Finite Group Databasebeta

← #14276821

Subgroups — #14276821

Order 1920.

528 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 117 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
1C2×#91235C211yesmaximal, characteristic
2D5⋊#830C211yesmaximal, characteristic
3C3×D5×C22⋊C8C211yesmaximal, characteristic
4#10598551—31nomaximal, Hall
5C23×ΓL(1,𝔽16)C412yes—
6C22×C3×C4×D5C2211yescharacteristic
7C2×D5⋊(C3⋊C8)—21no—
8C2×C3×C8×D5—21no—
9#91241C412yescomplemented
10#91235—21no—
11#91235—21no—
12#91232—21no—
13C3×C5×C22⋊C8C411yescharacteristic, complemented
14C3×C22⋊#168C411yescharacteristic, complemented
15C3×#3952—21no—
16#67674—51nomaximal, Hall
17C2×(C2×AGL(1,𝔽5))⋊C4—31no—
18D5⋊(C22⋊C8)—31no—
19D5×C22⋊C8D311yescharacteristic
20C23×C3×D5C2×C411yescharacteristic
21C22×ΓL(1,𝔽16)—22no—
22C22×ΓL(1,𝔽16)—22no—
23C22×ΓL(1,𝔽16)—42no—
24C22×ΓL(1,𝔽16)—42no—
25C22×ΓL(1,𝔽16)C814yescomplemented
26C22×C3×C4×C5C2×C411yescharacteristic
27C22×C3×Dic5C2×C411yescharacteristic
28C2×C3×C4×D5—42no—
29C2×C3×C4×D5D411yescharacteristic
30C2×C3×C4×D5D411yescharacteristic
31C2×C3×C4×D5D411yescharacteristic
32C2×C3×C4×D5Q811yescharacteristic
33C2×C3⋊#170—22no—
34D5⋊(C3⋊C8)—42no—
35C2×C3×C5×C8—21no—
36C2×C3×#168—21no—
37C3×C8×D5—42no—
38C2×C3×C22⋊C8—51no—
39C2×C3⋊#95—51no—
40C2×#830—51no—
41C23×AGL(1,𝔽5)—32no—
42C22×C4×D5C2×D311yescharacteristic
43C2×D5⋊C8—61no—
44C2×C8×D5—21no—
45C22⋊#170—32no—
46(C2×AGL(1,𝔽5))⋊C4—61no—
47(C2×AGL(1,𝔽5))⋊C4—61no—
48#4003—61no—
49C5×C22⋊C8Dic311yescharacteristic, complemented
50C22⋊#168Dic311yescharacteristic, complemented
51#3952—21no—
52#1280—151noSylow
53C23×C3×C5C4211yescharacteristic
54C22×C3×D5—22no—
55C22×C3×D5—21no—
56C22×C3×D5—21no—
57C22×C3×D5C22⋊C411yescharacteristic
58C22×C3×D5C4⋊C411yescharacteristic
59C22×C3×D5C2×C812yes—
60C22×C3×D5M1612yes—
61C2×ΓL(1,𝔽16)—24no—
62C2×ΓL(1,𝔽16)—44no—
63C2×ΓL(1,𝔽16)—42no—
64C2×ΓL(1,𝔽16)—42no—
65C2×ΓL(1,𝔽16)—44no—
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5C22⋊C411yescharacteristic
68C2×C3×C4×C5C4⋊C411yescharacteristic
69C2×C3×Dic5—41no—
70C2×C3×Dic5C22⋊C411yescharacteristic
71C2×C3×Dic5C4⋊C411yescharacteristic
72C3×C4×D5—22no—
73C3×C4×D5—22no—
74C3×C4×D5—41no—
75C3×C4×D5—41no—
76C3⋊#170—42no—
77C3×C5×C8—41no—
78C3×#168—41no—
79C23×C3×C4—51no—
80C23×Dic3—52no—
81C22×C3×C8—101no—
82C22×C3⋊C8—101no—
83C3×C22⋊C8—51no—
84C3×C22⋊C8—101no—
85C3×C22⋊C8AGL(1,𝔽5)11yescharacteristic, complemented
86C3⋊#95—101no—
87C3⋊#95—101no—
88#830—52no—
89#830—101no—
90C23×D5C4×D311yescharacteristic
91C22×AGL(1,𝔽5)—34no—
92C22×AGL(1,𝔽5)—62no—
93C22×AGL(1,𝔽5)—62no—
94C22×AGL(1,𝔽5)—122no—
95C22×AGL(1,𝔽5)—122no—
96C22×C4×C5C2×Dic311yescharacteristic
97C22×Dic5C4×D311yescharacteristic
98C2×C4×D5—42no—
99C2×C4×D5Dic611yescharacteristic
100C2×C4×D5D1211yescharacteristic
101C2×C4×D5#6711yescharacteristic
102C2×C4×D5#6711yescharacteristic
103C2×#170—62no—
104D5⋊C8—122no—
105C2×C5×C8—21no—
106C2×#168—21no—
107C8×D5—42no—
108C2×C22⋊C8—51no—
109C2×C22⋊C8—151no—
110C2×#95—151no—
