Finite Group Databasebeta

← #14435496

Subgroups — #14435496

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
1C5×#5557C211yesmaximal, characteristic
2C4×D3×Dic10C211yesmaximal, characteristic, complemented
3#11751119C211yesmaximal, characteristic, complemented
4C3×#65307C211yesmaximal, characteristic, complemented
5#11749155C211yesmaximal, characteristic
6#11749012C211yesmaximal, characteristic, complemented
7#11749006C211yesmaximal, characteristic, complemented
8#11748956C211yesmaximal, characteristic
9#11747495C211yesmaximal, characteristic, complemented
10#11747296C211yesmaximal, characteristic, complemented
11#11747290C211yesmaximal, characteristic, complemented
12#11747198C211yesmaximal, characteristic, complemented
13#11747093C211yesmaximal, characteristic, complemented
14#11747089C211yesmaximal, characteristic, complemented
15#11746878C211yesmaximal, characteristic, complemented
16#10614884—31nomaximal, Hall
17C2×D3×Dic10C2211yescharacteristic
18C3×C4×C5×D4C2211yescharacteristic
19C2×#6716C2211yescharacteristic
20C4×Dic30C2211yescharacteristic
21C5×#938C2211yescharacteristic
22C5×#936C2211yescharacteristic
23C4×C5×#67—21no—
24C5×#926—21no—
25C5×#897C2211yescharacteristic
26C5×#890C2211yescharacteristic
27C5×#883—21no—
28C5×#879—21no—
29C42×C5×D3C2211yescharacteristic
30C4×C5×Dic6C2211yescharacteristic
31C2×C3×#687C2211yescharacteristic
32C3×C4×Dic10C2211yescharacteristic
33C4×#1204—21no—
34D3×C4⋊Dic5C2211yescharacteristic
35D3×#683—21no—
36C4×D3×Dic5—21no—
37#91340C2211yescharacteristic
38Dic3×Dic10C2211yescharacteristic
39#91324—21no—
40C2×#6663C2211yescharacteristic
41C2×#6661C2211yescharacteristic
42#91116C2211yescharacteristic
43#91094C2211yescharacteristic
44#91091C2211yescharacteristic
45#91087C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×#3942C2211yescharacteristic
48C3×#3939C2211yescharacteristic
49C3×#3935C2211yescharacteristic
50#90986C2211yescharacteristic
51#90985C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90975C2211yescharacteristic
55#90973C2211yescharacteristic
56#90972C2211yescharacteristic
57#90970C2211yescharacteristic
58(C2×D3)⋊#168C2211yescharacteristic
59(C2×D3)⋊#168C2211yescharacteristic
60#79784—51nomaximal, Hall
61C5×#529—31no—
62C2×C4×Dic10—31no—
63#65352—31no—
64#65352—31no—
65#65343—31no—
66#65343—31no—
67#65339—31no—
68#65333—31no—
69#65329—31no—
70#65323—31no—
71#65319—31no—
72#65319—31no—
73#65307—31no—
74#65307D311yescharacteristic, complemented
75#65215—31no—
76C2×C3×C5×D4C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C2×Dic30C2311yescharacteristic
79C2×C5×#67—21no—
80C2×C4×C5×D3D411yescharacteristic
81C2×C4×C5×D3D411yescharacteristic
82C2×C4×C5×D3C2311yescharacteristic
83C2×C5×Dic6C2311yescharacteristic
84C2×C3×Dic10C2311yescharacteristic
85C2×#1204—21no—
86C2×D3×Dic5—21no—
87C2×D3×Dic5—21no—
88D3×Dic10—22no—
89D3×Dic10—22no—
90C3×C5×C4⋊C4C2311yescharacteristic
91C3×C5×C22⋊C4—21no—
92C3×C42×C5C2311yescharacteristic
93#6716—22no—
94C4⋊Dic15C2311yescharacteristic
95#6712—21no—
96C4×Dic15—21no—
97C2×C3⋊#168C2311yescharacteristic
