Finite Group Databasebeta

← #14294514

Subgroups — #14294514

Order 1920.

808 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#700C211yesmaximal, characteristic
2C2×#91909C211yesmaximal, characteristic
3#11753835C211yesmaximal, characteristic
4#11746746C211yesmaximal, characteristic, complemented
5C3×#64875C211yesmaximal, characteristic, complemented
6#11746526C211yesmaximal, characteristic, complemented
7#11746524C211yesmaximal, characteristic, complemented
8#10604373—31nomaximal, Hall
9C2×C4×D3×D5C2211yescharacteristic
10C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
11C2×#6758C2211yescharacteristic
12C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
13C2×C3×#700C2211yescharacteristic
14C2×#6740—21no—
15C2×D3×#170—21no—
16C2×Dic3⋊AGL(1,𝔽5)—21no—
17C2×(C2×D3)⋊AGL(1,𝔽5)—21no—
18D3×#700—22no—
19D3×#700C414yescomplemented
20#91909—22no—
21#91909C414yescomplemented
22C4⋊C4×D15C411yescharacteristic, complemented
23C5×#892C411yescharacteristic, complemented
24C3×#4038C2211yescharacteristic
25#91473—21no—
26#91437C411yescharacteristic, complemented
27C4×#1200—21no—
28#91398—21no—
29#91393—21no—
30#91358C2211yescharacteristic
31#91338C411yescharacteristic, complemented
32#68753—51nomaximal, Hall
33C2×#4130—31no—
34C22×#700—31no—
35D5×#117—31no—
36#64875—31no—
37#64875—31no—
38#64875—31no—
39#64875D311yescharacteristic, complemented
40C22×D3×D5D411yescharacteristic
41C22×ΓL(1,𝔽16)—21no—
42C22×C3×AGL(1,𝔽5)—21no—
43C2×C4×D15—21no—
44C2×C4×D15C2×C411yescharacteristic
45C2×C4×C5×D3C2×C411yescharacteristic
46C2×C3×C4×D5C2311yescharacteristic
47C2×#1200—21no—
48C2×#1200D411yescharacteristic
49C2×D3×Dic5D411yescharacteristic
50C2×D5×Dic3D411yescharacteristic
51C4×D3×D5C2×C412yes—
52C4×D3×D5C2×C412yes—
53C4×D3×D5D412yes—
54C4×D3×D5Q812yes—
55C2×C3⋊#170—21no—
56C4×ΓL(1,𝔽16)—21no—
57C4×ΓL(1,𝔽16)C2×C412yescomplemented
58#6758—21no—
59#6758C2×C412yescomplemented
60C2×C3×#170—21no—
61C3×C4×AGL(1,𝔽5)—21no—
62C3×C4×AGL(1,𝔽5)C2×C412yescomplemented
63C3×#700—21no—
64C3×#700C2×C412yescomplemented
65#6740—24no—
66D3×#170—24no—
67Dic3⋊AGL(1,𝔽5)—24no—
68(C2×D3)⋊AGL(1,𝔽5)—24no—
69C3×C5×C4⋊C4C2×C411yescharacteristic
70C4⋊Dic15C2×C411yescharacteristic
71#6712—21no—
72C5×(C2×D3)⋊C4—21no—
73C5×C4⋊Dic3C2×C411yescharacteristic
74C4×C5×Dic3—21no—
75C3×#685—21no—
76C3×C4⋊Dic5C2×C411yescharacteristic
77C3×C4×Dic5—21no—
78#6669—21no—
79(C2×D3)⋊Dic5—21no—
80#6665—21no—
81Dic3×Dic5—21no—
82Dic3×Dic5—21no—
83C2×D3×M16—51no—
84D3×#117—51no—
85C2×#872—51no—
86C3×#339—51no—
87#4555—51no—
88#4532—51no—
89#4523—51no—
90C22×C4×D5—31no—
91C2×C22⋊AGL(1,𝔽5)—61no—
92C22×#170—61no—
93#4130—34no—
94#4130—62no—
95C2×C4⋊AGL(1,𝔽5)—61no—
96C2×C4×AGL(1,𝔽5)—31no—
97C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
