Finite Group Databasebeta

← #14436149

Subgroups — #14436149

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5827C211yesmaximal, characteristic
2#11754195C211yesmaximal, characteristic, complemented
3#11751340C211yesmaximal, characteristic
4C3×#65528C211yesmaximal, characteristic
5#11749360C211yesmaximal, characteristic, complemented
6#11749333C211yesmaximal, characteristic, complemented
7#11749257C211yesmaximal, characteristic, complemented
8#11749256C211yesmaximal, characteristic, complemented
9#11749114C211yesmaximal, characteristic, complemented
10#11749088C211yesmaximal, characteristic, complemented
11#11749014C211yesmaximal, characteristic, complemented
12Dic3×#687C211yesmaximal, characteristic, complemented
13#11748461C211yesmaximal, characteristic, complemented
14#11748444C211yesmaximal, characteristic, complemented
15#11748330C211yesmaximal, characteristic, complemented
16#10614306—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×#6718C2211yescharacteristic
19C2×#6716C2211yescharacteristic
20#91813C2211yescharacteristic
21C5×Q8×Dic3C2211yescharacteristic
22C5×Q8×Dic3C2211yescharacteristic
23C5×D4×Dic3—21no—
24C5×D4×Dic3—21no—
25C5×D4×Dic3C2211yescharacteristic
26C5×D4×Dic3C2211yescharacteristic
27C5×#926—21no—
28C5×#926C2211yescharacteristic
29C2×C5×C4⋊Dic3—21no—
30C2×C5×C4⋊Dic3C2211yescharacteristic
31C2×C3×#689C2211yescharacteristic
32C2×C3×#687C2211yescharacteristic
33C3×#4070C2211yescharacteristic
34#91531—21no—
35#91530—21no—
36#91389C2211yescharacteristic
37#91381C2211yescharacteristic
38#91340C2211yescharacteristic
39#91336—21no—
40#91335—21no—
41Dic3×Dic10C2211yescharacteristic
42#91119C2211yescharacteristic
43#91116C2211yescharacteristic
44#91114C2211yescharacteristic
45C3×#3967C2211yescharacteristic
46C3×#3964C2211yescharacteristic
47C3×C22⋊#168C2211yescharacteristic
48#90989C2211yescharacteristic
49#90989C2211yescharacteristic
50#90985C2211yescharacteristic
51#90985C2211yescharacteristic
52Dic3⋊#168C2211yescharacteristic
53Dic3⋊#168C2211yescharacteristic
54#90975C2211yescharacteristic
55#90975C2211yescharacteristic
56#90970C2211yescharacteristic
57#90970C2211yescharacteristic
58#90953C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#80216—51nomaximal, Hall
61C5×#520—31no—
62#65852—31no—
63#65528—31no—
64#65528D311yescharacteristic
65#65320—31no—
66#65319—31no—
67C4×#689—31no—
68#65311—31no—
69#65308—31no—
70#65307—31no—
71C4×#687—31no—
72#65298—31no—
73#65289—31no—
74#65260—31no—
75#65259—31no—
76C3×C5×#41—22no—
77C3×C5×#41—22no—
78C2×C3×C5×Q8C2311yescharacteristic
79C2×C3×C5×D4—21no—
80C2×C3×C5×D4C2311yescharacteristic
81C22×C3×C4×C5—21no—
82C22×C3×C4×C5C2311yescharacteristic
83C2×Dic30C2311yescharacteristic
84C22×C5×Dic3—21no—
85C22×C5×Dic3—21no—
86C22×C5×Dic3—21no—
87C2×C3×Dic10C2311yescharacteristic
88#6719—21no—
89#6718—22no—
90#6716—22no—
91C4⋊Dic15C2311yescharacteristic
