Finite Group Databasebeta

← C2×#11747493 #14423340

Subgroups — C2×#11747493 #14423340

Order 1920.

1584 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×Dic6C211yesmaximal, characteristic, complemented
2C2×C3×#4041C211yesmaximal, characteristic
3C22×#6657C211yesmaximal, characteristic, complemented
4C22×#6655C211yesmaximal, characteristic, complemented
5C2×#91094C211yesmaximal, characteristic, complemented
6C2×C5×#810C211yesmaximal, characteristic, complemented
7C2×#90955C211yesmaximal, characteristic, complemented
8#11747493C218yesmaximal, direct product factor
9C2×#65095—31nomaximal, Hall
10C22×Dic30C2211yescharacteristic
11C22×C5×Dic6C2211yescharacteristic
12C22×C3×D20—21no—
13C22×C3×D20C2211yescharacteristic
14C22×C3×C4×D5C2211yescharacteristic
15C22×#1204—21no—
16C22×D5×Dic3—21no—
17C2×D5×Dic6—24no—
18C2×D5×Dic6—24no—
19C2×D5×Dic6—22no—
20C2×D5×Dic6C2214yescomplemented
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C22×C3⋊#168C2211yescharacteristic
23C22×C5×C3⋊C8C2211yescharacteristic
24C2×C3×#685—21no—
25C3×#4041—22no—
26C3×#4041C2214yes—
27C2×#6657—24no—
28C2×#6657C2214yescomplemented
29C2×#6655—24no—
30C2×#6655C2214yescomplemented
31#91094C2214yescomplemented
32C5×#810C2214yescomplemented
33#90955C2214yescomplemented
34C2×#5040—51nomaximal, Hall
35C22×Q8×D5—31no—
36C22×#688—31no—
37C22×#677—31no—
38C2×#4041D311yescharacteristic
39C2×C5×#103—31no—
40C2×#3952—31no—
41C2×#3942—31no—
42#65095—38no—
43C23×C3×D5—21no—
44C23×C3×D5D411yescharacteristic
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5C2311yescharacteristic
47C22×Dic15—21no—
48C2×Dic30—21no—
49C2×Dic30—22no—
50C2×Dic30D414yescomplemented
51C2×Dic30C2312yes—
52C22×C5×Dic3—21no—
53C2×C5×Dic6—21no—
54C2×C5×Dic6—22no—
55C2×C5×Dic6D414yescomplemented
56C2×C5×Dic6C2312yes—
57C22×C3×Dic5D411yescharacteristic
58C2×C3×D20—22no—
59C2×C3×D20—22no—
60C2×C3×D20—24no—
61C2×C3×D20—21no—
62C2×C3×D20—44no—
63C2×C3×D20C2312yes—
64C2×C3×C4×D5—22no—
65C2×C3×C4×D5—22no—
66C2×C3×C4×D5D412yes—
67C2×C3×C4×D5C2312yes—
68C2×#1204—28no—
69C2×#1204—24no—
70C2×D5×Dic3—28no—
71C2×D5×Dic3—24no—
72D5×Dic6—216no—
73D5×Dic6—28no—
74D5×Dic6—28no—
75C3×C5×C4⋊C4—21no—
76C3×C5×C4⋊C4C2312yes—
77C2×C3⋊#168—22no—
78C2×C3⋊#168C2312yes—
79C2×C5×C3⋊C8—22no—
80C2×C5×C3⋊C8C2312yes—
81C3×#685—24no—
82#6657—28no—
83#6655—28no—
84C23×Dic6—51no—
85C2×C3×#121—51no—
86C22×#214—51no—
87C22×#214—51no—
88C2×#830—51no—
89#5040—58no—
90C2×#810—51no—
91C2×#810D511yescharacteristic, complemented
92C22×C5×Q8—31no—
93C2×Q8×D5—34no—
94C2×Q8×D5—64no—
95C2×Q8×D5—64no—
96C2×Q8×D5—62no—
