Finite Group Databasebeta

← C2×#11747500 #14412504

Subgroups — C2×#11747500 #14412504

Order 1920.

1632 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6773C211yesmaximal, characteristic
2C2×C3×D5×C4⋊C4C211yesmaximal, characteristic, complemented
3C22×#6649C211yesmaximal, characteristic, complemented
4C2×#91093C211yesmaximal, characteristic, complemented
5C2×C5×#810C211yesmaximal, characteristic, complemented
6C2×#90972C211yesmaximal, characteristic, complemented
7C2×#90968C211yesmaximal, characteristic, complemented
8#11747500C218yesmaximal, direct product factor
9C2×#65092—31nomaximal, Hall
10C22×D60C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C22×C3×C4×D5—21no—
13C22×C3×C4×D5C2211yescharacteristic
14C22×#1202—21no—
15C22×#1200—21no—
16C2×#6773—24no—
17C2×#6773—22no—
18C2×#6773C418yescomplemented
19C2×#6773C2214yes—
20C2×C3×C5×C4⋊C4C2211yescharacteristic
21C22×C3⋊#168C2211yescharacteristic
22C22×C5×C3⋊C8C2211yescharacteristic
23C2×C3×C4⋊Dic5C2211yescharacteristic
24C2×C3×#683—21no—
25C3×D5×C4⋊C4—22no—
26C3×D5×C4⋊C4C2214yescomplemented
27C2×#6649—24no—
28C2×#6649C2214yescomplemented
29#91093C2214yescomplemented
30C5×#810C2214yescomplemented
31#90972C2214yescomplemented
32#90968C2214yescomplemented
33C2×#4966—51nomaximal, Hall
34C22×#713—31no—
35C22×#676—31no—
36C2×D5×C4⋊C4D311yescharacteristic, complemented
37C2×C5×#103—31no—
38C2×#3967—31no—
39C2×#3953—31no—
40C2×#3941—31no—
41#65092—38no—
42C23×D15—21no—
43C23×C3×D5D411yescharacteristic
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5C2311yescharacteristic
46C2×D60—21no—
47C2×D60—22no—
48C2×D60C2×C414yescomplemented
49C2×D60C2312yes—
50C22×C5×Dic3—21no—
51C2×C5×Dic6—21no—
52C2×C5×Dic6—22no—
53C2×C5×Dic6C2×C414yescomplemented
54C2×C5×Dic6C2312yes—
55C22×C3×Dic5—21no—
56C22×C3×Dic5D411yescharacteristic
57C2×C3×C4×D5—24no—
58C2×C3×C4×D5—44no—
59C2×C3×C4×D5C2×C414yes—
60C2×C3×C4×D5D412yes—
61C2×C3×C4×D5D414yes—
62C2×C3×C4×D5C2312yes—
63C2×#1202—28no—
64C2×#1202—24no—
65C2×#1200—28no—
66C2×#1200—24no—
67#6773—216no—
68#6773—28no—
69#6773C2×C4116yescomplemented
70C3×C5×C4⋊C4—21no—
71C3×C5×C4⋊C4C2312yes—
72C2×C3⋊#168—22no—
73C2×C3⋊#168C2312yes—
74C2×C5×C3⋊C8—22no—
75C2×C5×C3⋊C8C2312yes—
76C3×C4⋊Dic5—21no—
77C3×C4⋊Dic5C2312yes—
78C3×#683—24no—
79#6649—28no—
80C22×#235—51no—
81C22×C3×C4⋊C4—51no—
82C22×#208—51no—
83C2×#810—51no—
84C2×#810D511yescharacteristic, complemented
85#4966—58no—
86C2×#809—51no—
87C2×#809—51no—
88C22×C5×Q8—31no—
89C2×#713—38no—
90C2×#713—34no—
91C2×#713—64no—
