Finite Group Databasebeta

← #14300501

Subgroups — #14300501

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×C22⋊D5C211yesmaximal, characteristic
2C22×#6649C211yesmaximal, characteristic, complemented
3C2×#91114C211yesmaximal, characteristic, complemented
4C2×C5×#830C211yesmaximal, characteristic, complemented
5C2×#90955C211yesmaximal, characteristic, complemented
6#11745966C211yesmaximal, characteristic, complemented
7#11745966C211yesmaximal, characteristic, complemented
8#10600751—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C22×C3×C22⋊D5C411yescharacteristic
11C22×C3×C4×D5C2211yescharacteristic
12C22×C3⋊#168C2211yescharacteristic
13C22×C3⋊#168C2211yescharacteristic
14C22×C5×C3⋊C8C2211yescharacteristic
15C22×C5×C3⋊C8C2211yescharacteristic
16C2×C3×C22⋊Dic5C411yescharacteristic
17C3×C4×C22⋊D5—22no—
18C3×C4×C22⋊D5—22no—
19C2×C3×#685C411yescharacteristic
20C2×C3×#683C411yescharacteristic
21C2×C3×C4×Dic5C2211yescharacteristic
22C2×#6649—22no—
23C2×#6649—22no—
24C2×#6649—22no—
25#91114—22no—
26C5×#830—22no—
27#90955—22no—
28#71611—51nomaximal, Hall
29C2×C4×C22⋊D5D311yescharacteristic
30C22×#676—31no—
31C2×C5×C22⋊C8—31no—
32C2×C22⋊#168—31no—
33C2×#3952—31no—
34#64770—31no—
35#64770—31no—
36C24×C3×C5C2×C411yescharacteristic
37C23×C3×D5C2×C411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5C2×C411yescharacteristic
45C22×C3×C4×C5C2311yescharacteristic
46C2×C3×C22⋊D5—22no—
47C2×C3×C22⋊D5—22no—
48C2×C3×C22⋊D5—22no—
49C22×C3×Dic5C2×C411yescharacteristic
50C22×C3×Dic5C2×C411yescharacteristic
51C22×C3×Dic5C2×C411yescharacteristic
52C2×C3×C4×D5—21no—
53C2×C3×C4×D5—21no—
54C2×C3×C4×D5—21no—
55C2×C3×C4×D5—21no—
56C2×C3×C4×D5D412yes—
57C2×C3×C4×D5D412yes—
58C2×C3⋊#168—21no—
59C2×C3⋊#168—21no—
60C2×C3⋊#168—21no—
61C2×C3⋊#168—21no—
62C2×C3⋊#168—21no—
63C2×C3⋊#168D412yescomplemented
64C2×C5×C3⋊C8—21no—
65C2×C5×C3⋊C8—21no—
66C2×C5×C3⋊C8—21no—
67C2×C5×C3⋊C8—21no—
68C2×C5×C3⋊C8—21no—
69C2×C5×C3⋊C8D412yescomplemented
70C3×C22⋊Dic5—22no—
71C3×#685—22no—
72C3×#683—22no—
73C3×C4×Dic5—21no—
74C3×C4×Dic5—21no—
75#6649—28no—
76C2×C3×C4×D4—51no—
77C22×#208—51no—
78C2×#830—51no—
79C2×#830—51no—
80C2×#830D511yescharacteristic, complemented
81#4524—51no—
82#4524—51no—
83C23×C4×C5C2×D311yescharacteristic
84C22×C22⋊D5Dic311yescharacteristic
85C22×C4×D5C2×D311yescharacteristic
86C22×C5×C8—31no—
87C22×C5×C8—31no—
88C2×C22⋊Dic5Dic311yescharacteristic
89C4×C22⋊D5—22no—
90C4×C22⋊D5—22no—
91C2×#685Dic311yescharacteristic
92C2×#683Dic311yescharacteristic
93C2×C4×Dic5C2×D311yescharacteristic
94C22×#168—31no—
95C22×#168—31no—
96C2×#676—62no—
97C2×#676—62no—
98C2×#676—62no—
99C5×C22⋊C8—62no—
100C22⋊#168—62no—
101#3952—62no—
102#1870—151noSylow
103C23×C3×C5—21no—
104C23×C3×C5—21no—
105C23×C3×C5—21no—
106C23×C3×C5—21no—
107C23×C3×C5—21no—
108C23×C3×C5—21no—
109C23×C3×C5M1612yescomplemented
