Finite Group Databasebeta

← #14435489

Subgroups — #14435489

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
2#11752685C211yesmaximal, characteristic
3#11751129C211yesmaximal, characteristic, complemented
4C5×#5022C211yesmaximal, characteristic, complemented
5#11749291C211yesmaximal, characteristic, complemented
6#11749268C211yesmaximal, characteristic
7#11749250C211yesmaximal, characteristic, complemented
8#11749225C211yesmaximal, characteristic, complemented
9#11747269C211yesmaximal, characteristic, complemented
10#11747224C211yesmaximal, characteristic, complemented
11#11747169C211yesmaximal, characteristic, complemented
12#11747165C211yesmaximal, characteristic
13#11747065C211yesmaximal, characteristic, complemented
14#11746919C211yesmaximal, characteristic, complemented
15#11746871C211yesmaximal, characteristic, complemented
16#10612938—31nomaximal, Hall
17C2×C3×Q8×D5C2211yescharacteristic
18C3×C4×C5×Q8C2211yescharacteristic
19C2×#6718C2211yescharacteristic
20C2×#6717C2211yescharacteristic
21#91764C2211yescharacteristic
22C5×#870C2211yescharacteristic
23C3×Q8×Dic5C2211yescharacteristic
24C3×D5×C4⋊C4—21no—
25C3×D5×C4⋊C4C2211yescharacteristic
26C3×#4033—21no—
27C3×#4033C2211yescharacteristic
28C3×C42×D5—21no—
29C3×C42×D5C2211yescharacteristic
30C3×C4×Dic10—21no—
31C3×C4×Dic10C2211yescharacteristic
32#91450C2211yescharacteristic
33#91444—21no—
34#91418C2211yescharacteristic
35#91402—21no—
36#91387—21no—
37#91360C2211yescharacteristic
38#91348—21no—
39#91333C2211yescharacteristic
40C2×#6662C2211yescharacteristic
41C2×#6658C2211yescharacteristic
42#91094C2211yescharacteristic
43#91093C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#835C2211yescharacteristic
47C5×#808C2211yescharacteristic
48C5×#807C2211yescharacteristic
49C5×C4⋊(C3⋊C8)C2211yescharacteristic
50#90989C2211yescharacteristic
51#90986C2211yescharacteristic
52#90974C2211yescharacteristic
53#90970C2211yescharacteristic
54#90970C2211yescharacteristic
55#90968C2211yescharacteristic
56#90955C2211yescharacteristic
57#90955C2211yescharacteristic
58#90952C2211yescharacteristic
59#90952C2211yescharacteristic
60#82445—51nomaximal, Hall
61#66025—31no—
62C4×Q8×D5D311yescharacteristic, complemented
63C5×#479—31no—
64#65352—31no—
65#65317—31no—
66#65178—31no—
67#65173—31no—
68#65152—31no—
69#65142—31no—
70#65134—31no—
71#65124—31no—
72#65106—31no—
73#65097—31no—
74#65095—31no—
75#65078—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×D60C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C3×Q8×D5—22no—
80C3×Q8×D5—22no—
81C2×C3×C4×D5—21no—
82C2×C3×C4×D5—21no—
83C2×C3×C4×D5D411yescharacteristic
84C2×C3×C4×D5D411yescharacteristic
85C2×C3×C4×D5C2311yescharacteristic
86C2×C3×Dic10—21no—
87C2×C3×Dic10C2311yescharacteristic
88C2×#1202—21no—
89C2×#1200—21no—
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4C2311yescharacteristic
92C3×C42×C5—21no—
93C3×C42×C5C2311yescharacteristic
94#6718—22no—
95#6717—22no—
96#6714—21no—
97#6714—21no—
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C5×C4⋊Dic3C2311yescharacteristic
