Finite Group Databasebeta

← #14439195

Subgroups — #14439195

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#66002C211yesmaximal, characteristic, complemented
2C2×#91502C212yesmaximal, complemented
3C2×#91478C212yesmaximal, complemented
4D5×#874C211yesmaximal, characteristic, complemented
5#11751159C211yesmaximal, characteristic, complemented
6C5×#5058C211yesmaximal, characteristic, complemented
7#11749339C212yesmaximal, complemented
8#11749093C212yesmaximal, complemented
9#11747042C211yesmaximal, characteristic, complemented
10#11747036C211yesmaximal, characteristic, complemented
11#11747003C211yesmaximal, characteristic, complemented
12#10613576—31nomaximal, Hall
13C2×C3×#713C2211yescharacteristic
14C2×C3×#711C2211yescharacteristic
15C2×D5×D12—22no—
16C2×D5×D12C2212yes—
17C3×C5×#124C2211yescharacteristic, complemented
18C2×#6717C2212yescomplemented
19C2×#6715C2212yescomplemented
20#91763C2211yescharacteristic
21C2×C5×#215C2212yescomplemented
22C2×C5×#213C2212yescomplemented
23C5×#874C2211yescharacteristic
24C3×#4090C2211yescharacteristic, complemented
25C3×#4086C2211yescharacteristic, complemented
26C3×#4030—22no—
27C3×#4027—22no—
28C3×#4021C2211yescharacteristic, complemented
29C3×C42×D5C2211yescharacteristic
30#91502—28no—
31#91478—28no—
32#91451—22no—
33#91451C2212yes—
34C2×#6658C2212yescomplemented
35C2×#6656C2212yescomplemented
36C2×#6653C2212yescomplemented
37C2×#6652C2212yescomplemented
38C2×#6649C2212yes—
39#91087C2211yescharacteristic, complemented
40C5×#803C2211yescharacteristic, complemented
41Dic5×C3⋊C8C2212yescomplemented
42#83287—51nomaximal, Hall
43C2×#4060—32no—
44C2×#4057—32no—
45D5×#127—31no—
46#66002D311yescharacteristic, complemented
47C5×#496—31no—
48#65464—32no—
49#65440—32no—
50#65363—31no—
51#65347—31no—
52#65001—31no—
53#64996—31no—
54C22×D3×D5—22no—
55C2×C3×C5×Q8C2311yescharacteristic
56C2×C3×C5×D4C2311yescharacteristic
57C2×D60—22no—
58C2×D60C2312yes—
59C2×C5×D12—22no—
60C2×C5×D12C2312yes—
61C2×C3×C22⋊D5—21no—
62C2×C3×C22⋊D5—22no—
63C22×C3×Dic5—21no—
64C3×#713—24no—
65C3×#711—24no—
66C2×C3×D20—21no—
67C2×C3×D20C2311yescharacteristic
68C2×C3×C4×D5—21no—
69C2×C3×C4×D5D412yes—
70C2×C3×C4×D5C2311yescharacteristic
71C2×C3×Dic10C2311yescharacteristic
72C2×#1203—22no—
73C2×#1203—24no—
74D5×D12—24no—
75D5×D12—24no—
76D5×D12—48no—
77C3×C5×C22⋊C4—22no—
78C3×C42×C5C2311yescharacteristic
79#6717—24no—
80#6715—24no—
81C2×C3⋊#168C2312yes—
82C5×#215—24no—
83C5×#213—24no—
84C2×C5×C3⋊C8C2312yes—
85C3×#685—22no—
86C3×#683—22no—
87C3×C4×Dic5D412yes—
88C3×C4×Dic5C2311yescharacteristic
89#6658—24no—
90#6656—24no—
91#6653—24no—
