Finite Group Databasebeta

← #14317286

Subgroups — #14317286

Order 1920.

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

normal subgroups only

This group has 316 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
1C2×C5×#829C211yesmaximal, characteristic, complemented
2C3×#65480C211yesmaximal, characteristic
3Dic5×Dic12C211yesmaximal, characteristic, complemented
4C2×#90940C211yesmaximal, characteristic
5#11746385C211yesmaximal, characteristic, complemented
6#11745927C211yesmaximal, characteristic, complemented
7#11745892C211yesmaximal, characteristic
8#10602291—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10C2×C5×Dic12C2211yescharacteristic
11C3×#4093—21no—
12C2×C3×#688—21no—
13C2×C3×D40C2211yescharacteristic
14Dic5×Dic6—21no—
15#91102C2211yescharacteristic
16C2×C3⋊#672C2211yescharacteristic
17C5×#829—22no—
18C2×C5×C3⋊C16C2211yescharacteristic
19C3×C8×Dic5C2211yescharacteristic
20#90973—21no—
21#90940—22no—
22#71324—51nomaximal, Hall
23C2×C5×Q32—31no—
24#65480D311yescharacteristic
25Q16×Dic5—31no—
26C2×#3960—31no—
27#64784—31no—
28#64729—31no—
29#64721—31no—
30C2×C3×C5×Q8—21no—
31C2×C5×Dic6—21no—
32C2×C3×D20—21no—
33C3×C5×Q16—21no—
34C3×C5×Q16—21no—
35C2×C3×C5×C8C2311yescharacteristic
36C4⋊Dic15—21no—
37C5×Dic12—21no—
38C5×Dic12D412yes—
39C3×#688—42no—
40C3×#685—41no—
41C3×#685—41no—
42C3×C4×Dic5D411yescharacteristic
43C2×C3×#168D411yescharacteristic
44C3×D40—21no—
45C3×D40—21no—
46Dic3⋊Dic5—41no—
47Dic3×Dic5—41no—
48C3⋊#672—21no—
49C5×C3⋊C16—21no—
50C3×#495—51no—
51C2×#829D511yescharacteristic, complemented
52C2×#827—51no—
53C4×Dic12—51no—
54#4564—51no—
55#4562—51no—
56C4⋊(C3⋊C16)—51no—
57C2×C5×Q16—31no—
58C2×C5×Q16C2×D311yescharacteristic
59#4093—21no—
60Q8×Dic5—61no—
61C2×#688—21no—
62C2×D40C2×D311yescharacteristic
63C5×Q32—62no—
64C2×C5×C16—31no—
65#3967—61no—
66#3960—62no—
67#3950—31no—
68C8×Dic5C2×D311yescharacteristic
69C2×#672—31no—
70#2211—151noSylow
71C22×C3×D5—41no—
72C3×C5×Q8—41no—
73C3×C5×Q8—41no—
74C2×C3×C4×C5—41no—
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×Dic15—41no—
77C2×C5×Dic3—41no—
78C5×Dic6—22no—
79C5×Dic6—41no—
80C2×C3×Dic5D811yescharacteristic
81C2×C3×Dic5D811yescharacteristic
82C3×D20—41no—
83C3×D20—41no—
84C3×C5×C8C2×D411yescharacteristic
85C3×C5×C8#4111yescharacteristic
86C3×#168—21no—
87C2×C3×Q16C2×D511yescharacteristic
88C2×C3×SD16—101no—
89C2×C3×D8—51no—
90C3×#124—101no—
91C2×Dic12C2×D511yescharacteristic
92C4×Dic6—101no—
93C3×C4×C8—51no—
94#829—22no—
95#827—102no—
96#818—51no—
97#816—101no—
98C2×C3⋊C16—51no—
99C2×C3⋊C16C2×D511yescharacteristic
100C2×C5×Q8—21no—
101C2×C5×Q8—61no—
102C2×D20—21no—
103C5×Q16—21no—
104C5×Q16—21no—
105C5×Q16—32no—
106C5×Q16—61no—
107C2×C5×C8C22×D311yescharacteristic
108#688—42no—
109#685—41no—
110#685—41no—
111C4⋊Dic5—61no—
112C4⋊Dic5—121no—
113C4×Dic5—121no—
114C4×Dic5#6711yescharacteristic
115C2×#168#6711yescharacteristic
116D40—21no—
117D40—21no—
118C5×C16—61no—
119#672—61no—
120C2×Q32—31no—
121C2×SD32—151no—
122#495—51no—
123C4×Q16—151no—
124C4⋊C16—151no—
125#358—151no—
126#357—151no—
127C22×C3×C5C2×D811yescharacteristic
128C2×C3×D5—81no—
129C2×C3×D5—81no—
130C2×C3×D5—81no—
131C3×C4×C5—81no—
132C3×C4×C5#12111yescharacteristic
133C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
134Dic15—81no—
135C3×Dic5—21no—
136C3×Dic5—21no—
137C5×Dic3—42no—
138C2×C3×Q8—21no—
139C2×C3×D4—101no—
140C2×Dic6—21no—
141C3×Q16—21no—
142C3×Q16—21no—
143C3×SD16—202no—
144C3×D8—101no—
145C3×D8—101no—
146C2×C3×C8—51no—
147C2×C3×C8C22×D511yescharacteristic
