Finite Group Databasebeta

← #14308985

Subgroups — #14308985

Order 1920.

932 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756242C211yesmaximal, characteristic, complemented
2#11751056C211yesmaximal, characteristic
3#11751056C212yesmaximal
4C3×C5×#342C211yesmaximal, characteristic, complemented
5#11746348C212yesmaximal, complemented
6#10599764—31nomaximal, Hall
7C24×D15C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2212yes—
9C2×C3×C5×C22⋊C4C2211yescharacteristic
10C2×#6719C2211yescharacteristic
11C2×#6719C2212yes—
12C2×#6714—22no—
13C2×#6714—24no—
14#91813—22no—
15#91767—24no—
16#68971—51nomaximal, Hall
17#65817—31no—
18#65244—32no—
19#65244—31no—
20C5×#342D311yescharacteristic, complemented
21#64747—32no—
22C24×C3×C5C2311yescharacteristic
23C23×D15—21no—
24C23×D15—22no—
25C23×D15—22no—
26C23×D15—21no—
27C23×D15—44no—
28C23×D15Q812yescomplemented
29C22×C3×C4×C5—22no—
30C22×C3×C4×C5D412yes—
31C22×Dic15—21no—
32C22×Dic15D414yes—
33C2×Dic30—22no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C5×C22⋊C4—22no—
37#6719—22no—
38#6719—22no—
39#6719—22no—
40#6714—48no—
41#6714—44no—
42C4⋊Dic15—22no—
43#6712—24no—
44#5483—51no—
45#4955—52no—
46#4955—51no—
47C3×#342D511yescharacteristic, complemented
48#4527—52no—
49C24×D5—31no—
50C2×C5×C22⋊C4C2×D312yes—
51C2×C5×C22⋊C4C2×D311yescharacteristic
52C2×C22⋊Dic5—32no—
53C2×C22⋊Dic5—31no—
54C2×#685—64no—
55C2×#685—62no—
56#4070—62no—
57#4024—64no—
58#2029—151noSylow
59C23×C3×C5—42no—
60C23×C3×C5C2×D411yescharacteristic
61C23×C3×C5C2×D412yes—
62C23×C3×C5C2×Q811yescharacteristic
63C23×C3×C5#4112yes—
64C23×C3×C5#4111yescharacteristic
65C22×D15—24no—
66C22×D15—28no—
67C22×D15—24no—
68C22×D15—22no—
69C22×D15—44no—
70C22×D15—48no—
71C22×D15—44no—
72C22×D15—42no—
73C22×D15—44no—
74C22×D15—41no—
75C22×D15—41no—
76C22×D15—42no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—42no—
79C2×C3×C4×C5—44no—
80C2×C3×C4×C5—42no—
81C2×Dic15—24no—
82C2×Dic15—44no—
83C2×Dic15—42no—
84C2×Dic15—41no—
85Dic30—82no—
86C24×D3—51no—
87C2×C3×C22⋊C4C2×D512yes—
88C2×C3×C22⋊C4C2×D511yescharacteristic
89C2×#217—52no—
90C2×#217—51no—
91C2×(C2×D3)⋊C4—104no—
92C2×(C2×D3)⋊C4—102no—
93#924—102no—
94#878—104no—
95C24×C5C22×D311yescharacteristic
96C23×D5—32no—
97C23×D5—61no—
98C23×D5—62no—
99C23×D5—62no—
100C23×D5—61no—
101C23×D5—124no—
102C22×C4×C5—22no—
103C22×C4×C5D1212yes—
104C22×Dic5—34no—
105C22×Dic5—61no—
106C2×Dic10—62no—
107C5×C22⋊C4—22no—
108C5×C22⋊C4—22no—
109C5×C22⋊C4—22no—
110C22⋊Dic5—62no—
111C22⋊Dic5—62no—
112C22⋊Dic5—62no—
113#685—128no—
114#685—124no—
115C4⋊Dic5—62no—
116#683—64no—
117#543—151no—
118#379—152no—
119#379—151no—
120#342—152no—
121#342D1511yescharacteristic, complemented
122C22×C3×C5—22no—
123C22×C3×C5—24no—
