Finite Group Databasebeta

← #14277123

Subgroups — #14277123

Order 1920.

368 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 80 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#11752414C211yesmaximal, characteristic
2C3×D5⋊(C22⋊C8)C211yesmaximal, characteristic
3#11748499C211yesmaximal, characteristic
4#10598560—31nomaximal, Hall
5C22×C3×C4×D5C2211yescharacteristic
6C2×#6762—21no—
7C2×C3×D5⋊C8C412yes—
8C2×#6649—21no—
9#91232—21no—
10#91232C412yes—
11C3×C22⋊#170—21no—
12C3×#4003—21no—
13#91114C411yescharacteristic
14C5×#830C411yescharacteristic
15#90955—21no—
16#67679—51nomaximal, Hall
17#65755—31no—
18D5⋊(C22⋊C8)D311yescharacteristic
19#65015—31no—
20C23×C3×D5Q811yescharacteristic
21C22×C3×C4×C5C2×C411yescharacteristic
22C22×C3×Dic5D411yescharacteristic
23C2×C3×C4×D5—42no—
24C2×C3×C4×D5C2×C411yescharacteristic
25C2×C3×C4×D5C2×C411yescharacteristic
26C2×C3×C4×D5D411yescharacteristic
27C2×C3×C4×D5D411yescharacteristic
28#6762—42no—
29C2×C3⋊#170—22no—
30C2×C3×#170—22no—
31C3×D5⋊C8—42no—
32C2×C3⋊#168—21no—
33C2×C5×C3⋊C8—21no—
34#6649—42no—
35C2×C3×C22⋊C8—51no—
36#5207—51no—
37#5207—51no—
38C22×C4×D5C2×D311yescharacteristic
39C2×#704—61no—
40C2×D5⋊C8Dic312yes—
41C2×#676—61no—
42C22⋊#170—21no—
43#4003—21no—
44#4003—32no—
45#4003—61no—
46C5×C22⋊C8—31no—
47C22⋊#168—31no—
48#3952—61no—
49#1293—151noSylow
50C23×C3×C5C4⋊C411yescharacteristic
51C22×C3×D5—22no—
52C22×C3×D5—41no—
53C22×C3×D5—41no—
54C22×C3×D5C4⋊C411yescharacteristic
55C22×C3×D5C4⋊C411yescharacteristic
56C2×C3×C4×C5—41no—
57C2×C3×C4×C5C4211yescharacteristic
58C2×C3×C4×C5C22⋊C411yescharacteristic
59C2×C3×Dic5—22no—
60C2×C3×Dic5C22⋊C411yescharacteristic
61C2×C3×Dic5C22⋊C411yescharacteristic
62C3×C4×D5—22no—
63C3×C4×D5—22no—
64C3×C4×D5—41no—
65C3×C4×D5—41no—
66C3⋊#170—42no—
67C3×#170—42no—
68C3⋊#168—41no—
69C5×C3⋊C8—41no—
70C23×C3×C4—51no—
71C22×C3×C8—52no—
72C2×#208—101no—
73C2×#208—101no—
74C3×C22⋊C8—101no—
75C3×C22⋊C8—101no—
76#830—52no—
77#830—51no—
78#830—101no—
79#830—101no—
80#830AGL(1,𝔽5)11yescharacteristic
81C23×D5Dic611yescharacteristic
82C22×C4×C5C4×D311yescharacteristic
83C22×Dic5#6711yescharacteristic
84C2×C4×D5—42no—
85C2×C4×D5C4×D311yescharacteristic
86C2×C4×D5D1211yescharacteristic
87C2×C4×D5C2×Dic311yescharacteristic
88C2×C4×D5#6711yescharacteristic
89#704—122no—
90C2×#170—22no—
91C2×#170—62no—
92D5⋊C8—42no—
93C2×C5×C8—61no—
94C2×#168—61no—
95#676—122no—
96#407—151no—
97#407—151no—
98C2×C22⋊C8—51no—
99C22×C3×C5—21no—
100C22×C3×C5—21no—
101C22×C3×C5—21no—
102C22×C3×C5#9511yescharacteristic
103C2×C3×D5—21no—
104C2×C3×D5—21no—
105C2×C3×D5—21no—
106C2×C3×D5—21no—
107C2×C3×D5—21no—
108C2×C3×D5—44no—
109C2×C3×D5#10812yes—
110C3×C4×C5—21no—
111C3×C4×C5—21no—
112C3×Dic5—21no—
113C3×Dic5#9912yes—
114C24×C3—51no—
115C22×C3×C4—51no—
116C22×C3×C4—51no—
117C22×C3×C4—51no—
118C22×C3×C4—51no—
119C22×C3×C4—51no—
120C22×C3×C4—202no—
121C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
122C2×C3×C8—102no—
123C2×C3×C8—202no—
124#208—202no—
125#208—202no—
126C2×C3⋊C8—21no—
127C2×C3⋊C8—102no—
128C2×C3⋊C8—101no—
129C23×C5Dic3⋊C411yescharacteristic
130C22×D5—22no—
131C22×D5—41no—
132C22×D5—41no—
133C22×D5Dic3⋊C411yescharacteristic
134C22×D5C4⋊Dic311yescharacteristic
135C2×C4×C5—41no—
136C2×C4×C5C4×Dic311yescharacteristic
137C2×C4×C5(C2×D3)⋊C411yescharacteristic
138C2×Dic5—22no—
139C2×Dic5(C2×D3)⋊C411yescharacteristic
140C2×Dic5#21711yescharacteristic
141C4×D5—22no—
