Finite Group Databasebeta

← #14301646

Subgroups — #14301646

Order 1920.

1156 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#953C211yesmaximal, characteristic
2#11755410C211yesmaximal, characteristic, complemented
3#11751348C211yesmaximal, characteristic, complemented
4C3×#65536C211yesmaximal, characteristic, complemented
5C2×#90996C211yesmaximal, characteristic, complemented
6#11746020C211yesmaximal, characteristic, complemented
7#11746019C211yesmaximal, characteristic, complemented
8#10602462—31nomaximal, Hall
9C25×C3×C5C2211yescharacteristic
10C22×C5×#67—21no—
11C22×C5×#67C2211yescharacteristic
12C2×#6719—22no—
13C2×#6719C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C5×#953—22no—
16C5×#953C414yescomplemented
17C2×C5×#217—21no—
18C2×C5×#217C2211yescharacteristic
19C2×C3×C22⋊Dic5—22no—
20C2×C3×C22⋊Dic5C2211yescharacteristic
21C2×C3×C22⋊Dic5C2211yescharacteristic
22#67⋊Dic5—22no—
23D3×C22⋊Dic5—21no—
24Dic5×#67—22no—
25#91529—21no—
26#90996—22no—
27#69499—51nomaximal, Hall
28C2×C5×#120—31no—
29#66132—31no—
30#65536—31no—
31#65536D311yescharacteristic, complemented
32C2×#3966—31no—
33#64747—31no—
34#64747—31no—
35C24×C3×C5—21no—
36C24×C3×C5—21no—
37C24×C3×C5—21no—
38C24×C3×C5—21no—
39C24×C3×C5—21no—
40C24×C3×C5—21no—
41C24×C3×C5—44no—
42C24×C3×C5C2×C412yescomplemented
43C24×C3×C5C2311yescharacteristic
44C23×C5×D3D411yescharacteristic
45C22×Dic15—21no—
46C22×Dic15D412yescomplemented
47C2×C5×#67—21no—
48C2×C5×#67—21no—
49C2×C5×#67—21no—
50C2×C5×#67—21no—
51C2×C5×#67—24no—
52C2×C5×#67—44no—
53C2×C5×#67C2×C412yes—
54C2×C5×#67D412yes—
55C22×C5×Dic3—21no—
56C22×C5×Dic3D411yescharacteristic
57C22×C3×Dic5—21no—
58C22×C3×Dic5D412yescomplemented
59C2×D3×Dic5—22no—
60#6719—21no—
61#6719—21no—
62#6719—21no—
63#6719—21no—
64#6719—44no—
65C5×#217—21no—
66C5×#217—24no—
67C5×#217C2×C412yescomplemented
68C3×C22⋊Dic5—21no—
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5—21no—
71C3×C22⋊Dic5—21no—
72C3×C22⋊Dic5—44no—
73Dic3⋊Dic5—22no—
74(C2×D3)⋊Dic5—22no—
75Dic3×Dic5—22no—
76C2×#953D511yescharacteristic
77#5486—51no—
78C3×#379—51no—
79#5247—51no—
80C2×#806—51no—
81#4527—51no—
82#4526—51no—
83C25×C5C2×D311yescharacteristic
84C22×C5×D4—31no—
85C22×C5×D4—61no—
86C5×#120—34no—
87C5×#120—62no—
88C2×C5×C22⋊C4—31no—
89C2×C5×C22⋊C4—61no—
90C2×C22⋊Dic5—22no—
91C2×C22⋊Dic5—31no—
92C2×C22⋊Dic5—31no—
93C2×C22⋊Dic5—61no—
94C2×C22⋊Dic5—62no—
95C2×C22⋊Dic5C2×D311yescharacteristic
96C2×C22⋊Dic5C2×D311yescharacteristic
97D4×Dic5—62no—
98D4×Dic5—62no—
99#4072—61no—
100#3966—62no—
101#1889—151noSylow
102C23×C3×C5—24no—
103C23×C3×C5—24no—
104C23×C3×C5—24no—
105C23×C3×C5—22no—
106C23×C3×C5—22no—
107C23×C3×C5—22no—
108C23×C3×C5—44no—
109C23×C3×C5—42no—
110C23×C3×C5—42no—
111C23×C3×C5—42no—
112C23×C3×C5—42no—
113C23×C3×C5—44no—
114C23×C3×C5—44no—
115C23×C3×C5—44no—
