Finite Group Databasebeta

← #14417200

Subgroups — #14417200

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#11755140C211yesmaximal, characteristic, complemented
2C2×#91515C211yesmaximal, characteristic
3#11753336C211yesmaximal, characteristic
4#11750918C211yesmaximal, characteristic, complemented
5C5×#4789C211yesmaximal, characteristic, complemented
6C3×D5×#103C211yesmaximal, characteristic, complemented
7#11749265C211yesmaximal, characteristic, complemented
8#11749232C211yesmaximal, characteristic, complemented
9#11747829C211yesmaximal, characteristic, complemented
10#11747743C211yesmaximal, characteristic, complemented
11#11747646C211yesmaximal, characteristic, complemented
12#11747642C211yesmaximal, characteristic
13#11747453C211yesmaximal, characteristic, complemented
14#11747272C211yesmaximal, characteristic, complemented
15#11747266C211yesmaximal, characteristic, complemented
16#10611561—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C2×#6773C2211yescharacteristic
19Q8×Dic15C2211yescharacteristic
20C2×#6717C2211yescharacteristic
21#91782C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic
23C2×C5×#216C2211yescharacteristic
24C5×#887C2211yescharacteristic
25C2×C3×C8×D5C2211yescharacteristic
26C3×D5×C4⋊C4C2211yescharacteristic
27#91515C418yescomplemented
28#91444—21no—
29C4×#1202—21no—
30#91428C2211yescharacteristic
31#91404—21no—
32#91403—21no—
33#91358—21no—
34#91358C2211yescharacteristic
35#91357—21no—
36#91357C2211yescharacteristic
37#91344C2211yescharacteristic
38#91331—21no—
39#91331C2211yescharacteristic
40Dic3×Dic10—21no—
41Dic3×Dic10C2211yescharacteristic
42C2×#6661C2211yescharacteristic
43C2×#6658C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46#91105C2211yescharacteristic
47#91099C2211yescharacteristic
48#91091C2211yescharacteristic
49C5×#816C2211yescharacteristic
50C5×#815C2211yescharacteristic
51C5×#808C2211yescharacteristic
52C3×#3967C2211yescharacteristic
53C3×#3948C2211yescharacteristic
54C3×#3942C2211yescharacteristic
55#90990C2211yescharacteristic
56#90986C2211yescharacteristic
57#90973C2211yescharacteristic
58#90969C2211yescharacteristic
59#90951C2211yescharacteristic
60Dic3×#168C2211yescharacteristic
61#78774—51nomaximal, Hall
62C2×#4064—31no—
63#65908—31no—
64#65906—31no—
65C5×#441—31no—
66Q16×Dic5—31no—
67C4×#689—31no—
68C4×#688—31no—
69#65150—31no—
70#65141—31no—
71#65106—31no—
72#65093—31no—
73D5×#103D311yescharacteristic, complemented
74#65078—31no—
75#64999—31no—
76#64997—31no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×D60C2311yescharacteristic
79C2×C4×D15—21no—
80C2×C5×Dic6C2311yescharacteristic
81C3×Q8×D5—22no—