110C23×C3×C5C22×C411yescharacteristic
111C22×C3×D5—21no—
112C22×C3×D5—21no—
113C22×C3×D5—21no—
114C22×C3×D5—21no—
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5C22⋊C412yes—
118C2×C3×C4×C5—21no—
119C2×C3×C4×C5—21no—
120C2×C3×C4×C5—21no—
121C2×C3×C4×C5—41no—
122C2×C3×C4×C5—41no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5C2×D411yescharacteristic
126C2×C3×C4×C5C2×D411yescharacteristic
127C2×C3×C4×C5C2×D411yescharacteristic
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5#4111yescharacteristic
130C2×C3×C4×C5#4111yescharacteristic
131C3×C22⋊D5—28no—
132C2×C3×Dic5—21no—
133C2×C3×Dic5—21no—
134C2×C3×Dic5—21no—
135C2×C3×Dic5—21no—
136C2×C3×Dic5—21no—
137C2×C3×Dic5—21no—
138C2×C3×Dic5—21no—
139C2×C3×Dic5C22⋊C412yes—
140C2×C3×Dic5M1612yescomplemented
141C3×C4×D5—22no—
142C3×C4×D5—22no—
143C3×C4×D5—22no—
144C3×C4×D5—22no—
145C3⋊#168—22no—
146C3⋊#168—41no—
147C5×C3⋊C8—22no—
148C5×C3⋊C8—41no—
149C22×C3×D4—51no—
150C23×C3×C4—51no—
151C23×C3×C4C2×D511yescharacteristic
152C3×C4×D4—102no—
153C3×C4×D4—102no—
154C2×C3×C4⋊C4—51no—
155C2×C3×C22⋊C4—51no—
156C2×C3×C22⋊C4—51no—
157C2×C3×C42—51no—
158C2×#208—102no—
159C2×#208—102no—
160C2×#208—102no—
161C22×C3⋊C8—51no—
162C22×C3⋊C8—51no—
163C22×C3⋊C8C2×D511yescharacteristic
164C22×C3⋊C8C2×D511yescharacteristic
165#830—22no—
166#830—102no—
167#830—102no—
168C24×C5C2×Dic311yescharacteristic
169C23×D5C2×Dic311yescharacteristic
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5C2×Dic311yescharacteristic
177C22×C4×C5C22×D311yescharacteristic
178C2×C22⋊D5—22no—
179C2×C22⋊D5—22no—
180C2×C22⋊D5—22no—
181C22×Dic5C2×Dic311yescharacteristic
182C22×Dic5C2×Dic311yescharacteristic
183C22×Dic5C2×Dic311yescharacteristic
184C2×C4×D5—21no—
185C2×C4×D5—21no—
186C2×C4×D5—21no—
187C2×C4×D5—21no—
188C2×C4×D5#6712yes—
189C2×C4×D5#6712yes—
190C2×C5×C8—32no—
191C2×C5×C8—61no—
192C2×C5×C8—61no—
193C2×C5×C8—61no—
194C2×C5×C8—61no—
195C2×C5×C8—61no—
196C22⋊Dic5—22no—
197#685—22no—
198#683—22no—
199C4×Dic5—21no—
200C4×Dic5—21no—
201C2×#168—32no—
202C2×#168—61no—
203C2×#168—61no—
204C2×#168—61no—
205C2×#168—61no—
206C2×#168—61no—
207#676—68no—
208C22×M16—151no—
209C2×C4×D4—51no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—151no—
212C2×C22⋊C8—151no—
213#336—151no—
214#336—151no—
215C22×C3×C5—22no—
216C22×C3×C5—22no—
217C22×C3×C5—22no—
218C22×C3×C5—41no—
219C22×C3×C5—41no—
220C22×C3×C5—41no—
221C22×C3×C5—41no—
222C22×C3×C5C2×C22⋊C411yescharacteristic
223C22×C3×C5C4×D411yescharacteristic
224C22×C3×C5C4×D411yescharacteristic
225C22×C3×C5C2×M1611yescharacteristic
226C22×C3×C5C2×M1611yescharacteristic
227C22×C3×C5#13111yescharacteristic
228C22×C3×C5#13111yescharacteristic
229C2×C3×D5—22no—
230C2×C3×D5—22no—
231C2×C3×D5—22no—
232C2×C3×D5—41no—
233C2×C3×D5—41no—
234C2×C3×D5—41no—
235C2×C3×D5—41no—
236C3×C4×C5—41no—
237C3×C4×C5#12011yescharacteristic
