Finite Group Databasebeta

← C5×#69136 #14313128

Subgroups — C5×#69136 #14313128

Order 1920.

528 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5586C211yesmaximal, characteristic
2C5×#4745C211yesmaximal, characteristic, complemented
3C5×#4740C211yesmaximal, characteristic, complemented
4C3×C5×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C5×#4536C211yesmaximal, characteristic, complemented
6C5×#4476C211yesmaximal, characteristic, complemented
7C5×#4472C211yesmaximal, characteristic, complemented
8C5×#2120—31nomaximal, Hall
9C23×C5×Dic3C411yescharacteristic, complemented
10C2×C5×#237C2211yescharacteristic
11C3×C5×#120C2211yescharacteristic
12C5×#953C411yescharacteristic, complemented
13C5×#939—21no—
14C5×#935C2211yescharacteristic
15C5×D4×Dic3—21no—
16C5×D3×M16—21no—
17C5×#886C411yescharacteristic, complemented
18C5×#67⋊C4—21no—
19C5×#878—21no—
20C5×#877—21no—
21C5×#877C411yescharacteristic, complemented
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C5×#834C2211yescharacteristic
25C5×#833C2211yescharacteristic
26C5×#824—21no—
27C5×#806—21no—
28#69136C511yesmaximal, characteristic, direct product factor, Hall
29C5×#525—31no—
30C5×#413—31no—
31C5×#410—31no—
32C5×#352—31no—
33C5×#352—31no—
34C5×AΣL(1,𝔽16)—31no—
35C5×AΣL(1,𝔽16)D311yescharacteristic, complemented
36C24×C3×C5C2×C411yescharacteristic
37C2×C3×C5×D4—21no—
38C2×C3×C5×D4C2311yescharacteristic
39C2×C5×#67—21no—
40C2×C5×#67C2×C411yescharacteristic
41C2×C5×#67D411yescharacteristic
42C22×C5×Dic3—21no—
43C22×C5×Dic3—21no—
44C22×C5×Dic3—41no—
45C22×C5×Dic3—41no—
46C22×C5×Dic3C2×C411yescharacteristic
47C22×C5×Dic3C2×C411yescharacteristic
48C22×C5×Dic3D411yescharacteristic
49C5×#237—41no—
50C5×#237—41no—
51C2×C4×C5×D3D411yescharacteristic
52C2×C5×Dic6D411yescharacteristic
53C3×C5×M16—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C5×C22⋊C4C2×C411yescharacteristic
57C5×#217—21no—
58C5×#217—21no—
59C5×#217—21no—
60C5×#217C2×C411yescharacteristic
61C5×(C2×D3)⋊C4—21no—
62C5×C4⋊Dic3—21no—
63C5×Dic3⋊C4—21no—
64C5×Dic3⋊C4—21no—
65C5×Dic3⋊C4—41no—
66C4×C5×Dic3—21no—
67C4×C5×Dic3—41no—
68C5×#208—21no—
69C5×ΓL(1,𝔽25)—41no—
70C5×D3×C8—41no—
71#5586C2×C511yescharacteristic
72#4745C2×C511yescharacteristic, complemented
73#4740C2×C511yescharacteristic, complemented
74C3×AΣL(1,𝔽16)C2×C511yescharacteristic, complemented
75#4536C2×C511yescharacteristic, complemented
76#4476C2×C511yescharacteristic, complemented
77#4472C2×C511yescharacteristic, complemented
78C2×C5×#41—31no—
79C23×C4×C5—31no—
80C2×C5×M16—61no—
81C5×#123—31no—
82C5×#123—31no—
83C5×C22⋊Q8—61no—
84C5×#121—61no—
85C5×#120—31no—
86C5×#120C2×D311yescharacteristic
87C4×C5×D4—61no—
88C4×C5×D4—61no—
89C5×#117—31no—
90C5×#117—61no—
91C5×#101—61no—
92C5×#100—31no—
93C5×#100C2×D311yescharacteristic
94C5×#99—31no—
95C5×#99—61no—
96C5×#99C2×D311yescharacteristic
97#2120—31noSylow
98C23×C3×C5—21no—
99C23×C3×C5—41no—
100C23×C3×C5—42no—
101C23×C3×C5C22×C411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3C22⋊C411yescharacteristic
