Finite Group Databasebeta

← C2×#11756594 #14509959

Subgroups — C2×#11756594 #14509959

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×C3×C5×H(5,𝔽2)C211yesmaximal, characteristic, complemented
2C2×#92100C211yesmaximal, characteristic, complemented
3#11756594C2116yesmaximal, direct product factor
4C2×#91839C213yesmaximal, complemented
5C2×#91838C213yesmaximal, complemented
6C2×#91837C211yesmaximal, characteristic, complemented
7C2×#91821C213yesmaximal, complemented
8C22×#6715C213yesmaximal, complemented
9C2×#66169—31nomaximal, Hall
10C3×C5×H(5,𝔽2)—24no—
11C3×C5×H(5,𝔽2)C2218yescomplemented
12C2×C3×C5×#41—21no—
13C2×C3×C5×#41C2211yescharacteristic
14C2×C3×C5×#41C2213yescomplemented
15C22×C3×C5×D4—23no—
16C22×C3×C5×D4C2213yescomplemented
17#92100—24no—
18#92100C2218yescomplemented
19C2×#6821—21no—
20C2×D4×D15—23no—
21C2×#6817C2213yescomplemented
22C22×D60C2213yescomplemented
23#91839C22124yescomplemented
24#91838C22124yescomplemented
25#91837C2218yescomplemented
26C2×#6718C2211yescharacteristic, complemented
27C2×#6717C2213yescomplemented
28C2×#6716C2213yescomplemented
29#91821C22124yescomplemented
30C2×#6715C2213yescomplemented
31C2×#6715C2216yescomplemented
32C2×#6715C22124yescomplemented
33C2×#6710C2213yescomplemented
34C22×C3⋊#168C2213yescomplemented
35C2×#5835—51nomaximal, Hall
36C2×C5×H(5,𝔽2)D311yescharacteristic, complemented
37C2×#4149—31no—
38#66169—316no—
39C2×#4096—33no—
40C2×#4095—33no—
41C2×#4094—31no—
42C2×#4078—33no—
43C22×#686—33no—
44C24×C3×C5—23no—
45C23×D15—23no—
46C3×C5×#41—28no—
47C3×C5×#41—26no—
48C3×C5×#41D414yes—
49C3×C5×#41C2314yes—
50C3×C5×#41C23112yescomplemented
51C2×C3×C5×Q8D411yescharacteristic
52C2×C3×C5×Q8C2311yescharacteristic
53C2×C3×C5×D4—23no—
54C2×C3×C5×D4—224no—
55C2×C3×C5×D4—23no—
56C2×C3×C5×D4—26no—
57C2×C3×C5×D4D413yes—
58C2×C3×C5×D4C2313yes—
59C2×C3×C5×D4C23112yescomplemented
60C22×C3×C4×C5—23no—
61C22×C3×C4×C5C2313yes—
62C2×#1220—23no—
63#6821—28no—
64D4×D15—224no—
65#6817—26no—
66#6817C23112yescomplemented
67C2×D60—23no—
68C2×D60—26no—
69C2×D60C2313yes—
70C2×D60C23112yescomplemented
71C2×C4×D15—23no—
72C2×Dic30C2311yescharacteristic
73#6718C2314yescomplemented
74#6717C23112yescomplemented
75#6716C23112yescomplemented
76#6715C23112yescomplemented
77#6715C23124yescomplemented
78#6710C23112yescomplemented
79C2×C3⋊#168C2311yescharacteristic
80C2×C3⋊#168C2313yes—
81C2×C3⋊#168C23112yescomplemented
82C2×C3×H(5,𝔽2)D511yescharacteristic, complemented
83C2×#1009—51no—
84#5835—516no—
85C2×#950—53no—
86C2×#949—53no—
87C2×#948—51no—
88C2×#932—53no—
89C22×#213—53no—
90C5×H(5,𝔽2)—24no—
91C5×H(5,𝔽2)C2×D318yescomplemented
92C2×C5×#41—21no—
93C2×C5×#41C2×D311yescharacteristic
94C2×C5×#41C2×D313yescomplemented
95C22×C5×D4—23no—
96C22×C5×D4C2×D313yescomplemented
