Finite Group Databasebeta

← #14318552

Subgroups — #14318552

Order 1920.

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

normal subgroups only

This group has 268 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#11748061C211yesmaximal, characteristic, complemented
2#11747936C211yesmaximal, characteristic
3#11746335C211yesmaximal, characteristic, complemented
4C5×#4513C211yesmaximal, characteristic, complemented
5C3×#64736C211yesmaximal, characteristic, complemented
6#11745936C211yesmaximal, characteristic, complemented
7#11745915C211yesmaximal, characteristic, complemented
8#10600106—31nomaximal, Hall
9C2×#6705C2211yescharacteristic
10C2×C3×D40C2211yescharacteristic
11#91465—21no—
12#91292—21no—
13C3×C5×M32C2211yescharacteristic
14#91096C2211yescharacteristic
15C5×#819C2211yescharacteristic
16C5×#817C2211yescharacteristic
17C3×#3951C2211yescharacteristic
18#90992—21no—
19#90964—21no—
20#69257—51nomaximal, Hall
21#65182—31no—
22#65154—31no—
23C5×#365—31no—
24#64736D311yescharacteristic, complemented
25#64734—31no—
26#64715—31no—
27#64707—31no—
28C2×C4×D15D411yescharacteristic
29C2×C3×D20—21no—
30C2×#1202—41no—
31C2×C3×C5×C8C2311yescharacteristic
32C2×C3⋊#168D411yescharacteristic
33#6705—21no—
34#6705—21no—
35C5×C4⋊Dic3—21no—
36C5×#208—21no—
37C3×#681—21no—
38C3×D40—21no—
39C3×D40—21no—
40#6665—41no—
41#6651—41no—
42#6648—41no—
43C3×C5×C16—21no—
44C3⋊#672—21no—
45#5159—51no—
46#4893—51no—
47C3×#361—51no—
48#4563—51no—
49#4514—51no—
50#4513D511yescharacteristic, complemented
51#4494—51no—
52D5×M16—61no—
53C2×D40C2×D311yescharacteristic
54C2×#676—31no—
55#4041—61no—
56C5×M32C2×D311yescharacteristic
57C5×#108—31no—
58C5×#106—31no—
59#3954—61no—
60#3951C2×D311yescharacteristic
61#3944—31no—
62#3941—61no—
63#2238—151noSylow
64C22×D15SD1611yescharacteristic
65C22×C3×D5—41no—
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×Dic15SD1611yescharacteristic
68C4×D15—21no—
69C4×D15—21no—
70C2×C5×Dic3—41no—
71C3×D20—41no—
72C3×D20—41no—
73#1202—82no—
74C3×C5×C8#4111yescharacteristic
75C3×C5×C8#4111yescharacteristic
76C3⋊#168—21no—
77C3×#168—41no—
78C5×C3⋊C8—41no—
79C2×C3×D8—51no—
80#938—101no—
81D3×M16—101no—
82C2×ΓL(1,𝔽25)—51no—
83C3×M32C2×D511yescharacteristic
84C3×#108—51no—
85#832—101no—
86#822—101no—
87#819C2×D511yescharacteristic
88#817C2×D511yescharacteristic
89#812—51no—
90C2×D20—21no—
91C2×D20—121no—
92C2×C4×D5—31no—
93C5×M16—61no—
94C2×C5×C8C22×D311yescharacteristic
95C5×C4⋊C4—61no—
96#685—121no—
97#681—21no—
98C2×#168—31no—
99D40—21no—
100D40—21no—
101#676—61no—
102#676—61no—
103#676—121no—
104C8×D5—121no—
105C5×C16—21no—
106#672—61no—
107#469—151no—
108#430—151no—
109#365—31no—
110#365—151no—
111#361—51no—
112#361—151no—
113#349—151no—
114C22×C3×C5C2×SD1611yescharacteristic
115C2×D15—21no—
116C2×D15—41no—
117C2×C3×D5—81no—
118C2×C3×D5—81no—
119C2×C3×D5—81no—
120C3×C4×C5#12311yescharacteristic
121C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
122Dic15—21no—
123C5×Dic3—81no—
124C2×C3×D4—101no—
125C2×#67—201no—
126C2×C4×D3—51no—
127C3×D8—101no—
128C3×D8—101no—
129C3×M16—101no—
130C2×C3×C8C22×D511yescharacteristic
131#217—201no—
132C4⋊Dic3—21no—
133#208—21no—
134C2×C3⋊C8—51no—
135ΓL(1,𝔽25)—101no—
136ΓL(1,𝔽25)—101no—
