Finite Group Databasebeta

← #14329104

Subgroups — #14329104

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#893C211yesmaximal, characteristic, complemented
2C2×C3×#4038C211yesmaximal, characteristic, complemented
3C2×#91449C211yesmaximal, characteristic
4C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
5#11748915C212yesmaximal, complemented
6#11748910C212yesmaximal, complemented
7#11748858C211yesmaximal, characteristic, complemented
8#11748797C211yesmaximal, characteristic, complemented
9#11748714C212yesmaximal, complemented
10C4×(C2×D3)⋊Dic5C212yesmaximal, complemented
11C4×#6665C211yesmaximal, characteristic, complemented
12#10614072—31nomaximal, Hall
13C22×C5×D12C2211yescharacteristic
14C22×C4×C5×D3C2212yes—
15C22×C3×C4×D5C2211yescharacteristic
16C22×#1201C2212yes—
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4×Dic15C2211yescharacteristic
20C2×C4×Dic15C2212yes—
21C2×C5×(C2×D3)⋊C4C2212yes—
22C2×C4×C5×Dic3C2211yescharacteristic
23C5×#893—24no—
24C2×C3×#685C2212yes—
25C2×C3×C4⋊Dic5C2211yescharacteristic
26C2×C3×C4×Dic5C2212yes—
27C3×#4038—24no—
28C2×#6669C2212yes—
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×(C2×D3)⋊Dic5C2212yes—
31C2×(C2×D3)⋊Dic5C2212yes—
32C2×#6665C2211yescharacteristic
33C2×#6665C2211yescharacteristic
34#91449C418yescomplemented
35#91115C2212yes—
36#90994C2212yes—
37#90994C2211yescharacteristic
38#90994C2211yescharacteristic
39#82244—51nomaximal, Hall
40C2×C4×C5×D4—31no—
41C2×#4084—31no—
42C2×#4038D311yescharacteristic, complemented
43#65510—31no—
44#65502—32no—
45C4×C22⋊Dic5—32no—
46C4⋊C4×Dic5—31no—
47#65246—32no—
48#65233—32no—
49C4×#685—31no—
50#65217—31no—
51C23×C5×D3C2312yes—
52C23×C3×D5C2311yescharacteristic
53C22×C3×C4×C5C2312yes—
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2311yescharacteristic
56C22×Dic15C2312yes—
57C22×Dic15C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2311yescharacteristic
60C2×C5×D12—22no—
61C2×C5×D12—22no—
62C2×C5×D12C2×C414yes—
63C2×C4×C5×D3—24no—
64C2×C4×C5×D3—24no—
65C2×C4×C5×D3—42no—
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2311yescharacteristic
68C2×C3×C4×D5—22no—
69C2×C3×C4×D5—22no—
70C2×C3×C4×D5C2×C414yescomplemented
71C2×#1201—42no—
72C2×#1201—42no—
73C2×#1201C2×C418yescomplemented
74C3×C5×C4⋊C4D414yescomplemented
75C4⋊Dic15C2×C414yescomplemented
76C4×Dic15—22no—
77C4×Dic15—42no—
78C5×(C2×D3)⋊C4—24no—
79C4×C5×Dic3—22no—
80C3×#685—24no—
81C3×C4⋊Dic5—22no—
82C3×C4×Dic5—24no—
83#6669—42no—
84(C2×D3)⋊Dic5—24no—
