Finite Group Databasebeta

← #14430828

Subgroups — #14430828

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754910C211yesmaximal, characteristic
2#11753659C211yesmaximal, characteristic, complemented
3#11750862C211yesmaximal, characteristic, complemented
4C5×#4759C211yesmaximal, characteristic, complemented
5C3×#65059C211yesmaximal, characteristic
6#11749091C211yesmaximal, characteristic, complemented
7#11749087C211yesmaximal, characteristic, complemented
8D5×#832C211yesmaximal, characteristic
9#11747804C211yesmaximal, characteristic, complemented
10#11747784C211yesmaximal, characteristic, complemented
11#11747648C211yesmaximal, characteristic, complemented
12#11747619C211yesmaximal, characteristic, complemented
13#11747432C211yesmaximal, characteristic, complemented
14#11747253C211yesmaximal, characteristic, complemented
15#11747247C211yesmaximal, characteristic, complemented
16#10612698—31nomaximal, Hall
17C2×C3×D4×D5C2211yescharacteristic
18D4×Dic15C2211yescharacteristic
19#91777C2211yescharacteristic, complemented
20C5×D4×Dic3C2211yescharacteristic
21C5×#888C2211yescharacteristic, complemented
22C2×C3×#676C2211yescharacteristic
23C3×#4038C2211yescharacteristic
24#91559—21no—
25Dic3×C22⋊D5—21no—
26D5×#217—21no—
27C2×#6665—21no—
28#91434C2211yescharacteristic
29#91431—21no—
30Dic3×D20C2211yescharacteristic
31#91421—21no—
32D5×C4⋊Dic3C2211yescharacteristic
33#91384C2211yescharacteristic, complemented
34#91381C2211yescharacteristic, complemented
35#91378—21no—
36#91376—21no—
37#91358C2211yescharacteristic
38#91357C2211yescharacteristic
39C2×D5×C3⋊C8C2211yescharacteristic
40C3×C5×#102C2211yescharacteristic
41#91116C2211yescharacteristic
42#91101C2211yescharacteristic, complemented
43#91098C2211yescharacteristic, complemented
44#91092C2211yescharacteristic, complemented
45C5×#832C2211yescharacteristic
46C5×#818C2211yescharacteristic, complemented
47C5×Dic3⋊C8C2211yescharacteristic, complemented
48C5×#807C2211yescharacteristic, complemented
49C3×#3964C2211yescharacteristic
50C3×#3953C2211yescharacteristic
51C3×#3941C2211yescharacteristic
52#90990C2211yescharacteristic, complemented
53#90988C2211yescharacteristic, complemented
54#90986C2211yescharacteristic, complemented
55#90985C2211yescharacteristic, complemented
56Dic3⋊#168C2211yescharacteristic, complemented
57#90983C2211yescharacteristic, complemented
58#90965C2211yescharacteristic
59#90964C2211yescharacteristic
60#78918—51nomaximal, Hall
61#66063—31no—
62#65879—31no—
63C5×#474—31no—
64#65373—31no—
65#65298—31no—
66#65180—31no—
67#65179—31no—
68#65170—31no—
69#65169—31no—
70#65136—31no—
71#65128—31no—
72#65059D311yescharacteristic
73D5×#102—31no—
