Finite Group Databasebeta

← #14435522

Subgroups — #14435522

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×#5680C211yesmaximal, characteristic
2C4×D3×Dic10C211yesmaximal, characteristic, complemented
3#11751155C211yesmaximal, characteristic, complemented
4C3×#65343C211yesmaximal, characteristic, complemented
5#11749401C211yesmaximal, characteristic, complemented
6#11749260C211yesmaximal, characteristic, complemented
7#11749256C211yesmaximal, characteristic, complemented
8#11749202C211yesmaximal, characteristic, complemented
9#11749155C211yesmaximal, characteristic
10#11749014C211yesmaximal, characteristic, complemented
11#11749010C211yesmaximal, characteristic, complemented
12#11748956C211yesmaximal, characteristic
13#11746967C211yesmaximal, characteristic, complemented
14#11746919C211yesmaximal, characteristic, complemented
15#11746875C211yesmaximal, characteristic, complemented
16#10614884—31nomaximal, Hall
17C2×D3×Dic10C2211yescharacteristic
18C3×C5×#124C2211yescharacteristic
19C2×#6718C2211yescharacteristic
20C2×#6716C2211yescharacteristic
21C4×Dic30C2211yescharacteristic
22C5×#946C2211yescharacteristic
23C5×Q8×Dic3C2211yescharacteristic
24C5×#938C2211yescharacteristic
25C5×D4×Dic3C2211yescharacteristic
26C5×#883—21no—
27C5×#67⋊C4—21no—
28C5×#879—21no—
29C5×#877—21no—
30C42×C5×D3C2211yescharacteristic
31C5×#870C2211yescharacteristic
32C2×C3×#689C2211yescharacteristic
33C2×C3×#687C2211yescharacteristic
34C3×C4×Dic10C2211yescharacteristic
35C4×#1204—21no—
36D3×C4⋊Dic5C2211yescharacteristic
37D3×#683—21no—
38C4×D3×Dic5—21no—
39#91340C2211yescharacteristic
40Dic3×Dic10C2211yescharacteristic
41#91324—21no—
42#91119C2211yescharacteristic
43#91116C2211yescharacteristic
44C4⋊(C3⋊#168)C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×C4⋊#168C2211yescharacteristic
48#90989C2211yescharacteristic
49#90988C2211yescharacteristic
50#90986C2211yescharacteristic
51#90985C2211yescharacteristic
52#90975C2211yescharacteristic
53#90975C2211yescharacteristic
54#90970C2211yescharacteristic
55#90970C2211yescharacteristic
56(C2×D3)⋊#168C2211yescharacteristic
57(C2×D3)⋊#168C2211yescharacteristic
58#90953C2211yescharacteristic
59#90953C2211yescharacteristic
60#80571—51nomaximal, Hall
61C5×#529—31no—
62C2×C4×Dic10—31no—
63#65352—31no—
64#65352—31no—
65#65343—31no—
66#65343D311yescharacteristic, complemented
67#65339—31no—
68#65333—31no—
69#65329—31no—
70#65323—31no—
71#65319—31no—
72#65319—31no—
73#65307—31no—
74#65307—31no—
75#65215—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×D4C2311yescharacteristic
78C2×Dic30C2311yescharacteristic
79C2×C5×#67—21no—
80C22×C5×Dic3—21no—
81C2×C4×C5×D3D411yescharacteristic
82C2×C4×C5×D3D411yescharacteristic
83C2×C4×C5×D3C2311yescharacteristic
84C2×C3×Dic10C2311yescharacteristic
85C2×#1204—21no—
86C2×D3×Dic5—21no—
87C2×D3×Dic5—21no—
88D3×Dic10—22no—
89D3×Dic10—22no—
90C3×C5×C22⋊C4—21no—
91C3×C5×C22⋊C4—21no—
92C3×C42×C5C2311yescharacteristic
93#6718—22no—
94#6716—22no—
95C4⋊Dic15C2311yescharacteristic
96#6712—21no—
97C4×Dic15—21no—
98C2×C3⋊#168C2311yescharacteristic
99C2×C3⋊#168C2311yescharacteristic
100C5×#217—21no—
101C5×#217—21no—
102C5×(C2×D3)⋊C4—21no—
103C5×C4⋊Dic3—21no—
104C5×C4⋊Dic3C2311yescharacteristic
105C5×C4⋊Dic3C2311yescharacteristic
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4—21no—
108C5×Dic3⋊C4—21no—
109C4×C5×Dic3—21no—
110C4×C5×Dic3D411yescharacteristic
111C4×C5×Dic3D411yescharacteristic
112C4×C5×Dic3C2311yescharacteristic
113C3×#689—22no—
114C3×#687—22no—
115C3×C4⋊Dic5C2311yescharacteristic
116C3×#683—21no—
117C3×C4×Dic5—21no—
118C2×C3×#168C2311yescharacteristic
119C2×C3×#168C2311yescharacteristic
120Dic3⋊Dic5—21no—
121#6669—21no—
122#6668—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125#5680D511yescharacteristic
126C4×D3×Q8—51no—
127C3×#464—51no—
128#5186—51no—
129#5184—51no—
