Finite Group Databasebeta

← #14460067

Subgroups — #14460067

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752533C211yesmaximal, characteristic
2#11752486C211yesmaximal, characteristic, complemented
3C8×D60C211yesmaximal, characteristic, complemented
4C5×#4681C211yesmaximal, characteristic, complemented
5C3×C4×#677C211yesmaximal, characteristic, complemented
6#11748148C212yesmaximal, complemented
7#11748141C212yesmaximal, complemented
8#11747954C212yesmaximal, complemented
9#11747689C212yesmaximal, complemented
10#11747094C211yesmaximal, characteristic, complemented
11#11746886C211yesmaximal, characteristic, complemented
12#10613345—31nomaximal, Hall
13C2×#6766C2212yes—
14C2×C8×D15C2212yes—
15C4×D60C2211yescharacteristic
16C5×#869C2211yescharacteristic
17C5×#869C2211yescharacteristic
18C2×C3×#677C2211yescharacteristic
19C3×C4×D20C2211yescharacteristic
20C3×C4×Dic10C2211yescharacteristic
21#91450—21no—
22#91413—22no—
23D5×C4⋊Dic3—21no—
24#91390C2212yes—
25#91383C2212yes—
26#91375—21no—
27#91347C2212yes—
28#91337—22no—
29Dic5×Dic6—21no—
30C2×#6661C2212yes—
31C3×C4×C5×C8C2211yescharacteristic
32#91104C2212yes—
33C4⋊(C3⋊#168)C2211yescharacteristic
34C5×#816C2212yes—
35C5×#816C2212yes—
36C3×#3953C2211yescharacteristic
37C3×#3949C2211yescharacteristic
38C3×#3948C2211yescharacteristic
39#90989C2212yes—
40#90972C2212yes—
41#90964C2212yes—
42#79680—51nomaximal, Hall
43#66066—31no—
44#66060—31no—
45C5×#487—31no—
46#65379—31no—
47#65376—31no—
48#65104—32no—
49#65102—32no—
50#65099—32no—
51#65093—32no—
52C4×#677D311yescharacteristic, complemented
53C8×D20—31no—
54C2×D60D411yescharacteristic
55C2×C4×D15C2312yes—
56C2×C5×Dic6—21no—
57C2×C5×Dic6C2312yes—
58C2×C3×D20C2311yescharacteristic
59C2×C3×C4×D5—21no—
60C2×C3×Dic10C2311yescharacteristic
61C2×#1202—22no—
62C2×D5×Dic3—22no—
63#6766—24no—
64#6766—42no—
65C2×C3×C5×C8C2311yescharacteristic
66C2×C3×C5×C8C2311yescharacteristic
67C3×C42×C5C2311yescharacteristic
68#6714D412yes—
69C4⋊Dic15D411yescharacteristic
70C2×C3⋊#168C2312yes—
71C8×D15—42no—
72C5×C4⋊Dic3—21no—
73C5×C4⋊Dic3—21no—
74C5×C4⋊Dic3—21no—
75C5×C4⋊Dic3C2312yes—
76C3×#685—21no—
77C3×C4⋊Dic5C2311yescharacteristic
78C3×C4⋊Dic5C2311yescharacteristic
79C3×#683—21no—
80C3×C4×Dic5—21no—
81C3×#677—22no—
82Dic3⋊Dic5—22no—
83#6668—22no—
84#6667—22no—
85#6667—22no—
86#6667—22no—
87Dic3×Dic5—22no—
88#6661—42no—
89#5584—51no—
90#5555—51no—
91C3×C4×SD16—51no—
92#5173—52no—
93#5031—51no—
94#5007—51no—
95#4868—52no—
96#4813—52no—
97#4772—52no—
98C8×D12—51no—
99#4681D511yescharacteristic, complemented
100C2×#713—32no—
101C5×C4⋊Q8—31no—
102C5×C4⋊Q8—31no—
103#4093—61no—
104#4092—32no—
105Q8×Dic5—61no—
106C2×#689—32no—
107C2×#677C2×D311yescharacteristic
108C2×C8×D5—32no—
109#4044—62no—
110#4043—32no—
111#4041—61no—
112#4040—62no—
