Finite Group Databasebeta

← #14277198

Subgroups — #14277198

Order 1920.

492 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 88 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
1C4×#6763C211yesmaximal, characteristic
2C3×C4×C22⋊AGL(1,𝔽5)C211yesmaximal, characteristic
3#11748341C211yesmaximal, characteristic
4#10598785—31nomaximal, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×#6763—21no—
7C2×C4×ΓL(1,𝔽16)—21no—
8C2×C3×C22⋊AGL(1,𝔽5)—21no—
9C2×C3×C4×AGL(1,𝔽5)—21no—
10C2×#6710C411yescharacteristic, complemented
11C2×C5×#208C411yescharacteristic, complemented
12#91235C412yescomplemented
13C3×(C2×AGL(1,𝔽5))⋊C4C412yescomplemented
14#90955—21no—
15#90955—21no—
16#67618—51nomaximal, Hall
17C4×C22⋊AGL(1,𝔽5)—31no—
18C4×C22⋊AGL(1,𝔽5)D311yescharacteristic
19#65415—31no—
20C23×C3×D5D411yescharacteristic
21C22×ΓL(1,𝔽16)—22no—
22C22×C3×AGL(1,𝔽5)—22no—
23C22×C3×C4×C5C2×C411yescharacteristic
24C22×C3×Dic5Q811yescharacteristic
25C2×C3×C4×D5—41no—
26C2×C3×C4×D5—41no—
27C2×C3×C4×D5C2×C411yescharacteristic
28C2×C3×C4×D5C2×C411yescharacteristic
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31#6763—24no—
32C4×ΓL(1,𝔽16)—41no—
33C4×ΓL(1,𝔽16)—41no—
34C3×C22⋊AGL(1,𝔽5)—24no—
35C3×C4×AGL(1,𝔽5)—41no—
36C3×C4×AGL(1,𝔽5)—41no—
37#6710—41no—
38C2×C3⋊#168—21no—
39C5×#208—41no—
40C2×C5×C3⋊C8—21no—
41C3×C4×C22⋊C4—51no—
42C4×#217—51no—
43#5207—51no—
44C22×C4×D5C2×D311yescharacteristic
45C2×C22⋊AGL(1,𝔽5)—21no—
46C2×C22⋊AGL(1,𝔽5)—61no—
47C2×C4×AGL(1,𝔽5)—21no—
48C2×C4×AGL(1,𝔽5)—61no—
49C2×C5×M16—31no—
50C2×#681—31no—
51(C2×AGL(1,𝔽5))⋊C4—32no—
52(C2×AGL(1,𝔽5))⋊C4Dic312yescomplemented
53#3952—61no—
54#3952—61no—
55#1297—151noSylow
56C23×C3×C5C4⋊C411yescharacteristic
57C22×C3×D5—22no—
58C22×C3×D5—22no—
59C22×C3×D5—41no—
60C22×C3×D5C22⋊C411yescharacteristic
61C22×C3×D5C22⋊C411yescharacteristic
62C2×ΓL(1,𝔽16)—24no—
63C2×ΓL(1,𝔽16)—42no—
64C2×ΓL(1,𝔽16)—42no—
65C2×C3×AGL(1,𝔽5)—24no—
66C2×C3×AGL(1,𝔽5)—42no—
67C2×C3×AGL(1,𝔽5)—42no—
68C2×C3×C4×C5—21no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5C4211yescharacteristic
71C2×C3×C4×C5C22⋊C411yescharacteristic
72C2×C3×Dic5—41no—
73C2×C3×Dic5C4⋊C411yescharacteristic
74C2×C3×Dic5C4⋊C411yescharacteristic
75C3×C4×D5—21no—
76C3×C4×D5—21no—
77C3×C4×D5—21no—
78C3×C4×D5—21no—
79C3×C4×D5—41no—
80C3×C4×D5—41no—
81C3⋊#168—41no—
82C5×C3⋊C8—41no—
83C23×C3×C4—51no—
84C2×C3×C22⋊C4—101no—
85C2×C3×C42—101no—
86C2×#217—101no—
87C2×C4×Dic3—101no—
88C2×#208—51no—
89C2×#208AGL(1,𝔽5)11yescharacteristic, complemented
90C3×#95—52no—
91C3⋊#95—52no—
92#830—101no—
93#830—101no—
94C23×D5#6711yescharacteristic
95C22×AGL(1,𝔽5)—22no—
96C22×AGL(1,𝔽5)—62no—
97C22×C4×C5C4×D311yescharacteristic
98C22×Dic5Dic611yescharacteristic
99C2×C4×D5—41no—
100C2×C4×D5—41no—
101C2×C4×D5C4×D311yescharacteristic
102C2×C4×D5D1211yescharacteristic
103C2×C4×D5C2×Dic311yescharacteristic
104C2×C4×D5#6711yescharacteristic
105C22⋊AGL(1,𝔽5)—24no—
