Finite Group Databasebeta

← #14417309

Subgroups — #14417309

Order 1920.

940 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11754916C211yesmaximal, characteristic
2C2×#91488C211yesmaximal, characteristic
3#11753381C211yesmaximal, characteristic, complemented
4#11750873C211yesmaximal, characteristic
5C5×#4757C211yesmaximal, characteristic, complemented
6C3×#65046C211yesmaximal, characteristic, complemented
7Dic3×#687C211yesmaximal, characteristic, complemented
8Dic5×#214C211yesmaximal, characteristic, complemented
9#11747835C211yesmaximal, characteristic, complemented
10#11747832C211yesmaximal, characteristic, complemented
11#11747668C211yesmaximal, characteristic, complemented
12#11747609C211yesmaximal, characteristic, complemented
13#11747456C211yesmaximal, characteristic, complemented
14#11747275C211yesmaximal, characteristic, complemented
15#11747270C211yesmaximal, characteristic, complemented
16#10611507—31nomaximal, Hall
17C2×#6819C2211yescharacteristic
18C2×D15⋊Q8C2211yescharacteristic
19C2×C8×D15C2211yescharacteristic
20#91781C2211yescharacteristic
21C5×D4×Dic3C2211yescharacteristic
22C2×C5×#214C2211yescharacteristic
23C5×#887C2211yescharacteristic
24C3×D4×Dic5C2211yescharacteristic
25C2×C3×#687C2211yescharacteristic
26C3×#4033C2211yescharacteristic
27#91556—21no—
28#91552—21no—
29C2×#6669—21no—
30#91532—21no—
31#91488C418yescomplemented
32C4×#1204—21no—
33#91437C2211yescharacteristic
34#91403—21no—
35#91402—21no—
36#91386C2211yescharacteristic
37#91340C2211yescharacteristic
38#91333C2211yescharacteristic
39Dic5×Dic6C2211yescharacteristic
40Dic3×Dic10C2211yescharacteristic
41#91325—21no—
42C2×#6663C2211yescharacteristic
43C2×#6662C2211yescharacteristic
44C2×#6651C2211yescharacteristic
45C3×C5×#102C2211yescharacteristic
46#91116C2211yescharacteristic
47#91100C2211yescharacteristic
48#91094C2211yescharacteristic
49C5×#816C2211yescharacteristic
50C5×#815C2211yescharacteristic
51C5×#807C2211yescharacteristic
52C3×#3948C2211yescharacteristic
53C3×#3947C2211yescharacteristic
54C3×#3939C2211yescharacteristic
55#90987C2211yescharacteristic
56#90985C2211yescharacteristic
57#90972C2211yescharacteristic
58#90970C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60Dic5×C3⋊C8C2211yescharacteristic
61#79776—51nomaximal, Hall
62C2×#4061—31no—
63#65906—31no—
64#65880—31no—
65C5×#440—31no—
66SD16×Dic5—31no—
67C4×#689—31no—
68C4×#687—31no—
69#65170—31no—
70#65162—31no—
71D5×#103—31no—
72#65078—31no—
73#65061—31no—
74#65046D311yescharacteristic, complemented
75#65005—31no—
76#64997—31no—
77C2×C3×C5×D4C2311yescharacteristic
78C2×#1220—21no—
79C22×Dic15—21no—
80#6819—22no—
81#6819C2×C414yes—