238C3×C4×C5#12111yescharacteristic
239C3×C4×C5#12111yescharacteristic
240C3×C4×C5#12311yescharacteristic
241C3×Dic5—22no—
242C3×Dic5—22no—
243C3×Dic5—41no—
244C24×C3—51no—
245C24×C3C4×D511yescharacteristic
246C2×C3×D4—102no—
247C2×C3×D4—102no—
248C2×C3×D4—102no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—21no—
255C22×C3×C4—51no—
256C22×C3×C4—51no—
257C22×C3×C4—52no—
258C22×C3×C4—52no—
259C22×C3×C4—51no—
260C22×C3×C4—101no—
261C22×C3×C4—101no—
262C22×C3×C4—101no—
263C22×C3×C4—101no—
264C22×C3×C4C4×D511yescharacteristic
265C22×C3×C4C22×D511yescharacteristic
266C3×C4⋊C4—102no—
267C3×C22⋊C4—102no—
268C3×C22⋊C4—102no—
269C3×C42—101no—
270C3×C42—101no—
271#208—108no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—21no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—21no—
276C2×C3⋊C8—21no—
277C2×C3⋊C8—52no—
278C2×C3⋊C8—101no—
279C2×C3⋊C8—101no—
280C2×C3⋊C8—101no—
281C2×C3⋊C8—101no—
282C2×C3⋊C8—101no—
283C2×C3⋊C8C22⋊D512yescomplemented
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5#20812yescomplemented
291C23×C5C22×Dic311yescharacteristic
292C22×D5—21no—
293C22×D5—21no—
294C22×D5—21no—
295C22×D5—21no—
296C22×D5—21no—
297C22×D5—21no—
298C22×D5#21712yes—
299C2×C4×C5—21no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—41no—
303C2×C4×C5—41no—
304C2×C4×C5—41no—
305C2×C4×C5—41no—
306C2×C4×C5D3×D411yescharacteristic
307C2×C4×C5D3×D411yescharacteristic
308C2×C4×C5#23711yescharacteristic
309C2×C4×C5#23711yescharacteristic
310C2×C4×C5C2×#6711yescharacteristic
311C2×C4×C5C2×#6711yescharacteristic
312C22⋊D5—28no—
313C2×Dic5—21no—
314C2×Dic5—21no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5—21no—
320C2×Dic5#20812yescomplemented
321C2×Dic5#21712yes—
322C4×D5—22no—
323C4×D5—22no—
324C4×D5—22no—
325C4×D5—22no—
326C5×C8—62no—
327C5×C8—121no—
328#168—62no—
329#168—121no—
330C22×D4—51no—
331C23×C4—51no—
332C23×C4D3×D511yescharacteristic
333C2×M16—302no—
334C2×M16—302no—
335C2×M16—302no—
336C22×C8—31no—
337C22×C8—31no—
338C22×C8—151no—
339C22×C8—151no—
340C4×D4—102no—
341C4×D4—102no—
342C2×C4⋊C4—51no—
343C2×C22⋊C4—51no—
344C2×C22⋊C4—51no—
345C2×C42—51no—
346C22⋊C8—62no—
347C22⋊C8—302no—
348C22⋊C8—302no—
349C2×C3×C5—42no—
350C2×C3×C5#38611yescharacteristic
351C2×C3×C5#40711yescharacteristic
352C2×C3×C5#40811yescharacteristic
353C2×C3×C5#43511yescharacteristic
354C2×C3×C5#43511yescharacteristic
355C2×C3×C5#43611yescharacteristic
356C2×C3×C5#43611yescharacteristic
357C3×D5—42no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—21no—
363C23×C3—21no—
364C23×C3—52no—
365C23×C3—101no—
366C23×C3—101no—
367C23×C3—101no—
368C23×C3—101no—
369C23×C3—101no—
370C23×C3—101no—
371C23×C3#67612yescomplemented
372C23×C3C2×C4×D511yescharacteristic
373C3×D4—108no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—21no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—52no—
