Finite Group Databasebeta

← #14284452

Subgroups — #14284452

Order 1920.

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

normal subgroups only

This group has 476 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
1#11756427C211yesmaximal, characteristic
2#11750806C212yesmaximal, complemented
3C3×C5×#329C211yesmaximal, characteristic, complemented
4#11746361C211yesmaximal, characteristic, complemented
5#11746285C212yesmaximal, complemented
6#10599142—31nomaximal, Hall
7C2×#6821C411yescharacteristic
8C2×#6819C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10#91833C411yescharacteristic
11#91829C411yescharacteristic
12#91773—22no—
13#91770—22no—
14#91764C2211yescharacteristic
15C42×D15C2211yescharacteristic
16C3×C5×#97C2212yes—
17#91104—22no—
18#91098—22no—
19#91087C2212yes—
20#68349—51nomaximal, Hall
21#66002—31no—
22#64994—32no—
23C5×#329D311yescharacteristic, complemented
24#64760—31no—
25#64684—32no—
26C2×C3×C5×Q8C2×C411yescharacteristic
27C2×C3×C5×D4C2×C411yescharacteristic
28C2×#1220—21no—
29C2×#1220—22no—
30C22×Dic15—21no—
31#6821—42no—
32#6819—42no—
33C2×D60—21no—
34C2×D60C2×C411yescharacteristic
35C2×C4×D15—21no—
36C2×C4×D15C2×C411yescharacteristic
37C2×C4×D15D412yes—
38C2×Dic30C2×C411yescharacteristic
39C2×C3×C5×C8—22no—
40C3×C5×C22⋊C4—22no—
41C3×C42×C5C2311yescharacteristic
42#6714—22no—
43#6712—22no—
44C4×Dic15C2×C411yescharacteristic
45C4×Dic15D412yes—
46C2×C3⋊#168—22no—
47#5668—51no—
48#4705—52no—
49C3×#329D511yescharacteristic, complemented
50#4540—51no—
51#4464—52no—
52C2×#713—31no—
53C2×#711—31no—
54C5×#124C2×D311yescharacteristic
55#4090—31no—
56#4086—31no—
57#4030—62no—
58#4027—62no—
59#4021—31no—
60C42×D5—31no—
61C5×#97C2×D312yes—
62#3952—62no—
63#3946—62no—
64#3935—32no—
65#1536—151noSylow
66C23×C3×C5—21no—
67C22×D15—21no—
68C22×D15C22⋊C411yescharacteristic
69C3×C5×Q8—41no—
70C3×C5×D4—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5C22×C411yescharacteristic
73C2×C3×C4×C5C2×D412yes—
74#1220—44no—
75#1220—42no—
76C2×Dic15—21no—
77C2×Dic15—42no—
78C2×Dic15C22⋊C412yes—
79C2×Dic15C22⋊C411yescharacteristic
80D60—41no—
81D60—42no—
82C4×D15—22no—
83C4×D15—42no—
84C4×D15—42no—
85Dic30—41no—
86C3×C5×C8—42no—
87C3⋊#168—42no—
88C2×#239—51no—
89C2×#237—51no—
90C3×#124C2×D511yescharacteristic
91#944—51no—
92#940—51no—
93#884—102no—
94#67⋊C4—102no—
95#875—51no—
96C42×D3—51no—
97C3×#97C2×D512yes—
98(C2×D3)⋊C8—102no—
99Dic3⋊C8—102no—
100#803—52no—
101C2×C5×Q8C4×D311yescharacteristic
102C2×C5×D4C4×D311yescharacteristic
103C2×C22⋊D5—62no—
104C2×C22⋊D5—61no—
105C22×Dic5—61no—
106#713—122no—
107#711—122no—
108C2×D20—31no—
109C2×D20—61no—
110C2×C4×D5—31no—
111C2×C4×D5—32no—
112C2×C4×D5—61no—
113C2×Dic10—31no—
114C2×C5×C8—22no—
115C5×C22⋊C4—22no—
116C42×C5C22×D311yescharacteristic
117#685—62no—
118#683—62no—
119C4×Dic5—31no—
120C4×Dic5—32no—
121C2×#168—62no—
122#532—151no—
123#432—152no—
124#329—151no—
125#329—152no—
126#329D1511yescharacteristic, complemented
127C22×C3×C5—41no—
128C22×C3×C5—42no—
129C22×C3×C5C2×C22⋊C411yescharacteristic
130C2×D15—21no—
131C2×D15—22no—
132C2×D15—41no—
133C2×D15—42no—
134C3×C4×C5—21no—
135C3×C4×C5—22no—
136C3×C4×C5—41no—
137Dic15—22no—
138Dic15—41no—
139Dic15#10012yes—
140C2×C3×Q8C4×D511yescharacteristic
141C2×C3×D4C4×D511yescharacteristic
142C2×#67—102no—
143C2×#67—101no—
144C22×Dic3—101no—
145#239—202no—
146#237—202no—
147C2×D12—51no—
148C2×D12—101no—
149C2×C4×D3—51no—
150C2×C4×D3—52no—
151C2×C4×D3—101no—
152C2×Dic6—51no—
153C2×C3×C8—22no—
154C3×C22⋊C4—22no—
155C3×C42C22×D511yescharacteristic
156(C2×D3)⋊C4—102no—
157Dic3⋊C4—102no—
158C4×Dic3—51no—
159C4×Dic3—52no—