85(C2×D3)⋊Dic5—42no—
86(C2×D3)⋊Dic5C2×C418yescomplemented
87#6665—22no—
88#6665—22no—
89C2×C3×#117—51no—
90C2×#930—51no—
91C2×#893D511yescharacteristic, complemented
92C4×#217—51no—
93#4988—51no—
94Dic3×C4⋊C4—51no—
95#4972—51no—
96#4957—52no—
97#4956—52no—
98#4940—52no—
99C4×(C2×D3)⋊C4—52no—
100C22×C5×D4—31no—
101C23×C4×C5—32no—
102C22×C22⋊D5—32no—
103C22×C4×D5C2×D311yescharacteristic
104C4×C5×D4—64no—
105C2×C5×C4⋊C4C2×D311yescharacteristic
106C2×C5×C22⋊C4—32no—
107C2×C42×C5—31no—
108C2×C22⋊Dic5—32no—
109C2×C22⋊Dic5—32no—
110C2×C22⋊Dic5—32no—
111#4084—38no—
112C2×#685—31no—
113C2×#685—31no—
114C2×#685C2×D312yes—
115C2×C4⋊Dic5—31no—
116C2×C4⋊Dic5C2×D311yescharacteristic
117C2×#683—32no—
118C2×C4×Dic5—31no—
119C2×C4×Dic5—32no—
120C2×C4×Dic5C2×D312yes—
121#4038—24no—
122#3963—32no—
123#3963—32no—
124#3963—31no—
125#3963—31no—
126#2363—151noSylow
127C23×C3×C5C2411yescharacteristic
128C22×C5×D3—22no—
129C22×C5×D3—22no—
130C22×C5×D3—22no—
131C22×C5×D3—22no—
132C22×C5×D3—22no—
133C22×C5×D3—22no—
134C22×C5×D3C22×C414yes—
135C22×C3×D5—21no—
136C22×C3×D5—21no—
137C22×C3×D5—21no—
138C22×C3×D5—21no—
139C22×C3×D5—21no—
140C22×C3×D5—21no—
141C22×C3×D5C22×C412yes—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C22×C412yes—
145C2×C3×C4×C5C2×D414yes—
146C2×C3×C4×C5C2×D412yes—
147C2×C3×C4×C5#4112yes—
148C2×Dic15—21no—
149C2×Dic15—22no—
150C2×Dic15—21no—
151C2×Dic15—22no—
152C2×Dic15—21no—
153C2×Dic15—21no—
154C2×Dic15—21no—
155C2×Dic15C22×C414yes—
156C2×Dic15#4112yes—
157C2×C5×Dic3—21no—
158C2×C5×Dic3—21no—
159C2×C5×Dic3—21no—
160C2×C5×Dic3—21no—
161C2×C5×Dic3—21no—
162C2×C5×Dic3#4112yes—
163C5×D12—28no—
164C4×C5×D3—48no—
165C2×C3×Dic5—21no—
166C2×C3×Dic5—21no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5C22×C412yes—
171C3×C4×D5—28no—
172#1201—48no—
173C23×C3×C4—51no—
174C22×#67—52no—
175C22×D12C2×D511yescharacteristic
176C22×C4×D3C2×D512yes—
177C3×#117—104no—
178C2×C3×C4⋊C4—51no—
179C2×C3×C4⋊C4C2×D511yescharacteristic
180C2×C3×C22⋊C4—52no—
181C2×C3×C42—52no—
182C2×#217—51no—
183C2×#217—51no—
184#930—58no—
185C2×(C2×D3)⋊C4—52no—
186C2×(C2×D3)⋊C4—52no—
187C2×(C2×D3)⋊C4—52no—
188C2×(C2×D3)⋊C4C2×D512yes—
189C2×C4⋊Dic3—51no—
190C2×Dic3⋊C4—52no—
191C2×C4×Dic3—51no—
192C2×C4×Dic3—52no—
193C2×C4×Dic3C2×D511yescharacteristic
194#893—24no—
195C3⋊#95—52no—
196C3⋊#95—51no—
197C3⋊#95—52no—
198C3⋊#95—51no—
199C24×C5—32no—
200C23×D5C22×D311yescharacteristic
201C2×C5×D4—34no—
202C2×C5×D4—62no—
203C2×C5×D4—62no—
204C22×C4×C5—31no—
