Finite Group Databasebeta

← C5×#7618 #11930338

Subgroups — C5×#7618 #11930338

Order 1280.

494 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C5×#124C211yesmaximal, characteristic
2C5×#1831C211yesmaximal, characteristic, complemented
3C5×#1745C211yesmaximal, characteristic, complemented
4C5×#1272C212yesmaximal, complemented
5C5×#1270C212yesmaximal
6C2×C5×#124C411yescharacteristic
7C2×C4×C5×Q8C411yescharacteristic
8C2×C4×C5×D4C411yescharacteristic
9C2×C5×C4⋊C8—21no—
10C2×C5×#97—21no—
11C5×#391C2211yescharacteristic
12C5×#390C2211yescharacteristic
13C5×#388—21no—
14C5×#388—21no—
15C5×#382C411yescharacteristic
16C4×C5×C22⋊C4—21no—
17C4×C5×C22⋊C4—21no—
18C43×C5C2211yescharacteristic
19C5×#336—21no—
20C5×#336—21no—
21C5×#336C2212yes—
22C5×#336C2212yes—
23#7618C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×Q8C2×C411yescharacteristic
25C22×C5×D4C2×C411yescharacteristic
26C23×C4×C5—21no—
27C22×C5×C8—22no—
28C22×C5×C8—22no—
29C5×#124—22no—
30C5×#124—22no—
31C4×C5×Q8—42no—
32C4×C5×D4—42no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C22⋊C4—21no—
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C42×C5—21no—
42C2×C42×C5C2×C411yescharacteristic
43C2×C42×C5C2×C411yescharacteristic
44C2×C42×C5D411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C2×C42×C5D411yescharacteristic
48C2×C42×C5C2311yescharacteristic
49C5×C4⋊C8—42no—
50C5×#97—24no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54C5×#95—21no—
55C4×#124C2×C511yescharacteristic
56#1831C2×C511yescharacteristic, complemented
57#1745C2×C511yescharacteristic, complemented
58#1272C2×C512yescomplemented
59#1270C2×C512yes—
60C24×C5—21no—
61C2×C5×Q8—21no—
62C2×C5×Q8—41no—
63C2×C5×Q8—41no—
64C2×C5×Q8M1612yes—
65C2×C5×D4—21no—
66C2×C5×D4—41no—
67C2×C5×D4—41no—
68C2×C5×D4M1612yes—
69C22×C4×C5—21no—
70C22×C4×C5—21no—
71C22×C4×C5—21no—
72C22×C4×C5—42no—
73C22×C4×C5—42no—
74C22×C4×C5—42no—
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22⋊C411yescharacteristic
77C22×C4×C5C22⋊C411yescharacteristic
78C22×C4×C5C22⋊C411yescharacteristic
79C22×C4×C5C22×C411yescharacteristic
80C22×C4×C5C2×D411yescharacteristic
81C22×C4×C5C2×D411yescharacteristic
82C2×C5×C8—24no—
83C2×C5×C8—42no—
84C2×C5×C8—42no—
85C2×C5×C8—42no—
86C2×C5×C8—42no—
87C2×C5×C8—42no—
88C5×C4⋊C4—41no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—42no—
91C5×C22⋊C4—24no—
92C5×C22⋊C4—24no—
93C5×C22⋊C4—42no—
94C5×C22⋊C4—42no—
95C5×C22⋊C4—41no—
96C5×C22⋊C4—41no—
97C42×C5—22no—
98C42×C5—22no—
99C42×C5—21no—
100C42×C5—21no—
101C42×C5—22no—
102C42×C5—21no—
103C42×C5—21no—
104C42×C5—41no—
105C42×C5—41no—
106C42×C5—42no—
107C2×#124C4×C511yescharacteristic
108C2×C4×Q8C4×C511yescharacteristic
109C2×C4×D4C4×C511yescharacteristic
110C2×C4⋊C8—21no—
111C2×#97—21no—
112#391C22×C511yescharacteristic
113#390C22×C511yescharacteristic
114#388—21no—
115#388—21no—
116#382C4×C511yescharacteristic
117C4×C22⋊C4—21no—
118C4×C22⋊C4—21no—
119C43C22×C511yescharacteristic
120#336—21no—
121#336—21no—
122#336C22×C512yes—
123#336C22×C512yes—
124C23×C5—22no—
125C23×C5—41no—
126C23×C5—41no—
127C23×C5—41no—
128C23×C5—41no—
129C23×C5—41no—
130C23×C5—41no—
131C23×C5C2×C22⋊C411yescharacteristic
132C5×Q8—42no—
133C5×Q8—42no—
134C5×D4—42no—
135C5×D4—42no—
136C2×C4×C5—21no—
137C2×C4×C5—21no—
138C2×C4×C5—21no—
139C2×C4×C5—21no—
140C2×C4×C5—21no—
141C2×C4×C5—21no—
142C2×C4×C5—21no—
143C2×C4×C5—21no—
144C2×C4×C5—21no—
145C2×C4×C5—21no—
146C2×C4×C5—21no—
147C2×C4×C5—21no—
148C2×C4×C5—22no—
149C2×C4×C5—21no—
150C2×C4×C5—21no—
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—84no—
162C2×C4×C5#10012yes—
163C2×C4×C5#10412yes—
164C2×C4×C5C2×M1611yescharacteristic
165C2×C4×C5C2×M1611yescharacteristic
166C2×C4×C5#13512yes—
167C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C5#13711yescharacteristic
169C5×C8—44no—
170C5×C8—82no—
171C22×Q8C2×C4×C511yescharacteristic
172C22×D4C2×C4×C511yescharacteristic
173C23×C4—21no—
174C22×C8—22no—
175C22×C8—22no—
176#124—22no—
177#124—22no—
178C4×Q8—42no—
179C4×D4—42no—
