Finite Group Databasebeta

← #14302054

Subgroups — #14302054

Order 1920.

1196 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
1C2×#91570C211yesmaximal, characteristic
2C2×D3×C22⋊Dic5C211yesmaximal, characteristic, complemented
3C2×#91090C211yesmaximal, characteristic, complemented
4C5×#4955C211yesmaximal, characteristic, complemented
5C2×#90997C211yesmaximal, characteristic, complemented
6C3×#64747C211yesmaximal, characteristic, complemented
7#11746019C211yesmaximal, characteristic, complemented
8#10600289—31nomaximal, Hall
9C24×C5×D3C2211yescharacteristic
10C22×#1220C2211yescharacteristic
11C22×#1203C412yescomplemented
12C22×D3×Dic5—21no—
13C2×C3×C5×C22⋊C4C2211yescharacteristic
14C2×#6719C2211yescharacteristic
15C2×C5×#217C2211yescharacteristic
16C2×C5×(C2×D3)⋊C4—22no—
17C2×C3×C22⋊Dic5C2211yescharacteristic
18C2×C3×C22⋊Dic5C2211yescharacteristic
19#91570—21no—
20#91570—21no—
21#91570—22no—
22D3×C22⋊Dic5—22no—
23D3×C22⋊Dic5—22no—
24C2×(C2×D3)⋊Dic5—21no—
25C2×(C2×D3)⋊Dic5C412yescomplemented
26#91090—22no—
27#90997—22no—
28#68970—51nomaximal, Hall
29C2×#4099—31no—
30C22×C22⋊Dic5—31no—
31C5×#379—31no—
32C2×#3938—31no—
33C2×#3938—31no—
34#64747—31no—
35#64747D311yescharacteristic, complemented
36C24×C3×C5C2311yescharacteristic
37C23×D15C2×C411yescharacteristic, complemented
38C23×C5×D3—21no—
39C23×C5×D3—21no—
40C23×C5×D3—21no—
41C23×C5×D3—21no—
42C23×C5×D3—44no—
43C23×C5×D3C2×C412yes—
44C23×C5×D3D411yescharacteristic
45C23×C5×D3D412yes—
46C23×C5×D3D411yescharacteristic
47C22×C3×C4×C5—21no—
48C2×#1220—21no—
49C2×#1220—21no—
50C2×#1220—21no—
51C2×#1220—21no—
52C2×#1220—21no—
53C2×#1220—21no—
54C22×Dic15—21no—
55C22×Dic15C2×C411yescharacteristic, complemented
56C22×C5×Dic3—21no—
57C22×C3×Dic5—21no—
58C22×C3×Dic5C2×C412yescomplemented
59C2×#1203—22no—
60C2×#1203—22no—
61C2×#1203—44no—
62C2×D3×Dic5—24no—
63C2×D3×Dic5—44no—
64C3×C5×C22⋊C4—21no—
65C3×C5×C22⋊C4—21no—
66#6719—21no—
67#6719D412yescomplemented
68C5×#217—21no—
69C5×#217—21no—
70C5×(C2×D3)⋊C4—44no—
71C3×C22⋊Dic5—21no—
72C3×C22⋊Dic5—21no—
73C3×C22⋊Dic5—21no—
74C3×C22⋊Dic5D412yescomplemented
75(C2×D3)⋊Dic5—24no—
76(C2×D3)⋊Dic5—22no—
77(C2×D3)⋊Dic5—22no—
78C2×#882—51no—
79C2×D3×C22⋊C4—51no—
80#4955D511yescharacteristic, complemented
81C2×#806—51no—
82C2×#806—51no—
83C3×#342—51no—
84#4526—51no—
85C25×C5—31no—
86C22×C22⋊D5—31no—
87C22×C22⋊D5—32no—
88C23×Dic5—61no—
89C2×C5×C22⋊C4—31no—
90C2×C5×C22⋊C4—62no—
91C2×C5×C22⋊C4C2×D311yescharacteristic
92#4099—61no—
93#4099—62no—
94#4099—61no—
95C2×C22⋊Dic5—31no—
96C2×C22⋊Dic5—32no—
97C2×C22⋊Dic5—62no—
98C2×C22⋊Dic5—61no—
99C2×C22⋊Dic5—62no—
100C2×C22⋊Dic5C2×D311yescharacteristic
101C2×C22⋊Dic5C2×D311yescharacteristic
102#3938—62no—
103#3938—62no—
104#1898—151noSylow
105C23×C3×C5—42no—
106C23×C3×C5C22×C411yescharacteristic
107C23×C3×C5C2×D411yescharacteristic
108C23×C3×C5C2×D411yescharacteristic
109C23×C3×C5C2×D411yescharacteristic
110C23×C3×C5C2×D411yescharacteristic
