Finite Group Databasebeta

← #14319690

Subgroups — #14319690

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×C5×#892C211yesmaximal, characteristic
2C2×D3×C4⋊Dic5C211yesmaximal, characteristic
3C2×#91371C211yesmaximal, characteristic
4C4⋊C4×Dic15C211yesmaximal, characteristic, complemented
5C3×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
6#11748886C212yesmaximal
7Dic5×(C2×D3)⋊C4C212yesmaximal
8C4×Dic3⋊Dic5C212yesmaximal, complemented
9#11748699C211yesmaximal, characteristic, complemented
10Dic5×C4⋊Dic3C211yesmaximal, characteristic, complemented
11#11748667C212yesmaximal, complemented
12#10613954—31nomaximal, Hall
13C22×C4×C5×D3C2211yescharacteristic
14C22×D3×Dic5C2212yes—
15C2×C3×C5×C4⋊C4C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15C2212yes—
18C2×C4×Dic15C2211yescharacteristic
19C2×C5×(C2×D3)⋊C4C2212yes—
20C2×C5×C4⋊Dic3C2211yescharacteristic
21C2×C4×C5×Dic3C2212yes—
22C5×#892C418yescomplemented
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×C4×Dic5C2212yes—
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×Dic3⋊Dic5C2212yes—
27C2×Dic3⋊Dic5C2211yescharacteristic
28C2×Dic3⋊Dic5C2211yescharacteristic
29C2×(C2×D3)⋊Dic5C2211yescharacteristic
30C2×(C2×D3)⋊Dic5C2211yescharacteristic
31C2×Dic3×Dic5C2212yes—
32C2×Dic3×Dic5C2212yes—
33D3×C4⋊Dic5C418yescomplemented
34#91371C418yescomplemented
35#91115C2212yes—
36C3×#3963C2212yes—
37#90994C2212yes—
38#90994C2212yes—
39#73750—51nomaximal, Hall
40C2×C5×#117—31no—
41C2×#4072—31no—
42C22×C4⋊Dic5—31no—
43C4⋊C4×Dic5—31no—
44C4⋊C4×Dic5—31no—
45C4⋊C4×Dic5—31no—
46C4⋊C4×Dic5D311yescharacteristic, complemented
47C22⋊C4×Dic5—32no—
48C22⋊C4×Dic5—32no—
49C4×C4⋊Dic5—32no—
50C4×C4⋊Dic5—32no—
51C23×C5×D3C2311yescharacteristic
52C22×C3×C4×C5C2312yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×Dic15C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2311yescharacteristic
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2311yescharacteristic
59C2×C4×C5×D3C2×C414yes—
60C2×C4×C5×D3C2×C414yes—
61C2×C4×C5×D3C2×C414yes—
62C22×C3×Dic5C2311yescharacteristic
63C22×C3×Dic5C2312yes—
64C22×C3×Dic5C2311yescharacteristic
65C2×D3×Dic5—42no—
66C2×D3×Dic5—42no—
67C2×D3×Dic5C2×C418yes—
68C3×C5×C4⋊C4C2×C414yescomplemented
69C4⋊Dic15C2×C414yes—
70C4×Dic15—42no—
71C4×Dic15C2×C414yescomplemented
72C5×(C2×D3)⋊C4C2×C418yes—
73C5×C4⋊Dic3C2×C414yescomplemented
74C4×C5×Dic3C2×C418yescomplemented
75C3×C4⋊Dic5C2×C414yes—
76C3×C4×Dic5—42no—
77C3×C4×Dic5C2×C414yescomplemented
78Dic3⋊Dic5C2×C418yes—
79Dic3⋊Dic5C2×C414yescomplemented
80Dic3⋊Dic5C2×C414yescomplemented
81(C2×D3)⋊Dic5C2×C414yes—
82(C2×D3)⋊Dic5C2×C414yes—