82C3×Q8×D5C2×C414yescomplemented
83C2×C3×C4×D5—21no—
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5C2311yescharacteristic
86C2×C3×Dic10—21no—
87C2×C3×Dic10C2311yescharacteristic
88C2×#1202—21no—
89C2×#1200—21no—
90C2×#1200—21no—
91#6773—22no—
92#6773C2×C414yes—
93C2×C3×C5×C8C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95#6717C2×C414yescomplemented
96#6714—21no—
97C4⋊Dic15—21no—
98C4⋊Dic15C2311yescharacteristic
99C4×Dic15—21no—
100C4×Dic15C2311yescharacteristic
101C2×C3⋊#168C2311yescharacteristic
102C5×#216C2×C414yescomplemented
103C5×C4⋊Dic3—21no—
104C5×C4⋊Dic3C2311yescharacteristic
105C5×Dic3⋊C4—21no—
106C4×C5×Dic3—21no—
107C4×C5×Dic3—21no—
108C4×C5×Dic3C2311yescharacteristic
109C2×C5×C3⋊C8C2311yescharacteristic
110C3×C4⋊Dic5C2311yescharacteristic
111C3×#683—21no—
112C2×C3×#168C2311yescharacteristic
113C3×C8×D5—22no—
114Dic3⋊Dic5—21no—
115#6668—21no—
116#6668—21no—
117#6668D411yescharacteristic
118#6668D411yescharacteristic
119#6667—21no—
120#6665—21no—
121#6665D411yescharacteristic
122#6665D411yescharacteristic
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6661C2×C414yescomplemented
128#6658C2×C414yescomplemented
129#6649C2×C414yescomplemented
130#5812—51no—
131C2×#942—51no—
132#5504—51no—
133C2×C3×#103—51no—
134#5113—51no—
135#5101—51no—
136#4964—51no—
137#4817—51no—
138#4817—51no—
139#4790—51no—
140#4790—51no—
141#4789—51no—
142#4789D511yescharacteristic, complemented
143#4788—51no—
144#4788—51no—
145C2×#713—31no—
146C2×Q8×D5C2×D311yescharacteristic
147C2×C5×Q16—31no—
148C4×C5×Q8—31no—
149C4×C5×Q8—31no—
150Q8×Dic5—31no—
151Q8×Dic5—31no—
152C2×#689—31no—
153C2×#688—31no—
154#4064—38no—
155C2×#677—31no—
156C2×#676—31no—
157C2×C8×D5C2×D311yescharacteristic
158#4039—31no—
159#4039—61no—
160#4038—31no—
161#4038—61no—
162D5×C4⋊C4—61no—
163D5×C4⋊C4C2×D311yescharacteristic
164#4033—31no—
165#4033—61no—
166C4×D20—31no—
167C4×D20—61no—
168#4018—31no—
169#4018—61no—
170#4018—61no—
171C4×Dic10—31no—
172C4×Dic10—61no—
173C5×#106—31no—
174C5×#103—31no—
175C5×#103C2×D311yescharacteristic
176C5×#97—31no—
177#3967—31no—
178#3967C2×D311yescharacteristic
179#3953—31no—
180#3950—31no—
181#3948C2×D311yescharacteristic
182#3947—31no—
183C8×Dic5—31no—
184#3942C2×D311yescharacteristic
185#3941—31no—
186#3940—31no—
187#3939—31no—
188C4×#168—31no—
189#2947—151noSylow
190C22×D15—21no—
191C22×C3×D5C2×D411yescharacteristic
192C3×C5×Q8—21no—
193C3×C5×Q8C22×C412yes—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5C2411yescharacteristic
197C2×Dic15—21no—
198C2×Dic15C2×D411yescharacteristic
199C2×Dic15C2×D411yescharacteristic
200D60—21no—
201D60C22×C412yes—
