Finite Group Databasebeta

← #14329516

Subgroups — #14329516

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91764C211yesmaximal, characteristic
2C2×C4×D60C211yesmaximal, characteristic
3C2×C4×Dic30C211yesmaximal, characteristic, complemented
4C3×C4×C5×C4⋊C4C211yesmaximal, characteristic, complemented
5#11751091C212yesmaximal, complemented
6#11751090C212yesmaximal, complemented
7#11751040C211yesmaximal, characteristic
8C4×C4⋊Dic15C211yesmaximal, characteristic, complemented
9#11751030C211yesmaximal, characteristic, complemented
10#11750770C212yesmaximal, complemented
11#11750767C212yesmaximal, complemented
12#10605386—31nomaximal, Hall
13C22×D60C2211yescharacteristic
14C22×C4×D15C2212yes—
15C22×Dic30C2211yescharacteristic
16C2×C3×C5×C4⋊C4C2211yescharacteristic
17C2×C3×C5×C4⋊C4C2211yescharacteristic
18C2×C3×C42×C5C2211yescharacteristic
19C2×C3×C42×C5C2211yescharacteristic
20C2×C3×C42×C5C2211yescharacteristic
21C2×#6714C2212yes—
22C2×#6714C2212yes—
23C2×#6714C2212yes—
24C2×#6714C2212yes—
25C2×#6714C2212yes—
26C2×C4⋊Dic15C2211yescharacteristic
27C2×C4⋊Dic15C2211yescharacteristic
28C2×#6712C2212yes—
29C2×C4×Dic15C2212yes—
30C2×C4×Dic15C2212yes—
31#91764C418yescomplemented
32C4×D60—24no—
33C4×Dic30—24no—
34C3×C5×#95C2211yescharacteristic
35C3×C5×#95C2211yescharacteristic
36#91115C2212yes—
37#91115C2212yes—
38#91115C2212yes—
39#73655—51nomaximal, Hall
40C2×#4021—31no—
41C2×C4×D20—31no—
42C2×C4×Dic10—31no—
43C4×C5×C4⋊C4D311yescharacteristic, complemented
44#65279—32no—
45#65278—32no—
46#65228—31no—
47C4×C4⋊Dic5—31no—
48#65218—31no—
49#64958—32no—
50#64955—32no—
51C23×D15C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×C3×C4×C5C2311yescharacteristic
59C22×Dic15C2312yes—
60C22×Dic15C2312yes—
61C22×Dic15C2312yes—
62C2×D60—22no—
63C2×D60—22no—
64C2×D60C2×C414yes—
65C2×C4×D15—24no—
66C2×C4×D15—24no—
67C2×C4×D15—42no—
68C2×Dic30—22no—
69C2×Dic30—22no—
70C2×Dic30C2×C414yescomplemented
71C3×C5×C4⋊C4—22no—
72C3×C5×C4⋊C4—22no—
73C3×C42×C5—22no—
74C3×C42×C5—22no—
75C3×C42×C5C2×C414yescomplemented
76#6714—24no—
77#6714—24no—
78#6714—42no—
79#6714C2×C418yescomplemented
80#6714C2×C418yescomplemented
81C4⋊Dic15—22no—
82C4⋊Dic15D414yes—
83#6712—24no—
84C4×Dic15—24no—
85C4×Dic15—42no—
86C2×#875—51no—
87C2×C4×D12—51no—
88C2×C4×Dic6—51no—
89C3×C4×C4⋊C4D511yescharacteristic, complemented
90#4990—52no—
91#4989—52no—
92#4939—51no—
93C4×C4⋊Dic3—51no—
94#4929—51no—
95#4669—52no—
96#4666—52no—
97C22×D20—31no—
98C22×C4×D5—32no—
99C22×Dic10—31no—
100C2×C5×C4⋊C4C2×D311yescharacteristic
101C2×C5×C4⋊C4C2×D311yescharacteristic
102C2×C42×C5C2×D311yescharacteristic
103C2×C42×C5C2×D311yescharacteristic
104C2×C42×C5C2×D311yescharacteristic
105C2×#685—32no—
106C2×#685—32no—
107C2×#685—32no—
