Finite Group Databasebeta

← C2×#11755311 #14510013

Subgroups — C2×#11755311 #14510013

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92100C211yesmaximal, characteristic, complemented
2C2×C3×#4149C211yesmaximal, characteristic, complemented
3C2×C5×#948C211yesmaximal, characteristic, complemented
4#11755311C2116yesmaximal, direct product factor
5C2×#91312C213yesmaximal, complemented
6C2×#91311C213yesmaximal, complemented
7C2×#91301C213yesmaximal, complemented
8C22×#6653C213yesmaximal, complemented
9C2×#66086—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11#92100—24no—
12#92100C2218yescomplemented
13C2×#6821—21no—
14C2×D4×D15—23no—
15C2×#6817C2213yescomplemented
16C22×D60C2213yescomplemented
17C3×#4149—24no—
18C3×#4149C2218yescomplemented
19C2×C3×#713—21no—
20C2×C3×D4×D5—23no—
21C2×C3×#709C2213yescomplemented
22C22×C3×D20C2213yescomplemented
23C5×#948C2218yescomplemented
24C2×C5×#208C2213yescomplemented
25C22×C5×C3⋊C8C2213yescomplemented
26C2×#6662C2211yescharacteristic, complemented
27C2×#6658C2213yescomplemented
28#91312C22124yescomplemented
29#91311C22124yescomplemented
30C2×#6657C2213yescomplemented
31#91301C22124yescomplemented
32C2×#6653C2213yescomplemented
33C2×#6653C2216yescomplemented
34C2×#6653C22124yescomplemented
35C2×#5835—51nomaximal, Hall
36C2×#4149—31no—
37C2×#4149D311yescharacteristic, complemented
38C2×C5×#131—31no—
39#66086—316no—
40C2×#4054—33no—
41C2×#4054—33no—
42C2×#4050—33no—
43C22×D40—33no—
44C23×D15—23no—
45C23×C3×D5—23no—
46C3×C5×#41D414yes—
47C3×C5×#41C2314yes—
48C2×C3×C5×Q8D411yescharacteristic
49C2×C3×C5×D4D413yes—
50C22×C3×C4×C5C2313yes—
51C2×#1220—23no—
52#6821—28no—
53D4×D15—224no—
54#6817—26no—
55#6817C23112yescomplemented
56C2×D60—23no—
57C2×D60—26no—
58C2×D60C2313yes—
59C2×D60C23112yescomplemented
60C2×C4×D15—23no—
61C2×Dic30C2311yescharacteristic
62C2×C3×C22⋊D5—23no—
63C3×#713—28no—
64C3×D4×D5—224no—
65C3×#709—26no—
66C3×#709C23112yescomplemented
67C2×C3×D20—23no—
68C2×C3×D20—26no—
69C2×C3×D20C2313yes—
70C2×C3×D20C23112yescomplemented
71C2×C3×C4×D5—23no—
72C2×C3×Dic10C2311yescharacteristic
73C5×#208C23112yescomplemented
74C2×C5×C3⋊C8C2311yescharacteristic
75C2×C5×C3⋊C8C2313yes—
76C2×C5×C3⋊C8C23112yescomplemented
77#6662C2314yescomplemented
78#6658C23112yescomplemented
79#6657C23112yescomplemented
80#6653C23112yescomplemented
81#6653C23124yescomplemented
82C2×C3×H(5,𝔽2)—51no—
83C2×#1009—51no—
84#5835—516no—
85C2×#950—53no—
86C2×#949—53no—
87C2×#948D511yescharacteristic, complemented
88C2×#932—53no—
89C22×#213—53no—
90C2×C5×#41C2×D311yescharacteristic
91#4149—24no—
92#4149—38no—
93#4149—64no—
94#4149C2×D318yescomplemented
95C2×#713—21no—
96C2×#713—61no—
97C2×D4×D5—23no—
98C2×D4×D5—63no—
99C2×#709—33no—
100C2×#709C2×D313yescomplemented
101C22×D20—33no—
102C22×D20C2×D313yescomplemented
103C5×#131—38no—
104C2×C5×M16—33no—
105C22×C5×C8—33no—
106#4054—324no—
107#4054—324no—
108C2×Dic20—31no—
109#4050—324no—
110C2×D40—33no—
111C2×D40—36no—
112C2×D40—324no—
113C2×#677—33no—
114C2×#677—33no—
115C2×#576—151noSylow
