Finite Group Databasebeta

← #14300324

Subgroups — #14300324

Order 1920.

748 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11755406C211yesmaximal, characteristic
2#11751311C211yesmaximal, characteristic, complemented
3C5×#5210C211yesmaximal, characteristic, complemented
4C3×#65502C211yesmaximal, characteristic
5C2×#90995C211yesmaximal, characteristic
6#11746020C211yesmaximal, characteristic, complemented
7#11746018C211yesmaximal, characteristic, complemented
8#10600388—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C22×C3×C22⋊D5C2211yescharacteristic
11C2×#6719C2211yescharacteristic
12C2×#6719C2211yescharacteristic
13C2×#6712—21no—
14C2×C5×#217C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C2×C5×Dic3⋊C4—21no—
17C2×C3×C22⋊Dic5C2211yescharacteristic
18C2×C3×#685—21no—
19#91559—21no—
20#91559—21no—
21Dic3×C22⋊D5—21no—
22Dic3×C22⋊D5—21no—
23D5×#217—21no—
24#91528—21no—
25#91115—21no—
26C5×C3⋊#95—21no—
27C3×#3963—21no—
28#90995C414yescomplemented
29#69597—51nomaximal, Hall
30#65820—31no—
31C5×#385—31no—
32#65502D311yescharacteristic
33#65499—31no—
34C2×#3938—31no—
35#64747—31no—
36#64746—31no—
37C24×C3×C5C2311yescharacteristic
38C23×C3×D5D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—42no—
43C22×Dic15—21no—
44C22×Dic15D411yescharacteristic
45C22×Dic15D411yescharacteristic
46C22×C5×Dic3—21no—
47C22×C5×Dic3D411yescharacteristic
48C22×C5×Dic3D411yescharacteristic
49C2×C3×C22⋊D5—21no—
50C2×C3×C22⋊D5—21no—
51C2×C3×C22⋊D5—21no—
52C2×C3×C22⋊D5—21no—
53C2×C3×C22⋊D5C2×C412yes—
54C2×C3×C22⋊D5Q812yes—
55C22×C3×Dic5—21no—
56C22×C3×Dic5D411yescharacteristic
57C2×D5×Dic3—21no—
58C2×D5×Dic3—21no—
59#6719—21no—
60#6719—21no—
61#6719—21no—
62#6719C2×C412yescomplemented
63#6712—42no—
64C5×#217—21no—
65C5×#217—21no—
66C5×#217—21no—
67C5×#217C2×C412yescomplemented
68C5×Dic3⋊C4—42no—
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5—21no—
71C3×#685—42no—
72#6668—21no—
73#6668—21no—
74#6665—21no—
75#6665—21no—
76Dic3×Dic5—21no—
77Dic3×Dic5—21no—
78#5798—51no—
79C3×#386—51no—
80C2×#834—51no—
81#5210—51no—
82#5210D511yescharacteristic, complemented
83#4527—51no—
84#4527—51no—
85C23×C4×C5C2×D311yescharacteristic
86C22×C22⋊D5C2×D311yescharacteristic
87C2×C5×C4⋊C4—61no—
88C2×C5×C22⋊C4—31no—
89C2×C5×C22⋊C4—31no—
90C2×C22⋊Dic5—31no—
91C2×C22⋊Dic5—31no—
92C2×C22⋊Dic5C2×D311yescharacteristic
93C4×C22⋊D5—61no—
94C4×C22⋊D5—61no—
95C2×#685—21no—
96C2×#683—61no—
97#4027—61no—
98#4027—61no—
99D5×C22⋊C4—61no—
100#4023—61no—
101C5×#95—61no—
102#3963—21no—
103#3963—61no—
104#3938—34no—
105#1867—151noSylow
106C23×C3×C5—41no—
107C23×C3×C5—41no—
108C23×C3×C5C22×C411yescharacteristic
109C23×C3×C5C2×D411yescharacteristic
