Finite Group Databasebeta

← #14301490

Subgroups — #14301490

Order 1920.

648 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 648 conjugacy classes of subgroups — too many to draw. Only its 121 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#11756991C211yesmaximal, characteristic
2C3×D5×C4⋊Q8C211yesmaximal, characteristic
3D5⋊#836C211yesmaximal, characteristic
4#11752441C212yesmaximal
5#11746733C212yesmaximal
6#10604670—31nomaximal, Hall
7C2×C3×Q8×D5C2211yescharacteristic
8C2×C3×Q8×D5C2211yescharacteristic
9Q8×ΓL(1,𝔽16)—24no—
10#91989—22no—
11#91989C2212yes—
12D5⋊#208C2212yes—
13C3×C5×C4⋊Q8C411yescharacteristic, complemented
14C3×#4090C411yescharacteristic, complemented
15C3×#4090C411yescharacteristic, complemented
16C3×D5×C4⋊C4—22no—
17C3×#4034—22no—
18C3×C42×D5C2211yescharacteristic
19C3×#4015C411yescharacteristic, complemented
20#91238—24no—
21#91234—22no—
22#71784—51nomaximal, Hall
23#66262—31no—
24D5×C4⋊Q8D311yescharacteristic
25D5⋊#101—31no—
26#65782—32no—
27#64862—32no—
28C2×C3×C5×Q8C2×C411yescharacteristic
29C2×C3×C5×Q8C2×C411yescharacteristic
30C3×Q8×D5—22no—
31C3×Q8×D5—22no—
32C3×Q8×D5—22no—
33C3×Q8×D5—22no—
34C2×C3×C4×D5—21no—
35C2×C3×C4×D5—21no—
36C2×C3×C4×D5D412yes—
37C2×C3×C4×D5C2311yescharacteristic
38C2×C3×Dic10—21no—
39C2×C3×Dic10C2×C411yescharacteristic
40C2×C3×Dic10C2×C411yescharacteristic
41C2×C3×Dic10D412yes—
42#6763—22no—
43#6762—22no—
44C4⋊ΓL(1,𝔽16)—24no—
45C4⋊ΓL(1,𝔽16)D414yes—
46C4×ΓL(1,𝔽16)—24no—
47C4×ΓL(1,𝔽16)—22no—
48#6758—22no—
49D5⋊(C3⋊C8)—22no—
50C3×C5×C4⋊C4—22no—
51C3×C42×C5C2×C411yescharacteristic
52C3×C4⋊Dic5—22no—
53C3×#683—22no—
54C3×#683—22no—
55C3×C4×Dic5—21no—
56C3×C4×Dic5C2×C411yescharacteristic
57C2×C3×C4⋊Q8—51no—
58#5812—51no—
59C2×#836—51no—
60#5225—52no—
61#4523—52no—
62C2×Q8×D5C2×D311yescharacteristic
63C2×Q8×D5C2×D311yescharacteristic
64Q8×AGL(1,𝔽5)—64no—
65#4130—32no—
66#4130—62no—
67D5⋊M16—32no—
68C5×C4⋊Q8Dic311yescharacteristic, complemented
69#4090Dic311yescharacteristic, complemented
70#4090Dic311yescharacteristic, complemented
71D5×C4⋊C4—22no—
72#4034—22no—
73C42×D5C2×D311yescharacteristic
74#4015Dic311yescharacteristic, complemented
75#4009—64no—
76#4005—62no—
77#1886—151noSylow
78C22×C3×D5C2×D411yescharacteristic
79C2×ΓL(1,𝔽16)—24no—
80C3×C5×Q8—22no—
81C3×C5×Q8—22no—
82C2×C3×C4×C5—21no—
83C2×C3×C4×C5—21no—
84C2×C3×C4×C5C22⋊C412yes—
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×Dic5—21no—
87C2×C3×Dic5—21no—
88C2×C3×Dic5C22⋊C412yes—
89C2×C3×Dic5C2×D411yescharacteristic
90C3×C4×D5—24no—
91C3×C4×D5—22no—
92C3×C4×D5—22no—
93C3×C4×D5—41no—
94C3×C4×D5—41no—
95C3×C4×D5C2×D412yes—
96C3×C4×D5#4112yes—
97C3×Dic10—22no—
98C3×Dic10—24no—
99C3×Dic10—22no—
100C3×Dic10—42no—
101C3⋊#170—42no—
102C22×C3×Q8—51no—
103C22×C3×Q8—51no—
104C3×C4⋊Q8—51no—
105C3×C4⋊Q8—51no—
106C3×C4⋊Q8—51no—
107C3×C4⋊Q8—102no—
108C3×C4⋊Q8AGL(1,𝔽5)11yescharacteristic, complemented
109C2×C3×C4⋊C4—102no—
110C2×C3×C42—51no—
111Q8×Dic3—104no—
112#926—52no—
