Finite Group Databasebeta

← C2×#11756596 #14510026

Subgroups — C2×#11756596 #14510026

Order 1920.

2920 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×2−1+4C211yesmaximal, characteristic, complemented
2C2×#92100C211yesmaximal, characteristic, complemented
3#11756596C2116yesmaximal, direct product factor
4C2×#91839C213yesmaximal, complemented
5C2×#91838C213yesmaximal, complemented
6C2×#91837C211yesmaximal, characteristic, complemented
7C2×#91831C213yesmaximal, complemented
8C22×#6717C213yesmaximal, complemented
9C2×#66171—31nomaximal, Hall
10C3×C5×2−1+4—24no—
11C3×C5×2−1+4C2218yescomplemented
12C2×C3×C5×#41—23no—
13C2×C3×C5×#41C2211yescharacteristic
14C2×C3×C5×#41C2213yescomplemented
15C22×C3×C5×Q8—21no—
16C22×C3×C5×Q8C2213yescomplemented
17#92100—24no—
18#92100C2218yescomplemented
19C2×#6821—21no—
20C2×D4×D15—23no—
21C2×#6817C2213yes—
22C22×D60C2213yes—
23#91839C22124yescomplemented
24#91838C22124yescomplemented
25#91837C2218yescomplemented
26C2×#6718C2213yescomplemented
27#91831C22124yescomplemented
28C2×#6717C2213yescomplemented
29C2×#6717C2216yescomplemented
30C2×#6717C22124yescomplemented
31C2×#6716C2211yescharacteristic, complemented
32C2×#6715C2213yescomplemented
33C2×#6710C2213yescomplemented
34C22×C3⋊#168C2213yescomplemented
35C2×#5837—51nomaximal, Hall
36C2×C5×2−1+4D311yescharacteristic, complemented
37C2×#4149—31no—
38#66171—316no—
39C2×#4096—33no—
40C2×#4095—33no—
41C2×#4094—31no—
42C2×#4088—33no—
43C22×#688—33no—
44C23×D15—23no—
45C3×C5×#41—224no—
46C3×C5×#41—26no—
47C3×C5×#41D414yes—
48C3×C5×#41C2314yes—
49C3×C5×#41C23112yescomplemented
50C2×C3×C5×Q8—28no—
51C2×C3×C5×Q8—23no—
52C2×C3×C5×Q8—26no—
53C2×C3×C5×Q8D411yescharacteristic
54C2×C3×C5×Q8C2313yes—
55C2×C3×C5×Q8C23112yescomplemented
56C2×C3×C5×D4—23no—
57C2×C3×C5×D4D413yes—
58C2×C3×C5×D4C2311yescharacteristic
59C22×C3×C4×C5—23no—
60C22×C3×C4×C5—23no—
61C22×C3×C4×C5C2313yes—
62C2×#1220—23no—
63#6821—28no—
64D4×D15—224no—
65#6817—26no—
66#6817C23112yes—
67C2×D60—23no—
68C2×D60—26no—
69C2×D60C2313yes—
70C2×D60C23112yes—
71C2×C4×D15—23no—
72C2×Dic30C2311yescharacteristic
73#6718C23112yescomplemented
74#6717C23112yescomplemented
75#6717C23124yescomplemented
76#6716C2314yescomplemented
77#6715C23112yescomplemented
78#6710C23112yescomplemented
79C2×C3⋊#168C2311yescharacteristic
80C2×C3⋊#168C2313yes—
81C2×C3⋊#168C23112yescomplemented
82C2×C3×2−1+4D511yescharacteristic, complemented
83C2×#1009—51no—
84#5837—516no—
85C2×#950—53no—
86C2×#949—53no—
87C2×#948—51no—
88C2×#942—53no—
89C22×#215—53no—
90C5×2−1+4—24no—
91C5×2−1+4C2×D318yescomplemented
92C2×C5×#41—23no—
93C2×C5×#41C2×D311yescharacteristic
94C2×C5×#41C2×D313yescomplemented
95C22×C5×Q8—21no—
96C22×C5×Q8C2×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—33no—
107#4088—324no—
108C2×#688—33no—
109C2×#688—36no—
110C2×#688—324no—
111C2×#687—31no—
112C2×#686—33no—
113C2×#681—33no—
114C22×#168—33no—
115C2×#577—151noSylow
116C23×C3×C5—21no—
117C23×C3×C5C2×D413yes—
118C22×D15—23no—
119C22×D15—212no—
120C22×D15—86no—
121C3×C5×Q8—23no—
122C3×C5×Q8—212no—
