Finite Group Databasebeta

← C5×#7718 #11930438

Subgroups — C5×#7718 #11930438

Order 1280.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#2854C211yesmaximal, characteristic
2C5×#1817C211yesmaximal, characteristic, complemented
3C5×#1817C211yesmaximal, characteristic, complemented
4C5×#1271C212yesmaximal, complemented
5C5×#1270C212yesmaximal, complemented
6C2×C5×#123—21no—
7C2×C5×#121C411yescharacteristic
8C22×C42×C5C2211yescharacteristic
9C2×C5×C22⋊C8—21no—
10C2×C5×C22⋊C8—21no—
11C5×#390C411yescharacteristic
12C5×#390C2211yescharacteristic
13C5×#389C411yescharacteristic
14C5×#389C2211yescharacteristic
15C5×#388—21no—
16C5×#388—21no—
17C5×#386—21no—
18C5×#380C411yescharacteristic
19C5×#336—21no—
20C5×#336—21no—
21C5×#336C2212yes—
22C5×#336C2212yes—
23#7718C511yesmaximal, characteristic, direct product factor, Sylow
24C22×C5×D4—21no—
25C22×C5×D4C2×C411yescharacteristic
26C23×C4×C5C2×C411yescharacteristic
27C23×C4×C5D411yescharacteristic
28C23×C4×C5D411yescharacteristic
29C22×C5×C8—22no—
30C22×C5×C8—22no—
31C5×#123—44no—
32C5×#121—42no—
33C2×C5×C4⋊C4—21no—
34C2×C5×C4⋊C4—21no—
35C2×C5×C4⋊C4C2×C411yescharacteristic
36C2×C5×C4⋊C4C2×C411yescharacteristic
37C2×C5×C4⋊C4C2×C411yescharacteristic
38C2×C5×C22⋊C4—21no—
39C2×C5×C22⋊C4—21no—
40C2×C5×C22⋊C4—21no—
41C2×C5×C22⋊C4—21no—
42C2×C5×C22⋊C4—21no—
43C2×C5×C22⋊C4—21no—
44C2×C42×C5—42no—
45C2×C42×C5C2×C411yescharacteristic
46C2×C42×C5D411yescharacteristic
47C2×C42×C5D411yescharacteristic
48C2×C42×C5C2311yescharacteristic
49C5×C22⋊C8—42no—
50C5×C22⋊C8—42no—
51C5×#95—21no—
52C5×#95—21no—
53C5×#95—21no—
54#2854C2×C511yescharacteristic
55#1817C2×C511yescharacteristic, complemented
56#1817C2×C511yescharacteristic, complemented
57#1271C2×C512yescomplemented
58#1270C2×C512yescomplemented
59C24×C5—21no—
60C24×C5C22⋊C411yescharacteristic
61C2×C5×D4—22no—
62C2×C5×D4—41no—
63C2×C5×D4—41no—
64C2×C5×D4—42no—
65C2×C5×D4—42no—
66C2×C5×D4—42no—
67C22×C4×C5—22no—
68C22×C4×C5—22no—
69C22×C4×C5—22no—
70C22×C4×C5—22no—
71C22×C4×C5—22no—
72C22×C4×C5—22no—
73C22×C4×C5—21no—
74C22×C4×C5—21no—
75C22×C4×C5—21no—
76C22×C4×C5—41no—
77C22×C4×C5—41no—
78C22×C4×C5—41no—
79C22×C4×C5C22⋊C411yescharacteristic
80C22×C4×C5C22⋊C411yescharacteristic
81C22×C4×C5C22⋊C411yescharacteristic
82C22×C4×C5C22×C411yescharacteristic
83C22×C4×C5C2×D411yescharacteristic
84C22×C4×C5C2×D411yescharacteristic
85C2×C5×C8—42no—
86C2×C5×C8—42no—
87C2×C5×C8—42no—
88C2×C5×C8—42no—
89C2×C5×C8—42no—
90C2×C5×C8—42no—
91C5×C4⋊C4—22no—
92C5×C4⋊C4—41no—
93C5×C4⋊C4—41no—
94C5×C4⋊C4—42no—
95C5×C4⋊C4—42no—
96C5×C22⋊C4—42no—
97C5×C22⋊C4—42no—
98C5×C22⋊C4—42no—
99C5×C22⋊C4—42no—
100C5×C22⋊C4—42no—
101C5×C22⋊C4—42no—
102C42×C5—41no—
