Finite Group Databasebeta

← #14327147

Subgroups — #14327147

Order 1920.

1408 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×#67C211yesmaximal, characteristic
2C2×Dic5×#67C212yesmaximal
3#11751313C211yesmaximal, characteristic, complemented
4C2×C3×#3963C211yesmaximal, characteristic, complemented
5#11749509C212yesmaximal, complemented
6#11748903C212yesmaximal, complemented
7D3×#3963C211yesmaximal, characteristic, complemented
8#11748782C211yesmaximal, characteristic, complemented
9#11748693C212yesmaximal, complemented
10#11748667C211yesmaximal, characteristic, complemented
11#11748600C211yesmaximal, characteristic, complemented
12#10614064—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C5×#67C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C23×C3×Dic5C2212yes—
17C22×D3×Dic5C2212yes—
18C2×#6719C2212yes—
19C2×C4⋊Dic15C2212yes—
20C2×C5×#217C2211yescharacteristic
21C4×C5×#67C418yescomplemented
22C2×C5×(C2×D3)⋊C4C2211yescharacteristic
23C2×C5×Dic3⋊C4C2211yescharacteristic
24C2×C4×C5×Dic3C2211yescharacteristic
25Dic5×#67—28no—
26C2×Dic3⋊Dic5C2212yes—
27C2×Dic3⋊Dic5C2212yes—
28C2×Dic3⋊Dic5C2212yes—
29C2×(C2×D3)⋊Dic5C2212yes—
30C2×Dic3×Dic5C2212yes—
31#91115C2211yescharacteristic
32#91115C2211yescharacteristic
33C3×#3963C2211yescharacteristic
34C3×#3963C2212yes—
35C3×#3963C2211yescharacteristic
36#90994C2212yes—
37#90994C2212yes—
38#73369—51nomaximal, Hall
39C2×C4×C5×D4—31no—
40C2×D4×Dic5—32no—
41#65501—31no—
42#65501—31no—
43C2×#3963—31no—
44C2×#3963D311yescharacteristic, complemented
45#65274—32no—
46#65239—32no—
47#65239—32no—
48#65225—31no—
49C4×C4⋊Dic5—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×Dic15C2312yes—
57C22×Dic15C2312yes—
58C2×C5×#67C2×C414yes—
59C2×C5×#67D414yes—
60C2×C5×#67Q814yes—
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2311yescharacteristic
63C22×C5×Dic3C2311yescharacteristic
64C2×C4×C5×D3—42no—
65C2×C4×C5×D3C2×C414yescomplemented
66C22×C3×Dic5—24no—
67C22×C3×Dic5—24no—
68C22×C3×Dic5—42no—
69C22×C3×Dic5C2312yes—
70C22×C3×Dic5C2312yes—
71C2×D3×Dic5—24no—
72C2×D3×Dic5—24no—
73C2×D3×Dic5—42no—
74#6719—24no—
75C4⋊Dic15—42no—
76C5×#217C2×C414yescomplemented
77C5×(C2×D3)⋊C4C2×C414yescomplemented
78C5×Dic3⋊C4C2×C414yescomplemented
79C4×C5×Dic3C2×C414yescomplemented
80Dic3⋊Dic5—24no—
81Dic3⋊Dic5—24no—
82Dic3⋊Dic5—42no—
83(C2×D3)⋊Dic5—24no—
84Dic3×Dic5—24no—
85C2×C4×#67—52no—
86C2×C4×#67D511yescharacteristic
87C2×C3×#95—51no—
88#5212—51no—
89#5210—52no—
90#4668—52no—
91#4667—51no—
92D3×#95—51no—
93#4650—51no—
94#4649—51no—
95#4647—52no—
96C22×C5×D4—31no—
97C23×C4×C5—31no—
98C23×C4×C5C2×D311yescharacteristic
99C23×Dic5—32no—
100C23×Dic5C2×D312yes—
101C4×C5×D4—38no—
102C2×C5×C4⋊C4—31no—
103C2×C5×C22⋊C4—31no—