116C23×C3×C5C2×D413yes—
117C22×D15—23no—
118C22×D15—212no—
119C22×D15—86no—
120C22×C3×D5—23no—
121C22×C3×D5—212no—
122C22×C3×D5—86no—
123C3×C5×Q8C2×D414yes—
124C3×C5×D4C2×D4112yes—
125C2×C3×C4×C5C2×D413yes—
126C2×C3×C4×C5C2×D416yes—
127C2×C3×C4×C5C2411yescharacteristic
128C2×C3×C4×C5C2416yes—
129#1220—212no—
130C2×Dic15—21no—
131D60—23no—
132D60—212no—
133D60C2416yes—
134C4×D15—212no—
135Dic30—21no—
136Dic30C2412yes—
137C3×C22⋊D5—212no—
138C2×C3×Dic5—21no—
139C3×D20—23no—
140C3×D20—212no—
141C3×D20C2416yes—
142C3×C4×D5—212no—
143C3×Dic10—21no—
144C3×Dic10C2412yes—
145C5×C3⋊C8C2416yes—
146C5×C3⋊C8C2412yes—
147C3×H(5,𝔽2)—58no—
148C3×H(5,𝔽2)—104no—
149C2×C3×#41—53no—
150C2×C3×#41—101no—
151C2×C3×#41C2×D511yescharacteristic
152C22×C3×D4—53no—
153C22×C3×D4—103no—
154#1009—58no—
155#1009—104no—
156C2×#239—101no—
157C2×D3×D4—103no—
158C2×#235—53no—
159C22×D12—53no—
160#950—524no—
161#949—524no—
162#948C2×D518yescomplemented
163C2×#216—51no—
164C2×#215—53no—
165C2×#214—53no—
166#932—524no—
167C2×#213—53no—
168C2×#213—56no—
169C2×#213—524no—
170C2×#208C2×D513yescomplemented
171C22×C3⋊C8C2×D513yescomplemented
172C23×D5—23no—
173C23×D5—63no—
174C5×#41#6714yes—
175C5×#41C22×D314yes—
176C2×C5×Q8#6711yescharacteristic
177C2×C5×D4#6713yes—
178C22×C4×C5C22×D313yes—
179C2×C22⋊D5—23no—
180C2×C22⋊D5—63no—
181#713—28no—
182#713—68no—
183D4×D5—224no—
184D4×D5—624no—
185#709—26no—
186#709—312no—
187#709—66no—
188#709C22×D3112yescomplemented
189C2×D20—23no—
190C2×D20—26no—
191C2×D20—33no—
192C2×D20—312no—
193C2×D20—63no—
194C2×D20—66no—
195C2×D20C22×D313yes—
196C2×D20C22×D3112yescomplemented
197C2×C4×D5—23no—
198C2×C4×D5—63no—
199C2×Dic10—31no—
200C2×Dic10C22×D311yescharacteristic
201C5×M16—312no—
202C2×C5×C8—31no—
203C2×C5×C8—33no—
204C2×C5×C8—312no—
205Dic20—34no—
206D40—312no—
207D40—324no—
208#677—312no—
209#677—312no—
210C2×H(5,𝔽2)—51no—
211C2×H(5,𝔽2)—151no—
212#576—1516no—
213C2×AGL(1,ℤ/8)—153no—
214C2×AGL(1,ℤ/8)—153no—
215C2×#135—153no—
216C22×D8—153no—
217C2×#131—31no—
218C22×C3×C5—26no—
219C22×C3×C5C22×D416yes—
220C22×C3×C5C22×D411yescharacteristic
221C2×D15—26no—
222C2×D15—46no—
223C2×D15—812no—
224C2×C3×D5—26no—
225C2×C3×D5—46no—
226C2×C3×D5—812no—
227C3×C4×C5C22×D411yescharacteristic
228C3×C4×C5C22×D416yes—
229C3×C4×C5C2511yescharacteristic
230Dic15—22no—
231C3×Dic5—22no—
232C24×C3—103no—
233C23×D3—103no—
234C3×#41—512no—
235C3×#41—108no—
236C3×#41—106no—
237C3×#41D2014yes—
238C3×#41C22×D514yes—
239C2×C3×Q8—51no—
240C2×C3×Q8D2011yescharacteristic
241C2×C3×D4—53no—
242C2×C3×D4—512no—
243C2×C3×D4—103no—
244C2×C3×D4—1024no—
245C2×C3×D4—103no—
246C2×C3×D4—106no—
247C2×C3×D4D2013yes—
248C22×C3×C4—103no—
249C22×C3×C4C22×D513yes—
250C2×#67—103no—
251#239—108no—
252D3×D4—1024no—
253#235—512no—
254#235—106no—
255C2×D12—53no—
256C2×D12—512no—
257C2×D12—103no—
258C2×D12—106no—
259C2×C4×D3—103no—
260C2×Dic6—51no—
261#216—54no—
262#215—512no—
263#214—512no—
264#213—512no—
265#213—524no—
266#208C22×D5112yescomplemented
267C2×C3⋊C8C22×D511yescharacteristic
268C2×C3⋊C8C22×D513yes—
