Finite Group Databasebeta

← #10611456

Subgroups — #10611456

Order 640.

368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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#65912C212yesmaximal
2C4×C5×Q16C211yesmaximal, characteristic, complemented
3#65477C211yesmaximal, characteristic
4#65470C211yesmaximal, characteristic, complemented
5C4×#689C212yesmaximal, complemented
6#65176C211yesmaximal, characteristic
7#65163C211yesmaximal, characteristic, complemented
8#65102C212yesmaximal
9#65081C212yesmaximal, complemented
10C4×Dic20C211yesmaximal, characteristic, complemented
11C4×C8×D5C211yesmaximal, characteristic
12C2×C5×Q16C2211yescharacteristic
13C4×C5×Q8C2212yes—
14#4092C2212yes—
15#4090C2212yes—
16C2×#689C2212yes—
17C2×Dic20C2211yescharacteristic
18C2×C8×D5C2211yescharacteristic
19C2×C8×D5C2211yescharacteristic
20#4043C2212yes—
21#4042—22no—
22#4035—22no—
23#4034C2212yes—
24#4018—22no—
25C42×D5C2211yescharacteristic
26C4×Dic10—22no—
27C4×Dic10C2212yes—
28C5×#107C2211yescharacteristic
29C5×#103C2212yes—
30C4×C5×C8C2211yescharacteristic
31#3967C2212yes—
32#3950C2211yescharacteristic
33#3948C2212yes—
34C8×Dic5C2211yescharacteristic
35C8×Dic5C2211yescharacteristic
36#3942C2212yes—
37#3939C2212yes—
38C4×#168C2211yescharacteristic
39#3170—51nomaximal, Sylow
40C2×C5×Q8C2312yes—
41C2×C4×D5D411yescharacteristic
42C2×C4×D5D411yescharacteristic
43C2×C4×D5C2311yescharacteristic
44C2×Dic10—22no—
45C2×Dic10C2312yes—
46C5×Q16—22no—
47C2×C5×C8C2311yescharacteristic
48C2×C5×C8C2311yescharacteristic
49C5×C4⋊C4—22no—
50C5×C4⋊C4C2312yes—
51C42×C5—22no—
52C42×C5C2311yescharacteristic
53#689—24no—
54#685—22no—
55#685—22no—
56C4⋊Dic5—22no—
57C4⋊Dic5C2312yes—
58#683—22no—
59#683—22no—
60#683—22no—
61#683—22no—
62#683—22no—
63C4×Dic5—22no—
64C4×Dic5D411yescharacteristic
65C4×Dic5D411yescharacteristic
66C4×Dic5C2311yescharacteristic
67C2×#168C2311yescharacteristic
68C2×#168C2311yescharacteristic
69Dic20—22no—
70C8×D5—22no—
71C8×D5—22no—
72#533—52no—
73#500—51no—
74#494—51no—
75#487—52no—
76#467—51no—
77#467—51no—
78#467—52no—
79C4×Q16—52no—
80C4×Q16—51no—
81C4×Q16D511yescharacteristic, complemented
82C2×C4×C8—51no—
83C22×D5C2×D411yescharacteristic
84C5×Q8—22no—
85C5×Q8—22no—
86C2×C4×C5—22no—
87C2×C4×C5—22no—
88C2×C4×C5C2×D411yescharacteristic
89C2×C4×C5C2×D411yescharacteristic
90C2×C4×C5C2411yescharacteristic
91C2×Dic5—22no—
92C2×Dic5—22no—
93C2×Dic5C2×D411yescharacteristic
94C2×Dic5C2×D411yescharacteristic
95C2×Dic5C2×D411yescharacteristic
96C4×D5—21no—
97C4×D5—21no—
98C4×D5—22no—
99C4×D5Q1614yescomplemented
100Dic10—22no—
101Dic10—22no—
102Dic10—44no—
103C5×C8—21no—
104C5×C8#4112yes—
105#168—21no—
106#168#4112yes—
107C2×Q16—52no—
108C2×Q16—51no—
109C2×Q16C2×D511yescharacteristic
110C22×C8—51no—
111C22×C8—51no—
112C4⋊Q8—52no—
113C4⋊Q8—52no—
114#125—102no—
115C22⋊Q8—52no—
116C22⋊Q8—52no—
