Finite Group Databasebeta

← C5×#9893 #11932613

Subgroups — C5×#9893 #11932613

Order 1280.

388 conjugacy classes of subgroups.

The subgroup lattice has 298 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2864C211yesmaximal, characteristic
2C5×#1767C211yesmaximal, characteristic
3C5×#1745C211yesmaximal, characteristic
4C5×#1295C212yesmaximal
5C5×#1295C212yesmaximal
6C2×C5×C4⋊C8—21no—
7C2×C5×#97C2212yes—
8C2×C5×#97C2212yes—
9C5×#389C411yescharacteristic
10C5×#389C411yescharacteristic
11C5×#389C411yescharacteristic
12C5×#389C411yescharacteristic
13C5×#387—21no—
14C5×#387—21no—
15C5×#387—21no—
16C5×#387—21no—
17C5×#382C2211yescharacteristic
18C5×#382C2211yescharacteristic
19C43×C5C2211yescharacteristic
20C5×#336—21no—
21C5×#336—21no—
22C5×#336—21no—
23#9893C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×C8—22no—
25C22×C5×C8—22no—
26C2×C5×C4⋊C4—21no—
27C2×C5×C4⋊C4—21no—
28C2×C5×C4⋊C4—21no—
29C2×C5×C4⋊C4—21no—
30C2×C5×C4⋊C4C2×C411yescharacteristic
31C2×C5×C4⋊C4C2×C411yescharacteristic
32C2×C5×C4⋊C4C2×C411yescharacteristic
33C2×C5×C4⋊C4C2×C411yescharacteristic
34C2×C42×C5C2×C411yescharacteristic
35C2×C42×C5C2×C411yescharacteristic
36C2×C42×C5D411yescharacteristic
37C2×C42×C5D411yescharacteristic
38C2×C42×C5D411yescharacteristic
39C2×C42×C5D411yescharacteristic
40C2×C42×C5C2311yescharacteristic
41C5×C4⋊C8—24no—
42C5×#97—22no—
43C5×#97—24no—
44C5×#97Q814yes—
45C5×#95—21no—
46C5×#95—21no—
47C5×#95—21no—
48C5×#95—21no—
49C5×#95—21no—
50C5×#95—21no—
51C5×#95—21no—
52C5×#95—21no—
53#2864C2×C511yescharacteristic
54#1767C2×C511yescharacteristic
55#1745C2×C511yescharacteristic
56#1295C2×C512yes—
57#1295C2×C512yes—
58C22×C4×C5—21no—
59C22×C4×C5—21no—
60C22×C4×C5—21no—
61C22×C4×C5—21no—
62C22×C4×C5C22⋊C411yescharacteristic
63C22×C4×C5C22⋊C411yescharacteristic
64C22×C4×C5C22⋊C411yescharacteristic
65C22×C4×C5C22⋊C411yescharacteristic
66C22×C4×C5C22×C411yescharacteristic
67C22×C4×C5C2×D411yescharacteristic
68C22×C4×C5C2×D411yescharacteristic
69C2×C5×C8—24no—
70C2×C5×C8—24no—
71C2×C5×C8—42no—
72C2×C5×C8—42no—
73C2×C5×C8—42no—
74C2×C5×C8—42no—
75C5×C4⋊C4—41no—
76C5×C4⋊C4—41no—
77C5×C4⋊C4—41no—
78C5×C4⋊C4—41no—
79C5×C4⋊C4—42no—
80C5×C4⋊C4—42no—
81C5×C4⋊C4—42no—
82C5×C4⋊C4—42no—
83C42×C5—22no—
84C42×C5—41no—
85C42×C5—41no—
86C42×C5—41no—
87C42×C5—41no—
88C42×C5—41no—
89C42×C5C2×Q812yes—
90C42×C5#4112yes—
91C2×C4⋊C8—21no—
92C2×#97C22×C512yes—
93C2×#97C22×C512yes—
94#389C4×C511yescharacteristic
95#389C4×C511yescharacteristic
96#389C4×C511yescharacteristic
97#389C4×C511yescharacteristic
98#387—21no—
99#387—21no—
100#387—21no—
101#387—21no—
102#382C22×C511yescharacteristic
103#382C22×C511yescharacteristic
104C43C22×C511yescharacteristic
105#336—21no—
106#336—21no—
107#336—21no—
108C23×C5C2×C22⋊C411yescharacteristic
109C2×C4×C5—21no—
110C2×C4×C5—21no—
111C2×C4×C5—21no—
112C2×C4×C5—21no—
113C2×C4×C5—21no—
114C2×C4×C5—21no—
115C2×C4×C5—21no—
116C2×C4×C5—21no—
117C2×C4×C5—21no—
118C2×C4×C5—21no—
119C2×C4×C5—21no—
120C2×C4×C5—21no—
121C2×C4×C5—21no—
122C2×C4×C5—21no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—41no—
127C2×C4×C5—41no—
128C2×C4×C5—41no—
129C2×C4×C5—41no—
130C2×C4×C5—41no—
131C2×C4×C5—41no—
132C2×C4×C5—41no—
133C2×C4×C5—41no—
134C2×C4×C5—41no—
135C2×C4×C5—41no—
136C2×C4×C5—41no—
137C2×C4×C5—41no—
138C2×C4×C5#10412yes—
139C2×C4×C5C4×Q812yes—
140C2×C4×C5C22⋊Q812yes—