101C5×C4⋊Dic3C2311yescharacteristic
102C5×Dic3⋊C4—21no—
103C5×Dic3⋊C4—21no—
104C2×C5×C3⋊C8C2311yescharacteristic
105C2×C5×C3⋊C8C2311yescharacteristic
106C3×C4⋊Dic5—21no—
107C3×C4⋊Dic5C2311yescharacteristic
108C3×#683—21no—
109C3×#683—21no—
110C3×#683—21no—
111C3×C4×Dic5—21no—
112C3×C4×Dic5—21no—
113C3×C4×Dic5—21no—
114C3×C4×Dic5D411yescharacteristic
115C3×C4×Dic5D411yescharacteristic
116C3×C4×Dic5C2311yescharacteristic
117Dic3⋊Dic5—21no—
118#6669—21no—
119#6667—21no—
120#6667—21no—
121#6665—21no—
122Dic3×Dic5—21no—
123#6662—22no—
124#6658—22no—
125C2×C3×C4×Q8—51no—
126#5479—51no—
127#5228—51no—
128#5227—51no—
129#5030—51no—
130#5030—51no—
131#5028—51no—
132#5028—51no—
133#5026—51no—
134#5026—51no—
135#5022—51no—
136#5022D511yescharacteristic, complemented
137#4970—51no—
138#4968—51no—
139#4926—51no—
140C2×Q8×D5C2×D311yescharacteristic
141C5×#125—31no—
142C4×C5×Q8C2×D311yescharacteristic
143Q8×Dic5C2×D311yescharacteristic
144C2×#689—31no—
145C2×#688—31no—
146C2×Dic20—31no—
147C2×#677—31no—
148#4044—61no—
149#4043—31no—
150#4041—31no—
151#4040—61no—
152#4039—31no—
153#4039—61no—
154#4038—61no—
155D5×C4⋊C4—21no—
156D5×C4⋊C4C2×D311yescharacteristic
157#4033—21no—
158#4033—31no—
159#4033C2×D311yescharacteristic
160#4021—31no—
161C42×D5—21no—
162C42×D5C2×D311yescharacteristic
163C4×Dic10—21no—
164C4×Dic10C2×D311yescharacteristic
165C5×#107—31no—
166C5×#106—31no—
167C5×C4⋊C8—31no—
168C5×#103—31no—
169C5×#103—31no—
170#3953—31no—
171#3952—31no—
172#3952—31no—
173#3948—31no—
174#3947—31no—
175#3947—31no—
176#3942—31no—
177#3942—31no—
178#3942—31no—
179#3941—31no—
180#3940—31no—
181#3939—31no—
182C4⋊#168—31no—
183#3117—151noSylow
184C22×D15—21no—
185C22×C3×D5C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8#4112yes—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—21no—
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15—21no—
194D60—21no—
195D60—21no—
196Dic30—21no—
197Dic30—21no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C3×Dic5—21no—
201C2×C3×Dic5—21no—
202C2×C3×Dic5C2×D411yescharacteristic
203C2×C3×Dic5C2×D411yescharacteristic
204C2×C3×Dic5C2×D411yescharacteristic
205C3×C4×D5—24no—
206C3×C4×D5—22no—
207C3×C4×D5—21no—
208C3×C4×D5—21no—
209C3×C4×D5—41no—
210C3×C4×D5—42no—
211C3×Dic10—24no—
212C3×Dic10—21no—
213C3×Dic10#4112yes—
214#1202—42no—
215#1200—42no—
216C3⋊#168—21no—
217C3⋊#168—21no—
218C5×C3⋊C8—21no—
219C5×C3⋊C8—21no—
220C22×C3×Q8—51no—
221C3×C4×Q8—51no—
222C3×C4×Q8—51no—
223C3×C4×Q8—51no—
224C3×C4×Q8—101no—
225C3×C4×Q8—101no—
226C3×C4×Q8C2×D511yescharacteristic
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—101no—
229C2×C3×C42—51no—
230C2×C3×C42—101no—
231C2×#216—51no—
232C2×#216—51no—
233C2×#215—51no—
234C2×#215—51no—
235#930—51no—
236#929—101no—
237C4×#67—101no—
238#924—51no—
239#876—101no—
240#875—51no—
241C4×D12—51no—
242#872—101no—
243#870C2×D511yescharacteristic
244C4×Dic6—51no—
245#835—51no—
246#835—51no—
247#835C2×D511yescharacteristic
248#835C2×D511yescharacteristic
249#830—51no—
250#830—51no—
251#810—51no—
