Finite Group Databasebeta

← #14302452

Subgroups — #14302452

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
1C5×#5521C211yesmaximal, characteristic, complemented
2C2×#91299C211yesmaximal, characteristic
3C3×#65295C211yesmaximal, characteristic, complemented
4#11748421C211yesmaximal, characteristic, complemented
5#11748386C211yesmaximal, characteristic, complemented
6#11746354C211yesmaximal, characteristic, complemented
7#11745969C211yesmaximal, characteristic, complemented
8#10602444—31nomaximal, Hall
9C22×C5×D12C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12C2×#6710C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C5×#893—22no—
16C5×D3×C22⋊C4—22no—
17C4×C5×D12—22no—
18C3×#4072C2211yescharacteristic
19C2×#6656C412yescomplemented
20#91299—22no—
21#91299—22no—
22C2×#6652C412yescomplemented
23C3×#3938—22no—
24#90977—22no—
25#90966—22no—
26#70049—51nomaximal, Hall
27C5×#518—31no—
28C2×#4078—31no—
29#65504—31no—
30#65295D311yescharacteristic, complemented
31#65294—31no—
32#64753—31no—
33#64751—31no—
34C23×C5×D3—21no—
35C22×C3×C4×C5C2311yescharacteristic
36C2×C5×D12—21no—
37C2×C5×D12—21no—
38C2×C5×D12—21no—
39C2×C5×D12C2×C412yes—
40C2×C5×D12D412yes—
41C2×C5×D12D412yes—
42C2×C4×C5×D3—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#6710—21no—
55#6710—21no—
56#6710—21no—
57#6710—21no—
58C2×C3⋊#168—21no—
59C2×C3⋊#168C2×C412yescomplemented
60C5×#217—21no—
61C5×(C2×D3)⋊C4—24no—
62C5×C4⋊Dic3—21no—
63C4×C5×Dic3D412yes—
64C3×C22⋊Dic5—21no—
65C3×C4⋊Dic5—21no—
66C3×C4×Dic5—21no—
67#6656—24no—
68#6652—24no—
69C2×#949—51no—
70#5521D511yescharacteristic, complemented
71C3×#410—51no—
72#5236—51no—
73#5001—51no—
74#4533—51no—
75#4531—51no—
76C22×C5×D4—31no—
77C2×#709C2×D311yescharacteristic
78C4×C5×D4—62no—
79C4×C5×D4—62no—
80C5×#117—31no—
81C5×#117C2×D311yescharacteristic
82C2×C5×C22⋊C4—62no—
83C2×#687—32no—
84#4078—62no—
85#4078—62no—
86C2×#686—32no—
87#4072C2×D311yescharacteristic
88C2×#681—31no—
89C2×#681—31no—
90#3964—62no—
91#3938—22no—
92#3937—62no—
93#1904—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—22no—
96C22×C5×D3—22no—
97C22×C5×D3—22no—
98C22×C5×D3—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×C5×Dic3—22no—
108C5×D12—22no—
109C5×D12—22no—
110C5×D12—22no—
111C5×D12C22⋊C414yes—
112C4×C5×D3—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—
123C3⋊#168—22no—
124C3⋊#168—41no—
125C2×C3×#41—51no—
126C22×D12C2×D511yescharacteristic
127C3×#117—51no—
128C3×#117C2×D511yescharacteristic
129#949—102no—
130#949—102no—
131C2×#215—52no—
132C2×#213—52no—
133#926C2×D511yescharacteristic
134C2×#208—51no—
135C2×#208—51no—
136#893—22no—
137D3×C22⋊C4—22no—
138C4×D12—22no—
139C3×#99—102no—
140#837—102no—
141#809—102no—
142C24×C5—61no—
143C2×C5×D4—32no—
144C2×C5×D4—32no—
145C2×C5×D4—32no—
146C2×C5×D4—61no—
147C2×C5×D4—61no—
148C2×C5×D4—61no—
149C22×C4×C5—64no—
150C22×C4×C5C22×D311yescharacteristic
151C2×C22⋊D5—21no—
152#709—21no—
153#709—21no—
154#709—21no—
155#709—21no—
156C2×D20C4×D311yescharacteristic, complemented
