Finite Group Databasebeta

← #14295951

Subgroups — #14295951

Order 1920.

600 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#4094C211yesmaximal, characteristic
2#11751334C211yesmaximal, characteristic
3C2×C5×#837C211yesmaximal, characteristic
4#11748324C211yesmaximal, characteristic, complemented
5C2×Dic3×#168C211yesmaximal, characteristic, complemented
6#11745982C211yesmaximal, characteristic, complemented
7#11745976C211yesmaximal, characteristic, complemented
8#10601162—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10#91815C2211yescharacteristic
11C22×C3⋊#168C2211yescharacteristic
12C2×C4×C5×Dic3C2211yescharacteristic
13C2×C5×#208C2211yescharacteristic
14C3×#4094—22no—
15C3×#4094C414yescomplemented
16C2×C3×#681—21no—
17C2×C3×#681C2211yescharacteristic
18C22×C3×#168—21no—
19C22×C3×#168C2211yescharacteristic
20#91119C412yescomplemented
21#91116C412yescomplemented
22C5×#837C414yescomplemented
23#90954—21no—
24#90951—21no—
25Dic3×#168—22no—
26#72008—51nomaximal, Hall
27C2×#4094D311yescharacteristic
28C2×C5×#104—31no—
29#65522—31no—
30#65411—31no—
31C2×C4×#168—31no—
32#64778—31no—
33#64743—31no—
34C3×C5×#41—21no—
35C3×C5×#41—21no—
36C3×C5×#41C2×C412yes—
37C3×C5×#41C2×C412yes—
38C2×C3×C5×Q8C2×C411yescharacteristic
39C2×C3×C5×D4—21no—
40C2×C3×C5×D4C2×C411yescharacteristic
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5C2311yescharacteristic
43C22×C5×Dic3—21no—
44#6719—21no—
45C4⋊Dic15C2×C412yes—
46C4×Dic15—21no—
47C2×C3⋊#168—21no—
48C2×C3⋊#168—21no—
49C2×C3⋊#168C2×C412yes—
50C4×C5×Dic3—21no—
51C4×C5×Dic3C2×C412yes—
52C5×#208—21no—
53C5×#208C2×C412yes—
54C2×C5×C3⋊C8—21no—
55C3×#681—21no—
56C3×#681—24no—
57C3×#681C2×C412yes—
58C2×C3×#168—21no—
59C2×C3×#168—24no—
60C2×C3×#168C2×C412yes—
61C2×C3×#168D412yes—
62C2×C3×#168D411yescharacteristic
63C2×C3×#168D411yescharacteristic
64C2×C3×#131—51no—
65C2×#837D511yescharacteristic
66#5233—51no—
67#5101—51no—
68C2×C8×Dic3—51no—
69#4558—51no—
70#4555—51no—
71C2×C5×#41C2×D311yescharacteristic
72C2×C5×M16—31no—
73C2×C42×C5—31no—
74#4094—22no—
75#4094Dic314yescomplemented
76#4072—31no—
77C2×#681—21no—
78C2×#681C2×D311yescharacteristic
79C22×#168—21no—
80C22×#168—31no—
81C22×#168C2×D311yescharacteristic
82C5×#104—34no—
83#3967—32no—
84#3964—32no—
85#3947—61no—
86C8×Dic5—61no—
87C4×#168—62no—
88#1764—151noSylow
89C23×C3×C5—21no—
90C23×C3×C5#4111yescharacteristic
91C3×C5×Q8—21no—
92C3×C5×Q8C4212yes—
93C3×C5×D4—22no—
94C3×C5×D4—22no—
95C3×C5×D4—21no—
96C3×C5×D4C4212yes—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—22no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5C22×C411yescharacteristic
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C22×C411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5#4111yescharacteristic
106C2×Dic15—22no—
107C2×C5×Dic3—24no—
108C2×C5×Dic3—22no—
109C3⋊#168—22no—
110C3×#168—22no—
111C3×#168C22⋊C412yes—
112C3×#168C22⋊C412yes—
113C5×C3⋊C8—22no—
114C2×C3×#41C2×D511yescharacteristic
115C3×#131—54no—
116C3×#131—102no—
117C2×C3×M16—51no—
118C2×C3×M16—101no—
119C22×C3×C8—51no—
120C22×C3×C8—101no—
121#926—51no—
122C2×C4×Dic3C2×D511yescharacteristic
123C2×#208C2×D511yescharacteristic
124C22×C3⋊C8—51no—
125#837Dic514yescomplemented
126#835—52no—
127#832—52no—
128#815—101no—
129C8×Dic3—101no—
