Finite Group Databasebeta

← C5×#13323 #11936043

Subgroups — C5×#13323 #11936043

Order 1280.

534 conjugacy classes of subgroups.

The subgroup lattice has 420 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
3C2×C5×#472C211yesmaximal, characteristic, complemented
4C2×C5×#361C211yesmaximal, characteristic, complemented
5C5×#2143C211yesmaximal, characteristic, complemented
6C5×#2115C211yesmaximal, characteristic, complemented
7C5×#1388C211yesmaximal, characteristic, complemented
8C5×#575—21no—
9C2×C5×AGL(1,ℤ/8)—21no—
10C2×C5×#135C2211yescharacteristic
11C22×C5×D8C2211yescharacteristic
12C2×C5×#131C2211yescharacteristic
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—22no—
21C5×#472—22no—
22C5×#472—21no—
23C5×#471—22no—
24C2×C5×#108C2211yescharacteristic
25C2×C5×#108C2211yescharacteristic
26C5×#413—21no—
27C2×C5×#100—21no—
28C5×#361—22no—
29C5×#359—22no—
30C5×#349—22no—
31#13323C511yesmaximal, 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)—24no—
39C5×AGL(1,ℤ/8)—42no—
40C5×AGL(1,ℤ/8)—41no—
41C5×#135—21no—
42C5×#135—21no—
43C5×#135—21no—
44C5×#135—21no—
45C5×#135—42no—
46C2×C5×Q16D411yescharacteristic
47C2×C5×SD16—21no—
48C2×C5×SD16—41no—
49C2×C5×D8—21no—
50C2×C5×D8—21no—
51C2×C5×D8—21no—
52C2×C5×D8—21no—
53C2×C5×D8—21no—
54C2×C5×D8—41no—
55C2×C5×D8D411yescharacteristic
56C2×C5×D8D412yes—
57C5×#131—21no—
58C5×#131—21no—
59C5×#131—21no—
60C5×#131—21no—
61C2×C5×M16—21no—
62C2×C5×M16—21no—
63C2×C5×M16—21no—
64C2×C5×M16D411yescharacteristic
65C22×C5×C8—21no—
66C22×C5×C8C2311yescharacteristic
67C5×SD32—24no—
68C5×D16—24no—
69C5×M32—21no—
70C5×M32—21no—
71C5×M32—21no—
72C5×M32D412yes—
73C2×C5×C16—21no—
74C2×C5×C16—21no—
75C5×#108—21no—
76C5×#108—21no—
77C5×#108D412yes—
78C5×#108D412yes—
79C5×#101—22no—
80C5×#100—24no—
81C5×#100—22no—
82C2×#509C2×C511yescharacteristic, complemented
83#3067C2×C511yescharacteristic, complemented
84C2×#472C2×C511yescharacteristic, complemented
85C2×#361C2×C511yescharacteristic, complemented
86#2143C2×C511yescharacteristic, complemented
87#2115C2×C511yescharacteristic, complemented
88#1388C2×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—41no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C2×C5×D4—41no—
108C2×C5×D4—41no—
109C2×C5×D4D811yescharacteristic
110C22×C4×C5—21no—
111C22×C4×C5—41no—
112C22×C4×C5C2×D411yescharacteristic
113C5×Q16—21no—
114C5×Q16—21no—
115C5×Q16—42no—
116C5×SD16—42no—
117C5×SD16—44no—
118C5×SD16—42no—
119C5×SD16—41no—
120C5×SD16—41no—
121C5×D8—22no—
122C5×D8—21no—
123C5×D8—22no—
124C5×D8—21no—
125C5×D8—44no—
126C5×D8—42no—
127C5×D8—41no—
128C5×D8—41no—
129C5×M16—22no—
130C5×M16—22no—
131C5×M16—21no—
132C5×M16—21no—
133C5×M16—41no—
134C5×M16—41no—
135C5×M16—41no—
136C5×M16—41no—
137C2×C5×C8—21no—
138C2×C5×C8—41no—
139C2×C5×C8—41no—
140C2×C5×C8—41no—
141C2×C5×C8—41no—
142C2×C5×C8C2×D411yescharacteristic
