Finite Group Databasebeta

← #14307469

Subgroups — #14307469

Order 1920.

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

normal subgroups only

This group has 488 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#11752498C211yesmaximal, characteristic
2#11752340C211yesmaximal, characteristic
3C3×#65686C211yesmaximal, characteristic
4#11746526C214yesmaximal
5#10604588—31nomaximal, Hall
6C2×#6758C2212yes—
7C2×C3×C4×AGL(1,𝔽5)C2212yes—
8#91759C411yescharacteristic, complemented
9C5×#870C411yescharacteristic, complemented
10C3×C42×D5C2211yescharacteristic
11#91468C412yescomplemented
12#91358C2212yes—
13#91349—22no—
14#91323—22no—
15C4⋊(C3⋊#170)—22no—
16C3×(C2×AGL(1,𝔽5))⋊C4—22no—
17#69441—51nomaximal, Hall
18#66022—31no—
19#65686D311yescharacteristic
20#65681—31no—
21#64875—34no—
22C22×C3×AGL(1,𝔽5)—22no—
23C2×C3×C4×D5D412yes—
24C2×C3×C4×D5C2311yescharacteristic
25C2×#1204—22no—
26C2×C3⋊#170—22no—
27#6758—24no—
28C3×C4×AGL(1,𝔽5)—22no—
29C3×C4×AGL(1,𝔽5)Q814yescomplemented
30C3×C42×C5C2×C411yescharacteristic
31C4⋊Dic15C2×C412yes—
32#6712—22no—
33C5×C4⋊Dic3C2×C412yes—
34C5×Dic3⋊C4—22no—
35C3×C4×Dic5C2×C411yescharacteristic
36C3×C4×Dic5D412yes—
37#6668—22no—
38#6665—22no—
39Dic3×Dic5—22no—
40#5470—51no—
41C3×#376—51no—
42#4924—51no—
43#4523—54no—
44C2×C4×AGL(1,𝔽5)C2×D312yes—
45C2×#700—32no—
46C5×#125—31no—
47#4042—62no—
48#4038—32no—
49#4034—32no—
50#4033—62no—
51C42×D5C2×D311yescharacteristic
52#4016—31no—
53(C2×AGL(1,𝔽5))⋊C4—22no—
54C4⋊#170—62no—
55#1995—151noSylow
56C22×C3×D5C2×D411yescharacteristic
57C2×C3×AGL(1,𝔽5)—24no—
58C2×C3×AGL(1,𝔽5)—44no—
59C2×C3×C4×C5C22⋊C412yes—
60C2×C3×C4×C5C22×C411yescharacteristic
61C2×Dic15—22no—
62C2×C5×Dic3—22no—
63C2×C3×Dic5C22⋊C412yes—
64C2×C3×Dic5C2×D411yescharacteristic
65C3×C4×D5—42no—
66C3×C4×D5C2×Q812yes—
67C3×C4×D5#4112yes—
68#1204—44no—
69C3⋊#170—42no—
70C2×C3×C42—51no—
71C2×C3×C42—52no—
72#926—52no—
73#924—102no—
74C2×#208—52no—
75#870—51no—
76#870AGL(1,𝔽5)11yescharacteristic, complemented
77#869—52no—
78C4×Dic6—102no—
79C3×#95—102no—
80C4⋊(C3⋊C8)—102no—
81C22×AGL(1,𝔽5)—22no—
82C2×C4×D5#6712yes—
83C2×C4×D5C22×D311yescharacteristic
84C2×Dic10—62no—
85C2×#170—62no—
86C4×AGL(1,𝔽5)—22no—
87C4×AGL(1,𝔽5)Dic614yescomplemented
88#700—64no—
89C5×C4⋊C4—32no—
90C5×C4⋊C4—62no—
91C42×C5C4×D311yescharacteristic
92#685—62no—
93C4⋊Dic5—32no—
94#683—62no—
95#683—62no—
96C4×Dic5—62no—
97C4×Dic5C4×D311yescharacteristic
98C4×Dic5D1212yes—
99#533—151no—
100#423—151no—
101#376—51no—
102#339—154no—
103C22×C3×C5C2×C22⋊C411yescharacteristic
104C2×C3×D5—22no—
105C2×C3×D5C22⋊Q812yes—
106C3×AGL(1,𝔽5)—44no—
107C3×C4×C5—22no—
108C3×C4×C5C4×Q812yes—
109Dic15—42no—
110C3×Dic5—22no—
111C3×Dic5#12411yescharacteristic
112C3×Dic5C4⋊Q811yescharacteristic
113C5×Dic3—42no—
114C22×C3×C4—51no—
115C22×C3×C4—52no—
116C22×C3×C4—102no—
117C2×Dic6—102no—
118C3×C42—52no—
119C3×C42—51no—
120C3×C42—54no—
121C3×C42—102no—
122C3×C42C2×AGL(1,𝔽5)11yescharacteristic
123#217—102no—
124C4⋊Dic3—52no—
125C4⋊Dic3—102no—
126C4⋊Dic3C2×AGL(1,𝔽5)12yes—
127Dic3⋊C4—22no—
128Dic3⋊C4—102no—
129C4×Dic3—102no—
130#208—104no—
131C2×C3⋊C8—102no—
132C22×D5C2×#6711yescharacteristic
