Finite Group Databasebeta

← #14417711

Subgroups — #14417711

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×C5×#919C211yesmaximal, characteristic
2#11755220C212yesmaximal, complemented
3Q16×Dic15C211yesmaximal, characteristic, complemented
4C3×Q16×Dic5C211yesmaximal, characteristic, complemented
5#11749242C212yesmaximal, complemented
6#11749223C212yesmaximal, complemented
7#11749201C212yesmaximal, complemented
8#11747810C211yesmaximal, characteristic, complemented
9Dic5×D24C211yesmaximal, characteristic, complemented
10#11747653C211yesmaximal, characteristic, complemented
11D3×#3950C211yesmaximal, characteristic, complemented
12#10615629—31nomaximal, Hall
13C2×C5×#239C2212yes—
14C2×C3×C5×Q16C2211yescharacteristic
15Q8×Dic15C2212yes—
16C2×C5×#215C2212yes—
17C5×#919C418yescomplemented
18C2×C5×D24C2211yescharacteristic
19C2×C5×D3×C8C2211yescharacteristic
20C3×Q8×Dic5C2212yes—
21#91435—22no—
22#91435C2212yes—
23D3×C4⋊Dic5—22no—
24D3×C4⋊Dic5C2212yes—
25Dic5×D12—22no—
26Dic5×D12C2212yes—
27#91371—22no—
28#91371C2211yescharacteristic
29C2×#6650C2211yescharacteristic
30#91119C2212yes—
31#91102C2211yescharacteristic
32C8×Dic15C2211yescharacteristic
33C3×#3967C2212yes—
34C3×#3950C2211yescharacteristic
35C3×C8×Dic5C2211yescharacteristic
36#90990C2212yes—
37#90967C2212yes—
38#90966C2212yes—
39#90954C2211yescharacteristic
40#90952C2211yescharacteristic
41#79721—51nomaximal, Hall
42C2×C5×#135—31no—
43#66161—32no—
44#65521—32no—
45Q16×Dic5—31no—
46Q16×Dic5D311yescharacteristic, complemented
47#65453—32no—
48#65453—32no—
49D8×Dic5—31no—
50D8×Dic5—31no—
51C2×#3950—31no—
52#65390—31no—
53C2×C3×C5×Q8C2312yes—
54C5×#239—24no—
55C5×#239C2×C418yescomplemented
56C2×C5×D12—22no—
57C2×C5×D12C2312yes—
58C2×C4×C5×D3—22no—
59C2×C4×C5×D3C2311yescharacteristic
60C2×D3×Dic5—22no—
61C2×D3×Dic5—22no—
62C2×D3×Dic5—22no—
63C3×C5×Q16C2×C414yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65C4⋊Dic15—22no—
66C4⋊Dic15C2312yes—
67C4×Dic15—22no—
68C4×Dic15C2311yescharacteristic
69C2×C3⋊#168C2311yescharacteristic
70C5×#215C2×C418yescomplemented
71C2×C5×C3⋊C8C2311yescharacteristic
72C5×D24C2×C414yescomplemented
73C5×D3×C8C2×C414yescomplemented
74C3×C4⋊Dic5—22no—
75C3×C4⋊Dic5C2312yes—
76C3×C4×Dic5—22no—
77C3×C4×Dic5C2311yescharacteristic
78C2×C3×#168C2311yescharacteristic
79Dic3⋊Dic5—22no—
80Dic3⋊Dic5D411yescharacteristic
81Dic3⋊Dic5D411yescharacteristic
82(C2×D3)⋊Dic5—22no—
83(C2×D3)⋊Dic5—22no—
84(C2×D3)⋊Dic5D411yescharacteristic
85(C2×D3)⋊Dic5D411yescharacteristic
86#6650—22no—
87C2×#919D511yescharacteristic
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×D24—51no—
97#4689—51no—
98C2×C5×#41—32no—
99C5×#135—38no—
100C2×C5×Q16C2×D311yescharacteristic
101C2×C5×SD16—32no—
102C2×C5×D8—31no—
103C22×C5×C8—31no—
104Q8×Dic5—32no—
105Q8×Dic5C2×D312yes—
106D4×Dic5—32no—
107D4×Dic5—32no—
108D4×Dic5—62no—
109D4×Dic5—62no—
110#4072—31no—
