Finite Group Databasebeta

← #14290955

Subgroups — #14290955

Order 1920.

412 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 76 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×#66006C211yesmaximal, characteristic, complemented
2C5×#5058C211yesmaximal, characteristic
3#11746905C212yesmaximal, complemented
4#11746361C211yesmaximal, characteristic, complemented
5#11745849C212yesmaximal, complemented
6#10602121—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8C2×C5×#215—21no—
9C2×C5×#213—21no—
10C5×#874C2211yescharacteristic
11C3×#4090—21no—
12C3×#4081—21no—
13C3×#4025—22no—
14C3×#4024—22no—
15C3×#4016C2212yes—
16#91087C2212yes—
17C5×#803C2211yescharacteristic
18#90966—22no—
19#90966—22no—
20#71955—51nomaximal, Hall
21#66006D311yescharacteristic, complemented
22C5×#496—31no—
23#65360—32no—
24#64760—31no—
25#64685—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C2×C5×D12—22no—
29C2×C5×D12—21no—
30C22×C3×Dic5—21no—
31C2×C3×Dic10—21no—
32C3×C5×C22⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34C2×C3⋊#168—22no—
35C5×#215—42no—
36C5×#213—42no—
37C2×C5×C3⋊C8—21no—
38C3×C22⋊Dic5—22no—
39C3×C22⋊Dic5—21no—
40C3×C4⋊Dic5D412yes—
41C3×C4⋊Dic5D412yes—
42C3×#683—22no—
43C3×#683—22no—
44C3×#683—22no—
45C3×C4×Dic5—21no—
46C3×#563—51no—
47#5067—52no—
48#5058D511yescharacteristic
49#4543—52no—
50#4540—51no—
51C2×C5×SD16—61no—
52C2×C5×D8—61no—
53C5×#127—31no—
54C5×#124C2×D311yescharacteristic
55#4090—21no—
56#4081—21no—
57#4025—22no—
58#4024—22no—
59#4016C2×D312yes—
60C5×#97—31no—
61#3964—62no—
62#3964—62no—
63#3935—32no—
64#1657—151noSylow
65C23×C3×C5—21no—
66C22×C5×D3—41no—
67C3×C5×Q8—41no—
68C3×C5×D4—41no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5C2×D412yes—
71C2×C3×C4×C5C2×D411yescharacteristic
72C5×D12—41no—
73C5×D12—41no—
74C5×D12—44no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5—81no—
78C3×Dic10—81no—
79C3⋊#168—42no—
80C5×C3⋊C8—22no—
81C3×C4⋊Q8—101no—
82C3×#126—102no—
83C3×#125—52no—
84C3×#124C2×D511yescharacteristic
85C3×#123—101no—
86C3×C22⋊Q8—102no—
87C2×#215—21no—
88C2×#213—21no—
89#874C2×D511yescharacteristic
90#809—102no—
91#809—102no—
92#803—52no—
93#803C2×D511yescharacteristic
94C2×C5×Q8#6711yescharacteristic
95C2×C5×D4—61no—
96C2×C5×D4—62no—
97C2×C5×D4#6711yescharacteristic
98C22×Dic5—21no—
99C2×Dic10—21no—
100C5×SD16—122no—
101C5×D8—122no—
102C2×C5×C8—61no—
103C5×C22⋊C4—22no—
104C42×C5C22×D311yescharacteristic
105C22⋊Dic5—22no—
106C22⋊Dic5—21no—
107C4⋊Dic5#6712yes—
108C4⋊Dic5#6712yes—
109#683—22no—
110#683—22no—
111#683—22no—
112C4×Dic5—21no—
113C2×#168—62no—
114#563—51no—
115#496—31no—
116#490—152no—
117#330—152no—
118#329—151no—
119C22×C3×C5—41no—
120C22×C3×C5—42no—
121C22×C3×C5#12011yescharacteristic
122C2×C5×D3—81no—
123C2×C5×D3—82no—
124C3×C4×C5—21no—
125C3×C4×C5—22no—
126C3×C4×C5—41no—
127C3×Dic5—42no—
128C3×Dic5—42no—
129C2×C3×Q8—101no—
130C2×C3×Q8C22⋊D511yescharacteristic
131C2×C3×D4C22⋊D511yescharacteristic
132C22×C3×C4—101no—
133C2×D12—22no—
134C2×D12—21no—
135C3×C4⋊C4—52no—
136C3×C4⋊C4—52no—
137C3×C4⋊C4—102no—
138C3×C4⋊C4—102no—
139C3×C4⋊C4—102no—
140C3×C22⋊C4—22no—