113#4038—32no—
114D5×C4⋊C4—61no—
115C4×D20—31no—
116C4×D20C2×D311yescharacteristic
117C4×Dic10C2×D311yescharacteristic
118C5×#103—32no—
119C5×#103—32no—
120C4×C5×C8C2×D311yescharacteristic
121#3967—32no—
122#3953C2×D311yescharacteristic
123#3952—32no—
124#3949C2×D311yescharacteristic
125#3948C2×D311yescharacteristic
126#3941—32no—
127#3939—32no—
128C4⋊#168—31no—
129#3302—151noSylow
130C22×D15C2×D412yes—
131C22×C3×D5—21no—
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2×D411yescharacteristic
134C2×C3×C4×C5C2411yescharacteristic
135C2×Dic15C2×D412yes—
136D60—22no—
137C4×D15—22no—
138C4×D15—22no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C5×Dic6—22no—
142C5×Dic6—22no—
143C5×Dic6—42no—
144C2×C3×Dic5—21no—
145C2×C3×Dic5—21no—
146C2×C3×Dic5—21no—
147C3×D20—21no—
148C3×D20#4112yes—
149C3×C4×D5—42no—
150C3×Dic10—21no—
151C3×Dic10—21no—
152#1202—44no—
153D5×Dic3—44no—
154C3×C5×C8—21no—
155C3×C5×C8—21no—
156C3⋊#168—22no—
157C2×#237—52no—
158C2×C3×SD16—51no—
159C3×C4×Q8—51no—
160C3×C4×D4—51no—
161#946—52no—
162C2×#216—52no—
163#930—101no—
164C2×C4⋊Dic3—101no—
165C2×D3×C8—52no—
166#898—102no—
167#897—52no—
168#892—52no—
169#886—102no—
170#875—101no—
171C4×D12—51no—
172#869C2×D511yescharacteristic
173#869C2×D511yescharacteristic
174C4×Dic6—101no—
175C3×#106—51no—
176C3×#103—51no—
177C3×#102—51no—
178C3×C4×C8C2×D511yescharacteristic
179#832—52no—
180(C2×D3)⋊C8—52no—
181#816C2×D512yes—
182#816C2×D512yes—
183#810—52no—
184#807—52no—
185C4⋊(C3⋊C8)—51no—
186C2×C5×Q8—32no—
187C2×C5×Q8—61no—
188#713—64no—
189#713—122no—
190C2×D20—31no—
191C2×D20—62no—
192C2×D20C22×D311yescharacteristic
193C2×C4×D5—21no—
194C2×C4×D5—32no—
195C2×C4×D5—62no—
196C2×Dic10C22×D311yescharacteristic
197C2×C5×C8C22×D311yescharacteristic
198C2×C5×C8C22×D311yescharacteristic
199C5×C4⋊C4—32no—
200C5×C4⋊C4—61no—
201C5×C4⋊C4—61no—
202C5×C4⋊C4—61no—
203C42×C5C22×D311yescharacteristic
204#689—122no—
205#685—21no—
206#685—32no—
207#685—62no—
208#685—62no—
209#685—62no—
210C4⋊Dic5—31no—
211C4⋊Dic5—62no—
212C4⋊Dic5C22×D311yescharacteristic
213C4⋊Dic5C22×D311yescharacteristic
214#683—21no—
215#683—62no—
216C4×Dic5—21no—
217C4×Dic5—62no—
218C2×#168—32no—
219#677—22no—
220C8×D5—122no—
221#556—151no—
222#547—151no—
223#487—31no—
224#485—152no—
225#474—151no—
226#467—152no—
227#462—151no—
228#452—152no—
229C4×SD16—51no—
230C8×D4—151no—
231#416—152no—
232C22×C3×C5C22×D411yescharacteristic
233C2×D15—22no—
234C2×D15—22no—
235C2×D15—22no—
236C2×C3×D5—22no—
237C2×C3×D5—41no—
238C2×C3×D5—41no—
239C3×C4×C5—21no—
240C3×C4×C5#13512yes—
241C3×C4×C5C2×#4111yescharacteristic
242C3×C4×C5H(5,𝔽2)11yescharacteristic
243Dic15—22no—
244C3×Dic5—41no—
245C3×Dic5—41no—
246C3×Dic5—41no—
247C5×Dic3—42no—
248C5×Dic3—42no—
249C2×C3×Q8—51no—
250C2×C3×D4—51no—
251C22×C3×C4—101no—
252C2×#67—102no—
