Finite Group Databasebeta

← #14289399

Subgroups — #14289399

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×#66047C211yesmaximal, characteristic
2#11751177C211yesmaximal, characteristic
3#11746916C212yesmaximal, complemented
4C5×#4544C211yesmaximal, characteristic
5#11745840C212yesmaximal, complemented
6#10599197—31nomaximal, Hall
7C3×C5×#127C2211yescharacteristic
8C2×#6716—22no—
9#91758C2211yescharacteristic
10C3×#4082—22no—
11C3×#4081—22no—
12C3×D4×Dic5—22no—
13C3×C4×Dic10C2212yes—
14C4×C3⋊#168C2211yescharacteristic
15C5×C4⋊(C3⋊C8)C2212yes—
16#90990—22no—
17#90971—22no—
18#71944—51nomaximal, Hall
19#66047D311yescharacteristic
20#65365—31no—
21#65139—32no—
22C5×#331—31no—
23#64704—32no—
24C2×C3×C5×D4—22no—
25C2×C3×C5×D4D412yes—
26C2×Dic30—21no—
27C22×C3×Dic5—22no—
28C2×C3×Dic10D412yes—
29C3×C42×C5C2311yescharacteristic
30#6716—44no—
31C4⋊Dic15—22no—
32C2×C3⋊#168—21no—
33C2×C5×C3⋊C8—22no—
34C3×C22⋊Dic5—24no—
35C3×C22⋊Dic5—22no—
36C3×C4⋊Dic5D412yes—
37C3×#683—22no—
38C3×C4×Dic5—22no—
39C3×#559—51no—
40#5076—51no—
41#5021—52no—
42#4544D511yescharacteristic
43#4535—52no—
44C5×#127C2×D311yescharacteristic
45#4082—22no—
46#4081—22no—
47D4×Dic5—22no—
48C2×#687—62no—
49#4015—31no—
50C4×Dic10C2×D312yes—
51C5×C4⋊C8—32no—
52#3950—62no—
53#3948—62no—
54C4×#168—31no—
55#1630—151noSylow
56C23×C3×C5—22no—
57C3×C5×D4—42no—
58C3×C5×D4—42no—
59C3×C5×D4—42no—
60C2×C3×C4×C5C2×D411yescharacteristic
61C2×C3×C4×C5C2×D412yes—
62C2×Dic15—41no—
63Dic30—42no—
64C2×C3×Dic5—22no—
65C2×C3×Dic5—22no—
66C2×C3×Dic5—82no—
67C3×Dic10—22no—
68C3×Dic10—22no—
69C3⋊#168—22no—
70C5×C3⋊C8—42no—
71C3×#127C2×D511yescharacteristic
72C3×#124—102no—
73C3×#123—102no—
74C3×C4×Q8—52no—
75C3×C4×D4—102no—
76C2×#214—102no—
77#869—51no—
78#835—102no—
79#807—102no—
80C4⋊(C3⋊C8)C2×D512yes—
81C4×C3⋊C8—51no—
82C2×C5×D4—22no—
83C2×C5×D4#6712yes—
84C22×Dic5—22no—
85C2×Dic10—61no—
86C2×Dic10#6712yes—
87C2×C5×C8—62no—
88C42×C5C22×D311yescharacteristic
89C22⋊Dic5—24no—
90C22⋊Dic5—22no—
91#687—124no—
92C4⋊Dic5—62no—
93C4⋊Dic5#6712yes—
94#683—22no—
95C4×Dic5—22no—
96C2×#168—61no—
97#559—51no—
98#492—151no—
99#477—152no—
100#331—31no—
101Q8⋊C8—152no—
102C22×C3×C5—44no—
103C22×C3×C5—42no—
104C22×C3×C5#12011yescharacteristic
105C3×C4×C5—21no—
106C3×C4×C5#13512yes—
107C3×C4×C5#13712yes—
108Dic15—81no—
109C3×Dic5—42no—
110C3×Dic5—42no—
111C2×C3×Q8—52no—
112C2×C3×D4—22no—
113C2×C3×D4D2012yes—
114C22×C3×C4—102no—
115C2×Dic6—101no—
116C3×C4⋊C4—52no—
117C3×C4⋊C4—102no—
118C3×C22⋊C4—104no—
119C3×C22⋊C4—102no—
120C3×C42—102no—
121C3×C42C22×D511yescharacteristic
122#214—204no—
123C4⋊Dic3—102no—
124C2×C3⋊C8—22no—
125C2×C3⋊C8—101no—
126C23×C5—22no—
127C5×D4—42no—
128C5×D4—42no—
