Finite Group Databasebeta

← C5×#12805 #11935525

Subgroups — C5×#12805 #11935525

Order 1280.

434 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2929C211yesmaximal, characteristic
2C5×#2120C212yesmaximal
3C5×#1813C211yesmaximal, characteristic, complemented
4C5×#1812C211yesmaximal, characteristic, complemented
5C5×#1395C212yesmaximal, complemented
6C2×C5×#131C2211yescharacteristic
7C23×C5×C8C411yescharacteristic, complemented
8C5×#525C2211yescharacteristic
9C5×#435—21no—
10C5×#435—21no—
11C5×C8×D4—21no—
12C5×C8×D4—21no—
13C2×C5×#108—21no—
14C5×#427—21no—
15C5×#424C411yescharacteristic, complemented
16C5×#413C2212yes—
17C5×#410C2212yes—
18C5×#408C2211yescharacteristic
19C5×#407C411yescharacteristic, complemented
20C5×#405C411yescharacteristic, complemented
21C5×#352—22no—
22C5×AΣL(1,𝔽16)—22no—
23C5×#338—21no—
24C5×H(3,ℤ/4)—21no—
25#12805C511yesmaximal, characteristic, direct product factor, Sylow
26C2×C5×#41C2311yescharacteristic
27C23×C4×C5C2×C411yescharacteristic
28C5×#131—41no—
29C5×#131—41no—
30C2×C5×M16—22no—
31C2×C5×M16C2×C411yescharacteristic
32C2×C5×M16C2×C411yescharacteristic
33C2×C5×M16D411yescharacteristic
34C2×C5×M16D411yescharacteristic
35C22×C5×C8—21no—
36C22×C5×C8—21no—
37C22×C5×C8—41no—
38C22×C5×C8—41no—
39C22×C5×C8C2×C411yescharacteristic
40C22×C5×C8C2×C411yescharacteristic
41C22×C5×C8D411yescharacteristic
42C22×C5×C8D411yescharacteristic
43C5×#123D411yescharacteristic
44C5×#123Q811yescharacteristic
45C5×C22⋊Q8—21no—
46C5×#121—21no—
47C5×#120D411yescharacteristic
48C5×#120Q811yescharacteristic
49C4×C5×D4—21no—
50C4×C5×D4—21no—
51C5×#117—22no—
52C5×#117C2×C411yescharacteristic
53C5×#108—41no—
54C5×#108—41no—
55C5×#107—41no—
56C5×#106—41no—
57C5×C4⋊C8—21no—
58C5×C4⋊C8—21no—
59C5×#101—22no—
60C5×#100—22no—
61C5×#99—22no—
62C5×#99—22no—
63C5×C22⋊C8—21no—
64C5×C22⋊C8—21no—
65C5×C22⋊C8—21no—
66C5×C22⋊C8—21no—
67C5×#97—21no—
68C4×C5×C8—21no—
69#2929C2×C511yescharacteristic
70#2120C2×C512yes—
71#1813C2×C511yescharacteristic, complemented
72#1812C2×C511yescharacteristic, complemented
73#1395C2×C512yescomplemented
74C24×C5C4⋊C411yescharacteristic
75C5×#41—41no—
76C5×#41—41no—
77C2×C5×Q8#4111yescharacteristic
78C2×C5×D4—21no—
79C2×C5×D4—21no—
80C2×C5×D4C2×D411yescharacteristic
81C2×C5×D4C2×Q811yescharacteristic
82C2×C5×D4#4111yescharacteristic
83C22×C4×C5—21no—
84C22×C4×C5—21no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5C4⋊C411yescharacteristic
88C22×C4×C5C22×C411yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C22×C4×C5C2×D411yescharacteristic
91C5×M16—41no—
92C5×M16—41no—
93C5×M16—41no—
94C5×M16—41no—
95C5×M16—42no—
96C5×M16—42no—
97C2×C5×C8—21no—
98C2×C5×C8—21no—
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8—21no—
102C2×C5×C8—21no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—42no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C2×C5×C8—41no—
109C2×C5×C8—42no—
110C2×C5×C8C22⋊C411yescharacteristic
111C2×C5×C8C22⋊C411yescharacteristic
112C2×C5×C8C22⋊C411yescharacteristic
