Finite Group Databasebeta

← C2×#11749284 #14427643

Subgroups — C2×#11749284 #14427643

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91835C211yesmaximal, characteristic, complemented
2C22×C5×#215C211yesmaximal, characteristic, complemented
3C2×#91466C211yesmaximal, characteristic
4C22×#6648C211yesmaximal, characteristic, complemented
5C2×C3×#3967C211yesmaximal, characteristic, complemented
6#11749284C218yesmaximal, direct product factor
7C2×#90987C211yesmaximal, characteristic, complemented
8C2×#90967C211yesmaximal, characteristic, complemented
9C2×#65460—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C22×C4×D15C2211yescharacteristic
12C22×C5×D12C2211yescharacteristic
13C22×#1203—21no—
14#91835—22no—
15#91835C2214yescomplemented
16C2×#6714—21no—
17C2×C4⋊Dic15C2211yescharacteristic
18C2×#6712—21no—
19C2×C5×#215—24no—
20C2×C5×#215C2214yescomplemented
21C22×C5×C3⋊C8C2211yescharacteristic
22C2×C3×C4⋊Dic5C2211yescharacteristic
23C22×C3×#168C2211yescharacteristic
24C2×(C2×D3)⋊Dic5—21no—
25#91466—22no—
26#91466C2214yes—
27C2×#6648—24no—
28C2×#6648C2214yescomplemented
29C3×#3967C2214yescomplemented
30#90987C2214yescomplemented
31#90967C2214yescomplemented
32C2×#4807—51nomaximal, Hall
33C22×C5×SD16—31no—
34C2×#4092—31no—
35C2×#4084—31no—
36C22×C8×D5—31no—
37C2×#3967D311yescharacteristic, complemented
38C2×#3964—31no—
39#65460—38no—
40C2×#3949—31no—
41C23×D15D411yescharacteristic
42C23×C5×D3—21no—
43C2×C3×C5×Q8—21no—
44C2×C3×C5×Q8—22no—
45C2×C3×C5×Q8—22no—
46C2×C3×C5×Q8C2312yes—
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5C2311yescharacteristic
49C22×Dic15—21no—
50C22×Dic15D411yescharacteristic
51C2×C4×D15—22no—
52C2×C4×D15—22no—
53C2×C4×D15D412yes—
54C2×C4×D15C2312yes—
55C2×C5×D12—22no—
56C2×C5×D12—22no—
57C2×C5×D12—21no—
58C2×C5×D12C2312yes—
59C22×C3×Dic5—21no—
60C2×#1203—24no—
61C2×#1203—44no—
62#6714—24no—
63C4⋊Dic15—21no—
64C4⋊Dic15C2312yes—
65#6712—24no—
66C5×#215—28no—
67C2×C5×C3⋊C8D414yescomplemented
68C2×C5×C3⋊C8C2312yes—
69C3×C4⋊Dic5—21no—
70C3×C4⋊Dic5C2312yes—
71C2×C3×#168—22no—
72C2×C3×#168C2312yes—
73(C2×D3)⋊Dic5—24no—
74#6648—28no—
75C2×#946—51no—
76C22×#215D511yescharacteristic, complemented
77C22×D3×C8—51no—
78C2×#895—51no—
79C2×C3×#103—51no—
80C2×#821—51no—
81C2×#808—51no—
82#4807—58no—
83C22×C5×Q8C2×D311yescharacteristic
84C22×C5×D4—31no—
85C22×C22⋊D5—61no—
86C22×C4×D5—31no—
87C2×C5×SD16—34no—
88C2×C5×SD16—64no—
89C22×C5×C8—31no—
90C2×C22⋊Dic5—61no—
91#4092—34no—
92#4092—62no—
93#4084—34no—
94#4084—62no—
95C2×#685—61no—
96C2×C4⋊Dic5—31no—
97C2×C4⋊Dic5C2×D311yescharacteristic
98C2×#683—61no—
99C22×#168C2×D311yescharacteristic
100C2×C8×D5—34no—
101C2×C8×D5—64no—
102#3967C2×D314yescomplemented
103#3964—34no—
104#3949—34no—
105C2×#465—151noSylow
106C23×C3×C5C2×D411yescharacteristic
107C22×D15—22no—
108C22×D15—22no—
109C22×D15SD1614yescomplemented
110C22×D15C2×D412yes—
111C22×C5×D3—22no—
112C22×C5×D3—42no—
113C22×C5×D3—42no—
