Finite Group Databasebeta

← #14301731

Subgroups — #14301731

Order 1920.

684 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756578C211yesmaximal, characteristic, complemented
2C3×#66162C211yesmaximal, characteristic
3C5×#5237C211yesmaximal, characteristic, complemented
4#11748341C212yesmaximal, complemented
5#11745993C212yesmaximal, complemented
6#10600929—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C22×C3×C4×D5C2211yescharacteristic
9#91837—24no—
10C2×#6710—22no—
11C2×#6710C2212yes—
12C2×C5×#208C2212yes—
13C3×#4092—21no—
14C3×#4084—21no—
15C3×#4083C412yes—
16C3×#4081C412yes—
17C3×C4×C22⋊D5—22no—
18C3×#4072C2211yescharacteristic
19C5×#836—21no—
20C5×#833—21no—
21#90955—24no—
22#71714—51nomaximal, Hall
23#66162D311yescharacteristic
24#66153—31no—
25C5×#413—31no—
26#65415—32no—
27#64779—32no—
28C23×C3×D5C2×C411yescharacteristic
29C3×C5×#41—22no—
30C3×C5×#41—22no—
31C2×C3×C5×Q8D411yescharacteristic
32C2×C3×C5×D4C2×C412yes—
33C2×C3×C5×D4D411yescharacteristic
34C22×C3×C4×C5D412yes—
35C22×C3×C4×C5C2311yescharacteristic
36C2×C3×C22⋊D5—22no—
37C22×C3×Dic5C2×C411yescharacteristic
38C2×C3×C4×D5—21no—
39C2×C3×C4×D5—22no—
40C2×C3×C4×D5—21no—
41C2×C3×C4×D5—22no—
42#6710—24no—
43#6710—22no—
44#6710—22no—
45C2×C3⋊#168—24no—
46C2×C3⋊#168D414yescomplemented
47C5×#208—22no—
48C5×#208—22no—
49C2×C5×C3⋊C8—22no—
50C3×C22⋊Dic5—22no—
51C3×C22⋊Dic5C2×C412yes—
52C3×#685—22no—
53C3×C4⋊Dic5—21no—
54C3×#683—22no—
55C3×C4×Dic5—21no—
56C3×#525—51no—
57#5819—51no—
58#5237D511yescharacteristic, complemented
59#5207—52no—
60#4533—52no—
61C2×C5×#41C2×D311yescharacteristic
62C22×C4×D5C2×D311yescharacteristic
63C2×C5×M16—32no—
64#4094—64no—
65#4092—21no—
66#4084—21no—
67#4083Dic312yes—
68#4081Dic312yes—
69C4×C22⋊D5—22no—
70#4072C2×D311yescharacteristic
71C2×#681—32no—
72C2×#681—62no—
73C5×#101—61no—
74C5×#100—61no—
75#3952—64no—
76#1891—151noSylow
77C23×C3×C5C22⋊C412yes—
78C23×C3×C5C22×C411yescharacteristic
79C22×C3×D5—21no—
80C22×C3×D5—22no—
81C22×C3×D5—42no—
82C3×C5×Q8—22no—
83C3×C5×D4—24no—
84C3×C5×D4—22no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—22no—
87C2×C3×C4×C5C22⋊C412yes—
88C2×C3×C4×C5C2×D412yes—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4112yes—
92C3×C22⋊D5—44no—
93C2×C3×Dic5—22no—
94C2×C3×Dic5—21no—
95C2×C3×Dic5—22no—
96C3×C4×D5—41no—
97C3×C4×D5—42no—
98C3×C4×D5—41no—
99C3⋊#168—24no—
100C5×C3⋊C8—42no—
101C2×C3×#41C2×D511yescharacteristic
102C23×C3×C4—51no—
103C3×#123—52no—
104C3×C22⋊Q8—101no—
105C3×#121—101no—
106C3×#120—52no—
107C3×C4×D4—102no—
108C3×#117—51no—
109#948—104no—
110C2×#208—52no—
111C2×#208—102no—
112C2×#208C2×D512yes—
113#836—21no—
114#833—21no—
115#830—104no—
116C23×D5C2×Dic311yescharacteristic
117C5×#41—22no—
118C5×#41—22no—
119C2×C5×Q8#6711yescharacteristic
120C2×C5×D4C2×Dic312yes—
121C2×C5×D4#6711yescharacteristic
122C22×C4×C5#6712yes—
