Finite Group Databasebeta

← #14327186

Subgroups — #14327186

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×D20C211yesmaximal, characteristic
2C2×Dic3×D20C211yesmaximal, characteristic
3C2×Dic3×D20C211yesmaximal, characteristic
4#11751029C211yesmaximal, characteristic, complemented
5C4×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
6#11748891C212yesmaximal, complemented
7#11748885C212yesmaximal, complemented
8D5×C3⋊#95C212yesmaximal, complemented
9#11748858C211yesmaximal, characteristic, complemented
10#11748703C212yesmaximal, complemented
11#11748619C211yesmaximal, characteristic, complemented
12#10605501—31nomaximal, Hall
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2212yes—
15C22×D5×Dic3C2212yes—
16C22×D5×Dic3C2212yes—
17C2×C3×C42×C5C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×C4⋊Dic15C2211yescharacteristic
20C2×#6712C2212yes—
21C2×C5×Dic3⋊C4C2211yescharacteristic
22C2×C5×Dic3⋊C4C2211yescharacteristic
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C3×#685C2212yes—
26C2×C3×C4⋊Dic5C2211yescharacteristic
27C3×C4×D20—24no—
28C2×#6669C2212yes—
29C2×#6665C2212yes—
30C2×#6665C2212yes—
31Dic3×D20—24no—
32Dic3×D20C418yescomplemented
33#91115C2212yes—
34C5×C3⋊#95C2211yescharacteristic
35C5×C3⋊#95C2211yescharacteristic
36#90994C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#82334—51nomaximal, Hall
40C2×C4×D20—31no—
41C2×C4×D20—31no—
42C2×C4×D20D311yescharacteristic
43C4×C5×C4⋊C4—31no—
44#65278—32no—
45#65278—32no—
46#65225—31no—
47#65217—31no—
48#65217—31no—
49#64956—32no—
50D5×#95—32no—
51C23×C3×D5C2312yes—
52C22×C3×C4×C5C2311yescharacteristic
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C22×C5×Dic3C2311yescharacteristic
58C22×C5×Dic3C2311yescharacteristic
59C22×C5×Dic3C2311yescharacteristic
60C22×C5×Dic3C2311yescharacteristic
61C22×C3×Dic5C2312yes—
62C2×C3×D20C2×C414yes—
63C2×C3×D20D414yes—
64C2×C3×D20Q814yes—
65C2×C3×C4×D5—24no—
66C2×C3×C4×D5—24no—
67C2×C3×C4×D5—42no—
68C2×D5×Dic3—24no—
69C2×D5×Dic3—24no—
70C2×D5×Dic3—42no—
71C2×D5×Dic3—42no—
72C2×D5×Dic3—42no—
73C2×D5×Dic3C2×C418yescomplemented
74C3×C42×C5—22no—
75C4⋊Dic15—22no—
76C4⋊Dic15C2×C414yescomplemented
77#6712—42no—
78C5×Dic3⋊C4—22no—
79C5×Dic3⋊C4—22no—
80C4×C5×Dic3—22no—
81C4×C5×Dic3C2×C414yescomplemented
82C3×#685—24no—
83C3×C4⋊Dic5—22no—
84#6669—42no—
85#6665—24no—
86#6665C2×C418yescomplemented
87C2×C3×C4×D4—51no—
88C2×D4×Dic3—51no—
89C2×D4×Dic3—51no—
90#5210—52no—
91C2×C3⋊#95—52no—
92#4977—51no—
93#4972—51no—
94#4946—52no—
95#4942—52no—
96C4×Dic3⋊C4D511yescharacteristic, complemented
97#4928—51no—
98C22×D20C2×D311yescharacteristic
99C22×C4×D5—32no—
100C22×C4×D5—32no—
101C22×C4×D5C2×D312yes—
102C2×C5×C4⋊C4—31no—
103C2×C5×C4⋊C4—31no—
104C2×C42×C5—31no—
105C2×C42×C5—31no—
