Finite Group Databasebeta

← #14302450

Subgroups — #14302450

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
1#11756280C211yesmaximal, characteristic, complemented
2C2×#91301C211yesmaximal, characteristic
3C3×#65295C211yesmaximal, characteristic, complemented
4#11748420C211yesmaximal, characteristic, complemented
5#11748392C211yesmaximal, characteristic, complemented
6C5×#4533C211yesmaximal, characteristic, complemented
7#11745970C211yesmaximal, characteristic, complemented
8#10599820—31nomaximal, Hall
9C22×D60C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13#91782—22no—
14C22⋊C4×D15—22no—
15C4×D60—22no—
16C2×C5×#208C2211yescharacteristic
17C2×C5×#208C2211yescharacteristic
18C3×#4072C2211yescharacteristic
19C2×#6658C412yescomplemented
20#91301—22no—
21#91301—22no—
22C2×#6653C412yescomplemented
23C3×#3938—22no—
24#90976—22no—
25#90968—22no—
26#70049—51nomaximal, Hall
27C2×#4054—31no—
28#65855—31no—
29#65428—31no—
30#65420—31no—
31#65295D311yescharacteristic, complemented
32C5×#344—31no—
33#64777—31no—
34C23×D15—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×D60—21no—
37C2×D60—21no—
38C2×D60—21no—
39C2×D60C2×C412yes—
40C2×D60D412yes—
41C2×D60D412yes—
42C2×C4×D15—24no—
43C2×C3×C22⋊D5—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C3×#709—21no—
48C2×C3×D20C2×C411yescharacteristic, complemented
49C2×C3×C4×D5—21no—
50C2×C3×Dic10C2×C411yescharacteristic, complemented
51C3×C5×C4⋊C4—21no—
52C3×C5×C22⋊C4D412yes—
53C3×C42×C5—21no—
54#6719—21no—
55#6714—24no—
56C4⋊Dic15—21no—
57C4×Dic15D412yes—
58C5×#208—21no—
59C5×#208—21no—
60C5×#208—21no—
61C5×#208—21no—
62C2×C5×C3⋊C8—21no—
63C2×C5×C3⋊C8C2×C412yescomplemented
64C3×C22⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C3×C4×Dic5—21no—
67#6658—24no—
68#6653—24no—
69C2×#949—51no—
70#5521—51no—
71C3×#410—51no—
72#5236—51no—
73#5001—51no—
74#4533D511yescharacteristic, complemented
75#4531—51no—
76C2×#709C2×D311yescharacteristic
77C22×D20—31no—
78C2×C5×M16—31no—
79C2×C5×M16—31no—
80C5×#117C2×D311yescharacteristic
81#4072—31no—
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—22no—
93#1904—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—22no—
96C22×D15—22no—
97C22×D15—22no—
98C22×D15—82no—
99C22×C3×D5—21no—
100C2×C3×C4×C5—22no—
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×C3×C4×C5#4111yescharacteristic
107C2×Dic15—22no—
108D60—22no—
109D60—22no—
110D60—22no—
111D60C22⋊C414yes—
112C4×D15—84no—
113C3×C22⋊D5—41no—
114C3×C22⋊D5—41no—
115C2×C3×Dic5—21no—
116C2×C3×Dic5—41no—
117C3×D20—21no—
118C3×D20—21no—
119C3×C4×D5—41no—
120C3×C4×D5—41no—
121C3×Dic10—21no—
122C3×Dic10—21no—
123C5×C3⋊C8—22no—
124C5×C3⋊C8—41no—
125C2×C3×#41—51no—
126C22×D12—51no—
127C3×#117—51no—
128C3×#117C2×D511yescharacteristic
129#949—102no—
130#949—102no—
131C2×#215—52no—
132C2×#213—52no—
133#926—51no—
134C2×#208C2×D511yescharacteristic
135C2×#208C2×D511yescharacteristic
136#893—102no—
137D3×C22⋊C4—102no—
138C4×D12—102no—
139C3×#99—102no—
140#837—102no—
141#809—102no—
142C23×D5—61no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5—21no—
145#709—21no—
146#709—21no—
147#709—21no—
148#709—21no—
149C2×D20—32no—
150C2×D20—32no—
151C2×D20—32no—
152C2×D20—61no—
153C2×D20—61no—
154C2×D20—61no—
155C2×D20C4×D311yescharacteristic, complemented
156C2×C4×D5—21no—
157C2×C4×D5—64no—
158C2×Dic10C4×D311yescharacteristic, complemented
159C5×M16—61no—
160C5×M16—61no—
