Finite Group Databasebeta

← #14417645

Subgroups — #14417645

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×#912C211yesmaximal, characteristic
2#11754920C212yesmaximal, complemented
3D8×Dic15C211yesmaximal, characteristic, complemented
4C3×D8×Dic5C211yesmaximal, characteristic, complemented
5#11749020C212yesmaximal, complemented
6#11749001C212yesmaximal, complemented
7#11748955C212yesmaximal, complemented
8#11747886C211yesmaximal, characteristic, complemented
9Dic5×Dic12C211yesmaximal, characteristic, complemented
10#11747653C211yesmaximal, characteristic, complemented
11D3×#3950C211yesmaximal, characteristic, complemented
12#10615629—31nomaximal, Hall
13C2×C5×#237C2212yes—
14C2×C3×C5×D8C2211yescharacteristic
15D4×Dic15C2212yes—
16C2×C5×#214C2212yes—
17C5×#912C418yescomplemented
18C2×C5×Dic12C2211yescharacteristic
19C2×C5×D3×C8C2211yescharacteristic
20C3×D4×Dic5C2212yes—
21#67⋊Dic5—22no—
22Dic5×#67—22no—
23C2×Dic3⋊Dic5—22no—
24#91529—22no—
25D3×C4⋊Dic5C2212yes—
26#91371C2211yescharacteristic
27#91344C2212yes—
28Dic5×Dic6C2212yes—
29C2×#6650C2211yescharacteristic
30#91116C2212yes—
31#91102C2211yescharacteristic
32C8×Dic15C2211yescharacteristic
33C3×#3964C2212yes—
34C3×#3950C2211yescharacteristic
35C3×C8×Dic5C2211yescharacteristic
36#90990C2212yes—
37#90973C2212yes—
38#90972C2212yes—
39#90954C2211yescharacteristic
40#90952C2211yescharacteristic
41#79589—51nomaximal, Hall
42C2×C5×#135—31no—
43#66161—32no—
44#65521—32no—
45Q16×Dic5—31no—
46Q16×Dic5—31no—
47#65453—32no—
48#65453—32no—
49D8×Dic5—31no—
50D8×Dic5D311yescharacteristic, complemented
51C2×#3950—31no—
52#65390—31no—
53C2×C3×C5×D4C2312yes—
54C22×Dic15—22no—
55C2×C5×#67—22no—
56C22×C5×Dic3—22no—
57C5×#237—24no—
58C5×#237C2×C418yescomplemented
59C2×C4×C5×D3C2311yescharacteristic
60C2×C5×Dic6C2312yes—
61C22×C3×Dic5—22no—
62C2×D3×Dic5—22no—
63C3×C5×D8C2×C414yescomplemented
64C2×C3×C5×C8C2311yescharacteristic
65#6719—22no—
66C4⋊Dic15C2312yes—
67C4×Dic15C2311yescharacteristic
68C2×C3⋊#168C2311yescharacteristic
69C5×#214C2×C418yescomplemented
70C2×C5×C3⋊C8C2311yescharacteristic
71C5×Dic12C2×C414yescomplemented
72C5×D3×C8C2×C414yescomplemented
73C3×C22⋊Dic5—22no—
74C3×C4⋊Dic5C2312yes—
75C3×C4×Dic5C2311yescharacteristic
76C2×C3×#168C2311yescharacteristic
77Dic3⋊Dic5—22no—
78Dic3⋊Dic5—22no—
79Dic3⋊Dic5—22no—
80Dic3⋊Dic5D411yescharacteristic
81Dic3⋊Dic5D411yescharacteristic
82(C2×D3)⋊Dic5D411yescharacteristic
83(C2×D3)⋊Dic5D411yescharacteristic
84Dic3×Dic5—22no—
85Dic3×Dic5—22no—
86#6650—22no—
87C2×#912D511yescharacteristic
88#5546—52no—
89C3×C4×D8—51no—
90Dic3×D8—51no—
91#5018—52no—
92D3×#107—51no—
93#4873—51no—
94#4771—52no—
95#4757—52no—
96C4×Dic12—51no—
97#4689—51no—
98C2×C5×#41—32no—
99C5×#135—38no—
100C2×C5×Q16—31no—
101C2×C5×SD16—32no—
