Finite Group Databasebeta

← #14318584

Subgroups — #14318584

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
1C3×#65157C211yesmaximal, characteristic
2#11748057C211yesmaximal, characteristic
3#11746308C211yesmaximal, characteristic, complemented
4C5×#4487C211yesmaximal, characteristic, complemented
5#11745922C211yesmaximal, characteristic, complemented
6#11745921C211yesmaximal, characteristic, complemented
7#11745882C211yesmaximal, characteristic
8#10600107—31nomaximal, Hall
9C2×C3×Dic20C2211yescharacteristic
10C2×C3×#676C2211yescharacteristic
11C3×#4043—21no—
12D5×#208—21no—
13C3×C5×#106C2211yescharacteristic
14#91103C2211yescharacteristic
15#91096C2211yescharacteristic
16C5×#819C2211yescharacteristic
17C5×#812C2211yescharacteristic
18C3×#3942—21no—
19#90991—21no—
20#71090—51nomaximal, Hall
21#65182—31no—
22#65157D311yescharacteristic
23C5×#365—31no—
24#64737—31no—
25#64734—31no—
26#64716—31no—
27#64707—31no—
28C2×C3×C4×D5D411yescharacteristic
29C2×C3×Dic10—21no—
30C2×C3×C5×C8C2311yescharacteristic
31C3×C5×C4⋊C4—21no—
32#6710—21no—
33C5×#208—21no—
34C3×#685—41no—
35C3×C4⋊Dic5—41no—
36C2×C3×#168D411yescharacteristic
37C3×Dic20—21no—
38C3×Dic20—21no—
39C3×#676—21no—
40C3×#676—21no—
41#6649—41no—
42D5×C3⋊C8—41no—
43C3⋊#672—21no—
44C5×C3⋊C16—21no—
45C3×#470—51no—
46#5125—51no—
47#4565—51no—
48#4565—51no—
49#4553—51no—
50#4487—51no—
51#4487D511yescharacteristic, complemented
52D5×M16—61no—
53C2×Dic20C2×D311yescharacteristic
54C2×#676C2×D311yescharacteristic
55#4043—21no—
56C5×M32—31no—
57C5×#108—31no—
58C5×#106C2×D311yescharacteristic
59#3954—61no—
60#3951—31no—
61#3944—31no—
62#3942—21no—
63#2239—151noSylow
64C22×C3×D5SD1611yescharacteristic
65C2×C3×C4×C5—41no—
66C2×C3×C4×C5C2×D411yescharacteristic
67C2×C3×Dic5—41no—
68C2×C3×Dic5SD1611yescharacteristic
69C3×C4×D5—21no—
70C3×C4×D5—21no—
71C3×Dic10—41no—
72C3×Dic10—41no—
73C3×C5×C8#4111yescharacteristic
74C3×C5×C8#4111yescharacteristic
75C3⋊#168—41no—
76C3×#168—21no—
77C5×C3⋊C8—41no—
78C2×C3×Q16—51no—
79C2×C3×M16—51no—
80C3×C22⋊Q8—101no—
81C2×#208—101no—
82C3×#106C2×D511yescharacteristic
83C3×#103—101no—
84#819—51no—
85#819—101no—
86#819C2×D511yescharacteristic
87#812—51no—
88#812C2×D511yescharacteristic
89C2×C4×D5#6711yescharacteristic
90C2×Dic10—21no—
91C5×M16—61no—
92C2×C5×C8C22×D311yescharacteristic
93C5×C4⋊C4—21no—
94#685—41no—
95C4⋊Dic5—41no—
96#681—61no—
97C2×#168#6711yescharacteristic
98Dic20—21no—
99Dic20—21no—
100#676—21no—
101#676—21no—
102#676—121no—
103C8×D5—121no—
104C5×C16—61no—
105#672—61no—
106#470—51no—
107#430—151no—
108#365—31no—
109#365—151no—
110#362—151no—
111#362—151no—
112#349—151no—
113C22×C3×C5C2×SD1611yescharacteristic
114C2×C3×D5—21no—
115C2×C3×D5—41no—
116C3×C4×C5—81no—
117C3×C4×C5#12311yescharacteristic
118C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
119C3×Dic5—21no—
120C3×Dic5—81no—
121C2×C3×Q8—101no—
122C22×C3×C4—51no—
123C3×Q16—101no—
124C3×Q16—101no—
125C3×M16—101no—
126C3×M16—101no—
127C2×C3×C8—51no—
