Finite Group Databasebeta

← #13101708

Subgroups — #13101708

Order 1600.

384 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 70 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×D5×Dic10C211yesmaximal, characteristic, complemented
2C2×#87810C211yesmaximal, characteristic, complemented
3C5×#4084C211yesmaximal, characteristic
4C2×C5×#687C211yesmaximal, characteristic, complemented
5#11716608C211yesmaximal, characteristic, complemented
6#11716606C211yesmaximal, characteristic, complemented
7#11716597C211yesmaximal, characteristic, complemented
8C2×C52×D4C2211yescharacteristic
9C2×#6045C2211yescharacteristic
10C2×C5×C22⋊D5—21no—
11C2×C4×C5×D5C2211yescharacteristic
12C2×C5×Dic10C2211yescharacteristic
13C2×#6039—21no—
14C2×D5×Dic5—21no—
15D5×Dic10—22no—
16D5×Dic10—22no—
17#87810—22no—
18C2×#6029C2211yescharacteristic
19C5×C22⋊Dic5—21no—
20C5×#687—22no—
21C5×C4⋊Dic5C2211yescharacteristic
22C2×C5×#168C2211yescharacteristic
23#65459—51nomaximal
24#65329—51nomaximal
25C23×C52—21no—
26C22×C5×D5D411yescharacteristic
27C52×D4—21no—
28C52×D4—21no—
29C2×C4×C52C2311yescharacteristic
30C2×#1039—21no—
31#6045—21no—
32#6045D412yescomplemented
33C5×C22⋊D5—42no—
34C2×C5×Dic5—21no—
35C2×C5×Dic5—21no—
36C2×C5×Dic5D411yescharacteristic
37C4×C5×D5—21no—
38C4×C5×D5—21no—
39C5×Dic10—21no—
40C5×Dic10D412yescomplemented
41#6039—24no—
42D5×Dic5—24no—
43#6029—21no—
44C5×#168—21no—
45C2×Q8×D5—51no—
46C22×Dic10—51no—
47C2×C5×SD16—51no—
48C5×#121—51no—
49#4084D511yescharacteristic
50C2×#687—51no—
51C2×#687—51no—
52C2×#687—102no—
53C2×#687D511yescharacteristic, complemented
54#3967—51no—
55C22⋊#168—51no—
56#3952—51no—
57#3948—51no—
58#3942—51no—
59#3942—51no—
60C22×C52—41no—
61C22×C52—41no—
62C22×C52—41no—
63C22×C52C2×D411yescharacteristic
64C2×C5×D5—21no—
65C2×C5×D5—21no—
66C2×C5×D5SD1612yescomplemented
67C4×C52C2×D411yescharacteristic
68C4×C52C2×D411yescharacteristic
69#1039—22no—
70C5×Dic5—22no—
71C5×Dic5—21no—
72C5×Dic5—41no—
73C2×C5×Q8—51no—
74C2×C5×D4—22no—
75C2×C5×D4—101no—
76C2×C5×D4C2×D511yescharacteristic
77C2×C5×D4C2×D511yescharacteristic
78C22×C4×C5—51no—
79C2×C22⋊D5—21no—
80C22×Dic5—101no—
81Q8×D5—102no—
82Q8×D5—102no—
83C2×C4×D5—101no—
84C2×C4×D5C2×D511yescharacteristic
85C2×Dic10—51no—
86C2×Dic10—51no—
87C2×Dic10—102no—
88C2×Dic10—102no—
89C2×Dic10—101no—
90C2×Dic10—101no—
91C2×Dic10—102no—
92C2×Dic10C2×D511yescharacteristic
93C5×SD16—102no—
94C2×C5×C8—51no—
95C5×C4⋊C4—51no—
96C5×C22⋊C4—101no—
97C22⋊Dic5—21no—
98#687—22no—
99#687—102no—
100#687—102no—
101#687—108no—
102C4⋊Dic5C2×D511yescharacteristic
103C2×#168—51no—
104C2×#168—51no—
105C2×#168—102no—
106C2×#168C2×D511yescharacteristic
107#448—251noSylow
108C2×C52—81no—
109C2×C52#12011yescharacteristic
110C2×C52C2×SD1611yescharacteristic
111C2×C52#13711yescharacteristic
112C5×D5—22no—
113C23×C5—21no—
114C23×C5—21no—
115C23×C5—42no—
116C23×C5—51no—
117C22×D5C22⋊D511yescharacteristic
118C5×Q8—52no—
119C5×Q8—101no—
120C5×D4—24no—
121C5×D4—21no—
122C5×D4—21no—
123C5×D4—21no—
124C5×D4—21no—
125C5×D4—42no—
126C5×D4—202no—
127C2×C4×C5—22no—
128C2×C4×C5—51no—
129C2×C4×C5—101no—
130C2×C4×C5—101no—
131C2×C4×C5—101no—
132C2×C4×C5—101no—
133C2×C4×C5C22×D511yescharacteristic
134C2×C4×C5C22×D511yescharacteristic
135C22⋊D5—42no—
136C2×Dic5—21no—
137C2×Dic5—21no—
138C2×Dic5—104no—
139C2×Dic5—101no—
140C2×Dic5—101no—
