Finite Group Databasebeta

← C5×#9950 #11932670

Subgroups — C5×#9950 #11932670

Order 1280.

636 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3186C211yesmaximal, characteristic
2C2×C5×#481C211yesmaximal, characteristic, complemented
3C5×#2504C211yesmaximal, characteristic, complemented
4C5×#1964C211yesmaximal, characteristic, complemented
5C5×#1824C211yesmaximal, characteristic, complemented
6C5×#1519C211yesmaximal, characteristic, complemented
7C5×#1282C211yesmaximal, characteristic, complemented
8C2×C5×#121C2211yescharacteristic
9C2×C5×#121C2211yescharacteristic
10C22×C5×C4⋊C4C2211yescharacteristic
11C5×#481—22no—
12C5×#481—22no—
13C5×#480—21no—
14C5×#480—21no—
15C5×#466—22no—
16C5×#447—21no—
17C5×#447—21no—
18C2×C5×#106—21no—
19C2×C5×#102—21no—
20C2×C5×#99—22no—
21C2×C5×C22⋊C8C2211yescharacteristic
22C2×C5×C22⋊C8C2211yescharacteristic
23C5×#397—22no—
24C5×#390—21no—
25C5×#386—22no—
26C5×#382—21no—
27C5×#380C2211yescharacteristic
28C4×C5×C22⋊C4C2211yescharacteristic
29C5×#340—22no—
30C5×#327—22no—
31#9950C511yesmaximal, characteristic, direct product factor, Sylow
32C22×C5×D4—21no—
33C22×C5×D4—21no—
34C22×C5×D4D411yescharacteristic
35C22×C5×D4D411yescharacteristic
36C23×C4×C5—21no—
37C23×C4×C5C2311yescharacteristic
38C2×C5×D8—22no—
39C22×C5×C8—21no—
40C22×C5×C8D412yes—
41C5×#121—21no—
42C5×#121—21no—
43C5×#121—21no—
44C5×#121—21no—
45C5×#121—21no—
46C5×#121—21no—
47C5×#121—21no—
48C5×#121—21no—
49C2×C5×C4⋊C4—21no—
50C2×C5×C4⋊C4—21no—
51C2×C5×C4⋊C4—21no—
52C2×C5×C4⋊C4—21no—
53C2×C5×C4⋊C4—21no—
54C2×C5×C4⋊C4—21no—
55C2×C5×C4⋊C4D411yescharacteristic
56C2×C5×C4⋊C4D412yes—
57C2×C5×C4⋊C4D411yescharacteristic
58C2×C5×C22⋊C4—21no—
59C2×C5×C22⋊C4—21no—
60C2×C5×C22⋊C4—21no—
61C2×C5×C22⋊C4—24no—
62C2×C5×C22⋊C4D412yes—
63C2×C42×C5—21no—
64C5×#107—22no—
65C5×#106—24no—
66C5×#102—24no—
67C5×#102—22no—
68C5×#102—22no—
69C5×#99—44no—
70C5×C22⋊C8—21no—
71C5×C22⋊C8—21no—
72C5×C22⋊C8—21no—
73C5×C22⋊C8D412yes—
74C5×#95—24no—
75C5×#95—21no—
76C5×#95—21no—
77#3186C2×C511yescharacteristic
78C2×#481C2×C511yescharacteristic, complemented
79#2504C2×C511yescharacteristic, complemented
80#1964C2×C511yescharacteristic, complemented
81#1824C2×C511yescharacteristic, complemented
82#1519C2×C511yescharacteristic, complemented
83#1282C2×C511yescharacteristic, complemented
84C24×C5—21no—
85C24×C5—21no—
86C24×C5C2×D411yescharacteristic
87C2×C5×D4—21no—
88C2×C5×D4—21no—
89C2×C5×D4—21no—
90C2×C5×D4—21no—
91C2×C5×D4—42no—
92C2×C5×D4—42no—
93C2×C5×D4—41no—
94C2×C5×D4—41no—
95C2×C5×D4—41no—
96C2×C5×D4—41no—
97C2×C5×D4—42no—
98C2×C5×D4—42no—
99C2×C5×D4—42no—
100C2×C5×D4—42no—
101C22×C4×C5—22no—
102C22×C4×C5—22no—
103C22×C4×C5—21no—
104C22×C4×C5—21no—
105C22×C4×C5—42no—
106C22×C4×C5—41no—
107C22×C4×C5—41no—
108C22×C4×C5—41no—
109C22×C4×C5—82no—
110C22×C4×C5C2×D411yescharacteristic
111C22×C4×C5C2×D411yescharacteristic
112C22×C4×C5C2×D411yescharacteristic
113C22×C4×C5C2×D411yescharacteristic
114C22×C4×C5C2×D411yescharacteristic
115C22×C4×C5#4111yescharacteristic
116C5×D8—82no—
117C2×C5×C8—22no—
118C2×C5×C8—22no—
119C2×C5×C8—42no—
120C2×C5×C8—42no—
121C5×C4⋊C4—22no—
122C5×C4⋊C4—21no—
123C5×C4⋊C4—21no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—22no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4—42no—