124C22×C3×C5—41no—
125C22×C3×C5—42no—
126C22×C3×C5—41no—
127C22×C3×C5#12011yescharacteristic
128C22×C3×C5C22⋊Q812yes—
129C22×C3×C5C22⋊Q811yescharacteristic
130C22×C3×C5#12411yescharacteristic
131C22×C3×C5#12412yes—
132C2×D15—28no—
133C2×D15—24no—
134C2×D15—44no—
135C2×D15—48no—
136C2×D15—44no—
137C2×D15—42no—
138C2×D15—42no—
139C2×D15—44no—
140C3×C4×C5—42no—
141C3×C4×C5—82no—
142Dic15—44no—
143Dic15—81no—
144C24×C3C22×D511yescharacteristic
145C23×D3—52no—
146C23×D3—101no—
147C23×D3—102no—
148C23×D3—102no—
149C23×D3—101no—
150C23×D3—204no—
151C22×C3×C4—22no—
152C22×C3×C4D2012yes—
153C22×Dic3—54no—
154C22×Dic3—101no—
155C2×Dic6—102no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—22no—
158C3×C22⋊C4—22no—
159#217—102no—
160#217—102no—
161#217—102no—
162(C2×D3)⋊C4—208no—
163(C2×D3)⋊C4—204no—
164C4⋊Dic3—102no—
165Dic3⋊C4—104no—
166C23×C5—42no—
167C23×C5C2×D1211yescharacteristic
168C23×C5#23512yes—
169C23×C5D3×D412yes—
170C23×C5#23711yescharacteristic
171C23×C5D3×Q811yescharacteristic
172C22×D5—64no—
173C22×D5—68no—
174C22×D5—64no—
175C22×D5—62no—
176C22×D5—124no—
177C22×D5—128no—
178C22×D5—124no—
179C22×D5—122no—
180C22×D5—124no—
181C22×D5—121no—
182C22×D5—121no—
183C22×D5—122no—
184C2×C4×C5—22no—
185C2×C4×C5—42no—
186C2×C4×C5—44no—
187C2×C4×C5—42no—
188C2×Dic5—64no—
189C2×Dic5—124no—
190C2×Dic5—122no—
191C2×Dic5—121no—
192Dic10—242no—
193C25—151no—
194C22⋊Q8—304no—
195C22⋊Q8—302no—
196C2×C22⋊C4—152no—
197C2×C22⋊C4—151no—
198C2×C22⋊C4—304no—
199C2×C22⋊C4—302no—
200C2×C22⋊C4C2×D1512yes—
201C2×C22⋊C4C2×D1511yescharacteristic
202C2×C3×C5—21no—
203C2×C3×C5—22no—
204C2×C3×C5—22no—
205C2×C3×C5—21no—
206C2×C3×C5#39311yescharacteristic
207C2×C3×C5B(4,𝔽2)12yes—
208D15—44no—
209C23×C3—42no—
210C23×C3C2×D2011yescharacteristic
211C23×C3#70912yes—
212C23×C3D4×D512yes—
213C23×C3#71111yescharacteristic
214C23×C3Q8×D511yescharacteristic
215C22×D3—104no—
216C22×D3—108no—
217C22×D3—104no—
218C22×D3—102no—
219C22×D3—204no—
220C22×D3—208no—
221C22×D3—204no—
222C22×D3—202no—
223C22×D3—204no—
224C22×D3—201no—
225C22×D3—201no—
226C22×D3—202no—
227C2×C3×C4—22no—
228C2×C3×C4—42no—
229C2×C3×C4—44no—
230C2×C3×C4—42no—
231C2×Dic3—104no—
232C2×Dic3—204no—
233C2×Dic3—202no—
234C2×Dic3—201no—
235Dic6—402no—
236C22×C5—22no—
237C22×C5—24no—
238C22×C5—42no—
239C22×C5—41no—
240C22×C5—41no—
241C22×C5#87511yescharacteristic
242C22×C5#88211yescharacteristic
243C22×C5#88512yes—
244C22×C5#89612yes—
245C22×C5#89711yescharacteristic
246C2×D5—68no—
247C2×D5—64no—
248C2×D5—124no—
249C2×D5—128no—
250C2×D5—124no—
251C2×D5—122no—
252C2×D5—122no—
253C2×D5—124no—
254C4×C5—42no—
255C4×C5—82no—
256Dic5—124no—
257Dic5—241no—
258C24—152no—
259C24—301no—
260C24—302no—
261C24—302no—
262C24—301no—
263C24—604no—
