Finite Group Databasebeta

← C5×#9919 #11932639

Subgroups — C5×#9919 #11932639

Order 1280.

716 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#480C211yesmaximal, characteristic
2C5×#2618C211yesmaximal, characteristic
3C2×C5×#398C211yesmaximal, characteristic, complemented
4C5×#1823C211yesmaximal, characteristic, complemented
5C2×C5×#327C211yesmaximal, characteristic
6C2×C5×#324C211yesmaximal, characteristic, complemented
7C5×#1294C211yesmaximal, characteristic, complemented
8C2×C5×#123—21no—
9C2×C5×#121C2211yescharacteristic
10C22×C5×C4⋊C4—21no—
11C22×C5×C4⋊C4C2211yescharacteristic
12C22×C5×C4⋊C4C2211yescharacteristic
13C5×#480—22no—
14C5×#480—22no—
15C2×C5×#107—21no—
16C2×C5×#102—21no—
17C2×C5×C22⋊C8C2211yescharacteristic
18C2×C5×C22⋊C8C2211yescharacteristic
19C5×#398—22no—
20C5×#398—21no—
21C5×#398—22no—
22C5×#396—22no—
23C5×#394—21no—
24C5×#386—21no—
25C5×#380C2211yescharacteristic
26C2×C5×#95—21no—
27C2×C5×#95C2211yescharacteristic
28C5×#340—22no—
29C5×#327—22no—
30C5×#324—22no—
31#9919C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×D4—21no—
33C22×C5×D4D411yescharacteristic
34C23×C4×C5—21no—
35C23×C4×C5—21no—
36C23×C4×C5D411yescharacteristic
37C23×C4×C5D411yescharacteristic
38C23×C4×C5C2311yescharacteristic
39C22×C5×C8—21no—
40C22×C5×C8—21no—
41C5×#123—42no—
42C5×#123—42no—
43C5×#121—21no—
44C5×#121—21no—
45C5×#121—21no—
46C5×#121—21no—
47C2×C5×C4⋊C4—21no—
48C2×C5×C4⋊C4—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—22no—
52C2×C5×C4⋊C4—24no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4—21no—
56C2×C5×C4⋊C4—21no—
57C2×C5×C4⋊C4—21no—
58C2×C5×C4⋊C4—21no—
59C2×C5×C4⋊C4—21no—
60C2×C5×C4⋊C4—42no—
61C2×C5×C4⋊C4—42no—
62C2×C5×C4⋊C4D411yescharacteristic
63C2×C5×C4⋊C4D412yes—
64C2×C5×C4⋊C4D412yes—
65C2×C5×C22⋊C4—22no—
66C2×C5×C22⋊C4—21no—
67C2×C5×C22⋊C4—21no—
68C2×C5×C22⋊C4—22no—
69C5×#107—24no—
70C5×#102—24no—
71C5×C22⋊C8—21no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8—21no—
74C5×C22⋊C8D412yes—
75C5×#95—24no—
76C5×#95—22no—
77C5×#95—21no—
78C5×#95—21no—
79C5×#95D412yes—
80C2×#480C2×C511yescharacteristic
81#2618C2×C511yescharacteristic
82C2×#398C2×C511yescharacteristic, complemented
83#1823C2×C511yescharacteristic, complemented
84C2×#327C2×C511yescharacteristic
85C2×#324C2×C511yescharacteristic, complemented
86#1294C2×C511yescharacteristic, complemented
87C24×C5—21no—
88C24×C5C2×D411yescharacteristic
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4—42no—
92C2×C5×D4—41no—
93C2×C5×D4—41no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—41no—
98C22×C4×C5—24no—
99C22×C4×C5—21no—
100C22×C4×C5—22no—
101C22×C4×C5—21no—
102C22×C4×C5—21no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—21no—
106C22×C4×C5—22no—
107C22×C4×C5—21no—
108C22×C4×C5—22no—
109C22×C4×C5—21no—
110C22×C4×C5—21no—
111C22×C4×C5—21no—
112C22×C4×C5—42no—
113C22×C4×C5—42no—
114C22×C4×C5—41no—
115C22×C4×C5—41no—
116C22×C4×C5—42no—
117C22×C4×C5—41no—
118C22×C4×C5—41no—
119C22×C4×C5—41no—
120C22×C4×C5—41no—
121C22×C4×C5—41no—
122C22×C4×C5—41no—
123C22×C4×C5D812yes—
124C22×C4×C5C2×D411yescharacteristic
125C22×C4×C5C2×D411yescharacteristic
126C22×C4×C5C2×D411yescharacteristic
127C22×C4×C5C2×D411yescharacteristic
128C22×C4×C5C2×D411yescharacteristic
129C22×C4×C5#4111yescharacteristic
130C2×C5×C8—22no—
131C2×C5×C8—42no—
132C2×C5×C8—42no—
133C2×C5×C8—41no—
134C5×C4⋊C4—22no—
135C5×C4⋊C4—21no—
136C5×C4⋊C4—22no—
137C5×C4⋊C4—21no—
138C5×C4⋊C4—42no—
139C5×C4⋊C4—48no—
140C5×C4⋊C4—44no—
141C5×C4⋊C4—41no—
142C5×C4⋊C4—41no—
