Finite Group Databasebeta

← C2×#11752511 #14481256

Subgroups — C2×#11752511 #14481256

Order 1920.

2008 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×C4×Dic30C211yesmaximal, characteristic, complemented
2C2×C4×C5×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×#4018C211yesmaximal, characteristic
4C2×#91388C211yesmaximal, characteristic, complemented
5C2×#91382C212yesmaximal, complemented
6C2×#91379C212yesmaximal, complemented
7C2×#91376C211yesmaximal, characteristic, complemented
8C2×#91366C212yesmaximal
9C2×#91363C212yesmaximal
10C2×#91360C211yesmaximal, characteristic
11C2×#91359C211yesmaximal, characteristic
12#11752511C2116yesmaximal, direct product factor
13C2×#65917—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C2×C3×C42×C5C2211yescharacteristic
18C2×C4⋊Dic15C2211yescharacteristic
19C2×#6712C2212yes—
20C2×C4×Dic15C2212yes—
21C4×Dic30C2218yescomplemented
22C2×C5×C4⋊Dic3C2211yescharacteristic
23C2×C5×Dic3⋊C4C2212yes—
24C2×C4×C5×Dic3C2212yes—
25C4×C5×Dic6C2218yescomplemented
26C2×C3×#685C2211yescharacteristic
27C2×C3×#685C2211yescharacteristic
28C2×C3×#683C2211yescharacteristic
29C2×C3×#683C2211yescharacteristic
30C2×C3×C4×Dic5C2211yescharacteristic
31C3×#4018C2218yes—
32C2×Dic3⋊Dic5C2212yes—
33C2×Dic3⋊Dic5C2212yes—
34C2×#6669C2212yes—
35C2×#6669C2212yes—
36C2×#6668C2212yes—
37C2×#6668C2212yes—
38C2×#6665C2212yes—
39C2×#6665C2212yes—
40#91388C2218yescomplemented
41#91382C22116yescomplemented
42#91379C22116yescomplemented
43#91376C2218yescomplemented
44#91366C22116yes—
45#91363C22116yes—
46#91360C2218yes—
47#91359C2218yes—
48C2×#5518—51nomaximal, Hall
49C2×C4×C5×Q8—31no—
50C2×#4092—31no—
51C2×#4090—31no—
52#65917—316no—
53C2×#4044—32no—
54C2×#4043—31no—
55C2×#4036—31no—
56C2×#4035—32no—
57C2×#4022—32no—
58C2×#4018D311yescharacteristic
59C2×#4016—32no—
60C2×C4×Dic10—31no—
61C23×C3×D5C2311yescharacteristic
62C22×C3×C4×C5C2311yescharacteristic
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2312yes—
66C22×Dic15C2312yes—
67C2×Dic30—24no—
68C2×Dic30C2314yes—
69C22×C5×Dic3C2312yes—
70C22×C5×Dic3C2312yes—
71C2×C5×Dic6—24no—
72C2×C5×Dic6C2314yes—
73C22×C3×Dic5C2311yescharacteristic
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C2×C3×C4×D5—24no—
77C2×C3×C4×D5C2314yes—
78C3×C42×C5C2314yes—
79C4⋊Dic15C2314yes—
80#6712C2318yes—
81C4×Dic15C2318yes—
82C5×C4⋊Dic3C2314yes—
83C5×Dic3⋊C4C2318yes—
84C4×C5×Dic3C2318yes—
85C3×#685C2314yes—
86C3×#685C2314yes—
87C3×#683C2314yes—
88C3×#683C2314yes—
89C3×C4×Dic5C2314yes—
90Dic3⋊Dic5C2318yes—