92C2×#713—62no—
93C22×D20—31no—
94C22×D20—61no—
95C22×C4×D5—21no—
96C22×C4×D5—61no—
97C22×C4×D5C2×D311yescharacteristic
98C22×C5×C8—31no—
99C2×C5×C4⋊C4C2×D311yescharacteristic
100C2×C4⋊Dic5C2×D311yescharacteristic
101C2×#683—21no—
102C22×#168—31no—
103C2×#676—34no—
104C2×#676—64no—
105D5×C4⋊C4—22no—
106D5×C4⋊C4C2×D314yescomplemented
107C5×#103—34no—
108#3967—34no—
109#3953—34no—
110#3941—34no—
111C2×#417—151noSylow
112C23×C3×C5C2×D411yescharacteristic
113C22×D15—24no—
114C22×D15—22no—
115C22×D15—42no—
116C22×D15—42no—
117C22×C3×D5—22no—
118C22×C3×D5—22no—
119C22×C3×D5C22⋊C414yes—
120C22×C3×D5C2×D412yes—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—42no—
123C2×C3×C4×C5C22×C412yes—
124C2×C3×C4×C5C2×D411yescharacteristic
125C2×C3×C4×C5C2×D412yes—
126C2×C3×C4×C5C2411yescharacteristic
127D60—24no—
128D60—22no—
129D60C22×C414yescomplemented
130C2×C5×Dic3—24no—
131C2×C5×Dic3—22no—
132C5×Dic6—24no—
133C5×Dic6—22no—
134C5×Dic6C22×C414yescomplemented
135C2×C3×Dic5—22no—
136C2×C3×Dic5—42no—
137C2×C3×Dic5C22⋊C414yes—
138C2×C3×Dic5C2×D412yes—
139C3×C4×D5—48no—
140C3×C4×D5C22⋊C418yes—
141C3×C4×D5C22×C414yes—
142C3×C4×D5C2×D414yes—
143#1202—216no—
144#1200—216no—
145C3⋊#168—22no—
146C5×C3⋊C8—22no—
147C23×C3×C4—51no—
148C23×C3×C4—101no—
149C22×#67—101no—
150C2×#235—58no—
151C2×#235—54no—
152C2×#235—104no—
153C2×#235—102no—
154C22×D12—51no—
155C22×C4×D3—101no—
156C22×Dic6C2×D511yescharacteristic
157C2×C3×C4⋊C4—51no—
158C2×C3×C4⋊C4—54no—
159C2×C3×C4⋊C4—102no—
160C2×C3×C4⋊C4—101no—
161C2×C3×C4⋊C4C2×D511yescharacteristic
162C2×#208—54no—
163C2×#208—104no—
164C22×C3⋊C8—51no—
165C22×C3⋊C8C2×D511yescharacteristic
166#810—54no—
167#810C2×D514yescomplemented
168#809—54no—
169#809—54no—
170C23×D5—61no—
171C23×D5#6711yescharacteristic
172C2×C5×Q8—34no—
173C2×C5×Q8—32no—
174C2×C5×Q8—62no—
175C2×C5×Q8—61no—
176C22×C4×C5—21no—
177C22×C4×C5—61no—
178C22×C4×C5C22×D311yescharacteristic
179C22×Dic5—21no—
180C22×Dic5#6711yescharacteristic
181#713—316no—
182#713—616no—
183#713—68no—
184C2×D20—34no—
185C2×D20—32no—
186C2×D20—68no—
187C2×D20—64no—
188C2×D20—62no—
189C2×D20—61no—
190C2×C4×D5—24no—
191C2×C4×D5—44no—
192C2×C4×D5—68no—
193C2×C4×D5—64no—
194C2×C4×D5C4×D314yes—
195C2×C4×D5D1214yes—
196C2×C4×D5#6712yes—
197C2×C4×D5C22×D312yes—
198C2×C5×C8—32no—
199C2×C5×C8—62no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4C22×D312yes—
202C4⋊Dic5—21no—
203C4⋊Dic5C22×D312yes—
204#683—24no—
205C2×#168—32no—
206C2×#168—62no—
207#676—68no—
208C22×#41—151no—
209C22×M16—151no—
210C22×C4⋊C4—51no—
