Finite Group Databasebeta

← #14308982

Subgroups — #14308982

Order 1920.

932 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 932 conjugacy classes of subgroups — too many to draw. Only its 123 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
2C3×C5×#379C211yesmaximal, characteristic
3#11751348C212yesmaximal
4#11746348C212yesmaximal, complemented
5#11746347C211yesmaximal, characteristic, complemented
6#10600290—31nomaximal, Hall
7C25×C3×C5C2211yescharacteristic
8C2×C3×C5×C22⋊C4—22no—
9C2×C3×C5×C22⋊C4C2211yescharacteristic
10C2×C3×C5×C22⋊C4C2211yescharacteristic
11C2×#6719—24no—
12C2×#6719C2212yes—
13C2×#6719C2212yes—
14#91813—22no—
15#91767—24no—
16#69497—51nomaximal, Hall
17#65817—31no—
18C5×#379D311yescharacteristic
19#65536—32no—
20#64747—32no—
21#64746—31no—
22C24×C3×C5—22no—
23C24×C3×C5—21no—
24C24×C3×C5—21no—
25C24×C3×C5—22no—
26C24×C3×C5—44no—
27C24×C3×C5Q812yescomplemented
28C24×C3×C5C2311yescharacteristic
29C22×C3×C4×C5—21no—
30C22×C3×C4×C5D412yes—
31C22×Dic15—22no—
32C22×Dic15D414yes—
33C2×Dic30—22no—
34C3×C5×C22⋊C4—22no—
35C3×C5×C22⋊C4—22no—
36C3×C5×C22⋊C4—44no—
37#6719—22no—
38#6719—22no—
39#6719—22no—
40#6719—22no—
41#6719—48no—
42C4⋊Dic15—22no—
43#6712—24no—
44#5483—51no—
45C3×#379D511yescharacteristic
46#5247—52no—
47#4527—52no—
48#4526—51no—
49C25×C5C2×D311yescharacteristic
50C2×C5×C22⋊C4—22no—
51C2×C5×C22⋊C4C2×D311yescharacteristic
52C2×C5×C22⋊C4C2×D311yescharacteristic
53C2×C22⋊Dic5—32no—
54C2×C22⋊Dic5—32no—
55C2×C22⋊Dic5—64no—
56#4070—62no—
57#4024—64no—
58#2029—151noSylow
59C23×C3×C5—28no—
60C23×C3×C5—24no—
61C23×C3×C5—24no—
62C23×C3×C5—22no—
63C23×C3×C5—44no—
64C23×C3×C5—42no—
65C23×C3×C5—44no—
66C23×C3×C5—42no—
67C23×C3×C5—48no—
68C23×C3×C5—44no—
69C23×C3×C5—41no—
70C23×C3×C5—42no—
71C23×C3×C5—41no—
72C23×C3×C5C2×D412yes—
73C23×C3×C5C2×D411yescharacteristic
74C23×C3×C5C2×Q811yescharacteristic
75C23×C3×C5#4111yescharacteristic
76C23×C3×C5#4112yes—
77C2×C3×C4×C5—22no—
78C2×C3×C4×C5—42no—
79C2×C3×C4×C5—42no—
80C2×C3×C4×C5—41no—
81C2×Dic15—24no—
82C2×Dic15—44no—
83C2×Dic15—44no—
84C2×Dic15—42no—
85Dic30—82no—
86C25×C3C2×D511yescharacteristic
87C2×C3×C22⋊C4—22no—
88C2×C3×C22⋊C4C2×D511yescharacteristic
89C2×C3×C22⋊C4C2×D511yescharacteristic
90C2×#217—52no—
91C2×#217—52no—
92C2×#217—104no—
93#924—102no—
94#878—104no—
95C24×C5—22no—
96C24×C5—21no—
97C24×C5—21no—
98C24×C5—22no—
99C24×C5—44no—
100C24×C5Dic612yescomplemented
101C24×C5C22×D311yescharacteristic
102C22×C4×C5—21no—
103C22×C4×C5#6712yes—
104C22×Dic5—34no—
105C22×Dic5—62no—
106C2×Dic10—62no—
107C5×C22⋊C4—22no—
108C5×C22⋊C4—22no—
109C5×C22⋊C4—44no—
110C22⋊Dic5—62no—
111C22⋊Dic5—62no—
112C22⋊Dic5—62no—
113C22⋊Dic5—62no—
114C22⋊Dic5—128no—
115C4⋊Dic5—62no—
116#683—64no—
117#543—151no—
118#379—152no—
119#379D1511yescharacteristic