91Dic3⋊Dic5C2318yes—
92#6669C2318yes—
93#6669C2318yes—
94#6668C2318yes—
95#6668C2318yes—
96#6665C2318yes—
97#6665C2318yes—
98C2×C3×#117—51no—
99C2×#924—51no—
100C2×#924—51no—
101#5518—516no—
102C2×#889—52no—
103C2×#889—52no—
104C2×#879—52no—
105C2×#879—52no—
106C2×#870—51no—
107C2×#869—51no—
108C2×C4×Dic6—51no—
109C2×C4×Dic6D511yescharacteristic, complemented
110C22×C5×Q8—31no—
111C22×C4×D5C2×D311yescharacteristic
112C22×Dic10—31no—
113C4×C5×Q8—38no—
114C2×C5×C4⋊C4—32no—
115C2×C5×C4⋊C4—31no—
116C2×C42×C5—32no—
117C2×C42×C5C2×D311yescharacteristic
118#4092—38no—
119#4090—38no—
120C2×#685—32no—
121C2×#685—32no—
122C2×#685C2×D311yescharacteristic
123C2×#685C2×D311yescharacteristic
124C2×C4⋊Dic5—31no—
125C2×C4⋊Dic5—32no—
126C2×C4⋊Dic5—32no—
127C2×#683—32no—
128C2×#683—32no—
129C2×#683—32no—
130C2×#683—32no—
131C2×#683—32no—
132C2×#683C2×D311yescharacteristic
133C2×#683C2×D311yescharacteristic
134C2×C4×Dic5—32no—
135C2×C4×Dic5C2×D311yescharacteristic
136#4044—316no—
137#4043—38no—
138#4036—38no—
139#4035—316no—
140#4022—316no—
141#4018C2×D318yes—
142#4016—316no—
143C4×Dic10—38no—
144C2×#541—151noSylow
145C23×C3×C5C2411yescharacteristic
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5C2412yes—
150C2×C3×C4×C5—22no—
151C2×C3×C4×C5—22no—
152C2×C3×C4×C5#4114yes—
153C2×C3×C4×C5C2412yes—
154C2×C3×C4×C5C2412yes—
155C2×C3×C4×C5C2412yes—
156C2×Dic15—24no—
157C2×Dic15—24no—
158C2×Dic15C2414yes—
159C2×Dic15C2414yes—
160Dic30—28no—
161C2×C5×Dic3—24no—
162C2×C5×Dic3—24no—
163C2×C5×Dic3C2414yes—
164C2×C5×Dic3C2414yes—
165C5×Dic6—28no—
166C2×C3×Dic5—22no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5C2412yes—
170C2×C3×Dic5C2412yes—
171C2×C3×Dic5C2412yes—
172C3×C4×D5—28no—
173C23×C3×C4—51no—
174C22×Dic6—51no—
175C22×Dic6C2×D511yescharacteristic
176C3×#117—58no—
177C2×C3×C4⋊C4—51no—
178C2×C3×C4⋊C4—51no—
179C2×C3×C22⋊C4—51no—
180C2×C3×C22⋊C4—51no—
181C2×C3×C42—51no—
182C2×C3×C42C2×D511yescharacteristic
183C2×#217—52no—
184C2×#217—52no—
185C2×C4⋊Dic3—51no—
186C2×C4⋊Dic3—52no—
187C2×C4⋊Dic3—52no—
188C2×C4⋊Dic3C2×D511yescharacteristic
189#924—58no—
190#924—58no—
191C2×Dic3⋊C4—52no—
192C2×Dic3⋊C4—52no—
193C2×Dic3⋊C4—52no—
194C2×Dic3⋊C4—52no—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4C2×D512yes—
197C2×C4×Dic3—52no—
198C2×C4×Dic3C2×D512yes—
199#889—516no—
200#889—516no—
201#879—516no—
202#879—516no—
203#870—58no—
204#869—58no—
205C4×Dic6—58no—
206C4×Dic6C2×D518yescomplemented
207C23×D5C22×D311yescharacteristic
208C2×C5×Q8—34no—
209C2×C5×Q8—64no—
