Finite Group Databasebeta

← #14471804

Subgroups — #14471804

Order 1920.

724 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×#5539C211yesmaximal, characteristic, complemented
2#11752700C211yesmaximal, characteristic, complemented
3#11751117C211yesmaximal, characteristic, complemented
4C3×C4×#686C211yesmaximal, characteristic, complemented
5#11749099C211yesmaximal, characteristic
6#11749079C211yesmaximal, characteristic, complemented
7#11749011C211yesmaximal, characteristic, complemented
8#11748986C211yesmaximal, characteristic, complemented
9#11747403C211yesmaximal, characteristic, complemented
10#11747374C211yesmaximal, characteristic, complemented
11#11747292C211yesmaximal, characteristic, complemented
12#11747250C211yesmaximal, characteristic, complemented
13#11746913C211yesmaximal, characteristic, complemented
14#11746887C211yesmaximal, characteristic, complemented
15Dic6×#168C211yesmaximal, characteristic, complemented
16#10615374—31nomaximal, Hall
17C3×C4×C5×D4C2211yescharacteristic
18C2×#6716C2211yescharacteristic
19C2×#6715C2211yescharacteristic
20#91764C2211yescharacteristic
21C5×D4×Dic3C2211yescharacteristic
22C5×D4×Dic3C2211yescharacteristic
23C5×#924—21no—
24C2×C5×Dic3⋊C4—21no—
25C5×#890C2211yescharacteristic
26C5×#888C2211yescharacteristic
27C5×#878—21no—
28C5×#878—21no—
29C5×#870C2211yescharacteristic
30C4×C5×Dic6C2211yescharacteristic
31C2×C3×#686C2211yescharacteristic
32C3×C4×D20C2211yescharacteristic
33#91458C2211yescharacteristic
34#91455—21no—
35#91444—21no—
36#91428C2211yescharacteristic
37#91364C2211yescharacteristic
38#91356—21no—
39#91348—21no—
40#91340C2211yescharacteristic
41#91094C2211yescharacteristic
42#91093C2211yescharacteristic
43C4⋊(C3⋊#168)C2211yescharacteristic
44C3×#3964C2211yescharacteristic
45C3×#3941C2211yescharacteristic
46C3×#3939C2211yescharacteristic
47C3×C4×#168C2211yescharacteristic
48#90989C2211yescharacteristic
49#90986C2211yescharacteristic
50Dic3⋊#168C2211yescharacteristic
51Dic3⋊#168C2211yescharacteristic
52#90975C2211yescharacteristic
53#90975C2211yescharacteristic
54#90969C2211yescharacteristic
55#90969C2211yescharacteristic
56#90964C2211yescharacteristic
57#90964C2211yescharacteristic
58Dic3×#168C2211yescharacteristic
59Dic3×#168C2211yescharacteristic
60#79569—51nomaximal, Hall
61C5×#554—31no—
62#65919—31no—
63#65380—31no—
64#65377—31no—
65#65357—31no—
66#65357—31no—
67#65355—31no—
68#65355—31no—
69Q8×#168—31no—
70C4×#687—31no—
71#65305—31no—
72#65305—31no—
73#65304—31no—
74C4×#686—31no—
75C4×#686D311yescharacteristic, complemented
76C2×C3×C5×D4C2311yescharacteristic