252#810—51no—
253#809—51no—
254#809—51no—
255#808—51no—
256#808C2×D511yescharacteristic
257#807—51no—
258#807C2×D511yescharacteristic
259C4⋊(C3⋊C8)—51no—
260C4⋊(C3⋊C8)C2×D511yescharacteristic
261#803—51no—
262#803—51no—
263C2×C5×Q8C22×D311yescharacteristic
264Q8×D5—22no—
265Q8×D5—22no—
266C2×D20—31no—
267C2×D20—61no—
268C2×C4×D5—21no—
269C2×C4×D5—21no—
270C2×C4×D5—61no—
271C2×C4×D5#6711yescharacteristic
272C2×C4×D5#6711yescharacteristic
273C2×C4×D5C22×D311yescharacteristic
274C2×Dic10—21no—
275C2×Dic10—31no—
276C2×Dic10C22×D311yescharacteristic
277C2×C5×C8—31no—
278C2×C5×C8—31no—
279C5×C4⋊C4—21no—
280C5×C4⋊C4—31no—
281C5×C4⋊C4—31no—
282C5×C4⋊C4—61no—
283C5×C4⋊C4—61no—
284C5×C4⋊C4C22×D311yescharacteristic
285C42×C5—21no—
286C42×C5C22×D311yescharacteristic
287#689—62no—
288#688—62no—
289#685—61no—
290#685—61no—
291#685—61no—
292#685—61no—
293#685—61no—
294C4⋊Dic5—21no—
295C4⋊Dic5—61no—
296C4⋊Dic5C22×D311yescharacteristic
297#683—21no—
298#683—21no—
299#683—21no—
300#683—61no—
301C4×Dic5—21no—
302C4×Dic5—21no—
303C4×Dic5—21no—
304C4×Dic5—61no—
305C4×Dic5#6711yescharacteristic
306C4×Dic5#6711yescharacteristic
307C4×Dic5C22×D311yescharacteristic
308C2×#168—31no—
309C2×#168—31no—
310Dic20—62no—
311#677—62no—
312#529—151no—
313C2×C4×Q8—51no—
314#484—151no—
315#481—151no—
316#479—31no—
317#479—151no—
318#464—151no—
319#464—151no—
320#451—151no—
321#448—151no—
322#441—151no—
323#441—151no—
324#440—151no—
325#440—151no—
326#432—151no—
327C22×C3×C5C22×D411yescharacteristic
328C2×D15—41no—
329C2×D15—41no—
330C2×D15—41no—
331C2×C3×D5—21no—
332C2×C3×D5—21no—
333C2×C3×D5#13712yes—
334C3×C4×C5—22no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—41no—
338C3×C4×C5C2×#4111yescharacteristic
339C3×C4×C5C2×#4111yescharacteristic
340Dic15—41no—
341C3×Dic5—21no—
342C3×Dic5—22no—
343C3×Dic5—21no—
344C3×Dic5—21no—
345C3×Dic5—41no—
346C5×Dic3—41no—
347C5×Dic3—41no—
348C2×C3×Q8—51no—
349C2×C3×Q8—101no—
350C2×C3×Q8—102no—
351C2×C3×Q8—102no—
352C2×C3×Q8C22×D511yescharacteristic
353C22×C3×C4—51no—
354C22×C3×C4—51no—
355C22×C3×C4—51no—
356C22×C3×C4—101no—
357C22×C3×C4—101no—
358C2×#67—101no—
359C2×D12—51no—
360C2×C4×D3—101no—
361C2×Dic6—51no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—51no—
364C3×C4⋊C4—101no—
365C3×C4⋊C4—101no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4—101no—
368C3×C4⋊C4C22×D511yescharacteristic
369C3×C42—21no—
370C3×C42—51no—
371C3×C42—51no—
372C3×C42—51no—
373C3×C42—101no—
374C3×C42—101no—
375C3×C42—101no—
376C3×C42C22×D511yescharacteristic
377#217—101no—
378#216—102no—
379#216—102no—
380#215—102no—
381#215—102no—
382(C2×D3)⋊C4—101no—
383(C2×D3)⋊C4—101no—
384(C2×D3)⋊C4—101no—
385(C2×D3)⋊C4—101no—
386C4⋊Dic3C22×D511yescharacteristic
387C4⋊Dic3C22×D511yescharacteristic
388Dic3⋊C4—21no—
389Dic3⋊C4—21no—
390Dic3⋊C4—101no—
391Dic3⋊C4—101no—
392C4×Dic3—101no—
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395C2×C3⋊C8C22×D511yescharacteristic
396C2×C3⋊C8C22×D511yescharacteristic
397C22×D5—61no—
398C22×D5C2×#6711yescharacteristic
399C5×Q8—21no—
400C5×Q8#23512yes—
