Finite Group Databasebeta

← #14302953

Subgroups — #14302953

Order 1920.

628 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5516C211yesmaximal, characteristic, complemented
2#11754251C211yesmaximal, characteristic
3C3×#65294C211yesmaximal, characteristic
4#11748421C211yesmaximal, characteristic
5C2×#90962C211yesmaximal, characteristic, complemented
6#11746352C211yesmaximal, characteristic, complemented
7#11745971C211yesmaximal, characteristic, complemented
8#10602456—31nomaximal, Hall
9C22×C5×Dic6C2211yescharacteristic
10C2×C3×#709C2211yescharacteristic
11C3×C5×#117C2211yescharacteristic
12#91815C2211yescharacteristic
13C2×#6710C2211yescharacteristic
14C5×#926C2211yescharacteristic
15C5×#887—22no—
16C5×#877—22no—
17C4×C5×Dic6—22no—
18C2×C3×#681C2211yescharacteristic
19#91536—22no—
20#91385C412yescomplemented
21#91368C412yescomplemented
22#91359—22no—
23C3×#3937—22no—
24#90977—22no—
25#90962—22no—
26#70411—51nomaximal, Hall
27C5×#519—31no—
28#66150—31no—
29C2×#3968—31no—
30#65294—31no—
31#65294D311yescharacteristic
32#64751—31no—
33#64751—31no—
34C22×C3×C4×C5C2311yescharacteristic
35C22×C5×Dic3D412yes—
36C2×C5×Dic6—21no—
37C2×C5×Dic6—21no—
38C2×C5×Dic6—21no—
39C2×C5×Dic6—21no—
40C2×C5×Dic6C2×C412yes—
41C2×C5×Dic6D412yes—
42C2×C3×C22⋊D5—21no—
43C3×#709—21no—
44C3×#709—21no—
45C3×#709—21no—
46C3×#709—21no—
47C2×C3×D20C2×C411yescharacteristic
48C2×C3×C4×D5—21no—
49C2×C3×Dic10C2×C411yescharacteristic
50C3×C5×C4⋊C4—21no—
51C3×C5×C22⋊C4—21no—
52C3×C42×C5D412yes—
53#6719—21no—
54C4⋊Dic15—21no—
55C4×Dic15C2×C412yes—
56#6710—21no—
57#6710—21no—
58C2×C3⋊#168—21no—
59C5×#217—21no—
60C5×C4⋊Dic3—21no—
61C5×Dic3⋊C4—24no—
62C4×C5×Dic3—24no—
63C4×C5×Dic3D412yes—
64C3×#681—21no—
65C3×#681—21no—
66C2×C3×#168—21no—
67#6669—24no—
68#6665—24no—
69#5825—51no—
70#5516D511yescharacteristic, complemented
71C3×#421—51no—
72#5236—51no—
73C2×#824—51no—
74#4557—51no—
75#4531—51no—
76C22×C5×Q8—31no—
77C2×#709C2×D311yescharacteristic
78C4×C5×Q8—62no—
79C4×C5×Q8—62no—
80C5×#117—31no—
81C5×#117—62no—
82C5×#117C2×D311yescharacteristic
83#4093—32no—
84#4092—62no—
85#4090—32no—
86#4075—62no—
87#4072—31no—
88C2×#681—31no—
89C2×#681C2×D311yescharacteristic
90#3968—62no—
91#3937—22no—
92#3937—62no—
93#1912—151noSylow
94C23×C3×C5C2×D411yescharacteristic
95C22×C3×D5—21no—
96C2×C3×C4×C5—22no—
97C2×C3×C4×C5C22×C411yescharacteristic
98C2×C3×C4×C5C2×D411yescharacteristic
99C2×C3×C4×C5C2×D411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C2×C3×C4×C5#4111yescharacteristic
