Finite Group Databasebeta

← #14302449

Subgroups — #14302449

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
1C3×#65855C211yesmaximal, characteristic, complemented
2C2×#91312C211yesmaximal, characteristic
3#11751107C211yesmaximal, characteristic, complemented
4#11748429C211yesmaximal, characteristic, complemented
5#11748367C211yesmaximal, characteristic, complemented
6C5×#4533C211yesmaximal, characteristic, complemented
7#11745970C211yesmaximal, characteristic, complemented
8#10599820—31nomaximal, Hall
9C2×#6817C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C2×C5×#208C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C3×#4039—22no—
17C3×D5×C22⋊C4—22no—
18C3×C4×D20—22no—
19#91312—22no—
20#91312—22no—
21C2×#6657C412yescomplemented
22C2×#6653C412yescomplemented
23#91090—22no—
24#90981—22no—
25#90965—22no—
26#71651—51nomaximal, Hall
27C2×#4054—31no—
28#65855D311yescharacteristic, complemented
29#65428—31no—
30#65420—31no—
31#65295—31no—
32C5×#344—31no—
33#64777—31no—
34C23×C3×D5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×#1220—21no—
37#6817—21no—
38#6817—21no—
39#6817—21no—
40#6817—21no—
41C2×D60C2×C411yescharacteristic, complemented
42C2×C4×D15—21no—
43C2×Dic30C2×C411yescharacteristic, complemented
44C2×C3×D20—21no—
45C2×C3×D20—21no—
46C2×C3×D20—21no—
47C2×C3×D20C2×C412yes—
48C2×C3×D20D412yes—
49C2×C3×D20D412yes—
50C2×C3×C4×D5—24no—
51C3×C5×C4⋊C4—21no—
52C3×C5×C22⋊C4D412yes—
53C3×C42×C5—21no—
54#6719—21no—
55C4⋊Dic15—21no—
56C4×Dic15—21no—
57C5×#208—21no—
58C5×#208—21no—
59C5×#208—21no—
60C5×#208—21no—
61C2×C5×C3⋊C8—21no—
62C2×C5×C3⋊C8C2×C412yescomplemented
63C3×C22⋊Dic5—21no—
64C3×#685—24no—
65C3×C4⋊Dic5—21no—
66C3×C4×Dic5D412yes—
67#6657—24no—
68#6653—24no—
69C3×#518—51no—
70C2×#932—51no—
71#5215—51no—
72#5006—51no—
73#5005—51no—
74#4533D511yescharacteristic, complemented
75#4531—51no—
76C2×#709—31no—
77C22×D20C2×D311yescharacteristic
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—22no—
88D5×C22⋊C4—22no—
89C4×D20—22no—
90#3957—62no—
91#3953—62no—
92#3938—62no—
93#1904—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×D15—21no—
96C22×C3×D5—22no—
97C22×C3×D5—22no—
98C22×C3×D5—22no—
99C22×C3×D5—82no—
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
107#1220—41no—
108#1220—41no—
109C2×Dic15—21no—
110C2×Dic15—41no—
111D60—21no—
112D60—21no—
113C4×D15—41no—
114C4×D15—41no—
115Dic30—21no—
116Dic30—21no—
117C2×C3×Dic5—22no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20C22⋊C414yes—
122C3×C4×D5—84no—
123C5×C3⋊C8—22no—
124C5×C3⋊C8—41no—
125C22×C3×D4—51no—
126C2×#235—51no—
127C3×C4×D4—102no—
128C3×C4×D4—102no—
129C3×#117—51no—
130C3×#117C2×D511yescharacteristic
131C2×C3×C22⋊C4—102no—
132C2×#214—52no—
133#932—102no—
134#932—102no—
135C2×#213—52no—
136#926—51no—
137C2×#208C2×D511yescharacteristic
138C2×#208C2×D511yescharacteristic
139#832—102no—
140#806—102no—
141#805—102no—
142C23×D5—21no—
143C22×C4×C5C22×D311yescharacteristic
144C2×C22⋊D5—61no—
145#709—61no—
146#709—61no—
147#709—61no—
148#709—61no—
149C2×D20—21no—
150C2×D20—21no—
151C2×D20—21no—
152C2×D20—31no—
153C2×D20C4×D312yes—
154C2×D20D1212yes—