116C23×C3×C5—41no—
117C23×C3×C5—41no—
118C23×C3×C5—41no—
119C23×C3×C5—41no—
120C23×C3×C5C22×C411yescharacteristic
121C23×C3×C5C2×D411yescharacteristic
122C23×C3×C5C2×D411yescharacteristic
123C23×C3×C5C2×D411yescharacteristic
124C23×C3×C5C2×D411yescharacteristic
125C23×C3×C5#4111yescharacteristic
126C23×C3×C5#4111yescharacteristic
127C22×C5×D3—21no—
128C22×C5×D3—21no—
129C22×C5×D3—42no—
130C22×C5×D3C22⋊C412yescomplemented
131C2×Dic15—22no—
132C2×Dic15—42no—
133C2×Dic15—42no—
134C2×Dic15—41no—
135C5×#67—22no—
136C5×#67—22no—
137C5×#67—22no—
138C5×#67—22no—
139C5×#67—48no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—42no—
144C2×C5×Dic3C22⋊C412yescomplemented
145C2×C3×Dic5—22no—
146C2×C3×Dic5—42no—
147C2×C3×Dic5—42no—
148C2×C3×Dic5—41no—
149D3×Dic5—82no—
150C25×C3C2×D511yescharacteristic
151C22×#67—21no—
152C22×#67C2×D511yescharacteristic
153C2×C3×C22⋊C4—51no—
154C2×C3×C22⋊C4—51no—
155C2×C3×C22⋊C4—102no—
156#953—22no—
157#953Dic514yescomplemented
158C2×#217—21no—
159C2×#217—51no—
160C2×#217—51no—
161C2×#217—102no—
162C2×#217C2×D511yescharacteristic
163C4×#67—102no—
164#67⋊C4—102no—
165D3×C22⋊C4—101no—
166#877—101no—
167#806—102no—
168C24×C5—21no—
169C24×C5—21no—
170C24×C5—21no—
171C24×C5—21no—
172C24×C5—21no—
173C24×C5—21no—
174C24×C5—31no—
175C24×C5—44no—
176C24×C5C4×D312yescomplemented
177C24×C5C22×D311yescharacteristic
178C2×C5×D4—32no—
179C2×C5×D4—32no—
180C2×C5×D4—61no—
181C2×C5×D4—61no—
182C2×C5×D4—61no—
183C2×C5×D4—61no—
184C2×C5×D4—64no—
185C2×C5×D4—124no—
186C22×C4×C5—31no—
187C22×C4×C5—61no—
188C22×Dic5—21no—
189C22×Dic5—32no—
190C22×Dic5—62no—
191C22×Dic5—61no—
192C22×Dic5#6712yescomplemented
193C5×C22⋊C4—32no—
194C5×C22⋊C4—64no—
195C5×C22⋊C4—61no—
196C22⋊Dic5—21no—
197C22⋊Dic5—21no—
198C22⋊Dic5—21no—
199C22⋊Dic5—21no—
200C22⋊Dic5—44no—
201C22⋊Dic5—62no—
202C22⋊Dic5—61no—
203C22⋊Dic5—61no—
204C22⋊Dic5—61no—
205C22⋊Dic5—61no—
206C22⋊Dic5—124no—
207C4⋊Dic5—62no—
208C4×Dic5—62no—
209C2×#120—31no—
210#518—151no—
211C2×#99—151no—
212#379—51no—
213#379—151no—
214#342—151no—
215#342—151no—
216C22×C3×C5—22no—
217C22×C3×C5—22no—
218C22×C3×C5—22no—
219C22×C3×C5—24no—
220C22×C3×C5—24no—
221C22×C3×C5—24no—
222C22×C3×C5—41no—
223C22×C3×C5—41no—
224C22×C3×C5—41no—
225C22×C3×C5—41no—
226C22×C3×C5—42no—
227C22×C3×C5—44no—
228C22×C3×C5—44no—
229C22×C3×C5—44no—
230C22×C3×C5—42no—
231C22×C3×C5—42no—
232C22×C3×C5—42no—
233C22×C3×C5—44no—
234C22×C3×C5C2×C22⋊C411yescharacteristic
235C22×C3×C5C4×D411yescharacteristic
236C22×C3×C5C4×D411yescharacteristic
237C22×C3×C5#12011yescharacteristic
238C22×C3×C5#12111yescharacteristic
239C22×C3×C5#12111yescharacteristic
240C22×C3×C5#12311yescharacteristic
241C2×C5×D3—22no—
242C2×C5×D3—42no—
243C2×C5×D3—42no—
244C2×C5×D3—81no—
245Dic15—42no—
246Dic15—81no—
247C3×Dic5—42no—
248C3×Dic5—81no—
249C5×Dic3—22no—
