Finite Group Databasebeta

← C5×#10441 #11933161

Subgroups — C5×#10441 #11933161

Order 1280.

492 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#459C211yesmaximal, characteristic
2C5×#1800C211yesmaximal, characteristic, complemented
3C5×#1570C211yesmaximal, characteristic, complemented
4C5×#1545C211yesmaximal, characteristic, complemented
5C5×#1545C211yesmaximal, characteristic, complemented
6C5×#1478C211yesmaximal, characteristic, complemented
7C5×#1301C211yesmaximal, characteristic, complemented
8C22×C5×D8—21no—
9C2×C5×#127C2211yescharacteristic
10C2×C4×C5×D4C2211yescharacteristic
11C5×#459—22no—
12C5×#459—22no—
13C5×#431C2211yescharacteristic
14C5×#431C2211yescharacteristic
15C5×#423C2211yescharacteristic
16C5×#423C2211yescharacteristic
17C2×C5×C4⋊C8C2211yescharacteristic
18C2×C5×#102—21no—
19C2×C5×#100—21no—
20C5×#343—21no—
21C5×#334—22no—
22C5×#331—22no—
23C5×#331—22no—
24C5×D4⋊C8—22no—
25#10441C511yesmaximal, characteristic, direct product factor, Sylow
26C22×C5×D4—21no—
27C22×C5×D4—21no—
28C22×C5×D4—21no—
29C22×C5×D4D411yescharacteristic
30C23×C4×C5—21no—
31C2×C5×D8—24no—
32C2×C5×D8—42no—
33C2×C5×D8—42no—
34C2×C5×M16—21no—
35C2×C5×M16—21no—
36C22×C5×C8—21no—
37C5×#127—21no—
38C5×#127—21no—
39C5×#127—21no—
40C5×#127D412yes—
41C4×C5×D4—21no—
42C4×C5×D4—21no—
43C4×C5×D4—21no—
44C4×C5×D4—21no—
45C2×C5×C4⋊C4D411yescharacteristic
46C2×C5×C22⋊C4—21no—
47C2×C42×C5C2311yescharacteristic
48C5×C4⋊C8—21no—
49C5×C4⋊C8—21no—
50C5×C4⋊C8—21no—
51C5×C4⋊C8—21no—
52C5×C4⋊C8—21no—
53C5×C4⋊C8—21no—
54C5×C4⋊C8D412yes—
55C5×C4⋊C8D412yes—
56C5×#102—24no—
57C5×#100—42no—
58C5×C22⋊C8—21no—
59C5×C22⋊C8—21no—
60C4×C5×C8—21no—
61C4×C5×C8—21no—
62C2×#459C2×C511yescharacteristic
63#1800C2×C511yescharacteristic, complemented
64#1570C2×C511yescharacteristic, complemented
65#1545C2×C511yescharacteristic, complemented
66#1545C2×C511yescharacteristic, complemented
67#1478C2×C511yescharacteristic, complemented
68#1301C2×C511yescharacteristic, complemented
69C24×C5—21no—
70C24×C5—41no—
71C2×C5×D4—21no—
72C2×C5×D4—22no—
73C2×C5×D4—21no—
74C2×C5×D4—22no—
75C2×C5×D4—22no—
76C2×C5×D4—21no—
77C2×C5×D4—21no—
78C2×C5×D4—21no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—41no—
84C2×C5×D4—41no—
85C2×C5×D4—41no—
86C2×C5×D4—82no—
87C2×C5×D4—82no—
88C2×C5×D4SD1612yes—
89C22×C4×C5—21no—
90C22×C4×C5—41no—
91C22×C4×C5—41no—
92C22×C4×C5—82no—
93C22×C4×C5C2×D411yescharacteristic
94C22×C4×C5#4111yescharacteristic
95C22×C4×C5#4111yescharacteristic
96C5×D8—48no—
97C5×M16—41no—
98C5×M16—41no—
99C5×M16—41no—
100C5×M16—41no—
101C2×C5×C8—22no—
102C2×C5×C8—22no—
103C2×C5×C8—41no—
104C2×C5×C8—41no—
105C2×C5×C8—41no—
106C2×C5×C8—41no—
107C2×C5×C8—41no—
108C5×C4⋊C4—21no—
109C5×C4⋊C4—21no—
110C5×C22⋊C4—41no—
111C5×C22⋊C4—41no—
112C42×C5C2×D411yescharacteristic
113C42×C5C2×D411yescharacteristic
