Finite Group Databasebeta

← #14296874

Subgroups — #14296874

Order 1920.

1224 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#711C211yesmaximal, characteristic
2C2×#91118C211yesmaximal, characteristic, complemented
3C2×C5×#834C211yesmaximal, characteristic, complemented
4C2×#90995C212yesmaximal, complemented
5#11749471C212yesmaximal, complemented
6#10600820—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C22×C3×C22⋊D5C411yescharacteristic, complemented
9C22×C3×C22⋊D5C2211yescharacteristic
10C23×C3×Dic5C411yescharacteristic, complemented
11C23×C3×Dic5C2211yescharacteristic
12C2×C3×#711—22no—
13C2×C3×#711—22no—
14C2×C3×#711—24no—
15C2×C3×#711—24no—
16C22×C3×C4×D5C411yescharacteristic, complemented
17C22×C3×Dic10C411yescharacteristic, complemented
18C2×#6719C2212yes—
19C2×C5×#217C2212yes—
20#91118—22no—
21C5×#834—22no—
22#90995—24no—
23#90994—24no—
24#72139—51nomaximal, Hall
25C22×#711D311yescharacteristic
26C2×C5×#99—31no—
27C2×#3966—31no—
28C2×#3938—32no—
29#65232—32no—
30C24×C3×C5C2×C411yescharacteristic
31C24×C3×C5C2311yescharacteristic
32C23×C3×D5C2×C411yescharacteristic
33C2×C3×C5×D4—22no—
34C2×C3×C5×D4—22no—
35C2×C3×C5×D4D412yes—
36C2×C3×C5×D4D412yes—
37C22×C3×C4×C5C2×C411yescharacteristic
38C22×Dic15—22no—
39C22×C5×Dic3—22no—
40C2×C3×C22⋊D5—22no—
41C2×C3×C22⋊D5—22no—
42C2×C3×C22⋊D5—21no—
43C2×C3×C22⋊D5—21no—
44C2×C3×C22⋊D5—22no—
45C2×C3×C22⋊D5—22no—
46C2×C3×C22⋊D5D414yes—
47C22×C3×Dic5—22no—
48C22×C3×Dic5—21no—
49C22×C3×Dic5—22no—
50C22×C3×Dic5—21no—
51C22×C3×Dic5—22no—
52C22×C3×Dic5—22no—
53C22×C3×Dic5C2×C411yescharacteristic
54C22×C3×Dic5C2×C411yescharacteristic
55C22×C3×Dic5C2×C411yescharacteristic
56C22×C3×Dic5D414yes—
57C3×#711—216no—
58C3×#711—216no—
59C2×C3×C4×D5—22no—
60C2×C3×C4×D5—22no—
61C2×C3×C4×D5—22no—
62C2×C3×Dic10—22no—
63C2×C3×Dic10—22no—
64C2×C3×Dic10—22no—
65#6719—22no—
66#6719—22no—
67C5×#217—22no—
68C5×#217—22no—
69C22×C3×#41—51no—
70C2×#834—51no—
71C2×#834—52no—
72C2×#834D511yescharacteristic, complemented
73#5211—52no—
74C22×C5×D4C2×D311yescharacteristic
75C22×C22⋊D5Dic311yescharacteristic, complemented
76C22×C22⋊D5C2×D311yescharacteristic
77C23×Dic5Dic311yescharacteristic, complemented
78C23×Dic5C2×D311yescharacteristic
79C2×#711—22no—
80C2×#711—22no—
81C2×#711—24no—
82C2×#711—24no—
83C22×C4×D5Dic311yescharacteristic, complemented
84C22×Dic10Dic311yescharacteristic, complemented
85C2×C5×C22⋊C4—32no—
86C2×C22⋊Dic5—32no—
87C5×#99—62no—
88#3966—62no—
89#3963—64no—
90#3938—64no—
91#1782—151noSylow
92C23×C3×C5—21no—
93C23×C3×C5—21no—
94C23×C3×C5—42no—
95C23×C3×C5—42no—
96C23×C3×C5C22⋊C412yes—
97C23×C3×C5C22×C411yescharacteristic
98C23×C3×C5C2×D412yes—
99C23×C3×C5C2×D411yescharacteristic
100C23×C3×C5C2×D412yes—
101C23×C3×C5C2×D411yescharacteristic
102C22×C3×D5—21no—
103C22×C3×D5—21no—
104C22×C3×D5—42no—
105C22×C3×D5C22⋊C412yes—
106C3×C5×D4—24no—
107C3×C5×D4—24no—
108C2×C3×C4×C5—21no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5C22⋊C412yes—
111C2×Dic15—44no—
112C2×Dic15—42no—
