Finite Group Databasebeta

← C5×#12995 #11935715

Subgroups — C5×#12995 #11935715

Order 1280.

476 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3067C211yesmaximal, characteristic
2C5×#2916C211yesmaximal, characteristic, complemented
3C5×#2143C211yesmaximal, characteristic, complemented
4C2×C5×#359C211yesmaximal, characteristic, complemented
5C2×C5×#350C211yesmaximal, characteristic, complemented
6C5×#1388C211yesmaximal, characteristic, complemented
7C5×#1381C211yesmaximal, characteristic, complemented
8C5×#575—21no—
9C2×C5×#135C2211yescharacteristic
10C5×#568—21no—
11C2×C5×#131C2211yescharacteristic
12C2×C5×M32C2211yescharacteristic
13C22×C5×C16C2211yescharacteristic
14C5×#473C412yes—
15C5×#472C412yes—
16C5×#471—22no—
17C5×#430—22no—
18C5×#430—21no—
19C2×C5×#108—22no—
20C2×C5×#108C2211yescharacteristic
21C2×C5×#108C2211yescharacteristic
22C2×C5×#108C2211yescharacteristic
23C5×#413—21no—
24C5×#359—22no—
25C5×#359—22no—
26C5×#350—22no—
27#12995C511yesmaximal, characteristic, direct product factor, Sylow
28C2×C5×#41—21no—
29C2×C5×#41D411yescharacteristic
30C5×#137—22no—
31C5×#137—41no—
32C5×AGL(1,ℤ/8)—22no—
33C5×AGL(1,ℤ/8)—41no—
34C5×#135—21no—
35C5×#135—21no—
36C5×#135—21no—
37C5×#135—21no—
38C5×#135—42no—
39C2×C5×Q16C2×C411yescharacteristic
40C2×C5×SD16—21no—
41C2×C5×D8C2×C411yescharacteristic
42C5×#131—21no—
43C5×#131—21no—
44C5×#131—42no—
45C5×#131—42no—
46C5×#131C2×C412yes—
47C5×#131D412yes—
48C2×C5×M16—21no—
49C2×C5×M16—24no—
50C2×C5×M16—21no—
51C2×C5×M16—21no—
52C2×C5×M16—21no—
53C2×C5×M16D411yescharacteristic
54C22×C5×C8—21no—
55C22×C5×C8C2311yescharacteristic
56C5×M32—21no—
57C5×M32—21no—
58C2×C5×C16—21no—
59C2×C5×C16—21no—
60C2×C5×C16—21no—
61C2×C5×C16—21no—
62C5×#108—24no—
63C5×#108—21no—
64C5×#108—21no—
65C5×#108—21no—
66C5×#108C2×C412yes—
67C5×#108D412yes—
68C5×#108D412yes—
69C5×#101—22no—
70C5×#100—22no—
71#3067C2×C511yescharacteristic
72#2916C2×C511yescharacteristic, complemented
73#2143C2×C511yescharacteristic, complemented
74C2×#359C2×C511yescharacteristic, complemented
75C2×#350C2×C511yescharacteristic, complemented
76#1388C2×C511yescharacteristic, complemented
77#1381C2×C511yescharacteristic, complemented
78C5×#41—21no—
79C5×#41—21no—
80C5×#41—41no—
81C5×#41—41no—
82C5×#41—41no—
83C5×#41—41no—
84C5×#41C22⋊C412yes—
85C5×#41D812yes—
86C2×C5×Q8—21no—
87C2×C5×Q8SD1611yescharacteristic
88C2×C5×D4—21no—
89C2×C5×D4—21no—
90C2×C5×D4—41no—
91C2×C5×D4SD1611yescharacteristic
92C22×C4×C5—21no—
93C22×C4×C5—41no—
94C22×C4×C5C2×D411yescharacteristic
95C5×Q16—21no—
96C5×Q16—21no—
97C5×Q16—42no—
98C5×SD16—42no—
99C5×SD16—42no—
100C5×SD16—41no—
101C5×SD16—41no—
102C5×D8—21no—
103C5×D8—21no—
104C5×D8—42no—
105C5×M16—21no—
106C5×M16—22no—
107C5×M16—22no—
108C5×M16—22no—
109C5×M16—22no—
110C5×M16—22no—
111C5×M16—44no—
112C5×M16—41no—
113C5×M16—41no—
