Finite Group Databasebeta

← #14292682

Subgroups — #14292682

Order 1920.

320 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 82 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#11750939C211yesmaximal, characteristic
2#11747085C211yesmaximal, characteristic
3#11746947C211yesmaximal, characteristic, complemented
4#11746885C211yesmaximal, characteristic
5C5×#4481C211yesmaximal, characteristic, complemented
6C3×#64706C211yesmaximal, characteristic, complemented
7#11745868C211yesmaximal, characteristic, complemented
8#10599293—31nomaximal, Hall
9C2×#6705—21no—
10C4×D60C2211yescharacteristic
11C5×#869C2211yescharacteristic
12C3×#4015C2211yescharacteristic
13C2×#6658—21no—
14C3×C5×C4⋊C8C2211yescharacteristic
15#91104—21no—
16C4×C3⋊#168C2211yescharacteristic
17C5×C4⋊(C3⋊C8)C2211yescharacteristic
18C3×C4⋊#168C2211yescharacteristic
19#90986—21no—
20#90986—21no—
21#90985—21no—
22#90971—21no—
23#90969—21no—
24#68450—51nomaximal, Hall
25#65373—31no—
26#65368—31no—
27#65130—31no—
28#65127—31no—
29C5×#333—31no—
30#64706D311yescharacteristic, complemented
31#64699—31no—
32C2×D60D411yescharacteristic
33C2×C4×D15—21no—
34C2×C5×Dic6—21no—
35C2×C3×Dic10—21no—
36C2×C3×C5×C8—21no—
37C3×C42×C5C2311yescharacteristic
38#6714—21no—
39C4⋊Dic15D411yescharacteristic
40C2×C3⋊#168D411yescharacteristic
41C2×C3⋊#168D411yescharacteristic
42#6705—42no—
43C5×C4⋊Dic3—21no—
44C5×C4⋊Dic3—21no—
45C2×C5×C3⋊C8—21no—
46C3×C4⋊Dic5—21no—
47C3×C4⋊Dic5—21no—
48C2×C3×#168—21no—
49#6658—42no—
50#5083—51no—
51#5080—51no—
52#4842—51no—
53#4838—51no—
54C3×#332—51no—
55#4481D511yescharacteristic, complemented
56#4479—51no—
57C5×C4⋊Q8—31no—
58C2×#677—61no—
59C2×#676—61no—
60C4×D20—31no—
61#4015C2×D311yescharacteristic
62C5×C4⋊C8—31no—
63C5×C4⋊C8C2×D311yescharacteristic
64#3952—61no—
65#3948—61no—
66#3941—61no—
67#3940—61no—
68#3940—61no—
69#3940—61no—
70C4⋊#168C2×D311yescharacteristic
71C4×#168—31no—
72#1691—151noSylow
73C22×D15—21no—
74C2×C3×C4×C5C2×D411yescharacteristic
75C2×C3×C4×C5C2×D411yescharacteristic
76C2×C3×C4×C5#4111yescharacteristic
77C2×Dic15—21no—
78D60—21no—
79D60—21no—
80C4×D15—41no—
81C4×D15—41no—
82C2×C5×Dic3—41no—
83C5×Dic6—81no—
84C2×C3×Dic5—41no—
85C3×Dic10—41no—
86C3×Dic10—41no—
87C3×C5×C8—41no—
88C3⋊#168—21no—
89C3⋊#168SD1612yescomplemented
90C3×#168—41no—
91C5×C3⋊C8—41no—
92C3×C4⋊Q8—51no—
93C2×#215—101no—
94C2×ΓL(1,𝔽25)—101no—
95C4×D12—51no—
96#869C2×D511yescharacteristic
97C3×C4⋊C8—51no—
98C3×C4⋊C8C2×D511yescharacteristic
99#835—101no—
100#821—101no—
101(C2×D3)⋊C8—101no—
102#817—101no—
103#808—101no—
104#808—101no—
105C4⋊(C3⋊C8)C2×D511yescharacteristic
106C4×C3⋊C8—51no—
107C2×C5×Q8—61no—
108C2×D20—31no—
109C2×C4×D5—61no—
110C2×Dic10—21no—
111C2×C5×C8—21no—
112C2×C5×C8—61no—
113C5×C4⋊C4—61no—
114C5×C4⋊C4—61no—
115C42×C5C22×D311yescharacteristic
116#685—61no—
117C4⋊Dic5—21no—
118C4⋊Dic5—21no—
119C4⋊Dic5—31no—
120C2×#168—21no—
121C2×#168—31no—
122C2×#168—31no—
123#677—122no—
124#676—122no—
125#498—151no—
126#476—151no—
127#461—151no—
128#436—151no—
129#335—151no—
130#333—31no—
131#332—51no—
132C22×C3×C5#12111yescharacteristic
133C2×D15—41no—
134C2×D15—41no—
135C2×D15—41no—
136C3×C4×C5—21no—
137C3×C4×C5C2×SD1611yescharacteristic
138C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
139C3×C4×C5#13711yescharacteristic
140C3×C4×C5#13711yescharacteristic
141Dic15—41no—
142C3×Dic5—81no—
143C5×Dic3—81no—
144C2×C3×Q8—101no—
145C2×D12—51no—
146C2×C4×D3—101no—
147C2×Dic6—21no—
148C2×C3×C8—21no—
149C2×C3×C8—101no—
150C3×C4⋊C4—101no—
151C3×C4⋊C4—101no—
152C3×C42C22×D511yescharacteristic
153#215—202no—
154(C2×D3)⋊C4—101no—
155C4⋊Dic3—21no—
156C4⋊Dic3—21no—
157C4⋊Dic3—51no—
158C2×C3⋊C8—21no—
159C2×C3⋊C8—51no—
160C2×C3⋊C8—51no—