82C2×C4×D15C2311yescharacteristic
83C2×Dic30C2311yescharacteristic
84C22×C5×Dic3—21no—
85C2×C5×Dic6C2311yescharacteristic
86C22×C3×Dic5—21no—
87C2×C3×Dic10C2311yescharacteristic
88C2×#1204—21no—
89C2×#1200—21no—
90C2×#1200—21no—
91D15⋊Q8—22no—
92D15⋊Q8C2×C414yescomplemented
93C2×C3×C5×C8C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95#6714—21no—
96C4⋊Dic15C2311yescharacteristic
97C4×Dic15—21no—
98C2×C3⋊#168C2311yescharacteristic
99C8×D15—22no—
100C5×#217—21no—
101C5×#214C2×C414yescomplemented
102C5×C4⋊Dic3C2311yescharacteristic
103C5×Dic3⋊C4—21no—
104C4×C5×Dic3—21no—
105C4×C5×Dic3C2311yescharacteristic
106C2×C5×C3⋊C8C2311yescharacteristic
107C3×C22⋊Dic5—21no—
108C3×#687C2×C414yescomplemented
109C3×C4⋊Dic5C2311yescharacteristic
110C3×#683—21no—
111C3×C4×Dic5—21no—
112C3×C4×Dic5C2311yescharacteristic
113C2×C3×#168C2311yescharacteristic
114Dic3⋊Dic5—21no—
115#6669—21no—
116#6669—21no—
117#6669—21no—
118#6669D411yescharacteristic
119#6669D411yescharacteristic
120#6668—21no—
121#6667D411yescharacteristic
122#6667D411yescharacteristic
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6663C2×C414yescomplemented
128#6662C2×C414yescomplemented
129#6651C2×C414yescomplemented
130C2×#915—51no—
131#5572—51no—
132#5546—51no—
133C3×#440—51no—
134Dic3×SD16—51no—
135C4×#216—51no—
136C4×#214—51no—
137#4881—51no—
138#4873—51no—
139D3×#103—51no—
140#4789—51no—
141#4772—51no—
142#4757D511yescharacteristic, complemented
143#4716—51no—
144#4708—51no—
145C2×Q8×D5—31no—
146C2×#711—31no—
147C2×C5×SD16—31no—
148C4×C5×Q8—31no—
149C4×C5×D4—31no—
150Q8×Dic5—31no—
151C2×#689—31no—
152D4×Dic5C2×D311yescharacteristic
153C2×#687C2×D311yescharacteristic
154C4×C22⋊D5—61no—
155C2×#683—61no—
156#4061—38no—
157C2×Dic20—31no—
158C2×#676—31no—
159C2×C8×D5—31no—
160#4038—31no—
161#4038—61no—
162D5×C4⋊C4—31no—
163#4033—31no—
164#4033—61no—
165#4033C2×D311yescharacteristic
166#4027—61no—
167#4023—61no—
168#4018—31no—
169#4018—61no—
170C4×Dic10—31no—
171C4×Dic10—31no—
172C4×Dic10—61no—
173C5×#107—31no—
174C5×#103—31no—
175C5×#102C2×D311yescharacteristic
176C5×#97—31no—
177#3967—31no—
178#3964—31no—
179#3949—31no—
180#3948—31no—
181#3948C2×D311yescharacteristic
182#3947C2×D311yescharacteristic
183C8×Dic5—31no—
184#3942—31no—
185#3942—31no—
186#3940—31no—
187#3939C2×D311yescharacteristic
188C4×#168—31no—
189#2947—151noSylow
190C23×C3×C5—21no—
191C22×D15C2×D411yescharacteristic
192C3×C5×D4—21no—
193C3×C5×D4C22×C412yes—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5C2411yescharacteristic
196#1220—24no—
197C2×Dic15—21no—
198C2×Dic15—24no—
199C2×Dic15—21no—
200C2×Dic15C2×D411yescharacteristic
201C4×D15C22×C412yes—