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#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×C5—23no—
117C23×C3×C5—212no—
118C23×C3×C5—86no—
119C23×C3×C5C2×D413yes—
120C22×D15—23no—
121C22×D15—212no—
122C22×D15—86no—
123C3×C5×Q8—21no—
124C3×C5×Q8C2×D414yes—
125C3×C5×Q8C2412yes—
126C3×C5×D4—212no—
127C3×C5×D4—23no—
128C3×C5×D4—212no—
129C3×C5×D4C2×D4112yes—
130C3×C5×D4C2416yes—
131C2×C3×C4×C5—21no—
132C2×C3×C4×C5—212no—
133C2×C3×C4×C5C2×D413yes—
134C2×C3×C4×C5C2×D416yes—
135C2×C3×C4×C5C2411yescharacteristic
136C2×C3×C4×C5C2416yes—
137#1220—212no—
138C2×Dic15—21no—
139D60—23no—
140D60—212no—
141D60C2416yes—
142C4×D15—212no—
143Dic30—21no—
144Dic30C2412yes—
145C3⋊#168C2412yes—
146C3⋊#168C2416yes—
147C3×H(5,𝔽2)—24no—
148C3×H(5,𝔽2)C2×D518yescomplemented
149C2×C3×#41—21no—
150C2×C3×#41C2×D511yescharacteristic
151C2×C3×#41C2×D513yescomplemented
152C22×C3×D4—23no—
153C22×C3×D4C2×D513yescomplemented
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#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—23no—
173C23×D5—63no—
174C5×#41—28no—
175C5×#41—26no—
176C5×#41#6714yes—
177C5×#41C22×D314yes—
178C5×#41C22×D3112yescomplemented
179C2×C5×Q8#6711yescharacteristic
180C2×C5×Q8C22×D311yescharacteristic
181C2×C5×D4—23no—
182C2×C5×D4—224no—
183C2×C5×D4—23no—
184C2×C5×D4—26no—
185C2×C5×D4#6713yes—
186C2×C5×D4C22×D313yes—
187C2×C5×D4C22×D3112yescomplemented
188C22×C4×C5—23no—
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#681—312no—
207C2×#168—312no—
208C2×#168—31no—
209C2×#168—33no—
210C2×H(5,𝔽2)—151no—
211C2×H(5,𝔽2)D1511yescharacteristic, complemented
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×C5—26no—
220C22×C3×C5—46no—
221C22×C3×C5—812no—
222C22×C3×C5C22×D416yes—
223C22×C3×C5C22×D411yescharacteristic
224C2×D15—26no—
225C2×D15—46no—
226C2×D15—812no—
227C3×C4×C5—22no—
228C3×C4×C5C22×D411yescharacteristic
229C3×C4×C5C22×D416yes—
230C3×C4×C5C2511yescharacteristic
231Dic15—22no—
232C24×C3—23no—
233C23×D3—103no—
234C3×#41—28no—
235C3×#41—26no—
236C3×#41C22⋊D514yes—
237C3×#41C22×D514yes—
238C3×#41C22×D5112yescomplemented
239C2×C3×Q8C22⋊D511yescharacteristic
240C2×C3×Q8C22×D511yescharacteristic
241C2×C3×D4—23no—
242C2×C3×D4—224no—
243C2×C3×D4—23no—
244C2×C3×D4—26no—
245C2×C3×D4C22⋊D513yes—
246C2×C3×D4C22×D513yes—
247C2×C3×D4C22×D5112yescomplemented
248C22×C3×C4—23no—
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#208—512no—
267C2×C3⋊C8—51no—
268C2×C3⋊C8—53no—
269C2×C3⋊C8—512no—
270C23×C5—23no—
271C23×C5—212no—
272C23×C5—86no—
273C23×C5C2×#6713yes—
274C22×D5—63no—
275C22×D5—612no—
276C22×D5—246no—
277C5×Q8—21no—
278C5×Q8C2×#6714yes—
279C5×Q8C23×D312yes—
280C5×D4—212no—
281C5×D4—23no—
282C5×D4—212no—
283C5×D4C2×#67112yes—
284C5×D4C23×D316yes—
285C2×C4×C5—21no—
