Finite Group Databasebeta

← #14436187

Subgroups — #14436187

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
1#11756282C211yesmaximal, characteristic
2C3×#65852C211yesmaximal, characteristic, complemented
3C5×#5000C211yesmaximal, characteristic, complemented
4#11748552C211yesmaximal, characteristic
5#11748552C211yesmaximal, characteristic
6#11748445C211yesmaximal, characteristic, complemented
7#11748403C211yesmaximal, characteristic, complemented
8#11747104C211yesmaximal, characteristic, complemented
9#11747091C211yesmaximal, characteristic, complemented
10C4×#6662C211yesmaximal, characteristic, complemented
11#11747085C211yesmaximal, characteristic, complemented
12#11747054C211yesmaximal, characteristic, complemented
13C4×#6658C211yesmaximal, characteristic, complemented
14#11746951C211yesmaximal, characteristic, complemented
15#11746934C211yesmaximal, characteristic, complemented
16#10611116—31nomaximal, Hall
17C2×#6817C2211yescharacteristic
18C3×C5×#117C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20#91781—21no—
21C4⋊C4×D15—21no—
22#91770—21no—
23#91770—21no—
24C4×D60C2211yescharacteristic
25C4×D60C2211yescharacteristic
26C4×Dic30C2211yescharacteristic
27C4×Dic30C2211yescharacteristic
28C3×#4070C2211yescharacteristic
29C3×#4070C2211yescharacteristic
30C3×#4035—21no—
31C3×#4035—21no—
32C3×#4025—21no—
33C3×#4025—21no—
34C3×#4016C2211yescharacteristic
35C3×#4015C2211yescharacteristic
36C3×C4×Dic10C2211yescharacteristic
37C3×C4×Dic10C2211yescharacteristic
38C2×#6662C2211yescharacteristic
39C2×#6662C2211yescharacteristic
40C2×#6658C2211yescharacteristic
41C2×#6658C2211yescharacteristic
42C5×#830C2211yescharacteristic
43C5×#830C2211yescharacteristic
44C5×C4⋊(C3⋊C8)C2211yescharacteristic
45C5×C4⋊(C3⋊C8)C2211yescharacteristic
46C5×#803C2211yescharacteristic
47C4×C5×C3⋊C8C2211yescharacteristic
48#90990C2211yescharacteristic
49#90990C2211yescharacteristic
50#90987C2211yescharacteristic
51#90987C2211yescharacteristic
52#90974C2211yescharacteristic
53#90974C2211yescharacteristic
54#90971C2211yescharacteristic
55#90971C2211yescharacteristic
56#90971C2211yescharacteristic
57#90971C2211yescharacteristic
58#90968C2211yescharacteristic
59#90968C2211yescharacteristic
60#83446—51nomaximal, Hall
61#65857—31no—
62#65852D311yescharacteristic, complemented
63C5×#433—31no—
64#65138—31no—
65#65136—31no—
66#65130—31no—
67#65118—31no—
68#65022—31no—
69#65022—31no—
70#65011—31no—
71#65010—31no—
72#65005—31no—
73#64999—31no—
74C4×Dic20—31no—
75C4×#677—31no—
76C22×C3×C4×C5C2311yescharacteristic
77C2×#1220—21no—
78C22×Dic15—21no—
79#6817—22no—
80#6817—22no—
81C2×D60C2311yescharacteristic
82C2×C4×D15—21no—
83C2×C4×D15—21no—
84C2×C4×D15—21no—
85C2×Dic30C2311yescharacteristic
86C2×C3×Dic10C2311yescharacteristic
87C2×C3×Dic10C2311yescharacteristic
88C3×C5×C4⋊C4D411yescharacteristic
89C3×C5×C4⋊C4D411yescharacteristic
90C3×C5×C22⋊C4D411yescharacteristic
91C3×C5×C22⋊C4D411yescharacteristic
92C3×C42×C5C2311yescharacteristic
93C3×C42×C5C2311yescharacteristic
94#6714—21no—
