Finite Group Databasebeta

← D3×#65003 #14437874

Subgroups — D3×#65003 #14437874

Order 1920.

872 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#4021C211yesmaximal, characteristic
2D3×#4015C211yesmaximal, characteristic, complemented
3#11750815C211yesmaximal, characteristic, complemented
4C5×D3×#97C211yesmaximal, characteristic, complemented
5C3×#65003C211yesmaximal, characteristic, complemented
6D3×#3953C212yesmaximal
7#11748031C212yesmaximal, complemented
8#11747968C212yesmaximal, complemented
9D3×#3948C212yesmaximal, complemented
10#11746935C211yesmaximal, characteristic, complemented
11#11746893C211yesmaximal, characteristic, complemented
12C2×#65003—31nomaximal, Hall
13C2×D3×D20C2211yescharacteristic
14C2×D3×Dic10—21no—
15C2×D3×Dic10C2211yescharacteristic
16#91764C2211yescharacteristic
17#91758C2211yescharacteristic, complemented
18C2×C5×D3×C8C2212yes—
19C42×C5×D3C2211yescharacteristic
20C3×#4021C2211yescharacteristic
21C3×#4015C2211yescharacteristic, complemented
22D3×#685—21no—
23D3×#685—21no—
24#91469—21no—
25#91469C2212yescomplemented
26D3×C4⋊Dic5—21no—
27D3×C4⋊Dic5C2212yes—
28#91389—21no—
29#91374C2211yescharacteristic
30#91364C2211yescharacteristic
31#91353—21no—
32#91353—21no—
33C3×C5×#97C2211yescharacteristic, complemented
34#91105C2212yes—
35#91100C2212yescomplemented
36C5×#815C2212yescomplemented
37C5×#803C2211yescharacteristic, complemented
38C3×#3953C2212yes—
39C3×#3948C2212yescomplemented
40#90974C2212yescomplemented
41#90971C2212yescomplemented
42#90968C2212yes—
43#90965C2212yes—
44D3×#489—51nomaximal, Hall
45C2×#4021—31no—
46C2×#4015—31no—
47C2×C5×#97—31no—
48C2×#3953—32no—
49C2×#3948—32no—
50#65003—31no—
51#65003—31no—
52#65003—31no—
53#65003—32no—
54#65003—32no—
55#65003D311yescharacteristic, direct product factor
56C22×D3×D5—21no—
57C2×D60C2311yescharacteristic
58C2×Dic30—21no—
59C2×Dic30C2311yescharacteristic
60C2×C4×C5×D3D411yescharacteristic
61C2×C4×C5×D3D411yescharacteristic
62C2×C4×C5×D3C2311yescharacteristic
63C2×C3×D20C2311yescharacteristic
64C2×C3×Dic10—21no—
65C2×C3×Dic10C2311yescharacteristic
66C2×#1204—22no—
67C2×#1204—21no—
68C2×#1202—21no—
69C2×D3×Dic5—22no—
70C2×D3×Dic5—21no—
71D3×D20—24no—
72D3×Dic10—24no—
73D3×Dic10—44no—
74C2×C3×C5×C8C2312yes—
75C3×C42×C5C2311yescharacteristic
76#6714—21no—
77#6714—21no—
78C4⋊Dic15—21no—
79C4⋊Dic15C2312yes—
80C4×C5×Dic3D411yescharacteristic
81C4×C5×Dic3D411yescharacteristic
82C4×C5×Dic3C2311yescharacteristic
83C2×C5×C3⋊C8C2312yes—
84C5×D3×C8—24no—
85C3×#685—21no—
86C3×#685—21no—
87C3×C4⋊Dic5—21no—
88C3×C4⋊Dic5C2312yes—
89Dic3⋊Dic5—22no—
90Dic3⋊Dic5—22no—