102C2×C5×D8C2×D311yescharacteristic
103C22×C5×C8—31no—
104Q8×Dic5—32no—
105Q8×Dic5—32no—
106D4×Dic5—32no—
107D4×Dic5—62no—
108D4×Dic5—62no—
109D4×Dic5C2×D312yes—
110#4072—31no—
111#4072—62no—
112C2×C4⋊Dic5—32no—
113C2×C4⋊Dic5—62no—
114C2×#681—31no—
115#3967—32no—
116#3967—32no—
117#3964—32no—
118#3964C2×D312yes—
119#3950—31no—
120#3950—32no—
121#3950C2×D311yescharacteristic
122#3947—31no—
123#3947—31no—
124C8×Dic5—31no—
125C8×Dic5C2×D311yescharacteristic
126#2951—151noSylow
127C23×C3×C5—22no—
128C22×C5×D3C2×D411yescharacteristic
129C3×C5×D4—22no—
130C3×C5×D4C22×C414yes—
131C2×C3×C4×C5C2411yescharacteristic
132C2×Dic15—22no—
133C2×Dic15—82no—
134C2×Dic15C2×D411yescharacteristic
135C2×Dic15C2×D411yescharacteristic
136C5×#67—28no—
137C2×C5×Dic3—22no—
138C2×C5×Dic3—28no—
139C2×C5×Dic3C2×D411yescharacteristic
140C4×C5×D3C22×C412yes—
141C4×C5×D3#4112yes—
142C5×Dic6—22no—
143C5×Dic6C22×C414yes—
144C2×C3×Dic5—22no—
145C2×C3×Dic5—82no—
146C2×C3×Dic5C2×D411yescharacteristic
147C2×C3×Dic5C2×D411yescharacteristic
148D3×Dic5—82no—
149C3×C5×C8C22×C412yes—
150C3⋊#168—21no—
151C3×#168—21no—
152C5×C3⋊C8C22×C412yes—
153C2×#237C2×D512yes—
154C2×C3×D8C2×D511yescharacteristic
155C3×C4×D4—52no—
156D4×Dic3—52no—
157C2×#214C2×D512yes—
158C4×#67—102no—
159C2×Dic3⋊C4—102no—
160#912Dic518yescomplemented
161C2×Dic12C2×D511yescharacteristic
162C2×ΓL(1,𝔽25)—51no—
163C2×D3×C8C2×D511yescharacteristic
164D3×C4⋊C4—52no—
165#887—52no—
166#67⋊C4—102no—
167#877—102no—
168#872—51no—
169C4×Dic6—52no—
170C3×#107—51no—
171C3×#102—52no—
172C3×C4×C8—51no—
173#832—52no—
174#818—51no—
175#816—52no—
176#815—51no—
177C8×Dic3—51no—
178#810—52no—
179#807—52no—
180#803—51no—
181C5×#41—38no—
182C5×#41—64no—
183C2×C5×Q8—32no—
184C2×C5×D4—62no—
185C2×C5×D4C22×D312yes—
186C22×C4×C5—31no—
187C22×C4×C5—62no—
188C22×Dic5—22no—
189C22×Dic5—62no—
190C22×Dic5—62no—
191C5×Q16—34no—
192C5×SD16—38no—
193C5×D8C4×D314yescomplemented
194C2×C5×C8—31no—
195C2×C5×C8—34no—
196C2×C5×C8C22×D311yescharacteristic
197C22⋊Dic5—22no—
198C22⋊Dic5—31no—
199C22⋊Dic5—31no—
200C22⋊Dic5—62no—
201C4⋊Dic5—31no—
202C4⋊Dic5—31no—
203C4⋊Dic5—32no—
204C4⋊Dic5—62no—
205C4⋊Dic5—62no—
206C4⋊Dic5—62no—
207C4⋊Dic5C22×D312yes—
208C4×Dic5—31no—
209C4×Dic5—62no—
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—151no—
220C4×Q16—151no—
221C4×D8—51no—
222C4×D8—151no—
223C2×#107—151no—
224#417—152no—
225#405—151no—
226C22×C3×C5—24no—
227C22×C3×C5—42no—
228C22×C3×C5—42no—
229C22×C3×C5C22×D411yescharacteristic
230C2×C5×D3—21no—
231C2×C5×D3—21no—
232C2×C5×D3C4×D412yes—
233C3×C4×C5C23×C411yescharacteristic
234C3×C4×C5C2×#4111yescharacteristic
235Dic15—21no—
236Dic15—21no—
237Dic15—42no—
238C3×Dic5—21no—
239C3×Dic5—21no—
240C3×Dic5—42no—
241C5×Dic3—24no—
242C5×Dic3C4×D412yes—
243C2×C3×D4C22×D512yes—