111#4072—62no—
112C2×C4⋊Dic5—32no—
113C2×C4⋊Dic5—62no—
114C2×#681—31no—
115#3967—32no—
116#3967C2×D312yes—
117#3964—32no—
118#3964—32no—
119#3950—31no—
120#3950—32no—
121#3950C2×D311yescharacteristic
122#3947—31no—
123#3947—31no—
124C8×Dic5—31no—
125C8×Dic5C2×D311yescharacteristic
126#2951—151noSylow
127C22×C5×D3—22no—
128C22×C5×D3C2×D411yescharacteristic
129C3×C5×Q8—22no—
130C3×C5×Q8C22×C414yes—
131C2×C3×C4×C5—22no—
132C2×C3×C4×C5C2411yescharacteristic
133C2×Dic15—22no—
134C2×Dic15C2×D411yescharacteristic
135C2×Dic15C2×D411yescharacteristic
136C2×C5×Dic3C2×D411yescharacteristic
137C5×D12—28no—
138C5×D12—22no—
139C5×D12C22×C414yes—
140C4×C5×D3—28no—
141C4×C5×D3C22×C412yes—
142C4×C5×D3#4112yes—
143C2×C3×Dic5—22no—
144C2×C3×Dic5C2×D411yescharacteristic
145C2×C3×Dic5C2×D411yescharacteristic
146D3×Dic5—82no—
147D3×Dic5—82no—
148D3×Dic5—82no—
149C3×C5×C8C22×C412yes—
150C3⋊#168—21no—
151C3×#168—21no—
152C5×C3⋊C8C22×C412yes—
153C2×#239C2×D512yes—
154C2×C3×Q16C2×D511yescharacteristic
155C3×C4×Q8—52no—
156Q8×Dic3—52no—
157C2×#215C2×D512yes—
158#919Dic518yescomplemented
159C2×D24C2×D511yescharacteristic
160C2×ΓL(1,𝔽25)—51no—
161C2×D3×C8C2×D511yescharacteristic
162#893—52no—
163#893—102no—
164D3×C4⋊C4—52no—
165D3×C4⋊C4—102no—
166C4×D12—52no—
167C4×D12—102no—
168#872—51no—
169#872—102no—
170C3×#107—51no—
171C3×#103—52no—
172C3×C4×C8—51no—
173#835—52no—
174#821—52no—
175#818—51no—
176#815—51no—
177C8×Dic3—51no—
178#809—52no—
179#807—52no—
180#803—51no—
181C5×#41—38no—
182C5×#41—64no—
183C2×C5×Q8C22×D312yes—
184C2×C5×D4—32no—
185C2×C5×D4—62no—
186C22×C4×C5—31no—
187C22×C4×C5—62no—
188C22×Dic5—62no—
189C22×Dic5—62no—
190C22×Dic5—62no—
191C5×Q16C4×D314yescomplemented
192C5×SD16—38no—
193C5×D8—34no—
194C2×C5×C8—31no—
195C2×C5×C8—34no—
196C2×C5×C8C22×D311yescharacteristic
197C22⋊Dic5—31no—
198C22⋊Dic5—31no—
199C22⋊Dic5—62no—
200C22⋊Dic5—62no—
201C4⋊Dic5—22no—
202C4⋊Dic5—31no—
203C4⋊Dic5—31no—
204C4⋊Dic5—32no—
205C4⋊Dic5—62no—
206C4⋊Dic5—62no—
207C4⋊Dic5C22×D312yes—
208C4×Dic5—22no—
209C4×Dic5—31no—
210C4×Dic5—62no—
211C4×Dic5C22×D311yescharacteristic
212#681—62no—
213C2×#168—31no—
214C2×#168C22×D311yescharacteristic
215C2×#135—31no—
216#520—152no—
217#440—152no—
218#440—152no—
219C4×Q16—51no—
220C4×Q16—151no—
221C4×D8—151no—
222C4×D8—151no—
223C2×#107—151no—
224#417—152no—
225#405—151no—
226C22×C3×C5C22×D411yescharacteristic
227C2×C5×D3—21no—
228C2×C5×D3—21no—
229C2×C5×D3—24no—
230C2×C5×D3—42no—
231C2×C5×D3—42no—
232C2×C5×D3C4×D412yes—
233C3×C4×C5—24no—
234C3×C4×C5C23×C411yescharacteristic
235C3×C4×C5C2×#4111yescharacteristic
236Dic15—21no—
237Dic15—21no—
238Dic15—42no—
239C3×Dic5—21no—
240C3×Dic5—21no—
241C3×Dic5—42no—
242C5×Dic3C4×D412yes—
243C2×C3×Q8C22×D512yes—
244#239—24no—
245#239C2×Dic518yescomplemented
246C2×D12—22no—
247C2×D12C22×D512yes—
248C2×C4×D3—22no—
249C2×C4×D3—102no—
250C2×C4×D3—102no—