92#6712—21no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×#217—21no—
96C5×#217—21no—
97C5×#217D411yescharacteristic
98C5×#217D411yescharacteristic
99C5×C4⋊Dic3—21no—
100C5×C4⋊Dic3—21no—
101C5×C4⋊Dic3—21no—
102C5×C4⋊Dic3D411yescharacteristic
103C5×C4⋊Dic3D411yescharacteristic
104C5×C4⋊Dic3C2311yescharacteristic
105C5×C4⋊Dic3C2311yescharacteristic
106C4×C5×Dic3—21no—
107C4×C5×Dic3—21no—
108C4×C5×Dic3C2311yescharacteristic
109C4×C5×Dic3C2311yescharacteristic
110C3×C22⋊Dic5—21no—
111C3×#689—22no—
112C3×#687—22no—
113C3×C4⋊Dic5C2311yescharacteristic
114C3×#683—21no—
115C2×C3×#168C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117Dic3⋊Dic5—21no—
118Dic3⋊Dic5—21no—
119#6669—21no—
120#6669—21no—
121#6668—21no—
122#6668—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125#5827D511yescharacteristic
126#5625—51no—
127C3×#452—51no—
128#5239—51no—
129#5184—51no—
130#5182—51no—
131#5162—51no—
132Dic3×SD16—51no—
133#5044—51no—
134#4799—51no—
135#4790—51no—
136#4763—51no—
137#4757—51no—
138#4721—51no—
139#4720—51no—
140C2×C5×#41C2×D311yescharacteristic
141C4×C5×Q8—31no—
142C4×C5×Q8—31no—
143C4×C5×D4—31no—
144C4×C5×D4—31no—
145C4×C5×D4—61no—
146C4×C5×D4—61no—
147C5×#117—31no—
148C5×#117—61no—
149C2×C5×C4⋊C4—31no—
150C2×C5×C4⋊C4—61no—
151C2×#689—31no—
152C2×#689C2×D311yescharacteristic
153C2×#687—31no—
154C2×#687C2×D311yescharacteristic
155#4070—31no—
156#4070C2×D311yescharacteristic
157#4035—61no—
158#4035—61no—
159#4025—61no—
160#4025—61no—
161#4016—31no—
162#4015—31no—
163C4×Dic10—31no—
164C4×Dic10—31no—
165#3967—31no—
166#3967C2×D311yescharacteristic
167#3964—31no—
168#3964C2×D311yescharacteristic
169C22⋊#168—31no—
170C22⋊#168C2×D311yescharacteristic
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⋊#168—31no—
181#3935—31no—
182C4×#168—31no—
183#3120—151noSylow
184C23×C3×C5—21no—
185C23×C3×C5C2×D411yescharacteristic
186C3×C5×Q8—21no—
187C3×C5×Q8#4112yes—
188C3×C5×D4—24no—
189C3×C5×D4—21no—
190C3×C5×D4#4112yes—
191C2×C3×C4×C5—24no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5C2×D411yescharacteristic
196C2×C3×C4×C5C2411yescharacteristic
197C2×Dic15—21no—
198C2×Dic15—21no—
199Dic30—21no—
200Dic30—21no—
201C2×C5×Dic3—21no—
202C2×C5×Dic3—21no—
203C2×C5×Dic3—81no—
204C2×C5×Dic3—81no—
205C2×C5×Dic3—81no—
206C2×C5×Dic3C2×D411yescharacteristic
207C2×C5×Dic3C2×D411yescharacteristic
208C2×C5×Dic3C2×D411yescharacteristic
209C2×C5×Dic3C2×D411yescharacteristic
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C3×Dic10—21no—
213C3×Dic10—21no—
214C3⋊#168—21no—
215C3⋊#168—21no—
216C3×#168—21no—
217C3×#168—21no—
218C2×C3×#41C2×D511yescharacteristic
219C2×C3×Q16—51no—
220C2×C3×SD16—51no—
221C3×C22⋊Q8—51no—
222Q8×Dic3—51no—
223Q8×Dic3C2×D511yescharacteristic
224Q8×Dic3C2×D511yescharacteristic
225#944—51no—
226C2×#216—51no—
227D4×Dic3—21no—
228D4×Dic3—21no—
229D4×Dic3C2×D511yescharacteristic
230D4×Dic3C2×D511yescharacteristic
231C2×#214—51no—
232#926—21no—
