Finite Group Databasebeta

← #14279355

Subgroups — #14279355

Order 1920.

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

normal subgroups only

This group has 224 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×#5062C211yesmaximal, characteristic
2#11746361C211yesmaximal, characteristic, complemented
3C3×#64761C211yesmaximal, characteristic, complemented
4#10598262—31nomaximal, Hall
5C5×#1007C411yescharacteristic, complemented
6C3×C5×#124C2211yescharacteristic
7C5×#932—21no—
8#91087—21no—
9C5×#836C411yescharacteristic, complemented
10C5×#805—21no—
11C3×#3966—21no—
12#67542—51nomaximal, Hall
13C5×#454—31no—
14#64761D311yescharacteristic, complemented
15#64760—31no—
16C2×C3×C5×Q8C2×C411yescharacteristic
17C2×C3×C5×D4D411yescharacteristic
18C5×#239—41no—
19C5×D3×Q8—41no—
20C5×#235—21no—
21C5×#235—41no—
22C3×C5×C22⋊C4—41no—
23C3×C42×C5D411yescharacteristic
24C2×C3⋊#168—41no—
25C5×#214—41no—
26C5×#213—41no—
27C5×#208—21no—
28C3×C22⋊Dic5—41no—
29#5062D511yescharacteristic
30C3×#354—51no—
31#4540—51no—
32C5×2−1+4—31no—
33C5×AGL(1,ℤ/8)—61no—
34C5×#124C2×D311yescharacteristic
35C5×#104—61no—
36C5×#101—31no—
37#3966—21no—
38#3935—61no—
39#1404—151noSylow
40C23×C3×C5—21no—
41C3×C5×Q8—41no—
42C3×C5×D4—41no—
43C2×C3×C4×C5—21no—
44C2×C3×C4×C5—21no—
45C2×C3×C4×C5C22⋊C411yescharacteristic
46C5×#67—41no—
47C5×D12—21no—
48C5×D12—41no—
49C4×C5×D3—41no—
50C4×C5×D3—42no—
51C5×Dic6—21no—
52C5×Dic6—41no—
53C2×C3×Dic5—81no—
54C3⋊#168—42no—
55C5×C3⋊C8—41no—
56#1007Dic511yescharacteristic, complemented
57C3×#124C2×D511yescharacteristic
58#932—21no—
59C3×#99—101no—
60#836Dic511yescharacteristic, complemented
61#805—21no—
62#803—101no—
63C5×#41—61no—
64C5×#41—121no—
65C5×#41—121no—
66C2×C5×Q8—121no—
67C2×C5×Q8C4×D311yescharacteristic
68C2×C5×D4#6711yescharacteristic
69C5×SD16—121no—
70C5×D8—121no—
71C5×M16—61no—
72C5×C22⋊C4—41no—
73C42×C5D1211yescharacteristic
74C22⋊Dic5—41no—
75C2×#168—121no—
76#454—31no—
77#354—51no—
78#329—151no—
79C22×C3×C5—41no—
80C22×C3×C5—81no—
81C22×C3×C5#9911yescharacteristic
82C2×C5×D3—41no—
83C3×C4×C5—21no—
84C3×C4×C5—41no—
85C3×C4×C5—41no—
86C3×Dic5—161no—
87C5×Dic3—41no—
88C2×C3×Q8C2×Dic511yescharacteristic
89C2×C3×D4C22⋊D511yescharacteristic
90#239—41no—
91D3×Q8—41no—
92#235—21no—
93#235—41no—
94C3×C22⋊C4—41no—
95C3×C22⋊C4—201no—
96C3×C42C22⋊D511yescharacteristic
97#214—41no—
98#213—41no—
99#208—21no—
100C2×C3⋊C8—201no—
101C23×C5—21no—
102C5×Q8—41no—
103C5×Q8—61no—
104C5×Q8—121no—
105C5×D4—41no—
106C5×D4—61no—
107C5×D4—121no—
108C5×D4—121no—
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—121no—