128C5×C4⋊C4—41no—
129C5×C4⋊C4—41no—
130C5×C22⋊C4—22no—
131C5×C22⋊C4—22no—
132C5×C22⋊C4—41no—
133C5×C22⋊C4—41no—
134C5×C22⋊C4—41no—
135C5×C22⋊C4—41no—
136C5×C22⋊C4—42no—
137C5×C22⋊C4—84no—
138C42×C5—42no—
139C2×#121C22×C511yescharacteristic
140C2×#121C22×C511yescharacteristic
141C22×C4⋊C4C22×C511yescharacteristic
142#481—22no—
143#481—22no—
144#480—21no—
145#480—21no—
146#466—22no—
147#447—21no—
148#447—21no—
149C2×#106—21no—
150C2×#102—21no—
151C2×#99—22no—
152C2×C22⋊C8C22×C511yescharacteristic
153C2×C22⋊C8C22×C511yescharacteristic
154#397—22no—
155#390—21no—
156#386—22no—
157#382—21no—
158#380C22×C511yescharacteristic
159C4×C22⋊C4C22×C511yescharacteristic
160#340—22no—
161#327—22no—
162C23×C5—41no—
163C23×C5—41no—
164C23×C5—42no—
165C23×C5—42no—
166C23×C5—41no—
167C23×C5—41no—
168C23×C5—42no—
169C23×C5—42no—
170C23×C5—81no—
171C23×C5—81no—
172C23×C5#12011yescharacteristic
173C23×C5#12111yescharacteristic
174C23×C5#12711yescharacteristic
175C23×C5#13512yes—
176C23×C5AGL(1,ℤ/8)12yes—
177C5×D4—42no—
178C5×D4—42no—
179C5×D4—42no—
180C5×D4—81no—
181C5×D4—82no—
182C5×D4—82no—
183C5×D4—81no—
184C5×D4—81no—
185C5×D4—81no—
186C5×D4—81no—
187C2×C4×C5—22no—
188C2×C4×C5—22no—
189C2×C4×C5—22no—
190C2×C4×C5—41no—
191C2×C4×C5—41no—
192C2×C4×C5—41no—
193C2×C4×C5—42no—
194C2×C4×C5—42no—
195C2×C4×C5—44no—
196C2×C4×C5—41no—
197C2×C4×C5—41no—
198C2×C4×C5—42no—
199C2×C4×C5—42no—
200C2×C4×C5—42no—
201C2×C4×C5—42no—
202C2×C4×C5—82no—
203C2×C4×C5—82no—
204C2×C4×C5—81no—
205C2×C4×C5—81no—
206C2×C4×C5—81no—
207C2×C4×C5#12011yescharacteristic
208C2×C4×C5#12011yescharacteristic
209C2×C4×C5#12111yescharacteristic
210C2×C4×C5#12111yescharacteristic
211C5×C8—42no—
212C5×C8—42no—
213C22×D4—21no—
214C22×D4—21no—
215C22×D4C5×D411yescharacteristic
216C22×D4C5×D411yescharacteristic
217C23×C4—21no—
218C23×C4C23×C511yescharacteristic
219C2×D8—22no—
220C22×C8—21no—
221C22×C8C5×D412yes—
222#121—21no—
223#121—21no—
224#121—21no—
225#121—21no—
226#121—21no—
227#121—21no—
228#121—21no—
229#121—21no—
230C2×C4⋊C4—21no—
231C2×C4⋊C4—21no—
232C2×C4⋊C4—21no—
233C2×C4⋊C4—21no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—21no—
236C2×C4⋊C4C5×D412yes—
237C2×C4⋊C4C5×D411yescharacteristic
238C2×C4⋊C4C5×D411yescharacteristic
239C2×C22⋊C4—21no—
240C2×C22⋊C4—21no—
241C2×C22⋊C4—21no—
242C2×C22⋊C4—24no—
243C2×C22⋊C4C5×D412yes—
244C2×C42—21no—
245#107—22no—
246#106—24no—
247#102—24no—
248#102—22no—
249#102—22no—
250#99—44no—
251C22⋊C8—21no—
252C22⋊C8—21no—
253C22⋊C8—21no—
254C22⋊C8C5×D412yes—
255#95—24no—
256#95—21no—
257#95—21no—
258C22×C5—21no—
259C22×C5—21no—
260C22×C5—21no—
261C22×C5—21no—
262C22×C5—21no—
263C22×C5—21no—
264C22×C5—42no—
265C22×C5—42no—
266C22×C5—84no—
267C22×C5—81no—
268C22×C5—81no—
269C22×C5—81no—
270C22×C5—81no—
271C22×C5—81no—
272C22×C5—81no—
273C22×C5—162no—
274C22×C5#39211yescharacteristic
275C22×C5#44912yes—
276C22×C5#46312yes—
277C22×C5#49511yescharacteristic
278C22×C5#49611yescharacteristic
279C4×C5—21no—
280C4×C5—21no—
281C4×C5—21no—
282C4×C5—82no—
283C4×C5—82no—
284C4×C5—81no—
285C4×C5—81no—
286C4×C5—161no—
287C4×C5#45812yes—
288C24—21no—
289C24—21no—
290C24C2×C5×D411yescharacteristic
291C2×D4—21no—
292C2×D4—21no—
293C2×D4—21no—
294C2×D4—21no—
295C2×D4—42no—
