Finite Group Databasebeta

← #14322541

Subgroups — #14322541

Order 1920.

1760 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#237C211yesmaximal, characteristic
2C2×D3×C4⋊Dic5C211yesmaximal, characteristic, complemented
3C2×#91371C211yesmaximal, characteristic, complemented
4#11751322C211yesmaximal, characteristic, complemented
5C3×#65510C211yesmaximal, characteristic, complemented
6#11749519C214yesmaximal, complemented
7#11749513C214yesmaximal, complemented
8#11748607C211yesmaximal, characteristic, complemented
9#11748589C211yesmaximal, characteristic, complemented
10#10615818—31nomaximal, Hall
11C22×C3×C5×D4C2211yescharacteristic
12C22×C5×#67C2212yes—
13C23×C5×Dic3C2212yes—
14C2×C5×#237—24no—
15C2×C5×#237—24no—
16C2×C5×#237C418yescomplemented
17C22×C4×C5×D3C2211yescharacteristic
18C22×C5×Dic6C2211yescharacteristic
19C22×D3×Dic5C2212yes—
20C2×#6719C2214yes—
21C2×C4⋊Dic15C2211yescharacteristic
22C2×C4×Dic15C2211yescharacteristic
23C2×C3×C22⋊Dic5C2214yes—
24C2×C3×C4⋊Dic5C2211yescharacteristic
25C2×C3×C4×Dic5C2211yescharacteristic
26C2×Dic3⋊Dic5C2212yes—
27C2×Dic3⋊Dic5C2212yes—
28C2×(C2×D3)⋊Dic5C2212yes—
29D3×C4⋊Dic5—24no—
30#91371—24no—
31#90994C2214yes—
32#90994C2214yes—
33#76294—51nomaximal, Hall
34C22×C5×#41—31no—
35C2×#4072—31no—
36C22×C4⋊Dic5—31no—
37#65519—31no—
38#65519—31no—
39#65510—31no—
40#65510D311yescharacteristic, complemented
41#65509—34no—
42#65501—34no—
43C24×C3×C5C2312yes—
44C23×C5×D3C2311yescharacteristic
45C2×C3×C5×D4—22no—
46C2×C3×C5×D4—22no—
47C2×C3×C5×D4C2×C414yescomplemented
48C22×C3×C4×C5C2311yescharacteristic
49C22×Dic15C2312yes—
50C22×Dic15C2312yes—
51C2×C5×#67—24no—
52C2×C5×#67—24no—
53C2×C5×#67C2×C418yes—
54C22×C5×Dic3—24no—
55C22×C5×Dic3—24no—
56C22×C5×Dic3C2×C418yescomplemented
57C22×C5×Dic3C2312yes—
58C22×C5×Dic3C2311yescharacteristic
59C5×#237—232no—
60C2×C4×C5×D3C2×C414yes—
61C2×C4×C5×D3D414yes—
62C2×C4×C5×D3D414yes—
63C2×C5×Dic6—22no—
64C2×C5×Dic6—22no—
65C2×C5×Dic6C2×C414yescomplemented
66C22×C3×Dic5C2312yes—
67C22×C3×Dic5C2312yes—
68C2×D3×Dic5—24no—
69C2×D3×Dic5—44no—
70#6719—44no—
71C4⋊Dic15—22no—
72C4×Dic15—22no—
73C3×C22⋊Dic5—44no—
74C3×C4⋊Dic5—22no—
75C3×C4×Dic5—22no—
76Dic3⋊Dic5—24no—
77Dic3⋊Dic5—24no—
78(C2×D3)⋊Dic5—24no—
79C22×#237D511yescharacteristic
80C2×D3×C4⋊C4—51no—
81C2×#872—51no—
82C3×#390—51no—
83#5221—51no—
84#4973—51no—
85#4956—54no—
86#4942—54no—
87#4929—51no—
88C2×C5×#41—38no—
89C2×C5×#41—64no—
90C2×C5×#41—64no—
91C22×C5×Q8—31no—
92C22×C5×D4—32no—
93C22×C5×D4C2×D311yescharacteristic