157C2×C4×D5—21no—
158C2×Dic10C4×D311yescharacteristic, complemented
159C5×C4⋊C4—21no—
160C5×C4⋊C4—61no—
161C5×C22⋊C4—64no—
162C5×C22⋊C4—61no—
163C5×C22⋊C4#6712yes—
164C42×C5—21no—
165C42×C5—32no—
166C22⋊Dic5—21no—
167#687—64no—
168#686—64no—
169C4⋊Dic5—21no—
170C4×Dic5—21no—
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—31no—
179#421—151no—
180#418—151no—
181#410—51no—
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—24no—
189C2×C5×D3—44no—
190C2×C5×D3—82no—
191C2×C5×D3—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
199C3×Dic5—41no—
200C3×Dic5—81no—
201C5×Dic3—42no—
202C23×D3—21no—
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—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12C4×D512yes—
216C2×D12D2012yes—
217C2×D12C22⋊D512yes—
218C2×C4×D3—24no—
219C3×C4⋊C4—21no—
220C3×C4⋊C4—101no—
221C3×C22⋊C4—101no—
222C3×C22⋊C4C22⋊D512yes—
223C3×C42—21no—
224C3×C42—101no—
225#217—21no—
226#215—104no—
227#213—104no—
228(C2×D3)⋊C4—24no—
229C4⋊Dic3—21no—
230C4×Dic3C22⋊D512yes—
231#208—101no—
232#208—101no—
233#208—101no—
234#208—101no—
235C2×C3⋊C8—52no—
236C2×C3⋊C8—101no—
237C23×C5—62no—
238C23×C5—62no—
239C23×C5—62no—
240C23×C5—242no—
241C23×C5C2×#6711yescharacteristic
242C22×D5—21no—
243C5×D4—34no—
244C5×D4—62no—
245C5×D4—62no—
246C5×D4—62no—
247C2×C4×C5—22no—
248C2×C4×C5—62no—
249C2×C4×C5—244no—
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5#23511yescharacteristic
252C2×C4×C5D3×D411yescharacteristic
253C2×C4×C5D3×D411yescharacteristic
254C2×C4×C5D3×D411yescharacteristic
255C2×C4×C5#23711yescharacteristic
256C22⋊D5—41no—
257C22⋊D5—41no—
258C2×Dic5—21no—
259C2×Dic5—41no—
260D20—21no—
261D20—21no—
262C4×D5—41no—
263C4×D5—41no—
264Dic10—21no—
265Dic10—21no—
266#168—62no—
267#168—121no—
268C2×#41—51no—
269C22×D4—31no—
270AGL(1,ℤ/8)—302no—
271AGL(1,ℤ/8)—302no—
272C2×SD16—152no—
273C2×D8—152no—
274C2×M16—151no—
275C2×M16—151no—
276C4×D4—62no—
277C4×D4—62no—
278#117—31no—
279#117—51no—
280#117D3×D511yescharacteristic
281C2×C22⋊C4—62no—
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
289C3×D5—81no—
290C5×D3—44no—
291C23×C3—101no—
292C23×C3C2×C22⋊D511yescharacteristic
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—82no—
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×C4C2×D2011yescharacteristic
310C2×C3×C4#70911yescharacteristic
311C2×C3×C4#70911yescharacteristic
312C2×C3×C4C2×C22⋊D511yescharacteristic
313C2×C3×C4C2×C22⋊D511yescharacteristic
314C2×Dic3—22no—
315D12—22no—
316D12—22no—
317D12—22no—
318D12#68514yes—
319C4×D3—84no—
320C3⋊C8—102no—
321C3⋊C8—201no—
322C22×C5—41no—
323C22×C5—64no—
324C22×C5—124no—
325C22×C5—242no—
326C22×C5—242no—
327C22×C5C4×#6711yescharacteristic
328C22×C5#93711yescharacteristic
329C22×C5#93811yescharacteristic
330C2×D5—41no—
331C2×D5—81no—
332C4×C5—42no—
333C4×C5—122no—
334C4×C5D3×C22⋊C411yescharacteristic
335C4×C5#67⋊C411yescharacteristic
336C4×C5#88311yescharacteristic
337C4×C5#88411yescharacteristic
338Dic5—41no—