92#6652—24no—
93#6649D418yescomplemented
94C3×#532—51no—
95C2×#949—52no—
96C2×#949—52no—
97C2×#874—51no—
98#5085—52no—
99#5073—52no—
100#5058—51no—
101#5058—51no—
102#5058—51no—
103#5058D511yescharacteristic, complemented
104C4×#208—51no—
105C2×#713C2×D311yescharacteristic
106C2×#711C2×D311yescharacteristic
107C2×D4×D5—32no—
108C2×D4×D5—62no—
109C2×C5×SD16—32no—
110C2×C5×D8—32no—
111C5×#127—31no—
112C5×#124C2×D311yescharacteristic, complemented
113#4090C2×D311yescharacteristic, complemented
114C2×#688—32no—
115#4086—32no—
116#4086—62no—
117#4086C2×D311yescharacteristic, complemented
118C2×#687—32no—
119C2×#686—32no—
120C2×#686—32no—
121#4060—68no—
122#4057—68no—
123C2×D40—32no—
124C2×#677—32no—
125C2×#676—32no—
126#4030—22no—
127#4027—22no—
128#4021C2×D311yescharacteristic, complemented
129#4020—31no—
130C42×D5C2×D311yescharacteristic
131C5×#97—31no—
132C8×Dic5—32no—
133#3935—31no—
134#3151—151noSylow
135C23×C3×C5—21no—
136C22×D15—22no—
137C22×C5×D3—22no—
138C22×C3×D5—21no—
139C22×C3×D5C2×D411yescharacteristic
140C2×D3×D5—48no—
141C2×D3×D5—44no—
142C3×C5×Q8—22no—
143C3×C5×D4—22no—
144C2×C3×C4×C5—21no—
145C2×C3×C4×C5C2×D412yes—
146C2×C3×C4×C5C2411yescharacteristic
147D60—22no—
148D60—22no—
149D60—44no—
150C5×D12—22no—
151C5×D12—22no—
152C5×D12—44no—
153C3×C22⋊D5—42no—
154C3×C22⋊D5—44no—
155C2×C3×Dic5—21no—
156C2×C3×Dic5—42no—
157C2×C3×Dic5C2×D411yescharacteristic
158C2×C3×Dic5C2×D412yes—
159C3×D20—22no—
160C3×D20—42no—
161C3×C4×D5—24no—
162C3×C4×D5—42no—
163C3×C4×D5C2×D414yes—
164C3×Dic10—22no—
165#1203—44no—
166#1203—48no—
167C3⋊#168C2×D414yescomplemented
168C5×C3⋊C8C2×D414yescomplemented
169C2×C3×#41—51no—
170C2×C3×#41—51no—
171C22×D12—52no—
172C22×D12—102no—
173C3×C4⋊Q8—51no—
174C3×#127—51no—
175C3×#124—51no—
176C3×#124C2×D511yescharacteristic, complemented
177C3×#121—102no—
178C3×C4×D4—102no—
179C2×C3×C42—51no—
180#949—108no—
181#949—108no—
182C2×#215—52no—
183C2×#215—52no—
184C2×#215—52no—
185C2×#215C2×D512yescomplemented
186C2×#213—52no—
187C2×#213—52no—
188C2×#213—52no—
189C2×#213C2×D512yescomplemented
190C2×#208—52no—
191#874—52no—
192#874—51no—
193#874—102no—
194#874C2×D511yescharacteristic
195#803—51no—
196#803C2×D511yescharacteristic, complemented
197C4×C3⋊C8—52no—
198C23×D5—62no—
199C2×C5×Q8C22×D311yescharacteristic
200C2×C5×D4—32no—
201C2×C5×D4—62no—
202C2×C5×D4C22×D311yescharacteristic
203C2×C22⋊D5—21no—
204C2×C22⋊D5—22no—
205C2×C22⋊D5—62no—
206C2×C22⋊D5—64no—
207C22×Dic5—21no—
208#713—24no—
209#711—24no—
210D4×D5—64no—
211D4×D5—64no—
212D4×D5—128no—
213C2×D20—21no—
214C2×D20—32no—
215C2×D20—62no—
216C2×D20C22×D311yescharacteristic
