Finite Group Databasebeta

← #14417299

Subgroups — #14417299

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#11755217C211yesmaximal, characteristic
2C2×#91508C211yesmaximal, characteristic
3#11753397C211yesmaximal, characteristic, complemented
4#11750890C211yesmaximal, characteristic, complemented
5C5×#4789C211yesmaximal, characteristic, complemented
6C3×#65093C211yesmaximal, characteristic
7#11749265C211yesmaximal, characteristic, complemented
8#11749257C211yesmaximal, characteristic, complemented
9#11747742C211yesmaximal, characteristic, complemented
10#11747736C211yesmaximal, characteristic, complemented
11#11747646C211yesmaximal, characteristic, complemented
12D5×#816C211yesmaximal, characteristic, complemented
13#11747227C211yesmaximal, characteristic, complemented
14#11747221C211yesmaximal, characteristic, complemented
15#11747189C211yesmaximal, characteristic, complemented
16#10611561—31nomaximal, Hall
17C2×C3×#713C2211yescharacteristic
18C2×D5×Dic6C2211yescharacteristic
19Q8×Dic15C2211yescharacteristic
20C2×#6718C2211yescharacteristic
21#91776C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic
23C2×C5×#216C2211yescharacteristic
24C5×#887C2211yescharacteristic
25C2×C3×C8×D5C2211yescharacteristic
26C3×#4038C2211yescharacteristic
27#91508C418yescomplemented
28C4×#1204—21no—
29#91434—21no—
30#91434C2211yescharacteristic
31Dic3×D20—21no—
32Dic3×D20C2211yescharacteristic
33D5×C4⋊Dic3—21no—
34D5×C4⋊Dic3C2211yescharacteristic
35#91394—21no—
36#91393—21no—
37#91357—21no—
38#91357C2211yescharacteristic
39#91344C2211yescharacteristic
40#91340C2211yescharacteristic
41#91323—21no—
42C2×#6657C2211yescharacteristic
43C2×#6655C2211yescharacteristic
44C2×#6649C2211yescharacteristic
45C3×C5×#103C2211yescharacteristic
46#91100C2211yescharacteristic
47#91099C2211yescharacteristic
48#91092C2211yescharacteristic
49C5×#816C2211yescharacteristic
50C5×#815C2211yescharacteristic
51C5×#808C2211yescharacteristic
52C3×#3967C2211yescharacteristic
53C3×#3953C2211yescharacteristic
54C3×#3941C2211yescharacteristic
55#90990C2211yescharacteristic
56#90989C2211yescharacteristic
57#90975C2211yescharacteristic
58#90973C2211yescharacteristic
59#90951C2211yescharacteristic
60Dic3×#168C2211yescharacteristic
61#78821—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#65093D311yescharacteristic
73D5×#103—31no—
74#65078—31no—
75#64999—31no—
76#64997—31no—
77C2×C3×C5×Q8C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×Dic6C2311yescharacteristic
80C3×#713—22no—
81C3×#713C2×C414yes—
82C2×C3×D20—21no—
83C2×C3×D20C2311yescharacteristic
84C2×C3×C4×D5—21no—
85C2×C3×C4×D5C2311yescharacteristic
86C2×#1204—21no—
87C2×D5×Dic3—21no—
88C2×D5×Dic3—21no—
89C2×D5×Dic3—21no—
90C2×D5×Dic3—21no—
91D5×Dic6—22no—
92D5×Dic6C2×C414yescomplemented
93C2×C3×C5×C8C2311yescharacteristic
94C3×C5×C4⋊C4C2311yescharacteristic
95#6718C2×C414yescomplemented
96C4⋊Dic15—21no—
97C4⋊Dic15C2311yescharacteristic
98#6712—21no—
99C4×Dic15—21no—
100C4×Dic15—21no—
101C4×Dic15C2311yescharacteristic
102C2×C3⋊#168C2311yescharacteristic
103C5×#216C2×C414yescomplemented
104C5×C4⋊Dic3—21no—
105C5×C4⋊Dic3C2311yescharacteristic
106C5×Dic3⋊C4—21no—
