Finite Group Databasebeta

← #14300318

Subgroups — #14300318

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#11756245C211yesmaximal, characteristic
2#11751059C211yesmaximal, characteristic
3C2×#91090C211yesmaximal, characteristic
4#11751051C211yesmaximal, characteristic, complemented
5#11751047C211yesmaximal, characteristic, complemented
6C3×C5×#342C211yesmaximal, characteristic, complemented
7#11746348C211yesmaximal, characteristic, complemented
8#10599754—31nomaximal, Hall
9C22×#1220C2211yescharacteristic
10C23×Dic15C2211yescharacteristic
11C2×C3×C5×C22⋊C4C2211yescharacteristic
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×#6719C2211yescharacteristic
16C4×#1220—21no—
17C4×#1220—21no—
18C2×#6714—21no—
19C2×C4⋊Dic15—21no—
20C2×#6712—21no—
21#91770—21no—
22#91770—21no—
23C22⋊C4×D15—21no—
24#91766—21no—
25#91115—21no—
26#91115—21no—
27#91115—21no—
28#91090C414yescomplemented
29#68961—51nomaximal, Hall
30#65820—31no—
31#65247—31no—
32C2×#3938—31no—
33#65239—31no—
34#65235—31no—
35C5×#342D311yescharacteristic, complemented
36#64747—31no—
37C24×C3×C5C2311yescharacteristic
38C23×D15D411yescharacteristic
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5D411yescharacteristic
42C22×C3×C4×C5D411yescharacteristic
43C2×#1220—21no—
44C2×#1220—21no—
45C2×#1220—21no—
46C2×#1220—21no—
47C2×#1220C2×C412yes—
48C2×#1220Q812yes—
49C22×Dic15—21no—
50C22×Dic15—21no—
51C22×Dic15—21no—
52C22×Dic15—21no—
53C22×Dic15—42no—
54C22×Dic15D411yescharacteristic
55C22×Dic15D411yescharacteristic
56C22×Dic15D411yescharacteristic
57C2×C4×D15—21no—
58C2×C4×D15—21no—
59C3×C5×C22⋊C4—21no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62C3×C5×C22⋊C4—21no—
63C3×C5×C22⋊C4—21no—
64C3×C5×C22⋊C4C2×C412yescomplemented
65#6719—21no—
66#6719—21no—
67#6719—21no—
68#6719C2×C412yescomplemented
69#6714—21no—
70#6714—21no—
71#6714—42no—
72C4⋊Dic15—42no—
73#6712—21no—
74#6712—21no—
75#6712—42no—
76C4×Dic15—21no—
77C4×Dic15—21no—
78#5486—51no—
79#4958—51no—
80C2×#806—51no—
81#4950—51no—
82#4946—51no—
83C3×#342D511yescharacteristic, complemented
84#4527—51no—
85C22×C22⋊D5—31no—
86C23×Dic5—31no—
87C2×C5×C22⋊C4C2×D311yescharacteristic
88C2×C5×C22⋊C4C2×D311yescharacteristic
89C2×C5×C22⋊C4C2×D311yescharacteristic
90C2×C22⋊Dic5—31no—
91C2×C22⋊Dic5—31no—
92C4×C22⋊D5—61no—
93C4×C22⋊D5—61no—
94C2×#685—61no—
95C2×C4⋊Dic5—61no—
96C2×#683—61no—
97#4027—61no—
98#4027—61no—
99D5×C22⋊C4—61no—
100#4023—61no—
101#3963—61no—
102#3963—61no—
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×D15—21no—
116C22×D15—21no—
117C22×D15—41no—
118C22×D15—41no—
119C22×D15C4⋊C412yescomplemented
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—21no—
122C2×C3×C4×C5—21no—
123C2×C3×C4×C5—41no—
124C2×C3×C4×C5—41no—
125C2×C3×C4×C5—41no—
126C2×C3×C4×C5—41no—
127C2×C3×C4×C5—41no—
128C2×C3×C4×C5—41no—
129C2×C3×C4×C5—41no—
130#1220—22no—
131#1220—22no—
132#1220—22no—
133#1220—22no—
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—21no—
141C2×Dic15—21no—
142C2×Dic15—41no—
143C2×Dic15—41no—
144C2×Dic15—41no—
