Finite Group Databasebeta

← #14301665

Subgroups — #14301665

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
1C3×C5×#518C211yesmaximal, characteristic
2C2×#91824C211yesmaximal, characteristic
3C2×#91118C211yesmaximal, characteristic
4#11751044C212yesmaximal, complemented
5#11746347C212yesmaximal, complemented
6#10602448—31nomaximal, Hall
7C22×C3×C5×D4C2211yescharacteristic
8C23×Dic15C2211yescharacteristic
9C3×C4×C5×D4—24no—
10C3×C5×#117—21no—
11C2×C3×C5×C22⋊C4—21no—
12C2×C3×C5×C22⋊C4C2212yes—
13C2×#6719—21no—
14C2×#6719C2212yes—
15C2×#6719C2211yescharacteristic
16#91824—22no—
17#91824C414yescomplemented
18C2×#6712—21no—
19#91118—22no—
20#91115—24no—
21#71655—51nomaximal, Hall
22C5×#518D311yescharacteristic
23C2×#4081—31no—
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×C5—22no—
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D414yes—
36C22×Dic15—21no—
37C22×Dic15—21no—
38C22×Dic15—21no—
39C22×Dic15—22no—
40C22×Dic15—22no—
41C22×Dic15—22no—
42C22×Dic15C2×C412yescomplemented
43C3×C5×C4⋊C4—22no—
44C3×C5×C22⋊C4—22no—
45C3×C5×C22⋊C4—22no—
46C3×C5×C22⋊C4—22no—
47C3×C42×C5—22no—
48#6719—24no—
49#6719—21no—
50#6719—22no—
51#6719—22no—
52#6719C2×C412yescomplemented
53#6712—24no—
54C3×#518D511yescharacteristic
55C2×#935—51no—
56C2×#834—51no—
57#4943—52no—
58#4526—52no—
59C22×C5×D4C2×D311yescharacteristic
60C23×Dic5—31no—
61C4×C5×D4—24no—
62C5×#117—21no—
63C2×C5×C22⋊C4—21no—
64C2×C5×C22⋊C4C2×D312yes—
65C2×C22⋊Dic5—31no—
66C2×C22⋊Dic5—32no—
67C2×C22⋊Dic5—61no—
68#4081—34no—
69#4081—62no—
70C2×#683—61no—
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×C5—24no—
89C2×C3×C4×C5—44no—
90C2×C3×C4×C5—82no—
91C2×C3×C4×C5C22⋊C412yes—
92C2×Dic15—22no—
93C2×Dic15—22no—
94C2×Dic15—24no—
95C2×Dic15—42no—
96C2×Dic15—41no—
97C2×Dic15—42no—
98C2×Dic15—41no—
99C2×Dic15—44no—
100C2×Dic15—42no—
101C22×C3×D4C2×D511yescharacteristic
102C23×Dic3—51no—
103C3×C4×D4—24no—
104C3×#117—21no—
105C2×C3×C22⋊C4—21no—
106C2×C3×C22⋊C4C2×D512yes—
107C2×#217—51no—
108C2×#217—52no—
109C2×#217—101no—
110#935—54no—
111#935—102no—
112C2×Dic3⋊C4—101no—
113#834—102no—
114C3⋊#95—104no—
115C24×C5#6711yescharacteristic
116C24×C5C22×D311yescharacteristic
117C2×C5×D4—22no—
118C2×C5×D4—22no—
119C2×C5×D4C4×D312yes—
120C2×C5×D4D1212yes—
121C22×C4×C5—22no—
122C22×C4×C5#6711yescharacteristic
123C22×C4×C5#6714yes—
124C22×Dic5—32no—
125C22×Dic5—61no—
126C22×Dic5—62no—
127C22×Dic5—61no—
128C22×Dic5—61no—
129C22×Dic5—62no—
130C22×Dic5—62no—
131C5×C4⋊C4—22no—
132C5×C22⋊C4—22no—
133C5×C22⋊C4—22no—
134C5×C22⋊C4—22no—
135C42×C5—22no—
136C22⋊Dic5—32no—
137C22⋊Dic5—64no—
138C22⋊Dic5—61no—
139C22⋊Dic5—62no—
140C22⋊Dic5—62no—
141#683—64no—
142C2×#123—151no—
143#518D1511yescharacteristic
144C2×#99—151no—
145#381—152no—
146#342—152no—
147C22×C3×C5—24no—
148C22×C3×C5—22no—
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—
162C3×C4×C5—44no—
163Dic15—42no—
164Dic15—42no—
165Dic15—82no—
166C24×C3C22⋊D511yescharacteristic
167C24×C3C22×D511yescharacteristic
168C2×C3×D4—22no—
169C2×C3×D4—22no—
170C2×C3×D4C4×D512yes—
171C2×C3×D4D2012yes—
172C22×C3×C4—22no—
173C22×C3×C4C22⋊D511yescharacteristic
174C22×C3×C4C22⋊D514yes—
175C22×Dic3—52no—
176C22×Dic3—101no—
177C22×Dic3—102no—
178C22×Dic3—102no—
179C22×Dic3—101no—
180C22×Dic3—101no—
181C22×Dic3—102no—
182C3×C4⋊C4—22no—
183C3×C22⋊C4—22no—
184C3×C22⋊C4—22no—
185C3×C22⋊C4—22no—
186C3×C42—22no—
187#217—52no—
188#217—104no—
189#217—101no—
190#217—102no—
191#217—102no—
192Dic3⋊C4—104no—
193C23×C5—21no—
194C23×C5—21no—
195C23×C5—42no—
196C23×C5—42no—
197C23×C5(C2×D3)⋊C412yes—
198C23×C5C2×C4×D311yescharacteristic
199C23×C5C2×D1211yescharacteristic
200C23×C5#23512yes—
201C23×C5C2×#6711yescharacteristic
202C23×C5C2×#6712yes—
203C5×D4—24no—
204C5×D4—24no—