107C4×C5×Dic3—21no—
108C4×C5×Dic3—21no—
109C4×C5×Dic3C2311yescharacteristic
110C2×C5×C3⋊C8C2311yescharacteristic
111C3×#685—21no—
112C3×C4⋊Dic5C2311yescharacteristic
113C3×C4×Dic5—21no—
114C2×C3×#168C2311yescharacteristic
115C3×C8×D5—22no—
116Dic3⋊Dic5—21no—
117#6669—21no—
118#6668—21no—
119#6668D411yescharacteristic
120#6668D411yescharacteristic
121#6665—21no—
122#6665—21no—
123#6665D411yescharacteristic
124#6665D411yescharacteristic
125Dic3×Dic5—21no—
126Dic3×Dic5—21no—
127#6657C2×C414yescomplemented
128#6655C2×C414yescomplemented
129#6649C2×C414yescomplemented
130#5827—51no—
131C2×#951—51no—
132#5516—51no—
133C3×#416—51no—
134C2×#816—51no—
135#5101—51no—
136#4995—51no—
137#4790—51no—
138#4790—51no—
139#4789—51no—
140#4789D511yescharacteristic, complemented
141#4758—51no—
142#4758—51no—
143#4757—51no—
144#4757—51no—
145C2×#713C2×D311yescharacteristic
146C2×Q8×D5—31no—
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—61no—
161#4038C2×D311yescharacteristic
162D5×C4⋊C4—31no—
163D5×C4⋊C4—61no—
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#3953C2×D311yescharacteristic
180#3950—31no—
181#3948—31no—
182#3947—31no—
183C8×Dic5—31no—
184#3942—31no—
185#3941C2×D311yescharacteristic
186#3940—31no—
187#3939—31no—
188C4×#168—31no—
189#2947—151noSylow
190C22×C3×D5—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×Dic15—21no—
199C2×Dic15C2×D411yescharacteristic
200C2×Dic15C2×D411yescharacteristic
201Dic30—21no—
202Dic30C22×C412yes—
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×Dic5C2×D411yescharacteristic
211C3×D20—24no—
212C3×D20—21no—
213C3×D20C22×C412yes—
214C3×C4×D5—24no—
215C3×C4×D5C22×C412yes—
216C3×C4×D5#4112yes—
217#1204—24no—
218D5×Dic3—24no—
219D5×Dic3—81no—
220D5×Dic3—81no—
221D5×Dic3—81no—
222C3×C5×C8—21no—
223C3⋊#168C22×C412yes—
224C3×#168—21no—
225C5×C3⋊C8C22×C412yes—
226C2×C3×#41—51no—
227C22×Dic6—51no—
228C22×C3×C8—51no—
229C3×#117—51no—
230#951—58no—
231Q8×Dic3—51no—
232Q8×Dic3C2×D511yescharacteristic
233C2×#216—51no—
234C2×#216C2×D511yescharacteristic
235D4×Dic3—51no—
236D4×Dic3—51no—
237D4×Dic3—101no—
238D4×Dic3—101no—
239C2×#214—51no—
240C2×#214—51no—
241#926—51no—
242#926—101no—
243C2×C4⋊Dic3—51no—
244C2×C4⋊Dic3—101no—
245C2×#208—51no—
246#887—51no—
247#887—51no—
248#887—51no—
249#887C2×D511yescharacteristic
250#877—101no—
251#877—101no—
252C4×Dic6—101no—
253C4×Dic6—101no—
254C3×#103—51no—
255C3×#103C2×D511yescharacteristic
256C3×#102—51no—
257C3×#102—51no—
258#816—51no—
259#816—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—22no—
273#713C4×D314yes—
274Q8×D5—34no—
275Q8×D5—62no—
276C2×D20—21no—
277C2×D20C22×D311yescharacteristic
278C2×C4×D5—21no—
279C2×C4×D5—61no—
280C2×C4×D5—61no—
281C2×C4×D5—61no—
282C2×C4×D5—61no—
283C2×C4×D5C22×D311yescharacteristic
284C2×Dic10—31no—
285C2×Dic10—61no—
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—21no—
299#685—31no—
300#685—31no—
301#685—61no—
302#685—61no—
303C4⋊Dic5—31no—
304C4⋊Dic5—61no—
305C4⋊Dic5—61no—
306C4⋊Dic5C22×D311yescharacteristic
307#683—31no—
308#683—31no—
309#683—61no—
310#683—61no—
311#683—61no—
312C4×Dic5—21no—
313C4×Dic5—31no—
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—51no—