98C2×C3⋊#168C2311yescharacteristic
99C5×#217—21no—
100C5×#217—21no—
101C5×#217—21no—
102C5×(C2×D3)⋊C4—21no—
103C5×C4⋊Dic3—21no—
104C5×C4⋊Dic3—21no—
105C5×C4⋊Dic3C2311yescharacteristic
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4—21no—
108C4×C5×Dic3—21no—
109C4×C5×Dic3D411yescharacteristic
110C4×C5×Dic3D411yescharacteristic
111C4×C5×Dic3C2311yescharacteristic
112C3×#687—22no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×#683—21no—
115C3×C4×Dic5—21no—
116C2×C3×#168C2311yescharacteristic
117C2×C3×#168C2311yescharacteristic
118Dic3⋊Dic5—21no—
119#6669—21no—
120#6668—21no—
121Dic3×Dic5—21no—
122Dic3×Dic5—21no—
123#6663—22no—
124#6661—22no—
125C4×D3×Q8—51no—
126#5557D511yescharacteristic
127C3×#440—51no—
128#5170—51no—
129#5166—51no—
130#5030—51no—
131#5018—51no—
132#4884—51no—
133#4877—51no—
134#4809—51no—
135#4799—51no—
136#4777—51no—
137#4767—51no—
138#4716—51no—
139#4705—51no—
140C22×Dic10—31no—
141C5×#126—61no—
142C5×#125—31no—
143C5×#124—31no—
144C5×#123—61no—
145C5×C22⋊Q8—31no—
146C5×#121—31no—
147C4×C5×Q8—31no—
148C4×C5×D4—61no—
149C4×C5×D4C2×D311yescharacteristic
150C5×#117—61no—
151C2×C42×C5—31no—
152C2×#689—31no—
153C2×#689—31no—
154C2×#687—31no—
155C2×#687C2×D311yescharacteristic
156C2×C4⋊Dic5—31no—
157C2×#683—61no—
158C2×C4×Dic5—61no—
159C4×Dic10—31no—
160C4×Dic10—31no—
161C4×Dic10—31no—
162C4×Dic10—61no—
163C4×Dic10—61no—
164C4×Dic10C2×D311yescharacteristic
165#3967—31no—
166#3967—31no—
167#3964—31no—
168#3964C2×D311yescharacteristic
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3942—31no—
172#3942—31no—
173#3942—31no—
174#3942C2×D311yescharacteristic
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939C2×D311yescharacteristic
179C4⋊#168—31no—
180C4⋊#168—31no—
181#3935—31no—
182#3935C2×D311yescharacteristic
183#3117—151noSylow
184C23×C3×C5—21no—
185C22×C5×D3C2×D411yescharacteristic
186C3×C5×D4—21no—
187C3×C5×D4—21no—
188C2×C3×C4×C5—21no—
189C2×C3×C4×C5—42no—
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2411yescharacteristic
193C2×Dic15—21no—
194C2×Dic15—21no—
195Dic30—21no—
196Dic30#4112yes—
197C5×#67—42no—
198C2×C5×Dic3—21no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3C2×D411yescharacteristic
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
203C4×C5×D3—22no—
204C4×C5×D3—21no—
205C4×C5×D3—21no—
206C4×C5×D3—41no—
207C5×Dic6—21no—
208C5×Dic6—21no—
209C2×C3×Dic5—21no—
210C2×C3×Dic5—21no—
211C3×Dic10—21no—
212C3×Dic10#4112yes—
213#1204—24no—
214D3×Dic5—24no—
215D3×Dic5—42no—
216C3⋊#168—21no—
217C3⋊#168—21no—
218C3×#168—21no—
219C3×#168—21no—
220C2×D3×Q8—51no—
221C2×C3×SD16—51no—
222C3×C4×Q8—51no—
223C3×C4×D4C2×D511yescharacteristic
224Q8×Dic3—51no—
225C2×#216—51no—
226#938C2×D511yescharacteristic
227#936C2×D511yescharacteristic
228C2×#214—51no—
229C4×#67—21no—
230#926—21no—
231C2×Dic12—51no—
232#897C2×D511yescharacteristic
233D3×C4⋊C4—51no—
234D3×C4⋊C4—101no—
235#890C2×D511yescharacteristic
236#887—51no—
237#887—101no—
238#883—21no—
239#879—21no—
240C42×D3—101no—
241C42×D3C2×D511yescharacteristic
242C4×Dic6—51no—
243C4×Dic6—101no—
244C4×Dic6C2×D511yescharacteristic
