Finite Group Databasebeta

← C2×#11752638 #14495346

Subgroups — C2×#11752638 #14495346

Order 1920.

2304 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91764C211yesmaximal, characteristic, complemented
2C2×C5×#870C211yesmaximal, characteristic, complemented
3C2×C3×#4021C211yesmaximal, characteristic, complemented
4C2×#91459C212yesmaximal, complemented
5C2×#91431C212yesmaximal, complemented
6C2×#91413C212yesmaximal, complemented
7C2×#91411C212yesmaximal, complemented
8C2×#91409C212yesmaximal, complemented
9C2×#91356C212yesmaximal, complemented
10#11752638C2116yesmaximal, direct product factor
11C2×#66034—31nomaximal, Hall
12C22×D60C2211yescharacteristic
13C22×Dic30C2211yescharacteristic
14C22×C3×D20C2211yescharacteristic
15C22×C3×Dic10C2211yescharacteristic
16C22×#1202C2212yes—
17C22×#1202C2212yes—
18C22×#1200C2212yes—
19C22×D5×Dic3C2212yes—
20C2×C3×C42×C5C2211yescharacteristic
21C2×#6714C2212yes—
22C2×#6714C2212yes—
23#91764C2218yescomplemented
24C2×C5×C4⋊Dic3C2211yescharacteristic
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×Dic3⋊C4C2212yes—
27C2×C5×Dic3⋊C4C2212yes—
28C5×#870C2218yescomplemented
29C2×C3×#685C2212yes—
30C2×C3×#685C2212yes—
31C3×#4021C2218yescomplemented
32C2×#6669C2212yes—
33C2×#6668C2212yes—
34C2×#6667C2212yes—
35C2×#6665C2212yes—
36#91459C22116yescomplemented
37#91431C22116yescomplemented
38#91413C22116yescomplemented
39#91411C22116yescomplemented
40#91409C22116yescomplemented
41#91356C22116yescomplemented
42C2×#5684—51nomaximal, Hall
43C2×C5×#125—31no—
44#66034—316no—
45C2×#4042—32no—
46C2×#4042—32no—
47C2×#4041—32no—
48C2×#4041—32no—
49C2×#4040—32no—
50C2×#4040—32no—
51C2×#4021—31no—
52C2×#4021D311yescharacteristic, complemented
53C23×D15C2312yes—
54C23×C3×D5C2312yes—
55C22×C3×C4×C5C2311yescharacteristic
56C22×C3×C4×C5C2311yescharacteristic
57C22×C3×C4×C5C2311yescharacteristic
58C22×Dic15C2312yes—
59C2×D60—42no—
60C2×D60C2314yes—
61C2×Dic30—42no—
62C2×Dic30C2314yes—
63C22×C5×Dic3C2312yes—
64C22×C5×Dic3C2312yes—
65C22×C3×Dic5C2312yes—
66C2×C3×D20—42no—
67C2×C3×D20C2314yes—
68C2×C3×Dic10—42no—
69C2×C3×Dic10C2314yes—
70C2×#1202—44no—
71C2×#1202—44no—
72C2×#1202C2318yes—
73C2×#1202C2318yes—
74C2×#1200—44no—
75C2×#1200C2318yes—
76C2×D5×Dic3—44no—
77C2×D5×Dic3C2318yes—
78C3×C42×C5C2314yes—
79#6714C2318yes—
80#6714C2318yes—
81C5×C4⋊Dic3C2314yes—
82C5×C4⋊Dic3C2314yes—
83C5×Dic3⋊C4C2318yes—
84C5×Dic3⋊C4C2318yes—
85C3×#685C2318yes—
86C3×#685C2318yes—
87#6669C2318yes—
88#6668C2318yes—
