Finite Group Databasebeta

← #14279489

Subgroups — #14279489

Order 1920.

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

normal subgroups only

This group has 188 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
1C5×#5092C211yesmaximal, characteristic
2#11746369C211yesmaximal, characteristic
3C3×#64768C211yesmaximal, characteristic
4#10598286—31nomaximal, Hall
5C3×C5×C4⋊Q8C2211yescharacteristic
6C2×C5×#216—21no—
7C2×C5×#216—21no—
8C5×#869C411yescharacteristic
9#91120—21no—
10C4×C5×C3⋊C8C411yescharacteristic
11C3×#3968—21no—
12#67553—51nomaximal, Hall
13C5×#494—31no—
14#64768—31no—
15#64768D311yescharacteristic
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×Q8D411yescharacteristic
18C2×C5×Dic6—21no—
19C3×C5×C4⋊C4—41no—
20C3×C42×C5C2×C411yescharacteristic
21#6710—41no—
22C5×#216—42no—
23C5×#216—42no—
24C5×C4⋊Dic3—41no—
25C2×C5×C3⋊C8—21no—
26C3×#681—41no—
27#5092D511yescharacteristic
28C3×#356—51no—
29#4548—51no—
30C2×C5×Q16—61no—
31C2×C5×Q16—61no—
32C5×C4⋊Q8—31no—
33C5×C4⋊Q8C2×D311yescharacteristic
34C4×C5×C8—31no—
35#3968—21no—
36#3968—61no—
37#1411—151noSylow
38C3×C5×Q8—41no—
39C3×C5×Q8—41no—
40C2×C3×C4×C5—21no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5—21no—
43C2×C3×C4×C5C22⋊C411yescharacteristic
44C2×C5×Dic3—41no—
45C5×Dic6—41no—
46C5×Dic6—41no—
47C3⋊#168—81no—
48C3×#168—81no—
49C5×C3⋊C8—22no—
50C3×C4⋊Q8C2×D511yescharacteristic
51C2×#216—21no—
52C2×#216—21no—
53#869Dic511yescharacteristic
54C3×#101—101no—
55#836—101no—
56C4×C3⋊C8Dic511yescharacteristic
57C2×C5×Q8—61no—
58C2×C5×Q8D1211yescharacteristic
59C2×C5×Q8#6711yescharacteristic
60C5×Q16—122no—
61C5×Q16—122no—
62C2×C5×C8—61no—
63C5×C4⋊C4—41no—
64C5×C4⋊C4—121no—
65C42×C5C4×D311yescharacteristic
66#681—41no—
67#681—121no—
68#494—31no—
69#356—51no—
70#356—151no—
71C22×C3×C5#9911yescharacteristic
72C3×C4×C5—22no—
73C3×C4×C5—21no—
74C3×C4×C5—41no—
75C3×C4×C5—41no—
76C5×Dic3—81no—
77C2×C3×Q8C22⋊D511yescharacteristic
78C2×C3×Q8C22⋊D511yescharacteristic
79C2×Dic6—21no—
80C3×M16—201no—
81C3×C4⋊C4—41no—
82C3×C42C2×Dic511yescharacteristic
83#216—42no—
84#216—42no—
85C4⋊Dic3—41no—
86#208—201no—
87C2×C3⋊C8—21no—
88C5×Q8—41no—
89C5×Q8—41no—
90C5×Q8—121no—
91C5×Q8—121no—
92C2×C4×C5—21no—
93C2×C4×C5—21no—
94C2×C4×C5—21no—
95C2×C4×C5—121no—
96C2×C4×C5(C2×D3)⋊C411yescharacteristic
97C5×C8—62no—
98#168—81no—
99#168—241no—
100C2×Q16—61no—
101C2×Q16—61no—
102C4⋊Q8—31no—
103C4⋊Q8D3×D511yescharacteristic
104#101—101no—
105#101—301no—
106C4×C8—31no—
107C2×C3×C5—21no—
108C2×C3×C5#35311yescharacteristic
109C3×Q8—41no—
110C3×Q8—41no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4C22⋊Dic511yescharacteristic
115C2×Dic3—41no—
116Dic6—41no—
117Dic6—41no—
118C3×C8—401no—
119C3⋊C8—22no—
120C3⋊C8—401no—
121C22×C5#80611yescharacteristic
122C4×C5—22no—
123C4×C5—21no—
124C4×C5—41no—
125C4×C5—41no—
126C4×C5—241no—
127C2×Q8—61no—
128C2×Q8#120111yescharacteristic
129C2×Q8#120311yescharacteristic
130Q16—122no—
131Q16—122no—
132M16—201no—
133M16—601no—
134C2×C8—61no—
135C4⋊C4—41no—
136C4⋊C4—121no—
137C42D3×Dic511yescharacteristic
138C3×C5#141111yescharacteristic, complemented, Hall
139C22×C3#396611yescharacteristic
140C3×C4—22no—
141C3×C4—21no—
142C3×C4—41no—
143C3×C4—41no—
144Dic3—81no—
145C2×C5—21no—
146C2×C5#447411yescharacteristic
147Q8—41no—
148Q8—41no—
149Q8—121no—
150Q8—121no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—121no—
155C2×C4(C2×D3)⋊Dic511yescharacteristic
156C8—62no—
157C8—401no—
158C8—1201no—
159C2×C3—21no—
160C2×C3#6476511yescharacteristic
161C5#6755311yescharacteristic, complemented, Sylow
162C22#9099611yescharacteristic
163C4—22no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—241no—
168C3#1059828611yescharacteristic, complemented, Sylow
169C2—21no—
170C2#1174600711yescharacteristic
subgroupG/H
centerC2#11746007
commutatorC3×C42×C5C2×C4
Frattini, hypercenterC4⋊Q8D3×D5
Fitting, cosocleC3×C5×C4⋊Q8C22
socleC2×C3×C5#353
prime radicalC22×C3×C5#99
hypocenterC3×C5#1411
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
138. C3×C5#1411semidirect
161. C5#67553semidirect
168. C3#10598286semidirect

Maximal subgroups

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

subgroupindex
C5×#50922
#117463692
C3×#647682
#105982863
#675535