Finite Group Databasebeta

← C5×#65111 #13102083

Subgroups — C5×#65111 #13102083

Order 1600.

380 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 78 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×#4149C211yesmaximal, characteristic, complemented
2C5×#4095C211yesmaximal, characteristic, complemented
3C5×#4054C211yesmaximal, characteristic, complemented
4C5×#4020C211yesmaximal, characteristic, complemented
5C52×#104C211yesmaximal, characteristic, complemented
6C5×#3955C211yesmaximal, characteristic, complemented
7C5×#3937C211yesmaximal, characteristic, complemented
8C52×#41C2211yescharacteristic
9C5×#713—21no—
10C5×D4×D5—22no—
11C5×D4×D5—21no—
12C5×#709—21no—
13C5×#709C2211yescharacteristic
14C2×C5×D20—21no—
15C2×C5×D20—22no—
16C2×C5×D20C2211yescharacteristic
17C2×C5×D20C2211yescharacteristic, complemented
18C52×M16C2211yescharacteristic, complemented
19C42×C52C2211yescharacteristic, complemented
20C5×#688—21no—
21C5×#686—21no—
22C5×#681C2211yescharacteristic, complemented
23C5×D40—21no—
24C5×#677—21no—
25C5×#453—51nomaximal
26#65111C511yesmaximal, characteristic, direct product factor
27C22×C5×D5—22no—
28C22×C5×D5—21no—
29C22×C5×D5D412yes—
30C52×Q8D411yescharacteristic, complemented
31C52×D4—21no—
32C52×D4D411yescharacteristic, complemented
33C2×C4×C52—21no—
34C2×C4×C52—21no—
35C2×C4×C52C2311yescharacteristic
36C5×C22⋊D5—22no—
37C5×C22⋊D5—21no—
38C5×D20—22no—
39C5×D20—21no—
40C5×D20—21no—
41C5×D20—21no—
42C5×D20—21no—
43C5×D20—44no—
44C5×D20D411yescharacteristic, complemented
45C4×C5×D5—22no—
46C4×C5×D5—21no—
47C5×Dic10D411yescharacteristic, complemented
48C52×C8—21no—
49C5×#168—21no—
50C5×H(5,𝔽2)—51no—
51#4149C2×C511yescharacteristic, complemented
52C5×AGL(1,ℤ/8)—51no—
53C5×AGL(1,ℤ/8)—51no—
54C5×#127—51no—
55#4095C2×C511yescharacteristic, complemented
56#4054C2×C511yescharacteristic, complemented
57#4020C2×C511yescharacteristic, complemented
58C5×#104—22no—
59C5×#104—51no—
60C5×#104D511yescharacteristic, complemented
61C5×#104C2×C511yescharacteristic, complemented
62C5×#100—51no—
63#3955C2×C511yescharacteristic, complemented
64#3937C2×C511yescharacteristic, complemented
65C22×C52—21no—
66C22×C52C2×D411yescharacteristic
67C2×C5×D5—22no—
68C2×C5×D5—21no—
69C2×C5×D5—42no—
70C2×C5×D5—42no—
71C2×C5×D5—41no—
72C2×C5×D5—82no—
73C4×C52—22no—
74C4×C52—21no—
75C4×C52C2×D411yescharacteristic
76C4×C52C2×D411yescharacteristic
77C5×Dic5—21no—
78C5×#41—22no—
79C5×#41—51no—
80C5×#41—101no—
81C5×#41—101no—
82C5×#41C2×D511yescharacteristic
83C5×#41C22×C511yescharacteristic
84C2×C5×D4—51no—
85C2×C5×D4—51no—
86C2×C5×D4—101no—
87C2×C5×D4—102no—
88C2×C5×D4—102no—
89C2×C5×D4—101no—
90#713—21no—
91D4×D5—22no—
92D4×D5—21no—
93#709—21no—
94#709C22×C511yescharacteristic
95C2×D20—21no—
96C2×D20—22no—
97C2×D20C22×C511yescharacteristic
98C2×D20C22×C511yescharacteristic, complemented
99C5×SD16—101no—
100C5×SD16—101no—
101C5×D8—101no—
102C5×D8—101no—
103C5×M16—22no—
104C5×M16—51no—
105C5×M16C2×D511yescharacteristic, complemented
106C5×M16C22×C511yescharacteristic, complemented
107C42×C5—22no—
108C42×C5C2×D511yescharacteristic, complemented
109C42×C5C22×C511yescharacteristic, complemented
110#688—21no—
111#686—21no—
112#681C22×C511yescharacteristic, complemented
113D40—21no—
114#677—21no—
115#453—51noSylow
116C2×C52—21no—
117C2×C52—41no—
118C2×C52#12011yescharacteristic
119C5×D5—42no—
120C5×D5—41no—
121C5×D5—81no—
122C23×C5—52no—
123C23×C5—102no—
124C23×C5—101no—
125C22×D5—22no—
126C22×D5—21no—
127C22×D5C5×D412yes—
128C5×Q8—22no—