269C2×C3⋊C8C22×D5112yescomplemented
270C23×C5C2×#6713yes—
271C22×D5—23no—
272C22×D5—212no—
273C22×D5—63no—
274C22×D5—612no—
275C22×D5—86no—
276C22×D5—246no—
277C5×Q8C2×#6714yes—
278C5×D4C2×#67112yes—
279C2×C4×C5C2×#6713yes—
280C2×C4×C5C2×#6716yes—
281C2×C4×C5C23×D311yescharacteristic
282C2×C4×C5C23×D316yes—
283C22⋊D5—212no—
284C22⋊D5—612no—
285C2×Dic5—21no—
286C2×Dic5—61no—
287D20—23no—
288D20—212no—
289D20—36no—
290D20—63no—
291D20—612no—
292D20C23×D316yes—
293C4×D5—212no—
294C4×D5—612no—
295Dic10—21no—
296Dic10—32no—
297Dic10—61no—
298Dic10C23×D312yes—
299C5×C8—36no—
300C5×C8—32no—
301H(5,𝔽2)—58no—
302H(5,𝔽2)—104no—
303H(5,𝔽2)—158no—
304H(5,𝔽2)—304no—
305C2×#41—53no—
306C2×#41—101no—
307C2×#41—153no—
308C2×#41—301no—
309C2×#41D3×D511yescharacteristic
310C22×D4—53no—
311C22×D4—103no—
312C22×D4—153no—
313C22×D4—303no—
314AGL(1,ℤ/8)—1524no—
315AGL(1,ℤ/8)—1524no—
316#135—1524no—
317C2×Q16—151no—
318C2×SD16—153no—
319C2×SD16—153no—
320C2×D8—153no—
321C2×D8—156no—
322C2×D8—1524no—
323#131—38no—
324C2×M16—33no—
325C22×C8—33no—
326C2×C3×C5—26no—
327C2×C3×C5#57612yescomplemented
328C2×C3×C5C23×D411yescharacteristic
329D15—46no—
330C3×D5—46no—
331C23×C3—103no—
332C23×C3—1012no—
333C23×C3—406no—
334C23×C3C2×D2013yes—
335C22×D3—103no—
336C22×D3—1012no—
337C22×D3—406no—
338C3×Q8—52no—
339C3×Q8—101no—
340C3×Q8C2×D2014yes—
341C3×D4—56no—
342C3×D4—1012no—
343C3×D4—103no—
344C3×D4—1012no—
345C3×D4C2×D20112yes—
346C2×C3×C4—101no—
347C2×C3×C4—1012no—
348C2×C3×C4C2×D2013yes—
349C2×C3×C4C2×D2016yes—
350C2×C3×C4C23×D511yescharacteristic
351C2×C3×C4C23×D516yes—
352#67—1012no—
353C2×Dic3—101no—
354D12—56no—
355D12—103no—
356D12—1012no—
357C4×D3—1012no—
358Dic6—52no—
359Dic6—101no—
360C3⋊C8C23×D512yes—
361C3⋊C8C23×D516yes—
362C22×C5—26no—
363C22×C5C22×#6716yes—
364C22×C5C22×#6711yescharacteristic
365C2×D5—26no—
366C2×D5—46no—
367C2×D5—66no—
368C2×D5—812no—
369C2×D5—126no—
370C2×D5—2412no—
371C4×C5C22×#6711yescharacteristic
372C4×C5C22×#6716yes—
373C4×C5C24×D311yescharacteristic
374Dic5—22no—
375Dic5—62no—
376C24—103no—
377C24—303no—
378#41—512no—
379#41—108no—
380#41—106no—
381#41—1512no—
382#41—308no—
383#41—306no—
384#41#120214yes—
385#41C2×D3×D514yes—
386C2×Q8—51no—
387C2×Q8—151no—
388C2×Q8#120211yescharacteristic
389C2×D4—53no—
390C2×D4—512no—
391C2×D4—103no—
392C2×D4—1024no—
393C2×D4—103no—
394C2×D4—106no—
395C2×D4—153no—
396C2×D4—1512no—
397C2×D4—303no—
398C2×D4—3024no—
399C2×D4—303no—
400C2×D4—306no—
401C2×D4#120213yes—
402C22×C4—103no—
403C22×C4—303no—
404C22×C4C2×D3×D513yes—
405Q16—154no—
406SD16—1512no—
407SD16—1512no—
408D8—1512no—
409D8—1524no—
410M16—312no—
411C2×C8—31no—
412C2×C8—33no—
413C2×C8—312no—
414C3×C5C2×#57611yescharacteristic, complemented, Hall
415C22×C3—26no—
416C22×C3—106no—
417C22×C3—206no—
418C22×C3—4012no—
419C22×C3C22×D2016yes—
420C22×C3C22×D2011yescharacteristic
421C2×D3—106no—
422C2×D3—206no—
423C2×D3—4012no—
424C3×C4—102no—
425C3×C4C22×D2011yescharacteristic
426C3×C4C22×D2016yes—
427C3×C4C24×D511yescharacteristic
428Dic3—102no—