111C22×C3×C5—21no—
112C22×C3×C5—21no—
113C22×C3×C5#9511yescharacteristic
114C22×C3×C5C4×C811yescharacteristic
115C22×C3×C5#9711yescharacteristic
116C2×C3×D5—21no—
117C2×C3×D5—21no—
118C2×C3×D5—22no—
119C2×C3×D5—22no—
120C2×C3×D5—22no—
121C2×C3×D5—22no—
122C2×C3×D5C22⋊C812yes—
123C2×C3×D5#9912yes—
124C2×C3×D5#10011yescharacteristic
125C2×C3×D5#10111yescharacteristic
126C2×C3×D5C4⋊C812yes—
127ΓL(1,𝔽16)—44no—
128C3×C4×C5—21no—
129C3×C4×C5—21no—
130C3×Dic5—21no—
131C3×Dic5—21no—
132C24×C3—51no—
133C22×C3×C4—51no—
134C22×C3×C4—51no—
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C22×C3×C4—51no—
138C22×C3×C4—202no—
139C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
140C22×Dic3—54no—
141C22×Dic3—102no—
142C22×Dic3—102no—
143C22×Dic3—202no—
144C22×Dic3—202no—
145C2×C3×C8—21no—
146C2×C3×C8—101no—
147C2×C3×C8—202no—
148C2×C3⋊C8—102no—
149C2×C3⋊C8—202no—
150C23×C5C4×Dic311yescharacteristic
151C22×D5—22no—
152C22×D5—21no—
153C22×D5—21no—
154C22×D5D3×C812yes—
155C22×D5ΓL(1,𝔽25)12yes—
156C22×D5Dic3⋊C411yescharacteristic
157C22×D5(C2×D3)⋊C411yescharacteristic
158C2×AGL(1,𝔽5)—64no—
159C2×AGL(1,𝔽5)—124no—
160C2×AGL(1,𝔽5)—122no—
161C2×AGL(1,𝔽5)—122no—
162C2×AGL(1,𝔽5)—124no—
163C2×C4×C5—41no—
164C2×C4×C5C4⋊Dic311yescharacteristic
165C2×C4×C5#21711yescharacteristic
166C2×Dic5—41no—
167C2×Dic5Dic3⋊C411yescharacteristic
168C2×Dic5(C2×D3)⋊C411yescharacteristic
169C4×D5—22no—
170C4×D5—22no—
171C4×D5—41no—
172C4×D5—41no—
173#170—122no—
174C5×C8—41no—
175#168—41no—
176C23×C4—51no—
177C23×C4—152no—
178C22×C8—101no—
179C22×C8—301no—
180C22⋊C8—51no—
181C22⋊C8—101no—
182C22⋊C8—152no—
183C22⋊C8—301no—
184C22⋊C8ΓL(1,𝔽16)11yescharacteristic, complemented
185#95—301no—
186#95—301no—
187C2×C3×C5—21no—
188C2×C3×C5—21no—
189C2×C3×C5#33611yescharacteristic
190C2×C3×C5#34211yescharacteristic
191C2×C3×C5#34311yescharacteristic
192C3×D5—22no—
193C3×D5#32312yes—
194C3×D5#32412yes—
195C23×C3—51no—
196C23×C3—52no—
197C23×C3—52no—
198C23×C3—51no—
199C23×C3—101no—
200C23×C3—102no—
201C23×C3—101no—
202C23×C3C4×AGL(1,𝔽5)11yescharacteristic
203C2×C3×C4—41no—
204C2×C3×C4—51no—
205C2×C3×C4—51no—
206C2×C3×C4—102no—
207C2×C3×C4—102no—
208C2×C3×C4—201no—
209C2×C3×C4—201no—
210C2×C3×C4—201no—
211C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
212C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
213C2×Dic3—104no—
214C2×Dic3—202no—
215C2×Dic3—202no—
216C2×Dic3—204no—
217C2×Dic3—204no—
218C3×C8—41no—
219C3×C8—201no—
220C3⋊C8—202no—
221C22×C5—21no—
222C22×C5—21no—
223C22×C5C8×Dic311yescharacteristic
224C22×C5#81511yescharacteristic
225C22×C5C3⋊#9511yescharacteristic
226C2×D5—21no—
227C2×D5—21no—
228C2×D5—22no—
229C2×D5—22no—
230C2×D5—22no—
231C2×D5—22no—
232C2×D5#80612yes—
233C2×D5Dic3⋊C812yes—
234C2×D5(C2×D3)⋊C812yes—
235C2×D5#82311yescharacteristic
236C2×D5#82411yescharacteristic
237AGL(1,𝔽5)—124no—
238C4×C5—21no—
239C4×C5—21no—
240Dic5—21no—
241Dic5—21no—
242C24—51no—
243C22×C4—51no—
244C22×C4—51no—
245C22×C4—51no—
246C22×C4—51no—
247C22×C4—51no—