211#417—158no—
212C2×#103—31no—
213C2×#103—151no—
214C2×#102—151no—
215C2×#102—151no—
216C22×C3×C5C2×C22⋊C412yes—
217C22×C3×C5AGL(1,ℤ/8)12yes—
218C22×C3×C5#13712yes—
219C22×C3×C5C22×D411yescharacteristic
220C2×D15—24no—
221C2×D15—42no—
222C2×D15—42no—
223C2×D15—48no—
224C2×C3×D5—22no—
225C2×C3×D5—22no—
226C2×C3×D5—28no—
227C2×C3×D5C2×C22⋊C414yes—
228C3×C4×C5—42no—
229C3×C4×C5C2×C22⋊C412yes—
230C3×C4×C5C23×C411yescharacteristic
231C3×C4×C5C22×D411yescharacteristic
232C3×Dic5—42no—
233C3×Dic5C2×C22⋊C414yes—
234C5×Dic3—24no—
235C24×C3—51no—
236C23×D3—101no—
237C22×C3×C4—21no—
238C22×C3×C4—51no—
239C22×C3×C4—54no—
240C22×C3×C4—54no—
241C22×C3×C4—52no—
242C22×C3×C4—52no—
243C22×C3×C4—104no—
244C22×C3×C4—101no—
245C22×C3×C4—204no—
246C22×C3×C4C22×D511yescharacteristic
247C2×#67—104no—
248C2×#67—108no—
249C22×Dic3—21no—
250#235—516no—
251#235—108no—
252#235—1016no—
253C2×D12—54no—
254C2×D12—52no—
255C2×D12—102no—
256C2×D12—101no—
257C2×C4×D3—104no—
258C2×C4×D3—108no—
259C2×Dic6—22no—
260C2×Dic6—21no—
261C2×Dic6C4×D514yescomplemented
262C2×Dic6C22×D512yes—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—52no—
265C3×C4⋊C4—104no—
266C3×C4⋊C4—101no—
267C3×C4⋊C4C22×D512yes—
268#208—108no—
269C2×C3⋊C8—22no—
270C2×C3⋊C8—52no—
271C2×C3⋊C8—102no—
272C2×C3⋊C8C22×D512yes—
273C23×C5C2×#6711yescharacteristic
274C22×D5—22no—
275C22×D5—22no—
276C22×D5—64no—
277C22×D5—62no—
278C22×D5—122no—
279C22×D5—122no—
280C22×D5(C2×D3)⋊C414yes—
281C22×D5C2×#6712yes—
282C5×Q8—34no—
283C5×Q8—64no—
284C5×Q8—62no—
285C2×C4×C5—22no—
286C2×C4×C5—42no—
287C2×C4×C5—64no—
288C2×C4×C5—62no—
289C2×C4×C5C2×C4×D312yes—
290C2×C4×C5C2×D1212yes—
291C2×C4×C5C2×#6711yescharacteristic
292C2×C4×C5C23×D311yescharacteristic
293C2×Dic5—22no—
294C2×Dic5—42no—
295C2×Dic5(C2×D3)⋊C414yes—
296C2×Dic5C2×#6712yes—
297D20—34no—
298D20—616no—
299D20—64no—
300D20—62no—
301C4×D5—48no—
302C4×D5—616no—
303C4×D5(C2×D3)⋊C418yes—
304C4×D5C2×C4×D314yes—
305C4×D5C2×D1214yes—
306C5×C8—62no—
307#168—62no—
308C2×#41—154no—
309C2×#41—158no—
310C2×#41—304no—
311C2×#41—302no—
312C22×Q8—31no—
313C22×D4—151no—
314C22×D4—301no—
315C23×C4—51no—
316C23×C4—101no—
317C23×C4—301no—
318C2×M16—154no—
319C2×M16—304no—
320C22×C8—31no—
321C22×C8—151no—
322C2×C4⋊C4—51no—
323C2×C4⋊C4—54no—
324C2×C4⋊C4—102no—
325C2×C4⋊C4—101no—
326C2×C4⋊C4D3×D511yescharacteristic
327#103—34no—
328#103—154no—
329#102—154no—
330#102—154no—
331C2×C3×C5#41714yescomplemented
332C2×C3×C5C22×C22⋊C411yescharacteristic
333C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
