Finite Group Databasebeta

← #14327583

Subgroups — #14327583

Order 1920.

1176 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C5×#67C211yesmaximal, characteristic
2#11751313C211yesmaximal, characteristic, complemented
3C2×C3×#3963C211yesmaximal, characteristic, complemented
4#11749492C212yesmaximal
5Dic5×#217C212yesmaximal, complemented
6#11748777C211yesmaximal, characteristic, complemented
7#11748719C211yesmaximal, characteristic, complemented
8#11748686C212yesmaximal, complemented
9#11748684C212yesmaximal, complemented
10#11748643C211yesmaximal, characteristic, complemented
11#11748618C211yesmaximal, characteristic, complemented
12#10614067—31nomaximal, Hall
13C23×C3×C4×C5C2211yescharacteristic
14C22×C5×#67C2211yescharacteristic
15C22×C4×C5×D3C2211yescharacteristic
16C23×C3×Dic5C2212yes—
17C2×#6719C2212yes—
18C2×C4⋊Dic15C2212yes—
19C2×C5×#217C2211yescharacteristic
20C4×C5×#67C418yescomplemented
21C2×C5×(C2×D3)⋊C4C2211yescharacteristic
22C2×C5×Dic3⋊C4C2211yescharacteristic
23C2×C4×C5×Dic3C2211yescharacteristic
24C2×(C2×D3)⋊Dic5C2212yes—
25C2×(C2×D3)⋊Dic5C2212yes—
26C2×Dic3×Dic5C2212yes—
27C2×Dic3×Dic5C2212yes—
28#91115C2211yescharacteristic
29#91115C2211yescharacteristic
30C3×#3963C2211yescharacteristic
31C3×#3963C2211yescharacteristic
32C3×#3963C2212yes—
33#90994C2212yes—
34#90994C2212yes—
35#90994C2212yes—
36#90994C2212yes—
37#73336—51nomaximal, Hall
38C2×C4×C5×D4—31no—
39#65509—32no—
40#65501—31no—
41#65500—31no—
42C4×C22⋊Dic5—31no—
43C2×#3963D311yescharacteristic, complemented
44#65270—32no—
45#65240—32no—
46C22⋊C4×Dic5—32no—
47#65226—31no—
48#65221—31no—
49C24×C3×C5C2311yescharacteristic
50C23×C5×D3C2311yescharacteristic
51C22×C3×C4×C5—42no—
52C22×C3×C4×C5C2×C414yes—
53C22×C3×C4×C5C2311yescharacteristic
54C22×C3×C4×C5C2311yescharacteristic
55C22×Dic15C2312yes—
56C22×Dic15C2312yes—
57C2×C5×#67—22no—
58C2×C5×#67—22no—
59C2×C5×#67C2×C414yes—
60C22×C5×Dic3C2311yescharacteristic
61C22×C5×Dic3C2311yescharacteristic
62C22×C5×Dic3C2311yescharacteristic
63C2×C4×C5×D3—42no—
64C2×C4×C5×D3C2×C414yescomplemented
65C22×C3×Dic5—24no—
66C22×C3×Dic5—24no—
67C22×C3×Dic5—42no—
68C22×C3×Dic5C2312yes—
69C22×C3×Dic5C2312yes—
70#6719—24no—
71C4⋊Dic15—42no—
72C5×#217C2×C414yes—
73C5×(C2×D3)⋊C4C2×C414yescomplemented
74C5×Dic3⋊C4C2×C414yescomplemented
75C4×C5×Dic3C2×C414yescomplemented
76(C2×D3)⋊Dic5—24no—
77(C2×D3)⋊Dic5—42no—
78Dic3×Dic5—24no—
79Dic3×Dic5—42no—
80C2×C4×#67D511yescharacteristic
81C2×C3×#95—51no—
82#5213—52no—
83#5212—51no—
84C4×#217—52no—
85#4670—52no—
86#4666—51no—
87#4664—51no—
88#4655—52no—