113C2×C5×C8C22⋊C411yescharacteristic
114C5×C4⋊C4—21no—
115C5×C4⋊C4—21no—
116C5×C4⋊C4—21no—
117C5×C4⋊C4—42no—
118C5×C22⋊C4—21no—
119C5×C22⋊C4—21no—
120C5×C22⋊C4—21no—
121C5×C22⋊C4—21no—
122C5×C22⋊C4—42no—
123C5×C22⋊C4C4⋊C411yescharacteristic
124C5×C22⋊C4C4⋊C411yescharacteristic
125C42×C5—21no—
126C42×C5—42no—
127C2×#131C22×C511yescharacteristic
128C23×C8C4×C511yescharacteristic, complemented
129#525C22×C511yescharacteristic
130#435—21no—
131#435—21no—
132C8×D4—21no—
133C8×D4—21no—
134C2×#108—21no—
135#427—21no—
136#424C4×C511yescharacteristic, complemented
137#413C22×C512yes—
138#410C22×C512yes—
139#408C22×C511yescharacteristic
140#407C4×C511yescharacteristic, complemented
141#405C4×C511yescharacteristic, complemented
142#352—22no—
143AΣL(1,𝔽16)—22no—
144#338—21no—
145H(3,ℤ/4)—21no—
146C23×C5—21no—
147C23×C5—41no—
148C23×C5—42no—
149C23×C5C2×C4⋊C411yescharacteristic
150C23×C5#12111yescharacteristic
151C23×C5C22⋊Q811yescharacteristic
152C5×Q8—41no—
153C5×D4—41no—
154C5×D4—41no—
155C5×D4—41no—
156C5×D4—42no—
157C5×D4—42no—
158C2×C4×C5—21no—
159C2×C4×C5—21no—
160C2×C4×C5—21no—
161C2×C4×C5—21no—
162C2×C4×C5—21no—
163C2×C4×C5—21no—
164C2×C4×C5—21no—
165C2×C4×C5—21no—
166C2×C4×C5—21no—
167C2×C4×C5—42no—
168C2×C4×C5—41no—
169C2×C4×C5—41no—
170C2×C4×C5—41no—
171C2×C4×C5—82no—
172C2×C4×C5C2×C22⋊C411yescharacteristic
173C2×C4×C5#11711yescharacteristic
174C2×C4×C5#12111yescharacteristic
175C2×C4×C5C22⋊Q811yescharacteristic
176C5×C8—21no—
177C5×C8—21no—
178C5×C8—21no—
179C5×C8—41no—
180C5×C8—41no—
181C5×C8—82no—
182C5×C8#9911yescharacteristic
183C5×C8#9911yescharacteristic
184C2×#41C23×C511yescharacteristic
185C23×C4C2×C4×C511yescharacteristic
186#131—41no—
187#131—41no—
188C2×M16—22no—
189C2×M16C2×C4×C511yescharacteristic
190C2×M16C2×C4×C511yescharacteristic
191C2×M16C5×D411yescharacteristic
192C2×M16C5×D411yescharacteristic
193C22×C8—21no—
194C22×C8—21no—
195C22×C8—41no—
196C22×C8—41no—
197C22×C8C2×C4×C511yescharacteristic
198C22×C8C2×C4×C511yescharacteristic
199C22×C8C5×D411yescharacteristic
200C22×C8C5×D411yescharacteristic
201#123C5×D411yescharacteristic
202#123C5×Q811yescharacteristic
203C22⋊Q8—21no—
204#121—21no—
205#120C5×D411yescharacteristic
206#120C5×Q811yescharacteristic
207C4×D4—21no—
208C4×D4—21no—
209#117—22no—
210#117C2×C4×C511yescharacteristic
211#108—41no—
212#108—41no—
213#107—41no—
214#106—41no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217#101—22no—
218#100—22no—
219#99—22no—
220#99—22no—
221C22⋊C8—21no—
222C22⋊C8—21no—
223C22⋊C8—21no—
224C22⋊C8—21no—
225#97—21no—
226C4×C8—21no—
227C22×C5—22no—
228C22×C5—21no—
229C22×C5—21no—
230C22×C5—21no—
231C22×C5—41no—
232C22×C5—41no—
233C22×C5—41no—
234C22×C5—41no—
235C22×C5—42no—
236C22×C5—42no—
237C22×C5—41no—
238C22×C5#38011yescharacteristic
239C4×C5—21no—
240C4×C5—21no—
241C4×C5—21no—
242C4×C5—41no—
243C4×C5—41no—
244C4×C5—41no—
245C4×C5—162no—
246C4×C5C2×#9911yescharacteristic
247C4×C5#41011yescharacteristic
248C24C5×C4⋊C411yescharacteristic