114C42×C5C2×D411yescharacteristic
115C42×C5#4111yescharacteristic
116C22×D8—21no—
117C2×#127C22×C511yescharacteristic
118C2×C4×D4C22×C511yescharacteristic
119#459—22no—
120#459—22no—
121#431C22×C511yescharacteristic
122#431C22×C511yescharacteristic
123#423C22×C511yescharacteristic
124#423C22×C511yescharacteristic
125C2×C4⋊C8C22×C511yescharacteristic
126C2×#102—21no—
127C2×#100—21no—
128#343—21no—
129#334—22no—
130#331—22no—
131#331—22no—
132D4⋊C8—22no—
133C23×C5—22no—
134C23×C5—41no—
135C23×C5—41no—
136C23×C5—42no—
137C23×C5—81no—
138C23×C5—81no—
139C23×C5—82no—
140C23×C5—82no—
141C23×C5—81no—
142C23×C5—81no—
143C23×C5#12311yescharacteristic
144C5×D4—22no—
145C5×D4—22no—
146C5×D4—41no—
147C5×D4—42no—
148C5×D4—42no—
149C5×D4—41no—
150C5×D4—82no—
151C5×D4—82no—
152C5×D4—82no—
153C5×D4—81no—
154C5×D4—81no—
155C5×D4—82no—
156C2×C4×C5—22no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—82no—
160C2×C4×C5—82no—
161C2×C4×C5—81no—
162C2×C4×C5#12011yescharacteristic
163C2×C4×C5#12111yescharacteristic
164C2×C4×C5#12111yescharacteristic
165C2×C4×C5#12111yescharacteristic
166C2×C4×C5#12311yescharacteristic
167C2×C4×C5#12411yescharacteristic
168C2×C4×C5C2×SD1611yescharacteristic
169C2×C4×C5#13511yescharacteristic
170C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
172C5×C8—42no—
173C5×C8—42no—
174C5×C8—81no—
175C5×C8—81no—
176C5×C8—81no—
177C22×D4—21no—
178C22×D4—21no—
179C22×D4—21no—
180C22×D4C5×D411yescharacteristic
181C23×C4—21no—
182C2×D8—24no—
183C2×D8—42no—
184C2×D8—42no—
185C2×M16—21no—
186C2×M16—21no—
187C22×C8—21no—
188#127—21no—
189#127—21no—
190#127—21no—
191#127C5×D412yes—
192C4×D4—21no—
193C4×D4—21no—
194C4×D4—21no—
195C4×D4—21no—
196C2×C4⋊C4C5×D411yescharacteristic
197C2×C22⋊C4—21no—
198C2×C42C23×C511yescharacteristic
199C4⋊C8—21no—
200C4⋊C8—21no—
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8C5×D412yes—
206C4⋊C8C5×D412yes—
207#102—24no—
208#100—42no—
209C22⋊C8—21no—
210C22⋊C8—21no—
211C4×C8—21no—
212C4×C8—21no—
213C22×C5—21no—
214C22×C5—21no—
215C22×C5—42no—
216C22×C5—82no—
217C22×C5—82no—
218C22×C5—81no—
219C22×C5—81no—
220C22×C5—82no—
221C22×C5—82no—
222C22×C5—82no—
223C22×C5—162no—
224C22×C5—162no—
225C22×C5#39411yescharacteristic
226C22×C5#48111yescharacteristic
227C22×C5#48211yescharacteristic
228C4×C5—21no—
229C4×C5—21no—
230C4×C5—21no—
231C4×C5—81no—
232C4×C5#44911yescharacteristic
233C4×C5#45011yescharacteristic
234C4×C5#46511yescharacteristic
235C4×C5#46911yescharacteristic
236C4×C5#47212yes—
237C24—21no—
238C24—41no—
239C2×D4—21no—
240C2×D4—22no—
241C2×D4—21no—
242C2×D4—22no—
243C2×D4—22no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—21no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C2×D4—41no—
251C2×D4—41no—
252C2×D4—41no—
253C2×D4—41no—
254C2×D4—82no—
255C2×D4—82no—
256C2×D4C5×SD1612yes—
257C22×C4—21no—
