Finite Group Databasebeta

← #14458409

Subgroups — #14458409

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
1D12×D20C211yesmaximal, characteristic, complemented
2#11752676C211yesmaximal, characteristic, complemented
3#11750795C211yesmaximal, characteristic, complemented
4C5×C8×D12C211yesmaximal, characteristic, complemented
5C3×C4×D40C211yesmaximal, characteristic, complemented
6#11748112C212yesmaximal, complemented
7D3×#3953C212yesmaximal, complemented
8#11747909C212yesmaximal, complemented
9#11747627C212yesmaximal, complemented
10#11747028C211yesmaximal, characteristic, complemented
11#11746889C211yesmaximal, characteristic, complemented
12#10611169—31nomaximal, Hall
13C2×D3×D20C2212yes—
14C2×D5×D12—21no—
15C2×#6772—21no—
16#91763C2211yescharacteristic
17#91758C2211yescharacteristic, complemented
18C2×C5×D3×C8C2212yescomplemented
19C4×C5×D12C2211yescharacteristic
20C2×C3×D40C2211yescharacteristic
21C3×C4×D20C2211yescharacteristic
22C3×C4×D20C2211yescharacteristic, complemented
23#91476—22no—
24#91460C2212yes—
25#91457—22no—
26#91456C2212yescomplemented
27#91450—21no—
28D3×C4⋊Dic5C2212yescomplemented
29#91360—21no—
30C2×#6653C2212yescomplemented
31C3×C4×C5×C8C2211yescharacteristic, complemented
32#91105C2212yescomplemented
33#91105C2212yescomplemented
34C5×(C2×D3)⋊C8C2212yescomplemented
35C5×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
36C3×#3953C2211yescharacteristic
37C3×#3953C2211yescharacteristic, complemented
38C3×#3950C2211yescharacteristic, complemented
39#90990C2212yescomplemented
40#90968C2212yescomplemented
41#90965C2212yes—
42#79608—51nomaximal, Hall
43#65889—31no—
44D4×D20—31no—
45C5×C8×D4—31no—
46#65404—32no—
47C2×#3953—32no—
48#65135—31no—
49#65132—31no—
50#65025—32no—
51#65021—32no—
52#64983—31no—
53C4×D40D311yescharacteristic, complemented
54C22×D3×D5—22no—
55C2×D60—21no—
56C2×D60—21no—
57C2×D60C2312yes—
58C2×Dic30—21no—
59C2×C5×D12D411yescharacteristic
60C2×C4×C5×D3C2312yes—
61C2×C3×D20C2311yescharacteristic
62C2×C3×D20C2311yescharacteristic
63C2×C3×C4×D5—21no—
64C2×C3×C4×D5—21no—
65C2×#1203—22no—
66C2×#1202—22no—
67C2×#1201—22no—
68C2×D3×Dic5—22no—
69D3×D20—24no—
70D3×D20—42no—
71D5×D12—44no—
72#6772—44no—
73C2×C3×C5×C8C2311yescharacteristic
74C2×C3×C5×C8C2311yescharacteristic
75C3×C42×C5C2311yescharacteristic
76C4⋊Dic15—21no—
77C4⋊Dic15C2312yes—
78C5×(C2×D3)⋊C4D412yes—
79C5×C4⋊Dic3D411yescharacteristic
80C2×C5×C3⋊C8C2312yes—
81C5×D3×C8—42no—
82C3×#685—21no—
83C3×#685—21no—
84C3×C4⋊Dic5C2311yescharacteristic
85C3×C4⋊Dic5C2311yescharacteristic
86C3×D40—22no—
87Dic3⋊Dic5—22no—
88#6667—22no—
89#6665—22no—
90#6653—42no—
91#5551—51no—
92D4×D12—51no—
93C3×C4×D8—51no—
94#5156—52no—
95#5015—51no—
96#5007—51no—
97#4882—52no—
98#4775—52no—
99D3×#102—52no—
100#4694—51no—
101C8×D12D511yescharacteristic, complemented
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—32no—
111C2×D40C2×D311yescharacteristic
112#4043—61no—
113#4041—61no—
114#4032—62no—
115#4028—62no—
116#4020—31no—
117C4×D20C2×D311yescharacteristic
118C4×D20C2×D311yescharacteristic, complemented
119#4015—31no—
120C5×C4⋊C8—31no—
121C5×C22⋊C8—32no—
122C4×C5×C8C2×D311yescharacteristic, complemented
