Finite Group Databasebeta

← #14279384

Subgroups — #14279384

Order 1920.

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

normal subgroups only

This group has 212 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#11749393C211yesmaximal, characteristic
2#11746800C211yesmaximal, characteristic, complemented
3C3×#64931C211yesmaximal, characteristic, complemented
4#10598836—31nomaximal, Hall
5C5×#1007C411yescharacteristic
6C3×#4090C2211yescharacteristic
7#91309—21no—
8#91234—21no—
9C3×#4004—21no—
10#91120C411yescharacteristic
11#90979—21no—
12#67463—51nomaximal, Hall
13#65535—31no—
14#64931D311yescharacteristic, complemented
15#64929—31no—
16C2×C3×C5×Q8C2×C411yescharacteristic
17C5×#239—41no—
18C5×D3×Q8—41no—
19C5×#235—21no—
20C5×#235—41no—
21C2×C3×Dic10D411yescharacteristic
22#6762—41no—
23C2×C3×#170—41no—
24#6710—21no—
25C3×#683—41no—
26C3×C4×Dic5D411yescharacteristic
27#6661—41no—
28#6656—41no—
29#5095—51no—
30C3×#333—51no—
31#4548—51no—
32C5×2−1+4—31no—
33#4097—61no—
34#4090C2×D311yescharacteristic
35#4005—61no—
36#4004—21no—
37#3969—61no—
38#3968—31no—
39#1405—151noSylow
40C3×C5×Q8—41no—
41C2×C3×C4×C5—21no—
42C2×C3×C4×C5C22⋊C411yescharacteristic
43C5×#67—41no—
44C5×D12—21no—
45C5×D12—41no—
46C4×C5×D3—41no—
47C4×C5×D3—42no—
48C5×Dic6—21no—
49C5×Dic6—41no—
50C2×C3×Dic5—21no—
51C2×C3×Dic5—21no—
52C3×Dic10—41no—
53C3⋊#170—81no—
54C3×#170—81no—
55C3⋊#168—41no—
56#1007AGL(1,𝔽5)11yescharacteristic
57C3×C4⋊Q8—51no—
58#942—101no—
59C3×C4⋊C8—101no—
60#836—51no—
61#836—101no—
62#805—101no—
63C5×#41—61no—
64C5×#41—121no—
65C5×#41—121no—
66C2×C5×Q8—121no—
67C2×C5×Q8C4×D311yescharacteristic
68C2×Dic10D1211yescharacteristic
69#704—121no—
70C2×#170—41no—
71#689—121no—
72#687—121no—
73#683—41no—
74C4×Dic5#6711yescharacteristic
75#681—61no—
76#456—151no—
77#356—151no—
78#333—51no—
79C22×C3×C5#9911yescharacteristic
80C2×C5×D3—41no—
81C3×C4×C5—21no—
82C3×C4×C5—41no—
83C3×Dic5—21no—
84C3×Dic5—21no—
85C3×Dic5—41no—
86C5×Dic3—41no—
87C2×C3×Q8—51no—
88C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
89#239—41no—
90D3×Q8—41no—
91#235—21no—
92#235—41no—
93C2×C3×C8—201no—
94C3×C4⋊C4—201no—
95C3×C42—51no—
96#216—201no—
97#215—201no—
98#208—101no—
99#208—201no—
100C5×Q8—41no—
101C5×Q8—61no—
102C5×Q8—121no—
103C5×D4—61no—
104C5×D4—121no—
105C5×D4—121no—
106C2×C4×C5—21no—
107C2×C4×C5—121no—
108C2×C4×C5—122no—
109C2×C4×C5(C2×D3)⋊C411yescharacteristic
110C2×Dic5—21no—
111C2×Dic5—21no—
112Dic10—41no—
113#170—81no—
114#170—241no—
115#168—121no—
1162−1+4—31no—
117#137—301no—
118C4⋊Q8—51no—
119C4⋊C8—101no—
120#104—301no—
121#101—151no—
122#101—301no—
123C2×C3×C5—21no—
124C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
125C5×D3—81no—
126C3×Q8—41no—
127C3×Q8—201no—
128C2×C3×C4—21no—
129C2×C3×C4—101no—
130C2×C3×C4—101no—
131C2×C3×C4C22⋊AGL(1,𝔽5)11yescharacteristic
132#67—41no—
133D12—21no—
134D12—41no—
135C4×D3—41no—
136C4×D3—42no—
137Dic6—21no—
138Dic6—41no—
139C3×C8—401no—
140C3⋊C8—201no—
141C3⋊C8—401no—
142C22×C5—121no—
143C22×C5#80611yescharacteristic
144C4×C5—21no—
145C4×C5—41no—
146C4×C5—121no—
147Dic5—21no—
148Dic5—21no—
149Dic5—41no—
150#41—61no—
151#41—121no—
152#41—121no—
153C2×Q8—51no—
154C2×Q8—121no—
155C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
156Q16—601no—
157SD16—601no—
158M16—301no—
159M16—601no—
160C2×C8—201no—
161C4⋊C4—201no—
162C42—51no—
163C3×C5#140511yescharacteristic, complemented, Hall
164C22×C3#401111yescharacteristic
165C2×D3—41no—
166C3×C4—21no—
167C3×C4—41no—
168C3×C4—101no—
169C3×C4—101no—
170C3×C4—201no—
171Dic3—41no—
172C2×C5—21no—
173C2×C5—241no—
174C2×C5#447511yescharacteristic
175Q8—41no—
176Q8—61no—
177Q8—121no—
178Q8—201no—
179D4—61no—
180D4—121no—
181D4—121no—
182C2×C4—21no—
183C2×C4—101no—
184C2×C4—101no—
185C2×C4—121no—
186C2×C4—122no—
187C2×C4(C2×D3)⋊AGL(1,𝔽5)11yescharacteristic
188C8—401no—
189C8—601no—
190C8—1201no—
191C2×C3—21no—
192C2×C3#6493411yescharacteristic
193D3—81no—
194C5#6746311yescharacteristic, complemented, Sylow
195C22—121no—
196C22#9117211yescharacteristic
197C4—21no—
198C4—41no—
199C4—101no—
200C4—101no—
201C4—121no—
202C4—201no—
203C3#1059883611yescharacteristic, complemented, Sylow
204C2—21no—
205C2—241no—
206C2#1174657811yescharacteristic
subgroupG/H
centerC2#11746578
commutator, FittingC2×C3×C5×Q8C2×C4
Frattini, hypercenterC2×Q8D3×AGL(1,𝔽5)
socleC2×C3×C5AΣL(1,𝔽16)
prime radicalC5×#1007C4
cosocleC3×#4090C22
hypocenterC3×C5#1405
LCSG ▷ C2×C3×C5×Q8 ▷ C2×C3×C4×C5 ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. #11746800C2semidirect
3. C3×#64931C2semidirect
14. #64931D3semidirect
163. C3×C5#1405semidirect
194. C5#67463semidirect
203. C3#10598836semidirect

Maximal subgroups

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

subgroupindex
#117493932
#117468002
C3×#649312
#105988363
#674635