111C23×C3×C5#4111yescharacteristic
112C23×C3×C5#4111yescharacteristic
113C22×D15—21no—
114C22×D15—21no—
115C22×D15—21no—
116C22×D15—42no—
117C22×C5×D3—21no—
118C22×C5×D3—21no—
119C22×C5×D3—24no—
120C22×C5×D3—22no—
121C22×C5×D3—22no—
122C22×C5×D3—21no—
123C22×C5×D3—22no—
124C22×C5×D3—22no—
125C22×C5×D3—21no—
126C22×C5×D3—24no—
127C22×C5×D3—24no—
128C22×C5×D3—42no—
129C22×C5×D3—42no—
130C22×C5×D3—42no—
131C22×C5×D3—44no—
132C22×C5×D3—44no—
133C22×C5×D3—44no—
134C22×C5×D3—44no—
135C22×C5×D3C22⋊C412yes—
136C22×C5×D3C22⋊C412yes—
137C2×C3×C4×C5—42no—
138C2×C3×C4×C5—41no—
139#1220—41no—
140#1220—41no—
141#1220—41no—
142#1220—41no—
143C2×Dic15—21no—
144C2×Dic15—21no—
145C2×Dic15—21no—
146C2×Dic15—22no—
147C2×Dic15—42no—
148C2×C5×Dic3—42no—
149C2×C5×Dic3—41no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—42no—
153C2×C3×Dic5—42no—
154#1203—44no—
155#1203—44no—
156D3×Dic5—48no—
157C24×D3C2×D511yescharacteristic
158C22×#67—51no—
159C22×D12—52no—
160C22×C4×D3—101no—
161C2×C3×C22⋊C4—51no—
162C2×C3×C22⋊C4—51no—
163C2×C3×C22⋊C4C2×D511yescharacteristic
164C2×#217—51no—
165C2×#217C2×D511yescharacteristic
166C2×(C2×D3)⋊C4—22no—
167C2×(C2×D3)⋊C4—52no—
168C2×(C2×D3)⋊C4—101no—
169#882—101no—
170#882—101no—
171#882—102no—
172D3×C22⋊C4—102no—
173D3×C22⋊C4—102no—
174#806—102no—
175#806—102no—
176C24×C5—31no—
177C24×C5—32no—
178C24×C5—32no—
179C24×C5—31no—
180C24×C5—61no—
181C24×C5—61no—
182C24×C5—61no—
183C24×C5—61no—
184C24×C5—124no—
185C24×C5C22×D311yescharacteristic
186C23×D5—31no—
187C22×C4×C5—21no—
188C22×C4×C5—61no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—61no—
192C2×C22⋊D5—61no—
193C2×C22⋊D5—61no—
194C2×C22⋊D5—61no—
195C2×C22⋊D5—61no—
196C2×C22⋊D5—61no—
197C2×C22⋊D5—124no—
198C22×Dic5—21no—
199C22×Dic5—31no—
200C22×Dic5—64no—
201C22×Dic5—61no—
202C22×Dic5—124no—
203C22×Dic5C4×D312yescomplemented
204C5×C22⋊C4—21no—
205C5×C22⋊C4—21no—
206C5×C22⋊C4—61no—
207C5×C22⋊C4—61no—
208C5×C22⋊C4—124no—
209C22⋊Dic5—21no—
210C22⋊Dic5—21no—
211C22⋊Dic5—21no—
212C22⋊Dic5—32no—
213C22⋊Dic5—62no—
214C22⋊Dic5—62no—
215C22⋊Dic5—64no—
216C22⋊Dic5—61no—
217C22⋊Dic5D1212yescomplemented
218C2×#120—151no—
219C22×C22⋊C4—151no—
220C2×#99—151no—
221C2×#99—151no—
222#379—31no—
223#342—51no—
224#342—151no—
225C22×C3×C5—22no—
226C22×C3×C5—22no—
227C22×C3×C5—22no—
228C22×C3×C5—41no—
229C22×C3×C5—41no—
230C22×C3×C5—41no—
231C22×C3×C5—41no—
232C22×C3×C5C2×C22⋊C411yescharacteristic
233C22×C3×C5C4×D411yescharacteristic
234C22×C3×C5C4×D411yescharacteristic
235C22×C3×C5#12011yescharacteristic
236C22×C3×C5#12111yescharacteristic
237C22×C3×C5#12111yescharacteristic
238C22×C3×C5#12311yescharacteristic
239C2×D15—41no—
240C2×D15—42no—
241C2×D15—81no—
242C2×D15—81no—
243C2×C5×D3—24no—
244C2×C5×D3—24no—
245C2×C5×D3—22no—
246C2×C5×D3—22no—
247C2×C5×D3—22no—
248C2×C5×D3—22no—
249C2×C5×D3—22no—
250C2×C5×D3—44no—
251C2×C5×D3—44no—
252C2×C5×D3—44no—
253C2×C5×D3—44no—
254C2×C5×D3—42no—
255C2×C5×D3—42no—