123#3953—32no—
124#3953—32no—
125#3953—32no—
126#3953—32no—
127#3953C2×D311yescharacteristic
128#3953C2×D311yescharacteristic, complemented
129#3950—32no—
130#3950C2×D311yescharacteristic, complemented
131#3294—151noSylow
132C22×D15—22no—
133C22×C5×D3C2×D412yes—
134C22×C3×D5—21no—
135C22×C3×D5—21no—
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—22no—
143D60—22no—
144D60—22no—
145D60—42no—
146D60—81no—
147Dic30—42no—
148C2×C5×Dic3C2×D412yes—
149C5×D12D814yescomplemented
150C4×C5×D3—22no—
151C4×C5×D3—22no—
152C2×C3×Dic5—21no—
153C2×C3×Dic5—21no—
154C3×D20—21no—
155C3×D20—21no—
156C3×D20—21no—
157C3×D20#4112yescomplemented
158C3×C4×D5—42no—
159C3×C4×D5—42no—
160#1203—44no—
161#1202—44no—
162#1201—44no—
163D3×Dic5—44no—
164C3×C5×C8—21no—
165C3×C5×C8—21no—
166C5×C3⋊C8—22no—
167C2×D3×D4—52no—
168C2×#235—101no—
169C22×D12—101no—
170C2×C3×D8—51no—
171C3×C4×D4—51no—
172C3×C4×D4—51no—
173#938—52no—
174C2×#213—52no—
175#930—101no—
176#924—101no—
177C2×D3×C8C2×D512yescomplemented
178#895—52no—
179D3×C4⋊C4—52no—
180#883—102no—
181#882—102no—
182#874—51no—
183C4×D12C2×D511yescharacteristic
184#869—51no—
185C3×#107—51no—
186C3×#102—51no—
187C3×#102—51no—
188C3×C4×C8C2×D511yescharacteristic, complemented
189#832—52no—
190#821—52no—
191#821—52no—
192(C2×D3)⋊C8C2×D512yescomplemented
193#809—52no—
194#807—52no—
195C4⋊(C3⋊C8)C2×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—32no—
205C2×D20—64no—
206C2×D20—62no—
207C2×D20—61no—
208C2×D20—61no—
209C2×D20—122no—
210C2×D20C22×D311yescharacteristic
211C2×D20C22×D311yescharacteristic
212C2×C4×D5—21no—
213C2×C4×D5—21no—
214C2×Dic10—61no—
215C2×C5×C8—32no—
216C2×C5×C8—122no—
217C2×C5×C8C22×D311yescharacteristic
218C2×C5×C8C22×D311yescharacteristic
219C5×C4⋊C4—31no—
220C5×C22⋊C4—32no—
221C42×C5C22×D311yescharacteristic
222#685—21no—
223#685—21no—
224#685—62no—
225#685—62no—
226C4⋊Dic5—32no—
227C4⋊Dic5—62no—
228C4⋊Dic5—61no—
229C4⋊Dic5C22×D311yescharacteristic
230C4⋊Dic5C22×D311yescharacteristic
231D40—22no—
232D40—122no—
233#547—151no—
234D42—151no—
235#486—151no—
236#480—152no—
237#474—151no—
238#466—152no—
239#459—151no—
240#447—152no—
241C4×D8—51no—
242C8×D4—31no—
243C2×#102—152no—
244C22×C3×C5C22×D411yescharacteristic
245C2×D15—42no—
246C2×D15—42no—
247C2×D15—42no—
248C2×C5×D3—22no—
249C2×C5×D3—22no—
250C2×C5×D3C2×D814yes—
251C2×C3×D5—22no—
252C2×C3×D5—41no—
253C2×C3×D5—41no—
254C2×C3×D5—41no—
255C2×C3×D5—41no—
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—
263C3×Dic5—41no—
264C3×Dic5—41no—
265C5×Dic3—22no—
266C23×D3—102no—
267C2×C3×D4—51no—
268C2×C3×D4—51no—
269C22×C3×C4—101no—
270C22×C3×C4—101no—
271C2×#67—102no—
272C2×#67—102no—
273D3×D4—104no—
274D3×D4—202no—
275#235—204no—
276C2×D12—52no—
277C2×D12—102no—
278C2×D12—101no—
279C2×D12—101no—
280C2×D12—204no—
281C2×D12D2011yescharacteristic
282C2×C4×D3—102no—
283C2×C4×D3C22×D512yes—
284C2×Dic6—101no—
285C3×D8—102no—
286C2×C3×C8C22×D511yescharacteristic
287C2×C3×C8C22×D511yescharacteristic
288C3×C4⋊C4—51no—
289C3×C4⋊C4—51no—
290C3×C22⋊C4—101no—
291C3×C22⋊C4—101no—
292C3×C42C22×D511yescharacteristic
293#217—102no—
294#213—202no—
295(C2×D3)⋊C4—102no—