106C2×C42×C5C2×D311yescharacteristic
107C2×#685—32no—
108C2×#685—32no—
109C2×#685C2×D312yes—
110C2×C4⋊Dic5—31no—
111C2×C4⋊Dic5—31no—
112C2×C4⋊Dic5C2×D311yescharacteristic
113C2×#683—32no—
114C2×#683—32no—
115C4×D20—24no—
116C4×D20—38no—
117C4×D20—64no—
118C5×#95—31no—
119C5×#95—31no—
120#3963—32no—
121#3963—32no—
122#3963—32no—
123#3963—32no—
124#2349—151noSylow
125C23×C3×C5C2411yescharacteristic
126C22×C3×D5—22no—
127C22×C3×D5—22no—
128C22×C3×D5—22no—
129C22×C3×D5—22no—
130C22×C3×D5C22×C414yes—
131C22×C3×D5C2×D414yes—
132C22×C3×D5C2×Q814yes—
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×C5C22×C412yes—
139C2×C3×C4×C5C2×D412yes—
140C2×C3×C4×C5C2×Q812yes—
141C2×C3×C4×C5#4112yes—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C2×Dic15—22no—
145C2×Dic15—22no—
146C2×Dic15—22no—
147C2×Dic15C22×C414yes—
148C2×C5×Dic3—21no—
149C2×C5×Dic3—21no—
150C2×C5×Dic3—21no—
151C2×C5×Dic3—21no—
152C2×C5×Dic3—21no—
153C2×C5×Dic3—21no—
154C2×C5×Dic3—21no—
155C2×C5×Dic3—21no—
156C2×C5×Dic3—21no—
157C2×C5×Dic3C22×C412yes—
158C2×C5×Dic3C22×C412yes—
159C2×C5×Dic3#4112yes—
160C2×C3×Dic5—22no—
161C2×C3×Dic5—22no—
162C2×C3×Dic5—22no—
163C3×D20C4⋊C4116yescomplemented
164C3×C4×D5—48no—
165D5×Dic3—48no—
166D5×Dic3—48no—
167C22×C3×D4—51no—
168C23×C3×C4—52no—
169C23×Dic3—52no—
170C23×Dic3—52no—
171C3×C4×D4—104no—
172C2×C3×C4⋊C4—51no—
173C2×C3×C22⋊C4—52no—
174C2×C3×C42C2×D511yescharacteristic
175C2×#217—52no—
176C2×#217—52no—
177D4×Dic3—58no—
178D4×Dic3—104no—
179C2×C4⋊Dic3—51no—
180C2×C4⋊Dic3—51no—
181C2×Dic3⋊C4—52no—
182C2×Dic3⋊C4—52no—
183C2×Dic3⋊C4C2×D511yescharacteristic
184C2×Dic3⋊C4C2×D511yescharacteristic
185C2×C4×Dic3C2×D511yescharacteristic
186C2×C4×Dic3C2×D511yescharacteristic
187C3⋊#95—52no—
188C3⋊#95—52no—
189C3⋊#95—52no—
190C3⋊#95—52no—
191C3⋊#95C2×D511yescharacteristic
192C3⋊#95C2×D511yescharacteristic
193C23×D5C22×D312yes—
194C22×C4×C5—31no—
195C22×C4×C5—31no—
196C22×C4×C5—31no—
197C22×C4×C5—31no—
198C22×C4×C5C22×D311yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C22×C4×C5C22×D311yescharacteristic
201C22×Dic5—32no—
202C22×Dic5—32no—
203C22×Dic5C22×D312yes—
204C2×D20Dic614yes—
205C2×D20C4×D314yes—
206C2×D20#6714yes—
207C2×C4×D5—24no—
208C2×C4×D5—24no—
209C2×C4×D5—38no—
210C2×C4×D5—42no—
211C2×C4×D5—64no—
212C2×C4×D5—64no—
213C2×C4×D5—122no—
214C2×C4×D5—122no—
215C2×C4×D5—122no—
216C5×C4⋊C4—62no—
217C5×C4⋊C4—62no—
218C42×C5—22no—
219C42×C5—34no—
220C42×C5—62no—
221#685—24no—
222#685—38no—
223#685—64no—
224C4⋊Dic5—22no—
225C4⋊Dic5—34no—
226C4⋊Dic5—62no—
227#683—122no—
228#683—122no—
229C2×C4×D4—51no—
230C2×C4×D4—151no—
231C2×C4×D4—151no—
232#389—151no—
233#389—151no—
234#385—152no—
235#385—152no—
236#382—151no—
237#380—152no—
238C4×C4⋊C4—31no—
239C2×#95—152no—
240C22×C3×C5C23×C411yescharacteristic