253C22×Dic3—102no—
254#237—104no—
255#237—202no—
256C2×D12—51no—
257C2×C4×D3—52no—
258C2×Dic6—21no—
259C2×Dic6C22×D512yes—
260C3×SD16—102no—
261C2×C3×C8C22×D511yescharacteristic
262C2×C3×C8C22×D511yescharacteristic
263C3×C4⋊C4—51no—
264C3×C4⋊C4—51no—
265C3×C4⋊C4—101no—
266C3×C22⋊C4—101no—
267C3×C42—101no—
268C3×C42C22×D511yescharacteristic
269#216—202no—
270(C2×D3)⋊C4—52no—
271(C2×D3)⋊C4—102no—
272(C2×D3)⋊C4—102no—
273(C2×D3)⋊C4—102no—
274C4⋊Dic3—21no—
275C4⋊Dic3—21no—
276C4⋊Dic3—21no—
277C4⋊Dic3—51no—
278C4⋊Dic3—102no—
279C4⋊Dic3C22×D512yes—
280Dic3⋊C4—102no—
281C4×Dic3—102no—
282C2×C3⋊C8—52no—
283D3×C8—202no—
284C22×D5—21no—
285C22×D5—32no—
286C5×Q8—62no—
287C5×Q8—62no—
288C5×Q8—122no—
289C2×C4×C5—62no—
290C2×C4×C5—62no—
291C2×C4×C5D3×D411yescharacteristic
292C2×C4×C5D3×D411yescharacteristic
293C2×C4×C5C23×D311yescharacteristic
294C2×Dic5—21no—
295C2×Dic5—21no—
296C2×Dic5—21no—
297C2×Dic5—32no—
298D20—21no—
299D20—62no—
300D20—124no—
301D20#23512yes—
302C4×D5—42no—
303C4×D5—62no—
304C4×D5—62no—
305C4×D5—124no—
306Dic10—21no—
307Dic10—21no—
308C5×C8—21no—
309C5×C8—21no—
310#168—62no—
311C2×#41—152no—
312C2×Q16—152no—
313C2×SD16—51no—
314C22×C8—152no—
315C4⋊Q8—31no—
316C4⋊Q8—31no—
317#126—302no—
318#124—301no—
319#123—302no—
320C22⋊Q8—152no—
321C22⋊Q8—152no—
322#121—301no—
323C4×Q8—51no—
324C4×Q8—301no—
325C4×D4—51no—
326C4×D4—151no—
327#117—152no—
328C2×C4⋊C4—301no—
329#107—152no—
330#106—51no—
331C4⋊C8—151no—
332#103—32no—
333#103—32no—
334#103—51no—
335#103—152no—
336#102—51no—
337#102—152no—
338C22⋊C8—152no—
339C4×C8D3×D511yescharacteristic
340C2×C3×C5#54611yescharacteristic
341C2×C3×C5C2×#13511yescharacteristic
342C2×C3×C5#57811yescharacteristic
343D15—42no—
344C3×D5—42no—
345C23×C3—101no—
346C22×D3—52no—
347C3×Q8—101no—
348C3×Q8—101no—
349C3×D4—52no—
350C3×D4—101no—
351C2×C3×C4—101no—
352C2×C3×C4—101no—
353C2×C3×C4—101no—
354C2×C3×C4—202no—
355C2×C3×C4D4×D511yescharacteristic
356C2×C3×C4D4×D511yescharacteristic
357C2×C3×C4C23×D511yescharacteristic
358#67—204no—
359C2×Dic3—22no—
360C2×Dic3—22no—
361C2×Dic3—52no—
362C2×Dic3—204no—
363D12—102no—
364C4×D3—102no—
365C4×D3—102no—
366Dic6—22no—
367Dic6—22no—
368Dic6—42no—
369C3×C8—21no—
370C3×C8—21no—
371C3⋊C8—102no—
372C22×C5C2×D3×D411yescharacteristic
373C2×D5—22no—
374C2×D5—41no—
375C2×D5—41no—
376C2×D5—62no—
377C2×D5—62no—
378C2×D5—62no—
379C4×C5—21no—
380C4×C5—122no—
381C4×C5—122no—
382C4×C5#91612yes—
383C4×C5C2×#23511yescharacteristic
384C4×C5#100911yescharacteristic
385Dic5—41no—
386Dic5—41no—
387Dic5—41no—
388Dic5—62no—
389#41—304no—
390#41—602no—
391C2×Q8—32no—
392C2×Q8—51no—
393C2×Q8—61no—
394C2×D4—51no—
395C2×D4—151no—
396C2×D4—302no—
397C22×C4—101no—
398C22×C4—152no—
399C22×C4—302no—
400Q16—602no—
401SD16—102no—
402C2×C8—152no—
403C2×C8—602no—
