Finite Group Databasebeta

← #14285886

Subgroups — #14285886

Order 1920.

336 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 118 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#11752417C211yesmaximal, characteristic
2C2×C3×C4⋊#170C211yesmaximal, characteristic
3#11748316C211yesmaximal, characteristic
4#11746515C212yesmaximal, complemented
5#11746514C212yesmaximal, complemented
6#10603898—31nomaximal, Hall
7C2×#6762—21no—
8C22×C3×#170—21no—
9C2×C3×C4×Dic5C2211yescharacteristic
10#91233—21no—
11C4⋊(C3⋊#170)C2211yescharacteristic
12C4⋊(C3⋊#170)C2211yescharacteristic
13C3×C4⋊#170—21no—
14C3×C4⋊#170C2212yes—
15#91114C411yescharacteristic
16C5×#830C411yescharacteristic
17#90982C412yes—
18Dic5×C3⋊C8C2212yes—
19#70422—51nomaximal, Hall
20#65758—31no—
21C2×C4⋊#170D311yescharacteristic
22#65007—31no—
23#64884—32no—
24#64882—32no—
25C22×C3×C4×C5C2×C411yescharacteristic
26C22×C3×Dic5D411yescharacteristic
27C22×C3×Dic5Q811yescharacteristic
28#6762—42no—
29C2×C3⋊#170—21no—
30C2×C3⋊#170—21no—
31C2×C3×#170—22no—
32C2×C3×#170—42no—
33C2×C3⋊#168C2×C412yes—
34C2×C5×C3⋊C8C2×C412yes—
35C3×C4×Dic5C2×C411yescharacteristic
36C3×C4×Dic5D411yescharacteristic
37C3×C4×Dic5Q811yescharacteristic
38C3×C4×Dic5C2311yescharacteristic
39C2×C3×C4⋊C8—51no—
40#4925—51no—
41#4924—51no—
42#4479—52no—
43#4479—52no—
44C2×#704—61no—
45C22×#170—21no—
46C2×C4×Dic5C2×D311yescharacteristic
47#4004—61no—
48C4⋊#170—21no—
49C4⋊#170—31no—
50C4⋊#170—31no—
51C4⋊#170C2×D312yes—
52C5×C22⋊C8—31no—
53C22⋊#168—31no—
54#3946—32no—
55C8×Dic5—32no—
56#1571—151noSylow
57C23×C3×C5C4⋊C411yescharacteristic
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C4⋊C411yescharacteristic
60C2×C3×C4×C5C22×C411yescharacteristic
61C2×C3×Dic5—41no—
62C2×C3×Dic5C4⋊C411yescharacteristic
63C2×C3×Dic5C4⋊C411yescharacteristic
64C2×C3×Dic5D812yes—
65C2×C3×Dic5Q1612yes—
66C2×C3×Dic5C2×D411yescharacteristic
67C2×C3×Dic5C2×Q811yescharacteristic
68C3⋊#170—41no—
69C3⋊#170—41no—
70C3×#170—42no—
71C3⋊#168—22no—
72C5×C3⋊C8—22no—
73C22×C3×C8—101no—
74C2×C3×C42—51no—
75C2×#208—101no—
76C3×C4⋊C8—52no—
77C3×C4⋊C8—101no—
78#830—51no—
79#830AGL(1,𝔽5)11yescharacteristic
80C4⋊(C3⋊C8)—52no—
81C4⋊(C3⋊C8)—51no—
82C4⋊(C3⋊C8)—51no—
83C4⋊(C3⋊C8)—101no—
84C4×C3⋊C8—52no—
85C22×C4×C5C4×D311yescharacteristic
86C22×Dic5Dic611yescharacteristic
87C22×Dic5#6711yescharacteristic
88#704—122no—
89C2×#170—22no—
90C2×#170—42no—
91C2×#170—61no—
92C2×#170—61no—
93C2×C5×C8—32no—
94C4×Dic5Dic611yescharacteristic
95C4×Dic5C4×D311yescharacteristic
96C4×Dic5#6711yescharacteristic
97C4×Dic5C22×D311yescharacteristic
98C2×#168—32no—
99#431—151no—
100#423—151no—
101C2×C4⋊C8—51no—
102#335—152no—
103#335—152no—
104C22×C3×C5—21no—
105C22×C3×C5—21no—
106C22×C3×C5#10712yes—
107C22×C3×C5C2×C4⋊C411yescharacteristic
108C3×C4×C5—21no—
109C3×C4×C5#13112yes—
110C3×Dic5—21no—
111C3×Dic5—21no—
112C3×Dic5#10712yes—
113C3×Dic5C2×D811yescharacteristic
114C3×Dic5C2×Q1611yescharacteristic
115C22×C3×C4—51no—
116C22×C3×C4—51no—
117C22×C3×C4C2×AGL(1,𝔽5)11yescharacteristic
118C2×C3×C8—102no—
119C2×C3×C8—202no—
120C3×C42—51no—
121C3×C42—51no—
122C3×C42—51no—
123C3×C42—51no—
124#208—202no—
125C2×C3⋊C8—52no—
126C2×C3⋊C8—101no—
127C2×C3⋊C8—101no—
128C2×C3⋊C8C2×AGL(1,𝔽5)12yes—
129C23×C5Dic3⋊C411yescharacteristic
130C2×C4×C5—22no—
131C2×C4×C5Dic3⋊C411yescharacteristic