202C4×D15—81no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3C2×D411yescharacteristic
206C2×C5×Dic3C2×D411yescharacteristic
207C5×Dic6—21no—
208C5×Dic6C22×C412yes—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5C2×D411yescharacteristic
212C3×C4×D5—24no—
213C3×C4×D5—81no—
214C3×C4×D5C22×C412yes—
215C3×C4×D5#4112yes—
216C3×Dic10—21no—
217C3×Dic10—24no—
218C3×Dic10C22×C412yes—
219#1202—24no—
220#1200—24no—
221#1200—81no—
222C3×C5×C8—21no—
223C3⋊#168C22×C412yes—
224C3×#168—21no—
225C5×C3⋊C8C22×C412yes—
226C22×C3×Q8—51no—
227C2×#235—51no—
228C22×C3×C8—51no—
229C2×C3×C4⋊C4—51no—
230Q8×Dic3—51no—
231Q8×Dic3—51no—
232Q8×Dic3—51no—
233Q8×Dic3—101no—
234Q8×Dic3—101no—
235Q8×Dic3C2×D511yescharacteristic
236C2×#216—51no—
237C2×#216C2×D511yescharacteristic
238#942—58no—
239C2×#215—51no—
240C2×#215—51no—
241C4×#67—101no—
242C4×#67—101no—
243#926—51no—
244#926—51no—
245#926—101no—
246#926—101no—
247C2×#208—51no—
248#893—51no—
249#893—51no—
250#892—101no—
251D3×C4⋊C4—101no—
252#887—51no—
253#887C2×D511yescharacteristic
254C3×#103—51no—
255C3×#103—51no—
256C3×#103—51no—
257C3×#103C2×D511yescharacteristic
258#821—51no—
259#821—51no—
260#816—51no—
261#816C2×D511yescharacteristic
262#815—51no—
263#815C2×D511yescharacteristic
264C8×Dic3—51no—
265C8×Dic3—51no—
266#808—51no—
267#808C2×D511yescharacteristic
268#807—51no—
269#807—51no—
270C2×C5×Q8—31no—
271C2×C5×Q8C22×D311yescharacteristic
272#713—34no—
273#713—62no—
274Q8×D5—22no—
275Q8×D5C4×D314yescomplemented
276C2×D20—31no—
277C2×D20—61no—
278C2×C4×D5—21no—
279C2×C4×D5—21no—
280C2×C4×D5—61no—
281C2×C4×D5—61no—
282C2×C4×D5—61no—
283C2×C4×D5C22×D311yescharacteristic
284C2×Dic10—21no—
285C2×Dic10C22×D311yescharacteristic
286C5×Q16—34no—
287C2×C5×C8—31no—
288C2×C5×C8C22×D311yescharacteristic
289C5×C4⋊C4—31no—
290C5×C4⋊C4—61no—
291C5×C4⋊C4—61no—
292C5×C4⋊C4C22×D311yescharacteristic
293C42×C5—31no—
294C42×C5—61no—
295C42×C5—61no—
296#689—34no—
297#688—34no—
298#685—31no—
299#685—31no—
300#685—61no—
301#685—61no—
302#685—61no—
303C4⋊Dic5—31no—
304C4⋊Dic5—61no—
305C4⋊Dic5—61no—
306C4⋊Dic5C22×D311yescharacteristic
307#683—21no—
308#683—31no—
309#683—31no—
310#683—61no—
311#683—61no—
312C4×Dic5—31no—
313C4×Dic5—61no—
314C4×Dic5—61no—
315C4×Dic5—61no—
316C4×Dic5—61no—
317C4×Dic5—61no—
318C2×#168—31no—
319C2×#168C22×D311yescharacteristic
320#677—34no—
321#676—34no—
322C8×D5—22no—
323C2×#137—151no—
324#520—151no—
325#519—151no—
326#441—31no—
327#441—151no—
328#440—151no—
329#440—151no—
330C4×Q16—151no—
331C4×Q16—151no—
332C4×SD16—151no—
333C4×SD16—151no—
334#428—151no—
335#416—151no—
336C2×#103—51no—
337#405—151no—
338C22×C3×C5C22×D411yescharacteristic