336C2×#103—151no—
337#405—151no—
338C22×C3×C5C22×D411yescharacteristic
339C2×C3×D5—21no—
340C2×C3×D5—21no—
341C2×C3×D5—22no—
342C2×C3×D5—41no—
343C2×C3×D5—41no—
344C2×C3×D5C4×D412yes—
345C3×C4×C5—22no—
346C3×C4×C5—41no—
347C3×C4×C5C23×C411yescharacteristic
348C3×C4×C5C2×#4111yescharacteristic
349Dic15—22no—
350Dic15—21no—
351Dic15—21no—
352Dic15—41no—
353C3×Dic5—41no—
354C3×Dic5C4×D412yes—
355C5×Dic3—22no—
356C5×Dic3—21no—
357C5×Dic3—21no—
358C5×Dic3—41no—
359C3×#41—54no—
360C3×#41—102no—
361C2×C3×Q8C22×D511yescharacteristic
362C2×C3×D4—51no—
363C2×C3×D4—101no—
364C22×C3×C4—51no—
365C22×C3×C4—101no—
366C22×Dic3—101no—
367C22×Dic3—101no—
368C22×Dic3—101no—
369C22×Dic3—101no—
370C2×Dic6—51no—
371C2×Dic6—54no—
372C2×Dic6—102no—
373C2×Dic6—101no—
374C2×Dic6C22×D511yescharacteristic
375C2×C3×C8—51no—
376C2×C3×C8—102no—
377C2×C3×C8C22×D511yescharacteristic
378C3×C4⋊C4—51no—
379C3×C4⋊C4C22×D511yescharacteristic
380C3×C22⋊C4—101no—
381C3×C42—101no—
382#217—51no—
383#217—51no—
384#217—101no—
385#217—101no—
386#216—54no—
387#216C4×D514yescomplemented
388#214—54no—
389#214—54no—
390C4⋊Dic3—21no—
391C4⋊Dic3—51no—
392C4⋊Dic3—51no—
393C4⋊Dic3—51no—
394C4⋊Dic3—101no—
395C4⋊Dic3—101no—
396C4⋊Dic3C22×D511yescharacteristic
397Dic3⋊C4—21no—
398Dic3⋊C4—101no—
399Dic3⋊C4—101no—
400Dic3⋊C4—101no—
401C4×Dic3—21no—
402C4×Dic3—21no—
403C4×Dic3—51no—
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—21no—
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—31no—
427C2×Dic5—31no—
428C2×Dic5—61no—
429C2×Dic5—61no—
430C2×Dic5D3×D411yescharacteristic
431D20—24no—
432D20—21no—
433D20C2×C4×D312yes—
434C4×D5—24no—
435C4×D5—64no—
436C4×D5—241no—
437C4×D5—241no—
438C4×D5—241no—
439C4×D5C2×C4×D312yes—
440C4×D5#23712yes—
441Dic10—32no—
442Dic10—61no—
443Dic10—64no—
444C5×C8—21no—
445C5×C8—32no—
446#168—21no—
447#168—32no—
448C2×#41—51no—
449C22×Q8—151no—
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—51no—
470#117—151no—
471#117—301no—
472#117—301no—
473#117—301no—
474C2×C4⋊C4—151no—
475C2×C4⋊C4—301no—
476#107—151no—
477#107—151no—
478#106—31no—
479#106—151no—
480#103—31no—
481#103—51no—
482#103—151no—
483#103—151no—
484#103—151no—
485#103D3×D511yescharacteristic
486#102—51no—
487#102—51no—
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
495C3×D5—22no—
496C3×D5—42no—
497C23×C3—51no—
498C23×C3—101no—
499C3×Q8—21no—
500C3×Q8C2×C4×D512yes—
501C3×D4—52no—
502C3×D4—104no—
503C3×D4—101no—
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×C4C23×D511yescharacteristic
512C2×Dic3—21no—
513C2×Dic3—21no—
514C2×Dic3—51no—
515C2×Dic3—51no—
516C2×Dic3—104no—
517C2×Dic3—101no—
518C2×Dic3—101no—
519C2×Dic3—401no—
520C2×Dic3—401no—
521C2×Dic3—401no—
522C2×Dic3D4×D511yescharacteristic
523C2×Dic3D4×D511yescharacteristic
524Dic6—21no—
525Dic6—52no—
526Dic6—104no—
527Dic6—101no—
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—22no—
537C2×D5—41no—
538C2×D5—41no—
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—41no—
549Dic5—62no—
550Dic5—61no—
551Dic5—61no—
552Dic5—121no—
553Dic5#67⋊C412yes—
554#41—54no—
555#41—102no—
556C2×Q8—31no—
557C2×Q8—154no—
558C2×Q8—151no—
559C2×Q8—301no—
560C2×Q8—302no—