143C2×C5×C8C2×D411yescharacteristic
144C2×C5×C8C2×D411yescharacteristic
145C2×C5×C8C2×D411yescharacteristic
146C2×C5×C8C2×D411yescharacteristic
147C2×C5×C8#4111yescharacteristic
148C5×C16—22no—
149C5×C16—41no—
150#575—21no—
151C2×AGL(1,ℤ/8)—21no—
152C2×#135C22×C511yescharacteristic
153C22×D8C22×C511yescharacteristic
154C2×#131C22×C511yescharacteristic
155#509—22no—
156#509—22no—
157C2×SD32—21no—
158C2×D16—21no—
159C2×M32C22×C511yescharacteristic
160C2×M32C22×C511yescharacteristic
161#473—21no—
162#472—22no—
163#472—21no—
164#472—22no—
165#471—22no—
166C2×#108C22×C511yescharacteristic
167C2×#108C22×C511yescharacteristic
168#413—21no—
169C2×#100—21no—
170#361—22no—
171#359—22no—
172#349—22no—
173C23×C5—21no—
174C23×C5—41no—
175C23×C5—42no—
176C23×C5—81no—
177C23×C5—81no—
178C23×C5—162no—
179C23×C5#13511yescharacteristic
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—42no—
191C5×D4—41no—
192C5×D4—81no—
193C5×D4—81no—
194C5×D4—81no—
195C5×D4—81no—
196C2×C4×C5—21no—
197C2×C4×C5—41no—
198C2×C4×C5—41no—
199C2×C4×C5—41no—
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×C5AGL(1,ℤ/8)11yescharacteristic
207C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
208C5×C8—41no—
209C5×C8—42no—
210C5×C8—42no—
211C5×C8#12011yescharacteristic
212C5×C8#12111yescharacteristic
213C5×C8#12111yescharacteristic
214C5×C8#12711yescharacteristic
215C2×#41—21no—
216C2×#41C5×D411yescharacteristic
217C22×D4—21no—
218#137—22no—
219#137—41no—
220AGL(1,ℤ/8)—24no—
221AGL(1,ℤ/8)—22no—
222AGL(1,ℤ/8)—42no—
223AGL(1,ℤ/8)—41no—
224#135—21no—
225#135—21no—
226#135—21no—
227#135—21no—
228#135—42no—
229C2×Q16C5×D411yescharacteristic
230C2×SD16—21no—
231C2×SD16—41no—
232C2×D8—21no—
233C2×D8—21no—
234C2×D8—21no—
235C2×D8—21no—
236C2×D8—21no—
237C2×D8—41no—
238C2×D8C5×D412yes—
239C2×D8C5×D411yescharacteristic
240#131—21no—
241#131—21no—
242#131—21no—
243#131—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16—21no—
247C2×M16C5×D411yescharacteristic
248C22×C8—21no—
249C22×C8C23×C511yescharacteristic
250SD32—24no—
251D16—24no—
252M32—21no—
253M32—21no—
254M32—21no—
255M32C5×D412yes—
256C2×C16—21no—
257C2×C16—21no—
258#108—21no—
259#108—21no—
260#108C5×D412yes—
261#108C5×D412yes—
262#101—22no—
263#100—24no—
264#100—22no—
265C22×C5—41no—
266C22×C5—41no—
267C22×C5—81no—
268C22×C5—81no—
269C22×C5—82no—
270C22×C5—161no—
271C22×C5—162no—
272C22×C5—162no—
273C22×C5—162no—
274C22×C5#44911yescharacteristic
275C22×C5#44911yescharacteristic
276C22×C5#46611yescharacteristic
277C4×C5—41no—
278C4×C5—81no—
279C4×C5#39211yescharacteristic
280C4×C5#44711yescharacteristic
281C4×C5#44711yescharacteristic
282C4×C5#46911yescharacteristic
283C24—41no—
284#41—21no—
285#41—21no—
286#41—21no—
287#41—21no—
288#41—41no—
289#41—41no—
290#41—41no—
291#41—41no—
292C2×Q8—21no—
293C2×Q8C5×D811yescharacteristic
294C2×D4—21no—