133C2×AGL(1,𝔽5)—24no—
134C2×AGL(1,𝔽5)—44no—
135C2×C4×C5—62no—
136C2×C4×C5(C2×D3)⋊C412yes—
137C2×C4×C5C2×C4×D311yescharacteristic
138C2×Dic5—62no—
139C2×Dic5(C2×D3)⋊C412yes—
140C2×Dic5C2×D1211yescharacteristic
141C4×D5—42no—
142C4×D5C2×Dic612yes—
143C4×D5#23512yes—
144Dic10—124no—
145#170—122no—
146C2×M16—152no—
147C4⋊Q8—152no—
148#125—31no—
149#125—151no—
150C22⋊Q8—302no—
151C4×Q8—302no—
152#117—152no—
153C2×C42—51no—
154C2×C42—52no—
155C4⋊C8—302no—
156#95—102no—
157C2×C3×C5#39111yescharacteristic
158C2×C3×C5#42112yes—
159C3×D5—22no—
160C23×C3—51no—
161C2×C3×C4—51no—
162C2×C3×C4—52no—
163C2×C3×C4—52no—
164C2×C3×C4—52no—
165C2×C3×C4—104no—
166C2×C3×C4—202no—
167C2×C3×C4—204no—
168C2×C3×C4C22⋊AGL(1,𝔽5)12yes—
169C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
170C2×Dic3—22no—
171C2×Dic3—102no—
172Dic6—204no—
173C3⋊C8—202no—
174C22×C5C2×(C2×D3)⋊C411yescharacteristic
175C2×D5—22no—
176C2×D5#92412yes—
177AGL(1,𝔽5)—44no—
178C4×C5—22no—
179C4×C5—122no—
180C4×C5C4×Dic612yes—
181Dic5—22no—
182Dic5—122no—
183Dic5#86911yescharacteristic
184Dic5#87511yescharacteristic
185C2×Q8—302no—
186C22×C4—51no—
187C22×C4—52no—
188C22×C4—102no—
189M16—304no—
190C2×C8—302no—
191C4⋊C4—32no—
192C4⋊C4—62no—
193C4⋊C4—152no—
194C4⋊C4—302no—
195C4⋊C4—302no—
196C22⋊C4—302no—
197C42—52no—
198C42—51no—
199C42—54no—
200C42—102no—
201C42—302no—
202C42D3×AGL(1,𝔽5)11yescharacteristic
203C3×C5#199511yescharacteristic, complemented, Hall
204C22×C3—52no—
205C22×C3—102no—
206C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
207C3×C4—22no—
208C3×C4—51no—
209C3×C4—51no—
210C3×C4—102no—
211C3×C4—204no—
212C3×C4Q8×AGL(1,𝔽5)12yes—
213Dic3—42no—
214Dic3—202no—
215C2×C5#492911yescharacteristic
216C2×C5#500512yes—
217D5—22no—
218C23—51no—
219Q8—604no—
220C2×C4—51no—
221C2×C4—52no—
222C2×C4—52no—
223C2×C4—52no—
224C2×C4—62no—
225C2×C4—104no—
226C2×C4—202no—
227C2×C4—204no—
228C2×C4—302no—
229C2×C4(C2×D3)⋊AGL(1,𝔽5)12yes—
230C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
231C8—602no—
232C2×C3—102no—
233C2×C3(C2×AGL(1,𝔽5))⋊Q811yescharacteristic
234C2×C3#6579512yes—
235C5#6944111yescharacteristic, complemented, Sylow
236C22—52no—
237C22—102no—
238C22C2×(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
239C4—22no—
240C4—51no—
241C4—51no—
242C4—102no—
243C4—122no—
244C4—204no—
245C4—602no—
246C4AGL(1,𝔽5)×Dic612yes—
247C3#1060458811yescharacteristic, complemented, Sylow
248C2—102no—
249C2#1175172012yes—
250C2#1175174911yescharacteristic
subgroupG/H
centerC22C2×(C2×D3)⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC3×C42×C5C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×D5C2×D4
cosocleC2×C3×C4×D5C23
hypercenterC42D3×AGL(1,𝔽5)
hypocenterC3×C5#1995
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
8. #91759C4semidirect
9. C5×#870C4semidirect
11. #91468C4semidirect
29. C3×C4×AGL(1,𝔽5)Q8semidirect
76. #870AGL(1,𝔽5)semidirect
87. C4×AGL(1,𝔽5)Dic6semidirect
203. C3×C5#1995semidirect
235. C5#69441semidirect
247. C3#10604588semidirect

Maximal subgroups

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

subgroupindex
#117524982
#117523402
C3×#656862
#117465262
#106045883
#694415