205C22×C4×C5—31no—
206C22×C4×C5—64no—
207C22×C4×C5—64no—
208C22×C4×C5—122no—
209C22×C4×C5C22×D312yes—
210C22×C4×C5C22×D311yescharacteristic
211C2×C22⋊D5—38no—
212C2×C22⋊D5—122no—
213C2×C22⋊D5—122no—
214C22×Dic5—31no—
215C22×Dic5—32no—
216C22×Dic5—31no—
217C22×Dic5C22×D312yes—
218C22×Dic5C22×D311yescharacteristic
219C2×C4×D5—22no—
220C2×C4×D5—22no—
221C2×C4×D5C4×D314yescomplemented
222C5×C4⋊C4#6714yescomplemented
223C5×C22⋊C4—64no—
224C42×C5—62no—
225C22⋊Dic5—38no—
226C22⋊Dic5—64no—
227C22⋊Dic5—122no—
228#685—24no—
229#685—62no—
230#685—62no—
231C4⋊Dic5—22no—
232C4⋊Dic5—34no—
233#683—122no—
234C4×Dic5—24no—
235C4×Dic5—62no—
236C4×Dic5—122no—
237C2×#121—151no—
238C2×C4×D4—31no—
239C2×#117—51no—
240#390—152no—
241#390—151no—
242#389—151no—
243#388—152no—
244#386—152no—
245C4×C4⋊C4—151no—
246C4×C22⋊C4—151no—
247C4×C22⋊C4—152no—
248C22×C3×C5C23×C411yescharacteristic
249C22×C3×C5C22×D411yescharacteristic
250C22×C3×C5C2×#4111yescharacteristic
251C22×C3×C5C2×#4111yescharacteristic
252C22×C3×C5C2×#4111yescharacteristic
253C22×C3×C5H(5,𝔽2)11yescharacteristic
254C22×C3×C5H(5,𝔽2)11yescharacteristic
255C2×C5×D3—24no—
256C2×C5×D3—24no—
257C2×C5×D3—24no—
258C2×C5×D3—42no—
259C2×C5×D3—42no—
260C2×C5×D3—42no—
261C2×C5×D3—42no—
262C2×C3×D5—22no—
263C2×C3×D5—22no—
264C2×C3×D5—22no—
265C2×C3×D5—41no—
266C2×C3×D5—41no—
267C2×C3×D5—41no—
268C2×C3×D5—41no—
269C3×C4×C5—24no—
270C3×C4×C5C4×D414yes—
271Dic15—24no—
272Dic15—22no—
273Dic15—41no—
274C3×Dic5—22no—
275C3×Dic5—42no—
276C5×Dic3—22no—
277C5×Dic3—41no—
278C24×C3—51no—
279C23×D3C22×D512yes—
280C22×C3×C4—51no—
281C22×C3×C4—54no—
282C22×C3×C4—52no—
283C22×C3×C4—102no—
284C22×C3×C4—102no—
285C22×C3×C4C22×D512yes—
286C22×C3×C4C22×D511yescharacteristic
287C2×#67—58no—
288C2×#67—202no—
289C2×#67—202no—
290C22×Dic3—52no—
291C22×Dic3—51no—
292C22×Dic3—51no—
293C22×Dic3C22×D511yescharacteristic
294C22×Dic3C22×D511yescharacteristic
295C2×D12—22no—
296C2×D12—22no—
297C2×D12C4×D514yes—
298C2×C4×D3—24no—
299C2×C4×D3—24no—
300C2×C4×D3—42no—
301C3×C4⋊C4—102no—
302C3×C4⋊C4C22⋊D514yescomplemented
303C3×C22⋊C4—104no—
304C3×C42—104no—
305#217—102no—
306#217—102no—
307(C2×D3)⋊C4—24no—
308(C2×D3)⋊C4—58no—
309(C2×D3)⋊C4—104no—
310(C2×D3)⋊C4—202no—
311C4⋊Dic3—54no—
312Dic3⋊C4—202no—
313C4×Dic3—22no—
314C4×Dic3—102no—
315C4×Dic3—202no—
316C23×C5—34no—
317C23×C5—62no—
318C23×C5—62no—
319C23×C5—62no—
320C23×C5—62no—
321C23×C5—62no—
322C23×C5—62no—
323C23×C5C23×D311yescharacteristic
324C22×D5—21no—
325C22×D5—21no—
