Finite Group Databasebeta

← C5×#13030 #11935750

Subgroups — C5×#13030 #11935750

Order 1280.

476 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3414C211yesmaximal, characteristic
2C5×#2952C211yesmaximal, characteristic, complemented
3C5×#2145C211yesmaximal, characteristic, complemented
4C2×C5×#360C211yesmaximal, characteristic, complemented
5C5×#1976C211yesmaximal, characteristic, complemented
6C5×#1386C211yesmaximal, characteristic, complemented
7C5×#1378C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C2×C5×#135C2211yescharacteristic
10C5×#520—21no—
11C5×#510—21no—
12C5×#510C412yescomplemented
13C5×#509—21no—
14C5×#509C412yescomplemented
15C5×#508—22no—
16C2×C5×M32C2211yescharacteristic
17C2×C5×M32C2211yescharacteristic
18C5×#442—21no—
19C5×#441—21no—
20C4×C5×SD16—22no—
21C5×#427C2211yescharacteristic
22C2×C5×#106C2211yescharacteristic
23C5×#421—21no—
24C5×#417—21no—
25C5×#410—21no—
26C5×#405C2211yescharacteristic
27C5×#360—22no—
28C5×#360—22no—
29#13030C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41—21no—
31C2×C5×#41—21no—
32C5×#135—21no—
33C5×#135—21no—
34C5×#135—21no—
35C5×#135—21no—
36C5×#135—21no—
37C5×#135—21no—
38C5×#135C2×C412yes—
39C5×#135D412yes—
40C2×C5×Q16C2×C411yescharacteristic, complemented
41C2×C5×Q16D411yescharacteristic
42C2×C5×SD16—21no—
43C2×C5×SD16—21no—
44C2×C5×D8C2×C411yescharacteristic, complemented
45C2×C5×D8D411yescharacteristic
46C2×C5×M16D411yescharacteristic
47C22×C5×C8C2311yescharacteristic
48C4×C5×Q8—22no—
49C4×C5×D4—22no—
50C4×C5×D4—42no—
51C5×#117—21no—
52C5×#117—41no—
53C5×#117D411yescharacteristic
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—41no—
56C5×Q32—22no—
57C5×SD32—22no—
58C5×SD32—22no—
59C5×D16—22no—
60C5×M32—21no—
61C5×M32—21no—
62C5×M32—21no—
63C5×M32C2×C412yescomplemented
64C2×C5×C16—21no—
65C2×C5×C16—21no—
66C5×#107—21no—
67C5×#106—21no—
68C5×#106—21no—
69C5×#106D412yes—
70C5×#104—42no—
71C5×#103—22no—
72C5×#102—22no—
73C5×#99—42no—
74C5×#97—21no—
75C4×C5×C8—21no—
76#3414C2×C511yescharacteristic
77#2952C2×C511yescharacteristic, complemented
78#2145C2×C511yescharacteristic, complemented
79C2×#360C2×C511yescharacteristic, complemented
80#1976C2×C511yescharacteristic, complemented
81#1386C2×C511yescharacteristic, complemented
82#1378C2×C511yescharacteristic, complemented
83C5×#41—22no—
84C5×#41—22no—
85C5×#41—41no—
86C5×#41—41no—
87C5×#41—41no—
88C5×#41—41no—
89C5×#41—41no—
90C5×#41—41no—
91C2×C5×Q8—21no—
92C2×C5×Q8—21no—
93C2×C5×D4—21no—
94C2×C5×D4—21no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C22×C4×C5—42no—
98C22×C4×C5—41no—
99C22×C4×C5—41no—
100C22×C4×C5—41no—
101C22×C4×C5C2×D411yescharacteristic
102C5×Q16—21no—
103C5×Q16—21no—
104C5×Q16—21no—
105C5×Q16C22⋊C412yes—
106C5×SD16—22no—
107C5×SD16—22no—
108C5×SD16—41no—
109C5×SD16—41no—
110C5×D8—21no—
111C5×D8—21no—
112C5×D8—21no—
113C5×D8C22⋊C412yes—
114C5×M16—21no—
115C5×M16—21no—
116C2×C5×C8—21no—
117C2×C5×C8C22×C411yescharacteristic
118C2×C5×C8C2×D411yescharacteristic
119C2×C5×C8C2×D411yescharacteristic
120C2×C5×C8C2×D411yescharacteristic
121C2×C5×C8#4111yescharacteristic
