Finite Group Databasebeta

← #14284722

Subgroups — #14284722

Order 1920.

492 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 102 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#11756475C211yesmaximal, characteristic
2#11746859C212yesmaximal, complemented
3C5×#4544C211yesmaximal, characteristic, complemented
4C3×#64764C211yesmaximal, characteristic, complemented
5#11745863C212yesmaximal, complemented
6#10599175—31nomaximal, Hall
7C2×#6819C412yes—
8C3×C5×#127C2211yescharacteristic
9#91827—22no—
10#91825C412yes—
11D4×Dic15—22no—
12C42×D15C2211yescharacteristic
13#91758C2211yescharacteristic
14C5×C4⋊(C3⋊C8)C2212yes—
15C3×C4⋊#168C2212yes—
16#90957—22no—
17#90951—22no—
18#68382—51nomaximal, Hall
19#66050—31no—
20#65122—32no—
21C5×#331—31no—
22#64764D311yescharacteristic, complemented
23#64701—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4C2×C412yes—
26C2×#1220—22no—
27C22×Dic15—22no—
28#6819—44no—
29C2×C4×D15C2×C411yescharacteristic
30C2×C4×D15D412yes—
31C2×Dic30C2×C412yes—
32C3×C42×C5C2311yescharacteristic
33#6719—24no—
34C4⋊Dic15—22no—
35C4×Dic15C2×C411yescharacteristic
36C4×Dic15D412yes—
37C2×C5×C3⋊C8—22no—
38C2×C3×#168—22no—
39#5716—51no—
40#4833—52no—
41C3×#331—51no—
42#4544D511yescharacteristic, complemented
43#4481—52no—
44C2×#711—32no—
45C5×#127C2×D311yescharacteristic
46#4084—62no—
47#4082—32no—
48D4×Dic5—62no—
49C42×D5—31no—
50#4015—31no—
51C5×C4⋊C8—32no—
52#3952—62no—
53C8×Dic5—62no—
54C4⋊#168C2×D312yes—
55#1543—151noSylow
56C23×C3×C5—22no—
57C22×D15C22⋊C411yescharacteristic
58C3×C5×D4—42no—
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C2×C3×C4×C5C22×C411yescharacteristic
62C2×C3×C4×C5C2×D412yes—
63#1220—44no—
64C2×Dic15—22no—
65C2×Dic15—44no—
66C2×Dic15C22⋊C412yes—
67C2×Dic15C22⋊C411yescharacteristic
68C4×D15—22no—
69C4×D15—22no—
70C4×D15—22no—
71Dic30—42no—
72C3×#168—42no—
73C5×C3⋊C8—42no—
74C2×#237—52no—
75C3×#127C2×D511yescharacteristic
76#938—102no—
77#936—52no—
78D4×Dic3—102no—
79C42×D3—51no—
80#869—51no—
81C3×C4⋊C8—52no—
82(C2×D3)⋊C8—102no—
83C8×Dic3—102no—
84C4⋊(C3⋊C8)C2×D512yes—
85C2×C5×D4—22no—
86C2×C5×D4C4×D312yes—
87C2×C22⋊D5—62no—
88C22×Dic5—62no—
89#711—124no—
90C2×C4×D5—31no—
91C2×C4×D5—32no—
92C2×Dic10—32no—
93C2×C5×C8—62no—
94C42×C5C22×D311yescharacteristic
95C22⋊Dic5—64no—
96C4⋊Dic5—62no—
97C4×Dic5—31no—
98C4×Dic5—32no—
99C2×#168—22no—
100#532—151no—
101#431—152no—
102#333—152no—
103#331—31no—
104#331—51no—
105C22×C3×C5—42no—
106C22×C3×C5—44no—
107C22×C3×C5C2×C22⋊C411yescharacteristic
108C2×D15—21no—
109C2×D15—22no—
110C3×C4×C5—21no—
111C3×C4×C5#13512yes—
112C3×C4×C5#13512yes—
113Dic15—22no—
114Dic15—42no—
115Dic15#10012yes—
116C2×C3×D4—22no—
117C2×C3×D4C4×D512yes—
118C2×#67—102no—
119C22×Dic3—102no—
120#237—204no—
121C2×C4×D3—51no—
122C2×C4×D3—52no—
123C2×Dic6—52no—
124C2×C3×C8—102no—
125C3×C42C22×D511yescharacteristic
126#217—104no—
127C4⋊Dic3—102no—
128C4×Dic3—51no—
129C4×Dic3—52no—
130C2×C3⋊C8—22no—
131C23×C5—22no—
132C22×D5—31no—
133C5×D4—42no—
134C5×D4—42no—