145C2×Dic15—41no—
146C2×Dic15—41no—
147C2×Dic15—41no—
148C2×Dic15—41no—
149C2×Dic15—41no—
150C2×Dic15C4⋊C412yescomplemented
151C4×D15—81no—
152C4×D15—81no—
153C22×#67—51no—
154C23×Dic3—51no—
155C2×C3×C22⋊C4C2×D511yescharacteristic
156C2×C3×C22⋊C4C2×D511yescharacteristic
157C2×C3×C22⋊C4C2×D511yescharacteristic
158C2×#217—51no—
159C2×#217—51no—
160C4×#67—101no—
161C4×#67—101no—
162C2×(C2×D3)⋊C4—101no—
163C2×C4⋊Dic3—101no—
164C2×Dic3⋊C4—101no—
165#67⋊C4—101no—
166#67⋊C4—101no—
167D3×C22⋊C4—101no—
168#877—101no—
169C3⋊#95—101no—
170C3⋊#95—101no—
171C3⋊#95—101no—
172#806—54no—
173C24×C5C22×D311yescharacteristic
174C23×D5—31no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5D1211yescharacteristic
178C22×C4×C5D1211yescharacteristic
179C2×C22⋊D5—32no—
180C2×C22⋊D5—32no—
181C2×C22⋊D5—61no—
182C2×C22⋊D5—61no—
183C2×C22⋊D5—61no—
184C2×C22⋊D5—61no—
185C22×Dic5—31no—
186C22×Dic5—31no—
187C22×Dic5—31no—
188C22×Dic5—61no—
189C22×Dic5—61no—
190C22×Dic5—61no—
191C22×Dic5—61no—
192C22×Dic5—122no—
193C2×C4×D5—61no—
194C2×C4×D5—61no—
195C5×C22⋊C4—21no—
196C5×C22⋊C4—21no—
197C5×C22⋊C4—21no—
198C5×C22⋊C4—21no—
199C5×C22⋊C4—21no—
200C5×C22⋊C4C4×D312yescomplemented
201C22⋊Dic5—32no—
202C22⋊Dic5—61no—
203C22⋊Dic5—61no—
204C22⋊Dic5—61no—
205#685—61no—
206#685—61no—
207#685—122no—
208C4⋊Dic5—122no—
209#683—61no—
210#683—61no—
211#683—122no—
212C4×Dic5—61no—
213C4×Dic5—61no—
214#518—151no—
215C2×#99—151no—
216#386—151no—
217#385—151no—
218#385—151no—
219#342—151no—
220#342D1511yescharacteristic, complemented
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×D15—22no—
239C2×D15—41no—
240C2×D15—41no—
241C2×D15—42no—
242C2×D15—81no—
243C3×C4×C5—42no—
244C3×C4×C5—41no—
245C3×C4×C5—41no—
246C3×C4×C5—81no—
247Dic15—22no—
248Dic15—42no—
249Dic15—41no—
250Dic15—42no—
251Dic15—41no—
252C24×C3C22×D511yescharacteristic
253C23×D3—51no—
254C22×C3×C4—21no—
255C22×C3×C4—21no—
256C22×C3×C4D2011yescharacteristic
257C22×C3×C4D2011yescharacteristic
258C2×#67—52no—
259C2×#67—52no—
260C2×#67—101no—
261C2×#67—101no—
262C2×#67—101no—
263C2×#67—101no—
264C22×Dic3—51no—
265C22×Dic3—51no—
266C22×Dic3—51no—
267C22×Dic3—101no—
268C22×Dic3—101no—
269C22×Dic3—101no—
270C22×Dic3—101no—
271C22×Dic3—202no—
272C2×C4×D3—101no—
273C2×C4×D3—101no—
274C3×C22⋊C4—21no—
275C3×C22⋊C4—21no—
276C3×C22⋊C4—21no—
277C3×C22⋊C4—21no—
278C3×C22⋊C4—21no—
279C3×C22⋊C4C4×D512yescomplemented
280#217—52no—
281#217—101no—
282#217—101no—
283#217—101no—
284(C2×D3)⋊C4—101no—
285(C2×D3)⋊C4—101no—
286(C2×D3)⋊C4—202no—
287C4⋊Dic3—202no—
288Dic3⋊C4—101no—
289Dic3⋊C4—101no—
290Dic3⋊C4—202no—
291C4×Dic3—101no—
292C4×Dic3—101no—
293C23×C5—41no—
294C23×C5—41no—
295C23×C5C2×C4×D311yescharacteristic
296C23×C5C2×D1211yescharacteristic
297C23×C5#23511yescharacteristic
298C23×C5D3×D411yescharacteristic
299C23×C5D3×D411yescharacteristic
300C23×C5#23711yescharacteristic
301C23×C5D3×Q811yescharacteristic
302C22×D5—32no—
303C22×D5—61no—
304C22×D5—61no—
305C22×D5—121no—
306C22×D5—121no—
307C2×C4×C5—22no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