123C22×C4×C5C22×D311yescharacteristic
124C2×C22⋊D5—22no—
125C22×Dic5C2×Dic311yescharacteristic
126C2×C4×D5—22no—
127C2×C4×D5—22no—
128C2×C4×D5—21no—
129C2×C4×D5—21no—
130C5×M16—62no—
131C5×M16—62no—
132C2×C5×C8—62no—
133C22⋊Dic5—22no—
134C22⋊Dic5C2×Dic312yes—
135#685—22no—
136C4⋊Dic5—21no—
137#683—22no—
138C4×Dic5—21no—
139#681—64no—
140#681—62no—
141#681—62no—
142C2×#168—34no—
143C2×#168—64no—
144#568—151no—
145#525—51no—
146#413—31no—
147#407—152no—
148#344—152no—
149C22×C3×C5—22no—
150C22×C3×C5—41no—
151C22×C3×C5—42no—
152C22×C3×C5C2×C22⋊C411yescharacteristic
153C22×C3×C5C4×D412yes—
154C2×C3×D5—22no—
155C2×C3×D5—24no—
156C2×C3×D5—41no—
157C2×C3×D5—42no—
158C2×C3×D5—41no—
159C3×C4×C5—22no—
160C3×C4×C5#12011yescharacteristic
161C3×C4×C5#12112yes—
162C3×C4×C5#12311yescharacteristic
163C3×Dic5—42no—
164C3×Dic5—41no—
165C24×C3—51no—
166C3×#41—22no—
167C3×#41—22no—
168C2×C3×Q8C22⋊D511yescharacteristic
169C2×C3×D4—102no—
170C2×C3×D4C4×D512yes—
171C2×C3×D4C22⋊D511yescharacteristic
172C22×C3×C4—51no—
173C22×C3×C4—101no—
174C22×C3×C4—102no—
175C22×C3×C4—102no—
176C22×C3×C4—101no—
177C22×C3×C4D2012yes—
178C22×C3×C4C22×D511yescharacteristic
179C3×C4⋊C4—102no—
180C3×C4⋊C4—101no—
181C3×C22⋊C4—52no—
182C3×C22⋊C4—102no—
183C3×C22⋊C4—102no—
184C3×C42—101no—
185#208—22no—
186#208—22no—
187#208—104no—
188#208—102no—
189#208—102no—
190C2×C3⋊C8—22no—
191C2×C3⋊C8—54no—
192C2×C3⋊C8—104no—
193C23×C5#21712yes—
194C23×C5C22×Dic311yescharacteristic
195C22×D5—22no—
196C22×D5—21no—
197C22×D5—42no—
198C5×Q8—22no—
199C5×D4—24no—
200C5×D4—22no—
201C2×C4×C5—22no—
202C2×C4×C5—22no—
203C2×C4×C5#21712yes—
204C2×C4×C5D3×D412yes—
205C2×C4×C5#23712yes—
206C2×C4×C5C2×#6711yescharacteristic
207C2×C4×C5C2×#6711yescharacteristic
208C22⋊D5—44no—
209C2×Dic5—22no—
210C2×Dic5—22no—
211C2×Dic5—21no—
212C4×D5—41no—
213C4×D5—41no—
214C4×D5—42no—
215C5×C8—122no—
216#168—64no—
217C2×#41D3×D511yescharacteristic
218C23×C4—51no—
219#131—304no—
220C2×M16—32no—
221C2×M16—152no—
222C2×M16—302no—
223#123—52no—
224C22⋊Q8—101no—
225#121—101no—
226#120—52no—
227C4×D4—102no—
228#117—51no—
229#101—61no—
230#100—61no—
231C22⋊C8—304no—
232C2×C3×C5—21no—
233C2×C3×C5—22no—
234C2×C3×C5—42no—
235C2×C3×C5#38611yescharacteristic
236C3×D5—42no—
237C23×C3—102no—
238C23×C3—101no—
239C23×C3—202no—
240C23×C3#68512yes—
241C23×C3C2×C4×D511yescharacteristic
242C3×Q8—22no—
243C3×D4—24no—
244C3×D4—22no—
245C3×D4—204no—
246C2×C3×C4—22no—
247C2×C3×C4—22no—
248C2×C3×C4—102no—
249C2×C3×C4—102no—
250C2×C3×C4—101no—
251C2×C3×C4—201no—
252C2×C3×C4—201no—
253C2×C3×C4—202no—
254C2×C3×C4#68512yes—
255C2×C3×C4C2×D2011yescharacteristic
256C2×C3×C4D4×D512yes—
257C2×C3×C4#71112yes—
258C2×C3×C4C2×C22⋊D511yescharacteristic
259C3⋊C8—42no—
260C3⋊C8—104no—
261C22×C5—22no—
262C22×C5—41no—
263C22×C5—42no—
264C22×C5D4×Dic312yes—
265C22×C5C2×#21711yescharacteristic