244C22×C3×C4—102no—
245C2×#67—22no—
246C22×Dic3—22no—
247C22×Dic3—102no—
248#237—24no—
249#237C2×Dic518yescomplemented
250C2×C4×D3—102no—
251C2×C4×D3C22×D511yescharacteristic
252C2×Dic6C22×D512yes—
253C3×D8C2×Dic514yescomplemented
254C2×C3×C8—51no—
255C2×C3×C8C22×D511yescharacteristic
256C3×C4⋊C4—52no—
257C3×C22⋊C4—102no—
258C3×C42—51no—
259#217—102no—
260#214C2×Dic518yescomplemented
261(C2×D3)⋊C4—51no—
262(C2×D3)⋊C4—51no—
263C4⋊Dic3—52no—
264Dic3⋊C4—51no—
265Dic3⋊C4—51no—
266Dic3⋊C4—102no—
267Dic3⋊C4—102no—
268Dic3⋊C4—102no—
269C4×Dic3—51no—
270C4×Dic3—102no—
271C4×Dic3—102no—
272C2×C3⋊C8—51no—
273C2×C3⋊C8C22×D511yescharacteristic
274Dic12C2×Dic514yescomplemented
275ΓL(1,𝔽25)—102no—
276D3×C8C2×Dic514yescomplemented
277C23×C5—22no—
278C23×C5—31no—
279C5×Q8—34no—
280C5×Q8—62no—
281C5×D4—22no—
282C5×D4—68no—
283C5×D4C2×C4×D314yes—
284C2×C4×C5—31no—
285C2×C4×C5—32no—
286C2×C4×C5—32no—
287C2×C4×C5—68no—
288C2×C4×C5—62no—
289C2×C4×C5C23×D311yescharacteristic
290C2×Dic5—22no—
291C2×Dic5—31no—
292C2×Dic5—31no—
293C2×Dic5—62no—
294C2×Dic5—82no—
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×Q16—31no—
306C2×SD16—32no—
307C2×D8D3×D511yescharacteristic
308C2×M16—151no—
309C22×C8—31no—
310C4×Q8—152no—
311C4×Q8—152no—
312C4×D4—52no—
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—152no—
324#103—152no—
325#102—52no—
326#102—152no—
327#97—151no—
328#97—151no—
329C4×C8—51no—
330C4×C8—151no—
331C2×C3×C5—44no—
332C2×C3×C5C2×C4×D411yescharacteristic
333C2×C3×C5#57611yescharacteristic
334C2×C3×C5#57811yescharacteristic
335C5×D3—22no—
336C23×C3—22no—
337C22×D3D4×D511yescharacteristic
338C3×D4—22no—
339C3×D4C22×Dic514yes—
340C2×C3×C4—51no—
341C2×C3×C4—51no—
342C2×C3×C4—102no—
343C2×C3×C4—402no—
344C2×C3×C4C23×D511yescharacteristic
345#67—28no—
346C2×Dic3—22no—
347C2×Dic3—28no—
348C2×Dic3—51no—
349C2×Dic3—51no—
350C2×Dic3—102no—
351C2×Dic3—402no—
352C2×Dic3D4×D511yescharacteristic
353C4×D3—402no—
354C4×D3#71112yes—
355C4×D3C22×Dic512yes—
356Dic6—22no—
357Dic6C22×Dic514yes—
358C3×C8—101no—
359C3×C8C22×Dic512yes—
360C3⋊C8—101no—
361C3⋊C8C22×Dic512yes—
362C22×C5—24no—
363C22×C5—32no—
364C22×C5—42no—
365C22×C5—42no—
366C22×C5—61no—
367C22×C5—61no—
368C22×C5C2×D3×D411yescharacteristic
369C4×C5—32no—
370C4×C5—64no—
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×Q8—32no—
382C2×D4—62no—
383C2×D4C2×D3×D512yes—
384C22×C4—31no—
385C22×C4—62no—
386C22×C4—102no—
387C22×C4—302no—
388C22×C4—302no—
389Q16—34no—
390SD16—38no—
391D8D3×Dic514yescomplemented
392M16—302no—
393C2×C8—31no—
394C2×C8—34no—
395C2×C8—51no—
396C2×C8—151no—
397C2×C8C2×D3×D511yescharacteristic
398C4⋊C4—52no—
399C4⋊C4—151no—
400C4⋊C4—151no—
401C4⋊C4—152no—
402C4⋊C4—302no—
403C4⋊C4—302no—
404C4⋊C4—302no—
405C22⋊C4—102no—
406C22⋊C4—151no—
407C22⋊C4—151no—
