Finite Group Databasebeta

← C5×#13249 #11935969

Subgroups — C5×#13249 #11935969

Order 1280.

444 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#509C211yesmaximal, characteristic
2C2×C5×#365C211yesmaximal, characteristic, complemented
3C2×C5×#361C211yesmaximal, characteristic, complemented
4C2×C5×#360C211yesmaximal, characteristic, complemented
5C2×C5×#347C211yesmaximal, characteristic, complemented
6C5×#1975C211yesmaximal, characteristic, complemented
7C5×#1972C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C22×C5×D8C2211yescharacteristic
10C5×#509—22no—
11C5×#509—22no—
12C2×C5×SD32C412yescomplemented
13C2×C5×D16C412yescomplemented
14C2×C5×M32C2211yescharacteristic
15C2×C5×M32C2211yescharacteristic
16C2×C5×#108C2211yescharacteristic
17C2×C5×#106C2211yescharacteristic
18C2×C5×#104—21no—
19C2×C5×#102—21no—
20C5×#408—21no—
21C2×C5×#97C2211yescharacteristic
22C5×#390—21no—
23C5×#365—22no—
24C5×#361—22no—
25C5×#360—22no—
26C5×#347—22no—
27#13249C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C22×C5×D4—21no—
30C5×#135—21no—
31C5×#135—21no—
32C5×#135—21no—
33C5×#135—21no—
34C2×C5×Q16C2×C411yescharacteristic
35C2×C5×SD16—21no—
36C2×C5×D8—21no—
37C2×C5×D8—21no—
38C2×C5×D8—21no—
39C2×C5×D8—21no—
40C2×C5×D8—21no—
41C2×C5×D8C2×C411yescharacteristic
42C2×C5×D8C2×C412yes—
43C2×C5×M16—21no—
44C22×C5×C8D411yescharacteristic
45C22×C5×C8C2311yescharacteristic
46C2×C5×C4⋊C4—21no—
47C2×C5×C22⋊C4—42no—
48C2×C42×C5D411yescharacteristic
49C5×SD32—24no—
50C5×D16—24no—
51C5×M32—21no—
52C5×M32D412yes—
53C5×M32D412yes—
54C5×M32D412yes—
55C2×C5×C16—21no—
56C2×C5×C16C2×C412yes—
57C5×#108—21no—
58C5×#108—21no—
59C5×#106—21no—
60C5×#106—21no—
61C5×#104—42no—
62C5×#102—42no—
63C5×C22⋊C8—42no—
64C5×#97—21no—
65C5×#97—21no—
66C2×#509C2×C511yescharacteristic
67C2×#365C2×C511yescharacteristic, complemented
68C2×#361C2×C511yescharacteristic, complemented
69C2×#360C2×C511yescharacteristic, complemented
70C2×#347C2×C511yescharacteristic, complemented
71#1975C2×C511yescharacteristic, complemented
72#1972C2×C511yescharacteristic, complemented
73C24×C5—41no—
74C5×#41—41no—
75C5×#41—41no—
76C5×#41—41no—
77C5×#41—41no—
78C2×C5×Q8—21no—
79C2×C5×D4—22no—
80C2×C5×D4—21no—
81C2×C5×D4—41no—
82C2×C5×D4—41no—
83C2×C5×D4—41no—
84C2×C5×D4—41no—
85C2×C5×D4—41no—
86C2×C5×D4—41no—
87C22×C4×C5—21no—
88C22×C4×C5—41no—
89C22×C4×C5—41no—
90C22×C4×C5C2×D411yescharacteristic
91C5×Q16—21no—
92C5×Q16—21no—
93C5×SD16—41no—
94C5×SD16—41no—
95C5×D8—22no—
96C5×D8—21no—
97C5×D8—22no—
98C5×D8—21no—
99C5×D8—41no—
100C5×D8—41no—
101C5×M16—41no—
102C5×M16—41no—
103C2×C5×C8—21no—
104C2×C5×C8—21no—
105C2×C5×C8—21no—
106C2×C5×C8—41no—
107C2×C5×C8C22×C411yescharacteristic
108C2×C5×C8C2×D411yescharacteristic
109C2×C5×C8C2×D411yescharacteristic
110C2×C5×C8C2×D411yescharacteristic
111C2×C5×C8#4111yescharacteristic
112C2×C5×C8#4111yescharacteristic
