Finite Group Databasebeta

← #14283997

Subgroups — #14283997

Order 1920.

540 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 84 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#11754814C211yesmaximal, characteristic
2#11751907C212yesmaximal, complemented
3#11746792C211yesmaximal, characteristic, complemented
4C3×#64921C211yesmaximal, characteristic, complemented
5#11746505C212yesmaximal, complemented
6#10604993—31nomaximal, Hall
7C2×C5×#237C411yescharacteristic
8C2×#6769C411yescharacteristic
9C2×#6739—22no—
10#91829C411yescharacteristic
11C3×#4082C2211yescharacteristic
12#91558—22no—
13#91556—22no—
14C4×D3×Dic5C2211yescharacteristic
15#91385C411yescharacteristic
16#91375C2211yescharacteristic
17#91231C2212yes—
18C3×#4002C2212yes—
19Dic3×#170—22no—
20#68342—51nomaximal, Hall
21#66166—31no—
22C4×#704—32no—
23#64927—32no—
24#64921—31no—
25#64921D311yescharacteristic, complemented
26C2×C3×C5×D4C2×C411yescharacteristic
27C2×#1220—22no—
28C2×D60C2×C411yescharacteristic
29C2×C5×#67—21no—
30C22×C5×Dic3—21no—
31C5×#237—42no—
32C2×C4×C5×D3C2×C411yescharacteristic
33C2×C5×Dic6C2×C411yescharacteristic
34C2×C3×Dic10C2×C411yescharacteristic
35C2×#1203—21no—
36C2×#1200—21no—
37C2×D3×Dic5D412yes—
38#6769—42no—
39C2×C3⋊#170—22no—
40C2×C3×#170—22no—
41#6739—28no—
42C4×Dic15C2×C411yescharacteristic
43C3×C22⋊Dic5—22no—
44C3×C4×Dic5C2311yescharacteristic
45#6669—22no—
46#6667—22no—
47Dic3×Dic5D412yes—
48#5668—51no—
49#4707—52no—
50C3×#329—51no—
51#4540—51no—
52#4464—52no—
53C2×C5×#41—31no—
54C2×#709—31no—
55C2×#704—62no—
56#4093—31no—
57#4090—31no—
58#4086—31no—
59#4085—62no—
60#4082C2×D311yescharacteristic
61C4×C22⋊D5—62no—
62C2×C4×Dic5—31no—
63#4002—32no—
64#4002C2×D312yes—
65C4×#170—62no—
66#1525—151noSylow
67C23×C3×C5—21no—
68C22×D15—21no—
69C22×C5×D3C22⋊C411yescharacteristic
70C3×C5×D4—41no—
71C2×C3×C4×C5C22×C411yescharacteristic
72#1220—44no—
73C2×Dic15C22⋊C412yes—
74D60—41no—
75C5×#67—42no—
76C2×C5×Dic3—21no—
77C2×C5×Dic3—42no—
78C2×C5×Dic3C22⋊C411yescharacteristic
79C4×C5×D3—22no—
80C5×Dic6—41no—
81C2×C3×Dic5—21no—
82C2×C3×Dic5C2×D412yes—
83C3×Dic10—41no—
84#1203—42no—
85#1200—42no—
86D3×Dic5—24no—
87C3⋊#170—24no—
88C3×#170—24no—
89C2×#239—51no—
90C2×#237AGL(1,𝔽5)11yescharacteristic
91C3×#124—51no—
92#944—51no—
93#940—51no—
94C2×ΓL(1,𝔽25)—102no—
95#884—102no—
96#67⋊C4—102no—
97#875—51no—
98C42×D3—51no—
99C3×#97—52no—
100C8×Dic3—102no—
101#803—52no—
102C5×#41—122no—
103C2×C5×Q8—31no—
104C2×C5×D4—61no—
105C2×C5×D4C4×D311yescharacteristic
106C22×C4×C5—31no—
107C22×C4×C5—61no—
108C2×C22⋊D5—61no—
109C2×C22⋊D5—62no—
110C22×Dic5—32no—
111#709—122no—
112C2×D20—31no—
113C2×C4×D5—61no—
114C2×Dic10C4×D311yescharacteristic
115#704—68no—
116C2×#170—22no—
117C2×#170—62no—
118C22⋊Dic5—22no—
119#685—62no—
120#683—62no—
121C4×Dic5—31no—
122C4×Dic5—32no—
123C4×Dic5C22×D311yescharacteristic
124#532—151no—
125C4×M16—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×C5×D3—21no—
135C2×C5×D3—22no—
136C3×C4×C5—21no—
137Dic15#10414yes—
138C3×Dic5—22no—
139C3×Dic5—41no—
140C5×Dic3—41no—
141C5×Dic3#10012yes—
142C2×C3×Q8—51no—
143C2×C3×D4C2×AGL(1,𝔽5)11yescharacteristic
144C2×#67—21no—
145C2×#67—102no—
146C22×Dic3—21no—
147#239—202no—
148#237—42no—
149C2×D12—51no—
150C2×D12—101no—
151C2×C4×D3—52no—
152C2×C4×D3—101no—
153C2×C4×D3C2×AGL(1,𝔽5)11yescharacteristic
154C2×Dic6C2×AGL(1,𝔽5)11yescharacteristic
155C2×C3×C8—102no—
156C3×C22⋊C4—102no—
157C3×C42—51no—
158(C2×D3)⋊C4—102no—
159Dic3⋊C4—102no—
