Finite Group Databasebeta

← #14302454

Subgroups — #14302454

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×#91298C211yesmaximal, characteristic
3C5×#5006C211yesmaximal, characteristic, complemented
4#11748425C211yesmaximal, characteristic, complemented
5#11748366C211yesmaximal, characteristic, complemented
6#11746354C211yesmaximal, characteristic, complemented
7#11745969C211yesmaximal, characteristic, complemented
8#10600842—31nomaximal, Hall
9C2×C5×#235C2211yescharacteristic
10C22×C3×D20C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C3×#4072C2211yescharacteristic
16C3×#4039—22no—
17C3×D5×C22⋊C4—22no—
18C3×C4×D20—22no—
19C2×#6655C412yescomplemented
20#91298—22no—
21#91298—22no—
22C2×#6652C412yescomplemented
23C5×#806—22no—
24#90979—22no—
25#90964—22no—
26#71651—51nomaximal, Hall
27C2×#4095—31no—
28#65855D311yescharacteristic, complemented
29C5×#410—31no—
30#65525—31no—
31#65290—31no—
32#64753—31no—
33#64751—31no—
34C23×C3×D5—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×C5×#67—21no—
37C5×#235—21no—
38C5×#235—21no—
39C5×#235—21no—
40C5×#235—21no—
41C2×C5×D12C2×C411yescharacteristic, complemented
42C2×C4×C5×D3—21no—
43C2×C5×Dic6C2×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#6710—21no—
55#6710—21no—
56#6710—21no—
57#6710—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168C2×C412yescomplemented
60C5×#217—21no—
61C5×C4⋊Dic3—21no—
62C4×C5×Dic3—21no—
63C3×C22⋊Dic5—21no—
64C3×#685—24no—
65C3×C4⋊Dic5—21no—
66C3×C4×Dic5D412yes—
67#6655—24no—
68#6652—24no—
69C3×#518—51no—
70C2×#932—51no—
71#5215—51no—
72#5006D511yescharacteristic, complemented
73#5005—51no—
74#4533—51no—
75#4531—51no—
76C2×C5×#41—31no—
77C22×D20C2×D311yescharacteristic
78C5×#117—31no—
79C5×#117C2×D311yescharacteristic
80#4095—62no—
81#4095—62no—
82C2×#688—32no—
83C2×#686—32no—
84#4072C2×D311yescharacteristic
85C2×#681—31no—
86C2×#681—31no—
87#4039—22no—
88D5×C22⋊C4—22no—
89C4×D20—22no—
90C5×#99—62no—
91#3969—62no—
92#3941—62no—
93#1904—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—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
107C5×#67—41no—
108C5×#67—41no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—41no—
111C5×D12—21no—
112C5×D12—21no—
113C4×C5×D3—41no—
114C4×C5×D3—41no—
115C5×Dic6—21no—
116C5×Dic6—21no—
117C2×C3×Dic5—22no—
118C3×D20—22no—
119C3×D20—22no—
120C3×D20—22no—
121C3×D20C22⋊C414yes—
122C3×C4×D5—84no—
123C3⋊#168—22no—
124C3⋊#168—41no—
125C22×C3×D4—51no—
126C2×#235C2×D511yescharacteristic
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#926C2×D511yescharacteristic
137C2×#208—51no—
138C2×#208—51no—
139#832—102no—
140#806—22no—
141#805—102no—
142C23×D5—21no—
143C5×#41—61no—
144C5×#41—61no—
145C5×#41—61no—
146C5×#41—61no—
147C2×C5×Q8—31no—
148C2×C5×D4—31no—
149C2×C5×D4—61no—
150C22×C4×C5—61no—
151C22×C4×C5C22×D311yescharacteristic
152C2×D20—21no—
153C2×D20—21no—
154C2×D20—21no—
155C2×D20C4×D312yes—
156C2×D20D1212yes—
157C2×D20#6712yes—
158C2×C4×D5—24no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—61no—
161C5×C22⋊C4—61no—
162C5×C22⋊C4#6712yes—