94C23×C4×C5—31no—
95C23×C4×C5—32no—
96C23×Dic5—32no—
97C2×C22⋊Dic5—32no—
98C2×C22⋊Dic5—34no—
99C2×C22⋊Dic5C2×D314yes—
100#4072—64no—
101C2×C4⋊Dic5—31no—
102C2×C4⋊Dic5—32no—
103C2×C4⋊Dic5—32no—
104C2×C4⋊Dic5—64no—
105C2×C4⋊Dic5C2×D311yescharacteristic
106C2×C4×Dic5—31no—
107C2×C4×Dic5C2×D311yescharacteristic
108#3963—34no—
109#3963—34no—
110#2311—151noSylow
111C23×C3×C5—22no—
112C23×C3×C5—22no—
113C23×C3×C5—24no—
114C23×C3×C5—24no—
115C23×C3×C5C22×C414yes—
116C23×C3×C5C2411yescharacteristic
117C22×C5×D3—22no—
118C22×C5×D3—22no—
119C22×C5×D3C22×C412yes—
120C22×C5×D3C2×D412yes—
121C22×C5×D3C2×D412yes—
122C3×C5×D4—28no—
123C2×C3×C4×C5C22×C412yes—
124C2×C3×C4×C5C2×D412yes—
125C2×C3×C4×C5C2×D412yes—
126C2×Dic15—22no—
127C2×Dic15—22no—
128C2×Dic15—22no—
129C2×Dic15—24no—
130C2×Dic15—22no—
131C5×#67—216no—
132C2×C5×Dic3—22no—
133C2×C5×Dic3—22no—
134C2×C5×Dic3—216no—
135C2×C5×Dic3C22×C414yes—
136C2×C5×Dic3C22×C412yes—
137C2×C5×Dic3C2×D412yes—
138C2×C5×Dic3C2×D412yes—
139C4×C5×D3C22⋊C4116yescomplemented
140C5×Dic6—28no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C2×C3×Dic5—22no—
144C2×C3×Dic5—24no—
145C2×C3×Dic5—22no—
146D3×Dic5—48no—
147C22×C3×D4C2×D511yescharacteristic
148C22×#67C2×D512yes—
149C23×Dic3C2×D512yes—
150C2×#237—24no—
151C2×#237—24no—
152C2×#237Dic518yescomplemented
153C22×C4×D3—52no—
154C22×C4×D3C2×D511yescharacteristic
155C22×Dic6C2×D511yescharacteristic
156C2×C3×C4⋊C4—51no—
157C2×C3×C22⋊C4—54no—
158C2×C3×C42—51no—
159C2×#217—54no—
160C2×(C2×D3)⋊C4—52no—
161C2×C4⋊Dic3—51no—
162C2×Dic3⋊C4—52no—
163C2×Dic3⋊C4—52no—
164C2×C4×Dic3—51no—
165D3×C4⋊C4—104no—
166#872—104no—
167C3⋊#95—54no—
168C3⋊#95—54no—
169C24×C5—31no—
170C24×C5C22×D312yes—
171C5×#41—632no—
172C2×C5×Q8—34no—
173C2×C5×Q8—62no—
174C2×C5×Q8—62no—
175C2×C5×D4—22no—
176C2×C5×D4—22no—
177C2×C5×D4—38no—
178C2×C5×D4—64no—
179C2×C5×D4—64no—
180C2×C5×D4C4×D314yescomplemented
181C22×C4×C5—31no—
182C22×C4×C5—34no—
183C22×C4×C5—34no—
184C22×C4×C5—34no—
185C22×C4×C5—38no—
186C22×C4×C5—32no—
187C22×C4×C5—64no—
188C22×C4×C5—64no—
189C22×C4×C5C22×D311yescharacteristic
190C22×Dic5—32no—
191C22×Dic5—32no—
192C22×Dic5—64no—
193C22×Dic5—124no—
194C22×Dic5C22×D312yes—
195C22×Dic5C22×D312yes—
196C22⋊Dic5—44no—
197C22⋊Dic5—64no—
198C22⋊Dic5—124no—
199C4⋊Dic5—22no—
200C4⋊Dic5—64no—
201C4⋊Dic5—64no—
202C4⋊Dic5—62no—
203C4×Dic5—22no—
204C4×Dic5—62no—
205C22×#41—31no—
206C2×#117—151no—
207C22×C4⋊C4—151no—
208#391—151no—
209#391—151no—
210#390—51no—
211#390—151no—
212#386—154no—
213#380—154no—