95#6714—21no—
96C4⋊Dic15—21no—
97C4⋊Dic15C2311yescharacteristic
98C4⋊Dic15C2311yescharacteristic
99#6712—21no—
100#6712—21no—
101C4×Dic15—21no—
102C4×Dic15—21no—
103C2×C5×C3⋊C8C2311yescharacteristic
104C2×C5×C3⋊C8C2311yescharacteristic
105C2×C5×C3⋊C8C2311yescharacteristic
106C2×C5×C3⋊C8C2311yescharacteristic
107C3×C22⋊Dic5—21no—
108C3×C22⋊Dic5—21no—
109C3×C4⋊Dic5—21no—
110C3×C4⋊Dic5—21no—
111C3×C4⋊Dic5C2311yescharacteristic
112C3×C4⋊Dic5C2311yescharacteristic
113C3×#683—21no—
114C3×#683—21no—
115C3×#683—21no—
116C3×#683—21no—
117C3×#683—21no—
118C3×#683—21no—
119C3×C4×Dic5—21no—
120C3×C4×Dic5—21no—
121#6662—22no—
122#6662—22no—
123#6658—22no—
124#6658—22no—
125C3×#541—51no—
126#5523—51no—
127#5090—51no—
128#5083—51no—
129#5066—51no—
130#5063—51no—
131#5047—51no—
132#5047—51no—
133#5044—51no—
134#5043—51no—
135#5030—51no—
136C4×#216—51no—
137#5026—51no—
138C4×#215—51no—
139#5000D511yescharacteristic, complemented
140C2×#709—31no—
141C5×#117C2×D311yescharacteristic
142C2×C4⋊Dic5—31no—
143#4070C2×D311yescharacteristic
144#4070C2×D311yescharacteristic
145C2×Dic20—31no—
146C2×Dic20—31no—
147C2×#677—31no—
148C2×#677—31no—
149#4038—61no—
150D5×C4⋊C4—61no—
151#4035—21no—
152#4035—21no—
153#4027—61no—
154#4027—61no—
155#4025—21no—
156#4025—21no—
157C4×D20—31no—
158C4×D20—31no—
159#4016C2×D311yescharacteristic
160#4015C2×D311yescharacteristic
161C4×Dic10—31no—
162C4×Dic10—31no—
163C4×Dic10C2×D311yescharacteristic
164C4×Dic10C2×D311yescharacteristic
165C5×C4⋊C8—31no—
166C5×C4⋊C8—31no—
167C5×C22⋊C8—31no—
168C5×C22⋊C8—31no—
169C5×#97—31no—
170C4×C5×C8—31no—
171#3953—31no—
172#3953—31no—
173#3950—31no—
174#3950—31no—
175#3949—31no—
176#3949—31no—
177#3948—31no—
178#3948—31no—
179#3948—31no—
180#3948—31no—
181#3948—31no—
182#3948—31no—
183#3120—151noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×D15—21no—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—21no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2×D411yescharacteristic
191C2×C3×C4×C5C2×D411yescharacteristic
192C2×C3×C4×C5C2×D411yescharacteristic
193C2×C3×C4×C5C2411yescharacteristic
194#1220—24no—
195C2×Dic15—21no—
196C2×Dic15—21no—
197C2×Dic15—21no—
198C2×Dic15—81no—
199D60—21no—
200D60#4112yes—
201C4×D15—24no—
202C4×D15—81no—
203C4×D15—81no—
204Dic30—21no—
205Dic30#4112yes—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—21no—
209C2×C3×Dic5—21no—
210C3×Dic10—21no—
211C3×Dic10—21no—
212C3×Dic10—21no—
213C3×Dic10—21no—
214C5×C3⋊C8—21no—
215C5×C3⋊C8—21no—
216C5×C3⋊C8—21no—
217C5×C3⋊C8—21no—
218C2×#235—51no—
219C3×C4⋊Q8—51no—
220C3×#126—101no—
221C3×#126—101no—
222C3×#125—51no—
223C3×#125—101no—
224C3×#125—101no—
225C3×C22⋊Q8—51no—
226C3×C22⋊Q8—51no—
227C3×C4×Q8—51no—
228C3×C4×Q8—51no—
229C3×#117C2×D511yescharacteristic
230C2×#216—51no—
231C2×#216—51no—
232C2×#215—51no—
233C2×#215—51no—
234C2×C4⋊Dic3—51no—
235#892—101no—
236D3×C4⋊C4—101no—
237#67⋊C4—101no—
238#67⋊C4—101no—
239C4×D12—51no—
240C4×D12—51no—
241C4×Dic6—51no—
242C4×Dic6—51no—
243#835—51no—
244#835—51no—
245#835—51no—
