Finite Group Databasebeta

← C5×#13449 #11936169

Subgroups — C5×#13449 #11936169

Order 1280.

446 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
1C22×C5×SD32C211yesmaximal, characteristic
2C2×C5×C4⋊C16C211yesmaximal, characteristic, complemented
3C2×C5×#358C211yesmaximal, characteristic, complemented
4C2×C5×#357C211yesmaximal, characteristic
5C5×#1970C211yesmaximal, characteristic
6C5×#1969C211yesmaximal, characteristic, complemented
7C5×#1380C211yesmaximal, characteristic, complemented
8C22×C5×Q16C2211yescharacteristic
9C22×C5×D8C2211yescharacteristic
10C2×C5×SD32—22no—
11C2×C5×SD32—22no—
12C2×C5×SD32—22no—
13C22×C5×C16C2211yescharacteristic
14C22×C5×C16C2211yescharacteristic
15C2×C5×#107C2211yescharacteristic
16C2×C5×#107C2211yescharacteristic
17C2×C5×#103—21no—
18C2×C5×#102—21no—
19C2×C4×C5×C8C2211yescharacteristic
20C5×#391—21no—
21C5×#390—21no—
22C5×C4⋊C16—22no—
23C5×#358—22no—
24C5×#357—22no—
25#13449C511yesmaximal, characteristic, direct product factor, Sylow
26C22×C5×Q8—21no—
27C22×C5×D4—21no—
28C2×C5×Q16—21no—
29C2×C5×Q16—21no—
30C2×C5×Q16—21no—
31C2×C5×Q16—21no—
32C2×C5×Q16—21no—
33C2×C5×Q16D412yes—
34C2×C5×D8—21no—
35C2×C5×D8—21no—
36C2×C5×D8—21no—
37C2×C5×D8—21no—
38C2×C5×D8—21no—
39C2×C5×D8D412yes—
40C22×C5×C8D411yescharacteristic
41C22×C5×C8C2311yescharacteristic
42C2×C5×C4⋊C4—21no—
43C2×C5×C4⋊C4—21no—
44C2×C5×C22⋊C4—41no—
45C2×C5×C22⋊C4—41no—
46C2×C42×C5D411yescharacteristic
47C5×SD32—28no—
48C2×C5×C16—21no—
49C2×C5×C16—21no—
50C2×C5×C16—21no—
51C2×C5×C16—21no—
52C2×C5×C16—21no—
53C2×C5×C16D412yes—
54C5×#107—21no—
55C5×#107—21no—
56C5×#107—21no—
57C5×#107—21no—
58C5×#103—42no—
59C5×#102—42no—
60C4×C5×C8—21no—
61C4×C5×C8—21no—
62C5×#95—41no—
63C5×#95—41no—
64C22×SD32C2×C511yescharacteristic
65C2×C4⋊C16C2×C511yescharacteristic, complemented
66C2×#358C2×C511yescharacteristic, complemented
67C2×#357C2×C511yescharacteristic
68#1970C2×C511yescharacteristic
69#1969C2×C511yescharacteristic, complemented
70#1380C2×C511yescharacteristic, complemented
71C24×C5—41no—
72C2×C5×Q8—22no—
73C2×C5×Q8—41no—
74C2×C5×Q8—41no—
75C2×C5×Q8—41no—
76C2×C5×Q8—41no—
77C2×C5×Q8—41no—
78C2×C5×D4—22no—
79C2×C5×D4—41no—
80C2×C5×D4—41no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—41no—
84C22×C4×C5—41no—
85C22×C4×C5—41no—
86C22×C4×C5—41no—
87C22×C4×C5D811yescharacteristic
88C22×C4×C5D811yescharacteristic
89C22×C4×C5C2×D411yescharacteristic
90C5×Q16—22no—
91C5×Q16—22no—
92C5×Q16—41no—
93C5×Q16—41no—
94C5×D8—22no—
95C5×D8—22no—
96C5×D8—41no—
97C5×D8—41no—
98C2×C5×C8—21no—
99C2×C5×C8—21no—
100C2×C5×C8—21no—
101C2×C5×C8C2×D411yescharacteristic
102C2×C5×C8C2×D411yescharacteristic
103C2×C5×C8C2×D411yescharacteristic
104C2×C5×C8#4111yescharacteristic
105C2×C5×C8#4111yescharacteristic
106C2×C5×C8#4111yescharacteristic
107C5×C4⋊C4—41no—
108C5×C4⋊C4—41no—
109C5×C4⋊C4—41no—
110C5×C4⋊C4—41no—
111C5×C22⋊C4—82no—
112C5×C22⋊C4—82no—
113C42×C5—21no—
114C42×C5—21no—
115C5×C16—22no—
116C5×C16—41no—
117C22×Q16C22×C511yescharacteristic
