Finite Group Databasebeta

← #14319734

Subgroups — #14319734

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×#67C211yesmaximal, characteristic
2C2×#67⋊Dic5C212yesmaximal
3C2×#91115C211yesmaximal, characteristic, complemented
4C3×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
5#11749487C212yesmaximal, complemented
6D3×#3963C211yesmaximal, characteristic, complemented
7Dic5×(C2×D3)⋊C4C212yesmaximal, complemented
8#11748719C211yesmaximal, characteristic, complemented
9#11748667C211yesmaximal, characteristic, complemented
10#11748643C211yesmaximal, characteristic, complemented
11Dic5×Dic3⋊C4C212yesmaximal, complemented
12#10614048—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C23×Dic15C2212yes—
15C22×C5×#67C2211yescharacteristic
16C22×C4×C5×D3C2211yescharacteristic
17C22×D3×Dic5C2212yes—
18C2×C5×#217C2211yescharacteristic
19C4×C5×#67C418yescomplemented
20C2×C5×(C2×D3)⋊C4C2211yescharacteristic
21C2×C5×Dic3⋊C4C2211yescharacteristic
22C2×C4×C5×Dic3C2211yescharacteristic
23C2×C3×C22⋊Dic5C2212yes—
24C2×C3×C4×Dic5C2212yes—
25#67⋊Dic5C4116yescomplemented
26C2×Dic3⋊Dic5C2212yes—
27C2×(C2×D3)⋊Dic5C2212yes—
28C2×Dic3×Dic5C2212yes—
29C2×Dic3×Dic5C2212yes—
30C2×Dic3×Dic5C2212yes—
31#91115C2212yes—
32#91115C2211yescharacteristic
33#91115C2211yescharacteristic
34C3×#3963C2211yescharacteristic
35C3×#3963C2211yescharacteristic
36#90994C2212yes—
37#90994C2212yes—
38#73436—51nomaximal, Hall
39C2×C4×C5×D4—31no—
40C2×D4×Dic5—32no—
41C4×C22⋊Dic5—31no—
42C4×C22⋊Dic5D311yescharacteristic, complemented
43C2×#3963—31no—
44C2×#3963—31no—
45C4⋊C4×Dic5—32no—
46C22⋊C4×Dic5—32no—
47C22⋊C4×Dic5—32no—
48C4×C4⋊Dic5—31no—
49#65221—31no—
50C24×C3×C5C2311yescharacteristic
51C23×C5×D3C2311yescharacteristic
52C22×C3×C4×C5—42no—
53C22×C3×C4×C5C2×C414yescomplemented
54C22×C3×C4×C5C2311yescharacteristic
55C22×C3×C4×C5C2311yescharacteristic
56C22×Dic15—42no—
57C22×Dic15—42no—
58C22×Dic15C2×C418yescomplemented
59C22×Dic15C2312yes—
60C22×Dic15C2312yes—
61C2×C5×#67C2×C418yes—
62C2×C5×#67C2×C414yes—
63C22×C5×Dic3C2311yescharacteristic
64C22×C5×Dic3C2311yescharacteristic
65C22×C5×Dic3C2311yescharacteristic
66C2×C4×C5×D3—42no—
67C2×C4×C5×D3C2×C414yescomplemented
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2312yes—
70C2×D3×Dic5—42no—
71C2×D3×Dic5—42no—
72C2×D3×Dic5C2×C418yescomplemented
73C5×#217C2×C414yescomplemented
74C5×(C2×D3)⋊C4C2×C414yescomplemented
75C5×Dic3⋊C4C2×C414yescomplemented
76C4×C5×Dic3C2×C414yescomplemented
77C3×C22⋊Dic5C2×C418yescomplemented
78C3×C4×Dic5—42no—
79Dic3⋊Dic5C2×C418yescomplemented
80(C2×D3)⋊Dic5C2×C418yescomplemented
81Dic3×Dic5—42no—
82Dic3×Dic5—42no—
83Dic3×Dic5C2×C418yescomplemented
84C2×C4×#67D511yescharacteristic
85C2×#67⋊C4—52no—
86C3×C4×C22⋊C4—51no—
87C2×C3⋊#95—51no—
88Dic3×C22⋊C4—52no—
89C4×(C2×D3)⋊C4—52no—
90C4×Dic3⋊C4—52no—
91#4666—51no—
