Finite Group Databasebeta

← #14317238

Subgroups — #14317238

Order 1920.

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

normal subgroups only

This group has 340 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
1C3×#65161C211yesmaximal, characteristic, complemented
2#11747965C211yesmaximal, characteristic, complemented
3C2×#90940C211yesmaximal, characteristic, complemented
4C2×#90938C211yesmaximal, characteristic
5#11746312C211yesmaximal, characteristic, complemented
6C5×#4492C211yesmaximal, characteristic, complemented
7#11745927C211yesmaximal, characteristic, complemented
8#10600028—31nomaximal, Hall
9C2×D120C2211yescharacteristic
10C2×C5×Dic12C2211yescharacteristic
11C2×C3×D40C2211yescharacteristic
12C3×#4039—21no—
13#91375—21no—
14C2×#6660—21no—
15C3×C5×#107C2211yescharacteristic
16C2×C3⋊#672C2211yescharacteristic
17C2×C5×C3⋊C16C2211yescharacteristic
18C3×C8×Dic5C2211yescharacteristic
19C3×#3941—21no—
20#90940—22no—
21#90938—22no—
22#70890—51nomaximal, Hall
23#65480—31no—
24C2×#3960—31no—
25C2×D80—31no—
26#65161D311yescharacteristic, complemented
27C5×#358—31no—
28#64721—31no—
29#64711—31no—
30C2×D60—21no—
31C2×C5×Dic6—21no—
32C2×C3×D20—21no—
33C2×C3×C4×D5—41no—
34C2×C3×C5×C8C2311yescharacteristic
35C3×C5×C4⋊C4—21no—
36D120—21no—
37D120—21no—
38C5×Dic12—21no—
39C5×Dic12—21no—
40C3×#685—41no—
41C3×C4×Dic5D411yescharacteristic
42C2×C3×#168D411yescharacteristic
43C3×D40—21no—
44C3×D40D412yes—
45#6667—41no—
46#6667—41no—
47#6660—42no—
48C3⋊#672—21no—
49C5×C3⋊C16—21no—
50C3×C4×D8—51no—
51C2×#827—51no—
52C2×#826—51no—
53#4696—51no—
54#4492D511yescharacteristic, complemented
55#4491—51no—
56C4⋊(C3⋊C16)—51no—
57C2×C5×Q16—31no—
58#4093—61no—
59C2×#688—61no—
60C2×D40—31no—
61C2×D40C2×D311yescharacteristic
62#4039—21no—
63C2×C5×C16—31no—
64C5×#107C2×D311yescharacteristic
65#3960—62no—
66C8×Dic5C2×D311yescharacteristic
67C2×#672—31no—
68#3941—21no—
69D80—62no—
70#2210—151noSylow
71C22×D15—41no—
72C22×C3×D5—41no—
73C2×C3×C4×C5—41no—
74C2×C3×C4×C5C2×D411yescharacteristic
75D60—41no—
76D60—41no—
77C2×C5×Dic3—41no—
78C5×Dic6—41no—
79C5×Dic6—41no—
80C2×C3×Dic5D811yescharacteristic
81C2×C3×Dic5D811yescharacteristic
82C3×D20—22no—
83C3×D20—41no—
84C3×C4×D5—82no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3×#168—21no—
88C2×C3×D8—51no—
89C3×C4×D4—101no—
90C2×Dic12C2×D511yescharacteristic
91C2×D24—51no—
92C2×#204—101no—
93#875—101no—
94C3×#107C2×D511yescharacteristic
95C3×#102—101no—
96C3×C4×C8—51no—
97#827—102no—
98#826—102no—
99C2×C3⋊C16—51no—
100C2×C3⋊C16C2×D511yescharacteristic
101C2×C5×Q8—61no—
102C2×D20—21no—
103C2×D20—61no—
104C2×C4×D5—41no—
105C5×Q16—61no—
106C5×Q16—61no—
107C2×C5×C8C22×D311yescharacteristic
108C5×C4⋊C4—21no—
109#688—122no—
110#685—41no—
111#685—121no—
112#685—121no—
113C4×Dic5#6711yescharacteristic
114C2×#168#6711yescharacteristic
115D40—21no—
116D40—61no—
117D40—61no—
118D40D1212yes—
119C5×C16—61no—
120#672—61no—
121C2×SD32—151no—
122C2×D16—151no—
123#495—151no—
124C4×D8—51no—
125C4⋊C16—151no—
126#358—31no—
127#357—151no—
128C22×C3×C5C2×D811yescharacteristic
129C2×D15—81no—
130C2×D15—81no—
131C2×D15—81no—
132C2×C3×D5—42no—
133C2×C3×D5—81no—
134C2×C3×D5—81no—
135C3×C4×C5—81no—
136C3×C4×C5#12111yescharacteristic
137C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
138C3×Dic5—21no—
139C3×Dic5—21no—
140C5×Dic3—81no—
141C2×C3×D4—101no—
142C22×C3×C4—201no—
143C2×D12—101no—
144C2×Dic6—21no—
145C3×D8—52no—
146C3×D8—101no—
147C2×C3×C8—51no—
148C2×C3×C8C22×D511yescharacteristic
149C3×C4⋊C4—21no—
150C3×C22⋊C4—201no—
151C3×C42—51no—
152(C2×D3)⋊C4—201no—
153(C2×D3)⋊C4—201no—
154Dic12—21no—
155Dic12—21no—