97C22×D20—21no—
98C22×D20C2×D311yescharacteristic
99C22×C4×D5—61no—
100C22×C4×D5C2×D311yescharacteristic
101C22×Dic10—31no—
102C22×Dic10—61no—
103C22×C5×C8—31no—
104C2×C5×C4⋊C4C2×D311yescharacteristic
105C2×#688—34no—
106C2×#688—64no—
107C2×#685—21no—
108C22×#168—31no—
109C2×#677—34no—
110C2×#677—64no—
111#4041—22no—
112#4041C2×D314yes—
113C5×#103—34no—
114#3952—34no—
115#3942—34no—
116C2×#448—151noSylow
117C23×C3×C5C2×D411yescharacteristic
118C22×C3×D5—22no—
119C22×C3×D5—22no—
120C22×C3×D5—22no—
121C22×C3×D5—42no—
122C22×C3×D5—42no—
123C22×C3×D5—42no—
124C22×C3×D5SD1614yescomplemented
125C22×C3×D5C2×D412yes—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—42no—
128C2×C3×C4×C5C2×D411yescharacteristic
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2×D412yes—
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—24no—
133C2×Dic15—22no—
134Dic30—24no—
135Dic30—22no—
136Dic30C2×D414yescomplemented
137C2×C5×Dic3—24no—
138C2×C5×Dic3—22no—
139C5×Dic6—24no—
140C5×Dic6—22no—
141C5×Dic6C2×D414yescomplemented
142C2×C3×Dic5—22no—
143C2×C3×Dic5C2×D412yes—
144C3×D20—22no—
145C3×D20—22no—
146C3×D20—48no—
147C3×D20—42no—
148C3×C4×D5—24no—
149C3×C4×D5—22no—
150C3×C4×D5—22no—
151#1204—216no—
152D5×Dic3—216no—
153C3⋊#168—22no—
154C5×C3⋊C8—22no—
155C22×C3×D4—51no—
156C22×C3×D4—101no—
157C23×C3×C4—51no—
158C23×Dic3—101no—
159C22×Dic6—51no—
160C22×Dic6—54no—
161C22×Dic6—104no—
162C22×Dic6—102no—
163C22×Dic6—101no—
164C22×Dic6—104no—
165C22×Dic6C2×D511yescharacteristic
166C3×#121—54no—
167C3×#121—102no—
168C2×C3×C4⋊C4C2×D511yescharacteristic
169C2×C3×C22⋊C4—101no—
170C2×#214—54no—
171C2×#214—54no—
172C2×#214—104no—
173C2×#214—104no—
174C22×C3⋊C8—51no—
175C22×C3⋊C8C2×D511yescharacteristic
176#830—54no—
177#810—54no—
178#810C2×D514yescomplemented
179C23×D5—21no—
180C23×D5#6711yescharacteristic
181C2×C5×Q8—34no—
182C2×C5×Q8—32no—
183C2×C5×Q8—62no—
184C2×C5×Q8—61no—
185C22×C4×C5—21no—
186C22×C4×C5—61no—
187C22×C4×C5C22×D311yescharacteristic
188C22×Dic5—61no—
189C22×Dic5#6711yescharacteristic
190Q8×D5—68no—
191Q8×D5—68no—
192Q8×D5—616no—
193C2×D20—22no—
194C2×D20—22no—
195C2×D20—24no—
196C2×D20—21no—
197C2×D20—44no—
198C2×D20C22×D312yes—
199C2×C4×D5—22no—
200C2×C4×D5—22no—
201C2×C4×D5—68no—
202C2×C4×D5—64no—
203C2×C4×D5#6712yes—
204C2×C4×D5C22×D312yes—
205C2×Dic10—34no—
206C2×Dic10—32no—
207C2×Dic10—68no—
208C2×Dic10—62no—
209C2×Dic10—61no—
210C2×Dic10—64no—
211C2×C5×C8—32no—
212C2×C5×C8—62no—
213C5×C4⋊C4—21no—
214C5×C4⋊C4C22×D312yes—
215#688—68no—
216#685—24no—
217C2×#168—32no—
218C2×#168—62no—
219#677—68no—
220C23×Q8—151no—
