Finite Group Databasebeta

← #14430906

Subgroups — #14430906

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#11753837C211yesmaximal, characteristic
2#11753369C211yesmaximal, characteristic, complemented
3#11750971C211yesmaximal, characteristic, complemented
4C5×#4871C211yesmaximal, characteristic, complemented
5C3×#65150C211yesmaximal, characteristic, complemented
6#11748105C211yesmaximal, characteristic
7#11747817C211yesmaximal, characteristic, complemented
8#11747794C211yesmaximal, characteristic, complemented
9#11747648C211yesmaximal, characteristic, complemented
10D5×#809C211yesmaximal, characteristic
11#11747432C211yesmaximal, characteristic, complemented
12#11747419C211yesmaximal, characteristic, complemented
13#11747254C211yesmaximal, characteristic, complemented
14#11747250C211yesmaximal, characteristic, complemented
15#11747185C211yesmaximal, characteristic, complemented
16#10612900—31nomaximal, Hall
17C2×D5×D12C2211yescharacteristic
18#91782C2211yescharacteristic
19#91777C2211yescharacteristic, complemented
20C5×#893C2211yescharacteristic
21C5×#890C2211yescharacteristic, complemented
22C2×C3×#676C2211yescharacteristic
23C3×#4038C2211yescharacteristic
24C3×D5×C4⋊C4C2211yescharacteristic
25#91473—21no—
26D3×#685—21no—
27#91469C2211yescharacteristic, complemented
28C4×#1203—21no—
29#91435C2211yescharacteristic
30#91428C2211yescharacteristic
31#91405—21no—
32#91384C2211yescharacteristic, complemented
33#91360—21no—
34#91358C2211yescharacteristic
35#91357C2211yescharacteristic
36#91349—21no—
37#91335—21no—
38#91328—21no—
39C2×D5×C3⋊C8C2211yescharacteristic
40C3×C5×#106C2211yescharacteristic, complemented
41#91105C2211yescharacteristic
42#91098C2211yescharacteristic, complemented
43#91093C2211yescharacteristic
44#91092C2211yescharacteristic, complemented
45C5×#821C2211yescharacteristic
46C5×Dic3⋊C8C2211yescharacteristic, complemented
47C5×#809C2211yescharacteristic
48C5×#807C2211yescharacteristic, complemented
49C3×#3950C2211yescharacteristic, complemented
50C3×#3940C2211yescharacteristic, complemented
51C3×#3939C2211yescharacteristic, complemented
52#90990C2211yescharacteristic, complemented
53#90986C2211yescharacteristic, complemented
54Dic3⋊#168C2211yescharacteristic, complemented
55#90983C2211yescharacteristic, complemented
56#90969C2211yescharacteristic
57#90968C2211yescharacteristic
58#90967C2211yescharacteristic
59#90966C2211yescharacteristic
60#79242—51nomaximal, Hall
61#66023—31no—
62#65879—31no—
63C5×#478—31no—
64#65355—31no—
65#65297—31no—
66#65180—31no—
67#65169—31no—
68#65159—31no—
69#65150D311yescharacteristic, complemented
70#65135—31no—
71#65128—31no—
72#65059—31no—
73D5×#102—31no—
74#65055—31no—
75#65048—31no—
76C22×D3×D5—21no—
77C2×D60C2311yescharacteristic
78C2×C4×D15—21no—
79C2×Dic30—21no—
80C2×C5×D12C2311yescharacteristic
81C2×C4×C5×D3—21no—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5C2311yescharacteristic
84C2×#1204—21no—
85C2×#1203—21no—
86C2×#1200—21no—
87C2×D3×Dic5—21no—
88D5×D12—22no—
89D5×D12Q814yescomplemented
90C2×C3×C5×C8C2311yescharacteristic
