Finite Group Databasebeta

← #14471465

Subgroups — #14471465

Order 1920.

852 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752677C211yesmaximal, characteristic, complemented
2Dic6×D20C211yesmaximal, characteristic, complemented
3#11750795C211yesmaximal, characteristic, complemented
4C5×C8×Dic6C211yesmaximal, characteristic, complemented
5C3×C4×D40C211yesmaximal, characteristic, complemented
6#11748003C212yesmaximal, complemented
7#11747794C212yesmaximal, complemented
8#11747754C212yesmaximal, complemented
9#11747740C212yesmaximal, complemented
10#11747028C211yesmaximal, characteristic, complemented
11#11746889C211yesmaximal, characteristic, complemented
12#10611655—31nomaximal, Hall
13C2×#6773—21no—
14C2×D5×Dic6—21no—
15#91763C2211yescharacteristic
16#91758C2211yescharacteristic
17C4×C5×Dic6C2211yescharacteristic
18C2×C3×D40C2211yescharacteristic
19C3×C4×D20C2211yescharacteristic
20C3×C4×D20C2211yescharacteristic
21#91469C2212yes—
22#91459—22no—
23#91458C2212yes—
24#91450—21no—
25#91428C2212yes—
26Dic3×D20C2212yes—
27#91422—22no—
28#91360—21no—
29C2×#6653C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91105C2212yes—
32#91105C2212yes—
33C5×Dic3⋊C8C2212yes—
34C5×C8×Dic3C2212yes—
35C5×C4⋊(C3⋊C8)C2211yescharacteristic
36C3×#3953C2211yescharacteristic
37C3×#3953C2211yescharacteristic
38C3×#3950C2211yescharacteristic
39#90990C2212yes—
40#90968C2212yes—
41#90965C2212yes—
42#79567—51nomaximal, Hall
43#65911—31no—
44Q8×D20—31no—
45C5×C8×Q8—31no—
46#65135—31no—
47#65135—32no—
48#65132—32no—
49#65132—31no—
50#64983—31no—
51#64983—32no—
52C4×D40—32no—
53C4×D40D311yescharacteristic, complemented
54C2×D60—21no—
55C2×D60—21no—
56C2×D60C2312yes—
57C2×Dic30—21no—
58C2×C5×Dic6D411yescharacteristic
59C2×C3×D20C2311yescharacteristic
60C2×C3×D20C2311yescharacteristic
61C2×C3×C4×D5—21no—
62C2×C3×C4×D5—21no—
63C2×#1204—22no—
64C2×#1202—22no—
65C2×#1202—22no—
66C2×#1200—22no—
67C2×D5×Dic3—22no—
68#6773—44no—
69D5×Dic6—44no—
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72C3×C42×C5C2311yescharacteristic
73C4⋊Dic15—21no—
74C4⋊Dic15C2312yes—
75C5×C4⋊Dic3D411yescharacteristic
76C5×Dic3⋊C4D412yes—
77C4×C5×Dic3C2312yes—
78C2×C5×C3⋊C8C2312yes—
79C3×#685—21no—
80C3×#685—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×C4⋊Dic5C2311yescharacteristic
83C3×D40—22no—
84Dic3⋊Dic5—22no—
85#6667—22no—
86#6665—22no—
87#6653—24no—
88#5553—51no—
89D4×Dic6—51no—
90C3×C4×D8—51no—
91#5150—52no—
92#5015—51no—
93#5007—51no—
94#4890—52no—
95#4760—52no—
96#4756—52no—
97#4694—51no—
98C8×Dic6D511yescharacteristic, complemented
99C2×#713—61no—
100C2×Q8×D5—61no—
101C4×C5×Q8—31no—
102C2×D40—32no—
103C2×D40C2×D311yescharacteristic
104#4043—62no—
105#4043—61no—
106#4041—62no—
107#4041—61no—
108#4020—32no—
109#4020—31no—
110C4×D20—32no—
111C4×D20—32no—
112C4×D20C2×D311yescharacteristic
113C4×D20C2×D311yescharacteristic
114#4015—31no—
