Finite Group Databasebeta

← C5×#13319 #11936039

Subgroups — C5×#13319 #11936039

Order 1280.

572 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×D16C211yesmaximal, characteristic, complemented
2C2×C5×#472C211yesmaximal, characteristic, complemented
3C5×#3058C211yesmaximal, characteristic, complemented
4C2×C5×#361C211yesmaximal, characteristic, complemented
5C5×#2140C211yesmaximal, characteristic, complemented
6C2×C5×#350C211yesmaximal, characteristic, complemented
7C5×#1382C211yesmaximal, characteristic, complemented
8C2×C5×AGL(1,ℤ/8)—21no—
9C22×C5×D8C2211yescharacteristic
10C22×C5×D8C2211yescharacteristic
11C2×C5×#131C2211yescharacteristic
12C5×#535—21no—
13C2×C5×D16—22no—
14C2×C5×D16—22no—
15C2×C5×D16—22no—
16C2×C5×M32C2211yescharacteristic
17C22×C5×C16C2211yescharacteristic
18C5×#472—22no—
19C5×#472—22no—
20C5×#469—22no—
21C5×#466—22no—
22C2×C5×#108C2211yescharacteristic
23C5×#427C2211yescharacteristic
24C5×#418—21no—
25C2×C5×#100—21no—
26C5×#361—22no—
27C5×#357—22no—
28C5×#350—22no—
29#13319C511yesmaximal, characteristic, direct product factor, Sylow
30C2×C5×#41D411yescharacteristic
31C22×C5×D4—21no—
32C22×C5×D4—21no—
33C5×AGL(1,ℤ/8)—24no—
34C5×AGL(1,ℤ/8)—42no—
35C2×C5×SD16—41no—
36C2×C5×D8—21no—
37C2×C5×D8—21no—
38C2×C5×D8—21no—
39C2×C5×D8—21no—
40C2×C5×D8—21no—
41C2×C5×D8—21no—
42C2×C5×D8—21no—
43C2×C5×D8—21no—
44C2×C5×D8—21no—
45C2×C5×D8—21no—
46C2×C5×D8—41no—
47C2×C5×D8D412yes—
48C2×C5×D8D412yescomplemented
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×D16—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×#100—24no—
76C22×D16C2×C511yescharacteristic, complemented
77C2×#472C2×C511yescharacteristic, complemented
78#3058C2×C511yescharacteristic, complemented
79C2×#361C2×C511yescharacteristic, complemented
80#2140C2×C511yescharacteristic, complemented
81C2×#350C2×C511yescharacteristic, complemented
82#1382C2×C511yescharacteristic, complemented
83C24×C5—41no—
84C24×C5—41no—
85C5×#41—21no—
86C5×#41—21no—
87C5×#41—21no—
88C5×#41—21no—
89C2×C5×Q8D811yescharacteristic
90C2×C5×D4—21no—
91C2×C5×D4—22no—
92C2×C5×D4—22no—
93C2×C5×D4—44no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C2×C5×D4—41no—
99C2×C5×D4—41no—
100C2×C5×D4—41no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4D811yescharacteristic
105C22×C4×C5—21no—
106C22×C4×C5C2×D411yescharacteristic
107C5×SD16—44no—
108C5×D8—22no—
109C5×D8—22no—
110C5×D8—22no—
111C5×D8—22no—
112C5×D8—44no—
113C5×D8—41no—
114C5×D8—41no—
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×AGL(1,ℤ/8)—21no—
140C22×D8C22×C511yescharacteristic
141C22×D8C22×C511yescharacteristic
142C2×#131C22×C511yescharacteristic
143#535—21no—
144C2×D16—22no—
145C2×D16—22no—
146C2×D16—22no—
147C2×M32C22×C511yescharacteristic
148C22×C16C22×C511yescharacteristic