118C22×D8C22×C511yescharacteristic
119C2×SD32—22no—
120C2×SD32—22no—
121C2×SD32—22no—
122C22×C16C22×C511yescharacteristic
123C22×C16C22×C511yescharacteristic
124C2×#107C22×C511yescharacteristic
125C2×#107C22×C511yescharacteristic
126C2×#103—21no—
127C2×#102—21no—
128C2×C4×C8C22×C511yescharacteristic
129#391—21no—
130#390—21no—
131C4⋊C16—22no—
132#358—22no—
133#357—22no—
134C23×C5—42no—
135C23×C5—81no—
136C23×C5—81no—
137C23×C5—81no—
138C23×C5—81no—
139C23×C5—81no—
140C23×C5—81no—
141C23×C5C2×D811yescharacteristic
142C5×Q8—42no—
143C5×Q8—42no—
144C5×Q8—81no—
145C5×Q8—81no—
146C5×D4—42no—
147C5×D4—42no—
148C5×D4—81no—
149C5×D4—81no—
150C2×C4×C5—21no—
151C2×C4×C5—21no—
152C2×C4×C5—21no—
153C2×C4×C5—21no—
154C2×C4×C5—21no—
155C2×C4×C5—42no—
156C2×C4×C5—81no—
157C2×C4×C5—81no—
158C2×C4×C5—81no—
159C2×C4×C5—81no—
160C2×C4×C5—81no—
161C2×C4×C5—81no—
162C2×C4×C5—81no—
163C2×C4×C5—81no—
164C2×C4×C5SD3212yescomplemented
165C2×C4×C5#12111yescharacteristic
166C2×C4×C5#12111yescharacteristic
167C2×C4×C5#12111yescharacteristic
168C2×C4×C5#13511yescharacteristic
169C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
170C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
171C5×C8—41no—
172C5×C8#12011yescharacteristic
173C5×C8#12311yescharacteristic
174C5×C8#12311yescharacteristic
175C5×C8#12411yescharacteristic
176C22×Q8—21no—
177C22×D4—21no—
178C2×Q16—21no—
179C2×Q16—21no—
180C2×Q16—21no—
181C2×Q16—21no—
182C2×Q16—21no—
183C2×Q16C5×D412yes—
184C2×D8—21no—
185C2×D8—21no—
186C2×D8—21no—
187C2×D8—21no—
188C2×D8—21no—
189C2×D8C5×D412yes—
190C22×C8C5×D411yescharacteristic
191C22×C8C23×C511yescharacteristic
192C2×C4⋊C4—21no—
193C2×C4⋊C4—21no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—41no—
196C2×C42C5×D411yescharacteristic
197SD32—28no—
198C2×C16—21no—
199C2×C16—21no—
200C2×C16—21no—
201C2×C16—21no—
202C2×C16—21no—
203C2×C16C5×D412yes—
204#107—21no—
205#107—21no—
206#107—21no—
207#107—21no—
208#103—42no—
209#102—42no—
210C4×C8—21no—
211C4×C8—21no—
212#95—41no—
213#95—41no—
214C22×C5—82no—
215C22×C5—82no—
216C22×C5—82no—
217C22×C5—161no—
218C22×C5—161no—
219C22×C5—161no—
220C22×C5—161no—
221C22×C5#45911yescharacteristic
222C22×C5#45911yescharacteristic
223C22×C5#46611yescharacteristic
224C22×C5C2×SD3211yescharacteristic
225C22×C5#50811yescharacteristic
226C22×C5#50911yescharacteristic
227C22×C5#51011yescharacteristic
228C4×C5—22no—
229C4×C5—41no—
230C4×C5—82no—
231C4×C5—161no—
232C4×C5—161no—
233C4×C5#39411yescharacteristic
234C4×C5#46311yescharacteristic
235C4×C5#46311yescharacteristic
236C4×C5#46911yescharacteristic
237C24—41no—
238C2×Q8—22no—
239C2×Q8—41no—
240C2×Q8—41no—
241C2×Q8—41no—
242C2×Q8—41no—
243C2×Q8—41no—
244C2×D4—22no—
245C2×D4—41no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C2×D4—41no—
250C22×C4—41no—
251C22×C4—41no—
252C22×C4—41no—
253C22×C4C5×D811yescharacteristic
254C22×C4C5×D811yescharacteristic
255C22×C4C2×C5×D411yescharacteristic
256Q16—22no—
257Q16—22no—
258Q16—41no—
259Q16—41no—
260D8—22no—