202C4×D15#4112yes—
203Dic30—21no—
204Dic30C22×C412yes—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—21no—
207C2×C5×Dic3—81no—
208C2×C5×Dic3C2×D411yescharacteristic
209C2×C5×Dic3C2×D411yescharacteristic
210C5×Dic6—21no—
211C5×Dic6C22×C412yes—
212C2×C3×Dic5—21no—
213C2×C3×Dic5—21no—
214C2×C3×Dic5—81no—
215C2×C3×Dic5C2×D411yescharacteristic
216C2×C3×Dic5C2×D411yescharacteristic
217C3×Dic10—21no—
218C3×Dic10C22×C412yes—
219#1204—24no—
220#1200—24no—
221#1200—81no—
222C3×C5×C8—21no—
223C3⋊#168—21no—
224C3×#168C22×C412yes—
225C5×C3⋊C8C22×C412yes—
226C2×D3×Q8—51no—
227C2×#237—51no—
228C2×C3×SD16—51no—
229C3×C4×Q8—51no—
230C3×C4×D4—51no—
231Q8×Dic3—51no—
232C2×#216—51no—
233D4×Dic3C2×D511yescharacteristic
234C2×#214C2×D511yescharacteristic
235C4×#67—101no—
236C2×Dic3⋊C4—101no—
237#915—58no—
238C2×Dic12—51no—
239C2×ΓL(1,𝔽25)—51no—
240C2×D3×C8—51no—
241#892—51no—
242#892—101no—
243D3×C4⋊C4—51no—
244#887—51no—
245#887—101no—
246#887C2×D511yescharacteristic
247#67⋊C4—101no—
248#877—101no—
249#872—51no—
250#872—101no—
251C4×Dic6—51no—
252C4×Dic6—51no—
253C4×Dic6—101no—
254C3×#107—51no—
255C3×#103—51no—
256C3×#102C2×D511yescharacteristic
257C3×#97—51no—
258#835—51no—
259#832—51no—
260#817—51no—
261#816—51no—
262#816C2×D511yescharacteristic
263#815C2×D511yescharacteristic
264C8×Dic3—51no—
265#810—51no—
266#810—51no—
267#808—51no—
268#807C2×D511yescharacteristic
269C4×C3⋊C8—51no—
270C2×C5×Q8—31no—
271C2×C5×D4C22×D311yescharacteristic
272C22×C4×C5—61no—
273C2×C22⋊D5—61no—
274C22×Dic5—21no—
275C22×Dic5—61no—
276Q8×D5—34no—
277Q8×D5—62no—
278#711—34no—
279#711—62no—
280C2×C4×D5—31no—
281C2×C4×D5—61no—
282C2×C4×D5—61no—
283C2×Dic10—31no—
284C2×Dic10—61no—
285C2×Dic10C22×D311yescharacteristic
286C5×SD16—34no—
287C2×C5×C8—31no—
288C2×C5×C8C22×D311yescharacteristic
289C5×C4⋊C4—31no—
290C5×C4⋊C4—61no—
291C5×C4⋊C4C22×D311yescharacteristic
292C5×C22⋊C4—61no—
293C42×C5—31no—
294C42×C5—61no—
295C22⋊Dic5—21no—
296#689—34no—
297#687C4×D314yescomplemented
298#685—31no—
299#685—31no—
300#685—61no—
301C4⋊Dic5—31no—
302C4⋊Dic5—61no—
303C4⋊Dic5C22×D311yescharacteristic
304#683—21no—
305#683—31no—
306#683—31no—
307#683—61no—
308#683—61no—
309#683—61no—
310#683—61no—
311C4×Dic5—21no—
312C4×Dic5—61no—
313C4×Dic5—61no—
314C4×Dic5—61no—
315C4×Dic5—61no—
316C4×Dic5—61no—
317C4×Dic5C22×D311yescharacteristic
318C2×#168—31no—
319C2×#168C22×D311yescharacteristic
320Dic20—34no—
321#676—34no—
322C8×D5—62no—
323C2×#137—151no—
324#520—151no—
325#519—151no—
326#441—151no—
327#441—151no—
328#440—31no—
329#440—51no—
330C4×Q16—151no—
331C4×Q16—151no—
332C4×SD16—151no—
333C4×SD16—151no—
334#428—151no—
335#416—151no—
336C2×#103—151no—