92D3×#95—51no—
93#4649—51no—
94#4648—51no—
95C22×C5×D4—31no—
96C23×C4×C5—31no—
97C23×C4×C5C2×D311yescharacteristic
98C23×Dic5—32no—
99C23×Dic5—32no—
100C4×C5×D4—38no—
101C2×C5×C4⋊C4—31no—
102C2×C5×C22⋊C4—31no—
103C2×C5×C22⋊C4—31no—
104C2×C42×C5—31no—
105C2×C22⋊Dic5—32no—
106C2×C22⋊Dic5C2×D312yes—
107D4×Dic5—316no—
108C2×C4⋊Dic5—32no—
109C2×C4×Dic5—32no—
110C2×C4×Dic5—32no—
111C2×C4×Dic5—32no—
112C2×C4×Dic5C2×D312yes—
113#3963—31no—
114#3963—31no—
115#3963—32no—
116#3963—32no—
117#3963—32no—
118#3963C2×D311yescharacteristic
119#3963C2×D311yescharacteristic
120#2275—151noSylow
121C23×C3×C5—21no—
122C23×C3×C5—22no—
123C23×C3×C5—21no—
124C23×C3×C5C22×C414yes—
125C23×C3×C5C22×C412yes—
126C23×C3×C5C2411yescharacteristic
127C22×C5×D3—21no—
128C22×C5×D3—22no—
129C22×C5×D3—21no—
130C22×C5×D3C22×C414yes—
131C22×C5×D3C22×C412yes—
132C2×C3×C4×C5—22no—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—44no—
135C2×C3×C4×C5C22×C412yes—
136C2×C3×C4×C5C22×C412yes—
137C2×Dic15—22no—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—48no—
142C2×Dic15C22×C414yes—
143C2×Dic15C22×C414yes—
144C5×#67C42116yescomplemented
145C2×C5×Dic3—21no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—21no—
148C2×C5×Dic3C22×C412yes—
149C2×C5×Dic3C22×C412yes—
150C2×C5×Dic3C22×C414yes—
151C2×C5×Dic3C22×C412yes—
152C4×C5×D3—44no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5C22×C414yes—
158C2×C3×Dic5C22×C414yes—
159D3×Dic5—48no—
160C23×C3×C4C2×D511yescharacteristic
161C22×#67C2×D511yescharacteristic
162C23×Dic3—52no—
163C22×C4×D3—52no—
164C22×C4×D3C2×D511yescharacteristic
165C2×C3×C22⋊C4—52no—
166C2×C3×C42—52no—
167C2×#217C2×D511yescharacteristic
168C4×#67Dic518yescomplemented
169C2×(C2×D3)⋊C4—52no—
170C2×(C2×D3)⋊C4C2×D511yescharacteristic
171C2×Dic3⋊C4—52no—
172C2×Dic3⋊C4C2×D511yescharacteristic
173C2×C4×Dic3—52no—
174C2×C4×Dic3—52no—
175C2×C4×Dic3—52no—
176C2×C4×Dic3C2×D511yescharacteristic
177#67⋊C4—516no—
178C3×#95—51no—
179C3×#95—51no—
180C3⋊#95—51no—
181C3⋊#95—51no—
182C3⋊#95—52no—
183C3⋊#95—52no—
184C3⋊#95—52no—
185C24×C5—31no—
186C24×C5C22×D311yescharacteristic
187C2×C5×D4—34no—
188C2×C5×D4—38no—
189C22×C4×C5—31no—
190C22×C4×C5—31no—
191C22×C4×C5—31no—
192C22×C4×C5—34no—
193C22×C4×C5—42no—
194C22×C4×C5—122no—
195C22×C4×C5C4×D314yescomplemented
196C22×C4×C5C22×D311yescharacteristic
197C22×C4×C5C22×D311yescharacteristic
198C22×Dic5—32no—
199C22×Dic5—32no—
200C22×Dic5—38no—
201C22×Dic5—38no—
202C22×Dic5—122no—
203C22×Dic5—122no—
204C22×Dic5—122no—
205C22×Dic5—122no—
206C22×Dic5C22×D312yes—
207C22×Dic5C22×D312yes—
208C5×C4⋊C4—34no—
209C5×C22⋊C4—34no—
210C5×C22⋊C4—34no—
211C42×C5—34no—
212C22⋊Dic5—38no—
213C22⋊Dic5C4×D318yescomplemented
214C4⋊Dic5—38no—
215C4×Dic5—38no—
216C4×Dic5—42no—
217C4×Dic5—122no—
218C4×Dic5—122no—
219C2×C4×D4—31no—
220C2×C4×D4—152no—
221C4×C4⋊C4—151no—