339C2×D15—22no—
340C2×D15—41no—
341C2×D15—41no—
342C2×C3×D5—21no—
343C2×C3×D5—21no—
344C2×C3×D5C4×D412yes—
345C3×C4×C5—22no—
346C3×C4×C5—41no—
347C3×C4×C5C23×C411yescharacteristic
348C3×C4×C5C2×#4111yescharacteristic
349Dic15—21no—
350Dic15—21no—
351Dic15—41no—
352C3×Dic5—22no—
353C3×Dic5—41no—
354C3×Dic5C4×D412yes—
355C5×Dic3—22no—
356C5×Dic3—21no—
357C5×Dic3—21no—
358C5×Dic3—41no—
359C2×C3×Q8—54no—
360C2×C3×Q8—51no—
361C2×C3×Q8—101no—
362C2×C3×Q8—102no—
363C2×C3×Q8C22×D511yescharacteristic
364C22×C3×C4—51no—
365C22×C3×C4—101no—
366C22×C3×C4—101no—
367C2×#67—101no—
368#235—54no—
369#235—102no—
370C2×D12—51no—
371C2×C4×D3—101no—
372C2×C4×D3—101no—
373C2×C4×D3—101no—
374C2×Dic6C22×D511yescharacteristic
375C2×C3×C8—51no—
376C2×C3×C8—102no—
377C2×C3×C8C22×D511yescharacteristic
378C3×C4⋊C4—51no—
379C3×C4⋊C4—101no—
380C3×C4⋊C4C22×D511yescharacteristic
381#217—51no—
382#217—51no—
383#217—101no—
384#216—54no—
385#216C4×D514yescomplemented
386#215—54no—
387#215—54no—
388(C2×D3)⋊C4—101no—
389(C2×D3)⋊C4—101no—
390C4⋊Dic3—21no—
391C4⋊Dic3—51no—
392C4⋊Dic3—51no—
393C4⋊Dic3—51no—
394C4⋊Dic3—101no—
395C4⋊Dic3—101no—
396C4⋊Dic3—101no—
397C4⋊Dic3C22×D511yescharacteristic
398Dic3⋊C4—21no—
399Dic3⋊C4—101no—
400C4×Dic3—21no—
401C4×Dic3—21no—
402C4×Dic3—51no—
403C4×Dic3—101no—
404C4×Dic3—101no—
405C4×Dic3—101no—
406C4×Dic3—101no—
407C4×Dic3—101no—
408C4×Dic3C22×D511yescharacteristic
409#208—54no—
410C2×C3⋊C8—51no—
411C2×C3⋊C8C22×D511yescharacteristic
412C22×D5—61no—
413C22×D5D3×D411yescharacteristic
414C5×Q8—21no—
415C5×Q8—32no—
416C5×Q8—61no—
417C5×Q8C2×C4×D312yes—
418C2×C4×C5—21no—
419C2×C4×C5—21no—
420C2×C4×C5—31no—
421C2×C4×C5—31no—
422C2×C4×C5—61no—
423C2×C4×C5—61no—
424C2×C4×C5C23×D311yescharacteristic
425C2×Dic5—21no—
426C2×Dic5—21no—
427C2×Dic5—31no—
428C2×Dic5—31no—
429C2×Dic5—61no—
430C2×Dic5D3×D411yescharacteristic
431D20—32no—
432D20—64no—
433D20—61no—
434C4×D5—24no—
435C4×D5—64no—
436C4×D5—81no—
437C4×D5—241no—
438C4×D5—241no—
439C4×D5C2×C4×D312yes—
440C4×D5#23712yes—
441Dic10—21no—
442Dic10—24no—
443Dic10C2×C4×D312yes—
444C5×C8—21no—
445C5×C8—32no—
446#168—21no—
447#168—32no—
448C2×#41—151no—
449C22×Q8—51no—
450#137—158no—
451C2×Q16—31no—
452C2×Q16—151no—
453C2×SD16—151no—
454C2×SD16—151no—
455C2×M16—151no—
456C22×C8—51no—
457C4×Q8—31no—
458C4×Q8—31no—
459C4×Q8—151no—
460C4×Q8—151no—
461C4×Q8—151no—
462C4×Q8—151no—
463C4×Q8—301no—
464C4×Q8—301no—
465C4×D4—151no—
466C4×D4—151no—
467C4×D4—301no—
468C4×D4—301no—
469#117—151no—
470#117—151no—
471#117—301no—
472#117—301no—
473#117—301no—
474C2×C4⋊C4—51no—
475C2×C4⋊C4—301no—
476#107—151no—
477#107—151no—
478#106—31no—
479#106—151no—