334C2×C3×C5C2×#13711yescharacteristic
335D15—44no—
336C3×D5—24no—
337C23×C3—52no—
338C23×C3—54no—
339C23×C3—102no—
340C23×C3—102no—
341C23×C3D4×D511yescharacteristic
342C22×D3—102no—
343C22×D3—104no—
344C22×D3—202no—
345C22×D3—202no—
346C2×C3×C4—22no—
347C2×C3×C4—42no—
348C2×C3×C4—52no—
349C2×C3×C4—54no—
350C2×C3×C4—54no—
351C2×C3×C4—54no—
352C2×C3×C4—58no—
353C2×C3×C4—102no—
354C2×C3×C4—208no—
355C2×C3×C4—202no—
356C2×C3×C4C2×C4×D512yes—
357C2×C3×C4D4×D512yes—
358C2×C3×C4D4×D511yescharacteristic
359C2×C3×C4C23×D511yescharacteristic
360#67—1016no—
361C2×Dic3—22no—
362C2×Dic3—24no—
363D12—54no—
364D12—102no—
365D12—104no—
366C4×D3—1016no—
367Dic6—22no—
368Dic6—24no—
369Dic6C2×C4×D514yescomplemented
370C3⋊C8—22no—
371C3⋊C8—102no—
372C22×C5C2×(C2×D3)⋊C412yes—
373C22×C5#93212yes—
374C22×C5#94212yes—
375C22×C5C22×#6711yescharacteristic
376C2×D5—28no—
377C2×D5—22no—
378C2×D5—22no—
379C2×D5—64no—
380C2×D5—128no—
381C2×D5—122no—
382C2×D5—122no—
383C2×D5C2×(C2×D3)⋊C414yes—
384C4×C5—42no—
385C4×C5—64no—
386C4×C5C2×(C2×D3)⋊C412yes—
387C4×C5C22×C4×D311yescharacteristic
388C4×C5C22×D1211yescharacteristic
389Dic5—42no—
390Dic5C2×(C2×D3)⋊C414yes—
391C24—51no—
392C24—301no—
393#41—1516no—
394#41—3016no—
395#41—308no—
396C2×Q8—34no—
397C2×Q8—32no—
398C2×Q8—62no—
399C2×Q8—61no—
400C2×D4—154no—
401C2×D4—152no—
402C2×D4—308no—
403C2×D4—304no—
404C2×D4—302no—
405C2×D4—301no—
406C22×C4—21no—
407C22×C4—51no—
408C22×C4—54no—
409C22×C4—54no—
410C22×C4—52no—
411C22×C4—52no—
412C22×C4—61no—
413C22×C4—104no—
414C22×C4—101no—
415C22×C4—204no—
416C22×C4—308no—
417C22×C4—304no—
418C22×C4C2×D3×D511yescharacteristic
419M16—308no—
420C2×C8—32no—
421C2×C8—62no—
422C2×C8—152no—
423C2×C8—302no—
424C4⋊C4—21no—
425C4⋊C4—52no—
426C4⋊C4—104no—
427C4⋊C4—101no—
428C4⋊C4C2×D3×D512yes—
429C3×C5C2×#41711yescharacteristic, complemented, Hall
430C22×C3—54no—
431C22×C3—102no—
432C22×C3—102no—
433C22×C3—108no—
434C22×C3D5×C22⋊C412yes—
435C22×C3#406012yes—
436C22×C3#406412yes—
437C22×C3C2×D4×D511yescharacteristic
438C2×D3—104no—
439C2×D3—202no—
440C2×D3—202no—
441C2×D3—208no—
442C3×C4—42no—
443C3×C4—54no—
444C3×C4—202no—
445C3×C4D5×C22⋊C412yes—
446C3×C4C22×C4×D511yescharacteristic
447C3×C4C2×D4×D511yescharacteristic
448Dic3—24no—
449C2×C5#496614yescomplemented
450C2×C5C22×(C2×D3)⋊C411yescharacteristic
451C2×C5C2×#93211yescharacteristic
452C2×C5C2×#94211yescharacteristic
453D5—24no—
454D5—124no—
455C23—54no—
456C23—52no—
457C23—102no—
458C23—102no—
459C23—304no—
460C23—302no—
461C23—602no—
462C23—602no—