148C3×C22⋊C4—201no—
149C3×C22⋊C4—201no—
150C3×C42—51no—
151C4⋊Dic3—101no—
152Dic3⋊C4—201no—
153C4×Dic3—201no—
154Dic12—21no—
155Dic12C22⋊D512yes—
156C3⋊C16—21no—
157C3⋊C16—101no—
158C22×D5—41no—
159C5×Q8—41no—
160C5×Q8—41no—
161C5×Q8—62no—
162C5×Q8—121no—
163C2×C4×C5—41no—
164C2×C4×C5—121no—
165C2×C4×C5C2×#6711yescharacteristic
166C2×Dic5—121no—
167C2×Dic5#21311yescharacteristic
168C2×Dic5#21311yescharacteristic
169D20—41no—
170D20—41no—
171C5×C8D3×D411yescharacteristic
172C5×C8#23711yescharacteristic
173#168—21no—
174C2×Q16—31no—
175C2×Q16D3×D511yescharacteristic
176C2×SD16—101no—
177C2×D8—51no—
178#124—101no—
179C4×Q8—301no—
180Q32—62no—
181SD32—302no—
182C2×C16—31no—
183C2×C16—151no—
184#107—151no—
185#103—301no—
186C4×C8—51no—
187C2×C3×C5#45911yescharacteristic
188C2×C3×C5#50811yescharacteristic
189C2×C3×C5#51011yescharacteristic
190C3×D5—161no—
191C23×C3—201no—
192C3×Q8—41no—
193C3×Q8—41no—
194C3×D4—201no—
195C3×D4—201no—
196C2×C3×C4—41no—
197C2×C3×C4—51no—
198C2×C3×C4—51no—
199C2×C3×C4D4×D511yescharacteristic
200C2×Dic3—41no—
201C2×Dic3—201no—
202Dic6—22no—
203Dic6—41no—
204C3×C8—101no—
205C3×C8#71111yescharacteristic
206C3×C8C2×C22⋊D511yescharacteristic
207C22×C5C2×#21311yescharacteristic
208C2×D5—81no—
209C2×D5—81no—
210C2×D5—81no—
211C4×C5—81no—
212C4×C5—122no—
213C4×C5#93211yescharacteristic
214C4×C5#93811yescharacteristic
215Dic5—21no—
216Dic5—21no—
217Dic5—241no—
218C2×Q8—21no—
219C2×Q8—61no—
220C2×D4—101no—
221Q16—21no—
222Q16—21no—
223Q16—32no—
224Q16—61no—
225SD16—202no—
226D8—101no—
227D8—101no—
228C2×C8—51no—
229C2×C8C2×D3×D511yescharacteristic
230C4⋊C4—301no—
231C4⋊C4—601no—
232C22⋊C4—201no—
233C22⋊C4—201no—
234C42—51no—
235C42—601no—
236C16—61no—
237C16—301no—
238C3×C5#221111yescharacteristic, complemented, Hall
239C22×C3—401no—
240C22×C3—401no—
241C22×C3—401no—
242C22×C3D5×D811yescharacteristic
243C3×C4—81no—
244C3×C4—101no—
245C3×C4—101no—
246C3×C4#405711yescharacteristic
247C3×C4#408511yescharacteristic
248Dic3—42no—
249Dic3—401no—
250C2×C5#507211yescharacteristic
251C2×C5#519411yescharacteristic
252C2×C5#519511yescharacteristic
253D5—161no—
254C23—201no—
255Q8—41no—
256Q8—41no—
257Q8—62no—
258Q8—121no—
259D4—201no—
260D4—201no—
261C2×C4—41no—
262C2×C4—51no—
263C2×C4—51no—
264C2×C4—121no—
265C2×C4—601no—
266C2×C4D5×#6711yescharacteristic
267C8—101no—
268C8#678011yescharacteristic
269C8D3×C22⋊D511yescharacteristic
270C2×C3—801no—
271C2×C3#6520711yescharacteristic
272C2×C3#6520811yescharacteristic
273C2×C3#6543911yescharacteristic
274C5#7132411yescharacteristic, complemented, Sylow
275C22—401no—
276C22—401no—
277C22—401no—
278C22D5×#21311yescharacteristic
279C4—81no—
280C4—101no—
281C4—101no—
282C4—122no—
283C4—1201no—
284C4#9148911yescharacteristic
285C4#9156511yescharacteristic
286C3#1060229111yescharacteristic, complemented, Sylow
287C2—801no—
288C2#1174829511yescharacteristic
289C2#1174830311yescharacteristic
290C2#1174897411yescharacteristic
subgroupG/H
centerC22D5×#213
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×Q16C22
socleC22×C3×C5C2×D8
prime radicalC2×C3×D40C22
hypercenterC2×Q16D3×D5
hypocenterC3×C5#2211
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×C5×#829C2semidirect
3. Dic5×Dic12C2semidirect
5. #11746385C2semidirect
6. #11745927C2semidirect
51. C2×#829D5semidirect
238. C3×C5#2211semidirect
274. C5#71324semidirect
286. C3#10602291semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#8292
C3×#654802
Dic5×Dic122
C2×#909402
#117463852
#117459272
#117458922
#106022913
#713245