108C2×#685—32no—
109C2×#685—32no—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5—31no—
112C2×#683—32no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5—32no—
115#4021—38no—
116C4×D20—64no—
117C4×Dic10—64no—
118C5×#95C2×D311yescharacteristic
119C5×#95C2×D311yescharacteristic
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#2367—151noSylow
124C23×C3×C5C2411yescharacteristic
125C22×D15—22no—
126C22×D15—22no—
127C22×D15—22no—
128C22×D15—22no—
129C22×D15—22no—
130C22×D15—22no—
131C22×D15C22×C414yes—
132C2×C3×C4×C5—21no—
133C2×C3×C4×C5—21no—
134C2×C3×C4×C5—21no—
135C2×C3×C4×C5—21no—
136C2×C3×C4×C5—21no—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—21no—
140C2×C3×C4×C5—21no—
141C2×C3×C4×C5—21no—
142C2×C3×C4×C5—21no—
143C2×C3×C4×C5—21no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5—21no—
146C2×C3×C4×C5C22×C412yes—
147C2×C3×C4×C5C22×C412yes—
148C2×C3×C4×C5C22×C412yes—
149C2×C3×C4×C5C2×D412yes—
150C2×C3×C4×C5#4112yes—
151C2×C3×C4×C5#4112yes—
152C2×C3×C4×C5#4112yes—
153C2×Dic15—22no—
154C2×Dic15—22no—
155C2×Dic15—22no—
156C2×Dic15—22no—
157C2×Dic15—22no—
158C2×Dic15—22no—
159C2×Dic15—22no—
160C2×Dic15C22×C414yes—
161C2×Dic15C2×D414yes—
162D60—28no—
163C4×D15—48no—
164Dic30—28no—
165C22×D12—51no—
166C22×C4×D3—52no—
167C22×Dic6—51no—
168C2×C3×C4⋊C4C2×D511yescharacteristic
169C2×C3×C4⋊C4C2×D511yescharacteristic
170C2×C3×C42C2×D511yescharacteristic
171C2×C3×C42C2×D511yescharacteristic
172C2×C3×C42C2×D511yescharacteristic
173C2×(C2×D3)⋊C4—52no—
174C2×(C2×D3)⋊C4—52no—
175C2×(C2×D3)⋊C4—52no—
176C2×(C2×D3)⋊C4—52no—
177C2×(C2×D3)⋊C4—52no—
178C2×C4⋊Dic3—51no—
179C2×C4⋊Dic3—51no—
180C2×Dic3⋊C4—52no—
181C2×C4×Dic3—52no—
182C2×C4×Dic3—52no—
183#875—58no—
184C4×D12—104no—
185C4×Dic6—104no—
186C3×#95C2×D511yescharacteristic
187C3×#95C2×D511yescharacteristic
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C23×D5—32no—
192C22×C4×C5C22×D311yescharacteristic
193C22×C4×C5C22×D311yescharacteristic
194C22×C4×C5C22×D311yescharacteristic
195C22×C4×C5C22×D311yescharacteristic
196C22×C4×C5C22×D311yescharacteristic
197C22×C4×C5C22×D311yescharacteristic
198C22×C4×C5C22×D311yescharacteristic
199C22×Dic5—32no—
200C22×Dic5—32no—
201C22×Dic5—32no—
202C2×D20—34no—
203C2×D20—62no—
204C2×D20—62no—
205C2×C4×D5—64no—
206C2×C4×D5—64no—
207C2×C4×D5—122no—
208C2×Dic10—34no—
209C2×Dic10—62no—
210C2×Dic10—62no—
211C5×C4⋊C4—22no—
212C5×C4⋊C4—22no—
213C42×C5—22no—
214C42×C5—22no—
215C42×C5C4×D314yescomplemented
216#685—38no—
217#685—38no—
218#685—64no—
219#685—64no—
220#685—122no—
221C4⋊Dic5—34no—
222C4⋊Dic5—62no—
223#683—64no—
224C4×Dic5—64no—
225C4×Dic5—122no—
226C2×#124—151no—
227C2×C4×Q8—151no—
228C2×C4×D4—151no—
229#391—151no—
230#390—151no—
231#388—152no—
232#388—152no—
233#385—152no—