112C2×C4×C5—122no—
113C2×C4×C5(C2×D3)⋊C411yescharacteristic
114C2×Dic5—81no—
115C5×C8—121no—
116#168—122no—
1172−1+4—31no—
118AGL(1,ℤ/8)—61no—
119#124D3×D511yescharacteristic
120#104—61no—
121#101—31no—
122#99—101no—
123#97—301no—
124C2×C3×C5—21no—
125C2×C3×C5—81no—
126C2×C3×C5AΣL(1,𝔽16)11yescharacteristic
127C5×D3—81no—
128C23×C3—21no—
129C3×Q8—41no—
130C3×D4—41no—
131C2×C3×C4—21no—
132C2×C3×C4—21no—
133C2×C3×C4—401no—
134C2×C3×C4C22⋊Dic511yescharacteristic
135#67—41no—
136D12—21no—
137D12—41no—
138C4×D3—41no—
139C4×D3—42no—
140Dic6—21no—
141Dic6—41no—
142C3⋊C8—41no—
143C3⋊C8—202no—
144C22×C5—41no—
145C22×C5—81no—
146C22×C5—121no—
147C22×C5#80611yescharacteristic
148C4×C5—21no—
149C4×C5—41no—
150C4×C5—41no—
151C4×C5—121no—
152Dic5—161no—
153#41—61no—
154#41—121no—
155#41—121no—
156C2×Q8—121no—
157C2×Q8D3×Dic511yescharacteristic
158C2×D4#120111yescharacteristic
159SD16—121no—
160D8—121no—
161M16—61no—
162C2×C8—601no—
163C22⋊C4—41no—
164C22⋊C4—201no—
165C42#120311yescharacteristic
166C3×C5#140411yescharacteristic, complemented, Hall
167C22×C3—41no—
168C22×C3—81no—
169C22×C3#396611yescharacteristic
170C2×D3—41no—
171C3×C4—21no—
172C3×C4—41no—
173C3×C4—41no—
174C3×C4—801no—
175Dic3—41no—
176C2×C5—21no—
177C2×C5—81no—
178C2×C5—241no—
179C2×C5#447111yescharacteristic
180C23—21no—
181Q8—41no—
182Q8—61no—
183Q8—121no—
184D4—41no—
185D4—61no—
186D4—121no—
187D4—121no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—121no—
191C2×C4—122no—
192C2×C4—401no—
193C2×C4(C2×D3)⋊Dic511yescharacteristic
194C8—121no—
195C8—602no—
196C2×C3—21no—
197C2×C3—81no—
198C2×C3#6475611yescharacteristic
199D3—81no—
200C5#6754211yescharacteristic, complemented, Sylow
201C22—41no—
202C22—81no—
203C22—121no—
204C22#9099611yescharacteristic
205C4—21no—
206C4—41no—
207C4—41no—
208C4—121no—
209C4—801no—
210C3#1059826211yescharacteristic, complemented, Sylow
211C2—21no—
212C2—81no—
213C2—241no—
214C2#1174599611yescharacteristic
subgroupG/H
centerC2#11745996
commutatorC2×C3×C5×Q8C2×C4
Frattini, hypercenter#124D3×D5
Fitting, cosocleC3×C5×#124C22
socleC2×C3×C5AΣL(1,𝔽16)
prime radicalC5×#5062C2
hypocenterC3×C5#1404
LCSG ▷ C2×C3×C5×Q8 ▷ 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
2. #11746361C2semidirect
3. C3×#64761C2semidirect
5. C5×#1007C4semidirect
9. C5×#836C4semidirect
14. #64761D3semidirect
56. #1007Dic5semidirect
60. #836Dic5semidirect
166. C3×C5#1404semidirect
200. C5#67542semidirect
210. C3#10598262semidirect

Maximal subgroups

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

subgroupindex
C5×#50622
#117463612
C3×#647612
#105982623
#675425