249#41—41no—
250#41—41no—
251C2×Q8C5×#4111yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4C2×C5×D411yescharacteristic
255C2×D4C2×C5×Q811yescharacteristic
256C2×D4C5×#4111yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4C5×C4⋊C411yescharacteristic
262C22×C4C22×C4×C511yescharacteristic
263C22×C4C2×C5×D411yescharacteristic
264C22×C4C2×C5×D411yescharacteristic
265M16—41no—
266M16—41no—
267M16—41no—
268M16—41no—
269M16—42no—
270M16—42no—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8—21no—
277C2×C8—21no—
278C2×C8—21no—
279C2×C8—42no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—42no—
284C2×C8C5×C22⋊C411yescharacteristic
285C2×C8C5×C22⋊C411yescharacteristic
286C2×C8C5×C22⋊C411yescharacteristic
287C2×C8C5×C22⋊C411yescharacteristic
288C4⋊C4—21no—
289C4⋊C4—21no—
290C4⋊C4—21no—
291C4⋊C4—42no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—21no—
296C22⋊C4—42no—
297C22⋊C4C5×C4⋊C411yescharacteristic
298C22⋊C4C5×C4⋊C411yescharacteristic
299C42—21no—
300C42—42no—
301C2×C5—21no—
302C2×C5—41no—
303C2×C5—41no—
304C2×C5—42no—
305C2×C5—41no—
306C2×C5#179911yescharacteristic
307C23—21no—
308C23—41no—
309C23—42no—
310C23C2×C5×C4⋊C411yescharacteristic
311C23C5×#12111yescharacteristic
312C23C5×C22⋊Q811yescharacteristic
313Q8—41no—
314D4—41no—
315D4—41no—
316D4—41no—
317D4—42no—
318D4—42no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4—82no—
333C2×C4C2×C5×C22⋊C411yescharacteristic
334C2×C4C5×#11711yescharacteristic
335C2×C4C5×#12111yescharacteristic
336C2×C4C5×C22⋊Q811yescharacteristic
337C8—21no—
338C8—21no—
339C8—21no—
340C8—41no—
341C8—41no—
342C8—82no—
343C8C5×#9911yescharacteristic
344C8C5×#9911yescharacteristic
345C5#1280511yescharacteristic, direct product factor, Sylow
346C22—22no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—41no—
351C22—41no—
352C22—41no—
353C22—41no—
354C22—42no—
355C22—42no—
356C22—41no—
357C22C5×#38011yescharacteristic
358C4—21no—
359C4—21no—
360C4—21no—
361C4—41no—
362C4—41no—
363C4—41no—
364C4—162no—
365C4C2×C5×#9911yescharacteristic
366C4C5×#41011yescharacteristic
367C2—21no—
368C2—41no—
369C2—42no—
370C2—41no—
371C2—41no—
372C2C5×#179911yescharacteristic
subgroupG/H
centerC4×C5#410
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×#41C23×C5
socleC2×C5#1799
prime radicalC5×#525C22
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C5 ◁ C2×C5×C8 ◁ C2×C5×#131 ◁ G

Complements

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

NH ≅ G/Ntype
3. C5×#1813C2semidirect
4. C5×#1812C2semidirect
5. C5×#1395C2semidirect
7. C23×C5×C8C4semidirect
15. C5×#424C4semidirect
19. C5×#407C4semidirect
20. C5×#405C4semidirect
25. #12805C5direct (N × H)
71. #1813C2×C5semidirect
72. #1812C2×C5semidirect
73. #1395C2×C5semidirect
128. C23×C8C4×C5semidirect
136. #424C4×C5semidirect
140. #407C4×C5semidirect
141. #405C4×C5semidirect
345. C5#12805direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#29292
C5×#21202
C5×#18132
C5×#18122
C5×#13952
#128055