155C2×D20#6712yes—
156C2×C4×D5—24no—
157C2×C4×D5—61no—
158C2×Dic10—31no—
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—24no—
171C4⋊Dic5—21no—
172C4⋊Dic5—61no—
173C4×Dic5—61no—
174C4×Dic5#6712yes—
175D40—64no—
176#677—64no—
177C2×AGL(1,ℤ/8)—151no—
178#518—51no—
179#421—151no—
180#418—151no—
181#410—151no—
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—41no—
189C2×D15—81no—
190C2×C3×D5—24no—
191C2×C3×D5—44no—
192C2×C3×D5—82no—
193C2×C3×D5—82no—
194C3×C4×C5—42no—
195C3×C4×C5C2×C22⋊C411yescharacteristic
196C3×C4×C5C4×D411yescharacteristic
197C3×C4×C5#12111yescharacteristic
198C3×C4×C5#12311yescharacteristic
199Dic15—41no—
200Dic15—81no—
201C3×Dic5—42no—
202C24×C3—101no—
203C2×C3×D4—52no—
204C2×C3×D4—52no—
205C2×C3×D4—52no—
206C2×C3×D4—101no—
207C2×C3×D4—101no—
208C2×C3×D4—101no—
209C22×C3×C4—104no—
210C22×C3×C4C22×D511yescharacteristic
211C2×#67—101no—
212#235—101no—
213#235—101no—
214#235—101no—
215#235—101no—
216C2×D12—51no—
217C2×C4×D3—101no—
218C2×Dic6—51no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—101no—
221C3×C22⋊C4—104no—
222C3×C22⋊C4—101no—
223C3×C22⋊C4D2012yes—
224C3×C42—21no—
225C3×C42—52no—
226#217—101no—
227#214—104no—
228#213—104no—
229C4⋊Dic3—101no—
230C4×Dic3—101no—
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—22no—
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—61no—
242C22×D5—82no—
243C2×C4×C5—22no—
244C2×C4×C5C2×C4×D311yescharacteristic
245C2×C4×C5C2×D1211yescharacteristic
246C2×C4×C5#23511yescharacteristic
247C2×C4×C5#23511yescharacteristic
248C2×C4×C5C2×#6711yescharacteristic
249C2×C4×C5C2×#6711yescharacteristic
250C22⋊D5—121no—
251C22⋊D5—121no—
252C2×Dic5—22no—
253C2×Dic5—61no—
254C2×Dic5—121no—
255D20—22no—
256D20—22no—
257D20—22no—
258D20—61no—
259D20—61no—
260D20(C2×D3)⋊C414yes—
261C4×D5—84no—
262C4×D5—121no—
263C4×D5—121no—
264Dic10—61no—
265Dic10—61no—
266C5×C8—62no—
267C5×C8—121no—
268C2×#41—151no—
269C22×D4—51no—
270AGL(1,ℤ/8)—302no—
271AGL(1,ℤ/8)—302no—
272C2×SD16—152no—
273C2×D8—152no—
274C2×M16—31no—
275C2×M16—31no—
276C4×D4—102no—
277C4×D4—102no—
278#117—51no—
279#117—151no—
280#117D3×D511yescharacteristic
281C2×C22⋊C4—102no—
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—81no—
290C3×D5—44no—
291C23×C3—102no—
292C23×C3—102no—
293C23×C3—102no—
294C23×C3—402no—
295C23×C3C2×D2011yescharacteristic
296C22×D3—101no—
297C3×D4—54no—
298C3×D4—102no—
299C3×D4—102no—
300C3×D4—102no—
301C2×C3×C4—22no—
302C2×C3×C4—102no—
303C2×C3×C4—404no—
304C2×C3×C4C2×C4×D511yescharacteristic
305C2×C3×C4#70911yescharacteristic
306C2×C3×C4D4×D511yescharacteristic
307C2×C3×C4D4×D511yescharacteristic
308C2×C3×C4D4×D511yescharacteristic
309C2×C3×C4#71311yescharacteristic
310#67—201no—
311#67—201no—
312C2×Dic3—101no—
313C2×Dic3—201no—
314D12—101no—
315D12—101no—
316C4×D3—201no—
317C4×D3—201no—
318Dic6—101no—
319Dic6—101no—
320C3⋊C8—22no—
321C3⋊C8—41no—
322C22×C5—41no—
323C22×C5C4×#6711yescharacteristic
324C22×C5#93011yescharacteristic
325C22×C5#95311yescharacteristic
326C2×D5—24no—
327C2×D5—44no—
328C2×D5—82no—
329C2×D5—82no—
330C2×D5—121no—
331C2×D5—241no—
332C4×C5—42no—
333C4×C5C2×(C2×D3)⋊C411yescharacteristic