91#6667—21no—
92#6667—21no—
93#6665—21no—
94#6665—21no—
95D3×C4⋊Q8—51no—
96D3×#124—51no—
97C3×#489—51no—
98#5089—51no—
99#5055—51no—
100D3×#103—52no—
101#4794—52no—
102D3×#102—52no—
103#4765—52no—
104#4714—51no—
105D3×#97D511yescharacteristic, complemented
106C22×D20—31no—
107C22×Dic10—31no—
108C22×Dic10—61no—
109C22×C5×C8—32no—
110C2×C42×C5—31no—
111C2×#685—61no—
112C2×#685—61no—
113C2×C4⋊Dic5—32no—
114C2×C4⋊Dic5—61no—
115#4021—31no—
116#4021—31no—
117#4021—31no—
118#4021—61no—
119#4021—61no—
120#4021C2×D311yescharacteristic
121#4015—31no—
122#4015—32no—
123#4015—61no—
124#4015—61no—
125#4015C2×D311yescharacteristic, complemented
126C5×#97—32no—
127C5×#97—31no—
128C5×#97C2×D311yescharacteristic, complemented
129#3953—32no—
130#3953—32no—
131#3953—32no—
132#3953C2×D312yes—
133#3948—32no—
134#3948—32no—
135#3948—32no—
136#3948C2×D312yescomplemented
137C2×#489—151noSylow
138C22×D15—21no—
139C22×C5×D3C2×D411yescharacteristic
140C22×C3×D5—21no—
141C2×D3×D5—42no—
142C2×D3×D5—42no—
143C2×D3×D5—42no—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D411yescharacteristic
146C2×C3×C4×C5C2411yescharacteristic
147C2×Dic15—21no—
148C2×Dic15—22no—
149D60—22no—
150Dic30—22no—
151Dic30—42no—
152C2×C5×Dic3C2×D411yescharacteristic
153C2×C5×Dic3C2×D411yescharacteristic
154C2×C5×Dic3C2×D411yescharacteristic
155C4×C5×D3—22no—
156C4×C5×D3—22no—
157C4×C5×D3#4114yes—
158C2×C3×Dic5—21no—
159C2×C3×Dic5—22no—
160C3×D20—22no—
161C3×Dic10—22no—
162C3×Dic10—42no—
163#1204—44no—
164#1204—42no—
165#1202—42no—
166D3×Dic5—42no—
167D3×Dic5—44no—
168C3×C5×C8—22no—
169C5×C3⋊C8—22no—
170C2×D3×Q8—51no—
171C2×D3×Q8—101no—
172C2×D3×D4—51no—
173C3×C4⋊Q8—51no—
174C3×#124—51no—
175#947—51no—
176#944—101no—
177#936—51no—
178C2×D3×C8C2×D512yes—
179D3×C4⋊C4—52no—
180D3×C4⋊C4—101no—
181#888—52no—
182#888—101no—
183#885—101no—
184#885—101no—
185D3×C22⋊C4—101no—
186D3×C22⋊C4—101no—
187#875—51no—
188C42×D3C2×D511yescharacteristic
189#869—51no—
190C3×#103—52no—
191C3×#102—52no—
192C3×#97C2×D511yescharacteristic, complemented
193#835—52no—
194#832—52no—
195#821—52no—
196#816—52no—
197#815C2×D512yescomplemented
198#810—52no—
199#809—52no—
200#803C2×D511yescharacteristic, complemented
201C23×D5—61no—
202C22×C4×C5—31no—
203C22×C4×C5—31no—
204C22×C4×C5—31no—
205C22×Dic5—61no—
206C22×Dic5—62no—
207C2×D20—31no—
208C2×D20—64no—
209C2×D20—61no—
210C2×D20C22×D311yescharacteristic
211C2×Dic10—21no—
212C2×Dic10—31no—
213C2×Dic10—64no—
214C2×Dic10—61no—
215C2×Dic10—62no—
216C2×Dic10—61no—
217C2×Dic10—124no—
218C2×Dic10C22×D311yescharacteristic
219C2×C5×C8—32no—
220C2×C5×C8—64no—
221C2×C5×C8C22×D312yes—
