Finite Group Databasebeta

← C2×#11755305 #14510012

Subgroups — C2×#11755305 #14510012

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×C5×#1009C211yesmaximal, characteristic, complemented
3C2×C3×#4094C211yesmaximal, characteristic, complemented
4#11755305C2116yesmaximal, direct product factor
5C2×#91305C213yesmaximal, complemented
6C2×#91304C213yesmaximal, complemented
7C2×#91303C213yesmaximal, complemented
8C22×#6654C213yesmaximal, complemented
9C2×#66169—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11#92100—24no—
12#92100C2218yescomplemented
13C2×#6821—21no—
14C2×D4×D15—23no—
15C2×#6817C2213yescomplemented
16C22×D60C2213yescomplemented
17C5×#1009—24no—
18C5×#1009C2218yescomplemented
19C2×C5×#239—21no—
20C2×C5×D3×D4—23no—
21C2×C5×#235C2213yescomplemented
22C22×C5×D12C2213yescomplemented
23C3×#4094C2218yescomplemented
24C2×C3×#681C2213yescomplemented
25C22×C3×#168C2213yescomplemented
26C2×#6663C2211yescharacteristic, complemented
27C2×#6660C2213yescomplemented
28C2×#6659C2213yescomplemented
29#91305C22124yescomplemented
30#91304C22124yescomplemented
31#91303C22124yescomplemented
32C2×#6654C2213yescomplemented
33C2×#6654C2216yescomplemented
34C2×#6654C22124yescomplemented
35C2×#5752—51nomaximal, Hall
36C2×C5×H(5,𝔽2)—31no—
37C2×#4149—31no—
38#66169—316no—
39C2×#4096—33no—
40C2×#4095—33no—
41C2×#4094D311yescharacteristic, complemented
42C2×#4078—33no—
43C22×#686—33no—
44C23×D15—23no—
45C23×C5×D3—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×C5×#67—23no—
63C5×#239—28no—
64C5×D3×D4—224no—
65C5×#235—26no—
66C5×#235C23112yescomplemented
67C2×C5×D12—23no—
68C2×C5×D12—26no—
69C2×C5×D12C2313yes—
70C2×C5×D12C23112yescomplemented
71C2×C4×C5×D3—23no—
72C2×C5×Dic6C2311yescharacteristic
73C3×#681C23112yescomplemented
74C2×C3×#168C2311yescharacteristic
75C2×C3×#168C2313yes—
76C2×C3×#168C23112yescomplemented
77#6663C2314yescomplemented
78#6660C23112yescomplemented
79#6659C23112yescomplemented
80#6654C23112yescomplemented
81#6654C23124yescomplemented
82C2×#1009—51no—
83C2×#1009D511yescharacteristic, complemented
84C2×C3×#131—51no—
85#5752—516no—
86C2×#908—53no—
87C2×#908—53no—
88C2×#904—53no—
89C22×D24—53no—
90C5×H(5,𝔽2)—38no—
91C5×H(5,𝔽2)—64no—
92C2×C5×#41—33no—
93C2×C5×#41—61no—
94C2×C5×#41C2×D311yescharacteristic
95C22×C5×D4—33no—
96C22×C5×D4—63no—
97#4149—38no—
98#4149—64no—
99C2×#713—61no—
100C2×D4×D5—63no—
101C2×#709—33no—
102C22×D20—33no—
103#4096—324no—
104#4095—324no—
105#4094C2×D318yescomplemented
106C2×#689—31no—
107C2×#688—33no—
108C2×#687—33no—
109#4078—324no—
110C2×#686—33no—
111C2×#686—36no—
112C2×#686—324no—
113C2×#681C2×D313yescomplemented
114C22×#168C2×D313yescomplemented
115C2×#576—151noSylow
116C23×C3×C5C2×D413yes—
117C22×D15—23no—
118C22×D15—212no—
119C22×D15—86no—
120C22×C5×D3—23no—
