Finite Group Databasebeta

← #14279404

Subgroups — #14279404

Order 1920.

216 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 42 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×#65347C211yesmaximal, characteristic
2#11746362C211yesmaximal, characteristic, complemented
3C5×#4542C211yesmaximal, characteristic, complemented
4#10598039—31nomaximal, Hall
5C3×C5×#124C2211yescharacteristic
6C2×C3×#688—21no—
7C2×C3×#686—21no—
8C3×#4020C411yescharacteristic, complemented
9#91118—21no—
10C5×#836—21no—
11C3×#3935C411yescharacteristic, complemented
12#67797—51nomaximal, Hall
13#65347D311yescharacteristic
14C5×#355—31no—
15#64761—31no—
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C2×C3×D20—21no—
19C2×C3×D20—41no—
20C3×C5×C22⋊C4—41no—
21C3×C42×C5C2×C411yescharacteristic
22#6719—41no—
23C5×#208—41no—
24C3×#688—42no—
25C3×#686—42no—
26C2×C3×#168—21no—
27C3×#496—51no—
28#4542D511yescharacteristic, complemented
29#4541—51no—
30C5×#124C2×D311yescharacteristic
31C2×#688—21no—
32C2×#686—21no—
33#4020Dic311yescharacteristic, complemented
34C5×#101—61no—
35#3966—61no—
36#3935Dic311yescharacteristic, complemented
37#1406—151noSylow
38C23×C3×C5—21no—
39C22×C3×D5—41no—
40C3×C5×Q8—41no—
41C3×C5×D4—41no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5C22⋊C411yescharacteristic
45C2×Dic15—81no—
46C3×D20—41no—
47C3×D20—41no—
48C3×D20—82no—
49C3×#168—22no—
50C5×C3⋊C8—81no—
51C2×C3×SD16—101no—
52C2×C3×D8—101no—
53C3×#127—51no—
54C3×#124C2×D511yescharacteristic
55C3×#97—51no—
56#836—21no—
57#834—101no—
58C2×C5×Q8#6711yescharacteristic
59C2×C5×D4#6711yescharacteristic
60C2×D20—21no—
61C2×D20—41no—
62C5×M16—121no—
63C5×C22⋊C4—41no—
64C42×C5C2×Dic311yescharacteristic
65C22⋊Dic5—121no—
66#688—42no—
67#686—42no—
68C2×#168—21no—
69#496—51no—
70#355—31no—
71#354—151no—
72C22×C3×C5—41no—
73C22×C3×C5—81no—
74C22×C3×C5#9911yescharacteristic
75C2×C3×D5—82no—
76C2×C3×D5—81no—
77C3×C4×C5—21no—
78C3×C4×C5—41no—
79C3×C4×C5—41no—
80Dic15—161no—
81C2×C3×Q8C22⋊D511yescharacteristic
82C2×C3×D4—101no—
83C2×C3×D4—201no—
84C2×C3×D4D2011yescharacteristic
85C3×SD16—202no—
86C3×D8—202no—
87C2×C3×C8—101no—
88C3×C22⋊C4—41no—
89C3×C42C4×D511yescharacteristic
90#217—201no—
91#208—41no—
92C23×C5—21no—
93C22×D5—41no—
94C5×Q8—41no—
95C5×D4—41no—
96C2×C4×C5—21no—
97C2×C4×C5—21no—
98C2×C4×C5#21711yescharacteristic
99C2×Dic5—241no—
100D20—41no—
101D20—41no—
102D20—82no—
103C5×C8—241no—
104#168—22no—
105C2×SD16—101no—
106C2×D8—101no—
107#127—51no—
108#124D3×D511yescharacteristic
109#101—61no—
110#99—301no—
111#97—51no—
112C2×C3×C5—21no—
113C2×C3×C5—81no—
114C2×C3×C5#35311yescharacteristic
115C3×D5—161no—
116C23×C3—21no—
117C23×C3—201no—
118C3×Q8—41no—
119C3×D4—41no—
120C3×D4—201no—
121C3×D4—201no—
122C3×D4—402no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4#68511yescharacteristic
126C2×Dic3—401no—
127C3×C8—102no—
128C3⋊C8—81no—
129C22×C5—41no—
130C22×C5—81no—
131C22×C5#83411yescharacteristic
132C2×D5—82no—
133C2×D5—81no—
134C4×C5—21no—
135C4×C5—41no—
136C4×C5—41no—
137Dic5—481no—
138C2×Q8#120111yescharacteristic
139C2×D4—101no—
140C2×D4—201no—
141C2×D4#120211yescharacteristic
142SD16—202no—
143D8—202no—
144M16—121no—
145C2×C8—101no—
146C22⋊C4—41no—
147C22⋊C4—601no—
148C42D5×Dic311yescharacteristic
149C3×C5#140611yescharacteristic, complemented, Hall
150C22×C3—41no—
151C22×C3—81no—
152C22×C3—402no—
153C22×C3—401no—
154C22×C3#393811yescharacteristic
155C3×C4—21no—
156C3×C4—41no—
157C3×C4—41no—
158Dic3—801no—
159C2×C5—21no—
160C2×C5—81no—
161C2×C5#454511yescharacteristic
162D5—161no—
163C23—21no—
164C23—201no—
165Q8—41no—
166D4—41no—
167D4—201no—
168D4—201no—
169D4—402no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—1201no—
173C2×C4#666511yescharacteristic
174C8—102no—
175C8—241no—
176C2×C3—21no—
177C2×C3—81no—
178C2×C3—801no—
179C2×C3#6469411yescharacteristic
180C5#6779711yescharacteristic, complemented, Sylow
181C22—41no—
182C22—81no—
183C22—402no—
184C22—401no—
185C22#9099511yescharacteristic
186C4—21no—
187C4—41no—
188C4—41no—
189C4—2401no—
190C3#1059803911yescharacteristic, complemented, Sylow
191C2—21no—
192C2—81no—
193C2—801no—
194C2#1174600611yescharacteristic
subgroupG/H
centerC2#11746006
commutatorC3×C42×C5C2×C4
Frattini, hypercenter#124D3×D5
Fitting, cosocleC3×C5×#124C22
socleC2×C3×C5#353
prime radicalC3×#65347C2
hypocenterC3×C5#1406
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11746362C2semidirect
3. C5×#4542C2semidirect
8. C3×#4020C4semidirect
11. C3×#3935C4semidirect
28. #4542D5semidirect
33. #4020Dic3semidirect
36. #3935Dic3semidirect
149. C3×C5#1406semidirect
180. C5#67797semidirect
190. C3#10598039semidirect

Maximal subgroups

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

subgroupindex
C3×#653472
#117463622
C5×#45422
#105980393
#677975