Finite Group Databasebeta

← #14277356

Subgroups — #14277356

Order 1920.

792 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 792 conjugacy classes of subgroups — too many to draw. Only its 89 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#11752459C212yesmaximal
2C3×#65244C211yesmaximal, characteristic
3#10598705—31nomaximal, Hall
4C24×C3×D5C2211yescharacteristic
5C2×#6763—22no—
6C2×#6763—22no—
7C2×#6763C414yescomplemented
8C2×C3×C5×C22⋊C4C411yescharacteristic, complemented
9C2×C3×C22⋊Dic5C411yescharacteristic, complemented
10C2×C3×#685—22no—
11C3⋊#1304—51nomaximal, Hall
12#65800—32no—
13#65244D311yescharacteristic
14C24×C3×C5C2×C411yescharacteristic
15C23×C3×D5—44no—
16C23×C3×D5—41no—
17C23×C3×D5—41no—
18C23×C3×D5C2×C412yes—
19C23×C3×D5D411yescharacteristic
20C23×C3×D5D412yes—
21C23×C3×D5Q811yescharacteristic
22C22×ΓL(1,𝔽16)—24no—
23C22×C3×C4×C5—21no—
24C22×C3×Dic5—21no—
25#6763—42no—
26#6763—42no—
27#6763—44no—
28#6763—44no—
29C3×C5×C22⋊C4—41no—
30C3×C22⋊Dic5—41no—
31C3×#685—44no—
32C3×#379—51no—
33#5247—52no—
34C24×D5C2×D311yescharacteristic
35C2×C22⋊AGL(1,𝔽5)—34no—
36C2×C22⋊AGL(1,𝔽5)—62no—
37C2×C22⋊AGL(1,𝔽5)—62no—
38C2×C5×C22⋊C4Dic311yescharacteristic, complemented
39C2×C22⋊Dic5Dic311yescharacteristic, complemented
40C2×#685—22no—
41#1304—151noSylow
42C23×C3×C5—21no—
43C23×C3×C5—21no—
44C23×C3×C5—42no—
45C23×C3×C5C4211yescharacteristic
46C23×C3×C5C22⋊C411yescharacteristic
47C23×C3×C5C4⋊C411yescharacteristic
48C22×C3×D5—22no—
49C22×C3×D5—22no—
50C22×C3×D5—24no—
51C22×C3×D5—24no—
52C22×C3×D5—24no—
53C22×C3×D5—42no—
54C22×C3×D5—42no—
55C22×C3×D5—41no—
56C22×C3×D5—42no—
57C22×C3×D5—42no—
58C22×C3×D5—41no—
59C22×C3×D5—48no—
60C22×C3×D5—48no—
61C22×C3×D5C22⋊C412yes—
62C22×C3×D5C4⋊C412yes—
63C2×ΓL(1,𝔽16)—44no—
64C2×ΓL(1,𝔽16)—44no—
65C2×ΓL(1,𝔽16)—44no—
66C2×C3×C4×C5—42no—
67C2×C3×C4×C5—41no—
68C2×C3×Dic5—42no—
69C2×C3×Dic5—41no—
70C25×C3—51no—
71C2×C3×C22⋊C4—51no—
72C2×C3×C22⋊C4—102no—
73C2×C3×C22⋊C4AGL(1,𝔽5)11yescharacteristic, complemented
74C2×#217—54no—
75C2×#217—102no—
76C2×#217—102no—
77C24×C5C2×Dic311yescharacteristic
78C23×D5—44no—
79C23×D5—41no—
80C23×D5—41no—
81C23×D5Dic611yescharacteristic
82C23×D5C4×D312yes—
83C23×D5D1211yescharacteristic
84C23×D5#6712yes—
85C22×AGL(1,𝔽5)—64no—
86C22×C4×C5—21no—
87C22×Dic5—21no—
88C22⋊AGL(1,𝔽5)—122no—
89C22⋊AGL(1,𝔽5)—122no—
90C22⋊AGL(1,𝔽5)—124no—
91C22⋊AGL(1,𝔽5)—124no—
92C5×C22⋊C4—41no—
93C22⋊Dic5—41no—
94#685—44no—
95#379—51no—
96#379—152no—
97C22×C3×C5—22no—
98C22×C3×C5—22no—
99C22×C3×C5—22no—
100C22×C3×C5—21no—
101C22×C3×C5—21no—
102C22×C3×C5—42no—
103C22×C3×C5—42no—
104C22×C3×C5#9511yescharacteristic
105C22×C3×C5#9911yescharacteristic
106C22×C3×C5#9911yescharacteristic
