Finite Group Databasebeta

← C5×#13322 #11936042

Subgroups — C5×#13322 #11936042

Order 1280.

520 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×Q32C211yesmaximal, characteristic, complemented
2C2×C5×#473C211yesmaximal, characteristic
3C5×#3059C211yesmaximal, characteristic
4C2×C5×#362C211yesmaximal, characteristic, complemented
5C5×#2141C211yesmaximal, characteristic, complemented
6C2×C5×#350C211yesmaximal, characteristic
7C5×#1382C211yesmaximal, characteristic, complemented
8C2×C5×#137—21no—
9C22×C5×Q16C2211yescharacteristic
10C22×C5×Q16C2211yescharacteristic
11C2×C5×#131C2211yescharacteristic
12C5×#536—21no—
13C2×C5×Q32—22no—
14C2×C5×Q32—22no—
15C2×C5×Q32—22no—
16C2×C5×M32C2211yescharacteristic
17C22×C5×C16C2211yescharacteristic
18C5×#473—22no—
19C5×#473—22no—
20C5×#470—22no—
21C5×#467—22no—
22C2×C5×#108C2211yescharacteristic
23C5×#427C2211yescharacteristic
24C5×#419—21no—
25C2×C5×#101—21no—
26C5×#362—22no—
27C5×#358—22no—
28C5×#350—22no—
29#13322C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41D411yescharacteristic
31C22×C5×Q8—21no—
32C22×C5×Q8—21no—
33C5×#137—24no—
34C5×#137—42no—
35C2×C5×Q16—21no—
36C2×C5×Q16—21no—
37C2×C5×Q16—21no—
38C2×C5×Q16—21no—
39C2×C5×Q16—21no—
40C2×C5×Q16—21no—
41C2×C5×Q16—21no—
42C2×C5×Q16—21no—
43C2×C5×Q16—21no—
44C2×C5×Q16—21no—
45C2×C5×Q16—41no—
46C2×C5×Q16D412yes—
47C2×C5×Q16D412yes—
48C2×C5×SD16—41no—
49C5×#131—21no—
50C5×#131—21no—
51C5×#131—21no—
52C5×#131—21no—
53C2×C5×M16—21no—
54C2×C5×M16—21no—
55C2×C5×M16D411yescharacteristic
56C22×C5×C8—21no—
57C22×C5×C8C2311yescharacteristic
58C5×C4⋊Q8—41no—
59C5×#124—41no—
60C5×#123—42no—
61C5×C22⋊Q8—24no—
62C5×#117—21no—
63C5×Q32—28no—
64C5×M32—21no—
65C5×M32—21no—
66C2×C5×C16—21no—
67C2×C5×C16—21no—
68C2×C5×C16—21no—
69C2×C5×C16D412yes—
70C5×#108—21no—
71C5×#108D412yes—
72C5×#107D412yes—
73C5×#106—21no—
74C5×#103—24no—
75C5×#101—24no—
76C22×Q32C2×C511yescharacteristic, complemented
77C2×#473C2×C511yescharacteristic
78#3059C2×C511yescharacteristic
79C2×#362C2×C511yescharacteristic, complemented
80#2141C2×C511yescharacteristic, complemented
81C2×#350C2×C511yescharacteristic
82#1382C2×C511yescharacteristic, complemented
83C5×#41—21no—
84C5×#41—21no—
85C5×#41—21no—
86C5×#41—21no—
87C2×C5×Q8—22no—
88C2×C5×Q8—22no—
89C2×C5×Q8—41no—
90C2×C5×Q8—41no—
91C2×C5×Q8—41no—
92C2×C5×Q8—41no—
93C2×C5×Q8—41no—
94C2×C5×Q8—41no—
95C2×C5×Q8—41no—
96C2×C5×Q8—41no—
97C2×C5×Q8—41no—
98C2×C5×Q8—41no—
99C2×C5×Q8D811yescharacteristic
100C2×C5×D4—21no—
101C2×C5×D4D811yescharacteristic
102C22×C4×C5—21no—
103C22×C4×C5—41no—
104C22×C4×C5—41no—
105C22×C4×C5C2×D411yescharacteristic
106C5×Q16—22no—
107C5×Q16—22no—
108C5×Q16—22no—
109C5×Q16—22no—
110C5×Q16—44no—
111C5×Q16—41no—
112C5×Q16—41no—
113C5×Q16—41no—
114C5×Q16—41no—
115C5×SD16—44no—
116C5×M16—22no—
117C5×M16—21no—
118C5×M16—21no—
119C5×M16—41no—