264C24C22×D1511yescharacteristic
265C2×Q8—302no—
266C22×C4—22no—
267C22×C4—154no—
268C22×C4—301no—
269C22×C4D6012yes—
270C4⋊C4—304no—
271C4⋊C4—302no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—22no—
275C22⋊C4—302no—
276C22⋊C4—302no—
277C22⋊C4—302no—
278C22⋊C4—604no—
279C22⋊C4—608no—
280C3×C5#202911yescharacteristic, complemented, Hall
281C22×C3—22no—
282C22×C3—24no—
283C22×C3—42no—
284C22×C3—41no—
285C22×C3—41no—
286C22×C3#402111yescharacteristic
287C22×C3#402811yescharacteristic
288C22×C3#403112yes—
289C22×C3#404212yes—
290C22×C3#404311yescharacteristic
291C2×D3—108no—
292C2×D3—104no—
293C2×D3—204no—
294C2×D3—208no—
295C2×D3—204no—
296C2×D3—202no—
297C2×D3—204no—
298C2×D3—202no—
299C3×C4—42no—
300C3×C4—82no—
301Dic3—204no—
302Dic3—401no—
303C2×C5—21no—
304C2×C5—22no—
305C2×C5—22no—
306C2×C5—21no—
307C2×C5#467311yescharacteristic
308C2×C5#474112yes—
309D5—124no—
310C23—42no—
311C23—304no—
312C23—308no—
313C23—304no—
314C23—302no—
315C23—602no—
316C23—604no—
317C23—604no—
318C23—608no—
319C23—604no—
320C23—601no—
321C23—601no—
322C23—602no—
323C23C2×D6011yescharacteristic
324C23#681712yes—
325C23D4×D1512yes—
326C23#681911yescharacteristic
327C23Q8×D1511yescharacteristic
328Q8—1202no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—44no—
332C2×C4—42no—
333C2×C4—304no—
334C2×C4—604no—
335C2×C4—602no—
336C2×C4—601no—
337C2×C3—21no—
338C2×C3—22no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3#6496211yescharacteristic
342C2×C3#6503012yes—
343D3—204no—
344C5#6897111yescharacteristic, complemented, Sylow
345C22—22no—
346C22—24no—
347C22—42no—
348C22—41no—
349C22—41no—
350C22—308no—
351C22—304no—
352C22—608no—
353C22—604no—
354C22—604no—
355C22—602no—
356C22—602no—
357C22—604no—
358C22#9176411yescharacteristic
359C22#9177111yescharacteristic
360C22#9177412yes—
361C22#9178512yes—
362C22#9178611yescharacteristic
363C4—42no—
364C4—82no—
365C4—604no—
366C4—1201no—
367C3#1059976411yescharacteristic, complemented, Sylow
368C2—22no—
369C2—21no—
370C2—22no—
371C2—21no—
372C2—604no—
373C2#1175077411yescharacteristic
374C2#1175084212yes—
subgroupG/H
centerC22#91771
commutator, cosocleC24×C3×C5C23
FrattiniC24C22×D15
FittingC3×C5×#342C2
socleC22×C3×C5#120
prime radicalC24×D15C22
hypercenter#342D15
hypocenterC3×C5#2029
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
1. #11756242C2semidirect
4. C3×C5×#342C2semidirect
5. #11746348C2semidirect
20. C5×#342D3semidirect
28. C23×D15Q8semidirect
47. C3×#342D5semidirect
121. #342D15semidirect
280. C3×C5#2029semidirect
344. C5#68971semidirect
367. C3#10599764semidirect

Maximal subgroups

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

subgroupindex
#117562422
#117510562
C3×C5×#3422
#117463482
#105997643
#689715