Finite Group Databasebeta

← C5×#70407 #14302394

Subgroups — C5×#70407 #14302394

Order 1920.

692 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
1C2×C5×#949C211yesmaximal, characteristic
2C5×#5521C211yesmaximal, characteristic, complemented
3C3×C5×#421C211yesmaximal, characteristic, complemented
4C5×#5240C211yesmaximal, characteristic, complemented
5C5×#5131C211yesmaximal, characteristic, complemented
6C5×#4559C211yesmaximal, characteristic, complemented
7C5×#4531C211yesmaximal, characteristic, complemented
8C5×#1904—31nomaximal, Hall
9C2×C3×C5×#41C2211yescharacteristic
10C22×C5×D12C2211yescharacteristic
11C2×C3×C5×M16C2211yescharacteristic
12C3×C5×#117C2211yescharacteristic
13C5×#949—22no—
14C5×#949—22no—
15C2×C5×#215C412yescomplemented
16C2×C5×#213C412yescomplemented
17C5×#926C2211yescharacteristic
18C5×#926C2211yescharacteristic
19C2×C5×#208C2211yescharacteristic
20C5×#893—22no—
21C5×D3×C22⋊C4—22no—
22C4×C5×D12—22no—
23C3×C5×#104—22no—
24C5×#834—22no—
25C5×#821—22no—
26#70407C511yesmaximal, characteristic, direct product factor, Hall
27C2×C5×AGL(1,ℤ/8)—31no—
28C5×#518—31no—
29C5×#421D311yescharacteristic, complemented
30C5×#418—31no—
31C5×#410—31no—
32C5×#344—31no—
33C5×H(3,ℤ/4)—31no—
34C23×C5×D3—21no—
35C3×C5×#41—21no—
36C3×C5×#41—21no—
37C3×C5×#41—21no—
38C3×C5×#41—21no—
39C2×C3×C5×Q8C2×C411yescharacteristic, complemented
40C2×C3×C5×D4—21no—
41C2×C3×C5×D4C2×C411yescharacteristic, complemented
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5C2311yescharacteristic
44C2×C5×D12—21no—
45C2×C5×D12—21no—
46C2×C5×D12—21no—
47C2×C5×D12C2×C412yes—
48C2×C5×D12D412yes—
49C2×C5×D12D412yes—
50C2×C4×C5×D3—24no—
51C3×C5×M16—21no—
52C3×C5×M16—21no—
53C2×C3×C5×C8—21no—
54C3×C5×C4⋊C4—21no—
55C3×C5×C22⋊C4—21no—
56C3×C42×C5D412yes—
57C5×#217—21no—
58C5×#217D412yes—
59C5×#215—24no—
60C5×#213—24no—
61C5×(C2×D3)⋊C4—24no—
62C5×C4⋊Dic3—21no—
63C5×C4⋊Dic3—21no—
64C4×C5×Dic3—21no—
65C4×C5×Dic3—21no—
66C5×#208—21no—
67C5×#208—21no—
68C2×C5×C3⋊C8C2×C412yescomplemented
69C2×#949C2×C511yescharacteristic
70#5521C2×C511yescharacteristic, complemented
71C3×#421C2×C511yescharacteristic, complemented
72#5240C2×C511yescharacteristic, complemented
73#5131C2×C511yescharacteristic, complemented
74#4559C2×C511yescharacteristic, complemented
75#4531C2×C511yescharacteristic, complemented
76C2×C5×#41C2×D311yescharacteristic
77C22×C5×D4—31no—
78C5×AGL(1,ℤ/8)—62no—
79C5×AGL(1,ℤ/8)—62no—
80C2×C5×SD16—32no—
81C2×C5×D8—32no—
82C2×C5×M16—31no—
83C2×C5×M16C2×D311yescharacteristic
84C4×C5×D4—62no—
85C4×C5×D4—62no—
86C5×#117—31no—
87C5×#117—31no—
88C5×#117C2×D311yescharacteristic
89C2×C5×C22⋊C4—62no—
90C5×#104—22no—
91C5×#102—62no—
92C5×#99—62no—
93#1904—31noSylow
94C23×C3×C5—21no—
95C23×C3×C5C2×D411yescharacteristic
96C22×C5×D3—22no—
97C22×C5×D3—22no—
98C22×C5×D3—22no—
99C22×C5×D3—82no—
100C3×C5×Q8—21no—
101C3×C5×Q8—21no—
102C3×C5×D4—21no—
103C3×C5×D4—21no—
104C3×C5×D4—41no—
105C3×C5×D4—41no—
106C2×C3×C4×C5—21no—
107C2×C3×C4×C5—22no—
108C2×C3×C4×C5—41no—
109C2×C3×C4×C5—41no—
110C2×C3×C4×C5C22×C411yescharacteristic
111C2×C3×C4×C5C2×D411yescharacteristic
112C2×C3×C4×C5C2×D411yescharacteristic
113C2×C3×C4×C5C2×D411yescharacteristic
114C2×C3×C4×C5#4111yescharacteristic
115C2×C3×C4×C5#4111yescharacteristic
116C2×C5×Dic3—22no—
117C2×C5×Dic3—41no—
118C5×D12—22no—
119C5×D12—22no—
120C5×D12—22no—
121C5×D12C22⋊C414yes—
122C4×C5×D3—84no—
123C3×C5×C8—41no—
124C5×C3⋊C8—22no—
125C2×C3×#41C22×C511yescharacteristic
126C22×D12C22×C511yescharacteristic
127C2×C3×M16C22×C511yescharacteristic
128C3×#117C22×C511yescharacteristic
129#949—22no—
130#949—22no—
131C2×#215C4×C512yescomplemented