113C2×C5×Dic3—44no—
114C2×C5×Dic3—42no—
115C3×C22⋊D5—28no—
116C3×C22⋊D5—24no—
117C3×C22⋊D5—24no—
118C2×C3×Dic5—28no—
119C2×C3×Dic5—21no—
120C2×C3×Dic5—21no—
121C2×C3×Dic5—21no—
122C2×C3×Dic5—21no—
123C2×C3×Dic5—21no—
124C2×C3×Dic5—21no—
125C2×C3×Dic5—24no—
126C2×C3×Dic5—24no—
127C2×C3×Dic5C22⋊C412yes—
128C2×C3×Dic5C22⋊C412yes—
129C2×C3×Dic5C22⋊C412yes—
130C3×C4×D5—28no—
131C3×Dic10—28no—
132C2×C3×#41—104no—
133C2×C3×#41—104no—
134C2×C3×#41—102no—
135C2×C3×#41—102no—
136C22×C3×Q8—51no—
137C22×C3×D4—51no—
138C22×C3×D4—51no—
139C22×C3×D4C2×D511yescharacteristic
140C23×C3×C4—51no—
141C23×C3×C4—51no—
142C23×C3×C4—51no—
143C2×#217—52no—
144C2×#217C2×D512yes—
145#834—22no—
146#834—104no—
147#834—102no—
148C3⋊#95—104no—
149C24×C5C2×Dic311yescharacteristic
150C24×C5C22×D311yescharacteristic
151C23×D5C2×Dic311yescharacteristic
152C2×C5×D4—22no—
153C2×C5×D4—22no—
154C2×C5×D4#6712yes—
155C2×C5×D4#6712yes—
156C22×C4×C5—62no—
157C22×C4×C5C2×Dic311yescharacteristic
158C2×C22⋊D5—22no—
159C2×C22⋊D5—21no—
160C2×C22⋊D5—21no—
161C2×C22⋊D5—22no—
162C2×C22⋊D5—22no—
163C2×C22⋊D5—22no—
164C2×C22⋊D5#6714yes—
165C22×Dic5—22no—
166C22×Dic5—21no—
167C22×Dic5—21no—
168C22×Dic5—22no—
169C22×Dic5—22no—
170C22×Dic5—22no—
171C22×Dic5—62no—
172C22×Dic5C2×Dic311yescharacteristic
173C22×Dic5C2×Dic311yescharacteristic
174C22×Dic5C2×Dic311yescharacteristic
175C22×Dic5#6714yes—
176#711—216no—
177#711—216no—
178C2×C4×D5—22no—
179C2×C4×D5—22no—
180C2×C4×D5—22no—
181C2×Dic10—22no—
182C2×Dic10—22no—
183C2×Dic10—22no—
184C5×C22⋊C4—62no—
185C5×C22⋊C4—62no—
186C22⋊Dic5—62no—
187C22⋊Dic5—62no—
188C22×#41—51no—
189C2×#99—31no—
190C2×#99—152no—
191C2×#99—151no—
192#381—152no—
193C22×C3×C5—24no—
194C22×C3×C5—22no—
195C22×C3×C5—22no—
196C22×C3×C5—41no—
197C22×C3×C5—42no—
198C22×C3×C5—41no—
199C22×C3×C5—42no—
200C22×C3×C5—42no—
201C22×C3×C5—42no—
202C22×C3×C5C2×C22⋊C411yescharacteristic
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C22×C3×C5C2×C22⋊C411yescharacteristic
205C22×C3×C5#12012yes—
206C22×C3×C5#12012yes—
207C2×C3×D5—22no—
208C2×C3×D5—42no—
209C2×C3×D5—42no—
210C2×C3×D5—42no—
211C3×C4×C5—22no—
212Dic15—82no—
213C3×Dic5—22no—
214C3×Dic5—22no—
215C3×Dic5—22no—
216C5×Dic3—82no—
217C24×C3—51no—
218C24×C3C4×D511yescharacteristic
219C24×C3C22×D511yescharacteristic
220C3×#41—1016no—
221C3×#41—1016no—
222C2×C3×Q8—102no—
223C2×C3×Q8—102no—
224C2×C3×Q8—102no—
225C2×C3×D4—22no—
226C2×C3×D4—22no—
227C2×C3×D4—54no—
228C2×C3×D4—102no—
229C2×C3×D4—102no—
230C2×C3×D4—102no—
231C2×C3×D4—101no—
232C2×C3×D4—102no—
233C2×C3×D4—101no—
234C2×C3×D4D2012yes—
235C2×C3×D4C22⋊D512yes—
236C22×C3×C4—51no—
237C22×C3×C4—51no—
238C22×C3×C4—51no—
239C22×C3×C4—54no—
240C22×C3×C4—102no—
241C22×C3×C4—102no—
242C22×C3×C4—102no—
243C22×C3×C4—102no—
244C22×C3×C4—102no—
245C22×C3×C4—101no—
246C22×C3×C4—102no—
247C22×C3×C4—101no—
248C22×C3×C4—102no—
249C22×C3×C4C4×D511yescharacteristic
250C22×Dic3—22no—
251C22×Dic3—102no—
252#217—22no—
253#217—22no—
254#217—102no—
255#217—102no—
256C23×C5—21no—
