Finite Group Databasebeta

← #14308986

Subgroups — #14308986

Order 1920.

932 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 120 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
1C5×#5483C211yesmaximal, characteristic, complemented
2C3×#65244C211yesmaximal, characteristic
3#11749488C212yesmaximal
4#11746347C211yesmaximal, characteristic, complemented
5#11746018C212yesmaximal, complemented
6#10602690—31nomaximal, Hall
7C24×C3×D5C2211yescharacteristic
8C2×C3×C5×C22⋊C4C2211yescharacteristic
9C2×#6719C2212yes—
10C2×C5×#217C2212yes—
11C5×#924—22no—
12C5×#878—24no—
13C2×C3×C22⋊Dic5C2211yescharacteristic
14C2×C3×#685—22no—
15C2×#6665—24no—
16#69497—51nomaximal, Hall
17C5×#543—31no—
18#65244—32no—
19#65244D311yescharacteristic
20#64746—31no—
21#64746—32no—
22C24×C3×C5C2311yescharacteristic
23C23×C3×D5—22no—
24C23×C3×D5—21no—
25C23×C3×D5—21no—
26C23×C3×D5—22no—
27C23×C3×D5—44no—
28C23×C3×D5Q812yescomplemented
29C22×C3×C4×C5D412yes—
30C22×Dic15—22no—
31C22×C5×Dic3D414yes—
32C2×C5×Dic6—22no—
33C22×C3×Dic5—21no—
34C3×C5×C22⋊C4—22no—
35#6719—22no—
36#6719—22no—
37C5×#217—22no—
38C5×#217—22no—
39C5×C4⋊Dic3—22no—
40C5×Dic3⋊C4—24no—
41C3×C22⋊Dic5—22no—
42C3×#685—44no—
43#6665—48no—
44#5483D511yescharacteristic, complemented
45C3×#379—51no—
46#5247—52no—
47#4527—52no—
48#4526—51no—
49C24×D5C2×D311yescharacteristic
50C5×C22⋊Q8—64no—
51C5×C22⋊Q8—62no—
52C2×C5×C22⋊C4—32no—
53C2×C5×C22⋊C4C2×D311yescharacteristic
54C2×C22⋊Dic5—32no—
55C2×C22⋊Dic5C2×D311yescharacteristic
56C2×#685—22no—
57C2×#685—64no—
58#2029—151noSylow
59C23×C3×C5—42no—
60C23×C3×C5C2×D412yes—
61C23×C3×C5C2×D411yescharacteristic
62C23×C3×C5C2×Q811yescharacteristic
63C23×C3×C5#4111yescharacteristic
64C23×C3×C5#4112yes—
65C22×C3×D5—28no—
66C22×C3×D5—24no—
67C22×C3×D5—24no—
68C22×C3×D5—22no—
69C22×C3×D5—44no—
70C22×C3×D5—48no—
71C22×C3×D5—44no—
72C22×C3×D5—42no—
73C22×C3×D5—44no—
74C22×C3×D5—41no—
75C22×C3×D5—42no—
76C22×C3×D5—41no—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—42no—
79C2×Dic15—44no—
80C2×Dic15—42no—
81C2×C5×Dic3—24no—
82C2×C5×Dic3—44no—
83C5×Dic6—82no—
84C2×C3×Dic5—42no—
85C2×C3×Dic5—41no—
86C25×C3—51no—
87C2×C3×C22⋊C4—51no—
88C2×C3×C22⋊C4—102no—
89C2×C3×C22⋊C4C2×D511yescharacteristic
90C2×#217—52no—
91C2×#217—104no—
92C2×#217C2×D512yes—
93#924—22no—
94#878—24no—
95C24×C5C22×D311yescharacteristic
96C23×D5—22no—
97C23×D5—21no—
98C23×D5—21no—
99C23×D5—22no—
100C23×D5—44no—
101C23×D5Dic612yescomplemented
102C2×C5×Q8—62no—
103C22×C4×C5—34no—
104C22×C4×C5#6712yes—
105C22×Dic5—21no—
106C22×Dic5—62no—
107C5×C4⋊C4—64no—
108C5×C4⋊C4—62no—
109C5×C22⋊C4—22no—
110C5×C22⋊C4—62no—
111C5×C22⋊C4—62no—
112C22⋊Dic5—22no—
113C22⋊Dic5—62no—
114C22⋊Dic5—62no—
115#685—44no—
116#685—128no—
117#543—31no—