107C2×C3×D5—22no—
108C2×C3×D5—22no—
109C2×C3×D5—22no—
110C2×C3×D5—22no—
111C2×C3×D5—22no—
112C2×C3×D5—44no—
113C2×C3×D5—44no—
114C2×C3×D5—44no—
115C2×C3×D5—48no—
116C2×C3×D5—44no—
117C2×C3×D5#9914yes—
118ΓL(1,𝔽16)—84no—
119C3×C4×C5—81no—
120C3×Dic5—81no—
121C24×C3—51no—
122C24×C3—52no—
123C24×C3—52no—
124C24×C3—51no—
125C24×C3—201no—
126C24×C3—201no—
127C24×C3—204no—
128C24×C3C2×AGL(1,𝔽5)11yescharacteristic
129C22×C3×C4—21no—
130C22×C3×C4—101no—
131C22×Dic3—104no—
132C3×C22⋊C4—41no—
133C3×C22⋊C4—204no—
134C3×C22⋊C4—201no—
135#217—204no—
136#217—202no—
137#217—202no—
138#217—204no—
139C23×C5—21no—
140C23×C5—21no—
141C23×C5—42no—
142C23×C5C4×Dic311yescharacteristic
143C23×C5C4⋊Dic311yescharacteristic
144C23×C5#21711yescharacteristic
145C22×D5—22no—
146C22×D5—22no—
147C22×D5—24no—
148C22×D5—24no—
149C22×D5—24no—
150C22×D5—41no—
151C22×D5—42no—
152C22×D5—42no—
153C22×D5—42no—
154C22×D5—41no—
155C22×D5—42no—
156C22×D5—48no—
157C22×D5—48no—
158C22×D5Dic3⋊C412yes—
159C22×D5(C2×D3)⋊C412yes—
160C2×AGL(1,𝔽5)—124no—
161C2×AGL(1,𝔽5)—124no—
162C2×AGL(1,𝔽5)—124no—
163C2×C4×C5—42no—
164C2×C4×C5—41no—
165C2×Dic5—42no—
166C2×Dic5—41no—
167C25—51no—
168C2×C22⋊C4—51no—
169C2×C22⋊C4—102no—
170C2×C22⋊C4—154no—
171C2×C22⋊C4—302no—
172C2×C22⋊C4—302no—
173C2×C22⋊C4ΓL(1,𝔽16)11yescharacteristic, complemented
174C2×C3×C5—21no—
175C2×C3×C5—21no—
176C2×C3×C5—41no—
177C2×C3×C5—41no—
178C2×C3×C5#34212yes—
179C2×C3×C5#34211yescharacteristic
180C3×D5—24no—
181C3×D5—42no—
182C23×C3—21no—
183C23×C3—21no—
184C23×C3—42no—
185C23×C3—52no—
186C23×C3—52no—
187C23×C3—104no—
188C23×C3—104no—
189C23×C3—104no—
190C23×C3—102no—
191C23×C3—102no—
192C23×C3—202no—
193C23×C3—202no—
194C23×C3—202no—
195C23×C3—202no—
196C23×C3—201no—
197C23×C3—201no—
198C23×C3—208no—
199C23×C3—208no—
200C23×C3C4×AGL(1,𝔽5)11yescharacteristic
201C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
202C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
203C2×C3×C4—42no—
204C2×C3×C4—41no—
205C2×C3×C4—202no—
206C2×C3×C4—201no—
207C2×Dic3—204no—
208C2×Dic3—204no—
209C2×Dic3—204no—
210C22×C5—22no—
211C22×C5—21no—
212C22×C5—21no—
213C22×C5—22no—
214C22×C5—22no—
215C22×C5—42no—
216C22×C5—42no—
217C22×C5C3⋊#9511yescharacteristic
218C22×C5#83411yescharacteristic
219C22×C5#83411yescharacteristic
220C2×D5—22no—
221C2×D5—22no—
222C2×D5—22no—
223C2×D5—22no—
224C2×D5—22no—
225C2×D5—44no—
226C2×D5—44no—
227C2×D5—44no—
228C2×D5—48no—
229C2×D5—44no—
230C2×D5#80614yes—
231AGL(1,𝔽5)—244no—
232C4×C5—81no—
233Dic5—81no—
234C24—51no—
235C24—52no—
236C24—52no—
237C24—51no—
238C24—201no—
239C24—201no—
240C24—204no—
241C24C2×ΓL(1,𝔽16)11yescharacteristic
242C22×C4—21no—
243C22×C4—101no—
244C22×C4—304no—
245C22⋊C4—41no—