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C5×C4⋊C4C2311yescharacteristic
93#6714—21no—
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96C4×Dic15C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×(C2×D3)⋊C4—21no—
99C5×C4⋊Dic3—21no—
100C5×C4⋊Dic3C2311yescharacteristic
101C5×Dic3⋊C4—21no—
102C4×C5×Dic3C2311yescharacteristic
103C2×C5×C3⋊C8C2311yescharacteristic
104C3×#685—21no—
105C3×C4⋊Dic5C2311yescharacteristic
106C3×C4⋊Dic5C2311yescharacteristic
107C3×#683—21no—
108C3×C4×Dic5—21no—
109C2×C3×#168C2311yescharacteristic
110C3×#676—22no—
111Dic3⋊Dic5—21no—
112Dic3⋊Dic5—21no—
113#6668—21no—
114#6668D411yescharacteristic
115#6668D411yescharacteristic
116#6667—21no—
117(C2×D3)⋊Dic5—21no—
118#6665—21no—
119#6665D411yescharacteristic
120#6665D411yescharacteristic
121Dic3×Dic5—21no—
122D5×C3⋊C8—22no—
123#5521—51no—
124#5500—51no—
125C3×#428—51no—
126#5131—51no—
127#5119—51no—
128#4998—51no—
129C2×#809—51no—
130#4891—51no—
131#4891—51no—
132#4890—51no—
133#4890—51no—
134#4871—51no—
135#4871D511yescharacteristic, complemented
136#4870—51no—
137#4870—51no—
138C2×D4×D5—31no—
139C5×#125—31no—
140C4×C5×D4—31no—
141D4×Dic5—31no—
142C4×C22⋊D5—61no—
143C2×#685—61no—
144C2×#676C2×D311yescharacteristic
145C2×C8×D5—31no—
146#4043—61no—
147#4042—61no—
148#4039—31no—
149#4038—31no—
150#4038C2×D311yescharacteristic
151D5×C4⋊C4C2×D311yescharacteristic
152#4036—31no—
153#4035—61no—
154#4034—31no—
155#4034—61no—
156#4027—61no—
157D5×C22⋊C4—61no—
158C4×D20—31no—
159#4018—31no—
160#4015—31no—
161C5×#107—31no—
162C5×#106C2×D311yescharacteristic, complemented
163C5×C4⋊C8—31no—
164C5×#102—31no—
165C5×#102—31no—
166#3964—31no—
167#3964—31no—
168#3953—31no—
169#3953—31no—
170#3950—31no—
171#3950C2×D311yescharacteristic, complemented
172#3946—31no—
173#3946—31no—
174#3941—31no—
175#3941—31no—
176#3940—31no—
177#3940—31no—
178#3940C2×D311yescharacteristic, complemented
179#3939C2×D311yescharacteristic, complemented
180C4⋊#168—31no—
181#3081—151noSylow
182C22×D15—21no—
183C22×C5×D3—21no—
184C22×C3×D5C2×D411yescharacteristic
185C2×D3×D5—24no—
186C2×D3×D5—81no—
187C2×D3×D5—81no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15—21no—
192C2×Dic15C2×D411yescharacteristic
193C2×Dic15C2×D411yescharacteristic
194D60—21no—
195D60C2×Q812yes—
196C4×D15—81no—
197Dic30—81no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3C2×D411yescharacteristic
200C2×C5×Dic3C2×D411yescharacteristic
201C5×D12—21no—
202C5×D12C2×Q812yes—
203C4×C5×D3—81no—
204C2×C3×Dic5—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5C2×D411yescharacteristic
207C3×C4×D5—81no—
208C3×C4×D5C2×Q812yes—
209C3×C4×D5#4112yes—
210#1204—81no—
211#1203—24no—
212#1200—81no—
213D3×Dic5—81no—
214C3×C5×C8—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C5×C3⋊C8—21no—
218C22×D12—51no—
219C2×C3×M16—51no—
220C3×#117—51no—
221C2×C3×C4⋊C4—51no—
222#926—51no—
223#926—51no—
224#924—101no—
225#924—101no—
226C22×C3⋊C8—51no—
227#893—51no—
228#893—51no—
229#893—51no—
230#893C2×D511yescharacteristic
231#890—51no—
232#890—101no—
233#890C2×D511yescharacteristic, complemented