463C23D5×#6711yescharacteristic
464Q8—34no—
465Q8—64no—
466Q8—62no—
467D4—154no—
468D4—3016no—
469D4—304no—
470D4—302no—
471C2×C4—22no—
472C2×C4—42no—
473C2×C4—54no—
474C2×C4—52no—
475C2×C4—58no—
476C2×C4—54no—
477C2×C4—54no—
478C2×C4—64no—
479C2×C4—62no—
480C2×C4—102no—
481C2×C4—208no—
482C2×C4—202no—
483C2×C4—3016no—
484C2×C4C4×D3×D512yes—
485C2×C4D5×D1212yes—
486C2×C4D5×#6711yescharacteristic
487C2×C4C22×D3×D511yescharacteristic
488C8—62no—
489C8—302no—
490C2×C3—104no—
491C2×C3#6509214yescomplemented
492C2×C3C2×D5×C22⋊C411yescharacteristic
493C2×C3C2×#406011yescharacteristic
494C2×C3C2×#406411yescharacteristic
495D3—204no—
496C5C2×#496611yescharacteristic, complemented, Sylow
497C22—54no—
498C22—102no—
499C22—108no—
500C22—102no—
501C22—304no—
502C22—602no—
503C22—608no—
504C22—602no—
505C22D5×(C2×D3)⋊C412yes—
506C22#9149112yes—
507C22#9151512yes—
508C22C2×D5×#6711yescharacteristic
509C4—42no—
510C4—54no—
511C4—64no—
512C4—202no—
513C4D5×(C2×D3)⋊C412yes—
514C4C2×C4×D3×D511yescharacteristic
515C4C2×D5×D1211yescharacteristic
516C3C2×#6509211yescharacteristic, complemented, Sylow
517C2—104no—
518C2—604no—
519C2#1174750014yesdirect product factor
520C2C2×D5×(C2×D3)⋊C411yescharacteristic
521C2C2×#9149111yescharacteristic
522C2C2×#9151511yescharacteristic
subgroupG/H
centerC23D5×#67
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC22×#6773C2
cosocleC2×C3×C4×C5C24
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#417
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×D5×C4⋊C4C2semidirect
3. C22×#6649C2semidirect
4. C2×#91093C2semidirect
5. C2×C5×#810C2semidirect
6. C2×#90972C2semidirect
7. C2×#90968C2semidirect
8. #11747500C2direct (N × H)
18. C2×#6773C4semidirect
26. C3×D5×C4⋊C4C22semidirect
28. C2×#6649C22semidirect
29. #91093C22semidirect
30. C5×#810C22semidirect
31. #90972C22semidirect
32. #90968C22semidirect
36. C2×D5×C4⋊C4D3semidirect
48. C2×D60C2×C4semidirect
53. C2×C5×Dic6C2×C4semidirect
69. #6773C2×C4semidirect
84. C2×#810D5semidirect
106. D5×C4⋊C4C2×D3semidirect
129. D60C22×C4semidirect
134. C5×Dic6C22×C4semidirect
167. #810C2×D5semidirect
261. C2×Dic6C4×D5semidirect
331. C2×C3×C5#417semidirect
369. Dic6C2×C4×D5semidirect
429. C3×C5C2×#417semidirect
449. C2×C5#4966semidirect
491. C2×C3#65092semidirect
496. C5C2×#4966semidirect
516. C3C2×#65092semidirect
519. C2#11747500direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67732
C2×C3×D5×C4⋊C42
C22×#66492
C2×#910932
C2×C5×#8102
C2×#909722
C2×#909682
#117475002
C2×#650923
C2×#49665