Finite Group Databasebeta

← #14429244

Subgroups — #14429244

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4047C211yesmaximal, characteristic, complemented
2#11754605C211yesmaximal, characteristic
3#11754251C211yesmaximal, characteristic, complemented
4C2×#91321C211yesmaximal, characteristic, complemented
5#11751214C211yesmaximal, characteristic, complemented
6C2×C5×#816C211yesmaximal, characteristic, complemented
7#11748459C211yesmaximal, characteristic, complemented
8#11747941C212yesmaximal, complemented
9#11747940C212yesmaximal, complemented
10#11747939C212yesmaximal, complemented
11#11747938C212yesmaximal, complemented
12#10610531—31nomaximal, Hall
13C2×#6817C2211yescharacteristic
14C22×C5×Dic6C2211yescharacteristic
15C2×C3×#709C2211yescharacteristic
16C22×C3×C5×C8C2211yescharacteristic
17#91815C2211yescharacteristic
18C2×C5×C4⋊Dic3C2211yescharacteristic
19C2×C3×#681C2211yescharacteristic
20C3×#4047—24no—
21C2×C3×#676C2212yes—
22C2×C3×C8×D5C2212yes—
23#91569—22no—
24#91536—22no—
25#91465—21no—
26#91450C2212yes—
27#91390—21no—
28#91385—21no—
29#91368—21no—
30#91360C2212yes—
31#91359C2212yes—
32#91359C2212yes—
33#91321—24no—
34C2×#6663C2212yes—
35C2×#6660C2212yes—
36#91105C2211yescharacteristic
37#91105C2211yescharacteristic
38#91100C2211yescharacteristic
39#91100C2211yescharacteristic
40C5×#816C2212yes—
41C5×#816C2212yes—
42#90988C2212yes—
43#90985C2212yes—
44#83808—51nomaximal, Hall
45#66150—31no—
46C2×#4088—31no—
47C2×#4047D311yescharacteristic, complemented
48#65844—31no—
49C2×C5×#103—31no—
50#65402—31no—
51#65253—31no—
52#65105—32no—
53#65102—32no—
54#65101—32no—
55#65096—32no—
56C22×C3×C4×C5C2311yescharacteristic
57C2×#1220—21no—
58#6817—22no—
59#6817—22no—
60C2×D60C2311yescharacteristic
61C2×C4×D15—21no—
62C2×Dic30C2311yescharacteristic
63C22×C5×Dic3—21no—
64C22×C5×Dic3—21no—
65C2×C5×Dic6—22no—
66C2×C5×Dic6—22no—
67C2×C5×Dic6—21no—
68C2×C5×Dic6C2312yes—
69C2×C3×C22⋊D5D412yes—
70C3×#709—22no—
71C3×#709—22no—
72C2×C3×D20D411yescharacteristic
73C2×C3×C4×D5C2312yes—
74C2×C3×Dic10D411yescharacteristic
75C2×#1202—22no—
76C2×C3×C5×C8—22no—
77C2×C3×C5×C8C2311yescharacteristic
78C2×C3×C5×C8C2311yescharacteristic
79#6719—21no—
80C4⋊Dic15C2311yescharacteristic
81C4⋊Dic15C2311yescharacteristic
82C4×Dic15—21no—
83C5×C4⋊Dic3—21no—
84C5×C4⋊Dic3C2312yes—
85C3×#681D414yescomplemented
86C2×C3×#168C2312yes—
87C3×#676—24no—
88C3×C8×D5—24no—
89Dic3⋊Dic5—22no—
90#6669—22no—
91#6669—22no—
92#6667—22no—
93#6665—22no—
94#6665—22no—
95#6665—22no—
96#6663—24no—
97#6660—24no—
98C2×C3×#131—51no—
99#5833—51no—
100#5825—51no—
101C2×#909—51no—
102#5137—52no—
103#5134—52no—
104#5121—51no—
105#5116—52no—
106#5114—52no—
107#5113—51no—
108C2×#816D511yescharacteristic, complemented
109C22×C5×Q8—31no—
110C2×#709—31no—
111C2×#709C2×D311yescharacteristic
112C22×C5×C8C2×D311yescharacteristic
113C2×C5×C4⋊C4—31no—
114#4093—61no—
115#4092—32no—
116#4092—32no—
117#4090—61no—
118C2×#689—32no—
119#4088—64no—
120C2×#688—32no—
121#4076—62no—
122#4075—62no—
123#4072—31no—
124C2×#681C2×D311yescharacteristic
125#4047—24no—
126C2×#676C2×D312yes—
127C2×C8×D5C2×D312yes—
