Finite Group Databasebeta

← #12002382

Subgroups — #12002382

Order 1280.

392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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#10605950C211yesmaximal, characteristic
2#10600621C212yesmaximal
3#10600345C211yesmaximal, characteristic
4C5×#1295C211yesmaximal, characteristic
5#10598150C212yesmaximal
6C2×#4015C2211yescharacteristic
7C2×C5×#97C2212yes—
8C5×#382C2211yescharacteristic
9#65273—22no—
10C2×#3942—22no—
11#65225C2212yes—
12C2×#3935C2211yescharacteristic
13#64950—22no—
14#64946—22no—
15#64771—22no—
16#64771—22no—
17#10361—51nomaximal, Sylow
18C22×Dic10—21no—
19C22×C5×C8—22no—
20C2×C5×C4⋊C4D412yes—
21C2×C42×C5C2311yescharacteristic
22C2×C4⋊Dic5—22no—
23C2×C4⋊Dic5—22no—
24C2×C4⋊Dic5D412yes—
25C2×C4⋊Dic5D412yes—
26C2×#683—22no—
27C2×#683—22no—
28C22×#168—21no—
29#4015—22no—
30#4015—21no—
31#4015Q812yes—
32C5×#97—22no—
33C5×#97—22no—
34C5×#95—22no—
35#3963—22no—
36#3963—22no—
37#3963—22no—
38#3942—44no—
39#3935—22no—
40#2845—51no—
41#1993—52no—
42#1960—51no—
43#1295—52no—
44#1295D511yescharacteristic
45C22×C4×C5—22no—
46C22×C4×C5C2×D411yescharacteristic
47C22×C4×C5C2×D412yes—
48C22×Dic5—22no—
49C22×Dic5—22no—
50C22×Dic5—41no—
51C2×Dic10—22no—
52C2×Dic10—42no—
53C2×Dic10—42no—
54C2×Dic10—41no—
55C2×C5×C8—24no—
56C2×C5×C8—42no—
57C2×C5×C8—42no—
58C5×C4⋊C4—42no—
59C42×C5C2×Q811yescharacteristic
60C42×C5#4112yes—
61C42×C5#4111yescharacteristic
62C4⋊Dic5—24no—
63C4⋊Dic5—42no—
64C4⋊Dic5—42no—
65C4⋊Dic5—42no—
66C4⋊Dic5—82no—
67#683—82no—
68#683—82no—
69C2×#168—22no—
70C2×#168—41no—
71C2×#168—41no—
72C2×C4⋊Q8—51no—
73C2×#103—102no—
74C2×#97—51no—
75C2×#97C2×D512yes—
76#398—102no—
77#398—102no—
78#398—102no—
79#382—52no—
80#382C2×D511yescharacteristic
81#340—102no—
82#340—102no—
83C23×C5#12011yescharacteristic
84C2×C4×C5—21no—
85C2×C4×C5—21no—
86C2×C4×C5—22no—
87C2×C4×C5—22no—
88C2×C4×C5—42no—
89C2×C4×C5—42no—
90C2×C4×C5—42no—
91C2×C4×C5C22⋊Q812yes—
92C2×C4×C5C22⋊Q811yescharacteristic
93C2×C4×C5#12411yescharacteristic
94C2×C4×C5#12412yes—
95C2×Dic5—42no—
96C2×Dic5—42no—
97C2×Dic5—42no—
98C2×Dic5—42no—
99C2×Dic5—42no—
100C2×Dic5—42no—
101C2×Dic5—42no—
102C2×Dic5—81no—
103C2×Dic5—81no—
104Dic10—44no—
105Dic10—82no—
106C5×C8—44no—
107#168—42no—
108C22×Q8—101no—
109C22×C8—22no—
110C22×C8—101no—
111C4⋊Q8—52no—
112C4⋊Q8—102no—
113C4⋊Q8—101no—
114C2×C4⋊C4—52no—
115C2×C4⋊C4—52no—
116C2×C4⋊C4—102no—
117C2×C4⋊C4—102no—
118C2×C4⋊C4—102no—
119C2×C4⋊C4—102no—
120C2×C4⋊C4D2012yes—
121C2×C42C22×D511yescharacteristic
122#103—204no—
123#97—22no—
124#97—22no—
125#97—102no—
126#95—22no—
127#95—102no—
128#95—102no—
129#95—102no—
130C22×C5#39311yescharacteristic
131C22×C5#45311yescharacteristic
132C22×C5#45411yescharacteristic
133C22×C5#45512yes—
134C22×C5#45612yes—
135C4×C5—21no—
136C4×C5—21no—
137C4×C5—22no—
138C4×C5—22no—
139C4×C5—82no—
140Dic5—82no—
141Dic5—82no—
142Dic5—82no—
143C2×Q8—102no—
144C2×Q8—202no—
145C2×Q8—202no—
146C2×Q8—201no—
147C22×C4—22no—
148C22×C4—102no—
149C22×C4—102no—
150C22×C4—201no—
151C22×C4C2×D2011yescharacteristic
152C22×C4D4×D512yes—
153C2×C8—24no—
154C2×C8—42no—
155C2×C8—42no—
156C2×C8—102no—
157C2×C8—201no—
158C2×C8—201no—
159C4⋊C4—42no—
160C4⋊C4—104no—
161C4⋊C4—202no—
162C4⋊C4—202no—
163C4⋊C4—202no—
164C4⋊C4—402no—
165C4⋊C4—402no—
166C4⋊C4—402no—
167C42#70912yes—
168C42#71111yescharacteristic
169C42Q8×D511yescharacteristic
170C2×C5#166112yes—
171C2×C5#166211yescharacteristic
172C2×C5#166311yescharacteristic
173C2×C5#202711yescharacteristic
174C2×C5#202812yes—
175C23#402811yescharacteristic
176Q8—204no—
177Q8—402no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—202no—
186C2×C4—202no—
187C2×C4—202no—
188C2×C4—202no—
189C2×C4—202no—
190C2×C4—202no—
191C2×C4—202no—
192C2×C4—401no—
193C2×C4—401no—
194C2×C4#402111yescharacteristic
195C2×C4#403112yes—
196C2×C4#404212yes—
197C2×C4#404311yescharacteristic
198C8—44no—
199C8—202no—
200C5#1036111yescharacteristic, complemented, Sylow
201C22#6496211yescharacteristic
202C22#6503611yescharacteristic
203C22#6504211yescharacteristic
204C22#6511412yes—
205C22#6511512yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—402no—
212C4—402no—
213C4—402no—
214C2#1059914912yes—
215C2#1059916711yescharacteristic
216C2#1059917011yescharacteristic
217C2#1059956212yes—
218C2#1059978811yescharacteristic
subgroupG/H
centerC23#4028
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1295C2
socle, prime radicalC23×C5#120
hypercenter#1295D5
hypocenterC5#10361
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
200. C5#10361semidirect

Maximal subgroups

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

subgroupindex
#106059502
#106006212
#106003452
C5×#12952
#105981502
#103615