Finite Group Databasebeta

← C5×#9545 #11932265

Subgroups — C5×#9545 #11932265

Order 1280.

444 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#1954C211yesmaximal, characteristic
2C5×#1770C211yesmaximal, characteristic, complemented
3C4×C5×#102C211yesmaximal, characteristic
4C2×C5×#335C211yesmaximal, characteristic, complemented
5C2×C5×D4⋊C8C211yesmaximal, characteristic
6C5×#1279C211yesmaximal, characteristic, complemented
7C5×#1273C211yesmaximal, characteristic, complemented
8C2×C4×C5×D4C2211yescharacteristic
9C2×C5×C4⋊C8C2211yescharacteristic
10C2×C5×C4⋊C8C2211yescharacteristic
11C2×C5×#102C411yescharacteristic
12C2×C5×#102C411yescharacteristic
13C2×C5×C22⋊C8—21no—
14C2×C5×C22⋊C8—21no—
15C2×C5×#97—21no—
16C2×C4×C5×C8C2211yescharacteristic
17C2×C4×C5×C8C2211yescharacteristic
18C2×C4×C5×C8C2211yescharacteristic
19C4×C5×C4⋊C4C2211yescharacteristic
20C5×#340C411yescharacteristic
21C5×#340C411yescharacteristic
22C5×#336—21no—
23C5×#335—22no—
24C5×D4⋊C8—22no—
25#9545C511yesmaximal, characteristic, direct product factor, Sylow
26C22×C5×D4C2×C411yescharacteristic
27C23×C4×C5—21no—
28C22×C5×C8—21no—
29C22×C5×C8—21no—
30C22×C5×C8—21no—
31C22×C5×C8C2×C411yescharacteristic
32C22×C5×C8C2×C411yescharacteristic
33C22×C5×C8D411yescharacteristic
34C22×C5×C8D411yescharacteristic
35C4×C5×D4—21no—
36C4×C5×D4—21no—
37C4×C5×D4—21no—
38C4×C5×D4—21no—
39C2×C5×C4⋊C4C2×C411yescharacteristic
40C2×C5×C4⋊C4C2×C411yescharacteristic
41C2×C5×C4⋊C4C2×C411yescharacteristic
42C2×C5×C22⋊C4—21no—
43C2×C42×C5—21no—
44C2×C42×C5C2311yescharacteristic
45C5×C4⋊C8—21no—
46C5×C4⋊C8—21no—
47C5×C4⋊C8—21no—
48C5×C4⋊C8D412yes—
49C5×#102—22no—
50C5×#102—22no—
51C5×C22⋊C8—42no—
52C5×C22⋊C8—42no—
53C5×#97—42no—
54C4×C5×C8—21no—
55C4×C5×C8—21no—
56C4×C5×C8—21no—
57C4×C5×C8—21no—
58C4×C5×C8—21no—
59C4×C5×C8—21no—
60C5×#95—21no—
61#1954C2×C511yescharacteristic
62#1770C2×C511yescharacteristic, complemented
63C4×#102C2×C511yescharacteristic
64C2×#335C2×C511yescharacteristic, complemented
65C2×D4⋊C8C2×C511yescharacteristic
66#1279C2×C511yescharacteristic, complemented
67#1273C2×C511yescharacteristic, complemented
68C24×C5—21no—
69C2×C5×D4—21no—
70C2×C5×D4—21no—
71C2×C5×D4—21no—
72C2×C5×D4—21no—
73C2×C5×D4—21no—
74C2×C5×D4M1612yes—
75C22×C4×C5—21no—
76C22×C4×C5—21no—
77C22×C4×C5—21no—
78C22×C4×C5—41no—
79C22×C4×C5—41no—
80C22×C4×C5—41no—
81C22×C4×C5—41no—
82C22×C4×C5—41no—
83C22×C4×C5—41no—
84C22×C4×C5C22×C411yescharacteristic
85C22×C4×C5C2×D411yescharacteristic
86C22×C4×C5#4111yescharacteristic
87C2×C5×C8—21no—
88C2×C5×C8—21no—
89C2×C5×C8—21no—
90C2×C5×C8—21no—
91C2×C5×C8—22no—
92C2×C5×C8—21no—
93C2×C5×C8—22no—
94C2×C5×C8—21no—
95C2×C5×C8—21no—
96C2×C5×C8—21no—
97C2×C5×C8—21no—
98C2×C5×C8—21no—
99C2×C5×C8—41no—
100C2×C5×C8—41no—
101C2×C5×C8—41no—
102C2×C5×C8—41no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C2×C5×C8—41no—
106C2×C5×C8M1612yes—
107C2×C5×C8D812yes—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C4⋊C4—21no—
111C5×C4⋊C4—21no—
112C5×C4⋊C4—21no—
113C5×C4⋊C4—21no—
114C5×C22⋊C4—41no—
115C5×C22⋊C4—41no—
116C42×C5—41no—
117C42×C5—41no—
118C42×C5C2×D411yescharacteristic
119C42×C5#4111yescharacteristic
120C42×C5#4111yescharacteristic
121C42×C5#4111yescharacteristic
122C2×C4×D4C22×C511yescharacteristic
