Finite Group Databasebeta

← C5×#13026 #11935746

Subgroups — C5×#13026 #11935746

Order 1280.

486 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#510C211yesmaximal, characteristic
2C5×#2943C211yesmaximal, characteristic
3C2×C5×#360C211yesmaximal, characteristic
4C5×#2141C211yesmaximal, characteristic, complemented
5C5×#1971C211yesmaximal, characteristic, complemented
6C5×#1386C211yesmaximal, characteristic, complemented
7C5×#1377C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C22×C5×Q16C2211yescharacteristic
10C4×C5×#41—21no—
11C5×#510—22no—
12C5×#510C414yescomplemented
13C2×C5×Q32—21no—
14C2×C5×SD32—21no—
15C2×C5×M32C2211yescharacteristic
16C2×C5×M32C2211yescharacteristic
17C5×#442—21no—
18C5×#441—21no—
19C5×#440—22no—
20C5×#427C2211yescharacteristic
21C2×C5×#106C2211yescharacteristic
22C5×#416—21no—
23C2×C5×#103—21no—
24C2×C5×#97C2211yescharacteristic
25C5×#391—21no—
26C5×#360—22no—
27C5×#358—22no—
28#13026C511yesmaximal, characteristic, direct product factor, Sylow
29C2×C5×#41—21no—
30C22×C5×Q8—21no—
31C5×#135—21no—
32C5×#135—21no—
33C5×#135C2×C412yes—
34C5×#135D412yes—
35C2×C5×Q16—21no—
36C2×C5×Q16—21no—
37C2×C5×Q16—21no—
38C2×C5×Q16—21no—
39C2×C5×Q16—21no—
40C2×C5×Q16C2×C412yescomplemented
41C2×C5×Q16D411yescharacteristic
42C2×C5×SD16—21no—
43C2×C5×D8D411yescharacteristic
44C22×C5×C8D411yescharacteristic
45C22×C5×C8C2311yescharacteristic
46C4×C5×Q8—22no—
47C4×C5×D4—22no—
48C4×C5×D4—42no—
49C5×#117—21no—
50C5×#117—41no—
51C2×C5×C4⋊C4—21no—
52C2×C42×C5—41no—
53C2×C42×C5D411yescharacteristic
54C5×Q32—24no—
55C5×SD32—24no—
56C5×M32—21no—
57C5×M32—21no—
58C5×M32—21no—
59C5×M32C2×C412yescomplemented
60C2×C5×C16—21no—
61C2×C5×C16—21no—
62C5×#107D412yes—
63C5×#106—21no—
64C5×#106—21no—
65C5×#106—21no—
66C5×#103—22no—
67C5×#103—42no—
68C5×#102—22no—
69C5×#97—21no—
70C5×#97—21no—
71C5×#95—42no—
72C2×#510C2×C511yescharacteristic
73#2943C2×C511yescharacteristic
74C2×#360C2×C511yescharacteristic
75#2141C2×C511yescharacteristic, complemented
76#1971C2×C511yescharacteristic, complemented
77#1386C2×C511yescharacteristic, complemented
78#1377C2×C511yescharacteristic, complemented
79C5×#41—22no—
80C5×#41—22no—
81C5×#41—41no—
82C5×#41—41no—
83C2×C5×Q8—22no—
84C2×C5×Q8—21no—
85C2×C5×Q8—41no—
86C2×C5×Q8—41no—
87C2×C5×Q8—41no—
88C2×C5×Q8—41no—
89C2×C5×Q8—41no—
90C2×C5×D4—21no—
91C2×C5×D4—41no—
92C22×C4×C5—42no—
93C22×C4×C5—41no—
94C22×C4×C5—41no—
95C22×C4×C5—41no—
96C22×C4×C5D812yes—
97C22×C4×C5C2×D411yescharacteristic
98C5×Q16—22no—
99C5×Q16—22no—
100C5×Q16—21no—
101C5×Q16—41no—
102C5×Q16—41no—
103C5×Q16C22⋊C412yes—
104C5×SD16—22no—
105C5×SD16—22no—
106C5×D8—21no—
107C5×D8C22⋊C412yes—
108C2×C5×C8—21no—
109C2×C5×C8—21no—
110C2×C5×C8—21no—
111C2×C5×C8C22×C411yescharacteristic
112C2×C5×C8C2×D411yescharacteristic
113C2×C5×C8C2×D411yescharacteristic
114C2×C5×C8C2×D411yescharacteristic
115C2×C5×C8#4111yescharacteristic
