Finite Group Databasebeta

← #14290960

Subgroups — #14290960

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
2#11751159C211yesmaximal, characteristic
3#11746911C212yesmaximal, complemented
4C5×#4540C211yesmaximal, characteristic, complemented
5#11745849C212yesmaximal, complemented
6#10599147—31nomaximal, Hall
7C3×C5×#124C2211yescharacteristic
8C2×#6717—21no—
9C2×#6715—21no—
10#91763C2211yescharacteristic
11C3×#4090—21no—
12C3×#4081—21no—
13C3×#4025—22no—
14C3×#4024—22no—
15C3×#4016C2212yes—
16#91087C2211yescharacteristic
17C5×#803C2212yes—
18#90968—22no—
19#90968—22no—
20#71955—51nomaximal, Hall
21#66006D311yescharacteristic, complemented
22#65347—31no—
23#65002—32no—
24C5×#329—31no—
25#64685—32no—
26C2×C3×C5×Q8D411yescharacteristic
27C2×C3×C5×D4D411yescharacteristic
28C2×D60—22no—
29C2×D60—21no—
30C22×C3×Dic5—21no—
31C2×C3×Dic10—21no—
32C3×C5×C22⋊C4—22no—
33C3×C42×C5C2311yescharacteristic
34#6717—42no—
35#6715—42no—
36C2×C3⋊#168—21no—
37C2×C5×C3⋊C8—22no—
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#5058—51no—
49#4543—52no—
50#4540D511yescharacteristic, complemented
51C5×#124C2×D311yescharacteristic
52#4090—21no—
53C2×#688—61no—
54#4081—21no—
55C2×#686—61no—
56#4025—22no—
57#4024—22no—
58#4020—31no—
59#4016C2×D312yes—
60C5×#97—32no—
61#3953—62no—
62#3953—62no—
63#3935—31no—
64#1657—151noSylow
65C23×C3×C5—21no—
66C22×D15—41no—
67C3×C5×Q8—41no—
68C3×C5×D4—41no—
69C2×C3×C4×C5—21no—
70C2×C3×C4×C5C2×D411yescharacteristic
71C2×C3×C4×C5C2×D412yes—
72D60—41no—
73D60—41no—
74D60—44no—
75C2×C3×Dic5—22no—
76C2×C3×Dic5—22no—
77C2×C3×Dic5—81no—
78C3×Dic10—81no—
79C3⋊#168—22no—
80C5×C3⋊C8—42no—
81C3×C4⋊Q8—101no—
82C3×#126—102no—
83C3×#125—52no—
84C3×#124C2×D511yescharacteristic
85C3×#123—101no—
86C3×C22⋊Q8—102no—
87C2×#215—101no—
88C2×#213—101no—
89#874—51no—
90#809—102no—
91#809—102no—
92#803—51no—
93#803C2×D512yes—
94C2×C5×Q8#6711yescharacteristic
95C2×C5×D4#6711yescharacteristic
96C22×Dic5—21no—
97C2×D20—62no—
98C2×D20—61no—
99C2×Dic10—21no—
100C2×C5×C8—62no—
101C5×C22⋊C4—22no—
102C42×C5C22×D311yescharacteristic
103C22⋊Dic5—22no—
104C22⋊Dic5—21no—
105#688—122no—
106#686—122no—
107C4⋊Dic5#6712yes—
108C4⋊Dic5#6712yes—
109#683—22no—
110#683—22no—
111#683—22no—
112C4×Dic5—21no—
113C2×#168—61no—
114#563—51no—
115#496—151no—
116#490—152no—
117#330—152no—
118#329—31no—
119C22×C3×C5—41no—
120C22×C3×C5—42no—
121C22×C3×C5#12011yescharacteristic
122C2×D15—81no—
123C2×D15—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×Q8D2011yescharacteristic
131C2×C3×D4D2011yescharacteristic
132C22×C3×C4—101no—
133C2×D12—101no—
134C2×D12—102no—
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—202no—
146#213—202no—
147C2×C3⋊C8—22no—