98C2×#700—31no—
99C2×#700—34no—
100C2×#700—62no—
101C2×#700—61no—
102C2×#700C2×D311yescharacteristic
103C5×#117—31no—
104#4072—31no—
105#4038—31no—
106#4038C2×D311yescharacteristic
107D5×C4⋊C4—31no—
108D5×C4⋊C4—31no—
109D5×C22⋊C4—61no—
110#4023—61no—
111#4018—61no—
112C42×D5—61no—
113#1733—151noSylow
114C22×D15C22⋊C411yescharacteristic
115C22×C5×D3C22⋊C411yescharacteristic
116C22×C3×D5C2×D411yescharacteristic
117C2×D3×D5—41no—
118C2×D3×D5—41no—
119C2×D3×D5C22⋊C412yes—
120C2×D3×D5C4⋊C412yes—
121C2×ΓL(1,𝔽16)—22no—
122C2×ΓL(1,𝔽16)—41no—
123C2×ΓL(1,𝔽16)—41no—
124C2×C3×AGL(1,𝔽5)—22no—
125C2×C3×AGL(1,𝔽5)—41no—
126C2×C3×AGL(1,𝔽5)—41no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5C22×C411yescharacteristic
129C2×Dic15—21no—
130C2×Dic15C22⋊C411yescharacteristic
131C4×D15—42no—
132C4×D15C4212yes—
133C4×D15C4⋊C412yes—
134C2×C5×Dic3—21no—
135C2×C5×Dic3C22⋊C411yescharacteristic
136C4×C5×D3C4212yes—
137C4×C5×D3C4⋊C412yes—
138C2×C3×Dic5—21no—
139C2×C3×Dic5C2×D411yescharacteristic
140C3×C4×D5C22×C411yescharacteristic
141C3×C4×D5C22×C411yescharacteristic
142C3×C4×D5C2×D411yescharacteristic
143C3×C4×D5C2×Q811yescharacteristic
144#1200—42no—
145#1200C22⋊C412yes—
146#1200C4⋊C412yes—
147D3×Dic5C22⋊C412yes—
148D3×Dic5C4⋊C412yes—
149D5×Dic3C22⋊C412yes—
150D5×Dic3C4⋊C412yes—
151C3⋊#170—22no—
152C3×#170—22no—
153C22×C4×D3—51no—
154C2×C3×M16—51no—
155C3×#117—51no—
156C2×C3×C42—51no—
157C2×(C2×D3)⋊C4—101no—
158#926—51no—
159C2×Dic3⋊C4—101no—
160C2×C4×Dic3—51no—
161C2×#208—51no—
162D3×M16—54no—
163D3×M16—102no—
164C2×ΓL(1,𝔽25)—101no—
165C2×D3×C8—101no—
166#892—51no—
167#892AGL(1,𝔽5)11yescharacteristic, complemented
168D3×C4⋊C4—51no—
169D3×C4⋊C4—51no—
170D3×C22⋊C4—101no—
171#877—101no—
172#872—54no—
173#872—101no—
174#872—102no—
175C42×D3—101no—
176C23×D5—31no—
177C22×AGL(1,𝔽5)—21no—
178C22×AGL(1,𝔽5)—61no—
179C22×C4×C5—31no—
180C22×Dic5—31no—
181C2×C4×D5—31no—
182C2×C4×D5—31no—
183C2×C4×D5—31no—
184C2×C4×D5—32no—
185C2×C4×D5—32no—
186C2×C4×D5—32no—
187C2×C4×D5—32no—
188C2×C4×D5—61no—
189C2×C4×D5—61no—
190C2×C4×D5C22×D311yescharacteristic
191C22⋊AGL(1,𝔽5)—64no—
192C2×#170—21no—
193C2×#170—64no—
194C2×#170—61no—
195C4⋊AGL(1,𝔽5)—64no—
196C4×AGL(1,𝔽5)—21no—
197C4×AGL(1,𝔽5)—32no—
198C4×AGL(1,𝔽5)—61no—
199C4×AGL(1,𝔽5)C4×D312yescomplemented
200#700—21no—
201#700—32no—
202#700—64no—
203#700—61no—
204#700C4×D312yescomplemented
205C5×C4⋊C4—31no—
206C5×C4⋊C4C4×D311yescharacteristic
207C5×C22⋊C4—61no—
208C42×C5—61no—
209C22⋊Dic5—61no—
210#685—21no—
211#685—61no—
212C4⋊Dic5—31no—
213C4⋊Dic5C4×D311yescharacteristic
214#683—61no—
215#683—61no—
216C4×Dic5—21no—
217C4×Dic5—61no—
218C4×Dic5—61no—
219C22×M16—151no—
220C2×#117—151no—
221C2×#117—151no—
222#339—51no—
223#339—151no—
224#339—151no—