234#888—51no—
235#888—51no—
236#888—101no—
237D3×C22⋊C4—101no—
238D3×C22⋊C4—101no—
239C4×D12—101no—
240C4×D12—101no—
241C3×#107—51no—
242C3×#107—51no—
243C3×#106—51no—
244C3×#106C2×D511yescharacteristic, complemented
245#821—51no—
246#821—51no—
247#821—51no—
248#821C2×D511yescharacteristic
249Dic3⋊C8—51no—
250Dic3⋊C8—51no—
251Dic3⋊C8—51no—
252Dic3⋊C8C2×D511yescharacteristic, complemented
253#809—51no—
254#809—51no—
255#809—51no—
256#809C2×D511yescharacteristic
257#808—51no—
258#808—51no—
259#807—51no—
260#807C2×D511yescharacteristic, complemented
261C23×D5—61no—
262C2×C5×D4—31no—
263C22×C4×C5—61no—
264C2×C22⋊D5—61no—
265C22×Dic5—61no—
266D4×D5—34no—
267D4×D5—62no—
268C2×D20—31no—
269C2×C4×D5—21no—
270C2×C4×D5—61no—
271C2×C4×D5—61no—
272C2×C4×D5C22×D311yescharacteristic
273C2×Dic10—61no—
274C2×Dic10—61no—
275C2×C5×C8—31no—
276C2×C5×C8C22×D311yescharacteristic
277C5×C4⋊C4—31no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4C22×D311yescharacteristic
281C5×C4⋊C4C22×D311yescharacteristic
282C5×C22⋊C4—61no—
283C42×C5—31no—
284C22⋊Dic5—61no—
285#685—21no—
286#685—31no—
287#685—31no—
288#685—61no—
289#685—61no—
290#685—61no—
291C4⋊Dic5—31no—
292C4⋊Dic5—61no—
293C4⋊Dic5—61no—
294C4⋊Dic5C22×D311yescharacteristic
295C4⋊Dic5C22×D311yescharacteristic
296#683—21no—
297#683—31no—
298#683—31no—
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—31no—
311#478—151no—
312#478—151no—
313#478—151no—
314#476—151no—
315#476—151no—
316#474—151no—
317#474—151no—
318#428—51no—
319#427—151no—
320#424—151no—
321#418—151no—
322C2×#102—151no—
323C22×C3×C5C22×D411yescharacteristic
324C2×D15—22no—
325C2×D15—41no—
326C2×D15—41no—
327C2×C5×D3—22no—
328C2×C5×D3—41no—
329C2×C5×D3—41no—
330C2×C3×D5—21no—
331C2×C3×D5—21no—
332C2×C3×D5C22⋊Q812yes—
333D3×D5—84no—
334C3×C4×C5—41no—
335C3×C4×C5—41no—
336C3×C4×C5C22×Q811yescharacteristic
337C3×C4×C5C2×#4111yescharacteristic
338Dic15—21no—
339Dic15—21no—
340Dic15—41no—
341C3×Dic5—41no—
342C3×Dic5—41no—
343C3×Dic5C22⋊Q812yes—
344C5×Dic3—21no—
345C5×Dic3—21no—
346C5×Dic3—41no—
347C23×D3—101no—
348C22×C3×C4—51no—
349C22×C3×C4—101no—
350C2×D12—51no—
351C2×D12—54no—
352C2×D12—102no—
353C2×D12—101no—
354C2×D12C22×D511yescharacteristic
355C2×C4×D3—21no—
356C2×C4×D3—101no—
357C2×C4×D3—101no—
358C2×C4×D3—101no—
359C2×Dic6—101no—
360C2×Dic6—101no—
361C3×M16—102no—
362C2×C3×C8—51no—
363C2×C3×C8C22×D511yescharacteristic
364C3×C4⋊C4—51no—
365C3×C4⋊C4—51no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4C22×D511yescharacteristic
368C3×C4⋊C4C22×D511yescharacteristic
369C3×C22⋊C4—101no—
370C3×C42—101no—
371#217—51no—
372#217—51no—
373#217—101no—
374(C2×D3)⋊C4—21no—
375(C2×D3)⋊C4—101no—
376(C2×D3)⋊C4—101no—
377(C2×D3)⋊C4—101no—
378C4⋊Dic3—21no—
379C4⋊Dic3—51no—
380C4⋊Dic3—51no—
381C4⋊Dic3—51no—
382C4⋊Dic3—101no—
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—61no—
395C22×D5—61no—
396C22×D5—64no—
397C22×D5—241no—
398C22×D5—241no—
399C22×D5D3×D411yescharacteristic
400C5×D4—32no—
401C5×D4—61no—
402C2×C4×C5—21no—
403C2×C4×C5—21no—
404C2×C4×C5—31no—
405C2×C4×C5—31no—