132C2×#213C4×C512yescomplemented
133#926C22×C511yescharacteristic
134#926C22×C511yescharacteristic
135C2×#208C22×C511yescharacteristic
136#893—22no—
137D3×C22⋊C4—22no—
138C4×D12—22no—
139C3×#104—22no—
140#834—22no—
141#821—22no—
142C24×C5—61no—
143C5×#41—21no—
144C5×#41—21no—
145C5×#41—21no—
146C5×#41—21no—
147C2×C5×Q8C4×D311yescharacteristic, complemented
148C2×C5×D4—21no—
149C2×C5×D4—32no—
150C2×C5×D4—32no—
151C2×C5×D4—32no—
152C2×C5×D4—61no—
153C2×C5×D4—61no—
154C2×C5×D4—61no—
155C2×C5×D4C4×D311yescharacteristic, complemented
156C22×C4×C5—21no—
157C22×C4×C5—64no—
158C22×C4×C5C22×D311yescharacteristic
159C5×SD16—64no—
160C5×D8—64no—
161C5×M16—21no—
162C5×M16—21no—
163C5×M16—61no—
164C5×M16—61no—
165C2×C5×C8—21no—
166C2×C5×C8—32no—
167C5×C4⋊C4—21no—
168C5×C4⋊C4—61no—
169C5×C4⋊C4—61no—
170C5×C22⋊C4—21no—
171C5×C22⋊C4—32no—
172C5×C22⋊C4—64no—
173C5×C22⋊C4—61no—
174C42×C5—61no—
175C42×C5—61no—
176C42×C5#6712yes—
177C2×AGL(1,ℤ/8)—31no—
178#518—31no—
179#421C5×D311yescharacteristic, complemented
180#418—31no—
181#410—31no—
182#344—31no—
183H(3,ℤ/4)—31no—
184C22×C3×C5—41no—
185C22×C3×C5—41no—
186C22×C3×C5—81no—
187C22×C3×C5C4×D411yescharacteristic
188C22×C3×C5#12011yescharacteristic
189C22×C3×C5#12111yescharacteristic
190C2×C5×D3—24no—
191C2×C5×D3—44no—
192C2×C5×D3—82no—
193C2×C5×D3—82no—
194C3×C4×C5—42no—
195C3×C4×C5—41no—
196C3×C4×C5C2×C22⋊C411yescharacteristic
197C3×C4×C5C4×D411yescharacteristic
198C3×C4×C5#12111yescharacteristic
199C3×C4×C5#12311yescharacteristic
200C5×Dic3—42no—
201C5×Dic3—81no—
202C23×D3—21no—
203C3×#41—21no—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—21no—
207C2×C3×Q8C2×C4×C511yescharacteristic, complemented
208C2×C3×D4—21no—
209C2×C3×D4C2×C4×C511yescharacteristic, complemented
210C22×C3×C4—21no—
211C22×C3×C4C23×C511yescharacteristic
212C2×D12—21no—
213C2×D12—21no—
214C2×D12—21no—
215C2×D12C2×C4×C512yes—
216C2×D12C5×D412yes—
217C2×D12C5×D412yes—
218C2×C4×D3—24no—
219C3×M16—21no—
220C3×M16—21no—
221C2×C3×C8—21no—
222C3×C4⋊C4—21no—
223C3×C22⋊C4—21no—
224C3×C42C5×D412yes—
225#217—21no—
226#217C5×D412yes—
227#215—24no—
228#213—24no—
229(C2×D3)⋊C4—24no—
230C4⋊Dic3—21no—
231C4⋊Dic3—21no—
232C4×Dic3—21no—
233C4×Dic3—21no—
234#208—21no—
235#208—21no—
236C2×C3⋊C8C2×C4×C512yescomplemented
237C23×C5—21no—
238C23×C5—62no—
239C23×C5—62no—
240C23×C5—62no—
241C23×C5—242no—
242C23×C5D3×D411yescharacteristic
243C5×Q8—21no—
244C5×Q8—21no—
245C5×D4—21no—
246C5×D4—21no—
247C5×D4—34no—
248C5×D4—41no—
249C5×D4—41no—
250C5×D4—62no—
251C5×D4—62no—
252C5×D4—62no—
253C2×C4×C5—21no—
254C2×C4×C5—22no—
255C2×C4×C5—41no—
256C2×C4×C5—41no—
257C2×C4×C5—62no—
258C2×C4×C5—121no—
259C2×C4×C5—244no—
260C2×C4×C5C2×C4×D311yescharacteristic
261C2×C4×C5#23511yescharacteristic
262C2×C4×C5D3×D411yescharacteristic
263C2×C4×C5D3×D411yescharacteristic
264C2×C4×C5#23711yescharacteristic
265C2×C4×C5C2×#6711yescharacteristic
266C5×C8—41no—
267C5×C8—62no—
268C2×#41C2×C5×D311yescharacteristic
269C22×D4—31no—
270AGL(1,ℤ/8)—62no—
271AGL(1,ℤ/8)—62no—
272C2×SD16—32no—
273C2×D8—32no—
274C2×M16—31no—
275C2×M16C2×C5×D311yescharacteristic
276C4×D4—62no—
277C4×D4—62no—
278#117—31no—
279#117—31no—
280#117C2×C5×D311yescharacteristic
281C2×C22⋊C4—62no—
282#104—22no—
283#102—62no—
284#99—62no—
285C2×C3×C5—21no—
286C2×C3×C5—21no—
287C2×C3×C5—21no—
288C2×C3×C5—81no—
289C2×C3×C5#38611yescharacteristic
290C5×D3—44no—
291C23×C3—21no—
292C23×C3C2×C5×D411yescharacteristic
293C22×D3—22no—
294C22×D3—22no—
295C22×D3—22no—
296C22×D3—82no—
297C3×Q8—21no—
298C3×Q8—21no—
299C3×D4—21no—
300C3×D4—21no—
301C3×D4—41no—
302C3×D4—41no—
303C2×C3×C4—21no—
304C2×C3×C4—22no—
