Finite Group Databasebeta

← C5×#69979 #14283417

Subgroups — C5×#69979 #14283417

Order 1920.

572 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×#5791C211yesmaximal, characteristic
2C3×C5×#407C211yesmaximal, characteristic, complemented
3C5×#5212C211yesmaximal, characteristic, complemented
4C5×#4470C212yesmaximal, complemented
5C5×#4467C212yesmaximal, complemented
6C5×#1513—31nomaximal, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C2×C5×#235C411yescharacteristic, complemented
9C2×C3×C5×M16—21no—
10C5×#953—21no—
11C2×C5×#217—21no—
12C5×#930C411yescharacteristic, complemented
13C5×#930C2211yescharacteristic
14C5×#929—21no—
15C4×C5×#67—21no—
16C4×C5×#67—21no—
17C5×#926C411yescharacteristic, complemented
18C2×C5×C4⋊Dic3—21no—
19C5×#924C411yescharacteristic, complemented
20C5×#924C2211yescharacteristic
21C3×C5×C22⋊C8—21no—
22C3×C5×C22⋊C8C2212yes—
23C5×C3⋊#95C2212yes—
24#69979C511yesmaximal, characteristic, direct product factor, Hall
25C5×#525—31no—
26C5×#407D311yescharacteristic, complemented
27C5×#380—31no—
28C5×#328—32no—
29C5×#327—32no—
30C24×C3×C5D411yescharacteristic
31C22×C3×C4×C5—42no—
32C22×C3×C4×C5C2×C411yescharacteristic
33C22×C3×C4×C5C2×C411yescharacteristic
34C22×C3×C4×C5D411yescharacteristic
35C22×C3×C4×C5D411yescharacteristic
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5C2311yescharacteristic
38C2×C5×#67—21no—
39C2×C5×#67—21no—
40C2×C5×#67—21no—
41C22×C5×Dic3—22no—
42C5×#235—42no—
43C2×C5×D12C2×C411yescharacteristic
44C2×C4×C5×D3—21no—
45C2×C5×Dic6C2×C411yescharacteristic
46C3×C5×M16—42no—
47C2×C3×C5×C8—22no—
48C5×#217—21no—
49C5×#217—21no—
50C5×#217—21no—
51C5×#217—42no—
52C5×(C2×D3)⋊C4—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×C4⋊Dic3—42no—
55C5×C4⋊Dic3C2×C411yescharacteristic
56C5×C4⋊Dic3C2×C411yescharacteristic
57C5×Dic3⋊C4—21no—
58C5×Dic3⋊C4—21no—
59C4×C5×Dic3—21no—
60#5791C2×C511yescharacteristic
61C3×#407C2×C511yescharacteristic, complemented
62#5212C2×C511yescharacteristic, complemented
63#4470C2×C512yescomplemented
64#4467C2×C512yescomplemented
65C2×C5×#41—31no—
66C23×C4×C5C2×D311yescharacteristic
67C2×C5×M16—21no—
68C5×#123—61no—
69C5×C22⋊Q8—31no—
70C5×C22⋊Q8—31no—
71C5×#121—31no—
72C5×#121—31no—
73C5×#120—61no—
74C4×C5×D4—61no—
75C4×C5×D4—61no—
76C5×#117—31no—
77C2×C5×C4⋊C4—61no—
78C2×C5×C22⋊C4—61no—
79C5×C22⋊C8—21no—
80C5×C22⋊C8C2×D312yes—
81C5×#95—32no—
82#1513—31noSylow
83C23×C3×C5—21no—
84C23×C3×C5—21no—
85C23×C3×C5—41no—
86C23×C3×C5—41no—
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C22⋊C411yescharacteristic
89C23×C3×C5C2×D411yescharacteristic
90C22×C5×D3—21no—
91C2×C3×C4×C5—22no—
92C2×C3×C4×C5—22no—
93C2×C3×C4×C5—22no—
94C2×C3×C4×C5—41no—
95C2×C3×C4×C5—41no—
96C2×C3×C4×C5—41no—
97C2×C3×C4×C5C22⋊C411yescharacteristic
98C2×C3×C4×C5C22⋊C411yescharacteristic
99C2×C3×C4×C5C22×C411yescharacteristic
100C2×C3×C4×C5C2×D411yescharacteristic
101C5×#67—42no—
102C5×#67—42no—
103C5×#67—41no—
104C5×#67—41no—
