Finite Group Databasebeta

← C5×#68297 #14288389

Subgroups — C5×#68297 #14288389

Order 1920.

508 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×#5597C211yesmaximal, characteristic
2C5×#5033C211yesmaximal, characteristic, complemented
3C5×#4736C211yesmaximal, characteristic, complemented
4C5×#4661C211yesmaximal, characteristic, complemented
5C3×C5×#327C211yesmaximal, characteristic, complemented
6C5×#4469C211yesmaximal, characteristic, complemented
7C5×#4451C211yesmaximal, characteristic, complemented
8C5×#1610—31nomaximal, Hall
9C2×C5×#237—21no—
10C3×C5×#121C2211yescharacteristic
11C5×#939—21no—
12C5×#939—21no—
13C5×#930C2211yescharacteristic
14C2×C5×C4⋊Dic3—21no—
15C2×C5×C4⋊Dic3C2211yescharacteristic
16C2×C5×Dic3⋊C4C2211yescharacteristic
17C5×#896—21no—
18C5×#884—21no—
19C5×#878—21no—
20C3×C5×C22⋊C8C2211yescharacteristic
21C3×C5×#95C2211yescharacteristic
22C5×#832—21no—
23C5×C3⋊#95—21no—
24C5×#830C2211yescharacteristic
25C5×#821—21no—
26C5×#818—21no—
27C5×#807—21no—
28#68297C511yesmaximal, characteristic, direct product factor, Hall
29C5×#537—31no—
30C5×#480—31no—
31C5×#480—31no—
32C5×#398—31no—
33C5×#327—31no—
34C5×#327D311yescharacteristic, complemented
35C5×#324—31no—
36C2×C3×C5×D4—21no—
37C2×C3×C5×D4D411yescharacteristic
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5C2311yescharacteristic
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C2×C5×#67—21no—
43C22×C5×Dic3—21no—
44C22×C5×Dic3—21no—
45C22×C5×Dic3D411yescharacteristic
46C22×C5×Dic3D411yescharacteristic
47C5×#237—42no—
48C5×#237—42no—
49C2×C5×D12D411yescharacteristic
50C2×C4×C5×D3—21no—
51C2×C5×Dic6—21no—
52C2×C3×C5×C8—21no—
53C3×C5×C4⋊C4D411yescharacteristic
54C3×C5×C22⋊C4—21no—
55C5×#217—21no—
56C5×(C2×D3)⋊C4—21no—
57C5×(C2×D3)⋊C4—21no—
58C5×C4⋊Dic3—21no—
59C5×C4⋊Dic3—21no—
60C5×C4⋊Dic3—42no—
61C5×C4⋊Dic3D411yescharacteristic
62C5×Dic3⋊C4—21no—
63C5×Dic3⋊C4—21no—
64C5×Dic3⋊C4—21no—
65C2×C5×C3⋊C8—21no—
66#5597C2×C511yescharacteristic
67#5033C2×C511yescharacteristic, complemented
68#4736C2×C511yescharacteristic, complemented
69#4661C2×C511yescharacteristic, complemented
70C3×#327C2×C511yescharacteristic, complemented
71#4469C2×C511yescharacteristic, complemented
72#4451C2×C511yescharacteristic, complemented
73C2×C5×#41—61no—
74C5×C22⋊Q8—61no—
75C5×C22⋊Q8—61no—
76C5×#121—31no—
77C5×#121—61no—
78C5×#121—61no—
79C5×#121—61no—
80C5×#121C2×D311yescharacteristic
81C2×C5×C4⋊C4—31no—
82C2×C5×C4⋊C4—31no—
83C2×C5×C4⋊C4—61no—
84C5×#107—61no—
85C5×#107—61no—
86C5×#102—61no—
87C5×#102—61no—
88C5×C22⋊C8—31no—
89C5×C22⋊C8C2×D311yescharacteristic
90C5×#95—61no—
91C5×#95C2×D311yescharacteristic
92#1610—31noSylow
93C23×C3×C5—21no—
94C23×C3×C5C2×D411yescharacteristic
95C22×C5×D3—21no—
96C3×C5×D4—41no—
97C3×C5×D4—41no—
98C3×C5×D4—41no—