214C22×C3×C5—24no—
215C22×C3×C5—28no—
216C22×C3×C5—42no—
217C22×C3×C5—42no—
218C22×C3×C5—44no—
219C22×C3×C5C23×C411yescharacteristic
220C22×C3×C5C22×D411yescharacteristic
221C22×C3×C5C22×D411yescharacteristic
222C22×C3×C5H(5,𝔽2)12yes—
223C22×C3×C52−1+412yes—
224C2×C5×D3—24no—
225C2×C5×D3—22no—
226C2×C5×D3—22no—
227C2×C5×D3—24no—
228C2×C5×D3C2×C22⋊C414yes—
229C3×C4×C5C2×C22⋊C414yes—
230Dic15—42no—
231Dic15—42no—
232C3×Dic5—42no—
233C3×Dic5—42no—
234C5×Dic3—24no—
235C5×Dic3C2×C22⋊C414yes—
236C24×C3C22×D512yes—
237C23×D3C22×D511yescharacteristic
238C2×C3×D4—22no—
239C2×C3×D4—22no—
240C2×C3×D4C2×Dic514yescomplemented
241C22×C3×C4—52no—
242C22×C3×C4—52no—
243C22×C3×C4C22×D511yescharacteristic
244C2×#67—24no—
245C2×#67—24no—
246C2×#67C2×Dic518yes—
247C22×Dic3—24no—
248C22×Dic3—24no—
249C22×Dic3—52no—
250C22×Dic3—52no—
251C22×Dic3C2×Dic518yescomplemented
252C22×Dic3C22×D512yes—
253C22×Dic3C22×D511yescharacteristic
254#237—232no—
255C2×C4×D3—104no—
256C2×C4×D3—204no—
257C2×C4×D3C2×Dic514yes—
258C2×C4×D3C22⋊D514yes—
259C2×C4×D3C22⋊D514yes—
260C2×Dic6—22no—
261C2×Dic6—22no—
262C2×Dic6C2×Dic514yescomplemented
263C3×C4⋊C4—102no—
264C3×C22⋊C4—204no—
265C3×C42—102no—
266#217—204no—
267(C2×D3)⋊C4—104no—
268C4⋊Dic3—102no—
269Dic3⋊C4—104no—
270Dic3⋊C4—104no—
271C4×Dic3—102no—
272C23×C5—22no—
273C23×C5—22no—
274C23×C5—24no—
275C23×C5—24no—
276C23×C5—32no—
277C23×C5—32no—
278C23×C5—32no—
279C23×C5—62no—
280C23×C5—62no—
281C23×C5C2×C4×D314yes—
282C23×C5C23×D311yescharacteristic
283C5×Q8—68no—
284C5×D4—28no—
285C5×D4—616no—
286C2×C4×C5—32no—
287C2×C4×C5—32no—
288C2×C4×C5—32no—
289C2×C4×C5—316no—
290C2×C4×C5—34no—
291C2×C4×C5—616no—
292C2×C4×C5—62no—
293C2×C4×C5—62no—
294C2×C4×C5C2×C4×D312yes—
295C2×C4×C5D3×D412yes—
296C2×C4×C5D3×D412yes—
297C2×Dic5—22no—
298C2×Dic5—22no—
299C2×Dic5—22no—
300C2×Dic5—24no—
301C2×Dic5—22no—
302C2×Dic5—62no—
303C2×Dic5—62no—
304C2×Dic5—62no—
305C2×Dic5—64no—
306C2×Dic5—62no—
307C2×Dic5—128no—
308C2×#41—38no—
309C2×#41—64no—
310C2×#41—64no—
311C22×Q8—31no—
312C22×D4—32no—
313C22×D4D3×D511yescharacteristic
314C23×C4—31no—
315C23×C4—32no—
316C23×C4—152no—
317#117—304no—
318C2×C4⋊C4—51no—
319C2×C4⋊C4—152no—
320C2×C4⋊C4—152no—
321C2×C4⋊C4—151no—
322C2×C4⋊C4—304no—
323C2×C22⋊C4—54no—
324C2×C22⋊C4—152no—
325C2×C22⋊C4—154no—
326C2×C42—51no—
327C2×C42—151no—
328#95—154no—
329#95—154no—
330C2×C3×C5—44no—
331C2×C3×C5C22×C22⋊C411yescharacteristic
332C2×C3×C5#52012yes—
333C2×C3×C5#53511yescharacteristic
334C2×C3×C5#53611yescharacteristic
335C2×C3×C5#53712yes—
