Finite Group Databasebeta

← #14319689

Subgroups — #14319689

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91781C211yesmaximal, characteristic
2C2×#91437C211yesmaximal, characteristic
3C2×#91386C211yesmaximal, characteristic
4C5×Dic3×C4⋊C4C211yesmaximal, characteristic, complemented
5C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
6#11748881C212yesmaximal
7#11748875C212yesmaximal
8C4×#6669C212yesmaximal, complemented
9Dic3×C4⋊Dic5C211yesmaximal, characteristic, complemented
10Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#11748663C212yesmaximal, complemented
12#10605481—31nomaximal, Hall
13C22×C4×D15C2211yescharacteristic
14C22×#1200C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×#6714C2212yes—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×C4×Dic15C2212yes—
19#91781C418yescomplemented
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C4×C5×Dic3C2212yes—
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4×Dic5C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×#6669C2212yes—
27C2×#6669C2211yescharacteristic
28C2×#6669C2211yescharacteristic
29C2×#6667C2211yescharacteristic
30C2×#6667C2211yescharacteristic
31C2×Dic3×Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33#91437C418yescomplemented
34#91386C418yescomplemented
35C5×C3⋊#95C2212yes—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73750—51nomaximal, Hall
40C2×#4038—31no—
41C2×D5×C4⋊C4—31no—
42C2×#4018—31no—
43C4×C5×C4⋊C4—31no—
44C4⋊C4×Dic5—31no—
45C4⋊C4×Dic5D311yescharacteristic, complemented
46C4×#685—32no—
47C4×C4⋊Dic5—31no—
48C4×#683—32no—
49#64955—32no—
50#64938—32no—
51C23×D15C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2312yes—
55C22×Dic15C2311yescharacteristic
56C2×C4×D15C2×C414yes—
57C2×C4×D15C2×C414yes—
58C2×C4×D15C2×C414yes—
59C22×C5×Dic3C2311yescharacteristic
60C22×C5×Dic3C2312yes—
61C22×C5×Dic3C2311yescharacteristic
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C2×#1200—42no—
66C2×#1200—42no—
67C2×#1200C2×C418yes—
68C3×C5×C4⋊C4C2×C414yescomplemented
69#6714C2×C418yes—
70C4⋊Dic15C2×C414yescomplemented
71C4×Dic15C2×C418yescomplemented
72C5×C4⋊Dic3C2×C414yes—
73C4×C5×Dic3—42no—
74C4×C5×Dic3C2×C414yescomplemented
75C3×C4⋊Dic5C2×C414yes—
76C3×C4×Dic5—42no—
77C3×C4×Dic5C2×C414yescomplemented
78#6669C2×C418yes—
79#6669C2×C414yescomplemented
80#6669C2×C414yescomplemented
81#6667C2×C414yes—
82#6667C2×C414yes—
83Dic3×Dic5—42no—
84Dic3×Dic5—42no—
85C2×#892—51no—
86C2×D3×C4⋊C4—51no—
87C2×#872—51no—
88C3×C4×C4⋊C4—51no—
89Dic3×C4⋊C4—51no—
90Dic3×C4⋊C4D511yescharacteristic, complemented
91C4×(C2×D3)⋊C4—52no—
92C4×C4⋊Dic3—51no—
93C4×Dic3⋊C4—52no—
94#4666—52no—
95#4649—52no—
96C22×C4×D5—31no—
97C22×C4×D5—32no—
98C2×C5×C4⋊C4—31no—
99C2×C5×C4⋊C4C2×D311yescharacteristic
100C2×C42×C5—31no—
101C2×C42×C5—32no—