241C22×C3×C5C22×D411yescharacteristic
242C22×C3×C5C22×Q811yescharacteristic
243C22×C3×C5C2×#4111yescharacteristic
244C22×C3×C5C2×#4111yescharacteristic
245C22×C3×C5H(5,𝔽2)11yescharacteristic
246C22×C3×C5H(5,𝔽2)11yescharacteristic
247C2×C3×D5—24no—
248C2×C3×D5—24no—
249C2×C3×D5—24no—
250C2×C3×D5—24no—
251C2×C3×D5—24no—
252C2×C3×D5—24no—
253C2×C3×D5C2×C4⋊C418yes—
254C3×C4×C5—22no—
255C3×C4×C5—41no—
256C3×C4×C5C2×C4⋊C414yes—
257Dic15—24no—
258Dic15—42no—
259C3×Dic5—42no—
260C5×Dic3—22no—
261C5×Dic3—22no—
262C5×Dic3—22no—
263C5×Dic3—41no—
264C24×C3—52no—
265C2×C3×D4—54no—
266C2×C3×D4—54no—
267C2×C3×D4—54no—
268C22×C3×C4—52no—
269C22×C3×C4—104no—
270C22×C3×C4—104no—
271C22×C3×C4—202no—
272C22×C3×C4C22×D511yescharacteristic
273C22×C3×C4C22×D511yescharacteristic
274C22×C3×C4C22×D511yescharacteristic
275C22×Dic3—52no—
276C22×Dic3—58no—
277C22×Dic3—52no—
278C22×Dic3—104no—
279C22×Dic3—104no—
280C22×Dic3—202no—
281C22×Dic3—202no—
282C22×Dic3—202no—
283C22×Dic3C22×D511yescharacteristic
284C22×Dic3C22×D511yescharacteristic
285C22×Dic3C22×D511yescharacteristic
286C22×Dic3C22×D511yescharacteristic
287C3×C4⋊C4—102no—
288C3×C22⋊C4—104no—
289C3×C42—22no—
290#217—58no—
291#217—104no—
292C4⋊Dic3—54no—
293C4⋊Dic3—102no—
294Dic3⋊C4—22no—
295Dic3⋊C4—22no—
296Dic3⋊C4—202no—
297Dic3⋊C4—202no—
298C4×Dic3—22no—
299C4×Dic3C4×D514yescomplemented
300C23×C5C23×D311yescharacteristic
301C22×D5—22no—
302C22×D5—22no—
303C22×D5—22no—
304C22×D5—22no—
305C22×D5C2×Dic614yes—
306C22×D5C2×C4×D314yes—
307C22×D5C2×#6714yes—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—21no—
311C2×C4×C5—21no—
312C2×C4×C5—21no—
313C2×C4×C5—32no—
314C2×C4×C5—32no—
315C2×C4×C5—32no—
316C2×C4×C5—61no—
317C2×C4×C5—61no—
318C2×C4×C5—61no—
319C2×C4×C5—61no—
320C2×C4×C5—61no—
321C2×C4×C5—61no—
322C2×C4×C5—61no—
323C2×C4×C5—61no—
324C2×C4×C5—61no—
325C2×C4×C5C2×Dic612yes—
326C2×C4×C5C2×C4×D312yes—
327C2×C4×C5#23712yes—
328C2×C4×C5C2×#6712yes—
329C2×Dic5—22no—
330C2×Dic5—22no—
331C2×Dic5—22no—
332C2×Dic5—34no—
333C2×Dic5—62no—
334C2×Dic5—62no—
335C2×Dic5—62no—
336C2×Dic5—62no—
337C2×Dic5—62no—
338D20Dic3⋊C4116yescomplemented
339C4×D5—48no—
340C4×D5—128no—
341C4×D5—128no—
342C22×D4—51no—
343C23×C4—52no—
344C23×C4—152no—
345C23×C4—152no—
346C4×D4—104no—
347C4×D4—158no—
348C4×D4—304no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—51no—
352C2×C4⋊C4—151no—
353C2×C4⋊C4—151no—
354C2×C4⋊C4—152no—
355C2×C4⋊C4—152no—
356C2×C22⋊C4—52no—
357C2×C22⋊C4—152no—
358C2×C22⋊C4—152no—
359C2×C42—31no—
360C2×C42—31no—
361C2×C42D3×D511yescharacteristic
362#95—31no—
363#95—31no—
364#95—152no—
365#95—152no—
366#95—152no—
367#95—152no—
368C2×C3×C5C22×C4⋊C411yescharacteristic
369C2×C3×C5C4×#4111yescharacteristic
370C2×C3×C5#51811yescharacteristic
371C2×C3×C5#54611yescharacteristic
