Finite Group Databasebeta

← C5×#13311 #11936031

Subgroups — C5×#13311 #11936031

Order 1280.

520 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#510C211yesmaximal, characteristic, complemented
2C5×#3067C211yesmaximal, characteristic
3C5×#3059C211yesmaximal, characteristic, complemented
4C2×C5×#362C211yesmaximal, characteristic, complemented
5C5×#2145C211yesmaximal, characteristic, complemented
6C5×#2117C211yesmaximal, characteristic, complemented
7C5×#1389C211yesmaximal, characteristic, complemented
8C5×#575—21no—
9C2×C5×#135C2211yescharacteristic
10C22×C5×Q16C2211yescharacteristic
11C2×C5×#131C2211yescharacteristic
12C5×#536—21no—
13C5×#510—22no—
14C5×#510—22no—
15C2×C5×Q32—21no—
16C2×C5×SD32—21no—
17C2×C5×M32C2211yescharacteristic
18C2×C5×M32C2211yescharacteristic
19C5×#473—21no—
20C5×#472—21no—
21C5×#471—22no—
22C5×#470—22no—
23C5×#467—22no—
24C2×C5×#108C2211yescharacteristic
25C5×#427C2211yescharacteristic
26C5×#419—21no—
27C5×#413—21no—
28C5×#362—22no—
29C5×#360—22no—
30C5×#350—22no—
31#13311C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C2×C5×#41D411yescharacteristic
34C22×C5×Q8—21no—
35C5×#137—22no—
36C5×#137—41no—
37C5×AGL(1,ℤ/8)—22no—
38C5×AGL(1,ℤ/8)—41no—
39C5×#135—21no—
40C5×#135—21no—
41C5×#135—21no—
42C5×#135—21no—
43C5×#135—42no—
44C2×C5×Q16—21no—
45C2×C5×Q16—21no—
46C2×C5×Q16—21no—
47C2×C5×Q16—21no—
48C2×C5×Q16—21no—
49C2×C5×Q16D412yes—
50C2×C5×Q16D411yescharacteristic
51C2×C5×SD16—21no—
52C2×C5×D8D411yescharacteristic
53C5×#131—21no—
54C5×#131—21no—
55C5×#131—21no—
56C5×#131—21no—
57C2×C5×M16—21no—
58C2×C5×M16—21no—
59C2×C5×M16D411yescharacteristic
60C22×C5×C8—21no—
61C22×C5×C8C2311yescharacteristic
62C5×C4⋊Q8—41no—
63C5×#124—41no—
64C5×#123—42no—
65C5×C22⋊Q8—24no—
66C5×#117—21no—
67C5×Q32—24no—
68C5×SD32—24no—
69C5×M32—21no—
70C5×M32—21no—
71C5×M32—21no—
72C5×M32D412yes—
73C2×C5×C16—21no—
74C2×C5×C16—21no—
75C5×#108—21no—
76C5×#108D412yes—
77C5×#107—21no—
78C5×#106D412yes—
79C5×#103—24no—
80C5×#101—22no—
81C5×#100—22no—
82C2×#510C2×C511yescharacteristic, complemented
83#3067C2×C511yescharacteristic
84#3059C2×C511yescharacteristic, complemented
85C2×#362C2×C511yescharacteristic, complemented
86#2145C2×C511yescharacteristic, complemented
87#2117C2×C511yescharacteristic, complemented
88#1389C2×C511yescharacteristic, complemented
89C5×#41—21no—
90C5×#41—21no—
91C5×#41—21no—
92C5×#41—21no—
93C5×#41—41no—
94C5×#41—41no—
95C5×#41—41no—
96C5×#41—41no—
97C2×C5×Q8—22no—
98C2×C5×Q8—21no—
99C2×C5×Q8—41no—
100C2×C5×Q8—41no—
101C2×C5×Q8—41no—
102C2×C5×Q8—41no—
103C2×C5×Q8—41no—
104C2×C5×Q8D811yescharacteristic
105C2×C5×D4—21no—
106C2×C5×D4—21no—
107C2×C5×D4—41no—
108C2×C5×D4D811yescharacteristic
109C22×C4×C5—21no—
110C22×C4×C5—41no—
111C22×C4×C5—41no—
112C22×C4×C5C2×D411yescharacteristic
113C5×Q16—22no—
114C5×Q16—21no—
115C5×Q16—22no—
116C5×Q16—21no—
117C5×Q16—42no—
118C5×Q16—41no—
119C5×Q16—41no—
120C5×SD16—42no—
121C5×SD16—42no—
122C5×SD16—41no—
123C5×SD16—41no—
124C5×D8—21no—
125C5×D8—21no—
126C5×D8—42no—
127C5×M16—22no—
128C5×M16—21no—
129C5×M16—21no—
130C5×M16—41no—
131C5×M16—41no—
