Finite Group Databasebeta

← #14279080

Subgroups — #14279080

Order 1920.

332 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 69 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#11752434C211yesmaximal, characteristic
2#11752430C211yesmaximal, characteristic
3C3×#65029C211yesmaximal, characteristic
4#10598569—31nomaximal, Hall
5C2×C3×#711C2211yescharacteristic
6C2×#6762C411yescharacteristic, complemented
7C22×C3⋊#170C411yescharacteristic, complemented
8#91989—21no—
9C3×#4023—21no—
10#91241—21no—
11#91240—21no—
12#91240C412yescomplemented
13#91232—21no—
14C3×C5×#99C411yescharacteristic, complemented
15C3×#3966C411yescharacteristic, complemented
16C3×#3938—21no—
17#67696—51nomaximal, Hall
18#65775—31no—
19#65771—31no—
20#65029D311yescharacteristic
21C2×C3×C5×D4C2×C411yescharacteristic
22C2×C3×C22⋊D5C2×C411yescharacteristic
23C2×C3×C22⋊D5D411yescharacteristic
24C22×C3×Dic5C2×C411yescharacteristic
25C22×C3×Dic5D411yescharacteristic
26C3×#711—41no—
27C3×#711—41no—
28C2×C3×C4×D5D411yescharacteristic
29C2×C3×Dic10Q811yescharacteristic
30#6763—22no—
31#6762—41no—
32C2×C3⋊#170—21no—
33C2×C3⋊#170—21no—
34C2×C3⋊#170—41no—
35C4⋊ΓL(1,𝔽16)—41no—
36C4×ΓL(1,𝔽16)—41no—
37C3×C5×C22⋊C4—21no—
38C3×C22⋊Dic5—21no—
39C3×#683—41no—
40C3×C4×Dic5—41no—
41C3×#410—51no—
42#5240—51no—
43#5234—51no—
44C2×#711C2×D311yescharacteristic
45C2×#704—31no—
46C22×#170—31no—
47#4130—61no—
48#4023—21no—
49C22⋊#170—61no—
50#4011—32no—
51#4011—61no—
52#4003—61no—
53C5×#99Dic311yescharacteristic, complemented
54#3966Dic311yescharacteristic, complemented
55#3938—21no—
56#1391—151noSylow
57C23×C3×C5C4211yescharacteristic
58C23×C3×C5C22⋊C411yescharacteristic
59C22×C3×D5C22⋊C411yescharacteristic
60C2×ΓL(1,𝔽16)—42no—
61C3×C5×D4—41no—
62C2×C3×C4×C5—41no—
63C2×C3×C4×C5C4⋊C411yescharacteristic
64C3×C22⋊D5—41no—
65C3×C22⋊D5—41no—
66C2×C3×Dic5—21no—
67C2×C3×Dic5—21no—
68C2×C3×Dic5—21no—
69C2×C3×Dic5—21no—
70C2×C3×Dic5—41no—
71C2×C3×Dic5C22⋊C411yescharacteristic
72C2×C3×Dic5C4⋊C411yescharacteristic
73C2×C3×Dic5C4⋊C411yescharacteristic
74C3×C4×D5—21no—
75C3×C4×D5—21no—
76C3×Dic10—41no—
77C3⋊#170—41no—
78C3⋊#170—41no—
79C2×C3×#41—51no—
80C3×#117—101no—
81#926—101no—
82C2×#208—51no—
83C22×C3⋊C8—51no—
84C3×#99—51no—
85C3×#99—101no—
86C3×#99AGL(1,𝔽5)11yescharacteristic, complemented
87#834—52no—
88#834—101no—
89#830—101no—
90#830—101no—
91C2×C5×D4C2×Dic311yescharacteristic
92C2×C22⋊D5C4×D311yescharacteristic
93C2×C22⋊D5#6711yescharacteristic
94C22×Dic5C4×D311yescharacteristic
95C22×Dic5#6711yescharacteristic
96#711—41no—
97#711—41no—