336C5×D3—24no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3C22×Dic514yes—
342C23×C3C23×D511yescharacteristic
343C22×D3—22no—
344C22×D3—22no—
345C22×D3C22×Dic512yes—
346C22×D3C2×C22⋊D512yes—
347C22×D3C2×C22⋊D512yes—
348C3×D4—28no—
349C2×C3×C4—102no—
350C2×C3×C4—104no—
351C2×C3×C4—102no—
352C2×C3×C4—102no—
353C2×C3×C4—102no—
354C2×C3×C4C22×Dic512yes—
355C2×C3×C4C2×C22⋊D512yes—
356C2×C3×C4C2×C22⋊D512yes—
357#67—216no—
358C2×Dic3—22no—
359C2×Dic3—22no—
360C2×Dic3—216no—
361C2×Dic3—102no—
362C2×Dic3—104no—
363C2×Dic3—102no—
364C2×Dic3—102no—
365C2×Dic3—102no—
366C2×Dic3C22×Dic514yes—
367C2×Dic3C22×Dic512yes—
368C2×Dic3C2×C22⋊D512yes—
369C2×Dic3C2×C22⋊D512yes—
370C4×D3—208no—
371C4×D3C22⋊Dic5116yescomplemented
372Dic6—28no—
373C22×C5—24no—
374C22×C5—28no—
375C22×C5—34no—
376C22×C5—42no—
377C22×C5—42no—
378C22×C5—44no—
379C22×C5—62no—
380C22×C5—62no—
381C22×C5—64no—
382C22×C5—64no—
383C22×C5C22×C4×D311yescharacteristic
384C22×C5C2×D3×D411yescharacteristic
385C22×C5C2×D3×D411yescharacteristic
386C22×C5#100412yes—
387C22×C5#101012yes—
388C4×C5—34no—
389C4×C5—64no—
390C4×C5D3×C22⋊C414yes—
391Dic5—42no—
392Dic5—42no—
393Dic5—122no—
394Dic5—122no—
395C24—31no—
396C24C2×D3×D512yes—
397#41—632no—
398C2×Q8—34no—
399C2×Q8—62no—
400C2×Q8—62no—
401C2×D4—22no—
402C2×D4—22no—
403C2×D4—38no—
404C2×D4—64no—
405C2×D4—64no—
406C2×D4D3×Dic514yescomplemented
407C22×C4—31no—
408C22×C4—34no—
409C22×C4—34no—
410C22×C4—34no—
411C22×C4—38no—
412C22×C4—32no—
413C22×C4—52no—
414C22×C4—52no—
415C22×C4—64no—
416C22×C4—64no—
417C22×C4—152no—
418C22×C4—152no—
419C22×C4—304no—
420C22×C4—604no—
421C22×C4C2×D3×D511yescharacteristic
422C4⋊C4—102no—
423C4⋊C4—304no—
424C4⋊C4—304no—
425C4⋊C4—302no—
426C22⋊C4—204no—
427C22⋊C4—304no—
428C22⋊C4—604no—
429C42—102no—
430C42—302no—
431C3×C5#231111yescharacteristic, complemented, Hall
432C22×C3—28no—
433C22×C3—24no—
434C22×C3—42no—
435C22×C3—42no—
436C22×C3—44no—
437C22×C3#414912yes—
438C22×C3#415012yes—
439C22×C3C23×Dic511yescharacteristic
440C22×C3C22×C22⋊D511yescharacteristic
441C22×C3C22×C22⋊D511yescharacteristic
442C2×D3—22no—
443C2×D3—24no—
444C2×D3—22no—
445C2×D3—24no—
446C2×D3C2×C22⋊Dic514yes—
447C3×C4—202no—
448C3×C4—202no—
449C3×C4C2×C22⋊Dic514yes—
450Dic3—24no—
451Dic3—202no—
452Dic3—202no—
453Dic3C2×C22⋊Dic514yes—
454C2×C5—44no—
455C2×C5—64no—
456C2×C5C2×D3×C22⋊C411yescharacteristic
457C2×C5#554612yes—
458C2×C5#560812yes—
459C2×C5#567511yescharacteristic
460C2×C5#571511yescharacteristic
461C23—24no—
462C23—24no—
463C23—22no—