120#342—151no—
121#342—152no—
122C22×C3×C5—24no—
123C22×C3×C5—22no—
124C22×C3×C5—28no—
125C22×C3×C5—24no—
126C22×C3×C5—41no—
127C22×C3×C5—41no—
128C22×C3×C5—42no—
129C22×C3×C5—48no—
130C22×C3×C5—44no—
131C22×C3×C5—44no—
132C22×C3×C5—42no—
133C22×C3×C5—42no—
134C22×C3×C5—44no—
135C22×C3×C5#12011yescharacteristic
136C22×C3×C5C22⋊Q812yes—
137C22×C3×C5C22⋊Q811yescharacteristic
138C22×C3×C5#12412yes—
139C22×C3×C5#12411yescharacteristic
140C3×C4×C5—42no—
141C3×C4×C5—81no—
142Dic15—44no—
143Dic15—82no—
144C24×C3—22no—
145C24×C3—21no—
146C24×C3—21no—
147C24×C3—22no—
148C24×C3—44no—
149C24×C3Dic1012yescomplemented
150C24×C3C22×D511yescharacteristic
151C22×C3×C4—21no—
152C22×C3×C4C22⋊D512yes—
153C22×Dic3—54no—
154C22×Dic3—102no—
155C2×Dic6—102no—
156C3×C22⋊C4—22no—
157C3×C22⋊C4—22no—
158C3×C22⋊C4—44no—
159#217—102no—
160#217—102no—
161#217—102no—
162#217—102no—
163#217—208no—
164C4⋊Dic3—102no—
165Dic3⋊C4—104no—
166C23×C5—28no—
167C23×C5—24no—
168C23×C5—24no—
169C23×C5—22no—
170C23×C5—44no—
171C23×C5—42no—
172C23×C5—44no—
173C23×C5—42no—
174C23×C5—44no—
175C23×C5—48no—
176C23×C5—42no—
177C23×C5—41no—
178C23×C5—41no—
179C23×C5C2×Dic611yescharacteristic
180C23×C5#23511yescharacteristic
181C23×C5D3×D412yes—
182C23×C5#23712yes—
183C23×C5C2×#6711yescharacteristic
184C2×C4×C5—22no—
185C2×C4×C5—42no—
186C2×C4×C5—42no—
187C2×C4×C5—41no—
188C2×Dic5—64no—
189C2×Dic5—124no—
190C2×Dic5—124no—
191C2×Dic5—122no—
192Dic10—242no—
193C25C2×D1511yescharacteristic
194C22⋊Q8—304no—
195C22⋊Q8—302no—
196C2×C22⋊C4—22no—
197C2×C22⋊C4—152no—
198C2×C22⋊C4—152no—
199C2×C22⋊C4—304no—
200C2×C22⋊C4C2×D1511yescharacteristic
201C2×C22⋊C4C2×D1511yescharacteristic
202C2×C3×C5—22no—
203C2×C3×C5—21no—
204C2×C3×C5—22no—
205C2×C3×C5—21no—
206C2×C3×C5—44no—
207C2×C3×C5#39311yescharacteristic
208C2×C3×C5B(4,𝔽2)12yes—
209C23×C3—28no—
210C23×C3—24no—
211C23×C3—24no—
212C23×C3—22no—
213C23×C3—44no—
214C23×C3—42no—
215C23×C3—44no—
216C23×C3—42no—
217C23×C3—44no—
218C23×C3—48no—
219C23×C3—42no—
220C23×C3—41no—
221C23×C3—41no—
222C23×C3C2×Dic1011yescharacteristic
223C23×C3#70911yescharacteristic
224C23×C3D4×D512yes—
225C23×C3#71112yes—
226C23×C3C2×C22⋊D511yescharacteristic
227C2×C3×C4—22no—
228C2×C3×C4—42no—
229C2×C3×C4—42no—
230C2×C3×C4—41no—
231C2×Dic3—104no—
232C2×Dic3—204no—
233C2×Dic3—204no—
234C2×Dic3—202no—
235Dic6—402no—
236C22×C5—24no—
237C22×C5—22no—
238C22×C5—28no—
239C22×C5—24no—
240C22×C5—41no—
241C22×C5—41no—
242C22×C5—42no—
243C22×C5—48no—
244C22×C5—44no—
245C22×C5—44no—
246C22×C5—42no—
247C22×C5—42no—
248C22×C5—44no—
249C22×C5#87812yes—
250C22×C5#88512yes—
251C22×C5#92411yescharacteristic
252C22×C5#93611yescharacteristic
253C22×C5#93711yescharacteristic
254C4×C5—42no—
255C4×C5—81no—
256Dic5—124no—
257Dic5—242no—
258C24—22no—
259C24—21no—
260C24—21no—