89#6667C2318yes—
90#6665C2318yes—
91C2×C3×#124—51no—
92C2×#946—52no—
93C2×#939—52no—
94#5684—516no—
95C2×#886—52no—
96C2×#884—52no—
97C2×#883—52no—
98C2×#878—52no—
99C2×#875—51no—
100C2×#870D511yescharacteristic, complemented
101C22×D20—32no—
102C22×D20—32no—
103C22×D20—31no—
104C22×D20C2×D311yescharacteristic
105C22×C4×D5—32no—
106C22×C4×D5—32no—
107C22×Dic10—31no—
108C22×Dic10C2×D311yescharacteristic
109C5×#125—38no—
110C2×C5×C4⋊C4—31no—
111C2×C5×C4⋊C4—31no—
112C2×C5×C4⋊C4—32no—
113C2×C5×C4⋊C4—32no—
114C2×C42×C5C2×D311yescharacteristic
115C2×#685—32no—
116C2×#685—32no—
117C2×#685—32no—
118C2×#685—32no—
119C2×#685C2×D312yes—
120C2×#685C2×D312yes—
121C2×#683—32no—
122C2×#683—32no—
123#4042—316no—
124#4042—316no—
125#4041—316no—
126#4041—316no—
127#4040—316no—
128#4040—316no—
129#4021—38no—
130#4021C2×D318yescomplemented
131C2×#562—151noSylow
132C23×C3×C5C2411yescharacteristic
133C22×D15—24no—
134C22×D15—24no—
135C22×D15—24no—
136C22×D15C2414yes—
137C22×C3×D5—24no—
138C22×C3×D5—24no—
139C22×C3×D5—24no—
140C22×C3×D5C2414yes—
141C2×C3×C4×C5—22no—
142C2×C3×C4×C5—22no—
143C2×C3×C4×C5—22no—
144C2×C3×C4×C5C2412yes—
145C2×C3×C4×C5C2412yes—
146C2×C3×C4×C5C2412yes—
147C2×Dic15—24no—
148C2×Dic15C2414yes—
149D60—44no—
150Dic30—44no—
151C2×C5×Dic3—24no—
152C2×C5×Dic3—24no—
153C2×C5×Dic3C2414yes—
154C2×C5×Dic3C2414yes—
155C2×C3×Dic5—24no—
156C2×C3×Dic5C2414yes—
157C3×D20—44no—
158C3×Dic10—44no—
159#1202—48no—
160#1202—48no—
161#1200—48no—
162D5×Dic3—48no—
163C22×C3×Q8—51no—
164C22×C3×D4—51no—
165C22×#67—52no—
166C22×#67—52no—
167C23×Dic3—52no—
168C22×D12—51no—
169C22×C4×D3—52no—
170C22×Dic6—51no—
171C3×#124—58no—
172C2×C3×C22⋊C4—52no—
173C2×C3×C22⋊C4—52no—
174C2×C3×C42C2×D511yescharacteristic
175C2×#217—52no—
176#946—516no—
177#939—516no—
178C2×(C2×D3)⋊C4—52no—
179C2×(C2×D3)⋊C4—52no—
180C2×(C2×D3)⋊C4—52no—
181C2×C4⋊Dic3—52no—
182C2×C4⋊Dic3C2×D511yescharacteristic
183C2×C4⋊Dic3C2×D511yescharacteristic
184C2×Dic3⋊C4—52no—
185C2×Dic3⋊C4C2×D512yes—
186C2×Dic3⋊C4C2×D512yes—
187#886—516no—
188#884—516no—
189#883—516no—
190#878—516no—
191#875—58no—
192#870C2×D518yescomplemented
193C23×D5—32no—
194C23×D5C22×D312yes—
195C22×C4×C5—32no—
196C22×C4×C5—32no—
197C22×C4×C5C22×D311yescharacteristic
198C22×C4×C5C22×D311yescharacteristic
199C22×C4×C5C22×D311yescharacteristic
200C22×Dic5—32no—
201C22×Dic5C22×D312yes—
202C2×D20—38no—
203C2×D20—38no—
204C2×D20—34no—
205C2×D20—42no—
206C2×D20—122no—
207C2×D20—124no—
208C2×D20—124no—
209C2×D20C22×D314yes—
