Finite Group Databasebeta

← #14299672

Subgroups — #14299672

Order 1920.

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

normal subgroups only

This group has 504 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
1#11756985C211yesmaximal, characteristic
2#11752435C211yesmaximal, characteristic
3#11752388C212yesmaximal, complemented
4C3×#65034C211yesmaximal, characteristic
5#11746772C212yesmaximal, complemented
6#10603928—31nomaximal, Hall
7C2×C3×#711C2211yescharacteristic
8C2×#6762—22no—
9#91990—22no—
10#91990—22no—
11D5⋊#208C2212yes—
12C2×#6758C2211yescharacteristic
13C2×D5⋊(C3⋊C8)C2211yescharacteristic
14C3×D5×M16C2212yes—
15#91241—22no—
16#91225—22no—
17#91224—22no—
18C3×C5×#100C411yescharacteristic
19C3×#3965C411yescharacteristic
20C3×#3956C412yes—
21#70135—51nomaximal, Hall
22#66256—31no—
23#65776—31no—
24#65729—32no—
25#65034D311yescharacteristic
26#64901—32no—
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×C3×C22⋊D5Q812yes—
29C22×C3×Dic5D412yes—
30C3×#711—22no—
31C3×#711—22no—
32C2×C3×C4×D5C2311yescharacteristic
33C2×C3×Dic10C2×C411yescharacteristic
34#6762—24no—
35#6762—22no—
36C2×C3⋊#170—22no—
37C2×C3⋊#170—22no—
38C2×C3⋊#170—21no—
39C2×C3⋊#170—21no—
40#6758—22no—
41#6758D412yes—
42#6758D412yes—
43D5⋊(C3⋊C8)—22no—
44D5⋊(C3⋊C8)—22no—
45C3×C5×M16C2×C412yes—
46C3×#681C2×C412yes—
47C3×#676—22no—
48C3×C8×D5—22no—
49#5819—51no—
50C3×#413—51no—
51#5234—51no—
52#5125—52no—
53#4558—52no—
54C2×#711C2×D311yescharacteristic
55C2×#704—62no—
56#4131—62no—
57#4131—62no—
58D5⋊M16—32no—
59C2×#700—31no—
60C2×D5⋊C8—31no—
61D5×M16C2×D312yes—
62C22⋊#170—62no—
63#3996—62no—
64#3995—62no—
65C5×#100Dic311yescharacteristic
66#3965Dic311yescharacteristic
67#3956Dic312yes—
68#1858—151noSylow
69C23×C3×C5C4⋊C412yes—
70C22×C3×D5C2×Q811yescharacteristic
71C3×C5×D4—22no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C3×C22⋊D5—24no—
74C2×C3×Dic5—22no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5C4⋊C412yes—
77C2×C3×Dic5C2×D411yescharacteristic
78C3×C4×D5C2×D412yes—
79C3×C4×D5#4112yes—
80C3×Dic10—22no—
81C3⋊#170—22no—
82C3⋊#170—22no—
83C3⋊#170—41no—
84C3⋊#170—41no—
85C3×C5×C8—22no—
86C3×#168—22no—
87C2×C3×#41—51no—
88C2×C3×M16—52no—
89#948—102no—
90#948—102no—
91C2×#208—52no—
92C2×#208—51no—
93C2×#208—102no—
94C22×C3⋊C8—51no—
95C3×#101—52no—
96C3×#100—51no—
97C3×#100AGL(1,𝔽5)11yescharacteristic
98#830—102no—
99#819—102no—
100#819—102no—
101C2×C5×D4C2×Dic311yescharacteristic
102C2×C22⋊D5Dic612yes—
103C22×Dic5D1212yes—
104#711—22no—
105#711—22no—
106C2×C4×D5C22×D311yescharacteristic
107C2×Dic10C2×Dic311yescharacteristic
108#704—64no—
109#704—62no—
110C2×#170—62no—
111C2×#170—62no—
112C2×#170—61no—
113C2×#170—61no—
114#700—32no—
115#700—32no—
116#700—62no—
117D5⋊C8—62no—
118D5⋊C8—62no—
119C5×M16C2×Dic312yes—
120#681C2×Dic312yes—
121#676—22no—
122C8×D5—22no—
123#568—151no—
124#430—152no—
125#413—51no—
126#408—151no—
127#341—152no—
128C22×C3×C5—22no—
129C22×C3×C5—42no—
130C22×C3×C5C2×C4⋊C411yescharacteristic
131C2×C3×D5—41no—
132C2×C3×D5C22⋊Q812yes—
133C3×C4×C5C4×D412yes—
134C3×Dic5—22no—
135C3×Dic5#12011yescharacteristic
136C3×Dic5#12311yescharacteristic
137C3×#41—102no—
138C3×#41—102no—
139C2×C3×Q8—51no—
140C2×C3×D4—52no—
141C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
142C22×C3×C4—51no—
143C22×C3×C4—52no—
144C3×M16—52no—
145C3×M16—102no—
146C3×M16C2×AGL(1,𝔽5)12yes—
147C2×C3×C8—102no—
148#208—52no—
149#208—52no—
150#208—102no—
151#208—104no—
