Finite Group Databasebeta

← #14315910

Subgroups — #14315910

Order 1920.

308 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 64 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#11752390C211yesmaximal, characteristic, complemented
2#11751687C211yesmaximal, characteristic, complemented
3#11748276C211yesmaximal, characteristic
4C3×#64906C211yesmaximal, characteristic, complemented
5#11746473C211yesmaximal, characteristic, complemented
6#11746466C211yesmaximal, characteristic, complemented
7#11746455C211yesmaximal, characteristic, complemented
8#10604125—31nomaximal, Hall
9D4×ΓL(1,𝔽16)—21no—
10#91913—21no—
11C3×D5×D8C2211yescharacteristic
12#91270C2211yescharacteristic
13#91236—21no—
14#91222C2211yescharacteristic
15#91221C2211yescharacteristic
16C3×#3995C2211yescharacteristic
17C3×#3990C2211yescharacteristic
18#91155—21no—
19#91111C411yescharacteristic, complemented
20C5×#826C411yescharacteristic, complemented
21#90942C411yescharacteristic, complemented
22#90937C411yescharacteristic, complemented
23#90934C2211yescharacteristic
24#69254—51nomaximal, Hall
25#65733—31no—
26#65731—31no—
27#65200—31no—
28#64906D311yescharacteristic, complemented
29#64903—31no—
30#64847—31no—
31#64846—31no—
32C22×ΓL(1,𝔽16)—41no—
33C3×D4×D5—21no—
34#6772—21no—
35#6763—41no—
36C4⋊ΓL(1,𝔽16)—21no—
37C4×ΓL(1,𝔽16)D411yescharacteristic
38D5⋊(C3⋊C8)D411yescharacteristic
39C3×#700—21no—
40#6739—41no—
41D3×#170—41no—
42C3×C5×D8C2×C411yescharacteristic
43Dic60C2×C411yescharacteristic, complemented
44C5×D24C2×C411yescharacteristic, complemented
45C3×#686—21no—
46C3×D40C2×C411yescharacteristic
47C3×C8×D5C2311yescharacteristic
48#6659—21no—
49C3×#674—21no—
50C3⋊#672C2×C411yescharacteristic, complemented
51C5×C3⋊C16C2×C411yescharacteristic, complemented
52#5152—51no—
53#5147—51no—
54#4894—51no—
55C3×#361—51no—
56#4518—51no—
57#4512—51no—
58#4494—51no—
59D4×AGL(1,𝔽5)—61no—
60#4131—61no—
61#4058—31no—
62D5×D8C2×D311yescharacteristic
63#4008—61no—
64#4007—61no—
65#3995C2×D311yescharacteristic
66#3993—31no—
67#3992—31no—
68#3990C2×D311yescharacteristic
69C5×D16—31no—
70#3959—31no—
71#3958—31no—
72#3932—31no—
73#3930—31no—
74AGL(1,ℤ/16)—151noSylow
75C22×C3×D5—41no—
76C2×ΓL(1,𝔽16)—21no—
77C2×ΓL(1,𝔽16)—41no—
78C2×ΓL(1,𝔽16)—82no—
79C3×C5×D4—21no—
80Dic30—21no—
81C5×D12—21no—
82C3×C22⋊D5—41no—
83C3×D20—21no—
84C3×C4×D5C2×D411yescharacteristic
85#1201—41no—
86D3×Dic5—41no—
87C3⋊#170—21no—
88C3×#170—41no—
89C3×C5×C8C22×C411yescharacteristic
90C3×#168#4111yescharacteristic
91C2×C3×D8—51no—
92D4×Dic3—101no—