316C2×C4×C5—41no—
317C22⋊D5—62no—
318C22⋊D5—62no—
319C22⋊D5—62no—
320C22⋊D5—62no—
321C2×Dic5—32no—
322C2×Dic5—61no—
323C2×Dic5—61no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328C2×Dic5—61no—
329C2×Dic5—61no—
330C2×Dic5—121no—
331C2×Dic5—121no—
332C2×Dic5—121no—
333C2×Dic5—121no—
334C2×Dic5—121no—
335C2×Dic5—121no—
336C2×Dic5—121no—
337C2×Dic5—121no—
338C4×D5—241no—
339C4×D5—241no—
340C22×D4—151no—
341C23×C4—151no—
342C4×D4—301no—
343C4×D4—301no—
344C4×D4—301no—
345C4×D4—301no—
346#117—301no—
347C2×C4⋊C4—301no—
348C2×C4⋊C4—301no—
349C2×C22⋊C4—151no—
350C2×C22⋊C4—151no—
351C2×C22⋊C4—301no—
352C2×C22⋊C4—301no—
353C2×C22⋊C4C2×D1511yescharacteristic
354C2×C22⋊C4C2×D1511yescharacteristic
355C2×C22⋊C4C2×D1511yescharacteristic
356#99—154no—
357#95—301no—
358#95—301no—
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
369D15—42no—
370C23×C3—41no—
371C23×C3—41no—
372C23×C3C2×C4×D511yescharacteristic
373C23×C3C2×D2011yescharacteristic
374C23×C3#70911yescharacteristic
375C23×C3D4×D511yescharacteristic
376C23×C3D4×D511yescharacteristic
377C23×C3#71111yescharacteristic
378C23×C3Q8×D511yescharacteristic
379C22×D3—52no—
380C22×D3—101no—
381C22×D3—101no—
382C22×D3—201no—
383C22×D3—201no—
384C2×C3×C4—22no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394#67—102no—
395#67—102no—
396#67—102no—
397#67—102no—
398C2×Dic3—52no—
399C2×Dic3—101no—
400C2×Dic3—101no—
401C2×Dic3—102no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—101no—
406C2×Dic3—101no—
407C2×Dic3—201no—
408C2×Dic3—201no—
409C2×Dic3—201no—
410C2×Dic3—201no—
411C2×Dic3—201no—
412C2×Dic3—201no—
413C2×Dic3—201no—
414C2×Dic3—201no—
415C4×D3—401no—
416C4×D3—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×C5C4×D1211yescharacteristic
428C22×C5#67⋊C411yescharacteristic
429C22×C5#88211yescharacteristic
430C22×C5#88311yescharacteristic
431C22×C5D3×C4⋊C411yescharacteristic
432C22×C5#89611yescharacteristic
433C22×C5#89711yescharacteristic
434C2×D5—62no—
435C2×D5—121no—
436C2×D5—121no—
437C2×D5—122no—
438C2×D5—241no—
439C4×C5—42no—
440C4×C5—41no—
441C4×C5—41no—
442C4×C5—81no—
443Dic5—62no—
444Dic5—122no—
445Dic5—121no—
446Dic5—122no—
447Dic5—121no—
448C24—151no—
449C24C22×D1511yescharacteristic
450C2×D4—152no—
451C2×D4—152no—
452C2×D4—301no—
453C2×D4—301no—
454C2×D4—301no—
455C2×D4—301no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—151no—
459C22×C4—151no—
460C22×C4—151no—
461C22×C4—301no—
462C22×C4—301no—
463C22×C4—301no—
464C22×C4—301no—
465C22×C4—301no—
466C22×C4—301no—
467C22×C4—602no—
468C22×C4D6011yescharacteristic
469C22×C4D6011yescharacteristic
470C4⋊C4—301no—
471C4⋊C4—301no—
472C4⋊C4—602no—
473C4⋊C4—602no—
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—152no—
480C22⋊C4—301no—
481C22⋊C4—301no—
482C22⋊C4—301no—
483C22⋊C4—301no—
484C22⋊C4—301no—
485C22⋊C4—602no—
486C22⋊C4C4×D1512yescomplemented
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×C3C4×D2011yescharacteristic
501C22×C3#402711yescharacteristic
502C22×C3#402811yescharacteristic
503C22×C3#402911yescharacteristic