132C5×M16—41no—
133C2×C5×C8—21no—
134C2×C5×C8—41no—
135C2×C5×C8—41no—
136C2×C5×C8—41no—
137C2×C5×C8C2×D411yescharacteristic
138C2×C5×C8C2×D411yescharacteristic
139C2×C5×C8C2×D411yescharacteristic
140C2×C5×C8C2×D411yescharacteristic
141C2×C5×C8C2×D411yescharacteristic
142C2×C5×C8#4111yescharacteristic
143C5×C4⋊C4—22no—
144C5×C4⋊C4—44no—
145C5×C22⋊C4—44no—
146C5×C22⋊C4—41no—
147C42×C5—41no—
148C5×C16—22no—
149C5×C16—41no—
150#575—21no—
151C2×#135C22×C511yescharacteristic
152C22×Q16C22×C511yescharacteristic
153C2×#131C22×C511yescharacteristic
154#536—21no—
155#510—22no—
156#510—22no—
157C2×Q32—21no—
158C2×SD32—21no—
159C2×M32C22×C511yescharacteristic
160C2×M32C22×C511yescharacteristic
161#473—21no—
162#472—21no—
163#471—22no—
164#470—22no—
165#467—22no—
166C2×#108C22×C511yescharacteristic
167#427C22×C511yescharacteristic
168#419—21no—
169#413—21no—
170#362—22no—
171#360—22no—
172#350—22no—
173C23×C5—21no—
174C23×C5—41no—
175C23×C5AGL(1,ℤ/8)11yescharacteristic
176C5×Q8—21no—
177C5×Q8—21no—
178C5×Q8—41no—
179C5×Q8—42no—
180C5×Q8—41no—
181C5×Q8—42no—
182C5×Q8—81no—
183C5×Q8—81no—
184C5×D4—21no—
185C5×D4—21no—
186C5×D4—41no—
187C5×D4—41no—
188C5×D4—41no—
189C5×D4—41no—
190C5×D4—81no—
191C5×D4—81no—
192C2×C4×C5—21no—
193C2×C4×C5—41no—
194C2×C4×C5—41no—
195C2×C4×C5—42no—
196C2×C4×C5—42no—
197C2×C4×C5—41no—
198C2×C4×C5—81no—
199C2×C4×C5—81no—
200C2×C4×C5—81no—
201C2×C4×C5—81no—
202C2×C4×C5#12011yescharacteristic
203C2×C4×C5#12011yescharacteristic
204C2×C4×C5#12111yescharacteristic
205C2×C4×C5C2×D811yescharacteristic
206C2×C4×C5#13511yescharacteristic
207C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
208C5×C8—41no—
209C5×C8—42no—
210C5×C8#12011yescharacteristic
211C5×C8#12111yescharacteristic
212C5×C8#12111yescharacteristic
213C5×C8#12711yescharacteristic
214C2×#41—21no—
215C2×#41C5×D411yescharacteristic
216C22×Q8—21no—
217#137—22no—
218#137—41no—
219AGL(1,ℤ/8)—22no—
220AGL(1,ℤ/8)—41no—
221#135—21no—
222#135—21no—
223#135—21no—
224#135—21no—
225#135—42no—
226C2×Q16—21no—
227C2×Q16—21no—
228C2×Q16—21no—
229C2×Q16—21no—
230C2×Q16—21no—
231C2×Q16C5×D412yes—
232C2×Q16C5×D411yescharacteristic
233C2×SD16—21no—
234C2×D8C5×D411yescharacteristic
235#131—21no—
236#131—21no—
237#131—21no—
238#131—21no—
239C2×M16—21no—
240C2×M16—21no—
241C2×M16C5×D411yescharacteristic
242C22×C8—21no—
243C22×C8C23×C511yescharacteristic
244C4⋊Q8—41no—
245#124—41no—
246#123—42no—
247C22⋊Q8—24no—
248#117—21no—
249Q32—24no—
250SD32—24no—
251M32—21no—
252M32—21no—
253M32—21no—
254M32C5×D412yes—
255C2×C16—21no—
256C2×C16—21no—
257#108—21no—
258#108C5×D412yes—
259#107—21no—
260#106C5×D412yes—
261#103—24no—
262#101—22no—
263#100—22no—
264C22×C5—41no—
265C22×C5—42no—
266C22×C5—41no—
267C22×C5—81no—
268C22×C5—161no—
269C22×C5#44711yescharacteristic
270C22×C5#44911yescharacteristic
271C22×C5#46911yescharacteristic
272C4×C5—41no—
273C4×C5—82no—
274C4×C5—81no—
275C4×C5—82no—
276C4×C5#39211yescharacteristic
277C4×C5#44711yescharacteristic
278C4×C5#44911yescharacteristic
279C4×C5#46611yescharacteristic
280#41—21no—
281#41—21no—
282#41—21no—
283#41—21no—