114C5×M16—41no—
115C5×M16C22⋊C412yes—
116C2×C5×C8—21no—
117C2×C5×C8—22no—
118C2×C5×C8—22no—
119C2×C5×C8—44no—
120C2×C5×C8—41no—
121C2×C5×C8—41no—
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×C16—41no—
130C5×C16—41no—
131#575—21no—
132C2×#135C22×C511yescharacteristic
133#568—21no—
134C2×#131C22×C511yescharacteristic
135C2×M32C22×C511yescharacteristic
136C22×C16C22×C511yescharacteristic
137#473C4×C512yes—
138#472C4×C512yes—
139#471—22no—
140#430—21no—
141#430—22no—
142C2×#108—22no—
143C2×#108C22×C511yescharacteristic
144C2×#108C22×C511yescharacteristic
145C2×#108C22×C511yescharacteristic
146#413—21no—
147#359—22no—
148#359—22no—
149#350—22no—
150C23×C5—21no—
151C23×C5—41no—
152C23×C5#13711yescharacteristic
153C5×Q8—21no—
154C5×Q8—41no—
155C5×Q8—41no—
156C5×Q8#10212yes—
157C5×D4—22no—
158C5×D4—22no—
159C5×D4—21no—
160C5×D4—41no—
161C5×D4—41no—
162C5×D4—81no—
163C5×D4—81no—
164C5×D4#10212yes—
165C2×C4×C5—21no—
166C2×C4×C5—22no—
167C2×C4×C5—22no—
168C2×C4×C5—41no—
169C2×C4×C5—81no—
170C2×C4×C5—81no—
171C2×C4×C5C2×C22⋊C411yescharacteristic
172C2×C4×C5#12011yescharacteristic
173C2×C4×C5#12311yescharacteristic
174C2×C4×C5C2×D811yescharacteristic
175C2×C4×C5C2×SD1611yescharacteristic
176C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
177C5×C8—22no—
178C5×C8—42no—
179C5×C8—42no—
180C5×C8—42no—
181C5×C8C4×D411yescharacteristic
182C5×C8C4×D411yescharacteristic
183C5×C8#12111yescharacteristic
184C5×C8#12111yescharacteristic
185C2×#41—21no—
186C2×#41C5×D411yescharacteristic
187#137—22no—
188#137—41no—
189AGL(1,ℤ/8)—22no—
190AGL(1,ℤ/8)—41no—
191#135—21no—
192#135—21no—
193#135—21no—
194#135—21no—
195#135—42no—
196C2×Q16C2×C4×C511yescharacteristic
197C2×SD16—21no—
198C2×D8C2×C4×C511yescharacteristic
199#131—21no—
200#131—21no—
201#131—42no—
202#131—42no—
203#131C2×C4×C512yes—
204#131C5×D412yes—
205C2×M16—21no—
206C2×M16—24no—
207C2×M16—21no—
208C2×M16—21no—
209C2×M16—21no—
210C2×M16C5×D411yescharacteristic
211C22×C8—21no—
212C22×C8C23×C511yescharacteristic
213M32—21no—
214M32—21no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—21no—
218C2×C16—21no—
219#108—24no—
220#108—21no—
221#108—21no—
222#108—21no—
223#108C2×C4×C512yes—
224#108C5×D412yes—
225#108C5×D412yes—
226#101—22no—
227#100—22no—
228C22×C5—22no—
229C22×C5—41no—
230C22×C5—81no—
231C22×C5—81no—
232C22×C5—161no—
233C22×C5#41711yescharacteristic
234C22×C5#44811yescharacteristic
235C22×C5#48011yescharacteristic
236C4×C5—22no—
237C4×C5—81no—
238C4×C5#38611yescharacteristic
239C4×C5C2×#10211yescharacteristic
240C4×C5#44711yescharacteristic
241C4×C5#48111yescharacteristic
242#41—21no—
243#41—21no—
244#41—41no—
245#41—41no—
246#41—41no—
247#41—41no—
248#41C5×C22⋊C412yes—
249#41C5×D812yes—
250C2×Q8—21no—
251C2×Q8C5×SD1611yescharacteristic
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—41no—
