Finite Group Databasebeta

← #14417656

Subgroups — #14417656

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91279C211yesmaximal, characteristic
2#11752525C212yesmaximal, complemented
3#11750790C211yesmaximal, characteristic, complemented
4C4×C5×D24C211yesmaximal, characteristic, complemented
5C3×C4×Dic20C211yesmaximal, characteristic, complemented
6#11748146C212yesmaximal, complemented
7#11747883C211yesmaximal, characteristic, complemented
8#11747810C211yesmaximal, characteristic, complemented
9#11747738C212yesmaximal, complemented
10#11747636C211yesmaximal, characteristic, complemented
11#11747050C212yesmaximal, complemented
12#10611320—31nomaximal, Hall
13C2×#6768C2212yes—
14C2×#6705C2211yescharacteristic
15C2×C8×D15C2211yescharacteristic
16#91761C2211yescharacteristic
17C2×C5×D24C2211yescharacteristic
18C4×C5×D12C2212yes—
19C2×C3×Dic20C2211yescharacteristic
20C3×C4×Dic10C2212yes—
21#91446—22no—
22#91437C2212yes—
23#91435C2212yes—
24#91405—22no—
25D3×#683—22no—
26#91398—22no—
27#91331C2212yes—
28C2×#6656C2212yes—
29#91279C418yescomplemented
30C3×C4×C5×C8C2211yescharacteristic
31#91099C2211yescharacteristic
32C8×Dic15C2211yescharacteristic
33#91087C2211yescharacteristic
34C5×#821C2212yes—
35C5×#818C2211yescharacteristic
36C3×#3950C2211yescharacteristic
37C3×#3948C2212yes—
38#90989C2212yes—
39#90970C2212yes—
40#90966C2212yes—
41#79721—51nomaximal, Hall
42C2×#4058—31no—
43#65880—32no—
44C4×C5×D8—31no—
45D8×Dic5—31no—
46#65307—32no—
47D5×#107—31no—
48#65162—31no—
49#65060—32no—
50#65046—32no—
51C4×Dic20D311yescharacteristic, complemented
52#64978—31no—
53C2×C4×D15C2311yescharacteristic
54C2×C5×D12C2312yes—
55C2×C4×C5×D3—22no—
56C2×C3×Dic10C2312yes—
57C2×#1203—22no—
58C2×#1200—22no—
59C2×D3×Dic5—22no—
60C2×D3×Dic5—22no—
61#6768—24no—
62#6768C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C2×C3×C5×C8C2311yescharacteristic
65C3×C42×C5C2311yescharacteristic
66#6714D411yescharacteristic
67#6714D411yescharacteristic
68#6712D411yescharacteristic
69#6712D411yescharacteristic
70C4×Dic15C2311yescharacteristic
71C2×C3⋊#168C2311yescharacteristic
72C2×C3⋊#168C2311yescharacteristic
73#6705—22no—
74C8×D15C2×C414yescomplemented
75C5×(C2×D3)⋊C4—22no—
76C5×C4⋊Dic3C2312yes—
77C5×D24C2×C414yescomplemented
78C3×C4⋊Dic5C2312yes—
79C3×#683—22no—
80C3×C4×Dic5—22no—
81C3×Dic20C2×C414yescomplemented
82#6669—22no—
83#6668—22no—
84(C2×D3)⋊Dic5—22no—
85Dic3×Dic5—22no—
86#6656C2×C418yescomplemented
87C2×#919—51no—
88#5574—52no—
89C3×C4×Q16—51no—
90Dic3×Q16—51no—
91#5026—52no—
92D3×#107—51no—
93#4872—51no—
94#4817—52no—
95#4803—52no—
96C4×D24D511yescharacteristic, complemented
97#4689—51no—
98C2×#711—32no—
99C2×C5×D8—31no—
100C4×C5×D4—32no—
101D4×Dic5—32no—
102C2×#687—32no—
103C4×C22⋊D5—62no—
104C2×#683—62no—
105#4058—38no—
106C2×Dic20C2×D311yescharacteristic
107C2×#676—31no—
108C2×C8×D5—31no—
109D5×C4⋊C4—32no—