123C3×C5×Q8C2×D414yes—
124C3×C5×Q8C2416yes—
125C3×C5×D4—212no—
126C3×C5×D4—21no—
127C3×C5×D4C2×D4112yes—
128C3×C5×D4C2412yes—
129C2×C3×C4×C5—23no—
130C2×C3×C4×C5—212no—
131C2×C3×C4×C5—212no—
132C2×C3×C4×C5C2×D413yes—
133C2×C3×C4×C5C2×D416yes—
134C2×C3×C4×C5C2411yescharacteristic
135C2×C3×C4×C5C2416yes—
136#1220—212no—
137C2×Dic15—21no—
138D60—23no—
139D60—212no—
140D60C2416yes—
141C4×D15—212no—
142Dic30—21no—
143Dic30C2412yes—
144C3⋊#168C2412yes—
145C3⋊#168C2416yes—
146C3×2−1+4—24no—
147C3×2−1+4C2×D518yescomplemented
148C2×C3×#41—23no—
149C2×C3×#41C2×D511yescharacteristic
150C2×C3×#41C2×D513yescomplemented
151C22×C3×Q8—21no—
152C22×C3×Q8C2×D513yescomplemented
153#1009—58no—
154#1009—104no—
155C2×#239—101no—
156C2×D3×D4—103no—
157C2×#235—53no—
158C22×D12—53no—
159#950—524no—
160#949—524no—
161#948—58no—
162C2×#216—53no—
163#942—524no—
164C2×#215—53no—
165C2×#215—56no—
166C2×#215—524no—
167C2×#214—51no—
168C2×#213—53no—
169C2×#208—53no—
170C22×C3⋊C8—53no—
171C23×D5—63no—
172C5×#41—224no—
173C5×#41—26no—
174C5×#41#6714yes—
175C5×#41C22×D314yes—
176C5×#41C22×D3112yescomplemented
177C2×C5×Q8—28no—
178C2×C5×Q8—23no—
179C2×C5×Q8—26no—
180C2×C5×Q8#6711yescharacteristic
181C2×C5×Q8C22×D313yes—
182C2×C5×Q8C22×D3112yescomplemented
183C2×C5×D4—23no—
184C2×C5×D4#6713yes—
185C2×C5×D4C22×D311yescharacteristic
186C22×C4×C5—23no—
187C22×C4×C5—23no—
188C22×C4×C5C22×D313yes—
189C2×C22⋊D5—63no—
190#713—68no—
191D4×D5—624no—
192#709—312no—
193#709—66no—
194C2×D20—33no—
195C2×D20—312no—
196C2×D20—63no—
197C2×D20—66no—
198C2×C4×D5—63no—
199C2×Dic10—31no—
200#689—312no—
201#688—312no—
202#688—324no—
203#687—34no—
204#686—312no—
205#681—312no—
206C2×#168—312no—
207C2×#168—31no—
208C2×#168—33no—
209C2×2−1+4D1511yescharacteristic, complemented
210C2×H(5,𝔽2)—151no—
211#577—1516no—
212C2×#137—153no—
213C2×AGL(1,ℤ/8)—153no—
214C2×#135—153no—
215C22×SD16—153no—
216C2×#131—151no—
217C22×C3×C5—26no—
218C22×C3×C5—22no—
219C22×C3×C5—42no—
220C22×C3×C5C22×D416yes—
221C22×C3×C5C22×D411yescharacteristic
222C2×D15—26no—
223C2×D15—46no—
224C2×D15—812no—
225C3×C4×C5—26no—
226C3×C4×C5C22×D411yescharacteristic
227C3×C4×C5C22×D416yes—
228C3×C4×C5C2511yescharacteristic
229Dic15—22no—
230C23×D3—103no—
231C3×#41—224no—
232C3×#41—26no—
233C3×#41C22⋊D514yes—
234C3×#41C22×D514yes—
235C3×#41C22×D5112yescomplemented
236C2×C3×Q8—28no—
237C2×C3×Q8—23no—
238C2×C3×Q8—26no—
239C2×C3×Q8C22⋊D511yescharacteristic
240C2×C3×Q8C22×D513yes—
241C2×C3×Q8C22×D5112yescomplemented
242C2×C3×D4—23no—
243C2×C3×D4C22⋊D513yes—
244C2×C3×D4C22×D511yescharacteristic
245C22×C3×C4—23no—
246C22×C3×C4—23no—
247C22×C3×C4C22×D513yes—
248C2×#67—103no—
249#239—108no—
250D3×D4—1024no—
251#235—512no—
252#235—106no—
253C2×D12—53no—
254C2×D12—512no—
255C2×D12—103no—
256C2×D12—106no—
257C2×C4×D3—103no—
258C2×Dic6—51no—
259#216—512no—
260#215—512no—
261#215—524no—
262#214—54no—
263#213—512no—
264#208—512no—
265C2×C3⋊C8—51no—
266C2×C3⋊C8—53no—
267C2×C3⋊C8—512no—
268C23×C5—21no—
269C23×C5C2×#6713yes—
270C22×D5—63no—
271C22×D5—612no—
272C22×D5—246no—
