Finite Group Databasebeta

← C5×#8582 #11931302

Subgroups — C5×#8582 #11931302

Order 1280.

456 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#125C211yesmaximal, characteristic
2C5×#1767C211yesmaximal, characteristic
3C5×#1767C211yesmaximal, characteristic
4C2×C5×#330C212yesmaximal
5C5×#1295C212yesmaximal
6C2×C5×#125C2211yescharacteristic
7C2×C5×C4⋊C8—21no—
8C2×C5×C4⋊C8—21no—
9C2×C5×#97C2212yes—
10C2×C5×#97C2212yes—
11C5×#389C411yescharacteristic
12C5×#389C411yescharacteristic
13C5×#387—21no—
14C5×#387—21no—
15C5×#382C2211yescharacteristic
16C4×C5×C4⋊C4—21no—
17C4×C5×C4⋊C4—21no—
18C4×C5×C4⋊C4C411yescharacteristic
19C4×C5×C4⋊C4C411yescharacteristic
20C43×C5C2211yescharacteristic
21C5×#336—21no—
22C5×#336—21no—
23C5×#330—24no—
24#8582C511yesmaximal, characteristic, direct product factor, Sylow
25C22×C5×C8—22no—
26C22×C5×C8—22no—
27C5×#125—21no—
28C5×#125—21no—
29C5×#125D412yes—
30C5×#125Q812yes—
31C2×C5×C4⋊C4—21no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C4⋊C4C2×C411yescharacteristic
39C2×C42×C5—21no—
40C2×C42×C5—21no—
41C2×C42×C5C2×C411yescharacteristic
42C2×C42×C5C2×C411yescharacteristic
43C2×C42×C5D411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C2×C42×C5C2311yescharacteristic
48C5×C4⋊C8—24no—
49C5×C4⋊C8—24no—
50C5×#97—22no—
51C5×#97—22no—
52C5×#97—22no—
53C5×#97—22no—
54C5×#95—21no—
55C5×#95—21no—
56C5×#95—21no—
57C5×#95—21no—
58C5×#95—21no—
59C5×#95—21no—
60C4×#125C2×C511yescharacteristic
61#1767C2×C511yescharacteristic
62#1767C2×C511yescharacteristic
63C2×#330C2×C512yes—
64#1295C2×C512yes—
65C22×C4×C5—21no—
66C22×C4×C5—21no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5C22⋊C411yescharacteristic
70C22×C4×C5C22⋊C411yescharacteristic
71C22×C4×C5C22⋊C411yescharacteristic
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22×C411yescharacteristic
74C22×C4×C5C2×D411yescharacteristic
75C22×C4×C5C2×D411yescharacteristic
76C2×C5×C8—24no—
77C2×C5×C8—24no—
78C2×C5×C8—42no—
79C2×C5×C8—42no—
80C2×C5×C8—42no—
81C2×C5×C8—42no—
82C5×C4⋊C4—21no—
83C5×C4⋊C4—21no—
84C5×C4⋊C4—22no—
85C5×C4⋊C4—22no—
86C5×C4⋊C4—22no—
87C5×C4⋊C4—22no—
88C5×C4⋊C4—41no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—42no—
91C5×C4⋊C4—42no—
92C5×C4⋊C4C4⋊C412yes—
93C5×C4⋊C4C4⋊C412yes—
94C42×C5—22no—
95C42×C5—22no—
96C42×C5—22no—
97C42×C5—41no—
98C42×C5—41no—
99C42×C5—41no—
100C42×C5—42no—
101C42×C5—42no—
102C42×C5C2×D411yescharacteristic
103C42×C5C2×Q811yescharacteristic
104C42×C5#4111yescharacteristic
105C42×C5#4111yescharacteristic
106C2×#125C22×C511yescharacteristic
107C2×C4⋊C8—21no—
108C2×C4⋊C8—21no—
109C2×#97C22×C512yes—
110C2×#97C22×C512yes—
111#389C4×C511yescharacteristic
112#389C4×C511yescharacteristic
113#387—21no—
114#387—21no—
115#382C22×C511yescharacteristic
116C4×C4⋊C4—21no—
117C4×C4⋊C4—21no—
118C4×C4⋊C4C4×C511yescharacteristic
119C4×C4⋊C4C4×C511yescharacteristic
120C43C22×C511yescharacteristic
121#336—21no—
122#336—21no—
123#330—24no—
124C23×C5C2×C22⋊C411yescharacteristic
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—21no—
134C2×C4×C5—21no—
135C2×C4×C5—21no—
136C2×C4×C5—21no—
137C2×C4×C5—22no—
138C2×C4×C5—22no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—41no—
143C2×C4×C5—41no—
144C2×C4×C5—41no—
145C2×C4×C5—41no—
146C2×C4×C5—41no—
147C2×C4×C5—41no—
148C2×C4×C5—41no—
149C2×C4×C5—41no—
150C2×C4×C5—41no—
151C2×C4×C5—41no—
152C2×C4×C5#10112yes—
153C2×C4×C5#10412yes—
154C2×C4×C5#10412yes—
155C2×C4×C5C2×C4⋊C411yescharacteristic
156C2×C4×C5#11711yescharacteristic
157C2×C4×C5#12111yescharacteristic
158C2×C4×C5#12111yescharacteristic
159C2×C4×C5C22⋊Q811yescharacteristic
160C2×C4×C5C22⋊Q811yescharacteristic
161C5×C8—44no—
162C5×C8—44no—
163C22×C8—22no—
164C22×C8—22no—
165#125—21no—
166#125—21no—
167#125C5×D412yes—
