Finite Group Databasebeta

← C5×#69145 #14313297

Subgroups — C5×#69145 #14313297

Order 1920.

468 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5648C211yesmaximal, characteristic
2C5×#4745C211yesmaximal, characteristic
3C5×#4740C211yesmaximal, characteristic
4C3×C5×#352C211yesmaximal, characteristic, complemented
5C5×#4539C211yesmaximal, characteristic, complemented
6C5×#4476C211yesmaximal, characteristic, complemented
7C5×#4472C211yesmaximal, characteristic, complemented
8C5×#2123—31nomaximal, Hall
9C2×C5×#237C2211yescharacteristic
10C22×C5×Dic6C411yescharacteristic, complemented
11C3×C5×#123C2211yescharacteristic
12C5×#935C2211yescharacteristic
13C5×#929C411yescharacteristic, complemented
14C5×D3×M16—21no—
15C5×#896—21no—
16C5×#888—21no—
17C5×#886C411yescharacteristic, complemented
18C5×#885—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#69145C511yesmaximal, characteristic, direct product factor, Hall
29C5×#536—31no—
30C5×#413—31no—
31C5×#410—31no—
32C5×#352—31no—
33C5×#352—31no—
34C5×#352—31no—
35C5×#352D311yescharacteristic, complemented
36C2×C3×C5×D4C2311yescharacteristic
37C22×C3×C4×C5C2×C411yescharacteristic
38C2×C5×#67C2×C411yescharacteristic
39C2×C5×#67D411yescharacteristic
40C22×C5×Dic3C2×C411yescharacteristic
41C22×C5×Dic3C2×C411yescharacteristic
42C22×C5×Dic3D411yescharacteristic
43C5×#237—41no—
44C5×#237—41no—
45C2×C4×C5×D3D411yescharacteristic
46C2×C5×Dic6—21no—
47C2×C5×Dic6—21no—
48C2×C5×Dic6—41no—
49C2×C5×Dic6—41no—
50C2×C5×Dic6D411yescharacteristic
51C3×C5×M16—21no—
52C3×C5×C4⋊C4—21no—
53C3×C5×C22⋊C4—21no—
54C3×C5×C22⋊C4—21no—
55C3×C5×C22⋊C4C2×C411yescharacteristic
56C5×#217—21no—
57C5×#217—21no—
58C5×#217C2×C411yescharacteristic
59C5×(C2×D3)⋊C4—21no—
60C5×(C2×D3)⋊C4—21no—
61C5×C4⋊Dic3—21no—
62C5×Dic3⋊C4—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#5648C2×C511yescharacteristic
72#4745C2×C511yescharacteristic
73#4740C2×C511yescharacteristic
74C3×#352C2×C511yescharacteristic, complemented
75#4539C2×C511yescharacteristic, complemented
76#4476C2×C511yescharacteristic, complemented
77#4472C2×C511yescharacteristic, complemented
78C2×C5×#41—31no—
79C22×C5×Q8—31no—
80C2×C5×M16—61no—
81C5×C4⋊Q8—61no—
82C5×#124—61no—
83C5×#123—31no—
84C5×#123—31no—
85C5×#123—31no—
86C5×#123C2×D311yescharacteristic
87C5×C22⋊Q8—61no—
88C5×C22⋊Q8—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#2123—31noSylow
98C23×C3×C5C22×C411yescharacteristic
99C23×C3×C5C2×D411yescharacteristic
100C22×C5×D3C22⋊C411yescharacteristic
101C3×C5×D4—41no—
102C2×C3×C4×C5—21no—
103C2×C3×C4×C5—21no—
104C2×C3×C4×C5—41no—
105C2×C3×C4×C5—41no—
106C2×C3×C4×C5C2×D411yescharacteristic
107C5×#67—41no—