222C42×C5—31no—
223C42×C5—31no—
224C42×C5—31no—
225C42×C5C22×D311yescharacteristic
226#685—21no—
227#685—21no—
228#685—61no—
229#685—61no—
230#685—61no—
231#685—61no—
232#685—61no—
233#685—61no—
234C4⋊Dic5—21no—
235C4⋊Dic5—32no—
236C4⋊Dic5—62no—
237C4⋊Dic5—62no—
238C4⋊Dic5—61no—
239C4⋊Dic5C22×D312yes—
240C2×C4⋊Q8—151no—
241C2×#124—151no—
242#489—51no—
243#489—152no—
244#489—152no—
245#489—151no—
246#489—151no—
247#489—151no—
248C2×#103—152no—
249C2×#102—152no—
250C2×#97—31no—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15—41no—
253C2×D15—41no—
254C2×D15—41no—
255C2×C5×D3#12412yes—
256C2×C5×D3AGL(1,ℤ/8)12yes—
257C2×C5×D3#13712yes—
258C2×C3×D5—41no—
259C2×C3×D5—41no—
260C2×C3×D5—41no—
261D3×D5—84no—
262C3×C4×C5—21no—
263C3×C4×C5—21no—
264C3×C4×C5C2×#4112yes—
265Dic15—41no—
266Dic15—42no—
267C3×Dic5—41no—
268C3×Dic5—42no—
269C5×Dic3—21no—
270C5×Dic3—21no—
271C5×Dic3#12412yes—
272C23×D3—101no—
273C2×C3×Q8—51no—
274C2×C3×Q8—101no—
275C2×C3×D4—51no—
276C2×#67—101no—
277D3×Q8—104no—
278D3×Q8—204no—
279D3×D4—104no—
280C2×D12—51no—
281C2×C4×D3—101no—
282C2×C4×D3—102no—
283C2×C4×D3D2011yescharacteristic
284C2×C4×D3D2011yescharacteristic
285C2×C4×D3C22×D511yescharacteristic
286C2×Dic6—51no—
287C2×Dic6—101no—
288C2×Dic6—101no—
289C2×Dic6—102no—
290C2×C3×C8C22×D512yes—
291C3×C4⋊C4—52no—
292C3×C4⋊C4—101no—
293C3×C22⋊C4—101no—
294C3×C22⋊C4—101no—
295C3×C42C22×D511yescharacteristic
296#217—101no—
297#217—101no—
298(C2×D3)⋊C4—101no—
299(C2×D3)⋊C4—101no—
300(C2×D3)⋊C4—101no—
301(C2×D3)⋊C4—101no—
302C4⋊Dic3—52no—
303C4⋊Dic3—101no—
304Dic3⋊C4—102no—
305Dic3⋊C4—102no—
306C4×Dic3D2011yescharacteristic
307C4×Dic3D2011yescharacteristic
308C4×Dic3C22×D511yescharacteristic
309C2×C3⋊C8C22×D512yes—
310D3×C8—24no—
311C23×C5—31no—
312C22×D5—21no—
313C22×D5—61no—
314C22×D5—122no—
315C22×D5—122no—
316C22×D5—122no—
317C2×C4×C5—31no—
318C2×C4×C5—34no—
319C2×C4×C5—31no—
320C2×C4×C5—31no—
321C2×C4×C5—62no—
322C2×C4×C5—62no—
323C2×C4×C5D3×D411yescharacteristic
324C2×C4×C5D3×D411yescharacteristic
325C2×C4×C5C23×D311yescharacteristic
326C2×Dic5—22no—
327C2×Dic5—21no—
328C2×Dic5—62no—
329C2×Dic5—61no—
330C2×Dic5—122no—
331C2×Dic5—124no—
332D20—22no—
333D20—62no—
334D20—122no—
335Dic10—22no—
336Dic10—42no—
337Dic10—62no—
338Dic10—122no—
339Dic10—124no—
340Dic10—122no—
341C5×C8—22no—
342C5×C8—62no—
343C22×Q8—151no—
344C22×Q8—301no—
345C22×D4—151no—
346C22×C8—32no—
347C4⋊Q8—51no—
348C4⋊Q8—152no—
349C4⋊Q8—151no—
350C4⋊Q8—301no—
351C4⋊Q8—301no—
352#124—51no—
353#124—151no—
354#124—151no—
355#124—151no—
356#124—301no—
357#124—301no—
358C2×C4⋊C4—152no—
359C2×C4⋊C4—301no—