102C2×C3×C4×C5#4111yescharacteristic
103C2×Dic15—22no—
104C2×C5×Dic3—22no—
105C2×C5×Dic3—22no—
106C2×C5×Dic3—22no—
107C2×C5×Dic3C22⋊C414yes—
108C5×Dic6—22no—
109C5×Dic6—22no—
110C5×Dic6—22no—
111C5×Dic6—22no—
112C3×C22⋊D5—41no—
113C3×C22⋊D5—41no—
114C2×C3×Dic5—21no—
115C3×D20—21no—
116C3×D20—21no—
117C3×C4×D5—41no—
118C3×C4×D5—41no—
119C3×Dic10—21no—
120C3×Dic10—21no—
121C3⋊#168—41no—
122C3×#168—41no—
123C2×C3×#41—51no—
124C22×Dic6C2×D511yescharacteristic
125C2×C3×M16—51no—
126C3×#117C2×D511yescharacteristic
127#944—52no—
128#936—52no—
129#935—102no—
130#926—51no—
131#926C2×D511yescharacteristic
132#924—102no—
133C2×#208—51no—
134#887—22no—
135#877—22no—
136C4×Dic6—22no—
137C3×#104—102no—
138#837—102no—
139#824—102no—
140C2×C5×Q8—32no—
141C2×C5×Q8—32no—
142C2×C5×Q8—61no—
143C2×C5×Q8—61no—
144C2×C5×Q8—61no—
145C2×C5×Q8—61no—
146C22×C4×C5—32no—
147C22×C4×C5C22×D311yescharacteristic
148C2×C22⋊D5—21no—
149#709—21no—
150#709—21no—
151#709—21no—
152#709—21no—
153C2×D20C4×D311yescharacteristic
154C2×C4×D5—21no—
155C2×Dic10C4×D311yescharacteristic
156C5×C4⋊C4—21no—
157C5×C4⋊C4—64no—
158C5×C4⋊C4—61no—
159C5×C22⋊C4—21no—
160C5×C22⋊C4—61no—
161C42×C5—32no—
162C42×C5—64no—
163C42×C5#6712yes—
164C22⋊Dic5—61no—
165#685—64no—
166C4⋊Dic5—61no—
167#683—64no—
168C4×Dic5—32no—
169#681—21no—
170#681—21no—
171#681—61no—
172#681—61no—
173C2×#168—21no—
174C2×#168—61no—
175#536—151no—
176#519—31no—
177#421—51no—
178#421—151no—
179C2×#101—151no—
180H(3,ℤ/4)—151no—
181H(3,ℤ/4)—151no—
182C22×C3×C5—41no—
183C22×C3×C5C2×C22⋊C411yescharacteristic
184C22×C3×C5#12011yescharacteristic
185C22×C3×C5#12311yescharacteristic
186C2×C3×D5—42no—
187C2×C3×D5—41no—
188C3×C4×C5—42no—
189C3×C4×C5C4×D411yescharacteristic
190C3×C4×C5C4×D411yescharacteristic
191C3×C4×C5#12111yescharacteristic
192C3×C4×C5#12111yescharacteristic
193Dic15—42no—
194C3×Dic5—41no—
195C5×Dic3—24no—
196C5×Dic3—42no—
197C3×#41—101no—
198C3×#41—101no—
199C3×#41—101no—
200C3×#41—101no—
201C2×C3×Q8—51no—
202C2×C3×D4—51no—
203C2×C3×D4—101no—
204C22×C3×C4—101no—
205C22×C3×C4C22×D511yescharacteristic
206C22×Dic3C22⋊D512yes—
207C2×Dic6—21no—
208C2×Dic6—21no—
209C2×Dic6—21no—
210C2×Dic6—21no—
211C2×Dic6C4×D512yes—
212C2×Dic6D2012yes—
213C3×M16—101no—
214C3×M16—101no—
215C2×C3×C8—101no—
216C3×C4⋊C4—21no—
217C3×C22⋊C4—21no—
218C3×C42C22⋊D512yes—
219#217—21no—
220#217—101no—
221#217—104no—
222C4⋊Dic3—21no—
223C4⋊Dic3—101no—
224Dic3⋊C4—24no—
225Dic3⋊C4—104no—
226C4×Dic3—24no—
227C4×Dic3—52no—
