Finite Group Databasebeta

← C2×#11716902 #13104922

Subgroups — C2×#11716902 #13104922

Order 1600.

480 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 82 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
1C2×Q8×C5⋊D5C211yesmaximal, characteristic
2C2×C4⋊#1044C211yesmaximal, characteristic
3C2×#87862C211yesmaximal, characteristic
4#11716902C214yesmaximal, direct product factor
5C22×#1044—21no—
6C2×C52×Q8C411yescharacteristic, complemented
7Q8×C5⋊D5—21no—
8Q8×C5⋊D5—21no—
9Q8×C5⋊D5C412yescomplemented
10Q8×C5⋊D5C2212yes—
11C2×C4×C5⋊D5—21no—
12C2×C4×C5⋊D5C2211yescharacteristic
13C2×#6045—21no—
14C2×#6045C411yescharacteristic, complemented
15C2×#6034—21no—
16C4⋊#1044—21no—
17C4⋊#1044C2212yes—
18#87862—21no—
19#87862C2212yes—
20C2×#4009—52nomaximal
21C22×C5⋊D5D411yescharacteristic
22C2×#1044—22no—
23C2×#1044—42no—
24C52×Q8—21no—
25C52×Q8C2×C412yescomplemented
26C2×C4×C52—21no—
27C2×C4×C52C2×C411yescharacteristic
28C2×#1039—21no—
29C2×#1039D411yescharacteristic
30C4×C5⋊D5—22no—
31C4×C5⋊D5—22no—
32C4×C5⋊D5C2×C411yescharacteristic
33C4×C5⋊D5D411yescharacteristic
34C4×C5⋊D5D411yescharacteristic
35C4×C5⋊D5C2311yescharacteristic
36#6045—21no—
37#6045—22no—
38#6045—22no—
39#6045C2×C412yescomplemented
40#6034—22no—
41C2×Q8×D5—52no—
42C2×Q8×D5—102no—
43C2×C4⋊AGL(1,𝔽5)—52no—
44C2×D5⋊C8—52no—
45#4009—58no—
46C22×C52C22⋊C411yescharacteristic
47C2×C5⋊D5C22⋊C411yescharacteristic
48C2×C5⋊D5SD1612yes—
49C2×C5⋊D5Q1612yes—
50C2×C5⋊D5C2×D411yescharacteristic
51#1044—42no—
52C4×C52—22no—
53C4×C52C22⋊C411yescharacteristic
54C4×C52C22×C411yescharacteristic
55#1039—22no—
56#1039C22⋊C411yescharacteristic
57#1039C2×D411yescharacteristic
58C22×AGL(1,𝔽5)—102no—
59C2×C5×Q8—22no—
60C2×C5×Q8AGL(1,𝔽5)12yescomplemented
61Q8×D5—54no—
62Q8×D5—54no—
63Q8×D5—104no—
64Q8×D5—104no—
65Q8×D5—102no—
66Q8×D5—102no—
67Q8×D5—104no—
68Q8×D5—104no—
69C2×C4×D5—52no—
70C2×C4×D5—102no—
71C2×C4×D5—102no—
72C2×C4×D5—104no—
73C2×Dic10—52no—
74C2×Dic10—102no—
75C2×Dic10—102no—
76C2×Dic10—104no—
77C2×#170—102no—
78C4⋊AGL(1,𝔽5)—54no—
79C4⋊AGL(1,𝔽5)—102no—
80D5⋊C8—54no—
81D5⋊C8—102no—
82C2×#103—251noSylow
83C2×C52#10312yescomplemented
84C2×C52C2×C22⋊C411yescharacteristic
85C5⋊D5#10312yescomplemented
86C5⋊D5C2×SD1611yescharacteristic
87C5⋊D5C2×Q1611yescharacteristic
88C22×D5—52no—
89C22×D5—102no—
90C2×AGL(1,𝔽5)—104no—
91C2×AGL(1,𝔽5)—204no—
92C5×Q8—24no—
93C5×Q8—22no—
94C5×Q8—24no—
95C5×Q8C2×AGL(1,𝔽5)14yescomplemented
96C2×C4×C5—24no—
97C2×C4×C5—22no—
98C2×C4×C5—22no—
99C2×C4×C5C2×AGL(1,𝔽5)12yes—
100C2×Dic5—52no—
101C2×Dic5—102no—
102C2×Dic5—104no—
103C2×Dic5—102no—
104C4×D5—52no—
105C4×D5—52no—
106C4×D5—52no—
107C4×D5—52no—
108C4×D5—102no—
109C4×D5—102no—
110C4×D5—102no—