225#339—151no—
226C22×C3×C5C2×C22⋊C411yescharacteristic
227C2×D15—21no—
228C2×D15—21no—
229C2×D15#9512yes—
230C2×C5×D3—21no—
231C2×C5×D3—21no—
232C2×C5×D3#9512yes—
233C2×C3×D5—21no—
234C2×C3×D5—21no—
235C2×C3×D5C2×C22⋊C411yescharacteristic
236C2×C3×D5C2×C4⋊C411yescharacteristic
237D3×D5—42no—
238D3×D5—42no—
239ΓL(1,𝔽16)—42no—
240C3×AGL(1,𝔽5)—42no—
241C3×C4×C5—41no—
242C3×C4×C5C2×C4211yescharacteristic
243C3×C4×C5C2×C4⋊C411yescharacteristic
244Dic15—41no—
245Dic15#9512yes—
246C3×Dic5—41no—
247C3×Dic5C2×C22⋊C411yescharacteristic
248C3×Dic5C2×C4⋊C411yescharacteristic
249C5×Dic3—41no—
250C5×Dic3#9512yes—
251C23×D3—51no—
252C22×C3×C4—51no—
253C22×C3×C4—101no—
254C22×Dic3—51no—
255C22×Dic3—101no—
256C2×C4×D3—51no—
257C2×C4×D3—51no—
258C2×C4×D3—51no—
259C2×C4×D3—52no—
260C2×C4×D3—52no—
261C2×C4×D3—52no—
262C2×C4×D3—52no—
263C2×C4×D3—101no—
264C2×C4×D3—101no—
265C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
266C3×M16—52no—
267C3×M16—101no—
268C2×C3×C8—101no—
269C3×C4⋊C4—51no—
270C3×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic
271C3×C22⋊C4—101no—
272C3×C42—52no—
273C3×C42—101no—
274C3×C42—101no—
275#217—101no—
276(C2×D3)⋊C4—21no—
277(C2×D3)⋊C4—104no—
278(C2×D3)⋊C4—101no—
279C4⋊Dic3—51no—
280C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
281Dic3⋊C4—101no—
282Dic3⋊C4—101no—
283Dic3⋊C4—104no—
284C4×Dic3—21no—
285C4×Dic3—52no—
286C4×Dic3—101no—
287C4×Dic3—101no—
288C4×Dic3—101no—
289#208—52no—
290#208—101no—
291C2×C3⋊C8—101no—
292ΓL(1,𝔽25)—104no—
293D3×C8—104no—
294C23×C5—31no—
295C22×D5—31no—
296C22×D5—32no—
297C22×D5—32no—
298C22×D5—121no—
299C22×D5—121no—
300C22×D5D3×D411yescharacteristic
301C2×AGL(1,𝔽5)—22no—
302C2×AGL(1,𝔽5)—41no—
303C2×AGL(1,𝔽5)—41no—
304C2×AGL(1,𝔽5)—62no—
305C2×AGL(1,𝔽5)—121no—
306C2×AGL(1,𝔽5)—121no—
307C2×C4×C5—21no—
308C2×C4×C5—31no—
309C2×C4×C5—32no—
310C2×C4×C5—32no—
311C2×C4×C5—61no—
312C2×C4×C5C2×C4×D311yescharacteristic
313C2×Dic5—21no—
314C2×Dic5—31no—
315C2×Dic5—32no—
316C2×Dic5—32no—
317C2×Dic5—61no—
318C2×Dic5D3×D411yescharacteristic
319C4×D5—32no—
320C4×D5—32no—
321C4×D5—32no—
322C4×D5—32no—
323C4×D5—32no—
324C4×D5—32no—
325C4×D5—122no—
326C4×D5—122no—
327C4×D5C2×C4×D311yescharacteristic
328C4×D5C2×C4×D311yescharacteristic
329C4×D5D3×D411yescharacteristic
330C4×D5D3×Q811yescharacteristic
331#170—22no—
332#170—62no—
333C23×C4—151no—
334C2×M16—51no—
335C2×M16—154no—
336C2×M16—151no—
337C2×M16—301no—
338C2×M16—302no—
339C22×C8—301no—
340#117—31no—
341#117—51no—
342#117—154no—
343#117—151no—
344#117—151no—
345#117—301no—
346#117—301no—
347#117—302no—
348C2×C4⋊C4—151no—
349C2×C4⋊C4—151no—
350C2×C4⋊C4—301no—
351C2×C22⋊C4—301no—
352C2×C22⋊C4—301no—
353C2×C42—51no—
354C2×C42—151no—
355C2×C42—301no—
356C2×C3×C5C2×#9511yescharacteristic