106C22⋊AGL(1,𝔽5)—64no—
107C4×AGL(1,𝔽5)—41no—
108C4×AGL(1,𝔽5)—41no—
109C4×AGL(1,𝔽5)—121no—
110C4×AGL(1,𝔽5)—121no—
111C5×M16—121no—
112C2×C5×C8—61no—
113#681—121no—
114C2×#168—61no—
115#407—151no—
116C4×C22⋊C4—51no—
117C4×C22⋊C4—151no—
118C22×C3×C5—21no—
119C22×C3×C5—21no—
120C22×C3×C5—21no—
121C22×C3×C5#9511yescharacteristic
122C2×C3×D5—21no—
123C2×C3×D5—21no—
124C2×C3×D5—21no—
125C2×C3×D5—21no—
126C2×C3×D5—44no—
127C2×C3×D5#10412yes—
128C2×C3×D5#10412yes—
129ΓL(1,𝔽16)—44no—
130C3×AGL(1,𝔽5)—44no—
131C3×C4×C5—21no—
132C3×C4×C5#9911yescharacteristic
133C3×C4×C5#9911yescharacteristic
134C3×Dic5—21no—
135C3×Dic5—21no—
136C24×C3—51no—
137C22×C3×C4—51no—
138C22×C3×C4—51no—
139C22×C3×C4—51no—
140C22×C3×C4—51no—
141C22×C3×C4—51no—
142C22×C3×C4—102no—
143C22×C3×C4—201no—
144C22×C3×C4—201no—
145C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
146C22×Dic3—102no—
147C3×C22⋊C4—104no—
148C3×C42—201no—
149C3×C42—201no—
150#217—104no—
151C4×Dic3—201no—
152C4×Dic3—201no—
153#208—41no—
154#208—201no—
155C2×C3⋊C8—21no—
156C2×C3⋊C8—101no—
157C23×C5Dic3⋊C411yescharacteristic
158C22×D5—22no—
159C22×D5—22no—
160C22×D5—41no—
161C22×D5(C2×D3)⋊C411yescharacteristic
162C22×D5#21711yescharacteristic
163C2×AGL(1,𝔽5)—24no—
164C2×AGL(1,𝔽5)—42no—
165C2×AGL(1,𝔽5)—42no—
166C2×AGL(1,𝔽5)—64no—
167C2×AGL(1,𝔽5)—122no—
168C2×AGL(1,𝔽5)—122no—
169C2×C4×C5—21no—
170C2×C4×C5—21no—
171C2×C4×C5C4×Dic311yescharacteristic
172C2×C4×C5(C2×D3)⋊C411yescharacteristic
173C2×Dic5—41no—
174C2×Dic5Dic3⋊C411yescharacteristic
175C2×Dic5C4⋊Dic311yescharacteristic
176C4×D5—21no—
177C4×D5—21no—
178C4×D5—21no—
179C4×D5—21no—
180C4×D5—41no—
181C4×D5—41no—
182C5×C8—121no—
183#168—121no—
184C23×C4—51no—
185C2×M16—31no—
186C2×M16—151no—
187C2×C22⋊C4—101no—
188C2×C22⋊C4—301no—
189C2×C42—101no—
190C2×C42—301no—
191C22⋊C8—301no—
192C22⋊C8—301no—
193#95—52no—
194#95—152no—
195C2×C3×C5—41no—
196C2×C3×C5#33911yescharacteristic
197C2×C3×C5#33911yescharacteristic
198C2×C3×C5#34211yescharacteristic
199C3×D5—22no—
200C3×D5—22no—
201C23×C3—51no—
202C23×C3—51no—
203C23×C3—102no—
204C23×C3—102no—
205C23×C3—201no—
206C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4—51no—
210C2×C3×C4—51no—
211C2×C3×C4—101no—
212C2×C3×C4—101no—
213C2×C3×C4—101no—
214C2×C3×C4—101no—
215C2×C3×C4—104no—
216C2×C3×C4—201no—
217C2×C3×C4—201no—
218C2×C3×C4—201no—
219C2×C3×C4—202no—
220C2×C3×C4—202no—
221C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
222C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
223C2×Dic3—104no—
224C2×Dic3—202no—
225C2×Dic3—202no—
226C3⋊C8—41no—
227C3⋊C8—201no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5C3⋊#9511yescharacteristic
232C2×D5—21no—
233C2×D5—21no—
234C2×D5—21no—
235C2×D5—21no—
236C2×D5—44no—
237C2×D5#80512yes—
238C2×D5#83712yes—
239AGL(1,𝔽5)—44no—
240AGL(1,𝔽5)—124no—
241C4×C5—21no—
242C4×C5#80611yescharacteristic
243C4×C5#80611yescharacteristic
244Dic5—21no—