83Dic3×Dic5—42no—
84Dic3×Dic5—42no—
85C2×#892D511yescharacteristic
86C2×D3×C4⋊C4—51no—
87C2×#872—51no—
88C3×C4×C4⋊C4—51no—
89Dic3×C4⋊C4—51no—
90Dic3×C4⋊C4—51no—
91C4×(C2×D3)⋊C4—52no—
92C4×C4⋊Dic3—51no—
93C4×Dic3⋊C4—52no—
94#4666—52no—
95#4649—52no—
96C23×C4×C5—31no—
97C23×Dic5—32no—
98C5×#117—38no—
99C2×C5×C4⋊C4—31no—
100C2×C5×C4⋊C4C2×D311yescharacteristic
101C2×C5×C22⋊C4—32no—
102C2×C42×C5—32no—
103C2×C22⋊Dic5—31no—
104C2×C22⋊Dic5—31no—
105#4072—38no—
106C2×C4⋊Dic5—31no—
107C2×C4⋊Dic5—32no—
108C2×C4⋊Dic5—31no—
109C2×C4⋊Dic5—31no—
110C2×C4⋊Dic5—38no—
111C2×C4⋊Dic5C2×D311yescharacteristic
112C2×C4×Dic5—31no—
113C2×C4×Dic5—32no—
114C2×C4×Dic5—32no—
115C2×C4×Dic5—32no—
116C2×C4×Dic5C2×D312yes—
117C2×C4×Dic5C2×D311yescharacteristic
118#3963—32no—
119#3963—32no—
120#3963—32no—
121#3963C2×D312yes—
122#2274—151noSylow
123C23×C3×C5C2411yescharacteristic
124C22×C5×D3—21no—
125C22×C5×D3—21no—
126C22×C5×D3—21no—
127C22×C5×D3—21no—
128C22×C5×D3C22×C412yes—
129C22×C5×D3C22×C412yes—
130C22×C5×D3C22×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—21no—
138C2×Dic15—22no—
139C2×Dic15—21no—
140C2×Dic15—22no—
141C2×Dic15—21no—
142C2×Dic15—21no—
143C2×Dic15C22×C412yes—
144C2×Dic15C22×C412yes—
145C2×Dic15C22×C414yes—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3C22×C414yes—
149C2×C5×Dic3C22×C412yes—
150C2×C5×Dic3C22×C412yes—
151C2×C5×Dic3C22×C412yes—
152C4×C5×D3C42116yescomplemented
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—
162D3×Dic5—48no—
163C22×C4×D3—52no—
164C22×C4×D3C2×D511yescharacteristic
165C2×C3×C4⋊C4—51no—
166C2×C3×C4⋊C4C2×D511yescharacteristic
167C2×C3×C42—51no—
168C2×C3×C42—52no—
169C2×(C2×D3)⋊C4—51no—
170C2×(C2×D3)⋊C4—51no—
171C2×(C2×D3)⋊C4C2×D512yes—
172C2×C4⋊Dic3—51no—
173C2×C4⋊Dic3C2×D511yescharacteristic
174C2×Dic3⋊C4—51no—
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4—51no—
177C2×C4×Dic3—51no—
178C2×C4×Dic3—52no—
179C2×C4×Dic3—52no—
180C2×C4×Dic3—52no—
181C2×C4×Dic3C2×D512yes—
182#892Dic518yescomplemented
183D3×C4⋊C4—58no—
184#872—58no—
185C3×#95—52no—
186C3⋊#95—52no—
187C3⋊#95—52no—
188C3⋊#95—52no—
189C24×C5—31no—
190C22×C4×C5—31no—
191C22×C4×C5—34no—
192C22×C4×C5—34no—
193C22×C4×C5—34no—
194C22×C4×C5—32no—
195C22×C4×C5C22×D312yes—
196C22×C4×C5C22×D311yescharacteristic
197C22×Dic5—31no—
198C22×Dic5—31no—
199C22×Dic5—32no—
200C22×Dic5—38no—
201C22×Dic5—122no—
202C22×Dic5—122no—
203C22×Dic5C22×D311yescharacteristic
204C22×Dic5C22×D311yescharacteristic
205C22×Dic5C22×D312yes—
206C5×C4⋊C4—34no—
207C5×C4⋊C4C4×D314yescomplemented
208C5×C22⋊C4—38no—
209C42×C5—38no—
210C22⋊Dic5—34no—
211C22⋊Dic5—34no—
212C4⋊Dic5—34no—
213C4⋊Dic5—38no—
214C4⋊Dic5—34no—
