Finite Group Databasebeta

← C5×#13310 #11936030

Subgroups — C5×#13310 #11936030

Order 1280.

552 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#509C211yesmaximal, characteristic, complemented
2C5×#3067C211yesmaximal, characteristic, complemented
3C5×#3058C211yesmaximal, characteristic, complemented
4C2×C5×#361C211yesmaximal, characteristic, complemented
5C5×#2145C211yesmaximal, characteristic, complemented
6C5×#2117C211yesmaximal, characteristic, complemented
7C5×#1389C211yesmaximal, characteristic, complemented
8C5×#575—21no—
9C2×C5×#135C2211yescharacteristic
10C22×C5×D8C2211yescharacteristic
11C2×C5×#131C2211yescharacteristic
12C5×#535—21no—
13C5×#509—22no—
14C5×#509—22no—
15C2×C5×SD32—21no—
16C2×C5×D16—21no—
17C2×C5×M32C2211yescharacteristic
18C2×C5×M32C2211yescharacteristic
19C5×#473—21no—
20C5×#472—21no—
21C5×#471—22no—
22C5×#469—22no—
23C5×#466—22no—
24C2×C5×#108C2211yescharacteristic
25C5×#427C2211yescharacteristic
26C5×#418—21no—
27C5×#413—21no—
28C5×#361—22no—
29C5×#360—22no—
30C5×#350—22no—
31#13310C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C2×C5×#41D411yescharacteristic
34C22×C5×D4—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×Q16D411yescharacteristic, complemented
45C2×C5×SD16—21no—
46C2×C5×D8—21no—
47C2×C5×D8—21no—
48C2×C5×D8—21no—
49C2×C5×D8—21no—
50C2×C5×D8—21no—
51C2×C5×D8D412yes—
52C2×C5×D8D411yescharacteristic, complemented
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×#127—41no—
63C5×#124—41no—
64C5×#121—24no—
65C5×#120—42no—
66C5×#117—21no—
67C5×SD32—24no—
68C5×D16—24no—
69C5×M32—21no—
70C5×M32—21no—
71C5×M32—21no—
72C5×M32D412yescomplemented
73C2×C5×C16—21no—
74C2×C5×C16—21no—
75C5×#108—21no—
76C5×#108D412yescomplemented
77C5×#107—21no—
78C5×#106D412yes—
79C5×#102—24no—
80C5×#101—22no—
81C5×#100—22no—
82C2×#509C2×C511yescharacteristic, complemented
83#3067C2×C511yescharacteristic, complemented
84#3058C2×C511yescharacteristic, complemented
85C2×#361C2×C511yescharacteristic, complemented
86#2145C2×C511yescharacteristic, complemented
87#2117C2×C511yescharacteristic, complemented
88#1389C2×C511yescharacteristic, complemented
89C24×C5—41no—
90C5×#41—21no—
91C5×#41—21no—
92C5×#41—21no—
93C5×#41—21no—
94C5×#41—41no—
95C5×#41—41no—
96C5×#41—41no—
97C5×#41—41no—
98C2×C5×Q8—21no—
99C2×C5×Q8D811yescharacteristic
100C2×C5×D4—21no—
101C2×C5×D4—22no—
102C2×C5×D4—21no—
103C2×C5×D4—41no—
104C2×C5×D4—44no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4—41no—
108C2×C5×D4—41no—
109C2×C5×D4—41no—
110C2×C5×D4D811yescharacteristic
111C22×C4×C5—21no—
112C22×C4×C5—41no—
113C22×C4×C5C2×D411yescharacteristic
114C5×Q16—21no—
115C5×Q16—21no—
116C5×Q16—42no—
117C5×SD16—42no—
118C5×SD16—42no—
119C5×SD16—41no—
120C5×SD16—41no—
121C5×D8—22no—
122C5×D8—21no—
123C5×D8—22no—
124C5×D8—21no—
125C5×D8—42no—
126C5×D8—41no—
127C5×D8—41no—
128C5×M16—22no—
129C5×M16—21no—
130C5×M16—21no—
131C5×M16—41no—
132C5×M16—41no—
133C5×M16—41no—
134C2×C5×C8—21no—
135C2×C5×C8—41no—
136C2×C5×C8—41no—
137C2×C5×C8—41no—
138C2×C5×C8C2×D411yescharacteristic
139C2×C5×C8C2×D411yescharacteristic
140C2×C5×C8C2×D411yescharacteristic
141C2×C5×C8C2×D411yescharacteristic
142C2×C5×C8C2×D411yescharacteristic