110#4033—32no—
111#4027—62no—
112#4023—62no—
113#4018—31no—
114C4×Dic10C2×D312yes—
115C5×#107—31no—
116C5×#102—32no—
117C4×C5×C8C2×D311yescharacteristic
118#3964—32no—
119#3950C2×D311yescharacteristic
120#3948C2×D312yes—
121#3947—31no—
122C8×Dic5—31no—
123#3942—32no—
124#3939—32no—
125#3935—31no—
126#2951—151noSylow
127C22×D15C2×D411yescharacteristic
128C22×C5×D3—22no—
129C2×C3×C4×C5C2×D411yescharacteristic
130C2×C3×C4×C5C2×D411yescharacteristic
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15C2×D411yescharacteristic
133C2×Dic15C2×D411yescharacteristic
134C2×Dic15C2×D411yescharacteristic
135C4×D15C22×C412yes—
136C4×D15#4112yes—
137C2×C5×Dic3—22no—
138C5×D12—22no—
139C5×D12C22×C414yes—
140C4×C5×D3—82no—
141C2×C3×Dic5—22no—
142C2×C3×Dic5—22no—
143C3×Dic10—22no—
144C3×Dic10C22×C414yes—
145#1203—28no—
146#1200—82no—
147D3×Dic5—28no—
148D3×Dic5—82no—
149C3×C5×C8—21no—
150C3×C5×C8C22×C412yes—
151C3⋊#168—21no—
152C3⋊#168C22×C412yes—
153C2×#239—52no—
154C2×C3×Q16—51no—
155C3×C4×Q8—52no—
156Q8×Dic3—52no—
157C2×#215—52no—
158#919—58no—
159C2×D24C2×D511yescharacteristic
160C2×ΓL(1,𝔽25)—51no—
161C2×D3×C8—51no—
162#893—52no—
163#893—102no—
164D3×C4⋊C4—52no—
165D3×C4⋊C4—102no—
166C4×D12—102no—
167C4×D12C2×D512yes—
168#872—51no—
169#872—102no—
170C3×#107—51no—
171C3×#103—52no—
172C3×C4×C8C2×D511yescharacteristic
173#835—52no—
174#821C2×D512yes—
175#818C2×D511yescharacteristic
176#815—51no—
177C8×Dic3—51no—
178#809—52no—
179#807—52no—
180#803—51no—
181C2×C5×D4—32no—
182C22×C4×C5—62no—
183C2×C22⋊D5—62no—
184C22×Dic5—62no—
185C22×Dic5—62no—
186#711—38no—
187#711—64no—
188C2×C4×D5—31no—
189C2×C4×D5—62no—
190C2×Dic10C22×D312yes—
191C5×D8—34no—
192C2×C5×C8C22×D311yescharacteristic
193C2×C5×C8C22×D311yescharacteristic
194C5×C4⋊C4—32no—
195C5×C22⋊C4—62no—
196C42×C5C22×D311yescharacteristic
197C22⋊Dic5—62no—
198#687—38no—
199#685—31no—
200#685—31no—
201C4⋊Dic5C22×D312yes—
202#683—22no—
203#683—31no—
204#683—31no—
205#683—62no—
206#683—62no—
207C4×Dic5—22no—
208C4×Dic5—31no—
209C4×Dic5—62no—
210C2×#168—31no—
211C2×#168—31no—
212Dic20C4×D314yescomplemented
213#676—62no—
214C8×D5—34no—
215C2×#135—151no—
216#520—152no—
217#440—152no—
218#440—152no—
219C4×Q16—51no—
220C4×Q16—151no—
221C4×D8—31no—
222C4×D8—151no—
223C2×#107—151no—
224#417—152no—
225#405—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×D15—21no—
228C2×D15—21no—
229C2×D15C4×D412yes—
230C2×C5×D3—24no—
231C2×C5×D3—42no—
232C2×C5×D3—42no—
233C3×C4×C5—21no—
234C3×C4×C5—21no—
235C3×C4×C5C23×C411yescharacteristic
236C3×C4×C5C2×#4111yescharacteristic
237Dic15—21no—
238Dic15—21no—
239Dic15C4×D412yes—
240C3×Dic5—24no—
241C3×Dic5—42no—
242C5×Dic3—42no—
243C2×C3×Q8—52no—
244#239—58no—
245#239—104no—
246C2×D12—102no—
247C2×D12C22×D512yes—
248C2×C4×D3—22no—
249C2×C4×D3—51no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×C4×D3—102no—
253C3×Q16—54no—
