Finite Group Databasebeta

← #14458398

Subgroups — #14458398

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752745C211yesmaximal, characteristic, complemented
2#11752676C211yesmaximal, characteristic, complemented
3#11750947C211yesmaximal, characteristic, complemented
4C5×#4834C211yesmaximal, characteristic, complemented
5C3×#65132C211yesmaximal, characteristic, complemented
6#11748112C212yesmaximal, complemented
7D3×#3953C212yesmaximal, complemented
8#11747916C212yesmaximal, complemented
9#11747915C212yesmaximal, complemented
10C4×#6653C211yesmaximal, characteristic, complemented
11#11746890C211yesmaximal, characteristic, complemented
12#10611169—31nomaximal, Hall
13C2×#6777—21no—
14C2×D3×D20C2212yes—
15C2×#6772—21no—
16C4×D60C2211yescharacteristic
17#91758C2211yescharacteristic, complemented
18C2×C5×D3×C8C2212yescomplemented
19C4×C5×D12C2211yescharacteristic
20C2×C3×D40C2212yescomplemented
21C3×#4020C2211yescharacteristic
22C3×C4×D20C2211yescharacteristic, complemented
23#91474—22no—
24#91465—21no—
25#91457—22no—
26#91456C2212yes—
27#91456C2212yescomplemented
28D3×C4⋊Dic5C2212yescomplemented
29#91360—21no—
30C2×#6653C2211yescharacteristic
31C3×C5×C4⋊C8C2211yescharacteristic, complemented
32#91105C2212yes—
33#91102C2212yescomplemented
34C5×(C2×D3)⋊C8C2212yescomplemented
35C4×C5×C3⋊C8C2211yescharacteristic, complemented
36C3×#3953C2212yescomplemented
37#90990C2211yescharacteristic, complemented
38#90968C2211yescharacteristic
39#90965C2212yescomplemented
40#90965C2212yescomplemented
41#90965C2211yescharacteristic, complemented
42#80352—51nomaximal, Hall
43#65889—31no—
44D4×D20—31no—
45C5×C8×D4—31no—
46#65404—32no—
47C2×#3953—32no—
48#65135—31no—
49#65132D311yescharacteristic, complemented
50#65025—32no—
51#65021—32no—
52#64983—31no—
53C4×D40—31no—
54C22×D3×D5—22no—
55C2×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×Dic30—21no—
58C2×C5×D12D411yescharacteristic
59C2×C4×C5×D3C2312yes—
60C2×C3×D20—21no—
61C2×C3×D20—21no—
62C2×C3×D20C2312yes—
63C2×C3×D20C2311yescharacteristic
64C2×C3×C4×D5—21no—
65C2×#1202—22no—
66C2×#1201—22no—
67C2×#1201—22no—
68C2×D3×Dic5—22no—
69#6777—44no—
70D3×D20—24no—
71D3×D20—42no—
72#6772—44no—
73C2×C3×C5×C8C2312yes—
74C3×C42×C5C2311yescharacteristic
75#6714—21no—
76C4⋊Dic15—21no—
77C4⋊Dic15C2312yes—
78C4⋊Dic15C2311yescharacteristic
79C5×(C2×D3)⋊C4D412yes—
80C5×C4⋊Dic3D411yescharacteristic
81C2×C5×C3⋊C8C2311yescharacteristic
82C2×C5×C3⋊C8C2311yescharacteristic
83C5×D3×C8—42no—
84C3×#685—21no—
85C3×C4⋊Dic5C2311yescharacteristic
86C3×D40—42no—
87Dic3⋊Dic5—22no—
88#6665—22no—
89#6665—22no—
90#6653—22no—
91#5717—51no—
