Finite Group Databasebeta

← #14301402

Subgroups — #14301402

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756578C211yesmaximal, characteristic, complemented
2C3×#66166C211yesmaximal, characteristic
3C5×#5240C211yesmaximal, characteristic, complemented
4#11748421C212yesmaximal, complemented
5#11745977C212yesmaximal, complemented
6#10600838—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C2×C3×#709C2211yescharacteristic
9#91837—24no—
10C2×#6710—22no—
11C2×#6710C2212yes—
12C5×#926C2212yes—
13C3×#4093C411yescharacteristic, complemented
14C3×#4090C411yescharacteristic, complemented
15C3×#4086C411yescharacteristic, complemented
16C3×#4085—22no—
17C3×#4082C411yescharacteristic, complemented
18C3×C4×C22⋊D5—22no—
19C2×C3×C4×Dic5C2211yescharacteristic
20C5×#834—22no—
21#90977—24no—
22#71817—51nomaximal, Hall
23#66166D311yescharacteristic
24#66153—31no—
25C5×#410—31no—
26#65294—32no—
27#64752—32no—
28C3×C5×#41—22no—
29C3×C5×#41—22no—
30C2×C3×C5×Q8C2×C411yescharacteristic
31C2×C3×C5×D4C2×C411yescharacteristic
32C2×C3×C5×D4D412yes—
33C22×C3×C4×C5D412yes—
34C22×C3×C4×C5C2311yescharacteristic
35C2×C3×C22⋊D5—22no—
36C2×C3×C22⋊D5—21no—
37C22×C3×Dic5—21no—
38C3×#709—22no—
39C3×#709—22no—
40C2×C3×D20C2×C411yescharacteristic
41C2×C3×C4×D5—21no—
42C2×C3×Dic10C2×C411yescharacteristic
43#6710—24no—
44#6710—22no—
45#6710D414yescomplemented
46C2×C3⋊#168—24no—
47C2×C3⋊#168—22no—
48C5×#217—22no—
49C5×C4⋊Dic3—22no—
50C4×C5×Dic3—22no—
51C3×C22⋊Dic5—22no—
52C3×#685—22no—
53C3×#683—22no—
54C3×C4×Dic5—21no—
55C3×C4×Dic5C2×C411yescharacteristic
56C3×C4×Dic5C2×C411yescharacteristic
57C3×#532—51no—
58#5819—51no—
59#5240D511yescharacteristic, complemented
60#5236—52no—
61#4523—52no—
62C2×C5×#41C2×D311yescharacteristic
63C2×#709C2×D311yescharacteristic
64C5×#117—32no—
65#4094—64no—
66#4093Dic311yescharacteristic, complemented
67#4090Dic311yescharacteristic, complemented
68#4086Dic311yescharacteristic, complemented
69#4085—22no—
70#4082Dic311yescharacteristic, complemented
71C4×C22⋊D5—22no—
72C2×C4×Dic5C2×D311yescharacteristic
73C2×#681—32no—
74C2×#681—62no—
75C5×#99—62no—
76#3937—64no—
77#1884—151noSylow
78C23×C3×C5C22⋊C412yes—
79C23×C3×C5C2×D411yescharacteristic
80C22×C3×D5—21no—
81C3×C5×Q8—22no—
82C3×C5×D4—24no—
83C3×C5×D4—22no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5C22⋊C412yes—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C2×D412yes—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5#4112yes—
91C2×C5×Dic3—42no—
92C3×C22⋊D5—44no—
93C3×C22⋊D5—42no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—21no—
96C2×C3×Dic5—21no—
97C2×C3×Dic5—42no—
98C3×D20—22no—
99C3×C4×D5—41no—
100C3×C4×D5—41no—
101C3×Dic10—22no—
102C3⋊#168—24no—
103C2×C3×#41—51no—
104C2×C3×#41C2×D511yescharacteristic
105C3×C4⋊Q8—51no—
106C3×#127—51no—
107C3×#124—51no—
108C3×#124—51no—
109C3×#121—102no—
110C3×C4×D4—102no—
111C2×C3×C42—51no—
112#948—104no—
113#926C2×D512yes—
114C2×#208—52no—
115C2×#208—102no—
116#837—104no—
117#834—22no—
118C5×#41—22no—
119C5×#41—22no—
