Finite Group Databasebeta

← C5×#13321 #11936041

Subgroups — C5×#13321 #11936041

Order 1280.

552 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×SD32C211yesmaximal, characteristic, complemented
2C2×C5×#473C211yesmaximal, characteristic, complemented
3C5×#3058C211yesmaximal, characteristic
4C2×C5×#361C211yesmaximal, characteristic, complemented
5C5×#2141C211yesmaximal, characteristic, complemented
6C2×C5×#350C211yesmaximal, characteristic, complemented
7C5×#1382C211yesmaximal, characteristic, complemented
8C2×C5×#137—21no—
9C22×C5×Q16C2211yescharacteristic
10C22×C5×D8C2211yescharacteristic
11C2×C5×#131C2211yescharacteristic
12C5×#535—21no—
13C2×C5×SD32—22no—
14C2×C5×SD32—22no—
15C2×C5×SD32—22no—
16C2×C5×M32C2211yescharacteristic
17C22×C5×C16C2211yescharacteristic
18C5×#473—22no—
19C5×#473—22no—
20C5×#469—22no—
21C5×#466—22no—
22C2×C5×#108C2211yescharacteristic
23C5×#427C2211yescharacteristic
24C5×#418—21no—
25C2×C5×#101—21no—
26C5×#361—22no—
27C5×#358—22no—
28C5×#350—22no—
29#13321C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41D411yescharacteristic
31C22×C5×Q8—21no—
32C22×C5×D4—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—41no—
41C2×C5×Q16D412yescomplemented
42C2×C5×SD16—41no—
43C2×C5×D8—21no—
44C2×C5×D8—21no—
45C2×C5×D8—21no—
46C2×C5×D8—21no—
47C2×C5×D8—21no—
48C2×C5×D8D412yes—
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×#127—41no—
59C5×#124—41no—
60C5×#121—24no—
61C5×#120—42no—
62C5×#117—21no—
63C5×SD32—28no—
64C5×M32—21no—
65C5×M32—21no—
66C2×C5×C16—21no—
67C2×C5×C16—21no—
68C2×C5×C16—21no—
69C2×C5×C16D412yescomplemented
70C5×#108—21no—
71C5×#108D412yescomplemented
72C5×#107D412yes—
73C5×#106—21no—
74C5×#102—24no—
75C5×#101—24no—
76C22×SD32C2×C511yescharacteristic, complemented
77C2×#473C2×C511yescharacteristic, complemented
78#3058C2×C511yescharacteristic
79C2×#361C2×C511yescharacteristic, complemented
80#2141C2×C511yescharacteristic, complemented
81C2×#350C2×C511yescharacteristic, complemented
82#1382C2×C511yescharacteristic, complemented
83C24×C5—41no—
84C5×#41—21no—
85C5×#41—21no—
86C5×#41—21no—
87C5×#41—21no—
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×Q8D811yescharacteristic
95C2×C5×D4—21no—
96C2×C5×D4—22no—
97C2×C5×D4—44no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4D811yescharacteristic
104C22×C4×C5—21no—
105C22×C4×C5—41no—
106C22×C4×C5C2×D411yescharacteristic
107C5×Q16—22no—
108C5×Q16—22no—
109C5×Q16—44no—
110C5×Q16—41no—
111C5×Q16—41no—
112C5×SD16—44no—
113C5×D8—22no—
114C5×D8—22no—
115C5×D8—41no—
116C5×D8—41no—
117C5×M16—22no—
118C5×M16—21no—
119C5×M16—21no—
120C5×M16—41no—
121C5×M16—41no—
122C5×M16—41no—
123C2×C5×C8—21no—
124C2×C5×C8—41no—
125C2×C5×C8—41no—
126C2×C5×C8—41no—
127C2×C5×C8C2×D411yescharacteristic
128C2×C5×C8C2×D411yescharacteristic
129C2×C5×C8C2×D411yescharacteristic
130C2×C5×C8C2×D411yescharacteristic
131C2×C5×C8C2×D411yescharacteristic
