Finite Group Databasebeta

← #14416625

Subgroups — #14416625

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91279C211yesmaximal, characteristic
2#11753406C212yesmaximal, complemented
3#11750961C211yesmaximal, characteristic, complemented
4C5×#4869C211yesmaximal, characteristic, complemented
5C3×#65142C211yesmaximal, characteristic, complemented
6#11747870C211yesmaximal, characteristic, complemented
7#11747775C211yesmaximal, characteristic, complemented
8#11747603C211yesmaximal, characteristic, complemented
9#11747508C212yesmaximal, complemented
10#11747265C212yesmaximal, complemented
11#11747217C212yesmaximal, complemented
12#10611595—31nomaximal, Hall
13C2×#6768C2212yes—
14C2×C8×D15C2211yescharacteristic
15#91781C2212yes—
16C2×C5×D24C2211yescharacteristic
17C5×#893C2212yes—
18C2×C3×Dic20C2211yescharacteristic
19C3×#4033C2212yes—
20#91446—22no—
21Dic5×D12C2212yes—
22#91405—22no—
23C4×#1200C2211yescharacteristic
24#91400—22no—
25C4×D3×Dic5—22no—
26Dic3×Dic10C2212yes—
27C2×#6656C2212yes—
28C2×#6648C2211yescharacteristic
29#91279C418yescomplemented
30C3×C5×#106C2211yescharacteristic
31#91101C2211yescharacteristic
32#91091C2212yes—
33C5×#815C2211yescharacteristic
34C5×#809C2212yes—
35C3×#3947C2211yescharacteristic
36C3×#3942C2212yes—
37#90971C2212yes—
38#90967C2212yes—
39#90953C2211yescharacteristic
40#90952C2211yescharacteristic
41#79828—51nomaximal, Hall
42C2×#4058—31no—
43C4×#711—32no—
44C5×#442—31no—
45#65441—31no—
46#65307—32no—
47#65149—31no—
48#65142D311yescharacteristic, complemented
49#65061—32no—
50#65046—32no—
51#65005—31no—
52D5×#97—31no—
53C2×C4×D15C2311yescharacteristic
54C2×C5×D12C2312yes—
55C2×C4×C5×D3—22no—
56C2×C3×Dic10C2312yes—
57C2×#1203—22no—
58C2×#1200D412yes—
59C2×D3×Dic5—22no—
60C2×D3×Dic5—22no—
61#6768—24no—
62#6768C2×C418yescomplemented
63C2×C3×C5×C8C2311yescharacteristic
64C3×C5×C4⋊C4C2312yes—
65#6714—22no—
66C4⋊Dic15C2312yes—
67C4×Dic15—22no—
68C2×C3⋊#168C2311yescharacteristic
69C8×D15C2×C414yescomplemented
70C5×(C2×D3)⋊C4—22no—
71C4×C5×Dic3C2311yescharacteristic
72C2×C5×C3⋊C8C2311yescharacteristic
73C5×D24C2×C414yescomplemented
74C3×#683—22no—
75C3×C4×Dic5—22no—
76C3×C4×Dic5C2311yescharacteristic
77C2×C3×#168C2311yescharacteristic
78C3×Dic20C2×C414yescomplemented
79#6668—22no—
80(C2×D3)⋊Dic5—22no—
81Dic3×Dic5—22no—
82Dic3×Dic5D412yes—
83#6656C2×C418yescomplemented
84#6648—22no—
85C2×#919—51no—
86C4×#239—52no—
87C3×#441—51no—
88#5184—51no—
89#5026—52no—
90#4869D511yescharacteristic, complemented
91#4860—51no—
92#4817—52no—
93#4804—52no—
94#4711—51no—
95D3×#97—51no—
96C2×#711—32no—
97C2×C5×D8—31no—
98C4×C5×D4—32no—
99D4×Dic5—32no—
100C2×#687—32no—