129C5×Q8—51no—
130C5×Q8D2011yescharacteristic, complemented
131C5×Q8C5×D411yescharacteristic, complemented
132C5×D4—21no—
133C5×D4—21no—
134C5×D4—22no—
135C5×D4—42no—
136C5×D4—51no—
137C5×D4—102no—
138C5×D4—102no—
139C5×D4—101no—
140C5×D4—101no—
141C5×D4—101no—
142C5×D4—101no—
143C5×D4—101no—
144C5×D4—204no—
145C5×D4D2011yescharacteristic, complemented
146C5×D4C5×D411yescharacteristic, complemented
147C2×C4×C5—21no—
148C2×C4×C5—21no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
151C2×C4×C5—22no—
152C2×C4×C5—42no—
153C2×C4×C5—42no—
154C2×C4×C5—102no—
155C2×C4×C5—101no—
156C2×C4×C5C22×D511yescharacteristic
157C2×C4×C5C23×C511yescharacteristic
158C22⋊D5—22no—
159C22⋊D5—21no—
160D20—22no—
161D20—21no—
162D20—21no—
163D20—21no—
164D20—21no—
165D20—44no—
166D20C5×D411yescharacteristic, complemented
167C4×D5—22no—
168C4×D5—21no—
169Dic10C5×D411yescharacteristic, complemented
170C5×C8—21no—
171C5×C8—21no—
172C5×C8—42no—
173C5×C8—101no—
174#168—21no—
175H(5,𝔽2)—51no—
176AGL(1,ℤ/8)—51no—
177AGL(1,ℤ/8)—51no—
178#127—51no—
179#104—51no—
180#104C5×D511yescharacteristic, complemented
181#100—51no—
182C52#45311yescharacteristic, complemented, Sylow
183C22×C5—21no—
184C22×C5—21no—
185C22×C5—22no—
186C22×C5—42no—
187C22×C5—101no—
188C22×C5—102no—
189C22×C5—202no—
190C22×C5—202no—
191C22×C5—201no—
192C22×C5—402no—
193C22×C5D4×D511yescharacteristic
194C22×C5C2×C5×D411yescharacteristic
195C2×D5—22no—
196C2×D5—21no—
197C2×D5—42no—
198C2×D5—42no—
199C2×D5—41no—
200C2×D5—82no—
201C4×C5—22no—
202C4×C5—22no—
203C4×C5—21no—
204C4×C5—21no—
205C4×C5—22no—
206C4×C5—22no—
207C4×C5—42no—
208C4×C5—44no—
209C4×C5—101no—
210C4×C5C2×D2011yescharacteristic
211C4×C5D4×D511yescharacteristic
212C4×C5C2×C5×D411yescharacteristic
213C4×C5C2×C5×D411yescharacteristic
214Dic5—21no—
215#41—51no—
216#41—101no—
217#41—101no—
218#41C2×C5×D511yescharacteristic
219C2×D4—51no—
220C2×D4—51no—
221C2×D4—101no—
222C2×D4—102no—
223C2×D4—102no—
224C2×D4—101no—
225SD16—101no—
226SD16—101no—
227D8—101no—
228D8—101no—
229M16—51no—
230M16C2×C5×D511yescharacteristic, complemented
231C42C2×C5×D511yescharacteristic, complemented
232C2×C5—21no—
233C2×C5—21no—
234C2×C5—22no—
235C2×C5—42no—
236C2×C5—41no—
237C2×C5—41no—
238C2×C5—82no—
239C2×C5—202no—
240C2×C5—201no—
241C2×C5—401no—
242C2×C5#402811yescharacteristic
243C2×C5C5×#12011yescharacteristic
244D5—42no—
245D5—41no—
246D5—81no—
247C23—52no—
248C23—102no—
249C23—101no—
250Q8—51no—
251Q8C5×D2011yescharacteristic, complemented
252D4—21no—
253D4—51no—
254D4—102no—
255D4—102no—
256D4—101no—
257D4—101no—
258D4—101no—
259D4—101no—
260D4—101no—
261D4—204no—
262D4C5×D2011yescharacteristic, complemented
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—102no—
266C2×C4—101no—
267C2×C4C22×C5×D511yescharacteristic
268C8—21no—
269C8—101no—
270C5—22no—
271C5#6511111yescharacteristic, direct product factor
272C5C5×#45311yescharacteristic, complemented
273C22—21no—
274C22—101no—
275C22—102no—
276C22—202no—
277C22—202no—
278C22—201no—
279C22—402no—
280C22C5×D4×D511yescharacteristic
281C4—22no—
282C4—21no—
283C4—101no—
284C4C2×C5×D2011yescharacteristic
285C4C5×D4×D511yescharacteristic
286C2—21no—
287C2—41no—
288C2—202no—
289C2—201no—
290C2—401no—
291C2C5×#402811yescharacteristic
subgroupG/H
centerC2×C5#4028
commutator, cosocleC2×C4×C5C23×C5
FrattiniC2×C4C22×C5×D5
FittingC52×#104C2
socleC2×C52#120
hypercenterC5×#104D5
hypocenterC5C5×#453
LCSG ▷ C2×C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C5 ◁ C2×C4×C5 ◁ C5×#104