273C5×Q8—23no—
274C5×Q8—212no—
275C5×Q8C2×#6714yes—
276C5×Q8C23×D316yes—
277C5×D4—212no—
278C5×D4—21no—
279C5×D4C2×#67112yes—
280C5×D4C23×D312yes—
281C2×C4×C5—23no—
282C2×C4×C5—212no—
283C2×C4×C5—212no—
284C2×C4×C5C2×#6713yes—
285C2×C4×C5C2×#6716yes—
286C2×C4×C5C23×D311yescharacteristic
287C2×C4×C5C23×D316yes—
288C22⋊D5—612no—
289C2×Dic5—61no—
290D20—36no—
291D20—63no—
292D20—612no—
293C4×D5—612no—
294Dic10—32no—
295Dic10—61no—
296#168—32no—
297#168—36no—
2982−1+4—24no—
2992−1+4C2×D1518yescomplemented
300H(5,𝔽2)—158no—
301H(5,𝔽2)—304no—
302C2×#41—23no—
303C2×#41—153no—
304C2×#41—301no—
305C2×#41C2×D1511yescharacteristic
306C2×#41C2×D1513yescomplemented
307C22×Q8—21no—
308C22×Q8C2×D1513yescomplemented
309C22×D4—153no—
310C22×D4—303no—
311#137—1524no—
312AGL(1,ℤ/8)—1524no—
313#135—1524no—
314C2×Q16—153no—
315C2×SD16—153no—
316C2×SD16—156no—
317C2×SD16—1524no—
318C2×SD16—151no—
319C2×D8—153no—
320#131—158no—
321C2×M16—153no—
322C22×C8—153no—
323C2×C3×C5—26no—
324C2×C3×C5—42no—
325C2×C3×C5#57712yescomplemented
326C2×C3×C5C23×D411yescharacteristic
327D15—46no—
328C23×C3—21no—
329C23×C3C2×C22⋊D513yes—
330C22×D3—103no—
331C22×D3—1012no—
332C22×D3—406no—
333C3×Q8—23no—
334C3×Q8—212no—
335C3×Q8C2×C22⋊D514yes—
336C3×Q8C23×D516yes—
337C3×D4—212no—
338C3×D4—21no—
339C3×D4C2×C22⋊D5112yes—
340C3×D4C23×D512yes—
341C2×C3×C4—23no—
342C2×C3×C4—212no—
343C2×C3×C4—212no—
344C2×C3×C4C2×C22⋊D513yes—
345C2×C3×C4C2×C22⋊D516yes—
346C2×C3×C4C23×D511yescharacteristic
347C2×C3×C4C23×D516yes—
348#67—1012no—
349C2×Dic3—101no—
350D12—56no—
351D12—103no—
352D12—1012no—
353C4×D3—1012no—
354Dic6—52no—
355Dic6—101no—
356C3⋊C8—52no—
357C3⋊C8—56no—
358C22×C5—26no—
359C22×C5—22no—
360C22×C5—42no—
361C22×C5C22×#6716yes—
362C22×C5C22×#6711yescharacteristic
363C2×D5—66no—
364C2×D5—126no—
365C2×D5—2412no—
366C4×C5—26no—
367C4×C5C22×#6711yescharacteristic
368C4×C5C22×#6716yes—
369C4×C5C24×D311yescharacteristic
370Dic5—62no—
371C24—303no—
372#41—224no—
373#41—26no—
374#41—1512no—
375#41—308no—
376#41—306no—
377#41#122014yes—
378#41C22×D1514yes—
379#41C22×D15112yescomplemented
380C2×Q8—28no—
381C2×Q8—23no—
382C2×Q8—26no—
383C2×Q8—151no—
384C2×Q8#122011yescharacteristic
385C2×Q8C22×D1513yes—
386C2×Q8C22×D15112yescomplemented
387C2×D4—23no—
388C2×D4—153no—
389C2×D4—1512no—
390C2×D4—303no—
391C2×D4—3024no—
392C2×D4—303no—
393C2×D4—306no—
394C2×D4#122013yes—
395C2×D4C22×D1511yescharacteristic
396C22×C4—23no—
397C22×C4—23no—
398C22×C4—303no—
399C22×C4C22×D1513yes—
400Q16—1512no—
401SD16—1512no—
402SD16—1524no—
403SD16—154no—
404D8—1512no—
405M16—1512no—
406C2×C8—151no—
407C2×C8—153no—
408C2×C8—1512no—
409C3×C5C2×#57711yescharacteristic, complemented, Hall
410C22×C3—26no—
411C22×C3—22no—
412C22×C3—42no—
413C22×C3C22×C22⋊D516yes—
414C22×C3C22×C22⋊D511yescharacteristic
415C2×D3—106no—
416C2×D3—206no—
417C2×D3—4012no—
418C3×C4—26no—
419C3×C4C22×C22⋊D511yescharacteristic
420C3×C4C22×C22⋊D516yes—
421C3×C4C24×D511yescharacteristic
422Dic3—102no—
423C2×C5—26no—
424C2×C5—42no—
425C2×C5#583712yescomplemented