251C2×C4×D3—102no—
252C2×C4×D3C22×D511yescharacteristic
253C3×Q16C2×Dic514yescomplemented
254C2×C3×C8—51no—
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—52no—
257C3×C4⋊C4—102no—
258C3×C42—51no—
259C3×C42—102no—
260#215C2×Dic518yescomplemented
261(C2×D3)⋊C4—51no—
262(C2×D3)⋊C4—51no—
263(C2×D3)⋊C4—102no—
264(C2×D3)⋊C4—102no—
265C4⋊Dic3—52no—
266C4⋊Dic3—102no—
267Dic3⋊C4—51no—
268Dic3⋊C4—51no—
269Dic3⋊C4—102no—
270C4×Dic3—51no—
271C4×Dic3—102no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8C22×D511yescharacteristic
274D24C2×Dic514yescomplemented
275ΓL(1,𝔽25)—102no—
276D3×C8C2×Dic514yescomplemented
277C23×C5—31no—
278C23×C5—62no—
279C5×Q8—22no—
280C5×Q8C2×C4×D314yes—
281C5×D4—34no—
282C5×D4—68no—
283C5×D4—62no—
284C2×C4×C5—22no—
285C2×C4×C5—31no—
286C2×C4×C5—32no—
287C2×C4×C5—32no—
288C2×C4×C5—68no—
289C2×C4×C5C23×D311yescharacteristic
290C2×Dic5—22no—
291C2×Dic5—31no—
292C2×Dic5—31no—
293C2×Dic5—62no—
294C2×Dic5—242no—
295C2×Dic5—242no—
296C2×Dic5—242no—
297C2×Dic5D3×D411yescharacteristic
298C2×Dic5D3×D411yescharacteristic
299C5×C8—32no—
300C5×C8C2×C4×D312yes—
301#168—21no—
302#168—61no—
303C2×#41—32no—
304#135—38no—
305C2×Q16D3×D511yescharacteristic
306C2×SD16—32no—
307C2×D8—31no—
308C2×M16—151no—
309C22×C8—31no—
310C4×Q8—52no—
311C4×Q8—152no—
312C4×D4—152no—
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—51no—
321#107—152no—
322#107—151no—
323#103—52no—
324#103—152no—
325#102—152no—
326#102—152no—
327#97—151no—
328#97—151no—
329C4×C8—51no—
330C4×C8—151no—
331C2×C3×C5C2×C4×D411yescharacteristic
332C2×C3×C5#57611yescharacteristic
333C2×C3×C5#57811yescharacteristic
334C5×D3—22no—
335C5×D3—44no—
336C22×D3—22no—
337C22×D3D4×D511yescharacteristic
338C3×Q8—22no—
339C3×Q8C22×Dic514yes—
340C2×C3×C4—22no—
341C2×C3×C4—51no—
342C2×C3×C4—51no—
343C2×C3×C4—102no—
344C2×C3×C4C23×D511yescharacteristic
345C2×Dic3—51no—
346C2×Dic3—51no—
347C2×Dic3—102no—
348C2×Dic3D4×D511yescharacteristic
349D12—28no—
350D12—22no—
351D12C22×Dic514yes—
352C4×D3—28no—
353C4×D3—402no—
354C4×D3—402no—
355C4×D3—402no—
356C4×D3#71112yes—
357C4×D3C22×Dic512yes—
358C3×C8—101no—
359C3×C8C22×Dic512yes—
360C3⋊C8—101no—
361C3⋊C8C22×Dic512yes—
362C22×C5—32no—
363C22×C5—61no—
364C22×C5—61no—
365C22×C5—64no—
366C22×C5—122no—
367C22×C5—122no—
368C22×C5C2×D3×D411yescharacteristic
369C4×C5—24no—
370C4×C5—32no—
371C4×C5C22×C4×D311yescharacteristic
372C4×C5D3×#4111yescharacteristic
373Dic5—21no—
374Dic5—21no—
375Dic5—42no—
376Dic5—61no—
377Dic5—61no—
378Dic5—122no—
379#41—38no—
380#41—64no—
381C2×Q8C2×D3×D512yes—
382C2×D4—32no—
383C2×D4—62no—
384C22×C4—31no—
385C22×C4—62no—
386C22×C4—302no—
387C22×C4—302no—
388C22×C4—302no—
389Q16D3×Dic514yescomplemented
390SD16—38no—
391D8—34no—
392M16—302no—
393C2×C8—31no—
394C2×C8—34no—
395C2×C8—51no—
396C2×C8—151no—
397C2×C8C2×D3×D511yescharacteristic
398C4⋊C4—52no—
399C4⋊C4—102no—
400C4⋊C4—151no—
