Finite Group Databasebeta

← #14317234

Subgroups — #14317234

Order 1920.

340 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 74 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#11750973C211yesmaximal, characteristic, complemented
2#11747982C211yesmaximal, characteristic, complemented
3C2×#90943C211yesmaximal, characteristic, complemented
4C2×#90939C211yesmaximal, characteristic
5C5×#4491C211yesmaximal, characteristic, complemented
6C3×#64712C211yesmaximal, characteristic, complemented
7#11745928C211yesmaximal, characteristic, complemented
8#10599996—31nomaximal, Hall
9C2×D120C2211yescharacteristic
10#91782—21no—
11C2×C5×D24C2211yescharacteristic
12C2×C3×Dic20C2211yescharacteristic
13#91370—21no—
14C2×#6656—21no—
15C3×C5×#107C2211yescharacteristic
16C8×Dic15C2211yescharacteristic
17#91093—21no—
18C2×C5×C3⋊C16C2211yescharacteristic
19C2×C3×#672C2211yescharacteristic
20#90943—22no—
21#90939—22no—
22#69235—51nomaximal, Hall
23#65444—31no—
24C2×#3958—31no—
25C2×#3932—31no—
26#65161—31no—
27C5×#357—31no—
28#64721—31no—
29#64712D311yescharacteristic, complemented
30C2×D60—21no—
31C2×C4×D15—41no—
32C2×C5×D12—21no—
33C2×C3×Dic10—21no—
34C2×C3×C5×C8C2311yescharacteristic
35C3×C5×C4⋊C4—21no—
36#6714—41no—
37C4×Dic15D411yescharacteristic
38C2×C3⋊#168D411yescharacteristic
39D120—21no—
40D120D412yes—
41C5×D24—21no—
42C5×D24—21no—
43C3×Dic20—21no—
44C3×Dic20—21no—
45(C2×D3)⋊Dic5—41no—
46(C2×D3)⋊Dic5—41no—
47#6656—42no—
48C3×#672—21no—
49C5×C3⋊C16—21no—
50#5191—51no—
51C2×#828—51no—
52C2×D48—51no—
53#4872—51no—
54C3×#358—51no—
55Dic3⋊C16—51no—
56#4491D511yescharacteristic, complemented
57C2×C5×D8—31no—
58#4082—61no—
59C2×#687—61no—
60C2×Dic20C2×D311yescharacteristic
61C2×D40—31no—
62#4039—61no—
63C2×C5×C16—31no—
64C5×#107C2×D311yescharacteristic
65#3958—62no—
66C8×Dic5—31no—
67C2×#672C2×D311yescharacteristic
68#3941—61no—
69#3932—62no—
70#2210—151noSylow
71C22×D15—41no—
72C22×C5×D3—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×Dic15D811yescharacteristic
76C2×Dic15D811yescharacteristic
77D60—22no—
78D60—41no—
79C4×D15—82no—
80C5×D12—41no—
81C5×D12—41no—
82C2×C3×Dic5—41no—
83C3×Dic10—41no—
84C3×Dic10—41no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3⋊#168—21no—
88C2×C3×Q16—51no—
89#947—101no—
90C2×#215—101no—
91C2×D24—51no—
92C2×D24C2×D511yescharacteristic
93#893—101no—
94C2×C3×C16—51no—
95C3×#107C2×D511yescharacteristic
96#828—102no—
97C8×Dic3—51no—
98C2×C3⋊C16C2×D511yescharacteristic
99#809—101no—
100D48—102no—
101C2×C5×D4—61no—
102C2×D20—61no—
103C2×C4×D5—121no—
104C2×Dic10—21no—
105C5×D8—61no—
106C5×D8—61no—
107C2×C5×C8C22×D311yescharacteristic
108C5×C4⋊C4—21no—
109C22⋊Dic5—121no—
110C22⋊Dic5—121no—
111#687—122no—
112#685—121no—
113C4×Dic5—31no—
114C2×#168—31no—
115Dic20—21no—
116Dic20—21no—
117D40—32no—
118D40—61no—
119C5×C16—61no—
120#672—21no—
121C2×SD32—151no—
122C2×D16—151no—
123#495—151no—
124C4×D8—151no—
125C4⋊C16—151no—
126#358—51no—
127#357—31no—
128C22×C3×C5C2×D811yescharacteristic
129C2×D15—42no—
130C2×D15—81no—
131C2×D15—81no—
132C2×C5×D3—81no—
133C2×C5×D3—81no—
134C2×C5×D3—81no—
135C3×C4×C5—81no—
136C3×C4×C5#12111yescharacteristic
137C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
138Dic15—21no—
139Dic15—21no—
140C3×Dic5—81no—
141C2×C3×Q8—101no—
142C2×D12—21no—
143C2×D12—101no—
144C2×C4×D3—201no—
145C3×Q16—101no—
146C3×Q16—101no—
147C2×C3×C8C22×D511yescharacteristic
148C3×C4⋊C4—21no—
149#215—202no—
150(C2×D3)⋊C4—201no—
151(C2×D3)⋊C4—201no—
152(C2×D3)⋊C4—201no—
153C4×Dic3—51no—
154C2×C3⋊C8—51no—
155D24—21no—
156D24—21no—
157D24—52no—
158D24—101no—