305C2×C3×C4—41no—
306C2×C3×C4—41no—
307C2×C3×C4C22×C4×C511yescharacteristic
308C2×C3×C4C2×C5×D411yescharacteristic
309C2×C3×C4C2×C5×D411yescharacteristic
310C2×C3×C4C2×C5×D411yescharacteristic
311C2×C3×C4C5×#4111yescharacteristic
312C2×C3×C4C5×#4111yescharacteristic
313C2×Dic3—22no—
314C2×Dic3—41no—
315D12—22no—
316D12—22no—
317D12—22no—
318D12C5×C22⋊C414yes—
319C4×D3—84no—
320C3×C8—41no—
321C3⋊C8—22no—
322C22×C5—41no—
323C22×C5—41no—
324C22×C5—64no—
325C22×C5—81no—
326C22×C5—124no—
327C22×C5—242no—
328C22×C5—242no—
329C22×C5#67⋊C411yescharacteristic
330C22×C5#88411yescharacteristic
331C22×C5#93711yescharacteristic
332C4×C5—42no—
333C4×C5—41no—
334C4×C5—122no—
335C4×C5—241no—
336C4×C5D3×C22⋊C411yescharacteristic
337C4×C5#88311yescharacteristic
338C4×C5C4×#6711yescharacteristic
339C4×C5#93811yescharacteristic
340C24—61no—
341#41—21no—
342#41—21no—
343#41—21no—
344#41—21no—
345C2×Q8C4×C5×D311yescharacteristic, complemented
346C2×D4—21no—
347C2×D4—32no—
348C2×D4—32no—
349C2×D4—32no—
350C2×D4—61no—
351C2×D4—61no—
352C2×D4—61no—
353C2×D4C4×C5×D311yescharacteristic, complemented
354C22×C4—21no—
355C22×C4—64no—
356C22×C4C22×C5×D311yescharacteristic
357SD16—64no—
358D8—64no—
359M16—21no—
360M16—21no—
361M16—61no—
362M16—61no—
363C2×C8—21no—
364C2×C8—32no—
365C4⋊C4—21no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C22⋊C4—21no—
369C22⋊C4—32no—
370C22⋊C4—64no—
371C22⋊C4—61no—
372C42—61no—
373C42—61no—
374C42C5×#6712yes—
375C3×C5#190411yescharacteristic, complemented, Hall
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—81no—
379C22×C3C4×C5×D411yescharacteristic
380C22×C3C5×#12011yescharacteristic
381C22×C3C5×#12111yescharacteristic
382C2×D3—24no—
383C2×D3—44no—
384C2×D3—82no—
385C2×D3—82no—
386C3×C4—42no—
387C3×C4—41no—
388C3×C4C2×C5×C22⋊C411yescharacteristic
389C3×C4C4×C5×D411yescharacteristic
390C3×C4C5×#12111yescharacteristic
391C3×C4C5×#12311yescharacteristic
392Dic3—42no—
393Dic3—81no—
394C2×C5—21no—
395C2×C5—21no—
396C2×C5—21no—
397C2×C5—81no—
398C2×C5—124no—
399C2×C5#495611yescharacteristic
400C23—21no—
401C23—62no—
402C23—62no—
403C23—62no—
404C23—242no—
405C23C5×D3×D411yescharacteristic
406Q8—21no—
407Q8—21no—
408D4—21no—
409D4—21no—
410D4—34no—
411D4—41no—
412D4—41no—
413D4—62no—
414D4—62no—
415D4—62no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—41no—
419C2×C4—41no—
420C2×C4—62no—
421C2×C4—121no—
422C2×C4—244no—
423C2×C4C2×C4×C5×D311yescharacteristic
424C2×C4C5×#23511yescharacteristic
425C2×C4C5×D3×D411yescharacteristic
426C2×C4C5×D3×D411yescharacteristic
427C2×C4C5×#23711yescharacteristic
428C2×C4C2×C5×#6711yescharacteristic
429C8—41no—
430C8—62no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—81no—
435C2×C3C5×#38611yescharacteristic
436D3—44no—
437C5#7040711yescharacteristic, direct product factor, Sylow
438C22—41no—
439C22—41no—
440C22—64no—
441C22—81no—
442C22—124no—
443C22—242no—
444C22—242no—
445C22C5×#67⋊C411yescharacteristic
446C22C5×#88411yescharacteristic
447C22C5×#93711yescharacteristic
448C4—42no—
449C4—41no—
450C4—122no—
451C4—241no—
452C4C5×D3×C22⋊C411yescharacteristic
453C4C5×#88311yescharacteristic
454C4C4×C5×#6711yescharacteristic
455C4C5×#93811yescharacteristic
456C3C5×#190411yescharacteristic, complemented, Sylow
457C2—21no—
458C2—21no—
459C2—21no—
460C2—81no—
461C2—124no—
462C2C5×#495611yescharacteristic
subgroupG/H
centerC2×C5#4956
commutatorC2×C3×C4C22×C4×C5
FrattiniC22×C4C22×C5×D3
FittingC3×C5×#421C2
socleC2×C3×C5#386
prime radicalC2×C5×#949C2
cosocleC22×C3×C4C23×C5
hypercenterC5×#421D3
hypocenterC3C5×#1904
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C5 ◁ C22×C4×C5 ◁ C5×#421

