Finite Group Databasebeta

← #14284362

Subgroups — #14284362

Order 1920.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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
1D15×#125C211yesmaximal, characteristic
2#11750806C212yesmaximal
3C3×C5×#330C211yesmaximal, characteristic, complemented
4#11746364C211yesmaximal, characteristic, complemented
5#11746286C212yesmaximal, complemented
6#10599160—31nomaximal, Hall
7C3×C5×#125C2211yescharacteristic
8C4⋊C4×D15—22no—
9C4⋊C4×D15C412yes—
10#91779C412yes—
11#91778—22no—
12C42×D15C2211yescharacteristic
13#91759C2211yescharacteristic
14C3×C5×#97C2212yes—
15#91104—22no—
16#91098—22no—
17#91087C2212yes—
18#68367—51nomaximal, Hall
19D5×#125—31no—
20#64994—32no—
21C5×#330D311yescharacteristic, complemented
22#64763—31no—
23#64685—32no—
24C2×C4×D15—22no—
25C2×C4×D15C2×C411yescharacteristic
26C2×C4×D15D412yes—
27C2×C3×C5×C8—22no—
28C3×C5×C4⋊C4—22no—
29C3×C5×C4⋊C4C2×C412yes—
30C3×C42×C5C2311yescharacteristic
31C4⋊Dic15—22no—
32C4⋊Dic15C2×C412yes—
33#6712—22no—
34#6712—22no—
35#6712—22no—
36C4×Dic15C2×C411yescharacteristic
37C4×Dic15D412yes—
38C2×C3⋊#168—22no—
39D3×#125—51no—
40#4705—52no—
41C3×#330D511yescharacteristic, complemented
42#4543—51no—
43#4465—52no—
44C5×#125C2×D311yescharacteristic
45D5×C4⋊C4—32no—
46D5×C4⋊C4—62no—
47#4036—32no—
48#4035—62no—
49C42×D5—31no—
50#4016—31no—
51C5×#97C2×D312yes—
52#3952—62no—
53#3946—62no—
54#3935—32no—
55#1534—151noSylow
56C22×D15C22⋊C411yescharacteristic
57C2×C3×C4×C5—22no—
58C2×C3×C4×C5C22×C411yescharacteristic
59C2×C3×C4×C5C2×D412yes—
60C2×Dic15—22no—
61C2×Dic15C22⋊C412yes—
62C2×Dic15C22⋊C411yescharacteristic
63C4×D15—22no—
64C4×D15—42no—
65C4×D15—44no—
66C3×C5×C8—42no—
67C3⋊#168—42no—
68C3×#125C2×D511yescharacteristic
69D3×C4⋊C4—52no—
70D3×C4⋊C4—102no—
71#890—52no—
72#889—102no—
73C42×D3—51no—
74#870—51no—
75C3×#97C2×D512yes—
76(C2×D3)⋊C8—102no—
77Dic3⋊C8—102no—
78#803—52no—
79C2×C4×D5—31no—
80C2×C4×D5—32no—
81C2×C4×D5—62no—
82C2×C5×C8—22no—
83C5×C4⋊C4—22no—
84C5×C4⋊C4C4×D312yes—
85C42×C5C22×D311yescharacteristic
86C4⋊Dic5—32no—
87C4⋊Dic5—62no—
88#683—62no—
89#683—62no—
90#683—62no—
91C4×Dic5—31no—
92C4×Dic5—32no—
93C2×#168—62no—
94C2×#125—151no—
95#432—152no—
96#330—151no—
97#330—152no—
98#330D1511yescharacteristic, complemented
99C22×C3×C5C2×C22⋊C411yescharacteristic
100C2×D15—22no—
101C2×D15#10112yes—
102C3×C4×C5—21no—
103C3×C4×C5—22no—
104C3×C4×C5—42no—
105Dic15—21no—
106Dic15—22no—
107Dic15—42no—
108C2×C4×D3—51no—
109C2×C4×D3—52no—
110C2×C4×D3—102no—
111C2×C3×C8—22no—
112C3×C4⋊C4—22no—
113C3×C4⋊C4C4×D512yes—
114C3×C42C22×D511yescharacteristic
115C4⋊Dic3—52no—
116C4⋊Dic3—102no—
117Dic3⋊C4—102no—
118Dic3⋊C4—102no—
