Finite Group Databasebeta

← C5×#29657 #11952377

Subgroups — C5×#29657 #11952377

Order 1280.

1148 conjugacy classes of subgroups; only the 242 normal subgroups are shown.

normal subgroups only

This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 242 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×C5×#543C211yesmaximal, characteristic
2C5×#2483C213yesmaximal
3C5×#2062C214yesmaximal, complemented
4C5×#2030C214yesmaximal, complemented
5C5×#1819C213yesmaximal
6C5×#543—26no—
7C5×#543C2214yes—
8C2×C5×C22⋊Q8—23no—
9C2×C5×C22⋊Q8—23no—
10C22×C5×C22⋊C4C2211yescharacteristic
11C22×C5×C22⋊C4C2213yes—
12C5×#397—26no—
13C5×#385—23no—
14C5×#385C2216yes—
15C5×#381—23no—
16C5×#381C2216yes—
17C5×#379C2213yes—
18C5×#342C22112yes—
19#29657C511yesmaximal, characteristic, direct product factor, Sylow
20C25×C5C2311yescharacteristic
21C22×C5×Q8—21no—
22C22×C5×Q8—21no—
23C23×C4×C5D413yes—
24C23×C4×C5D413yes—
25C23×C4×C5C2311yescharacteristic
26C23×C4×C5C2311yescharacteristic
27C5×C22⋊Q8—212no—
28C5×C22⋊Q8—212no—
29C5×C22⋊Q8—212no—
30C5×C22⋊Q8—212no—
31C2×C5×C4⋊C4—23no—
32C2×C5×C4⋊C4—23no—
33C2×C5×C4⋊C4—26no—
34C2×C5×C22⋊C4—26no—
35C2×C5×C22⋊C4—26no—
36C2×C5×C22⋊C4—23no—
37C2×C5×C22⋊C4—23no—
38C2×C5×C22⋊C4—23no—
39C2×C5×C22⋊C4—23no—
40C2×C5×C22⋊C4D416yes—
41C2×C5×C22⋊C4C2316yes—
42C2×C5×C22⋊C4C2316yes—
43C5×#95—26no—
44C5×#95—26no—
45C5×#95—26no—
46C2×#543C2×C511yescharacteristic
47#2483C2×C513yes—
48#2062C2×C514yescomplemented
49#2030C2×C514yescomplemented
50#1819C2×C513yes—
51C24×C5—24no—
52C24×C5—42no—
53C24×C5—81no—
54C24×C5C2×D413yes—
55C24×C5C2×D413yes—
56C24×C5C2411yescharacteristic
57C2×C5×Q8—24no—
58C2×C5×Q8—24no—
59C2×C5×Q8—82no—
60C2×C5×Q8—82no—
61C22×C4×C5—23no—
62C22×C4×C5—23no—
63C22×C4×C5—23no—
64C22×C4×C5—23no—
65C22×C4×C5—26no—
66C22×C4×C5—23no—
67C22×C4×C5—23no—
68C22×C4×C5—24no—
69C22×C4×C5—46no—
70C22×C4×C5—81no—
71C22×C4×C5—83no—
72C22×C4×C5C2×D416yes—
73C22×C4×C5C2×D416yes—
74C5×C4⋊C4—212no—
75C5×C4⋊C4—212no—
76C5×C4⋊C4—86no—
77C5×C22⋊C4—212no—
78C5×C22⋊C4—212no—
79C5×C22⋊C4—212no—
80C5×C22⋊C4—46no—
81C5×C22⋊C4—43no—
82C5×C22⋊C4—41no—
83C5×C22⋊C4—83no—
84#543—26no—
85#543C22×C514yes—
86C2×C22⋊Q8—23no—
87C2×C22⋊Q8—23no—
88C22×C22⋊C4C22×C511yescharacteristic
89C22×C22⋊C4C22×C513yes—
90#397—26no—
91#385—23no—
92#385C22×C516yes—
93#381—23no—
94#381C22×C516yes—
95#379C22×C513yes—
96#342C22×C5112yes—
97C23×C5—26no—
98C23×C5—26no—
99C23×C5—26no—
100C23×C5—43no—
101C23×C5—41no—
102C23×C5—41no—
103C23×C5—43no—
104C23×C5—43no—
105C23×C5—88no—
106C23×C5#12013yes—
107C23×C5#12011yescharacteristic
108C23×C5C22×D413yes—
109C23×C52−1+414yes—
110C5×Q8—84no—
111C5×Q8—84no—
112C2×C4×C5—26no—
113C2×C4×C5—26no—
114C2×C4×C5—46no—
115C2×C4×C5—46no—
116C2×C4×C5—46no—
117C2×C4×C5—46no—
118C2×C4×C5—46no—
119C2×C4×C5—46no—
120C2×C4×C5—46no—
121C2×C4×C5—41no—
122C2×C4×C5—41no—
123C2×C4×C5—46no—
124C2×C4×C5—46no—
125C2×C4×C5—83no—
