Finite Group Databasebeta

← #14316362

Subgroups — #14316362

Order 1920.

432 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 80 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#11756507C211yesmaximal, characteristic
2C5×#5137C211yesmaximal, characteristic, complemented
3#11747562C212yesmaximal, complemented
4C3×#64773C211yesmaximal, characteristic, complemented
5#11745914C212yesmaximal, complemented
6#10601884—31nomaximal, Hall
7C2×#6817—21no—
8C2×C3×C5×M16C2211yescharacteristic
9#91798—22no—
10#91797—22no—
11#91793—21no—
12#91793C2212yes—
13C5×#924—21no—
14C2×C5×Dic12C2211yescharacteristic, complemented
15C5×#817C2211yescharacteristic, complemented
16C5×#816—21no—
17C3×#3944C2212yescomplemented
18#90948—22no—
19#90945—22no—
20#69121—51nomaximal, Hall
21#66082—31no—
22C5×#470—31no—
23#65468—32no—
24#64773D311yescharacteristic, complemented
25#64708—32no—
26C22×C3×C4×C5D411yescharacteristic
27C2×#1220—41no—
28#6817—22no—
29#6817—22no—
30#6817—41no—
31#6817—41no—
32C2×D60—21no—
33C2×C4×D15—41no—
34C2×Dic30—21no—
35C2×C5×Dic6—21no—
36C3×C5×M16—22no—
37C2×C3×C5×C8D411yescharacteristic
38C2×C3×C5×C8C2311yescharacteristic
39Dic60—21no—
40Dic60D412yes—
41D120—21no—
42D120D412yes—
43#6706—22no—
44#6706—22no—
45C5×#217—41no—
46C5×C4⋊Dic3—21no—
47C5×Dic3⋊C4—41no—
48C5×Dic12—22no—
49C3×#672—22no—
50#5748—51no—
51#5137D511yescharacteristic, complemented
52#4909—52no—
53C3×#349—51no—
54#4518—52no—
55C2×#709—61no—
56C2×C5×Q16—31no—
57C2×C5×M16C2×D311yescharacteristic
58C5×C22⋊Q8—61no—
59#4055—62no—
60#4054—62no—
61#4050—32no—
62#4050—61no—
63C5×#106—31no—
64C5×#103—61no—
65#3961—62no—
66#3960—62no—
67#3944C2×D312yescomplemented
68#2191—151noSylow
69C23×C3×C5D811yescharacteristic
70C22×D15—41no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—21no—
73C2×C3×C4×C5D811yescharacteristic
74C2×C3×C4×C5C2×D411yescharacteristic
75#1220—42no—
76#1220—42no—
77C2×Dic15—41no—
78D60—22no—
79D60—41no—
80C4×D15—42no—
81C4×D15—42no—
82Dic30—22no—
83Dic30—41no—
84C2×C5×Dic3—41no—
85C2×C5×Dic3—41no—
86C5×Dic6—41no—
87C5×Dic6—41no—
88C3×C5×C8—21no—
89C3×C5×C8C2×D412yes—
90C2×#235—101no—
91C2×C3×M16C2×D511yescharacteristic
92#924—21no—
93#909—102no—
94#908—102no—
95C2×Dic12C2×D511yescharacteristic, complemented
96#904—52no—
97#904—101no—
98C3×M32—52no—
99#817C2×D511yescharacteristic, complemented
100#816—21no—
101Dic24—102no—
102#800—102no—
103C2×C5×Q8—61no—
104C22×C4×C5D1211yescharacteristic
105C2×C22⋊D5—121no—
106#709—62no—
107#709—62no—
108#709—121no—
109#709—121no—
110C2×D20—61no—
111C2×C4×D5—121no—
112C2×Dic10—61no—
113C5×Q16—62no—
114C5×M16—22no—
115C2×C5×C8D1211yescharacteristic
116C2×C5×C8C22×D311yescharacteristic
117C5×C4⋊C4—61no—
118C5×C4⋊C4—121no—
119C5×C22⋊C4—121no—
120Dic20—32no—
121Dic20—61no—
122D40—32no—
123D40—61no—
124#677—62no—
125#677—62no—
126#672—22no—
127#575—151no—
128#510—152no—
129#470—31no—
130#360—152no—
131#349—51no—
132C22×C3×C5—21no—
133C22×C3×C5—41no—
134C22×C3×C5C2×D811yescharacteristic
135C2×D15—42no—
136C2×D15—82no—
137C3×C4×C5—21no—
138C3×C4×C5#12011yescharacteristic
139C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
140Dic15—42no—
141C5×Dic3—81no—
142C5×Dic3—81no—
143C22×C3×C4C22⋊D511yescharacteristic
144C2×#67—201no—
145#235—102no—
146#235—102no—
147#235—201no—
148#235—201no—
149C2×D12—101no—
150C2×C4×D3—201no—
151C2×Dic6—21no—
152C2×Dic6—101no—
153C3×M16—22no—
154C2×C3×C8C22⋊D511yescharacteristic
155C2×C3×C8C22×D511yescharacteristic
156#217—41no—
157C4⋊Dic3—21no—
158Dic3⋊C4—41no—
159Dic12—22no—
160Dic12—52no—
161Dic12—101no—
162D24—52no—
163D24—101no—
164#204—102no—
165#204—102no—
166C3×C16—102no—
167C23×C5D2411yescharacteristic
168C22×D5—121no—