210C2×C4×D5—38no—
211C2×C4×D5—38no—
212C2×C4×D5—124no—
213C2×C4×D5—124no—
214C2×Dic10—34no—
215C2×Dic10—42no—
216C2×Dic10—122no—
217C2×Dic10C22×D314yes—
218C5×C4⋊C4—38no—
219C5×C4⋊C4—38no—
220C5×C4⋊C4—34no—
221C5×C4⋊C4—34no—
222C42×C5C22×D314yes—
223#685—38no—
224#685—38no—
225#685—38no—
226#685—38no—
227#685C22×D318yes—
228#685C22×D318yes—
229#683—38no—
230#683—38no—
231#562—1516no—
232C2×#125—31no—
233C2×#124—51no—
234C2×#124—151no—
235C2×#123—152no—
236C2×#123—152no—
237C2×C22⋊Q8—152no—
238C2×C22⋊Q8—152no—
239C2×#121—152no—
240C2×#121—152no—
241C22×C3×C5H(5,𝔽2)12yes—
242C22×C3×C5H(5,𝔽2)12yes—
243C22×C3×C52−1+412yes—
244C22×C3×C5C2511yescharacteristic
245C2×D15—24no—
246C2×D15—24no—
247C2×D15—24no—
248C2×D15—48no—
249C2×C3×D5—24no—
250C2×C3×D5—24no—
251C2×C3×D5—24no—
252C2×C3×D5—48no—
253C3×C4×C5—22no—
254C3×C4×C5—22no—
255C3×C4×C5—22no—
256Dic15—24no—
257C3×Dic5—24no—
258C5×Dic3—24no—
259C5×Dic3—24no—
260C24×C3—52no—
261C23×D3—52no—
262C2×C3×Q8—54no—
263C2×C3×Q8—202no—
264C2×C3×D4—54no—
265C2×C3×D4—202no—
266C22×C3×C4—52no—
267C22×C3×C4C22×D511yescharacteristic
268C22×C3×C4C22×D511yescharacteristic
269C22×C3×C4C22×D511yescharacteristic
270C2×#67—58no—
271C2×#67—58no—
272C2×#67—204no—
273C2×#67—204no—
274C22×Dic3—52no—
275C22×Dic3—58no—
276C22×Dic3—204no—
277C22×Dic3C22×D512yes—
278C22×Dic3C22×D512yes—
279C2×D12—54no—
280C2×D12—202no—
281C2×C4×D3—58no—
282C2×C4×D3—204no—
283C2×Dic6—54no—
284C2×Dic6—202no—
285C3×C22⋊C4—58no—
286C3×C22⋊C4—58no—
287C3×C42C22×D514yes—
288#217—58no—
289(C2×D3)⋊C4—58no—
290(C2×D3)⋊C4—58no—
291(C2×D3)⋊C4—58no—
292C4⋊Dic3—58no—
293C4⋊Dic3C22×D514yes—
294C4⋊Dic3C22×D514yes—
295Dic3⋊C4—58no—
296Dic3⋊C4C22×D518yes—
297Dic3⋊C4C22×D518yes—
298C23×C5C23×D311yescharacteristic
299C22×D5—24no—
300C22×D5—24no—
301C22×D5—24no—
302C22×D5—34no—
303C22×D5—64no—
304C22×D5—64no—
305C22×D5—64no—
306C22×D5C23×D314yes—
307C2×C4×C5—22no—
308C2×C4×C5—22no—
309C2×C4×C5—22no—
310C2×C4×C5—34no—
311C2×C4×C5—34no—
312C2×C4×C5—64no—
313C2×C4×C5—64no—
314C2×C4×C5C23×D312yes—
315C2×C4×C5C23×D312yes—
316C2×C4×C5C23×D312yes—
317C2×Dic5—24no—
318C2×Dic5—34no—
319C2×Dic5—64no—
320C2×Dic5C23×D314yes—
321D20—44no—
322D20—124no—
323D20—128no—
324D20—128no—
325C4×D5—128no—
326C4×D5—128no—
327Dic10—44no—
328Dic10—124no—
329C22×Q8—51no—
330C22×Q8—151no—
331C22×D4—51no—
332C22×D4—152no—
333C22×D4—152no—
334C22×D4—151no—
335C23×C4—152no—
336C23×C4—152no—
337#125—38no—
338#124—58no—
339#124—158no—
340#123—1516no—
341#123—1516no—