337#405—151no—
338C22×C3×C5—22no—
339C22×C3×C5—41no—
340C22×C3×C5—41no—
341C22×C3×C5C22×D411yescharacteristic
342C2×D15—21no—
343C2×D15—21no—
344C2×D15C4×D412yes—
345C3×C4×C5—41no—
346C3×C4×C5C23×C411yescharacteristic
347C3×C4×C5C2×#4111yescharacteristic
348Dic15—22no—
349Dic15—41no—
350Dic15C4×D412yes—
351C3×Dic5—22no—
352C3×Dic5—21no—
353C3×Dic5—21no—
354C3×Dic5—41no—
355C5×Dic3—22no—
356C5×Dic3—21no—
357C5×Dic3—21no—
358C5×Dic3—41no—
359C2×C3×Q8—51no—
360C2×C3×D4C22×D511yescharacteristic
361C22×C3×C4—101no—
362C2×#67—101no—
363C22×Dic3—21no—
364C22×Dic3—101no—
365D3×Q8—54no—
366D3×Q8—102no—
367#237—54no—
368#237—102no—
369C2×C4×D3—51no—
370C2×C4×D3—101no—
371C2×C4×D3—101no—
372C2×Dic6—51no—
373C2×Dic6—101no—
374C2×Dic6C22×D511yescharacteristic
375C3×SD16—54no—
376C2×C3×C8—51no—
377C2×C3×C8C22×D511yescharacteristic
378C3×C4⋊C4—51no—
379C3×C4⋊C4—101no—
380C3×C4⋊C4C22×D511yescharacteristic
381C3×C22⋊C4—101no—
382C3×C42—51no—
383C3×C42—101no—
384#217—21no—
385#216—54no—
386#214C4×D514yescomplemented
387(C2×D3)⋊C4—51no—
388(C2×D3)⋊C4—51no—
389(C2×D3)⋊C4—101no—
390C4⋊Dic3—51no—
391C4⋊Dic3—101no—
392C4⋊Dic3C22×D511yescharacteristic
393Dic3⋊C4—21no—
394Dic3⋊C4—51no—
395Dic3⋊C4—51no—
396Dic3⋊C4—101no—
397Dic3⋊C4—101no—
398Dic3⋊C4—101no—
399Dic3⋊C4—101no—
400C4×Dic3—21no—
401C4×Dic3—101no—
402C4×Dic3—101no—
403C4×Dic3—101no—
404C4×Dic3—101no—
405C4×Dic3—101no—
406C4×Dic3C22×D511yescharacteristic
407C2×C3⋊C8—51no—
408C2×C3⋊C8C22×D511yescharacteristic
409Dic12—54no—
410ΓL(1,𝔽25)—54no—
411D3×C8—102no—
412C23×C5—21no—
413C22×D5—31no—
414C5×Q8—32no—
415C5×Q8—61no—
416C5×D4—21no—
417C5×D4C2×C4×D312yes—
418C2×C4×C5—21no—
419C2×C4×C5—31no—
420C2×C4×C5—31no—
421C2×C4×C5—61no—
422C2×C4×C5—61no—
423C2×C4×C5—241no—
424C2×C4×C5C23×D311yescharacteristic
425C22⋊D5—64no—
426C2×Dic5—21no—
427C2×Dic5—21no—
428C2×Dic5—31no—
429C2×Dic5—64no—
430C2×Dic5—61no—
431C2×Dic5—61no—
432C2×Dic5—81no—
433C2×Dic5D3×D411yescharacteristic
434C2×Dic5D3×D411yescharacteristic
435C4×D5—32no—
436C4×D5—32no—
437C4×D5—64no—
438C4×D5—241no—
439Dic10—21no—
440Dic10—32no—
441Dic10—64no—
442Dic10—61no—
443Dic10C2×C4×D312yes—
444C5×C8—21no—
445C5×C8—32no—
446#168—61no—
447#168C2×C4×D312yes—
448C2×#41—151no—
449C22×Q8—151no—
450#137—158no—
451C2×Q16—151no—
452C2×Q16—151no—
453C2×SD16—31no—
454C2×SD16—51no—
455C2×M16—151no—
456C22×C8—151no—
457C4×Q8—31no—
458C4×Q8—51no—
459C4×Q8—151no—
460C4×Q8—151no—
461C4×Q8—151no—
462C4×Q8—151no—
463C4×Q8—301no—
464C4×Q8—301no—
465C4×D4—31no—
466C4×D4—51no—
467C4×D4—301no—
468C4×D4—301no—
469#117—151no—
470#117—151no—
471#117—301no—
472#117—301no—
473#117—301no—
474C2×C4⋊C4—151no—
475C2×C4⋊C4—301no—