163C42×C5—21no—
164C42×C5—61no—
165C22⋊Dic5—21no—
166#688—64no—
167#686—64no—
168#685—24no—
169C4⋊Dic5—21no—
170C4×Dic5#6712yes—
171#681—61no—
172#681—61no—
173#681—61no—
174#681—61no—
175C2×#168—32no—
176C2×#168—61no—
177C2×AGL(1,ℤ/8)—151no—
178#518—51no—
179#421—151no—
180#418—151no—
181#410—31no—
182#344—151no—
183H(3,ℤ/4)—151no—
184C22×C3×C5—41no—
185C22×C3×C5C4×D411yescharacteristic
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5#12111yescharacteristic
188C2×C5×D3—41no—
189C2×C5×D3—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
199C3×Dic5—42no—
200C5×Dic3—41no—
201C5×Dic3—81no—
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—21no—
212#235—21no—
213#235—21no—
214#235—21no—
215#235—21no—
216C2×D12C4×D511yescharacteristic, complemented
217C2×C4×D3—21no—
218C2×Dic6C4×D511yescharacteristic, complemented
219C3×C4⋊C4—21no—
220C3×C4⋊C4—101no—
221C3×C22⋊C4—104no—
222C3×C22⋊C4—101no—
223C3×C22⋊C4C22⋊D512yes—
224C3×C42—21no—
225C3×C42—52no—
226#217—21no—
227#214—104no—
228#213—104no—
229C4⋊Dic3—21no—
230C4×Dic3—21no—
231#208—101no—
232#208—101no—
233#208—101no—
234#208—101no—
235C2×C3⋊C8—52no—
236C2×C3⋊C8—101no—
237C23×C5—61no—
238C23×C5C2×#6711yescharacteristic
239C22×D5—22no—
240C22×D5—22no—
241C22×D5—22no—
242C22×D5—82no—
243C5×Q8—61no—
244C5×Q8—61no—
245C5×D4—61no—
246C5×D4—61no—
247C5×D4—121no—
248C5×D4—121no—
249C2×C4×C5—22no—
250C2×C4×C5—61no—
251C2×C4×C5—121no—
252C2×C4×C5—121no—
253C2×C4×C5—121no—
254C2×C4×C5C2×C4×D311yescharacteristic
255C2×C4×C5C2×D1211yescharacteristic
256C2×C4×C5#23511yescharacteristic
257C2×C4×C5#23511yescharacteristic
258C2×C4×C5C2×#6711yescharacteristic
259C2×C4×C5C2×#6711yescharacteristic
260C2×Dic5—22no—
261D20—22no—
262D20—22no—
263D20—22no—
264D20(C2×D3)⋊C414yes—
265C4×D5—84no—
266#168—62no—
267#168—121no—
268C2×#41—31no—
269C22×D4—51no—
270AGL(1,ℤ/8)—302no—
271AGL(1,ℤ/8)—302no—
272C2×SD16—152no—
273C2×D8—152no—
274C2×M16—151no—
275C2×M16—151no—
276C4×D4—102no—
277C4×D4—102no—
278#117—31no—
279#117—51no—
280#117D3×D511yescharacteristic
281C2×C22⋊C4—102no—
282#104—302no—
283#102—302no—
284#99—62no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5#38611yescharacteristic
289C3×D5—44no—
290C5×D3—81no—
291C23×C3—102no—
292C23×C3—102no—
293C23×C3—102no—
294C23×C3—402no—
295C23×C3C2×C22⋊D511yescharacteristic
296C22×D3—21no—
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#71111yescharacteristic
310#67—41no—
311#67—41no—
312C2×Dic3—21no—
313C2×Dic3—41no—
314D12—21no—
315D12—21no—
316C4×D3—41no—
317C4×D3—41no—
318Dic6—21no—
319Dic6—21no—
320C3⋊C8—102no—
321C3⋊C8—201no—
322C22×C5—41no—
323C22×C5—121no—
324C22×C5—241no—
325C22×C5C4×#6711yescharacteristic
326C22×C5#93011yescharacteristic
327C22×C5#95311yescharacteristic
328C2×D5—24no—
329C2×D5—44no—
330C2×D5—82no—
331C2×D5—82no—
332C4×C5—42no—
333C4×C5—121no—
334C4×C5—241no—
335C4×C5C2×(C2×D3)⋊C411yescharacteristic
336C4×C5C4×#6711yescharacteristic
337C4×C5#92911yescharacteristic
338C4×C5#93011yescharacteristic
339Dic5—42no—
340C24—101no—
341#41—61no—
342#41—61no—
343#41—61no—
344#41—61no—