234C4×C4⋊C4—151no—
235C4×C4⋊C4D1511yescharacteristic, complemented
236C4×C22⋊C4—152no—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C2×#4111yescharacteristic
240C22×C3×C5C2×#4111yescharacteristic
241C22×C3×C5C2×#4111yescharacteristic
242C22×C3×C5H(5,𝔽2)11yescharacteristic
243C22×C3×C52−1+411yescharacteristic
244C2×D15—24no—
245C2×D15—24no—
246C2×D15—24no—
247C2×D15—42no—
248C2×D15—42no—
249C2×D15—42no—
250C2×D15—42no—
251C3×C4×C5—22no—
252C3×C4×C5—22no—
253C3×C4×C5—22no—
254C3×C4×C5—22no—
255C3×C4×C5—41no—
256C3×C4×C5—41no—
257C3×C4×C5C4×D414yes—
258Dic15—24no—
259Dic15—24no—
260Dic15—42no—
261C23×D3—52no—
262C22×C3×C4C22×D511yescharacteristic
263C22×C3×C4C22×D511yescharacteristic
264C22×C3×C4C22×D511yescharacteristic
265C22×C3×C4C22×D511yescharacteristic
266C22×C3×C4C22×D511yescharacteristic
267C22×C3×C4C22×D511yescharacteristic
268C22×C3×C4C22×D511yescharacteristic
269C22×Dic3—52no—
270C22×Dic3—52no—
271C22×Dic3—52no—
272C2×D12—54no—
273C2×D12—102no—
274C2×D12—102no—
275C2×C4×D3—104no—
276C2×C4×D3—104no—
277C2×C4×D3—202no—
278C2×Dic6—54no—
279C2×Dic6—102no—
280C2×Dic6—102no—
281C3×C4⋊C4—22no—
282C3×C4⋊C4—22no—
283C3×C42—22no—
284C3×C42—22no—
285C3×C42C4×D514yescomplemented
286(C2×D3)⋊C4—58no—
287(C2×D3)⋊C4—58no—
288(C2×D3)⋊C4—104no—
289(C2×D3)⋊C4—104no—
290(C2×D3)⋊C4—202no—
291C4⋊Dic3—54no—
292C4⋊Dic3—102no—
293Dic3⋊C4—104no—
294C4×Dic3—104no—
295C4×Dic3—202no—
296C23×C5C23×D311yescharacteristic
297C22×D5—34no—
298C22×D5—62no—
299C22×D5—62no—
300C22×D5—62no—
301C22×D5—62no—
302C22×D5—62no—
303C22×D5—62no—
304C2×C4×C5—21no—
305C2×C4×C5—21no—
306C2×C4×C5—21no—
307C2×C4×C5—21no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—21no—
318C2×C4×C5C2×C4×D312yes—
319C2×C4×C5C2×C4×D312yes—
320C2×C4×C5C2×C4×D312yes—
321C2×C4×C5#23512yes—
322C2×C4×C5#23512yes—
323C2×C4×C5D3×D412yes—
324C2×C4×C5#23912yes—
325C2×Dic5—34no—
326C2×Dic5—34no—
327C2×Dic5—62no—
328C2×Dic5—62no—
329C2×Dic5—62no—
330C2×Dic5—62no—
331C2×Dic5—62no—
332C2×Dic5—62no—
333C2×Dic5—62no—
334D20—68no—
335C4×D5—128no—
336Dic10—68no—
337C22×Q8—151no—
338C22×D4—151no—
339C23×C4—152no—
340#124—158no—
341C4×Q8—304no—
342C4×D4—304no—
343C2×C4⋊C4—151no—
344C2×C4⋊C4—152no—
345C2×C4⋊C4—151no—
346C2×C4⋊C4C2×D1511yescharacteristic
347C2×C4⋊C4C2×D1511yescharacteristic
348C2×C22⋊C4—152no—
349C2×C22⋊C4—152no—
350C2×C22⋊C4—152no—
351C2×C22⋊C4—152no—
352C2×C22⋊C4—152no—
353C2×C42—152no—
354C2×C42—152no—
355C2×C42C2×D1511yescharacteristic
356C2×C42C2×D1511yescharacteristic
357C2×C42C2×D1511yescharacteristic
358#95—152no—
359#95—152no—
360#95—152no—
361#95C2×D1511yescharacteristic
362#95C2×D1511yescharacteristic
363C2×C3×C5C2×C4×D411yescharacteristic
364C2×C3×C5C4×#4111yescharacteristic
365C2×C3×C5#52011yescharacteristic