401C2×C4×C5—21no—
402C2×C4×C5—21no—
403C2×C4×C5—61no—
404C2×C4×C5—61no—
405C2×C4×C5C2×#6711yescharacteristic
406C2×C4×C5C2×#6711yescharacteristic
407C2×C4×C5C23×D311yescharacteristic
408C2×Dic5—21no—
409C2×Dic5—21no—
410C2×Dic5—61no—
411C2×Dic5C2×#6711yescharacteristic
412C2×Dic5C2×#6711yescharacteristic
413C2×Dic5C2×#6711yescharacteristic
414D20—61no—
415D20—61no—
416D20—122no—
417C4×D5—24no—
418C4×D5—22no—
419C4×D5—21no—
420C4×D5—21no—
421C4×D5—41no—
422C4×D5—42no—
423C4×D5—122no—
424Dic10—24no—
425Dic10—21no—
426Dic10—61no—
427Dic10—61no—
428Dic10#23512yes—
429C5×C8—61no—
430C5×C8—61no—
431#168—61no—
432#168—61no—
433C22×Q8—51no—
434C2×Q16—151no—
435C2×Q16—151no—
436C2×SD16—151no—
437C2×SD16—151no—
438#126—301no—
439#125—31no—
440#124—151no—
441#123—301no—
442C22⋊Q8—151no—
443#121—151no—
444C4×Q8—51no—
445C4×Q8—51no—
446C4×Q8—51no—
447C4×Q8—101no—
448C4×Q8—101no—
449C4×Q8—151no—
450C4×Q8D3×D511yescharacteristic
451C4×D4—151no—
452C4×D4—301no—
453#117—301no—
454C2×C4⋊C4—51no—
455C2×C4⋊C4—101no—
456C2×C42—51no—
457C2×C42—101no—
458#107—31no—
459#107—151no—
460#106—31no—
461#106—151no—
462C4⋊C8—31no—
463C4⋊C8—151no—
464#103—31no—
465#103—31no—
466#103—151no—
467#103—151no—
468#103—151no—
469#103—151no—
470#102—151no—
471#102—151no—
472C22⋊C8—151no—
473C22⋊C8—151no—
474#97—151no—
475#97—151no—
476C2×C3×C5#52511yescharacteristic
477C2×C3×C5C2×#13711yescharacteristic
478C2×C3×C5#57511yescharacteristic
479D15—81no—
480C3×D5—22no—
481C23×C3—51no—
482C22×D3—101no—
483C3×Q8—21no—
484C3×Q8—52no—
485C3×Q8—104no—
486C3×Q8—101no—
487C3×Q8#71312yes—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—51no—
491C2×C3×C4—51no—
492C2×C3×C4—51no—
493C2×C3×C4—102no—
494C2×C3×C4—104no—
495C2×C3×C4—101no—
496C2×C3×C4—101no—
497C2×C3×C4—101no—
498C2×C3×C4—101no—
499C2×C3×C4—201no—
500C2×C3×C4—202no—
501C2×C3×C4D4×D511yescharacteristic
502C2×C3×C4D4×D511yescharacteristic
503C2×C3×C4C23×D511yescharacteristic
504#67—202no—
505C2×Dic3—21no—
506C2×Dic3—21no—
507C2×Dic3—101no—
508D12—101no—
509D12—101no—
510C4×D3—202no—
511Dic6—101no—
512Dic6—101no—
513C3⋊C8—21no—
514C3⋊C8—21no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5C22×#6711yescharacteristic
518C2×D5—21no—
519C2×D5—21no—
520C2×D5—121no—
521C2×D5—121no—
522C2×D5—121no—
523C2×D5#94212yes—
524C4×C5—22no—
525C4×C5—21no—
526C4×C5—21no—
527C4×C5—41no—
528C4×C5—121no—
529C4×C5—121no—
530C4×C5C2×#23511yescharacteristic
531C4×C5C2×#23511yescharacteristic
532Dic5—21no—
533Dic5—22no—
534Dic5—21no—
535Dic5—21no—
536Dic5—41no—
537Dic5—121no—
538C2×Q8—51no—
539C2×Q8—101no—
540C2×Q8—102no—
541C2×Q8—102no—
542C2×Q8—151no—
543C2×Q8C2×D3×D511yescharacteristic
544C2×D4—151no—
545C2×D4—301no—
546C22×C4—51no—
547C22×C4—51no—
548C22×C4—51no—
549C22×C4—101no—
550C22×C4—101no—
551C22×C4—301no—
552Q16—302no—
553Q16—302no—
554SD16—302no—
555SD16—302no—
556C2×C8—31no—
557C2×C8—31no—
558C2×C8—151no—
559C2×C8—151no—
560C4⋊C4—21no—
561C4⋊C4—31no—
562C4⋊C4—31no—
563C4⋊C4—51no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—101no—
567C4⋊C4—101no—
