Finite Group Databasebeta

← #14279161

Subgroups — #14279161

Order 1920.

324 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 73 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#11752420C211yesmaximal, characteristic
2#11752404C211yesmaximal, characteristic
3C3×#65399C211yesmaximal, characteristic
4#10598769—31nomaximal, Hall
5C2×C3×#709C2211yescharacteristic
6#91989—21no—
7D5⋊#208—21no—
8C22×C3×C5×C8C411yescharacteristic, complemented
9C2×C3×#681C411yescharacteristic, complemented
10#91242—21no—
11#91240—21no—
12#91234C412yescomplemented
13#91228C412yes—
14C3×#3952—21no—
15C3×#3952—21no—
16#67692—51nomaximal, Hall
17#65761—31no—
18#65745—31no—
19#65399D311yescharacteristic
20C22×C3×C4×C5C2×C411yescharacteristic
21C2×C3×C22⋊D5D411yescharacteristic
22C2×C3×C22⋊D5Q811yescharacteristic
23C3×#709—41no—
24C3×#709—41no—
25C2×C3×D20C2×C411yescharacteristic
26C2×C3×C4×D5D411yescharacteristic
27C2×C3×C4×D5D411yescharacteristic
28C2×C3×Dic10C2×C411yescharacteristic
29#6763—22no—
30#6762—22no—
31C4⋊ΓL(1,𝔽16)—41no—
32C4×ΓL(1,𝔽16)—41no—
33#6758—41no—
34D5⋊(C3⋊C8)—41no—
35C2×C3×C5×C8—21no—
36C2×C3×C5×C8—41no—
37C3×#681—41no—
38C2×C3×#168—21no—
39C3×#408—51no—
40#5240—51no—
41#5237—51no—
42C2×#709C2×D311yescharacteristic
43#4130—61no—
44D5⋊M16—61no—
45C22×C5×C8Dic311yescharacteristic, complemented
46C2×#681Dic311yescharacteristic, complemented
47#4013—61no—
48#4011—61no—
49#4005—32no—
50#3999—32no—
51#3952—21no—
52#3952—21no—
53#1395—151noSylow
54C23×C3×C5C4⋊C411yescharacteristic
55C22×C3×D5C22⋊C411yescharacteristic
56C22×C3×D5C4⋊C411yescharacteristic
57C2×ΓL(1,𝔽16)—42no—
58C2×C3×C4×C5—21no—
59C2×C3×C4×C5—21no—
60C2×C3×C4×C5C4211yescharacteristic
61C2×C3×C4×C5C22⋊C411yescharacteristic
62C3×C22⋊D5—41no—
63C3×C22⋊D5—41no—
64C2×C3×Dic5C22⋊C411yescharacteristic
65C2×C3×Dic5C4⋊C411yescharacteristic
66C3×D20—41no—
67C3×C4×D5—21no—
68C3×C4×D5—21no—
69C3×C4×D5—21no—
70C3×C4×D5—21no—
71C3×Dic10—41no—
72C3⋊#170—42no—
73C3×C5×C8—41no—
74C3×#168—41no—
75C2×C3×#41—51no—
76C2×C3×M16—51no—
77C22×C3×C8AGL(1,𝔽5)11yescharacteristic, complemented
78#926—101no—
79C2×#208—101no—
80C3×C22⋊C8—101no—
81C3×C22⋊C8—101no—
82#836—52no—
83#834—52no—
84#834—101no—
85#833—101no—
86C22×C4×C5C2×Dic311yescharacteristic
87C2×C22⋊D5Dic611yescharacteristic
88C2×C22⋊D5D1211yescharacteristic
89#709—41no—
90#709—41no—
91C2×D20C4×D311yescharacteristic
92C2×C4×D5#6711yescharacteristic
93C2×C4×D5#6711yescharacteristic
94C2×Dic10C4×D311yescharacteristic
95C22⋊AGL(1,𝔽5)—62no—
96#704—62no—
97C4⋊AGL(1,𝔽5)—121no—
98C4×AGL(1,𝔽5)—121no—
99#700—121no—
100D5⋊C8—121no—
101C2×C5×C8—21no—
102C2×C5×C8—41no—
103#681—41no—
104C2×#168—21no—
105#413—151no—
106#410—151no—
107#408—51no—
108C22×C3×C5—21no—
109C22×C3×C5—41no—
110C22×C3×C5#9511yescharacteristic
111C2×C3×D5—21no—
112C2×C3×D5—21no—
113C2×C3×D5—41no—
114C2×C3×D5—41no—
115ΓL(1,𝔽16)—82no—
116C3×C4×C5—21no—
117C3×C4×C5#9911yescharacteristic
118C3×C4×C5#9911yescharacteristic
119C3×Dic5—21no—
120C3×Dic5—21no—
121C3×#41—201no—
122C3×#41—201no—
123C2×C3×Q8—51no—
124C2×C3×D4—51no—
125C2×C3×D4—51no—
126C2×C3×D4—51no—
127C22×C3×C4—51no—
128C22×C3×C4—51no—
129C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
130C3×M16—201no—
131C2×C3×C8—21no—
132C2×C3×C8—41no—
133C2×C3×C8—101no—
134#217—102no—
135C4⋊Dic3—201no—
136C4×Dic3—201no—
137#208—102no—
138#208—201no—
139C2×C3⋊C8—201no—
140C23×C5C4⋊Dic311yescharacteristic
141C22×D5Dic3⋊C411yescharacteristic
142C22×D5(C2×D3)⋊C411yescharacteristic
143C2×AGL(1,𝔽5)—122no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5C4×Dic311yescharacteristic
147C2×C4×C5#21711yescharacteristic
