Finite Group Databasebeta

← #14315431

Subgroups — #14315431

Order 1920.

300 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 94 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×#65162C211yesmaximal, characteristic
2Dic5×Dic12C211yesmaximal, characteristic
3C2×#90946C211yesmaximal, characteristic
4#11746310C211yesmaximal, characteristic
5C5×#4492C211yesmaximal, characteristic
6#11745898C211yesmaximal, characteristic
7Dic5×C3⋊C16C211yesmaximal, characteristic
8#10600000—31nomaximal, Hall
9C2×C5×Dic12C2211yescharacteristic
10C2×C3×Dic20C2211yescharacteristic
11C3×#4033—21no—
12Dic5×Dic6—21no—
13C3×C5×#107C2211yescharacteristic
14#91102C2211yescharacteristic
15C2×C3⋊#672C2211yescharacteristic
16C2×C5×C3⋊C16C2211yescharacteristic
17C3×C8×Dic5C2211yescharacteristic
18C3×#3942—21no—
19#90973—21no—
20#90946C414yescomplemented
21C4×#829—51nomaximal, Hall
22Q16×Dic5—31no—
23C2×#3961—31no—
24#65162D311yescharacteristic
25C5×#358—31no—
26#64723—31no—
27C16×Dic5—31no—
28#64709—31no—
29C2×C5×Dic6—21no—
30C2×C3×Dic10—21no—
31C2×C3×C5×C8C2311yescharacteristic
32C3×C5×C4⋊C4—21no—
33C4⋊Dic15—21no—
34C5×Dic12—21no—
35C5×Dic12C2×C412yes—
36C3×#683—41no—
37C3×C4×Dic5—41no—
38C3×C4×Dic5D411yescharacteristic
39C2×C3×#168D411yescharacteristic
40C3×Dic20—21no—
41C3×Dic20C2×C412yes—
42Dic3⋊Dic5—41no—
43Dic3×Dic5—41no—
44C3⋊#672C2×C412yes—
45C5×C3⋊C16—21no—
46C3×C4×Q16—51no—
47C2×#829—51no—
48C4×Dic12—51no—
49#4564—51no—
50#4492D511yescharacteristic
51#4489—51no—
52C4×C3⋊C16—51no—
53C2×C5×Q16—31no—
54Q8×Dic5—61no—
55C2×Dic20C2×D311yescharacteristic
56#4033—21no—
57C2×C5×C16—31no—
58C5×#107C2×D311yescharacteristic
59#3967—61no—
60#3961—34no—
61#3950—31no—
62C8×Dic5C2×D311yescharacteristic
63C2×#672—31no—
64#3942—21no—
65C4×Q32—151noSylow
66C2×C3×C4×C5—41no—
67C2×C3×C4×C5C2×D411yescharacteristic
68C2×Dic15—41no—
69C2×C5×Dic3—41no—
70C5×Dic6—22no—
71C5×Dic6—41no—
72C2×C3×Dic5—41no—
73C2×C3×Dic5D811yescharacteristic
74C2×C3×Dic5D811yescharacteristic
75C3×Dic10—22no—
76C3×Dic10—41no—
77C3×C5×C8C22×C411yescharacteristic
78C3×C5×C8#4111yescharacteristic
79C3×#168—21no—
80C2×C3×Q16—51no—
81C3×C4×Q8—101no—
82C2×Dic12C2×D511yescharacteristic
83C4×Dic6—101no—
84C3×#107C2×D511yescharacteristic
85C3×#103—101no—
86C3×C4×C8—51no—
87#829—54no—
88#818—51no—
89#816—101no—
90C2×C3⋊C16—51no—
91C2×C3⋊C16C2×D511yescharacteristic
92C2×C5×Q8—61no—
93C2×Dic10—21no—
94C5×Q16—32no—
95C5×Q16—61no—
96C2×C5×C8C22×D311yescharacteristic
97C5×C4⋊C4—21no—
98C4⋊Dic5—61no—
99C4⋊Dic5—121no—
100#683—41no—
101C4×Dic5—41no—
102C4×Dic5—121no—
103C4×Dic5#6711yescharacteristic
104C2×#168#6711yescharacteristic
105Dic20—21no—
106Dic20C4×D312yes—
107C5×C16—61no—
108#672—32no—
109C2×Q32—151no—
110C4×Q16—51no—
111C4×Q16—151no—
112#366—151no—
113#358—31no—
114#358—151no—
115C4×C16—151no—
116C22×C3×C5C2×D811yescharacteristic
117C3×C4×C5—81no—
118C3×C4×C5C4×D411yescharacteristic
119C3×C4×C5#13511yescharacteristic
120Dic15—81no—
121C3×Dic5—21no—
122C3×Dic5—42no—
123C3×Dic5Q3212yescomplemented
124C5×Dic3—42no—
125C2×C3×Q8—101no—
126C2×Dic6—21no—
127C3×Q16—52no—