561C2×Q8C2×D3×D511yescharacteristic
562C2×D4—51no—
563C2×D4—101no—
564C22×C4—51no—
565C22×C4—101no—
566C22×C4—301no—
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—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—101no—
594C22⋊C4—151no—
595C22⋊C4—151no—
596C22⋊C4—301no—
597C22⋊C4—301no—
598C42—31no—
599C42—61no—
600C42—61no—
601C42—101no—
602C42—151no—
603C42—301no—
604C42—301no—
605C42—301no—
606C42—301no—
607C3×C5#294711yescharacteristic, complemented, Hall
608C22×C3—52no—
609C22×C3—101no—
610C22×C3—101no—
611C22×C3—102no—
612C22×C3—201no—
613C22×C3—201no—
614C22×C3C2×D4×D511yescharacteristic
615C3×C4—22no—
616C3×C4—41no—
617C3×C4—52no—
618C3×C4—201no—
619C3×C4C22×C4×D511yescharacteristic
620C3×C4D5×#4111yescharacteristic
621Dic3—21no—
622Dic3—21no—
623Dic3—22no—
624Dic3—41no—
625Dic3—101no—
626Dic3—101no—
627Dic3—102no—
628Dic3—201no—
629C2×C5C2×#67⋊C411yescharacteristic
630C2×C5#577011yescharacteristic
631C2×C5#577111yescharacteristic
632D5—22no—
633D5—42no—
634C23—51no—
635C23—101no—
636Q8—21no—
637Q8—32no—
638Q8—61no—
639Q8—152no—
640Q8—304no—
641Q8—301no—
642Q8C4×D3×D512yes—
643D4—52no—
644D4—104no—
645D4—101no—
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—151no—
658C2×C4—151no—
659C2×C4—304no—
660C2×C4—301no—
661C2×C4—301no—
662C2×C4—1201no—
663C2×C4—1201no—
664C2×C4—1201no—
665C2×C4C22×D3×D511yescharacteristic
666C8—21no—
667C8—32no—
668C8—101no—
669C8—152no—
670C2×C3—102no—
671C2×C3—202no—
672C2×C3C4×D4×D511yescharacteristic
673C2×C3#6611211yescharacteristic
674C2×C3#6611311yescharacteristic
675C5#7882111yescharacteristic, complemented, Sylow
676C22—52no—
677C22—101no—
678C22—101no—
679C22—102no—
680C22—201no—
681C22—201no—
682C22D3×D4×D511yescharacteristic
683C4—22no—
684C4—41no—
685C4—52no—
686C4—61no—
687C4—61no—
688C4—62no—
689C4—121no—
690C4—201no—
691C4—301no—
692C4—301no—
693C4—302no—
694C4—601no—
695C4C2×C4×D3×D511yescharacteristic
696C4D5×#23711yescharacteristic
697C3#1061156111yescharacteristic, complemented, Sylow
698C2—102no—
699C2—202no—
700C2D5×#67⋊C411yescharacteristic
701C2#1175409411yescharacteristic
702C2#1175411411yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#103C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×#713C22
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
3. #11753397C2semidirect
4. #11750890C2semidirect
5. C5×#4789C2semidirect
7. #11749265C2semidirect
8. #11749257C2semidirect
9. #11747742C2semidirect
10. #11747736C2semidirect
11. #11747646C2semidirect
12. D5×#816C2semidirect
13. #11747227C2semidirect
14. #11747221C2semidirect
15. #11747189C2semidirect
27. #91508C4semidirect
92. D5×Dic6C2×C4semidirect
95. #6718C2×C4semidirect
103. C5×#216C2×C4semidirect
127. #6657C2×C4semidirect
128. #6655C2×C4semidirect
129. #6649C2×C4semidirect
140. #4789D5semidirect
387. #216C4×D5semidirect
607. C3×C5#2947semidirect
675. C5#78821semidirect
697. C3#10611561semidirect

Maximal subgroups

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

subgroupindex
#117552172
C2×#915082
#117533972
#117508902
C5×#47892
C3×#650932
#117492652
#117492572
#117477422
#117477362
#117476462
D5×#8162
#117472272
#117472212
#117471892
#106115613
#788215