Finite Group Databasebeta

← #14279487

Subgroups — #14279487

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
1C3×#65381C211yesmaximal, characteristic
2#11746369C211yesmaximal, characteristic
3C5×#4548C211yesmaximal, characteristic
4#10598044—31nomaximal, Hall
5C3×C5×C4⋊Q8C2211yescharacteristic
6C2×C3×#689—21no—
7C2×C3×#689—21no—
8C3×#4015C411yescharacteristic
9#91120—21no—
10C5×#836—21no—
11C3×C4×#168C411yescharacteristic
12#67795—51nomaximal, Hall
13#65381D311yescharacteristic
14C5×#356—31no—
15#64768—31no—
16C2×C3×C5×Q8D411yescharacteristic
17C2×C3×C5×Q8D411yescharacteristic
18C2×C3×Dic10—21no—
19C3×C5×C4⋊C4—41no—
20C3×C42×C5C2×C411yescharacteristic
21#6710—41no—
22C5×#208—41no—
23C3×#689—42no—
24C3×#689—42no—
25C3×C4⋊Dic5—41no—
26C2×C3×#168—21no—
27C3×#494—51no—
28#4548—51no—
29#4548D511yescharacteristic
30C5×C4⋊Q8C2×D311yescharacteristic
31C2×#689—21no—
32C2×#689—21no—
33#4015Dic311yescharacteristic
34C5×#101—61no—
35#3968—61no—
36C4×#168Dic311yescharacteristic
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×C3×Dic5—41no—
45C3×Dic10—41no—
46C3×Dic10—41no—
47C3⋊#168—81no—
48C3×#168—22no—
49C5×C3⋊C8—81no—
50C2×C3×Q16—101no—
51C2×C3×Q16—101no—
52C3×C4⋊Q8—51no—
53C3×C4⋊Q8C2×D511yescharacteristic
54C3×C4×C8—51no—
55#836—21no—
56#836—101no—
57C2×C5×Q8#6711yescharacteristic
58C2×C5×Q8#6711yescharacteristic
59C2×Dic10—21no—
60C5×M16—121no—
61C5×C4⋊C4—41no—
62C42×C5C2×Dic311yescharacteristic
63#689—42no—
64#689—42no—
65C4⋊Dic5—41no—
66#681—121no—
67C2×#168—21no—
68#494—51no—
69#356—31no—
70#356—151no—
71C22×C3×C5#9911yescharacteristic
72C3×C4×C5—22no—
73C3×C4×C5—21no—
74C3×C4×C5—41no—
75C3×C4×C5—41no—
76C3×Dic5—81no—
77C2×C3×Q8—101no—
78C2×C3×Q8D2011yescharacteristic
79C2×C3×Q8C22⋊D511yescharacteristic
80C3×Q16—202no—
81C3×Q16—202no—
82C2×C3×C8—101no—
83C3×C4⋊C4—41no—
84C3×C4⋊C4—201no—
85C3×C42C4×D511yescharacteristic
86#208—41no—
87#208—201no—
88C5×Q8—41no—
89C5×Q8—41no—
90C2×C4×C5—21no—
91C2×C4×C5—21no—
92C2×C4×C5—21no—
93C2×C4×C5#21711yescharacteristic
94C2×Dic5—41no—
95Dic10—41no—
96Dic10—41no—
97C5×C8—241no—
98#168—22no—
99#168—241no—
100C2×Q16—101no—
101C2×Q16—101no—
102C4⋊Q8—51no—
103C4⋊Q8D3×D511yescharacteristic
104#101—61no—
105#101—301no—
106C4×C8—51no—
107C2×C3×C5—21no—
108C2×C3×C5#35311yescharacteristic
109C3×Q8—41no—
110C3×Q8—41no—
111C3×Q8—201no—
112C3×Q8—201no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—201no—
117C2×C3×C4#68511yescharacteristic
118C3×C8—102no—
119C3⋊C8—81no—
120C3⋊C8—401no—
121C22×C5#83411yescharacteristic
122C4×C5—22no—
123C4×C5—21no—
124C4×C5—41no—
125C4×C5—41no—
126Dic5—81no—
127C2×Q8—101no—
128C2×Q8#120111yescharacteristic
129C2×Q8#120211yescharacteristic
130Q16—202no—
131Q16—202no—
132M16—121no—
133M16—601no—
134C2×C8—101no—
135C4⋊C4—41no—
136C4⋊C4—201no—
137C42D5×Dic311yescharacteristic
138C3×C5#141111yescharacteristic, complemented, Hall
139C22×C3#393811yescharacteristic
140C3×C4—22no—
141C3×C4—21no—
142C3×C4—41no—
143C3×C4—41no—
144C3×C4—401no—
145C2×C5—21no—
146C2×C5#454511yescharacteristic
147Q8—41no—
148Q8—41no—
149Q8—201no—
150Q8—201no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—201no—
155C2×C4#666511yescharacteristic
156C8—102no—
157C8—241no—
158C8—1201no—
159C2×C3—21no—
160C2×C3#6469411yescharacteristic
161C5#6779511yescharacteristic, complemented, Sylow
162C22#9099511yescharacteristic
163C4—22no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—401no—
168C3#1059804411yescharacteristic, complemented, Sylow
169C2—21no—
170C2#1174600611yescharacteristic
subgroupG/H
centerC2#11746006
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#67795semidirect
168. C3#10598044semidirect

Maximal subgroups

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

subgroupindex
C3×#653812
#117463692
C5×#45482
#105980443
#677955