261D8—22no—
262D8—41no—
263D8—41no—
264C2×C8—21no—
265C2×C8—21no—
266C2×C8—21no—
267C2×C8C2×C5×D411yescharacteristic
268C2×C8C2×C5×D411yescharacteristic
269C2×C8C2×C5×D411yescharacteristic
270C2×C8C5×#4111yescharacteristic
271C2×C8C5×#4111yescharacteristic
272C2×C8C5×#4111yescharacteristic
273C4⋊C4—41no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C22⋊C4—82no—
278C22⋊C4—82no—
279C42—21no—
280C42—21no—
281C16—22no—
282C16—41no—
283C2×C5—162no—
284C2×C5#205411yescharacteristic
285C2×C5#220711yescharacteristic
286C2×C5#220811yescharacteristic
287C2×C5#221011yescharacteristic
288C2×C5#221111yescharacteristic
289C2×C5#221711yescharacteristic
290C2×C5#222011yescharacteristic
291C23—42no—
292C23—81no—
293C23—81no—
294C23—81no—
295C23—81no—
296C23—81no—
297C23—81no—
298C23C2×C5×D811yescharacteristic
299Q8—42no—
300Q8—42no—
301Q8—81no—
302Q8—81no—
303D4—42no—
304D4—42no—
305D4—81no—
306D4—81no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—81no—
316C2×C4—81no—
317C2×C4—81no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—81no—
321C2×C4C5×SD3212yescomplemented
322C2×C4C5×#12111yescharacteristic
323C2×C4C5×#12111yescharacteristic
324C2×C4C5×#12111yescharacteristic
325C2×C4C5×#13511yescharacteristic
326C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
327C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
328C8—41no—
329C8C5×#12011yescharacteristic
330C8C5×#12311yescharacteristic
331C8C5×#12311yescharacteristic
332C8C5×#12411yescharacteristic
333C5#1344911yescharacteristic, direct product factor, Sylow
334C22—82no—
335C22—82no—
336C22—82no—
337C22—161no—
338C22—161no—
339C22—161no—
340C22—161no—
341C22C5×#45911yescharacteristic
342C22C5×#45911yescharacteristic
343C22C5×#46611yescharacteristic
344C22C2×C5×SD3211yescharacteristic
345C22C5×#50811yescharacteristic
346C22C5×#50911yescharacteristic
347C22C5×#51011yescharacteristic
348C4—22no—
349C4—41no—
350C4—82no—
351C4—161no—
352C4—161no—
353C4C5×#39411yescharacteristic
354C4C5×#46311yescharacteristic
355C4C5×#46311yescharacteristic
356C4C5×#46911yescharacteristic
357C2—162no—
358C2C5×#205411yescharacteristic
359C2C5×#220711yescharacteristic
360C2C5×#220811yescharacteristic
361C2C5×#221011yescharacteristic
362C2C5×#221111yescharacteristic
363C2C5×#221711yescharacteristic
364C2C5×#222011yescharacteristic
subgroupG/H
center, socleC23×C5C2×D8
commutator, Frattini, cosocleC22×C8C23×C5
prime radicalC22×C5×D8C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C42×C5 ◁ C2×C4×C5×C8 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×C4⋊C16C2semidirect
3. C2×C5×#358C2semidirect
6. C5×#1969C2semidirect
7. C5×#1380C2semidirect
25. #13449C5direct (N × H)
65. C2×C4⋊C16C2×C5semidirect
66. C2×#358C2×C5semidirect
69. #1969C2×C5semidirect
70. #1380C2×C5semidirect
164. C2×C4×C5SD32semidirect
321. C2×C4C5×SD32semidirect
333. C5#13449direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×SD322
C2×C5×C4⋊C162
C2×C5×#3582
C2×C5×#3572
C5×#19702
C5×#19692
C5×#13802
#134495