Finite Group Databasebeta

← #14302459

Subgroups — #14302459

Order 1920.

692 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91797C211yesmaximal, characteristic
2#11754515C211yesmaximal, characteristic, complemented
3#11748626C211yesmaximal, characteristic, complemented
4#11748429C211yesmaximal, characteristic, complemented
5#11748392C211yesmaximal, characteristic, complemented
6C5×#4556C211yesmaximal, characteristic, complemented
7C3×#64777C211yesmaximal, characteristic, complemented
8#10599820—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×D60C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12#91797—22no—
13#91797—22no—
14C2×D120C412yescomplemented
15C2×#6706C412yescomplemented
16C5×#926C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C3×#4072C2211yescharacteristic
20#91561—22no—
21#91428—22no—
22#91418—22no—
23#90997—22no—
24#90981—22no—
25#90968—22no—
26#68704—51nomaximal, Hall
27C2×#4054—31no—
28#65855—31no—
29#65428—31no—
30#65420—31no—
31#65295—31no—
32C5×#344—31no—
33#64777D311yescharacteristic, complemented
34C23×D15—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220—21no—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41C2×D60—21no—
42C2×D60—21no—
43C2×D60—21no—
44C2×D60C2×C412yes—
45C2×D60C2×C411yescharacteristic, complemented
46C2×D60D412yes—
47C2×D60D412yes—
48C2×C4×D15—21no—
49C2×Dic30C2×C411yescharacteristic, complemented
50C2×#1200—24no—
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8C2×C412yescomplemented
54D120—24no—
55#6706—24no—
56C5×#217D412yes—
57C5×C4⋊Dic3—21no—
58C4×C5×Dic3—21no—
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8—21no—
62C3×C22⋊Dic5—21no—
63C3×C22⋊Dic5—21no—
64C3×C4⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C3×C4×Dic5—21no—
67C3×C4×Dic5D412yes—
68#6667—24no—
69C2×#908—51no—
70#5521—51no—
71#5006—51no—
72#5005—51no—
73#5001—51no—
74C3×H(3,ℤ/4)—51no—
75#4556D511yescharacteristic, complemented
76C2×#709—31no—
77C22×D20—31no—
78C2×C5×M16—31no—
79C2×C5×M16C2×D311yescharacteristic
80C5×#117—31no—
81#4072C2×D311yescharacteristic
82#4072C2×D311yescharacteristic
83#4054—62no—
84#4054—62no—
85C2×D40—32no—
86C2×#677—32no—
87#4039—62no—
88D5×C22⋊C4—62no—
89C4×D20—62no—
90#3957—62no—
91#3953—62no—
92#3938—62no—
93#1904—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—22no—
96C22×D15—22no—
97C22×D15—22no—
98C22×D15—21no—
99C22×D15—82no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C2×D411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5#4111yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106#1220—41no—
107#1220—41no—
108C2×Dic15—21no—
109D60—21no—
110D60—22no—
111D60—21no—
112D60—22no—
113D60—22no—
114D60C22⋊C414yes—
115C4×D15—41no—
116C4×D15—41no—
117Dic30—21no—
118Dic30—21no—
119C2×C5×Dic3—22no—
120C2×C3×Dic5—22no—
121C2×C3×Dic5—41no—
122#1200—84no—
123C3×C5×C8—22no—
124C5×C3⋊C8—41no—
125C2×#235—51no—
126C22×D12—51no—
127C2×C3×M16C2×D511yescharacteristic
128C3×#117—51no—
129C3×#117—51no—
130#926C2×D511yescharacteristic
131C2×#208C2×D511yescharacteristic
132#908—102no—
133#908—102no—
134C2×D24—52no—
135C2×#204—52no—
136#893—102no—
137D3×C22⋊C4—102no—
138C4×D12—102no—
139#809—102no—
140#806—102no—
141#805—102no—
142C23×D5—61no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5—61no—
145#709—61no—
146#709—61no—
147#709—61no—
148#709—61no—
149C2×D20—32no—
150C2×D20—32no—
151C2×D20—32no—
152C2×D20—31no—
153C2×D20—61no—
154C2×D20—61no—