110C23×C3×C5C2×D411yescharacteristic
111C23×C3×C5C2×D411yescharacteristic
112C23×C3×C5C2×Q811yescharacteristic
113C23×C3×C5#4111yescharacteristic
114C23×C3×C5#4111yescharacteristic
115C22×C3×D5—21no—
116C22×C3×D5—21no—
117C22×C3×D5—41no—
118C22×C3×D5—41no—
119C22×C3×D5C4⋊C412yescomplemented
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5—41no—
127C2×Dic15—22no—
128C2×Dic15—21no—
129C2×Dic15—21no—
130C2×Dic15—41no—
131C2×Dic15—41no—
132C2×Dic15—41no—
133C2×Dic15—41no—
134C2×C5×Dic3—22no—
135C2×C5×Dic3—21no—
136C2×C5×Dic3—21no—
137C2×C5×Dic3—41no—
138C2×C5×Dic3—41no—
139C2×C5×Dic3—41no—
140C2×C5×Dic3—41no—
141C3×C22⋊D5—22no—
142C3×C22⋊D5—22no—
143C3×C22⋊D5—22no—
144C3×C22⋊D5—22no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C2×C3×Dic5—41no—
148C2×C3×Dic5—41no—
149C2×C3×Dic5—41no—
150C2×C3×Dic5C4⋊C412yescomplemented
151D5×Dic3—81no—
152D5×Dic3—81no—
153C22×C3×D4—51no—
154C23×C3×C4C2×D511yescharacteristic
155C2×C3×C22⋊C4—51no—
156C2×C3×C22⋊C4—101no—
157C2×#217—51no—
158C2×#217—51no—
159C2×#217—101no—
160C2×#217C2×D511yescharacteristic
161C2×#217C2×D511yescharacteristic
162D4×Dic3—101no—
163D4×Dic3—101no—
164D4×Dic3—101no—
165D4×Dic3—101no—
166#926—101no—
167C2×Dic3⋊C4—21no—
168C2×Dic3⋊C4—101no—
169C3×#95—101no—
170#834—54no—
171C3⋊#95—21no—
172C3⋊#95—101no—
173C24×C5C22×D311yescharacteristic
174C23×D5#6711yescharacteristic
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—21no—
178C22×C4×C5—31no—
179C22×C4×C5—31no—
180C22×C4×C5—42no—
181C22×C4×C5—61no—
182C2×C22⋊D5—21no—
183C2×C22⋊D5—21no—
184C2×C22⋊D5—21no—
185C2×C22⋊D5—21no—
186C2×C22⋊D5Dic612yes—
187C2×C22⋊D5C4×D312yes—
188C22×Dic5—21no—
189C22×Dic5—31no—
190C22×Dic5—31no—
191C22×Dic5—61no—
192C22×Dic5#6711yescharacteristic
193C2×C4×D5—61no—
194C2×C4×D5—61no—
195C5×C4⋊C4—122no—
196C5×C22⋊C4—32no—
197C5×C22⋊C4—61no—
198C5×C22⋊C4—61no—
199C5×C22⋊C4—61no—
200C22⋊Dic5—21no—
201C22⋊Dic5—21no—
202C22⋊Dic5—32no—
203C22⋊Dic5—61no—
204C22⋊Dic5—61no—
205C22⋊Dic5—61no—
206#685—42no—
207#685—61no—
208#685—61no—
209#683—61no—
210#683—61no—
211#683—122no—
212C4×Dic5—61no—
213C4×Dic5—61no—
214#518—151no—
215C2×#99—151no—
216#386—51no—
217#385—31no—
218#385—151no—
219#342—151no—
220#342—151no—
221C22×C3×C5—21no—
222C22×C3×C5—21no—
223C22×C3×C5—21no—
224C22×C3×C5—21no—
225C22×C3×C5—21no—
226C22×C3×C5—21no—
227C22×C3×C5—41no—
228C22×C3×C5—41no—
229C22×C3×C5—41no—
230C22×C3×C5—41no—
231C22×C3×C5C2×C4⋊C411yescharacteristic
232C22×C3×C5C4×D411yescharacteristic
233C22×C3×C5C4×D411yescharacteristic
234C22×C3×C5#12011yescharacteristic
235C22×C3×C5C22⋊Q811yescharacteristic
236C22×C3×C5C22⋊Q811yescharacteristic
237C22×C3×C5#12311yescharacteristic
238C2×C3×D5—22no—