99C2×C3×C4×C5—22no—
100C2×C3×C4×C5—21no—
101C2×C3×C4×C5—41no—
102C2×C3×C4×C5—41no—
103C2×C3×C4×C5—41no—
104C2×C3×C4×C5C2×D411yescharacteristic
105C2×C3×C4×C5C2×D411yescharacteristic
106C5×#67—42no—
107C5×#67—41no—
108C5×#67—41no—
109C5×#67—81no—
110C2×C5×Dic3—21no—
111C2×C5×Dic3—21no—
112C2×C5×Dic3—21no—
113C2×C5×Dic3—21no—
114C2×C5×Dic3—42no—
115C2×C5×Dic3—41no—
116C2×C5×Dic3—41no—
117C2×C5×Dic3—41no—
118C2×C5×Dic3—41no—
119C2×C5×Dic3D812yes—
120C5×D12—41no—
121C4×C5×D3—42no—
122C5×Dic6—42no—
123C3×C5×C8—41no—
124C5×C3⋊C8—41no—
125C2×#237—21no—
126C3×#121C22×C511yescharacteristic
127#939—21no—
128#939—21no—
129#930C22×C511yescharacteristic
130C2×C4⋊Dic3—21no—
131C2×C4⋊Dic3C22×C511yescharacteristic
132C2×Dic3⋊C4C22×C511yescharacteristic
133#896—21no—
134#884—21no—
135#878—21no—
136C3×C22⋊C8C22×C511yescharacteristic
137C3×#95C22×C511yescharacteristic
138#832—21no—
139C3⋊#95—21no—
140#830C22×C511yescharacteristic
141#821—21no—
142#818—21no—
143#807—21no—
144C5×#41—122no—
145C5×#41—122no—
146C2×C5×Q8—61no—
147C2×C5×D4—21no—
148C2×C5×D4—31no—
149C2×C5×D4—61no—
150C2×C5×D4—61no—
151C2×C5×D4—61no—
152C2×C5×D4D1211yescharacteristic
153C22×C4×C5—21no—
154C22×C4×C5—31no—
155C22×C4×C5—31no—
156C22×C4×C5—61no—
157C22×C4×C5—61no—
158C22×C4×C5—61no—
159C22×C4×C5C22×D311yescharacteristic
160C2×C5×C8—21no—
161C2×C5×C8—61no—
162C5×C4⋊C4—31no—
163C5×C4⋊C4—61no—
164C5×C4⋊C4—61no—
165C5×C4⋊C4—61no—
166C5×C4⋊C4—61no—
167C5×C4⋊C4—61no—
168C5×C4⋊C4—122no—
169C5×C4⋊C4D1211yescharacteristic
170C5×C22⋊C4—21no—
171C5×C22⋊C4—61no—
172C5×C22⋊C4—61no—
173C5×C22⋊C4—61no—
174#537—31no—
175#480—31no—
176#480—31no—
177#398—31no—
178#327—31no—
179#327C5×D311yescharacteristic, complemented
180#324—31no—
181C22×C3×C5—21no—
182C22×C3×C5—21no—
183C22×C3×C5—41no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5#12011yescharacteristic
187C22×C3×C5C2×D811yescharacteristic
188C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
189C2×C5×D3—41no—
190C2×C5×D3—41no—
191C2×C5×D3—41no—
192C3×C4×C5—21no—
193C3×C4×C5—21no—
194C3×C4×C5—42no—
195C3×C4×C5—41no—
196C5×Dic3—22no—
197C5×Dic3—41no—
198C5×Dic3—41no—
199C5×Dic3—81no—
200C2×C3×D4—21no—
201C2×C3×D4C5×D411yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4C23×C511yescharacteristic
204C2×#67—21no—
205C2×#67—21no—
206C2×#67—21no—
207C22×Dic3—21no—
208C22×Dic3—21no—
209C22×Dic3C5×D411yescharacteristic
210C22×Dic3C5×D411yescharacteristic
211#237—42no—
212#237—42no—
213C2×D12C5×D411yescharacteristic
214C2×C4×D3—21no—
215C2×Dic6—21no—
216C2×C3×C8—21no—
217C3×C4⋊C4C5×D411yescharacteristic
218C3×C22⋊C4—21no—
219#217—21no—
220(C2×D3)⋊C4—21no—
221(C2×D3)⋊C4—21no—
222C4⋊Dic3—21no—
223C4⋊Dic3—21no—
224C4⋊Dic3—42no—
225C4⋊Dic3C5×D411yescharacteristic
226Dic3⋊C4—21no—
227Dic3⋊C4—21no—
