Finite Group Databasebeta

← #14301686

Subgroups — #14301686

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5798C211yesmaximal, characteristic
2C2×C3×#4081C211yesmaximal, characteristic
3C2×#91118C211yesmaximal, characteristic
4#11749471C212yesmaximal, complemented
5#11746018C212yesmaximal, complemented
6#10602448—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C23×C3×Dic5C2211yescharacteristic
9C2×#6719C2212yes—
10C2×C5×#217—21no—
11C2×C5×#217C2212yes—
12C5×D4×Dic3—24no—
13C5×#926—21no—
14C2×C3×C22⋊Dic5—21no—
15C2×C3×C22⋊Dic5C2211yescharacteristic
16C3×#4081—22no—
17C3×#4081C414yescomplemented
18C2×C3×#683—21no—
19#91118—22no—
20#90994—24no—
21#71704—51nomaximal, Hall
22C5×#518—31no—
23C2×#4081D311yescharacteristic
24C2×#3966—31no—
25#65232—32no—
26#64746—32no—
27C24×C3×C5D411yescharacteristic
28C24×C3×C5C2311yescharacteristic
29C2×C3×C5×D4—22no—
30C2×C3×C5×D4—22no—
31C2×C3×C5×D4C2×C412yes—
32C2×C3×C5×D4D412yes—
33C22×C3×C4×C5D411yescharacteristic
34C22×Dic15—22no—
35C22×C5×Dic3—22no—
36C22×C5×Dic3D414yes—
37C22×C3×Dic5—21no—
38C22×C3×Dic5—21no—
39C22×C3×Dic5—21no—
40C22×C3×Dic5—22no—
41C22×C3×Dic5—22no—
42C22×C3×Dic5C2×C412yescomplemented
43#6719—22no—
44#6719—22no—
45C5×#217—22no—
46C5×#217—22no—
47C5×#217—22no—
48C5×C4⋊Dic3—22no—
49C4×C5×Dic3—22no—
50C3×C22⋊Dic5—24no—
51C3×C22⋊Dic5—21no—
52C3×C22⋊Dic5C2×C412yescomplemented
53C3×#683—24no—
54C2×C3×#123—51no—
55#5798D511yescharacteristic
56C2×#834—51no—
57#5211—52no—
58#4527—52no—
59C22×C5×D4C2×D311yescharacteristic
60C23×Dic5C2×D311yescharacteristic
61C4×C5×D4—64no—
62C5×#117—61no—
63C2×C5×C22⋊C4—32no—
64C2×C5×C22⋊C4—61no—
65C2×C22⋊Dic5—21no—
66C2×C22⋊Dic5—32no—
67C2×C22⋊Dic5C2×D311yescharacteristic
68#4081—22no—
69#4081Dic314yescomplemented
70C2×#683—21no—
71#3966—62no—
72#3963—64no—
73#1890—151noSylow
74C23×C3×C5—21no—
75C23×C3×C5—21no—
76C23×C3×C5—42no—
77C23×C3×C5—42no—
78C23×C3×C5C22⋊C412yes—
79C23×C3×C5C22×C411yescharacteristic
80C23×C3×C5C2×D411yescharacteristic
81C23×C3×C5C2×D412yes—
82C23×C3×C5C2×D411yescharacteristic
83C23×C3×C5#4112yes—
84C3×C5×D4—24no—
85C3×C5×D4—24no—
86C2×C3×C4×C5—21no—
87C2×C3×C4×C5—21no—
88C2×C3×C4×C5C22⋊C412yes—
89C2×Dic15—44no—
90C2×Dic15—42no—
91C2×C5×Dic3—24no—
92C2×C5×Dic3—44no—
93C2×C5×Dic3—82no—
94C2×C3×Dic5—22no—
95C2×C3×Dic5—22no—
96C2×C3×Dic5—24no—
97C2×C3×Dic5—42no—
98C2×C3×Dic5—41no—
99C2×C3×Dic5—42no—
100C2×C3×Dic5—41no—
101C22×C3×D4C2×D511yescharacteristic
102C23×C3×C4—51no—
103C3×#123—54no—
104C3×#123—102no—
105C2×C3×C4⋊C4—101no—
106C2×C3×C22⋊C4—51no—
107C2×C3×C22⋊C4—101no—
108C2×#217—21no—
109C2×#217—52no—
110C2×#217C2×D512yes—
111D4×Dic3—24no—
112#926—21no—
113#834—102no—
114C3⋊#95—104no—
115C24×C5#6711yescharacteristic
116C24×C5C22×D311yescharacteristic
117C2×C5×D4—22no—
118C2×C5×D4—22no—
119C2×C5×D4C2×Dic312yes—
120C2×C5×D4#6712yes—
121C22×C4×C5—34no—
122C22×C4×C5—62no—
123C22×C4×C5#6711yescharacteristic
124C22×Dic5—22no—
125C22×Dic5—22no—
126C22×Dic5—21no—
127C22×Dic5—21no—
128C22×Dic5—21no—
129C22×Dic5—62no—
130C22×Dic5C2×Dic312yescomplemented
