Finite Group Databasebeta

← #14460116

Subgroups — #14460116

Order 1920.

796 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756322C211yesmaximal, characteristic, complemented
2#11756314C211yesmaximal, characteristic, complemented
3C3×C4×C5×D8C211yesmaximal, characteristic, complemented
4#11751259C212yesmaximal, complemented
5#11751120C211yesmaximal, characteristic, complemented
6#11751109C211yesmaximal, characteristic, complemented
7#11750989C212yesmaximal, complemented
8#11750879C212yesmaximal, complemented
9#11750873C212yesmaximal, complemented
10C8×D60C211yesmaximal, characteristic, complemented
11#11750782C211yesmaximal, characteristic, complemented
12#10611341—31nomaximal, Hall
13C2×#6819C2212yes—
14C2×C3×C5×D8C2211yescharacteristic
15C3×C4×C5×D4C2211yescharacteristic
16C3×C4×C5×D4C2211yescharacteristic
17#91827C2212yes—
18C2×#6716C2212yes—
19#91819—21no—
20#91819—21no—
21#91815—21no—
22C2×C4⋊Dic15—21no—
23C2×C8×D15C2212yes—
24#91786C2212yes—
25#91781C2212yes—
26#91775—22no—
27#91774—22no—
28C4×D60C2211yescharacteristic
29#91758C2211yescharacteristic
30#91758C2211yescharacteristic
31C3×C5×#107C2211yescharacteristic
32C3×C5×#102C2211yescharacteristic
33C3×C5×#102C2211yescharacteristic
34C3×C4×C5×C8C2211yescharacteristic
35#91116C2212yes—
36#91104C2212yes—
37#91100C2212yes—
38#91100C2212yes—
39#91094C2212yes—
40#91092C2212yes—
41C4⋊(C3⋊#168)C2211yescharacteristic
42#79610—51nomaximal, Hall
43#65897—31no—
44#65889—31no—
45C4×C5×D8D311yescharacteristic, complemented
46#65447—32no—
47#65308—31no—
48#65297—31no—
49#65177—32no—
50#65067—32no—
51#65061—32no—
52C8×D20—31no—
53#64970—31no—
54C2×C3×C5×D4C2311yescharacteristic
55C2×C3×C5×D4C2311yescharacteristic
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—21no—
58C2×#1220—22no—
59C2×#1220—22no—
60C22×Dic15—22no—
61#6819—24no—
62#6819—42no—
63C2×D60D411yescharacteristic
64C2×C4×D15C2312yes—
65C2×Dic30—21no—
66C2×Dic30C2312yes—
67C3×C5×D8—22no—
68C2×C3×C5×C8C2311yescharacteristic
69C2×C3×C5×C8C2311yescharacteristic
70C3×C5×C4⋊C4C2311yescharacteristic
71C3×C5×C4⋊C4C2311yescharacteristic
72C3×C5×C22⋊C4—21no—
73C3×C5×C22⋊C4—21no—
74C3×C42×C5C2311yescharacteristic
75#6719—22no—
76#6716—42no—
77#6714—22no—
78#6714—22no—
79#6714D412yes—
80C4⋊Dic15—21no—
81C4⋊Dic15—21no—
82C4⋊Dic15—21no—
83C4⋊Dic15—22no—
84C4⋊Dic15D411yescharacteristic
85C4⋊Dic15C2312yes—
86C4×Dic15—22no—
87C2×C3⋊#168C2312yes—
88C8×D15—42no—
89#5563—51no—
90#5555—51no—
91C3×C4×D8D511yescharacteristic, complemented
92#5158—52no—
93#5019—51no—
94#5008—51no—
95#4888—52no—
96#4778—52no—
97#4772—52no—
98C8×D12—51no—
99#4681—51no—
100C2×#711—32no—
101C2×C5×D8C2×D311yescharacteristic
102C4×C5×D4C2×D311yescharacteristic
103C4×C5×D4C2×D311yescharacteristic
104#4084—32no—
105C2×#687—32no—
106#4076—61no—
107#4076—61no—
108#4072—61no—
109C2×C4⋊Dic5—61no—
110C2×C8×D5—32no—
111#4043—32no—
112#4038—32no—
113#4032—62no—
114#4031—62no—
115C4×D20—31no—
116#4015—31no—
117#4015—31no—
118C5×#107C2×D311yescharacteristic
