Finite Group Databasebeta

← #14301627

Subgroups — #14301627

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×#91570C211yesmaximal, characteristic
2#11755413C211yesmaximal, characteristic, complemented
3C2×#91090C211yesmaximal, characteristic, complemented
4C5×#4955C211yesmaximal, characteristic, complemented
5#11749496C211yesmaximal, characteristic, complemented
6C3×#64747C211yesmaximal, characteristic, complemented
7#11746018C211yesmaximal, characteristic, complemented
8#10600292—31nomaximal, Hall
9C24×C5×D3C2211yescharacteristic
10C22×#1220C2211yescharacteristic
11C22×#1203—21no—
12C2×C3×C5×C22⋊C4C2211yescharacteristic
13C2×#6719C2211yescharacteristic
14C2×C5×#217C2211yescharacteristic
15C2×C5×(C2×D3)⋊C4—22no—
16C2×C3×C22⋊Dic5C2211yescharacteristic
17C2×C3×C22⋊Dic5C2211yescharacteristic
18#91570—22no—
19#91570C414yescomplemented
20#91561—21no—
21#91556—22no—
22#91552—22no—
23C2×(C2×D3)⋊Dic5—21no—
24C2×(C2×D3)⋊Dic5—22no—
25#91532—21no—
26#91090—22no—
27#68962—51nomaximal, Hall
28C2×#4099—31no—
29#65820—31no—
30C5×#379—31no—
31#65536—31no—
32C2×#3938—31no—
33#64747D311yescharacteristic, complemented
34#64746—31no—
35C24×C3×C5C2311yescharacteristic
36C23×D15D411yescharacteristic
37C23×C5×D3—21no—
38C23×C5×D3—21no—
39C23×C5×D3—21no—
40C23×C5×D3—21no—
41C23×C5×D3—21no—
42C23×C5×D3—21no—
43C23×C5×D3—44no—
44C23×C5×D3C2×C412yescomplemented
45C22×C3×C4×C5—21no—
46C2×#1220—21no—
47C2×#1220—21no—
48C2×#1220—21no—
49C2×#1220—21no—
50C2×#1220C2×C412yes—
51C2×#1220D412yes—
52C22×Dic15—21no—
53C22×Dic15D411yescharacteristic
54C22×C5×Dic3D412yescomplemented
55C22×C3×Dic5—21no—
56C22×C3×Dic5D412yescomplemented
57C2×#1203—24no—
58C2×#1203—44no—
59C2×#1200—22no—
60C3×C5×C22⋊C4—21no—
61C3×C5×C22⋊C4—21no—
62#6719—21no—
63#6719—21no—
64C5×#217—21no—
65C5×#217—21no—
66C5×(C2×D3)⋊C4—44no—
67C3×C22⋊Dic5—21no—
68C3×C22⋊Dic5—21no—
69C3×C22⋊Dic5—21no—
70C3×C22⋊Dic5C2×C412yescomplemented
71#6669—22no—
72#6667—22no—
73(C2×D3)⋊Dic5—24no—
74(C2×D3)⋊Dic5—44no—
75Dic3×Dic5—22no—
76C2×#882—51no—
77#5486—51no—
78#4955—51no—
79#4955D511yescharacteristic, complemented
80C2×#806—51no—
81C3×#342—51no—
82#4527—51no—
83C25×C5—31no—
84C22×C22⋊D5—31no—
85C22×C22⋊D5—61no—
86C2×C5×C22⋊C4—31no—
87C2×C5×C22⋊C4—62no—
88C2×C5×C22⋊C4C2×D311yescharacteristic
89#4099—34no—
90#4099—62no—
91C2×C22⋊Dic5—31no—
92C2×C22⋊Dic5—61no—
93C2×C22⋊Dic5—62no—
94C2×C22⋊Dic5C2×D311yescharacteristic
95C2×C22⋊Dic5C2×D311yescharacteristic
96C4×C22⋊D5—62no—
97#4027—62no—
98D5×C22⋊C4—61no—
99#4023—61no—
100#3938—62no—
101#1889—151noSylow
102C23×C3×C5—42no—
103C23×C3×C5C22×C411yescharacteristic
104C23×C3×C5C2×D411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×D411yescharacteristic