169C5×Q8—121no—
170C5×Q8—121no—
171C2×C4×C5—21no—
172C2×C4×C5—21no—
173C2×C4×C5—121no—
174C2×C4×C5—121no—
175C2×C4×C5D2411yescharacteristic
176C2×C4×C5C2×D1211yescharacteristic
177C22⋊D5—122no—
178C22⋊D5—122no—
179C2×Dic5—121no—
180D20—62no—
181D20—121no—
182C4×D5—122no—
183C4×D5—122no—
184Dic10—62no—
185Dic10—121no—
186C5×C8—21no—
187C5×C8D3×D412yes—
188C2×#41—301no—
189#137—302no—
190AGL(1,ℤ/8)—302no—
191#135—152no—
192#135—301no—
193C2×Q16—31no—
194C2×M16D3×D511yescharacteristic
195C22⋊Q8—61no—
196Q32—302no—
197SD32—302no—
198M32—52no—
199#106—31no—
200#103—61no—
201C2×C3×C5—21no—
202C2×C3×C5—41no—
203C2×C3×C5#44711yescharacteristic
204D15—82no—
205C23×C3#68611yescharacteristic
206C22×D3—201no—
207C2×C3×C4—21no—
208C2×C3×C4—21no—
209C2×C3×C4#68611yescharacteristic
210C2×C3×C4C2×C22⋊D511yescharacteristic
211#67—202no—
212#67—202no—
213C2×Dic3—41no—
214C2×Dic3—41no—
215C2×Dic3—201no—
216D12—102no—
217D12—201no—
218C4×D3—202no—
219C4×D3—202no—
220Dic6—41no—
221Dic6—41no—
222Dic6—102no—
223Dic6—201no—
224C3×C8—21no—
225C3×C8D4×D512yes—
226C22×C5—21no—
227C22×C5—41no—
228C22×C5C2×D2411yescharacteristic
229C2×D5—122no—
230C2×D5—242no—
231C4×C5—21no—
232C4×C5—241no—
233C4×C5—241no—
234C4×C5#88211yescharacteristic
235C4×C5#90811yescharacteristic
236Dic5—122no—
237#41—302no—
238#41—302no—
239#41—601no—
240#41—601no—
241C2×Q8—61no—
242C2×Q8—301no—
243C2×D4—301no—
244C2×D4—601no—
245C22×C4—601no—
246C22×C4#120311yescharacteristic
247Q16—62no—
248Q16—152no—
249Q16—301no—
250SD16—302no—
251SD16—302no—
252D8—152no—
253D8—301no—
254M16—22no—
255C2×C8#120311yescharacteristic
256C2×C8C2×D3×D511yescharacteristic
257C4⋊C4—61no—
258C4⋊C4—121no—
259C22⋊C4—121no—
260C16—102no—
261C3×C5#219111yescharacteristic, complemented, Hall
262C22×C3—21no—
263C22×C3—41no—
264C22×C3C2×#68611yescharacteristic
265C2×D3—202no—
266C2×D3—402no—
267C3×C4—21no—
268C3×C4#408311yescharacteristic
269C3×C4#409511yescharacteristic
270Dic3—81no—
271Dic3—81no—
272Dic3—202no—
273C2×C5—21no—
274C2×C5—41no—
275C2×C5#473211yescharacteristic
276D5—242no—
277C23—601no—
278C23#665411yescharacteristic
279Q8—121no—
280Q8—121no—
281Q8—302no—
282Q8—601no—
283D4—302no—
284D4—601no—
285D4—602no—
286D4—602no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—121no—
290C2×C4—121no—
291C2×C4—602no—
292C2×C4—601no—
293C2×C4—602no—
294C2×C4#665411yescharacteristic
295C2×C4C2×#120311yescharacteristic
296C8—21no—
297C8#679012yes—
298C2×C3—21no—
299C2×C3—41no—
300C2×C3#6532511yescharacteristic
301D3—402no—
302C5#6912111yescharacteristic, complemented, Sylow
303C22—21no—
304C22—41no—
305C22—602no—
306C22—1202no—
307C22C2×#665411yescharacteristic
308C4—21no—
309C4—241no—
310C4—241no—
311C4—602no—
312C4#9130511yescharacteristic
313C4#9157311yescharacteristic
314C3#1060188411yescharacteristic, complemented, Sylow
315C2—21no—
316C2—41no—
317C2—1202no—
318C2#1174852511yescharacteristic
subgroupG/H
centerC2#11748525
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×M16C22
socleC2×C3×C5#447
prime radical#11756507C2
hypercenterC2×M16D3×D5
hypocenterC3×C5#2191
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C5×#5137C2semidirect
3. #11747562C2semidirect
4. C3×#64773C2semidirect
5. #11745914C2semidirect
14. C2×C5×Dic12C22semidirect
15. C5×#817C22semidirect
17. C3×#3944C22semidirect
24. #64773D3semidirect
51. #5137D5semidirect
67. #3944C2×D3semidirect
95. C2×Dic12C2×D5semidirect
99. #817C2×D5semidirect
261. C3×C5#2191semidirect
302. C5#69121semidirect
314. C3#10601884semidirect

Maximal subgroups

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

subgroupindex
#117565072
C5×#51372
#117475622
C3×#647732
#117459142
#106018843
#691215