119C5×#102C2×D311yescharacteristic
120C5×#102C2×D311yescharacteristic
121C4×C5×C8C2×D311yescharacteristic
122#3964—32no—
123#3952—32no—
124#3948—32no—
125#3948—32no—
126#3942—32no—
127#3940—32no—
128C4⋊#168—31no—
129#3303—151noSylow
130C23×C3×C5—21no—
131C23×C3×C5—21no—
132C22×D15C2×D412yes—
133C3×C5×D4—21no—
134C3×C5×D4—21no—
135C3×C5×D4—21no—
136C3×C5×D4#4112yes—
137C2×C3×C4×C5—21no—
138C2×C3×C4×C5—21no—
139C2×C3×C4×C5—42no—
140C2×C3×C4×C5—42no—
141C2×C3×C4×C5C2×D411yescharacteristic
142C2×C3×C4×C5C2×D411yescharacteristic
143C2×C3×C4×C5C2411yescharacteristic
144#1220—44no—
145#1220—82no—
146C2×Dic15—22no—
147C2×Dic15—22no—
148C2×Dic15—44no—
149C2×Dic15C2×D412yes—
150D60—22no—
151C4×D15—22no—
152C4×D15—22no—
153Dic30—22no—
154Dic30—22no—
155Dic30—81no—
156C3×C5×C8—21no—
157C3×C5×C8—21no—
158C3⋊#168—22no—
159C2×#237—52no—
160C2×C3×D8C2×D511yescharacteristic
161C3×C4×D4C2×D511yescharacteristic
162C3×C4×D4C2×D511yescharacteristic
163#938—52no—
164C2×#214—52no—
165#930—101no—
166#930—101no—
167#926—101no—
168C2×C4⋊Dic3—101no—
169C2×D3×C8—52no—
170#897—52no—
171#892—52no—
172#886—102no—
173#885—102no—
174C4×D12—51no—
175#869—51no—
176#869—51no—
177C3×#107C2×D511yescharacteristic
178C3×#102C2×D511yescharacteristic
179C3×#102C2×D511yescharacteristic
180C3×C4×C8C2×D511yescharacteristic
181#832—52no—
182(C2×D3)⋊C8—52no—
183#816—52no—
184#816—52no—
185#810—52no—
186#808—52no—
187C4⋊(C3⋊C8)—51no—
188C2×C5×D4C22×D311yescharacteristic
189C2×C5×D4C22×D311yescharacteristic
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C2×C22⋊D5—62no—
193C2×C22⋊D5—62no—
194C22×Dic5—62no—
195#711—64no—
196#711—122no—
197C2×D20—31no—
198C2×C4×D5—32no—
199C2×Dic10—32no—
200C2×Dic10—61no—
201C5×D8—22no—
202C2×C5×C8C22×D311yescharacteristic
203C2×C5×C8C22×D311yescharacteristic
204C5×C4⋊C4C22×D311yescharacteristic
205C5×C4⋊C4C22×D311yescharacteristic
206C5×C22⋊C4—21no—
207C5×C22⋊C4—21no—
208C42×C5C22×D311yescharacteristic
209C22⋊Dic5—62no—
210#687—122no—
211#685—32no—
212#685—62no—
213#685—62no—
214C4⋊Dic5—31no—
215C4⋊Dic5—32no—
216C4⋊Dic5—62no—
217C4⋊Dic5—61no—
218C4⋊Dic5—61no—
219C4⋊Dic5—61no—
220C4×Dic5—62no—
221C2×#168—32no—
222C8×D5—122no—
223#555—151no—
224#547—151no—
225#487—151no—
226#485—152no—
227#476—151no—
228#465—152no—
229#461—151no—
230#449—152no—
231C4×D8D1511yescharacteristic, complemented
232C8×D4—151no—
233#416—152no—
234C22×C3×C5—22no—
235C22×C3×C5—41no—
236C22×C3×C5—41no—
237C22×C3×C5—41no—
238C22×C3×C5—41no—
239C22×C3×C5—41no—
240C22×C3×C5C22×D411yescharacteristic
241C2×D15—22no—
242C2×D15—22no—
243C2×D15—22no—
244C3×C4×C5—21no—
245C3×C4×C5—41no—
246C3×C4×C5—41no—
247C3×C4×C5#13512yes—
248C3×C4×C5C2×#4111yescharacteristic
249C3×C4×C5H(5,𝔽2)11yescharacteristic
250Dic15—22no—
251Dic15—42no—
252Dic15—42no—
253C2×C3×D4C22×D511yescharacteristic
254C2×C3×D4C22×D511yescharacteristic
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C2×#67—102no—
258C2×#67—102no—
259C22×Dic3—102no—
260#237—104no—
261#237—202no—
262C2×D12—51no—
263C2×C4×D3—52no—