108C23×C3×C5#4111yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C22×D15—21no—
111C22×D15—21no—
112C22×D15—42no—
113C22×D15C22⋊C412yescomplemented
114C22×C5×D3—24no—
115C22×C5×D3—24no—
116C22×C5×D3—24no—
117C22×C5×D3—22no—
118C22×C5×D3—22no—
119C22×C5×D3—22no—
120C22×C5×D3—44no—
121C22×C5×D3—44no—
122C22×C5×D3—44no—
123C22×C5×D3—44no—
124C22×C5×D3—42no—
125C22×C5×D3—42no—
126C22×C5×D3—42no—
127C22×C5×D3—41no—
128C22×C5×D3—41no—
129C22×C5×D3—41no—
130C22×C5×D3—41no—
131C2×C3×C4×C5—42no—
132C2×C3×C4×C5—41no—
133#1220—22no—
134#1220—22no—
135#1220—22no—
136#1220—22no—
137C2×Dic15—21no—
138C2×Dic15—21no—
139C2×Dic15—42no—
140C2×Dic15—41no—
141C2×Dic15C22⋊C412yescomplemented
142C2×C5×Dic3—22no—
143C2×C5×Dic3—42no—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—22no—
146C2×C3×Dic5—42no—
147C2×C3×Dic5—42no—
148#1203—48no—
149#1200—82no—
150C24×D3C2×D511yescharacteristic
151C22×#67—51no—
152C22×D12—101no—
153C2×C3×C22⋊C4—51no—
154C2×C3×C22⋊C4—51no—
155C2×C3×C22⋊C4C2×D511yescharacteristic
156C2×#217—51no—
157C2×#217C2×D511yescharacteristic
158C4×#67—102no—
159C2×(C2×D3)⋊C4—22no—
160C2×(C2×D3)⋊C4—101no—
161C2×(C2×D3)⋊C4—102no—
162#882—54no—
163#882—102no—
164#67⋊C4—102no—
165D3×C22⋊C4—101no—
166#877—101no—
167#806—102no—
168C24×C5—32no—
169C24×C5—61no—
170C24×C5—61no—
171C24×C5—61no—
172C24×C5—61no—
173C24×C5—61no—
174C24×C5—61no—
175C24×C5—124no—
176C24×C5C22×D311yescharacteristic
177C23×D5—31no—
178C22×C4×C5—21no—
179C22×C4×C5—32no—
180C2×C22⋊D5—32no—
181C2×C22⋊D5—32no—
182C2×C22⋊D5—64no—
183C2×C22⋊D5—61no—
184C2×C22⋊D5—61no—
185C2×C22⋊D5—61no—
186C2×C22⋊D5—61no—
187C2×C22⋊D5—124no—
188C22×Dic5—21no—
189C22×Dic5—31no—
190C22×Dic5—61no—
191C22×Dic5D1212yescomplemented
192C2×C4×D5—62no—
193C5×C22⋊C4—21no—
194C5×C22⋊C4—21no—
195C5×C22⋊C4—61no—
196C5×C22⋊C4—61no—
197C5×C22⋊C4—124no—
198C22⋊Dic5—21no—
199C22⋊Dic5—21no—
200C22⋊Dic5—21no—
201C22⋊Dic5—64no—
202C22⋊Dic5—61no—
203C22⋊Dic5—61no—
204C22⋊Dic5—124no—
205C22⋊Dic5C4×D312yescomplemented
206#685—62no—
207#683—62no—
208C4×Dic5—62no—
209C2×#120—151no—
210#518—151no—
211C2×#99—151no—
212#379—31no—
213#379—151no—
214#342—51no—
215#342—151no—
216C22×C3×C5—22no—
217C22×C3×C5—22no—
218C22×C3×C5—22no—
219C22×C3×C5—41no—
220C22×C3×C5—41no—
221C22×C3×C5—41no—
222C22×C3×C5—41no—
223C22×C3×C5C2×C22⋊C411yescharacteristic
224C22×C3×C5C4×D411yescharacteristic
225C22×C3×C5C4×D411yescharacteristic
226C22×C3×C5#12011yescharacteristic
227C22×C3×C5#12111yescharacteristic
228C22×C3×C5#12111yescharacteristic
229C22×C3×C5#12311yescharacteristic
230C2×D15—22no—
231C2×D15—42no—
232C2×D15—42no—
233C2×D15—81no—
234C2×C5×D3—24no—
235C2×C5×D3—24no—
236C2×C5×D3—24no—
237C2×C5×D3—42no—
238C2×C5×D3—44no—
239C2×C5×D3—44no—
240C2×C5×D3—42no—