228C4×Dic3C22⋊D512yes—
229#208—101no—
230#208—101no—
231C2×C3⋊C8—101no—
232C23×C5D3×D411yescharacteristic
233C22×D5—21no—
234C5×Q8—62no—
235C5×Q8—62no—
236C5×Q8—62no—
237C5×Q8—62no—
238C2×C4×C5—22no—
239C2×C4×C5—34no—
240C2×C4×C5—62no—
241C2×C4×C5—62no—
242C2×C4×C5—62no—
243C2×C4×C5C2×C4×D311yescharacteristic
244C2×C4×C5#23511yescharacteristic
245C2×C4×C5D3×D411yescharacteristic
246C2×C4×C5D3×D411yescharacteristic
247C2×C4×C5#23711yescharacteristic
248C2×C4×C5C2×#6711yescharacteristic
249C22⋊D5—41no—
250C22⋊D5—41no—
251C2×Dic5—21no—
252C2×Dic5—62no—
253D20—21no—
254D20—21no—
255C4×D5—41no—
256C4×D5—41no—
257Dic10—21no—
258Dic10—21no—
259#168—41no—
260#168—121no—
261C2×#41—51no—
262C22×Q8—31no—
263C2×M16—51no—
264C2×M16—151no—
265C4⋊Q8—152no—
266#124—152no—
267#123—302no—
268C22⋊Q8—302no—
269C4×Q8—62no—
270C4×Q8—62no—
271#117—31no—
272#117—62no—
273#117—151no—
274#117D3×D511yescharacteristic
275#104—102no—
276#104—302no—
277#101—302no—
278C2×C3×C5—21no—
279C2×C3×C5—21no—
280C2×C3×C5—21no—
281C2×C3×C5#38611yescharacteristic
282C3×D5—81no—
283C23×C3—101no—
284C23×C3C2×C22⋊D511yescharacteristic
285C3×Q8—101no—
286C3×Q8—101no—
287C3×D4—101no—
288C3×D4—101no—
289C3×D4—201no—
290C3×D4—201no—
291C2×C3×C4—22no—
292C2×C3×C4—101no—
293C2×C3×C4—201no—
294C2×C3×C4—201no—
295C2×C3×C4C2×C4×D511yescharacteristic
296C2×C3×C4C2×D2011yescharacteristic
297C2×C3×C4#70911yescharacteristic
298C2×C3×C4#70911yescharacteristic
299C2×C3×C4C2×C22⋊D511yescharacteristic
300C2×C3×C4C2×C22⋊D511yescharacteristic
301C2×Dic3—22no—
302C2×Dic3—22no—
303C2×Dic3—22no—
304C2×Dic3—102no—
305C2×Dic3#68514yes—
306Dic6—22no—
307Dic6—22no—
308Dic6—22no—
309Dic6—22no—
310C3×C8—201no—
311C3⋊C8—201no—
312C22×C5—41no—
313C22×C5D3×C22⋊C411yescharacteristic
314C22×C5#88311yescharacteristic
315C22×C5#93711yescharacteristic
316C2×D5—42no—
317C2×D5—41no—
318C4×C5—42no—
319C4×C5—64no—
320C4×C5—122no—
321C4×C5#67⋊C411yescharacteristic
322C4×C5#88411yescharacteristic
323C4×C5C4×#6711yescharacteristic
324C4×C5#93811yescharacteristic
325Dic5—41no—
326Dic5—122no—
327#41—101no—
328#41—101no—
329#41—101no—
330#41—101no—
331C2×Q8—32no—
332C2×Q8—32no—
333C2×Q8—51no—
334C2×Q8—61no—
335C2×Q8—61no—
336C2×Q8—61no—
337C2×Q8—61no—
338C2×D4—51no—
339C2×D4—101no—
340C22×C4—32no—
341C22×C4—101no—
342C22×C4C2×D3×D511yescharacteristic
343M16—101no—
344M16—101no—
345M16—301no—
346M16—301no—
347C2×C8—101no—
348C2×C8—301no—
349C4⋊C4—21no—
350C4⋊C4—64no—
351C4⋊C4—61no—
352C4⋊C4—304no—
353C4⋊C4—301no—