89#4651—51no—
90#4648—51no—
91C22×C5×D4—31no—
92C23×C4×C5—31no—
93C23×C4×C5C2×D311yescharacteristic
94C23×Dic5C2×D312yes—
95C4×C5×D4—38no—
96C2×C5×C4⋊C4—31no—
97C2×C5×C22⋊C4—31no—
98C2×C5×C22⋊C4—31no—
99C2×C42×C5—31no—
100C2×C22⋊Dic5—32no—
101C2×C22⋊Dic5—32no—
102C2×C22⋊Dic5—32no—
103C2×C4⋊Dic5—32no—
104C2×C4×Dic5—32no—
105C2×C4×Dic5—32no—
106#3963—31no—
107#3963—31no—
108#3963—32no—
109#3963—32no—
110#3963—32no—
111#3963—32no—
112#3963C2×D311yescharacteristic
113#3963C2×D311yescharacteristic
114#3963C2×D312yes—
115#2353—151noSylow
116C23×C3×C5—22no—
117C23×C3×C5—22no—
118C23×C3×C5C22×C412yes—
119C23×C3×C5#4112yes—
120C23×C3×C5#4112yes—
121C23×C3×C5C2411yescharacteristic
122C22×C5×D3—22no—
123C22×C5×D3—21no—
124C22×C5×D3—21no—
125C22×C5×D3—22no—
126C22×C5×D3C22×C412yes—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5—22no—
129C2×C3×C4×C5—44no—
130C2×C3×C4×C5C22×C412yes—
131C2×C3×C4×C5C22×C412yes—
132C2×Dic15—22no—
133C2×Dic15—22no—
134C2×Dic15—22no—
135C2×Dic15—22no—
136C2×Dic15—22no—
137C2×Dic15—22no—
138C5×#67—28no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—21no—
141C2×C5×Dic3—21no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3C22×C412yes—
144C2×C5×Dic3C22×C412yes—
145C2×C5×Dic3C22×C412yes—
146C4×C5×D3—44no—
147C2×C3×Dic5—22no—
148C2×C3×Dic5—22no—
149C2×C3×Dic5—22no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—48no—
153C2×C3×Dic5#4114yes—
154C23×C3×C4—52no—
155C23×C3×C4C2×D511yescharacteristic
156C22×#67C2×D511yescharacteristic
157C22×C4×D3C2×D511yescharacteristic
158C2×#217—52no—
159C2×#217C2×D511yescharacteristic
160C4×#67Dic518yescomplemented
161C2×(C2×D3)⋊C4—52no—
162C2×(C2×D3)⋊C4—52no—
163C2×(C2×D3)⋊C4C2×D511yescharacteristic
164C2×C4⋊Dic3—52no—
165C2×Dic3⋊C4C2×D511yescharacteristic
166C2×C4×Dic3—52no—
167C2×C4×Dic3—52no—
168C2×C4×Dic3C2×D511yescharacteristic
169C3×#95—51no—
170C3×#95—51no—
171C3×#95—52no—
172C3⋊#95—51no—
173C3⋊#95—51no—
174C3⋊#95—52no—
175C3⋊#95—52no—
176C3⋊#95—52no—
177C3⋊#95—52no—
178C24×C5—31no—
179C24×C5C22×D311yescharacteristic
180C2×C5×D4—34no—
181C2×C5×D4—62no—
182C2×C5×D4—62no—
183C22×C4×C5—31no—
184C22×C4×C5—31no—
185C22×C4×C5—31no—
186C22×C4×C5—34no—
187C22×C4×C5—42no—
188C22×C4×C5—122no—
189C22×C4×C5C4×D314yes—
190C22×C4×C5C22×D311yescharacteristic
191C22×C4×C5C22×D311yescharacteristic
192C22×Dic5—24no—
193C22×Dic5—24no—
194C22×Dic5—32no—
195C22×Dic5—32no—
196C22×Dic5—42no—
197C22×Dic5C22×D312yes—
198C22×Dic5C22×D312yes—
199C5×C4⋊C4—34no—
200C5×C22⋊C4—34no—
201C5×C22⋊C4—34no—
202C42×C5—34no—
203C22⋊Dic5—64no—
204C22⋊Dic5—64no—
205C22⋊Dic5—122no—