426C2×C5C23×#6711yescharacteristic
427D5—126no—
428C23—21no—
429C23—303no—
430C23—3012no—
431C23—1206no—
432C23C2×#122013yes—
433Q8—23no—
434Q8—212no—
435Q8—152no—
436Q8—301no—
437Q8C2×#122014yes—
438Q8C23×D1516yes—
439D4—212no—
440D4—21no—
441D4—156no—
442D4—3012no—
443D4—3012no—
444D4—303no—
445D4C2×#1220112yes—
446D4C23×D1512yes—
447C2×C4—212no—
448C2×C4—23no—
449C2×C4—212no—
450C2×C4—301no—
451C2×C4—3012no—
452C2×C4C2×#122016yes—
453C2×C4C2×#122013yes—
454C2×C4C23×D1516yes—
455C2×C4C23×D1511yescharacteristic
456C8—152no—
457C8—156no—
458C2×C3—26no—
459C2×C3—42no—
460C2×C3#6617112yescomplemented
461C2×C3C23×C22⋊D511yescharacteristic
462D3—206no—
463C5C2×#583711yescharacteristic, complemented, Sylow
464C22—26no—
465C22—22no—
466C22—42no—
467C22—306no—
468C22—606no—
469C22—12012no—
470C22C22×#122016yes—
471C22C22×#122011yescharacteristic
472C4—26no—
473C4—302no—
474C4C22×#122016yes—
475C4C22×#122011yescharacteristic
476C4C24×D1511yescharacteristic
477C3C2×#6617111yescharacteristic, complemented, Sylow
478C2—26no—
479C2—42no—
480C2—606no—
481C2#1175659612yesdirect product factor
482C2C23×#122011yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC3×C4×C5C25
FrattiniC4C24×D15
FittingC2×C3×C5×2−1+4C2
socleC22×C3×C5C22×D4
hypercenterC2×2−1+4D15
hypocenterC3×C5C2×#577
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×2−1+4C2semidirect
2. C2×#92100C2semidirect
3. #11756596C2direct (N × H)
4. C2×#91839C2semidirect
5. C2×#91838C2semidirect
6. C2×#91837C2semidirect
7. C2×#91831C2semidirect
8. C22×#6717C2semidirect
11. C3×C5×2−1+4C22semidirect
14. C2×C3×C5×#41C22semidirect
16. C22×C3×C5×Q8C22semidirect
18. #92100C22semidirect
23. #91839C22semidirect
24. #91838C22semidirect
25. #91837C22semidirect
26. C2×#6718C22semidirect
27. #91831C22semidirect
28. C2×#6717C22semidirect
29. C2×#6717C22semidirect
30. C2×#6717C22semidirect
31. C2×#6716C22semidirect
32. C2×#6715C22semidirect
33. C2×#6710C22semidirect
34. C22×C3⋊#168C22semidirect
36. C2×C5×2−1+4D3semidirect
49. C3×C5×#41C23semidirect
55. C2×C3×C5×Q8C23semidirect
73. #6718C23semidirect
74. #6717C23semidirect
75. #6717C23semidirect
76. #6716C23semidirect
77. #6715C23semidirect
78. #6710C23semidirect
81. C2×C3⋊#168C23semidirect
82. C2×C3×2−1+4D5semidirect
91. C5×2−1+4C2×D3semidirect
94. C2×C5×#41C2×D3semidirect
96. C22×C5×Q8C2×D3semidirect
147. C3×2−1+4C2×D5semidirect
150. C2×C3×#41C2×D5semidirect
152. C22×C3×Q8C2×D5semidirect
176. C5×#41C22×D3semidirect
182. C2×C5×Q8C22×D3semidirect
209. C2×2−1+4D15semidirect
235. C3×#41C22×D5semidirect
241. C2×C3×Q8C22×D5semidirect
299. 2−1+4C2×D15semidirect
306. C2×#41C2×D15semidirect
308. C22×Q8C2×D15semidirect
325. C2×C3×C5#577semidirect
379. #41C22×D15semidirect
386. C2×Q8C22×D15semidirect
409. C3×C5C2×#577semidirect
425. C2×C5#5837semidirect
460. C2×C3#66171semidirect
463. C5C2×#5837semidirect
477. C3C2×#66171semidirect
481. C2#11756596direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×2−1+42
C2×#921002
#117565962
C2×#918392
C2×#918382
C2×#918372
C2×#918312
C22×#67172
C2×#661713
C2×#58375