261C24—22no—
262C24—44no—
263C24Dic3012yescomplemented
264C24C22×D1511yescharacteristic
265C2×Q8—302no—
266C22×C4—21no—
267C22×C4—154no—
268C22×C4—302no—
269C22×C4#122012yes—
270C4⋊C4—304no—
271C4⋊C4—302no—
272C22⋊C4—22no—
273C22⋊C4—22no—
274C22⋊C4—44no—
275C22⋊C4—302no—
276C22⋊C4—302no—
277C22⋊C4—302no—
278C22⋊C4—302no—
279C22⋊C4—608no—
280C3×C5#202911yescharacteristic, complemented, Hall
281C22×C3—24no—
282C22×C3—22no—
283C22×C3—28no—
284C22×C3—24no—
285C22×C3—41no—
286C22×C3—41no—
287C22×C3—42no—
288C22×C3—48no—
289C22×C3—44no—
290C22×C3—44no—
291C22×C3—42no—
292C22×C3—44no—
293C22×C3—42no—
294C22×C3#402412yes—
295C22×C3#403112yes—
296C22×C3#407011yescharacteristic
297C22×C3#408211yescharacteristic
298C22×C3#408311yescharacteristic
299C3×C4—42no—
300C3×C4—81no—
301Dic3—204no—
302Dic3—402no—
303C2×C5—22no—
304C2×C5—21no—
305C2×C5—22no—
306C2×C5—21no—
307C2×C5—44no—
308C2×C5#494711yescharacteristic
309C2×C5#503212yes—
310C23—24no—
311C23—28no—
312C23—24no—
313C23—22no—
314C23—44no—
315C23—42no—
316C23—42no—
317C23—44no—
318C23—44no—
319C23—48no—
320C23—42no—
321C23—41no—
322C23—41no—
323C23C2×Dic3011yescharacteristic
324C23#681711yescharacteristic
325C23D4×D1512yes—
326C23#681912yes—
327C23C2×#122011yescharacteristic
328Q8—1202no—
329C2×C4—22no—
330C2×C4—42no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—304no—
334C2×C4—604no—
335C2×C4—604no—
336C2×C4—602no—
337C2×C3—22no—
338C2×C3—21no—
339C2×C3—22no—
340C2×C3—21no—
341C2×C3—44no—
342C2×C3#6523611yescharacteristic
343C2×C3#6532112yes—
344C5#6949711yescharacteristic, complemented, Sylow
345C22—22no—
346C22—24no—
347C22—28no—
348C22—24no—
349C22—41no—
350C22—41no—
351C22—42no—
352C22—44no—
353C22—48no—
354C22—44no—
355C22—42no—
356C22—42no—
357C22—44no—
358C22#9176712yes—
359C22#9177412yes—
360C22#9181311yescharacteristic
361C22#9182511yescharacteristic
362C22#9182611yescharacteristic
363C4—42no—
364C4—81no—
365C4—604no—
366C4—1202no—
367C3#1060029011yescharacteristic, complemented, Sylow
368C2—21no—
369C2—22no—
370C2—22no—
371C2—21no—
372C2—44no—
373C2#1175104811yescharacteristic
374C2#1175113312yes—
subgroupG/H
centerC22#91826
commutator, cosocleC24×C3×C5C23
FrattiniC24C22×D15
FittingC3×C5×#379C2
socleC22×C3×C5#120
prime radicalC25×C3×C5C22
hypercenter#379D15
hypocenterC3×C5#2029
LCSG ▷ C24×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #11756242C2semidirect
4. #11746348C2semidirect
5. #11746347C2semidirect
27. C24×C3×C5Q8semidirect
100. C24×C5Dic6semidirect
149. C24×C3Dic10semidirect
263. C24Dic30semidirect
280. C3×C5#2029semidirect
344. C5#69497semidirect
367. C3#10600290semidirect

Maximal subgroups

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

subgroupindex
#117562422
C3×C5×#3792
#117513482
#117463482
#117463472
#106002903
#694975