117C22⋊Q8—102no—
118C4×Q8—52no—
119C4×Q8—102no—
120C4×Q8C2×D512yes—
121#117—102no—
122C2×C42—51no—
123#107—51no—
124#107—52no—
125#107C2×D511yescharacteristic
126#103—52no—
127#103—52no—
128#103—52no—
129#103C2×D512yes—
130C4×C8—51no—
131C4×C8—51no—
132C4×C8—51no—
133C4×C8C2×D511yescharacteristic
134C22×C5C22×D411yescharacteristic
135C2×D5—21no—
136C2×D5—21no—
137C2×D5C2×Q1612yes—
138C4×C5—21no—
139C4×C5—42no—
140C4×C5—42no—
141C4×C5C2×Q1612yes—
142C4×C5C2×#4111yescharacteristic
143C4×C5C2×#4111yescharacteristic
144Dic5—21no—
145Dic5—42no—
146Dic5—42no—
147Dic5C2×Q1612yes—
148Dic5#13512yes—
149C2×Q8—52no—
150C2×Q8—102no—
151C2×Q8C22×D512yes—
152C22×C4—51no—
153C22×C4—51no—
154C22×C4—51no—
155Q16—22no—
156Q16—104no—
157Q16—102no—
158C2×C8—51no—
159C2×C8—51no—
160C2×C8—102no—
161C2×C8—102no—
162C2×C8C22×D511yescharacteristic
163C2×C8C22×D511yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—52no—
166C4⋊C4—102no—
167C4⋊C4—102no—
168C4⋊C4—102no—
169C4⋊C4—102no—
170C4⋊C4—102no—
171C4⋊C4—102no—
172C4⋊C4C22×D512yes—
173C22⋊C4—102no—
174C22⋊C4—102no—
175C42—22no—
176C42—51no—
177C42—51no—
178C42—51no—
179C42—102no—
180C42C22×D511yescharacteristic
181C2×C5#53211yescharacteristic
182C2×C5C22×Q1611yescharacteristic
183C2×C5C2×#13511yescharacteristic
184D5—22no—
185C23—51no—
186Q8—22no—
187Q8—22no—
188Q8—102no—
189Q8—102no—
190Q8—204no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—51no—
194C2×C4—51no—
195C2×C4—54no—
196C2×C4—51no—
197C2×C4—102no—
198C2×C4—101no—
199C2×C4—101no—
200C2×C4—102no—
201C2×C4—102no—
202C2×C4D4×D511yescharacteristic
203C2×C4D4×D511yescharacteristic
204C2×C4C23×D511yescharacteristic
205C8—21no—
206C8—52no—
207C8—101no—
208C8#70912yes—
209C5#317011yescharacteristic, complemented, Sylow
210C22—52no—
211C22—101no—
212C22—101no—
213C22C2×D4×D511yescharacteristic
214C4—21no—
215C4—42no—
216C4—42no—
217C4—52no—
218C4—52no—
219C4—101no—
220C4—202no—
221C4—202no—
222C4D5×Q1612yes—
223C4C2×#70911yescharacteristic
224C4D5×#4111yescharacteristic
225C2—102no—
226C2#6588211yescharacteristic
227C2C2×D5×Q1611yescharacteristic
228C2D5×#13511yescharacteristic
subgroupG/H
centerC2×C4D4×D5
commutator, cosocleC2×C4×C5C24
FrattiniC2×C4C23×D5
FittingC4×C5×Q16C2
socleC22×C5C22×D4
prime radicalC22×D5C2×D4
hypercenterC4×Q16D5
hypocenterC5#3170
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×Q16

Complements

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

NH ≅ G/Ntype
2. C4×C5×Q16C2semidirect
4. #65470C2semidirect
5. C4×#689C2semidirect
7. #65163C2semidirect
9. #65081C2semidirect
10. C4×Dic20C2semidirect
81. C4×Q16D5semidirect
99. C4×D5Q16semidirect
209. C5#3170semidirect

Maximal subgroups

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

subgroupindex
#659122
C4×C5×Q162
#654772
#654702
C4×#6892
#651762
#651632
#651022
#650812
C4×Dic202
C4×C8×D52
#31705