77C22×C3×C4×C5—21no—
78C2×D60C2311yescharacteristic
79C2×Dic30C2311yescharacteristic
80C22×C5×Dic3—21no—
81C22×C5×Dic3—21no—
82C2×C5×Dic6—21no—
83C2×C5×Dic6D411yescharacteristic
84C2×C3×D20C2311yescharacteristic
85C2×C3×C4×D5—21no—
86C2×#1202—21no—
87C2×#1202—21no—
88C2×#1200—21no—
89C3×C5×C4⋊C4C2311yescharacteristic
90C3×C5×C22⋊C4—21no—
91C3×C42×C5C2311yescharacteristic
92#6716—22no—
93#6715—22no—
94#6714—21no—
95#6714—21no—
96C2×C3⋊#168C2311yescharacteristic
97C2×C3⋊#168C2311yescharacteristic
98C5×#217—21no—
99C5×#217—21no—
100C5×C4⋊Dic3—21no—
101C5×C4⋊Dic3D411yescharacteristic
102C5×C4⋊Dic3C2311yescharacteristic
103C5×C4⋊Dic3C2311yescharacteristic
104C5×Dic3⋊C4—21no—
105C5×Dic3⋊C4—21no—
106C5×Dic3⋊C4—21no—
107C5×Dic3⋊C4—21no—
108C5×Dic3⋊C4D411yescharacteristic
109C5×Dic3⋊C4D411yescharacteristic
110C4×C5×Dic3C2311yescharacteristic
111C4×C5×Dic3C2311yescharacteristic
112C3×#686—22no—
113C3×#685—21no—
114C3×C4⋊Dic5C2311yescharacteristic
115C2×C3×#168C2311yescharacteristic
116C2×C3×#168C2311yescharacteristic
117#6669—21no—
118#6667—21no—
119#6665—21no—
120#6665—21no—
121Dic3×Dic5—21no—
122#5559—51no—
123#5539D511yescharacteristic, complemented
124C3×C4×D8—51no—
125#5153—51no—
126#5150—51no—
127#5016—51no—
128#5009—51no—
129#4891—51no—
130#4875—51no—
131#4768—51no—
132#4760—51no—
133#4758—51no—
134#4756—51no—
135#4697—51no—
136C8×Dic6—51no—
137C5×C4⋊Q8—31no—
138C5×#125—31no—
139C5×#125—31no—
140C5×C22⋊Q8—61no—
141C5×C22⋊Q8—61no—
142C5×C22⋊Q8—61no—
143C4×C5×Q8—31no—
144C4×C5×D4—31no—
145C4×C5×D4—31no—
146C4×C5×D4C2×D311yescharacteristic
147C2×C5×C4⋊C4—61no—
148#4093—61no—
149C2×#687—31no—
150C2×#686—31no—
151C2×#686C2×D311yescharacteristic
152#4040—61no—
153#4040—61no—
154#4039—61no—
155#4021—31no—
156#4021—31no—
157#4020—31no—
158C4×D20—31no—
159C4×D20C2×D311yescharacteristic
160C4×Dic10—31no—
161#3964C2×D311yescharacteristic
162#3942—31no—
163#3942—31no—
164#3942—31no—
165#3941—31no—
166#3941—31no—
167#3941—31no—
168#3941—31no—
169#3941—31no—
170#3941C2×D311yescharacteristic
171#3940—31no—
172#3939—31no—
173#3939C2×D311yescharacteristic
174C4⋊#168—31no—
175C4⋊#168—31no—
176C4⋊#168—31no—
177C4×#168—31no—
178C4×#168—31no—
179C4×#168C2×D311yescharacteristic
180#3361—151noSylow
181C23×C3×C5—21no—
182C22×D15—21no—
183C22×C3×D5—21no—
184C3×C5×D4—21no—
185C3×C5×D4#4112yes—
186C2×C3×C4×C5—21no—
187C2×C3×C4×C5—81no—
188C2×C3×C4×C5C2×D411yescharacteristic
189C2×C3×C4×C5C2×D411yescharacteristic
190C2×C3×C4×C5C2411yescharacteristic
191C2×Dic15—21no—
192D60—21no—
193D60—21no—
194Dic30—21no—