221C22×SD16—151no—
222C22×SD16—151no—
223C2×#121—51no—
224#448—158no—
225C2×#103—31no—
226C2×#103—151no—
227C2×C22⋊C8—151no—
228C22×C3×C5#12012yes—
229C22×C3×C5C2×SD1612yes—
230C22×C3×C5#13712yes—
231C22×C3×C5C22×D411yescharacteristic
232C2×C3×D5—22no—
233C2×C3×D5—22no—
234C2×C3×D5—28no—
235C2×C3×D5—42no—
236C2×C3×D5—42no—
237C2×C3×D5—42no—
238C2×C3×D5—84no—
239C2×C3×D5C2×SD1614yescomplemented
240C3×C4×C5—42no—
241C3×C4×C5#12012yes—
242C3×C4×C5C22×D411yescharacteristic
243C3×C4×C5C22×D411yescharacteristic
244Dic15—24no—
245C3×Dic5—22no—
246C5×Dic3—24no—
247C24×C3—51no—
248C24×C3—101no—
249C2×C3×D4—52no—
250C2×C3×D4—104no—
251C2×C3×D4—102no—
252C2×C3×D4—102no—
253C2×C3×D4—101no—
254C2×C3×D4—204no—
255C22×C3×C4—21no—
256C22×C3×C4—51no—
257C22×C3×C4—52no—
258C22×C3×C4—52no—
259C22×C3×C4—102no—
260C22×C3×C4—102no—
261C22×C3×C4C22×D511yescharacteristic
262C22×Dic3—21no—
263C22×Dic3—104no—
264C22×Dic3—108no—
265C22×Dic3—101no—
266C2×Dic6—22no—
267C2×Dic6—21no—
268C2×Dic6—54no—
269C2×Dic6—52no—
270C2×Dic6—108no—
271C2×Dic6—1016no—
272C2×Dic6—104no—
273C2×Dic6—108no—
274C2×Dic6—102no—
275C2×Dic6—101no—
276C2×Dic6—108no—
277C2×Dic6D2014yescomplemented
278C2×Dic6C22×D512yes—
279C3×C4⋊C4—21no—
280C3×C4⋊C4C22×D512yes—
281C3×C22⋊C4—104no—
282#214—108no—
283#214—108no—
284C2×C3⋊C8—22no—
285C2×C3⋊C8—52no—
286C2×C3⋊C8—102no—
287C2×C3⋊C8C22×D512yes—
288C23×C5C2×#6711yescharacteristic
289C22×D5—22no—
290C22×D5—22no—
291C22×D5—22no—
292C22×D5—42no—
293C22×D5—42no—
294C22×D5—42no—
295C22×D5#21414yescomplemented
296C22×D5C2×#6712yes—
297C5×Q8—34no—
298C5×Q8—64no—
299C5×Q8—62no—
300C2×C4×C5—22no—
301C2×C4×C5—42no—
302C2×C4×C5—64no—
303C2×C4×C5—62no—
304C2×C4×C5D3×D412yes—
305C2×C4×C5D3×D412yes—
306C2×C4×C5C2×#6711yescharacteristic
307C2×C4×C5C23×D311yescharacteristic
308C2×Dic5—22no—
309C2×Dic5—64no—
310C2×Dic5—62no—
311C2×Dic5C2×#6712yes—
312D20—22no—
313D20—22no—
314D20—48no—
315D20—42no—
316C4×D5—24no—
317C4×D5—22no—
318C4×D5—22no—
319C4×D5—616no—
320Dic10—34no—
321Dic10—616no—
322Dic10—64no—
323Dic10—62no—
324C5×C8—62no—
325#168—62no—
326C22×Q8—31no—
327C22×Q8—154no—
328C22×Q8—151no—
329C22×Q8—301no—
330C22×Q8—302no—
331C22×Q8—304no—
332C22×Q8—304no—
333C22×D4—51no—
334C22×D4—101no—
335C23×C4—51no—
336C23×C4—301no—
337C2×SD16—154no—
338C2×SD16—154no—
339C2×SD16—304no—
340C2×SD16—304no—
341C22×C8—31no—
342C22×C8—151no—
343#121—54no—
344#121—102no—
345C2×C4⋊C4D3×D511yescharacteristic
346C2×C22⋊C4—101no—
347#103—34no—
348#103—154no—
349C22⋊C8—154no—
350C2×C3×C5#44814yescomplemented
351C2×C3×C5C2×#12011yescharacteristic