206C4⋊Dic5—122no—
207C4×Dic5—64no—
208C4×Dic5—122no—
209C2×C4×D4—31no—
210#388—152no—
211#387—152no—
212#386—152no—
213#383—151no—
214#381—151no—
215#380—151no—
216C4×C22⋊C4—151no—
217C4×C22⋊C4—152no—
218#376—151no—
219C2×#95—51no—
220C22×C3×C5—22no—
221C22×C3×C5—22no—
222C22×C3×C5—24no—
223C22×C3×C5—24no—
224C22×C3×C5#11714yes—
225C22×C3×C5C23×C411yescharacteristic
226C22×C3×C5C2×#4111yescharacteristic
227C22×C3×C5C2×#4111yescharacteristic
228C22×C3×C5C2×#4112yes—
229C22×C3×C5H(5,𝔽2)12yes—
230C2×C5×D3—22no—
231C2×C5×D3—22no—
232C2×C5×D3—22no—
233C2×C5×D3—42no—
234C2×C5×D3—42no—
235C3×C4×C5—22no—
236C3×C4×C5—22no—
237Dic15—42no—
238Dic15—42no—
239C3×Dic5—24no—
240C3×Dic5—42no—
241C5×Dic3—22no—
242C5×Dic3—22no—
243C5×Dic3—22no—
244C24×C3C22×D511yescharacteristic
245C23×D3C22×D511yescharacteristic
246C22×C3×C4—42no—
247C22×C3×C4—52no—
248C22×C3×C4—52no—
249C22×C3×C4—104no—
250C22×C3×C4—104no—
251C22×C3×C4—202no—
252C22×C3×C4C2×Dic514yes—
253C22×C3×C4C22×D511yescharacteristic
254C22×C3×C4C22×D511yescharacteristic
255C2×#67—22no—
256C2×#67—22no—
257C2×#67C2×Dic514yes—
258C22×Dic3—52no—
259C22×Dic3—52no—
260C22×Dic3C22×D511yescharacteristic
261C22×Dic3C22×D511yescharacteristic
262C22×Dic3C22×D511yescharacteristic
263C2×C4×D3—42no—
264C2×C4×D3C2×Dic514yescomplemented
265#217—104no—
266#217C2×Dic514yes—
267(C2×D3)⋊C4—104no—
268(C2×D3)⋊C4—202no—
269(C2×D3)⋊C4C2×Dic514yescomplemented
270C4⋊Dic3—202no—
271Dic3⋊C4C2×Dic514yescomplemented
272C4×Dic3—104no—
273C4×Dic3—202no—
274C4×Dic3C2×Dic514yescomplemented
275C23×C5—22no—
276C23×C5—22no—
277C23×C5—32no—
278C23×C5—62no—
279C23×C5—61no—
280C23×C5—62no—
281C23×C5—61no—
282C23×C5C2×C4×D312yes—
283C23×C5#23712yes—
284C23×C5#23912yes—
285C23×C5C23×D311yescharacteristic
286C5×D4—68no—
287C2×C4×C5—22no—
288C2×C4×C5—22no—
289C2×C4×C5—32no—
290C2×C4×C5—32no—
291C2×C4×C5—32no—
292C2×C4×C5—44no—
293C2×C4×C5—62no—
294C2×C4×C5—61no—
295C2×C4×C5—62no—
296C2×C4×C5—61no—
297C2×C4×C5—124no—
298C2×C4×C5C2×C4×D312yes—
299C2×C4×C5C2×C4×D312yes—
300C2×Dic5—22no—
301C2×Dic5—22no—
302C2×Dic5—22no—
303C2×Dic5—22no—
304C2×Dic5—22no—
305C2×Dic5—48no—
306C2×Dic5—62no—
307C2×Dic5—62no—
308C2×Dic5—62no—
309C2×Dic5—62no—
310C2×Dic5—62no—
311C2×Dic5—62no—
312C2×Dic5#23514yes—
313C22×D4—31no—
314C23×C4—31no—
315C23×C4—52no—
316C23×C4D3×D511yescharacteristic
317C4×D4—38no—
318C2×C4⋊C4—31no—
319C2×C4⋊C4—152no—
320C2×C22⋊C4—31no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—152no—
323C2×C22⋊C4—152no—
324C2×C22⋊C4—152no—
325C2×C42—31no—
326C2×C42—152no—
327C2×C42—152no—
328#95—51no—
329#95—51no—