239C2×C3×D5—41no—
240C2×C3×D5—41no—
241C2×C3×D5—42no—
242C2×C3×D5—81no—
243C3×C4×C5—42no—
244Dic15—42no—
245Dic15—41no—
246Dic15—41no—
247C3×Dic5—22no—
248C3×Dic5—81no—
249C5×Dic3—42no—
250C5×Dic3—41no—
251C5×Dic3—41no—
252C24×C3—51no—
253C24×C3C22×D511yescharacteristic
254C2×C3×D4—52no—
255C2×C3×D4—52no—
256C2×C3×D4—101no—
257C2×C3×D4—101no—
258C2×C3×D4—101no—
259C2×C3×D4—101no—
260C22×C3×C4—21no—
261C22×C3×C4—21no—
262C22×C3×C4—21no—
263C22×C3×C4—42no—
264C22×C3×C4—51no—
265C22×C3×C4—101no—
266C22×Dic3—21no—
267C22×Dic3—51no—
268C22×Dic3—51no—
269C22×Dic3—101no—
270C22×Dic3—101no—
271C22×Dic3—101no—
272C22×Dic3C22⋊D511yescharacteristic
273C22×Dic3C22⋊D511yescharacteristic
274C3×C22⋊C4—101no—
275C3×C22⋊C4—101no—
276C3×C22⋊C4—202no—
277#217—21no—
278#217—21no—
279#217—21no—
280#217—52no—
281#217—101no—
282#217—101no—
283#217—101no—
284#217—101no—
285#217—101no—
286#217C4×D512yescomplemented
287C4⋊Dic3—101no—
288C4⋊Dic3—101no—
289Dic3⋊C4—42no—
290Dic3⋊C4—202no—
291C4×Dic3—101no—
292C4×Dic3—101no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5C2×Dic611yescharacteristic
296C23×C5C2×C4×D311yescharacteristic
297C23×C5D3×D411yescharacteristic
298C23×C5D3×D411yescharacteristic
299C23×C5#23711yescharacteristic
300C23×C5#23711yescharacteristic
301C23×C5C2×#6711yescharacteristic
302C22×D5—21no—
303C22×D5—21no—
304C22×D5—41no—
305C22×D5—41no—
306C22×D5Dic3⋊C412yescomplemented
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—62no—
315C2×C4×C5—61no—
316C2×C4×C5—61no—
317C2×C4×C5—121no—
318C2×C4×C5—121no—
319C2×C4×C5—121no—
320C2×C4×C5—121no—
321C22⋊D5—22no—
322C22⋊D5—22no—
323C22⋊D5—22no—
324C22⋊D5—22no—
325C2×Dic5—21no—
326C2×Dic5—21no—
327C2×Dic5—41no—
328C2×Dic5—41no—
329C2×Dic5—41no—
330C2×Dic5—62no—
331C2×Dic5—61no—
332C2×Dic5—61no—
333C2×Dic5—121no—
334C2×Dic5—121no—
335C2×Dic5—121no—
336C2×Dic5—121no—
337C2×Dic5Dic3⋊C412yescomplemented
338C4×D5—241no—
339C4×D5—241no—
340C22×D4—51no—
341C23×C4D3×D511yescharacteristic
342C4×D4—301no—
343C4×D4—301no—
344C4×D4—301no—
345C4×D4—301no—
346#117—301no—
347C2×C4⋊C4—61no—
348C2×C4⋊C4—301no—
349C2×C22⋊C4—31no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—51no—
352C2×C22⋊C4—101no—
353C2×C22⋊C4—151no—
354C2×C22⋊C4—151no—
355C2×C22⋊C4—301no—
356#99—154no—
357#95—61no—
358#95—101no—
359#95—301no—
360C2×C3×C5—21no—
361C2×C3×C5—21no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5—21no—
365C2×C3×C5—21no—
366C2×C3×C5#38511yescharacteristic
367C2×C3×C5B(4,𝔽2)11yescharacteristic
368C2×C3×C5#45811yescharacteristic
369C3×D5—42no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3—52no—
373C23×C3—101no—
374C23×C3—101no—
375C23×C3—201no—
376C23×C3—201no—
377C23×C3C2×C4×D511yescharacteristic