401C4⋊C4—151no—
402C4⋊C4—152no—
403C4⋊C4—302no—
404C4⋊C4—302no—
405C22⋊C4—151no—
406C22⋊C4—151no—
407C22⋊C4—302no—
408C22⋊C4—302no—
409C42—51no—
410C42—102no—
411C42—151no—
412C42—302no—
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3C2×D4×D511yescharacteristic
415C2×D3—21no—
416C2×D3—21no—
417C2×D3—24no—
418C2×D3—42no—
419C2×D3—42no—
420C2×D3D4×Dic512yes—
421C3×C4—24no—
422C3×C4—101no—
423C3×C4—101no—
424C3×C4—202no—
425C3×C4C2×#71111yescharacteristic
426C3×C4C23×Dic511yescharacteristic
427Dic3—101no—
428Dic3—101no—
429Dic3—202no—
430Dic3D4×Dic512yes—
431C2×C5—62no—
432C2×C5—124no—
433C2×C5C4×D3×D411yescharacteristic
434C2×C5#576611yescharacteristic
435C2×C5#576911yescharacteristic
436C23—31no—
437C23—62no—
438Q8—22no—
439Q8C2×D3×Dic514yes—
440D4—34no—
441D4—68no—
442D4—62no—
443C2×C4—22no—
444C2×C4—31no—
445C2×C4—32no—
446C2×C4—32no—
447C2×C4—51no—
448C2×C4—51no—
449C2×C4—68no—
450C2×C4—102no—
451C2×C4—151no—
452C2×C4—151no—
453C2×C4—302no—
454C2×C4—1202no—
455C2×C4—1202no—
456C2×C4—1202no—
457C2×C4C22×D3×D511yescharacteristic
458C8—32no—
459C8—101no—
460C8—301no—
461C8C2×D3×Dic512yes—
462C2×C3#6610311yescharacteristic
463C2×C3#6610511yescharacteristic
464C2×C3C2×D4×Dic511yescharacteristic
465D3—22no—
466D3—44no—
467C5#7972111yescharacteristic, complemented, Sylow
468C22—32no—
469C22—61no—
470C22—61no—
471C22—64no—
472C22—122no—
473C22—122no—
474C22D3×D4×D511yescharacteristic
475C4—24no—
476C4—32no—
477C4—101no—
478C4—101no—
479C4—202no—
480C4—301no—
481C4—301no—
482C4—602no—
483C4D3×#71111yescharacteristic
484C4C22×D3×Dic511yescharacteristic
485C3#1061562911yescharacteristic, complemented, Sylow
486C2—62no—
487C2—124no—
488C2#1175411011yescharacteristic
489C2#1175411511yescharacteristic
490C2D3×D4×Dic511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#919C2
cosocleC2×C3×C4×C5C24
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2951
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
2. #11755220C2semidirect
3. Q16×Dic15C2semidirect
4. C3×Q16×Dic5C2semidirect
5. #11749242C2semidirect
6. #11749223C2semidirect
7. #11749201C2semidirect
8. #11747810C2semidirect
9. Dic5×D24C2semidirect
10. #11747653C2semidirect
11. D3×#3950C2semidirect
17. C5×#919C4semidirect
46. Q16×Dic5D3semidirect
55. C5×#239C2×C4semidirect
63. C3×C5×Q16C2×C4semidirect
70. C5×#215C2×C4semidirect
72. C5×D24C2×C4semidirect
73. C5×D3×C8C2×C4semidirect
158. #919Dic5semidirect
191. C5×Q16C4×D3semidirect
245. #239C2×Dic5semidirect
253. C3×Q16C2×Dic5semidirect
260. #215C2×Dic5semidirect
274. D24C2×Dic5semidirect
276. D3×C8C2×Dic5semidirect
389. Q16D3×Dic5semidirect
413. C3×C5#2951semidirect
467. C5#79721semidirect
485. C3#10615629semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9192
#117552202
Q16×Dic152
C3×Q16×Dic52
#117492422
#117492232
#117492012
#117478102
Dic5×D242
#117476532
D3×#39502
#106156293
#797215