257C23×C5—21no—
258C23×C5—42no—
259C23×C5—42no—
260C23×C5#21712yes—
261C23×C5C22×Dic311yescharacteristic
262C23×C5C2×#6711yescharacteristic
263C23×C5C2×#6711yescharacteristic
264C23×C5C2×#6712yes—
265C23×C5C2×#6712yes—
266C22×D5—21no—
267C22×D5—21no—
268C22×D5—42no—
269C22×D5#21712yes—
270C5×D4—24no—
271C5×D4—24no—
272C2×C4×C5—21no—
273C2×C4×C5—21no—
274C2×C4×C5—124no—
275C2×C4×C5—122no—
276C2×C4×C5#21712yes—
277C22⋊D5—28no—
278C22⋊D5—24no—
279C22⋊D5—24no—
280C2×Dic5—28no—
281C2×Dic5—21no—
282C2×Dic5—21no—
283C2×Dic5—21no—
284C2×Dic5—21no—
285C2×Dic5—21no—
286C2×Dic5—21no—
287C2×Dic5—24no—
288C2×Dic5—24no—
289C2×Dic5—124no—
290C2×Dic5—122no—
291C2×Dic5#21712yes—
292C2×Dic5#21712yes—
293C2×Dic5#21712yes—
294C4×D5—28no—
295Dic10—28no—
296C2×#41—104no—
297C2×#41—104no—
298C2×#41—102no—
299C2×#41—102no—
300C22×Q8—51no—
301C22×D4—51no—
302C22×D4—51no—
303C22×D4D3×D511yescharacteristic
304C23×C4—51no—
305C23×C4—51no—
306C23×C4—51no—
307C2×C22⋊C4—32no—
308C2×C22⋊C4—152no—
309#99—62no—
310#99—304no—
311#99—302no—
312#95—304no—
313C2×C3×C5—22no—
314C2×C3×C5—22no—
315C2×C3×C5—21no—
316C2×C3×C5—21no—
317C2×C3×C5—42no—
318C2×C3×C5#37911yescharacteristic
319C2×C3×C5#41012yes—
320C3×D5—42no—
321C23×C3—21no—
322C23×C3—21no—
323C23×C3—42no—
324C23×C3—42no—
325C23×C3—52no—
326C23×C3—101no—
327C23×C3—101no—
328C23×C3—202no—
329C23×C3#68512yes—
330C23×C3C2×C4×D511yescharacteristic
331C23×C3C2×D2011yescharacteristic
332C23×C3D4×D512yes—
333C23×C3D4×D512yes—
334C23×C3C2×C22⋊D511yescharacteristic
335C3×Q8—108no—
336C3×D4—24no—
337C3×D4—24no—
338C3×D4—108no—
339C3×D4—104no—
340C3×D4—104no—
341C2×C3×C4—21no—
342C2×C3×C4—21no—
343C2×C3×C4—52no—
344C2×C3×C4—52no—
345C2×C3×C4—52no—
346C2×C3×C4—108no—
347C2×C3×C4—108no—
348C2×C3×C4—101no—
349C2×C3×C4—101no—
350C2×C3×C4—101no—
351C2×C3×C4—104no—
352C2×C3×C4—101no—
353C2×C3×C4—101no—
354C2×C3×C4—101no—
355C2×C3×C4—104no—
356C2×C3×C4#68512yes—
357C2×Dic3—44no—
358C2×Dic3—42no—
359C2×Dic3—204no—
360C2×Dic3—202no—
361C22×C5—24no—
362C22×C5—22no—
363C22×C5—22no—
364C22×C5—41no—
365C22×C5—41no—
366C22×C5—42no—
367C22×C5—42no—
368C22×C5—42no—
369C22×C5—42no—
370C22×C5C2×#21711yescharacteristic
371C22×C5C2×#21711yescharacteristic
372C22×C5C2×#21711yescharacteristic
373C22×C5#95312yes—
374C22×C5#95312yes—
375C2×D5—22no—
376C2×D5—42no—
377C2×D5—42no—
378C2×D5—42no—
379C4×C5—22no—
380C4×C5—242no—
381Dic5—22no—
382Dic5—22no—
383Dic5—22no—
384Dic5—242no—
385C24—51no—
386C24D5×Dic311yescharacteristic
387C24C2×D3×D511yescharacteristic
388#41—1016no—
389#41—1016no—
390C2×Q8—102no—
391C2×Q8—102no—
392C2×Q8—102no—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—54no—
396C2×D4—102no—
397C2×D4—102no—
398C2×D4—102no—
399C2×D4—101no—
400C2×D4—101no—
401C2×D4—102no—
402C2×D4#120112yes—
403C2×D4#120212yes—
404C22×C4—51no—
405C22×C4—51no—
406C22×C4—51no—
407C22×C4—54no—
408C22×C4—62no—
409C22×C4—102no—
410C22×C4—102no—
411C22×C4—102no—
412C22×C4—102no—
413C22×C4—102no—
414C22×C4—101no—
415C22×C4—101no—
416C22×C4—102no—