92#5551—51no—
93C3×#459—51no—
94#5157—52no—
95#5156—52no—
96#5070—51no—
97C4×#213—51no—
98#4846—51no—
99#4834D511yescharacteristic, complemented
100#4774—52no—
101D3×#102—52no—
102C2×#711—61no—
103C2×D4×D5—61no—
104C22×D20—32no—
105C22×C5×C8—32no—
106C4×C5×D4—31no—
107#4076—32no—
108#4076—32no—
109C2×C4⋊Dic5—32no—
110C2×D40—31no—
111C2×D40C2×D312yescomplemented
112#4043—61no—
113#4041—61no—
114#4032—62no—
115#4028—62no—
116#4020C2×D311yescharacteristic
117C4×D20—31no—
118C4×D20C2×D311yescharacteristic, complemented
119#4015—31no—
120C5×C4⋊C8C2×D311yescharacteristic, complemented
121C5×C22⋊C8—32no—
122C4×C5×C8—31no—
123#3953—32no—
124#3953—32no—
125#3953—31no—
126#3953—32no—
127#3953—31no—
128#3953C2×D312yescomplemented
129#3950—32no—
130#3950—31no—
131#3294—151noSylow
132C22×D15—21no—
133C22×C5×D3C2×D412yes—
134C22×C3×D5—21no—
135C22×C3×D5—22no—
136C2×D3×D5—44no—
137C2×D3×D5—44no—
138C2×D3×D5—82no—
139C2×C3×C4×C5C2×D411yescharacteristic
140C2×C3×C4×C5C2×D411yescharacteristic
141C2×C3×C4×C5C2411yescharacteristic
142C2×Dic15—21no—
143C2×Dic15—22no—
144D60—21no—
145D60#4112yescomplemented
146C4×D15—42no—
147Dic30—42no—
148C2×C5×Dic3C2×D412yes—
149C5×D12D814yescomplemented
150C4×C5×D3—22no—
151C4×C5×D3—22no—
152C2×C3×Dic5—21no—
153C3×D20—22no—
154C3×D20—21no—
155C3×D20—21no—
156C3×D20—22no—
157C3×D20—42no—
158C3×D20—81no—
159C3×C4×D5—42no—
160#1202—44no—
161#1201—44no—
162#1201—44no—
163D3×Dic5—44no—
164C3×C5×C8—22no—
165C5×C3⋊C8—21no—
166C5×C3⋊C8—21no—
167C2×D3×D4—52no—
168C2×D3×D4—101no—
169C2×#235—101no—
170C2×C3×D8—52no—
171C3×#127—51no—
172C3×C4×D4—51no—
173#938—52no—
174#938—52no—
175#938—101no—
176#937—102no—
177C2×#213—51no—
178#924—101no—
179C2×D3×C8C2×D512yescomplemented
180D3×C4⋊C4—52no—
181#883—102no—
182C4×D12—51no—
183C4×D12C2×D511yescharacteristic
184#869—51no—
185C3×C4⋊C8C2×D511yescharacteristic, complemented
186C3×#102—52no—
187#832—52no—
188#832—51no—
189#832—52no—
190#821—52no—
191(C2×D3)⋊C8C2×D512yescomplemented
192#818—52no—
193#809—51no—
194#807—51no—
195C4×C3⋊C8C2×D511yescharacteristic, complemented
196C23×D5—62no—
197C2×C5×D4—31no—
198C22×C4×C5—32no—
199C2×C22⋊D5—62no—
200C2×C22⋊D5—62no—
201C22×Dic5—62no—
202#711—124no—
203D4×D5—124no—
204C2×D20—21no—
205C2×D20—21no—
206C2×D20—31no—
207C2×D20—64no—
208C2×D20—62no—
209C2×D20—122no—
210C2×D20C22×D312yes—
211C2×D20C22×D311yescharacteristic
212C2×C4×D5—21no—
213C2×C4×D5—61no—
214C2×Dic10—61no—
215C2×C5×C8—31no—
216C2×C5×C8—31no—
217C2×C5×C8—122no—
218C2×C5×C8C22×D312yes—
219C5×C4⋊C4—31no—
220C5×C22⋊C4—32no—
221C42×C5C22×D311yescharacteristic
222#685—21no—
223#685—62no—
224#685—62no—
225#685—61no—