120C5×M16—41no—
121C5×M16—41no—
122C2×C5×C8—21no—
123C2×C5×C8—41no—
124C2×C5×C8—41no—
125C2×C5×C8—41no—
126C2×C5×C8C2×D411yescharacteristic
127C2×C5×C8C2×D411yescharacteristic
128C2×C5×C8C2×D411yescharacteristic
129C2×C5×C8C2×D411yescharacteristic
130C2×C5×C8C2×D411yescharacteristic
131C2×C5×C8#4111yescharacteristic
132C5×C4⋊C4—22no—
133C5×C4⋊C4—44no—
134C5×C22⋊C4—44no—
135C5×C22⋊C4—41no—
136C42×C5—41no—
137C5×C16—22no—
138C5×C16—41no—
139C2×#137—21no—
140C22×Q16C22×C511yescharacteristic
141C22×Q16C22×C511yescharacteristic
142C2×#131C22×C511yescharacteristic
143#536—21no—
144C2×Q32—22no—
145C2×Q32—22no—
146C2×Q32—22no—
147C2×M32C22×C511yescharacteristic
148C22×C16C22×C511yescharacteristic
149#473—22no—
150#473—22no—
151#470—22no—
152#467—22no—
153C2×#108C22×C511yescharacteristic
154#427C22×C511yescharacteristic
155#419—21no—
156C2×#101—21no—
157#362—22no—
158#358—22no—
159#350—22no—
160C23×C5—21no—
161C23×C5AGL(1,ℤ/8)11yescharacteristic
162C5×Q8—21no—
163C5×Q8—21no—
164C5×Q8—42no—
165C5×Q8—42no—
166C5×Q8—42no—
167C5×Q8—42no—
168C5×Q8—81no—
169C5×Q8—81no—
170C5×Q8—81no—
171C5×Q8—81no—
172C5×D4—21no—
173C5×D4—21no—
174C5×D4—41no—
175C5×D4—41no—
176C2×C4×C5—21no—
177C2×C4×C5—41no—
178C2×C4×C5—41no—
179C2×C4×C5—42no—
180C2×C4×C5—42no—
181C2×C4×C5—42no—
182C2×C4×C5—81no—
183C2×C4×C5—81no—
184C2×C4×C5—81no—
185C2×C4×C5—81no—
186C2×C4×C5#12011yescharacteristic
187C2×C4×C5#12011yescharacteristic
188C2×C4×C5#12111yescharacteristic
189C2×C4×C5C2×D811yescharacteristic
190C2×C4×C5#13511yescharacteristic
191C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
192C5×C8—41no—
193C5×C8—42no—
194C5×C8#12011yescharacteristic
195C5×C8#12111yescharacteristic
196C5×C8#12111yescharacteristic
197C5×C8#12711yescharacteristic
198C2×#41C5×D411yescharacteristic
199C22×Q8—21no—
200C22×Q8—21no—
201#137—24no—
202#137—42no—
203C2×Q16—21no—
204C2×Q16—21no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16—21no—
211C2×Q16—21no—
212C2×Q16—21no—
213C2×Q16—41no—
214C2×Q16C5×D412yes—
215C2×Q16C5×D412yes—
216C2×SD16—41no—
217#131—21no—
218#131—21no—
219#131—21no—
220#131—21no—
221C2×M16—21no—
222C2×M16—21no—
223C2×M16C5×D411yescharacteristic
224C22×C8—21no—
225C22×C8C23×C511yescharacteristic
226C4⋊Q8—41no—
227#124—41no—
228#123—42no—
229C22⋊Q8—24no—
230#117—21no—
231Q32—28no—
232M32—21no—
233M32—21no—
234C2×C16—21no—
235C2×C16—21no—
236C2×C16—21no—
237C2×C16C5×D412yes—
238#108—21no—
239#108C5×D412yes—
240#107C5×D412yes—
241#106—21no—
242#103—24no—
243#101—24no—
244C22×C5—22no—
245C22×C5—42no—
246C22×C5—41no—
247C22×C5#44711yescharacteristic
248C22×C5#44911yescharacteristic
249C22×C5#46911yescharacteristic
250C4×C5—41no—
251C4×C5—82no—
252C4×C5—82no—
253C4×C5—82no—
254C4×C5#39211yescharacteristic
255C4×C5#44711yescharacteristic
256C4×C5#44911yescharacteristic
257C4×C5#46611yescharacteristic
258#41—21no—