114C22×C5×D3—42no—
115C3×C5×Q8—22no—
116C3×C5×Q8—22no—
117C3×C5×Q8—42no—
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—42no—
120C2×C3×C4×C5C2×D411yescharacteristic
121C2×C3×C4×C5C2×D412yes—
122C2×C3×C4×C5#4112yes—
123C2×C3×C4×C5C2411yescharacteristic
124C2×Dic15—22no—
125C2×Dic15—22no—
126C2×Dic15—42no—
127C2×Dic15C2×D412yes—
128C4×D15—24no—
129C4×D15—22no—
130C4×D15—22no—
131C5×D12—22no—
132C5×D12—22no—
133C5×D12—42no—
134C2×C3×Dic5—22no—
135C2×C3×Dic5—42no—
136#1203—48no—
137C3×#168—22no—
138C5×C3⋊C8C2×D414yescomplemented
139C22×C3×Q8C2×D511yescharacteristic
140C22×D12—101no—
141C22×D12C2×D511yescharacteristic
142C22×C4×D3—51no—
143C22×C3×C8—51no—
144C2×C3×C4⋊C4—51no—
145#946—54no—
146#946—102no—
147C2×#215—24no—
148C2×#215C2×D514yescomplemented
149C2×(C2×D3)⋊C4—101no—
150C2×(C2×D3)⋊C4—101no—
151C2×C4⋊Dic3—51no—
152C2×Dic3⋊C4—101no—
153C22×C3⋊C8C2×D511yescharacteristic
154C2×D3×C8—54no—
155C2×D3×C8—104no—
156#895—54no—
157#895—102no—
158C3×#103—54no—
159#821—54no—
160#808—54no—
161C24×C5—61no—
162C23×D5—31no—
163C2×C5×Q8—21no—
164C2×C5×Q8—22no—
165C2×C5×Q8—22no—
166C2×C5×Q8C22×D312yes—
167C2×C5×D4—32no—
168C2×C5×D4—62no—
169C2×C5×D4—62no—
170C2×C5×D4—61no—
171C22×C4×C5—21no—
172C22×C4×C5C22×D311yescharacteristic
173C2×C22⋊D5—64no—
174C2×C22⋊D5—124no—
175C22×Dic5—21no—
176C22×Dic5—31no—
177C22×Dic5—61no—
178C2×C4×D5—32no—
179C2×C4×D5—32no—
180C2×C4×D5—62no—
181C2×C4×D5—62no—
182C5×SD16—68no—
183C2×C5×C8—34no—
184C2×C5×C8—32no—
185C22⋊Dic5—64no—
186#685—64no—
187C4⋊Dic5—21no—
188C4⋊Dic5—32no—
189C4⋊Dic5—61no—
190C4⋊Dic5C22×D312yes—
191#683—64no—
192C2×#168—22no—
193C2×#168C22×D312yes—
194C8×D5—68no—
195C22×SD16—31no—
196C23×C8—151no—
197C2×C22⋊Q8—151no—
198C2×#121—151no—
199#465—158no—
200C2×#106—151no—
201C2×#103—51no—
202C2×#102—151no—
203C22×C3×C5#12112yes—
204C22×C3×C5C2×SD1612yes—
205C22×C3×C5#13512yes—
206C22×C3×C5C22×D411yescharacteristic
207C2×D15—22no—
208C2×D15—22no—
209C2×D15—28no—
210C2×D15C2×SD1614yescomplemented
211C2×C5×D3—42no—
212C2×C5×D3—42no—
213C2×C5×D3—42no—
214C2×C5×D3—84no—
215C3×C4×C5—42no—
216C3×C4×C5#12112yes—
217C3×C4×C5C22×D411yescharacteristic
218C3×C4×C5C2×#4111yescharacteristic
219Dic15—22no—
220Dic15—42no—
221C3×Dic5—42no—
222C23×D3—21no—
223C23×D3—51no—
224C2×C3×Q8—21no—
225C2×C3×Q8—22no—
226C2×C3×Q8—22no—
227C2×C3×Q8C22×D512yes—
228C22×C3×C4—21no—
229C22×C3×C4—101no—
230C22×C3×C4C22×D511yescharacteristic
231C22×Dic3—51no—
232C22×Dic3—101no—
233C2×D12—22no—
234C2×D12—22no—
235C2×D12—21no—
236C2×D12—104no—
237C2×D12—204no—
238C2×D12C22×D512yes—
239C2×C4×D3—52no—
240C2×C4×D3—52no—
241C2×C4×D3—102no—
242C2×C4×D3—102no—
243C2×C3×C8—52no—
244C2×C3×C8—102no—
245C3×C4⋊C4—52no—
246C3×C4⋊C4—101no—
247#215—28no—
248(C2×D3)⋊C4—104no—
249(C2×D3)⋊C4—104no—
250C4⋊Dic3—52no—
251C4⋊Dic3—101no—
252Dic3⋊C4—104no—
253C2×C3⋊C8C22⋊D514yescomplemented
254C2×C3⋊C8C22×D512yes—
255D3×C8—108no—
256C23×C5—62no—
257C23×C5—122no—