113#926—102no—
114C2×#208—52no—
115#836—102no—
116#835—104no—
117C2×C5×Q8C2×Dic311yescharacteristic
118C2×C5×Q8C2×Dic311yescharacteristic
119Q8×D5—22no—
120Q8×D5—22no—
121Q8×D5—22no—
122Q8×D5—22no—
123C2×C4×D5—21no—
124C2×C4×D5—21no—
125C2×C4×D5#6712yes—
126C2×C4×D5C22×D311yescharacteristic
127C2×Dic10—21no—
128C2×Dic10C2×Dic311yescharacteristic
129C2×Dic10C2×Dic311yescharacteristic
130C2×Dic10#6712yes—
131C22⋊AGL(1,𝔽5)—62no—
132#704—62no—
133C4⋊AGL(1,𝔽5)—34no—
134C4⋊AGL(1,𝔽5)—64no—
135C4×AGL(1,𝔽5)—64no—
136C4×AGL(1,𝔽5)—62no—
137#700—62no—
138D5⋊C8—62no—
139C5×C4⋊C4—22no—
140C42×C5C2×Dic311yescharacteristic
141C4⋊Dic5—22no—
142#683—22no—
143#683—22no—
144C4×Dic5—21no—
145C4×Dic5C2×Dic311yescharacteristic
146C2×C4⋊Q8—51no—
147#519—151no—
148#419—152no—
149C2×#101—151no—
150#339—152no—
151C22×C3×C5C2×C22⋊C411yescharacteristic
152C2×C3×D5—22no—
153C2×C3×D5#12011yescharacteristic
154C2×C3×D5#12311yescharacteristic
155ΓL(1,𝔽16)—44no—
156C3×C4×C5—22no—
157C3×C4×C5—22no—
158C3×C4×C5—41no—
159C3×C4×C5C4×D412yes—
160C3×Dic5—22no—
161C3×Dic5—22no—
162C3×Dic5—41no—
163C3×Dic5#12112yes—
164C2×C3×Q8—52no—
165C2×C3×Q8—51no—
166C2×C3×Q8—51no—
167C2×C3×Q8—101no—
168C2×C3×Q8—102no—
169C2×C3×Q8—102no—
170C2×C3×Q8—102no—
171C2×C3×Q8—102no—
172C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
173C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
174C22×C3×C4—51no—
175C22×C3×C4—52no—
176C22×C3×C4—101no—
177C22×C3×C4—101no—
178C3×C4⋊C4—22no—
179C3×C4⋊C4—102no—
180C3×C4⋊C4—102no—
181C3×C4⋊C4—102no—
182C3×C42—51no—
183C3×C42—101no—
184C3×C42C2×AGL(1,𝔽5)11yescharacteristic
185#217—102no—
186C4⋊Dic3—54no—
187C4⋊Dic3—104no—
188C4×Dic3—102no—
189C4×Dic3—104no—
190#208—102no—
191#208—102no—
192C2×C3⋊C8—102no—
193C22×D5C2×#6711yescharacteristic
194C2×AGL(1,𝔽5)—64no—
195C5×Q8—22no—
196C5×Q8—22no—
197C2×C4×C5—21no—
198C2×C4×C5—21no—
199C2×C4×C5#21712yes—
200C2×C4×C5C22×Dic311yescharacteristic
201C2×Dic5—21no—
202C2×Dic5—21no—
203C2×Dic5#21712yes—
204C2×Dic5C2×#6711yescharacteristic
205C4×D5—24no—
206C4×D5—22no—
207C4×D5—22no—
208C4×D5—41no—
209C4×D5—41no—
210C4×D5D3×D412yes—
211C4×D5#23712yes—
212Dic10—22no—
213Dic10—24no—
214Dic10—22no—
215Dic10—42no—
216#170—122no—
217C22×Q8—51no—
218C22×Q8—51no—
219C2×M16—152no—
220C4⋊Q8—51no—
221C4⋊Q8—51no—
222C4⋊Q8—51no—
223C4⋊Q8—102no—
224C4⋊Q8ΓL(1,𝔽16)11yescharacteristic, complemented
225C4×Q8—304no—
226#117—152no—
227#117—302no—
228C2×C4⋊C4—102no—
229C2×C42—51no—
230#103—304no—
231#101—302no—
232C2×C3×C5—21no—
233C2×C3×C5#38611yescharacteristic
234C3×D5—21no—
235C3×D5#45612yes—
236C23×C3—51no—
237C3×Q8—22no—
238C3×Q8—22no—
239C3×Q8—104no—
240C3×Q8—102no—
241C3×Q8—102no—
242C3×Q8—202no—
243C2×C3×C4—21no—
244C2×C3×C4—21no—
245C2×C3×C4—51no—
246C2×C3×C4—52no—
247C2×C3×C4—52no—
248C2×C3×C4—52no—
249C2×C3×C4—102no—
250C2×C3×C4—102no—
251C2×C3×C4—104no—
252C2×C3×C4—101no—
253C2×C3×C4—101no—
254C2×C3×C4—201no—
255C2×C3×C4—201no—
256C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