118#379—51no—
119#379—152no—
120#342—152no—
121#342—151no—
122C22×C3×C5—22no—
123C22×C3×C5—24no—
124C22×C3×C5—41no—
125C22×C3×C5—41no—
126C22×C3×C5—42no—
127C22×C3×C5#12011yescharacteristic
128C22×C3×C5C22⋊Q812yes—
129C22×C3×C5C22⋊Q811yescharacteristic
130C22×C3×C5#12412yes—
131C22×C3×C5#12411yescharacteristic
132C2×C3×D5—28no—
133C2×C3×D5—24no—
134C2×C3×D5—44no—
135C2×C3×D5—48no—
136C2×C3×D5—44no—
137C2×C3×D5—42no—
138C2×C3×D5—42no—
139C2×C3×D5—44no—
140C3×C4×C5—42no—
141Dic15—82no—
142C3×Dic5—81no—
143C5×Dic3—44no—
144C24×C3—52no—
145C24×C3—102no—
146C24×C3—101no—
147C24×C3—102no—
148C24×C3—101no—
149C24×C3—204no—
150C24×C3C22×D511yescharacteristic
151C22×C3×C4—101no—
152C22×C3×C4C22⋊D512yes—
153C22×Dic3—102no—
154C22×Dic3C22⋊D514yes—
155C2×Dic6—22no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—102no—
158C3×C22⋊C4—204no—
159#217—22no—
160#217—22no—
161#217—102no—
162#217—102no—
163#217—208no—
164C4⋊Dic3—22no—
165Dic3⋊C4—24no—
166C23×C5—42no—
167C23×C5C2×Dic611yescharacteristic
168C23×C5#23511yescharacteristic
169C23×C5D3×D412yes—
170C23×C5#23712yes—
171C23×C5C2×#6711yescharacteristic
172C22×D5—24no—
173C22×D5—28no—
174C22×D5—24no—
175C22×D5—22no—
176C22×D5—44no—
177C22×D5—44no—
178C22×D5—48no—
179C22×D5—42no—
180C22×D5—44no—
181C22×D5—42no—
182C22×D5—41no—
183C22×D5—41no—
184C5×Q8—242no—
185C2×C4×C5—22no—
186C2×C4×C5—42no—
187C2×C4×C5—64no—
188C2×C4×C5—124no—
189C2×Dic5—42no—
190C2×Dic5—41no—
191C2×Dic5—124no—
192C2×Dic5—122no—
193C25—51no—
194C22⋊Q8—64no—
195C22⋊Q8—62no—
196C2×C22⋊C4—32no—
197C2×C22⋊C4—51no—
198C2×C22⋊C4—102no—
199C2×C22⋊C4—152no—
200C2×C22⋊C4—304no—
201C2×C22⋊C4D3×D511yescharacteristic
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—
208C3×D5—44no—
209C23×C3—42no—
210C23×C3—108no—
211C23×C3—104no—
212C23×C3—104no—
213C23×C3—102no—
214C23×C3—204no—
215C23×C3—202no—
216C23×C3—204no—
217C23×C3—208no—
218C23×C3—204no—
219C23×C3—201no—
220C23×C3—202no—
221C23×C3—201no—
222C23×C3Q8×D511yescharacteristic
223C23×C3#71312yes—
224C23×C3#71311yescharacteristic
225C23×C3C2×C22⋊D511yescharacteristic
226C23×C3C2×C22⋊D512yes—
227C2×C3×C4—22no—
228C2×C3×C4—42no—
229C2×C3×C4—202no—
230C2×C3×C4—201no—
231C2×Dic3—24no—
232C2×Dic3—44no—
233C2×Dic3—204no—
234C2×Dic3—202no—
235Dic6—82no—
236C22×C5—22no—
237C22×C5—24no—
238C22×C5—41no—
239C22×C5—41no—
240C22×C5—42no—
241C22×C5#87812yes—
242C22×C5#88512yes—
243C22×C5#92411yescharacteristic
244C22×C5#93611yescharacteristic
245C22×C5#93711yescharacteristic
246C2×D5—28no—
247C2×D5—24no—
248C2×D5—44no—
249C2×D5—48no—
250C2×D5—44no—
251C2×D5—42no—
252C2×D5—42no—
253C2×D5—44no—
254C4×C5—42no—
255C4×C5—124no—
256Dic5—81no—
257Dic5—242no—
258C24—52no—
259C24—101no—
260C24—102no—
261C24—102no—