105C2×C5×Dic3—21no—
106C2×C5×Dic3—21no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—42no—
109C2×C5×Dic3—42no—
110C2×C5×Dic3—42no—
111C5×D12—41no—
112C4×C5×D3—42no—
113C5×Dic6—41no—
114C3×C5×C8—42no—
115C23×C3×C4C22×C511yescharacteristic
116C2×#235C4×C511yescharacteristic, complemented
117C2×C3×M16—21no—
118#953—21no—
119C2×#217—21no—
120#930C4×C511yescharacteristic, complemented
121#930C22×C511yescharacteristic
122#929—21no—
123C4×#67—21no—
124C4×#67—21no—
125#926C4×C511yescharacteristic, complemented
126C2×C4⋊Dic3—21no—
127#924C4×C511yescharacteristic, complemented
128#924C22×C511yescharacteristic
129C3×C22⋊C8—21no—
130C3×C22⋊C8C22×C512yes—
131C3⋊#95C22×C512yes—
132C24×C5D1211yescharacteristic
133C5×#41—122no—
134C2×C5×Q8—31no—
135C2×C5×D4—31no—
136C2×C5×D4—61no—
137C2×C5×D4—61no—
138C2×C5×D4—61no—
139C22×C4×C5—42no—
140C22×C4×C5—61no—
141C22×C4×C5—62no—
142C22×C4×C5C4×D311yescharacteristic
143C22×C4×C5C4×D311yescharacteristic
144C22×C4×C5D1211yescharacteristic
145C22×C4×C5#6711yescharacteristic
146C22×C4×C5#6711yescharacteristic
147C22×C4×C5C22×D311yescharacteristic
148C5×M16—42no—
149C2×C5×C8—22no—
150C5×C4⋊C4—31no—
151C5×C4⋊C4—31no—
152C5×C4⋊C4—61no—
153C5×C4⋊C4—61no—
154C5×C4⋊C4—122no—
155C5×C22⋊C4—61no—
156C5×C22⋊C4—61no—
157C5×C22⋊C4—61no—
158C5×C22⋊C4—61no—
159C5×C22⋊C4—61no—
160C5×C22⋊C4—122no—
161C42×C5—61no—
162#525—31no—
163#407C5×D311yescharacteristic, complemented
164#380—31no—
165#328—32no—
166#327—32no—
167C22×C3×C5—21no—
168C22×C3×C5—21no—
169C22×C3×C5—21no—
170C22×C3×C5—21no—
171C22×C3×C5—21no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—42no—
176C22×C3×C5—42no—
177C22×C3×C5C2×C22⋊C411yescharacteristic
178C22×C3×C5AGL(1,ℤ/8)11yescharacteristic
179C22×C3×C5#13711yescharacteristic
180C2×C5×D3—41no—
181C2×C5×D3—41no—
182C2×C5×D3—41no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5—21no—
186C3×C4×C5#9912yes—
187C5×Dic3—41no—
188C5×Dic3—41no—
189C5×Dic3—41no—
190C5×Dic3—82no—
191C24×C3C5×D411yescharacteristic
192C22×C3×C4—42no—
193C22×C3×C4C2×C4×C511yescharacteristic
194C22×C3×C4C2×C4×C511yescharacteristic
195C22×C3×C4C5×D411yescharacteristic
196C22×C3×C4C5×D411yescharacteristic
197C22×C3×C4C5×D411yescharacteristic
198C22×C3×C4C23×C511yescharacteristic
199C2×#67—21no—
200C2×#67—21no—
201C2×#67—21no—
202C22×Dic3—22no—
203#235—42no—
204C2×D12C2×C4×C511yescharacteristic
205C2×C4×D3—21no—
206C2×Dic6C2×C4×C511yescharacteristic
207C3×M16—42no—
208C2×C3×C8—22no—
209#217—21no—
210#217—21no—
211#217—21no—
212#217—42no—
213(C2×D3)⋊C4—21no—
214(C2×D3)⋊C4—21no—
215C4⋊Dic3—42no—
216C4⋊Dic3C2×C4×C511yescharacteristic
217C4⋊Dic3C2×C4×C511yescharacteristic
218Dic3⋊C4—21no—
219Dic3⋊C4—21no—
220C4×Dic3—21no—
221C23×C5—21no—
222C23×C5—21no—
223C23×C5—41no—
224C23×C5—41no—
225C23×C5—61no—
226C23×C5(C2×D3)⋊C411yescharacteristic
227C23×C5(C2×D3)⋊C411yescharacteristic
228C23×C5C2×D1211yescharacteristic
229C5×Q8—121no—
230C5×D4—121no—
231C5×D4—122no—