156D24—101no—
157D24—101no—
158#204—202no—
159C3⋊C16—21no—
160C3⋊C16—101no—
161C22×D5—41no—
162C22×D5—121no—
163C5×Q8—121no—
164C5×Q8—121no—
165C2×C4×C5—41no—
166C2×C4×C5—121no—
167C2×C4×C5C2×#6711yescharacteristic
168C2×Dic5#21311yescharacteristic
169C2×Dic5#21311yescharacteristic
170D20—22no—
171D20—41no—
172D20—121no—
173D20—121no—
174C4×D5—82no—
175C5×C8C2×D1211yescharacteristic
176C5×C8#23511yescharacteristic
177#168—21no—
178C2×Q16—31no—
179C2×SD16—301no—
180C2×D8—51no—
181C2×D8—151no—
182#124—301no—
183C4×D4—101no—
184SD32—302no—
185D16—302no—
186C2×C16—31no—
187C2×C16—151no—
188#107D3×D511yescharacteristic
189#102—101no—
190C4×C8—51no—
191C2×C3×C5#45911yescharacteristic
192C2×C3×C5#50811yescharacteristic
193C2×C3×C5#50911yescharacteristic
194D15—161no—
195C3×D5—82no—
196C23×C3—201no—
197C22×D3—201no—
198C3×D4—102no—
199C3×D4—201no—
200C2×C3×C4—41no—
201C2×C3×C4—51no—
202C2×C3×C4—51no—
203C2×C3×C4—402no—
204C2×C3×C4D4×D511yescharacteristic
205C2×Dic3—41no—
206D12—201no—
207D12—201no—
208Dic6—41no—
209Dic6—41no—
210C3×C8—101no—
211C3×C8#70911yescharacteristic
212C3×C8D4×D511yescharacteristic
213C22×C5C2×#21311yescharacteristic
214C2×D5—42no—
215C2×D5—81no—
216C2×D5—81no—
217C2×D5—241no—
218C2×D5—241no—
219C2×D5—241no—
220C4×C5—81no—
221C4×C5—241no—
222C4×C5#93011yescharacteristic
223C4×C5#94911yescharacteristic
224Dic5—21no—
225Dic5—21no—
226C2×Q8—61no—
227C2×D4—101no—
228C2×D4—301no—
229C22×C4—201no—
230Q16—61no—
231Q16—61no—
232SD16—602no—
233D8—52no—
234D8—101no—
235D8—301no—
236D8—301no—
237C2×C8—51no—
238C2×C8C2×D3×D511yescharacteristic
239C4⋊C4—21no—
240C22⋊C4—201no—
241C22⋊C4—601no—
242C22⋊C4—601no—
243C42—51no—
244C16—61no—
245C16—301no—
246C3×C5#221011yescharacteristic, complemented, Hall
247C22×C3—202no—
248C22×C3—401no—
249C22×C3—401no—
250C22×C3D5×D811yescharacteristic
251C2×D3—401no—
252C2×D3—401no—
253C2×D3—401no—
254C3×C4—81no—
255C3×C4—101no—
256C3×C4—101no—
257C3×C4#403011yescharacteristic
258C3×C4#406011yescharacteristic
259Dic3—81no—
260C2×C5#501511yescharacteristic
261C2×C5#514711yescharacteristic
262C2×C5#519411yescharacteristic
263D5—82no—
264D5—481no—
265C23—201no—
266C23—601no—
267Q8—121no—
268Q8—121no—
269D4—102no—
270D4—201no—
271D4—601no—
272D4—601no—
273C2×C4—41no—
274C2×C4—51no—
275C2×C4—51no—
276C2×C4—121no—
277C2×C4—402no—
278C2×C4D5×#6711yescharacteristic
279C8—101no—
280C8#677111yescharacteristic
281C8D5×D1211yescharacteristic
282C2×C3—402no—
283C2×C3#6507511yescharacteristic
284C2×C3#6520311yescharacteristic
285C2×C3#6520811yescharacteristic
286D3—801no—
287C5#7089011yescharacteristic, complemented, Sylow
288C22—202no—
289C22—401no—
290C22—401no—
291C22—1201no—
292C22—1201no—
293C22—1201no—
294C22D5×#21311yescharacteristic
295C4—81no—
296C4—101no—
297C4—101no—
298C4—241no—
299C4#9144811yescharacteristic
300C4#9150211yescharacteristic
301C3#1060002811yescharacteristic, complemented, Sylow
302C2—402no—
303C2—2401no—
304C2#1174739911yescharacteristic
305C2#1174827811yescharacteristic
306C2#1174830311yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socleC22×C3×C5C2×D8
prime radicalC2×#90938C2
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. C3×#65161C2semidirect
2. #11747965C2semidirect
3. C2×#90940C2semidirect
5. #11746312C2semidirect
6. C5×#4492C2semidirect
7. #11745927C2semidirect
26. #65161D3semidirect
54. #4492D5semidirect
246. C3×C5#2210semidirect
287. C5#70890semidirect
301. C3#10600028semidirect

Maximal subgroups

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

subgroupindex
C3×#651612
#117479652
C2×#909402
C2×#909382
#117463122
C5×#44922
#117459272
#106000283
#708905