342C22⋊Q8—1516no—
343C22⋊Q8—1516no—
344#121—1516no—
345#121—1516no—
346C2×C4⋊C4—32no—
347C2×C4⋊C4—32no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—152no—
351C2×C4⋊C4—152no—
352C2×C22⋊C4—52no—
353C2×C22⋊C4—52no—
354C2×C22⋊C4—152no—
355C2×C22⋊C4—152no—
356C2×C22⋊C4—152no—
357C2×C22⋊C4—152no—
358C2×C42D3×D511yescharacteristic
359C2×C3×C5#56214yescomplemented
360C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
361C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
362C2×C3×C5C2×2−1+411yescharacteristic
363D15—44no—
364C3×D5—44no—
365C23×C3—54no—
366C23×C3—104no—
367C23×C3—104no—
368C23×C3—104no—
369C23×C3C23×D511yescharacteristic
370C22×D3—54no—
371C22×D3—104no—
372C22×D3—104no—
373C22×D3—104no—
374C3×Q8—204no—
375C3×D4—204no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—54no—
380C2×C3×C4—104no—
381C2×C3×C4C23×D512yes—
382C2×C3×C4C23×D512yes—
383C2×C3×C4C23×D512yes—
384#67—208no—
385#67—208no—
386C2×Dic3—24no—
387C2×Dic3—24no—
388C2×Dic3—54no—
389C2×Dic3—104no—
390C2×Dic3—208no—
391C2×Dic3C23×D514yes—
392C2×Dic3C23×D514yes—
393D12—204no—
394C4×D3—208no—
395Dic6—204no—
396C22×C5#100412yes—
397C22×C5#100912yes—
398C22×C5#101012yes—
399C22×C5C24×D311yescharacteristic
400C2×D5—24no—
401C2×D5—24no—
402C2×D5—24no—
403C2×D5—48no—
404C2×D5—64no—
405C2×D5—64no—
406C2×D5—64no—
407C2×D5—128no—
408C4×C5—22no—
409C4×C5—22no—
410C4×C5—22no—
411C4×C5—64no—
412C4×C5—64no—
413Dic5—24no—
414Dic5—64no—
415C24—52no—
416C24—152no—
417C2×Q8—54no—
418C2×Q8—154no—
419C2×Q8—202no—
420C2×Q8—602no—
421C2×D4—54no—
422C2×D4—158no—
423C2×D4—158no—
424C2×D4—154no—
425C2×D4—202no—
426C2×D4—602no—
427C2×D4—604no—
428C2×D4—604no—
429C22×C4—32no—
430C22×C4—32no—
431C22×C4—52no—
432C22×C4—158no—
433C22×C4—158no—
434C22×C4—152no—
435C22×C4—604no—
436C22×C4—604no—
437C22×C4C2×D3×D511yescharacteristic
438C22×C4C2×D3×D511yescharacteristic
439C22×C4C2×D3×D511yescharacteristic
440C4⋊C4—38no—
441C4⋊C4—38no—
442C4⋊C4—34no—
443C4⋊C4—34no—
444C4⋊C4—158no—
445C4⋊C4—158no—
446C22⋊C4—58no—
447C22⋊C4—58no—
448C22⋊C4—158no—
449C22⋊C4—158no—
450C22⋊C4—158no—
451C22⋊C4—158no—
452C42C2×D3×D514yes—
453C3×C5C2×#56211yescharacteristic, complemented, Hall
454C22×C3—104no—
455C22×C3—104no—
456C22×C3—104no—
457C22×C3—208no—
458C22×C3#414712yes—
459C22×C3#414912yes—
460C22×C3#414912yes—
461C22×C3C24×D511yescharacteristic
462C2×D3—104no—
463C2×D3—104no—
464C2×D3—104no—
465C2×D3—208no—
466C3×C4—22no—
467C3×C4—22no—
468C3×C4—22no—
469C3×C4—104no—
470Dic3—24no—
