Finite Group Databasebeta

← #14298909

Subgroups — #14298909

Order 1920.

376 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 108 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#11751824C212yesmaximal
2C8×D5×Dic3C211yesmaximal, characteristic
3#11746767C211yesmaximal, characteristic
4C3×#64896C211yesmaximal, characteristic
5#11746532C212yesmaximal
6#10603856—31nomaximal, Hall
7C2×#6758C2212yes—
8C2×C3×#700C2212yes—
9C2×C3×C8×D5C2211yescharacteristic
10C4×D5×Dic3C2211yescharacteristic
11C2×D5×C3⋊C8C2211yescharacteristic
12Dic3⋊#170—22no—
13Dic3⋊#170—22no—
14C8×Dic15C411yescharacteristic
15C5×C8×Dic3C411yescharacteristic
16#90951C411yescharacteristic
17Dic3×#168C411yescharacteristic
18#68928—51nomaximal, Hall
19#65681—32no—
20C4×C8×D5—31no—
21#64896—31no—
22#64896—32no—
23#64896D311yescharacteristic
24C2×C3×C4×D5C2311yescharacteristic
25C2×D5×Dic3Q811yescharacteristic
26C2×D5×Dic3Q811yescharacteristic
27C2×C3⋊#170—22no—
28#6758—22no—
29#6758—22no—
30C2×C3×#170—22no—
31C3×#700—22no—
32C3×#700—22no—
33C2×C3×C5×C8C2×C411yescharacteristic
34C4×Dic15C2×C411yescharacteristic
35C2×C3⋊#168C2×C411yescharacteristic
36C4×C5×Dic3C2×C411yescharacteristic
37C2×C5×C3⋊C8C2×C411yescharacteristic
38C2×C3×#168C2×C411yescharacteristic
39C3×C8×D5—22no—
40Dic3×Dic5D411yescharacteristic
41Dic3×Dic5D411yescharacteristic
42D5×C3⋊C8—22no—
43#5118—52no—
44C2×C8×Dic3—51no—
45C3×#341—51no—
46#4558—52no—
47#4552—51no—
48C2×#700—32no—
49C2×#700C2×D312yes—
50C2×C8×D5—31no—
51C2×C8×D5C2×D311yescharacteristic
52C42×D5—31no—
53C4⋊#170—62no—
54C4⋊#170—62no—
55C4×C5×C8—31no—
56C8×Dic5—31no—
57C8×Dic5—31no—
58C4×#168—31no—
59#1837—151noSylow
60C22×C3×D5C2×Q811yescharacteristic
61C2×C3×C4×C5C22×C411yescharacteristic
62C2×Dic15C4⋊C411yescharacteristic
63C2×Dic15C4⋊C411yescharacteristic
64C2×C5×Dic3C4⋊C411yescharacteristic
65C2×C5×Dic3C4⋊C411yescharacteristic
66C2×C3×Dic5C2×D411yescharacteristic
67C3×C4×D5#4112yes—
68C3×C4×D5#4112yes—
69D5×Dic3—22no—
70D5×Dic3—22no—
71C3⋊#170—42no—
72C3×#170—42no—
73C3×C5×C8—21no—
74C3⋊#168—21no—
75C3×#168—21no—
76C5×C3⋊C8—21no—
77C2×C3×M16—52no—
78C22×C3×C8—51no—
79C2×C4×Dic3—51no—
80C2×#208—52no—
81C22×C3⋊C8—51no—
82Dic3⋊C8—102no—
83Dic3⋊C8—102no—
84C8×Dic3—51no—
85C8×Dic3—51no—
86C8×Dic3—51no—
87C8×Dic3AGL(1,𝔽5)11yescharacteristic
88C2×C4×D5—31no—
89C2×C4×D5—31no—
90C2×C4×D5C22×D311yescharacteristic
91C2×#170—22no—
92C2×#170—62no—
93#700—22no—
94#700—22no—
95#700—62no—
96#700—62no—
97C2×C5×C8—31no—
98C2×C5×C8C4×D311yescharacteristic
99C42×C5—31no—
100C4×Dic5—31no—
101C4×Dic5—31no—
102C4×Dic5—31no—
103C2×#168—31no—
104C2×#168C4×D311yescharacteristic
105C8×D5—22no—
106C8×D5—62no—
107#423—152no—
108C2×C4×C8—151no—
109#341—51no—
110#341—151no—
111#341—152no—
112C22×C3×C5C2×C4⋊C411yescharacteristic
113C2×C3×D5—21no—
114C2×C3×D5—21no—
115C2×C3×D5#12512yes—
116C3×C4×C5#11711yescharacteristic
117C3×C4×C5#11711yescharacteristic
118Dic15—21no—
119Dic15—21no—
120C3×Dic5#12412yes—
121C5×Dic3#10812yes—
122C5×Dic3#10812yes—
123C22×C3×C4—51no—
124C22×Dic3—51no—
125C22×Dic3—51no—
126C3×M16—102no—
127C3×M16—102no—
128C2×C3×C8—51no—
129C2×C3×C8—102no—
130C2×C3×C8—102no—
131C2×C3×C8C2×AGL(1,𝔽5)11yescharacteristic
132C4×Dic3—51no—
133C4×Dic3—51no—
134C4×Dic3—51no—
135C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
136#208—102no—
137#208—102no—
138C2×C3⋊C8—51no—
139C2×C3⋊C8—102no—
140C2×C3⋊C8—102no—