215C4⋊Dic5—34no—
216C4⋊Dic5C4×D314yes—
217C4×Dic5—34no—
218C4×Dic5—42no—
219C4×Dic5—122no—
220C4×Dic5—122no—
221C4×Dic5—122no—
222C4×Dic5C4×D314yescomplemented
223C2×#117—31no—
224C2×#117—151no—
225C22×C4⋊C4—151no—
226C4×C4⋊C4—51no—
227C4×C4⋊C4—152no—
228C4×C4⋊C4—152no—
229C4×C4⋊C4—151no—
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×C5×D3—22no—
242C2×C5×D3—22no—
243C2×C5×D3—22no—
244C2×C5×D3—22no—
245C2×C5×D3—22no—
246C2×C5×D3—22no—
247C2×C5×D3C2×C4214yes—
248C3×C4×C5—24no—
249C3×C4×C5C2×C4214yes—
250Dic15—24no—
251Dic15—22no—
252Dic15—22no—
253C3×Dic5—24no—
254C3×Dic5—22no—
255C3×Dic5—22no—
256C5×Dic3—24no—
257C5×Dic3C2×C4214yes—
258C23×D3C22×D511yescharacteristic
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—51no—
266C22×Dic3—52no—
267C22×Dic3C22×D512yes—
268C22×Dic3C22×D511yescharacteristic
269C2×C4×D3—58no—
270C2×C4×D3—202no—
271C2×C4×D3—202no—
272C2×C4×D3C4×D514yes—
273C2×C4×D3C4×D514yes—
274C2×C4×D3C2×Dic514yes—
275C3×C4⋊C4—54no—
276C3×C4⋊C4C2×Dic514yescomplemented
277C3×C42—54no—
278C3×C42—202no—
279(C2×D3)⋊C4—54no—
280(C2×D3)⋊C4—54no—
281(C2×D3)⋊C4C2×Dic518yes—
282C4⋊Dic3—54no—
283C4⋊Dic3C2×Dic514yescomplemented
284Dic3⋊C4—58no—
285Dic3⋊C4—54no—
286Dic3⋊C4—54no—
287C4×Dic3—54no—
288C4×Dic3—202no—
289C4×Dic3—202no—
290C4×Dic3—202no—
291C4×Dic3C2×Dic518yescomplemented
292C23×C5—32no—
293C23×C5—32no—
294C23×C5—32no—
295C23×C5—61no—
296C23×C5—61no—
297C23×C5—61no—
298C23×C5—61no—
299C23×C5C23×D311yescharacteristic
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—32no—
303C2×C4×C5—32no—
304C2×C4×C5—32no—
305C2×C4×C5—316no—
306C2×C4×C5—34no—
307C2×C4×C5—62no—
308C2×C4×C5—62no—
309C2×C4×C5C2×C4×D312yes—
310C2×C4×C5C2×C4×D312yes—
311C2×C4×C5C2×C4×D314yes—
312C2×C4×C5C2×C4×D312yes—
313C2×Dic5—21no—
314C2×Dic5—22no—
315C2×Dic5—21no—
316C2×Dic5—21no—
317C2×Dic5—22no—
318C2×Dic5—21no—
319C2×Dic5—32no—
320C2×Dic5—32no—
321C2×Dic5—34no—
322C2×Dic5—61no—
323C2×Dic5—62no—
324C2×Dic5—61no—
325C2×Dic5—61no—
326C2×Dic5—62no—
327C2×Dic5—61no—
328C2×Dic5—128no—
329C2×Dic5C2×C4×D312yes—
330C2×Dic5C2×C4×D312yes—
331C2×Dic5C2×C4×D314yes—
332C23×C4—31no—
333C23×C4—152no—
334#117—38no—
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—32no—
345C2×C22⋊C4—151no—
346C2×C22⋊C4—151no—
347C2×C42—32no—
348C2×C42—51no—
349C2×C42—52no—
350C2×C42—151no—
351C2×C42—152no—
352C2×C42—152no—
353C2×C42—152no—
354#95—52no—
355#95—152no—
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
365C5×D3—24no—
366C23×C3C23×D511yescharacteristic
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—21no—
370C22×D3—21no—
371C22×D3C2×C4×D512yes—
372C22×D3C2×C4×D512yes—