104C3×C5×D4—41no—
105C3×C5×D4—42no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—41no—
108C2×C3×C4×C5C2×D411yescharacteristic
109C5×#67—41no—
110C5×#67—41no—
111C5×#67—42no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—21no—
116C2×C5×Dic3—21no—
117C2×C5×Dic3—21no—
118C2×C5×Dic3—42no—
119C2×C5×Dic3—41no—
120C2×C5×Dic3—41no—
121C2×C5×Dic3—41no—
122C2×C5×Dic3—41no—
123C2×C5×Dic3C22⋊C411yescharacteristic
124C2×C5×Dic3C22⋊C411yescharacteristic
125C2×C5×Dic3C22⋊C411yescharacteristic
126C4×C5×D3—21no—
127C4×C5×D3—21no—
128C5×Dic6—41no—
129C3×C5×C8—41no—
130C5×C3⋊C8—41no—
131C23×Dic3C4×C511yescharacteristic, complemented
132C2×#237C22×C511yescharacteristic
133C3×#120C22×C511yescharacteristic
134#953C4×C511yescharacteristic, complemented
135#939—21no—
136#935C22×C511yescharacteristic
137D4×Dic3—21no—
138D3×M16—21no—
139#886C4×C511yescharacteristic, complemented
140#67⋊C4—21no—
141#878—21no—
142#877—21no—
143#877C4×C511yescharacteristic, complemented
144C3×#100C22×C511yescharacteristic
145C3×#99C22×C511yescharacteristic
146#834C22×C511yescharacteristic
147#833C22×C511yescharacteristic
148#824—21no—
149#806—21no—
150C24×C5C4×D311yescharacteristic
151C5×#41—121no—
152C5×#41—121no—
153C2×C5×Q8—31no—
154C2×C5×D4—21no—
155C2×C5×D4—31no—
156C2×C5×D4—31no—
157C2×C5×D4—61no—
158C2×C5×D4C22×D311yescharacteristic
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5—31no—
162C22×C4×C5—31no—
163C22×C4×C5—61no—
164C22×C4×C5—61no—
165C22×C4×C5—121no—
166C22×C4×C5—121no—
167C5×M16—21no—
168C5×M16—61no—
169C5×M16—121no—
170C2×C5×C8—121no—
171C5×C4⋊C4—61no—
172C5×C4⋊C4—61no—
173C5×C4⋊C4—61no—
174C5×C4⋊C4—121no—
175C5×C22⋊C4—21no—
176C5×C22⋊C4—21no—
177C5×C22⋊C4—31no—
178C5×C22⋊C4—61no—
179C5×C22⋊C4—61no—
180C5×C22⋊C4—61no—
181C5×C22⋊C4—61no—
182C5×C22⋊C4C4×D311yescharacteristic
183C42×C5—61no—
184C42×C5—121no—
185#525—31no—
186#413—31no—
187#410—31no—
188#352—31no—
189#352—31no—
190AΣL(1,𝔽16)—31no—
191AΣL(1,𝔽16)C5×D311yescharacteristic, complemented
192C22×C3×C5—22no—
193C22×C3×C5—21no—
194C22×C3×C5—21no—
195C22×C3×C5—41no—
196C22×C3×C5—41no—
197C22×C3×C5—41no—
198C22×C3×C5—42no—
199C22×C3×C5—42no—
200C22×C3×C5—41no—
201C22×C3×C5C2×C22⋊C411yescharacteristic
202C2×C5×D3—21no—
203C2×C5×D3—41no—
204C3×C4×C5—21no—
205C3×C4×C5—41no—
206C3×C4×C5—81no—
207C5×Dic3—21no—
208C5×Dic3—21no—
209C5×Dic3—41no—
210C5×Dic3—41no—
211C5×Dic3—81no—
212C5×Dic3#9911yescharacteristic
213C5×Dic3#9911yescharacteristic
214C24×C3C2×C4×C511yescharacteristic
215C2×C3×D4—21no—
216C2×C3×D4C23×C511yescharacteristic
217C2×#67—21no—
218C2×#67C2×C4×C511yescharacteristic
219C2×#67C5×D411yescharacteristic
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—41no—
223C22×Dic3—41no—
224C22×Dic3C2×C4×C511yescharacteristic
225C22×Dic3C2×C4×C511yescharacteristic
226C22×Dic3C5×D411yescharacteristic
227#237—41no—
228#237—41no—
229C2×C4×D3C5×D411yescharacteristic
230C2×Dic6C5×D411yescharacteristic
231C3×M16—21no—
232C3×C22⋊C4—21no—
233C3×C22⋊C4—21no—
