Finite Group Databasebeta

← #14471464

Subgroups — #14471464

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#11752558C211yesmaximal, characteristic, complemented
2#11752554C211yesmaximal, characteristic, complemented
3C8×Dic30C211yesmaximal, characteristic, complemented
4C4×C5×D24C211yesmaximal, characteristic, complemented
5C3×#64983C211yesmaximal, characteristic, complemented
6#11748011C212yesmaximal, complemented
7#11748000C212yesmaximal, complemented
8#11747803C212yesmaximal, complemented
9#11747733C212yesmaximal, complemented
10#11747033C211yesmaximal, characteristic, complemented
11#11746900C211yesmaximal, characteristic, complemented
12#10611298—31nomaximal, Hall
13C2×D3×Dic10—21no—
14C2×#6765—21no—
15C4×Dic30C2211yescharacteristic
16C2×C5×D24C2211yescharacteristic
17C4×C5×D12C2211yescharacteristic
18C4×C5×D12C2211yescharacteristic
19C3×#4020C2211yescharacteristic
20C3×#4015C2211yescharacteristic
21#91470C2212yes—
22#91463C2212yes—
23#91456—21no—
24#91436—22no—
25#91435C2212yes—
26#91434C2212yes—
27#91408—22no—
28#91369—21no—
29C2×#6652C2212yes—
30C3×C4×C5×C8C2211yescharacteristic
31#91098C2212yes—
32C8×Dic15C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#821C2211yescharacteristic
35C5×#821C2211yescharacteristic
36C5×#818C2211yescharacteristic
37C3×#3953C2212yes—
38C3×#3953C2212yes—
39#90989C2212yes—
40#90966C2212yes—
41#90964C2212yes—
42#81584—51nomaximal, Hall
43#65887—31no—
44D4×Dic10—31no—
45C4×C5×D8—31no—
46#65439—32no—
47#65304—31no—
48#65296—31no—
49#65179—32no—
50#65049—32no—
51#65045—32no—
52#64983D311yescharacteristic, complemented
53C8×Dic10—31no—
54C2×Dic30D411yescharacteristic
55C2×C5×D12C2311yescharacteristic
56C2×C5×D12C2311yescharacteristic
57C2×C4×C5×D3—21no—
58C2×C4×C5×D3—21no—
59C2×C3×D20—21no—
60C2×C3×D20—21no—
61C2×C3×D20C2312yes—
62C2×C3×Dic10—21no—
63C2×#1204—22no—
64C2×#1201—22no—
65C2×#1201—22no—
66C2×D3×Dic5—22no—
67C2×D5×Dic3—22no—
68D3×Dic10—44no—
69#6765—44no—
70C2×C3×C5×C8C2311yescharacteristic
71C2×C3×C5×C8C2311yescharacteristic
72C3×C42×C5C2311yescharacteristic
73C4⋊Dic15D411yescharacteristic
74#6712D412yes—
75C4×Dic15C2312yes—
76C2×C3⋊#168C2312yes—
77C5×(C2×D3)⋊C4—21no—
78C5×(C2×D3)⋊C4—21no—
79C5×C4⋊Dic3C2311yescharacteristic
80C5×C4⋊Dic3C2311yescharacteristic
81C5×D24—22no—
82C3×C4⋊Dic5—21no—
83C3×C4⋊Dic5C2312yes—
84#6669—22no—
85(C2×D3)⋊Dic5—22no—
86#6665—22no—
87#6652—24no—
88#5727—51no—
89#5718—51no—
90C3×#486—51no—
91#5087—51no—
92#5072—51no—
93#4786—52no—
94#4760—52no—
95#4759—52no—
96#4756—52no—
97C4×D24D511yescharacteristic, complemented
98C8×Dic6—51no—
99C2×#709—61no—
100C22×Dic10—61no—
101C2×C5×D8—31no—
102C4×C5×D4—31no—
103C4×C5×D4—31no—
104#4086—32no—
105D4×Dic5—32no—
106C2×#686—32no—
107#4076—61no—
108#4070—61no—
109#4039—32no—
110#4034—32no—
111#4030—62no—
112#4024—62no—
113#4020C2×D311yescharacteristic
114#4015C2×D311yescharacteristic