93#907—101no—
94#904—51no—
95C3×M32—51no—
96C3×#108—51no—
97#832—101no—
98#827—51no—
99#827—51no—
100#826—51no—
101#826AGL(1,𝔽5)11yescharacteristic, complemented
102#825—101no—
103#817—51no—
104#815—51no—
105#812—51no—
106C22×AGL(1,𝔽5)—121no—
107#711—61no—
108D4×D5—21no—
109C22⋊AGL(1,𝔽5)—121no—
110#704—121no—
111C2×#170—121no—
112C4⋊AGL(1,𝔽5)—61no—
113C4×AGL(1,𝔽5)—31no—
114#700—21no—
115D5⋊C8—31no—
116C5×D8—31no—
117C5×D8C4×D311yescharacteristic
118#687—61no—
119#686—21no—
120Dic20—31no—
121D40C4×D311yescharacteristic
122C8×D5C22×D311yescharacteristic
123#674—21no—
124C5×C16—31no—
125#672—31no—
126#509—151no—
127#444—151no—
128#442—151no—
129#365—151no—
130#361—51no—
131#360—151no—
132#347—151no—
133C22×C3×C5—41no—
134C2×C5×D3—41no—
135C2×C3×D5—41no—
136C2×C3×D5—81no—
137C2×C3×D5—81no—
138C2×C3×D5AGL(1,ℤ/8)11yescharacteristic
139ΓL(1,𝔽16)—41no—
140ΓL(1,𝔽16)—81no—
141C3×C4×C5C4×D411yescharacteristic
142Dic15—41no—
143C3×Dic5AGL(1,ℤ/8)11yescharacteristic
144C2×C3×D4—101no—
145C22×Dic3—201no—
146#235—101no—
147C3×D8—51no—
148C3×D8—101no—
149C3×D8C2×AGL(1,𝔽5)11yescharacteristic
150C3×M16—101no—
151C2×C3×C8—51no—
152#217—201no—
153C4⋊Dic3—101no—
154C4×Dic3—51no—
155C2×C3⋊C8—51no—
156Dic12—51no—
157D24C2×AGL(1,𝔽5)11yescharacteristic, complemented
158#204—101no—
159ΓL(1,𝔽25)—201no—
160D3×C8—201no—
161C3×C16—101no—
162C3⋊C16—51no—
163C3⋊C16C2×AGL(1,𝔽5)11yescharacteristic, complemented
164C22×D5—41no—
165C2×AGL(1,𝔽5)—61no—
166C2×AGL(1,𝔽5)—121no—
167C2×AGL(1,𝔽5)—242no—
168C5×D4—21no—
169C5×D4—61no—
170C22⋊D5—41no—
171C22⋊D5—121no—
172C2×Dic5—121no—
173D20—21no—
174C4×D5D3×D411yescharacteristic
175Dic10—61no—
176#170—41no—
177#170—61no—
178C5×C8C2×C4×D311yescharacteristic
179#168#23711yescharacteristic
180#135—151no—
181C2×D8—51no—
182#131—301no—
183C4×D4—301no—
184SD32—151no—
185SD32—151no—
186D16—31no—
187D16—151no—
188M32—51no—
189M32—151no—
190#108—51no—
191#106—151no—
192#104—301no—
193#102—301no—
194#97—151no—
195C2×C3×C5—81no—
196C2×C3×C5#44211yescharacteristic
197C3×D5—21no—
198C3×D5—81no—
199C5×D3—81no—
200C23×C3—201no—
201C3×D4—21no—
202C3×D4—101no—
203C3×D4—201no—
204C2×C3×C4—51no—
205#67—201no—
206C2×Dic3—101no—
207C2×Dic3—201no—
208C2×Dic3—402no—
209D12—21no—
210C4×D3—201no—
211Dic6—101no—
212C3×C8—51no—
213C3×C8—201no—
214C3×C8C22×AGL(1,𝔽5)11yescharacteristic
215C3⋊C8—101no—
216C22×C5—41no—
217C22×C5—121no—
218C2×D5—41no—
219C2×D5—81no—
220C2×D5—81no—
221C2×D5#91411yescharacteristic
222AGL(1,𝔽5)—121no—
223AGL(1,𝔽5)—241no—
224C4×C5#67⋊C411yescharacteristic