226C4⋊Dic5—31no—
227C4⋊Dic5—32no—
228C4⋊Dic5—62no—
229C4⋊Dic5—61no—
230C4⋊Dic5C22×D311yescharacteristic
231D40—42no—
232D40—62no—
233#547—151no—
234D42—151no—
235#486—151no—
236#480—152no—
237#474—151no—
238#466—152no—
239#459—51no—
240#447—152no—
241C4×D8—151no—
242C8×D4—31no—
243C2×#102—152no—
244C22×C3×C5C22×D411yescharacteristic
245C2×D15—22no—
246C2×D15—41no—
247C2×D15—41no—
248C2×C5×D3—22no—
249C2×C5×D3—22no—
250C2×C5×D3C2×D814yes—
251C2×C3×D5—42no—
252C2×C3×D5—41no—
253C2×C3×D5—41no—
254C2×C3×D5—42no—
255C2×C3×D5—42no—
256C2×C3×D5—41no—
257D3×D5—88no—
258C3×C4×C5—21no—
259C3×C4×C5C2×D812yes—
260C3×C4×C5C2×#4111yescharacteristic
261C3×C4×C5H(5,𝔽2)11yescharacteristic
262Dic15—42no—
263Dic15—41no—
264C3×Dic5—41no—
265C5×Dic3—22no—
266C23×D3—102no—
267C2×C3×D4—52no—
268C2×C3×D4—51no—
269C2×C3×D4—101no—
270C2×C3×D4—101no—
271C22×C3×C4—101no—
272C2×#67—102no—
273C2×#67—102no—
274C2×#67—102no—
275D3×D4—104no—
276D3×D4—202no—
277D3×D4—204no—
278#235—204no—
279C2×D12—51no—
280C2×D12D2011yescharacteristic
281C2×C4×D3—102no—
282C2×C4×D3—101no—
283C2×C4×D3C22×D512yes—
284C2×Dic6—101no—
285C3×D8—202no—
286C2×C3×C8C22×D512yes—
287C3×C4⋊C4—51no—
288C3×C22⋊C4—101no—
289C3×C42C22×D511yescharacteristic
290#217—102no—
291#217—102no—
292#213—102no—
293(C2×D3)⋊C4—101no—
294(C2×D3)⋊C4D2012yes—
295C4⋊Dic3—51no—
296C4⋊Dic3—52no—
297C4⋊Dic3—101no—
298C4⋊Dic3D2011yescharacteristic
299Dic3⋊C4—102no—
300C2×C3⋊C8C22×D511yescharacteristic
301C2×C3⋊C8C22×D511yescharacteristic
302D3×C8—42no—
303C23×C5—32no—
304C22×D5—21no—
305C22×D5—22no—
306C22×D5—61no—
307C22×D5—124no—
308C22×D5—124no—
309C22×D5—242no—
310C5×D4—34no—
311C2×C4×C5—32no—
312C2×C4×C5—62no—
313C2×C4×C5—62no—
314C2×C4×C5D3×D411yescharacteristic
315C2×C4×C5D3×D411yescharacteristic
316C2×C4×C5C23×D311yescharacteristic
317C22⋊D5—124no—
318C22⋊D5—124no—
319C2×Dic5—21no—
320C2×Dic5—62no—
321C2×Dic5—61no—
322C2×Dic5—124no—
323D20—21no—
324D20—22no—
325D20—21no—
326D20—22no—
327D20—32no—
328D20—42no—
329D20—61no—
330D20—81no—
331D20—124no—
332C4×D5—42no—
333C4×D5—122no—
334Dic10—122no—
335C5×C8—22no—
336C5×C8—61no—
337C5×C8—61no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—52no—
342C2×D8—151no—
343C22×C8—32no—
344C4⋊Q8—151no—
345#127—51no—
346#123—302no—
347C22⋊Q8—301no—
348#121—152no—
349#121—152no—
350#121—301no—
351#120—302no—
352C4×D4—31no—
353C4×D4—51no—
354C4×D4—151no—
355C2×C4⋊C4—152no—
356#107—151no—
357#107—152no—
358C4⋊C8D3×D511yescharacteristic, complemented
359#102—52no—
360#102—151no—
361#102—152no—
362#102—151no—
363#102—152no—
364#102—152no—
365C22⋊C8—32no—
366C4×C8—31no—
367C2×C3×C5#54611yescharacteristic