258C22×C4—41no—
259C22×C4—41no—
260C22×C4—82no—
261C22×C4C2×C5×D411yescharacteristic
262C22×C4C5×#4111yescharacteristic
263C22×C4C5×#4111yescharacteristic
264D8—48no—
265M16—41no—
266M16—41no—
267M16—41no—
268M16—41no—
269C2×C8—22no—
270C2×C8—22no—
271C2×C8—41no—
272C2×C8—41no—
273C2×C8—41no—
274C2×C8—41no—
275C2×C8—41no—
276C4⋊C4—21no—
277C4⋊C4—21no—
278C22⋊C4—41no—
279C22⋊C4—41no—
280C42C2×C5×D411yescharacteristic
281C42C2×C5×D411yescharacteristic
282C42C2×C5×D411yescharacteristic
283C42C5×#4111yescharacteristic
284C2×C5—21no—
285C2×C5—21no—
286C2×C5—82no—
287C2×C5—162no—
288C2×C5#203411yescharacteristic
289C2×C5#204511yescharacteristic
290C2×C5#204811yescharacteristic
291C23—22no—
292C23—41no—
293C23—41no—
294C23—42no—
295C23—81no—
296C23—81no—
297C23—82no—
298C23—82no—
299C23—81no—
300C23—81no—
301C23C5×#12311yescharacteristic
302D4—22no—
303D4—22no—
304D4—41no—
305D4—42no—
306D4—42no—
307D4—41no—
308D4—82no—
309D4—82no—
310D4—82no—
311D4—81no—
312D4—81no—
313D4—82no—
314C2×C4—22no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—82no—
318C2×C4—82no—
319C2×C4—81no—
320C2×C4C5×#12011yescharacteristic
321C2×C4C5×#12111yescharacteristic
322C2×C4C5×#12111yescharacteristic
323C2×C4C5×#12111yescharacteristic
324C2×C4C5×#12311yescharacteristic
325C2×C4C5×#12411yescharacteristic
326C2×C4C2×C5×SD1611yescharacteristic
327C2×C4C5×#13511yescharacteristic
328C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
329C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
330C8—42no—
331C8—42no—
332C8—81no—
333C8—81no—
334C8—81no—
335C5#1044111yescharacteristic, direct product factor, Sylow
336C22—21no—
337C22—21no—
338C22—42no—
339C22—82no—
340C22—82no—
341C22—81no—
342C22—81no—
343C22—82no—
344C22—82no—
345C22—82no—
346C22—162no—
347C22—162no—
348C22C5×#39411yescharacteristic
349C22C5×#48111yescharacteristic
350C22C5×#48211yescharacteristic
351C4—21no—
352C4—21no—
353C4—21no—
354C4—81no—
355C4C5×#44911yescharacteristic
356C4C5×#45011yescharacteristic
357C4C5×#46511yescharacteristic
358C4C5×#46911yescharacteristic
359C4C5×#47212yes—
360C2—21no—
361C2—21no—
362C2—82no—
363C2—162no—
364C2C5×#203411yescharacteristic
365C2C5×#204511yescharacteristic
366C2C5×#204811yescharacteristic
subgroupG/H
center, socleC22×C5#394
commutator, Frattini, cosocleC2×C42C23×C5
prime radicalC2×C5×#459C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#1800C2semidirect
3. C5×#1570C2semidirect
4. C5×#1545C2semidirect
5. C5×#1545C2semidirect
6. C5×#1478C2semidirect
7. C5×#1301C2semidirect
25. #10441C5direct (N × H)
63. #1800C2×C5semidirect
64. #1570C2×C5semidirect
65. #1545C2×C5semidirect
66. #1545C2×C5semidirect
67. #1478C2×C5semidirect
68. #1301C2×C5semidirect
335. C5#10441direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4592
C5×#18002
C5×#15702
C5×#15452
C5×#14782
C5×#13012
#104415