406C2×C4×C5—61no—
407C2×C4×C5—241no—
408C2×C4×C5C23×D311yescharacteristic
409C22⋊D5—64no—
410C2×Dic5—21no—
411C2×Dic5—21no—
412C2×Dic5—31no—
413C2×Dic5—31no—
414C2×Dic5—61no—
415C2×Dic5—241no—
416C2×Dic5D3×D411yescharacteristic
417D20—32no—
418D20—61no—
419C4×D5—81no—
420C4×D5—241no—
421C4×D5—241no—
422C4×D5#23512yes—
423C4×D5D3×Q812yes—
424Dic10—241no—
425Dic10—241no—
426C5×C8—21no—
427C5×C8—61no—
428#168—21no—
429#168—61no—
430C22×D4—151no—
431C2×M16—51no—
432C22×C8—151no—
433C4⋊Q8—151no—
434C4⋊Q8—151no—
435C4⋊Q8—301no—
436#125—31no—
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—51no—
451C2×C22⋊C4—301no—
452C2×C22⋊C4—301no—
453#107—31no—
454#107—51no—
455#107—51no—
456#107—151no—
457#106—51no—
458#106—151no—
459#106—151no—
460#106D3×D511yescharacteristic, complemented
461C4⋊C8—31no—
462C4⋊C8—151no—
463C4⋊C8—151no—
464C4⋊C8—151no—
465#102—31no—
466#102—31no—
467#102—151no—
468#102—151no—
469#102—151no—
470#102—151no—
471#102—151no—
472#102—151no—
473C2×C3×C5C2×C22⋊Q811yescharacteristic
474C2×C3×C5#57611yescharacteristic
475C2×C3×C5#57711yescharacteristic
476D15—42no—
477C3×D5—22no—
478C5×D3—42no—
479C23×C3—51no—
480C22×D3—21no—
481C22×D3—104no—
482C22×D3—101no—
483C22×D3—401no—
484C22×D3—401no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—51no—
488C2×C3×C4—52no—
489C2×C3×C4—52no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4—401no—
493C2×C3×C4C23×D511yescharacteristic
494C2×Dic3—21no—
495C2×Dic3—51no—
496C2×Dic3—51no—
497C2×Dic3—101no—
498C2×Dic3D4×D511yescharacteristic
499C2×Dic3D4×D511yescharacteristic
500D12—21no—
501D12—52no—
502D12—104no—
503D12—101no—
504D12Q8×D512yes—
505C4×D3—81no—
506C4×D3—401no—
507C4×D3—401no—
508C4×D3—401no—
509Dic6—401no—
510Dic6—401no—
511C3×C8—21no—
512C3×C8—101no—
513C3⋊C8—21no—
514C3⋊C8—101no—
515C22×C5—62no—
516C22×C5—121no—
517C22×C5—121no—
518C22×C5C2×D3×D411yescharacteristic
519C2×D5—21no—
520C2×D5—21no—
521C2×D5—62no—
522C2×D5—121no—
523C2×D5—121no—
524C2×D5—244no—
525C2×D5#89612yes—
526C4×C5—41no—
527C4×C5—41no—
528C4×C5—61no—
529C4×C5—61no—
530C4×C5—121no—
531C4×C5C2×#23511yescharacteristic
532C4×C5C2×D3×Q811yescharacteristic
533Dic5—41no—
534Dic5—41no—
535Dic5—61no—
536Dic5—61no—
537Dic5—121no—
538Dic5#89612yes—
539C24—301no—
540C2×Q8—301no—
541C2×Q8—301no—
542C2×D4—31no—
543C2×D4—154no—
544C2×D4—151no—
545C2×D4—302no—
546C2×D4—301no—
547C22×C4—51no—
548C22×C4—61no—
549C22×C4—101no—
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—51no—
561C4⋊C4—51no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—101no—
565C4⋊C4—151no—
566C4⋊C4—151no—
567C4⋊C4—151no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4C2×D3×D511yescharacteristic
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—52no—
588C22×C3—101no—
589C22×C3—101no—
590C22×C3C2×D4×D511yescharacteristic
591C2×D3—22no—
592C2×D3—41no—
593C2×D3—41no—
594C2×D3—102no—
595C2×D3—201no—
596C2×D3—201no—
597C2×D3—404no—
598C3×C4—41no—
599C3×C4—41no—
600C3×C4—52no—
601C3×C4—201no—
602C3×C4—201no—
603C3×C4C2×Q8×D511yescharacteristic
604C3×C4D5×#4111yescharacteristic
605Dic3—21no—
