Finite Group Databasebeta

← #14285433

Subgroups — #14285433

Order 1920.

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

normal subgroups only

This group has 508 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#11747015C212yesmaximal, complemented
3C5×#4544C211yesmaximal, characteristic, complemented
4C3×#64764C211yesmaximal, characteristic, complemented
5#11745863C212yesmaximal, complemented
6#10599182—31nomaximal, Hall
7C2×#6819C412yes—
8C3×C5×#127C2211yescharacteristic
9#91827—22no—
10#91825C412yes—
11D4×Dic15—22no—
12C42×D15C2211yescharacteristic
13#91758C2211yescharacteristic
14C2×#6651—22no—
15C5×C4⋊(C3⋊C8)C2212yes—
16C3×C4⋊#168C2212yes—
17#90983—22no—
18#68389—51nomaximal, Hall
19#66050—31no—
20#65126—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#6651—44no—
40#5716—51no—
41#4837—52no—
42C3×#331—51no—
43#4544D511yescharacteristic, complemented
44#4481—52no—
45C2×#711—32no—
46C5×#127C2×D311yescharacteristic
47#4084—62no—
48#4082—32no—
49D4×Dic5—62no—
50C2×#676—62no—
51C42×D5—31no—
52#4015—31no—
53C5×C4⋊C8—32no—
54#3946—62no—
55C4⋊#168C2×D312yes—
56#1560—151noSylow
57C23×C3×C5—22no—
58C22×D15C22⋊C411yescharacteristic
59C3×C5×D4—42no—
60C3×C5×D4—42no—
61C3×C5×D4—42no—
62C2×C3×C4×C5C22×C411yescharacteristic
63C2×C3×C4×C5C2×D412yes—
64#1220—44no—
65C2×Dic15—22no—
66C2×Dic15—44no—
67C2×Dic15C22⋊C412yes—
68C2×Dic15C22⋊C411yescharacteristic
69C4×D15—22no—
70C4×D15—22no—
71C4×D15—22no—
72Dic30—42no—
73C3×#168—42no—
74C5×C3⋊C8—42no—
75C2×#237—52no—
76C3×#127C2×D511yescharacteristic
77#938—102no—
78#936—52no—
79D4×Dic3—102no—
80C2×ΓL(1,𝔽25)—102no—
81C42×D3—51no—
82#869—51no—
83C3×C4⋊C8—52no—
84Dic3⋊C8—102no—
85C4⋊(C3⋊C8)C2×D512yes—
86C2×C5×D4—22no—
87C2×C5×D4C4×D312yes—
88C2×C22⋊D5—62no—
89C22×Dic5—62no—
90#711—124no—
91C2×C4×D5—31no—
92C2×C4×D5—32no—
93C2×Dic10—32no—
94C2×C5×C8—62no—
95C42×C5C22×D311yescharacteristic
96C22⋊Dic5—64no—
97C4⋊Dic5—62no—
98C4×Dic5—31no—
99C4×Dic5—32no—
100C2×#168—22no—
101#676—124no—
102#532—151no—
103#423—152no—
104#333—152no—
105#331—31no—
106#331—51no—
107C22×C3×C5—42no—
108C22×C3×C5—44no—
109C22×C3×C5C2×C22⋊C411yescharacteristic
110C2×D15—21no—
111C2×D15—22no—
112C3×C4×C5—21no—
113C3×C4×C5AGL(1,ℤ/8)12yes—
114C3×C4×C5#13712yes—
115Dic15—22no—
116Dic15—42no—
117Dic15#10012yes—
118C2×C3×D4—22no—
119C2×C3×D4C4×D512yes—
120C2×#67—102no—
121C22×Dic3—102no—
122#237—204no—
123C2×C4×D3—51no—
124C2×C4×D3—52no—
125C2×Dic6—52no—
126C2×C3×C8—102no—
127C3×C42C22×D511yescharacteristic
128#217—104no—
129C4⋊Dic3—102no—
130C4×Dic3—51no—
131C4×Dic3—52no—
132C2×C3⋊C8—22no—
133ΓL(1,𝔽25)—204no—
134C23×C5—22no—
135C22×D5—31no—
136C5×D4—42no—
137C5×D4—42no—
138C5×D4—42no—
139C2×C4×C5C2×C4×D311yescharacteristic
140C2×C4×C5D3×D412yes—
141C22⋊D5—124no—
142C2×Dic5—31no—