233#926C2×D511yescharacteristic
234C2×C4⋊Dic3—21no—
235C2×C4⋊Dic3C2×D511yescharacteristic
236#924—51no—
237#890—51no—
238#890—101no—
239#889—101no—
240#887—51no—
241#879—101no—
242#879—101no—
243C3×#103—51no—
244C3×#102—51no—
245C3×C22⋊C8—51no—
246#835—51no—
247#835—51no—
248#835—51no—
249#832—51no—
250#830—51no—
251#817—51no—
252#817—51no—
253#816—51no—
254#816—51no—
255#815—51no—
256Dic3⋊C8—51no—
257Dic3⋊C8—51no—
258C8×Dic3—51no—
259#807—51no—
260#807—51no—
261C5×#41—22no—
262C5×#41—22no—
263C2×C5×Q8C22×D311yescharacteristic
264C2×C5×D4—21no—
265C2×C5×D4C22×D311yescharacteristic
266C22×C4×C5—21no—
267C22×C4×C5—61no—
268C22×C4×C5—61no—
269C22×C4×C5—61no—
270C22×C4×C5C22×D311yescharacteristic
271C2×Dic10—31no—
272C2×Dic10C22×D311yescharacteristic
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—31no—
277C5×C4⋊C4—61no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4—61no—
280C5×C22⋊C4—31no—
281C5×C22⋊C4—31no—
282C5×C22⋊C4—61no—
283C5×C22⋊C4—61no—
284C42×C5—31no—
285C42×C5—31no—
286C42×C5—61no—
287C42×C5—61no—
288C22⋊Dic5—21no—
289C22⋊Dic5—61no—
290#689—22no—
291#689—62no—
292#687—22no—
293#687—62no—
294C4⋊Dic5—31no—
295C4⋊Dic5—61no—
296C4⋊Dic5—61no—
297C4⋊Dic5C22×D311yescharacteristic
298#683—21no—
299#683—61no—
300#683—61no—
301#683—61no—
302#683—61no—
303#683—61no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C2×#168—31no—
307C2×#168—31no—
308C2×#168C22×D311yescharacteristic
309C2×#168C22×D311yescharacteristic
310#541—151no—
311#520—31no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—51no—
319#452—151no—
320#441—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—151no—
325C22×C3×C5—21no—
326C22×C3×C5—22no—
327C22×C3×C5—21no—
328C22×C3×C5—21no—
329C22×C3×C5—41no—
330C22×C3×C5—41no—
331C22×C3×C5C22×D411yescharacteristic
332C3×C4×C5—21no—
333C3×C4×C5—22no—
334C3×C4×C5C2×#4111yescharacteristic
335C3×C4×C5C2×#4111yescharacteristic
336Dic15—41no—
337Dic15—41no—
338C3×Dic5—41no—
339C3×Dic5—41no—
340C5×Dic3—21no—
341C5×Dic3—21no—
342C5×Dic3—21no—
343C5×Dic3—21no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C3×#41—22no—
347C3×#41—22no—
348C2×C3×Q8—51no—
349C2×C3×Q8C22×D511yescharacteristic
350C2×C3×D4—21no—
351C2×C3×D4C22×D511yescharacteristic
352C22×C3×C4—21no—
353C22×C3×C4C22×D511yescharacteristic
354C22×Dic3—21no—
355C22×Dic3—21no—
356C22×Dic3—21no—
357C2×Dic6—51no—
358C3×Q16—102no—
359C3×SD16—102no—
360C2×C3×C8—51no—
361C2×C3×C8—51no—
362C3×C4⋊C4—51no—
363C3×C4⋊C4—101no—
364C3×C22⋊C4—101no—
365#217—21no—
366#217—21no—
367#217—101no—
368#217C22⋊D511yescharacteristic
369#217C22⋊D511yescharacteristic
370#216—102no—
371#214—102no—
372C4⋊Dic3—21no—
373C4⋊Dic3—21no—
374C4⋊Dic3—21no—
375C4⋊Dic3—51no—
376C4⋊Dic3—101no—
377C4⋊Dic3—101no—
378C4⋊Dic3C22⋊D511yescharacteristic
379C4⋊Dic3C22⋊D511yescharacteristic
380C4⋊Dic3C22×D511yescharacteristic
381C4⋊Dic3C22×D511yescharacteristic
382Dic3⋊C4—101no—
