Finite Group Databasebeta

← C5×#19066 #11941786

Subgroups — C5×#19066 #11941786

Order 1280.

852 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3550C211yesmaximal, characteristic
2C5×#3237C211yesmaximal, characteristic, complemented
3C5×#3216C211yesmaximal, characteristic
4C5×#3162C211yesmaximal, characteristic, complemented
5C5×#1664C214yesmaximal, complemented
6C5×#1660C214yesmaximal, complemented
7C5×#1537C211yesmaximal, characteristic, complemented
8C5×#1531C211yesmaximal, characteristic, complemented
9C5×#1530C211yesmaximal, characteristic
10C5×#563C2214yes—
11C5×#559—21no—
12C5×Q82—21no—
13C5×#556—21no—
14C5×#556—21no—
15C5×D4×Q8—21no—
16C5×D4×Q8—21no—
17C5×#542—22no—
18C5×#542—22no—
19C5×#536—22no—
20C5×#533C2211yescharacteristic
21C5×#533C2211yescharacteristic
22C5×#533C2211yescharacteristic
23C5×#532C2211yescharacteristic
24C5×#501—21no—
25C5×#501—21no—
26C5×#501C2212yes—
27C5×#501C2212yes—
28C5×#501C2212yes—
29C5×#497C2212yes—
30C5×#491C2212yes—
31C5×#489C2212yes—
32C5×#485—22no—
33C5×#477—21no—
34C5×#475—21no—
35C5×#462—21no—
36C5×#460—21no—
37C5×#452—22no—
38C5×#432C2211yescharacteristic
39C5×#432C2211yescharacteristic
40C5×#427—22no—
41C2×C5×#97C2211yescharacteristic
42C5×#330C2214yes—
43C5×#330C2214yes—
44C5×#329C2214yes—
45#19066C511yesmaximal, characteristic, direct product factor, Sylow
46C2×C5×#41D412yes—
47C22×C5×Q8—22no—
48C2×C5×Q16—22no—
49C2×C5×SD16—22no—
50C22×C5×C8—21no—
51C5×C4⋊Q8—22no—
52C5×C4⋊Q8—22no—
53C5×C4⋊Q8—24no—
54C5×C4⋊Q8D411yescharacteristic
55C5×C4⋊Q8D411yescharacteristic
56C5×C4⋊Q8D411yescharacteristic
57C5×C4⋊Q8D411yescharacteristic
58C5×C4⋊Q8D411yescharacteristic
59C5×C4⋊Q8C2311yescharacteristic
60C5×C4⋊Q8C2311yescharacteristic
61C5×#127D411yescharacteristic
62C5×#126—24no—
63C5×#126—24no—
64C5×#125—21no—
65C5×#125C2312yes—
66C5×#125C2312yes—
67C5×#124—24no—
68C5×#124—22no—
69C5×#124—22no—
70C5×#124C2312yes—
71C5×#123—24no—
72C5×#123—24no—
73C5×C22⋊Q8—22no—
74C5×C22⋊Q8—22no—
75C5×C22⋊Q8—21no—
76C5×C22⋊Q8—21no—
77C5×C22⋊Q8—21no—
78C5×C22⋊Q8—21no—
79C5×C22⋊Q8—24no—
80C5×C22⋊Q8—24no—
81C5×C22⋊Q8—21no—
82C5×C22⋊Q8—21no—
83C5×#121—21no—
84C5×#121—21no—
85C4×C5×Q8—22no—
86C4×C5×Q8—22no—
87C4×C5×Q8—21no—
88C4×C5×Q8—21no—
89C4×C5×Q8—21no—
90C4×C5×Q8—21no—
91C4×C5×Q8—21no—
92C4×C5×Q8—21no—
93C4×C5×D4—22no—
94C4×C5×D4—22no—
95C4×C5×D4—21no—
96C4×C5×D4—21no—
97C5×#117—22no—
98C5×#117—21no—
99C5×#117D412yes—
100C5×#117D412yes—
101C2×C42×C5C2311yescharacteristic
102C5×#107—22no—
103C5×#107—22no—
104C5×#107—22no—
105C5×#106—22no—
106C5×#106—22no—
107C5×#106—22no—
108C5×C4⋊C8—21no—
109C5×C4⋊C8—21no—
110C5×#103—22no—
111C5×#103—22no—
