Finite Group Databasebeta

← #14319237

Subgroups — #14319237

Order 1920.

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

normal subgroups only

This group has 212 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#11746842C211yesmaximal, characteristic, complemented
2#11746839C211yesmaximal, characteristic, complemented
3D15×C32C211yesmaximal, characteristic, complemented
4C5×#4449C211yesmaximal, characteristic, complemented
5C3×#64669C211yesmaximal, characteristic, complemented
6#11745827C211yesmaximal, characteristic, complemented
7#11745818C211yesmaximal, characteristic, complemented
8#10600172—31nomaximal, Hall
9#91279—21no—
10#91277—21no—
11C16×D15C2211yescharacteristic
12C5×Dic24C2211yescharacteristic
13C5×D48C2211yescharacteristic
14C3×Dic40C2211yescharacteristic
15C3×D80C2211yescharacteristic
16#90941—21no—
17#90940—21no—
18C3×C5×C32C2211yescharacteristic
19C3⋊#3926C2211yescharacteristic
20#69379—51nomaximal, Hall
21#65208—31no—
22#65201—31no—
23C5×SD64—31no—
24#64742—31no—
25#64739—31no—
26#64669D311yescharacteristic, complemented
27D5×C32—31no—
28#6768—41no—
29#6766—41no—
30C8×D15D411yescharacteristic
31C5×Dic12—21no—
32C5×D24—21no—
33C3×Dic20—21no—
34C3×D40—21no—
35#6656—41no—
36#6655—41no—
37C3×C5×C16C2311yescharacteristic
38C3⋊#672D411yescharacteristic
39#4919—51no—
40#4912—51no—
41C3×SD64—51no—
42#4522—51no—
43#4519—51no—
44#4449D511yescharacteristic, complemented
45D3×C32—51no—
46#4065—61no—
47#4058—61no—
48C5×Q32—31no—
49C5×D16—31no—
50#3960—61no—
51#3959—61no—
52Dic40C2×D311yescharacteristic
53D80C2×D311yescharacteristic
54D5×C16—31no—
55C5×C32C2×D311yescharacteristic
56#3926—31no—
57#2262—151noSylow
58C4×D15D811yescharacteristic
59C5×D12—41no—
60C5×Dic6—41no—
61C3×D20—41no—
62C3×Dic10—41no—
63#1203—81no—
64#1202—81no—
65D3×Dic5—81no—
66D5×Dic3—81no—
67C3×C5×C8C2×D411yescharacteristic
68C3⋊#168D811yescharacteristic
69#919—101no—
70#912—101no—
71C3×Q32—51no—
72C3×D16—51no—
73#828—101no—
74#827—101no—
75Dic24C2×D511yescharacteristic
76D48C2×D511yescharacteristic
77D3×C16—51no—
78C3×C32C2×D511yescharacteristic
79C3⋊C32—51no—
80#713—121no—
81#711—121no—
82C5×Q16—61no—
83C5×D8—61no—
84#688—121no—
85#687—121no—
86Dic20—21no—
87D40—21no—
88C8×D5—31no—
89C5×C16C22×D311yescharacteristic
90#672—31no—
91#508—151no—
92#508—151no—
93Q64—151no—
94SD64—31no—
95SD64—51no—
96D32—151no—
97C2×C32—151no—
98C2×D15D1611yescharacteristic
99C2×C5×D3—81no—
100C2×C3×D5—81no—
101C3×C4×C5C2×D811yescharacteristic
102Dic15D1611yescharacteristic
103C3×Dic5—81no—
104C5×Dic3—81no—
105#239—201no—
106#237—201no—
107C3×Q16—101no—
108C3×D8—101no—
109#215—201no—
110#214—201no—
111Dic12—21no—
112D24—21no—
113D3×C8—51no—
114C3×C16C22×D511yescharacteristic
115C3⋊C16—51no—
116C5×Q8—121no—
117C5×D4—121no—
118C22⋊D5—241no—
119C2×Dic5—241no—
120D20—41no—
121D20—241no—
122C4×D5—31no—
123C4×D5—241no—
124Dic10—41no—
125C5×C8D3×D411yescharacteristic
126#168—31no—
127#135—301no—
128#135—301no—
129Q32—31no—
130Q32—51no—
131SD32—301no—
132SD32—301no—
133D16—31no—
134D16—51no—
135C2×C16—151no—
136C32—151no—
137C32D3×D511yescharacteristic
138C2×C3×C5C2×D1611yescharacteristic
139D15—21no—
140C3×D5—161no—
141C5×D3—161no—
142C3×Q8—201no—
143C3×D4—201no—
144#67—401no—
145C2×Dic3—401no—
146D12—41no—
147D12—401no—
148C4×D3—51no—
149C4×D3—401no—
150Dic6—41no—
151C3×C8D4×D511yescharacteristic
152C3⋊C8—51no—
153C22×C5—241no—
154C2×D5—31no—
155C2×D5—81no—
156C4×C5—241no—
157C4×C5D3×D811yescharacteristic
158Dic5—31no—
159Dic5—81no—
160#41—601no—
161#41—601no—
162Q16—61no—
163Q16—101no—
164SD16—601no—
165SD16—601no—
166D8—61no—
167D8—101no—
168C2×C8—151no—
169C16—151no—
170C16C2×D3×D511yescharacteristic
171C3×C5#226211yescharacteristic, complemented, Hall
172C22×C3—401no—
173C2×D3—51no—
174C2×D3—81no—
175C3×C4—401no—
176C3×C4D5×D811yescharacteristic
177Dic3—51no—
178Dic3—81no—
179C2×C5—481no—
180C2×C5D3×D1611yescharacteristic
181D5—61no—
182D5—161no—
183Q8—121no—
184Q8—201no—
185D4—121no—
186D4—201no—
187D4—1201no—
188D4—1201no—
189C2×C4—151no—
190C2×C4—1201no—
191C2×C4—1201no—
192C8—151no—
193C8#677711yescharacteristic
194C2×C3—801no—
195C2×C3D5×D1611yescharacteristic
196D3—101no—
197D3—161no—
198C5#6937911yescharacteristic, complemented, Sylow
199C22—151no—
200C22—241no—
201C22—401no—
202C4—151no—
203C4—241no—
204C4—401no—
205C4#9125611yescharacteristic
206C3#1060017211yescharacteristic, complemented, Sylow
207C2—301no—
208C2—481no—
209C2—801no—
210C2#1174682211yescharacteristic
subgroupG/H
centerC2#11746822
commutator, cosocleC3×C5×C16C23
FrattiniC16C2×D3×D5
FittingC3×C5×C32C22
socleC2×C3×C5C2×D16
hypercenterC32D3×D5
hypocenterC3×C5#2262
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
1. #11746842C2semidirect
2. #11746839C2semidirect
3. D15×C32C2semidirect
4. C5×#4449C2semidirect
5. C3×#64669C2semidirect
6. #11745827C2semidirect
7. #11745818C2semidirect
26. #64669D3semidirect
44. #4449D5semidirect
171. C3×C5#2262semidirect
198. C5#69379semidirect
206. C3#10600172semidirect

Maximal subgroups

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

subgroupindex
#117468422
#117468392
D15×C322
C5×#44492
C3×#646692
#117458272
#117458182
#106001723
#693795