122C2×C5×C8#4111yescharacteristic
123C5×C4⋊C4—21no—
124C5×C4⋊C4—22no—
125C5×C4⋊C4—42no—
126C5×C4⋊C4—41no—
127C5×C4⋊C4—41no—
128C5×C22⋊C4—42no—
129C5×C22⋊C4—41no—
130C5×C22⋊C4D812yes—
131C42×C5—21no—
132C42×C5—42no—
133C42×C5—41no—
134C5×C16—22no—
135C5×C16—41no—
136C2×#135C22×C511yescharacteristic
137C2×#135C22×C511yescharacteristic
138#520—21no—
139#510—21no—
140#510C4×C512yescomplemented
141#509—21no—
142#509C4×C512yescomplemented
143#508—22no—
144C2×M32C22×C511yescharacteristic
145C2×M32C22×C511yescharacteristic
146#442—21no—
147#441—21no—
148C4×SD16—22no—
149#427C22×C511yescharacteristic
150C2×#106C22×C511yescharacteristic
151#421—21no—
152#417—21no—
153#410—21no—
154#405C22×C511yescharacteristic
155#360—22no—
156#360—22no—
157C23×C5—41no—
158C23×C5—41no—
159C23×C5C2×D811yescharacteristic
160C5×Q8—22no—
161C5×Q8—41no—
162C5×Q8—41no—
163C5×Q8—41no—
164C5×D4—22no—
165C5×D4—42no—
166C5×D4—42no—
167C5×D4—41no—
168C5×D4—41no—
169C5×D4—41no—
170C5×D4—81no—
171C5×D4—81no—
172C2×C4×C5—22no—
173C2×C4×C5—41no—
174C2×C4×C5—42no—
175C2×C4×C5—42no—
176C2×C4×C5—41no—
177C2×C4×C5—42no—
178C2×C4×C5—81no—
179C2×C4×C5—81no—
180C2×C4×C5—81no—
181C2×C4×C5—162no—
182C2×C4×C5—161no—
183C2×C4×C5C4×D411yescharacteristic
184C2×C4×C5#12011yescharacteristic
185C2×C4×C5#12111yescharacteristic
186C2×C4×C5#13511yescharacteristic
187C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
188C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
189C5×C8—41no—
190C5×C8C2×C22⋊C411yescharacteristic
191C5×C8C4×D411yescharacteristic
192C5×C8#12111yescharacteristic
193C5×C8#12311yescharacteristic
194C2×#41—21no—
195C2×#41—21no—
196#135—21no—
197#135—21no—
198#135—21no—
199#135—21no—
200#135—21no—
201#135—21no—
202#135C2×C4×C512yes—
203#135C5×D412yes—
204C2×Q16C2×C4×C511yescharacteristic, complemented
205C2×Q16C5×D411yescharacteristic
206C2×SD16—21no—
207C2×SD16—21no—
208C2×D8C2×C4×C511yescharacteristic, complemented
209C2×D8C5×D411yescharacteristic
210C2×M16C5×D411yescharacteristic
211C22×C8C23×C511yescharacteristic
212C4×Q8—22no—
213C4×D4—22no—
214C4×D4—42no—
215#117—21no—
216#117—41no—
217#117C5×D411yescharacteristic
218C2×C4⋊C4—21no—
219C2×C4⋊C4—41no—
220Q32—22no—
221SD32—22no—
222SD32—22no—
223D16—22no—
224M32—21no—
225M32—21no—
226M32—21no—
227M32C2×C4×C512yescomplemented
228C2×C16—21no—
229C2×C16—21no—
230#107—21no—
231#106—21no—
232#106—21no—
233#106C5×D412yes—
234#104—42no—
235#103—22no—
236#102—22no—
237#99—42no—
238#97—21no—
239C4×C8—21no—
240C22×C5—41no—
241C22×C5—42no—
242C22×C5—81no—
243C22×C5—81no—
244C22×C5—81no—
245C22×C5—161no—
246C22×C5C4×D811yescharacteristic
247C22×C5#44711yescharacteristic
248C22×C5#45911yescharacteristic
249C4×C5—42no—
250C4×C5—42no—
251C4×C5—82no—
252C4×C5—81no—
253C4×C5—161no—
254C4×C5#38611yescharacteristic
255C4×C5#44211yescharacteristic
256C4×C5#44911yescharacteristic
257C4×C5#46311yescharacteristic
258#41—22no—
259#41—22no—
260#41—41no—
261#41—41no—
262#41—41no—
263#41—41no—
264#41—41no—
265#41—41no—
266C2×Q8—21no—
267C2×Q8—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—41no—
271C2×D4—41no—
272C22×C4—42no—
273C22×C4—41no—