121C22×C5×D3—212no—
122C22×C5×D3—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—
137C5×#67—212no—
138C2×C5×Dic3—21no—
139C5×D12—23no—
140C5×D12—212no—
141C5×D12C2416yes—
142C4×C5×D3—212no—
143C5×Dic6—21no—
144C5×Dic6C2412yes—
145C3×#168C2416yes—
146C3×#168C2412yes—
147C2×C3×#41C2×D511yescharacteristic
148#1009—24no—
149#1009—58no—
150#1009—104no—
151#1009C2×D518yescomplemented
152C2×#239—21no—
153C2×#239—101no—
154C2×D3×D4—23no—
155C2×D3×D4—103no—
156C2×#235—53no—
157C2×#235C2×D513yescomplemented
158C22×D12—53no—
159C22×D12C2×D513yescomplemented
160C3×#131—58no—
161C2×C3×M16—53no—
162C22×C3×C8—53no—
163#908—524no—
164#908—524no—
165C2×Dic12—51no—
166#904—524no—
167C2×D24—53no—
168C2×D24—56no—
169C2×D24—524no—
170C2×#204—53no—
171C2×#204—53no—
172C24×C5—63no—
173C23×D5—63no—
174C5×#41—312no—
175C5×#41—68no—
176C5×#41—66no—
177C5×#41D1214yes—
178C5×#41C22×D314yes—
179C2×C5×Q8—31no—
180C2×C5×Q8D1211yescharacteristic
181C2×C5×D4—33no—
182C2×C5×D4—312no—
183C2×C5×D4—63no—
184C2×C5×D4—624no—
185C2×C5×D4—63no—
186C2×C5×D4—66no—
187C2×C5×D4D1213yes—
188C22×C4×C5—63no—
189C22×C4×C5C22×D313yes—
190C2×C22⋊D5—63no—
191#713—68no—
192D4×D5—624no—
193#709—312no—
194#709—66no—
195C2×D20—33no—
196C2×D20—312no—
197C2×D20—63no—
198C2×D20—66no—
199C2×C4×D5—63no—
200C2×Dic10—31no—
201#689—34no—
202#688—312no—
203#687—312no—
204#686—312no—
205#686—324no—
206#681C22×D3112yescomplemented
207C2×#168C22×D311yescharacteristic
208C2×#168C22×D313yes—
209C2×#168C22×D3112yescomplemented
210C2×H(5,𝔽2)—31no—
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—51no—
218C22×C3×C5—26no—
219C22×C3×C5C22×D416yes—
220C22×C3×C5C22×D411yescharacteristic
221C2×D15—26no—
222C2×D15—46no—
223C2×D15—812no—
224C2×C5×D3—26no—
225C2×C5×D3—46no—
226C2×C5×D3—812no—
227C3×C4×C5C22×D411yescharacteristic
228C3×C4×C5C22×D416yes—
229C3×C4×C5C2511yescharacteristic
230Dic15—22no—
231C5×Dic3—22no—
232C23×D3—23no—
233C23×D3—103no—
234C3×#41C22⋊D514yes—
235C3×#41C22×D514yes—
236C2×C3×Q8C22⋊D511yescharacteristic
237C2×C3×D4C22⋊D513yes—
238C22×C3×C4C22×D513yes—
239C2×#67—23no—
240C2×#67—103no—
241#239—28no—
242#239—108no—
243D3×D4—224no—
244D3×D4—1024no—
245#235—26no—
246#235—512no—
247#235—106no—
248#235C22×D5112yescomplemented
249C2×D12—23no—
250C2×D12—26no—
251C2×D12—53no—
252C2×D12—512no—
253C2×D12—103no—
254C2×D12—106no—
255C2×D12C22×D513yes—
256C2×D12C22×D5112yescomplemented
257C2×C4×D3—23no—
258C2×C4×D3—103no—
259C2×Dic6—51no—
260C2×Dic6C22×D511yescharacteristic
261C3×M16—512no—
262C2×C3×C8—53no—
263C2×C3×C8—51no—
264C2×C3×C8—512no—
265Dic12—54no—
266D24—512no—
267D24—524no—
268#204—512no—
269#204—512no—
270C23×C5—63no—
271C23×C5—612no—
272C23×C5—246no—
273C23×C5C2×D1213yes—
274C22×D5—63no—
275C22×D5—612no—
276C22×D5—246no—
277C5×Q8—32no—
278C5×Q8—61no—