222C4×C4⋊C4—152no—
223C4×C22⋊C4—51no—
224C4×C22⋊C4—151no—
225C4×C22⋊C4—152no—
226C4×C22⋊C4—152no—
227#376—151no—
228C2×#95—151no—
229C2×#95—151no—
230C22×C3×C5—24no—
231C22×C3×C5—22no—
232C22×C3×C5—24no—
233C22×C3×C5—22no—
234C22×C3×C5C2×C4214yes—
235C22×C3×C5C23×C412yes—
236C22×C3×C5C23×C411yescharacteristic
237C22×C3×C5H(5,𝔽2)12yes—
238C22×C3×C5H(5,𝔽2)11yescharacteristic
239C22×C3×C52−1+411yescharacteristic
240C2×C5×D3—24no—
241C2×C5×D3—22no—
242C2×C5×D3—24no—
243C2×C5×D3—22no—
244C2×C5×D3C2×C4214yes—
245C3×C4×C5—22no—
246C3×C4×C5—22no—
247Dic15—24no—
248Dic15—24no—
249C3×Dic5—24no—
250C3×Dic5—24no—
251C5×Dic3—22no—
252C5×Dic3—22no—
253C5×Dic3C2×C4214yes—
254C24×C3C22×D511yescharacteristic
255C23×D3C22×D511yescharacteristic
256C22×C3×C4—42no—
257C22×C3×C4—52no—
258C22×C3×C4—52no—
259C22×C3×C4C2×Dic514yescomplemented
260C22×C3×C4C22×D511yescharacteristic
261C22×C3×C4C22×D511yescharacteristic
262C2×#67C4×D518yes—
263C2×#67C2×Dic514yes—
264C22×Dic3—52no—
265C22×Dic3—52no—
266C22×Dic3—58no—
267C22×Dic3—202no—
268C22×Dic3—202no—
269C22×Dic3C22×D511yescharacteristic
270C22×Dic3C22×D511yescharacteristic
271C22×Dic3C22×D511yescharacteristic
272C2×C4×D3—42no—
273C2×C4×D3—58no—
274C2×C4×D3—202no—
275C2×C4×D3—202no—
276C2×C4×D3C2×Dic514yescomplemented
277C3×C22⋊C4—58no—
278C3×C42—202no—
279#217C2×Dic514yescomplemented
280(C2×D3)⋊C4—58no—
281(C2×D3)⋊C4C2×Dic514yescomplemented
282Dic3⋊C4—58no—
283Dic3⋊C4C2×Dic514yescomplemented
284C4×Dic3—58no—
285C4×Dic3—202no—
286C4×Dic3—202no—
287C4×Dic3C2×Dic514yescomplemented
288C23×C5—22no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—34no—
292C23×C5—32no—
293C23×C5—62no—
294C23×C5—61no—
295C23×C5—61no—
296C23×C5C2×C4×D314yes—
297C23×C5C2×C4×D312yes—
298C23×C5C23×D311yescharacteristic
299C5×D4—316no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—34no—
303C2×C4×C5—32no—
304C2×C4×C5—32no—
305C2×C4×C5—32no—
306C2×C4×C5—44no—
307C2×C4×C5—62no—
308C2×C4×C5—61no—
309C2×C4×C5—61no—
310C2×C4×C5—124no—
311C2×C4×C5C2×C4×D312yes—
312C2×C4×C5C2×C4×D312yes—
313C2×Dic5—22no—
314C2×Dic5—22no—
315C2×Dic5—22no—
316C2×Dic5—22no—
317C2×Dic5—34no—
318C2×Dic5—34no—
319C2×Dic5—62no—
320C2×Dic5—62no—
321C2×Dic5—62no—
322C2×Dic5—62no—
323C2×Dic5—128no—
324C2×Dic5—128no—
325C2×Dic5C2×C4×D314yes—
326C2×Dic5C2×C4×D314yes—
327C22×D4—31no—
328C23×C4—31no—
329C23×C4—152no—
330C23×C4—152no—
331C23×C4D3×D511yescharacteristic
332C4×D4—38no—
333C4×D4—1516no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—152no—
336C2×C22⋊C4—31no—
337C2×C22⋊C4—31no—
338C2×C22⋊C4—52no—
339C2×C22⋊C4—152no—
340C2×C42—31no—
341C2×C42—52no—
342C2×C42—152no—
343C2×C42—152no—
344C2×C42—152no—
345#95—51no—
346#95—51no—
347#95—152no—
348#95—152no—
349#95—151no—
350#95—152no—
351#95—151no—
352C2×C3×C5—24no—
353C2×C3×C5C22×C4211yescharacteristic
354C2×C3×C5#51811yescharacteristic