274C22×C4—41no—
275C22×C4—41no—
276C22×C4C2×C5×D411yescharacteristic
277Q16—21no—
278Q16—21no—
279Q16—21no—
280Q16C5×C22⋊C412yes—
281SD16—22no—
282SD16—22no—
283SD16—41no—
284SD16—41no—
285D8—21no—
286D8—21no—
287D8—21no—
288D8C5×C22⋊C412yes—
289M16—21no—
290M16—21no—
291C2×C8—21no—
292C2×C8C22×C4×C511yescharacteristic
293C2×C8C2×C5×D411yescharacteristic
294C2×C8C2×C5×D411yescharacteristic
295C2×C8C2×C5×D411yescharacteristic
296C2×C8C5×#4111yescharacteristic
297C2×C8C5×#4111yescharacteristic
298C4⋊C4—21no—
299C4⋊C4—22no—
300C4⋊C4—42no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C22⋊C4—42no—
304C22⋊C4—41no—
305C22⋊C4C5×D812yes—
306C42—21no—
307C42—42no—
308C42—41no—
309C16—22no—
310C16—41no—
311C2×C5—21no—
312C2×C5—21no—
313C2×C5—21no—
314C2×C5—82no—
315C2×C5—161no—
316C2×C5#187911yescharacteristic
317C23—41no—
318C23—41no—
319C23C2×C5×D811yescharacteristic
320Q8—22no—
321Q8—41no—
322Q8—41no—
323Q8—41no—
324D4—22no—
325D4—42no—
326D4—42no—
327D4—41no—
328D4—41no—
329D4—41no—
330D4—81no—
331D4—81no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—42no—
335C2×C4—42no—
336C2×C4—41no—
337C2×C4—42no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—162no—
342C2×C4—161no—
343C2×C4C4×C5×D411yescharacteristic
344C2×C4C5×#12011yescharacteristic
345C2×C4C5×#12111yescharacteristic
346C2×C4C5×#13511yescharacteristic
347C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
348C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
349C8—41no—
350C8C2×C5×C22⋊C411yescharacteristic
351C8C4×C5×D411yescharacteristic
352C8C5×#12111yescharacteristic
353C8C5×#12311yescharacteristic
354C5#1303011yescharacteristic, direct product factor, Sylow
355C22—41no—
356C22—42no—
357C22—81no—
358C22—81no—
359C22—81no—
360C22—161no—
361C22C4×C5×D811yescharacteristic
362C22C5×#44711yescharacteristic
363C22C5×#45911yescharacteristic
364C4—42no—
365C4—42no—
366C4—82no—
367C4—81no—
368C4—161no—
369C4C5×#38611yescharacteristic
370C4C5×#44211yescharacteristic
371C4C5×#44911yescharacteristic
372C4C5×#46311yescharacteristic
373C2—21no—
374C2—21no—
375C2—21no—
376C2—82no—
377C2—161no—
378C2C5×#187911yescharacteristic
subgroupG/H
center, socleC2×C5#1879
commutatorC2×C8C22×C4×C5
Frattini, cosocleC22×C8C23×C5
prime radicalC5×#3414C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#405 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2952C2semidirect
3. C5×#2145C2semidirect
4. C2×C5×#360C2semidirect
5. C5×#1976C2semidirect
6. C5×#1386C2semidirect
7. C5×#1378C2semidirect
12. C5×#510C4semidirect
14. C5×#509C4semidirect
29. #13030C5direct (N × H)
40. C2×C5×Q16C2×C4semidirect
44. C2×C5×D8C2×C4semidirect
63. C5×M32C2×C4semidirect
77. #2952C2×C5semidirect
78. #2145C2×C5semidirect
79. C2×#360C2×C5semidirect
80. #1976C2×C5semidirect
81. #1386C2×C5semidirect
82. #1378C2×C5semidirect
140. #510C4×C5semidirect
142. #509C4×C5semidirect
204. C2×Q16C2×C4×C5semidirect
208. C2×D8C2×C4×C5semidirect
227. M32C2×C4×C5semidirect
354. C5#13030direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34142
C5×#29522
C5×#21452
C2×C5×#3602
C5×#19762
C5×#13862
C5×#13782
#130305