258C23×C5—122no—
259C23×C5—122no—
260C23×C5D3×D411yescharacteristic
261C22×D5—34no—
262C22×D5—32no—
263C22×D5—62no—
264C22×D5—62no—
265C5×Q8—22no—
266C5×Q8—22no—
267C5×Q8—42no—
268C5×D4—62no—
269C5×D4—62no—
270C5×D4—122no—
271C2×C4×C5—22no—
272C2×C4×C5—42no—
273C2×C4×C5#23512yes—
274C2×C4×C5D3×D412yes—
275C2×C4×C5D3×D411yescharacteristic
276C2×C4×C5C23×D311yescharacteristic
277C22⋊D5—128no—
278C2×Dic5—22no—
279C2×Dic5—32no—
280C2×Dic5—42no—
281C2×Dic5—62no—
282C2×Dic5—62no—
283C2×Dic5—122no—
284C4×D5—64no—
285C4×D5—62no—
286C4×D5—62no—
287C5×C8—34no—
288#168—22no—
289C22×Q8D3×D511yescharacteristic
290C22×D4—31no—
291C22×D4—301no—
292C23×C4—151no—
293C2×SD16—34no—
294C2×SD16—64no—
295C22×C8—31no—
296C22×C8—51no—
297C22×C8—154no—
298C22×C8—304no—
299C22⋊Q8—154no—
300C22⋊Q8—302no—
301#121—154no—
302#121—302no—
303C2×C4⋊C4—51no—
304C2×C4⋊C4—151no—
305C2×C4⋊C4—301no—
306C2×C22⋊C4—301no—
307C2×C22⋊C4—301no—
308#106—154no—
309#103—54no—
310#102—154no—
311C2×C3×C5#46514yescomplemented
312C2×C3×C5C2×#12111yescharacteristic
313C2×C3×C5C22×SD1611yescharacteristic
314C2×C3×C5C2×#13511yescharacteristic
315D15—24no—
316C5×D3—82no—
317C23×C3D4×D511yescharacteristic
318C22×D3—22no—
319C22×D3—42no—
320C22×D3—42no—
321C22×D3—42no—
322C22×D3—52no—
323C22×D3—54no—
324C22×D3—102no—
325C22×D3—102no—
326C3×Q8—22no—
327C3×Q8—22no—
328C3×Q8—42no—
329C2×C3×C4—22no—
330C2×C3×C4—42no—
331C2×C3×C4—102no—
332C2×C3×C4—202no—
333C2×C3×C4D4×D511yescharacteristic
334C2×C3×C4#71112yes—
335C2×C3×C4C2×C22⋊D512yes—
336C2×C3×C4C23×D511yescharacteristic
337C2×Dic3—52no—
338C2×Dic3—102no—
339C2×Dic3—102no—
340C2×Dic3—202no—
341D12—22no—
342D12—22no—
343D12—42no—
344D12—208no—
345C4×D3—102no—
346C4×D3—102no—
347C4×D3—104no—
348C3×C8—102no—
349C3⋊C8C2×C22⋊D514yescomplemented
350C22×C5—122no—
351C22×C5—122no—
352C22×C5—122no—
353C22×C5—244no—
354C22×C5#88412yes—
355C22×C5D3×SD1612yes—
356C22×C5#91912yes—
357C22×C5C2×D3×D411yescharacteristic
358C2×D5—34no—
359C2×D5—62no—
360C2×D5—62no—
361C2×D5—68no—
362C4×C5—42no—
363C4×C5#88412yes—
364C4×C5C2×#23511yescharacteristic
365C4×C5C2×D3×D411yescharacteristic
366Dic5—42no—
367Dic5—62no—
368Dic5—122no—
369C24—61no—
370C24—151no—
371C2×Q8—21no—
372C2×Q8—22no—
373C2×Q8—22no—
374C2×Q8C2×D3×D512yes—
375C2×D4—32no—
376C2×D4—62no—
377C2×D4—62no—
378C2×D4—61no—
379C2×D4—304no—
380C2×D4—604no—
381C22×C4—21no—
382C22×C4—101no—
383C22×C4—151no—
384C22×C4—152no—
385C22×C4—152no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—301no—
389C22×C4C2×D3×D511yescharacteristic
390SD16—68no—
391C2×C8—34no—
392C2×C8—32no—
393C2×C8—52no—
394C2×C8—102no—
395C2×C8—308no—
396C4⋊C4—52no—
397C4⋊C4—101no—
398C4⋊C4—152no—
399C4⋊C4—304no—
400C4⋊C4—301no—
401C22⋊C4—304no—
402C22⋊C4—304no—
403C3×C5C2×#46511yescharacteristic, complemented, Hall
404C22×C3D5×SD1612yes—
405C22×C3#406212yes—
406C22×C3#408412yes—
407C22×C3C2×D4×D511yescharacteristic
408C2×D3—42no—
409C2×D3—42no—
410C2×D3—42no—
