Finite Group Databasebeta

← C5×#29703 #11952423

Subgroups — C5×#29703 #11952423

Order 1280.

1074 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#3460C211yesmaximal, characteristic
2C5×#3079C212yesmaximal, complemented
3C5×#2542C211yesmaximal, characteristic, complemented
4C5×#2060C212yesmaximal, complemented
5C5×#2039C212yesmaximal, complemented
6C5×#2037C214yesmaximal, complemented
7C5×#1806C212yesmaximal, complemented
8C5×#1800C211yesmaximal, characteristic, complemented
9C5×#544C2211yescharacteristic
10C5×#542—22no—
11C5×#540—22no—
12C5×#538—22no—
13C5×#537C2211yescharacteristic
14C5×#535C2212yes—
15C5×#532—22no—
16C2×C5×C4⋊Q8C2211yescharacteristic
17C5×#529—22no—
18C5×#525—22no—
19C2×C5×C22⋊Q8—22no—
20C4×C5×#41C2212yes—
21C2×C4×C5×D4C2211yescharacteristic
22C5×#477—22no—
23C5×#476—22no—
24C5×#475—22no—
25C5×#474—22no—
26C5×#428C2214yes—
27C5×#423C2212yes—
28C2×C5×#104C2214yes—
29C5×#417C2214yes—
30C2×C5×#100C2212yes—
31C5×#399—22no—
32C5×#390C2212yes—
33C5×#384C2212yes—
34C4×C5×C4⋊C4C2211yescharacteristic
35C5×#343C2212yes—
36C5×#339C2214yes—
37#29703C511yesmaximal, characteristic, direct product factor, Sylow
38C2×C5×#41—22no—
39C2×C5×#41C2312yes—
40C22×C5×Q8—21no—
41C22×C5×D4C2311yescharacteristic
42C23×C4×C5D412yes—
43C2×C5×M16C2314yes—
44C5×C4⋊Q8—22no—
45C5×C4⋊Q8—22no—
46C5×C4⋊Q8—22no—
47C5×#127—22no—
48C5×#126—24no—
49C5×#125—22no—
50C5×#124—24no—
51C5×#124—22no—
52C5×#123—24no—
53C5×#123—24no—
54C5×C22⋊Q8—22no—
55C5×C22⋊Q8—22no—
56C5×C22⋊Q8—22no—
57C5×C22⋊Q8—48no—
58C5×#121—22no—
59C5×#121—24no—
60C5×#121—22no—
61C5×#121—22no—
62C5×#121—22no—
63C5×#121—22no—
64C5×#120—24no—
65C4×C5×Q8D412yes—
66C4×C5×Q8D412yes—
67C4×C5×D4—24no—
68C4×C5×D4—22no—
69C4×C5×D4—22no—
70C4×C5×D4—22no—
71C4×C5×D4—22no—
72C4×C5×D4D412yes—
73C4×C5×D4D412yes—
74C5×#117—22no—
75C5×#117—22no—
76C5×#117C2312yes—
77C2×C5×C4⋊C4—21no—
78C2×C5×C4⋊C4—24no—
79C2×C5×C4⋊C4—21no—
80C2×C5×C4⋊C4C2312yes—
81C2×C5×C4⋊C4C2311yescharacteristic
82C2×C5×C22⋊C4—24no—
83C2×C5×C22⋊C4D412yes—
84C2×C42×C5—22no—
85C2×C42×C5C2312yes—
86C2×C42×C5C2311yescharacteristic
87C5×#107—24no—
88C5×#106—24no—
89C5×C4⋊C8—22no—
90C5×C4⋊C8—22no—
91C5×#104—44no—
92C5×#103—24no—
93C5×#102—24no—
94C5×#100—42no—
95C5×#95—21no—
96#3460C2×C511yescharacteristic
97#3079C2×C512yescomplemented
98#2542C2×C511yescharacteristic, complemented
99#2060C2×C512yescomplemented
100#2039C2×C512yescomplemented
101#2037C2×C514yescomplemented
102#1806C2×C512yescomplemented
103#1800C2×C511yescharacteristic, complemented