383Dic3⋊C4—101no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387C4×Dic3—21no—
388C4×Dic3—21no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C4×Dic3C22×D511yescharacteristic
392C4×Dic3C22×D511yescharacteristic
393C2×C3⋊C8—51no—
394C2×C3⋊C8—51no—
395C23×C5—21no—
396C23×C5D3×D411yescharacteristic
397C5×Q8—21no—
398C5×Q8#23712yes—
399C5×D4—24no—
400C5×D4—21no—
401C5×D4#23712yes—
402C2×C4×C5—24no—
403C2×C4×C5—21no—
404C2×C4×C5—21no—
405C2×C4×C5—21no—
406C2×C4×C5—31no—
407C2×C4×C5—31no—
408C2×C4×C5—31no—
409C2×C4×C5—31no—
410C2×C4×C5—61no—
411C2×C4×C5—61no—
412C2×C4×C5—241no—
413C2×C4×C5—241no—
414C2×C4×C5—241no—
415C2×C4×C5D3×D411yescharacteristic
416C2×C4×C5C23×D311yescharacteristic
417C2×Dic5—21no—
418C2×Dic5—21no—
419C2×Dic5—61no—
420C2×Dic5—61no—
421Dic10—21no—
422Dic10—21no—
423Dic10—61no—
424Dic10—61no—
425#168—21no—
426#168—21no—
427#168—61no—
428#168—61no—
429C2×#41D3×D511yescharacteristic
430C2×Q16—51no—
431C2×Q16—151no—
432C2×SD16—51no—
433C2×SD16—151no—
434C4⋊Q8—151no—
435#126—301no—
436#126—301no—
437#125—151no—
438#125—301no—
439#125—301no—
440C22⋊Q8—51no—
441C22⋊Q8—151no—
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450#117—31no—
451#117—61no—
452C2×C4⋊C4—31no—
453C2×C4⋊C4—61no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460#103—51no—
461#103—151no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—51no—
467#102—151no—
468C22⋊C8—51no—
469C22⋊C8—151no—
470#97—151no—
471C4×C8—151no—
472C2×C3×C5—41no—
473C2×C3×C5—42no—
474C2×C3×C5#52511yescharacteristic
475C2×C3×C5#57711yescharacteristic
476C2×C3×C5#57811yescharacteristic
477C23×C3—21no—
478C23×C3C2×C22⋊D511yescharacteristic
479C3×Q8—21no—
480C3×Q8—101no—
481C3×Q8—101no—
482C3×Q8#70912yes—
483C3×D4—24no—
484C3×D4—21no—
485C3×D4#70912yes—
486C2×C3×C4—24no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—101no—
491C2×C3×C4—101no—
492C2×C3×C4C2×C22⋊D511yescharacteristic
493C2×C3×C4C23×D511yescharacteristic
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—81no—
497C2×Dic3—81no—
498C2×Dic3—81no—
499C2×Dic3—101no—
500C2×Dic3—101no—
501C2×Dic3C2×C22⋊D511yescharacteristic
502C2×Dic3C2×C22⋊D511yescharacteristic
503C2×Dic3C2×C22⋊D511yescharacteristic
504C2×Dic3C2×C22⋊D511yescharacteristic
505Dic6—101no—
506Dic6—101no—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5—22no—
515C22×C5—41no—
516C22×C5—41no—
517C22×C5C2×D3×D411yescharacteristic
518C4×C5—21no—
519C4×C5—22no—
520C4×C5—61no—
521C4×C5—61no—
522C4×C5—61no—
523C4×C5—61no—
524C4×C5—121no—
525C4×C5—121no—
526C4×C5C2×#23711yescharacteristic
527C4×C5C2×#23711yescharacteristic
528Dic5—41no—
529Dic5—41no—
530Dic5—121no—
531Dic5—121no—
532#41—22no—
533#41—22no—
534C2×Q8—51no—
535C2×Q8—151no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—21no—
538C2×D4C2×D3×D511yescharacteristic
539C22×C4—21no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—102no—
545Q16—302no—
546SD16—102no—
547SD16—302no—
548C2×C8—51no—