149#472—22no—
150#472—22no—
151#469—22no—
152#466—22no—
153C2×#108C22×C511yescharacteristic
154#427C22×C511yescharacteristic
155#418—21no—
156C2×#100—21no—
157#361—22no—
158#357—22no—
159#350—22no—
160C23×C5—21no—
161C23×C5—42no—
162C23×C5—42no—
163C23×C5—81no—
164C23×C5—81no—
165C23×C5—81no—
166C23×C5—81no—
167C23×C5—162no—
168C23×C5—162no—
169C23×C5AGL(1,ℤ/8)11yescharacteristic
170C5×Q8—21no—
171C5×Q8—21no—
172C5×D4—21no—
173C5×D4—21no—
174C5×D4—41no—
175C5×D4—41no—
176C5×D4—42no—
177C5×D4—42no—
178C5×D4—42no—
179C5×D4—42no—
180C5×D4—81no—
181C5×D4—81no—
182C5×D4—81no—
183C5×D4—81no—
184C5×D4—164no—
185C2×C4×C5—21no—
186C2×C4×C5—41no—
187C2×C4×C5—41no—
188C2×C4×C5—42no—
189C2×C4×C5#12011yescharacteristic
190C2×C4×C5#12011yescharacteristic
191C2×C4×C5#12111yescharacteristic
192C2×C4×C5C2×D811yescharacteristic
193C2×C4×C5#13511yescharacteristic
194C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
195C5×C8—41no—
196C5×C8—42no—
197C5×C8#12011yescharacteristic
198C5×C8#12111yescharacteristic
199C5×C8#12111yescharacteristic
200C5×C8#12711yescharacteristic
201C2×#41C5×D411yescharacteristic
202C22×D4—21no—
203C22×D4—21no—
204AGL(1,ℤ/8)—24no—
205AGL(1,ℤ/8)—42no—
206C2×SD16—41no—
207C2×D8—21no—
208C2×D8—21no—
209C2×D8—21no—
210C2×D8—21no—
211C2×D8—21no—
212C2×D8—21no—
213C2×D8—21no—
214C2×D8—21no—
215C2×D8—21no—
216C2×D8—21no—
217C2×D8—41no—
218C2×D8C5×D412yes—
219C2×D8C5×D412yescomplemented
220#131—21no—
221#131—21no—
222#131—21no—
223#131—21no—
224C2×M16—21no—
225C2×M16—21no—
226C2×M16C5×D411yescharacteristic
227C22×C8—21no—
228C22×C8C23×C511yescharacteristic
229#127—41no—
230#124—41no—
231#121—24no—
232#120—42no—
233#117—21no—
234D16—28no—
235M32—21no—
236M32—21no—
237C2×C16—21no—
238C2×C16—21no—
239C2×C16—21no—
240C2×C16C5×D412yescomplemented
241#108—21no—
242#108C5×D412yescomplemented
243#107C5×D412yes—
244#106—21no—
245#102—24no—
246#100—24no—
247C22×C5—22no—
248C22×C5—42no—
249C22×C5—41no—
250C22×C5—84no—
251C22×C5—82no—
252C22×C5—82no—
253C22×C5—162no—
254C22×C5—162no—
255C22×C5—162no—
256C22×C5—162no—
257C22×C5—162no—
258C22×C5#44711yescharacteristic
259C22×C5#44911yescharacteristic
260C22×C5#46911yescharacteristic
261C4×C5—41no—
262C4×C5—82no—
263C4×C5#39211yescharacteristic
264C4×C5#44711yescharacteristic
265C4×C5#44911yescharacteristic
266C4×C5#46611yescharacteristic
267C24—41no—
268C24—41no—
269#41—21no—
270#41—21no—
271#41—21no—
272#41—21no—
273C2×Q8C5×D811yescharacteristic
274C2×D4—21no—
275C2×D4—22no—
276C2×D4—22no—
277C2×D4—44no—
278C2×D4—41no—
279C2×D4—41no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4C5×D811yescharacteristic
289C22×C4—21no—
290C22×C4C2×C5×D411yescharacteristic
291SD16—44no—
292D8—22no—
293D8—22no—
294D8—22no—
295D8—22no—
296D8—44no—
297D8—41no—
298D8—41no—
299D8—41no—
