Finite Group Databasebeta

← #14318583

Subgroups — #14318583

Order 1920.

248 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 68 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
1C5×#4867C211yesmaximal, characteristic
2#11748059C211yesmaximal, characteristic
3#11746308C211yesmaximal, characteristic, complemented
4C3×#64707C211yesmaximal, characteristic, complemented
5#11745924C211yesmaximal, characteristic, complemented
6#11745923C211yesmaximal, characteristic, complemented
7#11745883C211yesmaximal, characteristic
8#10601883—31nomaximal, Hall
9C2×C5×Dic12C2211yescharacteristic
10C2×C5×ΓL(1,𝔽25)C2211yescharacteristic
11C5×#897—21no—
12D3×#681—21no—
13C3×C5×#106C2211yescharacteristic
14#91103C2211yescharacteristic
15#91096C2211yescharacteristic
16C5×#810—21no—
17C3×#3951C2211yescharacteristic
18C3×#3944C2211yescharacteristic
19#90993—21no—
20#69314—51nomaximal, Hall
21C5×#470—31no—
22#65414—31no—
23#64785—31no—
24#64785—31no—
25#64773—31no—
26#64707—31no—
27#64707D311yescharacteristic, complemented
28C2×C4×C5×D3D411yescharacteristic
29C2×C5×Dic6—21no—
30C2×C3×C5×C8C2311yescharacteristic
31C3×C5×C4⋊C4—21no—
32#6710—21no—
33C5×(C2×D3)⋊C4—41no—
34C5×C4⋊Dic3—41no—
35C2×C5×C3⋊C8D411yescharacteristic
36C5×Dic12—21no—
37C5×Dic12—21no—
38C5×ΓL(1,𝔽25)—21no—
39C5×ΓL(1,𝔽25)—21no—
40C3×#681—21no—
41#6650—41no—
42D3×#168—41no—
43C3⋊#672—21no—
44C3×#672—21no—
45#4893—51no—
46#4867D511yescharacteristic
47C3×#365—51no—
48#4517—51no—
49#4514—51no—
50#4496—51no—
51#4487—51no—
52C2×C5×Q16—31no—
53C2×C5×M16—31no—
54C5×C22⋊Q8—61no—
55C2×#681—61no—
56C5×#106C2×D311yescharacteristic
57C5×#103—61no—
58#3951—31no—
59#3951—61no—
60#3951C2×D311yescharacteristic
61#3944—31no—
62#3944C2×D311yescharacteristic
63#2239—151noSylow
64C22×C5×D3SD1611yescharacteristic
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×C5×Dic3—41no—
68C2×C5×Dic3SD1611yescharacteristic
69C4×C5×D3—21no—
70C4×C5×D3—21no—
71C5×Dic6—41no—
72C5×Dic6—41no—
73C3×C5×C8#4111yescharacteristic
74C3×C5×C8#4111yescharacteristic
75C3⋊#168—41no—
76C3×#168—41no—
77C5×C3⋊C8—21no—
78D3×M16—101no—
79C2×Dic12C2×D511yescharacteristic
80C2×ΓL(1,𝔽25)C2×D511yescharacteristic
81#897—21no—
82C3×M32—51no—
83C3×#108—51no—
84C3×#106C2×D511yescharacteristic
85#822—101no—
86#819—51no—
87#812—51no—
88#810—21no—
89C2×C5×Q8—61no—
90C22×C4×C5—31no—
91C5×Q16—61no—
92C5×Q16—61no—
93C5×M16—61no—
94C5×M16—61no—
95C2×C5×C8—31no—
96C2×C5×C8C22×D311yescharacteristic
97C5×C4⋊C4—21no—
98C5×C4⋊C4—121no—
99C5×C22⋊C4—121no—
100#681—21no—
101#681—61no—
102#681—121no—
103C2×#168—121no—
104#672—21no—
105#672—61no—
106#470—31no—
107#430—151no—
108#365—51no—
109#365—151no—
110#362—151no—
111#362—151no—
112#349—151no—
113C22×C3×C5C2×SD1611yescharacteristic
114C2×C5×D3—21no—
115C2×C5×D3—41no—
116C3×C4×C5—81no—
117C3×C4×C5#12311yescharacteristic
118C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
119C5×Dic3—21no—
120C5×Dic3—81no—
121C2×C4×D3C22⋊D511yescharacteristic
122C2×Dic6—21no—
123C3×M16—101no—
124C2×C3×C8C22×D511yescharacteristic
125C3×C4⋊C4—21no—
126(C2×D3)⋊C4—41no—