159C3×C16—101no—
160C3⋊C16—21no—
161C23×C5—121no—
162C22×D5—121no—
163C5×D4—121no—
164C5×D4—121no—
165C2×C4×C5—41no—
166C2×C4×C5D3×D411yescharacteristic
167C2×Dic5—31no—
168C2×Dic5—31no—
169C2×Dic5—41no—
170D20—62no—
171D20—121no—
172C4×D5—242no—
173Dic10—41no—
174Dic10—41no—
175C5×C8#23511yescharacteristic
176C5×C8D3×D411yescharacteristic
177#168—61no—
178C2×Q16—51no—
179C2×SD16—301no—
180C2×D8—31no—
181C2×D8—151no—
182#124—301no—
183C4×D4—301no—
184SD32—302no—
185D16—302no—
186C2×C16—31no—
187C2×C16—51no—
188#107D3×D511yescharacteristic
189#102—301no—
190C4×C8—151no—
191C2×C3×C5#45911yescharacteristic
192C2×C3×C5#50811yescharacteristic
193C2×C3×C5#50911yescharacteristic
194D15—82no—
195C5×D3—161no—
196C22×D3—41no—
197C22×D3—201no—
198C3×Q8—201no—
199C3×Q8—201no—
200C2×C3×C4—41no—
201C2×C3×C4—201no—
202C2×C3×C4D4×D511yescharacteristic
203C2×Dic3—51no—
204C2×Dic3—51no—
205D12—41no—
206D12—41no—
207D12—102no—
208D12—201no—
209C4×D3—402no—
210C3×C8#70911yescharacteristic
211C3×C8D4×D511yescharacteristic
212C3⋊C8—101no—
213C22×C5—241no—
214C22×C5—241no—
215C22×C5—241no—
216C22×C5D3×D811yescharacteristic
217C2×D5—122no—
218C2×D5—241no—
219C2×D5—241no—
220C4×C5—81no—
221C4×C5#88411yescharacteristic
222C4×C5#91411yescharacteristic
223Dic5—61no—
224Dic5—61no—
225Dic5—81no—
226C2×Q8—101no—
227C2×D4—61no—
228C2×D4—301no—
229C22×C4—601no—
230Q16—101no—
231Q16—101no—
232SD16—602no—
233D8—61no—
234D8—61no—
235D8—152no—
236D8—301no—
237C2×C8—151no—
238C2×C8C2×D3×D511yescharacteristic
239C4⋊C4—21no—
240C22⋊C4—601no—
241C22⋊C4—601no—
242C22⋊C4—601no—
243C42—151no—
244C16—61no—
245C16—101no—
246C3×C5#221011yescharacteristic, complemented, Hall
247C22×C3D5×D811yescharacteristic
248C2×D3—81no—
249C2×D3—81no—
250C2×D3—81no—
251C2×D3—202no—
252C2×D3—401no—
253C2×D3—401no—
254C3×C4—81no—
255C3×C4—401no—
256C3×C4#403011yescharacteristic
257C3×C4#406011yescharacteristic
258Dic3—101no—
259Dic3—101no—
260C2×C5—481no—
261C2×C5#478611yescharacteristic
262C2×C5#491411yescharacteristic
263C2×C5#491911yescharacteristic
264D5—242no—
265C23—121no—
266C23—601no—
267Q8—201no—
268Q8—201no—
269D4—121no—
270D4—121no—
271D4—302no—
272D4—601no—
273C2×C4—41no—
274C2×C4—151no—
275C2×C4—151no—
276C2×C4—201no—
277C2×C4—1202no—
278C2×C4#679011yescharacteristic
279C8—301no—
280C8#677111yescharacteristic
281C8#677711yescharacteristic
282C2×C3#6507511yescharacteristic
283C2×C3#6520011yescharacteristic
284C2×C3#6520511yescharacteristic
285D3—161no—
286D3—402no—
287C5#6923511yescharacteristic, complemented, Sylow
288C22—241no—
289C22—241no—
290C22—241no—
291C22—602no—
292C22—1201no—
293C22—1201no—
294C22#9148111yescharacteristic
295C4—81no—
296C4—301no—
297C4—301no—
298C4—401no—
299C4#9146111yescharacteristic
300C4#9150611yescharacteristic
301C3#1059999611yescharacteristic, complemented, Sylow
302C2—481no—
303C2—1202no—
304C2#1174740611yescharacteristic
305C2#1174828711yescharacteristic
306C2#1174831011yescharacteristic
subgroupG/H
centerC22#91481
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×#90939C2
hypercenter#107D3×D5
hypocenterC3×C5#2210
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #11750973C2semidirect
2. #11747982C2semidirect
3. C2×#90943C2semidirect
5. C5×#4491C2semidirect
6. C3×#64712C2semidirect
7. #11745928C2semidirect
29. #64712D3semidirect
56. #4491D5semidirect
246. C3×C5#2210semidirect
287. C5#69235semidirect
301. C3#10599996semidirect

Maximal subgroups

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

subgroupindex
#117509732
#117479822
C2×#909432
C2×#909392
C5×#44912
C3×#647122
#117459282
#105999963
#692355