357C2×C3×C5#42111yescharacteristic
358C2×C3×C5#42111yescharacteristic
359D15—22no—
360C3×D5—21no—
361C3×D5—21no—
362C5×D3—22no—
363C23×C3—51no—
364C22×D3—51no—
365C22×D3—52no—
366C22×D3—52no—
367C22×D3—201no—
368C22×D3—201no—
369C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
370C2×C3×C4—21no—
371C2×C3×C4—51no—
372C2×C3×C4—51no—
373C2×C3×C4—51no—
374C2×C3×C4—51no—
375C2×C3×C4—51no—
376C2×C3×C4—102no—
377C2×C3×C4—101no—
378C2×C3×C4—201no—
379C2×C3×C4—201no—
380C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
381C2×Dic3—21no—
382C2×Dic3—51no—
383C2×Dic3—52no—
384C2×Dic3—52no—
385C2×Dic3—102no—
386C2×Dic3—101no—
387C2×Dic3—201no—
388C2×Dic3—201no—
389C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
390C4×D3—52no—
391C4×D3—52no—
392C4×D3—52no—
393C4×D3—52no—
394C4×D3—52no—
395C4×D3—52no—
396C4×D3—202no—
397C4×D3—202no—
398C4×D3C4×AGL(1,𝔽5)12yes—
399C4×D3C4⋊AGL(1,𝔽5)12yes—
400C3×C8—102no—
401C3⋊C8—102no—
402C22×C5—32no—
403C22×C5—61no—
404C22×C5—61no—
405C22×C5D3×C22⋊C411yescharacteristic
406C2×D5—21no—
407C2×D5—21no—
408C2×D5—32no—
409C2×D5—61no—
410C2×D5—61no—
411C2×D5—122no—
412C2×D5—122no—
413C2×D5D3×C22⋊C411yescharacteristic
414C2×D5D3×C4⋊C411yescharacteristic
415AGL(1,𝔽5)—42no—
416AGL(1,𝔽5)—122no—
417C4×C5—32no—
418C4×C5—41no—
419C4×C5—121no—
420C4×C5C42×D311yescharacteristic
421C4×C5D3×C4⋊C411yescharacteristic
422Dic5—32no—
423Dic5—41no—
424Dic5—121no—
425Dic5D3×C22⋊C411yescharacteristic
426Dic5D3×C4⋊C411yescharacteristic
427C24—151no—
428C22×C4—31no—
429C22×C4—51no—
430C22×C4—101no—
431C22×C4—151no—
432C22×C4—152no—
433C22×C4—152no—
434C22×C4—152no—
435C22×C4—152no—
436C22×C4—151no—
437C22×C4—151no—
438C22×C4—151no—
439C22×C4—301no—
440C22×C4—301no—
441C22×C4—301no—
442M16—52no—
443M16—101no—
444M16—152no—
445M16—304no—
446M16—301no—
447C2×C8—101no—
448C2×C8—304no—
449C2×C8—301no—
450C4⋊C4—31no—
451C4⋊C4—51no—
452C4⋊C4—151no—
453C4⋊C4—301no—
454C4⋊C4—301no—
455C4⋊C4—304no—
456C4⋊C4D3×AGL(1,𝔽5)11yescharacteristic
457C22⋊C4—61no—
458C22⋊C4—101no—
459C22⋊C4—301no—
460C22⋊C4—301no—
461C22⋊C4—304no—
462C42—52no—
463C42—61no—
464C42—101no—
465C42—101no—
466C42—152no—
467C42—301no—
468C42—301no—
469C42—301no—
470C3×C5#173311yescharacteristic, complemented, Hall
471C22×C3—51no—
472C22×C3—51no—
473C22×C3—101no—
474C22×C3—101no—
475C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
476C2×D3—21no—
477C2×D3—21no—
478C2×D3—52no—
479C2×D3—101no—
480C2×D3—101no—
481C2×D3—202no—
482C2×D3—202no—
483C2×D3(C2×AGL(1,𝔽5))⋊C412yes—
484C3×C4—41no—
485C3×C4—51no—
486C3×C4—51no—
487C3×C4—202no—
488C3×C4—201no—
489C3×C4C2×C4×AGL(1,𝔽5)11yescharacteristic
490C3×C4C2×C4⋊AGL(1,𝔽5)11yescharacteristic
491Dic3—41no—
492Dic3—52no—
493Dic3—202no—
494Dic3—201no—