143C5×C4⋊C4—41no—
144C5×C4⋊C4—41no—
145C5×C4⋊C4—41no—
146C5×C4⋊C4—41no—
147C5×C22⋊C4—44no—
148C5×C22⋊C4—41no—
149C5×C22⋊C4—41no—
150C5×C22⋊C4—41no—
151C5×C22⋊C4—41no—
152C5×C22⋊C4—82no—
153C2×#123—21no—
154C2×#121C22×C511yescharacteristic
155C22×C4⋊C4—21no—
156C22×C4⋊C4C22×C511yescharacteristic
157C22×C4⋊C4C22×C511yescharacteristic
158#480—22no—
159#480—22no—
160C2×#107—21no—
161C2×#102—21no—
162C2×C22⋊C8C22×C511yescharacteristic
163C2×C22⋊C8C22×C511yescharacteristic
164#398—21no—
165#398—22no—
166#398—22no—
167#396—22no—
168#394—21no—
169#386—21no—
170#380C22×C511yescharacteristic
171C2×#95—21no—
172C2×#95C22×C511yescharacteristic
173#340—22no—
174#327—22no—
175#324—22no—
176C23×C5—22no—
177C23×C5—22no—
178C23×C5—41no—
179C23×C5—41no—
180C23×C5—41no—
181C23×C5—42no—
182C23×C5—42no—
183C23×C5#12011yescharacteristic
184C23×C5#12011yescharacteristic
185C23×C5#12111yescharacteristic
186C23×C5C2×D811yescharacteristic
187C23×C5#13511yescharacteristic
188C23×C5AGL(1,ℤ/8)11yescharacteristic
189C23×C5AGL(1,ℤ/8)11yescharacteristic
190C5×D4—42no—
191C5×D4—81no—
192C5×D4—81no—
193C5×D4—81no—
194C5×D4—81no—
195C5×D4—81no—
196C2×C4×C5—22no—
197C2×C4×C5—22no—
198C2×C4×C5—24no—
199C2×C4×C5—22no—
200C2×C4×C5—22no—
201C2×C4×C5—22no—
202C2×C4×C5—41no—
203C2×C4×C5—41no—
204C2×C4×C5—41no—
205C2×C4×C5—41no—
206C2×C4×C5—44no—
207C2×C4×C5—44no—
208C2×C4×C5—42no—
209C2×C4×C5—41no—
210C2×C4×C5—42no—
211C2×C4×C5—41no—
212C2×C4×C5—41no—
213C2×C4×C5—41no—
214C2×C4×C5—42no—
215C2×C4×C5—41no—
216C2×C4×C5—42no—
217C2×C4×C5—41no—
218C2×C4×C5—42no—
219C2×C4×C5—42no—
220C2×C4×C5—41no—
221C2×C4×C5—42no—
222C2×C4×C5—41no—
223C2×C4×C5—42no—
224C2×C4×C5—42no—
225C2×C4×C5—42no—
226C2×C4×C5—81no—
227C2×C4×C5—81no—
228C2×C4×C5—81no—
229C2×C4×C5—81no—
230C2×C4×C5—81no—
231C2×C4×C5#12011yescharacteristic
232C2×C4×C5#12111yescharacteristic
233C2×C4×C5#12111yescharacteristic
234C2×C4×C5#12711yescharacteristic
235C5×C8—42no—
236C5×C8—81no—
237C22×D4—21no—
238C22×D4C5×D411yescharacteristic
239C23×C4—21no—
240C23×C4—21no—
241C23×C4C5×D411yescharacteristic
242C23×C4C5×D411yescharacteristic
243C23×C4C23×C511yescharacteristic
244C22×C8—21no—
245C22×C8—21no—
246#123—42no—
247#123—42no—
248#121—21no—
249#121—21no—
250#121—21no—
251#121—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—21no—
255C2×C4⋊C4—21no—
256C2×C4⋊C4—24no—
257C2×C4⋊C4—22no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—21no—
262C2×C4⋊C4—21no—
263C2×C4⋊C4—21no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—42no—
266C2×C4⋊C4—42no—
267C2×C4⋊C4C5×D412yes—
268C2×C4⋊C4C5×D411yescharacteristic
269C2×C4⋊C4C5×D412yes—
270C2×C22⋊C4—22no—
271C2×C22⋊C4—21no—
272C2×C22⋊C4—21no—
273C2×C22⋊C4—22no—
274#107—24no—
275#102—24no—
276C22⋊C8—21no—
277C22⋊C8—21no—
278C22⋊C8—21no—
279C22⋊C8C5×D412yes—
280#95—24no—
281#95—22no—
282#95—21no—
283#95—21no—
284#95C5×D412yes—
285C22×C5—22no—
286C22×C5—22no—
287C22×C5—22no—
288C22×C5—22no—
289C22×C5—21no—
290C22×C5—21no—
291C22×C5—21no—
292C22×C5—21no—
293C22×C5—82no—
294C22×C5—82no—
295C22×C5—81no—
296C22×C5—81no—
297C22×C5—81no—
298C22×C5#39211yescharacteristic
299C22×C5#44711yescharacteristic
300C22×C5#44711yescharacteristic
301C22×C5#44911yescharacteristic
302C22×C5#44911yescharacteristic
303C22×C5#45612yes—
304C22×C5#45812yes—
305C22×C5#46611yescharacteristic
306C22×C5#46911yescharacteristic
307C4×C5—21no—
308C4×C5—21no—
309C4×C5—21no—
310C4×C5—21no—
311C4×C5—44no—
312C4×C5—42no—
313C4×C5—82no—
314C4×C5—82no—
315C4×C5—81no—
316C4×C5—81no—
317C24—21no—