373C22×D3C22×Dic512yes—
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—102no—
383C2×C3×C4—101no—
384C2×C3×C4—101no—
385C2×C3×C4C2×C4×D512yes—
386C2×C3×C4C2×C4×D512yes—
387C2×C3×C4C22×Dic514yes—
388C2×C3×C4C22×Dic512yes—
389C2×Dic3—22no—
390C2×Dic3—22no—
391C2×Dic3—52no—
392C2×Dic3—52no—
393C2×Dic3—54no—
394C2×Dic3—101no—
395C2×Dic3—101no—
396C2×Dic3—102no—
397C2×Dic3—102no—
398C2×Dic3—101no—
399C2×Dic3—101no—
400C2×Dic3C2×C4×D512yes—
401C2×Dic3C2×C4×D512yes—
402C2×Dic3C22×Dic514yes—
403C2×Dic3C22×Dic512yes—
404C4×D3—208no—
405C4×D3C4×Dic5116yescomplemented
406C22×C5—34no—
407C22×C5—62no—
408C22×C5—62no—
409C22×C5—62no—
410C22×C5—62no—
411C22×C5—62no—
412C22×C5—62no—
413C22×C5C22×C4×D311yescharacteristic
414C22×C5C22×C4×D311yescharacteristic
415C22×C5C22×C4×D311yescharacteristic
416C22×C5#100411yescharacteristic
417C22×C5#100711yescharacteristic
418C22×C5#100911yescharacteristic
419C22×C5#101011yescharacteristic
420C4×C5—24no—
421C4×C5—34no—
422C4×C5—64no—
423C4×C5C42×D314yes—
424Dic5—22no—
425Dic5—22no—
426Dic5—24no—
427Dic5—62no—
428Dic5—62no—
429Dic5—64no—
430C24—31no—
431C22×C4—31no—
432C22×C4—34no—
433C22×C4—34no—
434C22×C4—34no—
435C22×C4—32no—
436C22×C4—51no—
437C22×C4—52no—
438C22×C4—51no—
439C22×C4—158no—
440C22×C4—151no—
441C22×C4—151no—
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⋊C4D3×Dic514yescomplemented
454C22⋊C4—38no—
455C22⋊C4—154no—
456C22⋊C4—154no—
457C42—38no—
458C42—54no—
459C42—154no—
460C42—202no—
461C42—602no—
462C42—602no—
463C42—602no—
464C3×C5#227411yescharacteristic, complemented, Hall
465C22×C3C22×C4×D511yescharacteristic
466C22×C3C22×C4×D511yescharacteristic
467C22×C3#414911yescharacteristic
468C22×C3#414911yescharacteristic
469C22×C3#415011yescharacteristic
470C22×C3#415011yescharacteristic
471C22×C3C23×Dic511yescharacteristic
472C2×D3—22no—
473C2×D3—22no—
474C2×D3—22no—
475C2×D3—22no—
476C2×D3—22no—
477C2×D3—22no—
478C2×D3C2×C4×Dic514yes—
479C3×C4—24no—
480C3×C4—104no—
481C3×C4—102no—
482C3×C4—102no—
483C3×C4C2×C4×Dic514yes—
484Dic3—24no—
485Dic3—104no—
486Dic3—102no—
487Dic3—102no—
488Dic3C2×C4×Dic514yes—
489C2×C5—64no—
490C2×C5C2×C42×D311yescharacteristic
491C2×C5#550411yescharacteristic
492C2×C5#552311yescharacteristic
493C2×C5#554511yescharacteristic
494C2×C5#554611yescharacteristic
495C2×C5#557211yescharacteristic
496C2×C5#557411yescharacteristic
497C23—32no—
498C23—32no—
499C23—32no—
500C23—61no—
501C23—61no—
502C23—61no—
503C23—61no—
504C23C22×D3×D511yescharacteristic
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—316no—
511C2×C4—34no—
512C2×C4—52no—
513C2×C4—52no—
514C2×C4—54no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—101no—