217C2×C4×D5—21no—
218C2×C4×D5#6712yes—
219C2×C4×D5C22×D311yescharacteristic
220C2×Dic10C22×D311yescharacteristic
221C5×SD16—64no—
222C5×D8—64no—
223C2×C5×C8—32no—
224C5×C22⋊C4—22no—
225C42×C5C22×D311yescharacteristic
226#688—64no—
227#687—64no—
228#686—64no—
229#686—64no—
230#685—22no—
231#683—22no—
232C4×Dic5#6712yes—
233C4×Dic5C22×D311yescharacteristic
234C2×#168—32no—
235D40—64no—
236#677—64no—
237#676—38no—
238C2×AGL(1,ℤ/8)—152no—
239C2×AGL(1,ℤ/8)—152no—
240#532—51no—
241C2×#127—151no—
242#496—31no—
243#496—151no—
244#496—151no—
245#496—151no—
246#493—152no—
247#492—152no—
248C4×M16—151no—
249C22×C3×C5—41no—
250C22×C3×C5—42no—
251C22×C3×C5C22×D411yescharacteristic
252C2×D15—42no—
253C2×D15—44no—
254C2×C5×D3—42no—
255C2×C5×D3—44no—
256C2×C3×D5—22no—
257C2×C3×D5—41no—
258C2×C3×D5—42no—
259C2×C3×D5#12712yes—
260D3×D5—88no—
261C3×C4×C5—22no—
262C3×C4×C5—41no—
263C3×C4×C5C22×D412yes—
264C3×Dic5—41no—
265C3×Dic5#12712yes—
266C3×Dic5AGL(1,ℤ/8)14yescomplemented
267C23×D3—102no—
268C3×#41—104no—
269C3×#41—104no—
270C2×C3×Q8—51no—
271C2×C3×Q8C22×D511yescharacteristic
272C2×C3×D4—51no—
273C2×C3×D4—101no—
274C2×C3×D4—102no—
275C2×C3×D4—101no—
276C2×C3×D4C22×D511yescharacteristic
277C22×C3×C4—51no—
278C22×C3×C4—52no—
279C22×C3×C4—101no—
280C22×C3×C4—101no—
281C2×D12—22no—
282C2×D12—52no—
283C2×D12—104no—
284C2×D12—104no—
285C2×D12—104no—
286C2×D12—102no—
287C2×D12—102no—
288C2×D12—208no—
289C2×D12C22×D512yes—
290C3×C4⋊C4—102no—
291C3×C22⋊C4—22no—
292C3×C22⋊C4—102no—
293C3×C42—52no—
294C3×C42—51no—
295C3×C42C22×D511yescharacteristic
296#215—24no—
297#215—104no—
298#215—104no—
299#215—104no—
300#213—24no—
301#213—104no—
302#213—104no—
303#213—104no—
304#208—58no—
305C2×C3⋊C8—52no—
306C2×C3⋊C8C22×D512yes—
307C23×C5—21no—
308C23×C5—62no—
309C22×D5—21no—
310C22×D5—62no—
311C22×D5—128no—
312C22×D5—124no—
313C22×D5C2×#6711yescharacteristic
314C5×Q8—22no—
315C5×D4—22no—
316C5×D4—62no—
317C5×D4—62no—
318C5×D4—124no—
319C2×C4×C5—21no—
320C2×C4×C5C2×#6712yes—
321C2×C4×C5C23×D311yescharacteristic
322C22⋊D5—42no—
323C22⋊D5—44no—
324C22⋊D5—124no—
325C22⋊D5—128no—
326C2×Dic5—21no—
327C2×Dic5—42no—
328C2×Dic5C2×#6711yescharacteristic
329C2×Dic5C2×#6712yes—
330D20—22no—
331D20—42no—
332D20—62no—
333D20—62no—
334D20—124no—
335C4×D5—24no—
336C4×D5—42no—
337C4×D5D3×D414yes—
338Dic10—22no—
339C5×C8—34no—
340#168—34no—
341C2×#41—51no—
342C2×#41—51no—
343C22×D4—152no—
344C22×D4—302no—
345AGL(1,ℤ/8)—308no—
346AGL(1,ℤ/8)—308no—
347C2×SD16—32no—
348C2×SD16—152no—
349C2×SD16—152no—
350C2×SD16—152no—
351C2×D8—32no—
352C2×D8—152no—
353C2×D8—152no—
354C2×D8—152no—
355C2×M16—152no—
