Finite Group Databasebeta

← #14317073

Subgroups — #14317073

Order 1920.

348 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 79 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
1#11751252C211yesmaximal, characteristic
2C2×#91111C211yesmaximal, characteristic, complemented
3C2×#91084C211yesmaximal, characteristic, complemented
4#11750974C211yesmaximal, characteristic, complemented
5C3×C5×#357C211yesmaximal, characteristic, complemented
6#11746322C211yesmaximal, characteristic, complemented
7#11746312C211yesmaximal, characteristic, complemented
8#10599997—31nomaximal, Hall
9C2×C3×C5×D8C2211yescharacteristic
10#91829—21no—
11C2×#6715—21no—
12C2×Dic60C2211yescharacteristic
13C2×D120C2211yescharacteristic
14#91776—21no—
15C2×C3×C5×C16C2211yescharacteristic
16C3×C5×#107C2211yescharacteristic
17#91111—22no—
18C8×Dic15C2211yescharacteristic
19C2×C3⋊#672C2211yescharacteristic
20#91094—21no—
21#91084—22no—
22#69204—51nomaximal, Hall
23#65440—31no—
24C2×#3959—31no—
25C2×#3932—31no—
26#65162—31no—
27C5×#357D311yescharacteristic, complemented
28#64721—31no—
29#64711—31no—
30C2×C3×C5×D4—21no—
31C2×#1220—41no—
32C2×#1220—41no—
33C2×D60—21no—
34C2×Dic30—21no—
35C3×C5×D8—21no—
36C3×C5×D8—21no—
37C2×C3×C5×C8C2311yescharacteristic
38C3×C5×C4⋊C4—21no—
39#6715—42no—
40#6712—41no—
41C4×Dic15—41no—
42C4×Dic15D411yescharacteristic
43C2×C3⋊#168D411yescharacteristic
44Dic60—21no—
45Dic60D412yescomplemented
46D120—21no—
47D120—21no—
48C3×C5×C16—21no—
49C3⋊#672—21no—
50#5151—51no—
51C2×#827—51no—
52C2×#800—51no—
53#4873—51no—
54C3×#357D511yescharacteristic, complemented
55Dic3⋊C16—51no—
56#4491—51no—
57C2×C5×D8C2×D311yescharacteristic
58#4086—61no—
59C2×#686—61no—
60C2×Dic20—31no—
61C2×D40—31no—
62#4033—61no—
63C2×C5×C16C2×D311yescharacteristic
64C5×#107C2×D311yescharacteristic
65#3959—62no—
66C8×Dic5—31no—
67C2×#672—31no—
68#3942—61no—
69#3932—62no—
70#2207—151noSylow
71C23×C3×C5—41no—
72C22×D15—41no—
73C3×C5×D4—41no—
74C3×C5×D4—41no—
75C2×C3×C4×C5—41no—
76C2×C3×C4×C5C2×D411yescharacteristic
77#1220—82no—
78#1220—82no—
79C2×Dic15—41no—
80C2×Dic15D811yescharacteristic
81C2×Dic15D811yescharacteristic
82D60—41no—
83D60—41no—
84Dic30—22no—
85Dic30—41no—
86C3×C5×C8C2×D411yescharacteristic
87C3×C5×C8#4111yescharacteristic
88C3⋊#168—21no—
89C2×C3×D8C2×D511yescharacteristic
90#940—101no—
91C2×#213—101no—
92C2×Dic12—51no—
93C2×D24—51no—
94#887—101no—
95C2×C3×C16C2×D511yescharacteristic
96C3×#107C2×D511yescharacteristic
97#827—102no—
98C8×Dic3—51no—
99C2×C3⋊C16—51no—
100#810—101no—
101#800—102no—
102C2×C5×D4—21no—
103C2×C22⋊D5—121no—
104C2×C22⋊D5—121no—
105C2×D20—61no—
106C2×Dic10—61no—
107C5×D8—21no—
108C5×D8—21no—
109C2×C5×C8C22×D311yescharacteristic
110C5×C4⋊C4—21no—
111#686—122no—
112#683—121no—
113C4×Dic5—31no—
114C4×Dic5—121no—
115C2×#168—31no—
116Dic20—32no—
117Dic20—61no—
118D40—61no—
119D40—61no—
120C5×C16—21no—
121#672—61no—
122C2×SD32—151no—
123C2×SD32—151no—
124#493—151no—
125C4×Q16—151no—
126C4⋊C16—151no—
127#357—151no—
128#357D1511yescharacteristic, complemented
129C22×C3×C5—81no—
130C22×C3×C5—81no—
131C22×C3×C5—81no—
132C22×C3×C5C2×D811yescharacteristic
133C2×D15—81no—
134C2×D15—81no—
135C2×D15—81no—
136C3×C4×C5—81no—
137C3×C4×C5#12111yescharacteristic
138C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
139Dic15—21no—
140Dic15—42no—
141Dic15SD3212yescomplemented
142C2×C3×D4—21no—
143C2×#67—201no—
144C2×#67—201no—
145C2×D12—101no—
146C2×Dic6—101no—
147C3×D8—21no—
148C3×D8—21no—
149C2×C3×C8C22×D511yescharacteristic
150C3×C4⋊C4—21no—
151#213—202no—
152Dic3⋊C4—201no—
153C4×Dic3—51no—
154C4×Dic3—201no—
155C2×C3⋊C8—51no—
156Dic12—52no—
157Dic12—101no—
158D24—101no—
159D24—101no—
160C3×C16—21no—
161C3⋊C16—101no—
162C23×C5—41no—
163C22×D5—121no—
164C5×D4—41no—
165C5×D4—41no—
166C2×C4×C5—41no—
