Finite Group Databasebeta

← C5×#69137 #14313254

Subgroups — C5×#69137 #14313254

Order 1920.

532 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5592C211yesmaximal, characteristic
2C5×#4745C211yesmaximal, characteristic, complemented
3C5×#4740C211yesmaximal, characteristic, complemented
4C3×C5×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
5C5×#4536C211yesmaximal, characteristic, complemented
6C5×#4475C211yesmaximal, characteristic, complemented
7C5×#4471C211yesmaximal, characteristic, complemented
8C5×#2122—31nomaximal, Hall
9C22×C5×#67C411yescharacteristic, complemented
10C2×C5×#237C2211yescharacteristic
11C3×C5×#120C2211yescharacteristic
12C5×#953C411yescharacteristic, complemented
13C5×#940—21no—
14C5×#939—21no—
15C5×#937C2211yescharacteristic
16C5×D3×M16—21no—
17C5×#885—21no—
18C5×#884—21no—
19C5×#882C411yescharacteristic, complemented
20C5×#877—21no—
21C5×#877C411yescharacteristic, complemented
22C3×C5×#100C2211yescharacteristic
23C3×C5×#99C2211yescharacteristic
24C5×#834C2211yescharacteristic
25C5×#833C2211yescharacteristic
26C5×#824—21no—
27C5×#806—21no—
28#69137C511yesmaximal, characteristic, direct product factor, Hall
29C5×#535—31no—
30C5×#413—31no—
31C5×#410—31no—
32C5×AΣL(1,𝔽16)—31no—
33C5×AΣL(1,𝔽16)—31no—
34C5×AΣL(1,𝔽16)—31no—
35C5×AΣL(1,𝔽16)D311yescharacteristic, complemented
36C24×C3×C5C2×C411yescharacteristic
37C23×C5×D3C2×C411yescharacteristic
38C2×C3×C5×D4—21no—
39C2×C3×C5×D4C2311yescharacteristic
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C2×C5×#67—21no—
44C2×C5×#67—41no—
45C2×C5×#67—41no—
46C2×C5×#67C2×C411yescharacteristic
47C2×C5×#67D411yescharacteristic
48C22×C5×Dic3C2×C411yescharacteristic
49C22×C5×Dic3D411yescharacteristic
50C5×#237—41no—
51C5×#237—41no—
52C2×C5×D12—21no—
53C2×C4×C5×D3D411yescharacteristic
54C2×C5×Dic6D411yescharacteristic
55C3×C5×M16—21no—
56C3×C5×C22⋊C4—21no—
57C3×C5×C22⋊C4—21no—
58C3×C5×C22⋊C4C2×C411yescharacteristic
59C5×#217—21no—
60C5×#217—21no—
61C5×#217C2×C411yescharacteristic
62C5×(C2×D3)⋊C4—21no—
63C5×(C2×D3)⋊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#5592C2×C511yescharacteristic
72#4745C2×C511yescharacteristic, complemented
73#4740C2×C511yescharacteristic, complemented
74C3×AΣL(1,𝔽16)C2×C511yescharacteristic, complemented
75#4536C2×C511yescharacteristic, complemented
76#4475C2×C511yescharacteristic, complemented
77#4471C2×C511yescharacteristic, complemented
78C2×C5×#41—31no—
79C22×C5×D4—31no—
80C2×C5×M16—61no—
81C5×#127—61no—
82C5×#124—61no—
83C5×#121—61no—
84C5×#121—61no—
85C5×#120—31no—
86C5×#120—31no—
87C5×#120—31no—
88C5×#120C2×D311yescharacteristic
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#2122—31noSylow
98C23×C3×C5—21no—
99C23×C3×C5—41no—
100C23×C3×C5—81no—
101C23×C3×C5C22×C411yescharacteristic
102C23×C3×C5C2×D411yescharacteristic
103C22×C5×D3—21no—
104C22×C5×D3—41no—
105C22×C5×D3—81no—
106C22×C5×D3C22⋊C411yescharacteristic
107C3×C5×D4—41no—