104C2×C5×C22⋊C4—31no—
105C2×C42×C5—31no—
106C2×C22⋊Dic5—32no—
107C2×C22⋊Dic5—32no—
108D4×Dic5—68no—
109C2×C4⋊Dic5—32no—
110C2×C4⋊Dic5—32no—
111C2×C4⋊Dic5—32no—
112C2×C4⋊Dic5—32no—
113C2×C4×Dic5—32no—
114#3963—31no—
115#3963—31no—
116#3963—32no—
117#3963—32no—
118#3963C2×D311yescharacteristic
119#3963C2×D311yescharacteristic
120#3963C2×D312yes—
121#2349—151noSylow
122C23×C3×C5—22no—
123C23×C3×C5—22no—
124C23×C3×C5C22×C412yes—
125C23×C3×C5C2×D412yes—
126C23×C3×C5C2×Q812yes—
127C23×C3×C5C2411yescharacteristic
128C22×C5×D3—22no—
129C22×C5×D3—22no—
130C22×C5×D3C22×C412yes—
131C22×C5×D3C2×D412yes—
132C22×C5×D3C2×Q812yes—
133C2×C3×C4×C5—22no—
134C2×C3×C4×C5—22no—
135C2×C3×C4×C5—44no—
136C2×C3×C4×C5C22×C412yes—
137C2×C3×C4×C5C22×C412yes—
138C2×Dic15—22no—
139C2×Dic15—22no—
140C2×Dic15—22no—
141C2×Dic15—22no—
142C2×Dic15—22no—
143C2×Dic15—22no—
144C5×#67C4⋊C4116yescomplemented
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3C22×C412yes—
148C2×C5×Dic3C22×C412yes—
149C2×C5×Dic3C22×C412yes—
150C2×C5×Dic3C2×D412yes—
151C2×C5×Dic3C2×Q812yes—
152C4×C5×D3—44no—
153C2×C3×Dic5—22no—
154C2×C3×Dic5—22no—
155C2×C3×Dic5—22no—
156C2×C3×Dic5—22no—
157C2×C3×Dic5—22no—
158C2×C3×Dic5—48no—
159C2×C3×Dic5#4114yes—
160D3×Dic5—48no—
161C23×C3×C4—52no—
162C23×C3×C4C2×D511yescharacteristic
163C22×#67C2×D511yescharacteristic
164C22×C4×D3—52no—
165C22×C4×D3C2×D511yescharacteristic
166C2×#217—52no—
167C2×#217C2×D511yescharacteristic
168C4×#67—108no—
169C4×#67Dic518yescomplemented
170C2×(C2×D3)⋊C4—52no—
171C2×(C2×D3)⋊C4C2×D511yescharacteristic
172C2×C4⋊Dic3—52no—
173C2×Dic3⋊C4—52no—
174C2×Dic3⋊C4—52no—
175C2×Dic3⋊C4—52no—
176C2×Dic3⋊C4C2×D511yescharacteristic
177C2×C4×Dic3—52no—
178C2×C4×Dic3C2×D511yescharacteristic
179C3×#95—52no—
180C3×#95—51no—
181C3×#95—51no—
182C3⋊#95—51no—
183C3⋊#95—51no—
184C3⋊#95—52no—
185C3⋊#95—52no—
186C24×C5—31no—
187C24×C5C22×D311yescharacteristic
188C2×C5×D4—34no—
189C2×C5×D4—34no—
190C2×C5×D4—34no—
191C22×C4×C5—31no—
192C22×C4×C5—31no—
193C22×C4×C5—31no—
194C22×C4×C5—34no—
195C22×C4×C5—42no—
196C22×C4×C5—122no—
197C22×C4×C5C4×D314yescomplemented
198C22×C4×C5C22×D311yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C22×Dic5—24no—
201C22×Dic5—24no—
202C22×Dic5—32no—
203C22×Dic5—32no—
204C22×Dic5—42no—
205C22×Dic5—64no—
206C22×Dic5—64no—
207C22×Dic5—122no—
208C22×Dic5C22×D312yes—
209C22×Dic5C22×D312yes—
210C5×C4⋊C4—34no—
211C5×C22⋊C4—34no—
212C5×C22⋊C4—34no—
213C42×C5—34no—
214C22⋊Dic5—64no—
215C22⋊Dic5—64no—
216C4⋊Dic5—64no—
217C4⋊Dic5—64no—
218C4⋊Dic5—122no—
219C4⋊Dic5—122no—
220C4×Dic5—64no—
221C2×C4×D4—31no—
222C2×C4×D4—152no—
223#389—152no—
224#385—152no—
225#385—152no—
226#382—151no—
227#380—151no—
228#380—151no—
229C4×C4⋊C4—151no—
230C2×#95—51no—
231C2×#95—151no—