210C22×C4×C5—32no—
211C22×C4×C5—32no—
212C22×C4×C5C22×D311yescharacteristic
213C22×C4×C5C22×D311yescharacteristic
214C22×C4×C5C22×D311yescharacteristic
215C22×Dic5—32no—
216C22×Dic5—32no—
217C22×Dic5C22×D311yescharacteristic
218C22×Dic5C22×D311yescharacteristic
219C22×Dic5C22×D311yescharacteristic
220C2×C4×D5—24no—
221C2×C4×D5C22×D314yes—
222C2×Dic10—34no—
223C2×Dic10—64no—
224C5×C4⋊C4—38no—
225C5×C4⋊C4—34no—
226C42×C5—38no—
227C42×C5C22×D314yes—
228#685—38no—
229#685—38no—
230#685C22×D314yes—
231#685C22×D314yes—
232C4⋊Dic5—34no—
233C4⋊Dic5—38no—
234C4⋊Dic5—38no—
235#683—38no—
236#683—38no—
237#683—38no—
238#683—38no—
239#683—38no—
240#683C22×D314yes—
241#683C22×D314yes—
242C4×Dic5—38no—
243C4×Dic5C22×D314yes—
244#541—1516no—
245C2×C4⋊Q8—151no—
246C2×#126—152no—
247C2×#126—152no—
248C2×#125—152no—
249C2×#125—151no—
250C2×#125—152no—
251C2×C22⋊Q8—151no—
252C2×C22⋊Q8—151no—
253C2×C4×Q8—31no—
254C2×C4×Q8—151no—
255C2×#117—51no—
256C22×C3×C5C2×#4112yes—
257C22×C3×C52−1+412yes—
258C22×C3×C52−1+412yes—
259C22×C3×C5C2511yescharacteristic
260C2×C3×D5—22no—
261C2×C3×D5—22no—
262C2×C3×D5—22no—
263C2×C3×D5—44no—
264C3×C4×C5—22no—
265C3×C4×C5—22no—
266C3×C4×C5C2×#4114yes—
267Dic15—24no—
268Dic15—24no—
269C3×Dic5—22no—
270C3×Dic5—22no—
271C3×Dic5—22no—
272C5×Dic3—24no—
273C5×Dic3—24no—
274C24×C3—51no—
275C22×C3×C4—51no—
276C22×C3×C4—51no—
277C22×C3×C4—51no—
278C22×C3×C4—54no—
279C22×C3×C4—104no—
280C22×C3×C4C22×D511yescharacteristic
281C22×C3×C4C22×D511yescharacteristic
282C22×C3×C4C22×D511yescharacteristic
283C22×Dic3—52no—
284C22×Dic3—52no—
285C22×Dic3C22×D512yes—
286C22×Dic3C22×D512yes—
287C2×Dic6—24no—
288C2×Dic6—54no—
289C2×Dic6—104no—
290C2×Dic6C22×D514yes—
291C3×C4⋊C4—54no—
292C3×C4⋊C4—54no—
293C3×C22⋊C4—54no—
294C3×C22⋊C4—54no—
295C3×C42—54no—
296C3×C42C22×D514yes—
297#217—58no—
298#217—58no—
299C4⋊Dic3—54no—
300C4⋊Dic3—58no—
301C4⋊Dic3—58no—
302C4⋊Dic3C22×D514yes—
303Dic3⋊C4—58no—
304Dic3⋊C4—58no—
305Dic3⋊C4—58no—
306Dic3⋊C4—58no—
307Dic3⋊C4—58no—
308Dic3⋊C4C22×D518yes—
309C4×Dic3—58no—
310C4×Dic3C22×D518yes—
311C23×C5C23×D311yescharacteristic
312C22×D5—22no—
313C22×D5—22no—
314C22×D5—22no—
315C22×D5C23×D312yes—
316C5×Q8—68no—
317C2×C4×C5—22no—
318C2×C4×C5—22no—
319C2×C4×C5—34no—
320C2×C4×C5—34no—
321C2×C4×C5—64no—
322C2×C4×C5—64no—
323C2×C4×C5#23514yes—
324C2×C4×C5C23×D312yes—
325C2×C4×C5C23×D312yes—
326C2×C4×C5C23×D312yes—
327C2×Dic5—22no—
328C2×Dic5—22no—
329C2×Dic5—22no—
330C2×Dic5—34no—
331C2×Dic5—34no—
332C2×Dic5—64no—
333C2×Dic5—64no—