74#65055—31no—
75#65050—31no—
76C23×C3×D5—21no—
77C2×C3×C5×D4C2311yescharacteristic
78C22×Dic15—21no—
79C2×Dic30—21no—
80C22×C5×Dic3—21no—
81C2×C5×Dic6—21no—
82C2×C3×C22⋊D5—21no—
83C3×D4×D5—22no—
84C3×D4×D5Q814yescomplemented
85C2×C3×D20C2311yescharacteristic
86C2×C3×C4×D5C2311yescharacteristic
87C2×D5×Dic3—21no—
88C2×D5×Dic3—21no—
89C2×D5×Dic3—21no—
90C2×C3×C5×C8C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92#6719—21no—
93C4⋊Dic15C2311yescharacteristic
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96C4×Dic15C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#217—21no—
99C5×C4⋊Dic3C2311yescharacteristic
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C4×C5×Dic3C2311yescharacteristic
103C2×C5×C3⋊C8C2311yescharacteristic
104C3×#685—21no—
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4×Dic5—21no—
107C2×C3×#168C2311yescharacteristic
108C3×#676—22no—
109Dic3⋊Dic5—21no—
110#6669—21no—
111#6668—21no—
112#6668—21no—
113#6668—21no—
114#6668D411yescharacteristic
115#6668D411yescharacteristic
116#6665—21no—
117#6665—21no—
118#6665—21no—
119#6665D411yescharacteristic
120#6665D411yescharacteristic
121Dic3×Dic5—21no—
122D5×C3⋊C8—22no—
123#5798—51no—
124#5519—51no—
125C3×#418—51no—
126C2×#832—51no—
127#5121—51no—
128#5119—51no—
129#4998—51no—
130#4766—51no—
131#4766—51no—
132#4763—51no—
133#4763—51no—
134#4761—51no—
135#4761—51no—
136#4759—51no—
137#4759D511yescharacteristic, complemented
138C2×D4×D5C2×D311yescharacteristic
139C5×C4⋊Q8—31no—
140C4×C5×D4—31no—
141#4092—61no—
142#4090—61no—
143D4×Dic5—31no—
144C4×C22⋊D5—61no—
145C2×#685—61no—
146C2×#676C2×D311yescharacteristic
147C2×C8×D5—31no—
148#4042—61no—
149#4039—31no—
150#4038—31no—
151#4038C2×D311yescharacteristic
152D5×C4⋊C4—31no—
153#4036—31no—
154#4035—61no—
155#4034—31no—
156#4027—61no—
157D5×C22⋊C4—61no—
158C4×D20—31no—
159#4018—31no—
160#4016—31no—
161C5×#107—31no—
162C5×#107—31no—
163C5×C4⋊C8—31no—
164C5×#102—31no—
165C5×#102C2×D311yescharacteristic
166#3964—31no—
167#3964C2×D311yescharacteristic
168#3953—31no—
169#3953C2×D311yescharacteristic
170#3950—31no—
171#3949—31no—
172#3946—31no—
173#3946—31no—
174#3941—31no—
175#3941C2×D311yescharacteristic
176#3940—31no—
177#3940—31no—
178#3940—31no—
179#3939—31no—
180C4⋊#168—31no—
181#3081—151noSylow
182C23×C3×C5—21no—
183C22×C3×D5—21no—
184C22×C3×D5—24no—
185C22×C3×D5—81no—
186C22×C3×D5—81no—
187C22×C3×D5C2×D411yescharacteristic
188C3×C5×D4—21no—
189C3×C5×D4C2×Q812yes—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5C2411yescharacteristic
192C2×Dic15—21no—
193C2×Dic15—21no—
194C2×Dic15—81no—
195C2×Dic15C2×D411yescharacteristic
196C2×Dic15C2×D411yescharacteristic
