Finite Group Databasebeta

← #14317244

Subgroups — #14317244

Order 1920.

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

normal subgroups only

This group has 340 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
1C2×C3×#3932C211yesmaximal, characteristic, complemented
2#11747982C211yesmaximal, characteristic, complemented
3#11747809C211yesmaximal, characteristic, complemented
4C2×#90937C211yesmaximal, characteristic
5#11746322C211yesmaximal, characteristic, complemented
6C5×#4509C211yesmaximal, characteristic, complemented
7#11745897C211yesmaximal, characteristic, complemented
8#10599996—31nomaximal, Hall
9C2×C5×D24C2211yescharacteristic
10C2×C3×Dic20C2211yescharacteristic
11C2×C3×D40C2211yescharacteristic
12#91434—21no—
13#91370—21no—
14C2×#6656—21no—
15C2×C3×C5×C16C2211yescharacteristic
16C8×Dic15C2211yescharacteristic
17C2×C3⋊#672C2211yescharacteristic
18C5×#818C2211yescharacteristic
19C3×#3932—22no—
20#90964—21no—
21#90937—22no—
22#71477—51nomaximal, Hall
23#65444—31no—
24C2×#3958—31no—
25C2×#3932D311yescharacteristic, complemented
26#65161—31no—
27C5×#357—31no—
28#64721—31no—
29#64712—31no—
30C2×C5×D12—21no—
31C2×C3×D20—21no—
32C2×C3×Dic10—21no—
33C2×D5×Dic3—41no—
34C2×C3×C5×C8C2311yescharacteristic
35C4×Dic15D411yescharacteristic
36C2×C3⋊#168D411yescharacteristic
37C5×C4⋊Dic3—21no—
38C5×D24—21no—
39C5×D24—21no—
40C3×Dic20—21no—
41C3×Dic20—21no—
42C3×D40—21no—
43C3×D40D412yes—
44(C2×D3)⋊Dic5—41no—
45(C2×D3)⋊Dic5—41no—
46#6665—41no—
47#6656—42no—
48C3×C5×C16—21no—
49C3⋊#672—21no—
50C2×C3×SD32—51no—
51#5191—51no—
52Dic3×D8—51no—
53C2×#826—51no—
54#4564—51no—
55#4509D511yescharacteristic, complemented
56Dic3⋊C16—51no—
57C2×C5×D8—31no—
58#4082—61no—
59C2×#687—61no—
60C2×Dic20C2×D311yescharacteristic
61C2×D40C2×D311yescharacteristic
62#4039—61no—
63C2×C5×C16C2×D311yescharacteristic
64C5×#107—31no—
65#3958—62no—
66C8×Dic5—31no—
67C2×#672—31no—
68#3941—61no—
69#3932—22no—
70#2210—151noSylow
71C22×C5×D3—41no—
72C22×C3×D5—41no—
73C2×C3×C4×C5C2×D411yescharacteristic
74C2×Dic15D811yescharacteristic
75C2×Dic15D811yescharacteristic
76C2×C5×Dic3—41no—
77C5×D12—41no—
78C5×D12—41no—
79C2×C3×Dic5—41no—
80C3×D20—22no—
81C3×D20—41no—
82C3×Dic10—41no—
83C3×Dic10—41no—
84D5×Dic3—82no—
85C3×C5×C8C2×D411yescharacteristic
86C3×C5×C8#4111yescharacteristic
87C3⋊#168—21no—
88C2×C3×Q16—51no—
89C2×C3×D8—51no—
90#947—101no—
91C2×#215—101no—
92D4×Dic3—101no—
93C2×D24C2×D511yescharacteristic
94C3×SD32—102no—
95C2×C3×C16C2×D511yescharacteristic
96#832—101no—
97#826—102no—
98#818C2×D511yescharacteristic
99C8×Dic3—51no—
100C2×C3⋊C16—51no—
101C2×C5×D4—61no—
102C2×D20—21no—
103C2×C4×D5—121no—
104C2×Dic10—21no—
105C5×D8—61no—
106C5×D8—61no—
107C2×C5×C8C22×D311yescharacteristic
108C5×C4⋊C4—61no—
109C22⋊Dic5—121no—
110C22⋊Dic5—121no—
111#687—122no—
112#685—121no—
113C4×Dic5—31no—
114C2×#168—31no—
115Dic20—21no—
116Dic20—21no—
117D40—21no—
118D40#6712yes—
119C5×C16—21no—
120#672—61no—
121C2×SD32—51no—
122C2×D16—151no—
123#495—151no—
124C4×D8—151no—
125C4⋊C16—151no—
126#358—151no—
127#357—31no—
128C22×C3×C5C2×D811yescharacteristic
129C2×C5×D3—81no—
130C2×C5×D3—81no—
131C2×C5×D3—81no—
132C2×C3×D5—42no—
133C2×C3×D5—81no—
134C2×C3×D5—81no—
135C3×C4×C5#12111yescharacteristic
136C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
137Dic15—21no—
138Dic15—21no—
139C3×Dic5—81no—
140C5×Dic3—81no—
141C2×C3×Q8—101no—
142C2×C3×D4—101no—
143C22×Dic3—201no—
144C2×D12—21no—
145C3×Q16—101no—
146C3×Q16—101no—
147C3×D8—52no—
148C3×D8—101no—
149C2×C3×C8C22×D511yescharacteristic
150#217—201no—
151#215—202no—
152(C2×D3)⋊C4—201no—
153(C2×D3)⋊C4—201no—
154C4⋊Dic3—21no—
155C4×Dic3—51no—