143C2×C5×C8#4111yescharacteristic
144C5×C4⋊C4—22no—
145C5×C22⋊C4—44no—
146C5×C22⋊C4—41no—
147C42×C5—41no—
148C5×C16—22no—
149C5×C16—41no—
150#575—21no—
151C2×#135C22×C511yescharacteristic
152C22×D8C22×C511yescharacteristic
153C2×#131C22×C511yescharacteristic
154#535—21no—
155#509—22no—
156#509—22no—
157C2×SD32—21no—
158C2×D16—21no—
159C2×M32C22×C511yescharacteristic
160C2×M32C22×C511yescharacteristic
161#473—21no—
162#472—21no—
163#471—22no—
164#469—22no—
165#466—22no—
166C2×#108C22×C511yescharacteristic
167#427C22×C511yescharacteristic
168#418—21no—
169#413—21no—
170#361—22no—
171#360—22no—
172#350—22no—
173C23×C5—21no—
174C23×C5—42no—
175C23×C5—41no—
176C23×C5—81no—
177C23×C5—81no—
178C23×C5—162no—
179C23×C5AGL(1,ℤ/8)11yescharacteristic
180C5×Q8—21no—
181C5×Q8—21no—
182C5×Q8—41no—
183C5×Q8—41no—
184C5×D4—21no—
185C5×D4—21no—
186C5×D4—41no—
187C5×D4—41no—
188C5×D4—42no—
189C5×D4—41no—
190C5×D4—41no—
191C5×D4—42no—
192C5×D4—81no—
193C5×D4—81no—
194C5×D4—81no—
195C5×D4—81no—
196C5×D4—164no—
197C2×C4×C5—21no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
200C2×C4×C5—42no—
201C2×C4×C5—41no—
202C2×C4×C5—81no—
203C2×C4×C5—81no—
204C2×C4×C5#12011yescharacteristic
205C2×C4×C5#12011yescharacteristic
206C2×C4×C5#12111yescharacteristic
207C2×C4×C5C2×D811yescharacteristic
208C2×C4×C5#13511yescharacteristic
209C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
210C5×C8—41no—
211C5×C8—42no—
212C5×C8#12011yescharacteristic
213C5×C8#12111yescharacteristic
214C5×C8#12111yescharacteristic
215C5×C8#12711yescharacteristic
216C2×#41—21no—
217C2×#41C5×D411yescharacteristic
218C22×D4—21no—
219#137—22no—
220#137—41no—
221AGL(1,ℤ/8)—22no—
222AGL(1,ℤ/8)—41no—
223#135—21no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135—42no—
228C2×Q16C5×D411yescharacteristic, complemented
229C2×SD16—21no—
230C2×D8—21no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8C5×D412yes—
236C2×D8C5×D411yescharacteristic, complemented
237#131—21no—
238#131—21no—
239#131—21no—
240#131—21no—
241C2×M16—21no—
242C2×M16—21no—
243C2×M16C5×D411yescharacteristic
244C22×C8—21no—
245C22×C8C23×C511yescharacteristic
246#127—41no—
247#124—41no—
248#121—24no—
249#120—42no—
250#117—21no—
251SD32—24no—
252D16—24no—
253M32—21no—
254M32—21no—
255M32—21no—
256M32C5×D412yescomplemented
257C2×C16—21no—
258C2×C16—21no—
259#108—21no—
260#108C5×D412yescomplemented
261#107—21no—
262#106C5×D412yes—
263#102—24no—
264#101—22no—
265#100—22no—
266C22×C5—41no—
267C22×C5—42no—
268C22×C5—41no—
269C22×C5—84no—
270C22×C5—81no—
271C22×C5—82no—
272C22×C5—161no—
273C22×C5—162no—
274C22×C5—162no—
275C22×C5#44711yescharacteristic
276C22×C5#44911yescharacteristic
277C22×C5#46911yescharacteristic
278C4×C5—41no—
279C4×C5—82no—
280C4×C5—81no—
281C4×C5#39211yescharacteristic
282C4×C5#44711yescharacteristic
283C4×C5#44911yescharacteristic
284C4×C5#46611yescharacteristic
285C24—41no—
286#41—21no—
287#41—21no—
288#41—21no—
289#41—21no—
290#41—41no—
291#41—41no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×Q8C5×D811yescharacteristic
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—22no—
299C2×D4—41no—
300C2×D4—44no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4—41no—