197Dic30—81no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—81no—
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
203C5×Dic6—81no—
204C3×C22⋊D5—24no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5C2×D411yescharacteristic
207C3×D20—21no—
208C3×D20C2×Q812yes—
209C3×C4×D5C2×Q812yes—
210C3×C4×D5#4112yes—
211D5×Dic3—81no—
212D5×Dic3—81no—
213D5×Dic3—81no—
214C3×C5×C8—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C5×C3⋊C8—21no—
218C22×C3×D4—51no—
219C2×C3×M16—51no—
220C3×#117—51no—
221C2×#217—101no—
222C2×#217—101no—
223D4×Dic3—51no—
224D4×Dic3—51no—
225D4×Dic3—51no—
226D4×Dic3—101no—
227D4×Dic3—101no—
228D4×Dic3C2×D511yescharacteristic
229#926—51no—
230#926—51no—
231C2×C4⋊Dic3—51no—
232C22×C3⋊C8—51no—
233#890—51no—
234#890—51no—
235#888—51no—
236#888C2×D511yescharacteristic, complemented
237#878—101no—
238#878—101no—
239#870—101no—
240#869—101no—
241C3×#102—51no—
242C3×#102—51no—
243C3×#102—51no—
244C3×#102C2×D511yescharacteristic
245#832—51no—
246#832—51no—
247#832—51no—
248#832C2×D511yescharacteristic
249#818—51no—
250#818C2×D511yescharacteristic, complemented
251#817—51no—
252#817—51no—
253Dic3⋊C8—51no—
254Dic3⋊C8—51no—
255Dic3⋊C8—51no—
256Dic3⋊C8C2×D511yescharacteristic, complemented
257#808—51no—
258#808—51no—
259#807—51no—
260#807C2×D511yescharacteristic, complemented
261C23×D5—21no—
262C2×C5×Q8—61no—
263C2×C5×D4C22×D311yescharacteristic
264C22×C4×C5—61no—
265C2×C22⋊D5—21no—
266C22×Dic5—61no—
267D4×D5—22no—
268D4×D5Dic614yescomplemented
269C2×D20C22×D311yescharacteristic
270C2×C4×D5—61no—
271C2×C4×D5—61no—
272C2×C4×D5—61no—
273C2×C4×D5C22×D311yescharacteristic
274C2×Dic10—61no—
275C2×C5×C8—31no—
276C2×C5×C8C22×D311yescharacteristic
277C5×C4⋊C4—31no—
278C5×C4⋊C4—31no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4C22×D311yescharacteristic
281C5×C22⋊C4—61no—
282C42×C5—31no—
283C22⋊Dic5—61no—
284#685—21no—
285#685—31no—
286#685—31no—
287#685—61no—
288#685—61no—
289#685—61no—
290C4⋊Dic5—31no—
291C4⋊Dic5—31no—
292C4⋊Dic5—61no—
293C4⋊Dic5C22×D311yescharacteristic
294#683—31no—
295#683—31no—
296#683—61no—
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301C4×Dic5—21no—
302C4×Dic5—31no—
303C4×Dic5—61no—
304C2×#168—31no—
305C2×#168C22×D311yescharacteristic
306#676—22no—
307C8×D5—62no—
308#544—151no—
309#518—151no—
310#478—151no—
311#478—151no—
312#478—151no—
313#478—151no—
314#476—151no—
315#476—151no—
316#474—31no—
317#474—151no—
318#428—151no—
319#427—151no—
320#424—151no—
321#418—51no—
322C2×#102—151no—
323C22×C3×C5—22no—
324C22×C3×C5—41no—
325C22×C3×C5—41no—
326C22×C3×C5C22×D411yescharacteristic
327C2×C3×D5—21no—
328C2×C3×D5—21no—
329C2×C3×D5—22no—
330C2×C3×D5—41no—
331C2×C3×D5—41no—
332C2×C3×D5—84no—