103C42×C5—41no—
104C42×C5—41no—
105C42×C5—41no—
106C2×#123—21no—
107C2×#121C4×C511yescharacteristic
108C22×C42C22×C511yescharacteristic
109C2×C22⋊C8—21no—
110C2×C22⋊C8—21no—
111#390C4×C511yescharacteristic
112#390C22×C511yescharacteristic
113#389C4×C511yescharacteristic
114#389C22×C511yescharacteristic
115#388—21no—
116#388—21no—
117#386—21no—
118#380C4×C511yescharacteristic
119#336—21no—
120#336—21no—
121#336C22×C512yes—
122#336C22×C512yes—
123C23×C5—21no—
124C23×C5—21no—
125C23×C5—21no—
126C23×C5—21no—
127C23×C5—21no—
128C23×C5—21no—
129C23×C5—41no—
130C23×C5—41no—
131C23×C5—41no—
132C23×C5—41no—
133C23×C5—41no—
134C23×C5—41no—
135C23×C5—41no—
136C23×C5#9912yes—
137C23×C5C2×C22⋊C411yescharacteristic
138C5×D4—82no—
139C5×D4—84no—
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—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—44no—
156C2×C4×C5—44no—
157C2×C4×C5—44no—
158C2×C4×C5—41no—
159C2×C4×C5—41no—
160C2×C4×C5—41no—
161C2×C4×C5—41no—
162C2×C4×C5—41no—
163C2×C4×C5—41no—
164C2×C4×C5—41no—
165C2×C4×C5—41no—
166C2×C4×C5—41no—
167C2×C4×C5#13112yes—
168C2×C4×C5#13512yes—
169C2×C4×C5AGL(1,ℤ/8)12yes—
170C5×C8—82no—
171C5×C8—82no—
172C22×D4—21no—
173C22×D4C2×C4×C511yescharacteristic
174C23×C4C2×C4×C511yescharacteristic
175C23×C4C5×D411yescharacteristic
176C23×C4C5×D411yescharacteristic
177C22×C8—22no—
178C22×C8—22no—
179#123—44no—
180#121—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×C22⋊C4—21no—
192C2×C42—42no—
193C2×C42C2×C4×C511yescharacteristic
194C2×C42C5×D411yescharacteristic
195C2×C42C5×D411yescharacteristic
196C2×C42C23×C511yescharacteristic
197C22⋊C8—42no—
198C22⋊C8—42no—
199#95—21no—
200#95—21no—
201#95—21no—
202C22×C5—22no—
203C22×C5—22no—
204C22×C5—22no—
205C22×C5—41no—
206C22×C5—41no—
207C22×C5—41no—
208C22×C5—41no—
209C22×C5—81no—
210C22×C5—81no—
211C22×C5—81no—
212C22×C5—81no—
213C22×C5—81no—
214C22×C5—81no—
215C22×C5—81no—
216C22×C5#40811yescharacteristic
217C22×C5C2×#9911yescharacteristic
218C22×C5#41311yescharacteristic
219C22×C5#41611yescharacteristic
220C22×C5#41811yescharacteristic
221C22×C5#42111yescharacteristic
222C22×C5#42111yescharacteristic
223C4×C5—22no—
224C4×C5—22no—
225C4×C5—22no—
226C4×C5—41no—
227C4×C5—41no—
228C4×C5—41no—
229C4×C5—81no—
230C4×C5—81no—
231C4×C5—81no—
232C24—21no—
233C24C5×C22⋊C411yescharacteristic
234C2×D4—22no—
235C2×D4—41no—
236C2×D4—41no—
237C2×D4—42no—
238C2×D4—42no—
239C2×D4—42no—
240C22×C4—22no—
241C22×C4—22no—
242C22×C4—22no—
243C22×C4—22no—
244C22×C4—22no—
245C22×C4—22no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—21no—
249C22×C4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4C5×C22⋊C411yescharacteristic
253C22×C4C5×C22⋊C411yescharacteristic
