Finite Group Databasebeta

← #14317207

Subgroups — #14317207

Order 1920.

340 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 78 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
1C2×#91110C211yesmaximal, characteristic
2C3×#65444C211yesmaximal, characteristic, complemented
3#11747766C211yesmaximal, characteristic, complemented
4C2×#90943C211yesmaximal, characteristic, complemented
5C5×#4562C211yesmaximal, characteristic, complemented
6#11745927C211yesmaximal, characteristic, complemented
7#11745897C211yesmaximal, characteristic, complemented
8#10599996—31nomaximal, Hall
9C2×C3×C5×D8C2211yescharacteristic
10C2×D120C2211yescharacteristic
11C3×#4082—21no—
12C2×C3×#687—21no—
13C2×C3×Dic20C2211yescharacteristic
14#91418—21no—
15#91110—22no—
16C2×C3⋊#672C2211yescharacteristic
17C5×#818C2211yescharacteristic
18C2×C5×C3⋊C16C2211yescharacteristic
19C3×C8×Dic5C2211yescharacteristic
20#90969—21no—
21#90943—22no—
22#71323—51nomaximal, Hall
23#65444D311yescharacteristic, complemented
24C2×#3958—31no—
25C2×#3932—31no—
26#65161—31no—
27C5×#357—31no—
28#64721—31no—
29#64712—31no—
30C2×C3×C5×D4—21no—
31C2×D60—21no—
32C2×C3×Dic10—21no—
33C2×#1200—41no—
34C3×C5×D8—21no—
35C3×C5×D8—21no—
36C2×C3×C5×C8C2311yescharacteristic
37D120—21no—
38D120D412yes—
39C5×C4⋊Dic3—21no—
40C3×C22⋊Dic5—41no—
41C3×C22⋊Dic5—41no—
42C3×#687—42no—
43C3×C4×Dic5D411yescharacteristic
44C2×C3×#168D411yescharacteristic
45C3×Dic20—21no—
46C3×Dic20—21no—
47#6667—41no—
48C3⋊#672—21no—
49C5×C3⋊C16—21no—
50C3×#495—51no—
51C2×#828—51no—
52C2×#826—51no—
53C4×D24—51no—
54#4564—51no—
55#4562D511yescharacteristic, complemented
56C4⋊(C3⋊C16)—51no—
57C2×C5×D8C2×D311yescharacteristic
58#4082—21no—
59C2×#687—21no—
60C2×Dic20C2×D311yescharacteristic
61C2×D40—31no—
62#4039—61no—
63C2×C5×C16—31no—
64C5×#107—31no—
65#3958—62no—
66C8×Dic5C2×D311yescharacteristic
67C2×#672—31no—
68#3941—61no—
69#3932—62no—
70#2210—151noSylow
71C23×C3×C5—41no—
72C22×D15—41no—
73C3×C5×D4—41no—
74C3×C5×D4—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76D60—22no—
77D60—41no—
78C2×C5×Dic3—41no—
79C2×C3×Dic5—41no—
80C2×C3×Dic5D811yescharacteristic
81C2×C3×Dic5D811yescharacteristic
82C3×Dic10—41no—
83C3×Dic10—41no—
84#1200—82no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3×#168—21no—
88C2×C3×Q16—51no—
89C2×C3×SD16—101no—
90C2×C3×D8C2×D511yescharacteristic
91C3×#124—101no—
92C2×D24—51no—
93C4×D12—101no—
94C3×C4×C8—51no—
95#828—102no—
96#826—102no—
97#821—101no—
98#818C2×D511yescharacteristic
99C2×C3⋊C16—51no—
100C2×C3⋊C16C2×D511yescharacteristic
101C2×C5×D4—21no—
102C2×D20—61no—
103C2×C4×D5—121no—
104C2×Dic10—21no—
105C5×D8—21no—
106C5×D8—21no—
107C2×C5×C8C22×D311yescharacteristic
108C5×C4⋊C4—61no—
109C22⋊Dic5—41no—
110C22⋊Dic5—41no—
111#687—42no—
112#685—121no—
113C4×Dic5#6711yescharacteristic
114C2×#168#6711yescharacteristic
115Dic20—21no—
116Dic20—21no—
117D40—32no—
118D40—61no—
119C5×C16—61no—
120#672—61no—
121C2×SD32—151no—
122C2×D16—151no—
123#495—51no—
124C4×D8—151no—
125C4⋊C16—151no—
126#358—151no—
127#357—31no—
128C22×C3×C5—81no—
129C22×C3×C5—81no—
130C22×C3×C5—81no—
131C22×C3×C5C2×D811yescharacteristic
132C2×D15—42no—
133C2×D15—81no—
134C2×D15—81no—
135C3×C4×C5#12111yescharacteristic
136C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
137C3×Dic5—21no—
138C3×Dic5—21no—
139C3×Dic5—81no—
140C5×Dic3—81no—
141C2×C3×Q8—101no—
142C2×C3×D4—21no—
143C2×D12—101no—
144C2×C4×D3—201no—
145C3×Q16—101no—
146C3×Q16—101no—
147C3×SD16—202no—
148C3×D8—21no—
149C3×D8—21no—
150C2×C3×C8—51no—
151C2×C3×C8C22×D511yescharacteristic
152C3×C22⋊C4—201no—
153C3×C22⋊C4—201no—
154C3×C42—51no—
155(C2×D3)⋊C4—201no—
156C4⋊Dic3—21no—
157D24—52no—