156C2×C3⋊C8—51no—
157D24—21no—
158D24—21no—
159C3×C16—21no—
160C3⋊C16—101no—
161C23×C5—121no—
162C22×D5—41no—
163C5×D4—121no—
164C5×D4—121no—
165C2×C4×C5—121no—
166C2×C4×C5D3×D411yescharacteristic
167C2×Dic5—31no—
168C2×Dic5—31no—
169C2×Dic5—41no—
170D20—22no—
171D20—41no—
172C4×D5—242no—
173Dic10—41no—
174Dic10—41no—
175C5×C8#23711yescharacteristic
176C5×C8C2×#6711yescharacteristic
177#168—61no—
178C2×Q16—51no—
179C2×SD16—301no—
180C2×D8—31no—
181C2×D8—51no—
182#124—301no—
183C4×D4—301no—
184SD32—102no—
185D16—302no—
186C2×C16—151no—
187C2×C16D3×D511yescharacteristic
188#107—31no—
189#102—301no—
190C4×C8—151no—
191C2×C3×C5#45911yescharacteristic
192C2×C3×C5#50811yescharacteristic
193C2×C3×C5#50911yescharacteristic
194C3×D5—82no—
195C5×D3—161no—
196C23×C3—201no—
197C22×D3—41no—
198C3×Q8—201no—
199C3×Q8—201no—
200C3×D4—102no—
201C3×D4—201no—
202C2×C3×C4—201no—
203C2×C3×C4D4×D511yescharacteristic
204C2×Dic3—41no—
205C2×Dic3—51no—
206C2×Dic3—51no—
207C2×Dic3—402no—
208D12—41no—
209D12—41no—
210C3×C8#70911yescharacteristic
211C3×C8D4×D511yescharacteristic
212C3⋊C8—101no—
213C22×C5—241no—
214C22×C5—241no—
215C22×C5—241no—
216C22×C5D3×D811yescharacteristic
217C2×D5—42no—
218C2×D5—81no—
219C2×D5—81no—
220C4×C5—241no—
221C4×C5#91111yescharacteristic
222C4×C5#93911yescharacteristic
223Dic5—61no—
224Dic5—61no—
225Dic5—81no—
226C2×Q8—101no—
227C2×D4—61no—
228C2×D4—101no—
229C22×C4—601no—
230Q16—101no—
231Q16—101no—
232SD16—602no—
233D8—52no—
234D8—61no—
235D8—61no—
236D8—101no—
237C2×C8—151no—
238C2×C8C2×D3×D511yescharacteristic
239C4⋊C4—61no—
240C22⋊C4—601no—
241C22⋊C4—601no—
242C22⋊C4—601no—
243C42—151no—
244C16—21no—
245C16—301no—
246C3×C5#221011yescharacteristic, complemented, Hall
247C22×C3—202no—
248C22×C3—401no—
249C22×C3—401no—
250C22×C3D5×D811yescharacteristic
251C2×D3—81no—
252C2×D3—81no—
253C2×D3—81no—
254C3×C4—401no—
255C3×C4#403011yescharacteristic
256C3×C4#406011yescharacteristic
257Dic3—81no—
258Dic3—101no—
259Dic3—101no—
260C2×C5—481no—
261C2×C5#491411yescharacteristic
262C2×C5#491611yescharacteristic
263C2×C5#515011yescharacteristic
264D5—82no—
265C23—121no—
266C23—201no—
267Q8—201no—
268Q8—201no—
269D4—102no—
270D4—121no—
271D4—121no—
272D4—201no—
273C2×C4—121no—
274C2×C4—151no—
275C2×C4—151no—
276C2×C4—201no—
277C2×C4—1202no—
278C2×C4#677711yescharacteristic
279C8—301no—
280C8#676511yescharacteristic
281C8D5×#6711yescharacteristic
282C2×C3—402no—
283C2×C3#6507511yescharacteristic
284C2×C3#6520011yescharacteristic
285C2×C3#6520511yescharacteristic
286D3—161no—
287C5#7147711yescharacteristic, complemented, Sylow
288C22—202no—
289C22—241no—
290C22—241no—
291C22—241no—
292C22—401no—
293C22—401no—
294C22#9125611yescharacteristic
295C4—241no—
296C4—301no—
297C4—301no—
298C4—401no—
299C4#9125811yescharacteristic
300C4#9140811yescharacteristic
301C3#1059999611yescharacteristic, complemented, Sylow
302C2—402no—
303C2—481no—
304C2#1174682511yescharacteristic
305C2#1174684011yescharacteristic
306C2#1174775011yescharacteristic
subgroupG/H
centerC22#91256
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC2×C3×C5×C16C22
socleC22×C3×C5C2×D8
prime radicalC2×#90937C2
hypercenterC2×C16D3×D5
hypocenterC3×C5#2210
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3932C2semidirect
2. #11747982C2semidirect
3. #11747809C2semidirect
5. #11746322C2semidirect
6. C5×#4509C2semidirect
7. #11745897C2semidirect
25. C2×#3932D3semidirect
55. #4509D5semidirect
246. C3×C5#2210semidirect
287. C5#71477semidirect
301. C3#10599996semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#39322
#117479822
#117478092
C2×#909372
#117463222
C5×#45092
#117458972
#105999963
#714775