279C5×Q8C2×D1214yes—
280C5×D4—36no—
281C5×D4—612no—
282C5×D4—63no—
283C5×D4—612no—
284C5×D4C2×D12112yes—
285C2×C4×C5—61no—
286C2×C4×C5—612no—
287C2×C4×C5C2×D1213yes—
288C2×C4×C5C2×D1216yes—
289C2×C4×C5C23×D311yescharacteristic
290C2×C4×C5C23×D316yes—
291C22⋊D5—612no—
292C2×Dic5—61no—
293D20—36no—
294D20—63no—
295D20—612no—
296C4×D5—612no—
297Dic10—32no—
298Dic10—61no—
299#168C23×D312yes—
300#168C23×D316yes—
301H(5,𝔽2)—38no—
302H(5,𝔽2)—64no—
303H(5,𝔽2)—158no—
304H(5,𝔽2)—304no—
305C2×#41—33no—
306C2×#41—61no—
307C2×#41—153no—
308C2×#41—301no—
309C2×#41D3×D511yescharacteristic
310C22×D4—33no—
311C22×D4—63no—
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—58no—
324C2×M16—53no—
325C22×C8—53no—
326C2×C3×C5—26no—
327C2×C3×C5#57612yescomplemented
328C2×C3×C5C23×D411yescharacteristic
329D15—46no—
330C5×D3—46no—
331C23×C3C2×C22⋊D513yes—
332C22×D3—23no—
333C22×D3—212no—
334C22×D3—86no—
335C22×D3—103no—
336C22×D3—1012no—
337C22×D3—406no—
338C3×Q8C2×C22⋊D514yes—
339C3×D4C2×C22⋊D5112yes—
340C2×C3×C4C2×C22⋊D513yes—
341C2×C3×C4C2×C22⋊D516yes—
342C2×C3×C4C23×D511yescharacteristic
343C2×C3×C4C23×D516yes—
344#67—212no—
345#67—1012no—
346C2×Dic3—21no—
347C2×Dic3—101no—
348D12—23no—
349D12—212no—
350D12—56no—
351D12—103no—
352D12—1012no—
353D12C23×D516yes—
354C4×D3—212no—
355C4×D3—1012no—
356Dic6—21no—
357Dic6—52no—
358Dic6—101no—
359Dic6C23×D512yes—
360C3×C8—56no—
361C3×C8—52no—
362C22×C5—26no—
363C22×C5—66no—
364C22×C5—126no—
365C22×C5—2412no—
366C22×C5C22×D1216yes—
367C22×C5C22×D1211yescharacteristic
368C2×D5—66no—
369C2×D5—126no—
370C2×D5—2412no—
371C4×C5—62no—
372C4×C5C22×D1211yescharacteristic
373C4×C5C22×D1216yes—
374C4×C5C24×D311yescharacteristic
375Dic5—62no—
376C24—63no—
377C24—303no—
378#41—312no—
379#41—68no—
380#41—66no—
381#41—1512no—
382#41—308no—
383#41—306no—
384#41#120314yes—
385#41C2×D3×D514yes—
386C2×Q8—31no—
387C2×Q8—151no—
388C2×Q8#120311yescharacteristic
389C2×D4—33no—
390C2×D4—312no—
391C2×D4—63no—
392C2×D4—624no—
393C2×D4—63no—
394C2×D4—66no—
395C2×D4—153no—
396C2×D4—1512no—
397C2×D4—303no—
398C2×D4—3024no—
399C2×D4—303no—
400C2×D4—306no—
401C2×D4#120313yes—
402C22×C4—63no—
403C22×C4—303no—
404C22×C4C2×D3×D513yes—
405Q16—154no—
406SD16—1512no—
407SD16—1512no—
408D8—1512no—
409D8—1524no—
410M16—512no—
411C2×C8—51no—
412C2×C8—53no—
413C2×C8—512no—
414C3×C5C2×#57611yescharacteristic, complemented, Hall
415C22×C3—26no—
416C22×C3C22×C22⋊D516yes—
417C22×C3C22×C22⋊D511yescharacteristic
418C2×D3—26no—
419C2×D3—46no—
420C2×D3—812no—
421C2×D3—106no—
422C2×D3—206no—
423C2×D3—4012no—
424C3×C4C22×C22⋊D511yescharacteristic
425C3×C4C22×C22⋊D516yes—
426C3×C4C24×D511yescharacteristic
427Dic3—22no—
428Dic3—102no—
429C2×C5—26no—
430C2×C5—126no—
431C2×C5#575212yescomplemented
432C2×C5C23×D1211yescharacteristic
433D5—126no—
