Finite Group Databasebeta

← C2×#11755301 #14510011

Subgroups — C2×#11755301 #14510011

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×C5×#1009C211yesmaximal, characteristic, complemented
2C2×C3×#4149C211yesmaximal, characteristic, complemented
3C2×#91837C211yesmaximal, characteristic, complemented
4#11755301C2116yesmaximal, direct product factor
5C2×#91299C213yesmaximal, complemented
6C2×#91298C213yesmaximal, complemented
7C2×#91297C213yesmaximal, complemented
8C22×#6652C213yesmaximal, complemented
9C2×#66169—31nomaximal, Hall
10C2×C3×C5×#41C2211yescharacteristic
11C5×#1009—24no—
12C5×#1009C2218yescomplemented
13C2×C5×#239—21no—
14C2×C5×D3×D4—23no—
15C2×C5×#235C2213yescomplemented
16C22×C5×D12C2213yescomplemented
17C3×#4149—24no—
18C3×#4149C2218yescomplemented
19C2×C3×#713—21no—
20C2×C3×D4×D5—23no—
21C2×C3×#709C2213yescomplemented
22C22×C3×D20C2213yescomplemented
23#91837C2218yescomplemented
24C2×#6710C2213yescomplemented
25C22×C3⋊#168C2213yescomplemented
26C2×#6661C2211yescharacteristic, complemented
27C2×#6656C2213yescomplemented
28C2×#6655C2213yescomplemented
29#91299C22124yescomplemented
30#91298C22124yescomplemented
31#91297C22124yescomplemented
32C2×#6652C2213yescomplemented
33C2×#6652C2216yescomplemented
34C2×#6652C22124yescomplemented
35C2×#5835—51nomaximal, Hall
36C2×C5×H(5,𝔽2)—31no—
37C2×#4149D311yescharacteristic, complemented
38#66169—316no—
39C2×#4096—33no—
40C2×#4095—33no—
41C2×#4094—31no—
42C2×#4078—33no—
43C22×#686—33no—
44C23×C5×D3—23no—
45C23×C3×D5—23no—
46C3×C5×#41D414yes—
47C3×C5×#41C2314yes—
48C2×C3×C5×Q8D411yescharacteristic
49C2×C3×C5×D4D413yes—
50C22×C3×C4×C5C2313yes—
51C2×C5×#67—23no—
52C5×#239—28no—
53C5×D3×D4—224no—
54C5×#235—26no—
55C5×#235C23112yescomplemented
56C2×C5×D12—23no—
57C2×C5×D12—26no—
58C2×C5×D12C2313yes—
59C2×C5×D12C23112yescomplemented
60C2×C4×C5×D3—23no—
61C2×C5×Dic6C2311yescharacteristic
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
73#6710C23112yescomplemented
74C2×C3⋊#168C2311yescharacteristic
75C2×C3⋊#168C2313yes—
76C2×C3⋊#168C23112yescomplemented
77#6661C2314yescomplemented
78#6656C23112yescomplemented
79#6655C23112yescomplemented
80#6652C23112yescomplemented
81#6652C23124yescomplemented
82C2×C3×H(5,𝔽2)—51no—
83C2×#1009D511yescharacteristic, complemented
84#5835—516no—
85C2×#950—53no—
86C2×#949—53no—
87C2×#948—51no—
88C2×#932—53no—
89C22×#213—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—24no—
98#4149C2×D318yescomplemented
99C2×#713—21no—
100C2×D4×D5—23no—
101C2×#709C2×D313yescomplemented
102C22×D20C2×D313yescomplemented
103#4096—324no—
104#4095—324no—
105#4094—38no—
106C2×#689—31no—
107C2×#688—33no—
108C2×#687—33no—
109#4078—324no—
110C2×#686—33no—
111C2×#686—36no—
112C2×#686—324no—
113C2×#681—33no—
114C22×#168—33no—
115C2×#576—151noSylow
116C23×C3×C5C2×D413yes—