102C2×#685—32no—
103C2×#685—31no—
104C2×#685—31no—
105C2×C4⋊Dic5—31no—
106C2×C4⋊Dic5C2×D311yescharacteristic
107C2×#683—31no—
108C2×#683—31no—
109C2×#683—32no—
110C2×C4×Dic5—32no—
111C2×C4×Dic5—32no—
112C2×C4×Dic5—32no—
113C2×C4×Dic5C2×D312yes—
114C2×C4×Dic5C2×D311yescharacteristic
115#4038—38no—
116D5×C4⋊C4—38no—
117#4018—38no—
118C5×#95—32no—
119#3963—32no—
120#3963—32no—
121#3963C2×D312yes—
122#2274—151noSylow
123C23×C3×C5C2411yescharacteristic
124C22×D15—21no—
125C22×D15—21no—
126C22×D15—21no—
127C22×D15—21no—
128C22×D15C22×C412yes—
129C22×D15C22×C412yes—
130C22×D15C22×C412yes—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5C22×C414yes—
134C2×C3×C4×C5C22×C412yes—
135C2×C3×C4×C5C22×C412yes—
136C2×C3×C4×C5C22×C412yes—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15C22×C414yes—
140C2×Dic15C22×C412yes—
141C2×Dic15C22×C412yes—
142C2×Dic15C22×C412yes—
143C4×D15C42116yescomplemented
144C2×C5×Dic3—21no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—21no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3C22×C412yes—
151C2×C5×Dic3C22×C412yes—
152C2×C5×Dic3C22×C414yes—
153C2×C3×Dic5—21no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—21no—
158C2×C3×Dic5—21no—
159C2×C3×Dic5C22×C412yes—
160C2×C3×Dic5C22×C412yes—
161C2×C3×Dic5C22×C414yes—
162#1200—48no—
163C22×C4×D3—51no—
164C22×C4×D3—52no—
165C2×C3×C4⋊C4—51no—
166C2×C3×C4⋊C4C2×D511yescharacteristic
167C2×C3×C42—51no—
168C2×C3×C42—52no—
169C2×(C2×D3)⋊C4—52no—
170C2×(C2×D3)⋊C4—51no—
171C2×(C2×D3)⋊C4—51no—
172C2×C4⋊Dic3—51no—
173C2×C4⋊Dic3C2×D511yescharacteristic
174C2×Dic3⋊C4—51no—
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4—51no—
177C2×C4×Dic3—52no—
178C2×C4×Dic3—52no—
179C2×C4×Dic3—52no—
180C2×C4×Dic3C2×D512yes—
181C2×C4×Dic3C2×D511yescharacteristic
182#892—58no—
183D3×C4⋊C4—58no—
184#872—58no—
185C3×#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95C2×D512yes—
189C23×D5—31no—
190C22×C4×C5—31no—
191C22×C4×C5—32no—
192C22×C4×C5—31no—
193C22×C4×C5C22×D312yes—
194C22×C4×C5C22×D311yescharacteristic
195C22×Dic5—31no—
196C22×Dic5—32no—
197C22×Dic5C22×D312yes—
198C22×Dic5C22×D311yescharacteristic
199C22×Dic5C22×D311yescharacteristic
200C2×C4×D5—34no—
201C2×C4×D5—34no—
202C2×C4×D5—34no—
203C2×C4×D5—38no—
204C2×C4×D5—122no—
205C2×C4×D5—122no—
206C5×C4⋊C4—34no—
207C5×C4⋊C4C4×D314yescomplemented
208C42×C5—34no—
209C42×C5—122no—
210#685—38no—
211#685—34no—
212#685—34no—
213C4⋊Dic5—34no—
214C4⋊Dic5C4×D314yes—
215#683—38no—
216#683—34no—
217#683—34no—
218C4×Dic5—38no—
219C4×Dic5—42no—
220C4×Dic5—122no—
221C4×Dic5—122no—
222C4×Dic5C4×D314yescomplemented
223C2×#117—151no—
224C2×#117—151no—
225C22×C4⋊C4—151no—
226C4×C4⋊C4—31no—
227C4×C4⋊C4—51no—
228C4×C4⋊C4—152no—
229C4×C4⋊C4—152no—
230C4×C4⋊C4—151no—
231C4×C4⋊C4—151no—
232C4×C22⋊C4—152no—
233C4×C22⋊C4—152no—