Complements

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

NH ≅ G/Ntype
1. C5×#4149C2semidirect
2. C5×#4095C2semidirect
3. C5×#4054C2semidirect
4. C5×#4020C2semidirect
5. C52×#104C2semidirect
6. C5×#3955C2semidirect
7. C5×#3937C2semidirect
17. C2×C5×D20C22semidirect
18. C52×M16C22semidirect
19. C42×C52C22semidirect
22. C5×#681C22semidirect
26. #65111C5direct (N × H)
30. C52×Q8D4semidirect
32. C52×D4D4semidirect
44. C5×D20D4semidirect
47. C5×Dic10D4semidirect
51. #4149C2×C5semidirect
55. #4095C2×C5semidirect
56. #4054C2×C5semidirect
57. #4020C2×C5semidirect
60. C5×#104D5semidirect
61. C5×#104C2×C5semidirect
63. #3955C2×C5semidirect
64. #3937C2×C5semidirect
98. C2×D20C22×C5semidirect
105. C5×M16C2×D5semidirect
106. C5×M16C22×C5semidirect
108. C42×C5C2×D5semidirect
109. C42×C5C22×C5semidirect
112. #681C22×C5semidirect
130. C5×Q8D20semidirect
131. C5×Q8C5×D4semidirect
145. C5×D4D20semidirect
146. C5×D4C5×D4semidirect
166. D20C5×D4semidirect
169. Dic10C5×D4semidirect
180. #104C5×D5semidirect
182. C52#453semidirect
230. M16C2×C5×D5semidirect
231. C42C2×C5×D5semidirect
251. Q8C5×D20semidirect
262. D4C5×D20semidirect
271. C5#65111direct (N × H)
272. C5C5×#453semidirect

Maximal subgroups

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

subgroupindex
C5×#41492
C5×#40952
C5×#40542
C5×#40202
C52×#1042
C5×#39552
C5×#39372
C5×#4535
#651115