161ΓL(1,𝔽25)—202no—
162C22×D5—61no—
163C5×Q8—241no—
164C2×C4×C5—121no—
165C2×C4×C5#23511yescharacteristic
166C2×C4×C5D3×D411yescharacteristic
167C2×C4×C5D3×D411yescharacteristic
168C2×Dic5—41no—
169C2×Dic5—61no—
170D20—61no—
171D20—61no—
172C4×D5—121no—
173C4×D5—121no—
174Dic10—41no—
175Dic10—41no—
176C5×C8—41no—
177C5×C8—121no—
178#168—32no—
179#168—41no—
180#168—61no—
181C2×SD16—301no—
182C2×M16—301no—
183C4⋊Q8—31no—
184C4⋊Q8—51no—
185C4×D4—151no—
186#106—301no—
187#106—301no—
188#106—301no—
189C4⋊C8—31no—
190C4⋊C8—51no—
191C4⋊C8D3×D511yescharacteristic
192#103—301no—
193#102—301no—
194C22⋊C8—301no—
195C4×C8—151no—
196C2×C3×C5#46111yescharacteristic
197C2×C3×C5#46811yescharacteristic
198C2×C3×C5#47111yescharacteristic
199D15—81no—
200C22×D3—101no—
201C3×Q8—201no—
202C3×Q8—201no—
203C2×C3×C4—201no—
204C2×C3×C4#70911yescharacteristic
205C2×C3×C4D4×D511yescharacteristic
206C2×C3×C4D4×D511yescharacteristic
207C2×Dic3—41no—
208C2×Dic3—101no—
209D12—101no—
210D12—101no—
211C4×D3—201no—
212C4×D3—201no—
213Dic6—81no—
214C3×C8—41no—
215C3×C8—201no—
216C3⋊C8—41no—
217C3⋊C8—52no—
218C3⋊C8—101no—
219C22×C5#88411yescharacteristic
220C2×D5—121no—
221C2×D5—121no—
222C2×D5—121no—
223C4×C5—21no—
224C4×C5—241no—
225C4×C5#91111yescharacteristic
226C4×C5D3×SD1611yescharacteristic
227C4×C5#91511yescharacteristic
228C4×C5#91811yescharacteristic
229Dic5—81no—
230Dic5—121no—
231C2×Q8—61no—
232C2×Q8—101no—
233C2×D4—151no—
234C22×C4—301no—
235SD16—602no—
236M16—602no—
237C2×C8—21no—
238C2×C8—61no—
239C2×C8—101no—
240C2×C8—151no—
241C2×C8—151no—
242C4⋊C4—61no—
243C4⋊C4—61no—
244C4⋊C4—101no—
245C4⋊C4—101no—
246C4⋊C4—151no—
247C22⋊C4—301no—
248C42C2×D3×D511yescharacteristic
249C3×C5#169111yescharacteristic, complemented, Hall
250C22×C3#403011yescharacteristic
251C2×D3—201no—
252C2×D3—201no—
253C2×D3—201no—
254C3×C4—21no—
255C3×C4—401no—
256C3×C4D5×SD1611yescharacteristic
257C3×C4#406011yescharacteristic
258C3×C4#406411yescharacteristic
259C3×C4#406411yescharacteristic
260Dic3—81no—
261Dic3—201no—
262C2×C5#475411yescharacteristic
263C2×C5#478011yescharacteristic
264C2×C5#481811yescharacteristic
265D5—241no—
266C23—301no—
267Q8—201no—
268Q8—201no—
269Q8—241no—
270D4—301no—
271D4—301no—
272C2×C4—121no—
273C2×C4—201no—
274C2×C4—301no—
275C2×C4—601no—
276C2×C4—601no—
277C2×C4#677111yescharacteristic
278C2×C4#677711yescharacteristic
279C2×C4#679011yescharacteristic
280C8—41no—
281C8—121no—
282C8—152no—
283C8—201no—
284C8—301no—
285C2×C3#6503711yescharacteristic
286C2×C3#6510111yescharacteristic
287C2×C3#6510711yescharacteristic
288D3—401no—
289C5#6845011yescharacteristic, complemented, Sylow
290C22—601no—
291C22—601no—
292C22—601no—
293C22#9146111yescharacteristic
294C4—21no—
295C4—241no—
296C4—401no—
297C4—601no—
298C4#9125811yescharacteristic
299C4#9127811yescharacteristic
300C4#9148711yescharacteristic
301C4#9151211yescharacteristic
302C3#1059929311yescharacteristic, complemented, Sylow
303C2—1201no—
304C2#1174742611yescharacteristic
305C2#1174792711yescharacteristic
306C2#1174819911yescharacteristic
subgroupG/H
centerC22#91461
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊C8C22
socleC22×C3×C5#121
prime radicalC2×D60D4
hypercenterC4⋊C8D3×D5
hypocenterC3×C5#1691
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
3. #11746947C2semidirect
5. C5×#4481C2semidirect
6. C3×#64706C2semidirect
7. #11745868C2semidirect
30. #64706D3semidirect
55. #4481D5semidirect
89. C3⋊#168SD16semidirect
249. C3×C5#1691semidirect
289. C5#68450semidirect
302. C3#10599293semidirect

Maximal subgroups

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

subgroupindex
#117509392
#117470852
#117469472
#117468852
C5×#44812
C3×#647062
#117458682
#105992933
#684505