334C2×Dic5C23×D312yes—
335C2×Dic5C23×D312yes—
336C2×Dic5C23×D312yes—
337C4×D5—28no—
338Dic10—68no—
339C22×Q8—31no—
340C22×Q8—151no—
341C23×C4—51no—
342C4⋊Q8—158no—
343#126—1516no—
344#126—1516no—
345#125—1516no—
346#125—158no—
347#125—1516no—
348C22⋊Q8—158no—
349C22⋊Q8—158no—
350C4×Q8—38no—
351C4×Q8—158no—
352#117—58no—
353C2×C4⋊C4—31no—
354C2×C4⋊C4—32no—
355C2×C4⋊C4—51no—
356C2×C4⋊C4—51no—
357C2×C4⋊C4—152no—
358C2×C4⋊C4—152no—
359C2×C4⋊C4—152no—
360C2×C4⋊C4—152no—
361C2×C4⋊C4—152no—
362C2×C4⋊C4—152no—
363C2×C4⋊C4—151no—
364C2×C4⋊C4—152no—
365C2×C22⋊C4—51no—
366C2×C22⋊C4—51no—
367C2×C22⋊C4—152no—
368C2×C22⋊C4—152no—
369C2×C42—32no—
370C2×C42—51no—
371C2×C42—152no—
372C2×C42D3×D511yescharacteristic
373C2×C3×C5#54114yescomplemented
374C2×C3×C5C22×#4111yescharacteristic
375C2×C3×C5C2×2−1+411yescharacteristic
376C2×C3×C5C2×2−1+411yescharacteristic
377C3×D5—42no—
378C23×C3—52no—
379C23×C3—102no—
380C23×C3—102no—
381C23×C3—102no—
382C23×C3C23×D511yescharacteristic
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—52no—
386C2×C3×C4—52no—
387C2×C3×C4—52no—
388C2×C3×C4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—102no—
391C2×C3×C4—108no—
392C2×C3×C4#70914yes—
393C2×C3×C4C23×D512yes—
394C2×C3×C4C23×D512yes—
395C2×C3×C4C23×D512yes—
396C2×Dic3—24no—
397C2×Dic3—24no—
398C2×Dic3—54no—
399C2×Dic3—54no—
400C2×Dic3—104no—
401C2×Dic3—104no—
402C2×Dic3C23×D514yes—
403C2×Dic3C23×D514yes—
404Dic6—28no—
405Dic6—108no—
406C22×C5C2×#23512yes—
407C22×C5#101012yes—
408C22×C5#101012yes—
409C22×C5C24×D311yescharacteristic
410C2×D5—22no—
411C2×D5—22no—
412C2×D5—22no—
413C2×D5—44no—
414C4×C5—22no—
415C4×C5—22no—
416C4×C5—64no—
417C4×C5—64no—
418C4×C5C2×#23514yes—
419Dic5—22no—
420Dic5—22no—
421Dic5—22no—
422Dic5—64no—
423Dic5—64no—
424C24—51no—
425C2×Q8—34no—
426C2×Q8—64no—
427C2×Q8—154no—
428C2×Q8—304no—
429C22×C4—32no—
430C22×C4—32no—
431C22×C4—51no—
432C22×C4—51no—
433C22×C4—51no—
434C22×C4—54no—
435C22×C4—104no—
436C22×C4—152no—
437C22×C4—152no—
438C22×C4C2×D3×D511yescharacteristic
439C22×C4C2×D3×D511yescharacteristic
440C22×C4C2×D3×D511yescharacteristic
441C4⋊C4—34no—
442C4⋊C4—38no—
443C4⋊C4—54no—
444C4⋊C4—54no—
445C4⋊C4—158no—
446C4⋊C4—158no—
447C4⋊C4—158no—
448C4⋊C4—158no—
449C4⋊C4—158no—
450C4⋊C4—158no—
451C4⋊C4—154no—
452C4⋊C4—158no—
453C22⋊C4—54no—
454C22⋊C4—54no—
455C22⋊C4—158no—
456C22⋊C4—158no—
457C42—38no—
458C42—54no—
459C42—158no—
460C42C2×D3×D514yes—
461C3×C5C2×#54111yescharacteristic, complemented, Hall
462C22×C3—102no—
463C22×C3—102no—
464C22×C3—102no—
