Finite Group Databasebeta

← C5×#7614 #11930334

Subgroups — C5×#7614 #11930334

Order 1280.

504 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2293C211yesmaximal, characteristic
2C5×#1831C211yesmaximal, characteristic, complemented
3C5×#1767C211yesmaximal, characteristic, complemented
4C5×#1271C212yesmaximal, complemented
5C5×#1270C212yesmaximal
6C2×C4×C5×D4C411yescharacteristic
7C2×C5×#117—21no—
8C2×C5×C4⋊C8—21no—
9C2×C5×C4⋊C8—21no—
10C2×C5×#97—21no—
11C5×#390C411yescharacteristic
12C5×#390C2211yescharacteristic
13C5×#389C411yescharacteristic
14C5×#389C2211yescharacteristic
15C5×#388—21no—
16C5×#388—21no—
17C4×C5×C4⋊C4C411yescharacteristic
18C4×C5×C22⋊C4—21no—
19C43×C5C2211yescharacteristic
20C5×#336—21no—
21C5×#336C2212yes—
22C5×#336C2212yes—
23#7614C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×D4C2×C411yescharacteristic
25C23×C4×C5—21no—
26C22×C5×C8—22no—
27C22×C5×C8—22no—
28C4×C5×D4—22no—
29C4×C5×D4—22no—
30C5×#117—42no—
31C5×#117—42no—
32C2×C5×C4⋊C4—21no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4C2×C411yescharacteristic
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C22⋊C4—21no—
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C42×C5—21no—
43C2×C42×C5C2×C411yescharacteristic
44C2×C42×C5C2×C411yescharacteristic
45C2×C42×C5D411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C2×C42×C5D411yescharacteristic
48C2×C42×C5D411yescharacteristic
49C2×C42×C5C2311yescharacteristic
50C5×C4⋊C8—24no—
51C5×C4⋊C8—42no—
52C5×#97—42no—
53C5×#95—21no—
54C5×#95—21no—
55C5×#95—21no—
56#2293C2×C511yescharacteristic
57#1831C2×C511yescharacteristic, complemented
58#1767C2×C511yescharacteristic, complemented
59#1271C2×C512yescomplemented
60#1270C2×C512yes—
61C24×C5—21no—
62C2×C5×D4—21no—
63C2×C5×D4—41no—
64C2×C5×D4—41no—
65C2×C5×D4M1612yes—
66C22×C4×C5—24no—
67C22×C4×C5—21no—
68C22×C4×C5—21no—
69C22×C4×C5—21no—
70C22×C4×C5—42no—
71C22×C4×C5—42no—
72C22×C4×C5C22⋊C411yescharacteristic
73C22×C4×C5C22⋊C411yescharacteristic
74C22×C4×C5C22⋊C411yescharacteristic
75C22×C4×C5C22⋊C411yescharacteristic
76C22×C4×C5C22×C411yescharacteristic
77C22×C4×C5C2×D411yescharacteristic
78C22×C4×C5C2×D411yescharacteristic
79C2×C5×C8—24no—
80C2×C5×C8—42no—
81C2×C5×C8—42no—
82C2×C5×C8—42no—
83C2×C5×C8—42no—
84C2×C5×C8—42no—
85C5×C4⋊C4—21no—
86C5×C4⋊C4—41no—
87C5×C4⋊C4—41no—
88C5×C4⋊C4—42no—
89C5×C4⋊C4—41no—
90C5×C4⋊C4—41no—
91C5×C4⋊C4M1612yes—
92C5×C22⋊C4—24no—
93C5×C22⋊C4—42no—
94C5×C22⋊C4—42no—
95C5×C22⋊C4—41no—
96C5×C22⋊C4—41no—
97C5×C22⋊C4—41no—
98C5×C22⋊C4—41no—
99C42×C5—22no—
100C42×C5—21no—
101C42×C5—21no—
102C42×C5—21no—
103C42×C5—21no—
104C42×C5—41no—
105C42×C5—41no—
106C42×C5—41no—
107C42×C5—42no—
108C42×C5D812yes—
109C42×C5SD1612yes—
110C2×C4×D4C4×C511yescharacteristic
111C2×#117—21no—
112C2×C4⋊C8—21no—
113C2×C4⋊C8—21no—
114C2×#97—21no—
115#390C4×C511yescharacteristic
116#390C22×C511yescharacteristic
117#389C4×C511yescharacteristic
118#389C22×C511yescharacteristic
119#388—21no—
120#388—21no—
121C4×C4⋊C4C4×C511yescharacteristic
122C4×C22⋊C4—21no—
123C43C22×C511yescharacteristic
124#336—21no—
125#336C22×C512yes—
126#336C22×C512yes—
127C23×C5—22no—
128C23×C5—41no—
129C23×C5—41no—
130C23×C5—41no—
131C23×C5—41no—
132C23×C5—41no—
133C23×C5—41no—
134C23×C5C2×C22⋊C411yescharacteristic
135C5×D4—42no—
136C5×D4—42no—
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—21no—
149C2×C4×C5—21no—
150C2×C4×C5—22no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—48no—
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#10212yes—
163C2×C4×C5#10212yes—
164C2×C4×C5#10412yes—
165C2×C4×C5C2×M1611yescharacteristic
166C2×C4×C5C2×M1611yescharacteristic
167C2×C4×C5C2×D811yescharacteristic
168C2×C4×C5C2×SD1611yescharacteristic
169C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C5#13711yescharacteristic
171C5×C8—44no—
172C5×C8—82no—
173C22×D4C2×C4×C511yescharacteristic