123C2×C4⋊C8C22×C511yescharacteristic
124C2×C4⋊C8C22×C511yescharacteristic
125C2×#102C4×C511yescharacteristic
126C2×#102C4×C511yescharacteristic
127C2×C22⋊C8—21no—
128C2×C22⋊C8—21no—
129C2×#97—21no—
130C2×C4×C8C22×C511yescharacteristic
131C2×C4×C8C22×C511yescharacteristic
132C2×C4×C8C22×C511yescharacteristic
133C4×C4⋊C4C22×C511yescharacteristic
134#340C4×C511yescharacteristic
135#340C4×C511yescharacteristic
136#336—21no—
137#335—22no—
138D4⋊C8—22no—
139C23×C5—22no—
140C23×C5—41no—
141C23×C5—41no—
142C23×C5—41no—
143C23×C5—41no—
144C23×C5—41no—
145C23×C5—41no—
146C23×C5C4×D411yescharacteristic
147C5×D4—22no—
148C5×D4—22no—
149C5×D4—41no—
150C5×D4—41no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—41no—
154C2×C4×C5—41no—
155C2×C4×C5—41no—
156C2×C4×C5—41no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—81no—
163C2×C4×C5—81no—
164C2×C4×C5—81no—
165C2×C4×C5—81no—
166C2×C4×C5#11711yescharacteristic
167C2×C4×C5C4×D411yescharacteristic
168C2×C4×C5#12111yescharacteristic
169C2×C4×C5#12311yescharacteristic
170C2×C4×C5#12411yescharacteristic
171C2×C4×C5#12611yescharacteristic
172C2×C4×C5C2×M1611yescharacteristic
173C2×C4×C5C2×M1611yescharacteristic
174C2×C4×C5#13111yescharacteristic
175C2×C4×C5#13111yescharacteristic
176C2×C4×C5C2×D811yescharacteristic
177C2×C4×C5#13511yescharacteristic
178C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C5#13711yescharacteristic
180C5×C8—22no—
181C5×C8—22no—
182C5×C8—42no—
183C5×C8—41no—
184C5×C8—42no—
185C5×C8—41no—
186C5×C8—81no—
187C22×D4C2×C4×C511yescharacteristic
188C23×C4—21no—
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—21no—
192C22×C8C2×C4×C511yescharacteristic
193C22×C8C2×C4×C511yescharacteristic
194C22×C8C5×D411yescharacteristic
195C22×C8C5×D411yescharacteristic
196C4×D4—21no—
197C4×D4—21no—
198C4×D4—21no—
199C4×D4—21no—
200C2×C4⋊C4C2×C4×C511yescharacteristic
201C2×C4⋊C4C2×C4×C511yescharacteristic
202C2×C4⋊C4C2×C4×C511yescharacteristic
203C2×C22⋊C4—21no—
204C2×C42—21no—
205C2×C42C23×C511yescharacteristic
206C4⋊C8—21no—
207C4⋊C8—21no—
208C4⋊C8—21no—
209C4⋊C8C5×D412yes—
210#102—22no—
211#102—22no—
212C22⋊C8—42no—
213C22⋊C8—42no—
214#97—42no—
215C4×C8—21no—
216C4×C8—21no—
217C4×C8—21no—
218C4×C8—21no—
219C4×C8—21no—
220C4×C8—21no—
221#95—21no—
222C22×C5—42no—
223C22×C5—42no—
224C22×C5—42no—
225C22×C5—81no—
226C22×C5—81no—
227C22×C5—81no—
228C22×C5—81no—
229C22×C5#38811yescharacteristic
230C22×C5#43511yescharacteristic
231C22×C5#43611yescharacteristic
232C22×C5C4×D811yescharacteristic
233C22×C5#44011yescharacteristic
234C22×C5#44311yescharacteristic
235C22×C5#44411yescharacteristic
236C4×C5—21no—
237C4×C5—21no—
238C4×C5—81no—
239C4×C5—81no—
240C4×C5—81no—
241C4×C5#43211yescharacteristic
242C4×C5#43311yescharacteristic
243C4×C5#43511yescharacteristic
244C4×C5#43511yescharacteristic
245C4×C5#45911yescharacteristic
246C4×C5#46411yescharacteristic
247C4×C5#48011yescharacteristic
248C4×C5#48211yescharacteristic
249C24—21no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—21no—
255C2×D4C5×M1612yes—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—41no—
262C22×C4—41no—
263C22×C4—41no—
264C22×C4—41no—
265C22×C4C22×C4×C511yescharacteristic
266C22×C4C2×C5×D411yescharacteristic
267C22×C4C5×#4111yescharacteristic