382C2×C3×C4—52no—
383C2×C3×C4—101no—
384C2×C3×C4—101no—
385C2×C3×C4—101no—
386C2×C3×C4—101no—
387C2×C3×C4—102no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—101no—
392C2×C3×C4—101no—
393C2×C3×C4—101no—
394C2×C3×C4#70911yescharacteristic
395C2×C3×C4D4×D511yescharacteristic
396C2×C3×C4D4×D511yescharacteristic
397C2×C3×C4D4×D511yescharacteristic
398C2×C3×C4#71111yescharacteristic
399C2×C3×C4C2×C22⋊D511yescharacteristic
400C3⋊C8—22no—
401C3⋊C8—41no—
402C3⋊C8—102no—
403C3⋊C8—201no—
404C22×C5—22no—
405C22×C5—22no—
406C22×C5—22no—
407C22×C5—41no—
408C22×C5—41no—
409C22×C5—41no—
410C22×C5—41no—
411C22×C5C2×#20811yescharacteristic
412C22×C5C2×#20811yescharacteristic
413C22×C5D4×Dic311yescharacteristic
414C22×C5D4×Dic311yescharacteristic
415C22×C5#94811yescharacteristic
416C22×C5#94811yescharacteristic
417C22×C5C2×#21711yescharacteristic
418C2×D5—22no—
419C2×D5—22no—
420C2×D5—22no—
421C2×D5—41no—
422C2×D5—41no—
423C2×D5—41no—
424C2×D5—41no—
425C4×C5—41no—
426C4×C5#93511yescharacteristic
427C4×C5#93711yescharacteristic
428C4×C5#93911yescharacteristic
429C4×C5#93911yescharacteristic
430Dic5—22no—
431Dic5—22no—
432Dic5—41no—
433C24—51no—
434C24D5×Dic311yescharacteristic
435C2×D4—102no—
436C2×D4—102no—
437C2×D4—102no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—51no—
445C22×C4—51no—
446C22×C4—52no—
447C22×C4—52no—
448C22×C4—51no—
449C22×C4—101no—
450C22×C4—101no—
451C22×C4—101no—
452C22×C4—101no—
453C22×C4D5×Dic311yescharacteristic
454C22×C4C2×D3×D511yescharacteristic
455M16—308no—
456C2×C8—32no—
457C2×C8—61no—
458C2×C8—61no—
459C2×C8—61no—
460C2×C8—61no—
461C2×C8—61no—
462C2×C8—152no—
463C2×C8—301no—
464C2×C8—301no—
465C2×C8—301no—
466C2×C8—301no—
467C2×C8—301no—
468C4⋊C4—102no—
469C22⋊C4—102no—
470C22⋊C4—102no—
471C42—101no—
472C42—101no—
473C3×C5#187011yescharacteristic, complemented, Hall
474C22×C3—22no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—41no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—102no—
482C22×C3—102no—
483C22×C3—102no—
484C22×C3—201no—
485C22×C3—201no—
486C22×C3—201no—
487C22×C3—201no—
488C22×C3D5×C22⋊C411yescharacteristic
489C22×C3#402711yescharacteristic
490C22×C3C2×#67611yescharacteristic
491C22×C3#404711yescharacteristic
492C22×C3D5×M1611yescharacteristic
493C22×C3#405311yescharacteristic
494C22×C3C4×C22⋊D511yescharacteristic
495C3×C4—41no—
496C3×C4—102no—
497C3×C4—102no—
498C3×C4—201no—
499C3×C4#402911yescharacteristic
500C3×C4#403011yescharacteristic
501C3×C4#408311yescharacteristic
502C3×C4#408411yescharacteristic
503C2×C5—42no—
504C2×C5#501111yescharacteristic
505C2×C5#501111yescharacteristic
506C2×C5#501211yescharacteristic
507C2×C5#501211yescharacteristic
508C2×C5#520711yescharacteristic
509C2×C5#522011yescharacteristic
510C2×C5#523411yescharacteristic
511D5—42no—
512C23—21no—