296C2×D4—42no—
297C2×D4—41no—
298C2×D4—41no—
299C2×D4—41no—
300C2×D4—41no—
301C2×D4—42no—
302C2×D4—42no—
303C2×D4—42no—
304C2×D4—42no—
305C22×C4—21no—
306C22×C4—22no—
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—42no—
310C22×C4—41no—
311C22×C4—41no—
312C22×C4—41no—
313C22×C4—82no—
314C22×C4C2×C5×D411yescharacteristic
315C22×C4C2×C5×D411yescharacteristic
316C22×C4C2×C5×D411yescharacteristic
317C22×C4C2×C5×D411yescharacteristic
318C22×C4C2×C5×D411yescharacteristic
319C22×C4C5×#4111yescharacteristic
320D8—82no—
321C2×C8—22no—
322C2×C8—22no—
323C2×C8—42no—
324C2×C8—42no—
325C4⋊C4—22no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—22no—
330C4⋊C4—21no—
331C4⋊C4—42no—
332C4⋊C4—41no—
333C4⋊C4—41no—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—41no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—42no—
341C22⋊C4—84no—
342C42—42no—
343C2×C5—22no—
344C2×C5—21no—
345C2×C5—22no—
346C2×C5—21no—
347C2×C5—161no—
348C2×C5—161no—
349C2×C5#200811yescharacteristic
350C2×C5#201211yescharacteristic
351C2×C5#202211yescharacteristic
352C23—41no—
353C23—41no—
354C23—42no—
355C23—42no—
356C23—41no—
357C23—41no—
358C23—42no—
359C23—42no—
360C23—81no—
361C23—81no—
362C23C5×#12011yescharacteristic
363C23C5×#12111yescharacteristic
364C23C5×#12711yescharacteristic
365C23C5×#13512yes—
366C23C5×AGL(1,ℤ/8)12yes—
367D4—42no—
368D4—42no—
369D4—42no—
370D4—81no—
371D4—82no—
372D4—82no—
373D4—81no—
374D4—81no—
375D4—81no—
376D4—81no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—41no—
381C2×C4—41no—
382C2×C4—41no—
383C2×C4—42no—
384C2×C4—42no—
385C2×C4—44no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—42no—
390C2×C4—42no—
391C2×C4—42no—
392C2×C4—82no—
393C2×C4—82no—
394C2×C4—81no—
395C2×C4—81no—
396C2×C4—81no—
397C2×C4C5×#12011yescharacteristic
398C2×C4C5×#12011yescharacteristic
399C2×C4C5×#12111yescharacteristic
400C2×C4C5×#12111yescharacteristic
401C8—42no—
402C8—42no—
403C5#995011yescharacteristic, direct product factor, Sylow
404C22—21no—
405C22—21no—
406C22—21no—
407C22—21no—
408C22—21no—
409C22—21no—
410C22—42no—
411C22—42no—
412C22—84no—
413C22—81no—
414C22—81no—
415C22—81no—
416C22—81no—
417C22—81no—
418C22—81no—
419C22—162no—
420C22C5×#39211yescharacteristic
421C22C5×#44912yes—
422C22C5×#46312yes—
423C22C5×#49511yescharacteristic
424C22C5×#49611yescharacteristic
425C4—21no—
426C4—21no—
427C4—21no—
428C4—82no—
429C4—81no—
430C4—81no—
431C4—82no—
432C4—161no—
433C4C5×#45812yes—
434C2—22no—
435C2—21no—
436C2—22no—
437C2—21no—
438C2—161no—
439C2—161no—
440C2C5×#200811yescharacteristic
441C2C5×#201211yescharacteristic
442C2C5×#202211yescharacteristic
subgroupG/H
center, socleC22×C5#392
commutator, Frattini, cosocleC23×C4C23×C5
prime radicalC5×#3186C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C5×#481C2semidirect
3. C5×#2504C2semidirect
4. C5×#1964C2semidirect
5. C5×#1824C2semidirect
6. C5×#1519C2semidirect
7. C5×#1282C2semidirect
31. #9950C5direct (N × H)
78. C2×#481C2×C5semidirect
79. #2504C2×C5semidirect
80. #1964C2×C5semidirect
81. #1824C2×C5semidirect
82. #1519C2×C5semidirect
83. #1282C2×C5semidirect
403. C5#9950direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#31862
C2×C5×#4812
C5×#25042
C5×#19642
C5×#18242
C5×#15192
C5×#12822
#99505