Finite Group Databasebeta

← #14315435

Subgroups — #14315435

Order 1920.

300 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 88 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#11750974C211yesmaximal, characteristic
2#11747883C211yesmaximal, characteristic
3C2×#90947C211yesmaximal, characteristic
4C5×#4489C211yesmaximal, characteristic
5C3×#64712C211yesmaximal, characteristic
6#11745902C211yesmaximal, characteristic
7#11745872C211yesmaximal, characteristic
8#10600111—31nomaximal, Hall
9C2×Dic60C2211yescharacteristic
10#91776—21no—
11C2×C3×Dic20C2211yescharacteristic
12#91331—21no—
13C3×C5×#107C2211yescharacteristic
14C8×Dic15C2211yescharacteristic
15#91094—21no—
16C5×#818C2211yescharacteristic
17C2×C5×C3⋊C16C2211yescharacteristic
18C2×C3×#672C2211yescharacteristic
19#90970—21no—
20#90947C414yescomplemented
21#69207—51nomaximal, Hall
22C2×Dic40—31no—
23#65162—31no—
24#65162—31no—
25C5×#366—31no—
26C16×Dic5—31no—
27#64712—31no—
28#64712D311yescharacteristic
29C2×Dic30—21no—
30C2×C3×Dic10—21no—
31C2×C3×C5×C8C2311yescharacteristic
32C3×C5×C4⋊C4—21no—
33#6712—41no—
34C4×Dic15—41no—
35C4×Dic15D411yescharacteristic
36C2×C3⋊#168D411yescharacteristic
37Dic60—21no—
38Dic60C2×C412yes—
39C5×C4⋊Dic3—21no—
40C3×Dic20—21no—
41C3×Dic20C2×C412yes—
42#6668—41no—
43Dic3×Dic5—41no—
44C3×#672—21no—
45C5×C3⋊C16C2×C412yes—
46Dic3×Q16—51no—
47C2×#829—51no—
48#4873—51no—
49C3×#358—51no—
50#4503—51no—
51Dic3×C16—51no—
52#4489D511yescharacteristic
53C2×Dic20—31no—
54C2×Dic20C2×D311yescharacteristic
55#4033—61no—
56#4033—61no—
57C2×C5×C16—31no—
58C5×#107—31no—
59C5×#107C2×D311yescharacteristic
60C8×Dic5—31no—
61C2×#672C2×D311yescharacteristic
62#3942—61no—
63#3942—61no—
64Dic40—34no—
65C4×Q32—151noSylow
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×Dic15—41no—
69C2×Dic15D811yescharacteristic
70C2×Dic15D811yescharacteristic
71Dic30—22no—
72Dic30—41no—
73C2×C5×Dic3—41no—
74C2×C3×Dic5—41no—
75C3×Dic10—22no—
76C3×Dic10—41no—
77C3×C5×C8C22×C411yescharacteristic
78C3×C5×C8#4111yescharacteristic
79C3⋊#168—21no—
80C2×C3×Q16—51no—
81Q8×Dic3—101no—
82C2×Dic12—51no—
83#887—101no—
84C2×C3×C16—51no—
85C3×#107C2×D511yescharacteristic
86#835—101no—
87#829—54no—
88#818C2×D511yescharacteristic
89C8×Dic3—51no—
90C2×C3⋊C16C2×D511yescharacteristic
91#810—101no—
92C2×Dic10—21no—
93C2×Dic10—61no—
94C2×C5×C8C22×D311yescharacteristic
95C5×C4⋊C4—21no—
96C5×C4⋊C4—61no—
97#683—121no—
98#683—121no—
99C4×Dic5—31no—
100C4×Dic5—121no—
101C4×Dic5—121no—
102C2×#168—31no—
103Dic20—21no—
104Dic20—32no—
105Dic20—61no—
106Dic20C4×D312yes—
107C5×C16—32no—
108#672—21no—
109C2×Q32—151no—
110C4×Q16—151no—
111C4×Q16—151no—
112#366—31no—
113#358—51no—
114#358—151no—
115C4×C16—151no—
116C22×C3×C5C2×D811yescharacteristic
117C3×C4×C5—81no—
118C3×C4×C5C4×D411yescharacteristic
119C3×C4×C5#13511yescharacteristic
120Dic15—21no—
121Dic15—42no—
122Dic15Q3212yescomplemented
123C3×Dic5—42no—
124C5×Dic3—81no—
125C2×C3×Q8—101no—
126C2×Dic6—101no—
127C3×Q16—52no—
128C3×Q16—101no—
129C2×C3×C8C22×D511yescharacteristic
130C3×C4⋊C4—21no—
131C4⋊Dic3—21no—