141C2×C4×C5#12411yescharacteristic
142C2×C4×C5C4⋊Q811yescharacteristic
143C5×C8—44no—
144C5×C8—44no—
145C22×C8—22no—
146C22×C8—22no—
147C2×C4⋊C4—21no—
148C2×C4⋊C4—21no—
149C2×C4⋊C4—21no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4C2×C4×C511yescharacteristic
152C2×C4⋊C4C2×C4×C511yescharacteristic
153C2×C4⋊C4C2×C4×C511yescharacteristic
154C2×C4⋊C4C2×C4×C511yescharacteristic
155C2×C42C2×C4×C511yescharacteristic
156C2×C42C2×C4×C511yescharacteristic
157C2×C42C5×D411yescharacteristic
158C2×C42C5×D411yescharacteristic
159C2×C42C5×D411yescharacteristic
160C2×C42C5×D411yescharacteristic
161C2×C42C23×C511yescharacteristic
162C4⋊C8—24no—
163#97—22no—
164#97—24no—
165#97C5×Q814yes—
166#95—21no—
167#95—21no—
168#95—21no—
169#95—21no—
170#95—21no—
171#95—21no—
172#95—21no—
173#95—21no—
174C22×C5#39111yescharacteristic
175C22×C5#41311yescharacteristic
176C22×C5#41311yescharacteristic
177C22×C5C2×#10411yescharacteristic
178C22×C5#42111yescharacteristic
179C22×C5#42111yescharacteristic
180C22×C5#42111yescharacteristic
181C4×C5—21no—
182C4×C5—21no—
183C4×C5—22no—
184C4×C5—22no—
185C4×C5—22no—
186C4×C5—41no—
187C4×C5—41no—
188C4×C5—41no—
189C4×C5—81no—
190C4×C5—81no—
191C4×C5—81no—
192C4×C5—81no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—21no—
197C22×C4C5×C22⋊C411yescharacteristic
198C22×C4C5×C22⋊C411yescharacteristic
199C22×C4C5×C22⋊C411yescharacteristic
200C22×C4C5×C22⋊C411yescharacteristic
201C22×C4C22×C4×C511yescharacteristic
202C22×C4C2×C5×D411yescharacteristic
203C22×C4C2×C5×D411yescharacteristic
204C2×C8—24no—
205C2×C8—24no—
206C2×C8—42no—
207C2×C8—42no—
208C2×C8—42no—
209C2×C8—42no—
210C4⋊C4—41no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—42no—
216C4⋊C4—42no—
217C4⋊C4—42no—
218C42—22no—
219C42—41no—
220C42—41no—
221C42—41no—
222C42—41no—
223C42—41no—
224C42C2×C5×Q812yes—
225C42C5×#4112yes—
226C2×C5#152911yescharacteristic
227C2×C5#153211yescharacteristic
228C2×C5#153511yescharacteristic
229C2×C5#153511yescharacteristic
230C2×C5#198611yescharacteristic
231C2×C5#199511yescharacteristic
232C2×C5#199811yescharacteristic
233C23C2×C5×C22⋊C411yescharacteristic
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—41no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4C5×#10412yes—
264C2×C4C4×C5×Q812yes—
265C2×C4C5×C22⋊Q812yes—
266C2×C4C5×#12411yescharacteristic
267C2×C4C5×C4⋊Q811yescharacteristic
268C8—44no—
269C8—44no—
270C5#989311yescharacteristic, direct product factor, Sylow
271C22C5×#39111yescharacteristic
272C22C5×#41311yescharacteristic
273C22C5×#41311yescharacteristic
274C22C2×C5×#10411yescharacteristic
275C22C5×#42111yescharacteristic
276C22C5×#42111yescharacteristic
277C22C5×#42111yescharacteristic
278C4—22no—
279C4—21no—
280C4—21no—
281C4—22no—
282C4—22no—
283C4—41no—
284C4—41no—
285C4—41no—
286C4—81no—
287C4—81no—
288C4—81no—
289C4—81no—
290C2C5×#152911yescharacteristic
291C2C5×#153211yescharacteristic
292C2C5×#153511yescharacteristic
293C2C5×#153511yescharacteristic
294C2C5×#198611yescharacteristic
295C2C5×#199511yescharacteristic
296C2C5×#199811yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C43×C5 ◁ G

Complements

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

NH ≅ G/Ntype
23. #9893C5direct (N × H)
270. C5#9893direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28642
C5×#17672
C5×#17452
C5×#12952
#98935