155C2×D20—61no—
156C2×C4×D5—61no—
157C2×C4×D5—64no—
158C2×Dic10—31no—
159C5×M16—21no—
160C5×M16—21no—
161C5×M16—61no—
162C5×M16—61no—
163C2×C5×C8—61no—
164C2×C5×C8C4×D312yescomplemented
165C5×C4⋊C4—61no—
166C5×C22⋊C4—32no—
167C42×C5—61no—
168C22⋊Dic5—21no—
169C22⋊Dic5—21no—
170#685—64no—
171C4⋊Dic5—21no—
172C4⋊Dic5—21no—
173C4×Dic5—21no—
174C4×Dic5D1212yes—
175D40—64no—
176#677—64no—
177C2×AGL(1,ℤ/8)—151no—
178#518—151no—
179#421—151no—
180#418—151no—
181#410—151no—
182#344—31no—
183H(3,ℤ/4)—51no—
184C22×C3×C5—41no—
185C22×C3×C5C4×D411yescharacteristic
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#12111yescharacteristic
188C2×D15—24no—
189C2×D15—44no—
190C2×D15—41no—
191C2×D15—82no—
192C2×D15—82no—
193C2×D15—81no—
194C3×C4×C5C2×C22⋊C411yescharacteristic
195C3×C4×C5C4×D411yescharacteristic
196C3×C4×C5#12111yescharacteristic
197C3×C4×C5#12311yescharacteristic
198Dic15—41no—
199C3×Dic5—42no—
200C3×Dic5—81no—
201C5×Dic3—42no—
202C23×D3—101no—
203C22×C3×C4C22×D511yescharacteristic
204C2×#67—101no—
205#235—101no—
206#235—101no—
207#235—101no—
208#235—101no—
209C2×D12—52no—
210C2×D12—52no—
211C2×D12—52no—
212C2×D12—51no—
213C2×D12—101no—
214C2×D12—101no—
215C2×D12—101no—
216C2×C4×D3—101no—
217C2×C4×D3—104no—
218C2×Dic6—51no—
219C3×M16—21no—
220C3×M16—21no—
221C2×C3×C8C4×D512yescomplemented
222C3×C4⋊C4—101no—
223C3×C4⋊C4—101no—
224C3×C22⋊C4—101no—
225C3×C22⋊C4—101no—
226C3×C42—52no—
227C3×C42—101no—
228#217D2012yes—
229(C2×D3)⋊C4—104no—
230C4⋊Dic3—21no—
231C4×Dic3—21no—
232#208—21no—
233#208—21no—
234C2×C3⋊C8—21no—
235D24—104no—
236#204—104no—
237C23×C5D3×D411yescharacteristic
238C22×D5—62no—
239C22×D5—62no—
240C22×D5—62no—
241C22×D5—61no—
242C22×D5—242no—
243C2×C4×C5—62no—
244C2×C4×C5C2×C4×D311yescharacteristic
245C2×C4×C5C2×D1211yescharacteristic
246C2×C4×C5#23511yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5#23911yescharacteristic
250C22⋊D5—121no—
251C22⋊D5—121no—
252C2×Dic5—22no—
253C2×Dic5—41no—
254C2×Dic5—61no—
255D20—34no—
256D20—62no—
257D20—61no—
258D20—61no—
259D20—62no—
260D20—62no—
261C4×D5—121no—
262C4×D5—121no—
263C4×D5—244no—
264Dic10—61no—
265Dic10—61no—
266C5×C8—22no—
267C5×C8—121no—
268C2×#41—151no—
269C22×D4—151no—
270AGL(1,ℤ/8)—302no—
271AGL(1,ℤ/8)—302no—
272C2×SD16—152no—
273C2×D8—152no—
274C2×M16—31no—
275C2×M16D3×D511yescharacteristic
276C4×D4—302no—
277C4×D4—302no—
278#117—31no—
279#117—51no—
280#117—51no—
281C2×C22⋊C4—302no—
282#104—302no—
283#102—302no—
284#99—302no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5#38611yescharacteristic
289D15—44no—
290D15—81no—
291C23×C3C2×D2011yescharacteristic
292C22×D3—102no—
293C22×D3—102no—
294C22×D3—102no—
295C22×D3—101no—
296C22×D3—402no—
297C2×C3×C4—102no—
298C2×C3×C4—201no—
299C2×C3×C4C2×C4×D511yescharacteristic
300C2×C3×C4#70911yescharacteristic
301C2×C3×C4D4×D511yescharacteristic
302C2×C3×C4D4×D511yescharacteristic
303C2×C3×C4D4×D511yescharacteristic
304C2×C3×C4#71311yescharacteristic
305#67—201no—
306#67—201no—
307C2×Dic3—22no—
308C2×Dic3—101no—
309D12—54no—
310D12—101no—
311D12—102no—
312D12—102no—
313D12—101no—
314D12—102no—
315C4×D3—201no—
316C4×D3—201no—
317C4×D3—404no—
318Dic6—101no—
319Dic6—101no—
320C3×C8—22no—
321C3⋊C8—41no—
322C22×C5—41no—
323C22×C5#88211yescharacteristic
324C22×C5#88411yescharacteristic
325C22×C5#89311yescharacteristic
326C2×D5—64no—
327C2×D5—124no—
328C2×D5—121no—
329C2×D5—242no—
330C2×D5—242no—
331C2×D5—241no—
332C4×C5—122no—