256C2×C5×D3#9914yescomplemented
257C3×C4×C5—81no—
258Dic15—42no—
259Dic15—41no—
260C3×Dic5—42no—
261C3×Dic5—42no—
262C5×Dic3—81no—
263C24×C3C22×D511yescharacteristic
264C23×D3—21no—
265C23×D3—21no—
266C23×D3—21no—
267C23×D3—21no—
268C23×D3—44no—
269C23×D3—51no—
270C23×D3C4×D512yes—
271C23×D3D2011yescharacteristic
272C23×D3D2011yescharacteristic
273C23×D3C22⋊D512yes—
274C22×C3×C4—21no—
275C22×C3×C4—52no—
276C22×C3×C4—101no—
277C2×#67—101no—
278C2×#67—101no—
279C2×#67—101no—
280C2×#67—101no—
281C2×#67—101no—
282C2×#67—101no—
283C22×Dic3—21no—
284C22×Dic3—51no—
285C22×Dic3—101no—
286C2×D12—102no—
287C2×D12—102no—
288C2×D12—204no—
289C2×C4×D3—104no—
290C2×C4×D3—204no—
291C3×C22⋊C4—21no—
292C3×C22⋊C4—21no—
293C3×C22⋊C4—52no—
294C3×C22⋊C4—101no—
295C3×C22⋊C4—101no—
296C3×C22⋊C4—101no—
297#217—21no—
298#217—21no—
299#217—52no—
300#217—101no—
301(C2×D3)⋊C4—44no—
302(C2×D3)⋊C4—104no—
303(C2×D3)⋊C4—102no—
304(C2×D3)⋊C4—102no—
305C23×C5—32no—
306C23×C5—32no—
307C23×C5—42no—
308C23×C5—64no—
309C23×C5—64no—
310C23×C5—64no—
311C23×C5—61no—
312C23×C5—61no—
313C23×C5—62no—
314C23×C5—61no—
315C23×C5—62no—
316C23×C5—62no—
317C23×C5—61no—
318C23×C5—62no—
319C23×C5—122no—
320C23×C5—122no—
321C23×C5—122no—
322C23×C5—124no—
323C23×C5—124no—
324C23×C5—124no—
325C23×C5—124no—
326C23×C5C2×C4×D311yescharacteristic
327C23×C5C2×D1211yescharacteristic
328C23×C5#23511yescharacteristic
329C23×C5D3×D411yescharacteristic
330C23×C5D3×D411yescharacteristic
331C23×C5D3×D411yescharacteristic
332C23×C5#23911yescharacteristic
333C22×D5—61no—
334C22×D5—61no—
335C22×D5—61no—
336C22×D5—122no—
337C2×C4×C5—42no—
338C2×C4×C5—41no—
339C2×C4×C5—122no—
340C2×C4×C5—121no—
341C22⋊D5—124no—
342C22⋊D5—124no—
343C22⋊D5—121no—
344C22⋊D5—121no—
345C22⋊D5—121no—
346C22⋊D5—121no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—42no—
350C2×Dic5—42no—
351C2×Dic5—61no—
352C2×Dic5—61no—
353C2×Dic5—62no—
354C2×Dic5—61no—
355C2×Dic5—128no—
356C2×Dic5—122no—
357C25—31no—
358C22×D4—152no—
359C22×D4—151no—
360C23×C4—301no—
361#120—301no—
362#120—301no—
363#120—302no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—51no—
366C2×C22⋊C4—51no—
367C2×C22⋊C4—62no—
368C2×C22⋊C4—151no—
369C2×C22⋊C4—152no—
370C2×C22⋊C4—302no—
371C2×C22⋊C4—302no—
372C2×C22⋊C4—301no—
373C2×C22⋊C4D3×D511yescharacteristic
374#99—302no—
375#99—302no—
376C2×C3×C5—21no—
377C2×C3×C5—21no—
378C2×C3×C5—21no—
379C2×C3×C5—21no—
380C2×C3×C5—21no—
381C2×C3×C5—21no—
382C2×C3×C5#38611yescharacteristic
383C2×C3×C5C2×#9912yes—
384D15—81no—
385C5×D3—24no—
386C5×D3—42no—
387C23×C3—42no—
388C23×C3C2×C4×D511yescharacteristic
389C23×C3C2×D2011yescharacteristic
390C23×C3D4×D511yescharacteristic
391C23×C3D4×D511yescharacteristic
392C23×C3#71111yescharacteristic
393C23×C3#71111yescharacteristic
394C23×C3C2×C22⋊D511yescharacteristic
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—24no—
398C22×D3—22no—
399C22×D3—22no—
400C22×D3—21no—
401C22×D3—21no—
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—24no—