160C4×Dic3—51no—
161C4×Dic3—52no—
162C2×C3⋊C8—102no—
163ΓL(1,𝔽25)—108no—
164C23×C5—21no—
165C23×C5—31no—
166C22×D5—61no—
167C5×Q8—121no—
168C5×D4—41no—
169C5×D4—122no—
170C2×C4×C5—31no—
171C2×C4×C5—62no—
172C2×C4×C5—61no—
173C2×C4×C5—122no—
174C2×C4×C5C2×C4×D311yescharacteristic
175C22⋊D5—124no—
176C22⋊D5—122no—
177C2×Dic5—21no—
178C2×Dic5—32no—
179C2×Dic5—64no—
180C2×Dic5D3×D412yes—
181D20—121no—
182C4×D5—122no—
183Dic10—41no—
184#170—24no—
185#170—64no—
186C2×#41—31no—
187C2×#41—151no—
188C2×M16—302no—
189C4⋊Q8—151no—
190#127—151no—
191#124—51no—
192#124—151no—
193#121—302no—
194C4×D4—302no—
195C2×C42—151no—
196#97—52no—
197#97—152no—
198C4×C8—302no—
199C2×C3×C5—81no—
200C2×C3×C5C2×#10011yescharacteristic
201C2×C3×C5C2×#10412yes—
202D15—81no—
203C5×D3—41no—
204C23×C3—21no—
205C22×D3—101no—
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—
213#67—204no—
214C2×Dic3—21no—
215C2×Dic3—42no—
216C2×Dic3—52no—
217C2×Dic3C22⋊AGL(1,𝔽5)11yescharacteristic
218D12—201no—
219D12—202no—
220C4×D3—22no—
221C4×D3—104no—
222C4×D3—202no—
223Dic6—41no—
224C3×C8—104no—
225C3⋊C8—104no—
226C22×C5—41no—
227C22×C5—42no—
228C22×C5—61no—
229C22×C5—62no—
230C22×C5D3×C22⋊C411yescharacteristic
231C2×D5—121no—
232C2×D5—122no—
233C4×C5—21no—
234C4×C5—32no—
235C4×C5—121no—
236Dic5—22no—
237Dic5—34no—
238Dic5—41no—
239#41—122no—
240#41—602no—
241C2×Q8—31no—
242C2×Q8—51no—
243C2×D4—61no—
244C2×D4—151no—
245C2×D4—301no—
246C2×D4—302no—
247C2×D4D3×AGL(1,𝔽5)11yescharacteristic
248C22×C4—31no—
249C22×C4—61no—
250C22×C4—152no—
251C22×C4—301no—
252M16—308no—
253C2×C8—102no—
254C2×C8—302no—
255C4⋊C4—302no—
256C22⋊C4—102no—
257C22⋊C4—302no—
258C42—51no—
259C42—152no—
260C42—151no—
261C3×C5#152511yescharacteristic, complemented, Hall
262C22×C3—42no—
263C22×C3—41no—
264C22×C3C2×C22⋊AGL(1,𝔽5)11yescharacteristic
265C2×D3—22no—
266C2×D3—21no—
267C2×D3—202no—
268C2×D3—201no—
269C3×C4—21no—
270C3×C4—102no—
271C3×C4—201no—
272Dic3—41no—
273Dic3—54no—
274Dic3#401312yes—
275C2×C5—81no—
276C2×C5—121no—
277C2×C5D3×#10011yescharacteristic
278C2×C5D3×#10412yes—
279D5—241no—
280C23—21no—
281C23—31no—
282C23—301no—
283Q8—121no—
284Q8—201no—
285D4—41no—
286D4—122no—
287D4—601no—
288D4—604no—
289D4—602no—
290C2×C4—31no—
291C2×C4—52no—
292C2×C4—62no—
293C2×C4—61no—
294C2×C4—101no—
295C2×C4—122no—
296C2×C4—152no—
297C2×C4—304no—
298C2×C4—602no—
299C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
300C8—104no—
301C8—304no—
302C2×C3—81no—
303C2×C3D5⋊#10412yes—
304C2×C3C2×#401311yescharacteristic
305D3—41no—
306D3—401no—
307C5#6834211yescharacteristic, complemented, Sylow
308C22—41no—
309C22—42no—
310C22—61no—
311C22—62no—
312C22—601no—
313C22—602no—
314C22D3×C22⋊AGL(1,𝔽5)11yescharacteristic
315C4—21no—
316C4—32no—
317C4—102no—
318C4—121no—
319C4—154no—
320C4—201no—
321C3#1060499311yescharacteristic, complemented, Sylow
322C2—81no—
323C2—121no—
324C2—1201no—
325C2#1175193512yes—
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 radical#11754814C2
cosocleC3×C4×Dic5C23
hypercenterC2×D4D3×AGL(1,𝔽5)
hypocenterC3×C5#1525
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. #11751907C2semidirect
3. #11746792C2semidirect
4. C3×#64921C2semidirect
5. #11746505C2semidirect
25. #64921D3semidirect
261. C3×C5#1525semidirect
307. C5#68342semidirect
321. C3#10604993semidirect

Maximal subgroups

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

subgroupindex
#117548142
#117519072
#117467922
C3×#649212
#117465052
#106049933
#683425