245C3×#107—51no—
246C3×#103—51no—
247C3×#102—51no—
248C3×#97—51no—
249#835—51no—
250#832—51no—
251(C2×D3)⋊C8—51no—
252(C2×D3)⋊C8—51no—
253#817—51no—
254#816—51no—
255#816—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258#810—51no—
259#810—51no—
260#808—51no—
261#807—51no—
262#803—51no—
263C2×C5×Q8—31no—
264C2×C5×D4—61no—
265C2×C5×D4C22×D311yescharacteristic
266C22×C4×C5—21no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—31no—
270C22×Dic5—61no—
271C22×Dic5—61no—
272C2×Dic10—31no—
273C2×Dic10—62no—
274C2×Dic10—61no—
275C2×Dic10—62no—
276C2×Dic10C22×D311yescharacteristic
277C5×C4⋊C4—31no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4—61no—
281C5×C4⋊C4—61no—
282C5×C4⋊C4C22×D311yescharacteristic
283C5×C22⋊C4—21no—
284C5×C22⋊C4—61no—
285C5×C22⋊C4—61no—
286C5×C22⋊C4—61no—
287C5×C22⋊C4—61no—
288C42×C5—31no—
289C42×C5—31no—
290C42×C5—31no—
291C42×C5—61no—
292C42×C5C22×D311yescharacteristic
293#689—62no—
294#689—62no—
295#687—22no—
296#687—62no—
297C4⋊Dic5—31no—
298C4⋊Dic5—61no—
299C4⋊Dic5C22×D311yescharacteristic
300#683—21no—
301#683—61no—
302#683—61no—
303#683—61no—
304C4×Dic5—21no—
305C4×Dic5—61no—
306C4×Dic5—61no—
307C4×Dic5—61no—
308C2×#168—31no—
309C2×#168—31no—
310C2×#168C22×D311yescharacteristic
311C2×#168C22×D311yescharacteristic
312#529—31no—
313C2×C4×Q8—151no—
314#484—151no—
315#481—151no—
316#479—151no—
317#479—151no—
318#464—151no—
319#464—151no—
320#451—151no—
321#448—151no—
322#441—151no—
323#441—151no—
324#440—51no—
325#440—151no—
326#432—151no—
327C22×C3×C5—41no—
328C22×C3×C5—41no—
329C22×C3×C5—41no—
330C22×C3×C5C22×D411yescharacteristic
331C2×C5×D3—21no—
332C2×C5×D3—21no—
333C2×C5×D3#13712yes—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—41no—
337C3×C4×C5C2×#4111yescharacteristic
338C3×C4×C5C2×#4111yescharacteristic
339Dic15—22no—
340Dic15—41no—
341C3×Dic5—22no—
342C3×Dic5—41no—
343C5×Dic3—21no—
344C5×Dic3—21no—
345C5×Dic3—21no—
346C5×Dic3—41no—
347C5×Dic3—41no—
348C2×C3×Q8—51no—
349C2×C3×D4C22×D511yescharacteristic
350C22×C3×C4—21no—
351C2×#67—21no—
352D3×Q8—102no—
353D3×Q8—102no—
354C2×C4×D3—101no—
355C2×C4×D3—101no—
356C2×C4×D3C22⋊D511yescharacteristic
357C2×C4×D3C22⋊D511yescharacteristic
358C2×C4×D3C22×D511yescharacteristic
359C2×Dic6—51no—
360C2×Dic6—101no—
361C2×Dic6C22×D511yescharacteristic
362C3×SD16—102no—
363C2×C3×C8—51no—
364C2×C3×C8—51no—
365C3×C4⋊C4—51no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4C22×D511yescharacteristic
368C3×C22⋊C4—21no—
369C3×C42—101no—
370C3×C42C22×D511yescharacteristic
371#217—21no—
372#217—21no—
373#217—21no—
374#216—102no—
375#214—102no—
376(C2×D3)⋊C4—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—21no—
379C4⋊Dic3—51no—
380C4⋊Dic3—101no—
381C4⋊Dic3C22×D511yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387C4×Dic3—21no—
388C4×Dic3—101no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C4×Dic3C22⋊D511yescharacteristic
392C4×Dic3C22⋊D511yescharacteristic
393C4×Dic3C22×D511yescharacteristic
394C2×C3⋊C8—51no—
395C2×C3⋊C8—51no—
396Dic12—102no—
397C23×C5—21no—
398C23×C5—31no—
399C5×Q8—61no—
400C5×Q8—61no—
