Finite Group Databasebeta

← #12004331

Subgroups — #12004331

Order 1280.

316 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 93 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×#1570C211yesmaximal, characteristic
2#10601561C211yesmaximal, characteristic
3#10601308C211yesmaximal, characteristic
4#10601286C211yesmaximal, characteristic
5#10601239C211yesmaximal, characteristic
6#10601222C211yesmaximal, characteristic
7#10598228C211yesmaximal, characteristic
8#65804C2211yescharacteristic
9C5×#431C2211yescharacteristic
10C5×#423C2211yescharacteristic
11C2×C5×C4⋊C8C2211yescharacteristic
12C2×#3946—22no—
13#65221C2211yescharacteristic
14#65214C2211yescharacteristic
15C2×C4⋊#168C2211yescharacteristic
16C5×#334—22no—
17#64775—22no—
18#64704—22no—
19#64700—22no—
20#64676—22no—
21#10670—51nomaximal, Sylow
22C2×C5×M16—21no—
23C22×C5×C8—21no—
24C2×C42×C5C2311yescharacteristic
25#4072—21no—
26#4070—21no—
27#4070—21no—
28C2×C4×Dic5D412yes—
29C22×#168—21no—
30#4016—21no—
31#4015Q811yescharacteristic
32#4015Q811yescharacteristic
33C4×Dic10—21no—
34C4×Dic10—21no—
35C5×C4⋊C8—21no—
36C5×C4⋊C8—21no—
37C5×C4⋊C8—21no—
38C5×C4⋊C8—21no—
39C5×C4⋊C8—21no—
40C5×C22⋊C8—21no—
41C4×C5×C8D412yes—
42#3963—21no—
43#3963—21no—
44C22⋊#168—21no—
45#3946—44no—
46C4⋊#168—21no—
47C4⋊#168—21no—
48C4⋊#168—21no—
49C4×#168D412yes—
50#1995—51no—
51#1843—51no—
52#1570—51no—
53#1570D511yescharacteristic
54#1481—51no—
55#1481—51no—
56#1274—51no—
57C22×C4×C5C2×D411yescharacteristic
58C22×C4×C5#4111yescharacteristic
59C22×C4×C5#4111yescharacteristic
60C22×Dic5—22no—
61C2×Dic10—21no—
62C2×Dic10—21no—
63C5×M16—42no—
64C2×C5×C8—22no—
65C2×C5×C8—41no—
66C2×C5×C8—41no—
67C2×C5×C8—42no—
68C42×C5C2×D411yescharacteristic
69C42×C5C2×D411yescharacteristic
70C42×C5C2×Q811yescharacteristic
71C42×C5#4111yescharacteristic
72C22⋊Dic5—41no—
73C4⋊Dic5—21no—
74C4⋊Dic5—21no—
75C4⋊Dic5—21no—
76C4⋊Dic5—21no—
77#683—41no—
78#683—41no—
79C4×Dic5—22no—
80C4×Dic5—41no—
81C4×Dic5SD1614yes—
82C2×#168—22no—
83C2×#168—41no—
84C2×#168—42no—
85#533—51no—
86#431—51no—
87#431C2×D511yescharacteristic
88#423C2×D511yescharacteristic
89C2×C4⋊C8—51no—
90C2×C4⋊C8—102no—
91C2×C4⋊C8C2×D511yescharacteristic
92#376—51no—
93#339—102no—
94#334—22no—
95#334—102no—
96Q8⋊C8—102no—
97Q8⋊C8—102no—
98C23×C5#12311yescharacteristic
99C2×C4×C5—41no—
100C2×C4×C5—41no—
101C2×C4×C5C22⋊Q811yescharacteristic
102C2×C4×C5C22⋊Q811yescharacteristic
103C2×C4×C5C22⋊Q811yescharacteristic
104C2×C4×C5#12311yescharacteristic
105C2×C4×C5#12311yescharacteristic
106C2×C4×C5#12711yescharacteristic
107C2×C4×C5C2×SD1612yes—
108C2×C4×C5#13712yes—
109C2×Dic5—24no—
110C2×Dic5—42no—
111C2×Dic5—42no—
112C2×Dic5—41no—
113C2×Dic5—41no—
114Dic10—42no—
115Dic10—42no—
116C5×C8—42no—
117C5×C8—81no—
118C5×C8—81no—
