Finite Group Databasebeta

← #14315416

Subgroups — #14315416

Order 1920.

300 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 93 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
1Q16×Dic15C211yesmaximal, characteristic
2C2×#91113C211yesmaximal, characteristic
3#11750974C211yesmaximal, characteristic
4C3×C5×#358C211yesmaximal, characteristic
5#11746324C211yesmaximal, characteristic
6C16×Dic15C211yesmaximal, characteristic
7#11746310C211yesmaximal, characteristic
8#10600000—31nomaximal, Hall
9C2×C3×C5×Q16C2211yescharacteristic
10Q8×Dic15—21no—
11C2×Dic60C2211yescharacteristic
12#91776—21no—
13C2×C3×C5×C16C2211yescharacteristic
14C3×C5×#107C2211yescharacteristic
15#91119—21no—
16#91113C414yescomplemented
17#91102C2211yescharacteristic
18C8×Dic15C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20#91094—21no—
21#69207—51nomaximal, Hall
22Q16×Dic5—31no—
23C2×#3961—31no—
24#65162—31no—
25C5×#358D311yescharacteristic
26#64723—31no—
27C16×Dic5—31no—
28#64709—31no—
29C2×C3×C5×Q8—21no—
30C2×Dic30—21no—
31C3×C5×Q16—21no—
32C3×C5×Q16C2×C412yes—
33C2×C3×C5×C8C2311yescharacteristic
34C3×C5×C4⋊C4—21no—
35C4⋊Dic15—21no—
36C4⋊Dic15—41no—
37#6712—41no—
38C4×Dic15—41no—
39C4×Dic15—41no—
40C4×Dic15D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42Dic60—21no—
43Dic60C2×C412yes—
44C3×C5×C16—21no—
45C3⋊#672C2×C412yes—
46Dic3×Q16—51no—
47C2×#829—51no—
48#4873—51no—
49C3×#358D511yescharacteristic
50#4503—51no—
51Dic3×C16—51no—
52#4489—51no—
53C2×C5×Q16C2×D311yescharacteristic
54Q8×Dic5—61no—
55C2×Dic20—31no—
56#4033—61no—
57C2×C5×C16C2×D311yescharacteristic
58C5×#107C2×D311yescharacteristic
59#3967—61no—
60#3961—34no—
61#3950—31no—
62C8×Dic5—31no—
63C2×#672—31no—
64#3942—61no—
65C4×Q32—151noSylow
66C3×C5×Q8—22no—
67C3×C5×Q8—41no—
68C2×C3×C4×C5—41no—
69C2×C3×C4×C5—41no—
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×Dic15—41no—
72C2×Dic15—41no—
73C2×Dic15D811yescharacteristic
74C2×Dic15D811yescharacteristic
75Dic30—22no—
76Dic30—41no—
77C3×C5×C8C22×C411yescharacteristic
78C3×C5×C8#4111yescharacteristic
79C3⋊#168—21no—
80C2×C3×Q16C2×D511yescharacteristic
81Q8×Dic3—101no—
82C2×Dic12—51no—
83#887—101no—
84C2×C3×C16C2×D511yescharacteristic
85C3×#107C2×D511yescharacteristic
86#835—101no—
87#829—54no—
88#818—51no—
89C8×Dic3—51no—
90C2×C3⋊C16—51no—
91#810—101no—
92C2×C5×Q8—21no—
93C2×Dic10—61no—
94C5×Q16—21no—
95C5×Q16C4×D312yes—
96C2×C5×C8C22×D311yescharacteristic
97C5×C4⋊C4—21no—
98C4⋊Dic5—61no—
99C4⋊Dic5—121no—
100#683—121no—
101C4×Dic5—31no—
102C4×Dic5—121no—
103C4×Dic5—121no—
104C2×#168—31no—
105Dic20—32no—
106Dic20—61no—
107C5×C16—21no—
108#672—32no—
109C2×Q32—151no—
110C4×Q16—151no—
111C4×Q16—151no—
112#366—151no—
113#358—151no—
114#358D1511yescharacteristic
115C4×C16—151no—
116C22×C3×C5C2×D811yescharacteristic
117C3×C4×C5—42no—
118C3×C4×C5—81no—
119C3×C4×C5C4×D411yescharacteristic
120C3×C4×C5#13511yescharacteristic
121Dic15—21no—
122Dic15—42no—
123Dic15—81no—
124Dic15Q3212yescomplemented
125C2×C3×Q8—21no—
126C2×Dic6—101no—
127C3×Q16—21no—
128C3×Q16C4×D512yes—
129C2×C3×C8C22×D511yescharacteristic
130C3×C4⋊C4—21no—
131C4⋊Dic3—101no—
132C4⋊Dic3—201no—
133Dic3⋊C4—201no—
134C4×Dic3—51no—
135C4×Dic3—201no—
136C4×Dic3—201no—
137C2×C3⋊C8—51no—
