Finite Group Databasebeta

← #14436147

Subgroups — #14436147

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
1C3×#66161C211yesmaximal, characteristic
2#11754212C211yesmaximal, characteristic, complemented
3#11751340C211yesmaximal, characteristic
4C5×#5239C211yesmaximal, characteristic
5#11749350C211yesmaximal, characteristic, complemented
6#11749332C211yesmaximal, characteristic, complemented
7#11749247C211yesmaximal, characteristic, complemented
8#11749244C211yesmaximal, characteristic, complemented
9#11749103C211yesmaximal, characteristic, complemented
10#11749083C211yesmaximal, characteristic, complemented
11#11749004C211yesmaximal, characteristic, complemented
12Dic5×#214C211yesmaximal, characteristic, complemented
13#11748471C211yesmaximal, characteristic, complemented
14#11748450C211yesmaximal, characteristic, complemented
15#11748319C211yesmaximal, characteristic, complemented
16#10611947—31nomaximal, Hall
17C2×C3×C5×#41C2211yescharacteristic
18C2×#6718C2211yescharacteristic
19C2×#6716C2211yescharacteristic
20#91813C2211yescharacteristic
21C2×C5×#216C2211yescharacteristic
22C2×C5×#214C2211yescharacteristic
23C5×#924C2211yescharacteristic
24C3×Q8×Dic5C2211yescharacteristic
25C3×Q8×Dic5C2211yescharacteristic
26C3×D4×Dic5—21no—
27C3×D4×Dic5—21no—
28C3×D4×Dic5C2211yescharacteristic
29C3×D4×Dic5C2211yescharacteristic
30C3×#4072—21no—
31C3×#4072C2211yescharacteristic
32C2×C3×C4⋊Dic5—21no—
33C2×C3×C4⋊Dic5C2211yescharacteristic
34#91531—21no—
35#91530—21no—
36#91388C2211yescharacteristic
37#91376C2211yescharacteristic
38#91346—21no—
39#91339—21no—
40#91333C2211yescharacteristic
41Dic5×Dic6C2211yescharacteristic
42#91119C2211yescharacteristic
43#91116C2211yescharacteristic
44#91114C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#832C2211yescharacteristic
47C5×#830C2211yescharacteristic
48#90989C2211yescharacteristic
49#90989C2211yescharacteristic
50#90987C2211yescharacteristic
51#90987C2211yescharacteristic
52#90982C2211yescharacteristic
53#90982C2211yescharacteristic
54#90974C2211yescharacteristic
55#90974C2211yescharacteristic
56#90972C2211yescharacteristic
57#90972C2211yescharacteristic
58#90952C2211yescharacteristic
59Dic5×C3⋊C8C2211yescharacteristic
60#82575—51nomaximal, Hall
61#66161D311yescharacteristic
62#65959—31no—
63C5×#452—31no—
64#65528—31no—
65#65473—31no—
66#65471—31no—
67#65451—31no—
68SD16×Dic5—31no—
69#65333—31no—
70#65088—31no—
71#65079—31no—
72#65052—31no—
73#65046—31no—
74#65010—31no—
75#65009—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
84C2×C5×Dic6C2311yescharacteristic
85C22×C3×Dic5—21no—
86C22×C3×Dic5—21no—
87C22×C3×Dic5—21no—
88#6719—21no—
89#6718—22no—
90#6716—22no—
91C4⋊Dic15C2311yescharacteristic
92#6712—21no—
93C2×C3⋊#168C2311yescharacteristic
94C2×C3⋊#168C2311yescharacteristic
95C5×#217—21no—
96C5×#216—22no—
97C5×#214—22no—
98C5×C4⋊Dic3C2311yescharacteristic
99C5×Dic3⋊C4—21no—
100C2×C5×C3⋊C8C2311yescharacteristic
101C2×C5×C3⋊C8C2311yescharacteristic
102C3×C22⋊Dic5—21no—
103C3×C22⋊Dic5—21no—
104C3×C22⋊Dic5D411yescharacteristic
105C3×C22⋊Dic5D411yescharacteristic
106C3×C4⋊Dic5—21no—
107C3×C4⋊Dic5—21no—
108C3×C4⋊Dic5—21no—
109C3×C4⋊Dic5D411yescharacteristic
110C3×C4⋊Dic5D411yescharacteristic
111C3×C4⋊Dic5C2311yescharacteristic
112C3×C4⋊Dic5C2311yescharacteristic
113C3×C4×Dic5—21no—
114C3×C4×Dic5—21no—
115C3×C4×Dic5C2311yescharacteristic
116C3×C4×Dic5C2311yescharacteristic
117Dic3⋊Dic5—21no—
118Dic3⋊Dic5—21no—
