Finite Group Databasebeta

← C5×#13005 #11935725

Subgroups — C5×#13005 #11935725

Order 1280.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3067C211yesmaximal, characteristic
2C5×#2912C211yesmaximal, characteristic, complemented
3C5×#2145C211yesmaximal, characteristic, complemented
4C2×C5×#360C211yesmaximal, characteristic, complemented
5C5×#2117C211yesmaximal, characteristic, complemented
6C5×#1389C211yesmaximal, characteristic, complemented
7C5×#1383C211yesmaximal, characteristic, complemented
8C5×#575—21no—
9C2×C5×#135C2211yescharacteristic
10C2×C5×#131C2211yescharacteristic
11C5×#520—21no—
12C2×C5×M32C2211yescharacteristic
13C2×C5×M32C2211yescharacteristic
14C5×#473C412yescomplemented
15C5×#472C412yescomplemented
16C5×#471—22no—
17C2×C5×#108C2211yescharacteristic
18C5×#428—22no—
19C5×#428—21no—
20C5×#427—21no—
21C5×#427C2211yescharacteristic
22C2×C5×#106—21no—
23C2×C5×#106C2211yescharacteristic
24C5×#413—21no—
25C5×#360—22no—
26C5×#360—21no—
27C5×#360—21no—
28C5×#350—22no—
29#13005C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C2×C5×#41D411yescharacteristic
32C5×#137—22no—
33C5×#137—41no—
34C5×AGL(1,ℤ/8)—22no—
35C5×AGL(1,ℤ/8)—41no—
36C5×#135—21no—
37C5×#135—21no—
38C5×#135—21no—
39C5×#135—21no—
40C5×#135—42no—
41C2×C5×Q16C2×C411yescharacteristic, complemented
42C2×C5×SD16—21no—
43C2×C5×D8C2×C411yescharacteristic, complemented
44C5×#131—21no—
45C5×#131—21no—
46C5×#131C2×C412yes—
47C5×#131D412yes—
48C2×C5×M16—21no—
49C2×C5×M16—21no—
50C2×C5×M16D411yescharacteristic
51C22×C5×C8—21no—
52C22×C5×C8C2311yescharacteristic
53C4×C5×Q8—41no—
54C4×C5×D4—42no—
55C4×C5×D4—41no—
56C5×#117—22no—
57C5×#117—21no—
58C2×C5×C4⋊C4—22no—
59C2×C5×C4⋊C4—21no—
60C5×M32—21no—
61C5×M32—21no—
62C5×M32—21no—
63C5×M32—21no—
64C2×C5×C16—21no—
65C2×C5×C16—21no—
66C5×#108—21no—
67C5×#108C2×C412yescomplemented
68C5×#107—22no—
69C5×#107—21no—
70C5×#106—22no—
71C5×#106—21no—
72C5×#106D411yescharacteristic
73C5×#106D412yes—
74C5×#106D411yescharacteristic
75C5×#101—22no—
76C5×#100—22no—
77#3067C2×C511yescharacteristic
78#2912C2×C511yescharacteristic, complemented
79#2145C2×C511yescharacteristic, complemented
80C2×#360C2×C511yescharacteristic, complemented
81#2117C2×C511yescharacteristic, complemented
82#1389C2×C511yescharacteristic, complemented
83#1383C2×C511yescharacteristic, complemented
84C5×#41—21no—
85C5×#41—21no—
86C5×#41—41no—
87C5×#41—41no—
88C5×#41—41no—
89C5×#41—41no—
90C5×#41C22⋊C412yes—
91C5×#41SD1612yes—
92C2×C5×Q8—21no—
93C2×C5×Q8D811yescharacteristic
94C2×C5×D4—21no—
95C2×C5×D4—21no—
96C2×C5×D4—41no—
97C2×C5×D4D811yescharacteristic
98C22×C4×C5—21no—
99C22×C4×C5—42no—
100C22×C4×C5—41no—
101C22×C4×C5—41no—
102C22×C4×C5C2×D411yescharacteristic
103C5×Q16—21no—
104C5×Q16—21no—
105C5×Q16—42no—
106C5×SD16—42no—
107C5×SD16—42no—
108C5×SD16—41no—
109C5×SD16—41no—
110C5×D8—21no—
111C5×D8—21no—
112C5×D8—42no—
113C5×M16—21no—
114C5×M16—22no—
115C5×M16—22no—
116C5×M16—22no—
117C5×M16—41no—
118C5×M16C22⋊C412yes—
119C2×C5×C8—21no—
120C2×C5×C8—22no—
121C2×C5×C8—22no—
122C2×C5×C8—41no—
123C2×C5×C8C22×C411yescharacteristic
124C2×C5×C8C2×D411yescharacteristic
125C2×C5×C8C2×D411yescharacteristic
