Finite Group Databasebeta

← C5×#13332 #11936052

Subgroups — C5×#13332 #11936052

Order 1280.

566 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#510C211yesmaximal, characteristic, complemented
2C2×C5×#509C211yesmaximal, characteristic
3C2×C5×#495C211yesmaximal, characteristic, complemented
4C2×C5×#362C211yesmaximal, characteristic, complemented
5C2×C5×#361C211yesmaximal, characteristic, complemented
6C5×#1974C211yesmaximal, characteristic, complemented
7C5×#1376C211yesmaximal, characteristic, complemented
8C2×C5×#135C2211yescharacteristic
9C22×C5×Q16C2211yescharacteristic
10C22×C5×SD16—21no—
11C22×C5×D8C2211yescharacteristic
12C2×C5×#124—21no—
13C5×#510—22no—
14C5×#510—22no—
15C5×#509—22no—
16C5×#509—22no—
17C2×C5×Q32—21no—
18C2×C5×SD32—21no—
19C2×C5×SD32—21no—
20C2×C5×D16—21no—
21C2×C5×M32C2211yescharacteristic
22C2×C5×M32C2211yescharacteristic
23C5×#495—22no—
24C5×#495—22no—
25C2×C5×#108C2211yescharacteristic
26C2×C5×#104—21no—
27C5×#408—21no—
28C2×C4×C5×C8C2211yescharacteristic
29C5×#362—22no—
30C5×#361—22no—
31#13332C511yesmaximal, characteristic, direct product factor, Sylow
32C2×C5×#41—21no—
33C22×C5×Q8—21no—
34C22×C5×D4—21no—
35C5×#135—21no—
36C5×#135—21no—
37C5×#135—21no—
38C5×#135—21no—
39C2×C5×Q16—21no—
40C2×C5×Q16—21no—
41C2×C5×Q16—21no—
42C2×C5×Q16—21no—
43C2×C5×Q16—21no—
44C2×C5×Q16D412yes—
45C2×C5×Q16D411yescharacteristic
46C2×C5×SD16—24no—
47C2×C5×SD16—21no—
48C2×C5×SD16—42no—
49C2×C5×SD16—42no—
50C2×C5×D8—21no—
51C2×C5×D8—21no—
52C2×C5×D8—21no—
53C2×C5×D8—21no—
54C2×C5×D8—21no—
55C2×C5×D8D412yes—
56C2×C5×D8D411yescharacteristic
57C2×C5×M16—21no—
58C22×C5×C8D411yescharacteristic
59C22×C5×C8C2311yescharacteristic
60C5×#124—24no—
61C5×#124—42no—
62C2×C5×C22⋊C4—42no—
63C2×C42×C5D411yescharacteristic
64C5×Q32—24no—
65C5×SD32—24no—
66C5×SD32—24no—
67C5×D16—24no—
68C5×M32—21no—
69C5×M32—21no—
70C5×M32D412yes—
71C5×M32D412yes—
72C2×C5×C16—21no—
73C2×C5×C16—21no—
74C5×#108—21no—
75C5×#108—21no—
76C5×#104—42no—
77C5×C22⋊C8—42no—
78C4×C5×C8—21no—
79C4×C5×C8—21no—
80C2×#510C2×C511yescharacteristic, complemented
81C2×#509C2×C511yescharacteristic
82C2×#495C2×C511yescharacteristic, complemented
83C2×#362C2×C511yescharacteristic, complemented
84C2×#361C2×C511yescharacteristic, complemented
85#1974C2×C511yescharacteristic, complemented
86#1376C2×C511yescharacteristic, complemented
87C24×C5—41no—
88C5×#41—41no—
89C5×#41—41no—
90C5×#41—41no—
91C5×#41—41no—
92C2×C5×Q8—22no—
93C2×C5×Q8—21no—
94C2×C5×Q8—41no—
95C2×C5×Q8—41no—
96C2×C5×Q8—41no—
97C2×C5×Q8—41no—
98C2×C5×Q8—41no—
99C2×C5×D4—22no—
100C2×C5×D4—21no—
101C2×C5×D4—41no—
102C2×C5×D4—41no—
103C2×C5×D4—41no—
104C2×C5×D4—41no—
105C2×C5×D4—41no—
106C2×C5×D4—41no—
107C22×C4×C5—21no—
108C22×C4×C5—41no—
109C22×C4×C5—41no—
110C22×C4×C5C2×D411yescharacteristic
111C5×Q16—22no—
112C5×Q16—21no—
113C5×Q16—21no—
114C5×Q16—22no—
115C5×Q16—41no—
116C5×Q16—41no—
117C5×SD16—48no—
118C5×SD16—41no—
119C5×SD16—41no—
120C5×D8—22no—
121C5×D8—21no—
122C5×D8—21no—
123C5×D8—22no—
124C5×D8—41no—