117C22×C5×D3—23no—
118C22×C5×D3—212no—
119C22×C5×D3—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—
129C5×#67—212no—
130C2×C5×Dic3—21no—
131C5×D12—23no—
132C5×D12—212no—
133C5×D12C2416yes—
134C4×C5×D3—212no—
135C5×Dic6—21no—
136C5×Dic6C2412yes—
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—
145C3⋊#168C2416yes—
146C3⋊#168C2412yes—
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—24no—
155#1009C2×D518yescomplemented
156C2×#239—21no—
157C2×D3×D4—23no—
158C2×#235C2×D513yescomplemented
159C22×D12C2×D513yescomplemented
160#950—524no—
161#949—524no—
162#948—58no—
163C2×#216—51no—
164C2×#215—53no—
165C2×#214—53no—
166#932—524no—
167C2×#213—53no—
168C2×#213—56no—
169C2×#213—524no—
170C2×#208—53no—
171C22×C3⋊C8—53no—
172C24×C5—63no—
173C23×D5—23no—
174C5×#41—312no—
175C5×#41—68no—
176C5×#41—66no—
177C5×#41#6714yes—
178C5×#41C22×D314yes—
179C2×C5×Q8—31no—
180C2×C5×Q8#6711yescharacteristic
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×D4#6713yes—
188C22×C4×C5—63no—
189C22×C4×C5C22×D313yes—
190C2×C22⋊D5—23no—
191#713—28no—
192D4×D5—224no—
193#709—26no—
194#709C22×D3112yescomplemented
195C2×D20—23no—
196C2×D20—26no—
197C2×D20C22×D313yes—
198C2×D20C22×D3112yescomplemented
199C2×C4×D5—23no—
200C2×Dic10C22×D311yescharacteristic
201#689—34no—
202#688—312no—
203#687—312no—
204#686—312no—
205#686—324no—
206#681—312no—
207C2×#168—312no—
208C2×#168—31no—
209C2×#168—33no—
210C2×H(5,𝔽2)—31no—
211C2×H(5,𝔽2)—51no—
212#576—1516no—
213C2×AGL(1,ℤ/8)—153no—
214C2×AGL(1,ℤ/8)—153no—
215C2×#135—153no—
216C22×D8—153no—
217C2×#131—151no—
218C22×C3×C5—26no—
219C22×C3×C5C22×D416yes—
220C22×C3×C5C22×D411yescharacteristic
221C2×C5×D3—26no—
222C2×C5×D3—46no—
223C2×C5×D3—812no—
224C2×C3×D5—26no—
225C2×C3×D5—46no—
226C2×C3×D5—812no—
227C3×C4×C5C22×D411yescharacteristic
228C3×C4×C5C22×D416yes—
229C3×C4×C5C2511yescharacteristic
230C3×Dic5—22no—
231C5×Dic3—22no—
232C24×C3—103no—
233C23×D3—23no—
234C3×#41—512no—
235C3×#41—108no—
236C3×#41—106no—
237C3×#41C22⋊D514yes—
238C3×#41C22×D514yes—
239C2×C3×Q8—51no—
240C2×C3×Q8C22⋊D511yescharacteristic
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×D4C22⋊D513yes—
248C22×C3×C4—103no—
249C22×C3×C4C22×D513yes—
250C2×#67—23no—
251#239—28no—
252D3×D4—224no—
253#235—26no—
254#235C22×D5112yescomplemented
255C2×D12—23no—
256C2×D12—26no—
257C2×D12C22×D513yes—
258C2×D12C22×D5112yescomplemented
259C2×C4×D3—23no—
260C2×Dic6C22×D511yescharacteristic
261#216—54no—
262#215—512no—
263#214—512no—
264#213—512no—
265#213—524no—
266#208—512no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8—53no—
269C2×C3⋊C8—512no—
270C23×C5—63no—
271C23×C5—612no—
272C23×C5—246no—
273C23×C5C2×#6713yes—
274C22×D5—23no—
275C22×D5—212no—
276C22×D5—86no—
277C5×Q8—32no—
278C5×Q8—61no—
279C5×Q8C2×#6714yes—
280C5×D4—36no—
281C5×D4—612no—