148C22⋊D5—41no—
149C22⋊D5—41no—
150C2×Dic5Dic3⋊C411yescharacteristic
151C2×Dic5(C2×D3)⋊C411yescharacteristic
152D20—41no—
153C4×D5—21no—
154C4×D5—21no—
155C4×D5—21no—
156C4×D5—21no—
157Dic10—41no—
158#170—122no—
159C5×C8—41no—
160#168—41no—
161C2×#41—51no—
162C2×M16—51no—
163C2×M16—301no—
164C22×C8ΓL(1,𝔽16)11yescharacteristic, complemented
165#117—301no—
166#101—152no—
167#100—301no—
168#99—152no—
169#99—301no—
170C22⋊C8—101no—
171C22⋊C8—101no—
172C2×C3×C5—21no—
173C2×C3×C5—41no—
174C2×C3×C5#34211yescharacteristic
175C3×D5—41no—
176C3×D5—41no—
177C23×C3—51no—
178C23×C3—51no—
179C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
180C3×Q8—201no—
181C3×D4—201no—
182C3×D4—201no—
183C3×D4—201no—
184C2×C3×C4—21no—
185C2×C3×C4—21no—
186C2×C3×C4—51no—
187C2×C3×C4—51no—
188C2×C3×C4—101no—
189C2×C3×C4—101no—
190C2×C3×C4—101no—
191C2×C3×C4—101no—
192C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
193C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
194C2×Dic3—202no—
195C3×C8—41no—
196C3×C8—201no—
197C3⋊C8—202no—
198C22×C5—21no—
199C22×C5—41no—
200C22×C5C3⋊#9511yescharacteristic
201C2×D5—21no—
202C2×D5—21no—
203C2×D5—41no—
204C2×D5—41no—
205AGL(1,𝔽5)—242no—
206C4×C5—21no—
207C4×C5#83411yescharacteristic
208C4×C5#83411yescharacteristic
209Dic5—21no—
210Dic5—21no—
211#41—201no—
212#41—201no—
213C2×Q8—51no—
214C2×D4—51no—
215C2×D4—51no—
216C2×D4—51no—
217C22×C4—51no—
218C22×C4—51no—
219C22×C4C2×ΓL(1,𝔽16)11yescharacteristic
220M16—201no—
221M16—302no—
222M16—601no—
223C2×C8—21no—
224C2×C8—41no—
225C2×C8—101no—
226C2×C8—601no—
227C4⋊C4—601no—
228C22⋊C4—302no—
229C42—601no—
230C3×C5#139511yescharacteristic, complemented, Hall
231C22×C3—21no—
232C22×C3—41no—
233C22×C3—101no—
234C22×C3—101no—
235C22×C3—201no—
236C22×C3—201no—
237C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
238C3×C4—21no—
239C3×C4—101no—
240C3×C4—101no—
241C3×C4#399911yescharacteristic
242C3×C4#401111yescharacteristic
243Dic3—402no—
244C2×C5—21no—
245C2×C5—41no—
246C2×C5#452611yescharacteristic
247D5—41no—
248D5—41no—
249C23—51no—
250C23—51no—
251C23C4⋊ΓL(1,𝔽16)11yescharacteristic
252Q8—201no—
253D4—201no—
254D4—201no—
255D4—201no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—51no—
259C2×C4—51no—
260C2×C4—101no—
261C2×C4—101no—
262C2×C4—101no—
263C2×C4—101no—
264C2×C4—602no—
265C2×C4C4×ΓL(1,𝔽16)11yescharacteristic
266C2×C4#676311yescharacteristic
267C8—41no—
268C8—201no—
269C8—602no—
270C2×C3—21no—
271C2×C3—41no—
272C2×C3—201no—
273C2×C3—201no—
274C2×C3#6491711yescharacteristic
275C5#6769211yescharacteristic, complemented, Sylow
276C22—21no—
277C22—41no—
278C22—101no—
279C22—101no—
280C22—201no—
281C22—201no—
282C22#9123511yescharacteristic
283C4—21no—
284C4—101no—
285C4—101no—
286C4—1202no—
287C4#9122811yescharacteristic
288C4#9124011yescharacteristic
289C3#1059876911yescharacteristic, complemented, Sylow
290C2—21no—
291C2—41no—
292C2—201no—
293C2—201no—
294C2#1174678811yescharacteristic
subgroupG/H
centerC4#91228
commutatorC2×C3×C4×C5C42
FrattiniC22×C4C2×ΓL(1,𝔽16)
FittingC22×C3×C5×C8C4
socleC2×C3×C5#342
prime radical, cosocleC2×C3×#709C22
hypercenterC22×C8ΓL(1,𝔽16)
hypocenterC3×C5#1395
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
8. C22×C3×C5×C8C4semidirect
9. C2×C3×#681C4semidirect
12. #91234C4semidirect
45. C22×C5×C8Dic3semidirect
46. C2×#681Dic3semidirect
77. C22×C3×C8AGL(1,𝔽5)semidirect
164. C22×C8ΓL(1,𝔽16)semidirect
230. C3×C5#1395semidirect
275. C5#67692semidirect
289. C3#10598769semidirect

Maximal subgroups

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

subgroupindex
#117524202
#117524042
C3×#653992
#105987693
#676925