232C22×C3×C5—22no—
233C22×C3×C5—22no—
234C22×C3×C5—24no—
235C22×C3×C5—24no—
236C22×C3×C5C2×C4⋊C414yes—
237C22×C3×C5C23×C411yescharacteristic
238C22×C3×C5C22×D411yescharacteristic
239C22×C3×C5C22×Q811yescharacteristic
240C22×C3×C5C2×#4112yes—
241C22×C3×C5H(5,𝔽2)12yes—
242C2×C5×D3—22no—
243C2×C5×D3—22no—
244C2×C5×D3—24no—
245C2×C5×D3—24no—
246C2×C5×D3C2×C4⋊C414yes—
247C3×C4×C5—22no—
248C3×C4×C5—22no—
249Dic15—42no—
250Dic15—42no—
251C3×Dic5—24no—
252C3×Dic5—42no—
253C5×Dic3—22no—
254C5×Dic3—22no—
255C5×Dic3C2×C4⋊C414yes—
256C24×C3C22×D511yescharacteristic
257C23×D3C22×D511yescharacteristic
258C22×C3×C4—42no—
259C22×C3×C4—52no—
260C22×C3×C4—52no—
261C22×C3×C4—104no—
262C22×C3×C4—104no—
263C22×C3×C4—202no—
264C22×C3×C4C2×Dic514yescomplemented
265C22×C3×C4C22×D511yescharacteristic
266C22×C3×C4C22×D511yescharacteristic
267C2×#67Dic1014yes—
268C2×#67D2014yes—
269C2×#67C2×Dic514yes—
270C22×Dic3—52no—
271C22×Dic3—52no—
272C22×Dic3C22×D511yescharacteristic
273C22×Dic3C22×D511yescharacteristic
274C22×Dic3C22×D511yescharacteristic
275C2×C4×D3—42no—
276C2×C4×D3—104no—
277C2×C4×D3—104no—
278C2×C4×D3—202no—
279C2×C4×D3C2×Dic514yescomplemented
280#217—104no—
281#217C2×Dic514yescomplemented
282(C2×D3)⋊C4—104no—
283(C2×D3)⋊C4C2×Dic514yescomplemented
284C4⋊Dic3—202no—
285Dic3⋊C4—104no—
286Dic3⋊C4—104no—
287Dic3⋊C4—202no—
288Dic3⋊C4C2×Dic514yescomplemented
289C4×Dic3—104no—
290C4×Dic3C2×Dic514yescomplemented
291C23×C5—22no—
292C23×C5—22no—
293C23×C5—32no—
294C23×C5—32no—
295C23×C5—32no—
296C23×C5—62no—
297C23×C5—62no—
298C23×C5C2×C4×D312yes—
299C23×C5D3×D412yes—
300C23×C5D3×Q812yes—
301C23×C5C23×D311yescharacteristic
302C5×D4—316no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—32no—
306C2×C4×C5—32no—
307C2×C4×C5—32no—
308C2×C4×C5—32no—
309C2×C4×C5—32no—
310C2×C4×C5—44no—
311C2×C4×C5—62no—
312C2×C4×C5—62no—
313C2×C4×C5—124no—
314C2×C4×C5C2×C4×D312yes—
315C2×C4×C5C2×C4×D312yes—
316C2×Dic5—22no—
317C2×Dic5—22no—
318C2×Dic5—22no—
319C2×Dic5—22no—
320C2×Dic5—22no—
321C2×Dic5—48no—
322C2×Dic5—62no—
323C2×Dic5—62no—
324C2×Dic5—62no—
325C2×Dic5—62no—
326C2×Dic5—62no—
327C2×Dic5—62no—
328C2×Dic5—128no—
329C2×Dic5#23514yes—
330C22×D4—31no—
331C23×C4—31no—
332C23×C4—52no—
333C23×C4—152no—
334C23×C4D3×D511yescharacteristic
335C4×D4—38no—
336C4×D4—308no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—152no—
339C2×C4⋊C4—152no—
340C2×C4⋊C4—152no—
341C2×C4⋊C4—152no—
342C2×C22⋊C4—31no—
343C2×C22⋊C4—31no—
344C2×C22⋊C4—152no—
345C2×C22⋊C4—152no—
346C2×C42—31no—
347C2×C42—152no—
348#95—51no—
349#95—51no—
350#95—52no—
351#95—152no—
352#95—152no—
353#95—151no—
354#95—151no—
355C2×C3×C5—24no—
356C2×C3×C5C22×C4⋊C411yescharacteristic
357C2×C3×C5C4×#4111yescharacteristic
358C2×C3×C5#51811yescharacteristic