429C2×C5—26no—
430C2×C5#583512yescomplemented
431C2×C5C23×#6711yescharacteristic
432D5—46no—
433D5—126no—
434C23—103no—
435C23—1012no—
436C23—303no—
437C23—3012no—
438C23—406no—
439C23—1206no—
440C23C2×#120213yes—
441Q8—52no—
442Q8—101no—
443Q8—152no—
444Q8—301no—
445Q8C2×#120214yes—
446D4—56no—
447D4—1012no—
448D4—1012no—
449D4—103no—
450D4—156no—
451D4—3012no—
452D4—3012no—
453D4—303no—
454D4C2×#1202112yes—
455C2×C4—101no—
456C2×C4—1012no—
457C2×C4—301no—
458C2×C4—3012no—
459C2×C4C2×#120216yes—
460C2×C4C2×#120213yes—
461C2×C4C22×D3×D516yes—
462C2×C4C22×D3×D511yescharacteristic
463C8—32no—
464C8—36no—
465C2×C3—26no—
466C2×C3—206no—
467C2×C3#6608612yescomplemented
468C2×C3C23×D2011yescharacteristic
469D3—206no—
470C5C2×#583511yescharacteristic, complemented, Sylow
471C22—26no—
472C22—106no—
473C22—206no—
474C22—306no—
475C22—4012no—
476C22—606no—
477C22—12012no—
478C22C22×#120216yes—
479C22C22×#120211yescharacteristic
480C4—102no—
481C4—302no—
482C4C22×#120216yes—
483C4C22×#120211yescharacteristic
484C4C23×D3×D511yescharacteristic
485C3C2×#6608611yescharacteristic, complemented, Sylow
486C2—26no—
487C2—206no—
488C2—606no—
489C2#1175531112yesdirect product factor
490C2C23×#120211yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC3×C4×C5C25
FrattiniC4C23×D3×D5
FittingC2×C3×C5×#41C22
socleC22×C3×C5C22×D4
hypercenterC2×#41D3×D5
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#92100C2semidirect
2. C2×C3×#4149C2semidirect
3. C2×C5×#948C2semidirect
4. #11755311C2direct (N × H)
5. C2×#91312C2semidirect
6. C2×#91311C2semidirect
7. C2×#91301C2semidirect
8. C22×#6653C2semidirect
12. #92100C22semidirect
15. C2×#6817C22semidirect
16. C22×D60C22semidirect
18. C3×#4149C22semidirect
21. C2×C3×#709C22semidirect
22. C22×C3×D20C22semidirect
23. C5×#948C22semidirect
24. C2×C5×#208C22semidirect
25. C22×C5×C3⋊C8C22semidirect
26. C2×#6662C22semidirect
27. C2×#6658C22semidirect
28. #91312C22semidirect
29. #91311C22semidirect
30. C2×#6657C22semidirect
31. #91301C22semidirect
32. C2×#6653C22semidirect
33. C2×#6653C22semidirect
34. C2×#6653C22semidirect
37. C2×#4149D3semidirect
55. #6817C23semidirect
59. C2×D60C23semidirect
66. C3×#709C23semidirect
70. C2×C3×D20C23semidirect
73. C5×#208C23semidirect
76. C2×C5×C3⋊C8C23semidirect
77. #6662C23semidirect
78. #6658C23semidirect
79. #6657C23semidirect
80. #6653C23semidirect
81. #6653C23semidirect
87. C2×#948D5semidirect
94. #4149C2×D3semidirect
100. C2×#709C2×D3semidirect
102. C22×D20C2×D3semidirect
162. #948C2×D5semidirect
170. C2×#208C2×D5semidirect
171. C22×C3⋊C8C2×D5semidirect
188. #709C22×D3semidirect
196. C2×D20C22×D3semidirect
266. #208C22×D5semidirect
269. C2×C3⋊C8C22×D5semidirect
327. C2×C3×C5#576semidirect
414. C3×C5C2×#576semidirect
430. C2×C5#5835semidirect
467. C2×C3#66086semidirect
470. C5C2×#5835semidirect
485. C3C2×#66086semidirect
489. C2#11755311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#921002
C2×C3×#41492
C2×C5×#9482
#117553112
C2×#913122
C2×#913112
C2×#913012
C22×#66532
C2×#660863
C2×#58355