104C24×C5C2×D412yes—
105C5×#41—22no—
106C5×#41—22no—
107C5×#41—22no—
108C5×#41—22no—
109C5×#41—84no—
110C2×C5×Q8—22no—
111C2×C5×Q8—44no—
112C2×C5×Q8—41no—
113C2×C5×Q8—41no—
114C2×C5×Q8C2×D412yes—
115C2×C5×D4—22no—
116C2×C5×D4—24no—
117C2×C5×D4—24no—
118C2×C5×D4—22no—
119C2×C5×D4—22no—
120C2×C5×D4—21no—
121C2×C5×D4—21no—
122C2×C5×D4—22no—
123C2×C5×D4C2×D412yes—
124C22×C4×C5—22no—
125C22×C4×C5—22no—
126C22×C4×C5—22no—
127C22×C4×C5—22no—
128C22×C4×C5—22no—
129C22×C4×C5—22no—
130C22×C4×C5—22no—
131C22×C4×C5—44no—
132C22×C4×C5C2×D411yescharacteristic
133C22×C4×C5C2×D412yes—
134C22×C4×C5C2×D411yescharacteristic
135C22×C4×C5C2411yescharacteristic
136C5×M16—24no—
137C5×M16—24no—
138C2×C5×C8—24no—
139C5×C4⋊C4—24no—
140C5×C4⋊C4—22no—
141C5×C4⋊C4—22no—
142C5×C4⋊C4—24no—
143C5×C4⋊C4—22no—
144C5×C4⋊C4—22no—
145C5×C4⋊C4—22no—
146C5×C4⋊C4—24no—
147C5×C4⋊C4—48no—
148C5×C4⋊C4—42no—
149C5×C4⋊C4C2×D412yes—
150C5×C4⋊C4C2×D412yes—
151C5×C22⋊C4—24no—
152C5×C22⋊C4—24no—
153C5×C22⋊C4—24no—
154C5×C22⋊C4—22no—
155C5×C22⋊C4—24no—
156C5×C22⋊C4—22no—
157C5×C22⋊C4—22no—
158C5×C22⋊C4—48no—
159C42×C5—22no—
160C42×C5—22no—
161C42×C5—22no—
162C42×C5—22no—
163C42×C5—22no—
164C42×C5C2×D412yes—
165C42×C5C2×D412yes—
166#544C22×C511yescharacteristic
167#542—22no—
168#540—22no—
169#538—22no—
170#537C22×C511yescharacteristic
171#535C22×C512yes—
172#532—22no—
173C2×C4⋊Q8C22×C511yescharacteristic
174#529—22no—
175#525—22no—
176C2×C22⋊Q8—22no—
177C4×#41C22×C512yes—
178C2×C4×D4C22×C511yescharacteristic
179#477—22no—
180#476—22no—
181#475—22no—
182#474—22no—
183#428C22×C514yes—
184#423C22×C512yes—
185C2×#104C22×C514yes—
186#417C22×C514yes—
187C2×#100C22×C512yes—
188#399—22no—
189#390C22×C512yes—
190#384C22×C512yes—
191C4×C4⋊C4C22×C511yescharacteristic
192#343C22×C512yes—
193#339C22×C514yes—
194C23×C5—22no—
195C23×C5—22no—
196C23×C5—22no—
197C23×C5—22no—
198C23×C5—42no—
199C23×C5—42no—
200C23×C5C22×D411yescharacteristic
201C5×Q8—22no—
202C5×Q8—22no—
203C5×Q8—82no—
204C5×Q8—82no—
205C5×Q8—82no—
206C5×D4—22no—
207C5×D4—22no—
208C5×D4—42no—
209C5×D4—42no—
210C5×D4—42no—
211C5×D4—42no—
212C5×D4—84no—
213C5×D4—82no—
214C5×D4—84no—
215C2×C4×C5—22no—
216C2×C4×C5—24no—
217C2×C4×C5—22no—
218C2×C4×C5—22no—
219C2×C4×C5—22no—
220C2×C4×C5—22no—
221C2×C4×C5—41no—
222C2×C4×C5—42no—
223C2×C4×C5—42no—
224C2×C4×C5—42no—
225C2×C4×C5—42no—
226C2×C4×C5—44no—
227C2×C4×C5—44no—
228C2×C4×C5—42no—
229C2×C4×C5—44no—
230C2×C4×C5—42no—
231C2×C4×C5—82no—
232C2×C4×C5—82no—
233C2×C4×C5#12012yes—