359C2×C3×C5#54612yes—
360C2×C3×C5#55412yes—
361C5×D3—24no—
362C23×C3—22no—
363C23×C3—22no—
364C23×C3C2×Dic1012yes—
365C23×C3C2×D2012yes—
366C23×C3C22×Dic512yes—
367C23×C3C23×D511yescharacteristic
368C22×D3—22no—
369C22×D3—22no—
370C22×D3C2×Dic1012yes—
371C22×D3C2×D2012yes—
372C22×D3C22×Dic512yes—
373C2×C3×C4—22no—
374C2×C3×C4—22no—
375C2×C3×C4—44no—
376C2×C3×C4—54no—
377C2×C3×C4—102no—
378C2×C3×C4—102no—
379C2×C3×C4—102no—
380C2×C3×C4—102no—
381C2×C3×C4—102no—
382C2×C3×C4—208no—
383C2×C3×C4C22×Dic512yes—
384C2×C3×C4C22×Dic512yes—
385#67C4⋊Dic5116yescomplemented
386C2×Dic3—22no—
387C2×Dic3—22no—
388C2×Dic3—102no—
389C2×Dic3—102no—
390C2×Dic3—102no—
391C2×Dic3—102no—
392C2×Dic3—102no—
393C2×Dic3—102no—
394C2×Dic3C2×Dic1012yes—
395C2×Dic3C2×D2012yes—
396C2×Dic3C22×Dic512yes—
397C2×Dic3C22×Dic512yes—
398C2×Dic3C22×Dic512yes—
399C4×D3—44no—
400C4×D3—208no—
401C22×C5—22no—
402C22×C5—22no—
403C22×C5—24no—
404C22×C5—24no—
405C22×C5—34no—
406C22×C5—62no—
407C22×C5—62no—
408C22×C5—64no—
409C22×C5—64no—
410C22×C5D3×C4⋊C414yes—
411C22×C5C22×C4×D311yescharacteristic
412C22×C5C2×#23512yes—
413C22×C5C2×D3×D411yescharacteristic
414C22×C5#100412yes—
415C22×C5C2×D3×Q811yescharacteristic
416C4×C5—22no—
417C4×C5—22no—
418C4×C5—34no—
419C4×C5—62no—
420C4×C5—62no—
421Dic5—24no—
422Dic5—42no—
423Dic5—122no—
424Dic5—122no—
425C24—31no—
426C24C2×D3×D511yescharacteristic
427C2×D4—34no—
428C2×D4—34no—
429C2×D4—34no—
430C22×C4—31no—
431C22×C4—31no—
432C22×C4—31no—
433C22×C4—34no—
434C22×C4—42no—
435C22×C4—52no—
436C22×C4—52no—
437C22×C4—104no—
438C22×C4—104no—
439C22×C4—122no—
440C22×C4—152no—
441C22×C4—152no—
442C22×C4—202no—
443C22×C4—304no—
444C22×C4—304no—
445C22×C4—602no—
446C22×C4D3×Dic514yescomplemented
447C22×C4C2×D3×D511yescharacteristic
448C22×C4C2×D3×D511yescharacteristic
449C4⋊C4—34no—
450C4⋊C4—304no—
451C4⋊C4—304no—
452C4⋊C4—602no—
453C4⋊C4—602no—
454C22⋊C4—34no—
455C22⋊C4—34no—
456C22⋊C4—304no—
457C22⋊C4—304no—
458C42—34no—
459C42—304no—
460C3×C5#234911yescharacteristic, complemented, Hall
461C22×C3—24no—
462C22×C3—22no—
463C22×C3—24no—
464C22×C3—22no—
465C22×C3C2×C4⋊Dic514yes—
466C22×C3C22×Dic1011yescharacteristic
467C22×C3C22×D2011yescharacteristic
468C22×C3#414412yes—
469C22×C3D5×#4112yes—
470C22×C3C23×Dic511yescharacteristic
471C2×D3—24no—
472C2×D3—22no—
473C2×D3—24no—
474C2×D3—22no—
475C2×D3C2×C4⋊Dic514yes—
476C3×C4—22no—
477C3×C4—22no—
478C3×C4—104no—
479C3×C4—202no—
480Dic3—22no—
481Dic3—22no—
482Dic3—202no—
483Dic3—202no—
484Dic3C2×C4⋊Dic514yes—
485C2×C5—24no—
486C2×C5—64no—
487C2×C5C4×#23511yescharacteristic
488C2×C5#548611yescharacteristic
489C2×C5#549012yes—
490C2×C5C2×D3×C4⋊C411yescharacteristic
491C2×C5#551112yes—
492C23—22no—
493C23—22no—