130C8×Dic3—102no—
131C5×#41—21no—
132C5×#41—21no—
133C5×#41C4×D312yes—
134C5×#41C2×Dic312yes—
135C2×C5×Q8C4×D311yescharacteristic
136C2×C5×D4—21no—
137C2×C5×D4C4×D311yescharacteristic
138C22×C4×C5—21no—
139C22×C4×C5—61no—
140C22×C4×C5C22×D311yescharacteristic
141C5×M16—32no—
142C5×M16—61no—
143C2×C5×C8—61no—
144C42×C5—32no—
145C42×C5—61no—
146C22⋊Dic5—61no—
147C4⋊Dic5—32no—
148C4×Dic5—61no—
149#681—21no—
150#681—24no—
151#681C2×Dic312yes—
152C2×#168—21no—
153C2×#168—24no—
154C2×#168—32no—
155C2×#168—61no—
156C2×#168—61no—
157C2×#168C2×Dic312yes—
158C2×#168#6712yes—
159C2×#168#6711yescharacteristic
160C2×#168#6711yescharacteristic
161C2×#131—51no—
162C2×#104—31no—
163#416—151no—
164#405—151no—
165C2×C4×C8—151no—
166#341—151no—
167#339—151no—
168C22×C3×C5—22no—
169C22×C3×C5—22no—
170C22×C3×C5—42no—
171C22×C3×C5#11711yescharacteristic
172C22×C3×C5C4×D411yescharacteristic
173C22×C3×C5C4×D411yescharacteristic
174C3×C4×C5—22no—
175C3×C4×C5C2×C4211yescharacteristic
176C3×C4×C5C2×C22⋊C411yescharacteristic
177C3×C4×C5C4×D411yescharacteristic
178C3×C4×C5C4×D411yescharacteristic
179Dic15—42no—
180C5×Dic3—24no—
181C3×#41—21no—
182C3×#41—21no—
183C3×#41C4×D512yes—
184C3×#41C2×Dic512yes—
185C2×C3×Q8C4×D511yescharacteristic
186C2×C3×D4—21no—
187C2×C3×D4C4×D511yescharacteristic
188C22×C3×C4—21no—
189C22×C3×C4C22×D511yescharacteristic
190C22×Dic3—21no—
191C3×M16—52no—
192C3×M16—104no—
193C3×M16—101no—
194C2×C3×C8—52no—
195C2×C3×C8—51no—
196C2×C3×C8—52no—
197C2×C3×C8—51no—
198C2×C3×C8—104no—
199C2×C3×C8—101no—
200#217—101no—
201C4⋊Dic3—52no—
202C4×Dic3—21no—
203C4×Dic3—101no—
204C4×Dic3C2×Dic512yes—
205#208—21no—
206#208C2×Dic512yes—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—52no—
209C2×C3⋊C8—101no—
210C2×C3⋊C8—101no—
211C23×C5—21no—
212C23×C5#23511yescharacteristic
213C5×Q8—21no—
214C5×Q8C4×Dic312yes—
215C5×D4—22no—
216C5×D4—22no—
217C5×D4—21no—
218C5×D4C4×Dic312yes—
219C2×C4×C5—21no—
220C2×C4×C5—22no—
221C2×C4×C5—22no—
222C2×C4×C5—64no—
223C2×C4×C5—62no—
224C2×C4×C5C2×C4×D311yescharacteristic
225C2×C4×C5C2×C4×D311yescharacteristic
226C2×C4×C5#23511yescharacteristic
227C2×C4×C5C22×Dic311yescharacteristic
228C2×C4×C5C2×#6711yescharacteristic
229C2×C4×C5C2×#6711yescharacteristic
230C2×Dic5—62no—
231C5×C8—62no—
232#168—22no—
233#168—62no—
234#168#21712yes—
235#168#21712yes—
236C2×#41D3×D511yescharacteristic
237#131—54no—
238#131—102no—
239C2×M16—31no—
240C2×M16—51no—
241C2×M16—101no—
242C22×C8—51no—
243C22×C8—101no—
244C22×C8—151no—
245#117—151no—
246C2×C42—31no—
247#104—34no—
248#103—152no—
249#102—152no—
250#97—301no—
251C4×C8—302no—
252C4×C8—301no—
253C2×C3×C5—21no—
254C2×C3×C5—21no—
255C2×C3×C5—42no—
256C2×C3×C5C4×C22⋊C411yescharacteristic
257C2×C3×C5#44312yes—
258C23×C3—21no—
259C23×C3#71111yescharacteristic
260C3×Q8—21no—
261C3×Q8C4×Dic512yes—
262C3×D4—22no—
263C3×D4—22no—
264C3×D4—21no—
265C3×D4C4×Dic512yes—
266C2×C3×C4—21no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4C2×C4×D511yescharacteristic
270C2×C3×C4C2×C4×D511yescharacteristic
271C2×C3×C4D4×D511yescharacteristic
272C2×C3×C4D4×D511yescharacteristic
273C2×C3×C4#71111yescharacteristic
274C2×C3×C4C22×Dic511yescharacteristic
275C2×Dic3—24no—
276C2×Dic3—22no—
277C2×Dic3—102no—
278C3×C8—52no—
279C3×C8—52no—