378C23×C3#70911yescharacteristic
379C23×C3D4×D511yescharacteristic
380C23×C3D4×D511yescharacteristic
381C23×C3Q8×D511yescharacteristic
382C23×C3#71311yescharacteristic
383C23×C3C2×C22⋊D511yescharacteristic
384C3×D4—102no—
385C3×D4—102no—
386C3×D4—102no—
387C3×D4—102no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—52no—
396C2×C3×C4—101no—
397C2×C3×C4—101no—
398C2×C3×C4—201no—
399C2×C3×C4—201no—
400C2×C3×C4—201no—
401C2×Dic3—22no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406C2×Dic3—41no—
407C2×Dic3—41no—
408C2×Dic3—102no—
409C2×Dic3—101no—
410C2×Dic3—101no—
411C2×Dic3—201no—
412C2×Dic3—201no—
413C2×Dic3—201no—
414C2×Dic3—201no—
415C2×Dic3—401no—
416C2×Dic3—401no—
417C22×C5—21no—
418C22×C5—21no—
419C22×C5—21no—
420C22×C5—21no—
421C22×C5—21no—
422C22×C5—21no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5—41no—
426C22×C5—41no—
427C22×C5#87811yescharacteristic
428C22×C5#87811yescharacteristic
429C22×C5#67⋊C411yescharacteristic
430C22×C5#67⋊C411yescharacteristic
431C22×C5C2×Dic3⋊C411yescharacteristic
432C22×C5#93511yescharacteristic
433C22×C5#93711yescharacteristic
434C2×D5—22no—
435C2×D5—41no—
436C2×D5—41no—
437C2×D5—42no—
438C2×D5—81no—
439C4×C5—42no—
440C4×C5—122no—
441C4×C5—121no—
442C4×C5—121no—
443Dic5—22no—
444Dic5—81no—
445Dic5—122no—
446Dic5—121no—
447Dic5—121no—
448C24—51no—
449C24C2×D3×D511yescharacteristic
450C2×D4—52no—
451C2×D4—52no—
452C2×D4—101no—
453C2×D4—101no—
454C2×D4—101no—
455C2×D4—101no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—31no—
460C22×C4—31no—
461C22×C4—42no—
462C22×C4—51no—
463C22×C4—61no—
464C22×C4—101no—
465C22×C4—151no—
466C22×C4—151no—
467C22×C4—301no—
468C22×C4—301no—
469C22×C4—301no—
470C4⋊C4—122no—
471C4⋊C4—301no—
472C4⋊C4—301no—
473C4⋊C4—602no—
474C22⋊C4—32no—
475C22⋊C4—61no—
476C22⋊C4—61no—
477C22⋊C4—61no—
478C22⋊C4—101no—
479C22⋊C4—101no—
480C22⋊C4—152no—
481C22⋊C4—202no—
482C22⋊C4—301no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C22⋊C4—301no—
486C22⋊C4—301no—
487C42—301no—
488C42—301no—
489C3×C5#186711yescharacteristic, complemented, Hall
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3—102no—
501C22×C3—202no—
502C22×C3—201no—
503C22×C3—201no—
504C22×C3—401no—
505C22×C3D5×C4⋊C411yescharacteristic
506C22×C3#403911yescharacteristic
507C22×C3#404011yescharacteristic
508C22×C3#404211yescharacteristic
509C22×C3C4×C22⋊D511yescharacteristic
510C22×C3#408311yescharacteristic
511C22×C3#409211yescharacteristic
512C3×C4—42no—
513C3×C4—102no—
514C3×C4—401no—
515Dic3—42no—
516Dic3—41no—
517Dic3—41no—
518Dic3—202no—
519Dic3—201no—
520Dic3—201no—
521C2×C5—21no—
522C2×C5—21no—
523C2×C5—21no—
524C2×C5—21no—
525C2×C5—21no—
526C2×C5—21no—