228Dic3⋊C4—21no—
229C2×C3⋊C8—21no—
230C23×C5—21no—
231C23×C5—61no—
232C23×C5D3×D411yescharacteristic
233C5×Q8—122no—
234C5×D4—41no—
235C5×D4—41no—
236C5×D4—41no—
237C5×D4—121no—
238C5×D4—122no—
239C5×D4—121no—
240C5×D4—121no—
241C5×D4—241no—
242C2×C4×C5—22no—
243C2×C4×C5—21no—
244C2×C4×C5—32no—
245C2×C4×C5—41no—
246C2×C4×C5—41no—
247C2×C4×C5—41no—
248C2×C4×C5—61no—
249C2×C4×C5—61no—
250C2×C4×C5—61no—
251C2×C4×C5—61no—
252C2×C4×C5—122no—
253C2×C4×C5—122no—
254C2×C4×C5—121no—
255C2×C4×C5—121no—
256C2×C4×C5—121no—
257C2×C4×C5—121no—
258C2×C4×C5C2×D1211yescharacteristic
259C2×C4×C5D3×D411yescharacteristic
260C5×C8—41no—
261C5×C8—121no—
262C2×#41—61no—
263C22⋊Q8—61no—
264C22⋊Q8—61no—
265#121—31no—
266#121—61no—
267#121—61no—
268#121—61no—
269#121C2×C5×D311yescharacteristic
270C2×C4⋊C4—31no—
271C2×C4⋊C4—31no—
272C2×C4⋊C4—61no—
273#107—61no—
274#107—61no—
275#102—61no—
276#102—61no—
277C22⋊C8—31no—
278C22⋊C8C2×C5×D311yescharacteristic
279#95—61no—
280#95C2×C5×D311yescharacteristic
281C2×C3×C5—21no—
282C2×C3×C5—21no—
283C2×C3×C5—81no—
284C2×C3×C5#44711yescharacteristic
285C2×C3×C5#45611yescharacteristic
286C2×C3×C5#45811yescharacteristic
287C5×D3—81no—
288C23×C3—21no—
289C23×C3C2×C5×D411yescharacteristic
290C22×D3—21no—
291C3×D4—41no—
292C3×D4—41no—
293C3×D4—41no—
294C2×C3×C4—22no—
295C2×C3×C4—21no—
296C2×C3×C4—41no—
297C2×C3×C4—41no—
298C2×C3×C4—41no—
299C2×C3×C4C2×C5×D411yescharacteristic
300C2×C3×C4C2×C5×D411yescharacteristic
301#67—42no—
302#67—41no—
303#67—41no—
304#67—81no—
305C2×Dic3—21no—
306C2×Dic3—21no—
307C2×Dic3—21no—
308C2×Dic3—21no—
309C2×Dic3—42no—
310C2×Dic3—41no—
311C2×Dic3—41no—
312C2×Dic3—41no—
313C2×Dic3—41no—
314C2×Dic3C5×D812yes—
315D12—41no—
316C4×D3—42no—
317Dic6—42no—
318C3×C8—41no—
319C3⋊C8—41no—
320C22×C5—21no—
321C22×C5—21no—
322C22×C5—41no—
323C22×C5—41no—
324C22×C5—41no—
325C22×C5—121no—
326C22×C5—121no—
327C22×C5—121no—
328C22×C5#88211yescharacteristic
329C22×C5D3×D811yescharacteristic
330C22×C5#91411yescharacteristic
331C4×C5—21no—
332C4×C5—21no—
333C4×C5—42no—
334C4×C5—41no—
335C4×C5—62no—
336C4×C5—121no—
337C4×C5—121no—
338C4×C5—241no—
339#41—122no—
340#41—122no—
341C2×Q8—61no—
342C2×D4—21no—
343C2×D4—31no—
344C2×D4—61no—
345C2×D4—61no—
346C2×D4—61no—
347C2×D4C5×D1211yescharacteristic
348C22×C4—21no—
349C22×C4—31no—
350C22×C4—31no—
351C22×C4—61no—
352C22×C4—61no—
353C22×C4—61no—
354C22×C4C22×C5×D311yescharacteristic
355C2×C8—21no—
356C2×C8—61no—
357C4⋊C4—31no—
358C4⋊C4—61no—
359C4⋊C4—61no—
360C4⋊C4—61no—
361C4⋊C4—61no—
362C4⋊C4—61no—
363C4⋊C4—122no—
364C4⋊C4C5×D1211yescharacteristic
365C22⋊C4—21no—
366C22⋊C4—61no—
367C22⋊C4—61no—
368C22⋊C4—61no—
369C3×C5#161011yescharacteristic, complemented, Hall
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—41no—
373C22×C3—41no—