108C5×#67—41no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—21no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3C22⋊C411yescharacteristic
118C2×C5×Dic3C22⋊C411yescharacteristic
119C2×C5×Dic3C22⋊C411yescharacteristic
120C4×C5×D3—21no—
121C4×C5×D3—21no—
122C5×Dic6—41no—
123C5×Dic6—42no—
124C5×Dic6—41no—
125C5×Dic6—41no—
126C3×C5×C8—41no—
127C5×C3⋊C8—41no—
128C2×#237C22×C511yescharacteristic
129C22×Dic6C4×C511yescharacteristic, complemented
130C3×#123C22×C511yescharacteristic
131#935C22×C511yescharacteristic
132#929C4×C511yescharacteristic, complemented
133D3×M16—21no—
134#896—21no—
135#888—21no—
136#886C4×C511yescharacteristic, complemented
137#885—21no—
138#878—21no—
139#877—21no—
140#877C4×C511yescharacteristic, complemented
141C3×#100C22×C511yescharacteristic
142C3×#99C22×C511yescharacteristic
143#834C22×C511yescharacteristic
144#833C22×C511yescharacteristic
145#824—21no—
146#806—21no—
147C5×#41—121no—
148C5×#41—121no—
149C2×C5×Q8—31no—
150C2×C5×Q8—61no—
151C2×C5×Q8—61no—
152C2×C5×Q8—121no—
153C2×C5×Q8—121no—
154C2×C5×D4—31no—
155C2×C5×D4—31no—
156C2×C5×D4C22×D311yescharacteristic
157C22×C4×C5—31no—
158C22×C4×C5—31no—
159C22×C4×C5—31no—
160C22×C4×C5—31no—
161C22×C4×C5C4×D311yescharacteristic
162C5×M16—21no—
163C5×M16—61no—
164C5×M16—121no—
165C2×C5×C8—121no—
166C5×C4⋊C4—21no—
167C5×C4⋊C4—61no—
168C5×C4⋊C4—61no—
169C5×C4⋊C4—61no—
170C5×C4⋊C4—61no—
171C5×C4⋊C4—121no—
172C5×C22⋊C4—21no—
173C5×C22⋊C4—21no—
174C5×C22⋊C4—31no—
175C5×C22⋊C4—61no—
176C5×C22⋊C4—61no—
177C5×C22⋊C4—61no—
178C5×C22⋊C4—61no—
179C5×C22⋊C4C4×D311yescharacteristic
180C42×C5—61no—
181C42×C5—121no—
182#536—31no—
183#413—31no—
184#410—31no—
185#352—31no—
186#352—31no—
187#352—31no—
188#352C5×D311yescharacteristic, complemented
189C22×C3×C5—21no—
190C22×C3×C5—21no—
191C22×C3×C5—41no—
192C22×C3×C5—41no—
193C22×C3×C5C2×C22⋊C411yescharacteristic
194C2×C5×D3—21no—
195C2×C5×D3—41no—
196C3×C4×C5—21no—
197C3×C4×C5—41no—
198C3×C4×C5—41no—
199C3×C4×C5—81no—
200C5×Dic3—21no—
201C5×Dic3—21no—
202C5×Dic3—41no—
203C5×Dic3—41no—
204C5×Dic3—81no—
205C5×Dic3#9911yescharacteristic
206C5×Dic3#9911yescharacteristic
207C2×C3×D4C23×C511yescharacteristic
208C22×C3×C4C2×C4×C511yescharacteristic
209C2×#67C2×C4×C511yescharacteristic
210C2×#67C5×D411yescharacteristic
211C22×Dic3C2×C4×C511yescharacteristic
212C22×Dic3C2×C4×C511yescharacteristic
213C22×Dic3C5×D411yescharacteristic
214#237—41no—
215#237—41no—
216C2×C4×D3C5×D411yescharacteristic
217C2×Dic6—21no—
218C2×Dic6—21no—
219C2×Dic6—41no—
220C2×Dic6—41no—
221C2×Dic6C5×D411yescharacteristic
222C3×M16—21no—
223C3×C4⋊C4—21no—
224C3×C22⋊C4—21no—
225C3×C22⋊C4—21no—
226C3×C22⋊C4C2×C4×C511yescharacteristic
227#217—21no—
228#217—21no—
229#217C2×C4×C511yescharacteristic
230(C2×D3)⋊C4—21no—