120C2×C5×Q8C2×Dic311yescharacteristic
121C2×C5×D4C2×Dic311yescharacteristic
122C2×C5×D4#6712yes—
123C22×C4×C5#6712yes—
124C22×C4×C5C22×D311yescharacteristic
125C2×C22⋊D5—22no—
126C2×C22⋊D5—21no—
127C22×Dic5—21no—
128#709—22no—
129#709—22no—
130C2×D20C2×Dic311yescharacteristic
131C2×C4×D5—21no—
132C2×Dic10C2×Dic311yescharacteristic
133C5×C4⋊C4—62no—
134C5×C22⋊C4—62no—
135C42×C5—62no—
136C22⋊Dic5—22no—
137#685—22no—
138#683—22no—
139C4×Dic5—21no—
140C4×Dic5C2×Dic311yescharacteristic
141C4×Dic5C2×Dic311yescharacteristic
142#681—34no—
143#681—64no—
144#681—62no—
145C2×#168—64no—
146C2×#168—62no—
147#568—151no—
148#532—51no—
149#421—152no—
150#410—31no—
151#339—152no—
152C22×C3×C5—22no—
153C22×C3×C5—41no—
154C22×C3×C5—42no—
155C22×C3×C5C2×C22⋊C411yescharacteristic
156C22×C3×C5#12112yes—
157C2×C3×D5—42no—
158C2×C3×D5—41no—
159C3×C4×C5—22no—
160C3×C4×C5C4×D412yes—
161C3×C4×C5#12011yescharacteristic
162C3×C4×C5#12311yescharacteristic
163C3×Dic5—22no—
164C3×Dic5—41no—
165C3×Dic5—41no—
166C5×Dic3—82no—
167C3×#41—22no—
168C3×#41—22no—
169C3×#41—102no—
170C3×#41—102no—
171C2×C3×Q8—51no—
172C2×C3×Q8C4×D511yescharacteristic
173C2×C3×D4—51no—
174C2×C3×D4—102no—
175C2×C3×D4—101no—
176C2×C3×D4C4×D511yescharacteristic
177C2×C3×D4C22⋊D512yes—
178C22×C3×C4—101no—
179C22×C3×C4—101no—
180C22×C3×C4D2012yes—
181C22×C3×C4C22×D511yescharacteristic
182C3×C4⋊C4—102no—
183C3×C22⋊C4—102no—
184C3×C22⋊C4—102no—
185C3×C42—51no—
186C3×C42—51no—
187C3×C42—101no—
188#217—22no—
189C4⋊Dic3—22no—
190C4×Dic3—22no—
191#208—54no—
192#208—104no—
193#208—102no—
194C2×C3⋊C8—104no—
195C2×C3⋊C8—102no—
196C23×C5#21712yes—
197C23×C5C2×#6711yescharacteristic
198C22×D5—21no—
199C5×Q8—22no—
200C5×D4—24no—
201C5×D4—22no—
202C2×C4×C5—22no—
203C2×C4×C5—22no—
204C2×C4×C5—122no—
205C2×C4×C5#21712yes—
206C2×C4×C5D3×D412yes—
207C2×C4×C5#23712yes—
208C2×C4×C5C22×Dic311yescharacteristic
209C2×C4×C5C2×#6711yescharacteristic
210C22⋊D5—44no—
211C22⋊D5—42no—
212C2×Dic5—21no—
213C2×Dic5—21no—
214C2×Dic5—21no—
215C2×Dic5—42no—
216D20—22no—
217C4×D5—41no—
218C4×D5—41no—
219Dic10—22no—
220#168—64no—
221C2×#41—51no—
222C2×#41D3×D511yescharacteristic
223#131—304no—
224C2×M16—152no—
225C2×M16—302no—
226C4⋊Q8—51no—
227#127—51no—
228#124—51no—
229#124—51no—
230#121—102no—
231C4×D4—102no—
232#117—32no—
233C2×C42—51no—
234#104—304no—
235#99—62no—
236C2×C3×C5—22no—
237C2×C3×C5—21no—
238C2×C3×C5—42no—
239C2×C3×C5#38611yescharacteristic
240C3×D5—81no—
241C23×C3—101no—
242C23×C3#68512yes—
243C23×C3C2×C22⋊D511yescharacteristic
244C3×Q8—22no—
245C3×Q8—102no—
246C3×D4—24no—
247C3×D4—22no—
248C3×D4—102no—
249C3×D4—204no—
250C3×D4—202no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—101no—
254C2×C3×C4—101no—
255C2×C3×C4—101no—
256C2×C3×C4—202no—
257C2×C3×C4—201no—
258C2×C3×C4—201no—
259C2×C3×C4#68512yes—
260C2×C3×C4C2×C4×D511yescharacteristic
261C2×C3×C4C2×D2011yescharacteristic
262C2×C3×C4D4×D512yes—
263C2×C3×C4#71112yes—
264C2×Dic3—42no—
265C3⋊C8—104no—
266C22×C5—22no—
267C22×C5—41no—
268C22×C5—42no—
269C22×C5#93912yes—