255C2×D4C5×SD1611yescharacteristic
256C22×C4—21no—
257C22×C4—41no—
258C22×C4C2×C5×D411yescharacteristic
259Q16—21no—
260Q16—21no—
261Q16—42no—
262SD16—42no—
263SD16—42no—
264SD16—41no—
265SD16—41no—
266D8—21no—
267D8—21no—
268D8—42no—
269M16—21no—
270M16—22no—
271M16—22no—
272M16—22no—
273M16—22no—
274M16—22no—
275M16—44no—
276M16—41no—
277M16—41no—
278M16—41no—
279M16C5×C22⋊C412yes—
280C2×C8—21no—
281C2×C8—22no—
282C2×C8—22no—
283C2×C8—44no—
284C2×C8—41no—
285C2×C8—41no—
286C2×C8—41no—
287C2×C8C22×C4×C511yescharacteristic
288C2×C8C2×C5×D411yescharacteristic
289C2×C8C2×C5×D411yescharacteristic
290C2×C8C2×C5×D411yescharacteristic
291C2×C8C5×#4111yescharacteristic
292C2×C8C5×#4111yescharacteristic
293C16—41no—
294C16—41no—
295C2×C5—21no—
296C2×C5—21no—
297C2×C5—21no—
298C2×C5—42no—
299C2×C5—161no—
300C2×C5#187411yescharacteristic
301C23—21no—
302C23—41no—
303C23C5×#13711yescharacteristic
304Q8—21no—
305Q8—41no—
306Q8—41no—
307Q8C5×#10212yes—
308D4—22no—
309D4—22no—
310D4—21no—
311D4—41no—
312D4—41no—
313D4—81no—
314D4—81no—
315D4C5×#10212yes—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—22no—
319C2×C4—41no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4C2×C5×C22⋊C411yescharacteristic
323C2×C4C5×#12011yescharacteristic
324C2×C4C5×#12311yescharacteristic
325C2×C4C2×C5×D811yescharacteristic
326C2×C4C2×C5×SD1611yescharacteristic
327C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
328C8—22no—
329C8—42no—
330C8—42no—
331C8—42no—
332C8C4×C5×D411yescharacteristic
333C8C4×C5×D411yescharacteristic
334C8C5×#12111yescharacteristic
335C8C5×#12111yescharacteristic
336C5#1299511yescharacteristic, direct product factor, Sylow
337C22—22no—
338C22—41no—
339C22—81no—
340C22—81no—
341C22—161no—
342C22C5×#41711yescharacteristic
343C22C5×#44811yescharacteristic
344C22C5×#48011yescharacteristic
345C4—22no—
346C4—81no—
347C4C5×#38611yescharacteristic
348C4C2×C5×#10211yescharacteristic
349C4C5×#44711yescharacteristic
350C4C5×#48111yescharacteristic
351C2—21no—
352C2—21no—
353C2—21no—
354C2—42no—
355C2—161no—
356C2C5×#187411yescharacteristic
subgroupG/H
centerC4×C5#447
commutatorC2×C8C22×C4×C5
Frattini, cosocleC22×C8C23×C5
socleC2×C5#1874
prime radicalC5×#3067C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C5 ◁ C22×C4×C5 ◁ C2×C5×#131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#2916C2semidirect
3. C5×#2143C2semidirect
4. C2×C5×#359C2semidirect
5. C2×C5×#350C2semidirect
6. C5×#1388C2semidirect
7. C5×#1381C2semidirect
27. #12995C5direct (N × H)
72. #2916C2×C5semidirect
73. #2143C2×C5semidirect
74. C2×#359C2×C5semidirect
75. C2×#350C2×C5semidirect
76. #1388C2×C5semidirect
77. #1381C2×C5semidirect
336. C5#12995direct (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×#29162
C5×#21432
C2×C5×#3592
C2×C5×#3502
C5×#13882
C5×#13812
#129955