108C3×C5×D4—81no—
109C2×C3×C4×C5—21no—
110C2×C3×C4×C5—41no—
111C2×C3×C4×C5C2×D411yescharacteristic
112C5×#67—41no—
113C5×#67—41no—
114C5×#67—42no—
115C5×#67—41no—
116C5×#67—41no—
117C5×#67—81no—
118C5×#67—81no—
119C2×C5×Dic3—21no—
120C2×C5×Dic3—21no—
121C2×C5×Dic3—21no—
122C2×C5×Dic3—21no—
123C2×C5×Dic3—21no—
124C2×C5×Dic3—41no—
125C2×C5×Dic3C22⋊C411yescharacteristic
126C2×C5×Dic3C22⋊C411yescharacteristic
127C2×C5×Dic3C22⋊C411yescharacteristic
128C5×D12—81no—
129C4×C5×D3—21no—
130C4×C5×D3—21no—
131C5×Dic6—41no—
132C3×C5×C8—41no—
133C5×C3⋊C8—41no—
134C22×#67C4×C511yescharacteristic, complemented
135C2×#237C22×C511yescharacteristic
136C3×#120C22×C511yescharacteristic
137#953C4×C511yescharacteristic, complemented
138#940—21no—
139#939—21no—
140#937C22×C511yescharacteristic
141D3×M16—21no—
142#885—21no—
143#884—21no—
144#882C4×C511yescharacteristic, complemented
145#877—21no—
146#877C4×C511yescharacteristic, complemented
147C3×#100C22×C511yescharacteristic
148C3×#99C22×C511yescharacteristic
149#834C22×C511yescharacteristic
150#833C22×C511yescharacteristic
151#824—21no—
152#806—21no—
153C24×C5—31no—
154C24×C5C4×D311yescharacteristic
155C5×#41—121no—
156C5×#41—121no—
157C2×C5×Q8—31no—
158C2×C5×D4—21no—
159C2×C5×D4—31no—
160C2×C5×D4—31no—
161C2×C5×D4—61no—
162C2×C5×D4—61no—
163C2×C5×D4—61no—
164C2×C5×D4—61no—
165C2×C5×D4—61no—
166C2×C5×D4—121no—
167C2×C5×D4—121no—
168C2×C5×D4C22×D311yescharacteristic
169C22×C4×C5—31no—
170C22×C4×C5—31no—
171C22×C4×C5—31no—
172C5×M16—21no—
173C5×M16—61no—
174C5×M16—121no—
175C2×C5×C8—121no—
176C5×C4⋊C4—61no—
177C5×C4⋊C4—121no—
178C5×C22⋊C4—21no—
179C5×C22⋊C4—21no—
180C5×C22⋊C4—31no—
181C5×C22⋊C4—61no—
182C5×C22⋊C4—61no—
183C5×C22⋊C4—61no—
184C5×C22⋊C4—61no—
185C5×C22⋊C4C4×D311yescharacteristic
186C42×C5—61no—
187C42×C5—121no—
188#535—31no—
189#413—31no—
190#410—31no—
191AΣL(1,𝔽16)—31no—
192AΣL(1,𝔽16)—31no—
193AΣL(1,𝔽16)—31no—
194AΣL(1,𝔽16)C5×D311yescharacteristic, complemented
195C22×C3×C5—21no—
196C22×C3×C5—21no—
197C22×C3×C5—41no—
198C22×C3×C5—41no—
199C22×C3×C5—41no—
200C22×C3×C5—41no—
201C22×C3×C5—41no—
202C22×C3×C5—82no—
203C22×C3×C5C2×C22⋊C411yescharacteristic
204C2×C5×D3—21no—
205C2×C5×D3—41no—
206C2×C5×D3—41no—
207C2×C5×D3—41no—
208C2×C5×D3—41no—
209C2×C5×D3—82no—
210C3×C4×C5—21no—
211C3×C4×C5—41no—
212C3×C4×C5—81no—
213C5×Dic3—21no—
214C5×Dic3—21no—
215C5×Dic3—41no—
216C5×Dic3—81no—
217C5×Dic3#9911yescharacteristic
218C5×Dic3#9911yescharacteristic
219C24×C3C2×C4×C511yescharacteristic
220C23×D3C2×C4×C511yescharacteristic
221C2×C3×D4—21no—
222C2×C3×D4C23×C511yescharacteristic
223C2×#67—21no—
224C2×#67—21no—
225C2×#67—21no—
226C2×#67—21no—
227C2×#67—41no—
228C2×#67—41no—
229C2×#67C2×C4×C511yescharacteristic
230C2×#67C5×D411yescharacteristic
231C22×Dic3C2×C4×C511yescharacteristic
232C22×Dic3C5×D411yescharacteristic
233#237—41no—
234#237—41no—
235C2×D12—21no—
236C2×C4×D3C5×D411yescharacteristic
237C2×Dic6C5×D411yescharacteristic
