Finite Group Databasebeta

← #14317316

Subgroups — #14317316

Order 1920.

308 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 69 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#11751256C211yesmaximal, characteristic, complemented
2#11751248C211yesmaximal, characteristic
3#11751010C211yesmaximal, characteristic, complemented
4#11750996C211yesmaximal, characteristic, complemented
5C3×C5×#361C211yesmaximal, characteristic, complemented
6#11746332C211yesmaximal, characteristic, complemented
7#11746317C211yesmaximal, characteristic, complemented
8#10600055—31nomaximal, Hall
9C2×C3×C5×D8C2211yescharacteristic
10#91825—21no—
11C2×#6716—21no—
12#91796—21no—
13C2×Dic60C2211yescharacteristic
14#91793C2211yescharacteristic
15C3×C5×M32C2211yescharacteristic
16C3×C5×#108C2211yescharacteristic
17#91111—21no—
18#91110—21no—
19#91109—21no—
20C8×Dic15C2211yescharacteristic
21#91096C2211yescharacteristic
22Dic120—21no—
23#91084—21no—
24#69262—51nomaximal, Hall
25#65444—31no—
26#65436—31no—
27#65198—31no—
28#65184—31no—
29C5×#361D311yescharacteristic, complemented
30#64731—31no—
31#64716—31no—
32C2×C3×C5×D4—21no—
33#6817—21no—
34C2×Dic30—21no—
35C3×C5×D8—21no—
36C3×C5×D8—21no—
37C3×C5×M16—21no—
38C2×C3×C5×C8C2311yescharacteristic
39#6719—42no—
40#6716—41no—
41#6716—41no—
42C4×Dic15D411yescharacteristic
43C2×C3⋊#168D411yescharacteristic
44Dic60—21no—
45Dic60—21no—
46Dic60D411yescharacteristic
47D120D411yescharacteristic
48#6706—21no—
49#6705—41no—
50C8×D15—41no—
51C3×C5×C16—21no—
52C3⋊#672—21no—
53#5155—51no—
54#5147—51no—
55#4909—51no—
56#4895—51no—
57C3×#361D511yescharacteristic, complemented
58#4511—51no—
59#4496—51no—
60C2×C5×D8C2×D311yescharacteristic
61#4082—61no—
62C2×#687—61no—
63#4053—61no—
64C2×Dic20—31no—
65#4050—31no—
66C5×M32C2×D311yescharacteristic
67C5×#108C2×D311yescharacteristic
68#3959—61no—
69#3958—61no—
70#3957—61no—
71C8×Dic5—31no—
72#3944—31no—
73Dic40—61no—
74#3932—61no—
75#2212—151noSylow
76C23×C3×C5—41no—
77C3×C5×D4—41no—
78C3×C5×D4—41no—
79C2×C3×C4×C5C2×D411yescharacteristic
80#1220—41no—
81C2×Dic15—21no—
82C2×Dic15—41no—
83D60—21no—
84C4×D15—41no—
85Dic30—21no—
86Dic30—41no—
87Dic30—41no—
88C3×C5×C8—41no—
89C3×C5×C8C2×D411yescharacteristic
90C3×C5×C8#4111yescharacteristic
91C3⋊#168D811yescharacteristic
92C3⋊#168D811yescharacteristic
93C2×C3×D8C2×D511yescharacteristic
94#936—101no—
95C2×#214—101no—
96#907—101no—
97C2×Dic12—51no—
98#904—51no—
99C3×M32C2×D511yescharacteristic
100C3×#108C2×D511yescharacteristic
101#827—101no—
102#826—101no—
103#825—101no—
104C8×Dic3—51no—
105#812—51no—
106Dic24—101no—
107#800—101no—
108C2×C5×D4—21no—
109#709—61no—
110C2×Dic10—61no—
111C5×D8—21no—
112C5×D8—21no—
113C5×M16—21no—
114C2×C5×C8C22×D311yescharacteristic
115C22⋊Dic5—122no—
116#687—121no—
117#687—121no—
118C4×Dic5—31no—
119C2×#168—31no—
120Dic20—31no—
121Dic20—61no—
122Dic20—61no—
123D40—31no—
124#677—61no—
125#676—121no—
126C8×D5—121no—
127C5×C16—21no—
128#672—61no—
129#510—151no—
130#509—151no—
131#495—151no—
132#443—151no—
133#364—151no—
134#362—151no—
135#361D1511yescharacteristic, complemented
136C22×C3×C5—82no—
137C22×C3×C5—81no—
138C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
139C2×D15—41no—
140C3×C4×C5#12111yescharacteristic
141C3×C4×C5C2×D811yescharacteristic
142Dic15—41no—
143Dic15—41no—
144Dic15—81no—
145C2×C3×D4—21no—
146#235—101no—
147C2×Dic6—101no—
148C3×D8—21no—
149C3×D8—21no—
150C3×M16—21no—
151C2×C3×C8C22×D511yescharacteristic
152#217—202no—
153#214—201no—
154#214—201no—