232C5×D4—122no—
233C5×D4—121no—
234C5×D4—121no—
235C2×C4×C5—22no—
236C2×C4×C5—22no—
237C2×C4×C5—22no—
238C2×C4×C5—41no—
239C2×C4×C5—41no—
240C2×C4×C5—41no—
241C2×C4×C5—61no—
242C2×C4×C5—61no—
243C2×C4×C5—61no—
244C2×C4×C5—122no—
245C2×C4×C5—122no—
246C2×C4×C5—122no—
247C2×C4×C5—122no—
248C2×C4×C5(C2×D3)⋊C411yescharacteristic
249C2×C4×C5(C2×D3)⋊C411yescharacteristic
250C2×C4×C5C2×C4×D311yescharacteristic
251C2×C4×C5C2×#6711yescharacteristic
252C5×C8—42no—
253C2×#41—31no—
254C23×C4C2×C5×D311yescharacteristic
255C2×M16—21no—
256#123—61no—
257C22⋊Q8—31no—
258C22⋊Q8—31no—
259#121—31no—
260#121—31no—
261#120—61no—
262C4×D4—61no—
263C4×D4—61no—
264#117—31no—
265C2×C4⋊C4—61no—
266C2×C22⋊C4—61no—
267C22⋊C8—21no—
268C22⋊C8C2×C5×D312yes—
269#95—32no—
270C2×C3×C5—21no—
271C2×C3×C5—21no—
272C2×C3×C5—41no—
273C2×C3×C5—41no—
274C2×C3×C5C2×#9911yescharacteristic
275C2×C3×C5#41711yescharacteristic
276C2×C3×C5#42111yescharacteristic
277C5×D3—81no—
278C23×C3—21no—
279C23×C3—21no—
280C23×C3—41no—
281C23×C3—41no—
282C23×C3C5×C22⋊C411yescharacteristic
283C23×C3C5×C22⋊C411yescharacteristic
284C23×C3C2×C5×D411yescharacteristic
285C22×D3—21no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—41no—
290C2×C3×C4—41no—
291C2×C3×C4—41no—
292C2×C3×C4C5×C22⋊C411yescharacteristic
293C2×C3×C4C5×C22⋊C411yescharacteristic
294C2×C3×C4C22×C4×C511yescharacteristic
295C2×C3×C4C2×C5×D411yescharacteristic
296#67—42no—
297#67—42no—
298#67—41no—
299#67—41no—
300C2×Dic3—21no—
301C2×Dic3—21no—
302C2×Dic3—21no—
303C2×Dic3—42no—
304C2×Dic3—42no—
305C2×Dic3—42no—
306D12—41no—
307C4×D3—42no—
308Dic6—41no—
309C3×C8—42no—
310C22×C5—21no—
311C22×C5—21no—
312C22×C5—21no—
313C22×C5—21no—
314C22×C5—21no—
315C22×C5—21no—
316C22×C5—21no—
317C22×C5—21no—
318C22×C5—42no—
319C22×C5—42no—
320C22×C5—121no—
321C22×C5—121no—
322C22×C5—121no—
323C22×C5#90811yescharacteristic
324C22×C5#90911yescharacteristic
325C22×C5C2×(C2×D3)⋊C411yescharacteristic
326C4×C5—21no—
327C4×C5—21no—
328C4×C5—21no—
329C4×C5—121no—
330C4×C5—121no—
331C4×C5—121no—
332C4×C5—242no—
333C4×C5#80612yes—
334C24C5×D1211yescharacteristic
335#41—122no—
336C2×Q8—31no—
337C2×D4—31no—
338C2×D4—61no—
339C2×D4—61no—
340C2×D4—61no—
341C22×C4—42no—
342C22×C4—61no—
343C22×C4—62no—
344C22×C4C4×C5×D311yescharacteristic
345C22×C4C4×C5×D311yescharacteristic
346C22×C4C5×D1211yescharacteristic
347C22×C4C5×#6711yescharacteristic
348C22×C4C5×#6711yescharacteristic
349C22×C4C22×C5×D311yescharacteristic
350M16—42no—
351C2×C8—22no—
352C4⋊C4—31no—
353C4⋊C4—31no—
354C4⋊C4—61no—
355C4⋊C4—61no—
356C4⋊C4—122no—
357C22⋊C4—61no—
358C22⋊C4—61no—
359C22⋊C4—61no—
360C22⋊C4—61no—
361C22⋊C4—61no—
362C22⋊C4—122no—
363C42—61no—
364C3×C5#151311yescharacteristic, complemented, Hall
365C22×C3—21no—
366C22×C3—21no—
367C22×C3—21no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—42no—
374C22×C3—42no—
375C22×C3C2×C5×C22⋊C411yescharacteristic
376C22×C3C5×AGL(1,ℤ/8)11yescharacteristic