113C5×C4⋊C4—41no—
114C5×C4⋊C4—41no—
115C5×C22⋊C4—84no—
116C42×C5—21no—
117C42×C5—21no—
118C5×C16—22no—
119C5×C16C22⋊C414yescomplemented
120C2×#135C22×C511yescharacteristic
121C22×D8C22×C511yescharacteristic
122#509—22no—
123#509—22no—
124C2×SD32C4×C512yescomplemented
125C2×D16C4×C512yescomplemented
126C2×M32C22×C511yescharacteristic
127C2×M32C22×C511yescharacteristic
128C2×#108C22×C511yescharacteristic
129C2×#106C22×C511yescharacteristic
130C2×#104—21no—
131C2×#102—21no—
132#408—21no—
133C2×#97C22×C511yescharacteristic
134#390—21no—
135#365—22no—
136#361—22no—
137#360—22no—
138#347—22no—
139C23×C5—41no—
140C23×C5—42no—
141C23×C5—82no—
142C23×C5—82no—
143C23×C5—81no—
144C23×C5—81no—
145C23×C5AGL(1,ℤ/8)11yescharacteristic
146C5×Q8—41no—
147C5×Q8—41no—
148C5×D4—42no—
149C5×D4—41no—
150C5×D4—42no—
151C5×D4—41no—
152C5×D4—81no—
153C5×D4—81no—
154C5×D4—81no—
155C5×D4—81no—
156C2×C4×C5—42no—
157C2×C4×C5—41no—
158C2×C4×C5—41no—
159C2×C4×C5—81no—
160C2×C4×C5—81no—
161C2×C4×C5—82no—
162C2×C4×C5—81no—
163C2×C4×C5C4×D411yescharacteristic
164C2×C4×C5#12111yescharacteristic
165C2×C4×C5#12711yescharacteristic
166C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
167C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
168C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
169C5×C8—41no—
170C5×C8—81no—
171C5×C8C2×C22⋊C411yescharacteristic
172C5×C8C4×D411yescharacteristic
173C5×C8#12111yescharacteristic
174C5×C8#12411yescharacteristic
175C2×#41—21no—
176C22×D4—21no—
177#135—21no—
178#135—21no—
179#135—21no—
180#135—21no—
181C2×Q16C2×C4×C511yescharacteristic
182C2×SD16—21no—
183C2×D8—21no—
184C2×D8—21no—
185C2×D8—21no—
186C2×D8—21no—
187C2×D8—21no—
188C2×D8C2×C4×C512yes—
189C2×D8C2×C4×C511yescharacteristic
190C2×M16—21no—
191C22×C8C5×D411yescharacteristic
192C22×C8C23×C511yescharacteristic
193C2×C4⋊C4—21no—
194C2×C22⋊C4—42no—
195C2×C42C5×D411yescharacteristic
196SD32—24no—
197D16—24no—
198M32—21no—
199M32C5×D412yes—
200M32C5×D412yes—
201M32C5×D412yes—
202C2×C16—21no—
203C2×C16C2×C4×C512yes—
204#108—21no—
205#108—21no—
206#106—21no—
207#106—21no—
208#104—42no—
209#102—42no—
210C22⋊C8—42no—
211#97—21no—
212#97—21no—
213C22×C5—22no—
214C22×C5—82no—
215C22×C5—84no—
216C22×C5—81no—
217C22×C5—82no—
218C22×C5—162no—
219C22×C5—161no—
220C22×C5—161no—
221C22×C5#44211yescharacteristic
222C22×C5#46911yescharacteristic
223C22×C5#49611yescharacteristic
224C4×C5—81no—
225C4×C5—81no—
226C4×C5—161no—
227C4×C5#39011yescharacteristic
228C4×C5#44211yescharacteristic
229C4×C5#46911yescharacteristic
230C4×C5#49611yescharacteristic
231C24—41no—
232#41—41no—
233#41—41no—
234#41—41no—
235#41—41no—
236C2×Q8—21no—
237C2×D4—22no—
238C2×D4—21no—
239C2×D4—41no—
240C2×D4—41no—
241C2×D4—41no—
242C2×D4—41no—
243C2×D4—41no—
244C2×D4—41no—
245C22×C4—21no—
246C22×C4—41no—
247C22×C4—41no—
248C22×C4C2×C5×D411yescharacteristic
249Q16—21no—