333C2×C3×D5C22⋊Q812yes—
334C3×C4×C5—41no—
335C3×C4×C5C22×Q811yescharacteristic
336C3×C4×C5C2×#4111yescharacteristic
337Dic15—21no—
338Dic15—21no—
339Dic15—41no—
340Dic15—41no—
341C3×Dic5—41no—
342C3×Dic5C22⋊Q812yes—
343C5×Dic3—21no—
344C5×Dic3—21no—
345C5×Dic3—41no—
346C5×Dic3—41no—
347C24×C3—101no—
348C2×C3×D4—54no—
349C2×C3×D4—51no—
350C2×C3×D4—102no—
351C2×C3×D4—101no—
352C2×C3×D4C22×D511yescharacteristic
353C22×C3×C4—51no—
354C22×Dic3—21no—
355C22×Dic3—101no—
356C22×Dic3—101no—
357C22×Dic3—101no—
358C22×Dic3—101no—
359C2×Dic6—21no—
360C2×Dic6—101no—
361C3×M16—102no—
362C2×C3×C8—51no—
363C2×C3×C8C22×D511yescharacteristic
364C3×C4⋊C4—51no—
365C3×C4⋊C4C22×D511yescharacteristic
366C3×C22⋊C4—101no—
367C3×C42—101no—
368#217—21no—
369#217—51no—
370#217—51no—
371#217—101no—
372#217—101no—
373#217—101no—
374#217—101no—
375C4⋊Dic3—51no—
376C4⋊Dic3—51no—
377C4⋊Dic3—51no—
378C4⋊Dic3—51no—
379C4⋊Dic3—101no—
380C4⋊Dic3—101no—
381C4⋊Dic3—101no—
382C4⋊Dic3C22×D511yescharacteristic
383C4⋊Dic3C22×D511yescharacteristic
384Dic3⋊C4—21no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387Dic3⋊C4—101no—
388C4×Dic3—51no—
389C4×Dic3—101no—
390C4×Dic3C22×D511yescharacteristic
391C2×C3⋊C8—51no—
392C2×C3⋊C8—102no—
393C2×C3⋊C8C22×D511yescharacteristic
394C23×C5—21no—
395C22×D5—21no—
396C22×D5—24no—
397C22×D5—81no—
398C22×D5—81no—
399C22×D5D3×D411yescharacteristic
400C5×Q8—241no—
401C5×D4—21no—
402C5×D4C2×Dic612yes—
403C2×C4×C5—21no—
404C2×C4×C5—31no—
405C2×C4×C5—31no—
406C2×C4×C5—61no—
407C2×C4×C5—61no—
408C2×C4×C5—241no—
409C2×C4×C5C23×D311yescharacteristic
410C22⋊D5—24no—
411C2×Dic5—21no—
412C2×Dic5—31no—
413C2×Dic5—31no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—241no—
417C2×Dic5D3×D411yescharacteristic
418D20—21no—
419D20C2×Dic612yes—
420C4×D5—241no—
421C4×D5—241no—
422C4×D5—241no—
423C4×D5C2×Dic612yes—
424C4×D5#23712yes—
425Dic10—241no—
426C5×C8—21no—
427C5×C8—61no—
428#168—21no—
429#168—61no—
430C22×D4—51no—
431C2×M16—51no—
432C22×C8—151no—
433C4⋊Q8—31no—
434C4⋊Q8—151no—
435C4⋊Q8—301no—
436#125—151no—
437#125—151no—
438#125—301no—
439C22⋊Q8—301no—
440C22⋊Q8—301no—
441C4×D4—31no—
442C4×D4—151no—
443C4×D4—151no—
444C4×D4—151no—
445C4×D4—301no—
446C4×D4—301no—
447#117—51no—
448#117—151no—
449#117—151no—
450C2×C4⋊C4—151no—
451C2×C22⋊C4—301no—
452C2×C22⋊C4—301no—
453#107—31no—
454#107—31no—
455#107—151no—
456#107—151no—
457#106—151no—
458#106—151no—
459#106—151no—
460#106—151no—
461C4⋊C8—31no—
462C4⋊C8—151no—
463C4⋊C8—151no—
464C4⋊C8—151no—
465#102—31no—
466#102—51no—
467#102—51no—
468#102—51no—
469#102—151no—
470#102—151no—
471#102—151no—
472#102D3×D511yescharacteristic
473C2×C3×C5—42no—
474C2×C3×C5C2×C22⋊Q811yescharacteristic