119#6669—21no—
120#6669—21no—
121#6668—21no—
122#6668—21no—
123Dic3×Dic5—21no—
124Dic3×Dic5—21no—
125C3×#520—51no—
126#5518—51no—
127#5239—51no—
128#5239D511yescharacteristic
129#5031—51no—
130#5030—51no—
131C4×#216—51no—
132#5022—51no—
133#5019—51no—
134#5018—51no—
135C4×#214—51no—
136#5009—51no—
137#5000—51no—
138#4971—51no—
139#4970—51no—
140C2×C5×#41C2×D311yescharacteristic
141C2×C5×Q16—31no—
142C2×C5×SD16—31no—
143C5×C22⋊Q8—31no—
144Q8×Dic5—31no—
145Q8×Dic5C2×D311yescharacteristic
146Q8×Dic5C2×D311yescharacteristic
147#4090—31no—
148C2×#689—31no—
149D4×Dic5—21no—
150D4×Dic5—21no—
151D4×Dic5C2×D311yescharacteristic
152D4×Dic5C2×D311yescharacteristic
153C2×#687—31no—
154#4072—21no—
155#4072C2×D311yescharacteristic
156C2×C4⋊Dic5—21no—
157C2×C4⋊Dic5C2×D311yescharacteristic
158#4070—31no—
159#4036—31no—
160#4036—61no—
161#4035—61no—
162#4033—31no—
163#4025—61no—
164#4025—61no—
165C5×#103—31no—
166C5×#102—31no—
167C5×C22⋊C8—31no—
168#3967—31no—
169#3967—31no—
170#3967—31no—
171#3964—31no—
172C22⋊#168—31no—
173#3949—31no—
174#3949—31no—
175#3948—31no—
176#3948—31no—
177#3947—31no—
178#3946—31no—
179#3946—31no—
180C8×Dic5—31no—
181#3939—31no—
182#3939—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—
203C5×Dic6—21no—
204C5×Dic6—21no—
205C2×C3×Dic5—21no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—81no—
208C2×C3×Dic5—81no—
209C2×C3×Dic5—81no—
210C2×C3×Dic5C2×D411yescharacteristic
211C2×C3×Dic5C2×D411yescharacteristic
212C2×C3×Dic5C2×D411yescharacteristic
213C2×C3×Dic5C2×D411yescharacteristic
214C3⋊#168—21no—
215C3⋊#168—21no—
216C5×C3⋊C8—21no—
217C5×C3⋊C8—21no—
218C2×C3×#41C2×D511yescharacteristic
219C3×C4×Q8—51no—
220C3×C4×Q8—51no—
221C3×C4×D4—51no—
222C3×C4×D4—51no—
223C3×C4×D4—101no—
224C3×C4×D4—101no—
225C3×#117—51no—
226C3×#117—101no—
227C2×C3×C4⋊C4—51no—
228C2×C3×C4⋊C4—101no—
229C2×#216—51no—
230C2×#216C2×D511yescharacteristic
231C2×#214—51no—
232C2×#214C2×D511yescharacteristic
233#924—51no—
234#924C2×D511yescharacteristic
235#889—101no—
236#889—101no—
237#879—101no—
238#879—101no—
239#870—51no—
240#869—51no—
241C4×Dic6—51no—
242C4×Dic6—51no—
243#835—51no—
244#835C2×D511yescharacteristic
245#832—51no—
246#832C2×D511yescharacteristic
247#830—51no—
248#830C2×D511yescharacteristic
249#810—51no—
250#810—51no—
251#810—51no—
252#810—51no—
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)—51no—
258C4⋊(C3⋊C8)—51no—
259#803—51no—
260C4×C3⋊C8—51no—
261C5×#41—22no—
262C5×#41—22no—
263C2×C5×Q8—31no—
264C2×C5×Q8C22×D311yescharacteristic
265C2×C5×D4—21no—
266C2×C5×D4C22×D311yescharacteristic
267C22×C4×C5—21no—
268C22×C4×C5C22×D311yescharacteristic
269C22×Dic5—21no—
270C22×Dic5—21no—
271C22×Dic5—21no—
272C2×Dic10—31no—
273C5×Q16—62no—
274C5×SD16—62no—
275C2×C5×C8—31no—
276C2×C5×C8—31no—
277C5×C4⋊C4—31no—
278C5×C4⋊C4—61no—
279C5×C22⋊C4—61no—
280C22⋊Dic5—21no—
281C22⋊Dic5—21no—
282C22⋊Dic5—61no—
283C22⋊Dic5#6711yescharacteristic
284C22⋊Dic5#6711yescharacteristic
285#689—62no—
286#687—62no—
287C4⋊Dic5—21no—
288C4⋊Dic5—21no—
289C4⋊Dic5—21no—
290C4⋊Dic5—31no—
291C4⋊Dic5—61no—
292C4⋊Dic5—61no—
293C4⋊Dic5#6711yescharacteristic
294C4⋊Dic5#6711yescharacteristic
295C4⋊Dic5C22×D311yescharacteristic
296C4⋊Dic5C22×D311yescharacteristic
297#683—61no—
298#683—61no—
299#683—61no—
300#683—61no—
301#683—61no—
302C4×Dic5—21no—
303C4×Dic5—21no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306C4×Dic5C22×D311yescharacteristic
307C4×Dic5C22×D311yescharacteristic
308C2×#168—31no—