494C23—32no—
495C23—32no—
496C23—32no—
497C23—62no—
498C23—62no—
499C23D3×Dic1012yes—
500C23D3×D2012yes—
501C23C2×D3×Dic512yes—
502C23C22×D3×D511yescharacteristic
503D4—316no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—32no—
507C2×C4—32no—
508C2×C4—32no—
509C2×C4—32no—
510C2×C4—32no—
511C2×C4—44no—
512C2×C4—54no—
513C2×C4—62no—
514C2×C4—62no—
515C2×C4—102no—
516C2×C4—102no—
517C2×C4—102no—
518C2×C4—102no—
519C2×C4—102no—
520C2×C4—124no—
521C2×C4—208no—
522C2×C4—302no—
523C2×C4—302no—
524C2×C4—302no—
525C2×C4—302no—
526C2×C4—302no—
527C2×C4—302no—
528C2×C4—608no—
529C2×C4C2×D3×Dic512yes—
530C2×C4C2×D3×Dic512yes—
531C2×C3—24no—
532C2×C3#6587312yes—
533C2×C3#6588812yes—
534C2×C3C22×C4⋊Dic511yescharacteristic
535C2×C3#6613211yescharacteristic
536C2×C3#41×Dic511yescharacteristic
537D3—24no—
538C5#7336911yescharacteristic, complemented, Sylow
539C22—22no—
540C22—24no—
541C22—22no—
542C22—24no—
543C22—34no—
544C22—62no—
545C22—64no—
546C22—62no—
547C22—64no—
548C22D3×C4⋊Dic514yes—
549C22C2×D3×Dic1011yescharacteristic
550C22C2×D3×D2011yescharacteristic
551C22D5×#23512yes—
552C22C22×D3×Dic511yescharacteristic
553C22#9204912yes—
554C4—22no—
555C4—22no—
556C4—34no—
557C4—62no—
558C4—62no—
559C4—104no—
560C4—202no—
561C4—602no—
562C4—602no—
563C3#1061406411yescharacteristic, complemented, Sylow
564C2—24no—
565C2—64no—
566C2C2×D3×C4⋊Dic511yescharacteristic
567C2Dic5×#23511yescharacteristic
568C2#1175441112yes—
569C2#1175465912yes—
570C2#1175541011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC23×C3×C4×C5C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC23×C4D3×D5
hypocenterC3×C5#2349
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #11751313C2semidirect
4. C2×C3×#3963C2semidirect
5. #11749509C2semidirect
6. #11748903C2semidirect
7. D3×#3963C2semidirect
8. #11748782C2semidirect
9. #11748693C2semidirect
10. #11748667C2semidirect
11. #11748600C2semidirect
21. C4×C5×#67C4semidirect
44. C2×#3963D3semidirect
53. C22×C3×C4×C5C2×C4semidirect
65. C2×C4×C5×D3C2×C4semidirect
76. C5×#217C2×C4semidirect
77. C5×(C2×D3)⋊C4C2×C4semidirect
78. C5×Dic3⋊C4C2×C4semidirect
79. C4×C5×Dic3C2×C4semidirect
144. C5×#67C4⋊C4semidirect
169. C4×#67Dic5semidirect
197. C22×C4×C5C4×D3semidirect
264. C22×C3×C4C2×Dic5semidirect
279. C2×C4×D3C2×Dic5semidirect
281. #217C2×Dic5semidirect
283. (C2×D3)⋊C4C2×Dic5semidirect
288. Dic3⋊C4C2×Dic5semidirect
290. C4×Dic3C2×Dic5semidirect
385. #67C4⋊Dic5semidirect
446. C22×C4D3×Dic5semidirect
460. C3×C5#2349semidirect
538. C5#73369semidirect
563. C3#10614064semidirect

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×Dic5×#672
#117513132
C2×C3×#39632
#117495092
#117489032
D3×#39632
#117487822
#117486932
#117486672
#117486002
#106140643
#733695