408C22⋊C4—302no—
409C42—51no—
410C42—151no—
411C42—302no—
412C42—302no—
413C3×C5#295111yescharacteristic, complemented, Hall
414C22×C3—24no—
415C22×C3—42no—
416C22×C3—42no—
417C22×C3C2×D4×D511yescharacteristic
418C2×D3—21no—
419C2×D3—21no—
420C2×D3D4×Dic512yes—
421C3×C4—101no—
422C3×C4—101no—
423C3×C4—202no—
424C3×C4C2×#71111yescharacteristic
425C3×C4C23×Dic511yescharacteristic
426Dic3—24no—
427Dic3—101no—
428Dic3—101no—
429Dic3—202no—
430Dic3D4×Dic512yes—
431C2×C5—44no—
432C2×C5—62no—
433C2×C5C4×D3×D411yescharacteristic
434C2×C5#575711yescharacteristic
435C2×C5#577111yescharacteristic
436C23—22no—
437C23—31no—
438Q8—34no—
439Q8—62no—
440D4—22no—
441D4—68no—
442D4C2×D3×Dic514yes—
443C2×C4—31no—
444C2×C4—32no—
445C2×C4—32no—
446C2×C4—51no—
447C2×C4—51no—
448C2×C4—68no—
449C2×C4—62no—
450C2×C4—102no—
451C2×C4—151no—
452C2×C4—151no—
453C2×C4—302no—
454C2×C4—402no—
455C2×C4—1202no—
456C2×C4—1202no—
457C2×C4C22×D3×D511yescharacteristic
458C8—32no—
459C8—101no—
460C8—301no—
461C8C2×D3×Dic512yes—
462C2×C3—44no—
463C2×C3#6610311yescharacteristic
464C2×C3#6610511yescharacteristic
465C2×C3C2×D4×Dic511yescharacteristic
466D3—22no—
467C5#7958911yescharacteristic, complemented, Sylow
468C22—24no—
469C22—32no—
470C22—42no—
471C22—42no—
472C22—61no—
473C22—61no—
474C22D3×D4×D511yescharacteristic
475C4—32no—
476C4—64no—
477C4—101no—
478C4—101no—
479C4—202no—
480C4—301no—
481C4—301no—
482C4—602no—
483C4D3×#71111yescharacteristic
484C4C22×D3×Dic511yescharacteristic
485C3#1061562911yescharacteristic, complemented, Sylow
486C2—44no—
487C2—62no—
488C2#1175405811yescharacteristic
489C2#1175406311yescharacteristic
490C2D3×D4×Dic511yescharacteristic
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C22×D4
prime radicalC2×C5×#912C2
cosocleC2×C3×C4×C5C24
hypercenterC2×D8D3×D5
hypocenterC3×C5#2951
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. #11754920C2semidirect
3. D8×Dic15C2semidirect
4. C3×D8×Dic5C2semidirect
5. #11749020C2semidirect
6. #11749001C2semidirect
7. #11748955C2semidirect
8. #11747886C2semidirect
9. Dic5×Dic12C2semidirect
10. #11747653C2semidirect
11. D3×#3950C2semidirect
17. C5×#912C4semidirect
50. D8×Dic5D3semidirect
58. C5×#237C2×C4semidirect
63. C3×C5×D8C2×C4semidirect
69. C5×#214C2×C4semidirect
71. C5×Dic12C2×C4semidirect
72. C5×D3×C8C2×C4semidirect
160. #912Dic5semidirect
193. C5×D8C4×D3semidirect
249. #237C2×Dic5semidirect
253. C3×D8C2×Dic5semidirect
260. #214C2×Dic5semidirect
274. Dic12C2×Dic5semidirect
276. D3×C8C2×Dic5semidirect
391. D8D3×Dic5semidirect
413. C3×C5#2951semidirect
467. C5#79589semidirect
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×#9122
#117549202
D8×Dic152
C3×D8×Dic52
#117490202
#117490012
#117489552
#117478862
Dic5×Dic122
#117476532
D3×#39502
#106156293
#795895