238C3×M16—21no—
239C3×C22⋊C4—21no—
240C3×C22⋊C4—21no—
241C3×C22⋊C4C2×C4×C511yescharacteristic
242#217—21no—
243#217—21no—
244#217C2×C4×C511yescharacteristic
245(C2×D3)⋊C4—21no—
246(C2×D3)⋊C4—21no—
247Dic3⋊C4—21no—
248Dic3⋊C4—41no—
249C4×Dic3—21no—
250C4×Dic3—41no—
251#208—21no—
252ΓL(1,𝔽25)—41no—
253D3×C8—41no—
254C23×C5—21no—
255C23×C5—31no—
256C23×C5—41no—
257C23×C5—61no—
258C23×C5—81no—
259C23×C5—121no—
260C23×C5—241no—
261C23×C5C2×C4×D311yescharacteristic
262C23×C5D3×D411yescharacteristic
263C5×Q8—121no—
264C5×D4—41no—
265C5×D4—81no—
266C5×D4—121no—
267C5×D4—121no—
268C5×D4—121no—
269C5×D4—121no—
270C5×D4—122no—
271C5×D4—241no—
272C5×D4—241no—
273C5×D4—241no—
274C2×C4×C5—21no—
275C2×C4×C5—31no—
276C2×C4×C5—31no—
277C2×C4×C5—31no—
278C2×C4×C5—41no—
279C2×C4×C5—61no—
280C2×C4×C5—61no—
281C2×C4×C5—61no—
282C2×C4×C5—61no—
283C2×C4×C5—61no—
284C2×C4×C5—61no—
285C2×C4×C5—61no—
286C2×C4×C5—121no—
287C2×C4×C5D3×D411yescharacteristic
288C5×C8—41no—
289C5×C8—121no—
290C2×#41—31no—
291C22×D4—31no—
292C2×M16—61no—
293#127—61no—
294#124—61no—
295#121—61no—
296#121—61no—
297#120—31no—
298#120—31no—
299#120—31no—
300#120C2×C5×D311yescharacteristic
301#117—31no—
302#117—61no—
303#101—61no—
304#100—31no—
305#100C2×C5×D311yescharacteristic
306#99—31no—
307#99—61no—
308#99C2×C5×D311yescharacteristic
309C2×C3×C5—21no—
310C2×C3×C5—41no—
311C2×C3×C5—41no—
312C2×C3×C5—81no—
313C2×C3×C5C2×#9911yescharacteristic
314C5×D3—41no—
315C5×D3—81no—
316C23×C3—21no—
317C23×C3—41no—
318C23×C3—81no—
319C23×C3C22×C4×C511yescharacteristic
320C23×C3C2×C5×D411yescharacteristic
321C22×D3—21no—
322C22×D3—41no—
323C22×D3—81no—
324C22×D3C5×C22⋊C411yescharacteristic
325C3×D4—41no—
326C3×D4—81no—
327C2×C3×C4—21no—
328C2×C3×C4—41no—
329C2×C3×C4C2×C5×D411yescharacteristic
330#67—41no—
331#67—41no—
332#67—42no—
333#67—41no—
334#67—41no—
335#67—81no—
336#67—81no—
337C2×Dic3—21no—
338C2×Dic3—21no—
339C2×Dic3—21no—
340C2×Dic3—21no—
341C2×Dic3—21no—
342C2×Dic3—41no—
343C2×Dic3C5×C22⋊C411yescharacteristic
344C2×Dic3C5×C22⋊C411yescharacteristic
345C2×Dic3C5×C22⋊C411yescharacteristic
346D12—81no—
347C4×D3—21no—
348C4×D3—21no—
349Dic6—41no—
350C3×C8—41no—
351C3⋊C8—41no—
352C22×C5—21no—
353C22×C5—21no—
354C22×C5—41no—
355C22×C5—41no—
356C22×C5—41no—
357C22×C5—41no—
358C22×C5—41no—
359C22×C5—61no—
360C22×C5—82no—
361C22×C5—121no—
362C22×C5—121no—
363C22×C5—121no—
364C22×C5—121no—
365C22×C5—242no—
366C22×C5D3×C22⋊C411yescharacteristic
367C4×C5—21no—
368C4×C5—31no—
369C4×C5—31no—
370C4×C5—41no—
371C4×C5—61no—
372C4×C5—61no—
373C4×C5—81no—
374C4×C5—121no—
375C4×C5—241no—
376C24—31no—
377C24C4×C5×D311yescharacteristic
378#41—121no—
379#41—121no—
380C2×Q8—31no—
381C2×D4—21no—
382C2×D4—31no—
383C2×D4—31no—
384C2×D4—61no—
385C2×D4—61no—
386C2×D4—61no—
387C2×D4—61no—
388C2×D4—61no—
389C2×D4—121no—
390C2×D4—121no—
391C2×D4C22×C5×D311yescharacteristic
392C22×C4—31no—
393C22×C4—31no—
394C22×C4—31no—
395M16—21no—
396M16—61no—
