Finite Group Databasebeta

← C5×#7610 #11930330

Subgroups — C5×#7610 #11930330

Order 1280.

612 conjugacy classes of subgroups.

The subgroup lattice has 330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#389C211yesmaximal, characteristic
2C5×#1817C211yesmaximal, characteristic
3C5×#1728C211yesmaximal, characteristic
4C5×#1271C214yesmaximal, complemented
5C22×C5×M16—21no—
6C22×C5×C4⋊C4—21no—
7C22×C5×C4⋊C4C411yescharacteristic
8C22×C5×C4⋊C4C411yescharacteristic
9C22×C42×C5C2211yescharacteristic
10C2×C5×C22⋊C8—21no—
11C5×#389—21no—
12C5×#389—21no—
13C5×#389C412yes—
14C5×#389C2212yes—
15C2×C5×#95—21no—
16C5×#336—21no—
17C5×#336—21no—
18C5×#336C2212yes—
19C5×#336C2212yes—
20#7610C511yesmaximal, characteristic, direct product factor, Sylow
21C23×C4×C5—21no—
22C23×C4×C5—21no—
23C23×C4×C5C2×C411yescharacteristic
24C23×C4×C5D411yescharacteristic
25C23×C4×C5D411yescharacteristic
26C2×C5×M16—24no—
27C2×C5×M16—42no—
28C2×C5×M16—42no—
29C22×C5×C8—22no—
30C22×C5×C8—22no—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—24no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—22no—
35C2×C5×C4⋊C4—22no—
36C2×C5×C4⋊C4—42no—
37C2×C5×C4⋊C4—42no—
38C2×C5×C4⋊C4—42no—
39C2×C5×C4⋊C4C2×C412yes—
40C2×C5×C4⋊C4C2×C412yes—
41C2×C42×C5—42no—
42C2×C42×C5C2×C411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5C2311yescharacteristic
46C5×C22⋊C8—42no—
47C5×#95—22no—
48C5×#95—22no—
49C2×#389C2×C511yescharacteristic
50#1817C2×C511yescharacteristic
51#1728C2×C511yescharacteristic
52#1271C2×C514yescomplemented
53C24×C5C22⋊C411yescharacteristic
54C22×C4×C5—22no—
55C22×C4×C5—22no—
56C22×C4×C5—22no—
57C22×C4×C5—22no—
58C22×C4×C5—22no—
59C22×C4×C5—24no—
60C22×C4×C5—22no—
61C22×C4×C5—22no—
62C22×C4×C5—22no—
63C22×C4×C5—22no—
64C22×C4×C5—41no—
65C22×C4×C5—42no—
66C22×C4×C5—42no—
67C22×C4×C5—42no—
68C22×C4×C5—42no—
69C22×C4×C5—42no—
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5D812yes—
74C22×C4×C5SD1612yes—
75C22×C4×C5C22×C411yescharacteristic
76C22×C4×C5C2×D411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C5×M16—48no—
79C2×C5×C8—24no—
80C2×C5×C8—42no—
81C2×C5×C8—42no—
82C2×C5×C8—42no—
83C2×C5×C8—42no—
84C2×C5×C8—42no—
85C5×C4⋊C4—24no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—42no—
88C5×C4⋊C4—42no—
89C5×C4⋊C4—44no—
90C5×C4⋊C4—42no—
91C5×C4⋊C4—42no—
92C5×C4⋊C4M1614yescomplemented
93C42×C5—41no—
94C42×C5—41no—
95C42×C5—41no—
96C42×C5—41no—
97C22×M16—21no—
98C22×C4⋊C4—21no—
99C22×C4⋊C4C4×C511yescharacteristic
100C22×C4⋊C4C4×C511yescharacteristic
101C22×C42C22×C511yescharacteristic
102C2×C22⋊C8—21no—
103#389—21no—
104#389—21no—
105#389C4×C512yes—
106#389C22×C512yes—
107C2×#95—21no—
108#336—21no—
109#336—21no—
110#336C22×C512yes—
111#336C22×C512yes—
112C23×C5—21no—
113C23×C5—21no—
114C23×C5—21no—
115C23×C5—21no—
116C23×C5#9912yes—
117C23×C5#10212yes—
118C23×C5#10412yes—
119C23×C5C2×C22⋊C411yescharacteristic
120C2×C4×C5—28no—
121C2×C4×C5—24no—
122C2×C4×C5—24no—
123C2×C4×C5—21no—
124C2×C4×C5—21no—
125C2×C4×C5—21no—
126C2×C4×C5—21no—
127C2×C4×C5—21no—
128C2×C4×C5—21no—
129C2×C4×C5—21no—
130C2×C4×C5—21no—
131C2×C4×C5—21no—
132C2×C4×C5—21no—
133C2×C4×C5—24no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—44no—
138C2×C4×C5—48no—
139C2×C4×C5—42no—
140C2×C4×C5—42no—
141C2×C4×C5—42no—
142C2×C4×C5—42no—
143C2×C4×C5—42no—
144C2×C4×C5—84no—
145C2×C4×C5#10112yes—
146C2×C4×C5#10212yes—
147C2×C4×C5C2×M1612yes—
148C2×C4×C5C2×D811yescharacteristic
149C2×C4×C5C2×SD1611yescharacteristic
150C2×C4×C5#13712yes—
151C5×C8—44no—
152C5×C8—82no—
153C23×C4—21no—
154C23×C4—21no—
155C23×C4C2×C4×C511yescharacteristic
156C23×C4C5×D411yescharacteristic
157C23×C4C5×D411yescharacteristic
158C2×M16—24no—
159C2×M16—42no—
160C2×M16—42no—
161C22×C8—22no—
162C22×C8—22no—