128#4043—32no—
129#4043—61no—
130#4041—32no—
131#4041—61no—
132C5×#103—32no—
133C5×#103—32no—
134#3953—31no—
135#3953—31no—
136#3948—31no—
137#3948—31no—
138#3940—32no—
139#3939—32no—
140#3063—151noSylow
141C23×C3×C5C2×D411yescharacteristic
142C22×D15—21no—
143C22×C3×D5C2×D412yes—
144C2×C3×C4×C5C2×D411yescharacteristic
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5#4112yes—
147C2×C3×C4×C5C2411yescharacteristic
148#1220—42no—
149C2×Dic15—21no—
150C2×Dic15—21no—
151C2×Dic15—21no—
152D60—21no—
153D60—21no—
154C4×D15—42no—
155Dic30—21no—
156Dic30—21no—
157C2×C5×Dic3—22no—
158C2×C5×Dic3—22no—
159C2×C5×Dic3—42no—
160C2×C5×Dic3—81no—
161C5×Dic6—22no—
162C5×Dic6—22no—
163C5×Dic6—42no—
164C3×C22⋊D5—24no—
165C2×C3×Dic5C2×D412yes—
166C3×D20—22no—
167C3×C4×D5—22no—
168C3×C4×D5—22no—
169C3×Dic10—22no—
170#1202—82no—
171C3×C5×C8—21no—
172C3×C5×C8—21no—
173C3×#168C2×D414yes—
174C2×C3×#41—51no—
175C2×#235—51no—
176C22×Dic6C2×D511yescharacteristic
177C3×#131—104no—
178C2×C3×M16—51no—
179C2×C3×M16—52no—
180C22×C3×C8—52no—
181C22×C3×C8C2×D511yescharacteristic
182#946—101no—
183#944—101no—
184#939—102no—
185#938—101no—
186#936—101no—
187#935—102no—
188#930—52no—
189#926—51no—
190C2×C4⋊Dic3C2×D511yescharacteristic
191#924—52no—
192#924—52no—
193#924—52no—
194#909—104no—
195C2×Dic12—52no—
196C2×#204—52no—
197#821—51no—
198#821—51no—
199#818—52no—
200#817—52no—
201#816—51no—
202#816—51no—
203#816C2×D512yes—
204#816C2×D512yes—
205C2×C5×Q8—32no—
206C2×C5×Q8—61no—
207C2×C5×Q8—62no—
208C2×C5×Q8—62no—
209C22×C4×C5—61no—
210C22×C4×C5—61no—
211C22×C4×C5C22×D311yescharacteristic
212C2×C22⋊D5—61no—
213C2×C22⋊D5D1212yes—
214#709—22no—
215#709—22no—
216#709—62no—
217#709—62no—
218C2×D20—31no—
219C2×D20—62no—
220C2×D20D1211yescharacteristic
221C2×C4×D5—61no—
222C2×C4×D5C22×D312yes—
223C2×Dic10—31no—
224C2×Dic10D1211yescharacteristic
225C2×C5×C8—22no—
226C2×C5×C8C22×D311yescharacteristic
227C2×C5×C8C22×D311yescharacteristic
228C5×C4⋊C4—32no—
229C5×C4⋊C4—61no—
230C22⋊Dic5—61no—
231#689—64no—
232#688—64no—
233#685—62no—
234#685—62no—
235#685—62no—
236#685—62no—
237C4⋊Dic5—31no—
238C4⋊Dic5—31no—
239C4⋊Dic5—62no—
240#683—62no—
241#683—62no—
242C4×Dic5—61no—
243#681#6714yescomplemented
244C2×#168C22×D312yes—
245#676—24no—
246C8×D5—24no—
247C2×#137—151no—
248C2×#131—51no—
249#537—151no—
250#536—151no—
251#470—152no—
252#468—152no—
253#467—152no—
254#465—152no—
255#428—151no—
256#416—151no—
257C2×#103—31no—
258C22×C3×C5—21no—
259C22×C3×C5—21no—
260C22×C3×C5#12112yes—
261C22×C3×C5C22×D411yescharacteristic
262C2×D15—41no—
263C2×D15—41no—
264C2×D15—41no—
265C2×C3×D5—22no—
266C2×C3×D5—22no—
267C2×C3×D5—22no—
268C3×C4×C5#12112yes—
269C3×C4×C5C22×D411yescharacteristic
270C3×C4×C5C2×#4111yescharacteristic
271Dic15—41no—
272Dic15—41no—
273Dic15—41no—
274C3×Dic5—22no—
275C5×Dic3—42no—
276C5×Dic3—42no—
277C3×#41—102no—
278C3×#41—102no—
279C2×C3×Q8—51no—
280C2×C3×D4—52no—
281C2×C3×D4—51no—
282C22×C3×C4—52no—
283C22×C3×C4C22×D511yescharacteristic
284C2×#67—102no—
285C2×#67—101no—
286C22×Dic3—21no—
287C22×Dic3—21no—
288#235—102no—
289#235—102no—
290C2×D12—51no—