257C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
258C2×Dic3—104no—
259C3⋊C8—202no—
260C22×C5C2×#21711yescharacteristic
261C2×D5—22no—
262C2×D5#93511yescharacteristic
263C2×D5#93711yescharacteristic
264AGL(1,𝔽5)—124no—
265C4×C5—22no—
266C4×C5—22no—
267C4×C5—41no—
268C4×C5D4×Dic312yes—
269Dic5—22no—
270Dic5—22no—
271Dic5—41no—
272Dic5#93912yes—
273C2×Q8—52no—
274C2×Q8—51no—
275C2×Q8—51no—
276C2×Q8—101no—
277C2×Q8—102no—
278C2×Q8—102no—
279C2×Q8—102no—
280C2×Q8—102no—
281C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
282C2×Q8C2×ΓL(1,𝔽16)11yescharacteristic
283C22×C4—51no—
284C22×C4—52no—
285C22×C4—101no—
286C22×C4—101no—
287M16—302no—
288M16—302no—
289C2×C8—302no—
290C4⋊C4—22no—
291C4⋊C4—102no—
292C4⋊C4—102no—
293C4⋊C4—102no—
294C4⋊C4—154no—
295C4⋊C4—304no—
296C22⋊C4—302no—
297C42—51no—
298C42—101no—
299C42—302no—
300C42—304no—
301C42C2×ΓL(1,𝔽16)11yescharacteristic
302C3×C5#188611yescharacteristic, complemented, Hall
303C22×C3—51no—
304C22×C3—51no—
305C22×C3—102no—
306C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
307C3×C4—22no—
308C3×C4—22no—
309C3×C4—41no—
310C3×C4—52no—
311C3×C4—102no—
312C3×C4—102no—
313C3×C4—201no—
314C3×C4D4×AGL(1,𝔽5)12yes—
315Dic3—204no—
316C2×C5—21no—
317C2×C5#522011yescharacteristic
318D5—21no—
319D5#509512yes—
320C23—51no—
321Q8—22no—
322Q8—22no—
323Q8—104no—
324Q8—102no—
325Q8—102no—
326Q8—202no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—51no—
330C2×C4—52no—
331C2×C4—52no—
332C2×C4—52no—
333C2×C4—102no—
334C2×C4—102no—
335C2×C4—104no—
336C2×C4—101no—
337C2×C4—101no—
338C2×C4—201no—
339C2×C4—201no—
340C2×C4—304no—
341C2×C4#676312yes—
342C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
343C8—602no—
344C2×C3—21no—
345C2×C3—52no—
346C2×C3—101no—
347C2×C3#6577911yescharacteristic
348C5#7178411yescharacteristic, complemented, Sylow
349C22—51no—
350C22—51no—
351C22—102no—
352C22C2×#676311yescharacteristic
353C4—22no—
354C4—22no—
355C4—41no—
356C4—52no—
357C4—102no—
358C4—102no—
359C4—201no—
360C4—604no—
361C4D4×ΓL(1,𝔽16)12yes—
362C3#1060467011yescharacteristic, complemented, Sylow
363C2—21no—
364C2—52no—
365C2—101no—
366C2#1175243811yescharacteristic
subgroupG/H
centerC2#11752438
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×C4⋊Q8C4
socleC2×C3×C5#386
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC4⋊Q8ΓL(1,𝔽16)
hypocenterC3×C5#1886
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
13. C3×C5×C4⋊Q8C4semidirect
14. C3×#4090C4semidirect
15. C3×#4090C4semidirect
19. C3×#4015C4semidirect
68. C5×C4⋊Q8Dic3semidirect
69. #4090Dic3semidirect
70. #4090Dic3semidirect
74. #4015Dic3semidirect
108. C3×C4⋊Q8AGL(1,𝔽5)semidirect
224. C4⋊Q8ΓL(1,𝔽16)semidirect
302. C3×C5#1886semidirect
348. C5#71784semidirect
362. C3#10604670semidirect

Maximal subgroups

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

subgroupindex
#117569912
C3×D5×C4⋊Q82
D5⋊#8362
#117524412
#117467332
#106046703
#717845