138Dic12—52no—
139Dic12—101no—
140C3×C16—21no—
141C3⋊C16—52no—
142C5×Q8—22no—
143C5×Q8—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5D3×D411yescharacteristic
147C2×Dic5—31no—
148C2×Dic5—31no—
149C2×Dic5—121no—
150C2×Dic5—121no—
151Dic10—62no—
152Dic10—121no—
153C5×C8C2×C4×D311yescharacteristic
154C5×C8#23711yescharacteristic
155#168—61no—
156C2×Q16—151no—
157C2×Q16C2×D1511yescharacteristic
158C4×Q8—301no—
159C4×Q8—301no—
160Q32—154no—
161C2×C16—151no—
162C2×C16C2×D1511yescharacteristic
163#107—151no—
164#107C2×D1511yescharacteristic
165#103—301no—
166#103—301no—
167C4×C8—151no—
168C2×C3×C5C4×D811yescharacteristic
169C2×C3×C5C2×Q3211yescharacteristic
170C2×C3×C5#50811yescharacteristic
171C3×Q8—22no—
172C3×Q8—41no—
173C2×C3×C4—41no—
174C2×C3×C4—41no—
175C2×C3×C4D4×D511yescharacteristic
176C2×Dic3—51no—
177C2×Dic3—51no—
178C2×Dic3—201no—
179C2×Dic3—201no—
180Dic6—102no—
181Dic6—201no—
182C3×C8C2×C4×D511yescharacteristic
183C3×C8#71111yescharacteristic
184C3⋊C8—101no—
185C22×C5D3×D811yescharacteristic
186C4×C5—42no—
187C4×C5—81no—
188C4×C5#67⋊C411yescharacteristic
189C4×C5#91611yescharacteristic
190Dic5—32no—
191Dic5—61no—
192Dic5—122no—
193Dic5—241no—
194C2×Q8—21no—
195C2×Q8—301no—
196Q16—21no—
197Q16—152no—
198Q16—301no—
199Q16C4×D1512yes—
200C2×C8—151no—
201C2×C8C22×D1511yescharacteristic
202C4⋊C4—21no—
203C4⋊C4—301no—
204C4⋊C4—601no—
205C4⋊C4—601no—
206C42—151no—
207C42—601no—
208C42—601no—
209C16—21no—
210C16—152no—
211C3×C5C4×Q3211yescharacteristic, complemented, Hall
212C22×C3D5×D811yescharacteristic
213C3×C4—42no—
214C3×C4—81no—
215C3×C4#402711yescharacteristic
216C3×C4#406211yescharacteristic
217Dic3—52no—
218Dic3—101no—
219Dic3—202no—
220Dic3—401no—
221C2×C5#475611yescharacteristic
222C2×C5#491611yescharacteristic
223C2×C5D3×Q3211yescharacteristic
224Q8—22no—
225Q8—41no—
226Q8—302no—
227Q8—601no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—151no—
231C2×C4—151no—
232C2×C4—601no—
233C2×C4—601no—
234C2×C4D4×D1511yescharacteristic
235C8—301no—
236C8C2×C4×D1511yescharacteristic
237C8#681911yescharacteristic
238C2×C3#6504511yescharacteristic
239C2×C3#6520511yescharacteristic
240C2×C3D5×Q3211yescharacteristic
241C5#6920711yescharacteristic, complemented, Sylow
242C22D8×D1511yescharacteristic
243C4—42no—
244C4—81no—
245C4—152no—
246C4—301no—
247C4—602no—
248C4—1201no—
249C4#9177011yescharacteristic
250C4#9180511yescharacteristic
251C3#1060000011yescharacteristic, complemented, Sylow
252C2#1175085711yescharacteristic
253C2#1175101711yescharacteristic
254C2D15×Q3211yescharacteristic
subgroupG/H
centerC22D8×D15
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C22×D15
FittingC3×C5×#358C2
socle, prime radicalC22×C3×C5C2×D8
cosocleC2×C3×C5×C8C23
hypercenter#358D15
hypocenterC3×C5C4×Q32
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #358

Complements

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

NH ≅ G/Ntype
16. #91113C4semidirect
124. Dic15Q32semidirect
211. C3×C5C4×Q32semidirect
241. C5#69207semidirect
251. C3#10600000semidirect

Maximal subgroups

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

subgroupindex
Q16×Dic152
C2×#911132
#117509742
C3×C5×#3582
#117463242
C16×Dic152
#117463102
#106000003
#692075