234C3×C22⋊C4C2×C4×C511yescharacteristic
235#217—21no—
236#217—21no—
237#217—21no—
238#217C2×C4×C511yescharacteristic
239(C2×D3)⋊C4—21no—
240C4⋊Dic3—21no—
241Dic3⋊C4—21no—
242Dic3⋊C4—21no—
243Dic3⋊C4—41no—
244C4×Dic3—21no—
245C4×Dic3—41no—
246#208—21no—
247ΓL(1,𝔽25)—41no—
248D3×C8—41no—
249C23×C5—21no—
250C23×C5—31no—
251C23×C5—41no—
252C23×C5—42no—
253C23×C5C2×C4×D311yescharacteristic
254C23×C5D3×D411yescharacteristic
255C5×Q8—121no—
256C5×D4—41no—
257C5×D4—42no—
258C5×D4—121no—
259C5×D4—121no—
260C5×D4—122no—
261C2×C4×C5—21no—
262C2×C4×C5—31no—
263C2×C4×C5—31no—
264C2×C4×C5—31no—
265C2×C4×C5—41no—
266C2×C4×C5—61no—
267C2×C4×C5—61no—
268C2×C4×C5—61no—
269C2×C4×C5—61no—
270C2×C4×C5—61no—
271C2×C4×C5—61no—
272C2×C4×C5—61no—
273C2×C4×C5—61no—
274C2×C4×C5—121no—
275C2×C4×C5—121no—
276C2×C4×C5—122no—
277C2×C4×C5—121no—
278C2×C4×C5—121no—
279C2×C4×C5D3×D411yescharacteristic
280C5×C8—41no—
281C5×C8—121no—
282C2×#41—31no—
283C23×C4—31no—
284C2×M16—61no—
285#123—31no—
286#123—31no—
287C22⋊Q8—61no—
288#121—61no—
289#120—31no—
290#120C2×C5×D311yescharacteristic
291C4×D4—61no—
292C4×D4—61no—
293#117—31no—
294#117—61no—
295#101—61no—
296#100—31no—
297#100C2×C5×D311yescharacteristic
298#99—31no—
299#99—61no—
300#99C2×C5×D311yescharacteristic
301C2×C3×C5—21no—
302C2×C3×C5—41no—
303C2×C3×C5—42no—
304C2×C3×C5—41no—
305C2×C3×C5C2×#9911yescharacteristic
306C5×D3—41no—
307C23×C3—21no—
308C23×C3—41no—
309C23×C3—42no—
310C23×C3C22×C4×C511yescharacteristic
311C23×C3C2×C5×D411yescharacteristic
312C22×D3C5×C22⋊C411yescharacteristic
313C3×D4—41no—
314C3×D4—42no—
315C2×C3×C4—21no—
316C2×C3×C4—41no—
317C2×C3×C4C2×C5×D411yescharacteristic
318#67—41no—
319#67—41no—
320#67—42no—
321C2×Dic3—21no—
322C2×Dic3—21no—
323C2×Dic3—21no—
324C2×Dic3—21no—
325C2×Dic3—21no—
326C2×Dic3—21no—
327C2×Dic3—42no—
328C2×Dic3—41no—
329C2×Dic3—41no—
330C2×Dic3—41no—
331C2×Dic3—41no—
332C2×Dic3C5×C22⋊C411yescharacteristic
333C2×Dic3C5×C22⋊C411yescharacteristic
334C2×Dic3C5×C22⋊C411yescharacteristic
335C4×D3—21no—
336C4×D3—21no—
337Dic6—41no—
338C3×C8—41no—
339C3⋊C8—41no—
340C22×C5—22no—
341C22×C5—21no—
342C22×C5—21no—
343C22×C5—41no—
344C22×C5—41no—
345C22×C5—41no—
346C22×C5—42no—
347C22×C5—42no—
348C22×C5—41no—
349C22×C5—61no—
350C22×C5—121no—
351C22×C5D3×C22⋊C411yescharacteristic
352C4×C5—21no—
353C4×C5—31no—
354C4×C5—31no—
355C4×C5—41no—
356C4×C5—61no—
357C4×C5—61no—
358C4×C5—81no—
359C4×C5—121no—
360C4×C5—121no—
361C4×C5—241no—
362C24C4×C5×D311yescharacteristic
363#41—121no—
364#41—121no—
365C2×Q8—31no—
366C2×D4—21no—
367C2×D4—31no—
368C2×D4—31no—
369C2×D4—61no—
370C2×D4C22×C5×D311yescharacteristic
371C22×C4—31no—
372C22×C4—31no—
373C22×C4—31no—
374C22×C4—31no—
375C22×C4—61no—
376C22×C4—61no—
377C22×C4—121no—
378C22×C4—121no—
379M16—21no—
380M16—61no—
381M16—121no—
382C2×C8—121no—
383C4⋊C4—61no—
384C4⋊C4—61no—
385C4⋊C4—61no—
386C4⋊C4—121no—
387C22⋊C4—21no—
388C22⋊C4—21no—
389C22⋊C4—31no—
390C22⋊C4—61no—
391C22⋊C4—61no—
392C22⋊C4—61no—
393C22⋊C4—61no—
394C22⋊C4C4×C5×D311yescharacteristic