527C2×C5#494611yescharacteristic
528C2×C5#503211yescharacteristic
529C2×C5#505311yescharacteristic
530D5—42no—
531C23—41no—
532C23—41no—
533C23—52no—
534C23—101no—
535C23—101no—
536C23—201no—
537C23—201no—
538C23D5×Dic611yescharacteristic
539C23#676511yescharacteristic
540C23#676611yescharacteristic
541C23C4×D3×D511yescharacteristic
542C23D5×#6711yescharacteristic
543C23D3×C22⋊D511yescharacteristic
544C23#679011yescharacteristic
545D4—102no—
546D4—102no—
547D4—102no—
548D4—102no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—52no—
557C2×C4—62no—
558C2×C4—61no—
559C2×C4—61no—
560C2×C4—101no—
561C2×C4—101no—
562C2×C4—121no—
563C2×C4—121no—
564C2×C4—121no—
565C2×C4—121no—
566C2×C4—201no—
567C2×C4—201no—
568C2×C4—201no—
569C2×C4—302no—
570C2×C4—301no—
571C2×C4—301no—
572C2×C4—601no—
573C2×C4—601no—
574C2×C4—601no—
575C2×C4—601no—
576C2×C4—1201no—
577C2×C4—1201no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—21no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—202no—
585C2×C3#6527811yescharacteristic
586C2×C3#6532111yescharacteristic
587C2×C3#6534211yescharacteristic
588C5#6959711yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—102no—
600C22—202no—
601C22—201no—
602C22—201no—
603C22—401no—
604C22D5×Dic3⋊C411yescharacteristic
605C22#9139611yescharacteristic
606C22#9140711yescharacteristic
607C22#9142111yescharacteristic
608C22#9143111yescharacteristic
609C22#9144111yescharacteristic
610C22#9157711yescharacteristic
611C4—42no—
612C4—102no—
613C4—122no—
614C4—121no—
615C4—121no—
616C4—401no—
617C4—602no—
618C4—601no—
619C4—601no—
620C3#1060038811yescharacteristic, complemented, Sylow
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—202no—
628C2#1174889111yescharacteristic
629C2#1174893911yescharacteristic
630C2#1174952511yescharacteristic
subgroupG/H
centerC22#91577
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC23×C3×C4×C5C22
socleC22×C3×C5#120
prime radicalC22×C3×C22⋊D5C22
cosocleC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5#1867
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751311C2semidirect
3. C5×#5210C2semidirect
6. #11746020C2semidirect
7. #11746018C2semidirect
28. #90995C4semidirect
62. #6719C2×C4semidirect
67. C5×#217C2×C4semidirect
82. #5210D5semidirect
119. C22×C3×D5C4⋊C4semidirect
150. C2×C3×Dic5C4⋊C4semidirect
286. #217C4×D5semidirect
306. C22×D5Dic3⋊C4semidirect
337. C2×Dic5Dic3⋊C4semidirect
489. C3×C5#1867semidirect
588. C5#69597semidirect
620. C3#10600388semidirect

Maximal subgroups

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

subgroupindex
#117554062
#117513112
C5×#52102
C3×#655022
C2×#909952
#117460202
#117460182
#106003883
#695975