250C5×Dic3—42no—
251C24×C3—21no—
252C24×C3—21no—
253C24×C3—21no—
254C24×C3—21no—
255C24×C3—21no—
256C24×C3—21no—
257C24×C3—44no—
258C24×C3C2×Dic512yescomplemented
259C24×C3C22×D511yescharacteristic
260C23×D3C22⋊D511yescharacteristic
261C22×C3×C4—52no—
262C22×C3×C4—101no—
263C2×#67—21no—
264C2×#67—21no—
265C2×#67—21no—
266C2×#67—21no—
267C2×#67—24no—
268C2×#67—44no—
269C2×#67C2×Dic512yes—
270C2×#67C22⋊D512yes—
271C22×Dic3—21no—
272C22×Dic3—52no—
273C22×Dic3—101no—
274C22×Dic3C22⋊D511yescharacteristic
275C2×C4×D3—102no—
276C3×C22⋊C4—101no—
277C3×C22⋊C4—101no—
278C3×C22⋊C4—101no—
279C3×C22⋊C4—101no—
280C3×C22⋊C4—204no—
281#217—21no—
282#217—24no—
283#217—101no—
284#217—101no—
285#217—101no—
286#217—101no—
287#217—204no—
288#217C2×Dic512yescomplemented
289(C2×D3)⋊C4—102no—
290Dic3⋊C4—102no—
291C4×Dic3—102no—
292C23×C5—24no—
293C23×C5—24no—
294C23×C5—24no—
295C23×C5—22no—
296C23×C5—22no—
297C23×C5—22no—
298C23×C5—32no—
299C23×C5—44no—
300C23×C5—42no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5—42no—
304C23×C5—44no—
305C23×C5—44no—
306C23×C5—44no—
307C23×C5—41no—
308C23×C5—41no—
309C23×C5—41no—
310C23×C5—41no—
311C23×C5—61no—
312C23×C5—61no—
313C23×C5—122no—
314C23×C5C2×C4×D311yescharacteristic
315C23×C5#23511yescharacteristic
316C23×C5D3×D411yescharacteristic
317C23×C5D3×D411yescharacteristic
318C23×C5D3×D411yescharacteristic
319C23×C5#23711yescharacteristic
320C23×C5C2×#6711yescharacteristic
321C5×D4—62no—
322C5×D4—62no—
323C5×D4—62no—
324C5×D4—62no—
325C5×D4—128no—
326C2×C4×C5—32no—
327C2×C4×C5—61no—
328C2×C4×C5—61no—
329C2×C4×C5—62no—
330C2×C4×C5—122no—
331C2×Dic5—22no—
332C2×Dic5—42no—
333C2×Dic5—42no—
334C2×Dic5—41no—
335C2×Dic5—62no—
336C2×Dic5—122no—
337C2×Dic5—122no—
338C2×Dic5—121no—
339C2×Dic5—242no—
340C25D3×D511yescharacteristic
341C22×D4—31no—
342C22×D4—61no—
343#120—34no—
344#120—62no—
345C4×D4—302no—
346C4×D4—302no—
347#117—301no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—51no—
350C2×C22⋊C4—51no—
351C2×C22⋊C4—61no—
352C2×C22⋊C4—102no—
353C2×C22⋊C4—151no—
354C2×C22⋊C4—151no—
355C2×C22⋊C4—301no—
356C2×C22⋊C4—302no—
357#99—302no—
358C2×C3×C5—21no—
359C2×C3×C5—21no—
360C2×C3×C5—21no—
361C2×C3×C5—21no—
362C2×C3×C5—21no—
363C2×C3×C5—21no—
364C2×C3×C5—44no—
365C2×C3×C5#38611yescharacteristic
366C2×C3×C5B(4,𝔽2)12yes—
367C5×D3—42no—
368C23×C3—24no—
369C23×C3—24no—
370C23×C3—24no—
371C23×C3—22no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—44no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3—44no—
380C23×C3—44no—
381C23×C3—44no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3D4×D511yescharacteristic
387C23×C3D4×D511yescharacteristic
388C23×C3#71111yescharacteristic
389C23×C3#71111yescharacteristic
390C23×C3C22×Dic511yescharacteristic
391C23×C3C2×C22⋊D511yescharacteristic
392C23×C3C2×C22⋊D511yescharacteristic