101C4×C22⋊D5—62no—
102C2×C4×Dic5—62no—
103#4058—38no—
104C2×Dic20C2×D311yescharacteristic
105C2×C8×D5—31no—
106C2×C8×D5—31no—
107#4038—32no—
108#4033C2×D312yes—
109#4027—62no—
110#4023—62no—
111C42×D5—31no—
112C4×Dic10—32no—
113C5×#106C2×D311yescharacteristic
114C5×#102—32no—
115C5×#97—31no—
116#3964—32no—
117#3949—31no—
118#3948—32no—
119#3947—31no—
120#3947C2×D311yescharacteristic
121#3942C2×D312yes—
122#3939—32no—
123#3935—31no—
124#2943—151noSylow
125C22×D15C2×D411yescharacteristic
126C22×C5×D3—22no—
127C2×C3×C4×C5—22no—
128C2×C3×C4×C5C2411yescharacteristic
129C2×Dic15—22no—
130C2×Dic15C2×D411yescharacteristic
131C4×D15C22×C412yes—
132C4×D15#4112yes—
133C2×C5×Dic3C2×D412yes—
134C5×D12—22no—
135C5×D12C22×C414yes—
136C4×C5×D3—44no—
137C2×C3×Dic5—22no—
138C2×C3×Dic5C2×D412yes—
139C3×Dic10—22no—
140C3×Dic10C22×C414yes—
141#1203—28no—
142#1200—42no—
143D3×Dic5—28no—
144D3×Dic5—44no—
145C3×C5×C8C22×C412yes—
146C3⋊#168C22×C412yes—
147C3×#168—21no—
148C5×C3⋊C8—21no—
149C2×#239—52no—
150C2×C3×Q16—51no—
151C3×C4×Q8—52no—
152Q8×Dic3—52no—
153C2×#215—52no—
154#919—58no—
155C2×D24C2×D511yescharacteristic
156C2×D3×C8—51no—
157C2×D3×C8—51no—
158#893—102no—
159#893C2×D512yes—
160#892—52no—
161#892—102no—
162C4×D12—52no—
163C4×D12—102no—
164C42×D3—51no—
165C42×D3—102no—
166C3×#106C2×D511yescharacteristic
167C3×#103—52no—
168C3×#97—51no—
169#835—52no—
170#821—52no—
171#817—51no—
172#815—51no—
173#815C2×D511yescharacteristic
174#809C2×D512yes—
175#807—52no—
176#803—51no—
177C2×C5×D4—32no—
178C22×C4×C5—62no—
179C2×C22⋊D5—62no—
180C22×Dic5—62no—
181C22×Dic5—62no—
182#711—38no—
183#711—64no—
184C2×C4×D5—31no—
185C2×C4×D5—32no—
186C2×Dic10C22×D312yes—
187C5×D8—34no—
188C2×C5×C8—31no—
189C2×C5×C8C22×D311yescharacteristic
190C5×C4⋊C4C22×D312yes—
191C5×C22⋊C4—62no—
192C42×C5—31no—
193C22⋊Dic5—62no—
194#687—38no—
195#685—62no—
196C4⋊Dic5—32no—
197#683—22no—
198#683—62no—
199C4×Dic5—22no—
200C4×Dic5—32no—
201C4×Dic5—62no—
202C4×Dic5—62no—
203C4×Dic5C22×D311yescharacteristic
204C2×#168—31no—
205C2×#168C22×D311yescharacteristic
206Dic20C4×D314yescomplemented
207C8×D5—34no—
208C8×D5—62no—
209C2×#135—151no—
210C4×#41—152no—
211#442—31no—
212#442—151no—
213#441—51no—
214#441—151no—
215#440—152no—
216#440—152no—
217#427—151no—
218#416—152no—
219C2×#97—151no—
220C22×C3×C5C22×D411yescharacteristic
221C2×D15—22no—
222C2×D15C4×D412yes—
223C2×C5×D3—24no—
224C2×C5×D3—42no—
225C2×C5×D3—42no—
226C3×C4×C5—42no—
227C3×C4×C5C23×C411yescharacteristic
228C3×C4×C5C2×#4111yescharacteristic
229Dic15—42no—
230Dic15C4×D412yes—
231C3×Dic5—24no—
232C3×Dic5—22no—
233C5×Dic3—22no—
234C2×C3×Q8—52no—
235#239—58no—
236#239—104no—