282C5×D4—63no—
283C5×D4—612no—
284C5×D4C2×#67112yes—
285C2×C4×C5—61no—
286C2×C4×C5—612no—
287C2×C4×C5C2×#6713yes—
288C2×C4×C5C2×#6716yes—
289C2×C4×C5C23×D311yescharacteristic
290C2×C4×C5C23×D316yes—
291C22⋊D5—212no—
292C2×Dic5—21no—
293D20—23no—
294D20—212no—
295D20C23×D316yes—
296C4×D5—212no—
297Dic10—21no—
298Dic10C23×D312yes—
299#168—32no—
300#168—36no—
301H(5,𝔽2)—38no—
302H(5,𝔽2)—58no—
303H(5,𝔽2)—64no—
304H(5,𝔽2)—104no—
305C2×#41—33no—
306C2×#41—53no—
307C2×#41—61no—
308C2×#41—101no—
309C2×#41D3×D511yescharacteristic
310C22×D4—33no—
311C22×D4—53no—
312C22×D4—63no—
313C22×D4—103no—
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—158no—
324C2×M16—153no—
325C22×C8—153no—
326C2×C3×C5—26no—
327C2×C3×C5#57612yescomplemented
328C2×C3×C5C23×D411yescharacteristic
329C3×D5—46no—
330C5×D3—46no—
331C23×C3—103no—
332C23×C3—1012no—
333C23×C3—406no—
334C23×C3C2×C22⋊D513yes—
335C22×D3—23no—
336C22×D3—212no—
337C22×D3—86no—
338C3×Q8—52no—
339C3×Q8—101no—
340C3×Q8C2×C22⋊D514yes—
341C3×D4—56no—
342C3×D4—1012no—
343C3×D4—103no—
344C3×D4—1012no—
345C3×D4C2×C22⋊D5112yes—
346C2×C3×C4—101no—
347C2×C3×C4—1012no—
348C2×C3×C4C2×C22⋊D513yes—
349C2×C3×C4C2×C22⋊D516yes—
350C2×C3×C4C23×D511yescharacteristic
351C2×C3×C4C23×D516yes—
352#67—212no—
353C2×Dic3—21no—
354D12—23no—
355D12—212no—
356D12C23×D516yes—
357C4×D3—212no—
358Dic6—21no—
359Dic6C23×D512yes—
360C3⋊C8—52no—
361C3⋊C8—56no—
362C22×C5—26no—
363C22×C5—66no—
364C22×C5—126no—
365C22×C5—2412no—
366C22×C5C22×#6716yes—
367C22×C5C22×#6711yescharacteristic
368C2×D5—26no—
369C2×D5—46no—
370C2×D5—812no—
371C4×C5—62no—
372C4×C5C22×#6711yescharacteristic
373C4×C5C22×#6716yes—
374C4×C5C24×D311yescharacteristic
375Dic5—22no—
376C24—63no—
377C24—103no—
378#41—312no—
379#41—512no—
380#41—68no—
381#41—66no—
382#41—108no—
383#41—106no—
384#41#120114yes—
385#41C2×D3×D514yes—
386C2×Q8—31no—
387C2×Q8—51no—
388C2×Q8#120111yescharacteristic
389C2×D4—33no—
390C2×D4—312no—
391C2×D4—53no—
392C2×D4—512no—
393C2×D4—63no—
394C2×D4—624no—
395C2×D4—63no—
396C2×D4—66no—
397C2×D4—103no—
398C2×D4—1024no—
399C2×D4—103no—
400C2×D4—106no—
401C2×D4#120113yes—
402C22×C4—63no—
403C22×C4—103no—
404C22×C4C2×D3×D513yes—
405Q16—154no—
406SD16—1512no—
407SD16—1512no—
408D8—1512no—
409D8—1524no—
410M16—1512no—
411C2×C8—151no—
412C2×C8—153no—
413C2×C8—1512no—
414C3×C5C2×#57611yescharacteristic, complemented, Hall
415C22×C3—26no—
416C22×C3—106no—
417C22×C3—206no—
418C22×C3—4012no—
419C22×C3C22×C22⋊D516yes—
420C22×C3C22×C22⋊D511yescharacteristic
421C2×D3—26no—
422C2×D3—46no—
423C2×D3—812no—
424C3×C4—102no—
425C3×C4C22×C22⋊D511yescharacteristic
426C3×C4C22×C22⋊D516yes—
427C3×C4C24×D511yescharacteristic
428Dic3—22no—
429C2×C5—26no—
430C2×C5—126no—
431C2×C5#583512yescomplemented
432C2×C5C23×#6711yescharacteristic
433D5—46no—
434C23—63no—