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—42no—
396C22×D3C22⋊Dic512yescomplemented
397C2×C3×C4—102no—
398C2×C3×C4—202no—
399C2×C3×C4—202no—
400C2×C3×C4—201no—
401#67—22no—
402#67—22no—
403#67—22no—
404#67—22no—
405#67—48no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—42no—
410C2×Dic3—102no—
411C2×Dic3—202no—
412C2×Dic3—202no—
413C2×Dic3—201no—
414C2×Dic3C22⋊Dic512yescomplemented
415C4×D3—402no—
416C22×C5—22no—
417C22×C5—22no—
418C22×C5—22no—
419C22×C5—24no—
420C22×C5—24no—
421C22×C5—24no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5—41no—
426C22×C5—44no—
427C22×C5—44no—
428C22×C5—42no—
429C22×C5—42no—
430C22×C5—42no—
431C22×C5—44no—
432C22×C5—42no—
433C22×C5—44no—
434C22×C5—62no—
435C22×C5—122no—
436C22×C5—122no—
437C22×C5—241no—
438C22×C5D3×C22⋊C411yescharacteristic
439C22×C5#67⋊C411yescharacteristic
440C22×C5#88311yescharacteristic
441C22×C5#88411yescharacteristic
442C22×C5C4×#6711yescharacteristic
443C22×C5#93711yescharacteristic
444C22×C5#93811yescharacteristic
445C4×C5—62no—
446C4×C5—122no—
447Dic5—42no—
448Dic5—81no—
449Dic5—122no—
450Dic5—241no—
451C24—21no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—21no—
457C24—31no—
458C24—44no—
459C24D3×Dic512yescomplemented
460C24C2×D3×D511yescharacteristic
461C2×D4—32no—
462C2×D4—32no—
463C2×D4—61no—
464C2×D4—61no—
465C2×D4—61no—
466C2×D4—61no—
467C2×D4—64no—
468C2×D4—124no—
469C22×C4—31no—
470C22×C4—52no—
471C22×C4—61no—
472C22×C4—101no—
473C22×C4—152no—
474C22×C4—302no—
475C22×C4—301no—
476C4⋊C4—302no—
477C22⋊C4—32no—
478C22⋊C4—64no—
479C22⋊C4—61no—
480C22⋊C4—101no—
481C22⋊C4—101no—
482C22⋊C4—101no—
483C22⋊C4—101no—
484C22⋊C4—204no—
485C22⋊C4—302no—
486C22⋊C4—301no—
487C22⋊C4—301no—
488C22⋊C4—301no—
489C22⋊C4—301no—
490C22⋊C4—604no—
491C42—302no—
492C3×C5#188911yescharacteristic, complemented, Hall
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—24no—
497C22×C3—24no—
498C22×C3—24no—
499C22×C3—41no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—41no—
503C22×C3—42no—
504C22×C3—44no—
505C22×C3—44no—
506C22×C3—44no—
507C22×C3—42no—
508C22×C3—42no—
509C22×C3—44no—
510C22×C3—42no—
511C22×C3D4×Dic511yescharacteristic
512C22×C3D4×Dic511yescharacteristic
513C22×C3#408111yescharacteristic
514C22×C3#408311yescharacteristic
515C22×C3#408511yescharacteristic
516C22×C3#408511yescharacteristic
517C22×C3C2×C22⋊Dic511yescharacteristic
518C2×D3—22no—
519C2×D3—42no—
520C2×D3—42no—
521C2×D3—81no—
522C3×C4—202no—
523C3×C4—401no—
524Dic3—22no—
525Dic3—42no—
526Dic3—202no—
527Dic3—401no—
528C2×C5—21no—
529C2×C5—21no—
530C2×C5—21no—
531C2×C5—21no—
532C2×C5—21no—
533C2×C5—21no—
534C2×C5—44no—
535C2×C5—122no—
536C2×C5#495611yescharacteristic
537C2×C5#503212yes—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—22no—
542C23—22no—
543C23—22no—
544C23—32no—
545C23—44no—
