Finite Group Databasebeta

← C5×#13324 #11936044

Subgroups — C5×#13324 #11936044

Order 1280.

514 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#510C211yesmaximal, characteristic, complemented
2C5×#3067C211yesmaximal, characteristic
3C2×C5×#473C211yesmaximal, characteristic, complemented
4C2×C5×#362C211yesmaximal, characteristic, complemented
5C5×#2143C211yesmaximal, characteristic, complemented
6C5×#2115C211yesmaximal, characteristic, complemented
7C5×#1388C211yesmaximal, characteristic, complemented
8C5×#575—21no—
9C2×C5×#137—21no—
10C2×C5×#135C2211yescharacteristic
11C22×C5×Q16C2211yescharacteristic
12C2×C5×#131C2211yescharacteristic
13C5×#510—22no—
14C5×#510—22no—
15C2×C5×Q32—21no—
16C2×C5×SD32—21no—
17C2×C5×M32C2211yescharacteristic
18C2×C5×M32C2211yescharacteristic
19C5×#473—22no—
20C5×#473—22no—
21C5×#473—21no—
22C5×#472—21no—
23C5×#471—22no—
24C2×C5×#108C2211yescharacteristic
25C2×C5×#108C2211yescharacteristic
26C5×#413—21no—
27C2×C5×#101—21no—
28C5×#362—22no—
29C5×#359—22no—
30C5×#349—22no—
31#13324C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C2×C5×#41D411yescharacteristic
34C22×C5×Q8—21no—
35C5×#137—22no—
36C5×#137—24no—
37C5×#137—42no—
38C5×#137—41no—
39C5×AGL(1,ℤ/8)—22no—
40C5×AGL(1,ℤ/8)—41no—
41C5×#135—21no—
42C5×#135—21no—
43C5×#135—21no—
44C5×#135—21no—
45C5×#135—42no—
46C2×C5×Q16—21no—
47C2×C5×Q16—21no—
48C2×C5×Q16—21no—
49C2×C5×Q16—21no—
50C2×C5×Q16—21no—
51C2×C5×Q16—41no—
52C2×C5×Q16D411yescharacteristic
53C2×C5×Q16D412yes—
54C2×C5×SD16—21no—
55C2×C5×SD16—41no—
56C2×C5×D8D411yescharacteristic
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×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×#108—21no—
77C5×#108D412yes—
78C5×#108D412yes—
79C5×#101—24no—
80C5×#101—22no—
81C5×#100—22no—
82C2×#510C2×C511yescharacteristic, complemented
83#3067C2×C511yescharacteristic
84C2×#473C2×C511yescharacteristic, complemented
85C2×#362C2×C511yescharacteristic, complemented
86#2143C2×C511yescharacteristic, complemented
87#2115C2×C511yescharacteristic, complemented
88#1388C2×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—21no—
98C2×C5×Q8—22no—
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—44no—
118C5×Q16—42no—
119C5×Q16—41no—
120C5×Q16—41no—
121C5×SD16—44no—
122C5×SD16—42no—
123C5×SD16—42no—
124C5×SD16—41no—
125C5×SD16—41no—
126C5×D8—21no—
127C5×D8—21no—
128C5×D8—42no—
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×#137—21no—
152C2×#135C22×C511yescharacteristic
153C22×Q16C22×C511yescharacteristic
154C2×#131C22×C511yescharacteristic
155#510—22no—
156#510—22no—
157C2×Q32—21no—
158C2×SD32—21no—
159C2×M32C22×C511yescharacteristic
160C2×M32C22×C511yescharacteristic
161#473—22no—
162#473—21no—
163#473—22no—
164#472—21no—
165#471—22no—
166C2×#108C22×C511yescharacteristic
167C2×#108C22×C511yescharacteristic
168#413—21no—
169C2×#101—21no—
170#362—22no—
171#359—22no—
172#349—22no—
173C23×C5—21no—
174C23×C5—41no—
175C23×C5#13511yescharacteristic
176C5×Q8—21no—
177C5×Q8—21no—
178C5×Q8—41no—
179C5×Q8—42no—
180C5×Q8—42no—
181C5×Q8—41no—
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—41no—
196C2×C4×C5—42no—
197C2×C4×C5—81no—
198C2×C4×C5—81no—
199C2×C4×C5—81no—
200C2×C4×C5—81no—
201C2×C4×C5#12011yescharacteristic
202C2×C4×C5#12011yescharacteristic
203C2×C4×C5#12111yescharacteristic
204C2×C4×C5C2×D811yescharacteristic
205C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
206C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
207C5×C8—41no—
208C5×C8—42no—
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—24no—
218#137—22no—
219#137—42no—
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×Q16—21no—
229C2×Q16—21no—
230C2×Q16—21no—
231C2×Q16—21no—
232C2×Q16—21no—
233C2×Q16—41no—
234C2×Q16C5×D412yes—
235C2×Q16C5×D411yescharacteristic