246#835—51no—
247#830C2×D511yescharacteristic
248#830C2×D511yescharacteristic
249#810—51no—
250#810—51no—
251#809—51no—
252#809—51no—
253#808—51no—
254#808—51no—
255#807—51no—
256#807—51no—
257C4⋊(C3⋊C8)C2×D511yescharacteristic
258C4⋊(C3⋊C8)C2×D511yescharacteristic
259#803C2×D511yescharacteristic
260C4×C3⋊C8C2×D511yescharacteristic
261C22×C4×C5C22×D311yescharacteristic
262C2×C22⋊D5—61no—
263C22×Dic5—61no—
264#709—62no—
265#709—62no—
266C2×D20—31no—
267C2×C4×D5—61no—
268C2×C4×D5—61no—
269C2×C4×D5—61no—
270C2×Dic10—31no—
271C2×Dic10C22×D311yescharacteristic
272C2×Dic10C22×D311yescharacteristic
273C2×C5×C8—31no—
274C2×C5×C8—31no—
275C2×C5×C8—31no—
276C2×C5×C8—31no—
277C5×C4⋊C4#6711yescharacteristic
278C5×C4⋊C4#6711yescharacteristic
279C5×C22⋊C4#6711yescharacteristic
280C5×C22⋊C4#6711yescharacteristic
281C42×C5C22×D311yescharacteristic
282C42×C5C22×D311yescharacteristic
283C22⋊Dic5—21no—
284C22⋊Dic5—21no—
285#685—61no—
286#685—61no—
287C4⋊Dic5—21no—
288C4⋊Dic5—21no—
289C4⋊Dic5—31no—
290C4⋊Dic5—31no—
291C4⋊Dic5—61no—
292C4⋊Dic5C22×D311yescharacteristic
293C4⋊Dic5C22×D311yescharacteristic
294#683—21no—
295#683—21no—
296#683—21no—
297#683—21no—
298#683—21no—
299#683—21no—
300#683—61no—
301#683—61no—
302C4×Dic5—21no—
303C4×Dic5—21no—
304C4×Dic5—61no—
305C4×Dic5—61no—
306Dic20—62no—
307Dic20—62no—
308#677—62no—
309#677—62no—
310#541—51no—
311#520—151no—
312#484—151no—
313#483—151no—
314#479—151no—
315#478—151no—
316#462—151no—
317#461—151no—
318#452—151no—
319#452—151no—
320#441—151no—
321#440—151no—
322C4×Q16—151no—
323C4×SD16—151no—
324#433—31no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×D15—22no—
330C2×D15—41no—
331C2×D15—41no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5C2×#4111yescharacteristic
338C3×C4×C5C2×#4111yescharacteristic
339Dic15—22no—
340Dic15—41no—
341Dic15—41no—
342C3×Dic5—41no—
343C3×Dic5—41no—
344C3×Dic5—41no—
345C3×Dic5—41no—
346C2×C3×Q8—51no—
347C2×C3×Q8—51no—
348C22×C3×C4C22×D511yescharacteristic
349C2×#67—101no—
350C22×Dic3—101no—
351#235—102no—
352#235—102no—
353C2×D12—51no—
354C2×C4×D3—101no—
355C2×C4×D3—101no—
356C2×C4×D3—101no—
357C2×Dic6—51no—
358C3×C4⋊C4—51no—
359C3×C4⋊C4—51no—
360C3×C4⋊C4—101no—
361C3×C4⋊C4—101no—
362C3×C4⋊C4—101no—
363C3×C4⋊C4—101no—
364C3×C4⋊C4—101no—
365C3×C4⋊C4—101no—
366C3×C4⋊C4—101no—
367C3×C4⋊C4—101no—
368C3×C4⋊C4D2011yescharacteristic
369C3×C4⋊C4D2011yescharacteristic
370C3×C22⋊C4—101no—
371C3×C22⋊C4—101no—
372C3×C22⋊C4D2011yescharacteristic
373C3×C22⋊C4D2011yescharacteristic
374C3×C42—101no—
375C3×C42—101no—
376C3×C42C22×D511yescharacteristic
377C3×C42C22×D511yescharacteristic
378#216—102no—
379#216—102no—
380#215—102no—
381#215—102no—
382(C2×D3)⋊C4—101no—
383(C2×D3)⋊C4—101no—
384C4⋊Dic3—51no—
385C4⋊Dic3—51no—
386C4⋊Dic3—101no—
387Dic3⋊C4—101no—
388Dic3⋊C4—101no—
389C4×Dic3—101no—
390C4×Dic3—101no—
391C2×C3⋊C8C22×D511yescharacteristic
392C2×C3⋊C8C22×D511yescharacteristic
393C2×C3⋊C8C22×D511yescharacteristic
394C2×C3⋊C8C22×D511yescharacteristic
395C23×C5C2×#6711yescharacteristic