174C23×C4—21no—
175C22×C8—22no—
176C22×C8—22no—
177C4×D4—22no—
178C4×D4—22no—
179#117—42no—
180#117—42no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4C2×C4×C511yescharacteristic
184C2×C4⋊C4C2×C4×C511yescharacteristic
185C2×C4⋊C4C2×C4×C511yescharacteristic
186C2×C22⋊C4—21no—
187C2×C22⋊C4—21no—
188C2×C22⋊C4—21no—
189C2×C22⋊C4—21no—
190C2×C22⋊C4—21no—
191C2×C42—21no—
192C2×C42C2×C4×C511yescharacteristic
193C2×C42C2×C4×C511yescharacteristic
194C2×C42C5×D411yescharacteristic
195C2×C42C5×D411yescharacteristic
196C2×C42C5×D411yescharacteristic
197C2×C42C5×D411yescharacteristic
198C2×C42C23×C511yescharacteristic
199C4⋊C8—24no—
200C4⋊C8—42no—
201#97—42no—
202#95—21no—
203#95—21no—
204#95—21no—
205C22×C5—42no—
206C22×C5—42no—
207C22×C5—42no—
208C22×C5—81no—
209C22×C5—81no—
210C22×C5—81no—
211C22×C5—81no—
212C22×C5#40711yescharacteristic
213C22×C5#41011yescharacteristic
214C22×C5#41311yescharacteristic
215C22×C5C2×#10211yescharacteristic
216C22×C5#41711yescharacteristic
217C22×C5C2×#10411yescharacteristic
218C22×C5#42111yescharacteristic
219C4×C5—22no—
220C4×C5—21no—
221C4×C5—21no—
222C4×C5—22no—
223C4×C5—21no—
224C4×C5—21no—
225C4×C5—21no—
226C4×C5—21no—
227C4×C5—22no—
228C4×C5—42no—
229C4×C5—41no—
230C4×C5—81no—
231C4×C5—81no—
232C24—21no—
233C2×D4—21no—
234C2×D4—41no—
235C2×D4—41no—
236C2×D4C5×M1612yes—
237C22×C4—24no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—21no—
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—21no—
257C4⋊C4—41no—
258C4⋊C4—41no—
259C4⋊C4—41no—
260C4⋊C4—41no—
261C4⋊C4—42no—
262C4⋊C4C5×M1612yes—
263C22⋊C4—24no—
264C22⋊C4—41no—
265C22⋊C4—41no—
266C22⋊C4—41no—
267C22⋊C4—41no—
268C22⋊C4—42no—
269C22⋊C4—42no—
270C42—21no—
271C42—21no—
272C42—21no—
273C42—21no—
274C42—22no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42—42no—
279C42C5×D812yes—
280C42C5×SD1612yes—
281C2×C5—82no—
282C2×C5#146411yescharacteristic
283C2×C5#148611yescharacteristic
284C2×C5#148911yescharacteristic
285C2×C5#150211yescharacteristic
286C2×C5#151211yescharacteristic
287C2×C5#153211yescharacteristic
288C2×C5#154711yescharacteristic
289C23—22no—
290C23—41no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—41no—
296C23C2×C5×C22⋊C411yescharacteristic
297D4—42no—
298D4—42no—
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—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—22no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—48no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4C5×#10212yes—
325C2×C4C5×#10212yes—
326C2×C4C5×#10412yes—
327C2×C4C2×C5×M1611yescharacteristic
328C2×C4C2×C5×M1611yescharacteristic
329C2×C4C2×C5×D811yescharacteristic
330C2×C4C2×C5×SD1611yescharacteristic
331C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
332C2×C4C5×#13711yescharacteristic
333C8—44no—
334C8—82no—
335C5#761411yescharacteristic, direct product factor, Sylow
336C22—42no—
337C22—42no—
338C22—42no—
339C22—81no—
340C22—81no—
341C22—81no—
342C22—81no—
343C22C5×#40711yescharacteristic
344C22C5×#41011yescharacteristic
345C22C5×#41311yescharacteristic
346C22C2×C5×#10211yescharacteristic
347C22C5×#41711yescharacteristic
348C22C2×C5×#10411yescharacteristic
349C22C5×#42111yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—22no—
356C4—21no—
357C4—21no—
358C4—22no—
359C4—42no—
360C4—41no—
361C4—81no—
362C4—81no—
363C2—82no—
364C2C5×#146411yescharacteristic
365C2C5×#148611yescharacteristic
366C2C5×#148911yescharacteristic
367C2C5×#150211yescharacteristic
368C2C5×#151211yescharacteristic
369C2C5×#153211yescharacteristic
370C2C5×#154711yescharacteristic
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×#1767C2semidirect
4. C5×#1271C2semidirect
23. #7614C5direct (N × H)
57. #1831C2×C5semidirect
58. #1767C2×C5semidirect
59. #1271C2×C5semidirect
335. C5#7614direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#22932
C5×#18312
C5×#17672
C5×#12712
C5×#12702
#76145