333C4×C5C4×D1211yescharacteristic
334C4×C5D3×C22⋊C411yescharacteristic
335C4×C5#89411yescharacteristic
336C4×C5#89511yescharacteristic
337Dic5—42no—
338Dic5—81no—
339Dic5—121no—
340C24—301no—
341#41—301no—
342#41—301no—
343#41—301no—
344#41—301no—
345C2×Q8—151no—
346C2×D4—152no—
347C2×D4—151no—
348C2×D4—152no—
349C2×D4—152no—
350C2×D4—301no—
351C2×D4—301no—
352C2×D4—301no—
353C2×D4—301no—
354C22×C4—304no—
355C22×C4—301no—
356C22×C4C2×D3×D511yescharacteristic
357SD16—304no—
358D8—304no—
359M16—21no—
360M16—21no—
361M16—61no—
362M16—61no—
363C2×C8—61no—
364C2×C8#120012yescomplemented
365C4⋊C4—61no—
366C4⋊C4—101no—
367C4⋊C4—101no—
368C22⋊C4—32no—
369C22⋊C4—101no—
370C22⋊C4—101no—
371C22⋊C4—304no—
372C42—52no—
373C42—61no—
374C42—101no—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3C4×D2011yescharacteristic
378C22×C3#402811yescharacteristic
379C22×C3#404111yescharacteristic
380C2×D3—104no—
381C2×D3—204no—
382C2×D3—201no—
383C2×D3—402no—
384C2×D3—402no—
385C2×D3—401no—
386C3×C4—202no—
387C3×C4—401no—
388C3×C4D5×C22⋊C411yescharacteristic
389C3×C4#403011yescharacteristic
390C3×C4#403911yescharacteristic
391C3×C4#404011yescharacteristic
392Dic3—42no—
393Dic3—201no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5#466511yescharacteristic
398D5—124no—
399D5—241no—
400C23—302no—
401C23—302no—
402C23—302no—
403C23—301no—
404C23—1202no—
405C23D3×D2011yescharacteristic
406Q8—301no—
407Q8—301no—
408D4—154no—
409D4—302no—
410D4—301no—
411D4—302no—
412D4—302no—
413D4—301no—
414D4—601no—
415D4—601no—
416C2×C4—62no—
417C2×C4—102no—
418C2×C4—201no—
419C2×C4—301no—
420C2×C4—601no—
421C2×C4—601no—
422C2×C4—1204no—
423C2×C4#676911yescharacteristic
424C2×C4#677311yescharacteristic
425C2×C4D5×D1211yescharacteristic
426C2×C4C2×#120011yescharacteristic
427C2×C4#679011yescharacteristic
428C2×C4#679011yescharacteristic
429C8—22no—
430C8—121no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3#6495411yescharacteristic
435D3—204no—
436D3—401no—
437C5#6870411yescharacteristic, complemented, Sylow
438C22—41no—
439C22—304no—
440C22—604no—
441C22—601no—
442C22—1202no—
443C22—1202no—
444C22—1201no—
445C22#9142811yescharacteristic
446C22#9145911yescharacteristic
447C22#9147611yescharacteristic
448C4—122no—
449C4—202no—
450C4—401no—
451C4—601no—
452C4#9141811yescharacteristic
453C4#9142011yescharacteristic
454C4#9143311yescharacteristic
455C4#9156111yescharacteristic
456C3#1059982011yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—604no—
461C2—1201no—
462C2#1174890411yescharacteristic
subgroupG/H
centerC2#11748904
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#386
prime radicalC2×#91797C2
cosocleC22×C3×C4×C5C23
hypercenterC2×M16D3×D5
hypocenterC3×C5#1904
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #11754515C2semidirect
3. #11748626C2semidirect
4. #11748429C2semidirect
5. #11748392C2semidirect
6. C5×#4556C2semidirect
7. C3×#64777C2semidirect
14. C2×D120C4semidirect
15. C2×#6706C4semidirect
33. #64777D3semidirect
45. C2×D60C2×C4semidirect
49. C2×Dic30C2×C4semidirect
53. C2×C3×C5×C8C2×C4semidirect
75. #4556D5semidirect
164. C2×C5×C8C4×D3semidirect
221. C2×C3×C8C4×D5semidirect
364. C2×C8#1200semidirect
375. C3×C5#1904semidirect
437. C5#68704semidirect
456. C3#10599820semidirect

Maximal subgroups

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

subgroupindex
C2×#917972
#117545152
#117486262
#117484292
#117483922
C5×#45562
C3×#647772
#105998203
#687045