374C22×C3—41no—
375C22×C3C5×#12011yescharacteristic
376C22×C3C2×C5×D811yescharacteristic
377C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—41no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—42no—
384C3×C4—41no—
385Dic3—22no—
386Dic3—41no—
387Dic3—41no—
388Dic3—81no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—81no—
392C2×C5—241no—
393C2×C5#474211yescharacteristic
394C2×C5#477311yescharacteristic
395C2×C5#482611yescharacteristic
396C23—21no—
397C23—61no—
398C23C5×D3×D411yescharacteristic
399Q8—122no—
400D4—41no—
401D4—41no—
402D4—41no—
403D4—121no—
404D4—122no—
405D4—121no—
406D4—121no—
407D4—241no—
408C2×C4—22no—
409C2×C4—21no—
410C2×C4—32no—
411C2×C4—41no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—61no—
415C2×C4—61no—
416C2×C4—61no—
417C2×C4—61no—
418C2×C4—122no—
419C2×C4—122no—
420C2×C4—121no—
421C2×C4—121no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4C2×C5×D1211yescharacteristic
425C2×C4C5×D3×D411yescharacteristic
426C8—41no—
427C8—121no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—81no—
431C2×C3C5×#44711yescharacteristic
432C2×C3C5×#45611yescharacteristic
433C2×C3C5×#45811yescharacteristic
434D3—81no—
435C5#6829711yescharacteristic, direct product factor, Sylow
436C22—21no—
437C22—21no—
438C22—41no—
439C22—41no—
440C22—41no—
441C22—121no—
442C22—121no—
443C22—121no—
444C22C5×#88211yescharacteristic
445C22C5×D3×D811yescharacteristic
446C22C5×#91411yescharacteristic
447C4—21no—
448C4—21no—
449C4—42no—
450C4—41no—
451C4—62no—
452C4—121no—
453C4—121no—
454C4—241no—
455C3C5×#161011yescharacteristic, complemented, Sylow
456C2—21no—
457C2—21no—
458C2—81no—
459C2—241no—
460C2C5×#474211yescharacteristic
461C2C5×#477311yescharacteristic
462C2C5×#482611yescharacteristic
subgroupG/H
centerC22×C5#882
commutator, cosocleC22×C3×C4C23×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#327C2
socleC22×C3×C5#120
prime radicalC5×#5597C2
hypercenterC5×#327D3
hypocenterC3C5×#1610
LCSG ▷ C22×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C22×C4×C5 ◁ C5×#327

Complements

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

NH ≅ G/Ntype
2. C5×#5033C2semidirect
3. C5×#4736C2semidirect
4. C5×#4661C2semidirect
5. C3×C5×#327C2semidirect
6. C5×#4469C2semidirect
7. C5×#4451C2semidirect
28. #68297C5direct (N × H)
34. C5×#327D3semidirect
67. #5033C2×C5semidirect
68. #4736C2×C5semidirect
69. #4661C2×C5semidirect
70. C3×#327C2×C5semidirect
71. #4469C2×C5semidirect
72. #4451C2×C5semidirect
179. #327C5×D3semidirect
369. C3×C5#1610semidirect
435. C5#68297direct (N × H)
455. C3C5×#1610semidirect

Maximal subgroups

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

subgroupindex
C5×#55972
C5×#50332
C5×#47362
C5×#46612
C3×C5×#3272
C5×#44692
C5×#44512
C5×#16103
#682975