352C2×C3×C5C22×SD1611yescharacteristic
353C2×C3×C5C2×#13711yescharacteristic
354C3×D5—24no—
355C3×D5—82no—
356C23×C3—52no—
357C23×C3—54no—
358C23×C3—102no—
359C23×C3—102no—
360C23×C3—102no—
361C23×C3—202no—
362C23×C3—202no—
363C23×C3—202no—
364C23×C3D4×D511yescharacteristic
365C3×D4—102no—
366C3×D4—102no—
367C3×D4—208no—
368C3×D4—202no—
369C2×C3×C4—22no—
370C2×C3×C4—42no—
371C2×C3×C4—52no—
372C2×C3×C4—102no—
373C2×C3×C4—102no—
374C2×C3×C4—102no—
375C2×C3×C4—104no—
376C2×C3×C4C2×D2012yes—
377C2×C3×C4D4×D512yes—
378C2×C3×C4D4×D511yescharacteristic
379C2×C3×C4C23×D511yescharacteristic
380C2×Dic3—22no—
381C2×Dic3—24no—
382C2×Dic3—1016no—
383C2×Dic3—102no—
384C2×Dic3—104no—
385Dic6—22no—
386Dic6—24no—
387Dic6—54no—
388Dic6—1016no—
389Dic6—102no—
390Dic6—104no—
391Dic6C2×D2014yescomplemented
392C3⋊C8—22no—
393C3⋊C8—102no—
394C22×C5C2×#21412yes—
395C22×C5#93712yes—
396C22×C5#95112yes—
397C22×C5C22×#6711yescharacteristic
398C2×D5—22no—
399C2×D5—28no—
400C2×D5—22no—
401C2×D5—42no—
402C2×D5—42no—
403C2×D5—42no—
404C2×D5—84no—
405C2×D5C2×#21414yescomplemented
406C4×C5—42no—
407C4×C5—64no—
408C4×C5#93712yes—
409C4×C5C2×D3×D411yescharacteristic
410C4×C5C2×D3×D411yescharacteristic
411Dic5—22no—
412Dic5—64no—
413C24—51no—
414C24—101no—
415C2×Q8—34no—
416C2×Q8—32no—
417C2×Q8—62no—
418C2×Q8—61no—
419C2×Q8—154no—
420C2×Q8—152no—
421C2×Q8—304no—
422C2×Q8—308no—
423C2×Q8—308no—
424C2×Q8—308no—
425C2×Q8—3016no—
426C2×Q8—302no—
427C2×Q8—301no—
428C2×D4—52no—
429C2×D4—104no—
430C2×D4—102no—
431C2×D4—102no—
432C2×D4—101no—
433C2×D4—204no—
434C22×C4—21no—
435C22×C4—51no—
436C22×C4—52no—
437C22×C4—52no—
438C22×C4—61no—
439C22×C4—102no—
440C22×C4—102no—
441C22×C4—304no—
442C22×C4—308no—
443C22×C4—301no—
444C22×C4C2×D3×D511yescharacteristic
445SD16—308no—
446SD16—308no—
447C2×C8—32no—
448C2×C8—62no—
449C2×C8—152no—
450C2×C8—302no—
451C4⋊C4—21no—
452C4⋊C4C2×D3×D512yes—
453C22⋊C4—104no—
454C3×C5C2×#44811yescharacteristic, complemented, Hall
455C22×C3—54no—
456C22×C3—102no—
457C22×C3—102no—
458C22×C3—108no—
459C22×C3—202no—
460C22×C3—202no—
461C22×C3—202no—
462C22×C3—404no—
463C22×C3#402812yes—
464C22×C3D5×SD1612yes—
465C22×C3#406412yes—
466C22×C3C2×D4×D511yescharacteristic
467C3×C4—42no—
468C3×C4—102no—
469C3×C4#402812yes—
470C3×C4C22×D2011yescharacteristic
471C3×C4C2×D4×D511yescharacteristic
472Dic3—24no—
473Dic3—104no—
474C2×C5#504014yescomplemented
475C2×C5C22×#21411yescharacteristic
476C2×C5C2×#93711yescharacteristic
477C2×C5C2×#95111yescharacteristic
478D5—24no—
479D5—82no—
480C23—54no—
481C23—52no—
482C23—102no—
483C23—102no—
484C23—102no—