148C2×C3⋊C8—101no—
149C23×C5—21no—
150C22×D5—121no—
151C5×Q8—41no—
152C5×D4—41no—
153C2×C4×C5—21no—
154C2×C4×C5C2×#6711yescharacteristic
155C2×C4×C5C2×#6712yes—
156C2×Dic5—22no—
157C2×Dic5—22no—
158C2×Dic5—81no—
159D20—121no—
160D20—121no—
161D20—124no—
162Dic10—81no—
163C5×C8—122no—
164#168—62no—
165C2×SD16—301no—
166C2×D8—301no—
167C4⋊Q8—101no—
168#127—151no—
169#126—102no—
170#125—52no—
171#124D3×D511yescharacteristic
172#123—101no—
173C22⋊Q8—102no—
174#102—302no—
175#102—302no—
176#97—32no—
177#97—151no—
178C2×C3×C5—81no—
179C2×C3×C5#45311yescharacteristic
180C2×C3×C5#45412yes—
181D15—161no—
182C23×C3—21no—
183C22×D3—201no—
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×C4C2×D2011yescharacteristic
192C2×C3×C4D4×D512yes—
193D12—201no—
194D12—201no—
195D12—204no—
196C3⋊C8—42no—
197C3⋊C8—102no—
198C22×C5—41no—
199C22×C5—42no—
200C22×C5#95311yescharacteristic
201C2×D5—241no—
202C2×D5—242no—
203C4×C5—21no—
204C4×C5—22no—
205C4×C5—41no—
206Dic5—42no—
207Dic5—42no—
208C2×Q8—101no—
209C2×Q8#120211yescharacteristic
210C2×D4—301no—
211C2×D4—302no—
212C2×D4#120211yescharacteristic
213C22×C4—101no—
214SD16—602no—
215D8—602no—
216C2×C8—62no—
217C2×C8—301no—
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#402811yescharacteristic
232C2×D3—401no—
233C2×D3—402no—
234C3×C4—21no—
235C3×C4—22no—
236C3×C4—41no—
237C3×C4—202no—
238C3×C4—202no—
239C2×C5—81no—
240C2×C5#524111yescharacteristic
241C2×C5#524512yes—
242D5—481no—
243C23—21no—
244C23—601no—
245Q8—41no—
246Q8—401no—
247D4—41no—
248D4—601no—
249D4—601no—
250D4—604no—
251C2×C4—21no—
252C2×C4—102no—
253C2×C4—102no—
254C2×C4—401no—
255C2×C4C2×#120211yescharacteristic
256C2×C4D5×#6712yes—
257C8—122no—
258C8—302no—
259C2×C3—81no—
260C2×C3#6503611yescharacteristic
261C2×C3#6511612yes—
262D3—801no—
263C5#7195511yescharacteristic, complemented, Sylow
264C22—41no—
265C22—42no—
266C22—1201no—
267C22—1202no—
268C22#9156411yescharacteristic
269C4—21no—
270C4—22no—
271C4—41no—
272C4—202no—
273C4—202no—
274C3#1059914711yescharacteristic, complemented, Sylow
275C2—81no—
276C2—2401no—
277C2#1174913811yescharacteristic
278C2#1174945712yes—
subgroupG/H
centerC22#91564
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×#124C22
socleC22×C3×C5#120
prime radical#11751159C2
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. #11746911C2semidirect
4. C5×#4540C2semidirect
5. #11745849C2semidirect
21. #66006D3semidirect
50. #4540D5semidirect
228. C3×C5#1657semidirect
263. C5#71955semidirect
274. C3#10599147semidirect

Maximal subgroups

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

subgroupindex
C3×#660062
#117511592
#117469112
C5×#45402
#117458492
#105991473
#719555