195Dic30—21no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—42no—
199C2×C5×Dic3—81no—
200C2×C5×Dic3C2×D411yescharacteristic
201C2×C5×Dic3C2×D411yescharacteristic
202C2×C5×Dic3C2×D411yescharacteristic
203C2×C5×Dic3C2×D411yescharacteristic
204C5×Dic6—22no—
205C5×Dic6—81no—
206C2×C3×Dic5—21no—
207C3×D20—21no—
208C3×D20—21no—
209C3×C4×D5—81no—
210#1202—42no—
211#1202—81no—
212#1200—81no—
213C3⋊#168—21no—
214C3⋊#168—21no—
215C3×#168—21no—
216C3×#168—21no—
217C2×C3×D8—51no—
218C3×C4×D4—51no—
219C3×C4×D4C2×D511yescharacteristic
220#940—51no—
221#936—51no—
222D4×Dic3C2×D511yescharacteristic
223D4×Dic3C2×D511yescharacteristic
224C2×#214—51no—
225C2×#213—51no—
226#929—101no—
227C4×#67—101no—
228#924—21no—
229C2×Dic3⋊C4—21no—
230#893—51no—
231#890C2×D511yescharacteristic
232#888C2×D511yescharacteristic
233#887—51no—
234#885—101no—
235#883—101no—
236#878—21no—
237#878—21no—
238#875—51no—
239#870C2×D511yescharacteristic
240C4×Dic6C2×D511yescharacteristic
241C3×#107—51no—
242C3×#102—51no—
243C3×#102—51no—
244C3×C4×C8—51no—
245#832—51no—
246#832—51no—
247#821—51no—
248#821—51no—
249#816—51no—
250#816—51no—
251Dic3⋊C8—51no—
252Dic3⋊C8—51no—
253C8×Dic3—51no—
254C8×Dic3—51no—
255#810—51no—
256#809—51no—
257#808—51no—
258#807—51no—
259C4⋊(C3⋊C8)—51no—
260C2×C5×Q8—31no—
261C2×C5×Q8—61no—
262C2×C5×D4C22×D311yescharacteristic
263C22×C4×C5—21no—
264C22×C4×C5—61no—
265C22×C4×C5—61no—
266C2×D20—31no—
267C2×D20—61no—
268C2×D20—61no—
269C2×D20C22×D311yescharacteristic
270C2×C4×D5—21no—
271C2×C4×D5—61no—
272C2×Dic10—31no—
273C5×C4⋊C4—31no—
274C5×C4⋊C4—31no—
275C5×C4⋊C4—31no—
276C5×C4⋊C4—31no—
277C5×C4⋊C4—31no—
278C5×C4⋊C4—61no—
279C5×C4⋊C4—61no—
280C5×C4⋊C4—61no—
281C5×C4⋊C4—61no—
282C5×C4⋊C4—61no—
283C5×C4⋊C4C22×D311yescharacteristic
284C5×C22⋊C4—21no—
285C5×C22⋊C4—61no—
286C5×C22⋊C4—61no—
287C42×C5—31no—
288C42×C5—31no—
289C42×C5C22×D311yescharacteristic
290#687—62no—
291#686—22no—
292#686—62no—
293#685—21no—
294#685—61no—
295#685—61no—
296#685—61no—
297#685—61no—
298#685—61no—
299C4⋊Dic5C22×D311yescharacteristic
300#683—61no—
301C4×Dic5—61no—
302C2×#168—31no—
303C2×#168—31no—
304C2×#168C22×D311yescharacteristic
305C2×#168C22×D311yescharacteristic
306#559—151no—
307#554—31no—
308#488—151no—
309#488—151no—
310#486—151no—
311#478—151no—
312#478—151no—
313#477—151no—
314#463—151no—
315#463—151no—
316#459—151no—
317C8×Q8—151no—
318C4×SD16—151no—
319C4×D8—51no—
320C4×D8—151no—
321C22×C3×C5—22no—
322C22×C3×C5—41no—
323C22×C3×C5—41no—
324C22×C3×C5C22×D411yescharacteristic
325C2×D15—41no—
326C2×D15—41no—
327C2×D15—41no—
328C2×C3×D5—41no—
329C2×C3×D5—41no—