119Dic3⋊C4—102no—
120C4×Dic3—51no—
121C4×Dic3—52no—
122C2×C3⋊C8—102no—
123C22×D5—31no—
124C2×C4×C5—22no—
125C2×C4×C5C2×C4×D311yescharacteristic
126C2×C4×C5D3×D412yes—
127C2×Dic5—31no—
128C2×Dic5—32no—
129C2×Dic5—62no—
130C4×D5—62no—
131C4×D5—122no—
132C4×D5—124no—
133C5×C8—42no—
134#168—122no—
135#125—152no—
136#125—151no—
137#125—302no—
138#125C2×D1511yescharacteristic
139C2×C4⋊C4—152no—
140C2×C4⋊C4—302no—
141C2×C42—151no—
142C4⋊C8—302no—
143C22⋊C8—302no—
144#97—152no—
145#97C2×D1512yes—
146C2×C3×C5C2×#10111yescharacteristic
147C2×C3×C5#42112yes—
148D15—22no—
149C22×D3—51no—
150C2×C3×C4—22no—
151C2×C3×C4C2×C4×D511yescharacteristic
152C2×C3×C4D4×D512yes—
153C2×Dic3—51no—
154C2×Dic3—52no—
155C2×Dic3—102no—
156C4×D3—102no—
157C4×D3—202no—
158C4×D3—204no—
159C3×C8—42no—
160C3⋊C8—202no—
161C22×C5D3×C22⋊C411yescharacteristic
162C2×D5—32no—
163C2×D5—62no—
164C4×C5—21no—
165C4×C5—22no—
166C4×C5—42no—
167Dic5—61no—
168Dic5—62no—
169Dic5—122no—
170C22×C4—151no—
171C22×C4—152no—
172C22×C4—302no—
173C2×C8—22no—
174C2×C8—302no—
175C4⋊C4—22no—
176C4⋊C4—152no—
177C4⋊C4—302no—
178C4⋊C4—302no—
179C4⋊C4—302no—
180C4⋊C4—302no—
181C4⋊C4C4×D1512yes—
182C42—151no—
183C42—152no—
184C42C22×D1511yescharacteristic
185C3×C5#153411yescharacteristic, complemented, Hall
186C22×C3D5×C22⋊C411yescharacteristic
187C2×D3—52no—
188C2×D3—102no—
189C3×C4—21no—
190C3×C4—22no—
191C3×C4—42no—
192Dic3—101no—
193Dic3—102no—
194Dic3—202no—
195C2×C5D3×#10111yescharacteristic
196C2×C5#482112yes—
197D5—62no—
198C23—151no—
199C2×C4—22no—
200C2×C4—152no—
201C2×C4—151no—
202C2×C4—302no—
203C2×C4—302no—
204C2×C4—602no—
205C2×C4—604no—
206C2×C4C2×C4×D1511yescharacteristic
207C2×C4D4×D1512yes—
208C8—42no—
209C8—602no—
210C2×C3D5×#10111yescharacteristic
211C2×C3#6511012yes—
212D3—102no—
213C5#6836711yescharacteristic, complemented, Sylow
214C22—152no—
215C22—302no—
216C22C22⋊C4×D1511yescharacteristic
217C4—22no—
218C4—21no—
219C4—42no—
220C4—302no—
221C4—301no—
222C4—602no—
223C3#1059916011yescharacteristic, complemented, Sylow
224C2—302no—
225C2D15×#10111yescharacteristic
226C2#1175092212yes—
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#330C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenter#330D15
hypocenterC3×C5#1534
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. C3×C5×#330C2semidirect
4. #11746364C2semidirect
5. #11746286C2semidirect
21. C5×#330D3semidirect
41. C3×#330D5semidirect
98. #330D15semidirect
185. C3×C5#1534semidirect
213. C5#68367semidirect
223. C3#10599160semidirect

Maximal subgroups

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

subgroupindex
D15×#1252
#117508062
C3×C5×#3302
#117463642
#117462862
#105991603
#683675