241C2×C5×D3—42no—
242C2×C5×D3—44no—
243C2×C5×D3—42no—
244C2×C5×D3—44no—
245C3×C4×C5—81no—
246Dic15—22no—
247Dic15—81no—
248C3×Dic5—42no—
249C3×Dic5—42no—
250C5×Dic3—42no—
251C24×C3C22×D511yescharacteristic
252C23×D3—21no—
253C23×D3—21no—
254C23×D3—21no—
255C23×D3—21no—
256C23×D3—21no—
257C23×D3—21no—
258C23×D3—44no—
259C23×D3—51no—
260C23×D3C4×D512yescomplemented
261C22×C3×C4—21no—
262C22×C3×C4—52no—
263C22×C3×C4—101no—
264C2×#67—52no—
265C2×#67—52no—
266C2×#67—101no—
267C2×#67—101no—
268C2×#67—101no—
269C2×#67—101no—
270C22×Dic3—51no—
271C22×Dic3—101no—
272C22×Dic3C22⋊D512yescomplemented
273C2×D12—104no—
274C2×D12—204no—
275C2×C4×D3—102no—
276C3×C22⋊C4—21no—
277C3×C22⋊C4—21no—
278C3×C22⋊C4—52no—
279C3×C22⋊C4—101no—
280C3×C22⋊C4—101no—
281C3×C22⋊C4—101no—
282#217—21no—
283#217—21no—
284#217—101no—
285#217—101no—
286(C2×D3)⋊C4—44no—
287(C2×D3)⋊C4—102no—
288(C2×D3)⋊C4—104no—
289(C2×D3)⋊C4—204no—
290Dic3⋊C4—102no—
291C4×Dic3—102no—
292C23×C5—42no—
293C23×C5—64no—
294C23×C5—64no—
295C23×C5—64no—
296C23×C5—62no—
297C23×C5—62no—
298C23×C5—62no—
299C23×C5—122no—
300C23×C5—122no—
301C23×C5—122no—
302C23×C5—124no—
303C23×C5—124no—
304C23×C5—124no—
305C23×C5—124no—
306C23×C5—121no—
307C23×C5—121no—
308C23×C5—121no—
309C23×C5—121no—
310C23×C5C2×C4×D311yescharacteristic
311C23×C5C2×D1211yescharacteristic
312C23×C5#23511yescharacteristic
313C23×C5D3×D411yescharacteristic
314C23×C5D3×D411yescharacteristic
315C23×C5D3×D411yescharacteristic
316C23×C5#23911yescharacteristic
317C22×D5—32no—
318C22×D5—61no—
319C22×D5—61no—
320C22×D5—122no—
321C2×C4×C5—42no—
322C2×C4×C5—41no—
323C2×C4×C5—62no—
324C2×C4×C5—122no—
325C22⋊D5—62no—
326C22⋊D5—62no—
327C22⋊D5—62no—
328C22⋊D5—62no—
329C22⋊D5—128no—
330C2×Dic5—22no—
331C2×Dic5—22no—
332C2×Dic5—32no—
333C2×Dic5—42no—
334C2×Dic5—42no—
335C2×Dic5—61no—
336C2×Dic5—61no—
337C2×Dic5—122no—
338C2×Dic5—121no—
339C4×D5—242no—
340C25—31no—
341C22×D4—151no—
342C22×D4—301no—
343#120—154no—
344#120—302no—
345C4×D4—302no—
346C4×D4—302no—
347#117—301no—
348C2×C22⋊C4—31no—
349C2×C22⋊C4—51no—
350C2×C22⋊C4—51no—
351C2×C22⋊C4—62no—
352C2×C22⋊C4—151no—
353C2×C22⋊C4—301no—
354C2×C22⋊C4—301no—
355C2×C22⋊C4—302no—
356C2×C22⋊C4D3×D511yescharacteristic
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#38611yescharacteristic
365C2×C3×C5B(4,𝔽2)12yes—
366D15—42no—
367C5×D3—44no—
368C23×C3—42no—
369C23×C3C2×C4×D511yescharacteristic
370C23×C3#70911yescharacteristic
371C23×C3D4×D511yescharacteristic
372C23×C3D4×D511yescharacteristic
373C23×C3D4×D511yescharacteristic
374C23×C3#71111yescharacteristic
375C23×C3C2×C22⋊D511yescharacteristic
376C22×D3—24no—
377C22×D3—24no—
378C22×D3—24no—
379C22×D3—22no—
380C22×D3—22no—
381C22×D3—22no—
382C22×D3—44no—