549C2×C8—51no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—31no—
553C4⋊C4—31no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—51no—
557C4⋊C4—61no—
558C4⋊C4—61no—
559C4⋊C4—61no—
560C4⋊C4—101no—
561C4⋊C4—151no—
562C4⋊C4—301no—
563C4⋊C4—301no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4—301no—
568C4⋊C4—301no—
569C22⋊C4—31no—
570C22⋊C4—31no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4—101no—
574C22⋊C4—301no—
575C42—31no—
576C42—31no—
577C42—61no—
578C42—61no—
579C42—301no—
580C42—301no—
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—22no—
584C22×C3—21no—
585C22×C3—21no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3C22×C22⋊D511yescharacteristic
589C3×C4—21no—
590C3×C4—22no—
591C3×C4—201no—
592C3×C4—201no—
593C3×C4C2×#70911yescharacteristic
594C3×C4C2×#70911yescharacteristic
595Dic3—21no—
596Dic3—21no—
597Dic3—21no—
598Dic3—21no—
599Dic3—41no—
600Dic3—41no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5—42no—
605C2×C5#558611yescharacteristic
606C2×C5#577011yescharacteristic
607C2×C5#577911yescharacteristic
608C23—21no—
609C23D3×C22⋊D511yescharacteristic
610Q8—21no—
611Q8—101no—
612Q8—101no—
613Q8—301no—
614Q8—301no—
615Q8#677912yes—
616D4—24no—
617D4—21no—
618D4#677912yes—
619C2×C4—24no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—31no—
624C2×C4—31no—
625C2×C4—31no—
626C2×C4—31no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—241no—
632C2×C4—241no—
633C2×C4—241no—
634C2×C4—301no—
635C2×C4—301no—
636C2×C4D3×C22⋊D511yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—101no—
639C8—101no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3—42no—
644C2×C3#6612511yescharacteristic
645C2×C3#6617011yescharacteristic
646C2×C3#6617211yescharacteristic
647C5#8021611yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22C2×D3×C22⋊D511yescharacteristic
655C4—21no—
656C4—22no—
657C4—61no—
658C4—61no—
659C4—61no—
660C4—61no—
661C4—121no—
662C4—121no—
663C4—201no—
664C4—201no—
665C4—601no—
666C4—601no—
667C4C2×#677911yescharacteristic
668C4C2×#677911yescharacteristic
669C3#1061430611yescharacteristic, complemented, Sylow
670C2—41no—
671C2—42no—
672C2#1175534111yescharacteristic
673C2#1175534711yescharacteristic
674C2#1175538811yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #11754195C2semidirect
5. #11749360C2semidirect
6. #11749333C2semidirect
7. #11749257C2semidirect
8. #11749256C2semidirect
9. #11749114C2semidirect
10. #11749088C2semidirect
11. #11749014C2semidirect
12. Dic3×#687C2semidirect
13. #11748461C2semidirect
14. #11748444C2semidirect
15. #11748330C2semidirect
581. C3×C5#3120semidirect
647. C5#80216semidirect
669. C3#10614306semidirect

Maximal subgroups

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

subgroupindex
C5×#58272
#117541952
#117513402
C3×#655282
#117493602
#117493332
#117492572
#117492562
#117491142
#117490882
#117490142
Dic3×#6872
#117484612
#117484442
#117483302
#106143063
#802165