143C2×Dic5—32no—
144C2×Dic5—62no—
145C2×Dic5—124no—
146C4×D5—62no—
147C4×D5—62no—
148C4×D5—62no—
149Dic10—122no—
150C5×C8—122no—
151#168—42no—
152C2×#41—152no—
153C2×M16—302no—
154C4⋊Q8—151no—
155#127D3×D511yescharacteristic
156#124—152no—
157#121—302no—
158C4×D4—302no—
159C2×C42—151no—
160C4⋊C8—32no—
161C4⋊C8—52no—
162C4⋊C8—302no—
163C2×C3×C5—82no—
164C2×C3×C5C2×#10011yescharacteristic
165C2×C3×C5#41712yes—
166D15—41no—
167C23×C3—22no—
168C22×D3—51no—
169C3×D4—42no—
170C3×D4—42no—
171C3×D4—42no—
172C2×C3×C4C2×C4×D511yescharacteristic
173C2×C3×C4D4×D512yes—
174#67—204no—
175C2×Dic3—51no—
176C2×Dic3—52no—
177C2×Dic3—102no—
178C2×Dic3—204no—
179C4×D3—102no—
180C4×D3—102no—
181C4×D3—102no—
182Dic6—202no—
183C3×C8—202no—
184C3⋊C8—42no—
185C22×C5—42no—
186C22×C5—44no—
187C22×C5D3×C22⋊C411yescharacteristic
188C2×D5—61no—
189C2×D5—62no—
190C4×C5—21no—
191C4×C5#91112yes—
192C4×C5#91512yes—
193Dic5—32no—
194Dic5—62no—
195Dic5—122no—
196#41—604no—
197C2×Q8—152no—
198C2×D4—22no—
199C2×D4—302no—
200C2×D4#120012yes—
201C22×C4—151no—
202C22×C4—152no—
203C22×C4—302no—
204M16—604no—
205C2×C8—62no—
206C2×C8—102no—
207C4⋊C4—302no—
208C22⋊C4—304no—
209C42—151no—
210C42—152no—
211C42C2×D3×D511yescharacteristic
212C3×C5#156011yescharacteristic, complemented, Hall
213C22×C3—42no—
214C22×C3—44no—
215C22×C3D5×C22⋊C411yescharacteristic
216C2×D3—101no—
217C2×D3—102no—
218C3×C4—21no—
219C3×C4#405712yes—
220C3×C4#406112yes—
221Dic3—52no—
222Dic3—102no—
223Dic3—202no—
224C2×C5—82no—
225C2×C5D3×#10011yescharacteristic
226C2×C5#477112yes—
227D5—121no—
228C23—22no—
229C23—151no—
230Q8—602no—
231D4—42no—
232D4—42no—
233D4—42no—
234D4—604no—
235C2×C4—151no—
236C2×C4—152no—
237C2×C4—302no—
238C2×C4—302no—
239C2×C4—302no—
240C2×C4—302no—
241C2×C4—604no—
242C2×C4C2×#120011yescharacteristic
243C2×C4#679012yes—
244C8—122no—
245C8—202no—
246C2×C3—82no—
247C2×C3D5×#10011yescharacteristic
248C2×C3#6506012yes—
249D3—201no—
250C5#6838911yescharacteristic, complemented, Sylow
251C22—42no—
252C22—44no—
253C22—301no—
254C22—302no—
255C22#9156111yescharacteristic
256C4—21no—
257C4—152no—
258C4—302no—
259C4—602no—
260C4#9148212yes—
261C4#9148812yes—
262C3#1059918211yescharacteristic, complemented, Sylow
263C2—82no—
264C2—601no—
265C2#1174895912yes—
266C2#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#1560
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. #11747015C2semidirect
3. C5×#4544C2semidirect
4. C3×#64764C2semidirect
5. #11745863C2semidirect
22. #64764D3semidirect
43. #4544D5semidirect
212. C3×C5#1560semidirect
250. C5#68389semidirect
262. C3#10599182semidirect

Maximal subgroups

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

subgroupindex
#117564752
#117470152
C5×#45442
C3×#647642
#117458632
#105991823
#683895