115#4015—32no—
116C5×C4⋊C8—32no—
117C5×C4⋊C8—31no—
118C4×C5×C8—32no—
119C4×C5×C8C2×D311yescharacteristic
120#3953—32no—
121#3953—32no—
122#3953—32no—
123#3953—32no—
124#3953C2×D311yescharacteristic
125#3953C2×D311yescharacteristic
126#3950—32no—
127#3950C2×D311yescharacteristic
128#3358—151noSylow
129C22×D15—22no—
130C22×C3×D5—21no—
131C22×C3×D5—21no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15—22no—
136D60—22no—
137D60—22no—
138D60—42no—
139D60—81no—
140Dic30—42no—
141C2×C5×Dic3C2×D412yes—
142C2×C5×Dic3C2×D412yes—
143C5×Dic6D814yescomplemented
144C2×C3×Dic5—21no—
145C2×C3×Dic5—21no—
146C3×D20—21no—
147C3×D20—21no—
148C3×D20—21no—
149C3×D20#4112yescomplemented
150C3×C4×D5—42no—
151C3×C4×D5—42no—
152#1204—44no—
153#1202—44no—
154#1202—82no—
155#1200—44no—
156D5×Dic3—44no—
157C3×C5×C8—21no—
158C3×C5×C8—21no—
159C5×C3⋊C8—22no—
160C2×#235—101no—
161C22×Dic6—101no—
162C2×C3×D8—51no—
163C3×C4×D4—51no—
164C3×C4×D4—51no—
165#940—52no—
166D4×Dic3—52no—
167C2×#213—52no—
168#930—101no—
169#924—101no—
170#893—52no—
171#888—52no—
172#884—102no—
173#878—102no—
174#874—51no—
175#869—51no—
176C4×Dic6C2×D511yescharacteristic
177C3×#107—51no—
178C3×#102—51no—
179C3×#102—51no—
180C3×C4×C8C2×D511yescharacteristic
181#832—52no—
182#821—52no—
183#821—52no—
184Dic3⋊C8C2×D512yes—
185C8×Dic3C2×D512yes—
186#809—52no—
187#807—52no—
188C4⋊(C3⋊C8)C2×D511yescharacteristic
189C2×C5×Q8—31no—
190#713—124no—
191Q8×D5—124no—
192C2×D20—32no—
193C2×D20—62no—
194C2×D20—61no—
195C2×D20—62no—
196C2×D20—61no—
197C2×D20C22×D311yescharacteristic
198C2×D20C22×D311yescharacteristic
199C2×C4×D5—21no—
200C2×C4×D5—21no—
201C2×C4×D5—62no—
202C2×C4×D5—62no—
203C2×Dic10—62no—
204C2×Dic10—61no—
205C2×C5×C8—32no—
206C2×C5×C8C22×D311yescharacteristic
207C2×C5×C8C22×D311yescharacteristic
208C5×C4⋊C4—32no—
209C5×C4⋊C4—31no—
210C42×C5—32no—
211C42×C5C22×D311yescharacteristic
212#685—21no—
213#685—21no—
214#685—62no—
215#685—62no—
216C4⋊Dic5—32no—
217C4⋊Dic5—62no—
218C4⋊Dic5—61no—
219C4⋊Dic5C22×D311yescharacteristic
220C4⋊Dic5C22×D311yescharacteristic
221D40—22no—
222D40—64no—
223#550—151no—
224D4×Q8—151no—
225#486—152no—
226#486—151no—
227#474—152no—
228#474—151no—
229#459—151no—
230#459—152no—
231C8×Q8—31no—
232C4×D8—51no—
233C4×D8—152no—
234C22×C3×C5C22×D411yescharacteristic
235C2×D15—42no—
236C2×D15—42no—
237C2×D15—42no—
238C2×C3×D5—22no—
239C2×C3×D5—41no—
240C2×C3×D5—41no—
241C2×C3×D5—41no—
242C2×C3×D5—41no—
243C2×C3×D5—41no—
244C3×C4×C5—21no—
245C3×C4×C5C2×D812yes—
246C3×C4×C5C2×#4111yescharacteristic
247C3×C4×C52−1+411yescharacteristic
248Dic15—42no—
249C3×Dic5—41no—
250C3×Dic5—41no—
251C5×Dic3—22no—
252C5×Dic3C2×D814yes—
253C2×C3×D4—51no—
254C2×C3×D4—51no—
255C22×C3×C4—101no—
256C22×C3×C4—101no—
257C2×#67—102no—
258C2×#67—102no—
259C22×Dic3—102no—
260#235—204no—
261C2×D12—52no—
262C2×D12—101no—
263C2×D12—101no—
264C2×C4×D3—102no—
265C2×Dic6—101no—