485C23—202no—
486C23—202no—
487C23—202no—
488C23D5×#6711yescharacteristic
489Q8—34no—
490Q8—64no—
491Q8—62no—
492Q8—154no—
493Q8—3016no—
494Q8—304no—
495Q8—302no—
496D4—102no—
497D4—102no—
498D4—208no—
499D4—202no—
500C2×C4—22no—
501C2×C4—42no—
502C2×C4—52no—
503C2×C4—64no—
504C2×C4—62no—
505C2×C4—102no—
506C2×C4—104no—
507C2×C4—102no—
508C2×C4—102no—
509C2×C4—3016no—
510C2×C4—304no—
511C2×C4—302no—
512C2×C4D3×D2012yes—
513C2×C4#677712yes—
514C2×C4D5×#6711yescharacteristic
515C2×C4C22×D3×D511yescharacteristic
516C8—62no—
517C8—302no—
518C2×C3—104no—
519C2×C3—402no—
520C2×C3#6509514yescomplemented
521C2×C3C2×#402811yescharacteristic
522C2×C3C2×D5×SD1611yescharacteristic
523C2×C3C2×#406411yescharacteristic
524C5C2×#504011yescharacteristic, complemented, Sylow
525C22—54no—
526C22—102no—
527C22—102no—
528C22—108no—
529C22—202no—
530C22—202no—
531C22—202no—
532C22—404no—
533C22#9147412yes—
534C22D5×#21412yes—
535C22#9150812yes—
536C22C2×D5×#6711yescharacteristic
537C4—42no—
538C4—64no—
539C4—102no—
540C4—304no—
541C4#9147412yes—
542C4C2×D3×D2011yescharacteristic
543C4C2×#677711yescharacteristic
544C3C2×#6509511yescharacteristic, complemented, Sylow
545C2—104no—
546C2—402no—
547C2#1174749314yesdirect product factor
548C2C2×#9147411yescharacteristic
549C2C2×D5×#21411yescharacteristic
550C2C2×#9150811yescharacteristic
subgroupG/H
centerC23D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C2×D4
prime radicalC2×C3×#4041C2
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#448
LCSG ▷ C2×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
1. C22×D5×Dic6C2semidirect
3. C22×#6657C2semidirect
4. C22×#6655C2semidirect
5. C2×#91094C2semidirect
6. C2×C5×#810C2semidirect
7. C2×#90955C2semidirect
8. #11747493C2direct (N × H)
20. C2×D5×Dic6C22semidirect
28. C2×#6657C22semidirect
30. C2×#6655C22semidirect
31. #91094C22semidirect
32. C5×#810C22semidirect
33. #90955C22semidirect
50. C2×Dic30D4semidirect
55. C2×C5×Dic6D4semidirect
91. C2×#810D5semidirect
124. C22×C3×D5SD16semidirect
136. Dic30C2×D4semidirect
141. C5×Dic6C2×D4semidirect
178. #810C2×D5semidirect
239. C2×C3×D5C2×SD16semidirect
277. C2×Dic6D20semidirect
295. C22×D5#214semidirect
350. C2×C3×C5#448semidirect
391. Dic6C2×D20semidirect
405. C2×D5C2×#214semidirect
454. C3×C5C2×#448semidirect
474. C2×C5#5040semidirect
520. C2×C3#65095semidirect
524. C5C2×#5040semidirect
544. C3C2×#65095semidirect
547. C2#11747493direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×Dic62
C2×C3×#40412
C22×#66572
C22×#66552
C2×#910942
C2×C5×#8102
C2×#909552
#117474932
C2×#650953
C2×#50405