237C2×D12—102no—
238C2×D12C22×D512yes—
239C2×C4×D3—22no—
240C2×C4×D3—51no—
241C2×C4×D3—52no—
242C2×C4×D3—102no—
243C2×C4×D3—102no—
244C3×Q16—54no—
245C2×C3×C8—51no—
246C2×C3×C8C22×D511yescharacteristic
247C3×C4⋊C4—102no—
248C3×C4⋊C4C22×D512yes—
249C3×C42—51no—
250C3×C42—102no—
251#215—58no—
252(C2×D3)⋊C4—22no—
253(C2×D3)⋊C4—102no—
254(C2×D3)⋊C4—102no—
255C4⋊Dic3—52no—
256C4⋊Dic3—102no—
257C4×Dic3—52no—
258C4×Dic3—102no—
259C4×Dic3—102no—
260C4×Dic3C22×D511yescharacteristic
261C2×C3⋊C8—51no—
262C2×C3⋊C8C22×D511yescharacteristic
263D24C4×D514yescomplemented
264D3×C8—54no—
265D3×C8—102no—
266C23×C5—62no—
267C22×D5—31no—
268C5×D4—34no—
269C5×D4—62no—
270C2×C4×C5—22no—
271C2×C4×C5—32no—
272C2×C4×C5—124no—
273C2×C4×C5C23×D311yescharacteristic
274C22⋊D5—68no—
275C2×Dic5—22no—
276C2×Dic5—31no—
277C2×Dic5—68no—
278C2×Dic5—62no—
279C2×Dic5—124no—
280C2×Dic5D3×D412yes—
281C4×D5—32no—
282C4×D5—32no—
283C4×D5—122no—
284Dic10—22no—
285Dic10C2×C4×D314yes—
286C5×C8—61no—
287C5×C8C2×C4×D312yes—
288#168—21no—
289#168—32no—
290C2×#41—152no—
291#135—158no—
292C2×Q16—51no—
293C2×SD16—152no—
294C2×D8—31no—
295C22×C8—151no—
296C22×C8—151no—
297C4×Q8—52no—
298C4×Q8—152no—
299C4×D4—32no—
300C4×D4—152no—
301C4×D4—302no—
302C4×D4—302no—
303#117—152no—
304#117—302no—
305C2×C42—151no—
306C2×C42—302no—
307#107—152no—
308#106—151no—
309#106D3×D511yescharacteristic
310#103—52no—
311#103—152no—
312#102—32no—
313#102—152no—
314#97—31no—
315#97—51no—
316#97—151no—
317#97—151no—
318C2×C3×C5C2×C4×D411yescharacteristic
319C2×C3×C5#57512yes—
320D15—22no—
321C5×D3—44no—
322C22×D3—22no—
323C22×D3—51no—
324C3×Q8—54no—
325C3×Q8—102no—
326C2×C3×C4—22no—
327C2×C3×C4—52no—
328C2×C3×C4—102no—
329C2×C3×C4C23×D511yescharacteristic
330C2×Dic3—51no—
331C2×Dic3—102no—
332C2×Dic3D4×D512yes—
333D12—22no—
334D12—108no—
335D12C2×C4×D514yes—
336C4×D3—44no—
337C4×D3—52no—
338C4×D3—52no—
339C4×D3—108no—
340C4×D3—202no—
341C4×D3—204no—
342C3×C8—101no—
343C3×C8C2×C4×D512yes—
344C3⋊C8—21no—
345C3⋊C8—52no—
346C22×C5—64no—
347C22×C5—122no—
348C22×C5—122no—
349C22×C5C2×D3×D411yescharacteristic
350C2×D5—32no—
351C2×D5—62no—
352C4×C5—42no—
353C4×C5—62no—
354C4×C5C22×C4×D311yescharacteristic
355C4×C5D3×#4111yescharacteristic
356Dic5—22no—
357Dic5—24no—
358Dic5—32no—
359Dic5—122no—
360#41—158no—
361#41—304no—
362C2×Q8—52no—
363C2×D4—32no—
364C2×D4—302no—
365C22×C4—62no—
366C22×C4—152no—
367C22×C4—151no—
368C22×C4—302no—
369C22×C4—302no—
370Q16—54no—
371SD16—158no—
372D8—34no—
373C2×C8—31no—
374C2×C8—51no—
375C2×C8—151no—
376C2×C8—154no—
377C2×C8—302no—
378C2×C8C2×D3×D511yescharacteristic
379C4⋊C4—102no—
380C4⋊C4—152no—
381C4⋊C4—302no—
