Finite Group Databasebeta

← #10613046

Subgroups — #10613046

Order 640.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#65934C211yesmaximal, characteristic
2C2×#4034C211yesmaximal, characteristic, complemented
3C5×#481C211yesmaximal, characteristic
4#65323C211yesmaximal, characteristic
5#65259C211yesmaximal, characteristic, complemented
6#65145C212yesmaximal, complemented
7#65143C212yesmaximal, complemented
8#65054C212yesmaximal, complemented
9#65048C212yesmaximal, complemented
10#65011C211yesmaximal, characteristic, complemented
11#65008C211yesmaximal, characteristic, complemented
12C22×Dic10—21no—
13C5×#121C2211yescharacteristic
14C2×C5×C4⋊C4C2211yescharacteristic
15#4082C2211yescharacteristic
16#4081—21no—
17D4×Dic5—21no—
18D4×Dic5C2211yescharacteristic
19C2×C4⋊Dic5C2211yescharacteristic
20#4070C2211yescharacteristic
21C2×#683—21no—
22C2×C4×Dic5C2211yescharacteristic
23#4036C2211yescharacteristic
24#4034—21no—
25#4034—21no—
26#4034C2212yes—
27#4034C2212yes—
28#4033C2211yescharacteristic
29#4025—21no—
30#4023—21no—
31C5×#106C2212yes—
32C5×#102C2212yes—
33C5×C22⋊C8C2211yescharacteristic
34#3964C2212yes—
35C22⋊#168C2211yescharacteristic
36#3950C2212yes—
37#3948C2212yes—
38#3947C2212yes—
39#3946C2212yes—
40#3942C2212yes—
41#3940C2212yes—
42#3939C2212yes—
43#3239—51nomaximal, Sylow
44C2×C5×D4—21no—
45C2×C5×D4C2311yescharacteristic
46C22×C4×C5—21no—
47C22×C4×C5C2311yescharacteristic
48C22×Dic5—21no—
49C22×Dic5—21no—
50C22×Dic5D411yescharacteristic
51C22×Dic5D411yescharacteristic
52C2×Dic10—22no—
53C2×Dic10—22no—
54C2×Dic10—44no—
55C2×Dic10C2311yescharacteristic
56C2×C5×C8C2312yes—
57C5×C4⋊C4—21no—
58C5×C4⋊C4C2312yes—
59C5×C4⋊C4C2311yescharacteristic
60C5×C22⋊C4—21no—
61C22⋊Dic5—21no—
62C22⋊Dic5—21no—
63C22⋊Dic5—21no—
64C22⋊Dic5—21no—
65C4⋊Dic5—21no—
66C4⋊Dic5—21no—
67C4⋊Dic5C2311yescharacteristic
68C4⋊Dic5C2312yes—
69#683—21no—
70#683—21no—
71#683—21no—
72#683—22no—
73#683—22no—
74C4×Dic5—21no—
75C4×Dic5D411yescharacteristic
76C4×Dic5D411yescharacteristic
77C4×Dic5C2311yescharacteristic
78C4×Dic5C2311yescharacteristic
79C2×#168C2312yes—
80C2×C4⋊Q8—51no—
81#529—51no—
82#501—52no—
83#489—52no—
84#484—51no—
85#484—51no—
86#481—51no—
87#481D511yescharacteristic
88#475—52no—
89#474—52no—
90#432—51no—
91C23×C5—21no—
92C23×C5C2×D411yescharacteristic
93C5×D4—22no—
94C5×D4—42no—
95C2×C4×C5—22no—
96C2×C4×C5—21no—
97C2×C4×C5—22no—
98C2×C4×C5—42no—
99C2×C4×C5C2×D411yescharacteristic
100C2×C4×C5C2411yescharacteristic
101C2×Dic5—22no—
102C2×Dic5—22no—
103C2×Dic5—21no—
104C2×Dic5—21no—
105C2×Dic5—22no—
106C2×Dic5—42no—
107C2×Dic5—42no—
108C2×Dic5C2×D411yescharacteristic
109C2×Dic5C2×D411yescharacteristic
110C2×Dic5C2×D411yescharacteristic
111C2×Dic5C2×D411yescharacteristic
112Dic10—22no—
113Dic10—44no—
114Dic10—44no—
115C5×C8—22no—
116#168—22no—
117C22×Q8—101no—
118C4⋊Q8—52no—
119C4⋊Q8—52no—
120C4⋊Q8—101no—
121C4⋊Q8—101no—
122#126—101no—
123#125—51no—
124#124—51no—
125#123—101no—
126C22⋊Q8—51no—