495Dic3(C2×AGL(1,𝔽5))⋊C412yes—
496C2×C5—62no—
497C2×C5D3×#9511yescharacteristic
498C2×C5#482111yescharacteristic
499C2×C5#482111yescharacteristic
500D5—21no—
501D5—21no—
502D5—62no—
503C23—31no—
504C23—51no—
505C23—152no—
506C23—152no—
507C23—151no—
508C23—601no—
509C23—601no—
510C2×C4—21no—
511C2×C4—31no—
512C2×C4—32no—
513C2×C4—32no—
514C2×C4—51no—
515C2×C4—51no—
516C2×C4—51no—
517C2×C4—51no—
518C2×C4—51no—
519C2×C4—61no—
520C2×C4—102no—
521C2×C4—101no—
522C2×C4—152no—
523C2×C4—152no—
524C2×C4—152no—
525C2×C4—152no—
526C2×C4—152no—
527C2×C4—152no—
528C2×C4—151no—
529C2×C4—152no—
530C2×C4—152no—
531C2×C4—201no—
532C2×C4—201no—
533C2×C4—302no—
534C2×C4—301no—
535C2×C4—602no—
536C2×C4—602no—
537C2×C4—601no—
538C2×C4—601no—
539C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
540C8—102no—
541C8—302no—
542C2×C3—101no—
543C2×C3—101no—
544C2×C3C2×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
545C2×C3#6579511yescharacteristic
546C2×C3#6579511yescharacteristic
547D3—22no—
548D3—102no—
549C5#6875311yescharacteristic, complemented, Sylow
550C22—32no—
551C22—51no—
552C22—51no—
553C22—61no—
554C22—61no—
555C22—101no—
556C22—101no—
557C22—152no—
558C22—301no—
559C22—301no—
560C22—602no—
561C22—602no—
562C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
563C4—32no—
564C4—41no—
565C4—51no—
566C4—51no—
567C4—121no—
568C4—152no—
569C4—202no—
570C4—201no—
571C4—602no—
572C4—601no—
573C4C4×D3×AGL(1,𝔽5)11yescharacteristic
574C4D3×C4⋊AGL(1,𝔽5)11yescharacteristic
575C3#1060437311yescharacteristic, complemented, Sylow
576C2—62no—
577C2—101no—
578C2—101no—
579C2—302no—
580C2D3×(C2×AGL(1,𝔽5))⋊C411yescharacteristic
581C2#1175194911yescharacteristic
582C2#1175197311yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC3×C4×C5C2×C42
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C5×C4⋊C4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D3×D5D4
cosocleC2×C3×C4×D5C23
hypercenterC4⋊C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1733
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11746746C2semidirect
5. C3×#64875C2semidirect
6. #11746526C2semidirect
7. #11746524C2semidirect
19. D3×#700C4semidirect
21. #91909C4semidirect
22. C4⋊C4×D15C4semidirect
23. C5×#892C4semidirect
26. #91437C4semidirect
31. #91338C4semidirect
39. #64875D3semidirect
57. C4×ΓL(1,𝔽16)C2×C4semidirect
59. #6758C2×C4semidirect
62. C3×C4×AGL(1,𝔽5)C2×C4semidirect
64. C3×#700C2×C4semidirect
167. #892AGL(1,𝔽5)semidirect
199. C4×AGL(1,𝔽5)C4×D3semidirect
204. #700C4×D3semidirect
470. C3×C5#1733semidirect
549. C5#68753semidirect
575. C3#10604373semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#7002
C2×#919092
#117538352
#117467462
C3×#648752
#117465262
#117465242
#106043733
#687535