355C2×C3×C5#51812yes—
356C2×C3×C5#52012yes—
357C2×C3×C5#52011yescharacteristic
358C5×D3—24no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3C2×C4×D514yes—
363C23×C3C22×Dic512yes—
364C23×C3C23×D511yescharacteristic
365C22×D3—22no—
366C22×D3—21no—
367C22×D3—21no—
368C22×D3C2×C4×D514yes—
369C22×D3C22×Dic512yes—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—44no—
373C2×C3×C4—54no—
374C2×C3×C4—54no—
375C2×C3×C4—102no—
376C2×C3×C4—102no—
377C2×C3×C4—102no—
378C2×C3×C4—102no—
379C2×C3×C4C22×Dic512yes—
380C2×C3×C4C22×Dic512yes—
381#67C4×Dic5116yescomplemented
382C2×Dic3—22no—
383C2×Dic3—21no—
384C2×Dic3—21no—
385C2×Dic3—54no—
386C2×Dic3—54no—
387C2×Dic3—102no—
388C2×Dic3—102no—
389C2×Dic3—102no—
390C2×Dic3—102no—
391C2×Dic3—208no—
392C2×Dic3C2×C4×D514yes—
393C2×Dic3C22×Dic512yes—
394C2×Dic3C22×Dic512yes—
395C2×Dic3C22×Dic512yes—
396C4×D3—44no—
397C4×D3—208no—
398C22×C5—22no—
399C22×C5—22no—
400C22×C5—24no—
401C22×C5—24no—
402C22×C5—34no—
403C22×C5—62no—
404C22×C5—62no—
405C22×C5—64no—
406C22×C5—64no—
407C22×C5C42×D314yes—
408C22×C5C22×C4×D312yes—
409C22×C5C22×C4×D311yescharacteristic
410C22×C5#100412yes—
411C22×C5#100911yescharacteristic
412C22×C5#101011yescharacteristic
413C4×C5—22no—
414C4×C5—22no—
415C4×C5—34no—
416C4×C5—62no—
417C4×C5—62no—
418Dic5—24no—
419Dic5—24no—
420Dic5—64no—
421Dic5—64no—
422C24—31no—
423C24C2×D3×D511yescharacteristic
424C2×D4—38no—
425C2×D4—34no—
426C22×C4—31no—
427C22×C4—31no—
428C22×C4—31no—
429C22×C4—34no—
430C22×C4—42no—
431C22×C4—52no—
432C22×C4—52no—
433C22×C4—122no—
434C22×C4—158no—
435C22×C4—152no—
436C22×C4—152no—
437C22×C4—158no—
438C22×C4—602no—
439C22×C4—602no—
440C22×C4—602no—
441C22×C4—602no—
442C22×C4D3×Dic514yescomplemented
443C22×C4C2×D3×D511yescharacteristic
444C22×C4C2×D3×D511yescharacteristic
445C4⋊C4—34no—
446C4⋊C4—158no—
447C22⋊C4—34no—
448C22⋊C4—34no—
449C22⋊C4—58no—
450C22⋊C4—158no—
451C42—34no—
452C42—158no—
453C42—202no—
454C42—602no—
455C42—602no—
456C3×C5#227511yescharacteristic, complemented, Hall
457C22×C3—22no—
458C22×C3—24no—
459C22×C3—24no—
460C22×C3—22no—
461C22×C3C2×C4×Dic514yes—
462C22×C3C22×C4×D512yes—
463C22×C3#414412yes—
464C22×C3#414911yescharacteristic
465C22×C3#415011yescharacteristic
466C22×C3C23×Dic511yescharacteristic
467C2×D3—22no—
468C2×D3—24no—
469C2×D3—24no—
470C2×D3—22no—
471C2×D3C2×C4×Dic514yes—
472C3×C4—22no—
473C3×C4—22no—
474C3×C4—104no—
475C3×C4—104no—
476Dic3—22no—
477Dic3—22no—
478Dic3—104no—
479Dic3—104no—
480Dic3C2×C4×Dic514yes—
481C2×C5—24no—
482C2×C5—64no—
483C2×C5C2×C42×D311yescharacteristic
484C2×C5#548611yescharacteristic
485C2×C5#552311yescharacteristic
486C2×C5#554512yes—
487C2×C5#554612yes—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—34no—
492C23—32no—
493C23—61no—
494C23—61no—
495C23—62no—
496C23C4×D3×D514yes—
497C23C2×D3×Dic512yes—