125C5×D8—41no—
126C5×M16—41no—
127C5×M16—41no—
128C2×C5×C8—21no—
129C2×C5×C8—21no—
130C2×C5×C8—41no—
131C2×C5×C8D812yes—
132C2×C5×C8C2×D411yescharacteristic
133C2×C5×C8C2×D411yescharacteristic
134C2×C5×C8C2×D411yescharacteristic
135C2×C5×C8C2×D411yescharacteristic
136C2×C5×C8C2×D411yescharacteristic
137C2×C5×C8#4111yescharacteristic
138C5×C22⋊C4—48no—
139C42×C5—21no—
140C42×C5D812yes—
141C5×C16—22no—
142C5×C16—22no—
143C2×#135C22×C511yescharacteristic
144C22×Q16C22×C511yescharacteristic
145C22×SD16—21no—
146C22×D8C22×C511yescharacteristic
147C2×#124—21no—
148#510—22no—
149#510—22no—
150#509—22no—
151#509—22no—
152C2×Q32—21no—
153C2×SD32—21no—
154C2×SD32—21no—
155C2×D16—21no—
156C2×M32C22×C511yescharacteristic
157C2×M32C22×C511yescharacteristic
158#495—22no—
159#495—22no—
160C2×#108C22×C511yescharacteristic
161C2×#104—21no—
162#408—21no—
163C2×C4×C8C22×C511yescharacteristic
164#362—22no—
165#361—22no—
166C23×C5—42no—
167C23×C5—41no—
168C23×C5—84no—
169C23×C5—81no—
170C23×C5—81no—
171C23×C5AGL(1,ℤ/8)11yescharacteristic
172C5×Q8—41no—
173C5×Q8—42no—
174C5×Q8—42no—
175C5×Q8—41no—
176C5×Q8—81no—
177C5×Q8—81no—
178C5×D4—42no—
179C5×D4—41no—
180C5×D4—42no—
181C5×D4—41no—
182C5×D4—81no—
183C5×D4—81no—
184C5×D4—81no—
185C5×D4—81no—
186C2×C4×C5—22no—
187C2×C4×C5—42no—
188C2×C4×C5—42no—
189C2×C4×C5—41no—
190C2×C4×C5—81no—
191C2×C4×C5—81no—
192C2×C4×C5—81no—
193C2×C4×C5—81no—
194C2×C4×C5#12011yescharacteristic
195C2×C4×C5#12111yescharacteristic
196C2×C4×C5#12711yescharacteristic
197C2×C4×C5C2×D811yescharacteristic
198C2×C4×C5C2×D811yescharacteristic
199C2×C4×C5AGL(1,ℤ/8)11yescharacteristic
200C5×C8—22no—
201C5×C8—81no—
202C5×C8#12011yescharacteristic
203C5×C8#12011yescharacteristic
204C5×C8#12111yescharacteristic
205C5×C8#12111yescharacteristic
206C2×#41—21no—
207C22×Q8—21no—
208C22×D4—21no—
209#135—21no—
210#135—21no—
211#135—21no—
212#135—21no—
213C2×Q16—21no—
214C2×Q16—21no—
215C2×Q16—21no—
216C2×Q16—21no—
217C2×Q16—21no—
218C2×Q16C5×D412yes—
219C2×Q16C5×D411yescharacteristic
220C2×SD16—24no—
221C2×SD16—21no—
222C2×SD16—42no—
223C2×SD16—42no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—21no—
229C2×D8C5×D412yes—
230C2×D8C5×D411yescharacteristic
231C2×M16—21no—
232C22×C8C5×D411yescharacteristic
233C22×C8C23×C511yescharacteristic
234#124—24no—
235#124—42no—
236C2×C22⋊C4—42no—
237C2×C42C5×D411yescharacteristic
238Q32—24no—
239SD32—24no—
240SD32—24no—
241D16—24no—
242M32—21no—
243M32—21no—
244M32C5×D412yes—
245M32C5×D412yes—
246C2×C16—21no—
247C2×C16—21no—
248#108—21no—
249#108—21no—
250#104—42no—
251C22⋊C8—42no—
252C4×C8—21no—
253C4×C8—21no—
254C22×C5—22no—
255C22×C5—84no—
256C22×C5—82no—
257C22×C5—81no—
258C22×C5—82no—
259C22×C5—162no—
260C22×C5—162no—
261C22×C5#44711yescharacteristic
262C22×C5#45911yescharacteristic
263C22×C5#49611yescharacteristic
264C4×C5—42no—
265C4×C5—81no—
266C4×C5—82no—
267C4×C5#39211yescharacteristic
268C4×C5#44711yescharacteristic
269C4×C5#45911yescharacteristic
270C4×C5#49311yescharacteristic
271C24—41no—
272#41—41no—