158D24—101no—
159C3⋊C16—21no—
160C3⋊C16—101no—
161C23×C5—41no—
162C22×D5—121no—
163C5×D4—41no—
164C5×D4—41no—
165C2×C4×C5—121no—
166C2×C4×C5C2×#6711yescharacteristic
167C2×Dic5—41no—
168C2×Dic5#21311yescharacteristic
169C2×Dic5#21311yescharacteristic
170D20—62no—
171D20—121no—
172C4×D5—242no—
173Dic10—41no—
174Dic10—41no—
175C5×C8D3×D411yescharacteristic
176C5×C8#23711yescharacteristic
177#168—21no—
178C2×Q16—51no—
179C2×SD16—101no—
180C2×D8—151no—
181C2×D8D3×D511yescharacteristic
182#124—101no—
183C4×D4—301no—
184SD32—302no—
185D16—302no—
186C2×C16—31no—
187C2×C16—151no—
188#107—31no—
189#102—301no—
190C4×C8—51no—
191C2×C3×C5—161no—
192C2×C3×C5#45911yescharacteristic
193C2×C3×C5#50811yescharacteristic
194C2×C3×C5#50911yescharacteristic
195D15—82no—
196C23×C3—41no—
197C22×D3—201no—
198C3×Q8—201no—
199C3×Q8—201no—
200C3×D4—41no—
201C3×D4—41no—
202C2×C3×C4—51no—
203C2×C3×C4—51no—
204C2×C3×C4—201no—
205C2×C3×C4D4×D511yescharacteristic
206C2×Dic3—41no—
207D12—102no—
208D12—201no—
209C4×D3—402no—
210C3×C8—101no—
211C3×C8#70911yescharacteristic
212C3×C8D4×D511yescharacteristic
213C22×C5—81no—
214C22×C5—81no—
215C22×C5—81no—
216C22×C5C2×#21311yescharacteristic
217C2×D5—122no—
218C2×D5—241no—
219C2×D5—241no—
220C4×C5—241no—
221C4×C5#93211yescharacteristic
222C4×C5#93811yescharacteristic
223Dic5—21no—
224Dic5—21no—
225Dic5—81no—
226C2×Q8—101no—
227C2×D4—21no—
228C2×D4—301no—
229C22×C4—601no—
230Q16—101no—
231Q16—101no—
232SD16—202no—
233D8—21no—
234D8—21no—
235D8—152no—
236D8—301no—
237C2×C8—51no—
238C2×C8C2×D3×D511yescharacteristic
239C4⋊C4—61no—
240C22⋊C4—201no—
241C22⋊C4—201no—
242C22⋊C4—601no—
243C42—51no—
244C16—61no—
245C16—301no—
246C3×C5#221011yescharacteristic, complemented, Hall
247C22×C3—81no—
248C22×C3—81no—
249C22×C3—81no—
250C22×C3D5×D811yescharacteristic
251C2×D3—202no—
252C2×D3—401no—
253C2×D3—401no—
254C3×C4—101no—
255C3×C4—101no—
256C3×C4—401no—
257C3×C4#403011yescharacteristic
258C3×C4#406011yescharacteristic
259Dic3—81no—
260C2×C5—161no—
261C2×C5#507211yescharacteristic
262C2×C5#519311yescharacteristic
263C2×C5#519411yescharacteristic
264D5—242no—
265C23—41no—
266C23—601no—
267Q8—201no—
268Q8—201no—
269D4—41no—
270D4—41no—
271D4—302no—
272D4—601no—
273C2×C4—51no—
274C2×C4—51no—
275C2×C4—121no—
276C2×C4—201no—
277C2×C4—1202no—
278C2×C4D5×#6711yescharacteristic
279C8—101no—
280C8#677911yescharacteristic
281C8#679011yescharacteristic
282C2×C3—161no—
283C2×C3#6507511yescharacteristic
284C2×C3#6520011yescharacteristic
285C2×C3#6520511yescharacteristic
286D3—402no—
287C5#7132311yescharacteristic, complemented, Sylow
288C22—81no—
289C22—81no—
290C22—81no—
291C22—602no—
292C22—1201no—
293C22—1201no—
294C22D5×#21311yescharacteristic
295C4—101no—
296C4—101no—
297C4—241no—
298C4—401no—
299C4#9149111yescharacteristic
300C4#9153311yescharacteristic
301C3#1059999611yescharacteristic, complemented, Sylow
302C2—161no—
303C2—1202no—
304C2#1174826511yescharacteristic
305C2#1174827911yescharacteristic
306C2#1174897611yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×D8C22
socleC22×C3×C5C2×D8
prime radicalC2×#91110C2
hypercenterC2×D8D3×D5
hypocenterC3×C5#2210
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
2. C3×#65444C2semidirect
3. #11747766C2semidirect
4. C2×#90943C2semidirect
5. C5×#4562C2semidirect
6. #11745927C2semidirect
7. #11745897C2semidirect
23. #65444D3semidirect
55. #4562D5semidirect
246. C3×C5#2210semidirect
287. C5#71323semidirect
301. C3#10599996semidirect

Maximal subgroups

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

subgroupindex
C2×#911102
C3×#654442
#117477662
C2×#909432
C5×#45622
#117459272
#117458972
#105999963
#713235