231(C2×D3)⋊C4—21no—
232C4⋊Dic3—21no—
233Dic3⋊C4—21no—
234Dic3⋊C4—21no—
235Dic3⋊C4—21no—
236Dic3⋊C4—41no—
237C4×Dic3—21no—
238C4×Dic3—41no—
239#208—21no—
240ΓL(1,𝔽25)—41no—
241D3×C8—41no—
242C23×C5—31no—
243C23×C5C2×C4×D311yescharacteristic
244C23×C5D3×D411yescharacteristic
245C5×Q8—121no—
246C5×Q8—121no—
247C5×Q8—121no—
248C5×Q8—122no—
249C5×D4—41no—
250C5×D4—121no—
251C5×D4—121no—
252C2×C4×C5—21no—
253C2×C4×C5—21no—
254C2×C4×C5—31no—
255C2×C4×C5—31no—
256C2×C4×C5—31no—
257C2×C4×C5—41no—
258C2×C4×C5—41no—
259C2×C4×C5—61no—
260C2×C4×C5—61no—
261C2×C4×C5—61no—
262C2×C4×C5—61no—
263C2×C4×C5—61no—
264C2×C4×C5—61no—
265C2×C4×C5—61no—
266C2×C4×C5—61no—
267C2×C4×C5—121no—
268C2×C4×C5—121no—
269C2×C4×C5D3×D411yescharacteristic
270C5×C8—41no—
271C5×C8—121no—
272C2×#41—31no—
273C22×Q8—31no—
274C2×M16—61no—
275C4⋊Q8—61no—
276#124—61no—
277#123—31no—
278#123—31no—
279#123—31no—
280#123C2×C5×D311yescharacteristic
281C22⋊Q8—61no—
282C22⋊Q8—61no—
283#117—31no—
284#117—61no—
285#101—61no—
286#100—31no—
287#100C2×C5×D311yescharacteristic
288#99—31no—
289#99—61no—
290#99C2×C5×D311yescharacteristic
291C2×C3×C5—21no—
292C2×C3×C5—41no—
293C2×C3×C5—41no—
294C2×C3×C5C2×#9911yescharacteristic
295C5×D3—41no—
296C23×C3C22×C4×C511yescharacteristic
297C23×C3C2×C5×D411yescharacteristic
298C22×D3C5×C22⋊C411yescharacteristic
299C3×D4—41no—
300C2×C3×C4—21no—
301C2×C3×C4—21no—
302C2×C3×C4—41no—
303C2×C3×C4—41no—
304C2×C3×C4C2×C5×D411yescharacteristic
305#67—41no—
306#67—41no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—21no—
310C2×Dic3—21no—
311C2×Dic3—21no—
312C2×Dic3—21no—
313C2×Dic3—41no—
314C2×Dic3—41no—
315C2×Dic3C5×C22⋊C411yescharacteristic
316C2×Dic3C5×C22⋊C411yescharacteristic
317C2×Dic3C5×C22⋊C411yescharacteristic
318C4×D3—21no—
319C4×D3—21no—
320Dic6—41no—
321Dic6—42no—
322Dic6—41no—
323Dic6—41no—
324C3×C8—41no—
325C3⋊C8—41no—
326C22×C5—21no—
327C22×C5—21no—
328C22×C5—41no—
329C22×C5—41no—
330C22×C5—61no—
331C22×C5—121no—
332C22×C5D3×C22⋊C411yescharacteristic
333C4×C5—21no—
334C4×C5—31no—
335C4×C5—31no—
336C4×C5—41no—
337C4×C5—41no—
338C4×C5—61no—
339C4×C5—61no—
340C4×C5—81no—
341C4×C5—121no—
342C4×C5—121no—
343C4×C5—241no—
344#41—121no—
345#41—121no—
346C2×Q8—31no—
347C2×Q8—61no—
348C2×Q8—61no—
349C2×Q8—121no—
350C2×Q8—121no—
351C2×D4—31no—
352C2×D4—31no—
353C2×D4C22×C5×D311yescharacteristic
354C22×C4—31no—
355C22×C4—31no—
356C22×C4—31no—
357C22×C4—31no—
358C22×C4C4×C5×D311yescharacteristic
359M16—21no—
360M16—61no—
361M16—121no—
362C2×C8—121no—
363C4⋊C4—21no—
364C4⋊C4—61no—
365C4⋊C4—61no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C4⋊C4—121no—
369C22⋊C4—21no—
370C22⋊C4—21no—
371C22⋊C4—31no—
372C22⋊C4—61no—
373C22⋊C4—61no—
374C22⋊C4—61no—