160C2×C3⋊C8—102no—
161C23×C5—21no—
162C22×D5—31no—
163C22×D5—61no—
164C5×Q8—41no—
165C5×D4—41no—
166C2×C4×C5—21no—
167C2×C4×C5C2×C4×D311yescharacteristic
168C2×C4×C5D3×D412yes—
169C22⋊D5—124no—
170C22⋊D5—122no—
171C2×Dic5—31no—
172C2×Dic5—32no—
173C2×Dic5—61no—
174C2×Dic5—122no—
175D20—121no—
176D20—122no—
177C4×D5—62no—
178C4×D5—122no—
179C4×D5—122no—
180Dic10—121no—
181C5×C8—42no—
182#168—122no—
183C2×#41—151no—
184C2×#41—151no—
185C4⋊Q8—151no—
186#127—151no—
187#124—151no—
188#124C2×D1511yescharacteristic
189#121—302no—
190C4×D4—302no—
191C2×C42—151no—
192C4⋊C8—302no—
193C22⋊C8—302no—
194#97—152no—
195#97C2×D1512yes—
196C2×C3×C5—81no—
197C2×C3×C5C2×#10011yescharacteristic
198C2×C3×C5#42112yes—
199D15—41no—
200D15—81no—
201C23×C3—21no—
202C22×D3—51no—
203C22×D3—101no—
204C3×Q8—41no—
205C3×D4—41no—
206C2×C3×C4—21no—
207C2×C3×C4C2×C4×D511yescharacteristic
208C2×C3×C4D4×D512yes—
209#67—204no—
210#67—202no—
211C2×Dic3—51no—
212C2×Dic3—52no—
213C2×Dic3—101no—
214C2×Dic3—202no—
215D12—201no—
216D12—202no—
217C4×D3—102no—
218C4×D3—202no—
219C4×D3—202no—
220Dic6—201no—
221C3×C8—42no—
222C3⋊C8—202no—
223C22×C5—41no—
224C22×C5—42no—
225C22×C5D3×C22⋊C411yescharacteristic
226C2×D5—61no—
227C2×D5—62no—
228C2×D5—121no—
229C2×D5—122no—
230C4×C5—21no—
231C4×C5—22no—
232C4×C5—41no—
233Dic5—32no—
234Dic5—62no—
235Dic5—121no—
236#41—602no—
237#41—602no—
238C2×Q8—151no—
239C2×Q8C4×D1511yescharacteristic
240C2×D4—151no—
241C2×D4—301no—
242C2×D4—302no—
243C2×D4—301no—
244C2×D4C4×D1511yescharacteristic
245C22×C4—151no—
246C22×C4—152no—
247C22×C4—301no—
248C22×C4—301no—
249C2×C8—22no—
250C2×C8—302no—
251C4⋊C4—302no—
252C22⋊C4—22no—
253C22⋊C4—302no—
254C42—151no—
255C42—152no—
256C42C22×D1511yescharacteristic
257C3×C5#153611yescharacteristic, complemented, Hall
258C22×C3—41no—
259C22×C3—42no—
260C22×C3D5×C22⋊C411yescharacteristic
261C2×D3—101no—
262C2×D3—102no—
263C2×D3—201no—
264C2×D3—202no—
265C3×C4—21no—
266C3×C4—22no—
267C3×C4—41no—
268Dic3—52no—
269Dic3—102no—
270Dic3—201no—
271C2×C5—81no—
272C2×C5D3×#10011yescharacteristic
273C2×C5#482112yes—
274D5—121no—
275D5—241no—
276C23—21no—
277C23—151no—
278C23—301no—
279Q8—41no—
280Q8—601no—
281D4—41no—
282D4—601no—
283D4—602no—
284D4—604no—
285D4—602no—
286C2×C4—21no—
287C2×C4—151no—
288C2×C4—152no—
289C2×C4—302no—
290C2×C4—301no—
291C2×C4—602no—
292C2×C4—602no—
293C2×C4—602no—
294C2×C4C2×C4×D1511yescharacteristic
295C2×C4D4×D1512yes—
296C8—42no—
297C8—602no—
298C2×C3—81no—
299C2×C3D5×#10011yescharacteristic
300C2×C3#6511012yes—
301D3—201no—
302D3—401no—
303C5#6834911yescharacteristic, complemented, Sylow
304C22—42no—
305C22—41no—
306C22—302no—
307C22—301no—
308C22—602no—
309C22—601no—
310C22C22⋊C4×D1511yescharacteristic
311C4—22no—
312C4—21no—
313C4—41no—
314C4—152no—
315C4—302no—
316C4—601no—
317C3#1059914211yescharacteristic, complemented, Sylow
318C2—81no—
319C2—601no—
320C2—1201no—
321C2D15×#10011yescharacteristic
322C2#1175092212yes—
subgroupG/H
centerC22C22⋊C4×D15
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C22×D15
FittingC3×C5×#329C2
socleC22×C3×C5C2×C22⋊C4
prime radical#11756427C2
cosocleC3×C42×C5C23
hypercenter#329D15
hypocenterC3×C5#1536
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #11750806C2semidirect
3. C3×C5×#329C2semidirect
4. #11746361C2semidirect
5. #11746285C2semidirect
23. C5×#329D3semidirect
49. C3×#329D5semidirect
126. #329D15semidirect
257. C3×C5#1536semidirect
303. C5#68349semidirect
317. C3#10599142semidirect

Maximal subgroups

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

subgroupindex
#117564272
#117508062
C3×C5×#3292
#117463612
#117462852
#105991423
#683495