132C2×C4×C5C2×C4×D311yescharacteristic
133C2×Dic5—41no—
134C2×Dic5Dic3⋊C411yescharacteristic
135C2×Dic5Dic3⋊C411yescharacteristic
136C2×Dic5#21312yes—
137C2×Dic5#21612yes—
138C2×Dic5C2×Dic611yescharacteristic
139C2×Dic5C2×#6711yescharacteristic
140#170—42no—
141#170—121no—
142#170—121no—
143C5×C8—62no—
144#168—62no—
145C2×M16—301no—
146C22×C8—101no—
147C2×C42—51no—
148C4⋊C8—52no—
149C4⋊C8—101no—
150C4⋊C8—152no—
151C4⋊C8—151no—
152C4⋊C8—151no—
153C4⋊C8—301no—
154C22⋊C8—31no—
155C22⋊C8—151no—
156C4×C8—152no—
157C2×C3×C5—22no—
158C2×C3×C5#42411yescharacteristic
159C2×C3×C5C2×#10711yescharacteristic
160C2×C3×C5#43011yescharacteristic
161C23×C3C4⋊AGL(1,𝔽5)11yescharacteristic
162C2×C3×C4—22no—
163C2×C3×C4—51no—
164C2×C3×C4—51no—
165C2×C3×C4—52no—
166C2×C3×C4—52no—
167C2×C3×C4—51no—
168C2×C3×C4—51no—
169C2×C3×C4—201no—
170C2×C3×C4C4⋊AGL(1,𝔽5)11yescharacteristic
171C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
172C3×C8—202no—
173C3⋊C8—22no—
174C3⋊C8—102no—
175C3⋊C8—201no—
176C3⋊C8—201no—
177C22×C5—21no—
178C22×C5—21no—
179C22×C5#80712yes—
180C22×C5C2×Dic3⋊C411yescharacteristic
181C4×C5—21no—
182C4×C5#90112yes—
183Dic5—21no—
184Dic5—21no—
185Dic5#80712yes—
186Dic5C2×#21311yescharacteristic
187Dic5C2×#21611yescharacteristic
188C22×C4—51no—
189C22×C4—51no—
190C22×C4D3×AGL(1,𝔽5)11yescharacteristic
191M16—602no—
192C2×C8—32no—
193C2×C8—102no—
194C2×C8—152no—
195C2×C8—202no—
196C2×C8—301no—
197C2×C8—301no—
198C42—51no—
199C42—51no—
200C42—51no—
201C42—51no—
202C3×C5#157111yescharacteristic, complemented, Hall
203C22×C3—21no—
204C22×C3—21no—
205C22×C3#399412yes—
206C22×C3C2×C4⋊AGL(1,𝔽5)11yescharacteristic
207C3×C4—21no—
208C3×C4—52no—
209C3×C4—51no—
210C3×C4—51no—
211C3×C4—101no—
212C3×C4—101no—
213C3×C4#413112yes—
214C2×C5—22no—
215C2×C5C2×#80711yescharacteristic
216C2×C5#510211yescharacteristic
217C2×C5#512411yescharacteristic
218C23Dic3⋊AGL(1,𝔽5)11yescharacteristic
219C2×C4—22no—
220C2×C4—51no—
221C2×C4—51no—
222C2×C4—52no—
223C2×C4—52no—
224C2×C4—51no—
225C2×C4—51no—
226C2×C4—201no—
227C2×C4Dic3⋊AGL(1,𝔽5)11yescharacteristic
228C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
229C8—62no—
230C8—202no—
231C8—302no—
232C8—601no—
233C8—601no—
234C2×C3—22no—
235C2×C3#6569611yescharacteristic
236C2×C3C2×#399411yescharacteristic
237C2×C3#6572911yescharacteristic
238C5#7042211yescharacteristic, complemented, Sylow
239C22—21no—
240C22—21no—
241C22#9116012yes—
242C22C2×Dic3⋊AGL(1,𝔽5)11yescharacteristic
243C4—21no—
244C4—51no—
245C4—52no—
246C4—51no—
247C4—101no—
248C4—101no—
249C4#9192712yes—
250C3#1060389811yescharacteristic, complemented, Sylow
251C2—22no—
252C2C2×#9116011yescharacteristic
253C2#1175173211yescharacteristic
254C2#1175201111yescharacteristic
subgroupG/H
centerC22C2×Dic3⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC22×C3×C4×C5C2×C4
socleC22×C3×C5C2×C4⋊C4
prime radicalC23×C3×C5C4⋊C4
cosocleC3×C4×Dic5C23
hypercenterC22×C4D3×AGL(1,𝔽5)
hypocenterC3×C5#1571
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
4. #11746515C2semidirect
5. #11746514C2semidirect
202. C3×C5#1571semidirect
238. C5#70422semidirect
250. C3#10603898semidirect

Maximal subgroups

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

subgroupindex
#117524172
C2×C3×C4⋊#1702
#117483162
#117465152
#117465142
#106038983
#704225