112C5×#103—22no—
113C5×#102—22no—
114C5×C22⋊C8—21no—
115C5×C22⋊C8—21no—
116C5×#97—21no—
117C5×#97C2312yes—
118C5×#97C2312yes—
119C5×#97C2312yes—
120#3550C2×C511yescharacteristic
121#3237C2×C511yescharacteristic, complemented
122#3216C2×C511yescharacteristic
123#3162C2×C511yescharacteristic, complemented
124#1664C2×C514yescomplemented
125#1660C2×C514yescomplemented
126#1537C2×C511yescharacteristic, complemented
127#1531C2×C511yescharacteristic, complemented
128#1530C2×C511yescharacteristic
129C5×#41—82no—
130C2×C5×Q8—24no—
131C2×C5×Q8—21no—
132C2×C5×Q8—21no—
133C2×C5×Q8—21no—
134C2×C5×Q8—21no—
135C2×C5×Q8—21no—
136C2×C5×Q8—21no—
137C2×C5×Q8—84no—
138C2×C5×Q8C2×D412yes—
139C2×C5×D4—22no—
140C2×C5×D4—21no—
141C2×C5×D4—21no—
142C2×C5×D4C2×D412yes—
143C22×C4×C5—24no—
144C22×C4×C5—22no—
145C22×C4×C5C2×D411yescharacteristic
146C22×C4×C5C2×D411yescharacteristic
147C22×C4×C5C2×D411yescharacteristic
148C5×Q16—82no—
149C5×SD16—82no—
150C2×C5×C8—24no—
151C2×C5×C8—22no—
152C2×C5×C8—22no—
153C2×C5×C8—22no—
154C5×C4⋊C4—24no—
155C5×C4⋊C4—24no—
156C5×C4⋊C4—21no—
157C5×C4⋊C4—21no—
158C5×C4⋊C4—21no—
159C5×C4⋊C4—21no—
160C5×C4⋊C4—21no—
161C5×C4⋊C4—21no—
162C5×C4⋊C4—22no—
163C5×C4⋊C4—22no—
164C5×C4⋊C4—22no—
165C5×C4⋊C4—22no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—21no—
169C5×C4⋊C4—21no—
170C5×C4⋊C4—41no—
171C5×C4⋊C4—41no—
172C5×C4⋊C4C2×D412yes—
173C5×C4⋊C4C2×D412yes—
174C5×C4⋊C4C2×D412yes—
175C5×C4⋊C4C2×D412yes—
176C5×C22⋊C4—24no—
177C5×C22⋊C4—24no—
178C5×C22⋊C4—24no—
179C5×C22⋊C4—22no—
180C5×C22⋊C4—22no—
181C5×C22⋊C4—22no—
182C5×C22⋊C4—22no—
183C5×C22⋊C4—41no—
184C42×C5—24no—
185C42×C5—22no—
186C42×C5—22no—
187C42×C5—41no—
188C42×C5C2×D411yescharacteristic
189C42×C5C2×D411yescharacteristic
190C42×C5C2×D411yescharacteristic
191C42×C5C2411yescharacteristic
192#563C22×C514yes—
193#559—21no—
194Q82—21no—
195#556—21no—
196#556—21no—
197D4×Q8—21no—
198D4×Q8—21no—
199#542—22no—
200#542—22no—
201#536—22no—
202#533C22×C511yescharacteristic
203#533C22×C511yescharacteristic
204#533C22×C511yescharacteristic
205#532C22×C511yescharacteristic
206#501—21no—
207#501—21no—
208#501C22×C512yes—
209#501C22×C512yes—
210#501C22×C512yes—
211#497C22×C512yes—
212#491C22×C512yes—
213#489C22×C512yes—
214#485—22no—
215#477—21no—
216#475—21no—
217#462—21no—
218#460—21no—
219#452—22no—
220#432C22×C511yescharacteristic
221#432C22×C511yescharacteristic
222#427—22no—
223C2×#97C22×C511yescharacteristic
224#330C22×C514yes—
225#330C22×C514yes—
226#329C22×C514yes—
227C23×C5—22no—
228C23×C5#12011yescharacteristic
229C5×Q8—42no—
230C5×Q8—42no—
231C5×Q8—42no—
232C5×Q8—42no—
233C5×Q8—41no—
234C5×Q8—41no—