339Dic5—81no—
340C24—61no—
341#41—101no—
342#41—101no—
343#41—101no—
344#41—101no—
345C2×Q8—51no—
346C2×D4—32no—
347C2×D4—32no—
348C2×D4—32no—
349C2×D4—51no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4—101no—
354C22×C4—64no—
355C22×C4—101no—
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—64no—
369C22⋊C4—61no—
370C22⋊C4—101no—
371C22⋊C4#120112yes—
372C42—21no—
373C42—32no—
374C42—101no—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—201no—
378C22×C3—401no—
379C22×C3C4×C22⋊D511yescharacteristic
380C22×C3#407611yescharacteristic
381C22×C3#409911yescharacteristic
382C2×D3—24no—
383C2×D3—44no—
384C2×D3—82no—
385C2×D3—82no—
386C3×C4—42no—
387C3×C4—201no—
388C3×C4—401no—
389C3×C4C2×#68511yescharacteristic
390C3×C4C4×C22⋊D511yescharacteristic
391C3×C4#407511yescharacteristic
392C3×C4#407611yescharacteristic
393Dic3—42no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—124no—
398C2×C5#495611yescharacteristic
399D5—81no—
400C23—62no—
401C23—62no—
402C23—62no—
403C23—101no—
404C23—242no—
405C23C2×#120111yescharacteristic
406Q8—101no—
407Q8—101no—
408D4—34no—
409D4—62no—
410D4—62no—
411D4—62no—
412D4—101no—
413D4—101no—
414D4—201no—
415D4—201no—
416C2×C4—22no—
417C2×C4—62no—
418C2×C4—101no—
419C2×C4—201no—
420C2×C4—201no—
421C2×C4—201no—
422C2×C4—244no—
423C2×C4#676511yescharacteristic
424C2×C4#677111yescharacteristic
425C2×C4C4×D3×D511yescharacteristic
426C2×C4D3×D2011yescharacteristic
427C2×C4D3×C22⋊D511yescharacteristic
428C2×C4D3×C22⋊D511yescharacteristic
429C8—302no—
430C8—601no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—401no—
435C2×C3#6550211yescharacteristic
436D3—44no—
437C5#7004911yescharacteristic, complemented, Sylow
438C22—41no—
439C22—64no—
440C22—124no—
441C22—201no—
442C22—242no—
443C22—242no—
444C22—401no—
445C22C4×#120111yescharacteristic
446C22#9145611yescharacteristic
447C22#9156811yescharacteristic
448C4—42no—
449C4—122no—
450C4—201no—
451C4—401no—
452C4#9144111yescharacteristic
453C4#9145211yescharacteristic
454C4#9145411yescharacteristic
455C4D3×#68511yescharacteristic
456C3#1060244411yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—124no—
461C2—401no—
462C2#1174891011yescharacteristic
subgroupG/H
centerC2#11748910
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×#91299C2
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. C5×#5521C2semidirect
3. C3×#65295C2semidirect
4. #11748421C2semidirect
5. #11748386C2semidirect
6. #11746354C2semidirect
7. #11745969C2semidirect
19. C2×#6656C4semidirect
22. C2×#6652C4semidirect
30. #65295D3semidirect
48. C2×C3×D20C2×C4semidirect
50. C2×C3×Dic10C2×C4semidirect
59. C2×C3⋊#168C2×C4semidirect
70. #5521D5semidirect
156. C2×D20C4×D3semidirect
158. C2×Dic10C4×D3semidirect
375. C3×C5#1904semidirect
437. C5#70049semidirect
456. C3#10602444semidirect

Maximal subgroups

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

subgroupindex
C5×#55212
C2×#912992
C3×#652952
#117484212
#117483862
#117463542
#117459692
#106024443
#700495