Finite Group Databasebeta

← #14308990

Subgroups — #14308990

Order 1920.

932 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 118 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
1C3×#65817C211yesmaximal, characteristic, complemented
2#11751056C211yesmaximal, characteristic
3#11749502C212yesmaximal
4C5×#4526C211yesmaximal, characteristic, complemented
5#11746019C212yesmaximal, complemented
6#10599764—31nomaximal, Hall
7C24×D15C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×#6719C2211yescharacteristic
10C2×#6714—22no—
11C2×C5×#217C2212yes—
12C2×C3×C22⋊Dic5C2212yes—
13C3×#4070—22no—
14C3×#4024—24no—
15C2×#6667—24no—
16#71897—51nomaximal, Hall
17#65817D311yescharacteristic, complemented
18#65244—31no—
19#65244—32no—
20C5×#342—31no—
21#64747—32no—
22C24×C3×C5C2311yescharacteristic
23C23×D15—22no—
24C23×D15—21no—
25C23×D15—22no—
26C23×D15—21no—
27C23×D15—44no—
28C23×D15Q812yescomplemented
29C22×C3×C4×C5D412yes—
30C22×Dic15—21no—
31C22×C5×Dic3—22no—
32C22×C3×Dic5D414yes—
33C2×C3×Dic10—22no—
34C3×C5×C22⋊C4—22no—
35#6719—22no—
36#6714—44no—
37C5×#217—22no—
38C5×#217—22no—
39C3×C22⋊Dic5—22no—
40C3×C22⋊Dic5—22no—
41C3×C4⋊Dic5—22no—
42C3×#683—24no—
43#6667—48no—
44C3×#543—51no—
45#4955—51no—
46#4955—52no—
47#4526—52no—
48#4526D511yescharacteristic, complemented
49C24×D5—31no—
50C2×C5×C22⋊C4—32no—
51C2×C5×C22⋊C4C2×D311yescharacteristic
52C2×C22⋊Dic5—31no—
53C2×C22⋊Dic5C2×D312yes—
54C2×#685—62no—
55C2×#685—64no—
56#4070—22no—
57#4024—24no—
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—28no—
66C22×D15—24no—
67C22×D15—24no—
68C22×D15—22no—
69C22×D15—44no—
70C22×D15—48no—
71C22×D15—44no—
72C22×D15—44no—
73C22×D15—42no—
74C22×D15—41no—
75C22×D15—41no—
76C22×D15—42no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—42no—
79C2×Dic15—42no—
80C2×Dic15—41no—
81C2×C5×Dic3—44no—
82C2×C5×Dic3—42no—
83C2×C3×Dic5—24no—
84C2×C3×Dic5—44no—
85C3×Dic10—82no—
86C24×D3—51no—
87C3×C22⋊Q8—104no—
88C3×C22⋊Q8—102no—
89C2×C3×C22⋊C4—52no—
90C2×C3×C22⋊C4C2×D511yescharacteristic
91C2×#217—51no—
92C2×#217C2×D512yes—
93C2×(C2×D3)⋊C4—104no—
94C2×(C2×D3)⋊C4—102no—
95C24×C5C22×D311yescharacteristic
96C23×D5—32no—
97C23×D5—61no—
98C23×D5—62no—
99C23×D5—61no—
100C23×D5—62no—
101C23×D5—124no—
102C22×C4×C5—62no—
103C22×C4×C5#6712yes—
104C22×Dic5—61no—
105C22×Dic5#6714yes—
106C2×Dic10—22no—
107C5×C22⋊C4—22no—
108C5×C22⋊C4—62no—
109C5×C22⋊C4—62no—
110C22⋊Dic5—22no—
111C22⋊Dic5—22no—
112C22⋊Dic5—62no—
113#685—128no—
114#685—124no—
115C4⋊Dic5—22no—
116#683—24no—
117#543—51no—
118#379—152no—
119#379—151no—
120#342—31no—
121#342—152no—
122C22×C3×C5—24no—
123C22×C3×C5—22no—
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—48no—
135C2×D15—44no—
136C2×D15—44no—
137C2×D15—42no—
138C2×D15—42no—
139C2×D15—44no—
140C3×C4×C5—42no—
141Dic15—81no—
142C3×Dic5—44no—
143C5×Dic3—82no—
144C24×C3C22×D511yescharacteristic
145C23×D3—52no—
146C23×D3—101no—
147C23×D3—102no—
148C23×D3—102no—
149C23×D3—101no—
150C23×D3—204no—
151C2×C3×Q8—102no—
152C22×C3×C4—54no—
153C22×C3×C4D2012yes—
154C22×Dic3—22no—
155C22×Dic3—101no—
156C3×C4⋊C4—104no—
157C3×C4⋊C4—102no—
158C3×C22⋊C4—22no—
159C3×C22⋊C4—102no—
160C3×C22⋊C4—102no—
161#217—22no—
162#217—22no—
163#217—102no—
164(C2×D3)⋊C4—208no—
165(C2×D3)⋊C4—204no—
166C23×C5—42no—
167C23×C5D3×Q811yescharacteristic
168C23×C5#23911yescharacteristic
169C23×C5#23912yes—
170C23×C5C2×#6711yescharacteristic
171C23×C5C2×#6712yes—
172C22×D5—68no—
173C22×D5—64no—
174C22×D5—64no—
175C22×D5—62no—
176C22×D5—124no—
177C22×D5—124no—
178C22×D5—128no—
179C22×D5—124no—
180C22×D5—122no—
181C22×D5—122no—
182C22×D5—121no—
183C22×D5—121no—
184C2×C4×C5—22no—
185C2×C4×C5—42no—
186C2×C4×C5—124no—