326C22×D5—21no—
327C22×D5—21no—
328C22×D5—21no—
329C22×D5—21no—
330C22×D5C2×C4×D312yes—
331C5×D4—68no—
332C2×C4×C5—22no—
333C2×C4×C5—22no—
334C2×C4×C5—32no—
335C2×C4×C5—61no—
336C2×C4×C5—61no—
337C2×C4×C5—61no—
338C2×C4×C5—61no—
339C2×C4×C5—61no—
340C2×C4×C5—128no—
341C2×C4×C5C2×C4×D312yes—
342C2×C4×C5#23512yes—
343C2×C4×C5C2×#6714yes—
344C2×C4×C5C2×#6712yes—
345C22⋊D5—128no—
346C2×Dic5—21no—
347C2×Dic5—21no—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—22no—
351C2×Dic5—34no—
352C2×Dic5—32no—
353C2×Dic5—61no—
354C2×Dic5—61no—
355C2×Dic5—62no—
356C2×Dic5—62no—
357C2×Dic5—61no—
358C2×Dic5—61no—
359C2×Dic5—61no—
360C2×Dic5C2×C4×D312yes—
361C4×D5—28no—
362C22×D4—31no—
363C22×D4—152no—
364C23×C4—32no—
365C23×C4—51no—
366#121—158no—
367C4×D4—64no—
368#117—104no—
369C2×C4⋊C4—51no—
370C2×C4⋊C4—151no—
371C2×C4⋊C4—152no—
372C2×C4⋊C4D3×D511yescharacteristic
373C2×C22⋊C4—32no—
374C2×C22⋊C4—52no—
375C2×C22⋊C4—152no—
376C2×C22⋊C4—151no—
377C2×C22⋊C4—151no—
378C2×C22⋊C4—152no—
379C2×C22⋊C4—152no—
380C2×C42—31no—
381C2×C42—52no—
382C2×C42—151no—
383C2×C42—152no—
384#95—151no—
385#95—152no—
386#95—151no—
387#95—152no—
388C2×C3×C5C2×C4×D411yescharacteristic
389C2×C3×C5C4×#4111yescharacteristic
390C2×C3×C5#51811yescharacteristic
391C2×C3×C5#54611yescharacteristic
392C2×C3×C5#55011yescharacteristic
393C2×C3×C5#55311yescharacteristic
394C2×C3×C5#55511yescharacteristic
395C3×D5—42no—
396C5×D3—44no—
397C23×C3—52no—
398C23×C3—101no—
399C23×C3—101no—
400C23×C3—101no—
401C23×C3—101no—
402C23×C3—101no—
403C23×C3—101no—
404C23×C3C23×D511yescharacteristic
405C22×D3—22no—
406C22×D3—22no—
407C22×D3—22no—
408C22×D3—22no—
409C22×D3—22no—
410C22×D3—22no—
411C22×D3C2×C4×D514yes—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—52no—
415C2×C3×C4—101no—
416C2×C3×C4—101no—
417C2×C3×C4—108no—
418C2×C3×C4—102no—
419C2×C3×C4—102no—
420C2×C3×C4—102no—
421C2×C3×C4C2×C4×D512yes—
422C2×C3×C4#70912yes—
423C2×C3×C4C2×C22⋊D514yes—
424C2×C3×C4C2×C22⋊D512yes—
425#67—208no—
426C2×Dic3—21no—
427C2×Dic3—21no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—54no—
432C2×Dic3—52no—
433C2×Dic3—101no—
434C2×Dic3—101no—
435C2×Dic3—102no—
436C2×Dic3—102no—
437C2×Dic3—101no—
438C2×Dic3—101no—
439C2×Dic3—101no—
440C2×Dic3#71112yes—
441D12—28no—
442C4×D3—48no—
443C22×C5—64no—
444C22×C5—64no—
445C22×C5—64no—
446C22×C5—122no—
447C22×C5—122no—
448C22×C5—122no—
449C22×C5—122no—
450C22×C5C22×C4×D311yescharacteristic
451C22×C5C2×#23511yescharacteristic
452C22×C5D3×#4111yescharacteristic