250Q16—21no—
251SD16—41no—
252SD16—41no—
253D8—21no—
254D8—22no—
255D8—22no—
256D8—21no—
257D8—41no—
258D8—41no—
259M16—41no—
260M16—41no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—41no—
265C2×C8C22×C4×C511yescharacteristic
266C2×C8C2×C5×D411yescharacteristic
267C2×C8C2×C5×D411yescharacteristic
268C2×C8C2×C5×D411yescharacteristic
269C2×C8C5×#4111yescharacteristic
270C2×C8C5×#4111yescharacteristic
271C4⋊C4—41no—
272C4⋊C4—41no—
273C22⋊C4—84no—
274C42—21no—
275C42—21no—
276C16—22no—
277C16C5×C22⋊C414yescomplemented
278C2×C5—21no—
279C2×C5—21no—
280C2×C5—161no—
281C2×C5—162no—
282C2×C5#197211yescharacteristic
283C2×C5AGL(1,ℤ/16)12yes—
284C23—41no—
285C23—42no—
286C23—82no—
287C23—82no—
288C23—81no—
289C23—81no—
290C23C5×AGL(1,ℤ/8)11yescharacteristic
291Q8—41no—
292Q8—41no—
293D4—42no—
294D4—41no—
295D4—42no—
296D4—41no—
297D4—81no—
298D4—81no—
299D4—81no—
300D4—81no—
301C2×C4—42no—
302C2×C4—41no—
303C2×C4—41no—
304C2×C4—81no—
305C2×C4—81no—
306C2×C4—82no—
307C2×C4—81no—
308C2×C4C4×C5×D411yescharacteristic
309C2×C4C5×#12111yescharacteristic
310C2×C4C5×#12711yescharacteristic
311C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
312C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
313C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
314C8—41no—
315C8—81no—
316C8C2×C5×C22⋊C411yescharacteristic
317C8C4×C5×D411yescharacteristic
318C8C5×#12111yescharacteristic
319C8C5×#12411yescharacteristic
320C5#1324911yescharacteristic, direct product factor, Sylow
321C22—22no—
322C22—84no—
323C22—82no—
324C22—81no—
325C22—82no—
326C22—162no—
327C22—161no—
328C22—161no—
329C22C5×#44211yescharacteristic
330C22C5×#46911yescharacteristic
331C22C5×#49611yescharacteristic
332C4—81no—
333C4—81no—
334C4—161no—
335C4C5×#39011yescharacteristic
336C4C5×#44211yescharacteristic
337C4C5×#46911yescharacteristic
338C4C5×#49611yescharacteristic
339C2—21no—
340C2—21no—
341C2—162no—
342C2—161no—
343C2C5×#197211yescharacteristic
344C2C5×AGL(1,ℤ/16)12yes—
subgroupG/H
center, socleC22×C5#442
commutatorC2×C8C22×C4×C5
Frattini, cosocleC22×C8C23×C5
prime radicalC2×C5×#509C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#97 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#365C2semidirect
3. C2×C5×#361C2semidirect
4. C2×C5×#360C2semidirect
5. C2×C5×#347C2semidirect
6. C5×#1975C2semidirect
7. C5×#1972C2semidirect
12. C2×C5×SD32C4semidirect
13. C2×C5×D16C4semidirect
27. #13249C5direct (N × H)
67. C2×#365C2×C5semidirect
68. C2×#361C2×C5semidirect
69. C2×#360C2×C5semidirect
70. C2×#347C2×C5semidirect
71. #1975C2×C5semidirect
72. #1972C2×C5semidirect
119. C5×C16C22⋊C4semidirect
124. C2×SD32C4×C5semidirect
125. C2×D16C4×C5semidirect
277. C16C5×C22⋊C4semidirect
320. C5#13249direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5092
C2×C5×#3652
C2×C5×#3612
C2×C5×#3602
C2×C5×#3472
C5×#19752
C5×#19722
#132495