236C2×SD16—21no—
237C2×SD16—41no—
238C2×D8C5×D411yescharacteristic
239#131—21no—
240#131—21no—
241#131—21no—
242#131—21no—
243C2×M16—21no—
244C2×M16—21no—
245C2×M16—21no—
246C2×M16C5×D411yescharacteristic
247C22×C8—21no—
248C22×C8C23×C511yescharacteristic
249Q32—24no—
250SD32—24no—
251M32—21no—
252M32—21no—
253M32—21no—
254M32C5×D412yes—
255C2×C16—21no—
256C2×C16—21no—
257#108—21no—
258#108—21no—
259#108C5×D412yes—
260#108C5×D412yes—
261#101—24no—
262#101—22no—
263#100—22no—
264C22×C5—41no—
265C22×C5—41no—
266C22×C5—81no—
267C22×C5—81no—
268C22×C5—161no—
269C22×C5#44911yescharacteristic
270C22×C5#44911yescharacteristic
271C22×C5#46611yescharacteristic
272C4×C5—41no—
273C4×C5—81no—
274C4×C5—82no—
275C4×C5#39211yescharacteristic
276C4×C5#44711yescharacteristic
277C4×C5#44711yescharacteristic
278C4×C5#46911yescharacteristic
279#41—21no—
280#41—21no—
281#41—21no—
282#41—21no—
283#41—41no—
284#41—41no—
285#41—41no—
286#41—41no—
287C2×Q8—21no—
288C2×Q8—22no—
289C2×Q8—41no—
290C2×Q8—41no—
291C2×Q8—41no—
292C2×Q8—41no—
293C2×Q8—41no—
294C2×Q8C5×D811yescharacteristic
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—41no—
298C2×D4C5×D811yescharacteristic
299C22×C4—21no—
300C22×C4—41no—
301C22×C4—41no—
302C22×C4C2×C5×D411yescharacteristic
303Q16—22no—
304Q16—21no—
305Q16—22no—
306Q16—21no—
307Q16—44no—
308Q16—42no—
309Q16—41no—
310Q16—41no—
311SD16—44no—
312SD16—42no—
313SD16—42no—
314SD16—41no—
315SD16—41no—
316D8—21no—
317D8—21no—
318D8—42no—
319M16—21no—
320M16—22no—
321M16—21no—
322M16—22no—
323M16—41no—
324M16—41no—
325M16—41no—
326M16—41no—
327C2×C8—21no—
328C2×C8—41no—
329C2×C8—41no—
330C2×C8—41no—
331C2×C8—41no—
332C2×C8C2×C5×D411yescharacteristic
333C2×C8C2×C5×D411yescharacteristic
334C2×C8C2×C5×D411yescharacteristic
335C2×C8C2×C5×D411yescharacteristic
336C2×C8C2×C5×D411yescharacteristic
337C2×C8C5×#4111yescharacteristic
338C16—22no—
339C16—41no—
340C2×C5—21no—
341C2×C5—21no—
342C2×C5—21no—
343C2×C5—81no—
344C2×C5—161no—
345C2×C5#199911yescharacteristic
346C23—21no—
347C23—41no—
348C23C5×#13511yescharacteristic
349Q8—21no—
350Q8—21no—
351Q8—41no—
352Q8—42no—
353Q8—42no—
354Q8—41no—
355Q8—81no—
356Q8—81no—
357D4—21no—
358D4—21no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365C2×C4—21no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—42no—
370C2×C4—81no—
371C2×C4—81no—
372C2×C4—81no—
373C2×C4—81no—
374C2×C4C5×#12011yescharacteristic
375C2×C4C5×#12011yescharacteristic
376C2×C4C5×#12111yescharacteristic
377C2×C4C2×C5×D811yescharacteristic
378C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
379C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
380C8—41no—
381C8—42no—
382C8—42no—
383C8C5×#12011yescharacteristic
384C8C5×#12111yescharacteristic
385C8C5×#12111yescharacteristic
386C8C5×#12711yescharacteristic
387C5#1332411yescharacteristic, direct product factor, Sylow
388C22—41no—
389C22—41no—
390C22—81no—
391C22—81no—
392C22—161no—
393C22C5×#44911yescharacteristic
394C22C5×#44911yescharacteristic
395C22C5×#46611yescharacteristic
396C4—41no—
397C4—81no—
398C4—82no—
399C4C5×#39211yescharacteristic
400C4C5×#44711yescharacteristic
401C4C5×#44711yescharacteristic
402C4C5×#46911yescharacteristic
403C2—21no—
404C2—21no—
405C2—21no—
406C2—81no—
407C2—161no—
408C2C5×#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. C2×C5×#473C2semidirect
4. C2×C5×#362C2semidirect
5. C5×#2143C2semidirect
6. C5×#2115C2semidirect
7. C5×#1388C2semidirect
31. #13324C5direct (N × H)
82. C2×#510C2×C5semidirect
84. C2×#473C2×C5semidirect
85. C2×#362C2×C5semidirect
86. #2143C2×C5semidirect
87. #2115C2×C5semidirect
88. #1388C2×C5semidirect
387. C5#13324direct (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
C2×C5×#4732
C2×C5×#3622
C5×#21432
C5×#21152
C5×#13882
#133245