126C2×C5×C8C2×D411yescharacteristic
127C2×C5×C8#4111yescharacteristic
128C2×C5×C8#4111yescharacteristic
129C5×C4⋊C4—21no—
130C5×C4⋊C4—22no—
131C5×C4⋊C4—21no—
132C5×C4⋊C4—42no—
133C5×C4⋊C4—41no—
134C5×C22⋊C4—42no—
135C5×C22⋊C4—41no—
136C42×C5—42no—
137C42×C5—41no—
138C5×C16—41no—
139C5×C16—41no—
140#575—21no—
141C2×#135C22×C511yescharacteristic
142C2×#131C22×C511yescharacteristic
143#520—21no—
144C2×M32C22×C511yescharacteristic
145C2×M32C22×C511yescharacteristic
146#473C4×C512yescomplemented
147#472C4×C512yescomplemented
148#471—22no—
149C2×#108C22×C511yescharacteristic
150#428—21no—
151#428—22no—
152#427—21no—
153#427C22×C511yescharacteristic
154C2×#106—21no—
155C2×#106C22×C511yescharacteristic
156#413—21no—
157#360—22no—
158#360—21no—
159#360—21no—
160#350—22no—
161C23×C5—21no—
162C23×C5—41no—
163C23×C5AGL(1,ℤ/8)11yescharacteristic
164C5×Q8—21no—
165C5×Q8—41no—
166C5×Q8—41no—
167C5×Q8#10212yes—
168C5×D4—22no—
169C5×D4—22no—
170C5×D4—21no—
171C5×D4—41no—
172C5×D4—41no—
173C5×D4—81no—
174C5×D4—81no—
175C5×D4#10212yes—
176C2×C4×C5—21no—
177C2×C4×C5—22no—
178C2×C4×C5—22no—
179C2×C4×C5—41no—
180C2×C4×C5—41no—
181C2×C4×C5—42no—
182C2×C4×C5—41no—
183C2×C4×C5—81no—
184C2×C4×C5—81no—
185C2×C4×C5—161no—
186C2×C4×C5—162no—
187C2×C4×C5C2×C22⋊C411yescharacteristic
188C2×C4×C5#12011yescharacteristic
189C2×C4×C5#12311yescharacteristic
190C2×C4×C5C2×D811yescharacteristic
191C2×C4×C5C2×SD1611yescharacteristic
192C2×C4×C5#13711yescharacteristic
193C5×C8—22no—
194C5×C8—42no—
195C5×C8C4×D411yescharacteristic
196C5×C8C4×D411yescharacteristic
197C5×C8#12111yescharacteristic
198C5×C8#12111yescharacteristic
199C2×#41—21no—
200C2×#41C5×D411yescharacteristic
201#137—22no—
202#137—41no—
203AGL(1,ℤ/8)—22no—
204AGL(1,ℤ/8)—41no—
205#135—21no—
206#135—21no—
207#135—21no—
208#135—21no—
209#135—42no—
210C2×Q16C2×C4×C511yescharacteristic, complemented
211C2×SD16—21no—
212C2×D8C2×C4×C511yescharacteristic, complemented
213#131—21no—
214#131—21no—
215#131C2×C4×C512yes—
216#131C5×D412yes—
217C2×M16—21no—
218C2×M16—21no—
219C2×M16C5×D411yescharacteristic
220C22×C8—21no—
221C22×C8C23×C511yescharacteristic
222C4×Q8—41no—
223C4×D4—42no—
224C4×D4—41no—
225#117—22no—
226#117—21no—
227C2×C4⋊C4—22no—
228C2×C4⋊C4—21no—
229M32—21no—
230M32—21no—
231M32—21no—
232M32—21no—
233C2×C16—21no—
234C2×C16—21no—
235#108—21no—
236#108C2×C4×C512yescomplemented
237#107—22no—
238#107—21no—
239#106—22no—
240#106—21no—
241#106C5×D411yescharacteristic
242#106C5×D412yes—
243#106C5×D411yescharacteristic
244#101—22no—
245#100—22no—
246C22×C5—22no—
247C22×C5—41no—
248C22×C5—42no—
249C22×C5—81no—
250C22×C5—161no—
251C22×C5#41711yescharacteristic
252C22×C5#44711yescharacteristic
253C22×C5#48111yescharacteristic
254C4×C5—22no—
255C4×C5—81no—
256C4×C5—82no—
257C4×C5—81no—
258C4×C5—81no—
259C4×C5#38611yescharacteristic
260C4×C5C2×#10211yescharacteristic
261C4×C5#44811yescharacteristic
262C4×C5#48011yescharacteristic
263#41—21no—
264#41—21no—
265#41—41no—
266#41—41no—
267#41—41no—
268#41—41no—
269#41C5×C22⋊C412yes—
270#41C5×SD1612yes—
271C2×Q8—21no—
272C2×Q8C5×D811yescharacteristic
273C2×D4—21no—
274C2×D4—21no—
275C2×D4—41no—