141C3×C22⋊C4—102no—
142C3×C22⋊C4—101no—
143C3×C42—101no—
144C3×C42C22×D511yescharacteristic
145#215—42no—
146#213—42no—
147C2×C3⋊C8—21no—
148C2×C3⋊C8—102no—
149C23×C5—21no—
150C23×C5—121no—
151C5×Q8—41no—
152C5×D4—41no—
153C5×D4—121no—
154C5×D4—121no—
155C5×D4—124no—
156C2×C4×C5—21no—
157C2×C4×C5C2×#6711yescharacteristic
158C2×C4×C5C2×#6712yes—
159C2×Dic5—22no—
160C2×Dic5—22no—
161C2×Dic5—81no—
162Dic10—81no—
163C5×C8—62no—
164#168—122no—
165C2×SD16—61no—
166C2×D8—61no—
167C4⋊Q8—101no—
168#127—31no—
169#126—102no—
170#125—52no—
171#124D3×D511yescharacteristic
172#123—101no—
173C22⋊Q8—102no—
174#102—302no—
175#102—302no—
176#97—31no—
177#97—152no—
178C2×C3×C5—81no—
179C2×C3×C5#45311yescharacteristic
180C2×C3×C5#45412yes—
181C5×D3—161no—
182C23×C3—21no—
183C22×D3—41no—
184C3×Q8—41no—
185C3×Q8—401no—
186C3×D4—41no—
187C2×C3×C4—21no—
188C2×C3×C4—102no—
189C2×C3×C4—102no—
190C2×C3×C4—401no—
191C2×C3×C4D4×D512yes—
192C2×C3×C4C2×C22⋊D511yescharacteristic
193D12—41no—
194D12—41no—
195D12—44no—
196C3⋊C8—22no—
197C3⋊C8—202no—
198C22×C5—41no—
199C22×C5—42no—
200C22×C5—241no—
201C22×C5—242no—
202C22×C5#95311yescharacteristic
203C4×C5—21no—
204C4×C5—22no—
205C4×C5—41no—
206Dic5—42no—
207Dic5—42no—
208C2×Q8—101no—
209C2×Q8#120111yescharacteristic
210C2×D4—61no—
211C2×D4—62no—
212C2×D4#120111yescharacteristic
213C22×C4—101no—
214SD16—122no—
215D8—122no—
216C2×C8—61no—
217C2×C8—302no—
218C4⋊C4—52no—
219C4⋊C4—52no—
220C4⋊C4—102no—
221C4⋊C4—102no—
222C4⋊C4—102no—
223C22⋊C4—22no—
224C22⋊C4—102no—
225C22⋊C4—101no—
226C42—101no—
227C42C2×D3×D511yescharacteristic
228C3×C5#165711yescharacteristic, complemented, Hall
229C22×C3—41no—
230C22×C3—42no—
231C22×C3#408311yescharacteristic
232C2×D3—81no—
233C2×D3—82no—
234C3×C4—21no—
235C3×C4—22no—
236C3×C4—41no—
237C3×C4—202no—
238C3×C4—202no—
239C2×C5—81no—
240C2×C5—481no—
241C2×C5#524111yescharacteristic
242C2×C5#524512yes—
243C23—21no—
244C23—121no—
245Q8—41no—
246Q8—401no—
247D4—41no—
248D4—121no—
249D4—121no—
250D4—124no—
251C2×C4—21no—
252C2×C4—102no—
253C2×C4—102no—
254C2×C4—401no—
255C2×C4C2×#120111yescharacteristic
256C2×C4D5×#6712yes—
257C8—62no—
258C8—602no—
259C2×C3—81no—
260C2×C3#6536611yescharacteristic
261C2×C3#6549012yes—
262D3—161no—
263C5#7195511yescharacteristic, complemented, Sylow
264C22—41no—
265C22—42no—
266C22—241no—
267C22—242no—
268C22#9156311yescharacteristic
269C4—21no—
270C4—22no—
271C4—41no—
272C4—202no—
273C4—202no—
274C3#1060212111yescharacteristic, complemented, Sylow
275C2—81no—
276C2—481no—
277C2#1174913711yescharacteristic
278C2#1174945612yes—
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radicalC5×#5058C2
hypercenter#124D3×D5
hypocenterC3×C5#1657
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
1. C3×#66006C2semidirect
3. #11746905C2semidirect
4. #11746361C2semidirect
5. #11745849C2semidirect
21. #66006D3semidirect
228. C3×C5#1657semidirect
263. C5#71955semidirect
274. C3#10602121semidirect

Maximal subgroups

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

subgroupindex
C3×#660062
C5×#50582
#117469052
#117463612
#117458492
#106021213
#719555