405C22×D3—24no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3—42no—
409C22×D3—44no—
410C22×D3—44no—
411C22×D3—44no—
412C22×D3—44no—
413C22×D3—101no—
414C22×D3—101no—
415C22×D3—101no—
416C22×D3—202no—
417C22×D3#68512yes—
418C22×D3#68512yes—
419C2×C3×C4—42no—
420C2×C3×C4—41no—
421C2×C3×C4—102no—
422C2×C3×C4—102no—
423C2×C3×C4—202no—
424C2×C3×C4—202no—
425#67—201no—
426#67—201no—
427#67—201no—
428#67—201no—
429C2×Dic3—42no—
430C2×Dic3—41no—
431C2×Dic3—101no—
432C2×Dic3—101no—
433C2×Dic3—102no—
434C2×Dic3—101no—
435C2×Dic3—202no—
436D12—204no—
437D12—204no—
438C4×D3—208no—
439C22×C5—22no—
440C22×C5—22no—
441C22×C5—22no—
442C22×C5—34no—
443C22×C5—41no—
444C22×C5—41no—
445C22×C5—41no—
446C22×C5—41no—
447C22×C5—64no—
448C22×C5—64no—
449C22×C5—62no—
450C22×C5—62no—
451C22×C5—62no—
452C22×C5—62no—
453C22×C5—62no—
454C22×C5—124no—
455C22×C5—124no—
456C22×C5—124no—
457C22×C5—124no—
458C22×C5—122no—
459C22×C5—122no—
460C22×C5C4×D1211yescharacteristic
461C22×C5D3×C22⋊C411yescharacteristic
462C22×C5#88211yescharacteristic
463C22×C5#88411yescharacteristic
464C22×C5#89311yescharacteristic
465C22×C5#89411yescharacteristic
466C22×C5#89511yescharacteristic
467C2×D5—121no—
468C2×D5—122no—
469C2×D5—241no—
470C2×D5—241no—
471C4×C5—81no—
472C4×C5—241no—
473Dic5—42no—
474Dic5—42no—
475Dic5—122no—
476Dic5—121no—
477C24—31no—
478C24—32no—
479C24—32no—
480C24—31no—
481C24—61no—
482C24—61no—
483C24—61no—
484C24—61no—
485C24—124no—
486C24—151no—
487C24C2×D3×D511yescharacteristic
488C2×D4—302no—
489C2×D4—302no—
490C2×D4—301no—
491C2×D4—301no—
492C2×D4—301no—
493C2×D4—301no—
494C2×D4—301no—
495C2×D4—301no—
496C2×D4—604no—
497C22×C4—21no—
498C22×C4—52no—
499C22×C4—61no—
500C22×C4—101no—
501C22×C4—151no—
502C22×C4—304no—
503C22×C4—301no—
504C22×C4—604no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—52no—
508C22⋊C4—61no—
509C22⋊C4—61no—
510C22⋊C4—101no—
511C22⋊C4—101no—
512C22⋊C4—101no—
513C22⋊C4—124no—
514C22⋊C4—152no—
515C22⋊C4—302no—
516C22⋊C4—302no—
517C22⋊C4—304no—
518C22⋊C4—301no—
519C3×C5#189811yescharacteristic, complemented, Hall
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—41no—
526C22×C3—41no—
527C22×C3#402711yescharacteristic
528C22×C3#402711yescharacteristic
529C22×C3#402811yescharacteristic
530C22×C3#403211yescharacteristic
531C22×C3C2×#68511yescharacteristic
532C22×C3#408511yescharacteristic
533C22×C3#408511yescharacteristic
534C2×D3—24no—
535C2×D3—24no—
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—22no—
539C2×D3—22no—
540C2×D3—22no—
541C2×D3—44no—
542C2×D3—44no—
543C2×D3—44no—
544C2×D3—44no—
545C2×D3—42no—
546C2×D3—42no—
547C2×D3—202no—
548C2×D3—201no—
549C2×D3—401no—
550C2×D3—401no—
551C2×D3#393814yescomplemented
552C3×C4—81no—
553C3×C4—202no—
554C3×C4—202no—
555Dic3—81no—
556Dic3—202no—
557Dic3—201no—
558C2×C5—21no—
559C2×C5—21no—
560C2×C5—21no—
561C2×C5—21no—
562C2×C5—21no—
563C2×C5—21no—
564C2×C5—64no—
565C2×C5—122no—