Complements

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

NH ≅ G/Ntype
2. C5×#5521C2semidirect
3. C3×C5×#421C2semidirect
4. C5×#5240C2semidirect
5. C5×#5131C2semidirect
6. C5×#4559C2semidirect
7. C5×#4531C2semidirect
15. C2×C5×#215C4semidirect
16. C2×C5×#213C4semidirect
26. #70407C5direct (N × H)
29. C5×#421D3semidirect
39. C2×C3×C5×Q8C2×C4semidirect
41. C2×C3×C5×D4C2×C4semidirect
68. C2×C5×C3⋊C8C2×C4semidirect
70. #5521C2×C5semidirect
71. C3×#421C2×C5semidirect
72. #5240C2×C5semidirect
73. #5131C2×C5semidirect
74. #4559C2×C5semidirect
75. #4531C2×C5semidirect
131. C2×#215C4×C5semidirect
132. C2×#213C4×C5semidirect
147. C2×C5×Q8C4×D3semidirect
155. C2×C5×D4C4×D3semidirect
179. #421C5×D3semidirect
207. C2×C3×Q8C2×C4×C5semidirect
209. C2×C3×D4C2×C4×C5semidirect
236. C2×C3⋊C8C2×C4×C5semidirect
345. C2×Q8C4×C5×D3semidirect
353. C2×D4C4×C5×D3semidirect
375. C3×C5#1904semidirect
437. C5#70407direct (N × H)
456. C3C5×#1904semidirect

Maximal subgroups

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

subgroupindex
C2×C5×#9492
C5×#55212
C3×C5×#4212
C5×#52402
C5×#51312
C5×#45592
C5×#45312
C5×#19043
#704075