480#103—31no—
481#103—51no—
482#103—51no—
483#103—51no—
484#103—151no—
485#103D3×D511yescharacteristic
486#102—151no—
487#102—151no—
488#97—31no—
489#97—151no—
490C4×C8—151no—
491C4×C8—151no—
492C2×C3×C5C2×C4×D411yescharacteristic
493C2×C3×C5#57711yescharacteristic
494C2×C3×C5#57811yescharacteristic
495D15—42no—
496C3×D5—22no—
497C23×C3—51no—
498C22×D3—101no—
499C3×Q8—21no—
500C3×Q8—52no—
501C3×Q8—104no—
502C3×Q8—101no—
503C3×Q8C2×C4×D512yes—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—51no—
507C2×C3×C4—52no—
508C2×C3×C4—52no—
509C2×C3×C4—104no—
510C2×C3×C4—101no—
511C2×C3×C4—101no—
512C2×C3×C4—401no—
513C2×C3×C4C23×D511yescharacteristic
514#67—104no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—51no—
518C2×Dic3—51no—
519C2×Dic3—101no—
520C2×Dic3D4×D511yescharacteristic
521C2×Dic3D4×D511yescharacteristic
522D12—52no—
523D12—101no—
524C4×D3—104no—
525C4×D3—401no—
526C4×D3—401no—
527Dic6—21no—
528Dic6C2×C4×D512yes—
529C3×C8—21no—
530C3×C8—101no—
531C3⋊C8—52no—
532C3⋊C8C2×C4×D512yes—
533C22×C5C2×D3×D411yescharacteristic
534C2×D5—21no—
535C2×D5—21no—
536C2×D5—62no—
537C2×D5—121no—
538C2×D5—121no—
539C2×D5#67⋊C412yes—
540C4×C5—22no—
541C4×C5—41no—
542C4×C5—62no—
543C4×C5—61no—
544C4×C5—61no—
545C4×C5—121no—
546C4×C5C22×C4×D311yescharacteristic
547C4×C5C2×#23711yescharacteristic
548Dic5—22no—
549Dic5—41no—
550Dic5—61no—
551Dic5—61no—
552Dic5—121no—
553Dic5#67⋊C412yes—
554#41—154no—
555#41—302no—
556C2×Q8—31no—
557C2×Q8—54no—
558C2×Q8—51no—
559C2×Q8—101no—
560C2×Q8—102no—
561C2×Q8C2×D3×D511yescharacteristic
562C2×D4—151no—
563C2×D4—301no—
564C22×C4—51no—
565C22×C4—101no—
566C22×C4—101no—
567C22×C4—301no—
568C22×C4—301no—
569C22×C4—301no—
570Q16—34no—
571Q16—154no—
572SD16—154no—
573SD16—154no—
574M16—154no—
575C2×C8—31no—
576C2×C8—51no—
577C2×C8—102no—
578C2×C8—151no—
579C2×C8C2×D3×D511yescharacteristic
580C4⋊C4—31no—
581C4⋊C4—51no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—101no—
585C4⋊C4—151no—
586C4⋊C4—151no—
587C4⋊C4—151no—
588C4⋊C4—301no—
589C4⋊C4—301no—
590C4⋊C4—301no—
591C4⋊C4—301no—
592C4⋊C4C2×D3×D511yescharacteristic
593C22⋊C4—151no—
594C22⋊C4—151no—
595C22⋊C4—301no—
596C22⋊C4—301no—
597C22⋊C4—301no—
598C42—31no—
599C42—61no—
600C42—61no—
601C42—151no—
602C42—301no—
603C42—301no—
604C42—301no—
605C42—301no—
606C42—301no—
607C3×C5#294711yescharacteristic, complemented, Hall
608C22×C3—52no—
609C22×C3—101no—
610C22×C3—101no—
611C22×C3C2×D4×D511yescharacteristic
612C2×D3—102no—
613C2×D3—201no—
614C2×D3—201no—
615C3×C4—22no—
616C3×C4—41no—
617C3×C4—52no—
618C3×C4—102no—
619C3×C4—201no—
620C3×C4C22×C4×D511yescharacteristic
621C3×C4D5×#4111yescharacteristic