404C2×C8C2×D3×D511yescharacteristic
405C2×C8C2×D3×D511yescharacteristic
406C4⋊C4—32no—
407C4⋊C4—51no—
408C4⋊C4—51no—
409C4⋊C4—61no—
410C4⋊C4—61no—
411C4⋊C4—61no—
412C4⋊C4—101no—
413C4⋊C4—151no—
414C4⋊C4—302no—
415C4⋊C4—302no—
416C22⋊C4—101no—
417C22⋊C4—152no—
418C22⋊C4—302no—
419C22⋊C4—302no—
420C22⋊C4—302no—
421C42—101no—
422C42—302no—
423C42C2×D3×D511yescharacteristic
424C3×C5#330211yescharacteristic, complemented, Hall
425C22×C3—102no—
426C22×C3—201no—
427C22×C3—201no—
428C22×C3C2×D4×D511yescharacteristic
429C2×D3—102no—
430C2×D3—102no—
431C2×D3—102no—
432C3×C4—21no—
433C3×C4—201no—
434C3×C4—201no—
435C3×C4—201no—
436C3×C4#406212yes—
437C3×C4D5×#4111yescharacteristic
438C3×C4#414911yescharacteristic
439Dic3—42no—
440Dic3—42no—
441Dic3—102no—
442C2×C5#555011yescharacteristic
443C2×C5C2×#91611yescharacteristic
444C2×C5#577111yescharacteristic
445D5—42no—
446D5—122no—
447C23—101no—
448C23—152no—
449Q8—62no—
450Q8—62no—
451Q8—101no—
452Q8—101no—
453Q8—122no—
454D4—52no—
455D4—101no—
456D4—302no—
457D4—604no—
458C2×C4—62no—
459C2×C4—62no—
460C2×C4—101no—
461C2×C4—101no—
462C2×C4—101no—
463C2×C4—152no—
464C2×C4—202no—
465C2×C4—302no—
466C2×C4—302no—
467C2×C4—604no—
468C2×C4#677711yescharacteristic
469C2×C4#677711yescharacteristic
470C2×C4C22×D3×D511yescharacteristic
471C8—21no—
472C8—21no—
473C8—302no—
474C2×C3—202no—
475C2×C3#6601011yescharacteristic
476C2×C3C2×#406211yescharacteristic
477C2×C3#6610011yescharacteristic
478D3—202no—
479C5#7968011yescharacteristic, complemented, Sylow
480C22—102no—
481C22—201no—
482C22—201no—
483C22—302no—
484C22—302no—
485C22—302no—
486C22C2×#677711yescharacteristic
487C4—21no—
488C4—122no—
489C4—122no—
490C4—201no—
491C4—201no—
492C4—201no—
493C4—302no—
494C4#9127612yes—
495C4D5×#23511yescharacteristic
496C4#9201911yescharacteristic
497C3#1061334511yescharacteristic, complemented, Sylow
498C2—202no—
499C2—602no—
500C2#1175274811yescharacteristic
501C2C2×#9127611yescharacteristic
502C2#1175400811yescharacteristic
subgroupG/H
centerC22C2×#6777
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radical#11752533C2
hypercenterC4×C8D3×D5
hypocenterC3×C5#3302
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
2. #11752486C2semidirect
3. C8×D60C2semidirect
4. C5×#4681C2semidirect
5. C3×C4×#677C2semidirect
6. #11748148C2semidirect
7. #11748141C2semidirect
8. #11747954C2semidirect
9. #11747689C2semidirect
10. #11747094C2semidirect
11. #11746886C2semidirect
52. C4×#677D3semidirect
99. #4681D5semidirect
424. C3×C5#3302semidirect
479. C5#79680semidirect
497. C3#10613345semidirect

Maximal subgroups

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

subgroupindex
#117525332
#117524862
C8×D602
C5×#46812
C3×C4×#6772
#117481482
#117481412
#117479542
#117476892
#117470942
#117468862
#106133453
#796805