368C2×C3×C5C22×D811yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—42no—
371C3×D5—82no—
372C3×D5—81no—
373C5×D3—24no—
374C23×C3—101no—
375C23×C3—102no—
376C22×D3—101no—
377C22×D3—204no—
378C22×D3—204no—
379C22×D3—402no—
380C22×D3C2×D2012yes—
381C3×D4—101no—
382C3×D4—102no—
383C3×D4—101no—
384C3×D4—102no—
385C3×D4—202no—
386C3×D4—401no—
387C2×C3×C4—101no—
388C2×C3×C4—202no—
389C2×C3×C4C2×D2011yescharacteristic
390C2×C3×C4C2×D2011yescharacteristic
391C2×C3×C4C23×D511yescharacteristic
392#67—204no—
393#67—204no—
394#67—204no—
395C2×Dic3—102no—
396C2×Dic3—101no—
397C2×Dic3C2×D2012yes—
398D12—52no—
399D12—101no—
400D12D4014yescomplemented
401C4×D3—22no—
402C4×D3—22no—
403C4×D3—204no—
404C4×D3—202no—
405Dic6—202no—
406C3×C8—22no—
407C3⋊C8—21no—
408C3⋊C8—21no—
409C22×C5—34no—
410C22×C5—62no—
411C22×C5—62no—
412C22×C5C2×D3×D411yescharacteristic
413C2×D5—41no—
414C2×D5—42no—
415C2×D5—42no—
416C2×D5—41no—
417C2×D5—42no—
418C2×D5—41no—
419C2×D5—62no—
420C2×D5—121no—
421C2×D5—121no—
422C2×D5—248no—
423C4×C5—21no—
424C4×C5—62no—
425C4×C5D3×D812yes—
426C4×C5#100411yescharacteristic
427C4×C5D3×#4111yescharacteristic
428Dic5—41no—
429Dic5—122no—
430Dic5—121no—
431C24—302no—
432#41—604no—
433C2×Q8—301no—
434C2×D4—31no—
435C2×D4—52no—
436C2×D4—51no—
437C2×D4—101no—
438C2×D4—101no—
439C2×D4—151no—
440C2×D4—302no—
441C2×D4—304no—
442C2×D4—302no—
443C2×D4—302no—
444C2×D4—602no—
445C2×D4—604no—
446C22×C4—32no—
447C22×C4—101no—
448C22×C4—302no—
449C22×C4—301no—
450D8—202no—
451D8—302no—
452C2×C8—31no—
453C2×C8—31no—
454C2×C8—122no—
455C2×C8C2×D3×D512yes—
456C4⋊C4—31no—
457C4⋊C4—51no—
458C4⋊C4—152no—
459C4⋊C4—151no—
460C4⋊C4—302no—
461C4⋊C4—301no—
462C22⋊C4—32no—
463C22⋊C4—101no—
464C22⋊C4—302no—
465C22⋊C4—302no—
466C22⋊C4—301no—
467C42C2×D3×D511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—201no—
470C22×C3—202no—
471C22×C3—202no—
472C22×C3—201no—
473C22×C3—202no—
474C22×C3—201no—
475C22×C3C22×D2011yescharacteristic
476C2×D3—22no—
477C2×D3—22no—
478C2×D3—102no—
479C2×D3—201no—
480C2×D3—201no—
481C2×D3—408no—
482C2×D3C2×D4014yes—
483C3×C4—21no—
484C3×C4—201no—
485C3×C4C2×D4012yes—
486C3×C4#414411yescharacteristic
487C3×C4D5×#4111yescharacteristic
488Dic3—22no—
489Dic3—202no—
490Dic3—201no—
491C2×C5—64no—
492C2×C5#561211yescharacteristic
493C2×C5C2×D3×D811yescharacteristic
494C2×C5#577511yescharacteristic
495D5—82no—
496D5—81no—
497D5—122no—
498C23—32no—
499C23—101no—
500C23—102no—
501C23—301no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—602no—
506D4—34no—
507D4—101no—
508D4—102no—
509D4—101no—
510D4—102no—
511D4—152no—
512D4—202no—
513D4—301no—