622Dic3—21no—
623Dic3—21no—
624Dic3—22no—
625Dic3—41no—
626Dic3—101no—
627Dic3—101no—
628Dic3—201no—
629C2×C5C2×#67⋊C411yescharacteristic
630C2×C5#576211yescharacteristic
631C2×C5#576611yescharacteristic
632D5—22no—
633D5—122no—
634C23—51no—
635C23—301no—
636Q8—21no—
637Q8—32no—
638Q8—52no—
639Q8—61no—
640Q8—104no—
641Q8—101no—
642Q8C4×D3×D512yes—
643D4—152no—
644D4—304no—
645D4—301no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—31no—
649C2×C4—31no—
650C2×C4—51no—
651C2×C4—52no—
652C2×C4—52no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—104no—
656C2×C4—101no—
657C2×C4—101no—
658C2×C4—151no—
659C2×C4—151no—
660C2×C4—304no—
661C2×C4—301no—
662C2×C4—401no—
663C2×C4—1201no—
664C2×C4—1201no—
665C2×C4C22×D3×D511yescharacteristic
666C8—21no—
667C8—32no—
668C8—101no—
669C8—152no—
670C2×C3—102no—
671C2×C3C4×D4×D511yescharacteristic
672C2×C3#6611211yescharacteristic
673C2×C3#6611311yescharacteristic
674D3—202no—
675C5#7877411yescharacteristic, complemented, Sylow
676C22—52no—
677C22—101no—
678C22—101no—
679C22—302no—
680C22—601no—
681C22—601no—
682C22D3×D4×D511yescharacteristic
683C4—22no—
684C4—41no—
685C4—52no—
686C4—61no—
687C4—61no—
688C4—62no—
689C4—102no—
690C4—121no—
691C4—201no—
692C4—301no—
693C4—301no—
694C4—601no—
695C4C2×C4×D3×D511yescharacteristic
696C4D5×#23711yescharacteristic
697C3#1061156111yescharacteristic, complemented, Sylow
698C2—102no—
699C2—602no—
700C2D5×#67⋊C411yescharacteristic
701C2#1175408411yescharacteristic
702C2#1175410711yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×#6773C22
cosocleC2×C3×C4×C5C24
hypercenter#103D3×D5
hypocenterC3×C5#2947
LCSG ▷ 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
1. #11755140C2semidirect
4. #11750918C2semidirect
5. C5×#4789C2semidirect
6. C3×D5×#103C2semidirect
7. #11749265C2semidirect
8. #11749232C2semidirect
9. #11747829C2semidirect
10. #11747743C2semidirect
11. #11747646C2semidirect
13. #11747453C2semidirect
14. #11747272C2semidirect
15. #11747266C2semidirect
27. #91515C4semidirect
73. D5×#103D3semidirect
82. C3×Q8×D5C2×C4semidirect
95. #6717C2×C4semidirect
102. C5×#216C2×C4semidirect
127. #6661C2×C4semidirect
128. #6658C2×C4semidirect
129. #6649C2×C4semidirect
142. #4789D5semidirect
275. Q8×D5C4×D3semidirect
385. #216C4×D5semidirect
607. C3×C5#2947semidirect
675. C5#78774semidirect
697. C3#10611561semidirect

Maximal subgroups

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

subgroupindex
#117551402
C2×#915152
#117533362
#117509182
C5×#47892
C3×D5×#1032
#117492652
#117492322
#117478292
#117477432
#117476462
#117476422
#117474532
#117472722
#117472662
#106115613
#787745