300D8—41no—
301M16—21no—
302M16—22no—
303M16—21no—
304M16—41no—
305M16—41no—
306M16—41no—
307C2×C8—21no—
308C2×C8—41no—
309C2×C8—41no—
310C2×C8—41no—
311C2×C8C2×C5×D411yescharacteristic
312C2×C8C2×C5×D411yescharacteristic
313C2×C8C2×C5×D411yescharacteristic
314C2×C8C2×C5×D411yescharacteristic
315C2×C8C2×C5×D411yescharacteristic
316C2×C8C5×#4111yescharacteristic
317C4⋊C4—22no—
318C22⋊C4—44no—
319C22⋊C4—41no—
320C42—41no—
321C16—22no—
322C16—41no—
323C2×C5—21no—
324C2×C5—21no—
325C2×C5—81no—
326C2×C5—162no—
327C2×C5—162no—
328C2×C5#199911yescharacteristic
329C2×C5#219212yes—
330C23—21no—
331C23—42no—
332C23—42no—
333C23—81no—
334C23—81no—
335C23—81no—
336C23—81no—
337C23—162no—
338C23—162no—
339C23C5×AGL(1,ℤ/8)11yescharacteristic
340Q8—21no—
341Q8—21no—
342D4—21no—
343D4—21no—
344D4—41no—
345D4—41no—
346D4—42no—
347D4—42no—
348D4—42no—
349D4—42no—
350D4—81no—
351D4—81no—
352D4—81no—
353D4—81no—
354D4—164no—
355C2×C4—21no—
356C2×C4—41no—
357C2×C4—41no—
358C2×C4—42no—
359C2×C4C5×#12011yescharacteristic
360C2×C4C5×#12011yescharacteristic
361C2×C4C5×#12111yescharacteristic
362C2×C4C2×C5×D811yescharacteristic
363C2×C4C5×#13511yescharacteristic
364C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
365C8—41no—
366C8—42no—
367C8C5×#12011yescharacteristic
368C8C5×#12111yescharacteristic
369C8C5×#12111yescharacteristic
370C8C5×#12711yescharacteristic
371C5#1331911yescharacteristic, direct product factor, Sylow
372C22—22no—
373C22—42no—
374C22—41no—
375C22—84no—
376C22—82no—
377C22—82no—
378C22—162no—
379C22—162no—
380C22—162no—
381C22—162no—
382C22—162no—
383C22C5×#44711yescharacteristic
384C22C5×#44911yescharacteristic
385C22C5×#46911yescharacteristic
386C4—41no—
387C4—82no—
388C4C5×#39211yescharacteristic
389C4C5×#44711yescharacteristic
390C4C5×#44911yescharacteristic
391C4C5×#46611yescharacteristic
392C2—21no—
393C2—21no—
394C2—81no—
395C2—162no—
396C2—162no—
397C2C5×#199911yescharacteristic
398C2C5×#219212yes—
subgroupG/H
center, socleC22×C5#447
commutator, Frattini, cosocleC22×C8C23×C5
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×D16C2semidirect
2. C2×C5×#472C2semidirect
3. C5×#3058C2semidirect
4. C2×C5×#361C2semidirect
5. C5×#2140C2semidirect
6. C2×C5×#350C2semidirect
7. C5×#1382C2semidirect
29. #13319C5direct (N × H)
48. C2×C5×D8D4semidirect
69. C2×C5×C16D4semidirect
71. C5×#108D4semidirect
76. C22×D16C2×C5semidirect
77. C2×#472C2×C5semidirect
78. #3058C2×C5semidirect
79. C2×#361C2×C5semidirect
80. #2140C2×C5semidirect
81. C2×#350C2×C5semidirect
82. #1382C2×C5semidirect
219. C2×D8C5×D4semidirect
240. C2×C16C5×D4semidirect
242. #108C5×D4semidirect
371. C5#13319direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×D162
C2×C5×#4722
C5×#30582
C2×C5×#3612
C5×#21402
C2×C5×#3502
C5×#13822
#133195