453C22×C5D3×#4111yescharacteristic
454C22×C5#100911yescharacteristic
455C22×C5#100911yescharacteristic
456C22×C5C22×#6711yescharacteristic
457C2×D5—22no—
458C2×D5—22no—
459C2×D5—22no—
460C2×D5—41no—
461C2×D5—41no—
462C2×D5—41no—
463C2×D5—41no—
464C4×C5—24no—
465C4×C5—62no—
466C4×C5—121no—
467C4×C5C4×#6714yes—
468Dic5—22no—
469Dic5—42no—
470Dic5—64no—
471Dic5—62no—
472Dic5—121no—
473C24—32no—
474C24—51no—
475C2×D4—34no—
476C2×D4—62no—
477C2×D4—62no—
478C2×D4—158no—
479C2×D4—602no—
480C2×D4—602no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—51no—
484C22×C4—54no—
485C22×C4—52no—
486C22×C4—64no—
487C22×C4—64no—
488C22×C4—102no—
489C22×C4—102no—
490C22×C4—122no—
491C22×C4—152no—
492C22×C4—151no—
493C22×C4—151no—
494C22×C4C2×D3×D512yes—
495C22×C4C2×D3×D511yescharacteristic
496C4⋊C4—102no—
497C4⋊C4—154no—
498C4⋊C4—602no—
499C4⋊C4#120114yescomplemented
500C22⋊C4—64no—
501C22⋊C4—104no—
502C22⋊C4—158no—
503C22⋊C4—302no—
504C22⋊C4—302no—
505C22⋊C4—304no—
506C22⋊C4—602no—
507C42—62no—
508C42—104no—
509C42—302no—
510C42—602no—
511C3×C5#236311yescharacteristic, complemented, Hall
512C22×C3—102no—
513C22×C3—102no—
514C22×C3—102no—
515C22×C3—201no—
516C22×C3—201no—
517C22×C3—201no—
518C22×C3—201no—
519C22×C3C22×C4×D511yescharacteristic
520C22×C3C2×#70911yescharacteristic
521C22×C3C2×#71111yescharacteristic
522C22×C3#414411yescharacteristic
523C22×C3D5×#4111yescharacteristic
524C22×C3#414911yescharacteristic
525C22×C3C22×C22⋊D511yescharacteristic
526C2×D3—24no—
527C2×D3—24no—
528C2×D3—24no—
529C2×D3—42no—
530C2×D3—42no—
531C2×D3—42no—
532C2×D3—42no—
533C3×C4—24no—
534C3×C4—102no—
535C3×C4—202no—
536C3×C4C4×C22⋊D514yes—
537Dic3—22no—
538Dic3—41no—
539Dic3—104no—
540Dic3—102no—
541Dic3—201no—
542C2×C5—124no—
543C2×C5#552111yescharacteristic
544C2×C5#552211yescharacteristic
545C2×C5#553011yescharacteristic
546C2×C5#553211yescharacteristic
547C2×C5C2×C4×#6711yescharacteristic
548C2×C5#582911yescharacteristic
549C2×C5#583411yescharacteristic
550D5—42no—
551C23—34no—
552C23—52no—
553C23—62no—
554C23—62no—
555C23—62no—
556C23—62no—
557C23—62no—
558C23—62no—
559C23—101no—
560C23—101no—
561C23—101no—
562C23—101no—
563C23—101no—
564C23—101no—
565C23C22×D3×D511yescharacteristic
566D4—68no—
567D4—608no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—32no—
571C2×C4—52no—
572C2×C4—61no—
573C2×C4—61no—
574C2×C4—61no—
575C2×C4—61no—
576C2×C4—61no—
577C2×C4—101no—
578C2×C4—101no—
579C2×C4—108no—
580C2×C4—102no—
581C2×C4—102no—