330#95—52no—
331#95—152no—
332#95—152no—
333#95—152no—
334#95—152no—
335#95—151no—
336#95—151no—
337C2×C3×C5—24no—
338C2×C3×C5C2×#11711yescharacteristic
339C2×C3×C5C4×#4111yescharacteristic
340C2×C3×C5#51811yescharacteristic
341C2×C3×C5#55112yes—
342C2×C3×C5#55312yes—
343C5×D3—42no—
344C23×C3—22no—
345C23×C3—22no—
346C23×C3#70912yes—
347C23×C3#70912yes—
348C23×C3C22×Dic512yes—
349C23×C3C23×D511yescharacteristic
350C22×D3—21no—
351C22×D3—21no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3C22×Dic512yes—
355C2×C3×C4—22no—
356C2×C3×C4—22no—
357C2×C3×C4—44no—
358C2×C3×C4—54no—
359C2×C3×C4—102no—
360C2×C3×C4—102no—
361C2×C3×C4—102no—
362C2×C3×C4—102no—
363C2×C3×C4—102no—
364C2×C3×C4—208no—
365C2×C3×C4C22×Dic512yes—
366C2×C3×C4C22×Dic512yes—
367#67—28no—
368C2×Dic3—21no—
369C2×Dic3—21no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—102no—
373C2×Dic3—102no—
374C2×Dic3—102no—
375C2×Dic3—102no—
376C2×Dic3—102no—
377C2×Dic3—102no—
378C2×Dic3C22×Dic512yes—
379C2×Dic3C22×Dic512yes—
380C2×Dic3C22×Dic512yes—
381C4×D3—44no—
382C22×C5—22no—
383C22×C5—22no—
384C22×C5—24no—
385C22×C5—24no—
386C22×C5—62no—
387C22×C5—62no—
388C22×C5—62no—
389C22×C5—122no—
390C22×C5—122no—
391C22×C5#89214yes—
392C22×C5C22×C4×D311yescharacteristic
393C22×C5C2×#23512yes—
394C22×C5C2×#23711yescharacteristic
395C22×C5#100412yes—
396C22×C5C2×#23911yescharacteristic
397C4×C5—22no—
398C4×C5—22no—
399C4×C5—62no—
400C4×C5—62no—
401C4×C5—62no—
402Dic5—24no—
403Dic5—42no—
404Dic5—122no—
405Dic5—122no—
406C24—31no—
407C24C2×D3×D511yescharacteristic
408C2×D4—34no—
409C2×D4—62no—
410C2×D4—62no—
411C22×C4—31no—
412C22×C4—31no—
413C22×C4—31no—
414C22×C4—34no—
415C22×C4—42no—
416C22×C4—52no—
417C22×C4—52no—
418C22×C4—104no—
419C22×C4—104no—
420C22×C4—122no—
421C22×C4—152no—
422C22×C4—152no—
423C22×C4—202no—
424C22×C4D3×Dic514yes—
425C22×C4C2×D3×D511yescharacteristic
426C22×C4C2×D3×D511yescharacteristic
427C4⋊C4—34no—
428C4⋊C4—602no—
429C22⋊C4—34no—
430C22⋊C4—34no—
431C22⋊C4—304no—
432C22⋊C4—304no—
433C22⋊C4—602no—
434C42—34no—
435C42—304no—
436C42—602no—
437C3×C5#235311yescharacteristic, complemented, Hall
438C22×C3—24no—
439C22×C3—22no—
440C22×C3—24no—
441C22×C3—22no—
442C22×C3#407214yes—
443C22×C3C2×#70911yescharacteristic
444C22×C3C2×#70911yescharacteristic
445C22×C3#414412yes—
446C22×C3D5×#4112yes—
447C22×C3C23×Dic511yescharacteristic
448C2×D3—22no—
449C2×D3—22no—
450C2×D3—22no—
451C2×D3—42no—
452C2×D3—42no—
453C3×C4—22no—
454C3×C4—22no—
455C3×C4—104no—
456C3×C4—202no—
457Dic3—22no—
458Dic3—22no—
459Dic3—22no—
460Dic3—202no—
461Dic3—202no—