606Dic3—21no—
607Dic3—41no—
608Dic3—101no—
609Dic3—101no—
610Dic3—201no—
611C2×C5—122no—
612C2×C5C2×#89611yescharacteristic
613C2×C5#577411yescharacteristic
614C2×C5#577811yescharacteristic
615D5—22no—
616D5—122no—
617C23—51no—
618C23—61no—
619C23—304no—
620C23—301no—
621C23—1201no—
622C23—1201no—
623Q8—1201no—
624Q8—1201no—
625D4—32no—
626D4—61no—
627D4—152no—
628D4—304no—
629D4—301no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—31no—
633C2×C4—31no—
634C2×C4—51no—
635C2×C4—52no—
636C2×C4—52no—
637C2×C4—61no—
638C2×C4—101no—
639C2×C4—101no—
640C2×C4—151no—
641C2×C4—151no—
642C2×C4—241no—
643C2×C4—301no—
644C2×C4—401no—
645C2×C4—1201no—
646C2×C4—1201no—
647C2×C4—1201no—
648C2×C4C22×D3×D511yescharacteristic
649C8—21no—
650C8—61no—
651C8—101no—
652C8—301no—
653C2×C3—102no—
654C2×C3D5×C22⋊Q811yescharacteristic
655C2×C3#6610311yescharacteristic
656C2×C3#6610911yescharacteristic
657D3—42no—
658D3—202no—
659C5#7924211yescharacteristic, complemented, Sylow
660C22—52no—
661C22—62no—
662C22—101no—
663C22—101no—
664C22—121no—
665C22—121no—
666C22—302no—
667C22—601no—
668C22—601no—
669C22—1204no—
670C22D3×D4×D511yescharacteristic
671C4—41no—
672C4—41no—
673C4—52no—
674C4—61no—
675C4—61no—
676C4—121no—
677C4—201no—
678C4—201no—
679C4—301no—
680C4—301no—
681C4—601no—
682C4D5×#23511yescharacteristic
683C4D3×Q8×D511yescharacteristic
684C3#1061290011yescharacteristic, complemented, Sylow
685C2—102no—
686C2—122no—
687C2—602no—
688C2D5×#89611yescharacteristic
689C2#1175408911yescharacteristic
690C2#1175409011yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC2×D5×D12C22
hypercenter#106D3×D5
hypocenterC3×C5#3081
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
2. #11753369C2semidirect
3. #11750971C2semidirect
4. C5×#4871C2semidirect
5. C3×#65150C2semidirect
7. #11747817C2semidirect
8. #11747794C2semidirect
9. #11747648C2semidirect
11. #11747432C2semidirect
12. #11747419C2semidirect
13. #11747254C2semidirect
14. #11747250C2semidirect
15. #11747185C2semidirect
19. #91777C22semidirect
21. C5×#890C22semidirect
27. #91469C22semidirect
32. #91384C22semidirect
40. C3×C5×#106C22semidirect
42. #91098C22semidirect
44. #91092C22semidirect
46. C5×Dic3⋊C8C22semidirect
48. C5×#807C22semidirect
49. C3×#3950C22semidirect
50. C3×#3940C22semidirect
51. C3×#3939C22semidirect
52. #90990C22semidirect
53. #90986C22semidirect
54. Dic3⋊#168C22semidirect
55. #90983C22semidirect
69. #65150D3semidirect
89. D5×D12Q8semidirect
135. #4871D5semidirect
162. C5×#106C2×D3semidirect
171. #3950C2×D3semidirect
178. #3940C2×D3semidirect
179. #3939C2×D3semidirect
233. #890C2×D5semidirect
244. C3×#106C2×D5semidirect
252. Dic3⋊C8C2×D5semidirect
260. #807C2×D5semidirect
460. #106D3×D5semidirect
586. C3×C5#3081semidirect
659. C5#79242semidirect
684. C3#10612900semidirect

Maximal subgroups

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

subgroupindex
#117538372
#117533692
#117509712
C5×#48712
C3×#651502
#117481052
#117478172
#117477942
#117476482
D5×#8092
#117474322
#117474192
#117472542
#117472502
#117471852
#106129003
#792425