377C22×C3C5×#13711yescharacteristic
378C2×D3—41no—
379C2×D3—41no—
380C2×D3—41no—
381C3×C4—21no—
382C3×C4—21no—
383C3×C4—21no—
384C3×C4C5×#9912yes—
385Dic3—41no—
386Dic3—41no—
387Dic3—41no—
388Dic3—82no—
389C2×C5—21no—
390C2×C5—21no—
391C2×C5—41no—
392C2×C5—41no—
393C2×C5—241no—
394C2×C5C2×#80611yescharacteristic
395C2×C5#513311yescharacteristic
396C2×C5#513911yescharacteristic
397C23—21no—
398C23—21no—
399C23—41no—
400C23—41no—
401C23—61no—
402C23C5×(C2×D3)⋊C411yescharacteristic
403C23C5×(C2×D3)⋊C411yescharacteristic
404C23C2×C5×D1211yescharacteristic
405Q8—121no—
406D4—121no—
407D4—122no—
408D4—122no—
409D4—121no—
410D4—121no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—61no—
418C2×C4—61no—
419C2×C4—61no—
420C2×C4—122no—
421C2×C4—122no—
422C2×C4—122no—
423C2×C4—122no—
424C2×C4C5×(C2×D3)⋊C411yescharacteristic
425C2×C4C5×(C2×D3)⋊C411yescharacteristic
426C2×C4C2×C4×C5×D311yescharacteristic
427C2×C4C2×C5×#6711yescharacteristic
428C8—42no—
429C2×C3—21no—
430C2×C3—21no—
431C2×C3—41no—
432C2×C3—41no—
433C2×C3C2×C5×#9911yescharacteristic
434C2×C3C5×#41711yescharacteristic
435C2×C3C5×#42111yescharacteristic
436D3—81no—
437C5#6997911yescharacteristic, direct product factor, Sylow
438C22—21no—
439C22—21no—
440C22—21no—
441C22—21no—
442C22—21no—
443C22—21no—
444C22—21no—
445C22—21no—
446C22—42no—
447C22—42no—
448C22—121no—
449C22—121no—
450C22—121no—
451C22C5×#90811yescharacteristic
452C22C5×#90911yescharacteristic
453C22C2×C5×(C2×D3)⋊C411yescharacteristic
454C4—21no—
455C4—21no—
456C4—21no—
457C4—121no—
458C4—121no—
459C4—121no—
460C4—242no—
461C4C5×#80612yes—
462C3C5×#151311yescharacteristic, complemented, Sylow
463C2—21no—
464C2—21no—
465C2—41no—
466C2—41no—
467C2—241no—
468C2C2×C5×#80611yescharacteristic
469C2C5×#513311yescharacteristic
470C2C5×#513911yescharacteristic
subgroupG/H
centerC22×C5C2×(C2×D3)⋊C4
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#407C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC5×#5791C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#407D3
hypocenterC3C5×#1513
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C23×C4×C5 ◁ C5×#407

Complements

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

NH ≅ G/Ntype
2. C3×C5×#407C2semidirect
3. C5×#5212C2semidirect
4. C5×#4470C2semidirect
5. C5×#4467C2semidirect
8. C2×C5×#235C4semidirect
12. C5×#930C4semidirect
17. C5×#926C4semidirect
19. C5×#924C4semidirect
24. #69979C5direct (N × H)
26. C5×#407D3semidirect
61. C3×#407C2×C5semidirect
62. #5212C2×C5semidirect
63. #4470C2×C5semidirect
64. #4467C2×C5semidirect
116. C2×#235C4×C5semidirect
120. #930C4×C5semidirect
125. #926C4×C5semidirect
127. #924C4×C5semidirect
163. #407C5×D3semidirect
364. C3×C5#1513semidirect
437. C5#69979direct (N × H)
462. C3C5×#1513semidirect

Maximal subgroups

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

subgroupindex
C5×#57912
C3×C5×#4072
C5×#52122
C5×#44702
C5×#44672
C5×#15133
#699795