434C23—63no—
435C23—612no—
436C23—246no—
437C23—303no—
438C23—3012no—
439C23—1206no—
440C23C2×#120313yes—
441Q8—32no—
442Q8—61no—
443Q8—152no—
444Q8—301no—
445Q8C2×#120314yes—
446D4—36no—
447D4—612no—
448D4—612no—
449D4—63no—
450D4—156no—
451D4—3012no—
452D4—3012no—
453D4—303no—
454D4C2×#1203112yes—
455C2×C4—61no—
456C2×C4—612no—
457C2×C4—301no—
458C2×C4—3012no—
459C2×C4C2×#120316yes—
460C2×C4C2×#120313yes—
461C2×C4C22×D3×D516yes—
462C2×C4C22×D3×D511yescharacteristic
463C8—52no—
464C8—56no—
465C2×C3—26no—
466C2×C3#6616912yescomplemented
467C2×C3C23×C22⋊D511yescharacteristic
468D3—46no—
469D3—206no—
470C5C2×#575211yescharacteristic, complemented, Sylow
471C22—26no—
472C22—66no—
473C22—126no—
474C22—2412no—
475C22—306no—
476C22—606no—
477C22—12012no—
478C22C22×#120316yes—
479C22C22×#120311yescharacteristic
480C4—62no—
481C4—302no—
482C4C22×#120316yes—
483C4C22×#120311yescharacteristic
484C4C23×D3×D511yescharacteristic
485C3C2×#6616911yescharacteristic, complemented, Sylow
486C2—26no—
487C2—126no—
488C2—606no—
489C2#1175530512yesdirect product factor
490C2C23×#120311yescharacteristic
subgroupG/H
centerC22C22×#1203
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×C5×#1009C2semidirect
3. C2×C3×#4094C2semidirect
4. #11755305C2direct (N × H)
5. C2×#91305C2semidirect
6. C2×#91304C2semidirect
7. C2×#91303C2semidirect
8. C22×#6654C2semidirect
12. #92100C22semidirect
15. C2×#6817C22semidirect
16. C22×D60C22semidirect
18. C5×#1009C22semidirect
21. C2×C5×#235C22semidirect
22. C22×C5×D12C22semidirect
23. C3×#4094C22semidirect
24. C2×C3×#681C22semidirect
25. C22×C3×#168C22semidirect
26. C2×#6663C22semidirect
27. C2×#6660C22semidirect
28. C2×#6659C22semidirect
29. #91305C22semidirect
30. #91304C22semidirect
31. #91303C22semidirect
32. C2×#6654C22semidirect
33. C2×#6654C22semidirect
34. C2×#6654C22semidirect
41. C2×#4094D3semidirect
55. #6817C23semidirect
59. C2×D60C23semidirect
66. C5×#235C23semidirect
70. C2×C5×D12C23semidirect
73. C3×#681C23semidirect
76. C2×C3×#168C23semidirect
77. #6663C23semidirect
78. #6660C23semidirect
79. #6659C23semidirect
80. #6654C23semidirect
81. #6654C23semidirect
83. C2×#1009D5semidirect
105. #4094C2×D3semidirect
113. C2×#681C2×D3semidirect
114. C22×#168C2×D3semidirect
151. #1009C2×D5semidirect
157. C2×#235C2×D5semidirect
159. C22×D12C2×D5semidirect
206. #681C22×D3semidirect
209. C2×#168C22×D3semidirect
248. #235C22×D5semidirect
256. C2×D12C22×D5semidirect
327. C2×C3×C5#576semidirect
414. C3×C5C2×#576semidirect
431. C2×C5#5752semidirect
466. C2×C3#66169semidirect
470. C5C2×#5752semidirect
485. C3C2×#66169semidirect
489. C2#11755305direct (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×C5×#10092
C2×C3×#40942
#117553052
C2×#913052
C2×#913042
C2×#913032
C22×#66542
C2×#661693
C2×#57525