375C22⋊C4—61no—
376C22⋊C4C4×C5×D311yescharacteristic
377C42—61no—
378C42—121no—
379C3×C5#212311yescharacteristic, complemented, Hall
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3C2×C5×C22⋊C411yescharacteristic
385C2×D3—21no—
386C2×D3—41no—
387C3×C4—21no—
388C3×C4—41no—
389C3×C4—41no—
390C3×C4—81no—
391Dic3—21no—
392Dic3—21no—
393Dic3—41no—
394Dic3—41no—
395Dic3—81no—
396Dic3C5×#9911yescharacteristic
397Dic3C5×#9911yescharacteristic
398C2×C5—21no—
399C2×C5—41no—
400C2×C5—41no—
401C2×C5—121no—
402C2×C5D3×#9911yescharacteristic
403C23—31no—
404C23C2×C4×C5×D311yescharacteristic
405C23C5×D3×D411yescharacteristic
406Q8—121no—
407Q8—121no—
408Q8—121no—
409Q8—122no—
410D4—41no—
411D4—121no—
412D4—121no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—31no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—61no—
421C2×C4—61no—
422C2×C4—61no—
423C2×C4—61no—
424C2×C4—61no—
425C2×C4—61no—
426C2×C4—61no—
427C2×C4—61no—
428C2×C4—121no—
429C2×C4—121no—
430C2×C4C5×D3×D411yescharacteristic
431C8—41no—
432C8—121no—
433C2×C3—21no—
434C2×C3—41no—
435C2×C3—41no—
436C2×C3C2×C5×#9911yescharacteristic
437D3—41no—
438C5#6914511yescharacteristic, direct product factor, Sylow
439C22—21no—
440C22—21no—
441C22—41no—
442C22—41no—
443C22—61no—
444C22—121no—
445C22C5×D3×C22⋊C411yescharacteristic
446C4—21no—
447C4—31no—
448C4—31no—
449C4—41no—
450C4—41no—
451C4—61no—
452C4—61no—
453C4—81no—
454C4—121no—
455C4—121no—
456C4—241no—
457C3C5×#212311yescharacteristic, complemented, Sylow
458C2—21no—
459C2—41no—
460C2—41no—
461C2—121no—
462C2C5×D3×#9911yescharacteristic
subgroupG/H
centerC2×C5D3×#99
commutatorC23×C3C22×C4×C5
FrattiniC2×D4C22×C5×D3
FittingC3×C5×#352C2
socleC2×C3×C5C2×#99
prime radicalC2×C5×#237C22
cosocleC2×C3×D4C23×C5
hypercenterC5×#352D3
hypocenterC3C5×#2123
LCSG ▷ C23×C3 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C5 ◁ C2×C5×D4 ◁ C5×#352

Complements

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

NH ≅ G/Ntype
4. C3×C5×#352C2semidirect
5. C5×#4539C2semidirect
6. C5×#4476C2semidirect
7. C5×#4472C2semidirect
10. C22×C5×Dic6C4semidirect
13. C5×#929C4semidirect
17. C5×#886C4semidirect
21. C5×#877C4semidirect
28. #69145C5direct (N × H)
35. C5×#352D3semidirect
74. C3×#352C2×C5semidirect
75. #4539C2×C5semidirect
76. #4476C2×C5semidirect
77. #4472C2×C5semidirect
129. C22×Dic6C4×C5semidirect
132. #929C4×C5semidirect
136. #886C4×C5semidirect
140. #877C4×C5semidirect
188. #352C5×D3semidirect
379. C3×C5#2123semidirect
438. C5#69145direct (N × H)
457. C3C5×#2123semidirect

Maximal subgroups

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

subgroupindex
C5×#56482
C5×#47452
C5×#47402
C3×C5×#3522
C5×#45392
C5×#44762
C5×#44722
C5×#21233
#691455