Finite Group Databasebeta

← #14283877

Subgroups — #14283877

Order 1920.

568 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 568 conjugacy classes of subgroups — too many to draw. Only its 86 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#11754831C211yesmaximal, characteristic
2#11751873C212yesmaximal, complemented
3#11746792C211yesmaximal, characteristic, complemented
4C3×#64921C211yesmaximal, characteristic, complemented
5#11746505C212yesmaximal, complemented
6D5⋊#329—31nomaximal, Hall
7C2×D4×D15C411yescharacteristic
8C2×D15⋊Q8C411yescharacteristic
9C2×#6738—22no—
10C5×#936C411yescharacteristic
11C3×#4082C2211yescharacteristic
12#91561—22no—
13#91526—22no—
14C4×#1200C2211yescharacteristic
15#91375C2211yescharacteristic
16#91374C411yescharacteristic
17#91231C2212yescomplemented
18C3×#4002C2212yescomplemented
19#91169—22no—
20D3×#329—51nomaximal, Hall
21D5×#124—31no—
22#65676—32no—
23#64927—32no—
24#64921—31no—
25#64921D311yescharacteristic, complemented
26C23×D15—21no—
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×#1220—21no—
29D4×D15—42no—
30C2×D60C2×C411yescharacteristic
31C2×C4×D15C2×C411yescharacteristic
32C2×C5×Dic6C2×C411yescharacteristic
33C2×C3×Dic10C2×C411yescharacteristic
34C2×#1204—21no—
35C2×#1200—21no—
36C2×#1200D412yes—
37D15⋊Q8—42no—
38C2×C3⋊#170—22no—
39C2×C3×#170—22no—
40#6738—28no—
41C5×#217—22no—
42C4×C5×Dic3C2×C411yescharacteristic
43C3×C22⋊Dic5—22no—
44C3×C4×Dic5C2311yescharacteristic
45#6667—22no—
46#6667—22no—
47Dic3×Dic5D412yes—
48D3×#124—51no—
49D3×#97—52no—
50C3×#329—51no—
51#4540—51no—
52#4464—52no—
53C2×Q8×D5—31no—
54C2×D4×D5—31no—
55C2×D5⋊C8—62no—
56C5×#124—31no—
57#4093—31no—
58#4082C2×D311yescharacteristic
59#4031—62no—
60D5×C22⋊C4—62no—
61#4021—31no—
62C42×D5—31no—
63#4002—32no—
64#4002—62no—
65#4002C2×D312yescomplemented
66C2×#329—151noSylow
67C23×C3×C5—21no—
68C22×D15—21no—
69C22×D15—42no—
70C22×D15—44no—
71C22×D15C22⋊C411yescharacteristic
72C3×C5×D4—41no—
73C2×C3×C4×C5C22×C411yescharacteristic
74#1220—42no—
75C2×Dic15C22⋊C411yescharacteristic
76D60—41no—
77C4×D15—22no—
78C2×C5×Dic3—21no—
79C2×C5×Dic3C22⋊C412yes—
80C5×Dic6—41no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5C2×D412yes—
83C3×Dic10—41no—
84#1204—42no—
85#1200—24no—
86#1200—42no—
87C3⋊#170—24no—
88C3×#170—24no—
89C2×D3×Q8—51no—
90C2×D3×D4—51no—
91C3×#124—51no—
92#947—51no—
93#936AGL(1,𝔽5)11yescharacteristic
94C2×D3×C8—102no—
95#885—102no—
96D3×C22⋊C4—102no—
97#875—51no—
98C42×D3—51no—
99C3×#97—52no—
100#815—102no—
101#803—52no—
102C23×D5—61no—
103C2×C5×Q8—31no—
104C2×C5×D4C4×D311yescharacteristic
105C2×C22⋊D5—61no—
106Q8×D5—122no—
107D4×D5—122no—
108C2×D20—31no—
109C2×C4×D5—31no—
110C2×C4×D5—32no—
111C2×C4×D5—61no—
112C2×Dic10—61no—
113C2×Dic10C4×D311yescharacteristic
114C2×#170—22no—
115C2×#170—62no—
116D5⋊C8—68no—
117C5×C22⋊C4—62no—
118C42×C5—31no—
119C22⋊Dic5—22no—
120#685—62no—
121#685—62no—
122C4×Dic5—32no—
123C4×Dic5C22×D311yescharacteristic
124C2×#124—151no—
125C2×#97—152no—
126#329—51no—
127#329—152no—
128#329—151no—
129C22×C3×C5—41no—
130C22×C3×C5—42no—
131C22×C3×C5C2×C22⋊C411yescharacteristic
132C2×D15—41no—
133C2×D15—42no—
134C2×D15—84no—
135C2×D15#10012yes—
136C2×D15#10414yes—
137C3×C4×C5—21no—
138Dic15—21no—
139C3×Dic5—22no—
140C3×Dic5—41no—
141C5×Dic3—22no—
142C5×Dic3—41no—
143C23×D3—101no—
144C2×C3×Q8—51no—
145C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
146C2×#67—101no—
147D3×Q8—202no—
148D3×D4—202no—
149C2×D12—51no—
150C2×C4×D3—51no—
151C2×C4×D3—52no—
152C2×C4×D3—101no—
153C2×Dic6—101no—
154C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
155C2×C3×C8—102no—
156C3×C22⋊C4—102no—
157C3×C42—51no—
158#217—22no—
159(C2×D3)⋊C4—102no—
160(C2×D3)⋊C4—102no—
161C4×Dic3—52no—