98C2×C4×D5D1211yescharacteristic
99C2×Dic10Dic611yescharacteristic
100C22⋊AGL(1,𝔽5)—62no—
101#704—121no—
102C2×#170—61no—
103C2×#170—61no—
104C2×#170—121no—
105C4⋊AGL(1,𝔽5)—121no—
106C4×AGL(1,𝔽5)—121no—
107C5×C22⋊C4—21no—
108C22⋊Dic5—21no—
109#683—41no—
110C4×Dic5—41no—
111#410—51no—
112#410—151no—
113#408—151no—
114C22×C3×C5—21no—
115C22×C3×C5—21no—
116C22×C3×C5—41no—
117C22×C3×C5—41no—
118C22×C3×C5#9511yescharacteristic
119C2×C3×D5—21no—
120C2×C3×D5—41no—
121ΓL(1,𝔽16)—82no—
122C3×C4×C5—21no—
123C3×C4×C5—81no—
124C3×Dic5—21no—
125C3×Dic5—21no—
126C3×Dic5—81no—
127C3×Dic5#9911yescharacteristic
128C3×Dic5#9911yescharacteristic
129C3×#41—201no—
130C3×#41—201no—
131C2×C3×Q8—51no—
132C2×C3×D4—51no—
133C2×C3×D4—51no—
134C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
135C22×C3×C4—51no—
136C22×C3×C4—51no—
137C22×C3×C4—51no—
138C3×C4⋊C4—201no—
139C3×C22⋊C4—21no—
140C3×C22⋊C4—101no—
141C3×C42—201no—
142#217—102no—
143C4⋊Dic3—201no—
144C4×Dic3—201no—
145#208—201no—
146C2×C3⋊C8—101no—
147C2×C3⋊C8—101no—
148C2×C3⋊C8—201no—
149C23×C5C4×Dic311yescharacteristic
150C23×C5#21711yescharacteristic
151C22×D5(C2×D3)⋊C411yescharacteristic
152C2×AGL(1,𝔽5)—122no—
153C5×D4—41no—
154C2×C4×C5—41no—
155C2×C4×C5C4⋊Dic311yescharacteristic
156C22⋊D5—41no—
157C22⋊D5—41no—
158C2×Dic5—21no—
159C2×Dic5—21no—
160C2×Dic5—21no—
161C2×Dic5—21no—
162C2×Dic5—41no—
163C2×Dic5Dic3⋊C411yescharacteristic
164C2×Dic5Dic3⋊C411yescharacteristic
165C2×Dic5(C2×D3)⋊C411yescharacteristic
166C4×D5—21no—
167C4×D5—21no—
168Dic10—41no—
169#170—121no—
170#170—121no—
171C2×#41—51no—
172C2×M16—151no—
173C22×C8—151no—
174#117—101no—
175#117—301no—
176#99—51no—
177#99—101no—
178#99—152no—
179#99—301no—
180#99ΓL(1,𝔽16)11yescharacteristic, complemented
181C22⋊C8—301no—
182C22⋊C8—301no—
183C2×C3×C5—21no—
184C2×C3×C5—41no—
185C2×C3×C5—41no—
186C2×C3×C5#34211yescharacteristic
187C3×D5—41no—
188C23×C3—51no—
189C23×C3C4×AGL(1,𝔽5)11yescharacteristic
190C23×C3C22⋊AGL(1,𝔽5)11yescharacteristic
191C3×Q8—201no—
192C3×D4—41no—
193C3×D4—201no—
194C3×D4—201no—
195C2×C3×C4—41no—
196C2×C3×C4—51no—
197C2×C3×C4—51no—
198C2×C3×C4—51no—
199C2×C3×C4—101no—
200C2×C3×C4—101no—
201C2×C3×C4—101no—
202C2×C3×C4—101no—
203C2×C3×C4—101no—
204C2×C3×C4—101no—
205C2×C3×C4—201no—
206C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
207C2×Dic3—202no—
208C3⋊C8—201no—
209C3⋊C8—201no—
210C22×C5—21no—
211C22×C5—21no—
212C22×C5—41no—
213C22×C5—41no—
214C22×C5C3⋊#9511yescharacteristic
215C2×D5—21no—
216C2×D5—41no—
217AGL(1,𝔽5)—242no—
218C4×C5—21no—
219C4×C5—81no—
220Dic5—21no—
221Dic5—21no—