330C2×C3×D5—41no—
331C3×C4×C5—21no—
332C3×C4×C5—21no—
333C3×C4×C5—41no—
334C3×C4×C5C2×#4111yescharacteristic
335C3×C4×C52−1+411yescharacteristic
336Dic15—41no—
337C3×Dic5—41no—
338C5×Dic3—21no—
339C5×Dic3—21no—
340C5×Dic3—21no—
341C5×Dic3—41no—
342C5×Dic3—41no—
343C5×Dic3#13512yes—
344C2×C3×D4—51no—
345C2×C3×D4C22×D511yescharacteristic
346C22×C3×C4—21no—
347C22×C3×C4—101no—
348C2×#67—101no—
349C2×#67—101no—
350C22×Dic3—21no—
351C22×Dic3—21no—
352C2×D12—51no—
353C2×C4×D3—101no—
354C2×Dic6—21no—
355C2×Dic6—51no—
356C2×Dic6C22⋊D511yescharacteristic
357C3×D8—102no—
358C2×C3×C8—51no—
359C2×C3×C8—51no—
360C3×C4⋊C4—51no—
361C3×C4⋊C4C22×D511yescharacteristic
362C3×C22⋊C4—21no—
363C3×C22⋊C4—101no—
364C3×C42C22×D511yescharacteristic
365#217—21no—
366#217—21no—
367#217—101no—
368#217—101no—
369#214—102no—
370#213—102no—
371(C2×D3)⋊C4—101no—
372(C2×D3)⋊C4—101no—
373(C2×D3)⋊C4—101no—
374C4⋊Dic3—21no—
375C4⋊Dic3C22⋊D511yescharacteristic
376C4⋊Dic3C22×D511yescharacteristic
377C4⋊Dic3C22×D511yescharacteristic
378Dic3⋊C4—21no—
379Dic3⋊C4—21no—
380Dic3⋊C4—21no—
381Dic3⋊C4—21no—
382Dic3⋊C4—101no—
383Dic3⋊C4C22⋊D511yescharacteristic
384Dic3⋊C4C22⋊D511yescharacteristic
385C4×Dic3—101no—
386C4×Dic3C22×D511yescharacteristic
387C4×Dic3C22×D511yescharacteristic
388C2×C3⋊C8—51no—
389C2×C3⋊C8—51no—
390C23×C5—21no—
391C22×D5—21no—
392C22×D5—61no—
393C5×Q8—62no—
394C5×Q8—241no—
395C5×D4—21no—
396C5×D4#23512yes—
397C2×C4×C5—21no—
398C2×C4×C5—31no—
399C2×C4×C5—31no—
400C2×C4×C5—31no—
401C2×C4×C5—31no—
402C2×C4×C5—61no—
403C2×C4×C5—61no—
404C2×C4×C5—81no—
405C2×C4×C5—122no—
406C2×C4×C5—241no—
407C2×C4×C5D3×D411yescharacteristic
408C2×C4×C5D3×D411yescharacteristic
409C2×C4×C5C23×D311yescharacteristic
410C2×Dic5—21no—
411C2×Dic5—61no—
412D20—21no—
413D20—21no—
414D20—61no—
415D20—61no—
416D20—122no—
417D20—241no—
418C4×D5—81no—
419C4×D5—241no—
420Dic10—61no—
421Dic10—61no—
422#168—21no—
423#168—21no—
424#168—61no—
425#168—61no—
426C2×SD16—151no—
427C2×D8—51no—
428C2×D8—151no—
429C4⋊Q8—31no—
430#127—151no—
431#125—31no—
432#125—31no—
433#124—151no—
434#124—151no—
435#124—301no—
436#123—301no—
437#123—301no—
438C22⋊Q8—61no—
439C22⋊Q8—61no—
440C22⋊Q8—61no—
441C4×Q8—31no—
442C4×Q8—151no—
443C4×D4—31no—
444C4×D4—31no—
445C4×D4—51no—
446C4×D4—151no—
447C4×D4—301no—
448C4×D4D3×D511yescharacteristic
449C2×C4⋊C4—61no—
450#107—51no—
451#107—151no—
452#106—151no—
453C4⋊C8—151no—
454C4⋊C8—151no—
455C4⋊C8—151no—
456#103—151no—
457#103—151no—
458#103—151no—
459#102—51no—
460#102—51no—
461#102—151no—
462#102—151no—
463#102—151no—
464#102—151no—
465#102—151no—