126C2×C4×C5—83no—
127C25C23×C511yescharacteristic
128C22×Q8—21no—
129C22×Q8—21no—
130C23×C4C5×D413yes—
131C23×C4C5×D413yes—
132C23×C4C23×C511yescharacteristic
133C23×C4C23×C511yescharacteristic
134C22⋊Q8—212no—
135C22⋊Q8—212no—
136C22⋊Q8—212no—
137C22⋊Q8—212no—
138C2×C4⋊C4—23no—
139C2×C4⋊C4—23no—
140C2×C4⋊C4—26no—
141C2×C22⋊C4—26no—
142C2×C22⋊C4—26no—
143C2×C22⋊C4—23no—
144C2×C22⋊C4—23no—
145C2×C22⋊C4—23no—
146C2×C22⋊C4—23no—
147C2×C22⋊C4C5×D416yes—
148C2×C22⋊C4C23×C516yes—
149C2×C22⋊C4C23×C516yes—
150#95—26no—
151#95—26no—
152#95—26no—
153C22×C5—21no—
154C22×C5—23no—
155C22×C5—21no—
156C22×C5—23no—
157C22×C5—23no—
158C22×C5—23no—
159C22×C5—23no—
160C22×C5—44no—
161C22×C5—412no—
162C22×C5—86no—
163C22×C5#45812yes—
164C22×C5C2×#12011yescharacteristic
165C22×C5#53616yes—
166C4×C5—46no—
167C4×C5—46no—
168C4×C5—86no—
169C4×C5—81no—
170C4×C5—81no—
171C24—24no—
172C24—42no—
173C24—81no—
174C24C2×C5×D413yes—
175C24C2×C5×D413yes—
176C24C24×C511yescharacteristic
177C2×Q8—24no—
178C2×Q8—24no—
179C2×Q8—82no—
180C2×Q8—82no—
181C22×C4—23no—
182C22×C4—23no—
183C22×C4—23no—
184C22×C4—23no—
185C22×C4—23no—
186C22×C4—26no—
187C22×C4—23no—
188C22×C4—24no—
189C22×C4—46no—
190C22×C4—81no—
191C22×C4—83no—
192C22×C4C2×C5×D416yes—
193C22×C4C2×C5×D416yes—
194C4⋊C4—212no—
195C4⋊C4—212no—
196C4⋊C4—86no—
197C22⋊C4—212no—
198C22⋊C4—212no—
199C22⋊C4—212no—
200C22⋊C4—46no—
201C22⋊C4—43no—
202C22⋊C4—41no—
203C22⋊C4—83no—
204C2×C5—26no—
205C2×C5—22no—
206C2×C5—43no—
207C2×C5#261411yescharacteristic
208C2×C5C2×#45811yescharacteristic
209C2×C5#302611yescharacteristic
210C23—26no—
211C23—26no—
212C23—26no—
213C23—43no—
214C23—41no—
215C23—41no—
216C23—43no—
217C23—43no—
218C23—88no—
219C23C5×#12013yes—
220C23C5×#12011yescharacteristic
221C23C22×C5×D413yes—
222C23C5×2−1+414yes—
223Q8—84no—
224Q8—84no—
225C2×C4—26no—
226C2×C4—26no—
227C2×C4—46no—
228C2×C4—46no—
229C2×C4—46no—
230C2×C4—46no—
231C2×C4—46no—
232C2×C4—46no—
233C2×C4—46no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—46no—
237C2×C4—46no—
238C2×C4—83no—
239C2×C4—83no—
240C5#2965711yescharacteristic, direct product factor, Sylow
241C22—23no—
242C22—21no—
243C22—23no—
244C22—21no—
245C22—23no—
246C22—23no—
247C22—23no—
248C22—44no—
249C22—412no—
250C22—86no—
251C22C5×#45812yes—
252C22C2×C5×#12011yescharacteristic
253C22C5×#53616yes—
254C4—46no—
255C4—46no—
256C4—86no—
257C4—81no—
258C4—81no—
259C2—26no—
260C2—22no—
261C2—43no—
262C2C5×#261411yescharacteristic
263C2C2×C5×#45811yescharacteristic
264C2C5×#302611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC24C24×C5
prime radicalC25×C5C23
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#2062C2semidirect
4. C5×#2030C2semidirect
19. #29657C5direct (N × H)
48. #2062C2×C5semidirect
49. #2030C2×C5semidirect
240. C5#29657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5432
C5×#24832
C5×#20622
C5×#20302
C5×#18192
#296575