280C3×C8—102no—
281C3⋊C8—22no—
282C3⋊C8—102no—
283C22×C5—22no—
284C22×C5—22no—
285C22×C5—42no—
286C22×C5#92611yescharacteristic
287C22×C5C4×#6711yescharacteristic
288C22×C5C4×#6711yescharacteristic
289C4×C5—22no—
290C4×C5—64no—
291C4×C5C2×C4×Dic311yescharacteristic
292C4×C5C4×#6711yescharacteristic
293C4×C5C4×#6711yescharacteristic
294C4×C5C2×#21711yescharacteristic
295Dic5—122no—
296#41—21no—
297#41—21no—
298#41D5×Dic312yes—
299#41D3×Dic512yes—
300C2×Q8#120011yescharacteristic
301C2×D4—21no—
302C2×D4#120011yescharacteristic
303C22×C4—21no—
304C22×C4—61no—
305C22×C4C2×D3×D511yescharacteristic
306M16—32no—
307M16—52no—
308M16—61no—
309M16—104no—
310M16—101no—
311C2×C8—52no—
312C2×C8—52no—
313C2×C8—51no—
314C2×C8—51no—
315C2×C8—61no—
316C2×C8—104no—
317C2×C8—101no—
318C2×C8—152no—
319C2×C8—301no—
320C2×C8—301no—
321C4⋊C4—152no—
322C22⋊C4—301no—
323C42—32no—
324C42—61no—
325C42—301no—
326C3×C5#176411yescharacteristic, complemented, Hall
327C22×C3—22no—
328C22×C3—22no—
329C22×C3—42no—
330C22×C3#402311yescharacteristic
331C22×C3#402711yescharacteristic
332C22×C3D4×Dic511yescharacteristic
333C3×C4—22no—
334C3×C4D5×C22⋊C411yescharacteristic
335C3×C4#402711yescharacteristic
336C3×C4C2×C4×Dic511yescharacteristic
337C3×C4D4×Dic511yescharacteristic
338Dic3—24no—
339Dic3—202no—
340C2×C5—21no—
341C2×C5—21no—
342C2×C5—42no—
343C2×C5#514412yes—
344C2×C5C4×#21711yescharacteristic
345C23—21no—
346C23#678211yescharacteristic
347Q8—21no—
348Q8Dic3×Dic512yes—
349D4—22no—
350D4—22no—
351D4—21no—
352D4Dic3×Dic512yes—
353C2×C4—21no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—64no—
357C2×C4—62no—
358C2×C4—302no—
359C2×C4C2×D5×Dic311yescharacteristic
360C2×C4C2×D3×Dic511yescharacteristic
361C2×C4#678211yescharacteristic
362C2×C4C2×#120011yescharacteristic
363C2×C4D5×#6711yescharacteristic
364C2×C4D5×#6711yescharacteristic
365C8—52no—
366C8—52no—
367C8—62no—
368C8—102no—
369C8—302no—
370C2×C3—21no—
371C2×C3—21no—
372C2×C3—42no—
373C2×C3#6511312yes—
374C2×C3C22⋊C4×Dic511yescharacteristic
375C5#7200811yescharacteristic, complemented, Sylow
376C22—22no—
377C22—22no—
378C22—42no—
379C22#9152811yescharacteristic
380C22Dic5×#6711yescharacteristic
381C22#9155211yescharacteristic
382C4—22no—
383C4—64no—
384C4—602no—
385C4C2×Dic3×Dic511yescharacteristic
386C4D5×#21711yescharacteristic
387C4Dic5×#6711yescharacteristic
388C4#9155211yescharacteristic
389C3#1060116211yescharacteristic, complemented, Sylow
390C2—21no—
391C2—21no—
392C2—42no—
393C2#1174943412yes—
394C2Dic5×#21711yescharacteristic
subgroupG/H
centerC2×C4D5×#67
commutatorC3×C4×C5C2×C42
FrattiniC22×C4C2×D3×D5
Fitting, prime radicalC2×C3×C5×#41C22
socleC22×C3×C5C4×D4
cosocleC22×C3×C4×C5C23
hypercenterC2×#41D3×D5
hypocenterC3×C5#1764
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
4. #11748324C2semidirect
5. C2×Dic3×#168C2semidirect
6. #11745982C2semidirect
7. #11745976C2semidirect
15. C3×#4094C4semidirect
20. #91119C4semidirect
21. #91116C4semidirect
22. C5×#837C4semidirect
75. #4094Dic3semidirect
125. #837Dic5semidirect
326. C3×C5#1764semidirect
375. C5#72008semidirect
389. C3#10601162semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#40942
#117513342
C2×C5×#8372
#117483242
C2×Dic3×#1682
#117459822
#117459762
#106011623
#720085