401C5×D4—21no—
402C5×D4—21no—
403C5×D4—122no—
404C2×C4×C5—21no—
405C2×C4×C5—31no—
406C2×C4×C5—31no—
407C2×C4×C5—31no—
408C2×C4×C5—42no—
409C2×C4×C5—62no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—61no—
413C2×C4×C5—61no—
414C2×C4×C5—121no—
415C2×C4×C5D3×D411yescharacteristic
416C2×C4×C5D3×D411yescharacteristic
417C2×C4×C5C23×D311yescharacteristic
418C2×Dic5—21no—
419C2×Dic5—21no—
420C2×Dic5—64no—
421C2×Dic5—61no—
422C2×Dic5—61no—
423C2×Dic5—122no—
424Dic10—21no—
425Dic10—32no—
426Dic10—64no—
427Dic10—61no—
428Dic10#23512yes—
429#168—21no—
430#168—21no—
431#168—61no—
432#168—61no—
433C22×Q8—151no—
434C2×Q16—151no—
435C2×Q16—151no—
436C2×SD16—51no—
437C2×SD16—151no—
438#126—61no—
439#125—31no—
440#124—31no—
441#123—61no—
442C22⋊Q8—31no—
443#121—31no—
444C4×Q8—31no—
445C4×Q8—51no—
446C4×Q8—151no—
447C4×Q8—151no—
448C4×Q8—151no—
449C4×Q8—301no—
450C4×Q8—301no—
451C4×D4—61no—
452C4×D4D3×D511yescharacteristic
453#117—61no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—301no—
456C2×C42—31no—
457C2×C42—301no—
458#107—51no—
459#107—151no—
460#106—151no—
461#106—151no—
462C4⋊C8—151no—
463C4⋊C8—151no—
464#103—51no—
465#103—151no—
466#103—151no—
467#103—151no—
468#103—151no—
469#103—151no—
470#102—51no—
471#102—151no—
472C22⋊C8—151no—
473C22⋊C8—151no—
474#97—51no—
475#97—151no—
476C2×C3×C5—81no—
477C2×C3×C5#52511yescharacteristic
478C2×C3×C5C2×#13711yescharacteristic
479C2×C3×C5#57511yescharacteristic
480C5×D3—22no—
481C23×C3—21no—
482C22×D3C2×C22⋊D511yescharacteristic
483C3×Q8—52no—
484C3×Q8—101no—
485C3×D4—21no—
486C3×D4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—42no—
489C2×C3×C4—101no—
490C2×C3×C4—101no—
491C2×C3×C4C2×C22⋊D511yescharacteristic
492C2×C3×C4C2×C22⋊D511yescharacteristic
493C2×C3×C4C23×D511yescharacteristic
494#67—42no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—101no—
498C2×Dic3—101no—
499C2×Dic3C2×C22⋊D511yescharacteristic
500C2×Dic3C2×C22⋊D511yescharacteristic
501C2×Dic3C2×C22⋊D511yescharacteristic
502C4×D3—22no—
503C4×D3—21no—
504C4×D3—21no—
505C4×D3—41no—
506C4×D3—104no—
507C4×D3—202no—
508Dic6—21no—
509Dic6—21no—
510Dic6—52no—
511Dic6—104no—
512Dic6—101no—
513C3×C8—101no—
514C3×C8—101no—
515C3⋊C8—101no—
516C3⋊C8—101no—
517C22×C5—32no—
518C22×C5—41no—
519C22×C5—41no—
520C22×C5—41no—
521C22×C5—61no—
522C22×C5—61no—
523C22×C5C2×D3×D411yescharacteristic
524C4×C5—21no—
525C4×C5—21no—
526C4×C5—41no—
527C4×C5—61no—
528C4×C5—61no—
529C4×C5—61no—
530C4×C5—121no—
531C4×C5—121no—
532C4×C5C2×#23511yescharacteristic
533C4×C5D3×#4111yescharacteristic
534Dic5—22no—
535Dic5—41no—
536Dic5—62no—
537Dic5—121no—
538C2×Q8—31no—
539C2×Q8—51no—
540C2×Q8—151no—
541C2×Q8—301no—
542C2×Q8—302no—
543C2×Q8—302no—
544C2×D4—61no—
545C2×D4C2×D3×D511yescharacteristic
546C22×C4—21no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—31no—
550C22×C4—301no—
551C22×C4—301no—
552Q16—302no—
553Q16—302no—
554SD16—102no—
555SD16—302no—
556C2×C8—51no—
557C2×C8—51no—
558C2×C8—151no—
559C2×C8—151no—
560C4⋊C4—31no—
561C4⋊C4—51no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—101no—
567C4⋊C4—151no—