127#121C2×D511yescharacteristic
128C4×Q8—51no—
129C4×D4—51no—
130C4×D4—101no—
131#117—101no—
132C2×C4⋊C4—51no—
133C2×C4⋊C4—101no—
134C2×C4⋊C4C2×D511yescharacteristic
135C2×C42—51no—
136#107—52no—
137#107—52no—
138#106—52no—
139#106C2×D512yes—
140C4⋊C8—52no—
141#103—52no—
142#103—52no—
143#102—52no—
144#102C2×D512yes—
145C22⋊C8—51no—
146C22⋊C8C2×D511yescharacteristic
147#97—52no—
148C22×C5—21no—
149C22×C5—21no—
150C22×C5—41no—
151C22×C5—41no—
152C22×C5—41no—
153C22×C5#13712yes—
154C22×C5C22×D411yescharacteristic
155C4×C5—21no—
156C4×C5—42no—
157C4×C5—41no—
158C4×C52−1+412yes—
159Dic5—21no—
160Dic5—21no—
161Dic5—21no—
162Dic5—41no—
163Dic5—42no—
164Dic5—41no—
165Dic5AGL(1,ℤ/8)12yes—
166C2×Q8—51no—
167C2×Q8—102no—
168C2×Q8—102no—
169C2×Q8—204no—
170C2×D4—21no—
171C2×D4C22×D511yescharacteristic
172C22×C4—21no—
173C22×C4—51no—
174C22×C4—51no—
175C22×C4—101no—
176C22×C4—101no—
177C22×C4C22×D511yescharacteristic
178C2×C8—52no—
179C2×C8C22×D512yes—
180C4⋊C4—21no—
181C4⋊C4—52no—
182C4⋊C4—51no—
183C4⋊C4—102no—
184C4⋊C4—102no—
185C4⋊C4—101no—
186C4⋊C4—101no—
187C4⋊C4—101no—
188C4⋊C4—101no—
189C4⋊C4—101no—
190C4⋊C4C22×D512yes—
191C4⋊C4C22×D511yescharacteristic
192C22⋊C4—21no—
193C22⋊C4—101no—
194C22⋊C4—101no—
195C22⋊C4—101no—
196C22⋊C4—101no—
197C42—51no—
198C42—51no—
199C42—51no—
200C42—51no—
201C42—101no—
202C2×C5—22no—
203C2×C5—81no—
204C2×C5#53611yescharacteristic
205C2×C5C2×AGL(1,ℤ/8)11yescharacteristic
206C2×C5C2×#13711yescharacteristic
207C23—21no—
208C23D4×D511yescharacteristic
209Q8—102no—
210Q8—204no—
211Q8—204no—
212D4—22no—
213D4—42no—
214C2×C4—22no—
215C2×C4—21no—
216C2×C4—22no—
217C2×C4—42no—
218C2×C4—51no—
219C2×C4—51no—
220C2×C4—51no—
221C2×C4—51no—
222C2×C4—102no—
223C2×C4—102no—
224C2×C4—101no—
225C2×C4—101no—
226C2×C4—102no—
227C2×C4—202no—
228C2×C4—202no—
229C2×C4D4×D511yescharacteristic
230C2×C4C23×D511yescharacteristic
231C8—22no—
232C8—102no—
233C5#323911yescharacteristic, complemented, Sylow
234C22—21no—
235C22—21no—
236C22—41no—
237C22—41no—
238C22—41no—
239C22#406112yes—
240C22C2×D4×D511yescharacteristic
241C4—21no—
242C4—41no—
243C4—42no—
244C4—52no—
245C4—101no—
246C4—101no—
247C4—101no—
248C4—202no—
249C4—201no—
250C4—201no—
251C4#415012yes—
252C2—22no—
253C2—81no—
254C2#6598211yescharacteristic
255C2C2×#406111yescharacteristic
256C2D5×AGL(1,ℤ/8)11yescharacteristic
subgroupG/H
centerC22C2×D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC5×#481C2
socleC22×C5C22×D4
prime radicalC5×#121C22
hypercenter#481D5
hypocenterC5#3239
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#4034C2semidirect
5. #65259C2semidirect
6. #65145C2semidirect
7. #65143C2semidirect
8. #65054C2semidirect
9. #65048C2semidirect
10. #65011C2semidirect
11. #65008C2semidirect
233. C5#3239semidirect

Maximal subgroups

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

subgroupindex
#659342
C2×#40342
C5×#4812
#653232
#652592
#651452
#651432
#650542
#650482
#650112
#650082
#32395