514D4—401no—
515D4—604no—
516D4—604no—
517D4—604no—
518C2×C4—32no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—101no—
522C2×C4—202no—
523C2×C4—301no—
524C2×C4—302no—
525C2×C4—604no—
526C2×C4—602no—
527C2×C4D3×D2011yescharacteristic
528C2×C4D3×D2011yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—22no—
531C8—61no—
532C8—61no—
533C2×C3—402no—
534C2×C3—401no—
535C2×C3#6588811yescharacteristic
536C2×C3C22×D4011yescharacteristic
537C2×C3#6608511yescharacteristic
538D3—24no—
539D3—202no—
540C5#8035211yescharacteristic, complemented, Sylow
541C22—34no—
542C22—62no—
543C22—62no—
544C22—202no—
545C22—201no—
546C22—202no—
547C22—201no—
548C22—201no—
549C22—202no—
550C22—302no—
551C22—601no—
552C22—601no—
553C22—1208no—
554C22C2×D3×D2011yescharacteristic
555C4—21no—
556C4—62no—
557C4—201no—
558C4—601no—
559C4—602no—
560C4D3×D4012yes—
561C4#9202511yescharacteristic
562C4#9203411yescharacteristic
563C3#1061116911yescharacteristic, complemented, Sylow
564C2—64no—
565C2—402no—
566C2—401no—
567C2—602no—
568C2#1175388311yescharacteristic
569C2C2×D3×D4011yescharacteristic
570C2#1175403011yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5C22×D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#3294
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #11752745C2semidirect
2. #11752676C2semidirect
3. #11750947C2semidirect
4. C5×#4834C2semidirect
5. C3×#65132C2semidirect
6. #11748112C2semidirect
7. D3×#3953C2semidirect
8. #11747916C2semidirect
9. #11747915C2semidirect
10. C4×#6653C2semidirect
11. #11746890C2semidirect
17. #91758C22semidirect
18. C2×C5×D3×C8C22semidirect
20. C2×C3×D40C22semidirect
22. C3×C4×D20C22semidirect
27. #91456C22semidirect
28. D3×C4⋊Dic5C22semidirect
31. C3×C5×C4⋊C8C22semidirect
33. #91102C22semidirect
34. C5×(C2×D3)⋊C8C22semidirect
35. C4×C5×C3⋊C8C22semidirect
36. C3×#3953C22semidirect
37. #90990C22semidirect
39. #90965C22semidirect
40. #90965C22semidirect
41. #90965C22semidirect
49. #65132D3semidirect
99. #4834D5semidirect
111. C2×D40C2×D3semidirect
118. C4×D20C2×D3semidirect
120. C5×C4⋊C8C2×D3semidirect
128. #3953C2×D3semidirect
145. D60#41semidirect
149. C5×D12D8semidirect
179. C2×D3×C8C2×D5semidirect
185. C3×C4⋊C8C2×D5semidirect
191. (C2×D3)⋊C8C2×D5semidirect
195. C4×C3⋊C8C2×D5semidirect
358. C4⋊C8D3×D5semidirect
400. D12D40semidirect
468. C3×C5#3294semidirect
540. C5#80352semidirect
563. C3#10611169semidirect

Maximal subgroups

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

subgroupindex
#117527452
#117526762
#117509472
C5×#48342
C3×#651322
#117481122
D3×#39532
#117479162
#117479152
C4×#66532
#117468902
#106111693
#803525