127C4⋊Dic3—41no—
128#208—101no—
129C2×C3⋊C8C22⋊D511yescharacteristic
130Dic12—21no—
131Dic12—21no—
132ΓL(1,𝔽25)—21no—
133ΓL(1,𝔽25)—21no—
134ΓL(1,𝔽25)—201no—
135D3×C8—201no—
136C3×C16—101no—
137C3⋊C16—101no—
138C23×C5—31no—
139C5×Q8—121no—
140C5×Q8—121no—
141C2×C4×C5—31no—
142C2×C4×C5—41no—
143C2×C4×C5—61no—
144C2×C4×C5—61no—
145C2×C4×C5—121no—
146C2×C4×C5D3×D411yescharacteristic
147C5×C8—61no—
148C5×C8#23511yescharacteristic
149C5×C8#23911yescharacteristic
150#168—41no—
151#168—121no—
152C2×Q16—31no—
153C2×M16—31no—
154C2×M16—301no—
155C22⋊Q8—61no—
156M32—51no—
157M32—151no—
158#108—51no—
159#108—151no—
160#108—301no—
161#106D3×D511yescharacteristic
162#103—61no—
163C2×C3×C5—21no—
164C2×C3×C5#48111yescharacteristic
165C5×D3—41no—
166C22×D3#68711yescharacteristic
167C2×C3×C4—41no—
168C2×C3×C4C2×C22⋊D511yescharacteristic
169C2×Dic3—41no—
170C2×Dic3#68711yescharacteristic
171C4×D3—21no—
172C4×D3—21no—
173Dic6—41no—
174Dic6—41no—
175C3×C8—201no—
176C3×C8#71111yescharacteristic
177C3×C8#71111yescharacteristic
178C3⋊C8—21no—
179C3⋊C8—201no—
180C22×C5—61no—
181C22×C5—121no—
182C22×C5D3×SD1611yescharacteristic
183C4×C5—61no—
184C4×C5—81no—
185C4×C5—241no—
186C4×C5#89411yescharacteristic
187C4×C5#91411yescharacteristic
188C2×Q8—61no—
189C22×C4—31no—
190Q16—61no—
191Q16—61no—
192M16—61no—
193M16—61no—
194M16—101no—
195M16—301no—
196M16—601no—
197C2×C8—31no—
198C2×C8—601no—
199C2×C8C2×D3×D511yescharacteristic
200C4⋊C4—21no—
201C4⋊C4—121no—
202C22⋊C4—121no—
203C16—101no—
204C16—301no—
205C3×C5#223911yescharacteristic, complemented, Hall
206C22×C3C2×#68711yescharacteristic
207C2×D3—21no—
208C2×D3—41no—
209C3×C4—81no—
210C3×C4#408111yescharacteristic
211C3×C4#409511yescharacteristic
212Dic3—21no—
213Dic3—81no—
214C2×C5—21no—
215C2×C5—121no—
216C2×C5#486311yescharacteristic
217C23—31no—
218Q8—121no—
219Q8—121no—
220C2×C4—31no—
221C2×C4—41no—
222C2×C4—61no—
223C2×C4—61no—
224C2×C4—121no—
225C2×C4D3×C22⋊D511yescharacteristic
226C8—61no—
227C8—201no—
228C8—601no—
229C8#676811yescharacteristic
230C8#677211yescharacteristic
231C2×C3—21no—
232C2×C3#6532311yescharacteristic
233D3—41no—
234C5#6931411yescharacteristic, complemented, Sylow
235C22—61no—
236C22—121no—
237C22D3×#68711yescharacteristic
238C4—61no—
239C4—81no—
240C4—241no—
241C4#9142311yescharacteristic
242C4#9150411yescharacteristic
243C3#1060188311yescharacteristic, complemented, Sylow
244C2—21no—
245C2—121no—
246C2#1174719911yescharacteristic
subgroupG/H
centerC2#11747199
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#106C22
socleC2×C3×C5#481
prime radicalC22×C5×D3SD16
hypercenter#106D3×D5
hypocenterC3×C5#2239
LCSG ▷ C2×C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
3. #11746308C2semidirect
4. C3×#64707C2semidirect
5. #11745924C2semidirect
6. #11745923C2semidirect
27. #64707D3semidirect
205. C3×C5#2239semidirect
234. C5#69314semidirect
243. C3#10601883semidirect

Maximal subgroups

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

subgroupindex
C5×#48672
#117480592
#117463082
C3×#647072
#117459242
#117459232
#117458832
#106018833
#693145