130#5170—51no—
131#5164—51no—
132#5054—51no—
133#5022—51no—
134#4835—51no—
135#4829—51no—
136#4811—51no—
137#4789—51no—
138#4777—51no—
139#4757—51no—
140C22×Dic10—31no—
141C5×#126—61no—
142C5×#125—31no—
143C5×#124C2×D311yescharacteristic
144C5×#123—61no—
145C5×C22⋊Q8—31no—
146C5×#121—31no—
147C4×C5×Q8—31no—
148C4×C5×D4—31no—
149C4×C5×D4—61no—
150C5×#117—61no—
151C2×C42×C5—31no—
152C2×#689—31no—
153C2×#689C2×D311yescharacteristic
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#3967C2×D311yescharacteristic
167#3964—31no—
168#3964C2×D311yescharacteristic
169C22⋊#168—31no—
170C22⋊#168—31no—
171#3942—31no—
172#3942—31no—
173#3942—31no—
174#3942—31no—
175#3940—31no—
176#3940—31no—
177#3939—31no—
178#3939—31no—
179C4⋊#168—31no—
180C4⋊#168C2×D311yescharacteristic
181#3935—31no—
182#3935—31no—
183#3117—151noSylow
184C23×C3×C5—21no—
185C22×C5×D3C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C3×C5×D4—21no—
189C3×C5×D4—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2411yescharacteristic
194C2×Dic15—21no—
195C2×Dic15—21no—
196Dic30—21no—
197Dic30#4112yes—
198C5×#67—42no—
199C2×C5×Dic3—21no—
200C2×C5×Dic3—21no—
201C2×C5×Dic3—42no—
202C2×C5×Dic3C2×D411yescharacteristic
203C2×C5×Dic3C2×D411yescharacteristic
204C2×C5×Dic3C2×D411yescharacteristic
205C4×C5×D3—22no—
206C4×C5×D3—21no—
207C4×C5×D3—21no—
208C4×C5×D3—41no—
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×Q16—51no—
222C2×C3×SD16—51no—
223C3×#124C2×D511yescharacteristic
224C3×C4×Q8—51no—
225#946C2×D511yescharacteristic
226Q8×Dic3—51no—
227Q8×Dic3C2×D511yescharacteristic
228C2×#216—51no—
229#938C2×D511yescharacteristic
230D4×Dic3C2×D511yescharacteristic
231C2×#214—51no—
232D3×C4⋊C4—51no—
233D3×C4⋊C4—101no—
234#887—51no—
235#887—101no—
236#883—21no—
237#67⋊C4—21no—
238#879—21no—
239#877—21no—
240C42×D3—101no—
241C42×D3C2×D511yescharacteristic
242#870C2×D511yescharacteristic
243C4×Dic6—51no—
244C4×Dic6—101no—
245C3×C4⋊C8—51no—
246C3×#103—51no—
247C3×#102—51no—
248#835—51no—
249#835—51no—
250#835—51no—
251#832—51no—
252(C2×D3)⋊C8—51no—
253(C2×D3)⋊C8—51no—
254#818—51no—
255#817—51no—
256#816—51no—
257#816—51no—
258#815—51no—
259#815—51no—
260#808—51no—
261#807—51no—
262C4⋊(C3⋊C8)—51no—
263C2×C5×Q8C22×D311yescharacteristic
264C2×C5×D4—61no—
265C2×C5×D4C22×D311yescharacteristic
266C22×C4×C5—31no—
267C22×C4×C5—31no—
268C22×C4×C5—31no—
269C22×C4×C5—61no—
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—31no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4—61no—
281C5×C4⋊C4—61no—
282C5×C4⋊C4—61no—
283C5×C22⋊C4—21no—
284C5×C22⋊C4—21no—
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—22no—
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—51no—
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×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×Q8C22×D511yescharacteristic
350C2×C3×D4C22×D511yescharacteristic
351C2×#67—21no—
352C22×Dic3—21no—
353D3×Q8—102no—
354D3×Q8—102no—
355C2×C4×D3—101no—
356C2×C4×D3—101no—
357C2×C4×D3C22⋊D511yescharacteristic
358C2×C4×D3C22⋊D511yescharacteristic
359C2×C4×D3C22×D511yescharacteristic
360C2×Dic6—51no—
361C2×Dic6—101no—
362C3×Q16—102no—
363C3×SD16—102no—
364C2×C3×C8—51no—
365C2×C3×C8—51no—
366C3×C4⋊C4—51no—
367C3×C4⋊C4—101no—
368C3×C22⋊C4—21no—
369C3×C22⋊C4—21no—
370C3×C42—101no—
371C3×C42C22×D511yescharacteristic
372#217—21no—
373#217—21no—
374#216—102no—
375#214—102no—
376(C2×D3)⋊C4—21no—
377C4⋊Dic3—21no—
378C4⋊Dic3—51no—
379C4⋊Dic3—101no—
380C4⋊Dic3C22×D511yescharacteristic
381C4⋊Dic3C22×D511yescharacteristic
382Dic3⋊C4—21no—
383Dic3⋊C4—21no—
384Dic3⋊C4—21no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387Dic3⋊C4—101no—
388C4×Dic3—21no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C4×Dic3—101no—
392C4×Dic3C22⋊D511yescharacteristic
393C4×Dic3C22⋊D511yescharacteristic
394C4×Dic3C22×D511yescharacteristic
