Finite Group Databasebeta

← #14284353

Subgroups — #14284353

Order 1920.

496 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 496 conjugacy classes of subgroups — too many to draw. Only its 80 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
1D3×#4082C211yesmaximal, characteristic
2#11751803C212yesmaximal, complemented
3#11746792C211yesmaximal, characteristic, complemented
4C3×#64921C211yesmaximal, characteristic, complemented
5#11746504C212yesmaximal, complemented
6#10604916—31nomaximal, Hall
7C2×C5×D3×D4C411yescharacteristic
8C2×D3×Dic10C411yescharacteristic
9#91825C411yescharacteristic
10C3×#4082C2211yescharacteristic
11D3×C22⋊Dic5—22no—
12#91525—22no—
13C4×D3×Dic5C2211yescharacteristic
14#91373C2211yescharacteristic
15#91370C411yescharacteristic
16#91231C2212yescomplemented
17C3×#4002C2212yescomplemented
18#91177—22no—
19(C2×D3)⋊#170—22no—
20#68347—51nomaximal, Hall
21C2×#4082—31no—
22#65757—32no—
23#64921—31no—
24#64921—32no—
25#64921D311yescharacteristic, complemented
26C23×C5×D3—21no—
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×Dic30C2×C411yescharacteristic
29C2×C5×#67—21no—
30C5×D3×D4—42no—
31C2×C5×D12C2×C411yescharacteristic
32C2×C4×C5×D3C2×C411yescharacteristic
33C2×C3×Dic10C2×C411yescharacteristic
34C2×#1204—21no—
35C2×D3×Dic5—21no—
36C2×D3×Dic5D412yes—
37D3×Dic10—42no—
38C2×C3⋊#170—22no—
39C2×C3×#170—22no—
40#6719—22no—
41C4×Dic15C2×C411yescharacteristic
42C3×C22⋊Dic5—22no—
43C3×C4×Dic5C2311yescharacteristic
44(C2×D3)⋊Dic5—22no—
45(C2×D3)⋊Dic5—22no—
46Dic3×Dic5D412yes—
47D3×#124—51no—
48#4705—52no—
49C3×#329—51no—
50#4540—51no—
51#4464—52no—
52C22×C5×D4—31no—
53C22×Dic10—31no—
54C2×C22⋊Dic5—62no—
55#4082—31no—
56#4082—31no—
57#4082—31no—
58#4082—62no—
59#4082C2×D311yescharacteristic
60C2×C4×Dic5—31no—
61C22⋊#170—62no—
62#4004—62no—
63#4002—32no—
64#4002C2×D312yescomplemented
65#1533—151noSylow
66C23×C3×C5—21no—
67C22×C5×D3—21no—
68C22×C5×D3—44no—
69C22×C5×D3—42no—
70C22×C5×D3C22⋊C411yescharacteristic
71C3×C5×D4—41no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×Dic15—21no—
74C2×Dic15C22⋊C412yes—
75Dic30—41no—
76C5×#67—42no—
77C2×C5×Dic3C22⋊C411yescharacteristic
78C5×D12—41no—
79C4×C5×D3—22no—
80C2×C3×Dic5—21no—
81C2×C3×Dic5C2×D412yes—
82C3×Dic10—41no—
83#1204—42no—
84D3×Dic5—42no—
85D3×Dic5—42no—
86C3⋊#170—42no—
87C3×#170—42no—
88C2×D3×Q8—51no—
89C2×D3×D4AGL(1,𝔽5)11yescharacteristic
90C3×#124—51no—
91#947—51no—
92#936—51no—
93#885—102no—
94D3×C22⋊C4—102no—
95#875—51no—
96C42×D3—51no—
97C3×#97—52no—
98(C2×D3)⋊C8—102no—
99Dic3⋊C8—102no—
100#803—52no—
101C24×C5—61no—
102C2×C5×D4—31no—
103C2×C5×D4—61no—
104C2×C5×D4—122no—
105C2×C5×D4C4×D311yescharacteristic
106C22×C4×C5—31no—
107C22×Dic5—32no—
108C22×Dic5—61no—
109C2×Dic10—31no—
110C2×Dic10—61no—
111C2×Dic10—122no—
112C2×Dic10C4×D311yescharacteristic
113C2×#170—22no—
114C2×#170—62no—
115C22⋊Dic5—22no—
116C22⋊Dic5—62no—
117C22⋊Dic5—62no—
118C22⋊Dic5—62no—
119C4×Dic5—31no—
120C4×Dic5—32no—
121C4×Dic5C22×D311yescharacteristic
122C2×#124—151no—
123#432—152no—
124#329—51no—
125#329—152no—
126#329—151no—
127C22×C3×C5—41no—
128C22×C3×C5—42no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C2×C5×D3—22no—
131C2×C5×D3—41no—
132C2×C5×D3—42no—
133C2×C5×D3—84no—
134C2×C5×D3#10012yes—
135C3×C4×C5—21no—
136Dic15—22no—
137Dic15—41no—
138C3×Dic5—22no—
139C3×Dic5—41no—
140C5×Dic3—21no—
141C23×D3—21no—
142C2×C3×Q8—51no—
143C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
144C2×#67—21no—
145D3×Q8—202no—
146D3×D4—42no—
147C2×D12C2×AGL(1,𝔽5)11yescharacteristic
148C2×C4×D3—52no—
149C2×C4×D3—101no—
150C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
151C2×Dic6—51no—
152C2×Dic6—101no—
153C2×C3×C8—102no—
154C3×C22⋊C4—102no—
155C3×C42—51no—
156#217—102no—
157(C2×D3)⋊C4—102no—
158(C2×D3)⋊C4—102no—
159C4×Dic3—51no—
160C4×Dic3—52no—