304C2×D4—41no—
305C2×D4—41no—
306C2×D4C5×D811yescharacteristic
307C22×C4—21no—
308C22×C4—41no—
309C22×C4C2×C5×D411yescharacteristic
310Q16—21no—
311Q16—21no—
312Q16—42no—
313SD16—42no—
314SD16—42no—
315SD16—41no—
316SD16—41no—
317D8—21no—
318D8—22no—
319D8—22no—
320D8—21no—
321D8—42no—
322D8—41no—
323D8—41no—
324M16—21no—
325M16—22no—
326M16—21no—
327M16—41no—
328M16—41no—
329M16—41no—
330C2×C8—21no—
331C2×C8—41no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8C2×C5×D411yescharacteristic
335C2×C8C2×C5×D411yescharacteristic
336C2×C8C2×C5×D411yescharacteristic
337C2×C8C2×C5×D411yescharacteristic
338C2×C8C2×C5×D411yescharacteristic
339C2×C8C5×#4111yescharacteristic
340C4⋊C4—22no—
341C22⋊C4—44no—
342C22⋊C4—41no—
343C42—41no—
344C16—22no—
345C16—41no—
346C2×C5—21no—
347C2×C5—21no—
348C2×C5—21no—
349C2×C5—81no—
350C2×C5—162no—
351C2×C5—161no—
352C2×C5#199911yescharacteristic
353C23—21no—
354C23—42no—
355C23—41no—
356C23—81no—
357C23—81no—
358C23—162no—
359C23C5×AGL(1,ℤ/8)11yescharacteristic
360Q8—21no—
361Q8—21no—
362Q8—41no—
363Q8—41no—
364D4—21no—
365D4—21no—
366D4—41no—
367D4—41no—
368D4—42no—
369D4—41no—
370D4—41no—
371D4—42no—
372D4—81no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—164no—
377C2×C4—21no—
378C2×C4—41no—
379C2×C4—41no—
380C2×C4—42no—
381C2×C4—41no—
382C2×C4—81no—
383C2×C4—81no—
384C2×C4C5×#12011yescharacteristic
385C2×C4C5×#12011yescharacteristic
386C2×C4C5×#12111yescharacteristic
387C2×C4C2×C5×D811yescharacteristic
388C2×C4C5×#13511yescharacteristic
389C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
390C8—41no—
391C8—42no—
392C8C5×#12011yescharacteristic
393C8C5×#12111yescharacteristic
394C8C5×#12111yescharacteristic
395C8C5×#12711yescharacteristic
396C5#1331011yescharacteristic, direct product factor, Sylow
397C22—41no—
398C22—42no—
399C22—41no—
400C22—84no—
401C22—81no—
402C22—82no—
403C22—161no—
404C22—162no—
405C22—162no—
406C22C5×#44711yescharacteristic
407C22C5×#44911yescharacteristic
408C22C5×#46911yescharacteristic
409C4—41no—
410C4—82no—
411C4—81no—
412C4C5×#39211yescharacteristic
413C4C5×#44711yescharacteristic
414C4C5×#44911yescharacteristic
415C4C5×#46611yescharacteristic
416C2—21no—
417C2—21no—
418C2—21no—
419C2—81no—
420C2—162no—
421C2—161no—
422C2C5×#199911yescharacteristic
subgroupG/H
center, socleC2×C5#1999
commutator, Frattini, cosocleC22×C8C23×C5
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×#509C2semidirect
2. C5×#3067C2semidirect
3. C5×#3058C2semidirect
4. C2×C5×#361C2semidirect
5. C5×#2145C2semidirect
6. C5×#2117C2semidirect
7. C5×#1389C2semidirect
31. #13310C5direct (N × H)
44. C2×C5×Q16D4semidirect
52. C2×C5×D8D4semidirect
72. C5×M32D4semidirect
76. C5×#108D4semidirect
82. C2×#509C2×C5semidirect
83. #3067C2×C5semidirect
84. #3058C2×C5semidirect
85. C2×#361C2×C5semidirect
86. #2145C2×C5semidirect
87. #2117C2×C5semidirect
88. #1389C2×C5semidirect
228. C2×Q16C5×D4semidirect
236. C2×D8C5×D4semidirect
256. M32C5×D4semidirect
260. #108C5×D4semidirect
396. C5#13310direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#5092
C5×#30672
C5×#30582
C2×C5×#3612
C5×#21452
C5×#21172
C5×#13892
#133105