356C4⋊Q8—51no—
357#127—31no—
358#127—51no—
359#127—152no—
360#127—151no—
361#127—302no—
362#124—51no—
363#124D3×D511yescharacteristic, complemented
364#121—102no—
365C4×D4—102no—
366C2×C42—51no—
367#97—31no—
368#97—151no—
369C4×C8—152no—
370C2×C3×C5—81no—
371C2×C3×C5C2×#12711yescharacteristic
372C2×C3×C5C2×AGL(1,ℤ/8)12yes—
373D15—82no—
374C3×D5—22no—
375C3×D5—81no—
376C5×D3—82no—
377C23×C3—21no—
378C23×C3—51no—
379C23×C3—101no—
380C22×D3—22no—
381C22×D3—102no—
382C22×D3—204no—
383C22×D3—208no—
384C3×Q8—22no—
385C3×Q8—102no—
386C3×D4—22no—
387C3×D4—102no—
388C3×D4—202no—
389C3×D4—204no—
390C3×D4—202no—
391C2×C3×C4—21no—
392C2×C3×C4—52no—
393C2×C3×C4—51no—
394C2×C3×C4—54no—
395C2×C3×C4—104no—
396C2×C3×C4—101no—
397C2×C3×C4—202no—
398C2×C3×C4—202no—
399C2×C3×C4D4×D512yes—
400C2×C3×C4C23×D511yescharacteristic
401D12—22no—
402D12—22no—
403D12—44no—
404D12—102no—
405D12—102no—
406D12—204no—
407D12—204no—
408D12—208no—
409C3⋊C8—54no—
410C3⋊C8D4×D514yescomplemented
411C22×C5—41no—
412C22×C5—42no—
413C22×C5—122no—
414C22×C5—124no—
415C22×C5C22×#6711yescharacteristic
416C2×D5—22no—
417C2×D5—41no—
418C2×D5—42no—
419C2×D5—122no—
420C2×D5—124no—
421C2×D5—248no—
422C2×D5#94012yes—
423C4×C5—22no—
424C4×C5—41no—
425C4×C5C2×D3×D412yes—
426Dic5—41no—
427Dic5#94012yes—
428Dic5#94914yescomplemented
429C24—302no—
430#41—104no—
431#41—104no—
432C2×Q8—51no—
433C2×Q8C2×D3×D511yescharacteristic
434C2×D4—32no—
435C2×D4—51no—
436C2×D4—62no—
437C2×D4—101no—
438C2×D4—102no—
439C2×D4—101no—
440C2×D4—152no—
441C2×D4—304no—
442C2×D4—304no—
443C2×D4—304no—
444C2×D4—302no—
445C2×D4—302no—
446C2×D4—608no—
447C2×D4C2×D3×D511yescharacteristic
448C22×C4—51no—
449C22×C4—52no—
450C22×C4—101no—
451C22×C4—101no—
452SD16—64no—
453SD16—304no—
454SD16—304no—
455SD16—304no—
456D8—64no—
457D8—304no—
458D8—304no—
459D8—304no—
460M16—158no—
461C2×C8—32no—
462C2×C8—152no—
463C4⋊C4—102no—
464C22⋊C4—22no—
465C22⋊C4—102no—
466C42—52no—
467C42—51no—
468C42C2×D3×D511yescharacteristic
469C3×C5#315111yescharacteristic, complemented, Hall
470C22×C3—41no—
471C22×C3—42no—
472C22×C3—52no—
473C22×C3—102no—
474C22×C3—201no—
475C22×C3—202no—
476C22×C3C2×D4×D511yescharacteristic
477C2×D3—42no—
478C2×D3—44no—
479C2×D3—202no—
480C2×D3—204no—
481C2×D3—408no—
482C3×C4—22no—
483C3×C4—41no—
484C3×C4—52no—
485C3×C4—54no—
486C3×C4—201no—
487C3×C4C2×D4×D512yes—
488C2×C5—81no—
489C2×C5—242no—
490C2×C5C2×#94011yescharacteristic
491C2×C5C2×#94912yes—
492D5—22no—
493D5—81no—
494D5—242no—
495C23—21no—
496C23—51no—
497C23—62no—
498C23—101no—
499C23—302no—
500C23—604no—
501C23—608no—
502Q8—22no—
503Q8—102no—
504D4—22no—