498C23C22×D3×D511yescharacteristic
499D4—316no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—34no—
503C2×C4—32no—
504C2×C4—32no—
505C2×C4—32no—
506C2×C4—44no—
507C2×C4—54no—
508C2×C4—54no—
509C2×C4—61no—
510C2×C4—61no—
511C2×C4—62no—
512C2×C4—102no—
513C2×C4—102no—
514C2×C4—102no—
515C2×C4—102no—
516C2×C4—124no—
517C2×C4—154no—
518C2×C4—154no—
519C2×C4—302no—
520C2×C4—302no—
521C2×C4—302no—
522C2×C4—302no—
523C2×C4—608no—
524C2×C4—608no—
525C2×C4C2×D3×Dic512yes—
526C2×C4C2×D3×Dic512yes—
527C2×C3—24no—
528C2×C3#6587912yes—
529C2×C3#6588012yes—
530C2×C3C22×C4×Dic511yescharacteristic
531C2×C3#6613211yescharacteristic
532C2×C3#6616111yescharacteristic
533D3—24no—
534C5#7343611yescharacteristic, complemented, Sylow
535C22—22no—
536C22—24no—
537C22—24no—
538C22—22no—
539C22—34no—
540C22—62no—
541C22—64no—
542C22—64no—
543C22—62no—
544C22C4×D3×Dic514yes—
545C22#9200111yescharacteristic
546C22C2×C4×D3×D512yes—
547C22#9201911yescharacteristic
548C22C22×D3×Dic511yescharacteristic
549C22#9204912yes—
550C4—22no—
551C4—22no—
552C4—34no—
553C4—62no—
554C4—62no—
555C4—104no—
556C4—104no—
557C4—304no—
558C4—304no—
559C3#1061404811yescharacteristic, complemented, Sylow
560C2—24no—
561C2—64no—
562C2#1175428612yes—
563C2C2×C4×D3×Dic511yescharacteristic
564C2#1175451311yescharacteristic
565C2#1175462912yes—
566C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC2×C3×C5C22×C42
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2275
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. C2×#91115C2semidirect
4. C3×C4×C22⋊Dic5C2semidirect
5. #11749487C2semidirect
6. D3×#3963C2semidirect
7. Dic5×(C2×D3)⋊C4C2semidirect
8. #11748719C2semidirect
9. #11748667C2semidirect
10. #11748643C2semidirect
11. Dic5×Dic3⋊C4C2semidirect
19. C4×C5×#67C4semidirect
25. #67⋊Dic5C4semidirect
42. C4×C22⋊Dic5D3semidirect
53. C22×C3×C4×C5C2×C4semidirect
58. C22×Dic15C2×C4semidirect
67. C2×C4×C5×D3C2×C4semidirect
72. C2×D3×Dic5C2×C4semidirect
73. C5×#217C2×C4semidirect
74. C5×(C2×D3)⋊C4C2×C4semidirect
75. C5×Dic3⋊C4C2×C4semidirect
76. C4×C5×Dic3C2×C4semidirect
77. C3×C22⋊Dic5C2×C4semidirect
79. Dic3⋊Dic5C2×C4semidirect
80. (C2×D3)⋊Dic5C2×C4semidirect
83. Dic3×Dic5C2×C4semidirect
144. C5×#67C42semidirect
168. C4×#67Dic5semidirect
195. C22×C4×C5C4×D3semidirect
213. C22⋊Dic5C4×D3semidirect
259. C22×C3×C4C2×Dic5semidirect
276. C2×C4×D3C2×Dic5semidirect
279. #217C2×Dic5semidirect
281. (C2×D3)⋊C4C2×Dic5semidirect
283. Dic3⋊C4C2×Dic5semidirect
287. C4×Dic3C2×Dic5semidirect
381. #67C4×Dic5semidirect
442. C22×C4D3×Dic5semidirect
456. C3×C5#2275semidirect
534. C5#73436semidirect
559. C3#10614048semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×#672
C2×#67⋊Dic52
C2×#911152
C3×C4×C22⋊Dic52
#117494872
D3×#39632
Dic5×(C2×D3)⋊C42
#117487192
#117486672
#117486432
Dic5×Dic3⋊C42
#106140483
#734365