161C5×M16—61no—
162C5×M16—61no—
163C2×C5×C8—32no—
164C2×C5×C8—61no—
165C5×C4⋊C4—21no—
166C5×C22⋊C4#6712yes—
167C42×C5—21no—
168C22⋊Dic5—21no—
169C22⋊Dic5—61no—
170#685—64no—
171C4⋊Dic5—21no—
172C4⋊Dic5—61no—
173C4×Dic5—21no—
174C4×Dic5—32no—
175D40—64no—
176#677—64no—
177C2×AGL(1,ℤ/8)—151no—
178#518—151no—
179#421—151no—
180#418—151no—
181#410—51no—
182#344—31no—
183H(3,ℤ/4)—151no—
184C22×C3×C5—41no—
185C22×C3×C5C4×D411yescharacteristic
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#12111yescharacteristic
188C2×D15—24no—
189C2×D15—44no—
190C2×D15—82no—
191C2×D15—82no—
192C2×C3×D5—41no—
193C2×C3×D5—81no—
194C3×C4×C5—42no—
195C3×C4×C5C2×C22⋊C411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5#12111yescharacteristic
198C3×C4×C5#12311yescharacteristic
199Dic15—42no—
200C3×Dic5—41no—
201C3×Dic5—81no—
202C23×D3—101no—
203C3×#41—101no—
204C3×#41—101no—
205C3×#41—101no—
206C3×#41—101no—
207C2×C3×Q8—51no—
208C2×C3×D4—51no—
209C2×C3×D4—101no—
210C22×C3×C4—101no—
211C22×C3×C4C22×D511yescharacteristic
212C2×D12—52no—
213C2×D12—52no—
214C2×D12—52no—
215C2×D12—101no—
216C2×D12—101no—
217C2×D12—101no—
218C2×C4×D3—104no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—101no—
221C3×C22⋊C4—101no—
222C3×C22⋊C4D2012yes—
223C3×C42—21no—
224C3×C42—101no—
225#217—101no—
226#215—104no—
227#213—104no—
228(C2×D3)⋊C4—104no—
229C4⋊Dic3—101no—
230C4×Dic3—52no—
231#208—21no—
232#208—21no—
233#208—21no—
234#208—21no—
235C2×C3⋊C8—21no—
236C2×C3⋊C8C4×D512yescomplemented
237C23×C5C2×#6711yescharacteristic
238C22×D5—21no—
239C22×D5—62no—
240C22×D5—62no—
241C22×D5—62no—
242C22×D5—242no—
243C2×C4×C5—22no—
244C2×C4×C5C2×C4×D311yescharacteristic
245C2×C4×C5#23511yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5D3×D411yescharacteristic
248C2×C4×C5D3×D411yescharacteristic
249C2×C4×C5#23711yescharacteristic
250C22⋊D5—41no—
251C22⋊D5—41no—
252C2×Dic5—21no—
253C2×Dic5—41no—
254C2×Dic5—62no—
255D20—21no—
256D20—21no—
257D20—34no—
258D20—62no—
259D20—62no—
260D20—62no—
261C4×D5—41no—
262C4×D5—41no—
263C4×D5—244no—
264Dic10—21no—
265Dic10—21no—
266C5×C8—62no—
267C5×C8—121no—
268C2×#41—51no—
269C22×D4—151no—
270AGL(1,ℤ/8)—302no—
271AGL(1,ℤ/8)—302no—
272C2×SD16—152no—
273C2×D8—152no—
274C2×M16—31no—
275C2×M16—31no—
276C4×D4—302no—
277C4×D4—302no—
278#117—51no—
279#117—151no—
280#117D3×D511yescharacteristic
281C2×C22⋊C4—302no—
282#104—302no—
283#102—302no—
284#99—102no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5#38611yescharacteristic
289D15—44no—
290C3×D5—81no—
291C23×C3—101no—
292C23×C3C2×D2011yescharacteristic
293C22×D3—102no—
294C22×D3—102no—
295C22×D3—102no—
296C22×D3—402no—
297C3×Q8—101no—
298C3×Q8—101no—
299C3×D4—101no—
300C3×D4—101no—
301C3×D4—201no—
302C3×D4—201no—
303C2×C3×C4—22no—
304C2×C3×C4—101no—
305C2×C3×C4—201no—
306C2×C3×C4—201no—
307C2×C3×C4—201no—
308C2×C3×C4C2×C4×D511yescharacteristic
309C2×C3×C4#70911yescharacteristic
310C2×C3×C4D4×D511yescharacteristic
311C2×C3×C4D4×D511yescharacteristic
312C2×C3×C4D4×D511yescharacteristic
313C2×C3×C4#71311yescharacteristic
314C2×Dic3—102no—
315D12—54no—
316D12—102no—
317D12—102no—
318D12—102no—
319C4×D3—404no—
320C3⋊C8—22no—
321C3⋊C8—41no—
322C22×C5—41no—
323C22×C5C4×#6711yescharacteristic
324C22×C5#93711yescharacteristic
325C22×C5#93811yescharacteristic
326C2×D5—41no—
327C2×D5—64no—
328C2×D5—81no—
329C2×D5—124no—
330C2×D5—242no—
331C2×D5—242no—
332C4×C5—42no—