254C2×C3×C8C22×D511yescharacteristic
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—52no—
257C3×C4⋊C4—102no—
258C3×C42—102no—
259C3×C42C22×D511yescharacteristic
260#215—58no—
261(C2×D3)⋊C4—22no—
262(C2×D3)⋊C4—51no—
263(C2×D3)⋊C4—51no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—102no—
266C4⋊Dic3C22×D512yes—
267Dic3⋊C4—51no—
268Dic3⋊C4—51no—
269Dic3⋊C4—102no—
270C4×Dic3—51no—
271C4×Dic3—102no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8—51no—
274D24C4×D514yescomplemented
275ΓL(1,𝔽25)—102no—
276D3×C8—54no—
277C23×C5—62no—
278C22×D5—31no—
279C5×D4—34no—
280C5×D4—62no—
281C2×C4×C5—62no—
282C2×C4×C5—242no—
283C2×C4×C5D3×D411yescharacteristic
284C2×C4×C5D3×D411yescharacteristic
285C2×C4×C5C23×D311yescharacteristic
286C22⋊D5—68no—
287C2×Dic5—22no—
288C2×Dic5—22no—
289C2×Dic5—31no—
290C2×Dic5—31no—
291C2×Dic5—31no—
292C2×Dic5—68no—
293C2×Dic5—242no—
294C4×D5—32no—
295C4×D5—32no—
296C4×D5—242no—
297Dic10—22no—
298Dic10C2×C4×D314yes—
299C5×C8—21no—
300C5×C8C2×C4×D312yes—
301#168—32no—
302#168—61no—
303C2×#41—152no—
304#135—158no—
305C2×Q16—51no—
306C2×SD16—152no—
307C2×D8—31no—
308C2×M16—151no—
309C22×C8—151no—
310C4×Q8—52no—
311C4×Q8—152no—
312C4×D4—32no—
313C4×D4—152no—
314C4×D4—302no—
315C4×D4—302no—
316#117—151no—
317#117—302no—
318C2×C4⋊C4—152no—
319C2×C4⋊C4—302no—
320#107—31no—
321#107—51no—
322#107—152no—
323#103—52no—
324#103—152no—
325#102—32no—
326#102—152no—
327#97—151no—
328#97—151no—
329C4×C8—151no—
330C4×C8D3×D511yescharacteristic
331C2×C3×C5C2×C4×D411yescharacteristic
332C2×C3×C5#57611yescharacteristic
333C2×C3×C5#57811yescharacteristic
334D15—22no—
335C5×D3—44no—
336C22×D3—22no—
337C22×D3—51no—
338C3×Q8—54no—
339C3×Q8—102no—
340C2×C3×C4—102no—
341C2×C3×C4—102no—
342C2×C3×C4D4×D511yescharacteristic
343C2×C3×C4D4×D511yescharacteristic
344C2×C3×C4C23×D511yescharacteristic
345C2×Dic3—22no—
346C2×Dic3—51no—
347C2×Dic3—51no—
348C2×Dic3—51no—
349D12—22no—
350D12—108no—
351D12C2×C4×D514yes—
352C4×D3—52no—
353C4×D3—52no—
354C4×D3—82no—
355C4×D3—108no—
356C4×D3—402no—
357C4×D3—402no—
358C3×C8—21no—
359C3×C8C2×C4×D512yes—
360C3⋊C8—52no—
361C3⋊C8—101no—
362C22×C5—64no—
363C22×C5—122no—
364C22×C5—122no—
365C22×C5C2×D3×D411yescharacteristic
366C2×D5—32no—
367C2×D5—61no—
368C2×D5—61no—
369C4×C5—21no—
370C4×C5—21no—
371C4×C5—122no—
372C4×C5C22×C4×D311yescharacteristic
373C4×C5D3×#4111yescharacteristic
374Dic5—24no—
375Dic5—32no—
376Dic5—42no—
377Dic5—61no—
378Dic5—61no—
379#41—158no—
380#41—304no—
381C2×Q8—52no—
382C2×D4—32no—
383C2×D4—302no—
384C22×C4—62no—
385C22×C4—151no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389Q16—54no—
390SD16—158no—
391D8—34no—
392M16—302no—
393C2×C8—151no—
394C2×C8—154no—
395C2×C8—151no—
396C2×C8C2×D3×D511yescharacteristic
397C2×C8C2×D3×D511yescharacteristic
398C4⋊C4—32no—
399C4⋊C4—52no—
400C4⋊C4—102no—
401C4⋊C4—151no—
402C4⋊C4—151no—