116C2×C5×C8#4111yescharacteristic
117C5×C4⋊C4—22no—
118C5×C4⋊C4—42no—
119C5×C4⋊C4—41no—
120C5×C4⋊C4—41no—
121C5×C22⋊C4—42no—
122C5×C22⋊C4—41no—
123C42×C5—21no—
124C42×C5—21no—
125C42×C5—42no—
126C42×C5—41no—
127C5×C16—22no—
128C5×C16—41no—
129C2×#135C22×C511yescharacteristic
130C22×Q16C22×C511yescharacteristic
131C4×#41—21no—
132#510—22no—
133#510C4×C514yescomplemented
134C2×Q32—21no—
135C2×SD32—21no—
136C2×M32C22×C511yescharacteristic
137C2×M32C22×C511yescharacteristic
138#442—21no—
139#441—21no—
140#440—22no—
141#427C22×C511yescharacteristic
142C2×#106C22×C511yescharacteristic
143#416—21no—
144C2×#103—21no—
145C2×#97C22×C511yescharacteristic
146#391—21no—
147#360—22no—
148#358—22no—
149C23×C5—41no—
150C23×C5C2×D811yescharacteristic
151C5×Q8—22no—
152C5×Q8—41no—
153C5×Q8—42no—
154C5×Q8—42no—
155C5×Q8—81no—
156C5×Q8—81no—
157C5×D4—22no—
158C5×D4—42no—
159C5×D4—42no—
160C5×D4—41no—
161C2×C4×C5—22no—
162C2×C4×C5—41no—
163C2×C4×C5—42no—
164C2×C4×C5—42no—
165C2×C4×C5—42no—
166C2×C4×C5—42no—
167C2×C4×C5—42no—
168C2×C4×C5—84no—
169C2×C4×C5—81no—
170C2×C4×C5—81no—
171C2×C4×C5—82no—
172C2×C4×C5—81no—
173C2×C4×C5C4×D411yescharacteristic
174C2×C4×C5#12011yescharacteristic
175C2×C4×C5#12111yescharacteristic
176C2×C4×C5#13511yescharacteristic
177C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
178C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
179C5×C8—41no—
180C5×C8C2×C22⋊C411yescharacteristic
181C5×C8C4×D411yescharacteristic
182C5×C8#12111yescharacteristic
183C5×C8#12311yescharacteristic
184C2×#41—21no—
185C22×Q8—21no—
186#135—21no—
187#135—21no—
188#135C2×C4×C512yes—
189#135C5×D412yes—
190C2×Q16—21no—
191C2×Q16—21no—
192C2×Q16—21no—
193C2×Q16—21no—
194C2×Q16—21no—
195C2×Q16C2×C4×C512yescomplemented
196C2×Q16C5×D411yescharacteristic
197C2×SD16—21no—
198C2×D8C5×D411yescharacteristic
199C22×C8C5×D411yescharacteristic
200C22×C8C23×C511yescharacteristic
201C4×Q8—22no—
202C4×D4—22no—
203C4×D4—42no—
204#117—21no—
205#117—41no—
206C2×C4⋊C4—21no—
207C2×C42—41no—
208C2×C42C5×D411yescharacteristic
209Q32—24no—
210SD32—24no—
211M32—21no—
212M32—21no—
213M32—21no—
214M32C2×C4×C512yescomplemented
215C2×C16—21no—
216C2×C16—21no—
217#107C5×D412yes—
218#106—21no—
219#106—21no—
220#106—21no—
221#103—22no—
222#103—42no—
223#102—22no—
224#97—21no—
225#97—21no—
226#95—42no—
227C22×C5—22no—
228C22×C5—42no—
229C22×C5—82no—
230C22×C5C4×D811yescharacteristic
231C22×C5#44711yescharacteristic
232C22×C5#45911yescharacteristic
233C4×C5—42no—
234C4×C5—42no—
235C4×C5—82no—
236C4×C5—82no—
237C4×C5—161no—
238C4×C5#38611yescharacteristic
239C4×C5#44211yescharacteristic
240C4×C5#44911yescharacteristic
241C4×C5#46311yescharacteristic
242#41—22no—
243#41—22no—
244#41—41no—
245#41—41no—
246C2×Q8—22no—
247C2×Q8—21no—
248C2×Q8—41no—
249C2×Q8—41no—
250C2×Q8—41no—
251C2×Q8—41no—
252C2×Q8—41no—
253C2×D4—21no—
254C2×D4—41no—