333C4×C5D3×C22⋊C411yescharacteristic
334C4×C5#67⋊C411yescharacteristic
335C4×C5#88311yescharacteristic
336C4×C5#88411yescharacteristic
337Dic5—41no—
338Dic5—81no—
339Dic5—122no—
340C24—301no—
341#41—101no—
342#41—101no—
343#41—101no—
344#41—101no—
345C2×Q8—51no—
346C2×D4—51no—
347C2×D4—101no—
348C2×D4—152no—
349C2×D4—152no—
350C2×D4—152no—
351C2×D4—301no—
352C2×D4—301no—
353C2×D4—301no—
354C22×C4—101no—
355C22×C4—304no—
356C22×C4C2×D3×D511yescharacteristic
357SD16—304no—
358D8—304no—
359M16—61no—
360M16—61no—
361M16—61no—
362M16—61no—
363C2×C8—32no—
364C2×C8—61no—
365C4⋊C4—21no—
366C4⋊C4—101no—
367C4⋊C4—301no—
368C22⋊C4—101no—
369C22⋊C4—304no—
370C22⋊C4—301no—
371C22⋊C4#120212yes—
372C42—21no—
373C42—101no—
374C42—152no—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—201no—
378C22×C3—401no—
379C22×C3C4×D2011yescharacteristic
380C22×C3#402811yescharacteristic
381C22×C3#404111yescharacteristic
382C2×D3—104no—
383C2×D3—204no—
384C2×D3—402no—
385C2×D3—402no—
386C3×C4—42no—
387C3×C4—201no—
388C3×C4—401no—
389C3×C4D5×C22⋊C411yescharacteristic
390C3×C4#403011yescharacteristic
391C3×C4#403911yescharacteristic
392C3×C4#404011yescharacteristic
393Dic3—202no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5#495611yescharacteristic
398D5—81no—
399D5—124no—
400C23—101no—
401C23—302no—
402C23—302no—
403C23—302no—
404C23—1202no—
405C23C2×#120211yescharacteristic
406Q8—101no—
407Q8—101no—
408D4—101no—
409D4—101no—
410D4—154no—
411D4—201no—
412D4—201no—
413D4—302no—
414D4—302no—
415D4—302no—
416C2×C4—22no—
417C2×C4—101no—
418C2×C4—201no—
419C2×C4—201no—
420C2×C4—201no—
421C2×C4—302no—
422C2×C4—1204no—
423C2×C4#676611yescharacteristic
424C2×C4#677111yescharacteristic
425C2×C4C4×D3×D511yescharacteristic
426C2×C4#677711yescharacteristic
427C2×C4#679011yescharacteristic
428C2×C4#679011yescharacteristic
429C8—62no—
430C8—121no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—401no—
435C2×C3#6495411yescharacteristic
436D3—204no—
437C5#7004911yescharacteristic, complemented, Sylow
438C22—41no—
439C22—201no—
440C22—304no—
441C22—401no—
442C22—604no—
443C22—1202no—
444C22—1202no—
445C22C4×#120211yescharacteristic
446C22#9146511yescharacteristic
447C22#9157211yescharacteristic
448C4—42no—
449C4—201no—
450C4—401no—
451C4—602no—
452C4#9135411yescharacteristic
453C4#9139611yescharacteristic
454C4#9146111yescharacteristic
455C4#9147311yescharacteristic
456C3#1059982011yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—401no—
461C2—604no—
462C2#1174891711yescharacteristic
subgroupG/H
centerC2#11748917
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×#91301C2
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1904
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756280C2semidirect
3. C3×#65295C2semidirect
4. #11748420C2semidirect
5. #11748392C2semidirect
6. C5×#4533C2semidirect
7. #11745970C2semidirect
19. C2×#6658C4semidirect
22. C2×#6653C4semidirect
31. #65295D3semidirect
48. C2×C3×D20C2×C4semidirect
50. C2×C3×Dic10C2×C4semidirect
63. C2×C5×C3⋊C8C2×C4semidirect
74. #4533D5semidirect
155. C2×D20C4×D3semidirect
158. C2×Dic10C4×D3semidirect
236. C2×C3⋊C8C4×D5semidirect
375. C3×C5#1904semidirect
437. C5#70049semidirect
456. C3#10599820semidirect

Maximal subgroups

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

subgroupindex
#117562802
C2×#913012
C3×#652952
#117484202
#117483922
C5×#45332
#117459702
#105998203
#700495