475C2×C3×C5#57611yescharacteristic
476C2×C3×C5#57711yescharacteristic
477C3×D5—22no—
478C3×D5—42no—
479C23×C3—21no—
480C23×C3—51no—
481C23×C3—104no—
482C23×C3—101no—
483C23×C3—401no—
484C23×C3—401no—
485C3×D4—21no—
486C3×D4—52no—
487C3×D4—104no—
488C3×D4—101no—
489C3×D4Q8×D512yes—
490C2×C3×C4—21no—
491C2×C3×C4—51no—
492C2×C3×C4—52no—
493C2×C3×C4—52no—
494C2×C3×C4—101no—
495C2×C3×C4C23×D511yescharacteristic
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—51no—
499C2×Dic3—51no—
500C2×Dic3—81no—
501C2×Dic3—101no—
502C2×Dic3—101no—
503C2×Dic3—401no—
504C2×Dic3—401no—
505C2×Dic3—401no—
506C2×Dic3—401no—
507C2×Dic3D4×D511yescharacteristic
508C2×Dic3D4×D511yescharacteristic
509Dic6—81no—
510Dic6—401no—
511C3×C8—21no—
512C3×C8—101no—
513C3⋊C8—21no—
514C3⋊C8—101no—
515C22×C5—22no—
516C22×C5—41no—
517C22×C5—41no—
518C22×C5C2×D3×D411yescharacteristic
519C2×D5—21no—
520C2×D5—21no—
521C2×D5—22no—
522C2×D5—41no—
523C2×D5—41no—
524C2×D5—84no—
525C2×D5#87812yes—
526C4×C5—41no—
527C4×C5—61no—
528C4×C5—61no—
529C4×C5—121no—
530C4×C5—121no—
531C4×C5C22×Dic611yescharacteristic
532C4×C5C2×#23711yescharacteristic
533Dic5—41no—
534Dic5—61no—
535Dic5—61no—
536Dic5—121no—
537Dic5—121no—
538Dic5#87812yes—
539C24—101no—
540C2×Q8—61no—
541C2×Q8—301no—
542C2×D4—54no—
543C2×D4—51no—
544C2×D4—102no—
545C2×D4—101no—
546C2×D4C2×D3×D511yescharacteristic
547C22×C4—51no—
548C22×C4—61no—
549C22×C4—301no—
550C22×C4—301no—
551C22×C4—301no—
552C22×C4—301no—
553M16—102no—
554C2×C8—31no—
555C2×C8—51no—
556C2×C8—151no—
557C2×C8—302no—
558C2×C8C2×D3×D511yescharacteristic
559C4⋊C4—31no—
560C4⋊C4—31no—
561C4⋊C4—51no—
562C4⋊C4—61no—
563C4⋊C4—151no—
564C4⋊C4—151no—
565C4⋊C4—151no—
566C4⋊C4—151no—
567C4⋊C4—301no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4—301no—
573C4⋊C4C2×D3×D511yescharacteristic
574C22⋊C4—61no—
575C22⋊C4—101no—
576C22⋊C4—151no—
577C22⋊C4—151no—
578C22⋊C4—301no—
579C22⋊C4—301no—
580C22⋊C4—301no—
581C22⋊C4—301no—
582C42—31no—
583C42—101no—
584C42—151no—
585C42—301no—
586C3×C5#308111yescharacteristic, complemented, Hall
587C22×C3—22no—
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—52no—
591C22×C3—101no—
592C22×C3—101no—
593C22×C3—102no—
594C22×C3—201no—
595C22×C3—201no—
596C22×C3—404no—
597C22×C3C2×D4×D511yescharacteristic
598C3×C4—41no—
599C3×C4—52no—
600C3×C4—201no—
601C3×C4C2×Q8×D511yescharacteristic
602C3×C4D5×#4111yescharacteristic
603Dic3—21no—
604Dic3—21no—
605Dic3—41no—
606Dic3—41no—
607Dic3—101no—
608Dic3—101no—
609Dic3—201no—
610Dic3—201no—
611C2×C5—42no—
612C2×C5C2×#87811yescharacteristic
613C2×C5#577411yescharacteristic
614C2×C5#577511yescharacteristic
615D5—22no—
616D5—42no—
617C23—21no—
618C23—51no—