132C2×C5×C8#4111yescharacteristic
133C5×C4⋊C4—22no—
134C5×C22⋊C4—44no—
135C5×C22⋊C4—41no—
136C42×C5—41no—
137C5×C16—22no—
138C5×C16—41no—
139C2×#137—21no—
140C22×Q16C22×C511yescharacteristic
141C22×D8C22×C511yescharacteristic
142C2×#131C22×C511yescharacteristic
143#535—21no—
144C2×SD32—22no—
145C2×SD32—22no—
146C2×SD32—22no—
147C2×M32C22×C511yescharacteristic
148C22×C16C22×C511yescharacteristic
149#473—22no—
150#473—22no—
151#469—22no—
152#466—22no—
153C2×#108C22×C511yescharacteristic
154#427C22×C511yescharacteristic
155#418—21no—
156C2×#101—21no—
157#361—22no—
158#358—22no—
159#350—22no—
160C23×C5—21no—
161C23×C5—42no—
162C23×C5—81no—
163C23×C5—81no—
164C23×C5—162no—
165C23×C5AGL(1,ℤ/8)11yescharacteristic
166C5×Q8—21no—
167C5×Q8—21no—
168C5×Q8—42no—
169C5×Q8—42no—
170C5×Q8—81no—
171C5×Q8—81no—
172C5×D4—21no—
173C5×D4—21no—
174C5×D4—41no—
175C5×D4—41no—
176C5×D4—42no—
177C5×D4—42no—
178C5×D4—81no—
179C5×D4—81no—
180C5×D4—164no—
181C2×C4×C5—21no—
182C2×C4×C5—41no—
183C2×C4×C5—41no—
184C2×C4×C5—42no—
185C2×C4×C5—42no—
186C2×C4×C5—81no—
187C2×C4×C5—81no—
188C2×C4×C5#12011yescharacteristic
189C2×C4×C5#12011yescharacteristic
190C2×C4×C5#12111yescharacteristic
191C2×C4×C5C2×D811yescharacteristic
192C2×C4×C5#13511yescharacteristic
193C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
194C5×C8—41no—
195C5×C8—42no—
196C5×C8#12011yescharacteristic
197C5×C8#12111yescharacteristic
198C5×C8#12111yescharacteristic
199C5×C8#12711yescharacteristic
200C2×#41C5×D411yescharacteristic
201C22×Q8—21no—
202C22×D4—21no—
203#137—24no—
204#137—42no—
205C2×Q16—21no—
206C2×Q16—21no—
207C2×Q16—21no—
208C2×Q16—21no—
209C2×Q16—21no—
210C2×Q16—41no—
211C2×Q16C5×D412yescomplemented
212C2×SD16—41no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8C5×D412yes—
219#131—21no—
220#131—21no—
221#131—21no—
222#131—21no—
223C2×M16—21no—
224C2×M16—21no—
225C2×M16C5×D411yescharacteristic
226C22×C8—21no—
227C22×C8C23×C511yescharacteristic
228#127—41no—
229#124—41no—
230#121—24no—
231#120—42no—
232#117—21no—
233SD32—28no—
234M32—21no—
235M32—21no—
236C2×C16—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16C5×D412yescomplemented
240#108—21no—
241#108C5×D412yescomplemented
242#107C5×D412yes—
243#106—21no—
244#102—24no—
245#101—24no—
246C22×C5—22no—
247C22×C5—42no—
248C22×C5—41no—
249C22×C5—84no—
250C22×C5—82no—
251C22×C5—162no—
252C22×C5—162no—
253C22×C5#44711yescharacteristic
254C22×C5#44911yescharacteristic
255C22×C5#46911yescharacteristic
256C4×C5—41no—
257C4×C5—82no—
258C4×C5—82no—
259C4×C5#39211yescharacteristic
260C4×C5#44711yescharacteristic
261C4×C5#44911yescharacteristic
262C4×C5#46611yescharacteristic
263C24—41no—
264#41—21no—
265#41—21no—
266#41—21no—
267#41—21no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8C5×D811yescharacteristic
275C2×D4—21no—
276C2×D4—22no—
277C2×D4—44no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4C5×D811yescharacteristic