396C22×D5—61no—
397C2×C4×C5—21no—
398C2×C4×C5—21no—
399C2×C4×C5C2×#6711yescharacteristic
400C2×C4×C5C2×#6711yescharacteristic
401C2×C4×C5C2×#6711yescharacteristic
402C2×C4×C5C2×#6711yescharacteristic
403C2×C4×C5C2×#6711yescharacteristic
404C2×C4×C5C23×D311yescharacteristic
405C22⋊D5—64no—
406C2×Dic5—21no—
407C2×Dic5—21no—
408C2×Dic5—21no—
409C2×Dic5—21no—
410C2×Dic5—61no—
411C2×Dic5—61no—
412C2×Dic5—61no—
413C2×Dic5—241no—
414D20—32no—
415D20—61no—
416C4×D5—64no—
417C4×D5—241no—
418C4×D5—241no—
419Dic10—21no—
420Dic10—21no—
421Dic10—21no—
422Dic10—21no—
423Dic10—32no—
424Dic10—61no—
425C5×C8—61no—
426C5×C8—61no—
427C5×C8—61no—
428C5×C8—61no—
429C2×#41—151no—
430C2×Q16—151no—
431C2×Q16—151no—
432C2×SD16—151no—
433C2×SD16—151no—
434C4⋊Q8—51no—
435#126—101no—
436#126—101no—
437#125—51no—
438#125—101no—
439#125—101no—
440C22⋊Q8—51no—
441C22⋊Q8—51no—
442C4×Q8—51no—
443C4×Q8—51no—
444C4×Q8—151no—
445C4×Q8—151no—
446C4×D4—151no—
447C4×D4—151no—
448C4×D4—301no—
449C4×D4—301no—
450#117—301no—
451#117D3×D511yescharacteristic
452C2×C4⋊C4—151no—
453C2×C4⋊C4—301no—
454#107—151no—
455#107—151no—
456#106—151no—
457#106—151no—
458C4⋊C8—31no—
459C4⋊C8—31no—
460#103—151no—
461#103—151no—
462#103—151no—
463#103—151no—
464#103—151no—
465#103—151no—
466#102—151no—
467#102—151no—
468C22⋊C8—31no—
469C22⋊C8—31no—
470#97—31no—
471C4×C8—31no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476D15—42no—
477C23×C3C2×D2011yescharacteristic
478C22×D3—101no—
479C3×Q8—101no—
480C3×Q8—101no—
481C3×Q8—101no—
482C3×Q8—101no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—101no—
486C2×C3×C4—101no—
487C2×C3×C4—101no—
488C2×C3×C4—101no—
489C2×C3×C4C2×D2011yescharacteristic
490C2×C3×C4C2×D2011yescharacteristic
491C2×C3×C4C2×D2011yescharacteristic
492C2×C3×C4C2×D2011yescharacteristic
493C2×C3×C4C2×D2011yescharacteristic
494C2×C3×C4C23×D511yescharacteristic
495#67—104no—
496C2×Dic3—101no—
497C2×Dic3—101no—
498C2×Dic3—101no—
499C2×Dic3—401no—
500D12—52no—
501D12—101no—
502C4×D3—104no—
503C4×D3—401no—
504C4×D3—401no—
505Dic6—52no—
506Dic6—101no—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C3⋊C8—21no—
510C3⋊C8—21no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5C22×#6711yescharacteristic
515C2×D5—62no—
516C2×D5—121no—
517C2×D5—121no—
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5D3×#4111yescharacteristic
524C4×C5D3×#4111yescharacteristic
525Dic5—41no—
526Dic5—41no—
527Dic5—41no—
528Dic5—41no—
529Dic5—62no—
530Dic5—121no—
531Dic5—121no—
532#41—302no—
533#41—302no—
534C2×Q8—51no—
535C2×Q8—51no—
536C2×Q8—151no—
537C2×D4—151no—
538C2×D4—301no—
539C22×C4—301no—
540C22×C4—301no—
541C22×C4—301no—
542C22×C4—301no—
543C22×C4C2×D3×D511yescharacteristic
544Q16—302no—
545Q16—302no—
546SD16—302no—
547SD16—302no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—31no—
551C2×C8—31no—
552C4⋊C4—51no—
553C4⋊C4—51no—
554C4⋊C4—101no—
555C4⋊C4—101no—
556C4⋊C4—101no—
557C4⋊C4—101no—
558C4⋊C4—101no—
559C4⋊C4—101no—
560C4⋊C4—101no—
561C4⋊C4—101no—
562C4⋊C4—151no—
563C4⋊C4—151no—
564C4⋊C4—301no—