366C2×C3×C5#54611yescharacteristic
367C2×C3×C5#54811yescharacteristic
368C2×C3×C5#55611yescharacteristic
369C2×C3×C5#55911yescharacteristic
370D15—44no—
371C23×C3C23×D511yescharacteristic
372C22×D3—54no—
373C22×D3—102no—
374C22×D3—102no—
375C22×D3—102no—
376C22×D3—102no—
377C22×D3—102no—
378C22×D3—102no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4C2×C4×D512yes—
394C2×C3×C4C2×C4×D512yes—
395C2×C3×C4C2×C4×D512yes—
396C2×C3×C4#70912yes—
397C2×C3×C4#70912yes—
398C2×C3×C4D4×D512yes—
399C2×C3×C4#71312yes—
400C2×Dic3—54no—
401C2×Dic3—54no—
402C2×Dic3—102no—
403C2×Dic3—102no—
404C2×Dic3—102no—
405C2×Dic3—102no—
406C2×Dic3—102no—
407C2×Dic3—102no—
408C2×Dic3—102no—
409D12—108no—
410C4×D3—208no—
411Dic6—108no—
412C22×C5C22×C4×D311yescharacteristic
413C22×C5C2×#23511yescharacteristic
414C22×C5C2×#23511yescharacteristic
415C22×C5C2×D3×D411yescharacteristic
416C22×C5C2×#23911yescharacteristic
417C22×C5#100911yescharacteristic
418C22×C5#101011yescharacteristic
419C2×D5—64no—
420C2×D5—64no—
421C2×D5—64no—
422C2×D5—122no—
423C2×D5—122no—
424C2×D5—122no—
425C2×D5—122no—
426C4×C5—22no—
427C4×C5—22no—
428C4×C5—22no—
429C4×C5—22no—
430C4×C5—41no—
431C4×C5—41no—
432C4×C5#89314yes—
433Dic5—64no—
434Dic5—64no—
435Dic5—122no—
436C24—152no—
437C2×Q8—154no—
438C2×Q8—302no—
439C2×Q8—302no—
440C2×D4—154no—
441C2×D4—302no—
442C2×D4—302no—
443C22×C4—152no—
444C22×C4—152no—
445C22×C4—152no—
446C22×C4—304no—
447C22×C4—304no—
448C22×C4—602no—
449C22×C4C22×D1511yescharacteristic
450C22×C4C22×D1511yescharacteristic
451C22×C4C22×D1511yescharacteristic
452C22×C4C22×D1511yescharacteristic
453C22×C4C22×D1511yescharacteristic
454C22×C4C22×D1511yescharacteristic
455C22×C4C22×D1511yescharacteristic
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—154no—
459C4⋊C4—304no—
460C4⋊C4—302no—
461C22⋊C4—158no—
462C22⋊C4—158no—
463C22⋊C4—304no—
464C22⋊C4—304no—
465C22⋊C4—602no—
466C42—22no—
467C42—22no—
468C42—304no—
469C42—602no—
470C42C4×D1514yescomplemented
471C3×C5#236711yescharacteristic, complemented, Hall
472C22×C3C22×C4×D511yescharacteristic
473C22×C3C2×#70911yescharacteristic
474C22×C3C2×#70911yescharacteristic
475C22×C3C2×D4×D511yescharacteristic
476C22×C3C2×#71311yescharacteristic
477C22×C3#414911yescharacteristic
478C22×C3#415011yescharacteristic
479C2×D3—104no—
480C2×D3—104no—
481C2×D3—104no—
482C2×D3—202no—
483C2×D3—202no—
484C2×D3—202no—
485C2×D3—202no—
486C3×C4—22no—
487C3×C4—22no—
488C3×C4—22no—
489C3×C4—22no—
490C3×C4—41no—
491C3×C4—41no—
492C3×C4#403914yes—
493Dic3—104no—
494Dic3—104no—
495Dic3—202no—
496C2×C5C4×#23511yescharacteristic
497C2×C5C2×#89311yescharacteristic
498C2×C5#552311yescharacteristic
499C2×C5#555011yescharacteristic
500C2×C5#555211yescharacteristic