180C2×C4⋊C4—21no—
181C2×C4⋊C4C2×C4×C511yescharacteristic
182C2×C4⋊C4C2×C4×C511yescharacteristic
183C2×C22⋊C4—21no—
184C2×C22⋊C4—21no—
185C2×C22⋊C4—21no—
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C42—21no—
189C2×C42C2×C4×C511yescharacteristic
190C2×C42C2×C4×C511yescharacteristic
191C2×C42C5×D411yescharacteristic
192C2×C42C5×D411yescharacteristic
193C2×C42C5×D411yescharacteristic
194C2×C42C5×D411yescharacteristic
195C2×C42C23×C511yescharacteristic
196C4⋊C8—42no—
197#97—24no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202C22×C5—42no—
203C22×C5—42no—
204C22×C5—42no—
205C22×C5—81no—
206C22×C5—81no—
207C22×C5—81no—
208C22×C5—81no—
209C22×C5#40711yescharacteristic
210C22×C5#41011yescharacteristic
211C22×C5C2×#10011yescharacteristic
212C22×C5#41611yescharacteristic
213C22×C5#41711yescharacteristic
214C22×C5C2×#10411yescharacteristic
215C22×C5#42111yescharacteristic
216C4×C5—22no—
217C4×C5—21no—
218C4×C5—21no—
219C4×C5—22no—
220C4×C5—21no—
221C4×C5—21no—
222C4×C5—22no—
223C4×C5—42no—
224C4×C5—41no—
225C4×C5—41no—
226C4×C5—81no—
227C4×C5—81no—
228C24—21no—
229C2×Q8—21no—
230C2×Q8—41no—
231C2×Q8—41no—
232C2×Q8C5×M1612yes—
233C2×D4—21no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4C5×M1612yes—
237C22×C4—21no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—42no—
241C22×C4—42no—
242C22×C4—42no—
243C22×C4C5×C22⋊C411yescharacteristic
244C22×C4C5×C22⋊C411yescharacteristic
245C22×C4C5×C22⋊C411yescharacteristic
246C22×C4C5×C22⋊C411yescharacteristic
247C22×C4C22×C4×C511yescharacteristic
248C22×C4C2×C5×D411yescharacteristic
249C22×C4C2×C5×D411yescharacteristic
250C2×C8—24no—
251C2×C8—42no—
252C2×C8—42no—
253C2×C8—42no—
254C2×C8—42no—
255C2×C8—42no—
256C4⋊C4—41no—
257C4⋊C4—41no—
258C4⋊C4—42no—
259C22⋊C4—24no—
260C22⋊C4—24no—
261C22⋊C4—42no—
262C22⋊C4—41no—
263C22⋊C4—41no—
264C22⋊C4—42no—
265C42—21no—
266C42—21no—
267C42—22no—
268C42—21no—
269C42—21no—
270C42—22no—
271C42—22no—
272C42—41no—
273C42—41no—
274C42—42no—
275C2×C5—82no—
276C2×C5#146611yescharacteristic
277C2×C5#148811yescharacteristic
278C2×C5#148911yescharacteristic
279C2×C5#150011yescharacteristic
280C2×C5#151211yescharacteristic
281C2×C5#152711yescharacteristic
282C2×C5#155111yescharacteristic
283C23—22no—
284C23—41no—
285C23—41no—
286C23—41no—
287C23—41no—
288C23—41no—
289C23—41no—
290C23C2×C5×C22⋊C411yescharacteristic
291Q8—42no—
292Q8—42no—
293D4—42no—
294D4—42no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—22no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—84no—
321C2×C4C5×#10012yes—
322C2×C4C5×#10412yes—
323C2×C4C2×C5×M1611yescharacteristic
324C2×C4C2×C5×M1611yescharacteristic
325C2×C4C5×#13512yes—
326C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
327C2×C4C5×#13711yescharacteristic
328C8—44no—
329C8—82no—
330C5#761811yescharacteristic, direct product factor, Sylow
331C22—42no—
332C22—42no—
333C22—42no—
334C22—81no—
335C22—81no—
336C22—81no—
337C22—81no—
338C22C5×#40711yescharacteristic
339C22C5×#41011yescharacteristic
340C22C2×C5×#10011yescharacteristic
341C22C5×#41611yescharacteristic
342C22C5×#41711yescharacteristic
343C22C2×C5×#10411yescharacteristic
344C22C5×#42111yescharacteristic
345C4—22no—
346C4—21no—
347C4—21no—
348C4—22no—
349C4—22no—
350C4—21no—
351C4—21no—
352C4—42no—
353C4—41no—
354C4—41no—
355C4—81no—
356C4—81no—
357C2—82no—
358C2C5×#146611yescharacteristic
359C2C5×#148811yescharacteristic
360C2C5×#148911yescharacteristic
361C2C5×#150011yescharacteristic
362C2C5×#151211yescharacteristic
363C2C5×#152711yescharacteristic
364C2C5×#155111yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC22×C5×D4C2×C4
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
2. C5×#1831C2semidirect
3. C5×#1745C2semidirect
4. C5×#1272C2semidirect
23. #7618C5direct (N × H)
56. #1831C2×C5semidirect
57. #1745C2×C5semidirect
58. #1272C2×C5semidirect
330. C5#7618direct (N × H)

Maximal subgroups

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

subgroupindex
C4×C5×#1242
C5×#18312
C5×#17452
C5×#12722
C5×#12702
#76185