163C2×C4⋊C4—21no—
164C2×C4⋊C4—24no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—21no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4—42no—
169C2×C4⋊C4—42no—
170C2×C4⋊C4—42no—
171C2×C4⋊C4C2×C4×C512yes—
172C2×C4⋊C4C2×C4×C512yes—
173C2×C42—42no—
174C2×C42C2×C4×C511yescharacteristic
175C2×C42C5×D411yescharacteristic
176C2×C42C5×D411yescharacteristic
177C2×C42C23×C511yescharacteristic
178C22⋊C8—42no—
179#95—22no—
180#95—22no—
181C22×C5—22no—
182C22×C5—22no—
183C22×C5—22no—
184C22×C5—22no—
185C22×C5—22no—
186C22×C5—22no—
187C22×C5#32714yes—
188C22×C5#40711yescharacteristic
189C22×C5C2×#9911yescharacteristic
190C22×C5C2×#10111yescharacteristic
191C22×C5C2×#10211yescharacteristic
192C22×C5#41911yescharacteristic
193C22×C5C2×#10411yescharacteristic
194C22×C5#42111yescharacteristic
195C4×C5—22no—
196C4×C5—22no—
197C4×C5—21no—
198C4×C5—22no—
199C4×C5—21no—
200C4×C5—22no—
201C4×C5—44no—
202C4×C5—41no—
203C4×C5—82no—
204C24C5×C22⋊C411yescharacteristic
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—22no—
210C22×C4—24no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—22no—
214C22×C4—22no—
215C22×C4—41no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—42no—
221C22×C4C5×C22⋊C411yescharacteristic
222C22×C4C5×C22⋊C411yescharacteristic
223C22×C4C5×C22⋊C411yescharacteristic
224C22×C4C5×D812yes—
225C22×C4C5×SD1612yes—
226C22×C4C22×C4×C511yescharacteristic
227C22×C4C2×C5×D411yescharacteristic
228C22×C4C2×C5×D411yescharacteristic
229M16—48no—
230C2×C8—24no—
231C2×C8—42no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C4⋊C4—24no—
237C4⋊C4—22no—
238C4⋊C4—42no—
239C4⋊C4—42no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—44no—
243C4⋊C4C5×M1614yescomplemented
244C42—41no—
245C42—41no—
246C42—41no—
247C42—41no—
248C2×C5—24no—
249C2×C5#146311yescharacteristic
250C2×C5#148611yescharacteristic
251C2×C5#149111yescharacteristic
252C2×C5C2×#32711yescharacteristic
253C2×C5#151111yescharacteristic
254C2×C5#152811yescharacteristic
255C2×C5#154611yescharacteristic
256C23—21no—
257C23—21no—
258C23—21no—
259C23—21no—
260C23C5×#9912yes—
261C23C5×#10212yes—
262C23C5×#10412yes—
263C23C2×C5×C22⋊C411yescharacteristic
264C2×C4—28no—
265C2×C4—24no—
266C2×C4—24no—
267C2×C4—21no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—21no—
277C2×C4—24no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—44no—
282C2×C4—48no—
283C2×C4—42no—
284C2×C4—42no—
285C2×C4—42no—
286C2×C4—42no—
287C2×C4—42no—
288C2×C4—84no—
289C2×C4C5×#10112yes—
290C2×C4C5×#10212yes—
291C2×C4C2×C5×M1612yes—
292C2×C4C2×C5×D811yescharacteristic
293C2×C4C2×C5×SD1611yescharacteristic
294C2×C4C5×#13712yes—
295C8—44no—
296C8—82no—
297C5#761011yescharacteristic, direct product factor, Sylow
298C22—22no—
299C22—22no—
300C22—22no—
301C22—22no—
302C22—22no—
303C22—22no—
304C22C5×#32714yes—
305C22C5×#40711yescharacteristic
306C22C2×C5×#9911yescharacteristic
307C22C2×C5×#10111yescharacteristic
308C22C2×C5×#10211yescharacteristic
309C22C5×#41911yescharacteristic
310C22C2×C5×#10411yescharacteristic
311C22C5×#42111yescharacteristic
312C4—22no—
313C4—22no—
314C4—22no—
315C4—21no—
316C4—21no—
317C4—22no—
318C4—41no—
319C4—44no—
320C4—82no—
321C2—24no—
322C2C5×#146311yescharacteristic
323C2C5×#148611yescharacteristic
324C2C5×#149111yescharacteristic
325C2C2×C5×#32711yescharacteristic
326C2C5×#151111yescharacteristic
327C2C5×#152811yescharacteristic
328C2C5×#154611yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC24×C5C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#1271C2semidirect
20. #7610C5direct (N × H)
52. #1271C2×C5semidirect
92. C5×C4⋊C4M16semidirect
243. C4⋊C4C5×M16semidirect
297. C5#7610direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#3892
C5×#18172
C5×#17282
C5×#12712
#76105