273#41—41no—
274#41—41no—
275#41—41no—
276C2×Q8—22no—
277C2×Q8—21no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—22no—
284C2×D4—21no—
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—41no—
289C2×D4—41no—
290C2×D4—41no—
291C22×C4—21no—
292C22×C4—41no—
293C22×C4—41no—
294C22×C4C2×C5×D411yescharacteristic
295Q16—21no—
296Q16—22no—
297Q16—21no—
298Q16—22no—
299Q16—41no—
300Q16—41no—
301SD16—48no—
302SD16—41no—
303SD16—41no—
304D8—21no—
305D8—22no—
306D8—21no—
307D8—22no—
308D8—41no—
309D8—41no—
310M16—41no—
311M16—41no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—41no—
315C2×C8C5×D812yes—
316C2×C8C2×C5×D411yescharacteristic
317C2×C8C2×C5×D411yescharacteristic
318C2×C8C2×C5×D411yescharacteristic
319C2×C8C2×C5×D411yescharacteristic
320C2×C8C2×C5×D411yescharacteristic
321C2×C8C5×#4111yescharacteristic
322C22⋊C4—48no—
323C42—21no—
324C42C5×D812yes—
325C16—22no—
326C16—22no—
327C2×C5—21no—
328C2×C5—21no—
329C2×C5—161no—
330C2×C5—162no—
331C2×C5#201111yescharacteristic
332C2×C5#221212yes—
333C23—42no—
334C23—41no—
335C23—84no—
336C23—81no—
337C23—81no—
338C23C5×AGL(1,ℤ/8)11yescharacteristic
339Q8—41no—
340Q8—42no—
341Q8—42no—
342Q8—41no—
343Q8—81no—
344Q8—81no—
345D4—42no—
346D4—41no—
347D4—42no—
348D4—41no—
349D4—81no—
350D4—81no—
351D4—81no—
352D4—81no—
353C2×C4—22no—
354C2×C4—42no—
355C2×C4—42no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—81no—
361C2×C4C5×#12011yescharacteristic
362C2×C4C5×#12111yescharacteristic
363C2×C4C5×#12711yescharacteristic
364C2×C4C2×C5×D811yescharacteristic
365C2×C4C2×C5×D811yescharacteristic
366C2×C4C5×AGL(1,ℤ/8)11yescharacteristic
367C8—22no—
368C8—81no—
369C8C5×#12011yescharacteristic
370C8C5×#12011yescharacteristic
371C8C5×#12111yescharacteristic
372C8C5×#12111yescharacteristic
373C5#1333211yescharacteristic, direct product factor, Sylow
374C22—22no—
375C22—84no—
376C22—82no—
377C22—81no—
378C22—82no—
379C22—162no—
380C22—162no—
381C22C5×#44711yescharacteristic
382C22C5×#45911yescharacteristic
383C22C5×#49611yescharacteristic
384C4—42no—
385C4—81no—
386C4—82no—
387C4C5×#39211yescharacteristic
388C4C5×#44711yescharacteristic
389C4C5×#45911yescharacteristic
390C4C5×#49311yescharacteristic
391C2—21no—
392C2—21no—
393C2—162no—
394C2—161no—
395C2C5×#201111yescharacteristic
396C2C5×#221212yes—
subgroupG/H
center, socleC22×C5#459
commutator, Frattini, cosocleC22×C8C23×C5
prime radicalC2×C5×#509C2
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C2×C4×C5×C8 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#510C2semidirect
3. C2×C5×#495C2semidirect
4. C2×C5×#362C2semidirect
5. C2×C5×#361C2semidirect
6. C5×#1974C2semidirect
7. C5×#1376C2semidirect
31. #13332C5direct (N × H)
80. C2×#510C2×C5semidirect
82. C2×#495C2×C5semidirect
83. C2×#362C2×C5semidirect
84. C2×#361C2×C5semidirect
85. #1974C2×C5semidirect
86. #1376C2×C5semidirect
373. C5#13332direct (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
C2×C5×#5092
C2×C5×#4952
C2×C5×#3622
C2×C5×#3612
C5×#19742
C5×#13762
#133325