155C4×Dic3—51no—
156C2×C3⋊C8—51no—
157Dic12—51no—
158Dic12—101no—
159Dic12—101no—
160D24—51no—
161#204—101no—
162ΓL(1,𝔽25)—201no—
163D3×C8—201no—
164C3×C16—21no—
165C3⋊C16—101no—
166C23×C5—41no—
167C5×D4—41no—
168C5×D4—41no—
169C2×C4×C5D3×D411yescharacteristic
170C22⋊D5—121no—
171C2×Dic5—61no—
172C2×Dic5—121no—
173D20—61no—
174C4×D5—121no—
175Dic10—61no—
176Dic10—121no—
177Dic10—121no—
178C5×C8—41no—
179C5×C8#23511yescharacteristic
180C5×C8D3×D411yescharacteristic
181#168—31no—
182#168—31no—
183#135—151no—
184C2×Q16—151no—
185C2×SD16—301no—
186C2×D8C2×D1511yescharacteristic
187#131—301no—
188#124—301no—
189Q32—301no—
190SD32—301no—
191SD32—301no—
192D16—301no—
193M32—151no—
194M32C2×D1511yescharacteristic
195#108C2×D1511yescharacteristic
196#104—301no—
197C4×C8—151no—
198C2×C3×C5—21no—
199C2×C3×C5—161no—
200C2×C3×C5#45911yescharacteristic
201D15—81no—
202C23×C3—41no—
203C3×D4—41no—
204C3×D4—41no—
205C2×C3×C4D4×D511yescharacteristic
206#67—201no—
207C2×Dic3—101no—
208C2×Dic3—201no—
209D12—101no—
210C4×D3—201no—
211Dic6—101no—
212Dic6—201no—
213Dic6—201no—
214C3×C8—41no—
215C3×C8#70911yescharacteristic
216C3×C8D4×D511yescharacteristic
217C3⋊C8—51no—
218C3⋊C8—51no—
219C22×C5—82no—
220C22×C5—81no—
221C22×C5#91411yescharacteristic
222C2×D5—121no—
223C4×C5#88411yescharacteristic
224C4×C5D3×D811yescharacteristic
225Dic5—121no—
226Dic5—121no—
227Dic5—241no—
228#41—301no—
229C2×Q8—301no—
230C2×D4—21no—
231Q16—151no—
232Q16—301no—
233Q16—301no—
234SD16—301no—
235SD16—601no—
236SD16—601no—
237D8—21no—
238D8—21no—
239D8—151no—
240M16—21no—
241M16—601no—
242C2×C8—151no—
243C2×C8—601no—
244C2×C8C22×D1511yescharacteristic
245C22⋊C4—602no—
246C42—151no—
247C16—21no—
248C16—301no—
249C3×C5#221211yescharacteristic, complemented, Hall
250C22×C3—82no—
251C22×C3—81no—
252C22×C3#406011yescharacteristic
253C2×D3—201no—
254C3×C4#403011yescharacteristic
255C3×C4D5×D811yescharacteristic
256Dic3—201no—
257Dic3—201no—
258Dic3—401no—
259C2×C5—21no—
260C2×C5—161no—
261C2×C5#478611yescharacteristic
262D5—241no—
263C23—41no—
264Q8—301no—
265Q8—601no—
266Q8—601no—
267D4—41no—
268D4—41no—
269D4—301no—
270D4—601no—
271C2×C4—301no—
272C2×C4—601no—
273C2×C4—601no—
274C2×C4D4×D1511yescharacteristic
275C8—41no—
276C8—151no—
277C8—151no—
278C8#681711yescharacteristic
279C8D4×D1511yescharacteristic
280C2×C3—21no—
281C2×C3—161no—
282C2×C3#6507511yescharacteristic
283D3—401no—
284C5#6926211yescharacteristic, complemented, Sylow
285C22—82no—
286C22—81no—
287C22—601no—
288C22#9180311yescharacteristic
289C4—601no—
290C4—601no—
291C4—1201no—
292C4#9177311yescharacteristic
293C4D8×D1511yescharacteristic
294C3#1060005511yescharacteristic, complemented, Sylow
295C2—21no—
296C2—161no—
297C2—1201no—
298C2#1175088711yescharacteristic
subgroupG/H
centerC2#11750887
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C22×D15
FittingC3×C5×#361C2
socleC2×C3×C5#459
prime radical#11751248C2
hypercenter#361D15
hypocenterC3×C5#2212
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
1. #11751256C2semidirect
3. #11751010C2semidirect
4. #11750996C2semidirect
5. C3×C5×#361C2semidirect
6. #11746332C2semidirect
7. #11746317C2semidirect
29. C5×#361D3semidirect
57. C3×#361D5semidirect
135. #361D15semidirect
249. C3×C5#2212semidirect
284. C5#69262semidirect
294. C3#10600055semidirect

Maximal subgroups

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

subgroupindex
#117512562
#117512482
#117510102
#117509962
C3×C5×#3612
#117463322
#117463172
#106000553
#692625