225Dic5—121no—
226Dic5#91111yescharacteristic
227#41—301no—
228C2×D4—101no—
229C22×C4—601no—
230Q16—151no—
231SD16—301no—
232D8—31no—
233D8—51no—
234D8—101no—
235D8D3×AGL(1,𝔽5)11yescharacteristic
236M16—101no—
237M16—601no—
238C2×C8—51no—
239C2×C8—151no—
240C2×C8—601no—
241C4⋊C4—301no—
242C22⋊C4—601no—
243C42—151no—
244C16—31no—
245C16—101no—
246C16—151no—
247C3×C5AGL(1,ℤ/16)11yescharacteristic, complemented, Hall
248C22×C3—41no—
249C22×C3—51no—
250C22×C3—201no—
251C22×C3—401no—
252C22×C3—401no—
253C2×D3—41no—
254C3×C4—51no—
255C3×C4D4×AGL(1,𝔽5)11yescharacteristic
256Dic3—201no—
257Dic3—201no—
258Dic3—401no—
259C2×C5—81no—
260C2×C5—241no—
261C2×C5#478511yescharacteristic
262D5—21no—
263D5—81no—
264C23—201no—
265Q8—301no—
266D4—21no—
267D4—61no—
268D4—101no—
269D4—201no—
270D4—601no—
271C2×C4—51no—
272C2×C4—301no—
273C2×C4—601no—
274C2×C4—601no—
275C2×C4—1202no—
276C8—51no—
277C8—201no—
278C8—301no—
279C8C2×D3×AGL(1,𝔽5)11yescharacteristic
280C2×C3—81no—
281C2×C3—101no—
282C2×C3—401no—
283C2×C3#6573111yescharacteristic
284D3—81no—
285C5#6925411yescharacteristic, complemented, Sylow
286C22—41no—
287C22—51no—
288C22—121no—
289C22—201no—
290C22—401no—
291C22—401no—
292C4—51no—
293C4—601no—
294C4—601no—
295C4—1201no—
296C4#67⋊AGL(1,𝔽5)11yescharacteristic
297C3#1060412511yescharacteristic, complemented, Sylow
298C2—81no—
299C2—101no—
300C2—241no—
301C2—401no—
302C2#1175194211yescharacteristic
subgroupG/H
centerC2#11751942
commutatorC3×C5×C8C22×C4
FrattiniC8C2×D3×AGL(1,𝔽5)
FittingC3×C5×D8C2×C4
socleC2×C3×C5#442
prime radical#11748276C2
cosocleC3×C8×D5C23
hypercenterD8D3×AGL(1,𝔽5)
hypocenterC3×C5AGL(1,ℤ/16)
LCSG ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ D8

Complements

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

NH ≅ G/Ntype
1. #11752390C2semidirect
2. #11751687C2semidirect
4. C3×#64906C2semidirect
5. #11746473C2semidirect
6. #11746466C2semidirect
7. #11746455C2semidirect
19. #91111C4semidirect
20. C5×#826C4semidirect
21. #90942C4semidirect
22. #90937C4semidirect
28. #64906D3semidirect
43. Dic60C2×C4semidirect
44. C5×D24C2×C4semidirect
50. C3⋊#672C2×C4semidirect
51. C5×C3⋊C16C2×C4semidirect
101. #826AGL(1,𝔽5)semidirect
157. D24C2×AGL(1,𝔽5)semidirect
163. C3⋊C16C2×AGL(1,𝔽5)semidirect
247. C3×C5AGL(1,ℤ/16)semidirect
285. C5#69254semidirect
297. C3#10604125semidirect

Maximal subgroups

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

subgroupindex
#117523902
#117516872
#117482762
C3×#649062
#117464732
#117464662
#117464552
#106041253
#692545