395C2×C3⋊C8—51no—
396C2×C3⋊C8—51no—
397C23×C5—21no—
398C23×C5—31no—
399C5×Q8—21no—
400C5×Q8—21no—
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—62no—
409C2×C4×C5—61no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—61no—
413C2×C4×C5—121no—
414C2×C4×C5—122no—
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#23712yes—
429#168—21no—
430#168—21no—
431#168—61no—
432#168—61no—
433C22×Q8—151no—
434C2×Q16—51no—
435C2×Q16—151no—
436C2×SD16—51no—
437C2×SD16—151no—
438#126—61no—
439#125—31no—
440#124D3×D511yescharacteristic
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—31no—
452C4×D4—61no—
453#117—61no—
454C2×C4⋊C4—151no—
455C2×C4⋊C4—301no—
456C2×C42—31no—
457C2×C42—301no—
458#107—151no—
459#107—151no—
460#106—151no—
461#106—151no—
462C4⋊C8—51no—
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—151no—
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—21no—
484C3×Q8—21no—
485C3×Q8—52no—
486C3×Q8—101no—
487C3×D4—21no—
488C3×D4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4C2×C22⋊D511yescharacteristic
493C2×C3×C4C2×C22⋊D511yescharacteristic
494C2×C3×C4C23×D511yescharacteristic
495#67—42no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—42no—
499C2×Dic3—101no—
500C2×Dic3—101no—
501C2×Dic3C2×C22⋊D511yescharacteristic
502C2×Dic3C2×C22⋊D511yescharacteristic
503C2×Dic3C2×C22⋊D511yescharacteristic
504C4×D3—22no—
505C4×D3—21no—
506C4×D3—21no—
507C4×D3—41no—
508C4×D3—104no—
509C4×D3—202no—
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×#23711yescharacteristic
533C4×C5D3×#4111yescharacteristic
534Dic5—22no—
535Dic5—41no—
536Dic5—62no—
537Dic5—121no—
538C2×Q8—51no—
539C2×Q8—151no—
540C2×Q8—301no—
541C2×Q8—302no—
542C2×Q8—302no—
543C2×Q8C2×D3×D511yescharacteristic
544C2×D4—61no—
545C2×D4C2×D3×D511yescharacteristic
546C22×C4—31no—
547C22×C4—31no—
548C22×C4—31no—
549C22×C4—61no—
550C22×C4—301no—
551C22×C4—301no—
552Q16—102no—
553Q16—302no—
554SD16—102no—
555SD16—302no—
556C2×C8—51no—
557C2×C8—51no—
558C2×C8—151no—
559C2×C8—151no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—51no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—101no—
568C4⋊C4—151no—
569C4⋊C4—301no—
570C4⋊C4—301no—
571C4⋊C4—301no—
572C4⋊C4—301no—
573C22⋊C4—21no—
574C22⋊C4—21no—
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#560611yescharacteristic
612C2×C5#576811yescharacteristic
613C2×C5D3×#13711yescharacteristic
614C23—21no—
615C23—31no—
616Q8—21no—
617Q8—21no—
618Q8—52no—
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—62no—
631C2×C4—61no—
632C2×C4—61no—
633C2×C4—61no—
634C2×C4—61no—
635C2×C4—101no—
636C2×C4—101no—
637C2×C4—121no—
638C2×C4—122no—
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#8057111yescharacteristic, 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×#23711yescharacteristic
676C4#9202411yescharacteristic
677C3#1061488411yescharacteristic, complemented, Sylow
678C2—62no—
679C2—81no—
680C2#1175506511yescharacteristic
681C2#1175532211yescharacteristic
682C2D3×#409711yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
prime radicalC5×#938C22
hypercenter#124D3×D5
hypocenterC3×C5#3117
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C4×D3×Dic10C2semidirect
3. #11751155C2semidirect
4. C3×#65343C2semidirect
5. #11749401C2semidirect
6. #11749260C2semidirect
7. #11749256C2semidirect
8. #11749202C2semidirect
10. #11749014C2semidirect
11. #11749010C2semidirect
13. #11746967C2semidirect
14. #11746919C2semidirect
15. #11746875C2semidirect
66. #65343D3semidirect
587. C3×C5#3117semidirect
655. C5#80571semidirect
677. C3#10614884semidirect

Maximal subgroups

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

subgroupindex
C5×#56802
C4×D3×Dic102
#117511552
C3×#653432
#117494012
#117492602
#117492562
#117492022
#117491552
#117490142
#117490102
#117489562
#117469672
#117469192
#117468752
#106148843
#805715