128C2×C3×C8C22×D511yescharacteristic
129C3×C4⋊C4—21no—
130C3×C4⋊C4—201no—
131C3×C22⋊C4—201no—
132#208—21no—
133#208—101no—
134#208—201no—
135C2×C3⋊C8—201no—
136C3⋊C16—21no—
137C3⋊C16—101no—
138C22×D5#21411yescharacteristic
139C2×C4×C5—41no—
140C2×C4×C5C2×#6711yescharacteristic
141C2×Dic5—41no—
142C2×Dic5#21411yescharacteristic
143C4×D5—21no—
144C4×D5—21no—
145Dic10—41no—
146Dic10—41no—
147C5×C8—121no—
148C5×C8#23711yescharacteristic
149C5×C8#23711yescharacteristic
150#168—21no—
151#168—121no—
152C2×Q16—51no—
153C2×M16—51no—
154C2×M16—301no—
155C22⋊Q8—101no—
156M32—31no—
157M32—151no—
158#108—31no—
159#108—151no—
160#108—301no—
161#106D3×D511yescharacteristic
162#103—101no—
163C2×C3×C5—21no—
164C2×C3×C5#48111yescharacteristic
165C3×D5—41no—
166C23×C3—51no—
167C3×Q8—201no—
168C3×Q8—201no—
169C2×C3×C4—41no—
170C2×C3×C4—51no—
171C2×C3×C4—101no—
172C2×C3×C4—101no—
173C2×C3×C4—201no—
174C2×C3×C4D4×D511yescharacteristic
175C3×C8—101no—
176C3×C8#70911yescharacteristic
177C3×C8#71311yescharacteristic
178C3⋊C8—41no—
179C3⋊C8—201no—
180C22×C5C2×#21411yescharacteristic
181C2×D5—21no—
182C2×D5—41no—
183C4×C5—81no—
184C4×C5#93511yescharacteristic
185C4×C5#94911yescharacteristic
186Dic5—21no—
187Dic5—81no—
188C2×Q8—101no—
189C22×C4—51no—
190Q16—101no—
191Q16—101no—
192M16—61no—
193M16—101no—
194M16—101no—
195M16—301no—
196M16—601no—
197C2×C8—51no—
198C2×C8—601no—
199C2×C8C2×D3×D511yescharacteristic
200C4⋊C4—21no—
201C4⋊C4—201no—
202C22⋊C4—201no—
203C16—61no—
204C16—301no—
205C3×C5#223911yescharacteristic, complemented, Hall
206C22×C3—101no—
207C22×C3—201no—
208C22×C3D5×SD1611yescharacteristic
209C3×C4—81no—
210C3×C4—101no—
211C3×C4—401no—
212C3×C4#404011yescharacteristic
213C3×C4#406011yescharacteristic
214C2×C5—21no—
215C2×C5#503411yescharacteristic
216D5—41no—
217C23—51no—
218Q8—201no—
219Q8—201no—
220C2×C4—41no—
221C2×C4—51no—
222C2×C4—101no—
223C2×C4—101no—
224C2×C4—201no—
225C2×C4D5×#6711yescharacteristic
226C8—101no—
227C8—121no—
228C8—601no—
229C8#676511yescharacteristic
230C8#676611yescharacteristic
231C2×C3—21no—
232C2×C3—201no—
233C2×C3#6515211yescharacteristic
234C5#7109011yescharacteristic, complemented, Sylow
235C22—101no—
236C22—201no—
237C22D5×#21411yescharacteristic
238C4—81no—
239C4—101no—
240C4—401no—
241C4#9140711yescharacteristic
242C4#9150211yescharacteristic
243C3#1060010711yescharacteristic, complemented, Sylow
244C2—21no—
245C2—201no—
246C2#1174719511yescharacteristic
subgroupG/H
centerC2#11747195
commutator, cosocleC2×C3×C5×C8C23
FrattiniC2×C8C2×D3×D5
FittingC3×C5×#106C22
socleC2×C3×C5#481
prime radicalC22×C3×D5SD16
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. C5×#4487C2semidirect
5. #11745922C2semidirect
6. #11745921C2semidirect
51. #4487D5semidirect
205. C3×C5#2239semidirect
234. C5#71090semidirect
243. C3#10600107semidirect

Maximal subgroups

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

subgroupindex
C3×#651572
#117480572
#117463082
C5×#44872
#117459222
#117459212
#117458822
#106001073
#710905