372C2×C3×C5#54611yescharacteristic
373C2×C3×C5#55411yescharacteristic
374C2×C3×C5#55411yescharacteristic
375C3×D5—28no—
376C23×C3—54no—
377C23×C3—54no—
378C23×C3—54no—
379C23×C3—102no—
380C23×C3—102no—
381C23×C3—102no—
382C23×C3—102no—
383C23×C3C23×D511yescharacteristic
384C3×D4—516no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—102no—
391C2×C3×C4—102no—
392C2×C3×C4—102no—
393C2×C3×C4—208no—
394C2×C3×C4C2×C4×D512yes—
395C2×C3×C4#70912yes—
396C2×C3×C4D4×D512yes—
397C2×C3×C4Q8×D512yes—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—21no—
402C2×Dic3—21no—
403C2×Dic3—21no—
404C2×Dic3—21no—
405C2×Dic3—21no—
406C2×Dic3—21no—
407C2×Dic3—54no—
408C2×Dic3—102no—
409C2×Dic3—102no—
410C2×Dic3—102no—
411C2×Dic3—102no—
412C2×Dic3—102no—
413C2×Dic3—208no—
414C2×Dic3—208no—
415C2×Dic3C2×C4×D512yes—
416C2×Dic3C2×C4×D512yes—
417C2×Dic3#70912yes—
418C22×C5C22×Dic611yescharacteristic
419C22×C5C22×C4×D311yescharacteristic
420C22×C5C2×#23711yescharacteristic
421C22×C5#100411yescharacteristic
422C22×C5D3×#4111yescharacteristic
423C22×C5#100911yescharacteristic
424C22×C5C22×#6711yescharacteristic
425C2×D5—24no—
426C2×D5—24no—
427C2×D5—24no—
428C2×D5—24no—
429C2×D5—24no—
430C2×D5—24no—
431C2×D5C2×Dic3⋊C418yes—
432C4×C5—22no—
433C4×C5—41no—
434C4×C5—62no—
435C4×C5—62no—
436C4×C5—62no—
437C4×C5—121no—
438C4×C5C2×Dic3⋊C414yes—
439Dic5—42no—
440Dic5—64no—
441Dic5—122no—
442C24—52no—
443C2×D4—54no—
444C2×D4—54no—
445C2×D4—54no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—31no—
450C22×C4—52no—
451C22×C4—104no—
452C22×C4—104no—
453C22×C4—158no—
454C22×C4—152no—
455C22×C4—152no—
456C22×C4—202no—
457C22×C4—304no—
458C22×C4—304no—
459C22×C4—602no—
460C22×C4—602no—
461C22×C4—602no—
462C22×C4C2×D3×D511yescharacteristic
463C22×C4C2×D3×D511yescharacteristic
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—62no—
466C4⋊C4—62no—
467C4⋊C4—102no—
468C4⋊C4—154no—
469C4⋊C4—302no—
470C4⋊C4—602no—
471C4⋊C4—602no—
472C22⋊C4—104no—
473C22⋊C4—158no—
474C22⋊C4—304no—
475C42—22no—
476C42—34no—
477C42—62no—
478C3×C5#234911yescharacteristic, complemented, Hall
479C22×C3—58no—
480C22×C3—104no—
481C22×C3—104no—
482C22×C3—104no—
483C22×C3—104no—
484C22×C3—104no—
485C22×C3—104no—
486C22×C3C22×C4×D511yescharacteristic
487C22×C3C2×#70911yescharacteristic
488C22×C3C2×#70911yescharacteristic
489C22×C3C2×D4×D511yescharacteristic
490C22×C3C2×Q8×D511yescharacteristic
491C22×C3#414911yescharacteristic
492C22×C3#414911yescharacteristic
493C3×C4—22no—
494C3×C4—41no—
495C3×C4—202no—
496C3×C4D5×C4⋊C414yes—
497Dic3—22no—
498Dic3—22no—
499Dic3—22no—
500Dic3—41no—
501Dic3—104no—
502Dic3—202no—
503C2×C5C4×#23711yescharacteristic
504C2×C5#553911yescharacteristic
505C2×C5#554311yescharacteristic
506C2×C5#554511yescharacteristic