141C2×C3⋊C8C2×AGL(1,𝔽5)11yescharacteristic
142C22×D5D3×Q811yescharacteristic
143C2×C4×C5—31no—
144C2×C4×C5—31no—
145C2×C4×C5C2×C4×D311yescharacteristic
146C2×Dic5—31no—
147C2×Dic5—31no—
148C2×Dic5D3×D411yescharacteristic
149C4×D5—62no—
150C4×D5—62no—
151C4×D5#23512yes—
152C4×D5#23712yes—
153#170—42no—
154#170—122no—
155C5×C8—21no—
156C5×C8—61no—
157#168—21no—
158#168—61no—
159C2×M16—52no—
160C2×M16—152no—
161C22×C8—51no—
162C22×C8—151no—
163C2×C42—151no—
164C4⋊C8—302no—
165C4⋊C8—302no—
166C4×C8—31no—
167C4×C8—151no—
168C4×C8—151no—
169C4×C8—151no—
170C2×C3×C5#38211yescharacteristic
171C2×C3×C5C2×#10811yescharacteristic
172C2×C3×C5C2×#10811yescharacteristic
173C3×D5—22no—
174C23×C3—51no—
175C2×C3×C4—51no—
176C2×C3×C4—52no—
177C2×C3×C4—52no—
178C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
179C2×Dic3—51no—
180C2×Dic3—51no—
181C2×Dic3—102no—
182C2×Dic3—102no—
183C2×Dic3C4⋊AGL(1,𝔽5)11yescharacteristic
184C2×Dic3C4⋊AGL(1,𝔽5)11yescharacteristic
185C3×C8—21no—
186C3×C8—101no—
187C3×C8—202no—
188C3⋊C8—21no—
189C3⋊C8—101no—
190C3⋊C8—202no—
191C22×C5D3×C4⋊C411yescharacteristic
192C2×D5—21no—
193C2×D5—21no—
194C2×D5#88912yes—
195C4×C5—32no—
196C4×C5—32no—
197C4×C5#87211yescharacteristic
198C4×C5#87711yescharacteristic
199Dic5—61no—
200Dic5—61no—
201Dic5#88512yes—
202C22×C4—51no—
203C22×C4—151no—
204C22×C4—151no—
205M16—102no—
206M16—102no—
207M16—302no—
208M16—302no—
209C2×C8—31no—
210C2×C8—51no—
211C2×C8—102no—
212C2×C8—102no—
213C2×C8—151no—
214C2×C8—302no—
215C2×C8—302no—
216C2×C8D3×AGL(1,𝔽5)11yescharacteristic
217C42—31no—
218C42—151no—
219C42—151no—
220C42—151no—
221C3×C5#183711yescharacteristic, complemented, Hall
222C22×C3—52no—
223C22×C3—101no—
224C22×C3—101no—
225C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
226C3×C4—52no—
227C3×C4#413011yescharacteristic
228C3×C4#413011yescharacteristic
229Dic3—101no—
230Dic3—101no—
231Dic3#399512yes—
232Dic3#399612yes—
233C2×C5#465011yescharacteristic
234C2×C5D3×#10811yescharacteristic
235C2×C5D3×#10811yescharacteristic
236D5—22no—
237C23—51no—
238C2×C4—31no—
239C2×C4—31no—
240C2×C4—51no—
241C2×C4—52no—
242C2×C4—52no—
243C2×C4—151no—
244C2×C4—151no—
245C2×C4—302no—
246C2×C4—302no—
247C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
248C8—21no—
249C8—61no—
250C8—101no—
251C8—202no—
252C8—301no—
253C8—602no—
254C2×C3—102no—
255C2×C3#6568911yescharacteristic
256C2×C3C2×#399511yescharacteristic
257C2×C3C2×#399611yescharacteristic
258C5#6892811yescharacteristic, complemented, Sylow
259C22—52no—
260C22—101no—
261C22—101no—
262C22D3×C4⋊AGL(1,𝔽5)11yescharacteristic
263C4—32no—
264C4—32no—
265C4—52no—
266C4—301no—
267C4—301no—
268C4#9190911yescharacteristic
269C4#9192311yescharacteristic
270C3#1060385611yescharacteristic, complemented, Sylow
271C2—102no—
272C2D3×#399511yescharacteristic
273C2D3×#399611yescharacteristic
274C2#1175174611yescharacteristic
subgroupG/H
centerC22D3×C4⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×C8C2×C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC22×C3×D5C2×Q8
cosocleC2×C3×C4×D5C23
hypercenterC2×C8D3×AGL(1,𝔽5)
hypocenterC3×C5#1837
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
221. C3×C5#1837semidirect
258. C5#68928semidirect
270. C3#10603856semidirect

Maximal subgroups

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

subgroupindex
#117518242
C8×D5×Dic32
#117467672
C3×#648962
#117465322
#106038563
#689285