Finite Group Databasebeta

← #14289598

Subgroups — #14289598

Order 1920.

436 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 92 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×#66068C211yesmaximal, characteristic
2C5×#5092C211yesmaximal, characteristic, complemented
3#11746880C212yesmaximal, complemented
4#11746367C211yesmaximal, characteristic, complemented
5#11745835C212yesmaximal, complemented
6#10602097—31nomaximal, Hall
7C3×C5×C4⋊Q8C2211yescharacteristic
8C2×C5×#216—22no—
9C5×#869C2211yescharacteristic
10C3×#4093—22no—
11C3×#4041—22no—
12C3×#4038—22no—
13C3×C4×D20C2212yes—
14C4⋊(C3⋊#168)C2212yes—
15C4×C5×C3⋊C8C2211yescharacteristic
16#90986—22no—
17#90964—22no—
18#71928—51nomaximal, Hall
19#66068D311yescharacteristic
20C5×#494—31no—
21#65373—32no—
22#64766—31no—
23#64679—32no—
24C2×C3×C5×Q8D412yes—
25C2×C5×Dic6—21no—
26C2×C3×D20—22no—
27C2×C3×D20D412yes—
28C2×C3×C4×D5—22no—
29C3×C5×C4⋊C4—22no—
30C3×C42×C5C2311yescharacteristic
31C2×C3⋊#168—22no—
32C5×#216—44no—
33C5×C4⋊Dic3—22no—
34C2×C5×C3⋊C8—21no—
35C3×#685—24no—
36C3×#685—22no—
37C3×C4⋊Dic5D412yes—
38C3×C4×Dic5—22no—
39C3×#555—51no—
40#5092D511yescharacteristic, complemented
41#5008—52no—
42#4546—51no—
43D4⋊(C3⋊C8)—52no—
44C2×C5×Q16—62no—
45C5×C4⋊Q8—31no—
46C5×C4⋊Q8C2×D311yescharacteristic
47#4093—22no—
48#4041—22no—
49#4038—22no—
50C4×D20C2×D312yes—
51C4×C5×C8—31no—
52#3941—62no—
53#3940—62no—
54C4⋊#168—32no—
55#1634—151noSylow
56C22×C3×D5—22no—
57C3×C5×Q8—42no—
58C2×C3×C4×C5—22no—
59C2×C3×C4×C5C2×D411yescharacteristic
60C2×C3×C4×C5C2×D412yes—
61C2×C5×Dic3—41no—
62C5×Dic6—42no—
63C2×C3×Dic5—22no—
64C3×D20—22no—
65C3×D20—22no—
66C3×D20—82no—
67C3×C4×D5—42no—
68C3×C4×D5—42no—
69C3⋊#168—42no—
70C5×C3⋊C8—22no—
71C3×C4⋊Q8C2×D511yescharacteristic
72C3×#124—102no—
73C3×#121—102no—
74C3×C4×D4—52no—
75C3×#117—102no—
76C2×#216—22no—
77#869C2×D511yescharacteristic
78#832—102no—
79#808—102no—
80C4⋊(C3⋊C8)—52no—
81C4×C3⋊C8C2×D511yescharacteristic
82C2×C5×Q8—61no—
83C2×C5×Q8#6712yes—
84C2×D20—22no—
85C2×D20#6712yes—
86C2×C4×D5—22no—
87C5×Q16—124no—
88C2×C5×C8—61no—
89C5×C4⋊C4—22no—
90C5×C4⋊C4—62no—
91C42×C5C22×D311yescharacteristic
92#685—24no—
93#685—22no—
94C4⋊Dic5#6712yes—
95C4×Dic5—22no—
96C2×#168—62no—
97#555—51no—
98#494—31no—
99#476—152no—
100#333—151no—
101D4⋊C8—152no—
102C22×C3×C5#12011yescharacteristic
103C2×C3×D5—42no—
104C2×C3×D5—42no—
105C2×C3×D5—42no—
106C3×C4×C5—21no—
107C3×C4×C5—42no—
108C3×C4×C5#13512yes—
109C3×C4×C5#13712yes—
110C3×Dic5—42no—
111C5×Dic3—81no—
112C2×C3×Q8C22⋊D512yes—
113C2×C3×D4—52no—
114C2×C3×D4—102no—
115C22×C3×C4—102no—
116C2×Dic6—21no—
117C3×C4⋊C4—22no—
118C3×C4⋊C4—52no—
119C3×C22⋊C4—104no—
120C3×C22⋊C4—102no—
121C3×C42—102no—
122C3×C42C22×D511yescharacteristic
123#216—44no—
124C4⋊Dic3—22no—