417C22×C4—102no—
418C22×C4—302no—
419C22×C4D5×Dic311yescharacteristic
420C22⋊C4—62no—
421C22⋊C4—62no—
422C22⋊C4—302no—
423C22⋊C4—302no—
424C3×C5#178211yescharacteristic, complemented, Hall
425C22×C3—24no—
426C22×C3—22no—
427C22×C3—22no—
428C22×C3—41no—
429C22×C3—42no—
430C22×C3—41no—
431C22×C3—42no—
432C22×C3—42no—
433C22×C3—42no—
434C22×C3—102no—
435C22×C3—202no—
436C22×C3—202no—
437C22×C3—202no—
438C22×C3D5×C22⋊C411yescharacteristic
439C22×C3D5×C22⋊C411yescharacteristic
440C22×C3#402812yes—
441C22×C3C2×#68511yescharacteristic
442C22×C3#408312yes—
443C3×C4—22no—
444C3×C4—102no—
445C3×C4—102no—
446C3×C4—102no—
447Dic3—82no—
448Dic3—402no—
449C2×C5—22no—
450C2×C5—22no—
451C2×C5—21no—
452C2×C5—21no—
453C2×C5—42no—
454C2×C5#524012yes—
455C2×C5#524711yescharacteristic
456D5—42no—
457C23—21no—
458C23—21no—
459C23—42no—
460C23—42no—
461C23—52no—
462C23—101no—
463C23—101no—
464C23—202no—
465C23#666512yes—
466C23C2×D5×Dic311yescharacteristic
467C23C2×#120111yescharacteristic
468C23C2×#120211yescharacteristic
469C23D5×#6712yes—
470C23D5×#6712yes—
471Q8—108no—
472D4—24no—
473D4—24no—
474D4—108no—
475D4—104no—
476D4—104no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—52no—
480C2×C4—52no—
481C2×C4—52no—
482C2×C4—108no—
483C2×C4—108no—
484C2×C4—101no—
485C2×C4—101no—
486C2×C4—101no—
487C2×C4—101no—
488C2×C4—101no—
489C2×C4—101no—
490C2×C4—104no—
491C2×C4—104no—
492C2×C4—124no—
493C2×C4—122no—
494C2×C4—604no—
495C2×C4—602no—
496C2×C4#666512yes—
497C2×C3—22no—
498C2×C3—22no—
499C2×C3—21no—
500C2×C3—21no—
501C2×C3—42no—
502C2×C3—202no—
503C2×C3#6502912yes—
504C2×C3#6524411yescharacteristic
505C5#7213911yescharacteristic, complemented, Sylow
506C22—24no—
507C22—22no—
508C22—22no—
509C22—41no—
510C22—41no—
511C22—42no—
512C22—42no—
513C22—42no—
514C22—42no—
515C22—102no—
516C22—202no—
517C22—202no—
518C22—202no—
519C22C2×#666511yescharacteristic
520C22D5×#21711yescharacteristic
521C22D5×#21711yescharacteristic
522C22#9156312yes—
523C22#9156412yes—
524C4—22no—
525C4—102no—
526C4—102no—
527C4—102no—
528C4—242no—
529C4—1202no—
530C3#1060082011yescharacteristic, complemented, Sylow
531C2—22no—
532C2—22no—
533C2—21no—
534C2—21no—
535C2—42no—
536C2—202no—
537C2#1174917212yes—
538C2#1174948811yescharacteristic
subgroupG/H
centerC22D5×#217
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×#711C2
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1782
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91118C2semidirect
3. C2×C5×#834C2semidirect
4. C2×#90995C2semidirect
5. #11749471C2semidirect
8. C22×C3×C22⋊D5C4semidirect
10. C23×C3×Dic5C4semidirect
16. C22×C3×C4×D5C4semidirect
17. C22×C3×Dic10C4semidirect
72. C2×#834D5semidirect
75. C22×C22⋊D5Dic3semidirect
77. C23×Dic5Dic3semidirect
83. C22×C4×D5Dic3semidirect
84. C22×Dic10Dic3semidirect
424. C3×C5#1782semidirect
505. C5#72139semidirect
530. C3#10600820semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#7112
C2×#911182
C2×C5×#8342
C2×#909952
#117494712
#106008203
#721395