Finite Group Databasebeta

← #14279429

Subgroups — #14279429

Order 1920.

196 conjugacy classes of subgroups; only the 34 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 34 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#11747074C211yesmaximal, characteristic
2#11746727C211yesmaximal, characteristic
3C3×#64854C211yesmaximal, characteristic
4#10598541—31nomaximal, Hall
5#91758C411yescharacteristic, complemented
6C3×#4021C2211yescharacteristic
7C2×#6662—21no—
8C2×#6657—21no—
9#91234—21no—
10C3×#3999—21no—
11C5×#803C411yescharacteristic, complemented
12#67545—51nomaximal, Hall
13#65004—31no—
14#64856—31no—
15#64854D311yescharacteristic
16C2×Dic30—21no—
17C2×C3×D20D411yescharacteristic
18C2×C3×Dic10D411yescharacteristic
19#6762—41no—
20C3×C22⋊AGL(1,𝔽5)—41no—
21C3×C42×C5C2×C411yescharacteristic
22C4⋊Dic15—41no—
23C2×C5×C3⋊C8—21no—
24C3×#685—41no—
25#6662—42no—
26#6657—42no—
27#5060—51no—
28C3×#354—51no—
29#4542—51no—
30C2×Dic20—61no—
31C2×#677—61no—
32#4021C2×D311yescharacteristic
33#4015—31no—
34#4005—61no—
35#3999—21no—
36C5×#97—31no—
37#1407—151noSylow
38C22×C3×D5—21no—
39C2×C3×AGL(1,𝔽5)—81no—
40C2×C3×C4×C5—21no—
41C2×C3×C4×C5C22⋊C411yescharacteristic
42C2×Dic15—41no—
43Dic30—41no—
44Dic30—41no—
45C2×C3×Dic5—21no—
46C3×D20—41no—
47C3×Dic10—41no—
48C3⋊#170—81no—
49C5×C3⋊C8—22no—
50C3×#124—51no—
51C2×#216—101no—
52C2×#214—101no—
53#869—51no—
54C3×#99—101no—
55#836—101no—
56#803AGL(1,𝔽5)11yescharacteristic, complemented
57C2×D20#6711yescharacteristic
58C2×Dic10—61no—
59C2×Dic10D1211yescharacteristic
60C22⋊AGL(1,𝔽5)—41no—
61#704—121no—
62C2×C5×C8—61no—
63C42×C5C4×D311yescharacteristic
64#685—41no—
65C4⋊Dic5—121no—
66Dic20—122no—
67#677—122no—
68#497—151no—
69#355—151no—
70#354—51no—
71C22×C3×C5#9911yescharacteristic
72C2×C3×D5—41no—
73C2×C3×D5—81no—
74C3×AGL(1,𝔽5)—161no—
75C3×C4×C5—21no—
76C3×C4×C5—41no—
77Dic15—81no—
78C3×Dic5—41no—
79C2×C3×Q8—51no—
80C2×C3×D4—51no—
81C2×Dic6—101no—
82C3×C22⋊C4—201no—
83C3×C22⋊C4—201no—
84C3×C42C2×AGL(1,𝔽5)11yescharacteristic
85#216—202no—
86#214—202no—
87C4⋊Dic3—201no—
88#208—201no—
89C2×C3⋊C8—21no—
90C22×D5—21no—
91C2×AGL(1,𝔽5)—81no—
92C2×C4×C5—21no—
93C2×C4×C5(C2×D3)⋊C411yescharacteristic
94C2×Dic5—21no—
95C2×Dic5—121no—
96D20—41no—
97Dic10—41no—
98Dic10—121no—
99Dic10—121no—
100#170—241no—
101C5×C8—62no—
102C2×Q16—301no—
103C2×SD16—301no—
104C4⋊Q8—151no—
105#124—51no—
106#101—301no—
107#99—101no—
108#97—31no—
109C2×C3×C5—21no—
110C2×C3×C5#35311yescharacteristic
111C3×D5—81no—
112C23×C3—101no—
113C3×Q8—201no—
114C3×D4—201no—
115C2×C3×C4—21no—
116C2×C3×C4—101no—
117C2×C3×C4—401no—
118C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
119C2×Dic3—201no—
120Dic6—201no—
121Dic6—201no—
122C3⋊C8—22no—
123C3⋊C8—401no—
124C22×C5#80611yescharacteristic
125C2×D5—41no—
126C2×D5—81no—
127AGL(1,𝔽5)—161no—
128C4×C5—21no—
129C4×C5—41no—
130Dic5—41no—
131Dic5—241no—
132C2×Q8—51no—
133C2×Q8—301no—
134C2×D4—51no—
135Q16—602no—
136SD16—602no—
137M16—601no—
138C2×C8—61no—
139C4⋊C4—601no—
140C22⋊C4—201no—
141C22⋊C4—201no—
142C42D3×AGL(1,𝔽5)11yescharacteristic
143C3×C5#140711yescharacteristic, complemented, Hall
144C22×C3—201no—
145C22×C3—401no—
146C22×C3#399911yescharacteristic
147C3×C4—21no—
148C3×C4—41no—
149C3×C4—201no—
150C3×C4—801no—
151Dic3—401no—
152C2×C5—21no—
153C2×C5#447411yescharacteristic
154D5—81no—
155C23—101no—
156Q8—201no—
157Q8—601no—
158Q8—601no—
159D4—201no—
160C2×C4—21no—
161C2×C4—101no—
162C2×C4—401no—
163C2×C4—601no—
164C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
165C8—62no—
166C8—1201no—
167C2×C3—21no—
168C2×C3—401no—
169C2×C3#6485311yescharacteristic
170C5#6754511yescharacteristic, complemented, Sylow
171C22—201no—
172C22—401no—
173C22#9117311yescharacteristic
174C4—21no—
175C4—41no—
176C4—201no—
177C4—801no—
178C4—1201no—
179C3#1059854111yescharacteristic, complemented, Sylow
180C2—21no—
181C2—401no—
182C2#1174655511yescharacteristic
subgroupG/H
centerC2#11746555
commutator, FittingC3×C42×C5C2×C4
Frattini, hypercenterC42D3×AGL(1,𝔽5)
socleC2×C3×C5#353
prime radicalC2×C3×D20D4
cosocleC3×#4021C22
hypocenterC3×C5#1407
LCSG ▷ C3×C42×C5 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
5. #91758C4semidirect
11. C5×#803C4semidirect
56. #803AGL(1,𝔽5)semidirect
143. C3×C5#1407semidirect
170. C5#67545semidirect
179. C3#10598541semidirect

Maximal subgroups

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

subgroupindex
#117470742
#117467272
C3×#648542
#105985413
#675455