291C2×C4×D3—101no—
292C2×Dic6—22no—
293C2×Dic6—22no—
294C2×Dic6—21no—
295C2×Dic6—51no—
296C2×Dic6C22×D512yes—
297C3×M16—54no—
298C3×M16—104no—
299C2×C3×C8—22no—
300C2×C3×C8—52no—
301C2×C3×C8—104no—
302C2×C3×C8C22×D511yescharacteristic
303C2×C3×C8C22×D511yescharacteristic
304#217—102no—
305#217—102no—
306#217—102no—
307#217—101no—
308(C2×D3)⋊C4—102no—
309C4⋊Dic3—21no—
310C4⋊Dic3—51no—
311C4⋊Dic3—51no—
312C4⋊Dic3C22×D512yes—
313Dic3⋊C4—102no—
314Dic3⋊C4—102no—
315Dic3⋊C4—102no—
316C4×Dic3—101no—
317Dic12—104no—
318#204—104no—
319C23×C5C2×D1211yescharacteristic
320C22×D5—61no—
321C22×D5C2×D1212yes—
322C5×Q8—62no—
323C5×Q8—62no—
324C5×Q8—122no—
325C2×C4×C5—62no—
326C2×C4×C5—62no—
327C2×C4×C5—122no—
328C2×C4×C5—241no—
329C2×C4×C5C2×D1211yescharacteristic
330C2×C4×C5#23512yes—
331C2×C4×C5C2×#6712yes—
332C2×C4×C5C23×D311yescharacteristic
333C22⋊D5—24no—
334C22⋊D5—122no—
335C2×Dic5—61no—
336C2×Dic5—61no—
337C2×Dic5—61no—
338C2×Dic5C2×D1212yes—
339D20—22no—
340D20—61no—
341D20—61no—
342D20—242no—
343C4×D5—22no—
344C4×D5—22no—
345C4×D5—122no—
346Dic10—22no—
347Dic10—61no—
348Dic10—61no—
349C5×C8—21no—
350C5×C8—21no—
351#168C2×#6714yes—
352C2×#41—51no—
353C2×#41—151no—
354C22×Q8—31no—
355#137—304no—
356C2×Q16—152no—
357C2×SD16—152no—
358#131—104no—
359C2×M16—51no—
360C2×M16—52no—
361C22×C8—52no—
362C22×C8D3×D511yescharacteristic
363C4⋊Q8—301no—
364#124—301no—
365#123—302no—
366C22⋊Q8—152no—
367C22⋊Q8—152no—
368C22⋊Q8—152no—
369C22⋊Q8—301no—
370#121—152no—
371#121—301no—
372#121—302no—
373#117—151no—
374C2×C4⋊C4—31no—
375#107—152no—
376#106—152no—
377#103—32no—
378#103—32no—
379#103—151no—
380#103—151no—
381#102—151no—
382#102—151no—
383C2×C3×C5—22no—
384C2×C3×C5C2×#12111yescharacteristic
385C2×C3×C5#57711yescharacteristic
386C2×C3×C5#57811yescharacteristic
387D15—81no—
388C3×D5—42no—
389C23×C3—52no—
390C23×C3D4×D511yescharacteristic
391C22×D3—101no—
392C3×Q8—102no—
393C3×D4—104no—
394C3×D4—102no—
395C2×C3×C4—52no—
396C2×C3×C4—102no—
397C2×C3×C4—102no—
398C2×C3×C4#70912yes—
399C2×C3×C4D4×D511yescharacteristic
400C2×C3×C4D4×D512yes—
401C2×C3×C4C23×D511yescharacteristic
402#67—202no—
403#67—402no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—42no—
407C2×Dic3—81no—
408C2×Dic3—101no—
409C2×Dic3—101no—
410C2×Dic3—101no—
411D12—101no—
412D12—101no—
413C4×D3—202no—
414Dic6—22no—
415Dic6—22no—
416Dic6—42no—
417Dic6—101no—
418Dic6—101no—
419C3×C8—21no—
420C3×C8—21no—
421C3×C8—54no—
422C22×C5—21no—
423C22×C5—21no—
424C22×C5#93012yes—
425C22×C5C22×D1211yescharacteristic
426C2×D5—22no—
427C2×D5—22no—
428C2×D5—22no—
429C2×D5—121no—
430C2×D5—121no—
431C2×D5—121no—
432C4×C5—122no—
433C4×C5—122no—
434C4×C5#93012yes—
435C4×C5C2×#23511yescharacteristic
436C4×C5C22×#6711yescharacteristic
437Dic5—22no—
438Dic5—121no—
439Dic5—121no—
440Dic5—121no—
441#41—102no—
442#41—102no—
443#41—302no—
444#41—302no—
445C2×Q8—32no—
446C2×Q8—51no—
447C2×Q8—61no—
448C2×Q8—62no—
449C2×Q8—62no—
450C2×Q8—151no—
451C2×D4—52no—
452C2×D4—51no—
453C2×D4—151no—
454C2×D4—302no—
455C2×D4—301no—
456C22×C4—52no—
457C22×C4—61no—
458C22×C4—61no—
459C22×C4—301no—
460C22×C4C2×D3×D511yescharacteristic