234C2×C4×C5#12011yescharacteristic
235C2×C4×C5#12011yescharacteristic
236C2×C4×C5C22×D412yes—
237C2×C4×C5H(5,𝔽2)11yescharacteristic
238C2×C4×C52−1+411yescharacteristic
239C2×C4×C52−1+412yes—
240C5×C8—44no—
241C2×#41—22no—
242C2×#41C23×C512yes—
243C22×Q8—21no—
244C22×D4C23×C511yescharacteristic
245C23×C4C5×D412yes—
246C2×M16C23×C514yes—
247C4⋊Q8—22no—
248C4⋊Q8—22no—
249C4⋊Q8—22no—
250#127—22no—
251#126—24no—
252#125—22no—
253#124—24no—
254#124—22no—
255#123—24no—
256#123—24no—
257C22⋊Q8—22no—
258C22⋊Q8—22no—
259C22⋊Q8—22no—
260C22⋊Q8—48no—
261#121—22no—
262#121—24no—
263#121—22no—
264#121—22no—
265#121—22no—
266#121—22no—
267#120—24no—
268C4×Q8C5×D412yes—
269C4×Q8C5×D412yes—
270C4×D4—24no—
271C4×D4—22no—
272C4×D4—22no—
273C4×D4—22no—
274C4×D4—22no—
275C4×D4C5×D412yes—
276C4×D4C5×D412yes—
277#117—22no—
278#117—22no—
279#117C23×C512yes—
280C2×C4⋊C4—21no—
281C2×C4⋊C4—24no—
282C2×C4⋊C4—21no—
283C2×C4⋊C4C23×C512yes—
284C2×C4⋊C4C23×C511yescharacteristic
285C2×C22⋊C4—24no—
286C2×C22⋊C4C5×D412yes—
287C2×C42—22no—
288C2×C42C23×C512yes—
289C2×C42C23×C511yescharacteristic
290#107—24no—
291#106—24no—
292C4⋊C8—22no—
293C4⋊C8—22no—
294#104—44no—
295#103—24no—
296#102—24no—
297#100—42no—
298#95—21no—
299C22×C5—21no—
300C22×C5—21no—
301C22×C5—44no—
302C22×C5—42no—
303C22×C5—42no—
304C22×C5—42no—
305C22×C5—42no—
306C22×C5—42no—
307C22×C5—42no—
308C22×C5—82no—
309C22×C5C2×#12011yescharacteristic
310C22×C5#53611yescharacteristic
311C22×C5#53711yescharacteristic
312C4×C5—21no—
313C4×C5—22no—
314C4×C5—44no—
315C4×C5—42no—
316C4×C5—42no—
317C4×C5—42no—
318C4×C5—42no—
319C4×C5—82no—
320C4×C5#45312yes—
321C4×C5#53612yes—
322C4×C5#53712yes—
323C24C2×C5×D412yes—
324#41—22no—
325#41—22no—
326#41—22no—
327#41—22no—
328#41—84no—
329C2×Q8—22no—
330C2×Q8—44no—
331C2×Q8—41no—
332C2×Q8—41no—
333C2×Q8C2×C5×D412yes—
334C2×D4—22no—
335C2×D4—24no—
336C2×D4—24no—
337C2×D4—22no—
338C2×D4—22no—
339C2×D4—21no—
340C2×D4—21no—
341C2×D4—22no—
342C2×D4C2×C5×D412yes—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—44no—
351C22×C4C2×C5×D411yescharacteristic
352C22×C4C2×C5×D412yes—
353C22×C4C2×C5×D411yescharacteristic
354C22×C4C24×C511yescharacteristic
355M16—24no—
356M16—24no—
357C2×C8—24no—
358C4⋊C4—24no—
359C4⋊C4—22no—
360C4⋊C4—22no—
361C4⋊C4—24no—
362C4⋊C4—22no—
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—24no—
366C4⋊C4—48no—
367C4⋊C4—42no—
368C4⋊C4C2×C5×D412yes—
369C4⋊C4C2×C5×D412yes—
370C22⋊C4—24no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—22no—