465C22×C3—204no—
466C22×C3C2×#70912yes—
467C22×C3#414712yes—
468C22×C3#415012yes—
469C22×C3C24×D511yescharacteristic
470C3×C4—22no—
471C3×C4—22no—
472C3×C4—102no—
473C3×C4—102no—
474C3×C4—102no—
475C3×C4C2×#70914yes—
476Dic3—24no—
477Dic3—24no—
478Dic3—104no—
479Dic3—104no—
480C2×C5#551814yescomplemented
481C2×C5C22×#23511yescharacteristic
482C2×C5C2×#101011yescharacteristic
483C2×C5C2×#101011yescharacteristic
484D5—42no—
485C23—52no—
486C23—102no—
487C23—102no—
488C23—102no—
489C23C22×D3×D511yescharacteristic
490Q8—68no—
491Q8—308no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—34no—
495C2×C4—34no—
496C2×C4—52no—
497C2×C4—52no—
498C2×C4—52no—
499C2×C4—64no—
500C2×C4—64no—
501C2×C4—102no—
502C2×C4—102no—
503C2×C4—102no—
504C2×C4—108no—
505C2×C4—154no—
506C2×C4—154no—
507C2×C4—304no—
508C2×C4—304no—
509C2×C4#677114yes—
510C2×C4C22×D3×D512yes—
511C2×C4C22×D3×D512yes—
512C2×C4C22×D3×D512yes—
513C2×C3—202no—
514C2×C3#6591714yescomplemented
515C2×C3C22×#70911yescharacteristic
516C2×C3C2×#414711yescharacteristic
517C2×C3C2×#415011yescharacteristic
518C5C2×#551811yescharacteristic, complemented, Sylow
519C22—102no—
520C22—102no—
521C22—102no—
522C22—204no—
523C22#9200012yes—
524C22#9200112yes—
525C22C2×#677112yes—
526C22C23×D3×D511yescharacteristic
527C4—22no—
528C4—22no—
529C4—64no—
530C4—64no—
531C4—102no—
532C4—102no—
533C4—102no—
534C4—304no—
535C4—304no—
536C4C2×#677114yes—
537C3C2×#6591711yescharacteristic, complemented, Sylow
538C2—202no—
539C2#1175251114yesdirect product factor
540C2C2×#9200011yescharacteristic
541C2C2×#9200111yescharacteristic
542C2C22×#677111yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#541
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×C4×Dic30C2semidirect
2. C2×C4×C5×Dic6C2semidirect
4. C2×#91388C2semidirect
5. C2×#91382C2semidirect
6. C2×#91379C2semidirect
7. C2×#91376C2semidirect
12. #11752511C2direct (N × H)
21. C4×Dic30C22semidirect
25. C4×C5×Dic6C22semidirect
40. #91388C22semidirect
41. #91382C22semidirect
42. #91379C22semidirect
43. #91376C22semidirect
109. C2×C4×Dic6D5semidirect
206. C4×Dic6C2×D5semidirect
373. C2×C3×C5#541semidirect
461. C3×C5C2×#541semidirect
480. C2×C5#5518semidirect
514. C2×C3#65917semidirect
518. C5C2×#5518semidirect
537. C3C2×#65917semidirect
539. C2#11752511direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Dic302
C2×C4×C5×Dic62
C2×C3×#40182
C2×#913882
C2×#913822
C2×#913792
C2×#913762
C2×#913662
C2×#913632
C2×#913602
C2×#913592
#117525112
C2×#659173
C2×#55185