234C22×C3×C5C23×C411yescharacteristic
235C22×C3×C5C23×C411yescharacteristic
236C22×C3×C5C23×C411yescharacteristic
237C22×C3×C5H(5,𝔽2)11yescharacteristic
238C22×C3×C5H(5,𝔽2)11yescharacteristic
239C22×C3×C52−1+411yescharacteristic
240C22×C3×C52−1+411yescharacteristic
241C2×D15—22no—
242C2×D15—22no—
243C2×D15—22no—
244C2×D15—22no—
245C2×D15—22no—
246C2×D15—22no—
247C2×D15C2×C4214yes—
248C3×C4×C5—24no—
249C3×C4×C5C2×C4214yes—
250Dic15—24no—
251Dic15C2×C4214yes—
252C3×Dic5—24no—
253C3×Dic5—22no—
254C3×Dic5—22no—
255C5×Dic3—24no—
256C5×Dic3—22no—
257C5×Dic3—22no—
258C23×D3—51no—
259C22×C3×C4—51no—
260C22×C3×C4—52no—
261C22×C3×C4—51no—
262C22×C3×C4C22×D512yes—
263C22×C3×C4C22×D511yescharacteristic
264C22×Dic3—51no—
265C22×Dic3—52no—
266C22×Dic3C22×D511yescharacteristic
267C22×Dic3C22×D512yes—
268C22×Dic3C22×D511yescharacteristic
269C2×C4×D3—54no—
270C2×C4×D3—54no—
271C2×C4×D3—54no—
272C2×C4×D3—58no—
273C2×C4×D3—202no—
274C2×C4×D3—202no—
275C3×C4⋊C4—54no—
276C3×C4⋊C4C4×D514yescomplemented
277C3×C42—54no—
278C3×C42—202no—
279(C2×D3)⋊C4—58no—
280(C2×D3)⋊C4—54no—
281(C2×D3)⋊C4—54no—
282C4⋊Dic3—54no—
283C4⋊Dic3C4×D514yes—
284Dic3⋊C4—58no—
285Dic3⋊C4—54no—
286Dic3⋊C4—54no—
287C4×Dic3—42no—
288C4×Dic3—58no—
289C4×Dic3—202no—
290C4×Dic3—202no—
291C4×Dic3C4×D514yescomplemented
292C23×C5C23×D311yescharacteristic
293C22×D5—32no—
294C22×D5—32no—
295C22×D5—32no—
296C22×D5—61no—
297C22×D5—61no—
298C22×D5—61no—
299C22×D5—61no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—32no—
303C2×C4×C5—32no—
304C2×C4×C5—34no—
305C2×C4×C5—61no—
306C2×C4×C5—62no—
307C2×C4×C5—61no—
308C2×C4×C5—61no—
309C2×C4×C5—62no—
310C2×C4×C5—61no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5C2×C4×D312yes—
313C2×C4×C5C2×C4×D314yes—
314C2×C4×C5C2×C4×D312yes—
315C2×Dic5—21no—
316C2×Dic5—22no—
317C2×Dic5—21no—
318C2×Dic5—21no—
319C2×Dic5—22no—
320C2×Dic5—21no—
321C2×Dic5—32no—
322C2×Dic5—32no—
323C2×Dic5—32no—
324C2×Dic5—34no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5C2×C4×D312yes—
328C2×Dic5C2×C4×D312yes—
329C2×Dic5C2×C4×D314yes—
330C4×D5—316no—
331C4×D5—128no—
332C23×C4—152no—
333C23×C4—151no—
334#117—158no—
335#117—158no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—51no—
338C2×C4⋊C4—158no—
339C2×C4⋊C4—152no—
340C2×C4⋊C4—151no—
341C2×C4⋊C4—151no—
342C2×C4⋊C4—151no—
343C2×C4⋊C4D3×D511yescharacteristic
344C2×C22⋊C4—151no—
345C2×C22⋊C4—151no—
346C2×C22⋊C4—152no—
347C2×C42—31no—
348C2×C42—32no—
349C2×C42—51no—
350C2×C42—52no—
351C2×C42—152no—
352C2×C42—152no—
353C2×C42—152no—
354#95—32no—
355#95—52no—
356#95—152no—
357#95—152no—
358C2×C3×C5C22×C4211yescharacteristic
359C2×C3×C5#51811yescharacteristic
360C2×C3×C5#51911yescharacteristic
361C2×C3×C5#52011yescharacteristic
362C2×C3×C5#52011yescharacteristic
363C2×C3×C5#52011yescharacteristic