246C22⋊C4—204no—
247C22⋊C4—201no—
248C22⋊C4—604no—
249C22⋊C4—602no—
250C22⋊C4—602no—
251C22⋊C4—604no—
252C3×C5#130411yescharacteristic, complemented, Hall
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—22no—
256C22×C3—21no—
257C22×C3—21no—
258C22×C3—42no—
259C22×C3—42no—
260C22×C3—54no—
261C22×C3—102no—
262C22×C3—102no—
263C22×C3—102no—
264C22×C3—102no—
265C22×C3—102no—
266C22×C3—204no—
267C22×C3—204no—
268C22×C3—204no—
269C22×C3—208no—
270C22×C3—204no—
271C22×C3#399911yescharacteristic
272C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
273C22×C3#401111yescharacteristic
274C3×C4—81no—
275C3×C4—401no—
276Dic3—404no—
277C2×C5—21no—
278C2×C5—21no—
279C2×C5—41no—
280C2×C5—41no—
281C2×C5#452611yescharacteristic
282C2×C5#452712yes—
283D5—24no—
284D5—42no—
285C23—21no—
286C23—21no—
287C23—42no—
288C23—52no—
289C23—52no—
290C23—104no—
291C23—104no—
292C23—104no—
293C23—102no—
294C23—102no—
295C23—202no—
296C23—202no—
297C23—202no—
298C23—202no—
299C23—201no—
300C23—201no—
301C23—208no—
302C23—208no—
303C23C4×ΓL(1,𝔽16)11yescharacteristic
304C23C4⋊ΓL(1,𝔽16)11yescharacteristic
305C23#676311yescharacteristic
306C2×C4—42no—
307C2×C4—41no—
308C2×C4—202no—
309C2×C4—201no—
310C2×C4—604no—
311C2×C4—604no—
312C2×C4—604no—
313C2×C3—21no—
314C2×C3—21no—
315C2×C3—41no—
316C2×C3—41no—
317C2×C3—104no—
318C2×C3—202no—
319C2×C3#6486612yes—
320C2×C3#6491711yescharacteristic
321C5C3⋊#130411yescharacteristic, complemented, Sylow
322C22—22no—
323C22—22no—
324C22—22no—
325C22—21no—
326C22—21no—
327C22—42no—
328C22—42no—
329C22—54no—
330C22—102no—
331C22—102no—
332C22—102no—
333C22—102no—
334C22—102no—
335C22—204no—
336C22—204no—
337C22—204no—
338C22—208no—
339C22—204no—
340C22#9122811yescharacteristic
341C22#9123511yescharacteristic
342C22#9124011yescharacteristic
343C4—81no—
344C4—401no—
345C4—1204no—
346C3#1059870511yescharacteristic, complemented, Sylow
347C2—21no—
348C2—21no—
349C2—41no—
350C2—41no—
351C2—104no—
352C2—202no—
353C2#1174673712yes—
354C2#1174678811yescharacteristic
subgroupG/H
centerC22#91235
commutatorC23×C3×C5C42
FrattiniC24C2×ΓL(1,𝔽16)
FittingC2×C3×C5×C22⋊C4C4
socleC22×C3×C5#95
prime radical, cosocleC24×C3×D5C22
hypercenterC2×C22⋊C4ΓL(1,𝔽16)
hypocenterC3×C5#1304
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
7. C2×#6763C4semidirect
8. C2×C3×C5×C22⋊C4C4semidirect
9. C2×C3×C22⋊Dic5C4semidirect
38. C2×C5×C22⋊C4Dic3semidirect
39. C2×C22⋊Dic5Dic3semidirect
73. C2×C3×C22⋊C4AGL(1,𝔽5)semidirect
173. C2×C22⋊C4ΓL(1,𝔽16)semidirect
252. C3×C5#1304semidirect
321. C5C3⋊#1304semidirect
346. C3#10598705semidirect

Maximal subgroups

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

subgroupindex
#117524592
C3×#652442
#105987053
C3⋊#13045