111C4×D5—102no—
112C4×D5—104no—
113C4×D5—104no—
114C4×D5—108no—
115C4×D5—108no—
116Dic10—54no—
117Dic10—104no—
118Dic10—104no—
119Dic10—104no—
120Dic10—108no—
121Dic10—108no—
122Dic10—104no—
123Dic10—102no—
124#170—104no—
125C22×Q8—251no—
126C22×C8—251no—
127C2×C4⋊C4—251no—
128#103—254no—
129C52C2×#10311yescharacteristic, complemented, Sylow
130C22×C5—22no—
131C22×C5C22⋊AGL(1,𝔽5)12yes—
132C2×D5—52no—
133C2×D5—52no—
134C2×D5—54no—
135C2×D5—54no—
136C2×D5—102no—
137C2×D5—104no—
138C2×D5—104no—
139C2×D5—102no—
140AGL(1,𝔽5)—204no—
141C4×C5—28no—
142C4×C5—24no—
143C4×C5—22no—
144C4×C5—22no—
145C4×C5C22⋊AGL(1,𝔽5)12yes—
146C4×C5C22×AGL(1,𝔽5)12yes—
147Dic5—52no—
148Dic5—52no—
149Dic5—102no—
150Dic5—102no—
151Dic5—108no—
152Dic5—104no—
153C2×Q8—252no—
154C2×Q8—252no—
155C2×Q8—251no—
156C2×Q8—501no—
157C2×Q8—501no—
158C2×Q8—501no—
159C2×Q8#104411yescharacteristic, complemented
160C22×C4—251no—
161C22×C4—501no—
162C22×C4—501no—
163C2×C8—252no—
164C2×C8—501no—
165C2×C8—501no—
166C4⋊C4—252no—
167C4⋊C4—501no—
168C2×C5—24no—
169C2×C5—22no—
170C2×C5#400914yescomplemented
171C2×C5C2×C22⋊AGL(1,𝔽5)12yes—
172D5—54no—
173D5—52no—
174D5—52no—
175D5—104no—
176D5—102no—
177D5—102no—
178C23—251no—
179Q8—21no—
180Q8—252no—
181Q8—502no—
182Q8—502no—
183Q8—501no—
184Q8C2×#104412yescomplemented
185C2×C4—21no—
186C2×C4—251no—
187C2×C4—251no—
188C2×C4—251no—
189C2×C4—251no—
190C2×C4—251no—
191C2×C4—502no—
192C2×C4—502no—
193C2×C4—501no—
194C2×C4—502no—
195C2×C4—1002no—
196C2×C4C2×#104411yescharacteristic
197C8—502no—
198C5—22no—
199C5C2×#400912yescomplemented
200C22—252no—
201C22—252no—
202C22—251no—
203C22—251no—
204C22C22⋊#104411yescharacteristic
205C4—22no—
206C4—251no—
207C4—251no—
208C4—502no—
209C4—1002no—
210C4C22⋊#104411yescharacteristic
211C4C22×#104411yescharacteristic
212C2—251no—
213C2—252no—
214C2—251no—
215C2#1171690212yesdirect product factor
216C2C2×C22⋊#104411yescharacteristic
subgroupG/H
centerC22C22⋊#1044
commutatorC4×C52C22×C4
FrattiniC4C22×#1044
FittingC2×C52×Q8C4
socleC22×C52C22⋊C4
prime radicalC22×C5⋊D5D4
cosocleC4×C5⋊D5C23
hypercenterC2×Q8#1044
hypocenterC52C2×#103
LCSG ▷ C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
4. #11716902C2direct (N × H)
6. C2×C52×Q8C4semidirect
9. Q8×C5⋊D5C4semidirect
14. C2×#6045C4semidirect
25. C52×Q8C2×C4semidirect
39. #6045C2×C4semidirect
60. C2×C5×Q8AGL(1,𝔽5)semidirect
83. C2×C52#103semidirect
85. C5⋊D5#103semidirect
95. C5×Q8C2×AGL(1,𝔽5)semidirect
129. C52C2×#103semidirect
159. C2×Q8#1044semidirect
170. C2×C5#4009semidirect
184. Q8C2×#1044semidirect
199. C5C2×#4009semidirect
215. C2#11716902direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C5⋊D52
C2×C4⋊#10442
C2×#878622
#117169022
C2×#40095