264C2×Dic6—52no—
265C2×Dic6—101no—
266C3×D8—22no—
267C2×C3×C8C22×D511yescharacteristic
268C2×C3×C8C22×D511yescharacteristic
269C3×C4⋊C4C22×D511yescharacteristic
270C3×C4⋊C4C22×D511yescharacteristic
271C3×C22⋊C4—21no—
272C3×C22⋊C4—21no—
273C3×C42C22×D511yescharacteristic
274#217—102no—
275#214—202no—
276(C2×D3)⋊C4—52no—
277(C2×D3)⋊C4—102no—
278(C2×D3)⋊C4—102no—
279C4⋊Dic3—51no—
280C4⋊Dic3—52no—
281C4⋊Dic3—102no—
282C4⋊Dic3—101no—
283C4⋊Dic3—101no—
284C4⋊Dic3—101no—
285C4×Dic3—102no—
286C2×C3⋊C8—52no—
287D3×C8—202no—
288C23×C5—21no—
289C23×C5—21no—
290C22×D5—32no—
291C5×D4—21no—
292C5×D4—21no—
293C5×D4—21no—
294C5×D4#23512yes—
295C2×C4×C5—21no—
296C2×C4×C5—21no—
297C2×C4×C5—42no—
298C2×C4×C5—42no—
299C2×C4×C5D3×D411yescharacteristic
300C2×C4×C5D3×D411yescharacteristic
301C2×C4×C5C23×D311yescharacteristic
302C22⋊D5—124no—
303C22⋊D5—242no—
304C2×Dic5—32no—
305C2×Dic5—62no—
306C2×Dic5—62no—
307C2×Dic5—124no—
308D20—62no—
309C4×D5—62no—
310C4×D5—62no—
311Dic10—62no—
312Dic10—62no—
313Dic10—241no—
314C5×C8—21no—
315C5×C8—21no—
316#168—62no—
317C2×#41—152no—
318C2×SD16—152no—
319C2×D8C2×D1511yescharacteristic
320C22×C8—152no—
321C4⋊Q8—151no—
322C4⋊Q8—151no—
323#124—302no—
324#123—302no—
325C22⋊Q8—152no—
326#121—152no—
327#121—301no—
328#121—301no—
329C4×D4—151no—
330C4×D4C2×D1511yescharacteristic
331C4×D4C2×D1511yescharacteristic
332#117—152no—
333#117—301no—
334C2×C4⋊C4—301no—
335#107C2×D1511yescharacteristic
336#106—152no—
337C4⋊C8—151no—
338#103—152no—
339#103—152no—
340#103—152no—
341#102—152no—
342#102C2×D1511yescharacteristic
343#102C2×D1511yescharacteristic
344C22⋊C8—152no—
345C4×C8C2×D1511yescharacteristic
346C2×C3×C5—42no—
347C2×C3×C5—81no—
348C2×C3×C5#54611yescharacteristic
349C2×C3×C5C2×#13511yescharacteristic
350C2×C3×C5#57711yescharacteristic
351D15—42no—
352C23×C3—21no—
353C23×C3—21no—
354C22×D3—52no—
355C3×D4—21no—
356C3×D4—21no—
357C3×D4—21no—
358C3×D4#70912yes—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—42no—
362C2×C3×C4—42no—
363C2×C3×C4D4×D511yescharacteristic
364C2×C3×C4D4×D511yescharacteristic
365C2×C3×C4C23×D511yescharacteristic
366#67—204no—
367#67—402no—
368C2×Dic3—52no—
369C2×Dic3—102no—
370C2×Dic3—102no—
371C2×Dic3—204no—
372D12—102no—
373C4×D3—102no—
374C4×D3—102no—
375Dic6—102no—
376Dic6—102no—
377Dic6—401no—
378C3×C8—21no—
379C3×C8—21no—
380C3⋊C8—102no—
381C22×C5—22no—
382C22×C5—41no—
383C22×C5—41no—
384C22×C5—41no—
385C22×C5—41no—
386C22×C5—41no—
387C22×C5C2×D3×D411yescharacteristic
388C2×D5—62no—
389C2×D5—62no—
390C2×D5—62no—
391C4×C5—21no—
392C4×C5—41no—
393C4×C5—41no—
394C4×C5#91212yes—
395C4×C5C2×#23511yescharacteristic
396C4×C5#100911yescharacteristic
397Dic5—62no—
398Dic5—122no—
399Dic5—122no—
400#41—304no—
401#41—602no—
402C2×Q8—152no—
403C2×Q8—301no—
404C2×D4—151no—
405C2×D4—302no—
406C2×D4—302no—
407C2×D4C22×D1511yescharacteristic
408C2×D4C22×D1511yescharacteristic
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—152no—
412C22×C4—302no—
413SD16—602no—
414D8—22no—