131C5×C4⋊C4—62no—
132C5×C22⋊C4—62no—
133C5×C22⋊C4—62no—
134C5×C22⋊C4—62no—
135C42×C5—62no—
136C22⋊Dic5—24no—
137C22⋊Dic5—21no—
138C22⋊Dic5—62no—
139C22⋊Dic5—62no—
140C22⋊Dic5C2×Dic312yescomplemented
141#683—24no—
142C2×#123—51no—
143#518—31no—
144C2×#99—151no—
145#381—152no—
146#342—152no—
147C22×C3×C5—22no—
148C22×C3×C5—24no—
149C22×C3×C5—22no—
150C22×C3×C5—41no—
151C22×C3×C5—41no—
152C22×C3×C5—42no—
153C22×C3×C5—42no—
154C22×C3×C5—42no—
155C22×C3×C5—81no—
156C22×C3×C5C2×C22⋊C411yescharacteristic
157C22×C3×C5C4×D412yes—
158C22×C3×C5#12011yescharacteristic
159C22×C3×C5#12112yes—
160C22×C3×C5#12311yescharacteristic
161C3×C4×C5—22no—
162Dic15—82no—
163C3×Dic5—42no—
164C3×Dic5—42no—
165C5×Dic3—44no—
166C24×C3C22⋊D511yescharacteristic
167C24×C3C22×D511yescharacteristic
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4C4×D512yes—
171C2×C3×D4D2012yes—
172C22×C3×C4—52no—
173C22×C3×C4—101no—
174C22×C3×C4—102no—
175C22×C3×C4—102no—
176C22×C3×C4—101no—
177C22×C3×C4—101no—
178C22×C3×C4C22⋊D511yescharacteristic
179C22×Dic3—22no—
180C22×Dic3—102no—
181C22×Dic3C22⋊D514yes—
182C3×C4⋊C4—104no—
183C3×C22⋊C4—52no—
184C3×C22⋊C4—104no—
185C3×C22⋊C4—101no—
186#217—22no—
187#217—22no—
188#217—22no—
189#217—102no—
190#217—102no—
191C4⋊Dic3—22no—
192C4×Dic3—22no—
193C23×C5—21no—
194C23×C5—21no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5#21712yes—
198C23×C5D3×D412yes—
199C23×C5#23712yes—
200C23×C5C22×Dic311yescharacteristic
201C23×C5C2×#6711yescharacteristic
202C23×C5C2×#6711yescharacteristic
203C5×D4—24no—
204C5×D4—24no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—64no—
208C2×C4×C5—124no—
209C2×C4×C5—242no—
210C2×C4×C5#21712yes—
211C2×Dic5—24no—
212C2×Dic5—22no—
213C2×Dic5—22no—
214C2×Dic5—42no—
215C2×Dic5—41no—
216C2×Dic5—41no—
217C2×Dic5—42no—
218C2×Dic5—124no—
219C2×Dic5—122no—
220C22×D4D3×D511yescharacteristic
221C23×C4—51no—
222#123—54no—
223#123—102no—
224C4×D4—64no—
225#117—61no—
226C2×C4⋊C4—101no—
227C2×C22⋊C4—32no—
228C2×C22⋊C4—51no—
229C2×C22⋊C4—61no—
230C2×C22⋊C4—101no—
231C2×C22⋊C4—152no—
232#99—302no—
233#95—304no—
234C2×C3×C5—21no—
235C2×C3×C5—22no—
236C2×C3×C5—21no—
237C2×C3×C5—22no—
238C2×C3×C5—42no—
239C2×C3×C5#38611yescharacteristic
240C2×C3×C5#45812yes—
241C23×C3—21no—
242C23×C3—21no—
243C23×C3—42no—
244C23×C3—42no—
245C23×C3#68512yes—
246C23×C3C2×C4×D511yescharacteristic
247C23×C3C2×D2011yescharacteristic
248C23×C3#70912yes—
249C23×C3C2×C22⋊D511yescharacteristic
250C23×C3C2×C22⋊D512yes—
251C3×D4—24no—
252C3×D4—24no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—102no—
256C2×C3×C4—102no—
257C2×C3×C4—104no—
258C2×C3×C4—202no—
259C2×C3×C4—201no—
260C2×C3×C4—201no—
261C2×C3×C4—202no—
262C2×C3×C4#68512yes—
263C2×Dic3—24no—
264C2×Dic3—44no—
265C2×Dic3—82no—
266C2×Dic3—204no—
267C2×Dic3—202no—
268C22×C5—22no—
269C22×C5—24no—
270C22×C5—22no—
271C22×C5—42no—
272C22×C5—41no—
273C22×C5—41no—
274C22×C5—42no—
275C22×C5—42no—
276C22×C5—81no—
277C22×C5D4×Dic312yes—
278C22×C5#93511yescharacteristic
279C22×C5#93711yescharacteristic
280C22×C5#93912yes—
281C22×C5C2×#21711yescharacteristic