248C22×C4—154no—
249C22×C4—202no—
250C22×C4—302no—
251C22×C4—302no—
252C22×C4—602no—
253C22×C4—602no—
254C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
255C2×C8—21no—
256C2×C8—101no—
257C2×C8—202no—
258C2×C8—302no—
259C2×C8—602no—
260C3×C5#128011yescharacteristic, complemented, Hall
261C22×C3—21no—
262C22×C3—21no—
263C22×C3—52no—
264C22×C3—52no—
265C22×C3—51no—
266C22×C3—51no—
267C22×C3—52no—
268C22×C3—102no—
269C22×C3—102no—
270C22×C3—102no—
271C22×C3—102no—
272C22×C3—101no—
273C22×C3—101no—
274C22×C3C8×AGL(1,𝔽5)11yescharacteristic
275C22×C3#399211yescharacteristic
276C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
277C3×C4—21no—
278C3×C4—21no—
279C3×C4—101no—
280C3×C4—101no—
281Dic3—204no—
282C2×C5—21no—
283C2×C5—21no—
284C2×C5#452711yescharacteristic
285C2×C5#455011yescharacteristic
286C2×C5#455411yescharacteristic
287D5—22no—
288D5#446812yes—
289D5#446912yes—
290C23—51no—
291C23—52no—
292C23—52no—
293C23—51no—
294C23—102no—
295C23—101no—
296C23—101no—
297C23C4×ΓL(1,𝔽16)11yescharacteristic
298C2×C4—41no—
299C2×C4—51no—
300C2×C4—51no—
301C2×C4—102no—
302C2×C4—102no—
303C2×C4—201no—
304C2×C4—201no—
305C2×C4—201no—
306C2×C4—304no—
307C2×C4—602no—
308C2×C4—602no—
309C2×C4—604no—
310C2×C4—604no—
311C2×C4C4⋊ΓL(1,𝔽16)11yescharacteristic
312C2×C4#676311yescharacteristic
313C8—41no—
314C8—201no—
315C8—602no—
316C2×C3—21no—
317C2×C3—21no—
318C2×C3—52no—
319C2×C3—52no—
320C2×C3—102no—
321C2×C3#6486611yescharacteristic
322C2×C3(C2×AGL(1,𝔽5))⋊C811yescharacteristic
323C2×C3#6489911yescharacteristic
324C5#6767411yescharacteristic, complemented, Sylow
325C22—21no—
326C22—21no—
327C22—52no—
328C22—52no—
329C22—51no—
330C22—51no—
331C22—52no—
332C22—102no—
333C22—102no—
334C22—102no—
335C22—102no—
336C22—101no—
337C22—101no—
338C22C8×ΓL(1,𝔽16)11yescharacteristic
339C22#9122111yescharacteristic
340C22#9123511yescharacteristic
341C4—21no—
342C4—21no—
343C4—101no—
344C4—101no—
345C4—604no—
346C3#1059855111yescharacteristic, complemented, Sylow
347C2—21no—
348C2—21no—
349C2—52no—
350C2—52no—
351C2—102no—
352C2#1174673711yescharacteristic
353C2#1174676311yescharacteristic
354C2#1174677011yescharacteristic
subgroupG/H
centerC22#91235
commutatorC22×C3×C5C4×C8
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC3×C5×C22⋊C8C4
socleC22×C3×C5#95
prime radicalC23×C3×D5C2×C4
cosocleC22×C3×C4×D5C22
hypercenterC22⋊C8ΓL(1,𝔽16)
hypocenterC3×C5#1280
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊C8

Complements

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

NH ≅ G/Ntype
9. #91241C4semidirect
13. C3×C5×C22⋊C8C4semidirect
14. C3×C22⋊#168C4semidirect
25. C22×ΓL(1,𝔽16)C8semidirect
49. C5×C22⋊C8Dic3semidirect
50. C22⋊#168Dic3semidirect
85. C3×C22⋊C8AGL(1,𝔽5)semidirect
184. C22⋊C8ΓL(1,𝔽16)semidirect
260. C3×C5#1280semidirect
324. C5#67674semidirect
346. C3#10598551semidirect

Maximal subgroups

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

subgroupindex
C2×#912352
D5⋊#8302
C3×D5×C22⋊C82
#105985513
#676745