266C2×D5—22no—
267C2×D5—24no—
268C2×D5—41no—
269C2×D5—42no—
270C2×D5—41no—
271C4×C5—22no—
272C4×C5#93511yescharacteristic
273C4×C5#93711yescharacteristic
274C4×C5#93912yes—
275Dic5—42no—
276Dic5—41no—
277C24—51no—
278#41—22no—
279#41—22no—
280C2×Q8#120111yescharacteristic
281C2×D4—102no—
282C2×D4D5×Dic312yes—
283C2×D4#120111yescharacteristic
284C22×C4—51no—
285C22×C4—102no—
286C22×C4—101no—
287C22×C4—101no—
288C22×C4—102no—
289C22×C4#120212yes—
290C22×C4C2×D3×D511yescharacteristic
291M16—62no—
292M16—62no—
293M16—304no—
294M16—302no—
295M16—302no—
296C2×C8—62no—
297C2×C8—154no—
298C2×C8—304no—
299C4⋊C4—102no—
300C4⋊C4—101no—
301C22⋊C4—52no—
302C22⋊C4—102no—
303C22⋊C4—102no—
304C42—101no—
305C3×C5#189111yescharacteristic, complemented, Hall
306C22×C3—22no—
307C22×C3—41no—
308C22×C3—42no—
309C22×C3—102no—
310C22×C3—104no—
311C22×C3—201no—
312C22×C3—202no—
313C22×C3—201no—
314C22×C3#402712yes—
315C22×C3C2×#68511yescharacteristic
316C3×C4—22no—
317C3×C4—202no—
318C3×C4—201no—
319C3×C4#402811yescharacteristic
320C3×C4#403211yescharacteristic
321C3×C4#408512yes—
322C2×C5—21no—
323C2×C5—22no—
324C2×C5—42no—
325C2×C5#522011yescharacteristic
326D5—42no—
327C23—101no—
328C23—102no—
329C23—202no—
330C23#666512yes—
331C23C2×D5×Dic311yescharacteristic
332Q8—22no—
333D4—24no—
334D4—22no—
335D4—204no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—102no—
339C2×C4—101no—
340C2×C4—102no—
341C2×C4—201no—
342C2×C4—202no—
343C2×C4—201no—
344C2×C4#666512yes—
345C2×C4#678012yes—
346C2×C4C2×#120111yescharacteristic
347C2×C4C2×#120211yescharacteristic
348C2×C4#679012yes—
349C8—122no—
350C8—304no—
351C2×C3—21no—
352C2×C3—22no—
353C2×C3—42no—
354C2×C3—202no—
355C2×C3#6524711yescharacteristic
356C5#7171411yescharacteristic, complemented, Sylow
357C22—22no—
358C22—41no—
359C22—42no—
360C22—102no—
361C22—104no—
362C22—201no—
363C22—202no—
364C22—201no—
365C22C2×#666511yescharacteristic
366C22#9155912yes—
367C4—22no—
368C4—202no—
369C4—201no—
370C4#9153711yescharacteristic
371C4#9157112yes—
372C4#9157211yescharacteristic
373C3#1060092911yescharacteristic, complemented, Sylow
374C2—21no—
375C2—22no—
376C2—42no—
377C2—202no—
378C2#1174950011yescharacteristic
subgroupG/H
centerC4#91572
commutatorC23×C3×C5C22×C4
FrattiniC22×C4C2×D3×D5
FittingC2×C3×C5×#41C22
socleC2×C3×C5#386
prime radicalC3×#66162C2
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1891
LCSG ▷ C23×C3×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×#5237C2semidirect
4. #11748341C2semidirect
5. #11745993C2semidirect
46. C2×C3⋊#168D4semidirect
58. #5237D5semidirect
305. C3×C5#1891semidirect
356. C5#71714semidirect
373. C3#10600929semidirect

Maximal subgroups

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

subgroupindex
#117565782
C3×#661622
C5×#52372
#117483412
#117459932
#106009293
#717145