354C22⋊C4—21no—
355C22⋊C4—61no—
356C22⋊C4—304no—
357C22⋊C4—301no—
358C42—32no—
359C42—64no—
360C42—152no—
361C42#120112yes—
362C3×C5#191211yescharacteristic, complemented, Hall
363C22×C3—41no—
364C22×C3—202no—
365C22×C3—201no—
366C22×C3C2×#68511yescharacteristic
367C22×C3#407511yescharacteristic
368C22×C3#409911yescharacteristic
369C3×C4—42no—
370C3×C4—201no—
371C3×C4C4×C22⋊D511yescharacteristic
372C3×C4C4×C22⋊D511yescharacteristic
373C3×C4#407611yescharacteristic
374C3×C4#407611yescharacteristic
375Dic3—24no—
376Dic3—42no—
377Dic3—202no—
378C2×C5—21no—
379C2×C5—21no—
380C2×C5—21no—
381C2×C5#495611yescharacteristic
382D5—81no—
383C23—101no—
384C23D3×C22⋊D511yescharacteristic
385Q8—62no—
386Q8—62no—
387Q8—62no—
388Q8—62no—
389Q8—101no—
390Q8—101no—
391D4—101no—
392D4—101no—
393D4—201no—
394D4—201no—
395C2×C4—22no—
396C2×C4—34no—
397C2×C4—62no—
398C2×C4—62no—
399C2×C4—62no—
400C2×C4—101no—
401C2×C4—201no—
402C2×C4—201no—
403C2×C4—302no—
404C2×C4#676511yescharacteristic
405C2×C4#677111yescharacteristic
406C2×C4C4×D3×D511yescharacteristic
407C2×C4D3×D2011yescharacteristic
408C2×C4C2×#120111yescharacteristic
409C2×C4D3×C22⋊D511yescharacteristic
410C8—201no—
411C8—601no—
412C2×C3—21no—
413C2×C3—21no—
414C2×C3—21no—
415C2×C3—401no—
416C2×C3#6550211yescharacteristic
417C5#7041111yescharacteristic, complemented, Sylow
418C22—41no—
419C22—202no—
420C22—201no—
421C22#9145211yescharacteristic
422C22D3×#68511yescharacteristic
423C22#9156811yescharacteristic
424C4—42no—
425C4—64no—
426C4—122no—
427C4—201no—
428C4—602no—
429C4C4×#120111yescharacteristic
430C4#9144111yescharacteristic
431C4#9145411yescharacteristic
432C4#9145611yescharacteristic
433C3#1060245611yescharacteristic, complemented, Sylow
434C2—21no—
435C2—21no—
436C2—21no—
437C2—401no—
438C2#1174891011yescharacteristic
subgroupG/H
centerC2#11748910
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC3×C5×#117C22
socleC2×C3×C5#386
prime radicalC2×C3×#709C22
cosocleC22×C3×C4×C5C23
hypercenter#117D3×D5
hypocenterC3×C5#1912
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×#5516C2semidirect
5. C2×#90962C2semidirect
6. #11746352C2semidirect
7. #11745971C2semidirect
20. #91385C4semidirect
21. #91368C4semidirect
70. #5516D5semidirect
362. C3×C5#1912semidirect
417. C5#70411semidirect
433. C3#10602456semidirect

Maximal subgroups

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

subgroupindex
C5×#55162
#117542512
C3×#652942
#117484212
C2×#909622
#117463522
#117459712
#106024563
#704115