471Dic3—24no—
472Dic3—104no—
473C2×C5#568414yescomplemented
474C2×C5C2×#100411yescharacteristic
475C2×C5C2×#100911yescharacteristic
476C2×C5C2×#101011yescharacteristic
477D5—44no—
478D5—124no—
479C23—54no—
480C23—104no—
481C23—104no—
482C23—104no—
483C23—154no—
484C23—304no—
485C23—304no—
486C23—304no—
487C23C22×D3×D511yescharacteristic
488Q8—204no—
489Q8—604no—
490D4—204no—
491D4—604no—
492D4—608no—
493D4—608no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—34no—
498C2×C4—34no—
499C2×C4—54no—
500C2×C4—64no—
501C2×C4—64no—
502C2×C4—104no—
503C2×C4—154no—
504C2×C4—304no—
505C2×C4—608no—
506C2×C4—608no—
507C2×C4C22×D3×D512yes—
508C2×C4C22×D3×D512yes—
509C2×C4C22×D3×D512yes—
510C2×C3—204no—
511C2×C3#6603414yescomplemented
512C2×C3C2×#414711yescharacteristic
513C2×C3C2×#414911yescharacteristic
514C2×C3C2×#414911yescharacteristic
515D3—204no—
516C5C2×#568411yescharacteristic, complemented, Sylow
517C22—104no—
518C22—104no—
519C22—104no—
520C22—208no—
521C22—304no—
522C22—304no—
523C22—304no—
524C22—608no—
525C22#9200012yes—
526C22#9201712yes—
527C22#9201912yes—
528C22C23×D3×D511yescharacteristic
529C4—22no—
530C4—22no—
531C4—22no—
532C4—64no—
533C4—64no—
534C4—104no—
535C4—304no—
536C3C2×#6603411yescharacteristic, complemented, Sylow
537C2—204no—
538C2—604no—
539C2#1175263814yesdirect product factor
540C2C2×#9200011yescharacteristic
541C2C2×#9201711yescharacteristic
542C2C2×#9201911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#562
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91764C2semidirect
2. C2×C5×#870C2semidirect
3. C2×C3×#4021C2semidirect
4. C2×#91459C2semidirect
5. C2×#91431C2semidirect
6. C2×#91413C2semidirect
7. C2×#91411C2semidirect
8. C2×#91409C2semidirect
9. C2×#91356C2semidirect
10. #11752638C2direct (N × H)
23. #91764C22semidirect
28. C5×#870C22semidirect
31. C3×#4021C22semidirect
36. #91459C22semidirect
37. #91431C22semidirect
38. #91413C22semidirect
39. #91411C22semidirect
40. #91409C22semidirect
41. #91356C22semidirect
52. C2×#4021D3semidirect
100. C2×#870D5semidirect
130. #4021C2×D3semidirect
192. #870C2×D5semidirect
359. C2×C3×C5#562semidirect
453. C3×C5C2×#562semidirect
473. C2×C5#5684semidirect
511. C2×C3#66034semidirect
516. C5C2×#5684semidirect
536. C3C2×#66034semidirect
539. C2#11752638direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917642
C2×C5×#8702
C2×C3×#40212
C2×#914592
C2×#914312
C2×#914132
C2×#914112
C2×#914092
C2×#913562
#117526382
C2×#660343
C2×#56845