504C22×C3D5×C4⋊C411yescharacteristic
505C22×C3#404211yescharacteristic
506C22×C3#404311yescharacteristic
507C2×D3—102no—
508C2×D3—201no—
509C2×D3—201no—
510C2×D3—202no—
511C2×D3—401no—
512C3×C4—42no—
513C3×C4—41no—
514C3×C4—41no—
515C3×C4—81no—
516Dic3—102no—
517Dic3—202no—
518Dic3—201no—
519Dic3—202no—
520Dic3—201no—
521C2×C5—21no—
522C2×C5—21no—
523C2×C5—21no—
524C2×C5—21no—
525C2×C5—21no—
526C2×C5—21no—
527C2×C5#466811yescharacteristic
528C2×C5#474111yescharacteristic
529C2×C5#474211yescharacteristic
530D5—122no—
531C23—41no—
532C23—41no—
533C23—152no—
534C23—301no—
535C23—301no—
536C23—601no—
537C23—601no—
538C23C2×C4×D1511yescharacteristic
539C23C2×D6011yescharacteristic
540C23#681711yescharacteristic
541C23D4×D1511yescharacteristic
542C23D4×D1511yescharacteristic
543C23#681911yescharacteristic
544C23Q8×D1511yescharacteristic
545D4—302no—
546D4—302no—
547D4—302no—
548D4—302no—
549C2×C4—22no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—152no—
560C2×C4—301no—
561C2×C4—301no—
562C2×C4—302no—
563C2×C4—302no—
564C2×C4—302no—
565C2×C4—302no—
566C2×C4—301no—
567C2×C4—301no—
568C2×C4—601no—
569C2×C4—601no—
570C2×C4—601no—
571C2×C4—601no—
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#6495711yescharacteristic
585C2×C3#6503011yescharacteristic
586C2×C3#6503111yescharacteristic
587D3—202no—
588C5#6896111yescharacteristic, complemented, Sylow
589C22—21no—
590C22—21no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—302no—
600C22—602no—
601C22—601no—
602C22—601no—
603C22—1201no—
604C22C4×D6011yescharacteristic
605C22#9177011yescharacteristic
606C22#9177111yescharacteristic
607C22#9177211yescharacteristic
608C22C4⋊C4×D1511yescharacteristic
609C22#9178511yescharacteristic
610C22#9178611yescharacteristic
611C4—42no—
612C4—41no—
613C4—41no—
614C4—81no—
615C4—302no—
616C4—602no—
617C4—602no—
618C4—601no—
619C4—601no—
620C3#1059975411yescharacteristic, complemented, Sylow
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—21no—
626C2—21no—
627C2—602no—
628C2#1175076911yescharacteristic
629C2#1175084211yescharacteristic
630C2#1175084311yescharacteristic
subgroupG/H
centerC22#91771
commutatorC23×C3×C5C22×C4
FrattiniC24C22×D15
FittingC3×C5×#342C2
socleC22×C3×C5#120
prime radicalC22×#1220C22
cosocleC24×C3×C5C23
hypercenter#342D15
hypocenterC3×C5#1867
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
4. #11751051C2semidirect
5. #11751047C2semidirect
6. C3×C5×#342C2semidirect
7. #11746348C2semidirect
28. #91090C4semidirect
35. C5×#342D3semidirect
64. C3×C5×C22⋊C4C2×C4semidirect
68. #6719C2×C4semidirect
83. C3×#342D5semidirect
119. C22×D15C4⋊C4semidirect
150. C2×Dic15C4⋊C4semidirect
200. C5×C22⋊C4C4×D3semidirect
220. #342D15semidirect
279. C3×C22⋊C4C4×D5semidirect
486. C22⋊C4C4×D15semidirect
489. C3×C5#1867semidirect
588. C5#68961semidirect
620. C3#10599754semidirect

Maximal subgroups

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

subgroupindex
#117562452
#117510592
C2×#910902
#117510512
#117510472
C3×C5×#3422
#117463482
#105997543
#689615