466C4×C8—51no—
467C4×C8—151no—
468C4×C8—151no—
469C2×C3×C5—42no—
470C2×C3×C5#54811yescharacteristic
471C2×C3×C5C2×#13511yescharacteristic
472C2×C3×C5#57611yescharacteristic
473D15—81no—
474C3×D5—81no—
475C23×C3—21no—
476C23×C3—101no—
477C22×D3—101no—
478C3×D4—21no—
479C3×D4—101no—
480C3×D4—101no—
481C3×D4#71312yes—
482C2×C3×C4—21no—
483C2×C3×C4—81no—
484C2×C3×C4—101no—
485C2×C3×C4—401no—
486C2×C3×C4C2×C22⋊D511yescharacteristic
487C2×C3×C4C2×C22⋊D511yescharacteristic
488C2×C3×C4C23×D511yescharacteristic
489#67—202no—
490#67—401no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—42no—
494C2×Dic3—81no—
495C2×Dic3—101no—
496C2×Dic3C2×C22⋊D511yescharacteristic
497C2×Dic3C2×C22⋊D511yescharacteristic
498C2×Dic3C2×C22⋊D511yescharacteristic
499C2×Dic3C2×C22⋊D511yescharacteristic
500D12—101no—
501D12—101no—
502C4×D3—401no—
503Dic6—22no—
504Dic6—81no—
505Dic6—101no—
506Dic6—101no—
507C3×C8—101no—
508C3×C8—101no—
509C3⋊C8—101no—
510C3⋊C8—101no—
511C22×C5—22no—
512C22×C5—41no—
513C22×C5—41no—
514C22×C5C2×D3×D411yescharacteristic
515C2×D5—41no—
516C2×D5—41no—
517C2×D5—41no—
518C2×D5—121no—
519C2×D5—121no—
520C2×D5—121no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—32no—
524C4×C5—41no—
525C4×C5—61no—
526C4×C5—61no—
527C4×C5—61no—
528C4×C5—121no—
529C4×C5—121no—
530C4×C5C2×#23511yescharacteristic
531C4×C5#101011yescharacteristic
532Dic5—41no—
533Dic5—121no—
534C2×Q8—31no—
535C2×Q8—61no—
536C2×Q8—151no—
537C2×D4—51no—
538C2×D4—151no—
539C2×D4—301no—
540C2×D4—301no—
541C2×D4C2×D3×D511yescharacteristic
542C22×C4—21no—
543C22×C4—61no—
544C22×C4—61no—
545C22×C4—101no—
546C22×C4—301no—
547SD16—302no—
548D8—102no—
549D8—302no—
550C2×C8—51no—
551C2×C8—51no—
552C2×C8—151no—
553C2×C8—151no—
554C4⋊C4—31no—
555C4⋊C4—31no—
556C4⋊C4—31no—
557C4⋊C4—31no—
558C4⋊C4—31no—
559C4⋊C4—51no—
560C4⋊C4—61no—
561C4⋊C4—61no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—301no—
566C4⋊C4C2×D3×D511yescharacteristic
567C22⋊C4—21no—
568C22⋊C4—61no—
569C22⋊C4—61no—
570C22⋊C4—101no—
571C22⋊C4—301no—
572C22⋊C4—301no—
573C22⋊C4—301no—
574C22⋊C4—301no—
575C22⋊C4—301no—
576C42—31no—
577C42—31no—
578C42—301no—
579C42C2×D3×D511yescharacteristic
580C3×C5#336111yescharacteristic, complemented, Hall
581C22×C3—22no—
582C22×C3—41no—
583C22×C3—41no—
584C22×C3—201no—
585C22×C3—201no—
586C22×C3—201no—
587C22×C3C22×C22⋊D511yescharacteristic
588C2×D3—201no—
589C2×D3—201no—
590C2×D3—201no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—41no—
594C3×C4—201no—
595C3×C4C2×#71311yescharacteristic
596C3×C4#414711yescharacteristic
597Dic3—21no—
598Dic3—21no—