476#107—31no—
477#107—51no—
478#106—151no—
479#106—151no—
480#103—31no—
481#103—51no—
482#103—151no—
483#103—151no—
484#103—151no—
485#103—151no—
486#102—151no—
487#102D3×D511yescharacteristic
488#97—31no—
489#97—51no—
490C4×C8—151no—
491C4×C8—151no—
492C2×C3×C5—42no—
493C2×C3×C5C2×C4×D411yescharacteristic
494C2×C3×C5#57711yescharacteristic
495C2×C3×C5#57811yescharacteristic
496D15—22no—
497C23×C3—21no—
498C22×D3—51no—
499C3×Q8—52no—
500C3×Q8—101no—
501C3×D4—21no—
502C3×D4C2×C4×D512yes—
503C2×C3×C4—21no—
504C2×C3×C4—51no—
505C2×C3×C4—51no—
506C2×C3×C4—101no—
507C2×C3×C4—101no—
508C2×C3×C4—401no—
509C2×C3×C4C23×D511yescharacteristic
510#67—104no—
511C2×Dic3—21no—
512C2×Dic3—21no—
513C2×Dic3—51no—
514C2×Dic3—81no—
515C2×Dic3—104no—
516C2×Dic3—101no—
517C2×Dic3—101no—
518C2×Dic3D4×D511yescharacteristic
519C2×Dic3D4×D511yescharacteristic
520C4×D3—52no—
521C4×D3—52no—
522C4×D3—104no—
523C4×D3—401no—
524Dic6—21no—
525Dic6—52no—
526Dic6—104no—
527Dic6—101no—
528Dic6C2×C4×D512yes—
529C3×C8—21no—
530C3×C8—52no—
531C3⋊C8—101no—
532C3⋊C8C2×C4×D512yes—
533C22×C5—22no—
534C22×C5—41no—
535C22×C5—41no—
536C22×C5C2×D3×D411yescharacteristic
537C2×D5—32no—
538C2×D5—61no—
539C2×D5—61no—
540C4×C5—41no—
541C4×C5—61no—
542C4×C5—61no—
543C4×C5—62no—
544C4×C5—121no—
545C4×C5C22×C4×D311yescharacteristic
546C4×C5D3×#4111yescharacteristic
547Dic5—21no—
548Dic5—21no—
549Dic5—22no—
550Dic5—32no—
551Dic5—41no—
552Dic5—62no—
553Dic5—121no—
554#41—154no—
555#41—302no—
556C2×Q8—31no—
557C2×Q8—51no—
558C2×Q8—154no—
559C2×Q8—151no—
560C2×Q8—301no—
561C2×Q8—302no—
562C2×D4—301no—
563C2×D4C2×D3×D511yescharacteristic
564C22×C4—61no—
565C22×C4—101no—
566C22×C4—151no—
567C22×C4—301no—
568C22×C4—301no—
569C22×C4—301no—
570Q16—154no—
571Q16—154no—
572SD16—34no—
573SD16—54no—
574M16—154no—
575C2×C8—31no—
576C2×C8—51no—
577C2×C8—151no—
578C2×C8—302no—
579C2×C8C2×D3×D511yescharacteristic
580C4⋊C4—31no—
581C4⋊C4—51no—
582C4⋊C4—61no—
583C4⋊C4—101no—
584C4⋊C4—151no—
585C4⋊C4—151no—
586C4⋊C4—151no—
587C4⋊C4—301no—
588C4⋊C4—301no—
589C4⋊C4—301no—
590C4⋊C4—301no—
591C4⋊C4—301no—
592C4⋊C4C2×D3×D511yescharacteristic
593C22⋊C4—61no—
594C22⋊C4—101no—
595C22⋊C4—151no—
596C22⋊C4—151no—
597C22⋊C4—301no—
598C42—31no—
599C42—51no—
600C42—61no—
601C42—101no—
602C42—301no—
603C42—301no—
604C42—301no—
605C42—301no—
606C42—301no—
607C3×C5#294711yescharacteristic, complemented, Hall
608C22×C3—22no—
609C22×C3—41no—
610C22×C3—41no—
611C22×C3C2×D4×D511yescharacteristic
612C2×D3—52no—
613C2×D3—101no—
614C2×D3—101no—
615C3×C4—41no—
616C3×C4—101no—
617C3×C4—101no—
618C3×C4—102no—
619C3×C4—201no—
620C3×C4C22×C4×D511yescharacteristic
621C3×C4D5×#4111yescharacteristic
