Finite Group Databasebeta

← #12015580

Subgroups — #12015580

Order 1280.

342 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 79 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#10610379C211yesmaximal, characteristic
2#10600924C212yesmaximal
3C5×#1392C211yesmaximal, characteristic
4#10598192C212yesmaximal
5#10598182C211yesmaximal, characteristic
6#41×Dic5C2211yescharacteristic
7C5×#413C2212yes—
8C5×#408C2211yescharacteristic
9#65529C2212yes—
10#65523C2211yescharacteristic
11#65408C411yescharacteristic, complemented
12M16×Dic5C411yescharacteristic, complemented
13#65391C411yescharacteristic, complemented
14C2×C8×Dic5C411yescharacteristic, complemented
15#65009—22no—
16#65007—22no—
17#64777—22no—
18#64775—22no—
19#12864—51nomaximal, Sylow
20C2×C5×#41C2311yescharacteristic
21C2×C5×M16—22no—
22C2×C5×M16C2×C411yescharacteristic
23C22×C5×C8C2×C411yescharacteristic
24Q8×Dic5—21no—
25D4×Dic5—22no—
26D4×Dic5—21no—
27#4072—22no—
28#4072C2×C411yescharacteristic
29#4072D412yes—
30C2×C4×Dic5C2×C411yescharacteristic
31C2×C4×Dic5D412yes—
32C2×#681C2×C411yescharacteristic
33C22×#168C2×C411yescharacteristic
34C5×#101—22no—
35C5×#100—22no—
36C5×C22⋊C8—22no—
37#3966—22no—
38#3966—22no—
39C22⋊#168—22no—
40#3947—21no—
41#3946—22no—
42#3946—22no—
43C8×Dic5—21no—
44C8×Dic5—21no—
45C8×Dic5—21no—
46#2922—51no—
47#1827—52no—
48#1395—52no—
49#1392D511yescharacteristic
50#1391—51no—
51C5×#41—41no—
52C5×#41—41no—
53C2×C5×Q8#4111yescharacteristic
54C2×C5×D4#4112yes—
55C2×C5×D4#4111yescharacteristic
56C22×C4×C5C22×C411yescharacteristic
57C22×C4×C5C2×D412yes—
58C22×Dic5—21no—
59C22×Dic5—22no—
60C5×M16—41no—
61C5×M16—42no—
62C5×M16—42no—
63C2×C5×C8—21no—
64C2×C5×C8—21no—
65C2×C5×C8—41no—
66C2×C5×C8—42no—
67C22⋊Dic5—21no—
68C22⋊Dic5—22no—
69C22⋊Dic5—42no—
70C4⋊Dic5—21no—
71C4⋊Dic5—22no—
72C4⋊Dic5—42no—
73C4×Dic5—21no—
74C4×Dic5—22no—
75C4×Dic5—42no—
76C4×Dic5C22⋊C411yescharacteristic
77C4×Dic5C22⋊C411yescharacteristic
78C4×Dic5C22⋊C412yes—
79#681—41no—
80C2×#168—21no—
81C2×#168—21no—
82C2×#168—41no—
83C4×#41—51no—
84#433—102no—
85#431—102no—
86#424—51no—
87#424—51no—
88#413C2×D512yes—
89#410—52no—
90#408—51no—
91#408C2×D511yescharacteristic
92C4×M16—51no—
93C2×C4×C8—51no—
94#339—102no—
95H(3,ℤ/4)—102no—
96C23×C5#11711yescharacteristic
97C23×C5#12312yes—
98C5×Q8—41no—
99C5×D4—42no—
100C5×D4—41no—
101C2×C4×C5—21no—
102C2×C4×C5—21no—
103C2×C4×C5—22no—
104C2×C4×C5—22no—
105C2×C4×C5C2×C22⋊C411yescharacteristic
106C2×C4×C5#11711yescharacteristic
107C2×C4×C5#12312yes—
108C2×Dic5—21no—
109C2×Dic5—21no—
110C2×Dic5—22no—
111C2×Dic5—42no—
112C2×Dic5—44no—
113C2×Dic5—82no—
114C5×C8—41no—
115C5×C8—41no—
116C5×C8—82no—
117#168—41no—
118#168—41no—