125C2×C3⋊C8—21no—
126C2×C3⋊C8—102no—
127C22×D5—22no—
128C5×Q8—42no—
129C5×Q8—122no—
130C2×C4×C5—22no—
131C2×C4×C5—121no—
132C2×C4×C5C2×#6711yescharacteristic
133C2×C4×C5C2×#6712yes—
134C2×Dic5—22no—
135D20—22no—
136D20—22no—
137D20—82no—
138C4×D5—42no—
139C4×D5—42no—
140C5×C8—62no—
141#168—122no—
142C2×Q16—62no—
143C4⋊Q8—31no—
144C4⋊Q8D3×D511yescharacteristic
145#124—102no—
146#121—102no—
147C4×D4—52no—
148#117—102no—
149#106—302no—
150C4⋊C8—152no—
151#102—302no—
152C4×C8—31no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155C3×D5—82no—
156C23×C3—102no—
157C3×Q8—42no—
158C3×D4—102no—
159C3×D4—102no—
160C3×D4—402no—
161C2×C3×C4—22no—
162C2×C3×C4—102no—
163C2×C3×C4—202no—
164C2×C3×C4—202no—
165C2×C3×C4D4×D512yes—
166C2×C3×C4C2×C22⋊D511yescharacteristic
167C2×Dic3—41no—
168Dic6—42no—
169C3⋊C8—22no—
170C3⋊C8—202no—
171C22×C5#95311yescharacteristic
172C2×D5—42no—
173C2×D5—42no—
174C2×D5—42no—
175C4×C5—21no—
176C4×C5—42no—
177C4×C5—241no—
178C4×C5#95012yes—
179C4×C5#95112yes—
180Dic5—42no—
181C2×Q8—61no—
182C2×Q8#120112yes—
183C2×D4—52no—
184C2×D4—102no—
185C22×C4—102no—
186Q16—124no—
187C2×C8—61no—
188C2×C8—302no—
189C4⋊C4—22no—
190C4⋊C4—52no—
191C4⋊C4—62no—
192C22⋊C4—104no—
193C22⋊C4—102no—
194C42—102no—
195C42C2×D3×D511yescharacteristic
196C3×C5#163411yescharacteristic, complemented, Hall
197C22×C3—202no—
198C22×C3—202no—
199C22×C3—202no—
200C22×C3#408311yescharacteristic
201C3×C4—21no—
202C3×C4—42no—
203C3×C4—202no—
204C3×C4#406412yes—
205C3×C4#406512yes—
206Dic3—81no—
207C2×C5#523912yes—
208C2×C5#524111yescharacteristic
209D5—82no—
210C23—102no—
211Q8—42no—
212Q8—122no—
213D4—102no—
214D4—102no—
215D4—402no—
216C2×C4—22no—
217C2×C4—102no—
218C2×C4—121no—
219C2×C4—202no—
220C2×C4—202no—
221C2×C4C2×#120111yescharacteristic
222C2×C4D5×#6712yes—
223C8—62no—
224C8—602no—
225C2×C3—402no—
226C2×C3#6536611yescharacteristic
227C2×C3#6547612yes—
228C5#7192811yescharacteristic, complemented, Sylow
229C22—202no—
230C22—202no—
231C22—202no—
232C22#9156311yescharacteristic
233C4—21no—
234C4—42no—
235C4—202no—
236C4—241no—
237C4#9150812yes—
238C4#9151612yes—
239C3#1060209711yescharacteristic, complemented, Sylow
240C2—402no—
241C2#1174913711yescharacteristic
242C2#1174929412yes—
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC3×#66068C2
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1634
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. C5×#5092C2semidirect
3. #11746880C2semidirect
4. #11746367C2semidirect
5. #11745835C2semidirect
40. #5092D5semidirect
196. C3×C5#1634semidirect
228. C5#71928semidirect
239. C3#10602097semidirect

Maximal subgroups

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

subgroupindex
C3×#660682
C5×#50922
#117468802
#117463672
#117458352
#106020973
#719285