222Dic5—81no—
223Dic5#80611yescharacteristic
224Dic5#80611yescharacteristic
225#41—201no—
226#41—201no—
227C2×Q8—51no—
228C2×D4—51no—
229C2×D4—51no—
230C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
231C22×C4—51no—
232C22×C4—51no—
233C22×C4—51no—
234M16—601no—
235C2×C8—301no—
236C2×C8—301no—
237C2×C8—601no—
238C4⋊C4—201no—
239C4⋊C4—601no—
240C22⋊C4—21no—
241C22⋊C4—101no—
242C22⋊C4—302no—
243C42—201no—
244C42—601no—
245C3×C5#139111yescharacteristic, complemented, Hall
246C22×C3—21no—
247C22×C3—21no—
248C22×C3—41no—
249C22×C3—41no—
250C22×C3—101no—
251C22×C3—201no—
252C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
253C3×C4—21no—
254C3×C4—51no—
255C3×C4—51no—
256C3×C4—81no—
257C3×C4—101no—
258C3×C4—101no—
259C3×C4—401no—
260Dic3—402no—
261C2×C5—21no—
262C2×C5—41no—
263C2×C5—41no—
264C2×C5#452711yescharacteristic
265D5—41no—
266C23—51no—
267C23C4×ΓL(1,𝔽16)11yescharacteristic
268C23#676311yescharacteristic
269Q8—201no—
270D4—41no—
271D4—201no—
272D4—201no—
273C2×C4—41no—
274C2×C4—51no—
275C2×C4—51no—
276C2×C4—51no—
277C2×C4—101no—
278C2×C4—101no—
279C2×C4—101no—
280C2×C4—101no—
281C2×C4—101no—
282C2×C4—101no—
283C2×C4—201no—
284C2×C4—602no—
285C2×C4C4⋊ΓL(1,𝔽16)11yescharacteristic
286C8—601no—
287C8—601no—
288C2×C3—21no—
289C2×C3—41no—
290C2×C3—41no—
291C2×C3—201no—
292C2×C3#6486611yescharacteristic
293C5#6769611yescharacteristic, complemented, Sylow
294C22—21no—
295C22—21no—
296C22—41no—
297C22—41no—
298C22—101no—
299C22—201no—
300C22#9123511yescharacteristic
301C4—21no—
302C4—51no—
303C4—51no—
304C4—81no—
305C4—101no—
306C4—101no—
307C4—401no—
308C4—1202no—
309C3#1059856911yescharacteristic, complemented, Sylow
310C2—21no—
311C2—41no—
312C2—41no—
313C2—201no—
314C2#1174673711yescharacteristic
subgroupG/H
centerC2#11746737
commutatorC23×C3×C5C42
FrattiniC2×D4C2×ΓL(1,𝔽16)
FittingC3×C5×#99C4
socleC2×C3×C5#342
prime radical, cosocleC2×C3×#711C22
hypercenter#99ΓL(1,𝔽16)
hypocenterC3×C5#1391
LCSG ▷ C23×C3×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #99

Complements

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

NH ≅ G/Ntype
6. C2×#6762C4semidirect
7. C22×C3⋊#170C4semidirect
12. #91240C4semidirect
14. C3×C5×#99C4semidirect
15. C3×#3966C4semidirect
53. C5×#99Dic3semidirect
54. #3966Dic3semidirect
86. C3×#99AGL(1,𝔽5)semidirect
180. #99ΓL(1,𝔽16)semidirect
245. C3×C5#1391semidirect
293. C5#67696semidirect
309. C3#10598569semidirect

Maximal subgroups

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

subgroupindex
#117524342
#117524302
C3×#650292
#105985693
#676965