397M16—121no—
398C2×C8—121no—
399C4⋊C4—61no—
400C4⋊C4—121no—
401C22⋊C4—21no—
402C22⋊C4—21no—
403C22⋊C4—31no—
404C22⋊C4—61no—
405C22⋊C4—61no—
406C22⋊C4—61no—
407C22⋊C4—61no—
408C22⋊C4C4×C5×D311yescharacteristic
409C42—61no—
410C42—121no—
411C3×C5#212211yescharacteristic, complemented, Hall
412C22×C3—21no—
413C22×C3—21no—
414C22×C3—41no—
415C22×C3—41no—
416C22×C3—41no—
417C22×C3—41no—
418C22×C3—41no—
419C22×C3—82no—
420C22×C3C2×C5×C22⋊C411yescharacteristic
421C2×D3—21no—
422C2×D3—41no—
423C2×D3—41no—
424C2×D3—41no—
425C2×D3—41no—
426C2×D3—82no—
427C3×C4—21no—
428C3×C4—41no—
429C3×C4—81no—
430Dic3—21no—
431Dic3—21no—
432Dic3—41no—
433Dic3—81no—
434Dic3C5×#9911yescharacteristic
435Dic3C5×#9911yescharacteristic
436C2×C5—21no—
437C2×C5—41no—
438C2×C5—41no—
439C2×C5—81no—
440C2×C5—121no—
441C2×C5—241no—
442C2×C5D3×#9911yescharacteristic
443C23—21no—
444C23—31no—
445C23—41no—
446C23—61no—
447C23—81no—
448C23—121no—
449C23—241no—
450C23C2×C4×C5×D311yescharacteristic
451C23C5×D3×D411yescharacteristic
452Q8—121no—
453D4—41no—
454D4—81no—
455D4—121no—
456D4—121no—
457D4—121no—
458D4—121no—
459D4—122no—
460D4—241no—
461D4—241no—
462D4—241no—
463C2×C4—21no—
464C2×C4—31no—
465C2×C4—31no—
466C2×C4—31no—
467C2×C4—41no—
468C2×C4—61no—
469C2×C4—61no—
470C2×C4—61no—
471C2×C4—61no—
472C2×C4—61no—
473C2×C4—61no—
474C2×C4—61no—
475C2×C4—121no—
476C2×C4C5×D3×D411yescharacteristic
477C8—41no—
478C8—121no—
479C2×C3—21no—
480C2×C3—41no—
481C2×C3—41no—
482C2×C3—81no—
483C2×C3C2×C5×#9911yescharacteristic
484D3—41no—
485D3—81no—
486C5#6913711yescharacteristic, direct product factor, Sylow
487C22—21no—
488C22—21no—
489C22—41no—
490C22—41no—
491C22—41no—
492C22—41no—
493C22—41no—
494C22—61no—
495C22—82no—
496C22—121no—
497C22—121no—
498C22—121no—
499C22—121no—
500C22—242no—
501C22C5×D3×C22⋊C411yescharacteristic
502C4—21no—
503C4—31no—
504C4—31no—
505C4—41no—
506C4—61no—
507C4—61no—
508C4—81no—
509C4—121no—
510C4—241no—
511C3C5×#212211yescharacteristic, complemented, Sylow
512C2—21no—
513C2—41no—
514C2—41no—
515C2—81no—
516C2—121no—
517C2—241no—
518C2C5×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×#5592C2
cosocleC2×C3×D4C23×C5
hypercenterC5×AΣL(1,𝔽16)D3
hypocenterC3C5×#2122
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×#4475C2semidirect
7. C5×#4471C2semidirect
9. C22×C5×#67C4semidirect
12. C5×#953C4semidirect
19. C5×#882C4semidirect
21. C5×#877C4semidirect
28. #69137C5direct (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. #4475C2×C5semidirect
77. #4471C2×C5semidirect
134. C22×#67C4×C5semidirect
137. #953C4×C5semidirect
144. #882C4×C5semidirect
146. #877C4×C5semidirect
194. AΣL(1,𝔽16)C5×D3semidirect
411. C3×C5#2122semidirect
486. C5#69137direct (N × H)
511. C3C5×#2122semidirect

Maximal subgroups

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

subgroupindex
C5×#55922
C5×#47452
C5×#47402
C3×C5×AΣL(1,𝔽16)2
C5×#45362
C5×#44752
C5×#44712
C5×#21223
#691375