119#168—42no—
120#168—81no—
121C2×M16—21no—
122C22×C8—21no—
123C22×C8—101no—
124C4⋊Q8—51no—
125C4⋊Q8—51no—
126#125—101no—
127C22⋊Q8—101no—
128C22⋊Q8—101no—
129C4×Q8—101no—
130C4×Q8—101no—
131#117—101no—
132C2×C42—52no—
133C2×C42C22×D511yescharacteristic
134C4⋊C8—21no—
135C4⋊C8—21no—
136C4⋊C8—21no—
137C4⋊C8—21no—
138C4⋊C8—21no—
139C4⋊C8—101no—
140C4⋊C8—101no—
141C4⋊C8—101no—
142C4⋊C8—204no—
143C22⋊C8—21no—
144C22⋊C8—101no—
145C4×C8—52no—
146C4×C8C22⋊D512yes—
147#95—101no—
148#95—101no—
149C22×C5—21no—
150C22×C5—21no—
151C22×C5#39911yescharacteristic
152C22×C5#48312yes—
153C4×C5—21no—
154C4×C5—21no—
155C4×C5—21no—
156C4×C5—21no—
157C4×C5#47512yes—
158C4×C5#49211yescharacteristic
159C4×C5#49711yescharacteristic
160Dic5—44no—
161Dic5—81no—
162Dic5—81no—
163C2×Q8—101no—
164C2×Q8—101no—
165C22×C4—102no—
166C22×C4#70911yescharacteristic
167C22×C4D4×D511yescharacteristic
168C22×C4#71311yescharacteristic
169M16—42no—
170C2×C8—22no—
171C2×C8—42no—
172C2×C8—41no—
173C2×C8—41no—
174C2×C8—102no—
175C2×C8—202no—
176C2×C8—201no—
177C4⋊C4—101no—
178C4⋊C4—101no—
179C4⋊C4—101no—
180C4⋊C4—101no—
181C4⋊C4—201no—
182C4⋊C4—201no—
183C22⋊C4—201no—
184C42—54no—
185C42—102no—
186C42—201no—
187C42#70911yescharacteristic
188C42D4×D511yescharacteristic
189C42Q8×D511yescharacteristic
190C42C2×C22⋊D511yescharacteristic
191C2×C5—22no—
192C2×C5#209611yescharacteristic
193C2×C5#209811yescharacteristic
194C2×C5#209811yescharacteristic
195C23#404011yescharacteristic
196Q8—202no—
197Q8—202no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—104no—
201C2×C4—202no—
202C2×C4—202no—
203C2×C4—201no—
204C2×C4—201no—
205C2×C4#404011yescharacteristic
206C2×C4#404211yescharacteristic
207C2×C4#404211yescharacteristic
208C2×C4D5×SD1612yes—
209C2×C4#406112yes—
210C2×C4#407511yescharacteristic
211C2×C4#408611yescharacteristic
212C2×C4#409211yescharacteristic
213C8—42no—
214C8—81no—
215C8—81no—
216C8—202no—
217C8—401no—
218C5#1067011yescharacteristic, complemented, Sylow
219C22—21no—
220C22—21no—
221C22#6515112yes—
222C22#6528111yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—204no—
228C4—401no—
229C4—401no—
230C4#6514312yes—
231C4#6545611yescharacteristic
232C4#6546411yescharacteristic
233C2—22no—
234C2#1060134211yescharacteristic
235C2#1060138311yescharacteristic
236C2#1060153111yescharacteristic
subgroupG/H
centerC2×C4#4086
commutator, cosocleC2×C42×C5C23
FrattiniC2×C42C22×D5
FittingC5×#1570C2
socleC22×C5#399
prime radicalC23×C5#123
hypercenter#1570D5
hypocenterC5#10670
LCSG ▷ C2×C42×C5 ▷ C22×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
218. C5#10670semidirect

Maximal subgroups

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

subgroupindex
C5×#15702
#106015612
#106013082
#106012862
#106012392
#106012222
#105982282
#106705