235C5×Q8—42no—
236C5×Q8—42no—
237C5×Q8—84no—
238C5×D4—42no—
239C5×D4—42no—
240C5×D4—42no—
241C5×D4—82no—
242C2×C4×C5—22no—
243C2×C4×C5—22no—
244C2×C4×C5—22no—
245C2×C4×C5—22no—
246C2×C4×C5—22no—
247C2×C4×C5—22no—
248C2×C4×C5—41no—
249C2×C4×C5—41no—
250C2×C4×C5—44no—
251C2×C4×C5—41no—
252C2×C4×C5—41no—
253C2×C4×C5—84no—
254C2×C4×C5#12011yescharacteristic
255C2×C4×C5#12011yescharacteristic
256C2×C4×C5#12011yescharacteristic
257C2×C4×C5C22×D411yescharacteristic
258C2×C4×C5C22×D411yescharacteristic
259C2×C4×C5C22×D411yescharacteristic
260C5×C8—24no—
261C5×C8—42no—
262C5×C8—42no—
263C2×#41C5×D412yes—
264C22×Q8—22no—
265C2×Q16—22no—
266C2×SD16—22no—
267C22×C8—21no—
268C4⋊Q8—22no—
269C4⋊Q8—22no—
270C4⋊Q8—24no—
271C4⋊Q8C5×D411yescharacteristic
272C4⋊Q8C5×D411yescharacteristic
273C4⋊Q8C5×D411yescharacteristic
274C4⋊Q8C5×D411yescharacteristic
275C4⋊Q8C5×D411yescharacteristic
276C4⋊Q8C23×C511yescharacteristic
277C4⋊Q8C23×C511yescharacteristic
278#127C5×D411yescharacteristic
279#126—24no—
280#126—24no—
281#125—21no—
282#125C23×C512yes—
283#125C23×C512yes—
284#124—24no—
285#124—22no—
286#124—22no—
287#124C23×C512yes—
288#123—24no—
289#123—24no—
290C22⋊Q8—22no—
291C22⋊Q8—22no—
292C22⋊Q8—21no—
293C22⋊Q8—21no—
294C22⋊Q8—21no—
295C22⋊Q8—21no—
296C22⋊Q8—24no—
297C22⋊Q8—24no—
298C22⋊Q8—21no—
299C22⋊Q8—21no—
300#121—21no—
301#121—21no—
302C4×Q8—22no—
303C4×Q8—22no—
304C4×Q8—21no—
305C4×Q8—21no—
306C4×Q8—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×D4—22no—
311C4×D4—22no—
312C4×D4—21no—
313C4×D4—21no—
314#117—22no—
315#117—21no—
316#117C5×D412yes—
317#117C5×D412yes—
318C2×C42C23×C511yescharacteristic
319#107—22no—
320#107—22no—
321#107—22no—
322#106—22no—
323#106—22no—
324#106—22no—
325C4⋊C8—21no—
326C4⋊C8—21no—
327#103—22no—
328#103—22no—
329#103—22no—
330#102—22no—
331C22⋊C8—21no—
332C22⋊C8—21no—
333#97—21no—
334#97C23×C512yes—
335#97C23×C512yes—
336#97C23×C512yes—
337C22×C5—21no—
338C22×C5—21no—
339C22×C5—21no—
340C22×C5—42no—
341C22×C5—42no—
342C22×C5—42no—
343C22×C5C2×#12011yescharacteristic
344C4×C5—21no—
345C4×C5—21no—
346C4×C5—21no—
347C4×C5—21no—
348C4×C5—21no—
349C4×C5—42no—
350C4×C5—42no—
351C4×C5—42no—
352C4×C5—42no—
353C4×C5—42no—
354C4×C5—81no—
355C4×C5—81no—
356C4×C5#45612yes—
357#41—82no—
358C2×Q8—24no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—84no—
366C2×Q8C2×C5×D412yes—
367C2×D4—22no—
368C2×D4—21no—
369C2×D4—21no—
370C2×D4C2×C5×D412yes—
371C22×C4—24no—
372C22×C4—22no—
373C22×C4C2×C5×D411yescharacteristic
374C22×C4C2×C5×D411yescharacteristic
375C22×C4C2×C5×D411yescharacteristic
376Q16—82no—
377SD16—82no—