464C23—22no—
465C23—32no—
466C23—32no—
467C23—32no—
468C23—62no—
469C23—62no—
470C23C2×D3×Dic514yes—
471C23C22×D3×D511yescharacteristic
472Q8—68no—
473D4—28no—
474D4—616no—
475C2×C4—32no—
476C2×C4—32no—
477C2×C4—32no—
478C2×C4—316no—
479C2×C4—34no—
480C2×C4—616no—
481C2×C4—62no—
482C2×C4—62no—
483C2×C4—102no—
484C2×C4—102no—
485C2×C4—104no—
486C2×C4—102no—
487C2×C4—102no—
488C2×C4—302no—
489C2×C4—302no—
490C2×C4—304no—
491C2×C4—302no—
492C2×C4—302no—
493C2×C4—608no—
494C2×C4C2×D3×Dic512yes—
495C2×C4D3×C22⋊D512yes—
496C2×C4D3×C22⋊D512yes—
497C2×C3—44no—
498C2×C3#6615911yescharacteristic
499C2×C3#6616112yes—
500C2×C3#6616411yescharacteristic
501C2×C3#6616712yes—
502C2×C3C22×C22⋊Dic511yescharacteristic
503D3—24no—
504C5#7629411yescharacteristic, complemented, Sylow
505C22—24no—
506C22—28no—
507C22—34no—
508C22—42no—
509C22—42no—
510C22—44no—
511C22—62no—
512C22—62no—
513C22—64no—
514C22—64no—
515C22#9202012yes—
516C22#9202612yes—
517C22C22×D3×Dic511yescharacteristic
518C22C2×D3×C22⋊D511yescharacteristic
519C22C2×D3×C22⋊D511yescharacteristic
520C4—34no—
521C4—64no—
522C4—202no—
523C4—202no—
524C4—602no—
525C4—602no—
526C4D3×C22⋊Dic514yes—
527C3#1061581811yescharacteristic, complemented, Sylow
528C2—44no—
529C2—64no—
530C2#1175481211yescharacteristic
531C2#1175492012yes—
532C2#1175494512yes—
533C2#1175506811yescharacteristic
534C2C2×D3×C22⋊Dic511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D3×D5
commutatorC22×C3×C5C23×C4
FittingC22×C3×C5×D4C22
socle, cosocleC23×C3×C5C24
prime radicalC22×C5×#237C2
hypercenterC22×D4D3×D5
hypocenterC3×C5#2311
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×D3×C4⋊Dic5C2semidirect
3. C2×#91371C2semidirect
4. #11751322C2semidirect
5. C3×#65510C2semidirect
6. #11749519C2semidirect
7. #11749513C2semidirect
8. #11748607C2semidirect
9. #11748589C2semidirect
16. C2×C5×#237C4semidirect
40. #65510D3semidirect
47. C2×C3×C5×D4C2×C4semidirect
56. C22×C5×Dic3C2×C4semidirect
65. C2×C5×Dic6C2×C4semidirect
139. C4×C5×D3C22⋊C4semidirect
152. C2×#237Dic5semidirect
180. C2×C5×D4C4×D3semidirect
240. C2×C3×D4C2×Dic5semidirect
251. C22×Dic3C2×Dic5semidirect
262. C2×Dic6C2×Dic5semidirect
371. C4×D3C22⋊Dic5semidirect
406. C2×D4D3×Dic5semidirect
431. C3×C5#2311semidirect
504. C5#76294semidirect
527. C3#10615818semidirect

Maximal subgroups

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

subgroupindex
C22×C5×#2372
C2×D3×C4⋊Dic52
C2×#913712
#117513222
C3×#655102
#117495192
#117495132
#117486072
#117485892
#106158183
#762945