435C23—612no—
436C23—103no—
437C23—1012no—
438C23—246no—
439C23—406no—
440C23C2×#120113yes—
441Q8—32no—
442Q8—52no—
443Q8—61no—
444Q8—101no—
445Q8C2×#120114yes—
446D4—36no—
447D4—56no—
448D4—612no—
449D4—612no—
450D4—63no—
451D4—1012no—
452D4—1012no—
453D4—103no—
454D4C2×#1201112yes—
455C2×C4—61no—
456C2×C4—612no—
457C2×C4—101no—
458C2×C4—1012no—
459C2×C4C2×#120116yes—
460C2×C4C2×#120113yes—
461C2×C4C22×D3×D516yes—
462C2×C4C22×D3×D511yescharacteristic
463C8—152no—
464C8—156no—
465C2×C3—26no—
466C2×C3—206no—
467C2×C3#6616912yescomplemented
468C2×C3C23×C22⋊D511yescharacteristic
469D3—46no—
470C5C2×#583511yescharacteristic, complemented, Sylow
471C22—26no—
472C22—66no—
473C22—106no—
474C22—126no—
475C22—206no—
476C22—2412no—
477C22—4012no—
478C22C22×#120116yes—
479C22C22×#120111yescharacteristic
480C4—62no—
481C4—102no—
482C4C22×#120116yes—
483C4C22×#120111yescharacteristic
484C4C23×D3×D511yescharacteristic
485C3C2×#6616911yescharacteristic, complemented, Sylow
486C2—26no—
487C2—126no—
488C2—206no—
489C2#1175530112yesdirect product factor
490C2C23×#120111yescharacteristic
subgroupG/H
centerC22C22×#1201
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×C5×#1009C2semidirect
2. C2×C3×#4149C2semidirect
3. C2×#91837C2semidirect
4. #11755301C2direct (N × H)
5. C2×#91299C2semidirect
6. C2×#91298C2semidirect
7. C2×#91297C2semidirect
8. C22×#6652C2semidirect
12. C5×#1009C22semidirect
15. C2×C5×#235C22semidirect
16. C22×C5×D12C22semidirect
18. C3×#4149C22semidirect
21. C2×C3×#709C22semidirect
22. C22×C3×D20C22semidirect
23. #91837C22semidirect
24. C2×#6710C22semidirect
25. C22×C3⋊#168C22semidirect
26. C2×#6661C22semidirect
27. C2×#6656C22semidirect
28. C2×#6655C22semidirect
29. #91299C22semidirect
30. #91298C22semidirect
31. #91297C22semidirect
32. C2×#6652C22semidirect
33. C2×#6652C22semidirect
34. C2×#6652C22semidirect
37. C2×#4149D3semidirect
55. C5×#235C23semidirect
59. C2×C5×D12C23semidirect
66. C3×#709C23semidirect
70. C2×C3×D20C23semidirect
73. #6710C23semidirect
76. C2×C3⋊#168C23semidirect
77. #6661C23semidirect
78. #6656C23semidirect
79. #6655C23semidirect
80. #6652C23semidirect
81. #6652C23semidirect
83. C2×#1009D5semidirect
98. #4149C2×D3semidirect
101. C2×#709C2×D3semidirect
102. C22×D20C2×D3semidirect
155. #1009C2×D5semidirect
158. C2×#235C2×D5semidirect
159. C22×D12C2×D5semidirect
194. #709C22×D3semidirect
198. C2×D20C22×D3semidirect
254. #235C22×D5semidirect
258. C2×D12C22×D5semidirect
327. C2×C3×C5#576semidirect
414. C3×C5C2×#576semidirect
431. C2×C5#5835semidirect
467. C2×C3#66169semidirect
470. C5C2×#5835semidirect
485. C3C2×#66169semidirect
489. C2#11755301direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#10092
C2×C3×#41492
C2×#918372
#117553012
C2×#912992
C2×#912982
C2×#912972
C22×#66522
C2×#661693
C2×#58355