
318#417—151no—
319#416—31no—
320C22×C3×C5C22×D411yescharacteristic
321C2×C5×D3—21no—
322C2×C5×D3—21no—
323C2×C5×D3—22no—
324C2×C5×D3—41no—
325C2×C5×D3—41no—
326C2×C5×D3C22⋊Q812yes—
327C3×C4×C5—22no—
328C3×C4×C5—41no—
329C3×C4×C5C22×Q811yescharacteristic
330C3×C4×C5C2×#4111yescharacteristic
331Dic15—21no—
332Dic15—21no—
333Dic15—41no—
334Dic15—41no—
335C3×Dic5—21no—
336C3×Dic5—21no—
337C3×Dic5—41no—
338C3×Dic5—41no—
339C5×Dic3—41no—
340C5×Dic3C22⋊Q812yes—
341C2×C3×Q8C22×D511yescharacteristic
342#239—22no—
343#239Dic1014yescomplemented
344C2×D12—21no—
345C2×D12C22×D511yescharacteristic
346C2×C4×D3—21no—
347C2×C4×D3—101no—
348C2×C4×D3—101no—
349C2×C4×D3—101no—
350C2×C4×D3—101no—
351C2×C4×D3C22×D511yescharacteristic
352C2×Dic6—101no—
353C2×Dic6—101no—
354C2×C3×C8—51no—
355C2×C3×C8C22×D511yescharacteristic
356C3×C4⋊C4—51no—
357C3×C4⋊C4—51no—
358C3×C4⋊C4—101no—
359C3×C4⋊C4—101no—
360C3×C4⋊C4—101no—
361C3×C4⋊C4C22×D511yescharacteristic
362C3×C42—51no—
363C3×C42—101no—
364(C2×D3)⋊C4—21no—
365(C2×D3)⋊C4—51no—
366(C2×D3)⋊C4—51no—
367(C2×D3)⋊C4—101no—
368(C2×D3)⋊C4—101no—
369C4⋊Dic3—51no—
370C4⋊Dic3—51no—
371C4⋊Dic3—101no—
372C4⋊Dic3—101no—
373C4⋊Dic3—101no—
374C4⋊Dic3C22×D511yescharacteristic
375Dic3⋊C4—51no—
376Dic3⋊C4—51no—
377Dic3⋊C4—101no—
378Dic3⋊C4—101no—
379Dic3⋊C4—101no—
380Dic3⋊C4—101no—
381C4×Dic3—21no—
382C4×Dic3—51no—
383C4×Dic3—101no—
384C2×C3⋊C8—51no—
385C2×C3⋊C8C22×D511yescharacteristic
386ΓL(1,𝔽25)—102no—
387D3×C8—22no—
388C23×C5—31no—
389C23×C5—61no—
390C5×Q8—21no—
391C5×Q8D3×Q812yes—
392C5×D4—32no—
393C5×D4—64no—
394C5×D4—61no—
395C2×C4×C5—21no—
396C2×C4×C5—21no—
397C2×C4×C5—31no—
398C2×C4×C5—32no—
399C2×C4×C5—32no—
400C2×C4×C5—64no—
401C2×C4×C5—61no—
402C2×C4×C5C23×D311yescharacteristic
403C2×Dic5—21no—
404C2×Dic5—21no—
405C2×Dic5—31no—
406C2×Dic5—31no—
407C2×Dic5—61no—
408C2×Dic5—61no—
409C2×Dic5—241no—
410C2×Dic5—241no—
411C2×Dic5—241no—
412C2×Dic5—241no—
413C2×Dic5D3×D411yescharacteristic
414C2×Dic5D3×D411yescharacteristic
415Dic10—241no—
416Dic10—241no—
417C5×C8—21no—
418C5×C8—61no—
419#168—21no—
420#168—61no—
421C2×#41—31no—
422C2×M16—151no—
423C22×C8—31no—
424C4⋊Q8—151no—
425C4⋊Q8—151no—
426C4⋊Q8—301no—
427#125—51no—
428#125—151no—
429#125—301no—
430C22⋊Q8—301no—
431C22⋊Q8—301no—
432C4×Q8—51no—
433C4×Q8—151no—
434C4×D4—151no—
435C4×D4—151no—
436C4×D4—301no—
437C4×D4—301no—
438#117—31no—
439#117—151no—
440#117—301no—
441C2×C4⋊C4—151no—
442C2×C4⋊C4—151no—
443C2×C4⋊C4—301no—
444#107—51no—
445#107—151no—
446#106—51no—