309C2×#168—31no—
310#541—151no—
311#520—51no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—31no—
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—21no—
339C3×Dic5—21no—
340C3×Dic5—21no—
341C3×Dic5—21no—
342C3×Dic5—41no—
343C3×Dic5—41no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C3×#41—22no—
347C3×#41—22no—
348C2×C3×Q8C22×D511yescharacteristic
349C2×C3×D4—21no—
350C2×C3×D4C22×D511yescharacteristic
351C22×C3×C4—21no—
352C22×C3×C4—101no—
353C22×C3×C4—101no—
354C22×C3×C4—101no—
355C22×C3×C4C22×D511yescharacteristic
356C2×Dic6—51no—
357C2×Dic6C22×D511yescharacteristic
358C3×C4⋊C4—51no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4—51no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4—101no—
365C3×C22⋊C4—51no—
366C3×C22⋊C4—51no—
367C3×C22⋊C4—101no—
368C3×C22⋊C4—101no—
369C3×C42—51no—
370C3×C42—51no—
371C3×C42—101no—
372C3×C42—101no—
373#217—21no—
374#217—101no—
375#216—22no—
376#216—102no—
377#214—22no—
378#214—102no—
379C4⋊Dic3—51no—
380C4⋊Dic3—101no—
381C4⋊Dic3—101no—
382C4⋊Dic3C22×D511yescharacteristic
383Dic3⋊C4—21no—
384Dic3⋊C4—101no—
385Dic3⋊C4—101no—
386Dic3⋊C4—101no—
387Dic3⋊C4—101no—
388Dic3⋊C4—101no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C2×C3⋊C8—51no—
392C2×C3⋊C8—51no—
393C2×C3⋊C8C22×D511yescharacteristic
394C2×C3⋊C8C22×D511yescharacteristic
395C23×C5—21no—
396C23×C5C2×#6711yescharacteristic
397C5×Q8—21no—
398C5×Q8—61no—
399C5×Q8—61no—
400C5×Q8#23512yes—
401C5×D4—24no—
402C5×D4—21no—
403C5×D4#23512yes—
404C2×C4×C5—24no—
405C2×C4×C5—21no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—61no—
409C2×C4×C5—61no—
410C2×C4×C5C2×#6711yescharacteristic
411C2×C4×C5C23×D311yescharacteristic
412C2×Dic5—21no—
413C2×Dic5—21no—
414C2×Dic5—61no—
415C2×Dic5—61no—
416C2×Dic5—81no—
417C2×Dic5—81no—
418C2×Dic5—81no—
419C2×Dic5C2×#6711yescharacteristic
420C2×Dic5C2×#6711yescharacteristic
421C2×Dic5C2×#6711yescharacteristic
422C2×Dic5C2×#6711yescharacteristic
423Dic10—61no—
424Dic10—61no—
425C5×C8—61no—
426C5×C8—61no—
427#168—61no—
428#168—61no—
429C2×#41D3×D511yescharacteristic
430C2×Q16—31no—
431C2×Q16—151no—
432C2×SD16—31no—
433C2×SD16—151no—
434C4⋊Q8—151no—
435#126—301no—
436#126—301no—
437#125—151no—
438#125—301no—
439#125—301no—
440C22⋊Q8—31no—
441C22⋊Q8—151no—
442C4×Q8—51no—
443C4×Q8—51no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—51no—
447C4×D4—51no—
448C4×D4—101no—
449C4×D4—101no—
450#117—51no—
451#117—101no—
452C2×C4⋊C4—51no—
453C2×C4⋊C4—101no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—151no—
459C4⋊C8—151no—
460#103—31no—
461#103—151no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—31no—
467#102—151no—
468C22⋊C8—31no—
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×C3D4×D511yescharacteristic
479C3×Q8—21no—
480C3×Q8#71112yes—
481C3×D4—24no—
482C3×D4—21no—
483C3×D4#71112yes—
484C2×C3×C4—24no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—51no—
489C2×C3×C4—51no—
490C2×C3×C4—51no—
491C2×C3×C4—51no—
492C2×C3×C4—101no—
493C2×C3×C4—101no—
494C2×C3×C4—401no—
495C2×C3×C4—401no—
496C2×C3×C4—401no—
497C2×C3×C4D4×D511yescharacteristic
498C2×C3×C4C23×D511yescharacteristic
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—101no—
502C2×Dic3—101no—
503Dic6—21no—
504Dic6—21no—
505Dic6—101no—
506Dic6—101no—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—21no—
512C22×C5—22no—
513C22×C5—21no—
514C22×C5—21no—
515C22×C5—41no—
516C22×C5—41no—
517C22×C5C22×#6711yescharacteristic
518C4×C5—21no—