566C2×C5#466511yescharacteristic
567C2×C5D3×#9912yes—
568D5—241no—
569C23—32no—
570C23—32no—
571C23—42no—
572C23—64no—
573C23—64no—
574C23—64no—
575C23—61no—
576C23—61no—
577C23—62no—
578C23—62no—
579C23—62no—
580C23—61no—
581C23—61no—
582C23—62no—
583C23—122no—
584C23—122no—
585C23—122no—
586C23—124no—
587C23—124no—
588C23—124no—
589C23—124no—
590C23—301no—
591C23—301no—
592C23—301no—
593C23—602no—
594C23#676811yescharacteristic
595C23C4×D3×D511yescharacteristic
596C23D5×D1211yescharacteristic
597C23D3×D2011yescharacteristic
598C23#678211yescharacteristic
599C23D3×C22⋊D511yescharacteristic
600C23#679011yescharacteristic
601D4—604no—
602D4—604no—
603D4—601no—
604D4—601no—
605D4—601no—
606D4—601no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—102no—
610C2×C4—102no—
611C2×C4—122no—
612C2×C4—121no—
613C2×C4—202no—
614C2×C4—202no—
615C2×C4—301no—
616C2×C4—301no—
617C2×C4—301no—
618C2×C4—302no—
619C2×C4—608no—
620C2×C4—602no—
621C2×C3—21no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3C2×#393812yes—
628C2×C3#6524711yescharacteristic
629D3—24no—
630D3—42no—
631D3—401no—
632C5#6897011yescharacteristic, complemented, Sylow
633C22—22no—
634C22—22no—
635C22—22no—
636C22—34no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—64no—
642C22—64no—
643C22—62no—
644C22—62no—
645C22—62no—
646C22—62no—
647C22—62no—
648C22—124no—
649C22—124no—
650C22—124no—
651C22—124no—
652C22—122no—
653C22—122no—
654C22—601no—
655C22—602no—
656C22—1201no—
657C22—1201no—
658C22#9140511yescharacteristic
659C22#9140611yescharacteristic
660C22#9141611yescharacteristic
661C22#9142711yescharacteristic
662C22D3×#68511yescharacteristic
663C22#9147611yescharacteristic
664C22#9155811yescharacteristic
665C4—81no—
666C4—202no—
667C4—202no—
668C4—241no—
669C4—602no—
670C4—601no—
671C3#1060028911yescharacteristic, complemented, Sylow
672C2—21no—
673C2—21no—
674C2—21no—
675C2—21no—
676C2—21no—
677C2—21no—
678C2—64no—
679C2—122no—
680C2—1201no—
681C2D3×#393812yes—
682C2#1174888311yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×#91570C2
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1898
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×D3×C22⋊Dic5C2semidirect
3. C2×#91090C2semidirect
4. C5×#4955C2semidirect
5. C2×#90997C2semidirect
6. C3×#64747C2semidirect
7. #11746019C2semidirect
11. C22×#1203C4semidirect
25. C2×(C2×D3)⋊Dic5C4semidirect
35. #64747D3semidirect
37. C23×D15C2×C4semidirect
55. C22×Dic15C2×C4semidirect
58. C22×C3×Dic5C2×C4semidirect
67. #6719D4semidirect
74. C3×C22⋊Dic5D4semidirect
80. #4955D5semidirect
203. C22×Dic5C4×D3semidirect
217. C22⋊Dic5D12semidirect
256. C2×C5×D3#99semidirect
519. C3×C5#1898semidirect
551. C2×D3#3938semidirect
632. C5#68970semidirect
671. C3#10600289semidirect

Maximal subgroups

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

subgroupindex
C2×#915702
C2×D3×C22⋊Dic52
C2×#910902
C5×#49552
C2×#909972
C3×#647472
#117460192
#106002893
#689705