318C24C2×C5×D411yescharacteristic
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—42no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C22×C4—24no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—21no—
335C22×C4—21no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—21no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—41no—
345C22×C4—41no—
346C22×C4—42no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4—41no—
351C22×C4—41no—
352C22×C4—41no—
353C22×C4C5×D812yes—
354C22×C4C2×C5×D411yescharacteristic
355C22×C4C2×C5×D411yescharacteristic
356C22×C4C2×C5×D411yescharacteristic
357C22×C4C2×C5×D411yescharacteristic
358C22×C4C2×C5×D411yescharacteristic
359C22×C4C5×#4111yescharacteristic
360C2×C8—22no—
361C2×C8—42no—
362C2×C8—42no—
363C2×C8—41no—
364C4⋊C4—22no—
365C4⋊C4—21no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—42no—
369C4⋊C4—48no—
370C4⋊C4—44no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—41no—
376C4⋊C4—41no—
377C22⋊C4—44no—
378C22⋊C4—41no—
379C22⋊C4—41no—
380C22⋊C4—41no—
381C22⋊C4—41no—
382C22⋊C4—82no—
383C2×C5—21no—
384C2×C5—21no—
385C2×C5—21no—
386C2×C5—21no—
387C2×C5—161no—
388C2×C5#160912yes—
389C2×C5#161012yes—
390C2×C5#199911yescharacteristic
391C2×C5#200511yescharacteristic
392C2×C5#202211yescharacteristic
393C23—22no—
394C23—22no—
395C23—41no—
396C23—41no—
397C23—41no—
398C23—42no—
399C23—42no—
400C23C5×#12011yescharacteristic
401C23C5×#12011yescharacteristic
402C23C5×#12111yescharacteristic
403C23C2×C5×D811yescharacteristic
404C23C5×#13511yescharacteristic
405C23C5×AGL(1,ℤ/8)11yescharacteristic
406C23C5×AGL(1,ℤ/8)11yescharacteristic
407D4—42no—
408D4—81no—
409D4—81no—
410D4—81no—
411D4—81no—
412D4—81no—
413C2×C4—22no—
414C2×C4—22no—
415C2×C4—24no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—44no—
425C2×C4—44no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—42no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—81no—
444C2×C4—81no—
445C2×C4—81no—
446C2×C4—81no—
447C2×C4—81no—
448C2×C4C5×#12011yescharacteristic
449C2×C4C5×#12111yescharacteristic
450C2×C4C5×#12111yescharacteristic
451C2×C4C5×#12711yescharacteristic
452C8—42no—
453C8—81no—
454C5#991911yescharacteristic, direct product factor, Sylow
455C22—21no—
456C22—21no—
457C22—22no—
458C22—22no—
459C22—22no—
460C22—22no—
461C22—21no—
462C22—21no—
463C22—81no—
464C22—82no—
465C22—82no—
466C22—81no—
467C22—81no—
468C22C5×#39211yescharacteristic
469C22C5×#44711yescharacteristic
470C22C5×#44711yescharacteristic
471C22C5×#44911yescharacteristic
472C22C5×#44911yescharacteristic
473C22C5×#45612yes—
474C22C5×#45812yes—
475C22C5×#46611yescharacteristic
476C22C5×#46911yescharacteristic
477C4—21no—
478C4—21no—
479C4—21no—
480C4—21no—
481C4—44no—
482C4—42no—
483C4—81no—
484C4—82no—
485C4—82no—
486C4—81no—
487C2—21no—
488C2—21no—
489C2—21no—
490C2—21no—
491C2—161no—
492C2C5×#160912yes—
493C2C5×#161012yes—
494C2C5×#199911yescharacteristic
495C2C5×#200511yescharacteristic
496C2C5×#202211yescharacteristic
subgroupG/H
center, socleC23×C5#120
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC2×C5×#121C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×C5×#398C2semidirect
4. C5×#1823C2semidirect
6. C2×C5×#324C2semidirect
7. C5×#1294C2semidirect
31. #9919C5direct (N × H)
82. C2×#398C2×C5semidirect
83. #1823C2×C5semidirect
85. C2×#324C2×C5semidirect
86. #1294C2×C5semidirect
454. C5#9919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4802
C5×#26182
C2×C5×#3982
C5×#18232
C2×C5×#3272
C2×C5×#3242
C5×#12942
#99195