Finite Group Databasebeta

← #14279426

Subgroups — #14279426

Order 1920.

196 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 40 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#11751161C211yesmaximal, characteristic
2C5×#4542C211yesmaximal, characteristic
3C3×#64761C211yesmaximal, characteristic
4#10598040—31nomaximal, Hall
5C3×C5×#124C2211yescharacteristic
6C2×#6718—21no—
7C2×#6716—21no—
8#91758C411yescharacteristic, complemented
9#91087C411yescharacteristic, complemented
10C5×#836—21no—
11C3×#3966—21no—
12#67545—51nomaximal, Hall
13#65349—31no—
14C5×#355—31no—
15#64761D311yescharacteristic
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C2×Dic30—21no—
19C3×C5×C22⋊C4—41no—
20C3×C42×C5C2×C411yescharacteristic
21#6718—42no—
22#6716—42no—
23C4⋊Dic15—41no—
24C2×C3⋊#168—21no—
25C5×#208—41no—
26C3×C22⋊Dic5—41no—
27#5060—51no—
28C3×#354—51no—
29#4542D511yescharacteristic
30C5×#124C2×D311yescharacteristic
31C2×#689—61no—
32C2×#687—61no—
33#4015—31no—
34C5×#101—61no—
35#3966—21no—
36#3935—31no—
37#1407—151noSylow
38C23×C3×C5—21no—
39C3×C5×Q8—41no—
40C3×C5×D4—41no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×Dic15—41no—
45Dic30—41no—
46Dic30—41no—
47C2×C3×Dic5—81no—
48C3⋊#168—22no—
49C5×C3⋊C8—81no—
50C3×#124C2×D511yescharacteristic
51C2×#216—101no—
52C2×#214—101no—
53#869—51no—
54C3×#99—101no—
55#836—21no—
56#803—51no—
57C2×C5×Q8D1211yescharacteristic
58C2×C5×D4#6711yescharacteristic
59C2×Dic10—61no—
60C5×M16—121no—
61C5×C22⋊C4—41no—
62C42×C5C4×D311yescharacteristic
63C22⋊Dic5—41no—
64#689—122no—
65#687—122no—
66C4⋊Dic5—121no—
67C2×#168—61no—
68#497—151no—
69#355—31no—
70#354—51no—
71C22×C3×C5—41no—
72C22×C3×C5—81no—
73C22×C3×C5#9911yescharacteristic
74C3×C4×C5—21no—
75C3×C4×C5—41no—
76C3×C4×C5—41no—
77Dic15—81no—
78C3×Dic5—161no—
79C2×C3×Q8C22⋊D511yescharacteristic
80C2×C3×D4D2011yescharacteristic
81C2×Dic6—101no—
82C3×C22⋊C4—41no—
83C3×C22⋊C4—201no—
84C3×C42C4×D511yescharacteristic
85#216—202no—
86#214—202no—
87C4⋊Dic3—201no—
88#208—41no—
89C2×C3⋊C8—101no—
90C23×C5—21no—
91C5×Q8—41no—
92C5×D4—41no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5(C2×D3)⋊C411yescharacteristic
96C2×Dic5—81no—
97C2×Dic5—121no—
98Dic10—121no—
99Dic10—121no—
100C5×C8—241no—
101#168—62no—
102C2×Q16—301no—
103C2×SD16—301no—
104C4⋊Q8—151no—
105#124D3×D511yescharacteristic
106#101—61no—
107#99—101no—
108#97—151no—
109C2×C3×C5—21no—
110C2×C3×C5—81no—
111C2×C3×C5#35311yescharacteristic
112C23×C3—21no—
113C3×Q8—41no—
114C3×D4—41no—
115C2×C3×C4—21no—
116C2×C3×C4—21no—
117C2×C3×C4—401no—
118C2×C3×C4#68511yescharacteristic
119C2×Dic3—201no—
120Dic6—201no—
121Dic6—201no—
122C3⋊C8—81no—
123C3⋊C8—102no—
124C22×C5—41no—
125C22×C5—81no—
126C22×C5#80611yescharacteristic
127C4×C5—21no—
128C4×C5—41no—
129C4×C5—41no—
130Dic5—161no—
131Dic5—241no—
132C2×Q8—301no—
133C2×Q8#120311yescharacteristic
134C2×D4#120211yescharacteristic
135Q16—602no—
136SD16—602no—
137M16—121no—
138C2×C8—301no—
139C4⋊C4—601no—
140C22⋊C4—41no—
141C22⋊C4—201no—
142C42#120011yescharacteristic
143C3×C5#140711yescharacteristic, complemented, Hall
144C22×C3—41no—
145C22×C3—81no—
146C22×C3#393811yescharacteristic
147C3×C4—21no—
148C3×C4—41no—
149C3×C4—41no—
150C3×C4—801no—
151Dic3—401no—
152C2×C5—21no—
153C2×C5—81no—
154C2×C5#447411yescharacteristic
155C23—21no—
156Q8—41no—
157Q8—601no—
158Q8—601no—
159D4—41no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—401no—
163C2×C4—601no—
164C2×C4#666711yescharacteristic
165C8—241no—
166C8—302no—
167C2×C3—21no—
168C2×C3—81no—
169C2×C3#6469411yescharacteristic
170C5#6754511yescharacteristic, complemented, Sylow
171C22—41no—
172C22—81no—
173C22#9099711yescharacteristic
174C4—21no—
175C4—41no—
176C4—41no—
177C4—801no—
178C4—1201no—
179C3#1059804011yescharacteristic, complemented, Sylow
180C2—21no—
181C2—81no—
182C2#1174600811yescharacteristic
subgroupG/H
centerC2#11746008
commutatorC3×C42×C5C2×C4
Frattini, hypercenter#124D3×D5
Fitting, cosocleC3×C5×#124C22
socleC2×C3×C5#353
prime radicalC2×C3×C5×D4D4
hypocenterC3×C5#1407
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
8. #91758C4semidirect
9. #91087C4semidirect
143. C3×C5#1407semidirect
170. C5#67545semidirect
179. C3#10598040semidirect

Maximal subgroups

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

subgroupindex
#117511612
C5×#45422
C3×#647612
#105980403
#675455