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—101no—
141C3⋊C16C4×D512yes—
142C2×C4×C5—41no—
143C2×C4×C5—121no—
144C2×C4×C5D3×D411yescharacteristic
145C2×Dic5—31no—
146C2×Dic5—31no—
147C2×Dic5—41no—
148C2×Dic5—121no—
149Dic10—22no—
150Dic10—41no—
151Dic10—62no—
152Dic10—121no—
153C5×C8C2×C4×D311yescharacteristic
154C5×C8#23711yescharacteristic
155#168—61no—
156C2×Q16—51no—
157C2×Q16—151no—
158C4×Q8—301no—
159C4×Q8—301no—
160Q32—154no—
161C2×C16—31no—
162C2×C16—51no—
163#107—31no—
164#107D3×D511yescharacteristic
165#103—301no—
166#103—301no—
167C4×C8—151no—
168C2×C3×C5C4×D811yescharacteristic
169C2×C3×C5C2×Q3211yescharacteristic
170C2×C3×C5#50811yescharacteristic
171C3×Q8—102no—
172C3×Q8—201no—
173C2×C3×C4—41no—
174C2×C3×C4—201no—
175C2×C3×C4D4×D511yescharacteristic
176C2×Dic3—41no—
177C2×Dic3—51no—
178C2×Dic3—51no—
179C2×Dic3—201no—
180Dic6—102no—
181Dic6—201no—
182C3×C8C2×C4×D511yescharacteristic
183C3×C8#71311yescharacteristic
184C3⋊C8—101no—
185C22×C5D3×D811yescharacteristic
186C4×C5—81no—
187C4×C5—241no—
188C4×C5#67⋊C411yescharacteristic
189C4×C5#91611yescharacteristic
190Dic5—32no—
191Dic5—42no—
192Dic5—61no—
193Dic5—122no—
194C2×Q8—101no—
195C2×Q8—301no—
196Q16—52no—
197Q16—101no—
198Q16—152no—
199Q16—301no—
200C2×C8—151no—
201C2×C8C2×D3×D511yescharacteristic
202C4⋊C4—21no—
203C4⋊C4—61no—
204C4⋊C4—601no—
205C4⋊C4—601no—
206C42—151no—
207C42—601no—
208C42—601no—
209C16—32no—
210C16—101no—
211C3×C5C4×Q3211yescharacteristic, complemented, Hall
212C22×C3D5×D811yescharacteristic
213C3×C4—81no—
214C3×C4—202no—
215C3×C4#403911yescharacteristic
216C3×C4#406511yescharacteristic
217Dic3—52no—
218Dic3—81no—
219Dic3—101no—
220Dic3—202no—
221C2×C5#475611yescharacteristic
222C2×C5#491611yescharacteristic
223C2×C5D3×Q3211yescharacteristic
224Q8—102no—
225Q8—201no—
226Q8—302no—
227Q8—601no—
228C2×C4—41no—
229C2×C4—121no—
230C2×C4—151no—
231C2×C4—151no—
232C2×C4—201no—
233C2×C4—601no—
234C2×C4#679011yescharacteristic
235C8—301no—
236C8#676611yescharacteristic
237C8C4×D3×D511yescharacteristic
238C2×C3#6516111yescharacteristic
239C2×C3#6520111yescharacteristic
240C2×C3D5×Q3211yescharacteristic
241C5#6920711yescharacteristic, complemented, Sylow
242C22#9148111yescharacteristic
243C4—81no—
244C4—152no—
245C4—202no—
246C4—241no—
247C4—301no—
248C4—602no—
249C4#9139611yescharacteristic
250C4#9152111yescharacteristic
251C3#1060011111yescharacteristic, complemented, Sylow
252C2#1174722611yescharacteristic
253C2#1174828611yescharacteristic
254C2#1174829811yescharacteristic
subgroupG/H
centerC22#91481
commutatorC3×C5×C8C22×C4
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#107C22
socle, prime radicalC22×C3×C5C2×D8
cosocleC2×C3×C5×C8C23
hypercenter#107D3×D5
hypocenterC3×C5C4×Q32
LCSG ▷ 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
20. #90947C4semidirect
122. Dic15Q32semidirect
211. C3×C5C4×Q32semidirect
241. C5#69207semidirect
251. C3#10600111semidirect

Maximal subgroups

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

subgroupindex
#117509742
#117478832
C2×#909472
C5×#44892
C3×#647122
#117459022
#117458722
#106001113
#692075