135C5×D4—42no—
136C2×C4×C5C2×C4×D311yescharacteristic
137C2×C4×C5D3×D412yes—
138C22⋊D5—124no—
139C2×Dic5—31no—
140C2×Dic5—32no—
141C2×Dic5—62no—
142C2×Dic5—124no—
143C4×D5—62no—
144C4×D5—62no—
145C4×D5—62no—
146Dic10—122no—
147C5×C8—122no—
148#168—42no—
149C2×#41—152no—
150C4⋊Q8—151no—
151#127D3×D511yescharacteristic
152#124—152no—
153#121—302no—
154C4×D4—302no—
155C2×C42—151no—
156C4⋊C8—32no—
157C4⋊C8—52no—
158C22⋊C8—302no—
159C4×C8—302no—
160C2×C3×C5—82no—
161C2×C3×C5C2×#10011yescharacteristic
162C2×C3×C5#41612yes—
163D15—41no—
164C23×C3—22no—
165C22×D3—51no—
166C3×D4—42no—
167C3×D4—42no—
168C3×D4—42no—
169C2×C3×C4C2×C4×D511yescharacteristic
170C2×C3×C4D4×D512yes—
171#67—204no—
172C2×Dic3—51no—
173C2×Dic3—52no—
174C2×Dic3—102no—
175C2×Dic3—204no—
176C4×D3—102no—
177C4×D3—102no—
178C4×D3—102no—
179Dic6—202no—
180C3×C8—202no—
181C3⋊C8—42no—
182C22×C5—42no—
183C22×C5—44no—
184C22×C5D3×C22⋊C411yescharacteristic
185C2×D5—61no—
186C2×D5—62no—
187C4×C5—21no—
188C4×C5#91212yes—
189C4×C5#91612yes—
190Dic5—32no—
191Dic5—62no—
192Dic5—122no—
193#41—604no—
194C2×Q8—152no—
195C2×D4—22no—
196C2×D4—302no—
197C2×D4#120012yes—
198C22×C4—151no—
199C22×C4—152no—
200C22×C4—302no—
201C2×C8—62no—
202C2×C8—102no—
203C4⋊C4—302no—
204C22⋊C4—304no—
205C42—151no—
206C42—152no—
207C42C2×D3×D511yescharacteristic
208C3×C5#154311yescharacteristic, complemented, Hall
209C22×C3—42no—
210C22×C3—44no—
211C22×C3D5×C22⋊C411yescharacteristic
212C2×D3—101no—
213C2×D3—102no—
214C3×C4—21no—
215C3×C4#405812yes—
216C3×C4#406212yes—
217Dic3—52no—
218Dic3—102no—
219Dic3—202no—
220C2×C5—82no—
221C2×C5D3×#10011yescharacteristic
222C2×C5#477212yes—
223D5—121no—
224C23—22no—
225C23—151no—
226Q8—602no—
227D4—42no—
228D4—42no—
229D4—42no—
230D4—604no—
231C2×C4—151no—
232C2×C4—152no—
233C2×C4—302no—
234C2×C4—302no—
235C2×C4—302no—
236C2×C4—302no—
237C2×C4—604no—
238C2×C4C2×#120011yescharacteristic
239C2×C4#679012yes—
240C8—122no—
241C8—202no—
242C2×C3—82no—
243C2×C3D5×#10011yescharacteristic
244C2×C3#6506112yes—
245D3—201no—
246C5#6838211yescharacteristic, complemented, Sylow
247C22—42no—
248C22—44no—
249C22—301no—
250C22—302no—
251C22#9156111yescharacteristic
252C4—21no—
253C4—152no—
254C4—302no—
255C4—602no—
256C4#9149712yes—
257C4#9149912yes—
258C3#1059917511yescharacteristic, complemented, Sylow
259C2—82no—
260C2—601no—
261C2#1174896912yes—
262C2#1174912711yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#127C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756475C2
cosocleC3×C42×C5C23
hypercenter#127D3×D5
hypocenterC3×C5#1543
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
2. #11746859C2semidirect
3. C5×#4544C2semidirect
4. C3×#64764C2semidirect
5. #11745863C2semidirect
22. #64764D3semidirect
42. #4544D5semidirect
208. C3×C5#1543semidirect
246. C5#68382semidirect
258. C3#10599175semidirect

Maximal subgroups

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

subgroupindex
#117564752
#117468592
C5×#45442
C3×#647642
#117458632
#105991753
#683825