568C4⋊C4—101no—
569C4⋊C4—101no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4C2×D3×D511yescharacteristic
573C22⋊C4—301no—
574C22⋊C4—301no—
575C22⋊C4—301no—
576C22⋊C4—301no—
577C22⋊C4—301no—
578C42—21no—
579C42—51no—
580C42—51no—
581C42—51no—
582C42—101no—
583C42—101no—
584C42—101no—
585C42—301no—
586C42C2×D3×D511yescharacteristic
587C3×C5#311711yescharacteristic, complemented, Hall
588C22×C3—52no—
589C22×C3—101no—
590C22×C3—101no—
591C22×C3C2×D4×D511yescharacteristic
592C2×D3—201no—
593C2×D3—201no—
594C2×D3—201no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—22no—
598C3×C4—41no—
599C3×C4—101no—
600C3×C4—101no—
601C3×C4—101no—
602C3×C4—102no—
603C3×C4—201no—
604C3×C4C2×#71311yescharacteristic
605C3×C4D5×#4111yescharacteristic
606Dic3—41no—
607Dic3—41no—
608Dic3—201no—
609C2×C5#579111yescharacteristic
610C2×C5C2×#94211yescharacteristic
611C2×C5#582211yescharacteristic
612D5—22no—
613D5—241no—
614C23—51no—
615C23—301no—
616Q8—21no—
617Q8—52no—
618Q8—104no—
619Q8—101no—
620Q8—301no—
621Q8—301no—
622Q8#677312yes—
623D4—301no—
624D4—301no—
625D4—602no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—51no—
629C2×C4—51no—
630C2×C4—51no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—102no—
634C2×C4—104no—
635C2×C4—101no—
636C2×C4—101no—
637C2×C4—101no—
638C2×C4—101no—
639C2×C4—201no—
640C2×C4—202no—
641C2×C4—301no—
642C2×C4—602no—
643C2×C4D5×#6711yescharacteristic
644C2×C4D5×#6711yescharacteristic
645C2×C4C22×D3×D511yescharacteristic
646C8—61no—
647C8—61no—
648C8—301no—
649C8—301no—
650C2×C3—102no—
651C2×C3#6596111yescharacteristic
652C2×C3#6610211yescharacteristic
653C2×C3D5×#13711yescharacteristic
654D3—401no—
655C5#8244511yescharacteristic, complemented, Sylow
656C22—52no—
657C22—101no—
658C22—101no—
659C22—601no—
660C22—601no—
661C22—601no—
662C22C2×D5×#6711yescharacteristic
663C4—22no—
664C4—21no—
665C4—21no—
666C4—41no—
667C4—101no—
668C4—102no—
669C4—101no—
670C4—101no—
671C4—121no—
672C4—121no—
673C4—201no—
674C4—601no—
675C4C2×#677311yescharacteristic
676C4D5×#23511yescharacteristic
677C3#1061293811yescharacteristic, complemented, Sylow
678C2—102no—
679C2—1201no—
680C2#1175452711yescharacteristic
681C2D5×#94211yescharacteristic
682C2#1175531511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radical#91450C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C3×C4×Q8×D5C2semidirect
3. #11751129C2semidirect
4. C5×#5022C2semidirect
5. #11749291C2semidirect
7. #11749250C2semidirect
8. #11749225C2semidirect
9. #11747269C2semidirect
10. #11747224C2semidirect
11. #11747169C2semidirect
13. #11747065C2semidirect
14. #11746919C2semidirect
15. #11746871C2semidirect
62. C4×Q8×D5D3semidirect
136. #5022D5semidirect
587. C3×C5#3117semidirect
655. C5#82445semidirect
677. C3#10612938semidirect

Maximal subgroups

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

subgroupindex
C3×C4×Q8×D52
#117526852
#117511292
C5×#50222
#117492912
#117492682
#117492502
#117492252
#117472692
#117472242
#117471692
#117471652
#117470652
#117469192
#117468712
#106129383
#824455