360C2×C22⋊C4—301no—
361C2×C22⋊C4—301no—
362C2×C42—31no—
363#103—52no—
364#103—152no—
365#103—152no—
366#103—152no—
367#102—52no—
368#102—152no—
369#102—152no—
370#102—152no—
371#97—32no—
372#97—31no—
373#97D3×D511yescharacteristic, complemented
374C2×C3×C5C2×#12411yescharacteristic
375C2×C3×C5C2×AGL(1,ℤ/8)11yescharacteristic
376C2×C3×C5C2×#13711yescharacteristic
377D15—81no—
378C3×D5—81no—
379C5×D3#48914yescomplemented
380C23×C3—101no—
381C22×D3—101no—
382C22×D3—202no—
383C22×D3—202no—
384C22×D3—202no—
385C22×D3C2×D2011yescharacteristic
386C3×Q8—102no—
387C3×Q8—202no—
388C3×D4—102no—
389C2×C3×C4—102no—
390C2×C3×C4—101no—
391C2×C3×C4C2×D2011yescharacteristic
392C2×C3×C4C2×D2011yescharacteristic
393C2×C3×C4C23×D511yescharacteristic
394#67—202no—
395C2×Dic3—102no—
396C2×Dic3—101no—
397C2×Dic3C2×D2011yescharacteristic
398C2×Dic3C2×D2011yescharacteristic
399C2×Dic3C2×D2011yescharacteristic
400D12—102no—
401C4×D3—22no—
402C4×D3—22no—
403C4×D3—202no—
404C4×D3—204no—
405C4×D3#70914yes—
406Dic6—102no—
407Dic6—204no—
408Dic6—202no—
409Dic6—202no—
410C3×C8—22no—
411C3⋊C8—22no—
412C22×C5—32no—
413C22×C5—32no—
414C22×C5—32no—
415C22×C5C2×D3×D411yescharacteristic
416C2×D5—41no—
417C2×D5—41no—
418C2×D5—41no—
419C2×D5—121no—
420C2×D5—121no—
421C2×D5—121no—
422C2×D5—244no—
423C4×C5—21no—
424C4×C5—21no—
425C4×C5—32no—
426C4×C5—61no—
427C4×C5—61no—
428C4×C5D3×#4112yes—
429Dic5—41no—
430Dic5—42no—
431Dic5—121no—
432Dic5—122no—
433C24—301no—
434C2×Q8—51no—
435C2×Q8—101no—
436C2×Q8—151no—
437C2×Q8—301no—
438C2×Q8—302no—
439C2×Q8—304no—
440C2×Q8—301no—
441C2×Q8—604no—
442C2×D4—51no—
443C2×D4—151no—
444C2×D4—304no—
445C2×D4—301no—
446C22×C4—31no—
447C22×C4—31no—
448C22×C4—31no—
449C22×C4—301no—
450C22×C4—302no—
451C2×C8—32no—
452C2×C8—64no—
453C2×C8C2×D3×D512yes—
454C4⋊C4—52no—
455C4⋊C4—101no—
456C4⋊C4—152no—
457C4⋊C4—302no—
458C4⋊C4—302no—
459C4⋊C4—301no—
460C22⋊C4—101no—
461C22⋊C4—101no—
462C22⋊C4—301no—
463C22⋊C4—301no—
464C22⋊C4—301no—
465C22⋊C4—301no—
466C22⋊C4—301no—
467C22⋊C4—301no—
468C42—31no—
469C42—31no—
470C42—31no—
471C42C2×D3×D511yescharacteristic
472C3×C5C2×#48911yescharacteristic, complemented, Hall
473C22×C3—201no—
474C22×C3—201no—
475C22×C3—201no—
476C22×C3C22×D2011yescharacteristic
477C2×D3—201no—
478C2×D3—201no—
479C2×D3—201no—
480C2×D3—404no—
481C2×D3#402112yes—
482C2×D3#405412yes—
483C2×D3#405512yes—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—201no—
487C3×C4—202no—
488C3×C4C2×#70912yes—
489Dic3—21no—
490Dic3—21no—
491Dic3—201no—
492Dic3—202no—
493Dic3#402112yes—
494C2×C5—34no—
495C2×C5D3×#12411yescharacteristic