622Dic3—21no—
623Dic3—21no—
624Dic3—22no—
625Dic3—41no—
626Dic3—52no—
627Dic3—102no—
628Dic3—201no—
629C2×C5—42no—
630C2×C5C4×D3×D411yescharacteristic
631C2×C5#577511yescharacteristic
632C2×C5#577911yescharacteristic
633D5—62no—
634C23—21no—
635C23—151no—
636Q8—32no—
637Q8—52no—
638Q8—61no—
639Q8—101no—
640Q8—152no—
641Q8—304no—
642Q8—301no—
643D4—21no—
644D4—304no—
645D4C4×D3×D512yes—
646C2×C4—21no—
647C2×C4—31no—
648C2×C4—31no—
649C2×C4—51no—
650C2×C4—51no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—101no—
654C2×C4—101no—
655C2×C4—151no—
656C2×C4—152no—
657C2×C4—152no—
658C2×C4—241no—
659C2×C4—304no—
660C2×C4—304no—
661C2×C4—301no—
662C2×C4—301no—
663C2×C4—401no—
664C2×C4—1201no—
665C2×C4C22×D3×D511yescharacteristic
666C8—21no—
667C8—32no—
668C8—52no—
669C8—301no—
670C2×C3—42no—
671C2×C3C4×D4×D511yescharacteristic
672C2×C3#6610911yescharacteristic
673C2×C3#6611311yescharacteristic
674D3—102no—
675C5#7977611yescharacteristic, complemented, Sylow
676C22—22no—
677C22—41no—
678C22—41no—
679C22—152no—
680C22—301no—
681C22—301no—
682C22D3×D4×D511yescharacteristic
683C4—41no—
684C4—61no—
685C4—61no—
686C4—62no—
687C4—101no—
688C4—101no—
689C4—102no—
690C4—121no—
691C4—152no—
692C4—201no—
693C4—302no—
694C4—601no—
695C4C2×C4×D3×D511yescharacteristic
696C4#9202411yescharacteristic
697C3#1061150711yescharacteristic, complemented, Sylow
698C2—42no—
699C2—302no—
700C2#1175320311yescharacteristic
701C2#1175405711yescharacteristic
702C2#1175408611yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#102C22
socleC22×C3×C5C22×D4
prime radicalC2×#6819C22
cosocleC2×C3×C4×C5C24
hypercenter#102D3×D5
hypocenterC3×C5#2947
LCSG ▷ 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
3. #11753381C2semidirect
5. C5×#4757C2semidirect
6. C3×#65046C2semidirect
7. Dic3×#687C2semidirect
8. Dic5×#214C2semidirect
9. #11747835C2semidirect
10. #11747832C2semidirect
11. #11747668C2semidirect
12. #11747609C2semidirect
13. #11747456C2semidirect
14. #11747275C2semidirect
15. #11747270C2semidirect
31. #91488C4semidirect
74. #65046D3semidirect
92. D15⋊Q8C2×C4semidirect
101. C5×#214C2×C4semidirect
108. C3×#687C2×C4semidirect
127. #6663C2×C4semidirect
128. #6662C2×C4semidirect
129. #6651C2×C4semidirect
142. #4757D5semidirect
297. #687C4×D3semidirect
386. #214C4×D5semidirect
607. C3×C5#2947semidirect
675. C5#79776semidirect
697. C3#10611507semidirect

Maximal subgroups

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

subgroupindex
#117549162
C2×#914882
#117533812
#117508732
C5×#47572
C3×#650462
Dic3×#6872
Dic5×#2142
#117478352
#117478322
#117476682
#117476092
#117474562
#117472752
#117472702
#106115073
#797765