507C2×C5C22×Dic3⋊C411yescharacteristic
508C2×C5#580611yescharacteristic
509C2×C5#582911yescharacteristic
510D5—28no—
511C23—54no—
512C23—54no—
513C23—54no—
514C23—102no—
515C23—102no—
516C23—102no—
517C23—102no—
518C23C22×D3×D511yescharacteristic
519D4—516no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—32no—
526C2×C4—32no—
527C2×C4—32no—
528C2×C4—61no—
529C2×C4—61no—
530C2×C4—61no—
531C2×C4—61no—
532C2×C4—61no—
533C2×C4—61no—
534C2×C4—61no—
535C2×C4—61no—
536C2×C4—61no—
537C2×C4—102no—
538C2×C4—102no—
539C2×C4—102no—
540C2×C4—154no—
541C2×C4—208no—
542C2×C4—302no—
543C2×C4—302no—
544C2×C4—302no—
545C2×C4—302no—
546C2×C4—302no—
547C2×C4—608no—
548C2×C4—608no—
549C2×C4D5×Dic612yes—
550C2×C4#676512yes—
551C2×C4C4×D3×D512yes—
552C2×C4D5×#6712yes—
553C2×C3—108no—
554C2×C3C4×#70911yescharacteristic
555C2×C3C2×D5×C4⋊C411yescharacteristic
556C2×C3#6585511yescharacteristic
557C2×C3#6588411yescharacteristic
558C2×C3#6588411yescharacteristic
559C2×C3#6591311yescharacteristic
560C2×C3#6591311yescharacteristic
561C5#8233411yescharacteristic, complemented, Sylow
562C22—58no—
563C22—104no—
564C22—104no—
565C22—104no—
566C22—104no—
567C22—104no—
568C22—104no—
569C22C2×D5×Dic611yescharacteristic
570C22C2×#676511yescharacteristic
571C22C2×C4×D3×D511yescharacteristic
572C22D3×#70911yescharacteristic
573C22#9201711yescharacteristic
574C22#9201911yescharacteristic
575C22C2×D5×#6711yescharacteristic
576C4—22no—
577C4—41no—
578C4—62no—
579C4—62no—
580C4—62no—
581C4—121no—
582C4—202no—
583C4—304no—
584C4—602no—
585C4D5×Dic3⋊C414yes—
586C3#1060550111yescharacteristic, complemented, Sylow
587C2—108no—
588C2C4×#676511yescharacteristic
589C2#1175259711yescharacteristic
590C2#1175265711yescharacteristic
591C2#1175272711yescharacteristic
592C2C2×D5×Dic3⋊C411yescharacteristic
593C2#1175430511yescharacteristic
594C2#1175463811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC2×C3×C42×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C3×D20C22
hypercenterC2×C42D3×D5
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #11751029C2semidirect
5. C4×C5×Dic3⋊C4C2semidirect
6. #11748891C2semidirect
7. #11748885C2semidirect
8. D5×C3⋊#95C2semidirect
9. #11748858C2semidirect
10. #11748703C2semidirect
11. #11748619C2semidirect
32. Dic3×D20C4semidirect
73. C2×D5×Dic3C2×C4semidirect
76. C4⋊Dic15C2×C4semidirect
81. C4×C5×Dic3C2×C4semidirect
86. #6665C2×C4semidirect
96. C4×Dic3⋊C4D5semidirect
163. C3×D20C4⋊C4semidirect
299. C4×Dic3C4×D5semidirect
338. D20Dic3⋊C4semidirect
478. C3×C5#2349semidirect
561. C5#82334semidirect
586. C3#10605501semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×D202
C2×Dic3×D202
#117510292
C4×C5×Dic3⋊C42
#117488912
#117488852
D5×C3⋊#952
#117488582
#117487032
#117486192
#106055013
#823345