462C2×C5—24no—
463C2×C5—122no—
464C2×C5C4×#23511yescharacteristic
465C2×C5#548611yescharacteristic
466C2×C5#549512yes—
467C2×C5C2×#89211yescharacteristic
468C2×C5#551412yes—
469C23—22no—
470C23—22no—
471C23—32no—
472C23—61no—
473C23—61no—
474C23—62no—
475C23—62no—
476C23#676512yes—
477C23#676912yes—
478C23C2×D3×Dic512yes—
479C23C22×D3×D511yescharacteristic
480D4—68no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—32no—
484C2×C4—32no—
485C2×C4—32no—
486C2×C4—44no—
487C2×C4—54no—
488C2×C4—61no—
489C2×C4—61no—
490C2×C4—62no—
491C2×C4—62no—
492C2×C4—102no—
493C2×C4—102no—
494C2×C4—102no—
495C2×C4—102no—
496C2×C4—102no—
497C2×C4—124no—
498C2×C4—208no—
499C2×C4—302no—
500C2×C4—302no—
501C2×C4—302no—
502C2×C4—302no—
503C2×C4—302no—
504C2×C4—302no—
505C2×C4C2×D3×Dic512yes—
506C2×C4C2×D3×Dic512yes—
507C2×C3—24no—
508C2×C3#6587412yes—
509C2×C3#6589012yes—
510C2×C3C2×#407211yescharacteristic
511C2×C3#6613211yescharacteristic
512C2×C3#41×Dic511yescharacteristic
513D3—42no—
514C5#7333611yescharacteristic, complemented, Sylow
515C22—22no—
516C22—24no—
517C22—22no—
518C22—24no—
519C22—62no—
520C22—62no—
521C22—62no—
522C22—122no—
523C22—122no—
524C22#9133814yes—
525C22C2×#676511yescharacteristic
526C22C2×#676911yescharacteristic
527C22D5×#23512yes—
528C22C22×D3×Dic511yescharacteristic
529C22#9204912yes—
530C4—22no—
531C4—22no—
532C4—62no—
533C4—62no—
534C4—62no—
535C4—104no—
536C4—202no—
537C4—602no—
538C4—602no—
539C3#1061406711yescharacteristic, complemented, Sylow
540C2—24no—
541C2—122no—
542C2C2×#9133811yescharacteristic
543C2#1175439912yes—
544C2Dic5×#23511yescharacteristic
545C2#1175441612yes—
546C2#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#2353
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. #11751313C2semidirect
3. C2×C3×#3963C2semidirect
5. Dic5×#217C2semidirect
6. #11748777C2semidirect
7. #11748719C2semidirect
8. #11748686C2semidirect
9. #11748684C2semidirect
10. #11748643C2semidirect
11. #11748618C2semidirect
20. C4×C5×#67C4semidirect
43. C2×#3963D3semidirect
64. C2×C4×C5×D3C2×C4semidirect
73. C5×(C2×D3)⋊C4C2×C4semidirect
74. C5×Dic3⋊C4C2×C4semidirect
75. C4×C5×Dic3C2×C4semidirect
160. C4×#67Dic5semidirect
264. C2×C4×D3C2×Dic5semidirect
269. (C2×D3)⋊C4C2×Dic5semidirect
271. Dic3⋊C4C2×Dic5semidirect
274. C4×Dic3C2×Dic5semidirect
437. C3×C5#2353semidirect
514. C5#73336semidirect
539. C3#10614067semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C5×#672
#117513132
C2×C3×#39632
#117494922
Dic5×#2172
#117487772
#117487192
#117486862
#117486842
#117486432
#117486182
#106140673
#733365