501C2×C5#558411yescharacteristic
502C2×C5#558511yescharacteristic
503D5—124no—
504C23—154no—
505C23—302no—
506C23—302no—
507C23—302no—
508C23—302no—
509C23—302no—
510C23—302no—
511C23C23×D1511yescharacteristic
512Q8—308no—
513D4—308no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—154no—
529C2×C4—154no—
530C2×C4—302no—
531C2×C4—302no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4—302no—
535C2×C4—302no—
536C2×C4—302no—
537C2×C4—608no—
538C2×C4C2×C4×D1512yes—
539C2×C4C2×C4×D1512yes—
540C2×C4C2×C4×D1512yes—
541C2×C4#681712yes—
542C2×C4#681712yes—
543C2×C4D4×D1512yes—
544C2×C4#682112yes—
545C2×C3C4×#70911yescharacteristic
546C2×C3C2×#403911yescharacteristic
547C2×C3#6585711yescharacteristic
548C2×C3#6588411yescharacteristic
549C2×C3#6588611yescharacteristic
550C2×C3#6591811yescharacteristic
551C2×C3#6591911yescharacteristic
552D3—204no—
553C5#7365511yescharacteristic, complemented, Sylow
554C22—304no—
555C22—304no—
556C22—304no—
557C22—602no—
558C22—602no—
559C22—602no—
560C22—602no—
561C22C22×C4×D1511yescharacteristic
562C22C2×#681711yescharacteristic
563C22C2×#681711yescharacteristic
564C22C2×D4×D1511yescharacteristic
565C22C2×#682111yescharacteristic
566C22#9210011yescharacteristic
567C22#9210111yescharacteristic
568C4—22no—
569C4—22no—
570C4—22no—
571C4—22no—
572C4—41no—
573C4—41no—
574C4—304no—
575C4—304no—
576C4—602no—
577C4#9178214yes—
578C3#1060538611yescharacteristic, complemented, Sylow
579C2—604no—
580C2C4×#681711yescharacteristic
581C2C2×#9178211yescharacteristic
582C2#1175628211yescharacteristic
583C2#1175630911yescharacteristic
584C2#1175631111yescharacteristic
585C2#1175634311yescharacteristic
586C2#1175634411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D15
commutatorC22×C3×C5C23×C4
FittingC3×C4×C5×C4⋊C4C2
socle, cosocleC23×C3×C5C24
prime radicalC22×D60C22
hypercenterC4×C4⋊C4D15
hypocenterC3×C5#2367
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4×Dic30C2semidirect
4. C3×C4×C5×C4⋊C4C2semidirect
5. #11751091C2semidirect
6. #11751090C2semidirect
8. C4×C4⋊Dic15C2semidirect
9. #11751030C2semidirect
10. #11750770C2semidirect
11. #11750767C2semidirect
31. #91764C4semidirect
43. C4×C5×C4⋊C4D3semidirect
70. C2×Dic30C2×C4semidirect
75. C3×C42×C5C2×C4semidirect
79. #6714C2×C4semidirect
80. #6714C2×C4semidirect
89. C3×C4×C4⋊C4D5semidirect
215. C42×C5C4×D3semidirect
235. C4×C4⋊C4D15semidirect
285. C3×C42C4×D5semidirect
470. C42C4×D15semidirect
471. C3×C5#2367semidirect
553. C5#73655semidirect
578. C3#10605386semidirect

Maximal subgroups

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

subgroupindex
C2×#917642
C2×C4×D602
C2×C4×Dic302
C3×C4×C5×C4⋊C42
#117510912
#117510902
#117510402
C4×C4⋊Dic152
#117510302
#117507702
#117507672
#106053863
#736555