403C4⋊C4—302no—
404C4⋊C4—302no—
405C22⋊C4—62no—
406C22⋊C4—151no—
407C22⋊C4—151no—
408C22⋊C4—302no—
409C42—102no—
410C42—151no—
411C42—302no—
412C42C2×D3×D511yescharacteristic
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3C2×D4×D511yescharacteristic
415C2×D3—24no—
416C2×D3—42no—
417C2×D3—42no—
418C2×D3—52no—
419C2×D3—101no—
420C2×D3—101no—
421C3×C4—21no—
422C3×C4—21no—
423C3×C4—104no—
424C3×C4—202no—
425C3×C4C22×C4×D511yescharacteristic
426C3×C4D5×#4111yescharacteristic
427Dic3—42no—
428Dic3—52no—
429Dic3—101no—
430Dic3—101no—
431C2×C5—124no—
432C2×C5C4×D3×D411yescharacteristic
433C2×C5#576611yescharacteristic
434C2×C5#576911yescharacteristic
435D5—62no—
436C23—62no—
437C23—151no—
438Q8—54no—
439Q8—102no—
440D4—34no—
441D4—62no—
442D4—308no—
443C2×C4—62no—
444C2×C4—102no—
445C2×C4—102no—
446C2×C4—151no—
447C2×C4—152no—
448C2×C4—152no—
449C2×C4—151no—
450C2×C4—151no—
451C2×C4—242no—
452C2×C4—308no—
453C2×C4—1202no—
454C2×C4—1202no—
455C2×C4#677711yescharacteristic
456C2×C4#677711yescharacteristic
457C2×C4C22×D3×D511yescharacteristic
458C8—21no—
459C8—152no—
460C8—301no—
461C8C4×D3×D512yes—
462C2×C3C4×D4×D511yescharacteristic
463C2×C3#6609111yescharacteristic
464C2×C3#6610511yescharacteristic
465D3—44no—
466D3—102no—
467C5#7972111yescharacteristic, complemented, Sylow
468C22—64no—
469C22—122no—
470C22—122no—
471C22—152no—
472C22—301no—
473C22—301no—
474C22C2×#677711yescharacteristic
475C4—21no—
476C4—21no—
477C4—104no—
478C4—122no—
479C4—152no—
480C4—202no—
481C4—301no—
482C4—301no—
483C4C2×C4×D3×D511yescharacteristic
484C4#9201611yescharacteristic
485C3#1061132011yescharacteristic, complemented, Sylow
486C2—124no—
487C2—302no—
488C2C4×#677711yescharacteristic
489C2#1175398311yescharacteristic
490C2#1175401111yescharacteristic
subgroupG/H
centerC22C2×#6777
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×C8C22
socleC22×C3×C5C22×D4
prime radicalC2×#91279C2
cosocleC2×C3×C4×C5C24
hypercenterC4×C8D3×D5
hypocenterC3×C5#2951
LCSG ▷ 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. #11752525C2semidirect
3. #11750790C2semidirect
4. C4×C5×D24C2semidirect
5. C3×C4×Dic20C2semidirect
6. #11748146C2semidirect
7. #11747883C2semidirect
8. #11747810C2semidirect
9. #11747738C2semidirect
10. #11747636C2semidirect
11. #11747050C2semidirect
29. #91279C4semidirect
51. C4×Dic20D3semidirect
62. #6768C2×C4semidirect
74. C8×D15C2×C4semidirect
77. C5×D24C2×C4semidirect
81. C3×Dic20C2×C4semidirect
86. #6656C2×C4semidirect
96. C4×D24D5semidirect
212. Dic20C4×D3semidirect
274. D24C4×D5semidirect
413. C3×C5#2951semidirect
467. C5#79721semidirect
485. C3#10611320semidirect

Maximal subgroups

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

subgroupindex
C2×#912792
#117525252
#117507902
C4×C5×D242
C3×C4×Dic202
#117481462
#117478832
#117478102
#117477382
#117476362
#117470502
#106113203
#797215