345C2×Q8—31no—
346C2×D4—31no—
347C2×D4—52no—
348C2×D4—52no—
349C2×D4—52no—
350C2×D4—61no—
351C2×D4—101no—
352C2×D4—101no—
353C2×D4—101no—
354C22×C4—61no—
355C22×C4—104no—
356C22×C4C2×D3×D511yescharacteristic
357SD16—304no—
358D8—304no—
359M16—301no—
360M16—301no—
361M16—301no—
362M16—301no—
363C2×C8—152no—
364C2×C8—301no—
365C4⋊C4—21no—
366C4⋊C4—61no—
367C4⋊C4—101no—
368C22⋊C4—61no—
369C22⋊C4—104no—
370C22⋊C4—101no—
371C22⋊C4#120112yes—
372C42—21no—
373C42—52no—
374C42—61no—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—104no—
378C22×C3—204no—
379C22×C3—402no—
380C22×C3—402no—
381C22×C3C4×C22⋊D511yescharacteristic
382C22×C3#408311yescharacteristic
383C22×C3#408411yescharacteristic
384C2×D3—41no—
385C2×D3—81no—
386C3×C4—42no—
387C3×C4—202no—
388C3×C4D5×C22⋊C411yescharacteristic
389C3×C4#402711yescharacteristic
390C3×C4#402911yescharacteristic
391C3×C4#403011yescharacteristic
392Dic3—41no—
393Dic3—81no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—241no—
398C2×C5#521311yescharacteristic
399D5—44no—
400C23—61no—
401C23—102no—
402C23—102no—
403C23—102no—
404C23—402no—
405C23C2×#120111yescharacteristic
406Q8—61no—
407Q8—61no—
408D4—54no—
409D4—61no—
410D4—61no—
411D4—102no—
412D4—102no—
413D4—102no—
414D4—121no—
415D4—121no—
416C2×C4—22no—
417C2×C4—61no—
418C2×C4—102no—
419C2×C4—121no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—404no—
423C2×C4#677111yescharacteristic
424C2×C4#677211yescharacteristic
425C2×C4C4×D3×D511yescharacteristic
426C2×C4D5×D1211yescharacteristic
427C2×C4D5×#6711yescharacteristic
428C2×C4D5×#6711yescharacteristic
429C8—302no—
430C8—601no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—204no—
435C2×C3#6524511yescharacteristic
436D3—81no—
437C5#7165111yescharacteristic, complemented, Sylow
438C22—41no—
439C22—104no—
440C22—121no—
441C22—204no—
442C22—241no—
443C22—402no—
444C22—402no—
445C22C4×#120111yescharacteristic
446C22#9144911yescharacteristic
447C22#9156311yescharacteristic
448C4—42no—
449C4—121no—
450C4—202no—
451C4—241no—
452C4#9144011yescharacteristic
453C4#9144711yescharacteristic
454C4#9144811yescharacteristic
455C4D5×(C2×D3)⋊C411yescharacteristic
456C3#1060084211yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—204no—
461C2—241no—
462C2#1174890511yescharacteristic
subgroupG/H
centerC2#11748905
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×#91298C2
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. C5×#5006C2semidirect
4. #11748425C2semidirect
5. #11748366C2semidirect
6. #11746354C2semidirect
7. #11745969C2semidirect
19. C2×#6655C4semidirect
22. C2×#6652C4semidirect
28. #65855D3semidirect
41. C2×C5×D12C2×C4semidirect
43. C2×C5×Dic6C2×C4semidirect
59. C2×C3⋊#168C2×C4semidirect
72. #5006D5semidirect
216. C2×D12C4×D5semidirect
218. C2×Dic6C4×D5semidirect
375. C3×C5#1904semidirect
437. C5#71651semidirect
456. C3#10600842semidirect

Maximal subgroups

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

subgroupindex
C3×#658552
C2×#912982
C5×#50062
#117484252
#117483662
#117463542
#117459692
#106008423
#716515