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—52no—
519C23—101no—
520C23—101no—
521C23—101no—
522C23—101no—
523C23—101no—
524C23—101no—
525C23#664912yescomplemented
526C23C2×D5×Dic311yescharacteristic
527D4—108no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—52no—
536C2×C4—52no—
537C2×C4—101no—
538C2×C4—101no—
539C2×C4—101no—
540C2×C4—101no—
541C2×C4—102no—
542C2×C4—102no—
543C2×C4—102no—
544C2×C4—102no—
545C2×C4—101no—
546C2×C4—101no—
547C2×C4—101no—
548C2×C4#677911yescharacteristic
549C2×C4#678011yescharacteristic
550C2×C4D5×#6711yescharacteristic
551C2×C4D5×#6711yescharacteristic
552C2×C4D3×C22⋊D511yescharacteristic
553C2×C4#679011yescharacteristic
554C8—62no—
555C8—121no—
556C8—302no—
557C8—601no—
558C2×C3—42no—
559C2×C3—202no—
560C2×C3#6501511yescharacteristic
561C2×C3#6501611yescharacteristic
562C2×C3#6501811yescharacteristic
563C2×C3#6501911yescharacteristic
564C2×C3#6524511yescharacteristic
565C2×C3#6540011yescharacteristic
566C2×C3#6541711yescharacteristic
567C5#7161111yescharacteristic, complemented, Sylow
568C22—22no—
569C22—22no—
570C22—22no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—102no—
576C22—102no—
577C22—102no—
578C22—201no—
579C22—201no—
580C22—201no—
581C22—201no—
582C22D5×#20811yescharacteristic
583C22#9128311yescharacteristic
584C22#9128411yescharacteristic
585C22C2×#664911yescharacteristic
586C22D5×#21711yescharacteristic
587C22Dic3×C22⋊D511yescharacteristic
588C22#9155911yescharacteristic
589C4—41no—
590C4—102no—
591C4—102no—
592C4—201no—
593C4#9154811yescharacteristic
594C4#9154911yescharacteristic
595C4#9155011yescharacteristic
596C4#9157711yescharacteristic
597C3#1060075111yescharacteristic, complemented, Sylow
598C2—42no—
599C2—202no—
600C2#1174833911yescharacteristic
601C2#1174848211yescharacteristic
602C2#1174849911yescharacteristic
603C2#1174850311yescharacteristic
604C2#1174850411yescharacteristic
605C2#1174850711yescharacteristic
606C2#1174951811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C2×D3×D5
commutator, socleC23×C3×C5C22×C4
FittingC23×C3×C4×C5C22
prime radicalC22×C3×C22⋊D5C4
cosocleC22×C3×C4×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1870
LCSG ▷ C23×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C22×#6649C2semidirect
3. C2×#91114C2semidirect
4. C2×C5×#830C2semidirect
5. C2×#90955C2semidirect
6. #11745966C2semidirect
7. #11745966C2semidirect
63. C2×C3⋊#168D4semidirect
69. C2×C5×C3⋊C8D4semidirect
80. C2×#830D5semidirect
109. C23×C3×C5M16semidirect
140. C2×C3×Dic5M16semidirect
283. C2×C3⋊C8C22⋊D5semidirect
290. C23×C5#208semidirect
320. C2×Dic5#208semidirect
371. C23×C3#676semidirect
473. C3×C5#1870semidirect
525. C23#6649semidirect
567. C5#71611semidirect
597. C3#10600751semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×C22⋊D52
C22×#66492
C2×#911142
C2×C5×#8302
C2×#909552
#117459662
#106007513
#716115