378C2×C8—24no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C4⋊C4—24no—
383C4⋊C4—24no—
384C4⋊C4—21no—
385C4⋊C4—21no—
386C4⋊C4—21no—
387C4⋊C4—21no—
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—22no—
391C4⋊C4—22no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—21no—
395C4⋊C4—21no—
396C4⋊C4—21no—
397C4⋊C4—21no—
398C4⋊C4—41no—
399C4⋊C4—41no—
400C4⋊C4C2×C5×D412yes—
401C4⋊C4C2×C5×D412yes—
402C4⋊C4C2×C5×D412yes—
403C4⋊C4C2×C5×D412yes—
404C22⋊C4—24no—
405C22⋊C4—24no—
406C22⋊C4—24no—
407C22⋊C4—22no—
408C22⋊C4—22no—
409C22⋊C4—22no—
410C22⋊C4—22no—
411C22⋊C4—41no—
412C42—24no—
413C42—22no—
414C42—22no—
415C42—41no—
416C42C2×C5×D411yescharacteristic
417C42C2×C5×D411yescharacteristic
418C42C2×C5×D411yescharacteristic
419C42C24×C511yescharacteristic
420C2×C5—41no—
421C2×C5—82no—
422C2×C5C2×#45611yescharacteristic
423C2×C5#301911yescharacteristic
424C2×C5#302011yescharacteristic
425C23—22no—
426C23C5×#12011yescharacteristic
427Q8—42no—
428Q8—42no—
429Q8—42no—
430Q8—42no—
431Q8—41no—
432Q8—41no—
433Q8—42no—
434Q8—42no—
435Q8—84no—
436D4—42no—
437D4—42no—
438D4—42no—
439D4—82no—
440C2×C4—22no—
441C2×C4—22no—
442C2×C4—22no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—22no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—44no—
449C2×C4—41no—
450C2×C4—41no—
451C2×C4—84no—
452C2×C4C5×#12011yescharacteristic
453C2×C4C5×#12011yescharacteristic
454C2×C4C5×#12011yescharacteristic
455C2×C4C22×C5×D411yescharacteristic
456C2×C4C22×C5×D411yescharacteristic
457C2×C4C22×C5×D411yescharacteristic
458C8—24no—
459C8—42no—
460C8—42no—
461C5#1906611yescharacteristic, direct product factor, Sylow
462C22—21no—
463C22—21no—
464C22—21no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22C2×C5×#12011yescharacteristic
469C4—21no—
470C4—21no—
471C4—21no—
472C4—21no—
473C4—21no—
474C4—42no—
475C4—42no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—81no—
480C4—81no—
481C4C5×#45612yes—
482C2—41no—
483C2—82no—
484C2C2×C5×#45611yescharacteristic
485C2C5×#301911yescharacteristic
486C2C5×#302011yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC42C24×C5
prime radicalC5×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3237C2semidirect
4. C5×#3162C2semidirect
5. C5×#1664C2semidirect
6. C5×#1660C2semidirect
7. C5×#1537C2semidirect
8. C5×#1531C2semidirect
45. #19066C5direct (N × H)
121. #3237C2×C5semidirect
123. #3162C2×C5semidirect
124. #1664C2×C5semidirect
125. #1660C2×C5semidirect
126. #1537C2×C5semidirect
127. #1531C2×C5semidirect
461. C5#19066direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#35502
C5×#32372
C5×#32162
C5×#31622
C5×#16642
C5×#16602
C5×#15372
C5×#15312
C5×#15302
#190665