518C2×C4—101no—
519C2×C4—102no—
520C2×C4—101no—
521C2×C4—101no—
522C2×C4—102no—
523C2×C4—152no—
524C2×C4—152no—
525C2×C4—154no—
526C2×C4—301no—
527C2×C4—301no—
528C2×C4—302no—
529C2×C4—301no—
530C2×C4—301no—
531C2×C4—302no—
532C2×C4—608no—
533C2×C4C4×D3×D512yes—
534C2×C4C4×D3×D512yes—
535C2×C4C2×D3×Dic514yes—
536C2×C4C2×D3×Dic512yes—
537C2×C3#6585011yescharacteristic
538C2×C3#6585511yescharacteristic
539C2×C3#6585711yescharacteristic
540C2×C3#6585711yescharacteristic
541C2×C3C22×C4×Dic511yescharacteristic
542C2×C3#6616111yescharacteristic
543C2×C3#6616111yescharacteristic
544D3—24no—
545C5#7375011yescharacteristic, complemented, Sylow
546C22—34no—
547C22—62no—
548C22—62no—
549C22—62no—
550C22—62no—
551C22—62no—
552C22—62no—
553C22C2×C4×D3×D511yescharacteristic
554C22C2×C4×D3×D511yescharacteristic
555C22#9202011yescharacteristic
556C22#9202611yescharacteristic
557C22#9203011yescharacteristic
558C22#9203511yescharacteristic
559C22C22×D3×Dic511yescharacteristic
560C4—24no—
561C4—34no—
562C4—64no—
563C4—104no—
564C4—102no—
565C4—102no—
566C4—304no—
567C4—302no—
568C4—302no—
569C4C4×D3×Dic514yes—
570C3#1061395411yescharacteristic, complemented, Sylow
571C2—64no—
572C2#1175340511yescharacteristic
573C2#1175366811yescharacteristic
574C2#1175367011yescharacteristic
575C2#1175383911yescharacteristic
576C2C2×C4×D3×Dic511yescharacteristic
577C2#1175492011yescharacteristic
578C2#1175522011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC2×C3×C5×C4⋊C4C22
socle, cosocleC23×C3×C5C24
prime radicalC23×C5×D3C23
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. C4⋊C4×Dic15C2semidirect
5. C3×C4⋊C4×Dic5C2semidirect
8. C4×Dic3⋊Dic5C2semidirect
9. #11748699C2semidirect
10. Dic5×C4⋊Dic3C2semidirect
11. #11748667C2semidirect
22. C5×#892C4semidirect
33. D3×C4⋊Dic5C4semidirect
34. #91371C4semidirect
46. C4⋊C4×Dic5D3semidirect
68. C3×C5×C4⋊C4C2×C4semidirect
71. C4×Dic15C2×C4semidirect
73. C5×C4⋊Dic3C2×C4semidirect
74. C4×C5×Dic3C2×C4semidirect
77. C3×C4×Dic5C2×C4semidirect
79. Dic3⋊Dic5C2×C4semidirect
80. Dic3⋊Dic5C2×C4semidirect
152. C4×C5×D3C42semidirect
182. #892Dic5semidirect
207. C5×C4⋊C4C4×D3semidirect
222. C4×Dic5C4×D3semidirect
276. C3×C4⋊C4C2×Dic5semidirect
283. C4⋊Dic3C2×Dic5semidirect
291. C4×Dic3C2×Dic5semidirect
405. C4×D3C4×Dic5semidirect
453. C4⋊C4D3×Dic5semidirect
464. C3×C5#2274semidirect
545. C5#73750semidirect
570. C3#10613954semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8922
C2×D3×C4⋊Dic52
C2×#913712
C4⋊C4×Dic152
C3×C4⋊C4×Dic52
#117488862
Dic5×(C2×D3)⋊C42
C4×Dic3⋊Dic52
#117486992
Dic5×C4⋊Dic32
#117486672
#106139543
#737505