254C22×C4C5×C22⋊C411yescharacteristic
255C22×C4C22×C4×C511yescharacteristic
256C22×C4C2×C5×D411yescharacteristic
257C22×C4C2×C5×D411yescharacteristic
258C2×C8—42no—
259C2×C8—42no—
260C2×C8—42no—
261C2×C8—42no—
262C2×C8—42no—
263C2×C8—42no—
264C4⋊C4—22no—
265C4⋊C4—41no—
266C4⋊C4—41no—
267C4⋊C4—42no—
268C4⋊C4—42no—
269C22⋊C4—42no—
270C22⋊C4—42no—
271C22⋊C4—42no—
272C22⋊C4—42no—
273C22⋊C4—42no—
274C22⋊C4—42no—
275C42—41no—
276C42—41no—
277C42—41no—
278C42—41no—
279C2×C5—42no—
280C2×C5—161no—
281C2×C5#146811yescharacteristic
282C2×C5#148211yescharacteristic
283C2×C5#149611yescharacteristic
284C2×C5#151011yescharacteristic
285C2×C5#151611yescharacteristic
286C2×C5#153511yescharacteristic
287C2×C5#155311yescharacteristic
288C23—21no—
289C23—21no—
290C23—21no—
291C23—21no—
292C23—21no—
293C23—21no—
294C23—41no—
295C23—41no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23—41no—
301C23C5×#9912yes—
302C23C2×C5×C22⋊C411yescharacteristic
303D4—82no—
304D4—84no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—44no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—41no—
328C2×C4—41no—
329C2×C4—41no—
330C2×C4—41no—
331C2×C4—41no—
332C2×C4C5×#13112yes—
333C2×C4C5×#13512yes—
334C2×C4C5×AGL(1,ℤ/8)12yes—
335C8—82no—
336C8—82no—
337C5#771811yescharacteristic, direct product factor, Sylow
338C22—22no—
339C22—22no—
340C22—22no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—81no—
346C22—81no—
347C22—81no—
348C22—81no—
349C22—81no—
350C22—81no—
351C22—81no—
352C22C5×#40811yescharacteristic
353C22C2×C5×#9911yescharacteristic
354C22C5×#41311yescharacteristic
355C22C5×#41611yescharacteristic
356C22C5×#41811yescharacteristic
357C22C5×#42111yescharacteristic
358C22C5×#42111yescharacteristic
359C4—22no—
360C4—22no—
361C4—22no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—81no—
366C4—81no—
367C4—81no—
368C2—42no—
369C2—161no—
370C2C5×#146811yescharacteristic
371C2C5×#148211yescharacteristic
372C2C5×#149611yescharacteristic
373C2C5×#151011yescharacteristic
374C2C5×#151611yescharacteristic
375C2C5×#153511yescharacteristic
376C2C5×#155311yescharacteristic
subgroupG/H
center, socleC23×C5C2×C22⋊C4
commutatorC22×C4C22×C4×C5
Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#121C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C22×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1817C2semidirect
3. C5×#1817C2semidirect
4. C5×#1271C2semidirect
5. C5×#1270C2semidirect
23. #7718C5direct (N × H)
55. #1817C2×C5semidirect
56. #1817C2×C5semidirect
57. #1271C2×C5semidirect
58. #1270C2×C5semidirect
337. C5#7718direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#28542
C5×#18172
C5×#12712
C5×#12702
#77185