161C2×C3⋊C8—102no—
162C23×C5—21no—
163C23×C5—31no—
164C23×C5—61no—
165C23×C5—122no—
166C23×C5—124no—
167C5×D4—41no—
168C5×D4—121no—
169C5×D4—122no—
170C2×C4×C5—31no—
171C2×C4×C5—62no—
172C2×C4×C5C2×C4×D311yescharacteristic
173C2×Dic5—21no—
174C2×Dic5—32no—
175C2×Dic5—61no—
176C2×Dic5—122no—
177C2×Dic5—122no—
178C2×Dic5D3×D412yes—
179Dic10—41no—
180Dic10—122no—
181Dic10—121no—
182#170—42no—
183#170—122no—
184C22×Q8—151no—
185C22×D4—31no—
186#124—51no—
187#124—151no—
188#124—151no—
189#124—151no—
190#124—302no—
191C2×C22⋊C4—302no—
192C2×C42—151no—
193C4⋊C8—302no—
194C22⋊C8—302no—
195#97—52no—
196#97—152no—
197C2×C3×C5—81no—
198C2×C3×C5C2×#10011yescharacteristic
199C2×C3×C5#42112yes—
200C5×D3—22no—
201C5×D3—81no—
202C23×C3—21no—
203C22×D3—21no—
204C22×D3—44no—
205C22×D3—42no—
206C22×D3C22⋊AGL(1,𝔽5)11yescharacteristic
207C3×Q8—201no—
208C3×D4—41no—
209C2×C3×C4—52no—
210C2×C3×C4—101no—
211C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
212#67—42no—
213C2×Dic3—52no—
214C2×Dic3—101no—
215C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
216D12—41no—
217C4×D3—22no—
218C4×D3—202no—
219C4×D3—202no—
220Dic6—202no—
221Dic6—201no—
222C3×C8—202no—
223C3⋊C8—202no—
224C22×C5—32no—
225C22×C5—41no—
226C22×C5—42no—
227C22×C5—62no—
228C22×C5—121no—
229C22×C5—122no—
230C22×C5—244no—
231C22×C5D3×C22⋊C411yescharacteristic
232C4×C5—21no—
233C4×C5—61no—
234Dic5—22no—
235Dic5—41no—
236Dic5—62no—
237Dic5—121no—
238C24—61no—
239C2×Q8—51no—
240C2×Q8—151no—
241C2×Q8—301no—
242C2×Q8—602no—
243C2×D4—31no—
244C2×D4—61no—
245C2×D4—122no—
246C2×D4D3×AGL(1,𝔽5)11yescharacteristic
247C22×C4—31no—
248C22×C4—152no—
249C22×C4—301no—
250C2×C8—102no—
251C2×C8—302no—
252C22⋊C4—102no—
253C22⋊C4—302no—
254C22⋊C4—302no—
255C22⋊C4—302no—
256C42—51no—
257C42—152no—
258C42—151no—
259C3×C5#153311yescharacteristic, complemented, Hall
260C22×C3—41no—
261C22×C3—42no—
262C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
263C2×D3—22no—
264C2×D3—41no—
265C2×D3—42no—
266C2×D3—84no—
267C2×D3#401312yes—
268C3×C4—21no—
269C3×C4—102no—
270C3×C4—201no—
271Dic3—21no—
272Dic3—102no—
273Dic3—201no—
274C2×C5—62no—
275C2×C5—81no—
276C2×C5—241no—
277C2×C5D3×#10011yescharacteristic
278C2×C5#482112yes—
279C23—21no—
280C23—31no—
281C23—61no—
282C23—122no—
283C23—124no—
284Q8—201no—
285Q8—601no—
286Q8—602no—
287D4—41no—
288D4—121no—
289D4—122no—
290C2×C4—31no—
291C2×C4—52no—
292C2×C4—62no—
293C2×C4—101no—
294C2×C4—152no—
295C2×C4—301no—
296C2×C4—602no—
297C2×C4—602no—
298C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
299C8—202no—
300C8—602no—
301C2×C3—81no—
302C2×C3#6576912yes—
303C2×C3C2×#401311yescharacteristic
304D3—22no—
305D3—81no—
306C5#6834711yescharacteristic, complemented, Sylow
307C22—32no—
308C22—42no—
309C22—41no—
310C22—62no—
311C22—122no—
312C22—121no—
313C22—244no—
314C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
315C4—21no—
316C4—61no—
317C4—102no—
318C4—201no—
319C4—302no—
320C4—601no—
321C3#1060491611yescharacteristic, complemented, Sylow
322C2—62no—
323C2—81no—
324C2—241no—
325C2#1175195012yes—
326C2D3×#401311yescharacteristic
subgroupG/H
centerC22D3×C22⋊AGL(1,𝔽5)
commutatorC2×C3×C4×C5C22×C4
FrattiniC2×C4C2×D3×AGL(1,𝔽5)
FittingC2×C3×C5×D4C2×C4
socleC22×C3×C5C2×C22⋊C4
prime radicalC2×C5×D3×D4C4
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1533
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #11751803C2semidirect
3. #11746792C2semidirect
4. C3×#64921C2semidirect
5. #11746504C2semidirect
16. #91231C22semidirect
17. C3×#4002C22semidirect
25. #64921D3semidirect
64. #4002C2×D3semidirect
259. C3×C5#1533semidirect
306. C5#68347semidirect
321. C3#10604916semidirect

Maximal subgroups

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

subgroupindex
D3×#40822
#117518032
#117467922
C3×#649212
#117465042
#106049163
#683475