447#106—151no—
448#106—151no—
449#106—151no—
450#106—151no—
451#106—151no—
452C4⋊C8—51no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—31no—
457#103—51no—
458#103—151no—
459#103D3×D511yescharacteristic
460#102—31no—
461#102—31no—
462#102—151no—
463#102—151no—
464C2×C3×C5C2×C22⋊Q811yescharacteristic
465C2×C3×C5#57711yescharacteristic
466C2×C3×C5#57711yescharacteristic
467C5×D3—22no—
468C5×D3—42no—
469C22×D3—21no—
470C22×D3D4×D511yescharacteristic
471C3×Q8—21no—
472C3×Q8C2×Dic1012yes—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—51no—
476C2×C3×C4—51no—
477C2×C3×C4—101no—
478C2×C3×C4—101no—
479C2×C3×C4C23×D511yescharacteristic
480C2×Dic3—21no—
481C2×Dic3—51no—
482C2×Dic3—51no—
483C2×Dic3—101no—
484C2×Dic3—101no—
485C2×Dic3D4×D511yescharacteristic
486D12—24no—
487D12—21no—
488D12C2×Dic1012yes—
489C4×D3—24no—
490C4×D3—401no—
491C4×D3—401no—
492C4×D3—401no—
493C4×D3—401no—
494C4×D3C2×Dic1012yes—
495C4×D3#71112yes—
496Dic6—401no—
497Dic6—401no—
498C3×C8—21no—
499C3×C8—101no—
500C3⋊C8—21no—
501C3⋊C8—101no—
502C22×C5—32no—
503C22×C5—61no—
504C22×C5—61no—
505C22×C5—62no—
506C22×C5—121no—
507C22×C5—121no—
508C22×C5C2×D3×D411yescharacteristic
509C4×C5—22no—
510C4×C5—32no—
511C4×C5—41no—
512C4×C5—121no—
513C4×C5C2×D3×Q811yescharacteristic
514C4×C5D3×#4111yescharacteristic
515Dic5—21no—
516Dic5—21no—
517Dic5—41no—
518Dic5—41no—
519Dic5—61no—
520Dic5—61no—
521Dic5—121no—
522Dic5—121no—
523#41—34no—
524#41—62no—
525C2×Q8—301no—
526C2×Q8—301no—
527C2×Q8C2×D3×D511yescharacteristic
528C2×D4—31no—
529C2×D4—61no—
530C22×C4—31no—
531C22×C4—61no—
532C22×C4—301no—
533C22×C4—301no—
534C22×C4—301no—
535C22×C4—301no—
536M16—302no—
537C2×C8—31no—
538C2×C8—51no—
539C2×C8—62no—
540C2×C8—151no—
541C2×C8C2×D3×D511yescharacteristic
542C4⋊C4—31no—
543C4⋊C4—51no—
544C4⋊C4—51no—
545C4⋊C4—101no—
546C4⋊C4—101no—
547C4⋊C4—101no—
548C4⋊C4—151no—
549C4⋊C4—151no—
550C4⋊C4—151no—
551C4⋊C4—151no—
552C4⋊C4—301no—
553C4⋊C4—301no—
554C4⋊C4—301no—
555C4⋊C4—301no—
556C4⋊C4—301no—
557C4⋊C4—301no—
558C4⋊C4—301no—
559C4⋊C4C2×D3×D511yescharacteristic
560C22⋊C4—61no—
561C22⋊C4—151no—
562C22⋊C4—151no—
563C22⋊C4—301no—
564C22⋊C4—301no—
565C42—51no—
566C42—61no—
567C42—101no—
568C42—151no—
569C42—301no—
570C3×C5#308411yescharacteristic, complemented, Hall
571C22×C3C2×D4×D511yescharacteristic
572C2×D3—21no—
573C2×D3—21no—
574C2×D3—22no—
575C2×D3—41no—
576C2×D3—41no—
577C2×D3#402412yes—
578C3×C4—22no—
579C3×C4—41no—
580C3×C4—101no—
581C3×C4—101no—
582C3×C4—201no—
583C3×C4—201no—
