Finite Group Databasebeta

← #11988610

Subgroups — #11988610

Order 1280.

350 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 87 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×#2809C211yesmaximal, characteristic
2#10600477C211yesmaximal, characteristic
3#10600405C212yesmaximal
4#10598133C211yesmaximal, characteristic
5#10598129C212yesmaximal
6C5×#400—21no—
7C5×#398—22no—
8C5×#391—21no—
9C5×#391C2211yescharacteristic
10C5×#389C2212yes—
11C5×#387—22no—
12C2×#3967—21no—
13C2×#3939—21no—
14#65224C2211yescharacteristic
15#64749—22no—
16#64749—22no—
17#64744C2211yescharacteristic
18#64744C2212yes—
19#7831—51nomaximal, Sylow
20C22×C5×Q8D411yescharacteristic
21C2×C5×C4⋊C4—22no—
22C2×C5×C4⋊C4—21no—
23C2×C5×C4⋊C4—21no—
24C2×C5×C4⋊C4D412yes—
25C2×C5×C4⋊C4D412yes—
26C2×C5×C4⋊C4D411yescharacteristic
27C2×C42×C5—21no—
28C2×C42×C5C2311yescharacteristic
29C2×C4⋊Dic5—21no—
30C2×C4⋊Dic5—22no—
31C22×#168—21no—
32C22×#168—22no—
33C5×#95—21no—
34C5×#95—22no—
35C5×#95—22no—
36C5×#95—22no—
37C5×#95—22no—
38#3967—42no—
39#3939—42no—
40#2809D511yescharacteristic
41#2100—52no—
42#2095—51no—
43#1272—51no—
44#1271—52no—
45C2×C5×Q8—21no—
46C2×C5×Q8—41no—
47C2×C5×Q8—41no—
48C2×C5×Q8Q1612yes—
49C22×C4×C5—21no—
50C22×C4×C5—22no—
51C22×C4×C5—22no—
52C22×C4×C5—21no—
53C22×C4×C5C2×D411yescharacteristic
54C22×C4×C5C2×D412yes—
55C22×Dic5—41no—
56C5×C4⋊C4—22no—
57C5×C4⋊C4—22no—
58C5×C4⋊C4—42no—
59C5×C4⋊C4—41no—
60C5×C4⋊C4—42no—
61C5×C4⋊C4—42no—
62C5×C4⋊C4—81no—
63C5×C4⋊C4—81no—
64C42×C5—41no—
65C42×C5—81no—
66C4⋊Dic5—41no—
67C4⋊Dic5—41no—
68C4⋊Dic5—44no—
69C2×#168—22no—
70C2×#168—41no—
71C2×#168—41no—
72C2×#168—42no—
73C2×#168—42no—
74C2×#168—42no—
75C2×#107—101no—
76C2×#103—101no—
77#400—21no—
78#398—22no—
79#391—21no—
80#391C2×D511yescharacteristic
81#389C2×D512yes—
82#387—22no—
83#384—51no—
84#340—102no—
85#340—102no—
86#336—51no—
87#336—52no—
88C23×C5#12011yescharacteristic
89C5×Q8—42no—
90C5×Q8—81no—
91C2×C4×C5—21no—
92C2×C4×C5—22no—
93C2×C4×C5—22no—
94C2×C4×C5—21no—
95C2×C4×C5—22no—
96C2×C4×C5—41no—
97C2×C4×C5—41no—
98C2×C4×C5—42no—
99C2×C4×C5—42no—
100C2×C4×C5—42no—
101C2×C4×C5—41no—
102C2×C4×C5—42no—
103C2×C4×C5—42no—
104C2×C4×C5—42no—
105C2×C4×C5—42no—
106C2×C4×C5C2×Q1611yescharacteristic
107C2×C4×C5#13512yes—
108C2×C4×C5#13712yes—
109C2×C4×C5#13711yescharacteristic
110C2×Dic5—81no—
111C2×Dic5—82no—
112#168—42no—
113#168—82no—
114C22×Q8C22⋊D511yescharacteristic
115C22×C8—101no—
116C22×C8—102no—
117C2×C4⋊C4—22no—
118C2×C4⋊C4—21no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—102no—
121C2×C4⋊C4—101no—
122C2×C4⋊C4C22⋊D512yes—
123C2×C4⋊C4C22⋊D512yes—
124C2×C4⋊C4C22⋊D511yescharacteristic
125C2×C42—21no—
126C2×C42C22×D511yescharacteristic
127#107—202no—
128#103—202no—
129#95—21no—
130#95—22no—
131#95—22no—
132#95—22no—
133#95—22no—
134C22×C5#45111yescharacteristic
135C22×C5#45212yes—
136C22×C5#45311yescharacteristic
137C22×C5#45412yes—
138C22×C5#45811yescharacteristic
139C4×C5—21no—
140C4×C5—21no—
141C4×C5—22no—
142C4×C5—22no—
143C4×C5—42no—
144C4×C5—82no—
145C4×C5—82no—
146C4×C5—81no—
147Dic5—161no—
148C2×Q8—21no—
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8#68912yes—
152C22×C4—21no—
153C22×C4—21no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—201no—
157C22×C4C2×C22⋊D512yes—
158C22×C4C2×C22⋊D511yescharacteristic
159C2×C8—102no—
160C2×C8—201no—
161C2×C8—201no—
162C2×C8—202no—
163C2×C8—202no—
164C2×C8—202no—
165C4⋊C4—22no—
166C4⋊C4—22no—
167C4⋊C4—41no—
168C4⋊C4—42no—
169C4⋊C4—42no—
170C4⋊C4—42no—
171C4⋊C4—81no—
172C4⋊C4—81no—
173C4⋊C4—201no—
174C4⋊C4—201no—
175C4⋊C4—204no—
176C42—41no—
177C42—81no—
178C2×C5#161411yescharacteristic
179C2×C5#161512yes—
180C2×C5#163411yescharacteristic
181C2×C5#163612yes—
182C2×C5#165711yescharacteristic
183C23#409911yescharacteristic
184Q8—42no—
185Q8—81no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—42no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—401no—
202C2×C4—402no—
203C2×C4#408811yescharacteristic
204C2×C4C2×#68911yescharacteristic
205C2×C4#409612yes—
206C2×C4#409712yes—
207C8—202no—
208C8—402no—
209C5#783111yescharacteristic, complemented, Sylow
210C22#6551711yescharacteristic
211C22#6552812yes—
212C22#6553011yescharacteristic
213C22#6553211yescharacteristic
214C22#6553412yes—
215C4—22no—
216C4—22no—
217C4—21no—
218C4—21no—
219C4—42no—
220C4—82no—
221C4—82no—
222C4—81no—
223C4—801no—
224C2#1060268012yes—
225C2#1060268411yescharacteristic
226C2#1060272111yescharacteristic
227C2#1060272912yes—
228C2#1060274811yescharacteristic
subgroupG/H
centerC23#4099
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#2809C2
socle, prime radicalC23×C5#120
hypercenter#2809D5
hypocenterC5#7831
LCSG ▷ C2×C42×C5 ▷ C23×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2809

Complements

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

NH ≅ G/Ntype
209. C5#7831semidirect

Maximal subgroups

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

subgroupindex
C5×#28092
#106004772
#106004052
#105981332
#105981292
#78315