Finite Group Databasebeta

← #14283992

Subgroups — #14283992

Order 1920.

540 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 540 conjugacy classes of subgroups — too many to draw. Only its 90 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#11746844C212yesmaximal, complemented
3C5×#4540C211yesmaximal, characteristic, complemented
4C3×#64760C211yesmaximal, characteristic, complemented
5#11745848C212yesmaximal, complemented
6#10599135—31nomaximal, Hall
7C2×#6821C411yescharacteristic
8C2×#6819C411yescharacteristic
9C3×C5×#124C2211yescharacteristic
10#91833C411yescharacteristic
11#91829C411yescharacteristic
12#91773—22no—
13#91770—22no—
14#91764C2211yescharacteristic
15C42×D15C2211yescharacteristic
16C2×#6651—22no—
17C5×#803C2212yes—
18C3×#3935C2212yes—
19#90951—22no—
20#68342—51nomaximal, Hall
21#66002—31no—
22#64996—32no—
23C5×#329—31no—
24#64760D311yescharacteristic, complemented
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
39C3×C5×C22⋊C4—22no—
40C3×C42×C5C2311yescharacteristic
41#6714—22no—
42#6712—22no—
43C4×Dic15C2×C411yescharacteristic
44C4×Dic15D412yes—
45C2×C5×C3⋊C8—22no—
46C2×C3×#168—22no—
47#6651—28no—
48#5668—51no—
49#4707—52no—
50C3×#329—51no—
51#4540D511yescharacteristic, complemented
52#4464—52no—
53C2×#713—31no—
54C2×#711—31no—
55C5×#124C2×D311yescharacteristic
56#4090—31no—
57#4086—31no—
58C2×#676—62no—
59#4030—62no—
60#4027—62no—
61#4021—31no—
62C42×D5—31no—
63C5×#97—32no—
64C8×Dic5—62no—
65#3935C2×D312yes—
66#1525—151noSylow
67C23×C3×C5—21no—
68C22×D15—21no—
69C22×D15C22⋊C411yescharacteristic
70C3×C5×Q8—41no—
71C3×C5×D4—41no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5C22×C411yescharacteristic
74C2×C3×C4×C5C2×D412yes—
75#1220—42no—
76#1220—44no—
77C2×Dic15—21no—
78C2×Dic15—42no—
79C2×Dic15C22⋊C411yescharacteristic
80C2×Dic15C22⋊C412yes—
81D60—41no—
82D60—42no—
83C4×D15—22no—
84C4×D15—24no—
85C4×D15—42no—
86Dic30—41no—
87C3×#168—24no—
88C5×C3⋊C8—24no—
89C2×#239—51no—
90C2×#237—51no—
91C3×#124C2×D511yescharacteristic
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#803C2×D512yes—
102C2×C5×Q8C4×D311yescharacteristic
103C2×C5×D4C4×D311yescharacteristic
104C2×C22⋊D5—62no—
105C2×C22⋊D5—61no—
106C22×Dic5—61no—
107#713—122no—
108#711—122no—
109C2×D20—31no—
110C2×D20—61no—
111C2×C4×D5—31no—
112C2×C4×D5—32no—
113C2×C4×D5—61no—
114C2×Dic10—31no—
115C2×C5×C8—62no—
116C5×C22⋊C4—22no—
117C42×C5C22×D311yescharacteristic
118#685—62no—
119#683—62no—
120C4×Dic5—31no—
121C4×Dic5—32no—
122C2×#168—22no—
123#676—68no—
124#532—151no—
125C4×M16—152no—
126#329—31no—
127#329—51no—
128#329—152no—
129C22×C3×C5—41no—
130C22×C3×C5—42no—
131C22×C3×C5C2×C22⋊C411yescharacteristic
132C2×D15—21no—
133C2×D15—22no—
134C2×D15—41no—
135C2×D15—42no—
136C3×C4×C5—21no—
137C3×C4×C5—22no—
138C3×C4×C5—41no—
139Dic15—41no—
140Dic15#10012yes—
141Dic15#10414yes—
142C2×C3×Q8C4×D511yescharacteristic
143C2×C3×D4C4×D511yescharacteristic
144C2×#67—102no—
145C2×#67—101no—
146C22×Dic3—101no—
147#239—202no—
148#237—202no—
149C2×D12—51no—
150C2×D12—101no—
151C2×C4×D3—51no—
152C2×C4×D3—52no—
153C2×C4×D3—101no—
154C2×Dic6—51no—
155C2×C3×C8—102no—
156C3×C22⋊C4—22no—
157C3×C42C22×D511yescharacteristic
158(C2×D3)⋊C4—102no—
159Dic3⋊C4—102no—
160C4×Dic3—51no—
161C4×Dic3—52no—
162C2×C3⋊C8—22no—
163ΓL(1,𝔽25)—108no—
164C23×C5—21no—
165C22×D5—31no—
166C22×D5—61no—
167C5×Q8—41no—
168C5×D4—41no—
169C2×C4×C5—21no—