115C4×Dic10—31no—
116C5×#107—31no—
117C5×#102—31no—
118C5×#102—31no—
119C4×C5×C8C2×D311yescharacteristic
120#3964—32no—
121#3953C2×D312yes—
122#3953C2×D312yes—
123#3946—32no—
124C8×Dic5—32no—
125#3941—32no—
126#3939—32no—
127C4⋊#168—31no—
128#3358—151noSylow
129C22×C5×D3—21no—
130C22×C5×D3—21no—
131C22×C3×D5—22no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15C2×D412yes—
136C2×Dic15C2×D412yes—
137Dic30D814yescomplemented
138C2×C5×Dic3—21no—
139C2×C5×Dic3—21no—
140C5×D12—21no—
141C5×D12—21no—
142C5×D12—21no—
143C5×D12#4112yescomplemented
144C4×C5×D3—42no—
145C4×C5×D3—42no—
146C2×C3×Dic5—22no—
147C3×D20—22no—
148C3×D20—22no—
149C3×D20—42no—
150C3×D20—81no—
151C3×Dic10—42no—
152#1204—44no—
153#1201—44no—
154#1201—82no—
155D3×Dic5—44no—
156D5×Dic3—44no—
157C3×C5×C8—21no—
158C3×C5×C8—21no—
159C3⋊#168—22no—
160C2×D3×Q8—101no—
161C2×#237—101no—
162C3×C4⋊Q8—51no—
163C3×#127—51no—
164#946—101no—
165#940—52no—
166#939—102no—
167#938—101no—
168D4×Dic3—52no—
169C2×#213—52no—
170C2×D24C2×D511yescharacteristic
171#896—102no—
172#893—52no—
173#888—52no—
174C4×D12C2×D511yescharacteristic
175C4×D12C2×D511yescharacteristic
176C4×Dic6—51no—
177C3×#102—52no—
178C3×#102—52no—
179C3×C4×C8C2×D511yescharacteristic
180#832—52no—
181#821C2×D511yescharacteristic
182#821C2×D511yescharacteristic
183#818C2×D511yescharacteristic
184Dic3⋊C8—52no—
185C8×Dic3—52no—
186#809—52no—
187#807—52no—
188C4⋊(C3⋊C8)—51no—
189C2×C5×D4—31no—
190C2×C5×D4—31no—
191C22×C4×C5—61no—
192C22×C4×C5—61no—
193C2×C22⋊D5—62no—
194C2×C22⋊D5—62no—
195C22×Dic5—62no—
196#709—124no—
197C2×D20—21no—
198C2×D20—21no—
199C2×D20C22×D312yes—
200C2×C4×D5—62no—
201C2×Dic10—21no—
202C2×Dic10—31no—
203C2×Dic10—62no—
204C2×Dic10—124no—
205C5×D8—62no—
206C2×C5×C8C22×D311yescharacteristic
207C2×C5×C8C22×D311yescharacteristic
208C5×C4⋊C4—31no—
209C5×C4⋊C4—31no—
210C5×C22⋊C4—61no—
211C5×C22⋊C4—61no—
212C42×C5C22×D311yescharacteristic
213C22⋊Dic5—62no—
214#686—64no—
215#685—62no—
216C4⋊Dic5—21no—
217C4⋊Dic5—31no—
218C4⋊Dic5C22×D312yes—
219#683—32no—
220#683—62no—
221C4×Dic5—32no—
222C2×#168—32no—
223#550—151no—
224D4×Q8—151no—
225#486—51no—
226#486—152no—
227#474—152no—
228#474—151no—
229#459—152no—
230#459—151no—
231C8×Q8—151no—
232C4×D8—31no—
233C4×D8—152no—
234C22×C3×C5C22×D411yescharacteristic
235C2×C5×D3—22no—
236C2×C5×D3—41no—
237C2×C5×D3—41no—
238C2×C5×D3—41no—
239C2×C5×D3—41no—
240C2×C5×D3—41no—
241C2×C3×D5—42no—
242C2×C3×D5—42no—
243C2×C3×D5—42no—
244C3×C4×C5—21no—
245C3×C4×C5C2×D812yes—
246C3×C4×C5C2×#4111yescharacteristic
247C3×C4×C52−1+411yescharacteristic
248Dic15—22no—
249Dic15C2×D814yes—
250C3×Dic5—42no—
251C5×Dic3—41no—
252C5×Dic3—41no—
253C2×C3×Q8—101no—
254C2×C3×D4—52no—
255C2×C3×D4—101no—
256C2×C3×D4—101no—
257C2×#67—102no—
258C2×#67—102no—
259C22×Dic3—102no—
260D3×Q8—204no—
261#237—204no—
262C2×D12C22×D511yescharacteristic
263C2×D12C22×D511yescharacteristic