411C2×D3—54no—
412C2×D3—84no—
413C2×D3—102no—
414C2×D3—102no—
415C2×D3—108no—
416C3×C4—42no—
417C3×C4—202no—
418C3×C4#408412yes—
419C3×C4C2×#71111yescharacteristic
420C3×C4C22×C22⋊D511yescharacteristic
421Dic3—102no—
422Dic3—202no—
423C2×C5—242no—
424C2×C5#480714yescomplemented
425C2×C5C2×#88411yescharacteristic
426C2×C5C2×D3×SD1611yescharacteristic
427C2×C5C2×#91911yescharacteristic
428D5—64no—
429C23—62no—
430C23—122no—
431C23—122no—
432C23—122no—
433C23—154no—
434C23—152no—
435C23—302no—
436C23—302no—
437C23#679011yescharacteristic
438Q8—22no—
439Q8—22no—
440Q8—42no—
441D4—62no—
442D4—62no—
443D4—122no—
444D4—608no—
445C2×C4—22no—
446C2×C4—42no—
447C2×C4—102no—
448C2×C4—152no—
449C2×C4—202no—
450C2×C4—302no—
451C2×C4—302no—
452C2×C4—302no—
453C2×C4—304no—
454C2×C4—302no—
455C2×C4—602no—
456C2×C4#678212yes—
457C2×C4D3×C22⋊D512yes—
458C2×C4#679011yescharacteristic
459C2×C4C22×D3×D511yescharacteristic
460C8—34no—
461C8—102no—
462C2×C3#6546014yescomplemented
463C2×C3C2×D5×SD1611yescharacteristic
464C2×C3C2×#406211yescharacteristic
465C2×C3C2×#408411yescharacteristic
466D3—82no—
467D3—104no—
468C5C2×#480711yescharacteristic, complemented, Sylow
469C22—122no—
470C22—122no—
471C22—122no—
472C22—154no—
473C22—244no—
474C22—302no—
475C22—302no—
476C22—308no—
477C22#9150512yes—
478C22#9152312yes—
479C22#9155712yes—
480C22C2×#679011yescharacteristic
481C4—42no—
482C4—202no—
483C4—302no—
484C4—602no—
485C4#9155712yes—
486C4C2×#678211yescharacteristic
487C4C2×D3×C22⋊D511yescharacteristic
488C3C2×#6546011yescharacteristic, complemented, Sylow
489C2—242no—
490C2—304no—
491C2#1174928414yesdirect product factor
492C2C2×#9150511yescharacteristic
493C2C2×#9152311yescharacteristic
494C2C2×#9155711yescharacteristic
subgroupG/H
centerC23#6790
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C2×D4
prime radicalC2×#91466C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#465
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#91835C2semidirect
2. C22×C5×#215C2semidirect
4. C22×#6648C2semidirect
5. C2×C3×#3967C2semidirect
6. #11749284C2direct (N × H)
7. C2×#90987C2semidirect
8. C2×#90967C2semidirect
15. #91835C22semidirect
20. C2×C5×#215C22semidirect
28. C2×#6648C22semidirect
29. C3×#3967C22semidirect
30. #90987C22semidirect
31. #90967C22semidirect
37. C2×#3967D3semidirect
67. C2×C5×C3⋊C8D4semidirect
76. C22×#215D5semidirect
102. #3967C2×D3semidirect
109. C22×D15SD16semidirect
138. C5×C3⋊C8C2×D4semidirect
148. C2×#215C2×D5semidirect
210. C2×D15C2×SD16semidirect
253. C2×C3⋊C8C22⋊D5semidirect
311. C2×C3×C5#465semidirect
349. C3⋊C8C2×C22⋊D5semidirect
403. C3×C5C2×#465semidirect
424. C2×C5#4807semidirect
462. C2×C3#65460semidirect
468. C5C2×#4807semidirect
488. C3C2×#65460semidirect
491. C2#11749284direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918352
C22×C5×#2152
C2×#914662
C22×#66482
C2×C3×#39672
#117492842
C2×#909872
C2×#909672
C2×#654603
C2×#48075