519C4×C5—22no—
520C4×C5—121no—
521C4×C5—121no—
522C4×C5C2×#23511yescharacteristic
523C4×C5C2×#23511yescharacteristic
524Dic5—21no—
525Dic5—21no—
526Dic5—21no—
527Dic5—21no—
528Dic5—41no—
529Dic5—41no—
530Dic5—121no—
531Dic5—121no—
532#41—22no—
533#41—22no—
534C2×Q8—31no—
535C2×Q8—151no—
536C2×Q8C2×D3×D511yescharacteristic
537C2×D4—21no—
538C2×D4C2×D3×D511yescharacteristic
539C22×C4—21no—
540C22×C4—101no—
541C22×C4—101no—
542C22×C4—101no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—62no—
545Q16—302no—
546SD16—62no—
547SD16—302no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—151no—
551C2×C8—151no—
552C4⋊C4—31no—
553C4⋊C4—51no—
554C4⋊C4—51no—
555C4⋊C4—51no—
556C4⋊C4—51no—
557C4⋊C4—61no—
558C4⋊C4—101no—
559C4⋊C4—101no—
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—51no—
570C22⋊C4—51no—
571C22⋊C4—61no—
572C22⋊C4—101no—
573C22⋊C4—101no—
574C22⋊C4—301no—
575C42—51no—
576C42—51no—
577C42—101no—
578C42—101no—
579C42—301no—
580C42—301no—
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—22no—
586C22×C3—41no—
587C22×C3—41no—
588C22×C3C2×D4×D511yescharacteristic
589C3×C4—21no—
590C3×C4—22no—
591C3×C4—101no—
592C3×C4—101no—
593C3×C4—101no—
594C3×C4—101no—
595C3×C4—201no—
596C3×C4—201no—
597C3×C4C2×#71111yescharacteristic
598C3×C4C2×#71111yescharacteristic
599Dic3—41no—
600Dic3—41no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5—42no—
605C2×C5#579111yescharacteristic
606C2×C5#583611yescharacteristic
607C2×C5#583811yescharacteristic
608C23—21no—
609C23D5×#6711yescharacteristic
610Q8—21no—
611Q8—61no—
612Q8—61no—
613Q8—301no—
614Q8—301no—
615Q8#678212yes—
616D4—24no—
617D4—21no—
618D4#678212yes—
619C2×C4—24no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—51no—
624C2×C4—51no—
625C2×C4—51no—
626C2×C4—51no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—101no—
630C2×C4—101no—
631C2×C4—301no—
632C2×C4—301no—
633C2×C4—401no—
634C2×C4—401no—
635C2×C4—401no—
636C2×C4D5×#6711yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—61no—
639C8—61no—
640C8—301no—
641C8—301no—
642C2×C3—41no—
643C2×C3—42no—
644C2×C3#6592011yescharacteristic
645C2×C3#6610411yescharacteristic
646C2×C3#6611311yescharacteristic
647C5#8257511yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—22no—
652C22—41no—
653C22—41no—
654C22C2×D5×#6711yescharacteristic
655C4—21no—
656C4—22no—
657C4—101no—
658C4—101no—
659C4—101no—
660C4—101no—
661C4—121no—
662C4—121no—
663C4—201no—
664C4—201no—
665C4—601no—
666C4—601no—
667C4C2×#678211yescharacteristic
668C4C2×#678211yescharacteristic
669C3#1061194711yescharacteristic, complemented, Sylow
670C2—41no—
671C2—42no—
672C2#1175533611yescharacteristic
673C2#1175533711yescharacteristic
674C2#1175538511yescharacteristic
subgroupG/H
centerC22C2×D5×#67
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. #11754212C2semidirect
5. #11749350C2semidirect
6. #11749332C2semidirect
7. #11749247C2semidirect
8. #11749244C2semidirect
9. #11749103C2semidirect
10. #11749083C2semidirect
11. #11749004C2semidirect
12. Dic5×#214C2semidirect
13. #11748471C2semidirect
14. #11748450C2semidirect
15. #11748319C2semidirect
581. C3×C5#3120semidirect
647. C5#82575semidirect
669. C3#10611947semidirect

Maximal subgroups

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

subgroupindex
C3×#661612
#117542122
#117513402
C5×#52392
#117493502
#117493322
#117492472
#117492442
#117491032
#117490832
#117490042
Dic5×#2142
#117484712
#117484502
#117483192
#106119473
#825755