284#41—41no—
285#41—41no—
286#41—41no—
287#41—41no—
288C2×Q8—21no—
289C2×Q8—22no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8—41no—
295C2×Q8C5×D811yescharacteristic
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4C5×D811yescharacteristic
300C22×C4—21no—
301C22×C4—41no—
302C22×C4—41no—
303C22×C4C2×C5×D411yescharacteristic
304Q16—22no—
305Q16—21no—
306Q16—22no—
307Q16—21no—
308Q16—42no—
309Q16—41no—
310Q16—41no—
311SD16—42no—
312SD16—42no—
313SD16—41no—
314SD16—41no—
315D8—21no—
316D8—21no—
317D8—42no—
318M16—21no—
319M16—22no—
320M16—21no—
321M16—41no—
322M16—41no—
323M16—41no—
324C2×C8—21no—
325C2×C8—41no—
326C2×C8—41no—
327C2×C8—41no—
328C2×C8C2×C5×D411yescharacteristic
329C2×C8C2×C5×D411yescharacteristic
330C2×C8C2×C5×D411yescharacteristic
331C2×C8C2×C5×D411yescharacteristic
332C2×C8C2×C5×D411yescharacteristic
333C2×C8C5×#4111yescharacteristic
334C4⋊C4—22no—
335C4⋊C4—44no—
336C22⋊C4—44no—
337C22⋊C4—41no—
338C42—41no—
339C16—22no—
340C16—41no—
341C2×C5—21no—
342C2×C5—21no—
343C2×C5—21no—
344C2×C5—81no—
345C2×C5—161no—
346C2×C5#199911yescharacteristic
347C23—21no—
348C23—41no—
349C23C5×AGL(1,ℤ/8)11yescharacteristic
350Q8—21no—
351Q8—21no—
352Q8—41no—
353Q8—42no—
354Q8—41no—
355Q8—42no—
356Q8—81no—
357Q8—81no—
358D4—21no—
359D4—21no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—41no—
364D4—81no—
365D4—81no—
366C2×C4—21no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—42no—
371C2×C4—41no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—81no—
376C2×C4C5×#12011yescharacteristic
377C2×C4C5×#12011yescharacteristic
378C2×C4C5×#12111yescharacteristic
379C2×C4C2×C5×D811yescharacteristic
380C2×C4C5×#13511yescharacteristic
381C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
382C8—41no—
383C8—42no—
384C8C5×#12011yescharacteristic
385C8C5×#12111yescharacteristic
386C8C5×#12111yescharacteristic
387C8C5×#12711yescharacteristic
388C5#1331111yescharacteristic, direct product factor, Sylow
389C22—41no—
390C22—42no—
391C22—41no—
392C22—81no—
393C22—161no—
394C22C5×#44711yescharacteristic
395C22C5×#44911yescharacteristic
396C22C5×#46911yescharacteristic
397C4—41no—
398C4—82no—
399C4—81no—
400C4—82no—
401C4C5×#39211yescharacteristic
402C4C5×#44711yescharacteristic
403C4C5×#44911yescharacteristic
404C4C5×#46611yescharacteristic
405C2—21no—
406C2—21no—
407C2—21no—
408C2—81no—
409C2—161no—
410C2C5×#199911yescharacteristic
subgroupG/H
center, socleC2×C5#1999
commutator, Frattini, cosocleC22×C8C23×C5
prime radicalC5×#3067C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C2×C5×#131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#510C2semidirect
3. C5×#3059C2semidirect
4. C2×C5×#362C2semidirect
5. C5×#2145C2semidirect
6. C5×#2117C2semidirect
7. C5×#1389C2semidirect
31. #13311C5direct (N × H)
82. C2×#510C2×C5semidirect
84. #3059C2×C5semidirect
85. C2×#362C2×C5semidirect
86. #2145C2×C5semidirect
87. #2117C2×C5semidirect
88. #1389C2×C5semidirect
388. C5#13311direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5102
C5×#30672
C5×#30592
C2×C5×#3622
C5×#21452
C5×#21172
C5×#13892
#133115