619C23—104no—
620C23—101no—
621C23—401no—
622C23—401no—
623Q8—241no—
624Q8—1201no—
625D4—21no—
626D4—52no—
627D4—104no—
628D4—101no—
629D4D5×Dic612yes—
630C2×C4—21no—
631C2×C4—31no—
632C2×C4—31no—
633C2×C4—51no—
634C2×C4—52no—
635C2×C4—52no—
636C2×C4—61no—
637C2×C4—61no—
638C2×C4—101no—
639C2×C4—151no—
640C2×C4—151no—
641C2×C4—241no—
642C2×C4—301no—
643C2×C4—301no—
644C2×C4—1201no—
645C2×C4—1201no—
646C2×C4—1201no—
647C2×C4—1201no—
648C2×C4C22×D3×D511yescharacteristic
649C8—21no—
650C8—61no—
651C8—101no—
652C8—301no—
653C2×C3—42no—
654C2×C3—102no—
655C2×C3—202no—
656C2×C3D5×C22⋊Q811yescharacteristic
657C2×C3#6609111yescharacteristic
658C2×C3#6611211yescharacteristic
659C5#7891811yescharacteristic, complemented, Sylow
660C22—22no—
661C22—41no—
662C22—41no—
663C22—52no—
664C22—101no—
665C22—101no—
666C22—102no—
667C22—201no—
668C22—201no—
669C22—404no—
670C22D3×D4×D511yescharacteristic
671C4—41no—
672C4—52no—
673C4—61no—
674C4—61no—
675C4—121no—
676C4—121no—
677C4—201no—
678C4—301no—
679C4—301no—
680C4—601no—
681C4—601no—
682C4C2×D5×Dic611yescharacteristic
683C4D5×#23711yescharacteristic
684C3#1061269811yescharacteristic, complemented, Sylow
685C2—42no—
686C2—102no—
687C2—202no—
688C2D5×#87811yescharacteristic
689C2#1175405611yescharacteristic
690C2#1175408811yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D4×D5C22
hypercenter#102D3×D5
hypocenterC3×C5#3081
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #11753659C2semidirect
3. #11750862C2semidirect
4. C5×#4759C2semidirect
6. #11749091C2semidirect
7. #11749087C2semidirect
9. #11747804C2semidirect
10. #11747784C2semidirect
11. #11747648C2semidirect
12. #11747619C2semidirect
13. #11747432C2semidirect
14. #11747253C2semidirect
15. #11747247C2semidirect
19. #91777C22semidirect
21. C5×#888C22semidirect
33. #91384C22semidirect
34. #91381C22semidirect
42. #91101C22semidirect
43. #91098C22semidirect
44. #91092C22semidirect
46. C5×#818C22semidirect
47. C5×Dic3⋊C8C22semidirect
48. C5×#807C22semidirect
52. #90990C22semidirect
53. #90988C22semidirect
54. #90986C22semidirect
55. #90985C22semidirect
56. Dic3⋊#168C22semidirect
57. #90983C22semidirect
84. C3×D4×D5Q8semidirect
137. #4759D5semidirect
236. #888C2×D5semidirect
250. #818C2×D5semidirect
256. Dic3⋊C8C2×D5semidirect
260. #807C2×D5semidirect
268. D4×D5Dic6semidirect
586. C3×C5#3081semidirect
659. C5#78918semidirect
684. C3#10612698semidirect

Maximal subgroups

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

subgroupindex
#117549102
#117536592
#117508622
C5×#47592
C3×#650592
#117490912
#117490872
D5×#8322
#117478042
#117477842
#117476482
#117476192
#117474322
#117472532
#117472472
#106126983
#789185