286C2×C4×C5—212no—
287C2×C4×C5C2×#6713yes—
288C2×C4×C5C2×#6716yes—
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#168—32no—
300#168—36no—
301H(5,𝔽2)—24no—
302H(5,𝔽2)—158no—
303H(5,𝔽2)—304no—
304H(5,𝔽2)C2×D1518yescomplemented
305C2×#41—21no—
306C2×#41—153no—
307C2×#41—301no—
308C2×#41C2×D1511yescharacteristic
309C2×#41C2×D1513yescomplemented
310C22×D4—23no—
311C22×D4—153no—
312C22×D4—303no—
313C22×D4C2×D1513yescomplemented
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—46no—
328C2×C3×C5#57612yescomplemented
329C2×C3×C5C23×D411yescharacteristic
330D15—46no—
331C23×C3—23no—
332C23×C3—212no—
333C23×C3—86no—
334C23×C3C2×C22⋊D513yes—
335C22×D3—103no—
336C22×D3—1012no—
337C22×D3—406no—
338C3×Q8—21no—
339C3×Q8C2×C22⋊D514yes—
340C3×Q8C23×D512yes—
341C3×D4—212no—
342C3×D4—23no—
343C3×D4—212no—
344C3×D4C2×C22⋊D5112yes—
345C3×D4C23×D516yes—
346C2×C3×C4—21no—
347C2×C3×C4—212no—
348C2×C3×C4C2×C22⋊D513yes—
349C2×C3×C4C2×C22⋊D516yes—
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⋊C8—52no—
361C3⋊C8—56no—
362C22×C5—26no—
363C22×C5—26no—
364C22×C5—46no—
365C22×C5—812no—
366C22×C5C22×#6716yes—
367C22×C5C22×#6711yescharacteristic
368C2×D5—66no—
369C2×D5—126no—
370C2×D5—2412no—
371C4×C5—22no—
372C4×C5C22×#6711yescharacteristic
373C4×C5C22×#6716yes—
374C4×C5C24×D311yescharacteristic
375Dic5—62no—
376C24—23no—
377C24—303no—
378#41—28no—
379#41—26no—
380#41—1512no—
381#41—308no—
382#41—306no—
383#41#122014yes—
384#41C22×D1514yes—
385#41C22×D15112yescomplemented
386C2×Q8—151no—
387C2×Q8#122011yescharacteristic
388C2×Q8C22×D1511yescharacteristic
389C2×D4—23no—
390C2×D4—224no—
391C2×D4—23no—
392C2×D4—26no—
393C2×D4—153no—
394C2×D4—1512no—
395C2×D4—303no—
396C2×D4—3024no—
397C2×D4—303no—
398C2×D4—306no—
399C2×D4#122013yes—
400C2×D4C22×D1513yes—
401C2×D4C22×D15112yescomplemented
402C22×C4—23no—
403C22×C4—303no—
404C22×C4C22×D1513yes—
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—26no—
417C22×C3—46no—
418C22×C3—812no—
419C22×C3C22×C22⋊D516yes—
420C22×C3C22×C22⋊D511yescharacteristic
421C2×D3—106no—
422C2×D3—206no—
423C2×D3—4012no—
424C3×C4—22no—
425C3×C4C22×C22⋊D511yescharacteristic
426C3×C4C22×C22⋊D516yes—
427C3×C4C24×D511yescharacteristic
428Dic3—102no—
429C2×C5—26no—
430C2×C5—46no—
431C2×C5#583512yescomplemented
432C2×C5C23×#6711yescharacteristic
433D5—126no—
434C23—23no—
435C23—212no—
436C23—86no—
437C23—303no—
438C23—3012no—
439C23—1206no—
440C23C2×#122013yes—
441Q8—21no—
442Q8—152no—
443Q8—301no—
444Q8C2×#122014yes—
445Q8C23×D1512yes—
446D4—212no—
447D4—23no—
448D4—212no—
449D4—156no—
450D4—3012no—
451D4—3012no—
452D4—303no—
453D4C2×#1220112yes—
454D4C23×D1516yes—
455C2×C4—21no—
456C2×C4—212no—
457C2×C4—301no—
458C2×C4—3012no—
459C2×C4C2×#122016yes—
460C2×C4C2×#122013yes—
461C2×C4C23×D1516yes—