187C2×C4×C5—122no—
188C2×Dic5—24no—
189C2×Dic5—44no—
190C2×Dic5—122no—
191C2×Dic5—121no—
192Dic10—82no—
193C25—151no—
194C22⋊Q8—104no—
195C22⋊Q8—102no—
196C2×C22⋊C4—32no—
197C2×C22⋊C4—52no—
198C2×C22⋊C4—151no—
199C2×C22⋊C4—304no—
200C2×C22⋊C4—302no—
201C2×C22⋊C4D3×D511yescharacteristic
202C2×C3×C5—22no—
203C2×C3×C5—21no—
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—108no—
216C22×D3—104no—
217C22×D3—104no—
218C22×D3—102no—
219C22×D3—204no—
220C22×D3—208no—
221C22×D3—204no—
222C22×D3—204no—
223C22×D3—202no—
224C22×D3—201no—
225C22×D3—201no—
226C22×D3—202no—
227C3×Q8—402no—
228C2×C3×C4—22no—
229C2×C3×C4—42no—
230C2×C3×C4—104no—
231C2×C3×C4—204no—
232C2×Dic3—44no—
233C2×Dic3—42no—
234C2×Dic3—202no—
235C2×Dic3—201no—
236C22×C5—24no—
237C22×C5—22no—
238C22×C5—41no—
239C22×C5—41no—
240C22×C5—42no—
241C22×C5#94612yes—
242C22×C5#94611yescharacteristic
243C22×C5#94712yes—
244C22×C5#94711yescharacteristic
245C22×C5#95311yescharacteristic
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—242no—
256Dic5—44no—
257Dic5—241no—
258C24—152no—
259C24—301no—
260C24—302no—
261C24—301no—
262C24—302no—
263C24—604no—
264C24C2×D3×D511yescharacteristic
265C2×Q8—102no—
266C22×C4—54no—
267C22×C4—62no—
268C22×C4—301no—
269C22×C4#120212yes—
270C4⋊C4—104no—
271C4⋊C4—102no—
272C22⋊C4—22no—
273C22⋊C4—62no—
274C22⋊C4—62no—
275C22⋊C4—102no—
276C22⋊C4—102no—
277C22⋊C4—302no—
278C22⋊C4—604no—
279C22⋊C4—608no—
280C3×C5#202911yescharacteristic, complemented, Hall
281C22×C3—24no—
282C22×C3—22no—
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—208no—
294C2×D3—204no—
295C2×D3—204no—
296C2×D3—202no—
297C2×D3—204no—
298C2×D3—202no—
299C3×C4—42no—
300C3×C4—204no—
301Dic3—82no—
302Dic3—401no—
303C2×C5—21no—
304C2×C5—22no—
305C2×C5—22no—
306C2×C5—21no—
307C2×C5#523111yescharacteristic
308C2×C5#524412yes—
309D5—124no—
310C23—42no—
311C23—304no—
312C23—308no—
313C23—304no—
314C23—302no—
315C23—602no—
316C23—604no—
317C23—604no—
318C23—604no—
319C23—608no—
320C23—601no—
321C23—602no—
322C23—601no—
323C23#676811yescharacteristic
324C23#676912yes—
325C23D15⋊Q811yescharacteristic
326C23C2×#120211yescharacteristic
327C23D5×#6712yes—
328Q8—402no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—104no—
332C2×C4—124no—
333C2×C4—122no—
334C2×C4—204no—
335C2×C4—602no—
336C2×C4—601no—
337C2×C3—22no—
338C2×C3—21no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3#6496211yescharacteristic
342C2×C3#6503012yes—
343D3—204no—
344C5#7189711yescharacteristic, complemented, Sylow
345C22—22no—
346C22—24no—
347C22—41no—
348C22—42no—
349C22—41no—
350C22—308no—
351C22—304no—
352C22—608no—
353C22—604no—
354C22—604no—
355C22—602no—
356C22—604no—
357C22—602no—
358C22#9132612yes—
359C22#9137411yescharacteristic
360C22#9139011yescharacteristic
361C22#9141112yes—
362C22#9156411yescharacteristic
363C4—42no—
364C4—204no—
365C4—242no—
366C4—1201no—
367C3#1059976411yescharacteristic, complemented, Sylow
368C2—22no—
369C2—21no—
370C2—22no—
371C2—21no—
372C2—604no—
373C2#1174875311yescharacteristic
374C2#1174917612yes—
subgroupG/H
centerC22#91564
commutator, cosocleC24×C3×C5C23
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
prime radicalC24×D15C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5#2029
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C3×#65817C2semidirect
4. C5×#4526C2semidirect
5. #11746019C2semidirect
17. #65817D3semidirect
28. C23×D15Q8semidirect
48. #4526D5semidirect
280. C3×C5#2029semidirect
344. C5#71897semidirect
367. C3#10599764semidirect

Maximal subgroups

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

subgroupindex
C3×#658172
#117510562
#117495022
C5×#45262
#117460192
#105997643
#718975