565C4⋊C4—301no—
566C4⋊C4—301no—
567C4⋊C4#120211yescharacteristic
568C4⋊C4#120211yescharacteristic
569C22⋊C4—101no—
570C22⋊C4—101no—
571C22⋊C4—301no—
572C22⋊C4—301no—
573C22⋊C4#120211yescharacteristic
574C22⋊C4#120211yescharacteristic
575C42—101no—
576C42—101no—
577C42—301no—
578C42—301no—
579C42C2×D3×D511yescharacteristic
580C42C2×D3×D511yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3C22×D2011yescharacteristic
586C2×D3—102no—
587C2×D3—201no—
588C2×D3—201no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—201no—
595C3×C4—201no—
596C3×C4—201no—
597C3×C4—201no—
598C3×C4D5×#4111yescharacteristic
599C3×C4D5×#4111yescharacteristic
600Dic3—102no—
601Dic3—201no—
602Dic3—201no—
603C2×C5—41no—
604C2×C5#582811yescharacteristic
605C2×C5#583711yescharacteristic
606C2×C5#583811yescharacteristic
607D5—122no—
608C23—301no—
609C23C2×#120211yescharacteristic
610Q8—101no—
611Q8—101no—
612Q8—101no—
613Q8—101no—
614Q8—152no—
615Q8—301no—
616D4—152no—
617D4—304no—
618D4—301no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—101no—
622C2×C4—101no—
623C2×C4—101no—
624C2×C4—101no—
625C2×C4—304no—
626C2×C4—301no—
627C2×C4—301no—
628C2×C4—301no—
629C2×C4—1201no—
630C2×C4—1201no—
631C2×C4—1201no—
632C2×C4C2×#120211yescharacteristic
633C2×C4C2×#120211yescharacteristic
634C2×C4C2×#120211yescharacteristic
635C2×C4C2×#120211yescharacteristic
636C2×C4C2×#120211yescharacteristic
637C2×C4C22×D3×D511yescharacteristic
638C8—61no—
639C8—61no—
640C8—61no—
641C8—61no—
642C2×C3—41no—
643C2×C3#6585811yescharacteristic
644C2×C3#6608511yescharacteristic
645C2×C3#6608711yescharacteristic
646D3—202no—
647C5#8344611yescharacteristic, complemented, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—302no—
652C22—601no—
653C22—601no—
654C22C22×#120211yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—201no—
661C4—201no—
662C4—201no—
663C4—201no—
664C4—302no—
665C4—601no—
666C4—601no—
667C4#9201611yescharacteristic
668C4#9201611yescharacteristic
669C3#1061111611yescharacteristic, complemented, Sylow
670C2—41no—
671C2—602no—
672C2#1175459011yescharacteristic
673C2#1175531011yescharacteristic
674C2#1175531211yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#117C22
socleC22×C3×C5C22×D4
prime radicalC2×#6817C22
hypercenter#117D3×D5
hypocenterC3×C5#3120
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#65852C2semidirect
3. C5×#5000C2semidirect
6. #11748445C2semidirect
7. #11748403C2semidirect
8. #11747104C2semidirect
9. #11747091C2semidirect
10. C4×#6662C2semidirect
11. #11747085C2semidirect
12. #11747054C2semidirect
13. C4×#6658C2semidirect
14. #11746951C2semidirect
15. #11746934C2semidirect
62. #65852D3semidirect
139. #5000D5semidirect
581. C3×C5#3120semidirect
647. C5#83446semidirect
669. C3#10611116semidirect

Maximal subgroups

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

subgroupindex
#117562822
C3×#658522
C5×#50002
#117485522
#117484452
#117484032
#117471042
#117470912
C4×#66622
#117470852
#117470542
C4×#66582
#117469512
#117469342
#106111163
#834465