141C2×Dic5—202no—
142C2×Dic5C22⋊D511yescharacteristic
143C4×D5—21no—
144C4×D5—21no—
145C4×D5—104no—
146Dic10—21no—
147Dic10—52no—
148Dic10—52no—
149Dic10—104no—
150Dic10—104no—
151Dic10—104no—
152Dic10—101no—
153Dic10—101no—
154Dic10—202no—
155Dic10C22⋊D512yescomplemented
156C5×C8—101no—
157#168—21no—
158#168—104no—
159#168—101no—
160#168—101no—
161C22×Q8—251no—
162C2×SD16—51no—
163C2×SD16—251no—
164#121—51no—
165#103—251no—
166#103—251no—
167C22⋊C8—251no—
168C52#44811yescharacteristic, complemented, Sylow
169C22×C5—22no—
170C22×C5—44no—
171C22×C5—41no—
172C22×C5—41no—
173C22×C5—41no—
174C22×C5—41no—
175C22×C5—41no—
176C22×C5—41no—
177C22×C5—52no—
178C22×C5—82no—
179C22×C5—82no—
180C22×C5—101no—
181C22×C5—101no—
182C22×C5D4×D511yescharacteristic
183C22×C5C2×C22⋊D511yescharacteristic
184C2×D5—21no—
185C2×D5—21no—
186C2×D5#68712yescomplemented
187C4×C5—22no—
188C4×C5—22no—
189C4×C5—101no—
190C4×C5—102no—
191C4×C5—201no—
192C4×C5D4×D511yescharacteristic
193C4×C5D4×D511yescharacteristic
194C4×C5D4×D511yescharacteristic
195C4×C5C2×C22⋊D511yescharacteristic
196Dic5—22no—
197Dic5—21no—
198Dic5—41no—
199Dic5—102no—
200Dic5—102no—
201Dic5—204no—
202C2×Q8—51no—
203C2×Q8—251no—
204C2×Q8—501no—
205C2×Q8—502no—
206C2×Q8—502no—
207C2×D4—101no—
208C2×D4D5211yescharacteristic
209C22×C4—51no—
210C22×C4—501no—
211SD16—102no—
212SD16—502no—
213C2×C8—51no—
214C2×C8—251no—
215C4⋊C4—51no—
216C22⋊C4—101no—
217C2×C5—22no—
218C2×C5—22no—
219C2×C5—22no—
220C2×C5—84no—
221C2×C5—81no—
222C2×C5—81no—
223C2×C5—102no—
224C2×C5D5×SD1611yescharacteristic
225C2×C5#406111yescharacteristic
226C2×C5C2×#68711yescharacteristic
227C2×C5#408311yescharacteristic
228C2×C5#408311yescharacteristic
229C2×C5#409711yescharacteristic
230D5—22no—
231C23—21no—
232C23—51no—
233Q8—52no—
234Q8—101no—
235Q8—252no—
236Q8—504no—
237Q8—501no—
238D4—21no—
239D4—21no—
240D4—202no—
241C2×C4—51no—
242C2×C4—101no—
243C2×C4—101no—
244C2×C4—101no—
245C2×C4—101no—
246C2×C4—504no—
247C2×C4—501no—
248C2×C4C2×D5211yescharacteristic
249C8—101no—
250C8—501no—
251C5—22no—
252C5#6532911yescharacteristic, complemented
253C5#6545911yescharacteristic, complemented
254C22—41no—
255C22—41no—
256C22—41no—
257C22—52no—
258C22—101no—
259C22—101no—
260C22D5×C22⋊D511yescharacteristic
261C4—101no—
262C4—102no—
263C4—201no—
264C4—502no—
265C4D5×C22⋊D511yescharacteristic
266C4#8788611yescharacteristic
267C2—81no—
268C2—102no—
269C2D5×#68711yescharacteristic
270C2#1171704711yescharacteristic
271C2#1171710111yescharacteristic
subgroupG/H
centerC22D5×C22⋊D5
commutator, cosocleC2×C4×C52C23
FrattiniC2×C4C2×D52
FittingC2×C52×D4C22
socleC22×C52C2×D4
prime radicalC5×#4084C2
hypercenterC2×D4D52
hypocenterC52#448
LCSG ▷ C2×C4×C52 ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
1. C2×D5×Dic10C2semidirect
2. C2×#87810C2semidirect
4. C2×C5×#687C2semidirect
5. #11716608C2semidirect
6. #11716606C2semidirect
7. #11716597C2semidirect
32. #6045D4semidirect
40. C5×Dic10D4semidirect
53. C2×#687D5semidirect
66. C2×C5×D5SD16semidirect
155. Dic10C22⋊D5semidirect
168. C52#448semidirect
186. C2×D5#687semidirect
252. C5#65329semidirect
253. C5#65459semidirect

Maximal subgroups

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

subgroupindex
C2×D5×Dic102
C2×#878102
C5×#40842
C2×C5×#6872
#117166082
#117166062
#117165972
#654595
#653295