568C4⋊C4—301no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4C2×D3×D511yescharacteristic
573C22⋊C4—21no—
574C22⋊C4—61no—
575C22⋊C4—61no—
576C22⋊C4—61no—
577C22⋊C4—61no—
578C42—31no—
579C42—31no—
580C42—31no—
581C42—61no—
582C42—101no—
583C42—301no—
584C42—301no—
585C42—301no—
586C42C2×D3×D511yescharacteristic
587C3×C5#311711yescharacteristic, complemented, Hall
588C22×C3—41no—
589C22×C3—41no—
590C22×C3—41no—
591C22×C3C22×C22⋊D511yescharacteristic
592C2×D3—21no—
593C2×D3—21no—
594C2×D3#409712yes—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—41no—
598C3×C4—102no—
599C3×C4—201no—
600C3×C4D5×#4111yescharacteristic
601C3×C4D5×#4111yescharacteristic
602Dic3—21no—
603Dic3—21no—
604Dic3—21no—
605Dic3—41no—
606Dic3—41no—
607Dic3—102no—
608Dic3—201no—
609C2×C5—62no—
610C2×C5—81no—
611C2×C5#554711yescharacteristic
612C2×C5#577311yescharacteristic
613C2×C5D3×#13711yescharacteristic
614C23—21no—
615C23—31no—
616Q8—52no—
617Q8—61no—
618Q8—61no—
619Q8—101no—
620Q8—152no—
621Q8—304no—
622Q8—301no—
623D4—21no—
624D4—21no—
625D4—122no—
626C2×C4—21no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—42no—
631C2×C4—62no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—61no—
636C2×C4—101no—
637C2×C4—101no—
638C2×C4—121no—
639C2×C4—304no—
640C2×C4—301no—
641C2×C4—301no—
642C2×C4—602no—
643C2×C4D3×C22⋊D511yescharacteristic
644C2×C4D3×C22⋊D511yescharacteristic
645C2×C4C22×D3×D511yescharacteristic
646C8—101no—
647C8—101no—
648C8—301no—
649C8—301no—
650C2×C3—81no—
651C2×C3#6615611yescharacteristic
652C2×C3C2×#409711yescharacteristic
653C2×C3#6616211yescharacteristic
654D3—22no—
655C5#7978411yescharacteristic, complemented, Sylow
656C22—32no—
657C22—41no—
658C22—41no—
659C22—41no—
660C22—61no—
661C22—61no—
662C22C2×D3×C22⋊D511yescharacteristic
663C4—21no—
664C4—21no—
665C4—41no—
666C4—61no—
667C4—61no—
668C4—61no—
669C4—102no—
670C4—121no—
671C4—121no—
672C4—201no—
673C4—302no—
674C4—601no—
675C4D5×#23511yescharacteristic
676C4#9201611yescharacteristic
677C3#1061488411yescharacteristic, complemented, Sylow
678C2—62no—
679C2—81no—
680C2#1175464911yescharacteristic
681C2#1175469611yescharacteristic
682C2D3×#409711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radicalC5×#938C22
hypercenterC4×D4D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D4

Complements

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

NH ≅ G/Ntype
2. C4×D3×Dic10C2semidirect
3. #11751119C2semidirect
4. C3×#65307C2semidirect
6. #11749012C2semidirect
7. #11749006C2semidirect
9. #11747495C2semidirect
10. #11747296C2semidirect
11. #11747290C2semidirect
12. #11747198C2semidirect
13. #11747093C2semidirect
14. #11747089C2semidirect
15. #11746878C2semidirect
74. #65307D3semidirect
587. C3×C5#3117semidirect
655. C5#79784semidirect
677. C3#10614884semidirect

Maximal subgroups

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

subgroupindex
C5×#55572
C4×D3×Dic102
#117511192
C3×#653072
#117491552
#117490122
#117490062
#117489562
#117474952
#117472962
#117472902
#117471982
#117470932
#117470892
#117468782
#106148843
#797845