295C2×D4—22no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—41no—
302C2×D4—41no—
303C2×D4C5×D811yescharacteristic
304C22×C4—21no—
305C22×C4—41no—
306C22×C4C2×C5×D411yescharacteristic
307Q16—21no—
308Q16—21no—
309Q16—42no—
310SD16—42no—
311SD16—44no—
312SD16—42no—
313SD16—41no—
314SD16—41no—
315D8—21no—
316D8—22no—
317D8—22no—
318D8—21no—
319D8—44no—
320D8—42no—
321D8—41no—
322D8—41no—
323M16—21no—
324M16—21no—
325M16—22no—
326M16—22no—
327M16—41no—
328M16—41no—
329M16—41no—
330M16—41no—
331C2×C8—21no—
332C2×C8—41no—
333C2×C8—41no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8C2×C5×D411yescharacteristic
337C2×C8C2×C5×D411yescharacteristic
338C2×C8C2×C5×D411yescharacteristic
339C2×C8C2×C5×D411yescharacteristic
340C2×C8C2×C5×D411yescharacteristic
341C2×C8C5×#4111yescharacteristic
342C16—22no—
343C16—41no—
344C2×C5—21no—
345C2×C5—21no—
346C2×C5—21no—
347C2×C5—81no—
348C2×C5—161no—
349C2×C5—162no—
350C2×C5#199911yescharacteristic
351C23—21no—
352C23—41no—
353C23—42no—
354C23—81no—
355C23—81no—
356C23—162no—
357C23C5×#13511yescharacteristic
358Q8—21no—
359Q8—21no—
360Q8—41no—
361Q8—41no—
362D4—21no—
363D4—21no—
364D4—41no—
365D4—41no—
366D4—42no—
367D4—41no—
368D4—42no—
369D4—41no—
370D4—81no—
371D4—81no—
372D4—81no—
373D4—81no—
374C2×C4—21no—
375C2×C4—41no—
376C2×C4—41no—
377C2×C4—41no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4C5×#12011yescharacteristic
381C2×C4C5×#12011yescharacteristic
382C2×C4C5×#12111yescharacteristic
383C2×C4C2×C5×D811yescharacteristic
384C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
385C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
386C8—41no—
387C8—42no—
388C8—42no—
389C8C5×#12011yescharacteristic
390C8C5×#12111yescharacteristic
391C8C5×#12111yescharacteristic
392C8C5×#12711yescharacteristic
393C5#1332311yescharacteristic, direct product factor, Sylow
394C22—41no—
395C22—41no—
396C22—81no—
397C22—81no—
398C22—82no—
399C22—162no—
400C22—161no—
401C22—162no—
402C22—162no—
403C22C5×#44911yescharacteristic
404C22C5×#44911yescharacteristic
405C22C5×#46611yescharacteristic
406C4—41no—
407C4—81no—
408C4C5×#39211yescharacteristic
409C4C5×#44711yescharacteristic
410C4C5×#44711yescharacteristic
411C4C5×#46911yescharacteristic
412C2—21no—
413C2—21no—
414C2—21no—
415C2—81no—
416C2—162no—
417C2—161no—
418C2C5×#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. C2×C5×#472C2semidirect
4. C2×C5×#361C2semidirect
5. C5×#2143C2semidirect
6. C5×#2115C2semidirect
7. C5×#1388C2semidirect
31. #13323C5direct (N × H)
82. C2×#509C2×C5semidirect
83. #3067C2×C5semidirect
84. C2×#472C2×C5semidirect
85. C2×#361C2×C5semidirect
86. #2143C2×C5semidirect
87. #2115C2×C5semidirect
88. #1388C2×C5semidirect
393. C5#13323direct (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
C2×C5×#4722
C2×C5×#3612
C5×#21432
C5×#21152
C5×#13882
#133235