496C2×C5D3×AGL(1,ℤ/8)11yescharacteristic
497C2×C5D3×#13711yescharacteristic
498D5—81no—
499D5—241no—
500C23—31no—
501C23—101no—
502C23—301no—
503C23—602no—
504C23—602no—
505C23—602no—
506Q8—102no—
507Q8—202no—
508Q8—302no—
509Q8—602no—
510Q8—602no—
511Q8—604no—
512D4—102no—
513D4—302no—
514D4—602no—
515C2×C4—31no—
516C2×C4—34no—
517C2×C4—31no—
518C2×C4—31no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—101no—
522C2×C4—102no—
523C2×C4—301no—
524C2×C4—302no—
525C2×C4—602no—
526C2×C4—604no—
527C2×C4D3×D2011yescharacteristic
528C2×C4D3×D2011yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—22no—
531C8—62no—
532C2×C3—401no—
533C2×C3C2×#402111yescharacteristic
534C2×C3C2×#405411yescharacteristic
535C2×C3C2×#405511yescharacteristic
536D3—401no—
537D3#6500314yesdirect product factor
538C5D3×#48911yescharacteristic, complemented, Sylow
539C22—32no—
540C22—32no—
541C22—32no—
542C22—201no—
543C22—201no—
544C22—201no—
545C22—601no—
546C22—601no—
547C22—601no—
548C22—1204no—
549C22C2×D3×D2011yescharacteristic
550C4—21no—
551C4—21no—
552C4—32no—
553C4—61no—
554C4—61no—
555C4—201no—
556C4—202no—
557C4—601no—
558C4—602no—
559C4D3×#70912yes—
560C3C2×#6500311yescharacteristic, complemented, Sylow
561C2—34no—
562C2—401no—
563C2—1201no—
564C2D3×#402111yescharacteristic
565C2D3×#405411yescharacteristic
566C2D3×#405511yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#97C22
socleC22×C3×C5C22×D4
prime radicalC2×D3×D20C22
hypercenter#97D3×D5
hypocenterC3×C5C2×#489
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
2. D3×#4015C2semidirect
3. #11750815C2semidirect
4. C5×D3×#97C2semidirect
5. C3×#65003C2semidirect
7. #11748031C2semidirect
8. #11747968C2semidirect
9. D3×#3948C2semidirect
10. #11746935C2semidirect
11. #11746893C2semidirect
17. #91758C22semidirect
21. C3×#4015C22semidirect
25. #91469C22semidirect
33. C3×C5×#97C22semidirect
35. #91100C22semidirect
36. C5×#815C22semidirect
37. C5×#803C22semidirect
39. C3×#3948C22semidirect
40. #90974C22semidirect
41. #90971C22semidirect
55. #65003D3direct (N × H)
105. D3×#97D5semidirect
125. #4015C2×D3semidirect
128. C5×#97C2×D3semidirect
136. #3948C2×D3semidirect
192. C3×#97C2×D5semidirect
197. #815C2×D5semidirect
200. #803C2×D5semidirect
373. #97D3×D5semidirect
379. C5×D3#489semidirect
472. C3×C5C2×#489semidirect
537. D3#65003direct (N × H)
538. C5D3×#489semidirect
560. C3C2×#65003semidirect

Maximal subgroups

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

subgroupindex
D3×#40212
D3×#40152
#117508152
C5×D3×#972
C3×#650032
D3×#39532
#117480312
#117479682
D3×#39482
#117469352
#117468932
C2×#650033
D3×#4895