142C4×D5—22no—
143C4×D5—41no—
144C4×D5—41no—
145#170—42no—
146#170—122no—
147C5×C8—121no—
148#168—121no—
149C23×C4—51no—
150C2×M16—301no—
151C2×M16—301no—
152C22×C8—52no—
153C22⋊C8—31no—
154C22⋊C8—101no—
155C22⋊C8—101no—
156C22⋊C8—152no—
157C22⋊C8—151no—
158C22⋊C8—301no—
159C22⋊C8—301no—
160C2×C3×C5—41no—
161C2×C3×C5#33811yescharacteristic
162C2×C3×C5#34111yescharacteristic
163C2×C3×C5#34211yescharacteristic
164C3×D5—22no—
165C3×D5—41no—
166C23×C3—51no—
167C23×C3—51no—
168C23×C3—102no—
169C23×C3—201no—
170C23×C3—201no—
171C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
172C2×C3×C4—41no—
173C2×C3×C4—51no—
174C2×C3×C4—51no—
175C2×C3×C4—102no—
176C2×C3×C4—102no—
177C2×C3×C4—102no—
178C2×C3×C4—201no—
179C2×C3×C4—201no—
180C2×C3×C4C4×AGL(1,𝔽5)11yescharacteristic
181C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
182C3×C8—202no—
183C3⋊C8—41no—
184C3⋊C8—201no—
185C3⋊C8—202no—
186C22×C5—21no—
187C22×C5—21no—
188C22×C5—21no—
189C22×C5C3⋊#9511yescharacteristic
190C2×D5—21no—
191C2×D5—21no—
192C2×D5—21no—
193C2×D5—21no—
194C2×D5—21no—
195C2×D5—44no—
196C2×D5#81912yes—
197C4×C5—21no—
198C4×C5—21no—
199Dic5—21no—
200Dic5#83412yes—
201C24—51no—
202C22×C4—51no—
203C22×C4—51no—
204C22×C4—51no—
205C22×C4—51no—
206C22×C4—51no—
207C22×C4—202no—
208C22×C4D3×AGL(1,𝔽5)11yescharacteristic
209M16—602no—
210M16—602no—
211C2×C8—61no—
212C2×C8—102no—
213C2×C8—202no—
214C2×C8—302no—
215C2×C8—301no—
216C3×C5#129311yescharacteristic, complemented, Hall
217C22×C3—21no—
218C22×C3—21no—
219C22×C3—21no—
220C22×C3—52no—
221C22×C3—101no—
222C22×C3—101no—
223C22×C3—101no—
224C22×C3—101no—
225C22×C3—101no—
226C22×C3—204no—
227C22×C3(C2×AGL(1,𝔽5))⋊C411yescharacteristic
228C3×C4—21no—
229C3×C4—21no—
230C3×C4—52no—
231C3×C4—101no—
232C2×C5—41no—
233C2×C5#452611yescharacteristic
234C2×C5#455211yescharacteristic
235C2×C5C3⋊#33811yescharacteristic
236D5—22no—
237D5—41no—
238C23—51no—
239C23—51no—
240C23—102no—
241C23—201no—
242C23—201no—
243C23Dic3⋊AGL(1,𝔽5)11yescharacteristic
244C2×C4—41no—
245C2×C4—51no—
246C2×C4—51no—
247C2×C4—102no—
248C2×C4—102no—
249C2×C4—102no—
250C2×C4—201no—
251C2×C4—201no—
252C2×C4Dic3×AGL(1,𝔽5)11yescharacteristic
253C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
254C8—121no—
255C8—202no—
256C8—601no—
257C8—602no—
258C2×C3—41no—
259C2×C3—102no—
260C2×C3—201no—
261C2×C3#6486611yescharacteristic
262C2×C3#6489711yescharacteristic
263C2×C3#6490111yescharacteristic
264C5#6767911yescharacteristic, complemented, Sylow
265C22—21no—
266C22—21no—
267C22—21no—
268C22—52no—
269C22—101no—
270C22—101no—
271C22—101no—
272C22—101no—
273C22—101no—
274C22—204no—
275C22(C2×AGL(1,𝔽5))⋊Dic311yescharacteristic
276C4—21no—
277C4—21no—
278C4—52no—
279C4—101no—
280C3#1059856011yescharacteristic, complemented, Sylow
281C2—41no—
282C2—102no—
283C2—201no—
284C2#1174652111yescharacteristic
285C2#1174653311yescharacteristic
286C2#1174657111yescharacteristic
subgroupG/H
centerC22(C2×AGL(1,𝔽5))⋊Dic3
commutatorC2×C3×C4×C5C42
Frattini, hypercenterC22×C4D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5#95
prime radicalC23×C3×D5Q8
cosocleC22×C3×C4×D5C22
hypocenterC3×C5#1293
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
216. C3×C5#1293semidirect
264. C5#67679semidirect
280. C3#10598560semidirect

Maximal subgroups

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

subgroupindex
#117524142
C3×D5⋊(C22⋊C8)2
#117484992
#105985603
#676795