282C4×C5—22no—
283C4×C5—124no—
284Dic5—42no—
285Dic5—42no—
286Dic5—242no—
287C24#120111yescharacteristic
288C24C2×D3×D511yescharacteristic
289C2×D4—22no—
290C2×D4—22no—
291C2×D4D5×Dic312yes—
292C2×D4#120212yes—
293C22×C4—34no—
294C22×C4—52no—
295C22×C4—62no—
296C22×C4—102no—
297C22×C4—101no—
298C22×C4—101no—
299C22×C4—101no—
300C22×C4—102no—
301C22×C4—302no—
302C22×C4#120111yescharacteristic
303C4⋊C4—62no—
304C4⋊C4—104no—
305C22⋊C4—52no—
306C22⋊C4—62no—
307C22⋊C4—62no—
308C22⋊C4—62no—
309C22⋊C4—104no—
310C22⋊C4—101no—
311C22⋊C4—302no—
312C22⋊C4—302no—
313C42—62no—
314C3×C5#189011yescharacteristic, complemented, Hall
315C22×C3—24no—
316C22×C3—22no—
317C22×C3—22no—
318C22×C3—41no—
319C22×C3—41no—
320C22×C3—42no—
321C22×C3—42no—
322C22×C3—42no—
323C22×C3—81no—
324C22×C3C2×#68511yescharacteristic
325C22×C3C4×C22⋊D512yes—
326C22×C3#407511yescharacteristic
327C22×C3#407612yes—
328C22×C3#409911yescharacteristic
329C3×C4—22no—
330C3×C4—202no—
331C3×C4—202no—
332Dic3—44no—
333Dic3—402no—
334C2×C5—21no—
335C2×C5—22no—
336C2×C5—21no—
337C2×C5—22no—
338C2×C5—42no—
339C2×C5#505312yes—
340C2×C5#522011yescharacteristic
341C23—21no—
342C23—21no—
343C23—42no—
344C23—42no—
345C23#666512yes—
346C23C2×D5×Dic311yescharacteristic
347C23#677912yes—
348C23C2×#120111yescharacteristic
349C23C2×#120211yescharacteristic
350C23D3×C22⋊D512yes—
351D4—24no—
352D4—24no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—64no—
356C2×C4—102no—
357C2×C4—102no—
358C2×C4—104no—
359C2×C4—124no—
360C2×C4—202no—
361C2×C4—201no—
362C2×C4—201no—
363C2×C4—202no—
364C2×C4—242no—
365C2×C4—604no—
366C2×C4—602no—
367C2×C4#666512yes—
368C2×C3—22no—
369C2×C3—21no—
370C2×C3—21no—
371C2×C3—22no—
372C2×C3—42no—
373C2×C3#6550211yescharacteristic
374C2×C3#6553212yes—
375C5#7170411yescharacteristic, complemented, Sylow
376C22—24no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—42no—
381C22—41no—
382C22—42no—
383C22—42no—
384C22—81no—
385C22C2×#666511yescharacteristic
386C22#9153611yescharacteristic
387C22Dic3×C22⋊D512yes—
388C22#9156811yescharacteristic
389C22#9156912yes—
390C4—22no—
391C4—124no—
392C4—202no—
393C4—202no—
394C4—1202no—
395C3#1060244811yescharacteristic, complemented, Sylow
396C2—21no—
397C2—22no—
398C2—21no—
399C2—22no—
400C2—42no—
401C2#1174918312yes—
402C2#1174949511yescharacteristic
subgroupG/H
centerC22#91568
commutatorC23×C3×C5C22×C4
FrattiniC24C2×D3×D5
Fitting, prime radicalC22×C3×C5×D4C22
socleC22×C3×C5#120
cosocleC24×C3×C5C23
hypercenterC22×D4D3×D5
hypocenterC3×C5#1890
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
4. #11749471C2semidirect
5. #11746018C2semidirect
17. C3×#4081C4semidirect
42. C22×C3×Dic5C2×C4semidirect
52. C3×C22⋊Dic5C2×C4semidirect
69. #4081Dic3semidirect
130. C22×Dic5C2×Dic3semidirect
140. C22⋊Dic5C2×Dic3semidirect
314. C3×C5#1890semidirect
375. C5#71704semidirect
395. C3#10602448semidirect

Maximal subgroups

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

subgroupindex
C5×#57982
C2×C3×#40812
C2×#911182
#117494712
#117460182
#106024483
#717045