Finite Group Databasebeta

← C5×#29656 #11952376

Subgroups — C5×#29656 #11952376

Order 1280.

1428 conjugacy classes of subgroups; only the 242 normal subgroups are shown.

normal subgroups only

This group has 1428 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, complemented
2C5×#2405C213yesmaximal
3C5×#2062C214yesmaximal, complemented
4C5×#2029C214yesmaximal, complemented
5C5×#1819C213yesmaximal, complemented
6C23×C5×D4C2211yescharacteristic
7C5×#543—26no—
8C5×#543C2214yes—
9C2×C5×#123—23no—
10C2×C5×C22⋊Q8—23no—
11C2×C5×C22⋊Q8—23no—
12C22×C5×C22⋊C4C2213yes—
13C5×#394—26no—
14C5×#386—23no—
15C5×#385C2216yes—
16C5×#379C2216yes—
17C5×#379C2213yes—
18C5×#342C22112yes—
19#29656C511yesmaximal, characteristic, direct product factor, Sylow
20C25×C5C2311yescharacteristic
21C25×C5C2311yescharacteristic
22C22×C5×Q8—21no—
23C22×C5×Q8—21no—
24C22×C5×D4—23no—
25C22×C5×D4—23no—
26C22×C5×D4—44no—
27C23×C4×C5D413yes—
28C23×C4×C5D413yes—
29C23×C4×C5C2311yescharacteristic
30C5×#123—412no—
31C5×C22⋊Q8—212no—
32C5×C22⋊Q8—212no—
33C5×C22⋊Q8—212no—
34C5×C22⋊Q8—212no—
35C2×C5×C4⋊C4—23no—
36C2×C5×C4⋊C4—23no—
37C2×C5×C4⋊C4—26no—
38C2×C5×C22⋊C4—26no—
39C2×C5×C22⋊C4—26no—
40C2×C5×C22⋊C4—23no—
41C2×C5×C22⋊C4—26no—
42C2×C5×C22⋊C4—23no—
43C2×C5×C22⋊C4—26no—
44C2×C5×C22⋊C4D416yes—
45C2×C5×C22⋊C4C2316yes—
46C2×C5×C22⋊C4C2316yes—
47C5×#95—26no—
48C2×#543C2×C511yescharacteristic, complemented
49#2405C2×C513yes—
50#2062C2×C514yescomplemented
51#2029C2×C514yescomplemented
52#1819C2×C513yescomplemented
53C24×C5—24no—
54C24×C5—23no—
55C24×C5—24no—
56C24×C5—42no—
57C24×C5—42no—
58C24×C5—81no—
59C24×C5—81no—
60C24×C5C2×D413yes—
61C24×C5C2×D413yes—
62C24×C5C2411yescharacteristic
63C2×C5×Q8—24no—
64C2×C5×Q8—24no—
65C2×C5×Q8—82no—
66C2×C5×Q8—82no—
67C2×C5×D4—212no—
68C2×C5×D4—46no—
69C2×C5×D4—46no—
70C2×C5×D4—46no—
71C2×C5×D4—43no—
72C2×C5×D4—41no—
73C22×C4×C5—23no—
74C22×C4×C5—23no—
75C22×C4×C5—23no—
76C22×C4×C5—23no—
77C22×C4×C5—23no—
78C22×C4×C5—26no—
79C22×C4×C5—42no—
80C22×C4×C5—46no—
81C22×C4×C5—83no—
82C22×C4×C5C2×D416yes—
83C22×C4×C5C2×D416yes—
84C5×C4⋊C4—212no—
85C5×C4⋊C4—212no—
86C5×C4⋊C4—412no—
87C5×C22⋊C4—212no—
88C5×C22⋊C4—212no—
89C5×C22⋊C4—212no—
90C5×C22⋊C4—412no—
91C5×C22⋊C4—46no—
92C5×C22⋊C4—86no—
93C5×C22⋊C4—83no—
94C23×D4C22×C511yescharacteristic
95#543—26no—
96#543C22×C514yes—
97C2×#123—23no—
98C2×C22⋊Q8—23no—
99C2×C22⋊Q8—23no—
100C22×C22⋊C4C22×C513yes—
101#394—26no—
102#386—23no—
103#385C22×C516yes—
104#379C22×C513yes—
105#379C22×C516yes—
106#342C22×C5112yes—
107C23×C5—26no—
108C23×C5—26no—
109C23×C5—26no—
110C23×C5—26no—
111C23×C5—41no—
112C23×C5—43no—
113C23×C5—41no—
114C23×C5—43no—
115C23×C5—43no—
116C23×C5—46no—
117C23×C5—43no—
118C23×C5—41no—
119C23×C5—46no—
120C23×C5—88no—
121C23×C5—88no—
122C23×C5#12013yes—
123C23×C5#12011yescharacteristic
124C23×C5C22×D413yes—
125C23×C52−1+414yes—
126C5×Q8—84no—
127C5×Q8—84no—
128C5×D4—412no—
129C5×D4—44no—
130C2×C4×C5—26no—
131C2×C4×C5—26no—
132C2×C4×C5—26no—
133C2×C4×C5—43no—
134C2×C4×C5—46no—
135C2×C4×C5—41no—
136C2×C4×C5—46no—
137C2×C4×C5—46no—
138C2×C4×C5—46no—
139C2×C4×C5—46no—
140C2×C4×C5—46no—
141C2×C4×C5—46no—
142C2×C4×C5—83no—
143C2×C4×C5—83no—
144C25C23×C511yescharacteristic
145C25C23×C511yescharacteristic
146C22×Q8—21no—
147C22×Q8—21no—
148C22×D4—23no—
149C22×D4—23no—