415C2×C8—152no—
416C2×C8—602no—
417C2×C8C22×D1511yescharacteristic
418C2×C8C22×D1511yescharacteristic
419C4⋊C4—151no—
420C4⋊C4—152no—
421C4⋊C4—302no—
422C4⋊C4—301no—
423C4⋊C4—301no—
424C4⋊C4—301no—
425C4⋊C4C22×D1511yescharacteristic
426C4⋊C4C22×D1511yescharacteristic
427C22⋊C4—21no—
428C22⋊C4—21no—
429C22⋊C4—152no—
430C22⋊C4—302no—
431C22⋊C4—302no—
432C22⋊C4—302no—
433C42—302no—
434C42C22×D1511yescharacteristic
435C3×C5#330311yescharacteristic, complemented, Hall
436C22×C3—22no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—41no—
440C22×C3—41no—
441C22×C3—41no—
442C22×C3C2×D4×D511yescharacteristic
443C2×D3—102no—
444C2×D3—102no—
445C2×D3—102no—
446C3×C4—21no—
447C3×C4—41no—
448C3×C4—41no—
449C3×C4#405812yes—
450C3×C4C2×#70911yescharacteristic
451C3×C4#414911yescharacteristic
452Dic3—102no—
453Dic3—202no—
454Dic3—202no—
455C2×C5—42no—
456C2×C5—81no—
457C2×C5#555011yescharacteristic
458C2×C5C2×#91211yescharacteristic
459C2×C5#577011yescharacteristic
460D5—122no—
461C23—21no—
462C23—21no—
463C23—152no—
464Q8—302no—
465Q8—302no—
466Q8—1201no—
467D4—21no—
468D4—21no—
469D4—21no—
470D4—302no—
471D4—604no—
472D4—1202no—
473D4#681712yes—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—152no—
479C2×C4—302no—
480C2×C4—302no—
481C2×C4—302no—
482C2×C4—302no—
483C2×C4—604no—
484C2×C4D4×D1511yescharacteristic
485C2×C4D4×D1511yescharacteristic
486C2×C4C23×D1511yescharacteristic
487C8—21no—
488C8—21no—
489C8—302no—
490C2×C3—42no—
491C2×C3—81no—
492C2×C3#6588411yescharacteristic
493C2×C3C2×#405811yescharacteristic
494C2×C3#6610411yescharacteristic
495D3—202no—
496C5#7961011yescharacteristic, complemented, Sylow
497C22—22no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—302no—
504C22—302no—
505C22—302no—
506C22C2×D4×D1511yescharacteristic
507C4—21no—
508C4—41no—
509C4—41no—
510C4—302no—
511C4—602no—
512C4—602no—
513C4#9180112yes—
514C4C2×#681711yescharacteristic
515C4#9210011yescharacteristic
516C3#1061134111yescharacteristic, complemented, Sylow
517C2—42no—
518C2—81no—
519C2—602no—
520C2#1175630911yescharacteristic
521C2C2×#9180111yescharacteristic
522C2#1175652911yescharacteristic
subgroupG/H
centerC22C2×D4×D15
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C4×C5×D8C2
socleC22×C3×C5C22×D4
hypercenterC4×D8D15
hypocenterC3×C5#3303
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #11756322C2semidirect
2. #11756314C2semidirect
3. C3×C4×C5×D8C2semidirect
4. #11751259C2semidirect
5. #11751120C2semidirect
6. #11751109C2semidirect
7. #11750989C2semidirect
8. #11750879C2semidirect
9. #11750873C2semidirect
10. C8×D60C2semidirect
11. #11750782C2semidirect
45. C4×C5×D8D3semidirect
91. C3×C4×D8D5semidirect
231. C4×D8D15semidirect
435. C3×C5#3303semidirect
496. C5#79610semidirect
516. C3#10611341semidirect

Maximal subgroups

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

subgroupindex
#117563222
#117563142
C3×C4×C5×D82
#117512592
#117511202
#117511092
#117509892
#117508792
#117508732
C8×D602
#117507822
#106113413
#796105