Finite Group Databasebeta

← #14290945

Subgroups — #14290945

Order 1920.

412 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 87 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×C5×#563C211yesmaximal, characteristic, complemented
2#11751168C212yesmaximal, complemented
3#11751159C211yesmaximal, characteristic
4#11746364C212yesmaximal, complemented
5#11746361C211yesmaximal, characteristic, complemented
6#10602748—31nomaximal, Hall
7C3×C5×C4⋊Q8—21no—
8C3×C5×#126—22no—
9C3×C5×#125C2212yes—
10C3×C5×#124C2211yescharacteristic
11C3×C5×#123—21no—
12C3×C5×C22⋊Q8—22no—
13C2×#6717—21no—
14C2×#6715—21no—
15#91763C2211yescharacteristic
16#91093—22no—
17#91093—22no—
18#91087C2212yes—
19#91087C2211yescharacteristic
20#71955—51nomaximal, Hall
21C5×#563D311yescharacteristic, complemented
22#65356—32no—
23#65347—31no—
24#64763—32no—
25#64760—31no—
26C2×C3×C5×Q8—21no—
27C2×C3×C5×Q8D411yescharacteristic
28C2×C3×C5×D4D411yescharacteristic
29C22×C3×C4×C5—21no—
30C2×D60—21no—
31C2×D60—22no—
32C3×C5×C4⋊C4—22no—
33C3×C5×C4⋊C4—22no—
34C3×C5×C4⋊C4—22no—
35C3×C5×C4⋊C4D412yes—
36C3×C5×C4⋊C4D412yes—
37C3×C5×C22⋊C4—22no—
38C3×C5×C22⋊C4—21no—
39C3×C5×C22⋊C4—22no—
40C3×C42×C5—21no—
41C3×C42×C5C2311yescharacteristic
42#6717—42no—
43#6715—42no—
44C2×C3⋊#168—21no—
45C2×C3⋊#168—22no—
46C3×#563D511yescharacteristic, complemented
47#5067—52no—
48#5058—51no—
49#4543—52no—
50#4540—51no—
51C5×C4⋊Q8—21no—
52C5×#126—22no—
53C5×#125C2×D312yes—
54C5×#124C2×D311yescharacteristic
55C5×#123—21no—
56C5×C22⋊Q8—22no—
57C2×#688—61no—
58C2×#686—61no—
59#4020—31no—
60#3941—62no—
61#3941—62no—
62#3935—31no—
63#3935—32no—
64#1657—151noSylow
65C23×C3×C5—21no—
66C22×D15—41no—
67C3×C5×Q8—41no—
68C3×C5×Q8—81no—
69C3×C5×D4—41no—
70C2×C3×C4×C5—22no—
71C2×C3×C4×C5—21no—
72C2×C3×C4×C5—22no—
73C2×C3×C4×C5—81no—
74C2×C3×C4×C5C2×D412yes—
75C2×C3×C4×C5C2×D411yescharacteristic
76D60—41no—
77D60—41no—
78D60—44no—
79C3⋊#168—22no—
80C3⋊#168—42no—
81C3×C4⋊Q8—21no—
82C3×#126—22no—
83C3×#125C2×D512yes—
84C3×#124C2×D511yescharacteristic
85C3×#123—21no—
86C3×C22⋊Q8—22no—
87C2×#215—101no—
88C2×#213—101no—
89#874—51no—
90#809—102no—
91#809—102no—
92#803—52no—
93#803—51no—
94C2×C5×Q8—21no—
95C2×C5×Q8#6711yescharacteristic
96C2×C5×D4#6711yescharacteristic
97C22×C4×C5—21no—
98C2×D20—62no—
99C2×D20—61no—
100C5×C4⋊C4—22no—
101C5×C4⋊C4—22no—
102C5×C4⋊C4—22no—
103C5×C4⋊C4#6712yes—
104C5×C4⋊C4#6712yes—
105C5×C22⋊C4—22no—
106C5×C22⋊C4—21no—
107C5×C22⋊C4—22no—
108C42×C5—21no—
109C42×C5C22×D311yescharacteristic
110#688—122no—
111#686—122no—
112C2×#168—61no—
113C2×#168—62no—
114#563D1511yescharacteristic, complemented
115#496—151no—
116#490—152no—
117#330—152no—
118#329—151no—
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—42no—
127C3×C4×C5—41no—
128C3×C4×C5—42no—
129C2×C3×Q8—21no—
130C2×C3×Q8C22⋊D511yescharacteristic
131C2×C3×D4C22⋊D511yescharacteristic
132C22×C3×C4—21no—
133C2×D12—102no—
134C2×D12—101no—
135C3×C4⋊C4—22no—
136C3×C4⋊C4—22no—
137C3×C4⋊C4—22no—
138C3×C4⋊C4C22⋊D512yes—
139C3×C4⋊C4C22⋊D512yes—
140C3×C22⋊C4—22no—
141C3×C22⋊C4—21no—