150C22×D4—44no—
151C23×C4C5×D413yes—
152C23×C4C5×D413yes—
153C23×C4C23×C511yescharacteristic
154#123—412no—
155C22⋊Q8—212no—
156C22⋊Q8—212no—
157C22⋊Q8—212no—
158C22⋊Q8—212no—
159C2×C4⋊C4—23no—
160C2×C4⋊C4—23no—
161C2×C4⋊C4—26no—
162C2×C22⋊C4—26no—
163C2×C22⋊C4—26no—
164C2×C22⋊C4—23no—
165C2×C22⋊C4—26no—
166C2×C22⋊C4—23no—
167C2×C22⋊C4—26no—
168C2×C22⋊C4C5×D416yes—
169C2×C22⋊C4C23×C516yes—
170C2×C22⋊C4C23×C516yes—
171#95—26no—
172C22×C5—21no—
173C22×C5—23no—
174C22×C5—21no—
175C22×C5—23no—
176C22×C5—23no—
177C22×C5—23no—
178C22×C5—23no—
179C22×C5—44no—
180C22×C5—412no—
181C22×C5—412no—
182C22×C5—42no—
183C22×C5—86no—
184C22×C5—86no—
185C22×C5—81no—
186C22×C5—81no—
187C22×C5B(4,𝔽2)12yes—
188C22×C5C2×#12011yescharacteristic
189C22×C5#53616yes—
190C4×C5—42no—
191C4×C5—46no—
192C4×C5—46no—
193C4×C5—86no—
194C24—24no—
195C24—23no—
196C24—24no—
197C24—42no—
198C24—42no—
199C24—81no—
200C24—81no—
201C24C2×C5×D413yes—
202C24C2×C5×D413yes—
203C24C24×C511yescharacteristic
204C2×Q8—24no—
205C2×Q8—24no—
206C2×Q8—82no—
207C2×Q8—82no—
208C2×D4—212no—
209C2×D4—46no—
210C2×D4—46no—
211C2×D4—46no—
212C2×D4—43no—
213C2×D4—41no—
214C22×C4—23no—
215C22×C4—23no—
216C22×C4—23no—
217C22×C4—23no—
218C22×C4—23no—
219C22×C4—26no—
220C22×C4—42no—
221C22×C4—46no—
222C22×C4—83no—
223C22×C4C2×C5×D416yes—
224C22×C4C2×C5×D416yes—
225C4⋊C4—212no—
226C4⋊C4—212no—
227C4⋊C4—412no—
228C22⋊C4—212no—
229C22⋊C4—212no—
230C22⋊C4—212no—
231C22⋊C4—412no—
232C22⋊C4—46no—
233C22⋊C4—86no—
234C22⋊C4—83no—
235C2×C5—26no—
236C2×C5—22no—
237C2×C5—43no—
238C2×C5—82no—
239C2×C5#261411yescharacteristic
240C2×C5C2×B(4,𝔽2)11yescharacteristic
241C2×C5#302611yescharacteristic
242C23—26no—
243C23—26no—
244C23—26no—
245C23—26no—
246C23—41no—
247C23—43no—
248C23—41no—
249C23—43no—
250C23—43no—
251C23—46no—
252C23—43no—
253C23—41no—
254C23—46no—
255C23—88no—
256C23—88no—
257C23C5×#12013yes—
258C23C5×#12011yescharacteristic
259C23C22×C5×D413yes—
260C23C5×2−1+414yes—
261Q8—84no—
262Q8—84no—
263D4—412no—
264D4—44no—
265C2×C4—26no—
266C2×C4—26no—
267C2×C4—26no—
268C2×C4—43no—
269C2×C4—46no—
270C2×C4—46no—
271C2×C4—41no—
272C2×C4—46no—
273C2×C4—46no—
274C2×C4—46no—
275C2×C4—46no—
276C2×C4—46no—
277C2×C4—83no—
278C2×C4—83no—
279C5#2965611yescharacteristic, direct product factor, Sylow
280C22—23no—
281C22—21no—
282C22—23no—
283C22—21no—
284C22—23no—
285C22—23no—
286C22—23no—
287C22—44no—
288C22—412no—
289C22—412no—
290C22—42no—
291C22—86no—
292C22—86no—
293C22—81no—
294C22—81no—
295C22C5×B(4,𝔽2)12yes—
296C22C2×C5×#12011yescharacteristic
297C22C5×#53616yes—
298C4—42no—
299C4—46no—
300C4—46no—
301C4—86no—
302C2—26no—
303C2—22no—
304C2—43no—
305C2—82no—
306C2C5×#261411yescharacteristic
307C2C2×C5×B(4,𝔽2)11yescharacteristic
308C2C5×#302611yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC24C24×C5
prime radicalC23×C5×D4C22
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C25×C5 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#543C2semidirect
3. C5×#2062C2semidirect
4. C5×#2029C2semidirect
5. C5×#1819C2semidirect
19. #29656C5direct (N × H)
48. C2×#543C2×C5semidirect
50. #2062C2×C5semidirect
51. #2029C2×C5semidirect
52. #1819C2×C5semidirect
279. C5#29656direct (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×#24052
C5×#20622
C5×#20292
C5×#18192
#296565