255C22×C4—42no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—41no—
259C22×C4C5×D812yes—
260C22×C4C2×C5×D411yescharacteristic
261Q16—22no—
262Q16—22no—
263Q16—21no—
264Q16—41no—
265Q16—41no—
266Q16C5×C22⋊C412yes—
267SD16—22no—
268SD16—22no—
269D8—21no—
270D8C5×C22⋊C412yes—
271C2×C8—21no—
272C2×C8—21no—
273C2×C8—21no—
274C2×C8C22×C4×C511yescharacteristic
275C2×C8C2×C5×D411yescharacteristic
276C2×C8C2×C5×D411yescharacteristic
277C2×C8C2×C5×D411yescharacteristic
278C2×C8C5×#4111yescharacteristic
279C2×C8C5×#4111yescharacteristic
280C4⋊C4—22no—
281C4⋊C4—42no—
282C4⋊C4—41no—
283C4⋊C4—41no—
284C22⋊C4—42no—
285C22⋊C4—41no—
286C42—21no—
287C42—21no—
288C42—42no—
289C42—41no—
290C16—22no—
291C16—41no—
292C2×C5—21no—
293C2×C5—21no—
294C2×C5—82no—
295C2×C5#187911yescharacteristic
296C2×C5#219112yes—
297C23—41no—
298C23C2×C5×D811yescharacteristic
299Q8—22no—
300Q8—41no—
301Q8—42no—
302Q8—42no—
303Q8—81no—
304Q8—81no—
305D4—22no—
306D4—42no—
307D4—42no—
308D4—41no—
309C2×C4—22no—
310C2×C4—41no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—42no—
314C2×C4—42no—
315C2×C4—42no—
316C2×C4—84no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—82no—
320C2×C4—81no—
321C2×C4C4×C5×D411yescharacteristic
322C2×C4C5×#12011yescharacteristic
323C2×C4C5×#12111yescharacteristic
324C2×C4C5×#13511yescharacteristic
325C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
326C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
327C8—41no—
328C8C2×C5×C22⋊C411yescharacteristic
329C8C4×C5×D411yescharacteristic
330C8C5×#12111yescharacteristic
331C8C5×#12311yescharacteristic
332C5#1302611yescharacteristic, direct product factor, Sylow
333C22—22no—
334C22—42no—
335C22—82no—
336C22C4×C5×D811yescharacteristic
337C22C5×#44711yescharacteristic
338C22C5×#45911yescharacteristic
339C4—42no—
340C4—42no—
341C4—82no—
342C4—82no—
343C4—161no—
344C4C5×#38611yescharacteristic
345C4C5×#44211yescharacteristic
346C4C5×#44911yescharacteristic
347C4C5×#46311yescharacteristic
348C2—21no—
349C2—21no—
350C2—82no—
351C2C5×#187911yescharacteristic
352C2C5×#219112yes—
subgroupG/H
center, socleC22×C5#447
commutatorC2×C8C22×C4×C5
Frattini, cosocleC22×C8C23×C5
prime radicalC2×C5×#135C22
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#97 ◁ G

Complements

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

NH ≅ G/Ntype
4. C5×#2141C2semidirect
5. C5×#1971C2semidirect
6. C5×#1386C2semidirect
7. C5×#1377C2semidirect
12. C5×#510C4semidirect
28. #13026C5direct (N × H)
40. C2×C5×Q16C2×C4semidirect
59. C5×M32C2×C4semidirect
75. #2141C2×C5semidirect
76. #1971C2×C5semidirect
77. #1386C2×C5semidirect
78. #1377C2×C5semidirect
133. #510C4×C5semidirect
195. C2×Q16C2×C4×C5semidirect
214. M32C2×C4×C5semidirect
332. C5#13026direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5102
C5×#29432
C2×C5×#3602
C5×#21412
C5×#19712
C5×#13862
C5×#13772
#130265