334C4×C5C4×#6711yescharacteristic
335C4×C5#92911yescharacteristic
336C4×C5#93011yescharacteristic
337Dic5—42no—
338Dic5—121no—
339Dic5—241no—
340C24—101no—
341#41—301no—
342#41—301no—
343#41—301no—
344#41—301no—
345C2×Q8—151no—
346C2×D4—52no—
347C2×D4—52no—
348C2×D4—52no—
349C2×D4—101no—
350C2×D4—101no—
351C2×D4—101no—
352C2×D4—151no—
353C2×D4—301no—
354C22×C4—104no—
355C22×C4—301no—
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—104no—
369C22⋊C4—101no—
370C22⋊C4—301no—
371C22⋊C4#120212yes—
372C42—21no—
373C42—52no—
374C42—301no—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—104no—
378C22×C3—204no—
379C22×C3—402no—
380C22×C3—402no—
381C22×C3C4×D2011yescharacteristic
382C22×C3#402811yescharacteristic
383C22×C3#404111yescharacteristic
384C2×D3—201no—
385C2×D3—401no—
386C3×C4—42no—
387C3×C4—202no—
388C3×C4D5×C22⋊C411yescharacteristic
389C3×C4#403011yescharacteristic
390C3×C4#403911yescharacteristic
391C3×C4#404011yescharacteristic
392Dic3—201no—
393Dic3—401no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5#521311yescharacteristic
398D5—44no—
399D5—241no—
400C23—102no—
401C23—102no—
402C23—102no—
403C23—301no—
404C23—402no—
405C23C2×#120211yescharacteristic
406Q8—301no—
407Q8—301no—
408D4—54no—
409D4—102no—
410D4—102no—
411D4—102no—
412D4—301no—
413D4—301no—
414D4—601no—
415D4—601no—
416C2×C4—22no—
417C2×C4—102no—
418C2×C4—301no—
419C2×C4—404no—
420C2×C4—601no—
421C2×C4—601no—
422C2×C4—601no—
423C2×C4#677111yescharacteristic
424C2×C4#677311yescharacteristic
425C2×C4C4×D3×D511yescharacteristic
426C2×C4D5×D1211yescharacteristic
427C2×C4D5×#6711yescharacteristic
428C2×C4D5×#6711yescharacteristic
429C8—62no—
430C8—121no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—204no—
435C2×C3#6495411yescharacteristic
436D3—401no—
437C5#7165111yescharacteristic, complemented, Sylow
438C22—41no—
439C22—104no—
440C22—204no—
441C22—402no—
442C22—402no—
443C22—601no—
444C22—1201no—
445C22C4×#120211yescharacteristic
446C22#9145011yescharacteristic
447C22#9156411yescharacteristic
448C4—42no—
449C4—202no—
450C4—601no—
451C4—1201no—
452C4#9134811yescharacteristic
453C4#9144411yescharacteristic
454C4#9144811yescharacteristic
455C4D5×(C2×D3)⋊C411yescharacteristic
456C3#1059982011yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—204no—
461C2—1201no—
462C2#1174890711yescharacteristic
subgroupG/H
centerC2#11748907
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×#91312C2
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. C3×#65855C2semidirect
3. #11751107C2semidirect
4. #11748429C2semidirect
5. #11748367C2semidirect
6. C5×#4533C2semidirect
7. #11745970C2semidirect
21. C2×#6657C4semidirect
22. C2×#6653C4semidirect
28. #65855D3semidirect
41. C2×D60C2×C4semidirect
43. C2×Dic30C2×C4semidirect
62. C2×C5×C3⋊C8C2×C4semidirect
74. #4533D5semidirect
236. C2×C3⋊C8C4×D5semidirect
375. C3×C5#1904semidirect
437. C5#71651semidirect
456. C3#10599820semidirect

Maximal subgroups

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

subgroupindex
C3×#658552
C2×#913122
#117511072
#117484292
#117483672
C5×#45332
#117459702
#105998203
#716515