245Dic5—21no—
246C24—51no—
247C22×C4—51no—
248C22×C4—51no—
249C22×C4—51no—
250C22×C4—51no—
251C22×C4—51no—
252C22×C4—102no—
253C22×C4—201no—
254C22×C4—201no—
255C22×C4—302no—
256C22×C4D3×AGL(1,𝔽5)11yescharacteristic
257M16—121no—
258M16—601no—
259C2×C8—61no—
260C2×C8—301no—
261C22⋊C4—104no—
262C22⋊C4—304no—
263C42—201no—
264C42—201no—
265C42—601no—
266C42—601no—
267C3×C5#129711yescharacteristic, complemented, Hall
268C22×C3—21no—
269C22×C3—21no—
270C22×C3—21no—
271C22×C3—52no—
272C22×C3—52no—
273C22×C3—101no—
274C22×C3—101no—
275C22×C3—101no—
276C22×C3—101no—
277C22×C3—204no—
278C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
279C3×C4—21no—
280C3×C4—101no—
281C3×C4—101no—
282C3×C4—204no—
283C3×C4#399911yescharacteristic
284C3×C4#401111yescharacteristic
285Dic3—204no—
286C2×C5—41no—
287C2×C5#452311yescharacteristic
288C2×C5#452711yescharacteristic
289C2×C5#453211yescharacteristic
290D5—22no—
291D5—22no—
292C23—51no—
293C23—51no—
294C23—102no—
295C23—102no—
296C23—201no—
297C23Dic3⋊AGL(1,𝔽5)11yescharacteristic
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—51no—
301C2×C4—51no—
302C2×C4—101no—
303C2×C4—101no—
304C2×C4—101no—
305C2×C4—101no—
306C2×C4—104no—
307C2×C4—201no—
308C2×C4—201no—
309C2×C4—201no—
310C2×C4—202no—
311C2×C4—202no—
312C2×C4—304no—
313C2×C4—602no—
314C2×C4—602no—
315C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
316C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
317C8—121no—
318C8—601no—
319C2×C3—41no—
320C2×C3—102no—
321C2×C3—102no—
322C2×C3#6490011yescharacteristic
323C2×C3#6490011yescharacteristic
324C2×C3#6491711yescharacteristic
325C5#6761811yescharacteristic, complemented, Sylow
326C22—21no—
327C22—21no—
328C22—21no—
329C22—52no—
330C22—52no—
331C22—101no—
332C22—101no—
333C22—101no—
334C22—101no—
335C22—204no—
336C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
337C4—21no—
338C4—101no—
339C4—101no—
340C4—204no—
341C4—604no—
342C4#9117211yescharacteristic
343C4#9117311yescharacteristic
344C3#1059878511yescharacteristic, complemented, Sylow
345C2—41no—
346C2—102no—
347C2—102no—
348C2#1174652211yescharacteristic
349C2#1174652711yescharacteristic
350C2#1174657311yescharacteristic
subgroupG/H
centerC2×C4(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C42
Frattini, hypercenterC22×C4D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5#95
prime radicalC23×C3×D5D4
cosocleC22×C3×C4×D5C22
hypocenterC3×C5#1297
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
10. C2×#6710C4semidirect
11. C2×C5×#208C4semidirect
12. #91235C4semidirect
13. C3×(C2×AGL(1,𝔽5))⋊C4C4semidirect
52. (C2×AGL(1,𝔽5))⋊C4Dic3semidirect
89. C2×#208AGL(1,𝔽5)semidirect
267. C3×C5#1297semidirect
325. C5#67618semidirect
344. C3#10598785semidirect

Maximal subgroups

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

subgroupindex
C4×#67632
C3×C4×C22⋊AGL(1,𝔽5)2
#117483412
#105987853
#676185