266C2×Dic6—102no—
267C2×Dic6—204no—
268C2×Dic6D2011yescharacteristic
269C3×D8—102no—
270C2×C3×C8C22×D511yescharacteristic
271C2×C3×C8C22×D511yescharacteristic
272C3×C4⋊C4—51no—
273C3×C4⋊C4—51no—
274C3×C22⋊C4—101no—
275C3×C22⋊C4—101no—
276C3×C42C22×D511yescharacteristic
277#217—102no—
278#213—104no—
279(C2×D3)⋊C4—102no—
280C4⋊Dic3—52no—
281C4⋊Dic3—101no—
282C4⋊Dic3D2011yescharacteristic
283Dic3⋊C4—102no—
284Dic3⋊C4D2012yes—
285C4×Dic3C22×D512yes—
286C2×C3⋊C8C22×D512yes—
287C22×D5—21no—
288C22×D5—21no—
289C22×D5—62no—
290C5×Q8—34no—
291C2×C4×C5—32no—
292C2×C4×C5—32no—
293C2×C4×C5D3×D411yescharacteristic
294C2×C4×C5D3×D411yescharacteristic
295C2×C4×C5C23×D311yescharacteristic
296C2×Dic5—21no—
297C2×Dic5—21no—
298C2×Dic5—62no—
299D20—21no—
300D20—21no—
301D20—21no—
302D20—62no—
303D20—62no—
304D20—124no—
305D20—122no—
306D20—241no—
307D20—242no—
308D20#23512yescomplemented
309C4×D5—42no—
310C4×D5—42no—
311C4×D5—124no—
312C4×D5—124no—
313Dic10—124no—
314Dic10—122no—
315C5×C8—21no—
316C5×C8—21no—
317C5×C8—62no—
318C2×#41—301no—
319C22×Q8—301no—
320C2×D8—51no—
321C2×D8—152no—
322C4⋊Q8—152no—
323C4⋊Q8—151no—
324#127—152no—
325#127—151no—
326C22⋊Q8—302no—
327C22⋊Q8—301no—
328#121—302no—
329#121—301no—
330C4×Q8—31no—
331C4×D4—51no—
332C4×D4—51no—
333C4×D4—152no—
334C4×D4—152no—
335#107—51no—
336#107—152no—
337C4⋊C8—32no—
338C4⋊C8—31no—
339#102—51no—
340#102—51no—
341#102—152no—
342#102—152no—
343#102—152no—
344#102—152no—
345C4×C8—32no—
346C4×C8D3×D511yescharacteristic
347C2×C3×C5#54811yescharacteristic
348C2×C3×C5C22×D811yescharacteristic
349C2×C3×C5#57711yescharacteristic
350D15—82no—
351C3×D5—42no—
352C3×D5—81no—
353C23×C3—101no—
354C23×C3—101no—
355C22×D3—102no—
356C3×D4—52no—
357C3×D4—101no—
358C3×D4—101no—
359C3×D4—101no—
360C2×C3×C4—101no—
361C2×C3×C4—101no—
362C2×C3×C4—202no—
363C2×C3×C4—202no—
364C2×C3×C4C2×D2011yescharacteristic
365C2×C3×C4C2×D2011yescharacteristic
366C2×C3×C4C23×D511yescharacteristic
367#67—204no—
368#67—402no—
369C2×Dic3—102no—
370C2×Dic3—204no—
371C2×Dic3C2×D2012yes—
372C2×Dic3C2×D2012yes—
373D12—102no—
374D12—102no—
375D12—202no—
376D12—401no—
377C4×D3—204no—
378Dic6—202no—
379Dic6—204no—
380Dic6D4014yescomplemented
381C3×C8—21no—
382C3×C8—21no—
383C3⋊C8—22no—
384C22×C5C2×D3×D411yescharacteristic
385C2×D5—22no—
386C2×D5—41no—
387C2×D5—41no—
388C2×D5—41no—
389C2×D5—41no—
390C2×D5—41no—
391C2×D5—122no—
392C2×D5—122no—
393C2×D5—122no—
394C4×C5—21no—
395C4×C5—34no—
396C4×C5—62no—
397C4×C5D3×D812yes—
398C4×C5C2×#23511yescharacteristic
399C4×C5#101011yescharacteristic
400Dic5—41no—
401Dic5—41no—
402Dic5—122no—
403#41—604no—
404C2×Q8—31no—
405C2×Q8—302no—
406C2×Q8—301no—
407C2×Q8—604no—
408C2×D4—51no—
409C2×D4—51no—
410C2×D4—152no—
411C2×D4—302no—
412C2×D4—302no—
413C2×D4—301no—
414C2×D4—301no—
415C22×C4—101no—
416C22×C4—101no—
417C22×C4—302no—
418C22×C4—302no—
419D8—102no—
420D8—304no—
421C2×C8—32no—