383C22×D3—44no—
384C22×D3—44no—
385C22×D3—44no—
386C22×D3—42no—
387C22×D3—42no—
388C22×D3—42no—
389C22×D3—41no—
390C22×D3—41no—
391C22×D3—41no—
392C22×D3—41no—
393C22×D3—52no—
394C22×D3—101no—
395C22×D3—101no—
396C22×D3—202no—
397C2×C3×C4—42no—
398C2×C3×C4—41no—
399C2×C3×C4—102no—
400C2×C3×C4—102no—
401C2×C3×C4—202no—
402C2×C3×C4—202no—
403#67—102no—
404#67—102no—
405#67—102no—
406#67—102no—
407C2×Dic3—22no—
408C2×Dic3—42no—
409C2×Dic3—52no—
410C2×Dic3—101no—
411C2×Dic3—101no—
412C2×Dic3—202no—
413C2×Dic3—201no—
414D12—208no—
415C4×D3—402no—
416C22×C5—22no—
417C22×C5—22no—
418C22×C5—22no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—64no—
424C22×C5—64no—
425C22×C5—64no—
426C22×C5—122no—
427C22×C5—124no—
428C22×C5—124no—
429C22×C5—124no—
430C22×C5—122no—
431C22×C5—122no—
432C22×C5—122no—
433C22×C5—124no—
434C22×C5C4×D1211yescharacteristic
435C22×C5D3×C22⋊C411yescharacteristic
436C22×C5#88211yescharacteristic
437C22×C5#88411yescharacteristic
438C22×C5#89311yescharacteristic
439C22×C5#89411yescharacteristic
440C22×C5#89511yescharacteristic
441C2×D5—62no—
442C2×D5—122no—
443C2×D5—122no—
444C2×D5—241no—
445C4×C5—81no—
446C4×C5—122no—
447Dic5—42no—
448Dic5—42no—
449Dic5—62no—
450Dic5—241no—
451C24—32no—
452C24—61no—
453C24—61no—
454C24—61no—
455C24—61no—
456C24—61no—
457C24—61no—
458C24—124no—
459C24—151no—
460C24C2×D3×D511yescharacteristic
461C2×D4—152no—
462C2×D4—152no—
463C2×D4—304no—
464C2×D4—301no—
465C2×D4—301no—
466C2×D4—301no—
467C2×D4—301no—
468C2×D4—604no—
469C22×C4—21no—
470C22×C4—32no—
471C22×C4—52no—
472C22×C4—101no—
473C22×C4—151no—
474C22×C4—302no—
475C22×C4—301no—
476C4⋊C4—302no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—52no—
480C22⋊C4—61no—
481C22⋊C4—61no—
482C22⋊C4—101no—
483C22⋊C4—101no—
484C22⋊C4—101no—
485C22⋊C4—124no—
486C22⋊C4—302no—
487C22⋊C4—304no—
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—41no—
497C22×C3—41no—
498C22×C3—41no—
499C22×C3—41no—
500C22×C3D5×C22⋊C411yescharacteristic
501C22×C3#402711yescharacteristic
502C22×C3#402911yescharacteristic
503C22×C3#403011yescharacteristic
504C22×C3C4×C22⋊D511yescharacteristic
505C22×C3#408311yescharacteristic
506C22×C3#408411yescharacteristic
507C2×D3—24no—
508C2×D3—24no—
509C2×D3—24no—
510C2×D3—44no—
511C2×D3—44no—
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—44no—
516C2×D3—44no—
517C2×D3—42no—
518C2×D3—102no—
519C2×D3—202no—
520C2×D3—202no—
521C2×D3—401no—
522C3×C4—81no—
523C3×C4—202no—
524C3×C4—202no—
525Dic3—42no—
526Dic3—102no—
527Dic3—401no—
528C2×C5—21no—
529C2×C5—21no—
530C2×C5—21no—
531C2×C5—21no—
532C2×C5—21no—
533C2×C5—21no—
534C2×C5—124no—
535C2×C5#466511yescharacteristic
536C2×C5#474112yes—
537D5—122no—
538C23—42no—
539C23—64no—
540C23—64no—