364C2×C3×C5#52011yescharacteristic
365D15—24no—
366C23×C3C23×D511yescharacteristic
367C22×D3—52no—
368C22×D3—52no—
369C22×D3—52no—
370C22×D3—101no—
371C22×D3—101no—
372C22×D3—101no—
373C22×D3—101no—
374C2×C3×C4—22no—
375C2×C3×C4—22no—
376C2×C3×C4—52no—
377C2×C3×C4—52no—
378C2×C3×C4—54no—
379C2×C3×C4—101no—
380C2×C3×C4—102no—
381C2×C3×C4—101no—
382C2×C3×C4—101no—
383C2×C3×C4—102no—
384C2×C3×C4—101no—
385C2×C3×C4C2×C4×D512yes—
386C2×C3×C4C2×C4×D512yes—
387C2×C3×C4C2×C4×D514yes—
388C2×C3×C4C2×C4×D512yes—
389C2×Dic3—21no—
390C2×Dic3—22no—
391C2×Dic3—21no—
392C2×Dic3—21no—
393C2×Dic3—22no—
394C2×Dic3—21no—
395C2×Dic3—52no—
396C2×Dic3—52no—
397C2×Dic3—52no—
398C2×Dic3—54no—
399C2×Dic3—102no—
400C2×Dic3—102no—
401C2×Dic3C2×C4×D512yes—
402C2×Dic3C2×C4×D512yes—
403C2×Dic3C2×C4×D514yes—
404C4×D3—516no—
405C4×D3—208no—
406C22×C5C22×C4×D311yescharacteristic
407C22×C5C22×C4×D311yescharacteristic
408C22×C5C22×C4×D311yescharacteristic
409C22×C5#100411yescharacteristic
410C22×C5#100711yescharacteristic
411C22×C5#100911yescharacteristic
412C22×C5#101011yescharacteristic
413C2×D5—34no—
414C2×D5—62no—
415C2×D5—62no—
416C2×D5—62no—
417C2×D5—62no—
418C2×D5—62no—
419C2×D5—62no—
420C4×C5—24no—
421C4×C5—62no—
422C4×C5—62no—
423C4×C5—64no—
424C4×C5C42×D314yes—
425Dic5—22no—
426Dic5—22no—
427Dic5—24no—
428Dic5—34no—
429Dic5—64no—
430C24—151no—
431C22×C4—31no—
432C22×C4—32no—
433C22×C4—31no—
434C22×C4—51no—
435C22×C4—52no—
436C22×C4—51no—
437C22×C4—158no—
438C22×C4—151no—
439C22×C4—154no—
440C22×C4—154no—
441C22×C4—154no—
442C22×C4—152no—
443C22×C4—602no—
444C22×C4—602no—
445C22×C4C2×D3×D512yes—
446C22×C4C2×D3×D511yescharacteristic
447C4⋊C4—34no—
448C4⋊C4—54no—
449C4⋊C4—158no—
450C4⋊C4—154no—
451C4⋊C4—154no—
452C4⋊C4—154no—
453C4⋊C4#120014yescomplemented
454C22⋊C4—154no—
455C22⋊C4—154no—
456C22⋊C4—158no—
457C42—34no—
458C42—54no—
459C42—122no—
460C42—158no—
461C42—202no—
462C42—602no—
463C42—602no—
464C3×C5#227411yescharacteristic, complemented, Hall
465C22×C3C22×C4×D511yescharacteristic
466C22×C3C22×C4×D511yescharacteristic
467C22×C3C22×C4×D511yescharacteristic
468C22×C3#414411yescharacteristic
469C22×C3#414711yescharacteristic
470C22×C3#414911yescharacteristic
471C22×C3#415011yescharacteristic
472C2×D3—54no—
473C2×D3—102no—
474C2×D3—102no—
475C2×D3—102no—
476C2×D3—102no—
477C2×D3—102no—
478C2×D3—102no—
479C3×C4—24no—
480C3×C4—102no—
481C3×C4—102no—
482C3×C4—104no—
483C3×C4C42×D514yes—
484Dic3—22no—
485Dic3—22no—
486Dic3—24no—
487Dic3—54no—
488Dic3—104no—
489C2×C5C2×C42×D311yescharacteristic
490C2×C5#550411yescharacteristic
491C2×C5#552311yescharacteristic
492C2×C5#554511yescharacteristic
493C2×C5#554611yescharacteristic
494C2×C5#557211yescharacteristic
495C2×C5#557411yescharacteristic
496D5—64no—
497C23—152no—
498C23—152no—
499C23—152no—
500C23—301no—
501C23—301no—