374C22⋊C4—24no—
375C22⋊C4—22no—
376C22⋊C4—22no—
377C22⋊C4—48no—
378C42—22no—
379C42—22no—
380C42—22no—
381C42—22no—
382C42—22no—
383C42C2×C5×D412yes—
384C42C2×C5×D412yes—
385C2×C5—21no—
386C2×C5—21no—
387C2×C5—82no—
388C2×C5—82no—
389C2×C5#261611yescharacteristic
390C2×C5C2×#45311yescharacteristic
391C2×C5#302211yescharacteristic
392C23—22no—
393C23—22no—
394C23—22no—
395C23—22no—
396C23—42no—
397C23—42no—
398C23C22×C5×D411yescharacteristic
399Q8—22no—
400Q8—22no—
401Q8—82no—
402Q8—82no—
403Q8—82no—
404D4—22no—
405D4—22no—
406D4—42no—
407D4—42no—
408D4—42no—
409D4—42no—
410D4—82no—
411D4—84no—
412D4—84no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—22no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—44no—
423C2×C4—44no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—44no—
428C2×C4—42no—
429C2×C4—82no—
430C2×C4—82no—
431C2×C4C5×#12012yes—
432C2×C4C5×#12011yescharacteristic
433C2×C4C5×#12011yescharacteristic
434C2×C4C22×C5×D412yes—
435C2×C4C5×H(5,𝔽2)11yescharacteristic
436C2×C4C5×2−1+411yescharacteristic
437C2×C4C5×2−1+412yes—
438C8—44no—
439C5#2970311yescharacteristic, direct product factor, Sylow
440C22—21no—
441C22—21no—
442C22—44no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22—42no—
449C22—82no—
450C22C2×C5×#12011yescharacteristic
451C22C5×#53611yescharacteristic
452C22C5×#53711yescharacteristic
453C4—21no—
454C4—22no—
455C4—44no—
456C4—42no—
457C4—42no—
458C4—42no—
459C4—42no—
460C4—82no—
461C4C5×#45312yes—
462C4C5×#53612yes—
463C4C5×#53712yes—
464C2—21no—
465C2—21no—
466C2—82no—
467C2—82no—
468C2C5×#261611yescharacteristic
469C2C2×C5×#45311yescharacteristic
470C2C5×#302211yescharacteristic
subgroupG/H
center, socleC22×C5C2×#120
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC5×#3460C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C5 ◁ C2×C42×C5 ◁ G

Complements

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

NH ≅ G/Ntype
2. C5×#3079C2semidirect
3. C5×#2542C2semidirect
4. C5×#2060C2semidirect
5. C5×#2039C2semidirect
6. C5×#2037C2semidirect
7. C5×#1806C2semidirect
8. C5×#1800C2semidirect
37. #29703C5direct (N × H)
97. #3079C2×C5semidirect
98. #2542C2×C5semidirect
99. #2060C2×C5semidirect
100. #2039C2×C5semidirect
101. #2037C2×C5semidirect
102. #1806C2×C5semidirect
103. #1800C2×C5semidirect
439. C5#29703direct (N × H)

Maximal subgroups

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

subgroupindex
C5×#34602
C5×#30792
C5×#25422
C5×#20602
C5×#20392
C5×#20372
C5×#18062
C5×#18002
#297035