137ΓL(1,𝔽25)—201no—
138D3×C8—201no—
139C3×C16—21no—
140C3⋊C16—101no—
141C22×D5—31no—
142C22×D5—41no—
143C2×C4×C5—121no—
144C2×C4×C5D3×D411yescharacteristic
145C2×Dic5—31no—
146D20—41no—
147D20—41no—
148D20—242no—
149C4×D5—61no—
150C4×D5—61no—
151C5×C8—121no—
152C5×C8#23511yescharacteristic
153C5×C8#23711yescharacteristic
154#168—41no—
155#168—61no—
156C2×D8—51no—
157C2×M16—151no—
158C2×M16—301no—
159#121—301no—
160M32—151no—
161M32D3×D511yescharacteristic
162#108—31no—
163#108—51no—
164#108—301no—
165#106—31no—
166#102—301no—
167C2×C3×C5—21no—
168C2×C3×C5#48111yescharacteristic
169D15—41no—
170C3×D5—161no—
171C23×C3—201no—
172C22×D3—51no—
173C3×D4—201no—
174C3×D4—201no—
175C2×C3×C4D4×D511yescharacteristic
176#67—402no—
177C2×Dic3—41no—
178C2×Dic3—51no—
179C4×D3—101no—
180C4×D3—101no—
181C3×C8—201no—
182C3×C8#70911yescharacteristic
183C3×C8#71311yescharacteristic
184C3⋊C8—41no—
185C3⋊C8—101no—
186C22×C5D3×SD1611yescharacteristic
187C2×D5—61no—
188C2×D5—81no—
189C2×D5—81no—
190C2×D5—81no—
191C2×D5—121no—
192C4×C5—241no—
193C4×C5#88311yescharacteristic
194C4×C5#91111yescharacteristic
195Dic5—61no—
196C2×D4—101no—
197C2×D4—601no—
198C22×C4—151no—
199D8—101no—
200D8—101no—
201M16—61no—
202M16—101no—
203M16—301no—
204M16—301no—
205M16—601no—
206C2×C8—151no—
207C2×C8—601no—
208C2×C8C2×D3×D511yescharacteristic
209C4⋊C4—61no—
210C22⋊C4—601no—
211C16—21no—
212C16—301no—
213C3×C5#223811yescharacteristic, complemented, Hall
214C22×C3—401no—
215C22×C3—401no—
216C22×C3—401no—
217C22×C3D5×SD1611yescharacteristic
218C2×D3—101no—
219C2×D3—201no—
220C3×C4#404011yescharacteristic
221C3×C4#406011yescharacteristic
222Dic3—81no—
223Dic3—101no—
224C2×C5—21no—
225C2×C5#477711yescharacteristic
226D5—121no—
227D5—161no—
228C23—151no—
229C23—201no—
230D4—201no—
231D4—201no—
232D4—1202no—
233C2×C4—121no—
234C2×C4—151no—
235C2×C4—301no—
236C2×C4—301no—
237C2×C4#677711yescharacteristic
238C8—121no—
239C8—201no—
240C8—301no—
241C8#677311yescharacteristic
242C8#677911yescharacteristic
243C2×C3—21no—
244C2×C3—801no—
245C2×C3#6515211yescharacteristic
246D3—201no—
247C5#6925711yescharacteristic, complemented, Sylow
248C22—301no—
249C22—401no—
250C22—401no—
251C22—401no—
252C22—601no—
253C22#9125511yescharacteristic
254C4—241no—
255C4—301no—
256C4#9125811yescharacteristic
257C4#9135611yescharacteristic
258C3#1060010611yescharacteristic, complemented, Sylow
259C2—21no—
260C2—601no—
261C2—801no—
262C2#1174757011yescharacteristic
subgroupG/H
centerC2#11747570
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×M32C22
socleC2×C3×C5#481
prime radical#11747936C2
hypercenterM32D3×D5
hypocenterC3×C5#2238
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ M32

Complements

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

NH ≅ G/Ntype
1. #11748061C2semidirect
3. #11746335C2semidirect
4. C5×#4513C2semidirect
5. C3×#64736C2semidirect
6. #11745936C2semidirect
7. #11745915C2semidirect
24. #64736D3semidirect
50. #4513D5semidirect
213. C3×C5#2238semidirect
247. C5#69257semidirect
258. C3#10600106semidirect

Maximal subgroups

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

subgroupindex
#117480612
#117479362
#117463352
C5×#45132
C3×#647362
#117459362
#117459152
#106001063
#692575