284C22×C4—21no—
285C22×C4—41no—
286C22×C4C2×C5×D411yescharacteristic
287Q16—22no—
288Q16—22no—
289Q16—44no—
290Q16—41no—
291Q16—41no—
292SD16—44no—
293D8—22no—
294D8—22no—
295D8—41no—
296D8—41no—
297M16—21no—
298M16—22no—
299M16—21no—
300M16—41no—
301M16—41no—
302M16—41no—
303C2×C8—21no—
304C2×C8—41no—
305C2×C8—41no—
306C2×C8—41no—
307C2×C8C2×C5×D411yescharacteristic
308C2×C8C2×C5×D411yescharacteristic
309C2×C8C2×C5×D411yescharacteristic
310C2×C8C2×C5×D411yescharacteristic
311C2×C8C2×C5×D411yescharacteristic
312C2×C8C5×#4111yescharacteristic
313C4⋊C4—22no—
314C22⋊C4—44no—
315C22⋊C4—41no—
316C42—41no—
317C16—22no—
318C16—41no—
319C2×C5—21no—
320C2×C5—21no—
321C2×C5—81no—
322C2×C5—162no—
323C2×C5#199911yescharacteristic
324C2×C5#219412yes—
325C23—21no—
326C23—42no—
327C23—81no—
328C23—81no—
329C23—162no—
330C23C5×AGL(1,ℤ/8)11yescharacteristic
331Q8—21no—
332Q8—21no—
333Q8—42no—
334Q8—42no—
335Q8—81no—
336Q8—81no—
337D4—21no—
338D4—21no—
339D4—41no—
340D4—41no—
341D4—42no—
342D4—42no—
343D4—81no—
344D4—81no—
345D4—164no—
346C2×C4—21no—
347C2×C4—41no—
348C2×C4—41no—
349C2×C4—42no—
350C2×C4—42no—
351C2×C4—81no—
352C2×C4—81no—
353C2×C4C5×#12011yescharacteristic
354C2×C4C5×#12011yescharacteristic
355C2×C4C5×#12111yescharacteristic
356C2×C4C2×C5×D811yescharacteristic
357C2×C4C5×#13511yescharacteristic
358C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
359C8—41no—
360C8—42no—
361C8C5×#12011yescharacteristic
362C8C5×#12111yescharacteristic
363C8C5×#12111yescharacteristic
364C8C5×#12711yescharacteristic
365C5#1332111yescharacteristic, direct product factor, Sylow
366C22—22no—
367C22—42no—
368C22—41no—
369C22—84no—
370C22—82no—
371C22—162no—
372C22—162no—
373C22C5×#44711yescharacteristic
374C22C5×#44911yescharacteristic
375C22C5×#46911yescharacteristic
376C4—41no—
377C4—82no—
378C4—82no—
379C4C5×#39211yescharacteristic
380C4C5×#44711yescharacteristic
381C4C5×#44911yescharacteristic
382C4C5×#46611yescharacteristic
383C2—21no—
384C2—21no—
385C2—81no—
386C2—162no—
387C2C5×#199911yescharacteristic
388C2C5×#219412yes—
subgroupG/H
center, socleC22×C5#447
commutator, Frattini, cosocleC22×C8C23×C5
prime radicalC5×#3058C2
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×SD32C2semidirect
2. C2×C5×#473C2semidirect
4. C2×C5×#361C2semidirect
5. C5×#2141C2semidirect
6. C2×C5×#350C2semidirect
7. C5×#1382C2semidirect
29. #13321C5direct (N × H)
41. C2×C5×Q16D4semidirect
69. C2×C5×C16D4semidirect
71. C5×#108D4semidirect
76. C22×SD32C2×C5semidirect
77. C2×#473C2×C5semidirect
79. C2×#361C2×C5semidirect
80. #2141C2×C5semidirect
81. C2×#350C2×C5semidirect
82. #1382C2×C5semidirect
211. C2×Q16C5×D4semidirect
239. C2×C16C5×D4semidirect
241. #108C5×D4semidirect
365. C5#13321direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×SD322
C2×C5×#4732
C5×#30582
C2×C5×#3612
C5×#21412
C2×C5×#3502
C5×#13822
#133215