162C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
163C2×C3⋊C8—102no—
164D3×C8—108no—
165C23×C5—21no—
166C22×D5—31no—
167C22×D5—61no—
168C22×D5—122no—
169C22×D5—124no—
170C5×Q8—121no—
171C5×D4—41no—
172C2×C4×C5—32no—
173C2×C4×C5—61no—
174C2×C4×C5C2×C4×D311yescharacteristic
175C22⋊D5—122no—
176C2×Dic5—21no—
177C2×Dic5—31no—
178C2×Dic5D3×D412yes—
179D20—121no—
180C4×D5—64no—
181C4×D5—62no—
182C4×D5—122no—
183Dic10—41no—
184Dic10—122no—
185#170—24no—
186#170—64no—
187C22×Q8—151no—
188C22×D4—151no—
189C22×C8—302no—
190#124—31no—
191#124—51no—
192#124—151no—
193#124—151no—
194#124—302no—
195C2×C22⋊C4—302no—
196C2×C42—151no—
197#97—52no—
198#97—152no—
199#97—302no—
200C2×C3×C5—81no—
201C2×C3×C5C2×#10011yescharacteristic
202C2×C3×C5C2×#10412yes—
203D15—81no—
204D15#32914yescomplemented
205C23×C3—21no—
206C22×D3—51no—
207C22×D3—101no—
208C22×D3—202no—
209C22×D3—204no—
210C3×Q8—201no—
211C3×D4—41no—
212C2×C3×C4—52no—
213C2×C3×C4—101no—
214C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
215#67—202no—
216C2×Dic3—21no—
217C2×Dic3—51no—
218C2×Dic3C22⋊AGL(1,𝔽5)12yes—
219D12—201no—
220C4×D3—104no—
221C4×D3—102no—
222C4×D3—202no—
223Dic6—41no—
224Dic6—202no—
225C3×C8—104no—
226C3⋊C8—104no—
227C22×C5—41no—
228C22×C5—42no—
229C22×C5D3×C22⋊C411yescharacteristic
230C2×D5—32no—
231C2×D5—34no—
232C2×D5—121no—
233C2×D5—122no—
234C2×D5—244no—
235C4×C5—21no—
236C4×C5—62no—
237C4×C5—121no—
238Dic5—22no—
239Dic5—41no—
240Dic5—61no—
241C24—301no—
242C2×Q8—31no—
243C2×Q8—51no—
244C2×Q8—301no—
245C2×Q8—602no—
246C2×D4—151no—
247C2×D4—301no—
248C2×D4—602no—
249C2×D4D3×AGL(1,𝔽5)11yescharacteristic
250C22×C4—152no—
251C22×C4—151no—
252C22×C4—301no—
253C2×C8—102no—
254C2×C8—308no—
255C2×C8—302no—
256C22⋊C4—62no—
257C22⋊C4—102no—
258C22⋊C4—302no—
259C22⋊C4—302no—
260C42—31no—
261C42—51no—
262C42—152no—
263C3×C5C2×#32911yescharacteristic, complemented, Hall
264C22×C3—42no—
265C22×C3—41no—
266C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
267C2×D3—54no—
268C2×D3—52no—
269C2×D3—202no—
270C2×D3—201no—
271C2×D3—404no—
272C3×C4—21no—
273C3×C4—102no—
274C3×C4—201no—
275Dic3—22no—
276Dic3—41no—
277Dic3—101no—
278C2×C5—81no—
279C2×C5D3×#10011yescharacteristic
280C2×C5D3×#10412yes—
281D5—34no—
282D5—241no—
283C23—21no—
284C23—151no—
285C23—301no—
286C23—602no—
287C23—604no—
288Q8—121no—
289Q8—201no—
290Q8—602no—
291D4—41no—
292D4—601no—
293D4—602no—
294C2×C4—32no—
295C2×C4—52no—
296C2×C4—61no—
297C2×C4—101no—
298C2×C4—151no—
299C2×C4—302no—
300C2×C4—304no—
301C2×C4—602no—
302C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
303C8—104no—
304C8—304no—
305C2×C3—81no—
306C2×C3D5⋊#10011yescharacteristic
307C2×C3D5⋊#10412yes—
308D3—54no—
309D3—401no—
310C5D3×#32911yescharacteristic, complemented, Sylow
311C22—41no—
312C22—42no—
313C22—152no—
314C22—154no—
315C22—601no—
316C22—602no—
317C22—1204no—
318C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
319C4—21no—
320C4—62no—
321C4—102no—
322C4—121no—
323C4—201no—
324C4—301no—
325C3D5⋊#32911yescharacteristic, complemented, Sylow
326C2—81no—
327C2—154no—
328C2—1201no—
329C2#1175193512yes—
330C2#1175205011yescharacteristic
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×D4×D15C4
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5C2×#329
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. #11751873C2semidirect
3. #11746792C2semidirect
4. C3×#64921C2semidirect
5. #11746505C2semidirect
17. #91231C22semidirect
18. C3×#4002C22semidirect
25. #64921D3semidirect
65. #4002C2×D3semidirect
204. D15#329semidirect
263. C3×C5C2×#329semidirect
310. C5D3×#329semidirect
325. C3D5⋊#329semidirect

Maximal subgroups

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

subgroupindex
#117548312
#117518732
#117467922
C3×#649212
#117465052
D5⋊#3293
D3×#3295