599Dic3—21no—
600Dic3—41no—
601Dic3—41no—
602Dic3—201no—
603Dic3#409612yes—
604C2×C5—42no—
605C2×C5#555211yescharacteristic
606C2×C5#575711yescharacteristic
607C2×C5D3×#13511yescharacteristic
608D5—81no—
609D5—241no—
610C23—21no—
611C23—101no—
612C23—301no—
613Q8—62no—
614Q8—241no—
615Q8—301no—
616Q8—301no—
617D4—21no—
618D4—101no—
619D4—101no—
620D4—301no—
621D4—301no—
622D4—602no—
623D4—1201no—
624D4#677312yes—
625C2×C4—21no—
626C2×C4—31no—
627C2×C4—31no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—61no—
631C2×C4—61no—
632C2×C4—81no—
633C2×C4—101no—
634C2×C4—122no—
635C2×C4—241no—
636C2×C4—301no—
637C2×C4—401no—
638C2×C4—1201no—
639C2×C4D3×C22⋊D511yescharacteristic
640C2×C4D3×C22⋊D511yescharacteristic
641C2×C4C22×D3×D511yescharacteristic
642C8—101no—
643C8—101no—
644C8—301no—
645C8—301no—
646C2×C3—42no—
647C2×C3—401no—
648C2×C3#6615111yescharacteristic
649C2×C3C2×#409611yescharacteristic
650C2×C3#6616911yescharacteristic
651D3—401no—
652C5#7956911yescharacteristic, complemented, Sylow
653C22—22no—
654C22—41no—
655C22—41no—
656C22—201no—
657C22—201no—
658C22—201no—
659C22—601no—
660C22—601no—
661C22—601no—
662C22C2×D3×C22⋊D511yescharacteristic
663C4—21no—
664C4—21no—
665C4—32no—
666C4—41no—
667C4—61no—
668C4—61no—
669C4—61no—
670C4—121no—
671C4—121no—
672C4—201no—
673C4—601no—
674C4#9200011yescharacteristic
675C4C2×#677311yescharacteristic
676C3#1061537411yescharacteristic, complemented, Sylow
677C2—42no—
678C2—401no—
679C2—1201no—
680C2#1175454411yescharacteristic
681C2#1175469711yescharacteristic
682C2D3×#409611yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊D5
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×D4C22
socleC22×C3×C5C22×D4
prime radical#11749099C2
hypercenterC4×D4D3×D5
hypocenterC3×C5#3361
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
1. C5×#5539C2semidirect
2. #11752700C2semidirect
3. #11751117C2semidirect
4. C3×C4×#686C2semidirect
6. #11749079C2semidirect
7. #11749011C2semidirect
8. #11748986C2semidirect
9. #11747403C2semidirect
10. #11747374C2semidirect
11. #11747292C2semidirect
12. #11747250C2semidirect
13. #11746913C2semidirect
14. #11746887C2semidirect
15. Dic6×#168C2semidirect
75. C4×#686D3semidirect
123. #5539D5semidirect
580. C3×C5#3361semidirect
652. C5#79569semidirect
676. C3#10615374semidirect

Maximal subgroups

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

subgroupindex
C5×#55392
#117527002
#117511172
C3×C4×#6862
#117490992
#117490792
#117490112
#117489862
#117474032
#117473742
#117472922
#117472502
#117469132
#117468872
Dic6×#1682
#106153743
#795695