Finite Group Databasebeta

← #14319312

Subgroups — #14319312

Order 1920.

208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 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#11746839C211yesmaximal, characteristic
2#11746831C211yesmaximal, characteristic, complemented
3#11746268C211yesmaximal, characteristic, complemented
4C5×Dic48C211yesmaximal, characteristic, complemented
5C3×#64669C211yesmaximal, characteristic, complemented
6#11745827C211yesmaximal, characteristic, complemented
7#11745821C211yesmaximal, characteristic, complemented
8#10600177—31nomaximal, Hall
9#91277—21no—
10#91264—21no—
11C16×D15C2211yescharacteristic
12C5×Dic24C2211yescharacteristic
13C5×Dic24C2211yescharacteristic
14C3×Dic40C2211yescharacteristic
15C3×D80C2211yescharacteristic
16#90946—21no—
17#90940—21no—
18C3×C5×C32C2211yescharacteristic
19C3⋊#3926C2211yescharacteristic
20#69381—51nomaximal, Hall
21#65208—31no—
22D5×Q32—31no—
23C5×Q64—31no—
24#64742—31no—
25#64741—31no—
26#64669D311yescharacteristic, complemented
27#64667—31no—
28D15⋊Q8—41no—
29#6766—41no—
30C8×D15D411yescharacteristic
31C5×Dic12—21no—
32C5×Dic12—21no—
33C3×Dic20—21no—
34C3×D40—21no—
35#6661—41no—
36#6655—41no—
37C3×C5×C16C2311yescharacteristic
38C3⋊#672D411yescharacteristic
39D3×Q32—51no—
40#4912—51no—
41C3×SD64—51no—
42#4522—51no—
43#4520—51no—
44Dic48D511yescharacteristic, complemented
45#4447—51no—
46#4065—61no—
47D5×Q16—61no—
48C5×Q32—31no—
49C5×Q32—31no—
50#3961—61no—
51#3960—61no—
52Dic40C2×D311yescharacteristic
53D80C2×D311yescharacteristic
54D5×C16—31no—
55C5×C32C2×D311yescharacteristic
56#3926—31no—
57#2264—151noSylow
58C4×D15D811yescharacteristic
59C5×Dic6—41no—
60C5×Dic6—41no—
61C3×D20—41no—
62C3×Dic10—41no—
63#1204—81no—
64#1202—81no—
65#1200—81no—
66D5×Dic3—81no—
67C3×C5×C8C2×D411yescharacteristic
68C3⋊#168D811yescharacteristic
69D3×Q16—101no—
70#912—101no—
71C3×Q32—51no—
72C3×D16—51no—
73#829—101no—
74#827—101no—
75Dic24C2×D511yescharacteristic
76Dic24C2×D511yescharacteristic
77D3×C16—51no—
78C3×C32C2×D511yescharacteristic
79C3⋊C32—51no—
80#713—121no—
81Q8×D5—121no—
82C5×Q16—61no—
83C5×Q16—61no—
84#689—121no—
85#688—121no—
86Dic20—21no—
87D40—21no—
88C8×D5—31no—
89C5×C16C22×D311yescharacteristic
90#672—31no—
91#508—151no—
92C2×Q32—151no—
93Q64—31no—
94Q64—151no—
95SD64—51no—
96SD64—151no—
97M64—151no—
98C2×D15D1611yescharacteristic
99C2×C3×D5—81no—
100C3×C4×C5C2×D811yescharacteristic
101Dic15D1611yescharacteristic
102C3×Dic5—81no—
103C5×Dic3—81no—
104C5×Dic3—81no—
105D3×Q8—201no—
106#237—201no—
107C3×Q16—101no—
108C3×D8—101no—
109#216—201no—
110#214—201no—
111Dic12—21no—
112Dic12—21no—
113D3×C8—51no—
114C3×C16C22×D511yescharacteristic
115C3⋊C16—51no—
116C5×Q8—121no—
117C5×Q8—121no—
118D20—41no—
119D20—241no—
120C4×D5—31no—
121C4×D5—241no—
122C4×D5—241no—
123Dic10—41no—
124Dic10—241no—
125C5×C8D3×D411yescharacteristic
126#168—31no—
127#135—301no—
128C2×Q16—301no—
129Q32—31no—
130Q32—31no—
131Q32—51no—
132Q32—301no—
133SD32—301no—
134D16—51no—
135C2×C16—151no—
136C32—151no—
137C32D3×D511yescharacteristic
138C2×C3×C5C2×D1611yescharacteristic
139D15—21no—
140C3×D5—161no—
141C3×Q8—201no—
142C3×D4—201no—
143#67—401no—
144C2×Dic3—401no—
145C4×D3—51no—
146C4×D3—401no—
147Dic6—41no—
148Dic6—41no—
149Dic6—401no—
150C3×C8D4×D511yescharacteristic
151C3⋊C8—51no—
152C2×D5—31no—
153C2×D5—81no—
154C4×C5—241no—
155C4×C5—241no—
156C4×C5D3×D811yescharacteristic
157Dic5—31no—
158Dic5—81no—
159#41—601no—
160C2×Q8—601no—
161Q16—61no—
162Q16—61no—
163Q16—101no—
164Q16—601no—
165SD16—601no—
166D8—101no—
167C2×C8—151no—
168C16—151no—
169C16C2×D3×D511yescharacteristic
170C3×C5#226411yescharacteristic, complemented, Hall
171C22×C3—401no—
172C2×D3—51no—
173C3×C4—401no—
174C3×C4D5×D811yescharacteristic
175Dic3—51no—
176Dic3—81no—
177Dic3—81no—
178C2×C5D3×D1611yescharacteristic
179D5—61no—
180D5—161no—
181Q8—121no—
182Q8—121no—
183Q8—201no—
184Q8—1201no—
185D4—201no—
186D4—1201no—
187C2×C4—151no—
188C2×C4—1201no—
189C2×C4—1201no—
190C8—151no—
191C8#677711yescharacteristic
192C2×C3—801no—
193C2×C3D5×D1611yescharacteristic
194D3—101no—
195C5#6938111yescharacteristic, complemented, Sylow
196C22—151no—
197C22—401no—
198C4—151no—
199C4—241no—
200C4—241no—
201C4—401no—
202C4#9125611yescharacteristic
203C3#1060017711yescharacteristic, complemented, Sylow
204C2—301no—
205C2—801no—
206C2#1174682211yescharacteristic
subgroupG/H
centerC2#11746822
commutator, cosocleC3×C5×C16C23
FrattiniC16C2×D3×D5
FittingC3×C5×C32C22
socleC2×C3×C5C2×D16
prime radical#11746839C2
hypercenterC32D3×D5
hypocenterC3×C5#2264
LCSG ▷ C3×C5×C16 ▷ C3×C5×C8 ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ C16 ◁ C32

Complements

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

NH ≅ G/Ntype
2. #11746831C2semidirect
3. #11746268C2semidirect
4. C5×Dic48C2semidirect
5. C3×#64669C2semidirect
6. #11745827C2semidirect
7. #11745821C2semidirect
26. #64669D3semidirect
44. Dic48D5semidirect
170. C3×C5#2264semidirect
195. C5#69381semidirect
203. C3#10600177semidirect

Maximal subgroups

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

subgroupindex
#117468392
#117468312
#117462682
C5×Dic482
C3×#646692
#117458272
#117458212
#106001773
#693815