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—102no—
267C2×Dic6—51no—
268C2×Dic6—102no—
269C2×C3×C8C22×D511yescharacteristic
270C2×C3×C8C22×D511yescharacteristic
271C3×C4⋊C4—52no—
272C3×C4⋊C4—101no—
273C3×C42C22×D511yescharacteristic
274#217—102no—
275#213—104no—
276(C2×D3)⋊C4—21no—
277(C2×D3)⋊C4—21no—
278(C2×D3)⋊C4—102no—
279C4⋊Dic3—51no—
280C4⋊Dic3C22×D511yescharacteristic
281C4⋊Dic3C22×D511yescharacteristic
282Dic3⋊C4—52no—
283Dic3⋊C4—102no—
284C4×Dic3—52no—
285C2×C3⋊C8—52no—
286D24—22no—
287C23×C5—61no—
288C23×C5—61no—
289C22×D5—22no—
290C5×D4—32no—
291C5×D4—61no—
292C5×D4—61no—
293C5×D4—61no—
294C2×C4×C5—61no—
295C2×C4×C5—61no—
296C2×C4×C5—122no—
297C2×C4×C5—122no—
298C2×C4×C5D3×D411yescharacteristic
299C2×C4×C5D3×D411yescharacteristic
300C2×C4×C5C23×D311yescharacteristic
301C22⋊D5—124no—
302C22⋊D5—242no—
303C2×Dic5—22no—
304C2×Dic5—32no—
305C2×Dic5—32no—
306C2×Dic5—124no—
307D20—22no—
308D20—22no—
309D20—42no—
310D20—81no—
311C4×D5—124no—
312Dic10—34no—
313Dic10—42no—
314Dic10—124no—
315C5×C8—21no—
316C5×C8—21no—
317#168—62no—
318C2×#41—301no—
319C22×Q8—301no—
320C2×D8—31no—
321C2×D8—152no—
322C4⋊Q8—51no—
323C4⋊Q8—152no—
324#127—51no—
325#127—152no—
326C22⋊Q8—302no—
327C22⋊Q8—301no—
328#121—302no—
329#121—301no—
330C4×Q8—151no—
331C4×D4—31no—
332C4×D4—31no—
333C4×D4—152no—
334C4×D4—152no—
335#107—31no—
336#107—152no—
337C4⋊C8—152no—
338C4⋊C8—151no—
339#102—31no—
340#102—31no—
341#102—52no—
342#102—52no—
343#102—152no—
344#102—152no—
345C4×C8—152no—
346C4×C8D3×D511yescharacteristic
347C2×C3×C5#54811yescharacteristic
348C2×C3×C5C22×D811yescharacteristic
349C2×C3×C5#57711yescharacteristic
350C3×D5—82no—
351C5×D3—42no—
352C5×D3—81no—
353C23×C3—102no—
354C22×D3—21no—
355C22×D3—21no—
356C3×Q8—202no—
357C3×D4—102no—
358C3×D4—102no—
359C3×D4—202no—
360C3×D4—401no—
361C2×C3×C4—102no—
362C2×C3×C4D4×D511yescharacteristic
363C2×C3×C4D4×D511yescharacteristic
364C2×C3×C4C23×D511yescharacteristic
365#67—204no—
366#67—402no—
367C2×Dic3—21no—
368C2×Dic3—21no—
369C2×Dic3—52no—
370C2×Dic3—52no—
371C2×Dic3—204no—
372D12—21no—
373D12—21no—
374D12—21no—
375D12#70912yescomplemented
376C4×D3—42no—
377C4×D3—42no—
378C4×D3—204no—
379Dic6—54no—
380Dic6—204no—
381C3×C8—21no—
382C3×C8—21no—
383C3⋊C8—102no—
384C22×C5—62no—
385C22×C5—121no—
386C22×C5—121no—
387C22×C5—121no—
388C22×C5—121no—
389C22×C5—121no—
390C22×C5C2×D3×D411yescharacteristic
391C2×D5—42no—
392C2×D5—42no—
393C2×D5—42no—
394C4×C5—21no—
395C4×C5—121no—
396C4×C5—121no—
397C4×C5D3×D812yes—
398C4×C5D3×#4111yescharacteristic
399C4×C5#101011yescharacteristic
400Dic5—34no—
401Dic5—42no—
402Dic5—62no—
403#41—604no—
404C2×Q8—101no—
405C2×Q8—151no—
406C2×Q8—302no—
407C2×Q8—604no—
408C2×D4—31no—
409C2×D4—31no—
410C2×D4—52no—
411C2×D4—101no—
412C2×D4—101no—
413C2×D4—302no—
414C2×D4—302no—
415C22×C4—61no—
416C22×C4—61no—
417C22×C4—302no—
418C22×C4—302no—
419D8—62no—