422C2×C8C2×D3×D511yescharacteristic
423C2×C8C2×D3×D511yescharacteristic
424C4⋊C4—32no—
425C4⋊C4—31no—
426C4⋊C4—51no—
427C4⋊C4—51no—
428C4⋊C4—152no—
429C4⋊C4—302no—
430C4⋊C4—301no—
431C22⋊C4—101no—
432C22⋊C4—101no—
433C22⋊C4—302no—
434C22⋊C4—302no—
435C42—32no—
436C42C2×D3×D511yescharacteristic
437C3×C5#335811yescharacteristic, complemented, Hall
438C22×C3—102no—
439C22×C3—201no—
440C22×C3—201no—
441C22×C3—201no—
442C22×C3—201no—
443C22×C3—201no—
444C22×C3C22×D2011yescharacteristic
445C2×D3—202no—
446C2×D3—202no—
447C2×D3—202no—
448C3×C4—21no—
449C3×C4—201no—
450C3×C4—201no—
451C3×C4C2×D4012yes—
452C3×C4#414711yescharacteristic
453C3×C4D5×#4111yescharacteristic
454Dic3—22no—
455Dic3—202no—
456Dic3C2×D4014yes—
457C2×C5#555211yescharacteristic
458C2×C5C2×D3×D811yescharacteristic
459C2×C5#577011yescharacteristic
460D5—42no—
461D5—81no—
462D5—242no—
463C23—101no—
464C23—101no—
465C23—302no—
466Q8—34no—
467Q8—604no—
468Q8—602no—
469D4—52no—
470D4—101no—
471D4—101no—
472D4—101no—
473D4—302no—
474D4—302no—
475D4—604no—
476D4—602no—
477D4—1201no—
478D4—1202no—
479C2×C4—32no—
480C2×C4—32no—
481C2×C4—101no—
482C2×C4—101no—
483C2×C4—202no—
484C2×C4—202no—
485C2×C4—302no—
486C2×C4—604no—
487C2×C4—604no—
488C2×C4D3×D2011yescharacteristic
489C2×C4D3×D2011yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—21no—
492C8—21no—
493C8—62no—
494C2×C3—202no—
495C2×C3—401no—
496C2×C3#6591011yescharacteristic
497C2×C3C22×D4011yescharacteristic
498C2×C3#6608511yescharacteristic
499D3—402no—
500C5#7956711yescharacteristic, complemented, Sylow
501C22—102no—
502C22—201no—
503C22—201no—
504C22—201no—
505C22—201no—
506C22—201no—
507C22—602no—
508C22—602no—
509C22—602no—
510C22C2×D3×D2011yescharacteristic
511C4—21no—
512C4—34no—
513C4—62no—
514C4—201no—
515C4—201no—
516C4—602no—
517C4D3×D4012yes—
518C4#9200011yescharacteristic
519C4D5×#23511yescharacteristic
520C3#1061165511yescharacteristic, complemented, Sylow
521C2—202no—
522C2—401no—
523C2—1202no—
524C2#1175254111yescharacteristic
525C2C2×D3×D4011yescharacteristic
526C2#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#3358
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. #11752677C2semidirect
2. Dic6×D20C2semidirect
3. #11750795C2semidirect
4. C5×C8×Dic6C2semidirect
5. C3×C4×D40C2semidirect
6. #11748003C2semidirect
7. #11747794C2semidirect
8. #11747754C2semidirect
9. #11747740C2semidirect
10. #11747028C2semidirect
11. #11746889C2semidirect
53. C4×D40D3semidirect
98. C8×Dic6D5semidirect
143. C5×Dic6D8semidirect
149. C3×D20#41semidirect
308. D20#235semidirect
380. Dic6D40semidirect
437. C3×C5#3358semidirect
500. C5#79567semidirect
520. C3#10611655semidirect

Maximal subgroups

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

subgroupindex
#117526772
Dic6×D202
#117507952
C5×C8×Dic62
C3×C4×D402
#117480032
#117477942
#117477542
#117477402
#117470282
#117468892
#106116553
#795675