270C22×C5C2×#21711yescharacteristic
271C2×D5—42no—
272C2×D5—41no—
273C4×C5—22no—
274C4×C5—242no—
275C4×C5D4×Dic312yes—
276C4×C5#93511yescharacteristic
277C4×C5#93711yescharacteristic
278Dic5—22no—
279Dic5—41no—
280Dic5—41no—
281#41—22no—
282#41—22no—
283#41—102no—
284#41—102no—
285C2×Q8—51no—
286C2×Q8D5×Dic311yescharacteristic
287C2×D4—51no—
288C2×D4—102no—
289C2×D4—101no—
290C2×D4D5×Dic311yescharacteristic
291C2×D4#120112yes—
292C22×C4—101no—
293C22×C4—101no—
294C22×C4#120212yes—
295C22×C4C2×D3×D511yescharacteristic
296M16—154no—
297M16—304no—
298M16—302no—
299C2×C8—304no—
300C2×C8—302no—
301C4⋊C4—62no—
302C4⋊C4—102no—
303C22⋊C4—62no—
304C22⋊C4—102no—
305C22⋊C4—102no—
306C42—51no—
307C42—51no—
308C42—62no—
309C42—101no—
310C3×C5#188411yescharacteristic, complemented, Hall
311C22×C3—22no—
312C22×C3—41no—
313C22×C3—42no—
314C22×C3—202no—
315C22×C3—201no—
316C22×C3C2×#68511yescharacteristic
317C22×C3#408512yes—
318C3×C4—22no—
319C3×C4—102no—
320C3×C4—201no—
321C3×C4—201no—
322C3×C4#402712yes—
323C3×C4#402811yescharacteristic
324C3×C4#403211yescharacteristic
325Dic3—82no—
326C2×C5—21no—
327C2×C5—22no—
328C2×C5—42no—
329C2×C5#522011yescharacteristic
330D5—81no—
331C23—101no—
332C23#666512yes—
333C23C2×#120111yescharacteristic
334Q8—22no—
335Q8—102no—
336D4—24no—
337D4—22no—
338D4—102no—
339D4—204no—
340D4—202no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—101no—
344C2×C4—101no—
345C2×C4—101no—
346C2×C4—122no—
347C2×C4—202no—
348C2×C4—201no—
349C2×C4—201no—
350C2×C4#666512yes—
351C2×C4C2×D5×Dic311yescharacteristic
352C2×C4#678012yes—
353C2×C4C2×#120211yescharacteristic
354C2×C4#679012yes—
355C8—304no—
356C2×C3—22no—
357C2×C3—21no—
358C2×C3—42no—
359C2×C3—401no—
360C2×C3#6524711yescharacteristic
361C5#7181711yescharacteristic, complemented, Sylow
362C22—22no—
363C22—41no—
364C22—42no—
365C22—202no—
366C22—201no—
367C22C2×#666511yescharacteristic
368C22#9157112yes—
369C4—22no—
370C4—102no—
371C4—201no—
372C4—201no—
373C4—242no—
374C4#9153711yescharacteristic
375C4#9155912yes—
376C4#9157211yescharacteristic
377C3#1060083811yescharacteristic, complemented, Sylow
378C2—21no—
379C2—22no—
380C2—42no—
381C2—401no—
382C2#1174950011yescharacteristic
subgroupG/H
centerC4#91572
commutatorC2×C3×C4×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#386
prime radicalC3×#66166C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1884
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #11756578C2semidirect
3. C5×#5240C2semidirect
4. #11748421C2semidirect
5. #11745977C2semidirect
13. C3×#4093C4semidirect
14. C3×#4090C4semidirect
15. C3×#4086C4semidirect
17. C3×#4082C4semidirect
45. #6710D4semidirect
59. #5240D5semidirect
66. #4093Dic3semidirect
67. #4090Dic3semidirect
68. #4086Dic3semidirect
70. #4082Dic3semidirect
310. C3×C5#1884semidirect
361. C5#71817semidirect
377. C3#10600838semidirect

Maximal subgroups

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

subgroupindex
#117565782
C3×#661662
C5×#52402
#117484212
#117459772
#106008383
#718175