505D4—62no—
506D4—62no—
507D4—102no—
508D4—124no—
509D4—202no—
510D4—204no—
511D4—202no—
512D4—302no—
513D4—302no—
514D4—604no—
515D4—604no—
516D4—608no—
517C2×C4—21no—
518C2×C4—52no—
519C2×C4—51no—
520C2×C4—54no—
521C2×C4—104no—
522C2×C4—101no—
523C2×C4—202no—
524C2×C4—202no—
525C2×C4D5×#6712yes—
526C2×C4C22×D3×D511yescharacteristic
527C8—34no—
528C8—154no—
529C2×C3—81no—
530C2×C3—102no—
531C2×C3—401no—
532C2×C3D5×#12711yescharacteristic
533C2×C3D5×AGL(1,ℤ/8)12yes—
534D3—82no—
535D3—402no—
536C5#8328711yescharacteristic, complemented, Sylow
537C22—41no—
538C22—42no—
539C22—52no—
540C22—102no—
541C22—122no—
542C22—124no—
543C22—201no—
544C22—202no—
545C22—602no—
546C22—604no—
547C22—1208no—
548C22C2×D5×#6711yescharacteristic
549C4—22no—
550C4—41no—
551C4—52no—
552C4—54no—
553C4—201no—
554C4D3×D4×D512yes—
555C3#1061357611yescharacteristic, complemented, Sylow
556C2—81no—
557C2—102no—
558C2—242no—
559C2—401no—
560C2—1202no—
561C2D5×#94011yescharacteristic
562C2D5×#94912yes—
subgroupG/H
centerC22C2×D5×#67
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C22×D4
hypercenter#124D3×D5
hypocenterC3×C5#3151
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#66002C2semidirect
2. C2×#91502C2semidirect
3. C2×#91478C2semidirect
4. D5×#874C2semidirect
5. #11751159C2semidirect
6. C5×#5058C2semidirect
7. #11749339C2semidirect
8. #11749093C2semidirect
9. #11747042C2semidirect
10. #11747036C2semidirect
11. #11747003C2semidirect
17. C3×C5×#124C22semidirect
18. C2×#6717C22semidirect
19. C2×#6715C22semidirect
21. C2×C5×#215C22semidirect
22. C2×C5×#213C22semidirect
24. C3×#4090C22semidirect
25. C3×#4086C22semidirect
28. C3×#4021C22semidirect
34. C2×#6658C22semidirect
35. C2×#6656C22semidirect
36. C2×#6653C22semidirect
37. C2×#6652C22semidirect
39. #91087C22semidirect
40. C5×#803C22semidirect
41. Dic5×C3⋊C8C22semidirect
46. #66002D3semidirect
93. #6649D4semidirect
103. #5058D5semidirect
112. C5×#124C2×D3semidirect
113. #4090C2×D3semidirect
117. #4086C2×D3semidirect
128. #4021C2×D3semidirect
167. C3⋊#168C2×D4semidirect
168. C5×C3⋊C8C2×D4semidirect
176. C3×#124C2×D5semidirect
185. C2×#215C2×D5semidirect
189. C2×#213C2×D5semidirect
196. #803C2×D5semidirect
266. C3×Dic5AGL(1,ℤ/8)semidirect
363. #124D3×D5semidirect
410. C3⋊C8D4×D5semidirect
428. Dic5#949semidirect
469. C3×C5#3151semidirect
536. C5#83287semidirect
555. C3#10613576semidirect

Maximal subgroups

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

subgroupindex
C3×#660022
C2×#915022
C2×#914782
D5×#8742
#117511592
C5×#50582
#117493392
#117490932
#117470422
#117470362
#117470032
#106135763
#832875