170C2×C4×C5C2×C4×D311yescharacteristic
171C2×C4×C5D3×D412yes—
172C22⋊D5—124no—
173C22⋊D5—122no—
174C2×Dic5—32no—
175C2×Dic5—31no—
176C2×Dic5—61no—
177C2×Dic5—122no—
178D20—121no—
179D20—122no—
180C4×D5—64no—
181C4×D5—62no—
182C4×D5—122no—
183Dic10—121no—
184C5×C8—64no—
185#168—24no—
186C2×#41—151no—
187C2×#41—151no—
188C2×M16—302no—
189C4⋊Q8—151no—
190#127—151no—
191#124—151no—
192#124D3×D511yescharacteristic
193#121—302no—
194C4×D4—302no—
195C2×C42—151no—
196#97—32no—
197#97—52no—
198C4×C8—302no—
199C2×C3×C5—81no—
200C2×C3×C5C2×#10011yescharacteristic
201C2×C3×C5C2×#10412yes—
202D15—41no—
203D15—81no—
204C23×C3—21no—
205C22×D3—51no—
206C22×D3—101no—
207C3×Q8—41no—
208C3×D4—41no—
209C2×C3×C4—21no—
210C2×C3×C4C2×C4×D511yescharacteristic
211C2×C3×C4D4×D512yes—
212#67—204no—
213#67—202no—
214C2×Dic3—52no—
215C2×Dic3—51no—
216C2×Dic3—101no—
217C2×Dic3—202no—
218D12—201no—
219D12—202no—
220C4×D3—104no—
221C4×D3—102no—
222C4×D3—202no—
223Dic6—201no—
224C3×C8—104no—
225C3⋊C8—24no—
226C22×C5—41no—
227C22×C5—42no—
228C22×C5D3×C22⋊C411yescharacteristic
229C2×D5—61no—
230C2×D5—62no—
231C2×D5—121no—
232C2×D5—122no—
233C4×C5—21no—
234C4×C5—22no—
235C4×C5—41no—
236Dic5—32no—
237Dic5—34no—
238Dic5—121no—
239#41—602no—
240#41—602no—
241C2×Q8—151no—
242C2×Q8#120011yescharacteristic
243C2×D4—151no—
244C2×D4—301no—
245C2×D4—302no—
246C2×D4—301no—
247C2×D4#120011yescharacteristic
248C22×C4—151no—
249C22×C4—152no—
250C22×C4—301no—
251C22×C4—301no—
252M16—308no—
253C2×C8—62no—
254C2×C8—102no—
255C4⋊C4—302no—
256C22⋊C4—22no—
257C22⋊C4—302no—
258C42—151no—
259C42—152no—
260C42C2×D3×D511yescharacteristic
261C3×C5#152511yescharacteristic, complemented, Hall
262C22×C3—41no—
263C22×C3—42no—
264C22×C3D5×C22⋊C411yescharacteristic
265C2×D3—101no—
266C2×D3—102no—
267C2×D3—201no—
268C2×D3—202no—
269C3×C4—21no—
270C3×C4—22no—
271C3×C4—41no—
272Dic3—52no—
273Dic3—54no—
274Dic3—201no—
275C2×C5—81no—
276C2×C5D3×#10011yescharacteristic
277C2×C5D3×#10412yes—
278D5—121no—
279D5—241no—
280C23—21no—
281C23—151no—
282C23—301no—
283Q8—41no—
284Q8—601no—
285D4—41no—
286D4—601no—
287D4—602no—
288D4—604no—
289D4—602no—
290C2×C4—21no—
291C2×C4—152no—
292C2×C4—151no—
293C2×C4—304no—
294C2×C4—302no—
295C2×C4—301no—
296C2×C4—602no—
297C2×C4—602no—
298C2×C4C2×#120011yescharacteristic
299C2×C4#679012yes—
300C8—64no—
301C8—104no—
302C2×C3—81no—
303C2×C3D5×#10011yescharacteristic
304C2×C3D5×#10412yes—
305D3—201no—
306D3—401no—
307C5#6834211yescharacteristic, complemented, Sylow
308C22—41no—
309C22—42no—
310C22—301no—
311C22—302no—
312C22—601no—
313C22—602no—
314C22#9156111yescharacteristic
315C4—21no—
316C4—22no—
317C4—41no—
318C4—152no—
319C4—154no—
320C4—601no—
321C3#1059913511yescharacteristic, complemented, Sylow
322C2—81no—
323C2—601no—
324C2—1201no—
325C2#1174912711yescharacteristic
326C2#1174943012yes—
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5C2×C22⋊C4
prime radical#11756427C2
cosocleC3×C42×C5C23
hypercenter#124D3×D5
hypocenterC3×C5#1525
LCSG ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11746844C2semidirect
3. C5×#4540C2semidirect
4. C3×#64760C2semidirect
5. #11745848C2semidirect
24. #64760D3semidirect
51. #4540D5semidirect
261. C3×C5#1525semidirect
307. C5#68342semidirect
321. C3#10599135semidirect

Maximal subgroups

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

subgroupindex
#117564272
#117468442
C5×#45402
C3×#647602
#117458482
#105991353
#683425