420D8—304no—
421C2×C8—152no—
422C2×C8C2×D3×D511yescharacteristic
423C2×C8C2×D3×D511yescharacteristic
424C4⋊C4—31no—
425C4⋊C4—31no—
426C4⋊C4—52no—
427C4⋊C4—101no—
428C4⋊C4—152no—
429C4⋊C4—151no—
430C4⋊C4—302no—
431C22⋊C4—61no—
432C22⋊C4—61no—
433C22⋊C4—302no—
434C22⋊C4—302no—
435C42—152no—
436C42C2×D3×D511yescharacteristic
437C3×C5#335811yescharacteristic, complemented, Hall
438C22×C3—202no—
439C22×C3—202no—
440C22×C3—202no—
441C22×C3C2×D4×D511yescharacteristic
442C2×D3—22no—
443C2×D3—41no—
444C2×D3—41no—
445C2×D3—41no—
446C2×D3—41no—
447C2×D3—41no—
448C3×C4—21no—
449C3×C4—202no—
450C3×C4D5×D812yes—
451C3×C4C2×#70911yescharacteristic
452C3×C4#415011yescharacteristic
453Dic3—41no—
454Dic3—41no—
455Dic3—54no—
456Dic3—102no—
457C2×C5—122no—
458C2×C5—241no—
459C2×C5#567711yescharacteristic
460C2×C5C2×D3×D811yescharacteristic
461C2×C5#576211yescharacteristic
462D5—82no—
463C23—61no—
464C23—61no—
465C23—102no—
466Q8—154no—
467Q8—202no—
468Q8—604no—
469D4—32no—
470D4—61no—
471D4—61no—
472D4—61no—
473D4—102no—
474D4—102no—
475D4—202no—
476D4—401no—
477D4—604no—
478D4—1202no—
479C2×C4—61no—
480C2×C4—61no—
481C2×C4—102no—
482C2×C4—122no—
483C2×C4—122no—
484C2×C4—152no—
485C2×C4—152no—
486C2×C4—604no—
487C2×C4—604no—
488C2×C4#677711yescharacteristic
489C2×C4#677711yescharacteristic
490C2×C4C22×D3×D511yescharacteristic
491C8—21no—
492C8—21no—
493C8—302no—
494C2×C3—402no—
495C2×C3#6588611yescharacteristic
496C2×C3C2×D5×D811yescharacteristic
497C2×C3#6610411yescharacteristic
498D3—42no—
499D3—81no—
500C5#8158411yescharacteristic, complemented, Sylow
501C22—62no—
502C22—121no—
503C22—121no—
504C22—121no—
505C22—121no—
506C22—121no—
507C22—202no—
508C22—202no—
509C22—202no—
510C22C2×#677711yescharacteristic
511C4—21no—
512C4—121no—
513C4—121no—
514C4—154no—
515C4—202no—
516C4—302no—
517C4#9125612yes—
518C4#9200111yescharacteristic
519C4D3×#70911yescharacteristic
520C3#1061129811yescharacteristic, complemented, Sylow
521C2—122no—
522C2—241no—
523C2—402no—
524C2#1175255511yescharacteristic
525C2C2×#9125611yescharacteristic
526C2#1175398011yescharacteristic
subgroupG/H
centerC22C2×#6777
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. #11752558C2semidirect
2. #11752554C2semidirect
3. C8×Dic30C2semidirect
4. C4×C5×D24C2semidirect
5. C3×#64983C2semidirect
6. #11748011C2semidirect
7. #11748000C2semidirect
8. #11747803C2semidirect
9. #11747733C2semidirect
10. #11747033C2semidirect
11. #11746900C2semidirect
52. #64983D3semidirect
97. C4×D24D5semidirect
137. Dic30D8semidirect
143. C5×D12#41semidirect
375. D12#709semidirect
437. C3×C5#3358semidirect
500. C5#81584semidirect
520. C3#10611298semidirect

Maximal subgroups

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

subgroupindex
#117525582
#117525542
C8×Dic302
C4×C5×D242
C3×#649832
#117480112
#117480002
#117478032
#117477332
#117470332
#117469002
#106112983
#815845