129C5×D4—42no—
130C2×C4×C5C2×#6711yescharacteristic
131C2×C4×C5C2×#6712yes—
132C2×Dic5—22no—
133C2×Dic5—22no—
134C2×Dic5—82no—
135C2×Dic5—121no—
136Dic10—22no—
137Dic10—22no—
138Dic10—122no—
139C5×C8—122no—
140#168—62no—
141C2×SD16—302no—
142C4⋊Q8—151no—
143#127D3×D511yescharacteristic
144#124—102no—
145#123—102no—
146C4×Q8—52no—
147C4×D4—102no—
148#107—302no—
149C4⋊C8—32no—
150#103—302no—
151C4×C8—151no—
152C2×C3×C5—82no—
153C2×C3×C5#45212yes—
154C2×C3×C5#45311yescharacteristic
155C23×C3—22no—
156C3×Q8—102no—
157C3×Q8—102no—
158C3×D4—42no—
159C3×D4—42no—
160C3×D4—42no—
161C2×C3×C4—102no—
162C2×C3×C4—102no—
163C2×C3×C4—402no—
164C2×C3×C4C2×D2011yescharacteristic
165C2×C3×C4D4×D512yes—
166C2×Dic3—201no—
167Dic6—202no—
168C3⋊C8—42no—
169C3⋊C8—102no—
170C22×C5—44no—
171C22×C5—42no—
172C22×C5#95311yescharacteristic
173C4×C5—21no—
174C4×C5#95012yes—
175C4×C5#95112yes—
176Dic5—42no—
177Dic5—42no—
178Dic5—241no—
179C2×Q8—52no—
180C2×Q8—301no—
181C2×D4—22no—
182C2×D4#120212yes—
183C22×C4—102no—
184SD16—604no—
185C2×C8—62no—
186C2×C8—301no—
187C4⋊C4—52no—
188C4⋊C4—102no—
189C4⋊C4—302no—
190C22⋊C4—104no—
191C22⋊C4—102no—
192C42—102no—
193C42C2×D3×D511yescharacteristic
194C3×C5#163011yescharacteristic, complemented, Hall
195C22×C3—42no—
196C22×C3—44no—
197C22×C3#402811yescharacteristic
198C3×C4—21no—
199C3×C4—202no—
200C3×C4—202no—
201C3×C4#405812yes—
202C3×C4#406112yes—
203Dic3—401no—
204C2×C5—82no—
205C2×C5#523912yes—
206C2×C5#524111yescharacteristic
207C23—22no—
208Q8—102no—
209Q8—102no—
210Q8—602no—
211D4—42no—
212D4—42no—
213D4—42no—
214C2×C4—102no—
215C2×C4—102no—
216C2×C4—402no—
217C2×C4—601no—
218C2×C4C2×#120211yescharacteristic
219C2×C4D5×#6712yes—
220C8—122no—
221C8—302no—
222C2×C3—82no—
223C2×C3#6503611yescharacteristic
224C2×C3#6507212yes—
225C5#7194411yescharacteristic, complemented, Sylow
226C22—42no—
227C22—44no—
228C22#9156411yescharacteristic
229C4—21no—
230C4—202no—
231C4—202no—
232C4—1201no—
233C4#9148412yes—
234C4#9149012yes—
235C3#1059919711yescharacteristic, complemented, Sylow
236C2—82no—
237C2#1174904912yes—
238C2#1174913811yescharacteristic
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
Fitting, prime radicalC3×C5×#127C22
socleC22×C3×C5#120
hypercenter#127D3×D5
hypocenterC3×C5#1630
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #127

Complements

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

NH ≅ G/Ntype
3. #11746916C2semidirect
5. #11745840C2semidirect
194. C3×C5#1630semidirect
225. C5#71944semidirect
235. C3#10599197semidirect

Maximal subgroups

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

subgroupindex
C3×#660472
#117511772
#117469162
C5×#45442
#117458402
#105991973
#719445