205C2×C4×C5—21no—
206C2×C4×C5—21no—
207C2×C4×C5—24no—
208C2×C4×C5—44no—
209C2×C4×C5—82no—
210C2×C4×C5(C2×D3)⋊C412yes—
211C2×Dic5—62no—
212C2×Dic5—62no—
213C2×Dic5—64no—
214C2×Dic5—122no—
215C2×Dic5—121no—
216C2×Dic5—122no—
217C2×Dic5—121no—
218C2×Dic5—124no—
219C2×Dic5—122no—
220C22×D4C2×D1511yescharacteristic
221C23×C4—151no—
222#123—154no—
223#123—302no—
224C4×D4—24no—
225#117—21no—
226C2×C4⋊C4—301no—
227C2×C22⋊C4—21no—
228C2×C22⋊C4—151no—
229C2×C22⋊C4—152no—
230C2×C22⋊C4—301no—
231C2×C22⋊C4C2×D1512yes—
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—24no—
256C2×C3×C4—44no—
257C2×C3×C4—82no—
258C2×C3×C4#68512yes—
259C2×Dic3—102no—
260C2×Dic3—102no—
261C2×Dic3—104no—
262C2×Dic3—202no—
263C2×Dic3—201no—
264C2×Dic3—201no—
265C2×Dic3—202no—
266C2×Dic3—204no—
267C2×Dic3—202no—
268C22×C5—24no—
269C22×C5—22no—
270C22×C5—22no—
271C22×C5—41no—
272C22×C5—41no—
273C22×C5—42no—
274C22×C5—42no—
275C22×C5—42no—
276C22×C5—81no—
277C22×C5C2×(C2×D3)⋊C411yescharacteristic
278C22×C5C4×#6712yes—
279C22×C5#92911yescharacteristic
280C22×C5#93012yes—
281C22×C5#95311yescharacteristic
282C4×C5—22no—
283C4×C5—44no—
284Dic5—122no—
285Dic5—122no—
286Dic5—242no—
287C24#122011yescharacteristic
288C24C22×D1511yescharacteristic
289C2×D4—22no—
290C2×D4—22no—
291C2×D4C4×D1512yes—
292C2×D4D6012yes—
293C22×C4—22no—
294C22×C4—152no—
295C22×C4—301no—
296C22×C4—302no—
297C22×C4—302no—
298C22×C4—301no—
299C22×C4—301no—
300C22×C4—302no—
301C22×C4#122011yescharacteristic
302C22×C4#122014yes—
303C4⋊C4—22no—
304C4⋊C4—304no—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—22no—
308C22⋊C4—152no—
309C22⋊C4—304no—
310C22⋊C4—301no—
311C22⋊C4—302no—
312C22⋊C4—302no—
313C42—22no—
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—44no—
331Dic3—202no—
332Dic3—202no—
333Dic3—402no—
334C2×C5—21no—
335C2×C5—22no—
336C2×C5—21no—
337C2×C5—22no—
338C2×C5—42no—
339C2×C5#521311yescharacteristic
340C2×C5#524312yes—
341C23—21no—
342C23—21no—
343C23—42no—
344C23—42no—
345C23#671412yes—
346C23C2×C4×D1511yescharacteristic
347C23C2×D6011yescharacteristic
348C23#681712yes—
349C23C2×#122011yescharacteristic
350C23C2×#122012yes—
351D4—24no—
352D4—24no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—24no—
356C2×C4—44no—
357C2×C4—82no—
358C2×C4—302no—
359C2×C4—302no—
360C2×C4—304no—
361C2×C4—602no—
362C2×C4—601no—
363C2×C4—602no—
364C2×C4—601no—
365C2×C4—604no—
366C2×C4—602no—
367C2×C4#671412yes—
368C2×C3—21no—
369C2×C3—22no—
370C2×C3—21no—
371C2×C3—22no—
372C2×C3—42no—
373C2×C3#6550211yescharacteristic
374C2×C3#6553212yes—
375C5#7165511yescharacteristic, complemented, Sylow
376C22—24no—
377C22—22no—
378C22—22no—
379C22—41no—
380C22—41no—
381C22—42no—
382C22—42no—
383C22—42no—
384C22—81no—
385C22C2×#671411yescharacteristic
386C22C4×#122012yes—
387C22#9181811yescharacteristic
388C22#9181912yes—
389C22#9184211yescharacteristic
390C4—22no—
391C4—44no—
392C4—602no—
393C4—602no—
394C4—1202no—
395C3#1060244811yescharacteristic, complemented, Sylow
396C2—21no—
397C2—22no—
398C2—21no—
399C2—22no—
400C2—42no—
401C2#1175131411yescharacteristic
402C2#1175134412yes—
subgroupG/H
centerC22#91842
commutatorC23×C3×C5C22×C4
FrattiniC24C22×D15
FittingC3×C5×#518C2
socleC22×C3×C5#120
prime radicalC22×C3×C5×D4C22
cosocleC24×C3×C5C23
hypercenter#518D15
hypocenterC3×C5#1890
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #518

Complements

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

NH ≅ G/Ntype
4. #11751044C2semidirect
5. #11746347C2semidirect
17. #91824C4semidirect
42. C22×Dic15C2×C4semidirect
52. #6719C2×C4semidirect
314. C3×C5#1890semidirect
375. C5#71655semidirect
395. C3#10602448semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5182
C2×#918242
C2×#911182
#117510442
#117463472
#106024483
#716555