462C2×C4C23×D1511yescharacteristic
463C8—152no—
464C8—156no—
465C2×C3—26no—
466C2×C3—46no—
467C2×C3#6616912yescomplemented
468C2×C3C23×C22⋊D511yescharacteristic
469D3—206no—
470C5C2×#583511yescharacteristic, complemented, Sylow
471C22—26no—
472C22—26no—
473C22—46no—
474C22—812no—
475C22—306no—
476C22—606no—
477C22—12012no—
478C22C22×#122016yes—
479C22C22×#122011yescharacteristic
480C4—22no—
481C4—302no—
482C4C22×#122016yes—
483C4C22×#122011yescharacteristic
484C4C24×D1511yescharacteristic
485C3C2×#6616911yescharacteristic, complemented, Sylow
486C2—26no—
487C2—46no—
488C2—606no—
489C2#1175659412yesdirect product factor
490C2C23×#122011yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC3×C4×C5C25
FrattiniC4C24×D15
FittingC2×C3×C5×H(5,𝔽2)C2
socleC22×C3×C5C22×D4
hypercenterC2×H(5,𝔽2)D15
hypocenterC3×C5C2×#576
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×H(5,𝔽2)

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×H(5,𝔽2)C2semidirect
2. C2×#92100C2semidirect
3. #11756594C2direct (N × H)
4. C2×#91839C2semidirect
5. C2×#91838C2semidirect
6. C2×#91837C2semidirect
7. C2×#91821C2semidirect
8. C22×#6715C2semidirect
11. C3×C5×H(5,𝔽2)C22semidirect
14. C2×C3×C5×#41C22semidirect
16. C22×C3×C5×D4C22semidirect
18. #92100C22semidirect
21. C2×#6817C22semidirect
22. C22×D60C22semidirect
23. #91839C22semidirect
24. #91838C22semidirect
25. #91837C22semidirect
26. C2×#6718C22semidirect
27. C2×#6717C22semidirect
28. C2×#6716C22semidirect
29. #91821C22semidirect
30. C2×#6715C22semidirect
31. C2×#6715C22semidirect
32. C2×#6715C22semidirect
33. C2×#6710C22semidirect
34. C22×C3⋊#168C22semidirect
36. C2×C5×H(5,𝔽2)D3semidirect
50. C3×C5×#41C23semidirect
59. C2×C3×C5×D4C23semidirect
66. #6817C23semidirect
70. C2×D60C23semidirect
73. #6718C23semidirect
74. #6717C23semidirect
75. #6716C23semidirect
76. #6715C23semidirect
77. #6715C23semidirect
78. #6710C23semidirect
81. C2×C3⋊#168C23semidirect
82. C2×C3×H(5,𝔽2)D5semidirect
91. C5×H(5,𝔽2)C2×D3semidirect
94. C2×C5×#41C2×D3semidirect
96. C22×C5×D4C2×D3semidirect
148. C3×H(5,𝔽2)C2×D5semidirect
151. C2×C3×#41C2×D5semidirect
153. C22×C3×D4C2×D5semidirect
178. C5×#41C22×D3semidirect
187. C2×C5×D4C22×D3semidirect
211. C2×H(5,𝔽2)D15semidirect
238. C3×#41C22×D5semidirect
247. C2×C3×D4C22×D5semidirect
304. H(5,𝔽2)C2×D15semidirect
309. C2×#41C2×D15semidirect
313. C22×D4C2×D15semidirect
328. C2×C3×C5#576semidirect
385. #41C22×D15semidirect
401. C2×D4C22×D15semidirect
414. C3×C5C2×#576semidirect
431. C2×C5#5835semidirect
467. C2×C3#66169semidirect
470. C5C2×#5835semidirect
485. C3C2×#66169semidirect
489. C2#11756594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×H(5,𝔽2)2
C2×#921002
#117565942
C2×#918392
C2×#918382
C2×#918372
C2×#918212
C22×#67152
C2×#661693
C2×#58355