395C42—61no—
396C42—121no—
397C3×C5#212011yescharacteristic, complemented, Hall
398C22×C3—22no—
399C22×C3—21no—
400C22×C3—21no—
401C22×C3—41no—
402C22×C3—41no—
403C22×C3—41no—
404C22×C3—42no—
405C22×C3—42no—
406C22×C3—41no—
407C22×C3C2×C5×C22⋊C411yescharacteristic
408C2×D3—21no—
409C2×D3—41no—
410C3×C4—21no—
411C3×C4—41no—
412C3×C4—81no—
413Dic3—21no—
414Dic3—21no—
415Dic3—41no—
416Dic3—41no—
417Dic3—81no—
418Dic3C5×#9911yescharacteristic
419Dic3C5×#9911yescharacteristic
420C2×C5—21no—
421C2×C5—41no—
422C2×C5—42no—
423C2×C5—41no—
424C2×C5—121no—
425C2×C5D3×#9911yescharacteristic
426C23—21no—
427C23—31no—
428C23—41no—
429C23—42no—
430C23C2×C4×C5×D311yescharacteristic
431C23C5×D3×D411yescharacteristic
432Q8—121no—
433D4—41no—
434D4—42no—
435D4—121no—
436D4—121no—
437D4—122no—
438C2×C4—21no—
439C2×C4—31no—
440C2×C4—31no—
441C2×C4—31no—
442C2×C4—41no—
443C2×C4—61no—
444C2×C4—61no—
445C2×C4—61no—
446C2×C4—61no—
447C2×C4—61no—
448C2×C4—61no—
449C2×C4—61no—
450C2×C4—61no—
451C2×C4—121no—
452C2×C4—121no—
453C2×C4—122no—
454C2×C4—121no—
455C2×C4—121no—
456C2×C4C5×D3×D411yescharacteristic
457C8—41no—
458C8—121no—
459C2×C3—21no—
460C2×C3—41no—
461C2×C3—42no—
462C2×C3—41no—
463C2×C3C2×C5×#9911yescharacteristic
464D3—41no—
465C5#6913611yescharacteristic, direct product factor, Sylow
466C22—22no—
467C22—21no—
468C22—21no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—42no—
473C22—42no—
474C22—41no—
475C22—61no—
476C22—121no—
477C22C5×D3×C22⋊C411yescharacteristic
478C4—21no—
479C4—31no—
480C4—31no—
481C4—41no—
482C4—61no—
483C4—61no—
484C4—81no—
485C4—121no—
486C4—121no—
487C4—241no—
488C3C5×#212011yescharacteristic, complemented, Sylow
489C2—21no—
490C2—41no—
491C2—42no—
492C2—41no—
493C2—121no—
494C2C5×D3×#9911yescharacteristic
subgroupG/H
centerC2×C5D3×#99
commutatorC23×C3C22×C4×C5
FrattiniC2×D4C22×C5×D3
FittingC3×C5×AΣL(1,𝔽16)C2
socleC2×C3×C5C2×#99
prime radicalC5×#5586C2
cosocleC2×C3×D4C23×C5
hypercenterC5×AΣL(1,𝔽16)D3
hypocenterC3C5×#2120
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C5 ◁ C2×C5×D4 ◁ C5×AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. C5×#4745C2semidirect
3. C5×#4740C2semidirect
4. C3×C5×AΣL(1,𝔽16)C2semidirect
5. C5×#4536C2semidirect
6. C5×#4476C2semidirect
7. C5×#4472C2semidirect
9. C23×C5×Dic3C4semidirect
12. C5×#953C4semidirect
17. C5×#886C4semidirect
21. C5×#877C4semidirect
28. #69136C5direct (N × H)
35. C5×AΣL(1,𝔽16)D3semidirect
72. #4745C2×C5semidirect
73. #4740C2×C5semidirect
74. C3×AΣL(1,𝔽16)C2×C5semidirect
75. #4536C2×C5semidirect
76. #4476C2×C5semidirect
77. #4472C2×C5semidirect
131. C23×Dic3C4×C5semidirect
134. #953C4×C5semidirect
139. #886C4×C5semidirect
143. #877C4×C5semidirect
191. AΣL(1,𝔽16)C5×D3semidirect
397. C3×C5#2120semidirect
465. C5#69136direct (N × H)
488. C3C5×#2120semidirect

Maximal subgroups

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

subgroupindex
C5×#55862
C5×#47452
C5×#47402
C3×C5×AΣL(1,𝔽16)2
C5×#45362
C5×#44762
C5×#44722
C5×#21203
#691365