259#41—21no—
260#41—21no—
261#41—21no—
262C2×Q8—22no—
263C2×Q8—22no—
264C2×Q8—41no—
265C2×Q8—41no—
266C2×Q8—41no—
267C2×Q8—41no—
268C2×Q8—41no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8C5×D811yescharacteristic
275C2×D4—21no—
276C2×D4C5×D811yescharacteristic
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4C2×C5×D411yescharacteristic
281Q16—22no—
282Q16—22no—
283Q16—22no—
284Q16—22no—
285Q16—44no—
286Q16—41no—
287Q16—41no—
288Q16—41no—
289Q16—41no—
290SD16—44no—
291M16—21no—
292M16—22no—
293M16—21no—
294M16—41no—
295M16—41no—
296M16—41no—
297C2×C8—21no—
298C2×C8—41no—
299C2×C8—41no—
300C2×C8—41no—
301C2×C8C2×C5×D411yescharacteristic
302C2×C8C2×C5×D411yescharacteristic
303C2×C8C2×C5×D411yescharacteristic
304C2×C8C2×C5×D411yescharacteristic
305C2×C8C2×C5×D411yescharacteristic
306C2×C8C5×#4111yescharacteristic
307C4⋊C4—22no—
308C4⋊C4—44no—
309C22⋊C4—44no—
310C22⋊C4—41no—
311C42—41no—
312C16—22no—
313C16—41no—
314C2×C5—21no—
315C2×C5—21no—
316C2×C5—81no—
317C2×C5#199911yescharacteristic
318C2×C5#219512yes—
319C23—21no—
320C23C5×AGL(1,ℤ/8)11yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—42no—
324Q8—42no—
325Q8—42no—
326Q8—42no—
327Q8—81no—
328Q8—81no—
329Q8—81no—
330Q8—81no—
331D4—21no—
332D4—21no—
333D4—41no—
334D4—41no—
335C2×C4—21no—
336C2×C4—41no—
337C2×C4—41no—
338C2×C4—42no—
339C2×C4—42no—
340C2×C4—42no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4C5×#12011yescharacteristic
346C2×C4C5×#12011yescharacteristic
347C2×C4C5×#12111yescharacteristic
348C2×C4C2×C5×D811yescharacteristic
349C2×C4C5×#13511yescharacteristic
350C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
351C8—41no—
352C8—42no—
353C8C5×#12011yescharacteristic
354C8C5×#12111yescharacteristic
355C8C5×#12111yescharacteristic
356C8C5×#12711yescharacteristic
357C5#1332211yescharacteristic, direct product factor, Sylow
358C22—22no—
359C22—42no—
360C22—41no—
361C22C5×#44711yescharacteristic
362C22C5×#44911yescharacteristic
363C22C5×#46911yescharacteristic
364C4—41no—
365C4—82no—
366C4—82no—
367C4—82no—
368C4C5×#39211yescharacteristic
369C4C5×#44711yescharacteristic
370C4C5×#44911yescharacteristic
371C4C5×#46611yescharacteristic
372C2—21no—
373C2—21no—
374C2—81no—
375C2C5×#199911yescharacteristic
376C2C5×#219512yes—
subgroupG/H
center, socleC22×C5#447
commutator, Frattini, cosocleC22×C8C23×C5
prime radicalC2×C5×#41D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C5×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C5×Q32C2semidirect
4. C2×C5×#362C2semidirect
5. C5×#2141C2semidirect
7. C5×#1382C2semidirect
29. #13322C5direct (N × H)
76. C22×Q32C2×C5semidirect
79. C2×#362C2×C5semidirect
80. #2141C2×C5semidirect
82. #1382C2×C5semidirect
357. C5#13322direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×Q322
C2×C5×#4732
C5×#30592
C2×C5×#3622
C5×#21412
C2×C5×#3502
C5×#13822
#133225