168#125C5×Q812yes—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—21no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C2×C4×C511yescharacteristic
174C2×C4⋊C4C2×C4×C511yescharacteristic
175C2×C4⋊C4C2×C4×C511yescharacteristic
176C2×C4⋊C4C2×C4×C511yescharacteristic
177C2×C42—21no—
178C2×C42—21no—
179C2×C42C2×C4×C511yescharacteristic
180C2×C42C2×C4×C511yescharacteristic
181C2×C42C5×D411yescharacteristic
182C2×C42C5×D411yescharacteristic
183C2×C42C5×D411yescharacteristic
184C2×C42C5×D411yescharacteristic
185C2×C42C23×C511yescharacteristic
186C4⋊C8—24no—
187C4⋊C8—24no—
188#97—22no—
189#97—22no—
190#97—22no—
191#97—22no—
192#95—21no—
193#95—21no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198C22×C5#38011yescharacteristic
199C22×C5C2×#10111yescharacteristic
200C22×C5#41311yescharacteristic
201C22×C5C2×#10411yescharacteristic
202C22×C5C2×#10411yescharacteristic
203C22×C5#42111yescharacteristic
204C22×C5#42111yescharacteristic
205C4×C5—21no—
206C4×C5—21no—
207C4×C5—21no—
208C4×C5—21no—
209C4×C5—21no—
210C4×C5—21no—
211C4×C5—22no—
212C4×C5—22no—
213C4×C5—22no—
214C4×C5—42no—
215C4×C5—42no—
216C4×C5—41no—
217C4×C5—81no—
218C4×C5—81no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—21no—
223C22×C4C5×C22⋊C411yescharacteristic
224C22×C4C5×C22⋊C411yescharacteristic
225C22×C4C5×C22⋊C411yescharacteristic
226C22×C4C5×C22⋊C411yescharacteristic
227C22×C4C22×C4×C511yescharacteristic
228C22×C4C2×C5×D411yescharacteristic
229C22×C4C2×C5×D411yescharacteristic
230C2×C8—24no—
231C2×C8—24no—
232C2×C8—42no—
233C2×C8—42no—
234C2×C8—42no—
235C2×C8—42no—
236C4⋊C4—21no—
237C4⋊C4—21no—
238C4⋊C4—22no—
239C4⋊C4—22no—
240C4⋊C4—22no—
241C4⋊C4—22no—
242C4⋊C4—41no—
243C4⋊C4—41no—
244C4⋊C4—42no—
245C4⋊C4—42no—
246C4⋊C4C5×C4⋊C412yes—
247C4⋊C4C5×C4⋊C412yes—
248C42—22no—
249C42—22no—
250C42—22no—
251C42—41no—
252C42—41no—
253C42—41no—
254C42—42no—
255C42—42no—
256C42C2×C5×D411yescharacteristic
257C42C2×C5×Q811yescharacteristic
258C42C5×#4111yescharacteristic
259C42C5×#4111yescharacteristic
260C2×C5#152411yescharacteristic
261C2×C5#152811yescharacteristic
262C2×C5#153111yescharacteristic
263C2×C5#153511yescharacteristic
264C2×C5#180111yescharacteristic
265C2×C5#180611yescharacteristic
266C2×C5#180611yescharacteristic
267C23C2×C5×C22⋊C411yescharacteristic
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—21no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—41no—
287C2×C4—41no—
288C2×C4—41no—
289C2×C4—41no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4—41no—
295C2×C4C5×#10112yes—
296C2×C4C5×#10412yes—
297C2×C4C5×#10412yes—
298C2×C4C2×C5×C4⋊C411yescharacteristic
299C2×C4C5×#11711yescharacteristic
300C2×C4C5×#12111yescharacteristic
301C2×C4C5×#12111yescharacteristic
302C2×C4C5×C22⋊Q811yescharacteristic
303C2×C4C5×C22⋊Q811yescharacteristic
304C8—44no—
305C8—44no—
306C5#858211yescharacteristic, direct product factor, Sylow
307C22C5×#38011yescharacteristic
308C22C2×C5×#10111yescharacteristic
309C22C5×#41311yescharacteristic
310C22C2×C5×#10411yescharacteristic
311C22C2×C5×#10411yescharacteristic
312C22C5×#42111yescharacteristic
313C22C5×#42111yescharacteristic
314C4—22no—
315C4—22no—
316C4—22no—
317C4—21no—
318C4—21no—
319C4—21no—
320C4—21no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—42no—
325C4—42no—
326C4—81no—
327C4—81no—
328C2C5×#152411yescharacteristic
329C2C5×#152811yescharacteristic
330C2C5×#153111yescharacteristic
331C2C5×#153511yescharacteristic
332C2C5×#180111yescharacteristic
333C2C5×#180611yescharacteristic
334C2C5×#180611yescharacteristic
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
24. #8582C5direct (N × H)
306. C5#8582direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×#1252
C5×#17672
C2×C5×#3302
C5×#12952
#85825