546C23—42no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—44no—
551C23—44no—
552C23—44no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—61no—
558C23—61no—
559C23—122no—
560C23#678011yescharacteristic
561C23C2×D3×Dic511yescharacteristic
562C23#678211yescharacteristic
563C23D5×#6711yescharacteristic
564C23D3×C22⋊D511yescharacteristic
565C23D3×C22⋊D511yescharacteristic
566C23#679011yescharacteristic
567D4—62no—
568D4—62no—
569D4—62no—
570D4—62no—
571D4—128no—
572C2×C4—32no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—62no—
576C2×C4—102no—
577C2×C4—122no—
578C2×C4—202no—
579C2×C4—202no—
580C2×C4—201no—
581C2×C4—302no—
582C2×C4—602no—
583C2×C4—602no—
584C2×C4—601no—
585C2×C4—1202no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—44no—
593C2×C3#6532112yes—
594C2×C3#6550911yescharacteristic
595D3—42no—
596C5#6949911yescharacteristic, complemented, Sylow
597C22—22no—
598C22—22no—
599C22—22no—
600C22—24no—
601C22—24no—
602C22—24no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—42no—
608C22—44no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—44no—
613C22—42no—
614C22—44no—
615C22—62no—
616C22—122no—
617C22—122no—
618C22—241no—
619C22Dic5×#6711yescharacteristic
620C22D3×C22⋊Dic511yescharacteristic
621C22#9155511yescharacteristic
622C22#9155811yescharacteristic
623C22#67⋊Dic511yescharacteristic
624C22#9156511yescharacteristic
625C22#9157711yescharacteristic
626C4—62no—
627C4—122no—
628C4—202no—
629C4—401no—
630C4—602no—
631C4—1201no—
632C3#1060246211yescharacteristic, complemented, Sylow
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—44no—
640C2—122no—
641C2#1174951911yescharacteristic
642C2#1174952512yes—
subgroupG/H
centerC22#91577
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC25×C3×C5C22
socleC22×C3×C5#120
prime radicalC2×C5×#953C2
cosocleC24×C3×C5C23
hypercenterC25D3×D5
hypocenterC3×C5#1889
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C25

Complements

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

NH ≅ G/Ntype
2. #11755410C2semidirect
3. #11751348C2semidirect
4. C3×#65536C2semidirect
5. C2×#90996C2semidirect
6. #11746020C2semidirect
7. #11746019C2semidirect
16. C5×#953C4semidirect
31. #65536D3semidirect
42. C24×C3×C5C2×C4semidirect
46. C22×Dic15D4semidirect
58. C22×C3×Dic5D4semidirect
67. C5×#217C2×C4semidirect
130. C22×C5×D3C22⋊C4semidirect
144. C2×C5×Dic3C22⋊C4semidirect
157. #953Dic5semidirect
176. C24×C5C4×D3semidirect
192. C22×Dic5#67semidirect
258. C24×C3C2×Dic5semidirect
288. #217C2×Dic5semidirect
396. C22×D3C22⋊Dic5semidirect
414. C2×Dic3C22⋊Dic5semidirect
459. C24D3×Dic5semidirect
492. C3×C5#1889semidirect
596. C5#69499semidirect
632. C3#10602462semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9532
#117554102
#117513482
C3×#655362
C2×#909962
#117460202
#117460192
#106024623
#694995