276C2×D4C5×D811yescharacteristic
277C22×C4—21no—
278C22×C4—42no—
279C22×C4—41no—
280C22×C4—41no—
281C22×C4C2×C5×D411yescharacteristic
282Q16—21no—
283Q16—21no—
284Q16—42no—
285SD16—42no—
286SD16—42no—
287SD16—41no—
288SD16—41no—
289D8—21no—
290D8—21no—
291D8—42no—
292M16—21no—
293M16—22no—
294M16—22no—
295M16—22no—
296M16—41no—
297M16C5×C22⋊C412yes—
298C2×C8—21no—
299C2×C8—22no—
300C2×C8—22no—
301C2×C8—41no—
302C2×C8C22×C4×C511yescharacteristic
303C2×C8C2×C5×D411yescharacteristic
304C2×C8C2×C5×D411yescharacteristic
305C2×C8C2×C5×D411yescharacteristic
306C2×C8C5×#4111yescharacteristic
307C2×C8C5×#4111yescharacteristic
308C4⋊C4—21no—
309C4⋊C4—22no—
310C4⋊C4—21no—
311C4⋊C4—42no—
312C4⋊C4—41no—
313C22⋊C4—42no—
314C22⋊C4—41no—
315C42—42no—
316C42—41no—
317C16—41no—
318C16—41no—
319C2×C5—21no—
320C2×C5—21no—
321C2×C5—21no—
322C2×C5—42no—
323C2×C5—161no—
324C2×C5#187411yescharacteristic
325C23—21no—
326C23—41no—
327C23C5×AGL(1,ℤ/8)11yescharacteristic
328Q8—21no—
329Q8—41no—
330Q8—41no—
331Q8C5×#10212yes—
332D4—22no—
333D4—22no—
334D4—21no—
335D4—41no—
336D4—41no—
337D4—81no—
338D4—81no—
339D4C5×#10212yes—
340C2×C4—21no—
341C2×C4—22no—
342C2×C4—22no—
343C2×C4—41no—
344C2×C4—41no—
345C2×C4—42no—
346C2×C4—41no—
347C2×C4—81no—
348C2×C4—81no—
349C2×C4—161no—
350C2×C4—162no—
351C2×C4C2×C5×C22⋊C411yescharacteristic
352C2×C4C5×#12011yescharacteristic
353C2×C4C5×#12311yescharacteristic
354C2×C4C2×C5×D811yescharacteristic
355C2×C4C2×C5×SD1611yescharacteristic
356C2×C4C5×#13711yescharacteristic
357C8—22no—
358C8—42no—
359C8C4×C5×D411yescharacteristic
360C8C4×C5×D411yescharacteristic
361C8C5×#12111yescharacteristic
362C8C5×#12111yescharacteristic
363C5#1300511yescharacteristic, direct product factor, Sylow
364C22—22no—
365C22—41no—
366C22—42no—
367C22—81no—
368C22—161no—
369C22C5×#41711yescharacteristic
370C22C5×#44711yescharacteristic
371C22C5×#48111yescharacteristic
372C4—22no—
373C4—82no—
374C4—81no—
375C4—81no—
376C4—81no—
377C4C5×#38611yescharacteristic
378C4C2×C5×#10211yescharacteristic
379C4C5×#44811yescharacteristic
380C4C5×#48011yescharacteristic
381C2—21no—
382C2—21no—
383C2—21no—
384C2—42no—
385C2—161no—
386C2C5×#187411yescharacteristic
subgroupG/H
center, socleC2×C5#1874
commutatorC2×C8C22×C4×C5
Frattini, cosocleC22×C8C23×C5
prime radicalC5×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C2×C5×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2912C2semidirect
3. C5×#2145C2semidirect
4. C2×C5×#360C2semidirect
5. C5×#2117C2semidirect
6. C5×#1389C2semidirect
7. C5×#1383C2semidirect
14. C5×#473C4semidirect
15. C5×#472C4semidirect
29. #13005C5direct (N × H)
41. C2×C5×Q16C2×C4semidirect
43. C2×C5×D8C2×C4semidirect
67. C5×#108C2×C4semidirect
78. #2912C2×C5semidirect
79. #2145C2×C5semidirect
80. C2×#360C2×C5semidirect
81. #2117C2×C5semidirect
82. #1389C2×C5semidirect
83. #1383C2×C5semidirect
146. #473C4×C5semidirect
147. #472C4×C5semidirect
210. C2×Q16C2×C4×C5semidirect
212. C2×D8C2×C4×C5semidirect
236. #108C2×C4×C5semidirect
363. C5#13005direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#30672
C5×#29122
C5×#21452
C2×C5×#3602
C5×#21172
C5×#13892
C5×#13832
#130055