382C4⋊C4C2×D3×D512yes—
383C22⋊C4—62no—
384C22⋊C4—302no—
385C22⋊C4—302no—
386C42—31no—
387C42—51no—
388C42—102no—
389C42—152no—
390C42—302no—
391C42—302no—
392C3×C5#294311yescharacteristic, complemented, Hall
393C22×C3C2×D4×D511yescharacteristic
394C2×D3—24no—
395C2×D3—42no—
396C2×D3—42no—
397C2×D3—52no—
398C2×D3—102no—
399C3×C4—42no—
400C3×C4—102no—
401C3×C4—104no—
402C3×C4C22×C4×D511yescharacteristic
403C3×C4D5×#4111yescharacteristic
404Dic3—22no—
405Dic3—52no—
406Dic3—202no—
407C2×C5—124no—
408C2×C5C4×D3×D411yescharacteristic
409C2×C5#577712yes—
410D5—62no—
411C23—62no—
412C23—151no—
413Q8—54no—
414Q8—102no—
415D4—34no—
416D4—62no—
417D4—308no—
418C2×C4—22no—
419C2×C4—32no—
420C2×C4—52no—
421C2×C4—102no—
422C2×C4—124no—
423C2×C4—151no—
424C2×C4—152no—
425C2×C4—152no—
426C2×C4—308no—
427C2×C4—302no—
428C2×C4—602no—
429C2×C4—604no—
430C2×C4C22×D3×D511yescharacteristic
431C8—61no—
432C8—101no—
433C8—152no—
434C8C4×D3×D512yes—
435C2×C3C4×D4×D511yescharacteristic
436C2×C3#6610712yes—
437D3—44no—
438D3—102no—
439C5#7982811yescharacteristic, complemented, Sylow
440C22—64no—
441C22—122no—
442C22—122no—
443C22—152no—
444C22—302no—
445C22D3×D4×D511yescharacteristic
446C4—42no—
447C4—62no—
448C4—102no—
449C4—104no—
450C4—152no—
451C4—602no—
452C4C2×C4×D3×D511yescharacteristic
453C4#9203411yescharacteristic
454C3#1061159511yescharacteristic, complemented, Sylow
455C2—124no—
456C2—302no—
457C2#1175384011yescharacteristic
458C2#1175407412yes—
subgroupG/H
centerC22D3×D4×D5
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C22×D3×D5
FittingC3×C5×#106C22
socleC22×C3×C5C22×D4
prime radicalC2×#91279C2
cosocleC2×C3×C4×C5C24
hypercenter#106D3×D5
hypocenterC3×C5#2943
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ #106

Complements

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

NH ≅ G/Ntype
2. #11753406C2semidirect
3. #11750961C2semidirect
4. C5×#4869C2semidirect
5. C3×#65142C2semidirect
6. #11747870C2semidirect
7. #11747775C2semidirect
8. #11747603C2semidirect
9. #11747508C2semidirect
10. #11747265C2semidirect
11. #11747217C2semidirect
29. #91279C4semidirect
48. #65142D3semidirect
62. #6768C2×C4semidirect
69. C8×D15C2×C4semidirect
73. C5×D24C2×C4semidirect
78. C3×Dic20C2×C4semidirect
83. #6656C2×C4semidirect
90. #4869D5semidirect
206. Dic20C4×D3semidirect
263. D24C4×D5semidirect
392. C3×C5#2943semidirect
439. C5#79828semidirect
454. C3#10611595semidirect

Maximal subgroups

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

subgroupindex
C2×#912792
#117534062
#117509612
C5×#48692
C3×#651422
#117478702
#117477752
#117476032
#117475082
#117472652
#117472172
#106115953
#798285