262C24—101no—
263C24—204no—
264C24C2×D3×D511yescharacteristic
265C2×Q8—62no—
266C22×C4—34no—
267C22×C4—101no—
268C22×C4—302no—
269C22×C4#120112yes—
270C4⋊C4—64no—
271C4⋊C4—62no—
272C22⋊C4—22no—
273C22⋊C4—62no—
274C22⋊C4—62no—
275C22⋊C4—102no—
276C22⋊C4—204no—
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—608no—
280C3×C5#202911yescharacteristic, complemented, Hall
281C22×C3—24no—
282C22×C3—22no—
283C22×C3—41no—
284C22×C3—42no—
285C22×C3—41no—
286C22×C3—108no—
287C22×C3—104no—
288C22×C3—208no—
289C22×C3—204no—
290C22×C3—204no—
291C22×C3—202no—
292C22×C3—202no—
293C22×C3—204no—
294C22×C3#409212yes—
295C22×C3#409211yescharacteristic
296C22×C3#409312yes—
297C22×C3#409311yescharacteristic
298C22×C3#409911yescharacteristic
299C3×C4—42no—
300C3×C4—401no—
301Dic3—44no—
302Dic3—402no—
303C2×C5—21no—
304C2×C5—22no—
305C2×C5—22no—
306C2×C5—21no—
307C2×C5#494711yescharacteristic
308C2×C5#503212yes—
309D5—44no—
310C23—42no—
311C23—104no—
312C23—108no—
313C23—104no—
314C23—102no—
315C23—202no—
316C23—204no—
317C23—204no—
318C23—208no—
319C23—204no—
320C23—202no—
321C23—201no—
322C23—201no—
323C23D5×Dic611yescharacteristic
324C23#676612yes—
325C23#677311yescharacteristic
326C23C2×#120111yescharacteristic
327C23D3×C22⋊D512yes—
328Q8—242no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—64no—
332C2×C4—124no—
333C2×C4—202no—
334C2×C4—201no—
335C2×C4—604no—
336C2×C4—602no—
337C2×C3—22no—
338C2×C3—21no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3—204no—
342C2×C3#6552011yescharacteristic
343C2×C3#6553312yes—
344C5#6949711yescharacteristic, complemented, Sylow
345C22—22no—
346C22—24no—
347C22—41no—
348C22—42no—
349C22—41no—
350C22—108no—
351C22—104no—
352C22—204no—
353C22—208no—
354C22—204no—
355C22—202no—
356C22—204no—
357C22—202no—
358C22#9135911yescharacteristic
359C22#9136811yescharacteristic
360C22#9142112yes—
361C22#9145512yes—
362C22#9156811yescharacteristic
363C4—42no—
364C4—124no—
365C4—401no—
366C4—1202no—
367C3#1060269011yescharacteristic, complemented, Sylow
368C2—21no—
369C2—22no—
370C2—22no—
371C2—21no—
372C2—204no—
373C2#1174877311yescharacteristic
374C2#1174917712yes—
subgroupG/H
centerC22#91568
commutator, cosocleC24×C3×C5C23
FrattiniC24C2×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
prime radicalC24×C3×D5C22
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. C5×#5483C2semidirect
4. #11746347C2semidirect
5. #11746018C2semidirect
28. C23×C3×D5Q8semidirect
44. #5483D5semidirect
101. C23×D5Dic6semidirect
280. C3×C5#2029semidirect
344. C5#69497semidirect
367. C3#10602690semidirect

Maximal subgroups

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

subgroupindex
C5×#54832
C3×#652442
#117494882
#117463472
#117460182
#106026903
#694975