584C3×C4C22×Dic1011yescharacteristic
585C3×C4C2×#71111yescharacteristic
586Dic3—41no—
587Dic3—101no—
588Dic3—101no—
589Dic3—201no—
590Dic3—201no—
591Dic3#402412yes—
592C2×C5—62no—
593C2×C5—122no—
594C2×C5D3×C22⋊Q811yescharacteristic
595C2×C5#577011yescharacteristic
596C2×C5#577811yescharacteristic
597C23—31no—
598C23—61no—
599Q8—21no—
600Q8—1201no—
601Q8—1201no—
602Q8D3×Dic1012yes—
603D4—32no—
604D4—64no—
605D4—61no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—31no—
609C2×C4—32no—
610C2×C4—32no—
611C2×C4—51no—
612C2×C4—51no—
613C2×C4—64no—
614C2×C4—61no—
615C2×C4—101no—
616C2×C4—101no—
617C2×C4—151no—
618C2×C4—151no—
619C2×C4—301no—
620C2×C4—301no—
621C2×C4—1201no—
622C2×C4—1201no—
623C2×C4—1201no—
624C2×C4—1201no—
625C2×C4C22×D3×D511yescharacteristic
626C8—21no—
627C8—61no—
628C8—101no—
629C8—301no—
630C2×C3C2×#402411yescharacteristic
631C2×C3#6610411yescharacteristic
632C2×C3#6610411yescharacteristic
633D3—22no—
634D3—42no—
635C5#8123511yescharacteristic, complemented, Sylow
636C22—32no—
637C22—61no—
638C22—61no—
639C22—62no—
640C22—121no—
641C22—121no—
642C22D3×D4×D511yescharacteristic
643C4—22no—
644C4—32no—
645C4—41no—
646C4—101no—
647C4—101no—
648C4—121no—
649C4—201no—
650C4—201no—
651C4—301no—
652C4—301no—
653C4—601no—
654C4—601no—
655C4C2×D3×Dic1011yescharacteristic
656C4D3×#71111yescharacteristic
657C3#1061055511yescharacteristic, complemented, Sylow
658C2—62no—
659C2—122no—
660C2D3×#402411yescharacteristic
661C2#1175409511yescharacteristic
662C2#1175411211yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#239C22
hypercenter#103D3×D5
hypocenterC3×C5#3084
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #103

Complements

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

NH ≅ G/Ntype
2. #11753665C2semidirect
3. #11750900C2semidirect
5. C3×#65088C2semidirect
6. #11749361C2semidirect
7. #11749348C2semidirect
9. #11747808C2semidirect
10. #11747758C2semidirect
11. #11747655C2semidirect
12. D3×#3949C2semidirect
13. #11747258C2semidirect
14. #11747241C2semidirect
15. #11747190C2semidirect
69. #65088D3semidirect
78. C5×#239Q8semidirect
343. #239Dic10semidirect
570. C3×C5#3084semidirect
635. C5#81235semidirect
657. C3#10610555semidirect

Maximal subgroups

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

subgroupindex
#117552202
#117536652
#117509002
C5×#48042
C3×#650882
#117493612
#117493482
#117492012
#117478082
#117477582
#117476552
D3×#39492
#117472582
#117472412
#117471902
#106105553
#812355