296(C2×D3)⋊C4D2012yes—
297C4⋊Dic3—52no—
298C4⋊Dic3—101no—
299C4⋊Dic3D2011yescharacteristic
300Dic3⋊C4—102no—
301C2×C3⋊C8C22×D512yes—
302D3×C8—42no—
303C23×C5—32no—
304C22×D5—21no—
305C22×D5—21no—
306C22×D5—62no—
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—21no—
321C2×Dic5—62no—
322C2×Dic5—124no—
323D20—21no—
324D20—21no—
325D20—21no—
326D20—62no—
327D20—62no—
328D20—124no—
329D20—122no—
330D20—241no—
331D20#23512yescomplemented
332C4×D5—42no—
333C4×D5—42no—
334Dic10—122no—
335C5×C8—21no—
336C5×C8—21no—
337C5×C8—62no—
338C2×#41—301no—
339C22×D4—152no—
340C22×D4—301no—
341C2×D8—51no—
342C2×D8—152no—
343C22×C8—32no—
344C4⋊Q8—151no—
345#127—151no—
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—51no—
355C2×C4⋊C4—152no—
356#107—51no—
357#107—152no—
358C4⋊C8—31no—
359#102—51no—
360#102—51no—
361#102—152no—
362#102—152no—
363#102—152no—
364#102—152no—
365C22⋊C8—32no—
366C4×C8D3×D511yescharacteristic, complemented
367C2×C3×C5#54611yescharacteristic
368C2×C3×C5C22×D811yescharacteristic
369C2×C3×C5#57711yescharacteristic
370D15—82no—
371C3×D5—42no—
372C3×D5—81no—
373C5×D3—24no—
374C23×C3—101no—
375C23×C3—101no—
376C22×D3—102no—
377C22×D3—204no—
378C22×D3—204no—
379C22×D3—402no—
380C22×D3C2×D2012yes—
381C3×D4—52no—
382C3×D4—101no—
383C3×D4—101no—
384C3×D4—101no—
385C2×C3×C4—101no—
386C2×C3×C4—101no—
387C2×C3×C4—202no—
388C2×C3×C4—202no—
389C2×C3×C4C2×D2011yescharacteristic
390C2×C3×C4C2×D2011yescharacteristic
391C2×C3×C4C23×D511yescharacteristic
392#67—204no—
393#67—204no—
394C2×Dic3—102no—
395C2×Dic3C2×D2012yes—
396D12—102no—
397D12—102no—
398D12—204no—
399D12—202no—
400D12—401no—
401D12D4014yescomplemented
402C4×D3—22no—
403C4×D3—22no—
404C4×D3—204no—
405Dic6—202no—
406C3×C8—21no—
407C3×C8—21no—
408C3⋊C8—22no—
409C22×C5—34no—
410C22×C5—62no—
411C22×C5—62no—
412C22×C5C2×D3×D411yescharacteristic
413C2×D5—22no—
414C2×D5—41no—
415C2×D5—41no—
416C2×D5—41no—
417C2×D5—41no—
418C2×D5—41no—
419C2×D5—122no—
420C2×D5—122no—
421C2×D5—122no—
422C2×D5—248no—
423C4×C5—21no—
424C4×C5—62no—
425C4×C5D3×D812yes—
426C4×C5C2×#23511yescharacteristic
427C4×C5#100911yescharacteristic
428Dic5—41no—
429Dic5—41no—
430Dic5—122no—
431C24—302no—
432#41—604no—
433C2×Q8—301no—
434C2×D4—31no—
435C2×D4—51no—
436C2×D4—51no—
437C2×D4—152no—
438C2×D4—302no—
439C2×D4—304no—
440C2×D4—302no—
441C2×D4—302no—
442C2×D4—301no—
443C2×D4—301no—
444C2×D4—602no—
445C2×D4—604no—
446C22×C4—32no—
447C22×C4—101no—
448C22×C4—101no—
449C22×C4—302no—
450D8—102no—
451D8—602no—
452C2×C8—32no—
453C2×C8—122no—
454C2×C8C2×D3×D511yescharacteristic
455C2×C8C2×D3×D511yescharacteristic
456C4⋊C4—31no—
457C4⋊C4—51no—
458C4⋊C4—51no—
459C4⋊C4—152no—
460C4⋊C4—302no—
461C4⋊C4—301no—
462C22⋊C4—32no—
463C22⋊C4—101no—
464C22⋊C4—101no—
465C22⋊C4—302no—
466C22⋊C4—302no—
467C42C2×D3×D511yescharacteristic
468C3×C5#329411yescharacteristic, complemented, Hall
469C22×C3—102no—
470C22×C3—201no—
471C22×C3—201no—
472C22×C3—201no—
473C22×C3—201no—
474C22×C3—201no—
475C22×C3C22×D2011yescharacteristic
476C2×D3—22no—
477C2×D3—22no—
478C2×D3—202no—
479C2×D3—202no—
480C2×D3—202no—
481C2×D3—408no—
482C2×D3C2×D4014yes—
483C3×C4—21no—
484C3×C4—201no—