128C3×Q16—101no—
129C2×C3×C8—51no—
130C2×C3×C8C22×D511yescharacteristic
131C3×C4⋊C4—21no—
132C3×C4⋊C4—201no—
133C3×C42—51no—
134C3×C42—201no—
135C4⋊Dic3—101no—
136Dic3⋊C4—201no—
137C4×Dic3—201no—
138Dic12—21no—
139Dic12C4×D512yes—
140C3⋊C16—21no—
141C3⋊C16—52no—
142C5×Q8—62no—
143C5×Q8—121no—
144C2×C4×C5—41no—
145C2×C4×C5—121no—
146C2×C4×C5C2×#6711yescharacteristic
147C2×Dic5—41no—
148C2×Dic5—121no—
149C2×Dic5#21311yescharacteristic
150C2×Dic5#21311yescharacteristic
151Dic10—22no—
152Dic10—41no—
153C5×C8C2×C4×D311yescharacteristic
154C5×C8#23511yescharacteristic
155#168—21no—
156C2×Q16—31no—
157C2×Q16—51no—
158C4×Q8—101no—
159C4×Q8—301no—
160Q32—154no—
161C2×C16—31no—
162C2×C16—151no—
163#107—151no—
164#107D3×D511yescharacteristic
165#103—101no—
166#103—301no—
167C4×C8—51no—
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—51no—
175C2×C3×C4—51no—
176C2×C3×C4—201no—
177C2×C3×C4D4×D511yescharacteristic
178C2×Dic3—41no—
179C2×Dic3—201no—
180Dic6—22no—
181Dic6—41no—
182C3×C8—101no—
183C3×C8C2×C4×D511yescharacteristic
184C3×C8#71111yescharacteristic
185C22×C5C2×#21311yescharacteristic
186C4×C5—81no—
187C4×C5—122no—
188C4×C5C4×#6711yescharacteristic
189C4×C5#95011yescharacteristic
190Dic5—21no—
191Dic5—42no—
192Dic5—241no—
193Dic5#82912yescomplemented
194C2×Q8—61no—
195C2×Q8—101no—
196Q16—32no—
197Q16—52no—
198Q16—61no—
199Q16—101no—
200C2×C8—51no—
201C2×C8C2×D3×D511yescharacteristic
202C4⋊C4—21no—
203C4⋊C4—201no—
204C4⋊C4—301no—
205C4⋊C4—601no—
206C42—51no—
207C42—201no—
208C42—601no—
209C16—61no—
210C16—152no—
211C3×C5C4×Q3211yescharacteristic, complemented, Hall
212C22×C3D5×D811yescharacteristic
213C3×C4—52no—
214C3×C4—81no—
215C3×C4—101no—
216C3×C4—202no—
217C3×C4#402711yescharacteristic
218C3×C4#406211yescharacteristic
219Dic3—42no—
220Dic3—401no—
221C2×C5C4×#21311yescharacteristic
222C2×C5C2×#82911yescharacteristic
223C2×C5#519411yescharacteristic
224Q8—62no—
225Q8—102no—
226Q8—121no—
227Q8—201no—
228C2×C4—41no—
229C2×C4—51no—
230C2×C4—51no—
231C2×C4—121no—
232C2×C4—201no—
233C2×C4—601no—
234C2×C4D5×#6711yescharacteristic
235C8—101no—
236C8#677211yescharacteristic
237C8C4×D3×D511yescharacteristic
238C2×C3#6504511yescharacteristic
239C2×C3#6520511yescharacteristic
240C2×C3D5×Q3211yescharacteristic
241C5C4×#82911yescharacteristic, complemented, Sylow
242C22D5×#21311yescharacteristic
243C4—52no—
244C4—81no—
245C4—101no—
246C4—122no—
247C4—202no—
248C4—1201no—
249C4#9144011yescharacteristic
250C4#9151411yescharacteristic
251C3#1060000011yescharacteristic, complemented, Sylow
252C2#1174721611yescharacteristic
253C2#1174827911yescharacteristic
254C2D5×#82911yescharacteristic
subgroupG/H
centerC22D5×#213
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. #90946C4semidirect
123. C3×Dic5Q32semidirect
193. Dic5#829semidirect
211. C3×C5C4×Q32semidirect
241. C5C4×#829semidirect
251. C3#10600000semidirect

Maximal subgroups

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

subgroupindex
C3×#651622
Dic5×Dic122
C2×#909462
#117463102
C5×#44922
#117458982
Dic5×C3⋊C162
#106000003
C4×#8295