461Q16—304no—
462SD16—304no—
463M16—54no—
464M16—104no—
465C2×C8—22no—
466C2×C8—52no—
467C2×C8—104no—
468C2×C8C2×D3×D511yescharacteristic
469C2×C8C2×D3×D511yescharacteristic
470C4⋊C4—32no—
471C4⋊C4—61no—
472C4⋊C4—151no—
473C4⋊C4—151no—
474C4⋊C4—302no—
475C4⋊C4—302no—
476C4⋊C4—302no—
477C22⋊C4—302no—
478C22⋊C4—302no—
479C22⋊C4—302no—
480C22⋊C4—302no—
481C22⋊C4—301no—
482C42—301no—
483C3×C5#306311yescharacteristic, complemented, Hall
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—102no—
487C22×C3—102no—
488C22×C3—102no—
489C22×C3#403012yes—
490C22×C3C2×D4×D511yescharacteristic
491C2×D3—201no—
492C2×D3—201no—
493C2×D3—201no—
494C3×C4—102no—
495C3×C4#403012yes—
496C3×C4C2×#70911yescharacteristic
497C3×C4C2×D4×D511yescharacteristic
498Dic3—42no—
499Dic3—42no—
500Dic3—201no—
501Dic3—201no—
502Dic3—201no—
503C2×C5—22no—
504C2×C5#575111yescharacteristic
505C2×C5#575311yescharacteristic
506C2×C5C2×#93011yescharacteristic
507D5—42no—
508D5—241no—
509C23—52no—
510C23—301no—
511C23D5×D1211yescharacteristic
512Q8—62no—
513Q8—62no—
514Q8—102no—
515Q8—122no—
516Q8—301no—
517Q8—301no—
518D4—104no—
519D4—102no—
520D4—301no—
521D4—301no—
522D4—602no—
523D4—1202no—
524C2×C4—52no—
525C2×C4—62no—
526C2×C4—62no—
527C2×C4—102no—
528C2×C4—102no—
529C2×C4—122no—
530C2×C4—241no—
531C2×C4—301no—
532C2×C4—301no—
533C2×C4—301no—
534C2×C4—602no—
535C2×C4#677112yes—
536C2×C4D5×D1211yescharacteristic
537C2×C4D5×#6712yes—
538C2×C4C22×D3×D511yescharacteristic
539C8—21no—
540C8—21no—
541C8—54no—
542C2×C3—22no—
543C2×C3—202no—
544C2×C3C2×#403011yescharacteristic
545C2×C3#6609611yescharacteristic
546C2×C3#6610011yescharacteristic
547D3—401no—
548C5#8380811yescharacteristic, complemented, Sylow
549C22—21no—
550C22—21no—
551C22—102no—
552C22—102no—
553C22—102no—
554C22—601no—
555C22—601no—
556C22—601no—
557C22#9144812yes—
558C22C2×D5×D1211yescharacteristic
559C4—102no—
560C4—122no—
561C4—122no—
562C4—601no—
563C4—601no—
564C4—601no—
565C4#9144812yes—
566C4C2×#677111yescharacteristic
567C4C2×D5×#6711yescharacteristic
568C3#1061053111yescharacteristic, complemented, Sylow
569C2—22no—
570C2—202no—
571C2—1201no—
572C2#1175396011yescharacteristic
573C2#1175398711yescharacteristic
574C2C2×#9144811yescharacteristic
subgroupG/H
centerC22C2×D5×D12
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC22×C3×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11754605C2
hypercenterC22×C8D3×D5
hypocenterC3×C5#3063
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#4047C2semidirect
3. #11754251C2semidirect
4. C2×#91321C2semidirect
5. #11751214C2semidirect
6. C2×C5×#816C2semidirect
7. #11748459C2semidirect
8. #11747941C2semidirect
9. #11747940C2semidirect
10. #11747939C2semidirect
11. #11747938C2semidirect
47. C2×#4047D3semidirect
85. C3×#681D4semidirect
108. C2×#816D5semidirect
243. #681#67semidirect
483. C3×C5#3063semidirect
548. C5#83808semidirect
568. C3#10610531semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40472
#117546052
#117542512
C2×#913212
#117512142
C2×C5×#8162
#117484592
#117479412
#117479402
#117479392
#117479382
#106105313
#838085