268C2×C8—21no—
269C2×C8—21no—
270C2×C8—21no—
271C2×C8—21no—
272C2×C8—22no—
273C2×C8—21no—
274C2×C8—22no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—21no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8C5×M1612yes—
288C2×C8C5×D812yes—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—21no—
292C4⋊C4—21no—
293C4⋊C4—21no—
294C4⋊C4—21no—
295C22⋊C4—41no—
296C22⋊C4—41no—
297C42—41no—
298C42—41no—
299C42C2×C5×D411yescharacteristic
300C42C5×#4111yescharacteristic
301C42C5×#4111yescharacteristic
302C42C5×#4111yescharacteristic
303C2×C5—82no—
304C2×C5#158111yescharacteristic
305C2×C5#158511yescharacteristic
306C2×C5#158911yescharacteristic
307C2×C5#159211yescharacteristic
308C2×C5#192411yescharacteristic
309C2×C5#192511yescharacteristic
310C2×C5#192911yescharacteristic
311C23—22no—
312C23—41no—
313C23—41no—
314C23—41no—
315C23—41no—
316C23—41no—
317C23—41no—
318C23C4×C5×D411yescharacteristic
319D4—22no—
320D4—22no—
321D4—41no—
322D4—41no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—81no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4C5×#11711yescharacteristic
339C2×C4C4×C5×D411yescharacteristic
340C2×C4C5×#12111yescharacteristic
341C2×C4C5×#12311yescharacteristic
342C2×C4C5×#12411yescharacteristic
343C2×C4C5×#12611yescharacteristic
344C2×C4C2×C5×M1611yescharacteristic
345C2×C4C2×C5×M1611yescharacteristic
346C2×C4C5×#13111yescharacteristic
347C2×C4C5×#13111yescharacteristic
348C2×C4C2×C5×D811yescharacteristic
349C2×C4C5×#13511yescharacteristic
350C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
351C2×C4C5×#13711yescharacteristic
352C8—22no—
353C8—22no—
354C8—42no—
355C8—41no—
356C8—42no—
357C8—41no—
358C8—81no—
359C5#954511yescharacteristic, direct product factor, Sylow
360C22—42no—
361C22—42no—
362C22—42no—
363C22—81no—
364C22—81no—
365C22—81no—
366C22—81no—
367C22C5×#38811yescharacteristic
368C22C5×#43511yescharacteristic
369C22C5×#43611yescharacteristic
370C22C4×C5×D811yescharacteristic
371C22C5×#44011yescharacteristic
372C22C5×#44311yescharacteristic
373C22C5×#44411yescharacteristic
374C4—21no—
375C4—21no—
376C4—81no—
377C4—81no—
378C4—81no—
379C4C5×#43211yescharacteristic
380C4C5×#43311yescharacteristic
381C4C5×#43511yescharacteristic
382C4C5×#43511yescharacteristic
383C4C5×#45911yescharacteristic
384C4C5×#46411yescharacteristic
385C4C5×#48011yescharacteristic
386C4C5×#48211yescharacteristic
387C2—82no—
388C2C5×#158111yescharacteristic
389C2C5×#158511yescharacteristic
390C2C5×#158911yescharacteristic
391C2C5×#159211yescharacteristic
392C2C5×#192411yescharacteristic
393C2C5×#192511yescharacteristic
394C2C5×#192911yescharacteristic
subgroupG/H
centerC22×C4×C5C2×D4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
socleC23×C5C4×D4
prime radicalC22×C5×D4C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4×C5 ◁ C2×C4×C5×C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1770C2semidirect
4. C2×C5×#335C2semidirect
6. C5×#1279C2semidirect
7. C5×#1273C2semidirect
25. #9545C5direct (N × H)
62. #1770C2×C5semidirect
64. C2×#335C2×C5semidirect
66. #1279C2×C5semidirect
67. #1273C2×C5semidirect
359. C5#9545direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#19542
C5×#17702
C4×C5×#1022
C2×C5×#3352
C2×C5×D4⋊C82
C5×#12792
C5×#12732
#95455