582C2×C4—102no—
583C2×C4—128no—
584C2×C4—154no—
585C2×C4—152no—
586C2×C4—301no—
587C2×C4—301no—
588C2×C4—302no—
589C2×C4—302no—
590C2×C4—301no—
591C2×C4—301no—
592C2×C4—301no—
593C2×C4#677112yes—
594C2×C4C4×D3×D512yes—
595C2×C4C2×#120114yes—
596C2×C4C2×#120112yes—
597C2×C3—202no—
598C2×C3C4×#71111yescharacteristic
599C2×C3#6587911yescharacteristic
600C2×C3#6589211yescharacteristic
601C2×C3#6589711yescharacteristic
602C2×C3C2×C4×C22⋊D511yescharacteristic
603C2×C3#6614011yescharacteristic
604C2×C3#6616811yescharacteristic
605D3—44no—
606C5#8224411yescharacteristic, complemented, Sylow
607C22—64no—
608C22—64no—
609C22—64no—
610C22—102no—
611C22—102no—
612C22—102no—
613C22—122no—
614C22—122no—
615C22—122no—
616C22—122no—
617C22—201no—
618C22—201no—
619C22—201no—
620C22—201no—
621C22C2×#677111yescharacteristic
622C22C2×C4×D3×D511yescharacteristic
623C22D3×#71111yescharacteristic
624C22#9202711yescharacteristic
625C22#9203411yescharacteristic
626C22#9203511yescharacteristic
627C22C22×#120111yescharacteristic
628C4—24no—
629C4—62no—
630C4—102no—
631C4—121no—
632C4—202no—
633C4—302no—
634C4—304no—
635C4—601no—
636C4C4×#120114yes—
637C3#1061407211yescharacteristic, complemented, Sylow
638C2—124no—
639C2—202no—
640C2#1175340211yescharacteristic
641C2#1175376711yescharacteristic
642C2#1175380611yescharacteristic
643C2#1175383711yescharacteristic
644C2C2×C4×#120111yescharacteristic
645C2#1175496811yescharacteristic
646C2#1175525411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC2×#91449C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5#2363
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C5×#893C2semidirect
2. C2×C3×#4038C2semidirect
4. C4⋊C4×Dic15C2semidirect
5. #11748915C2semidirect
6. #11748910C2semidirect
7. #11748858C2semidirect
8. #11748797C2semidirect
9. #11748714C2semidirect
10. C4×(C2×D3)⋊Dic5C2semidirect
11. C4×#6665C2semidirect
34. #91449C4semidirect
42. C2×#4038D3semidirect
70. C2×C3×C4×D5C2×C4semidirect
73. C2×#1201C2×C4semidirect
74. C3×C5×C4⋊C4D4semidirect
75. C4⋊Dic15C2×C4semidirect
86. (C2×D3)⋊Dic5C2×C4semidirect
91. C2×#893D5semidirect
221. C2×C4×D5C4×D3semidirect
222. C5×C4⋊C4#67semidirect
302. C3×C4⋊C4C22⋊D5semidirect
499. C4⋊C4#1201semidirect
511. C3×C5#2363semidirect
606. C5#82244semidirect
637. C3#10614072semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8932
C2×C3×#40382
C2×#914492
C4⋊C4×Dic152
#117489152
#117489102
#117488582
#117487972
#117487142
C4×(C2×D3)⋊Dic52
C4×#66652
#106140723
#822445