152#208—102no—
153C2×C3⋊C8—102no—
154C2×C3⋊C8—102no—
155C2×C3⋊C8—102no—
156C2×C3⋊C8—101no—
157C2×C3⋊C8—101no—
158C2×C3⋊C8—102no—
159C23×C5C4⋊Dic312yes—
160C22×D5C2×Dic611yescharacteristic
161C5×D4—22no—
162C2×C4×C5C22×Dic311yescharacteristic
163C22⋊D5—24no—
164C2×Dic5—22no—
165C2×Dic5—22no—
166C2×Dic5C4⋊Dic312yes—
167C2×Dic5C2×D1211yescharacteristic
168C4×D5D3×D412yes—
169C4×D5#23712yes—
170Dic10—22no—
171#170—62no—
172#170—62no—
173#170—121no—
174#170—121no—
175C5×C8—22no—
176#168—22no—
177C2×#41—51no—
178#131—302no—
179#131—302no—
180C2×M16—52no—
181C2×M16—152no—
182C2×M16—151no—
183C2×M16—302no—
184C22×C8—151no—
185#108—302no—
186#108—302no—
187#101—52no—
188#100—51no—
189#100ΓL(1,𝔽16)11yescharacteristic
190C22⋊C8—302no—
191C2×C3×C5—21no—
192C2×C3×C5—42no—
193C2×C3×C5#38511yescharacteristic
194C3×D5—22no—
195C23×C3—51no—
196C23×C3C4⋊AGL(1,𝔽5)12yes—
197C3×Q8—102no—
198C3×D4—22no—
199C3×D4—104no—
200C2×C3×C4—51no—
201C2×C3×C4—52no—
202C2×C3×C4—52no—
203C2×C3×C4—52no—
204C2×C3×C4—102no—
205C2×C3×C4—102no—
206C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
207C3×C8—22no—
208C3×C8—102no—
209C3⋊C8—102no—
210C3⋊C8—102no—
211C3⋊C8—201no—
212C3⋊C8—201no—
213C22×C5—22no—
214C22×C5—42no—
215C22×C5C2×C4⋊Dic311yescharacteristic
216C2×D5—41no—
217C2×D5#87812yes—
218C4×C5D4×Dic312yes—
219Dic5—22no—
220Dic5#88211yescharacteristic
221Dic5#88611yescharacteristic
222#41—102no—
223#41—102no—
224C2×Q8—51no—
225C2×D4—52no—
226C2×D4C2×ΓL(1,𝔽16)11yescharacteristic
227C22×C4—51no—
228C22×C4—52no—
229M16—52no—
230M16—102no—
231M16—152no—
232M16—152no—
233M16—302no—
234M16—304no—
235M16—302no—
236M16C2×ΓL(1,𝔽16)12yes—
237C2×C8—102no—
238C2×C8—302no—
239C2×C8—302no—
240C2×C8—302no—
241C2×C8—301no—
242C2×C8—301no—
243C2×C8—302no—
244C3×C5#185811yescharacteristic, complemented, Hall
245C22×C3—22no—
246C22×C3—42no—
247C22×C3—52no—
248C22×C3—201no—
249C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
250C3×C4—51no—
251C3×C4—51no—
252C3×C4—102no—
253C3×C4D4×AGL(1,𝔽5)12yes—
254C2×C5—21no—
255C2×C5—42no—
256C2×C5#495011yescharacteristic
257D5—22no—
258C23—51no—
259C23C4⋊ΓL(1,𝔽16)12yes—
260Q8—102no—
261D4—22no—
262D4—104no—
263C2×C4—51no—
264C2×C4—52no—
265C2×C4—52no—
266C2×C4—52no—
267C2×C4—102no—
268C2×C4—102no—
269C2×C4C22×ΓL(1,𝔽16)11yescharacteristic
270C8—22no—
271C8—102no—
272C8—302no—
273C8—302no—
274C8—601no—
275C8—601no—
276C2×C3—21no—
277C2×C3—42no—
278C2×C3—102no—
279C2×C3#6569911yescharacteristic
280C5#7013511yescharacteristic, complemented, Sylow
281C22—22no—
282C22—42no—
283C22—52no—
284C22—201no—
285C22C2×C4⋊ΓL(1,𝔽16)11yescharacteristic
286C4—51no—
287C4—51no—
288C4—102no—
289C4D4×ΓL(1,𝔽16)12yes—
290C3#1060392811yescharacteristic, complemented, Sylow
291C2—21no—
292C2—42no—
293C2—102no—
294C2#1175235811yescharacteristic
subgroupG/H
centerC2#11752358
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C22×ΓL(1,𝔽16)
FittingC3×C5×#100C4
socleC2×C3×C5#385
prime radicalC2×C3×#711C22
cosocleC2×C3×C4×D5C23
hypercenter#100ΓL(1,𝔽16)
hypocenterC3×C5#1858
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ #100

Complements

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

NH ≅ G/Ntype
3. #11752388C2semidirect
5. #11746772C2semidirect
244. C3×C5#1858semidirect
280. C5#70135semidirect
290. C3#10603928semidirect

Maximal subgroups

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

subgroupindex
#117569852
#117524352
#117523882
C3×#650342
#117467722
#106039283
#701355