485C3×C4—201no—
486C3×C4C2×D4012yes—
487C3×C4#414411yescharacteristic
488C3×C4D5×#4111yescharacteristic
489Dic3—22no—
490Dic3—202no—
491C2×C5—64no—
492C2×C5#555011yescharacteristic
493C2×C5C2×D3×D811yescharacteristic
494C2×C5#577011yescharacteristic
495D5—42no—
496D5—81no—
497D5—242no—
498C23—32no—
499C23—101no—
500C23—101no—
501C23—302no—
502C23—604no—
503C23—604no—
504C23—1202no—
505Q8—602no—
506D4—34no—
507D4—52no—
508D4—101no—
509D4—101no—
510D4—101no—
511D4—302no—
512D4—302no—
513D4—604no—
514D4—604no—
515D4—604no—
516D4—602no—
517D4—1201no—
518C2×C4—32no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—101no—
522C2×C4—101no—
523C2×C4—202no—
524C2×C4—202no—
525C2×C4—302no—
526C2×C4—604no—
527C2×C4D3×D2011yescharacteristic
528C2×C4D3×D2011yescharacteristic
529C2×C4C22×D3×D511yescharacteristic
530C8—21no—
531C8—21no—
532C8—62no—
533C2×C3—202no—
534C2×C3—401no—
535C2×C3#6588811yescharacteristic
536C2×C3C22×D4011yescharacteristic
537C2×C3#6608511yescharacteristic
538D3—24no—
539D3—402no—
540C5#7960811yescharacteristic, complemented, Sylow
541C22—34no—
542C22—62no—
543C22—62no—
544C22—102no—
545C22—201no—
546C22—201no—
547C22—201no—
548C22—201no—
549C22—201no—
550C22—602no—
551C22—602no—
552C22—602no—
553C22—1208no—
554C22C2×D3×D2011yescharacteristic
555C4—21no—
556C4—62no—
557C4—201no—
558C4—201no—
559C4—602no—
560C4D3×D4012yes—
561C4D5×#23511yescharacteristic
562C4#9201811yescharacteristic
563C3#1061116911yescharacteristic, complemented, Sylow
564C2—64no—
565C2—202no—
566C2—401no—
567C2—1202no—
568C2#1175274011yescharacteristic
569C2C2×D3×D4011yescharacteristic
570C2#1175397211yescharacteristic
subgroupG/H
centerC22C2×D3×D20
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×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. D12×D20C2semidirect
2. #11752676C2semidirect
3. #11750795C2semidirect
4. C5×C8×D12C2semidirect
5. C3×C4×D40C2semidirect
6. #11748112C2semidirect
7. D3×#3953C2semidirect
8. #11747909C2semidirect
9. #11747627C2semidirect
10. #11747028C2semidirect
11. #11746889C2semidirect
17. #91758C22semidirect
18. C2×C5×D3×C8C22semidirect
22. C3×C4×D20C22semidirect
26. #91456C22semidirect
28. D3×C4⋊Dic5C22semidirect
30. C2×#6653C22semidirect
31. C3×C4×C5×C8C22semidirect
32. #91105C22semidirect
33. #91105C22semidirect
34. C5×(C2×D3)⋊C8C22semidirect
35. C5×C4⋊(C3⋊C8)C22semidirect
37. C3×#3953C22semidirect
38. C3×#3950C22semidirect
39. #90990C22semidirect
40. #90968C22semidirect
53. C4×D40D3semidirect
101. C8×D12D5semidirect
118. C4×D20C2×D3semidirect
122. C4×C5×C8C2×D3semidirect
128. #3953C2×D3semidirect
130. #3950C2×D3semidirect
149. C5×D12D8semidirect
157. C3×D20#41semidirect
177. C2×D3×C8C2×D5semidirect
188. C3×C4×C8C2×D5semidirect
192. (C2×D3)⋊C8C2×D5semidirect
195. C4⋊(C3⋊C8)C2×D5semidirect
331. D20#235semidirect
366. C4×C8D3×D5semidirect
401. D12D40semidirect
468. C3×C5#3294semidirect
540. C5#79608semidirect
563. C3#10611169semidirect

Maximal subgroups

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

subgroupindex
D12×D202
#117526762
#117507952
C5×C8×D122
C3×C4×D402
#117481122
D3×#39532
#117479092
#117476272
#117470282
#117468892
#106111693
#796085