541C23—64no—
542C23—62no—
543C23—62no—
544C23—62no—
545C23—122no—
546C23—122no—
547C23—122no—
548C23—124no—
549C23—124no—
550C23—124no—
551C23—124no—
552C23—121no—
553C23—121no—
554C23—121no—
555C23—121no—
556C23—152no—
557C23—301no—
558C23—301no—
559C23—602no—
560C23#676911yescharacteristic
561C23C4×D3×D511yescharacteristic
562C23D5×D1211yescharacteristic
563C23#677711yescharacteristic
564C23#678211yescharacteristic
565C23D3×C22⋊D511yescharacteristic
566C23#679011yescharacteristic
567D4—302no—
568D4—302no—
569D4—302no—
570D4—302no—
571D4—608no—
572C2×C4—42no—
573C2×C4—41no—
574C2×C4—62no—
575C2×C4—102no—
576C2×C4—102no—
577C2×C4—122no—
578C2×C4—152no—
579C2×C4—202no—
580C2×C4—202no—
581C2×C4—301no—
582C2×C4—301no—
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#6524511yescharacteristic
593C2×C3#6532112yes—
594D3—44no—
595D3—202no—
596C5#6896211yescharacteristic, complemented, Sylow
597C22—22no—
598C22—22no—
599C22—22no—
600C22—41no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—64no—
605C22—64no—
606C22—64no—
607C22—124no—
608C22—122no—
609C22—124no—
610C22—122no—
611C22—122no—
612C22—124no—
613C22—122no—
614C22—124no—
615C22—302no—
616C22—602no—
617C22—602no—
618C22—1201no—
619C22#9140511yescharacteristic
620C22#9142011yescharacteristic
621C22#9143811yescharacteristic
622C22#9144611yescharacteristic
623C22#9147311yescharacteristic
624C22#9147511yescharacteristic
625C22#9155711yescharacteristic
626C4—81no—
627C4—122no—
628C4—202no—
629C4—202no—
630C4—302no—
631C4—1201no—
632C3#1060029211yescharacteristic, complemented, Sylow
633C2—21no—
634C2—21no—
635C2—21no—
636C2—21no—
637C2—21no—
638C2—21no—
639C2—124no—
640C2—602no—
641C2#1174713412yes—
642C2#1174891911yescharacteristic
subgroupG/H
centerC22#91475
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#91570C2
cosocleC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#1889
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. #11755413C2semidirect
3. C2×#91090C2semidirect
4. C5×#4955C2semidirect
5. #11749496C2semidirect
6. C3×#64747C2semidirect
7. #11746018C2semidirect
19. #91570C4semidirect
33. #64747D3semidirect
44. C23×C5×D3C2×C4semidirect
54. C22×C5×Dic3D4semidirect
56. C22×C3×Dic5D4semidirect
70. C3×C22⋊Dic5C2×C4semidirect
79. #4955D5semidirect
113. C22×D15C22⋊C4semidirect
141. C2×Dic15C22⋊C4semidirect
191. C22×Dic5D12semidirect
205. C22⋊Dic5C4×D3semidirect
260. C23×D3C4×D5semidirect
272. C22×Dic3C22⋊D5semidirect
492. C3×C5#1889semidirect
596. C5#68962semidirect
632. C3#10600292semidirect

Maximal subgroups

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

subgroupindex
C2×#915702
#117554132
C2×#910902
C5×#49552
#117494962
C3×#647472
#117460182
#106002923
#689625