167C2×C4×C5D3×D411yescharacteristic
168C22⋊D5—242no—
169C22⋊D5—242no—
170C2×Dic5—31no—
171C2×Dic5—31no—
172C2×Dic5—121no—
173D20—121no—
174D20—121no—
175Dic10—62no—
176Dic10—121no—
177C5×C8#23511yescharacteristic
178C5×C8D3×D411yescharacteristic
179#168—61no—
180C2×Q16—151no—
181C2×D8—151no—
182C2×D8—301no—
183C2×D8C2×D1511yescharacteristic
184#127—301no—
185C4×Q8—301no—
186SD32—302no—
187SD32—302no—
188C2×C16—151no—
189C2×C16C2×D1511yescharacteristic
190#107C2×D1511yescharacteristic
191#103—301no—
192C4×C8—151no—
193C2×C3×C5—161no—
194C2×C3×C5#45911yescharacteristic
195C2×C3×C5C2×SD3211yescharacteristic
196C2×C3×C5#50911yescharacteristic
197D15—161no—
198C23×C3—41no—
199C22×D3—201no—
200C3×D4—41no—
201C3×D4—41no—
202C2×C3×C4—41no—
203C2×C3×C4D4×D511yescharacteristic
204#67—402no—
205#67—402no—
206C2×Dic3—51no—
207C2×Dic3—51no—
208C2×Dic3—201no—
209D12—201no—
210D12—201no—
211Dic6—102no—
212Dic6—201no—
213C3×C8#70911yescharacteristic
214C3×C8D4×D511yescharacteristic
215C3⋊C8—101no—
216C22×C5—81no—
217C22×C5—81no—
218C22×C5—81no—
219C22×C5D3×D811yescharacteristic
220C2×D5—241no—
221C2×D5—241no—
222C2×D5—241no—
223C4×C5—81no—
224C4×C5#88411yescharacteristic
225C4×C5#91411yescharacteristic
226Dic5—32no—
227Dic5—61no—
228Dic5—122no—
229C2×Q8—301no—
230C2×D4—21no—
231C2×D4—301no—
232C2×D4—601no—
233C2×D4—601no—
234Q16—152no—
235Q16—301no—
236D8—21no—
237D8—21no—
238D8—301no—
239D8—301no—
240D8—602no—
241C2×C8—151no—
242C2×C8C22×D1511yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—601no—
245C42—151no—
246C42—601no—
247C16—21no—
248C16—301no—
249C3×C5#220711yescharacteristic, complemented, Hall
250C22×C3—81no—
251C22×C3—81no—
252C22×C3—81no—
253C22×C3D5×D811yescharacteristic
254C2×D3—401no—
255C2×D3—401no—
256C2×D3—401no—
257C3×C4—81no—
258C3×C4#403011yescharacteristic
259C3×C4#406011yescharacteristic
260Dic3—52no—
261Dic3—101no—
262Dic3—202no—
263C2×C5—161no—
264C2×C5#478611yescharacteristic
265C2×C5#491111yescharacteristic
266C2×C5D3×SD3211yescharacteristic
267D5—481no—
268C23—41no—
269C23—601no—
270Q8—302no—
271Q8—601no—
272D4—41no—
273D4—41no—
274D4—601no—
275D4—601no—
276D4—1202no—
277D4—1202no—
278C2×C4—41no—
279C2×C4—151no—
280C2×C4—151no—
281C2×C4—601no—
282C2×C4D4×D1511yescharacteristic
283C8—301no—
284C8#681711yescharacteristic
285C8D4×D1511yescharacteristic
286C2×C3—161no—
287C2×C3#6507511yescharacteristic
288C2×C3#6520011yescharacteristic
289C2×C3D5×SD3211yescharacteristic
290D3—801no—
291C5#6920411yescharacteristic, complemented, Sylow
292C22—81no—
293C22—81no—
294C22—81no—
295C22—1201no—
296C22—1201no—
297C22—1201no—
298C22D8×D1511yescharacteristic
299C4—81no—
300C4—152no—
301C4—301no—
302C4—602no—
303C4#9177311yescharacteristic
304C4#9180311yescharacteristic
305C3#1059999711yescharacteristic, complemented, Sylow
306C2—161no—
307C2—2401no—
308C2#1175088711yescharacteristic
309C2#1175101211yescharacteristic
310C2D15×SD3211yescharacteristic
subgroupG/H
centerC22D8×D15
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#357C2
socleC22×C3×C5C2×D8
prime radical#11751252C2
hypercenter#357D15
hypocenterC3×C5#2207
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #357

Complements

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

NH ≅ G/Ntype
2. C2×#91111C2semidirect
3. C2×#91084C2semidirect
4. #11750974C2semidirect
5. C3×C5×#357C2semidirect
6. #11746322C2semidirect
7. #11746312C2semidirect
27. C5×#357D3semidirect
45. Dic60D4semidirect
54. C3×#357D5semidirect
128. #357D15semidirect
141. Dic15SD32semidirect
249. C3×C5#2207semidirect
291. C5#69204semidirect
305. C3#10599997semidirect

Maximal subgroups

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

subgroupindex
#117512522
C2×#911112
C2×#910842
#117509742
C3×C5×#3572
#117463222
#117463122
#105999973
#692045