502C23—301no—
503C23—301no—
504C23C22×D3×D511yescharacteristic
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—34no—
510C2×C4—52no—
511C2×C4—52no—
512C2×C4—54no—
513C2×C4—61no—
514C2×C4—61no—
515C2×C4—62no—
516C2×C4—61no—
517C2×C4—61no—
518C2×C4—62no—
519C2×C4—101no—
520C2×C4—101no—
521C2×C4—102no—
522C2×C4—101no—
523C2×C4—101no—
524C2×C4—102no—
525C2×C4—152no—
526C2×C4—152no—
527C2×C4—152no—
528C2×C4—1516no—
529C2×C4—154no—
530C2×C4—302no—
531C2×C4—302no—
532C2×C4—608no—
533C2×C4C4×D3×D512yes—
534C2×C4C4×D3×D512yes—
535C2×C4C2×#120014yes—
536C2×C4C2×#120012yes—
537C2×C3C2×C42×D511yescharacteristic
538C2×C3#6583811yescharacteristic
539C2×C3#6585711yescharacteristic
540C2×C3#6587911yescharacteristic
541C2×C3#6588011yescharacteristic
542C2×C3#6590611yescharacteristic
543C2×C3#6590811yescharacteristic
544D3—104no—
545C5#7375011yescharacteristic, complemented, Sylow
546C22—154no—
547C22—302no—
548C22—302no—
549C22—302no—
550C22—302no—
551C22—302no—
552C22—302no—
553C22C2×C4×D3×D511yescharacteristic
554C22C2×C4×D3×D511yescharacteristic
555C22#9202011yescharacteristic
556C22#9202511yescharacteristic
557C22#9202911yescharacteristic
558C22#9203511yescharacteristic
559C22C22×#120011yescharacteristic
560C4—24no—
561C4—64no—
562C4—62no—
563C4—62no—
564C4—104no—
565C4—102no—
566C4—102no—
567C4—154no—
568C4—304no—
569C4C4×#120014yes—
570C3#1060548111yescharacteristic, complemented, Sylow
571C2—304no—
572C2#1175338111yescharacteristic
573C2#1175366711yescharacteristic
574C2#1175367011yescharacteristic
575C2#1175384111yescharacteristic
576C2C2×C4×#120011yescharacteristic
577C2#1175491611yescharacteristic
578C2#1175514911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×D15C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2274
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. C5×Dic3×C4⋊C4C2semidirect
5. C3×C4⋊C4×Dic5C2semidirect
8. C4×#6669C2semidirect
9. Dic3×C4⋊Dic5C2semidirect
10. Dic5×C4⋊Dic3C2semidirect
11. #11748663C2semidirect
19. #91781C4semidirect
33. #91437C4semidirect
34. #91386C4semidirect
45. C4⋊C4×Dic5D3semidirect
68. C3×C5×C4⋊C4C2×C4semidirect
70. C4⋊Dic15C2×C4semidirect
71. C4×Dic15C2×C4semidirect
74. C4×C5×Dic3C2×C4semidirect
77. C3×C4×Dic5C2×C4semidirect
79. #6669C2×C4semidirect
80. #6669C2×C4semidirect
90. Dic3×C4⋊C4D5semidirect
143. C4×D15C42semidirect
207. C5×C4⋊C4C4×D3semidirect
222. C4×Dic5C4×D3semidirect
276. C3×C4⋊C4C4×D5semidirect
291. C4×Dic3C4×D5semidirect
453. C4⋊C4#1200semidirect
464. C3×C5#2274semidirect
545. C5#73750semidirect
570. C3#10605481semidirect

Maximal subgroups

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

subgroupindex
C2×#917812
C2×#914372
C2×#913862
C5×Dic3×C4⋊C42
C3×C4⋊C4×Dic52
#117488812
#117488752
C4×#66692
Dic3×C4⋊Dic52
Dic5×C4⋊Dic32
#117486632
#106054813
#737505