119C2×#41C22×D511yescharacteristic
120C2×M16—22no—
121C2×M16—51no—
122C2×M16C4×D511yescharacteristic
123C22×C8—51no—
124C22×C8C4×D511yescharacteristic
125C4×Q8—101no—
126C4×D4—102no—
127C4×D4—101no—
128#117—51no—
129#117—52no—
130#117—102no—
131C2×C42—51no—
132C2×C42—52no—
133C4⋊C8—102no—
134C4⋊C8—102no—
135#101—22no—
136#100—22no—
137#99—102no—
138#99—102no—
139C22⋊C8—22no—
140C22⋊C8—102no—
141#97—101no—
142C4×C8—101no—
143C4×C8—101no—
144C4×C8—101no—
145C22×C5—22no—
146C22×C5—21no—
147C22×C5—41no—
148C22×C5—42no—
149C22×C5#38111yescharacteristic
150C4×C5—22no—
151C4×C5—21no—
152C4×C5#41011yescharacteristic
153C4×C5#41011yescharacteristic
154Dic5—22no—
155Dic5—41no—
156Dic5—42no—
157Dic5—162no—
158#41—41no—
159#41—41no—
160C2×Q8#71111yescharacteristic
161C2×D4#70912yes—
162C2×D4#71311yescharacteristic
163C22×C4—101no—
164C22×C4—102no—
165C22×C4C2×C4×D511yescharacteristic
166C22×C4D4×D512yes—
167M16—41no—
168M16—42no—
169M16—42no—
170M16—201no—
171C2×C8—21no—
172C2×C8—21no—
173C2×C8—41no—
174C2×C8—42no—
175C2×C8—101no—
176C2×C8—101no—
177C2×C8—201no—
178C4⋊C4—102no—
179C4⋊C4—101no—
180C4⋊C4—202no—
181C22⋊C4—101no—
182C22⋊C4—102no—
183C22⋊C4—202no—
184C42—51no—
185C42—51no—
186C42—52no—
187C42—102no—
188C42—101no—
189C42—202no—
190C2×C5—21no—
191C2×C5—42no—
192C2×C5—41no—
193C2×C5#182011yescharacteristic
194C23#401811yescharacteristic
195C23#404012yes—
196Q8—41no—
197D4—42no—
198D4—41no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—101no—
204C2×C4—101no—
205C2×C4—102no—
206C2×C4—202no—
207C2×C4—204no—
208C2×C4—402no—
209C2×C4D5×C22⋊C411yescharacteristic
210C2×C4#402912yes—
211C2×C4#403811yescharacteristic
212C8—41no—
213C8—41no—
214C8—82no—
215C8—201no—
216C8—201no—
217C5#1286411yescharacteristic, complemented, Sylow
218C22—22no—
219C22—21no—
220C22—41no—
221C22—42no—
222C22#6495311yescharacteristic
223C4—22no—
224C4—21no—
225C4—102no—
226C4—201no—
227C4—202no—
228C4—802no—
229C4#6502911yescharacteristic
230C4#6502911yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1059974611yescharacteristic
subgroupG/H
centerC4#65029
commutatorC22×C4×C5C22×C4
FrattiniC2×#41C22×D5
FittingC5×#1392C2
socleC2×C5#1820
prime radical, cosocleC2×C5×#41C23
hypercenter#1392D5
hypocenterC5#12864
LCSG ▷ C22×C4×C5 ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1392

Complements

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

NH ≅ G/Ntype
11. #65408C4semidirect
12. M16×Dic5C4semidirect
13. #65391C4semidirect
14. C2×C8×Dic5C4semidirect
217. C5#12864semidirect

Maximal subgroups

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

subgroupindex
#106103792
#106009242
C5×#13922
#105981922
#105981822
#128645