142C3×C22⋊C4—22no—
143C3×C42—21no—
144C3×C42C22×D511yescharacteristic
145#215—202no—
146#213—202no—
147C2×C3⋊C8—101no—
148C2×C3⋊C8—102no—
149C23×C5—21no—
150C22×D5—121no—
151C5×Q8—41no—
152C5×Q8—81no—
153C5×D4—41no—
154C2×C4×C5—22no—
155C2×C4×C5—21no—
156C2×C4×C5—22no—
157C2×C4×C5—81no—
158C2×C4×C5C2×#6712yes—
159C2×C4×C5C2×#6711yescharacteristic
160D20—121no—
161D20—121no—
162D20—124no—
163#168—62no—
164#168—122no—
165C2×SD16—301no—
166C2×D8—301no—
167C4⋊Q8—21no—
168#127—151no—
169#126—22no—
170#125C2×D1512yes—
171#124C2×D1511yescharacteristic
172#123—21no—
173C22⋊Q8—22no—
174#102—302no—
175#102—302no—
176#97—152no—
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—81no—
186C3×D4—41no—
187C2×C3×C4—22no—
188C2×C3×C4—21no—
189C2×C3×C4—22no—
190C2×C3×C4—81no—
191C2×C3×C4C2×C22⋊D512yes—
192C2×C3×C4C2×C22⋊D511yescharacteristic
193D12—201no—
194D12—201no—
195D12—204no—
196C3⋊C8—102no—
197C3⋊C8—202no—
198C22×C5—41no—
199C22×C5—42no—
200C22×C5#95311yescharacteristic
201C2×D5—241no—
202C2×D5—242no—
203C4×C5—21no—
204C4×C5—22no—
205C4×C5—42no—
206C4×C5—41no—
207C4×C5—42no—
208C2×Q8—21no—
209C2×Q8#122011yescharacteristic
210C2×D4—302no—
211C2×D4—301no—
212C2×D4#122011yescharacteristic
213C22×C4—21no—
214SD16—602no—
215D8—602no—
216C2×C8—301no—
217C2×C8—302no—
218C4⋊C4—22no—
219C4⋊C4—22no—
220C4⋊C4—22no—
221C4⋊C4#122012yes—
222C4⋊C4#122012yes—
223C22⋊C4—22no—
224C22⋊C4—21no—
225C22⋊C4—22no—
226C42—21no—
227C42C22×D1511yescharacteristic
228C3×C5#165711yescharacteristic, complemented, Hall
229C22×C3—41no—
230C22×C3—42no—
231C22×C3#409911yescharacteristic
232C2×D3—401no—
233C2×D3—402no—
234C3×C4—21no—
235C3×C4—22no—
236C3×C4—42no—
237C3×C4—41no—
238C3×C4—42no—
239C2×C5—81no—
240C2×C5#524111yescharacteristic
241C2×C5#524512yes—
242D5—481no—
243C23—21no—
244C23—601no—
245Q8—41no—
246Q8—81no—
247D4—41no—
248D4—601no—
249D4—601no—
250D4—604no—
251C2×C4—22no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—81no—
255C2×C4C2×#122012yes—
256C2×C4C2×#122011yescharacteristic
257C8—302no—
258C8—602no—
259C2×C3—81no—
260C2×C3#6553011yescharacteristic
261C2×C3#6553412yes—
262D3—801no—
263C5#7195511yescharacteristic, complemented, Sylow
264C22—41no—
265C22—42no—
266C22—1201no—
267C22—1202no—
268C22#9184211yescharacteristic
269C4—21no—
270C4—22no—
271C4—42no—
272C4—41no—
273C4—42no—
274C3#1060274811yescharacteristic, complemented, Sylow
275C2—81no—
276C2—2401no—
277C2#1175134211yescharacteristic
278C2#1175134612yes—
subgroupG/H
centerC22#91842
commutator, cosocleC3×C42×C5C23
FrattiniC42C22×D15
FittingC3×C5×#563C2
socleC22×C3×C5#120
prime radical#11751159C2
hypercenter#563D15
hypocenterC3×C5#1657
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
1. C3×C5×#563C2semidirect
2. #11751168C2semidirect
4. #11746364C2semidirect
5. #11746361C2semidirect
21. C5×#563D3semidirect
46. C3×#563D5semidirect
114. #563D15semidirect
228. C3×C5#1657semidirect
263. C5#71955semidirect
274. C3#10602748semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5632
#117511682
#117511592
#117463642
#117463612
#106027483
#719555