Finite Group Databasebeta

← C5×#70148 #14313623

Subgroups — C5×#70148 #14313623

Order 1920.

500 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C5×#5832C211yesmaximal, characteristic
2C3×C5×#413C211yesmaximal, characteristic, complemented
3C5×#5237C211yesmaximal, characteristic, complemented
4C5×#4478C212yesmaximal, complemented
5C5×#4477C212yesmaximal, complemented
6C5×#2132—31nomaximal, Hall
7C2×C3×C5×#41C2211yescharacteristic
8C2×C5×#235C411yescharacteristic
9C2×C3×C5×M16—21no—
10C5×#947C2211yescharacteristic
11C5×#944C2211yescharacteristic
12C5×#940C411yescharacteristic
13C5×#939—21no—
14C5×#939—21no—
15C5×#936C411yescharacteristic
16C4×C5×#67—21no—
17C4×C5×#67—21no—
18C2×C4×C5×Dic3C411yescharacteristic
19C2×C5×#208—21no—
20C3×C5×#101C2212yes—
21C3×C5×#100—21no—
22C5×#836C2212yes—
23C5×#833—21no—
24#70148C511yesmaximal, characteristic, direct product factor, Hall
25C5×#532—31no—
26C5×#413—31no—
27C5×#413D311yescharacteristic, complemented
28C5×#356—32no—
29C5×#355—32no—
30C3×C5×#41—41no—
31C3×C5×#41—41no—
32C2×C3×C5×Q8C2311yescharacteristic
33C2×C3×C5×D4C2×C411yescharacteristic
34C2×C3×C5×D4D411yescharacteristic
35C2×C3×C5×D4D411yescharacteristic
36C22×C3×C4×C5C2×C411yescharacteristic
37C22×C3×C4×C5D411yescharacteristic
38C22×C3×C4×C5D411yescharacteristic
39C2×C5×#67—21no—
40C2×C5×#67—21no—
41C2×C5×#67—21no—
42C22×C5×Dic3—21no—
43C5×#235—41no—
44C5×#235—41no—
45C2×C5×D12C2×C411yescharacteristic
46C2×C4×C5×D3—21no—
47C2×C5×Dic6C2×C411yescharacteristic
48C3×C5×M16—22no—
49C3×C5×M16—41no—
50C2×C3×C5×C8—41no—
51C5×#217—21no—
52C5×#217—21no—
53C5×(C2×D3)⋊C4—21no—
54C5×(C2×D3)⋊C4—21no—
55C5×Dic3⋊C4—21no—
56C5×Dic3⋊C4—21no—
57C4×C5×Dic3—21no—
58C4×C5×Dic3C2×C411yescharacteristic
59C4×C5×Dic3C2×C411yescharacteristic
60C5×#208—22no—
61C5×#208—41no—
62C2×C5×C3⋊C8—41no—
63#5832C2×C511yescharacteristic
64C3×#413C2×C511yescharacteristic, complemented
65#5237C2×C511yescharacteristic, complemented
66#4478C2×C512yescomplemented
67#4477C2×C512yescomplemented
68C2×C5×#41—31no—
69C2×C5×#41C2×D311yescharacteristic
70C2×C5×M16—21no—
71C2×C5×M16—61no—
72C5×C4⋊Q8—31no—
73C5×#127—31no—
74C5×#124—31no—
75C5×#124—31no—
76C5×#121—61no—
77C5×#121—61no—
78C4×C5×D4—61no—
79C4×C5×D4—61no—
80C2×C42×C5—31no—
81C5×#101—32no—
82C5×#101C2×D312yes—
83C5×#100—21no—
84C5×#100—61no—
85#2132—31noSylow
86C23×C3×C5C22⋊C411yescharacteristic
87C23×C3×C5C22⋊C411yescharacteristic
88C23×C3×C5C22⋊C411yescharacteristic
89C22×C5×D3—21no—
90C3×C5×Q8—41no—
91C3×C5×D4—41no—
92C3×C5×D4—41no—
93C3×C5×D4—41no—
94C2×C3×C4×C5—21no—
95C2×C3×C4×C5—21no—
96C2×C3×C4×C5—21no—
97C2×C3×C4×C5—21no—
98C2×C3×C4×C5—21no—
99C2×C3×C4×C5—21no—
100C2×C3×C4×C5C22⋊C411yescharacteristic
101C2×C3×C4×C5C22×C411yescharacteristic
102C2×C3×C4×C5C2×D411yescharacteristic
103C2×C3×C4×C5C2×D411yescharacteristic
104C5×#67—42no—
105C5×#67—42no—
106C5×#67—42no—
107C2×C5×Dic3—21no—
108C2×C5×Dic3—21no—
109C2×C5×Dic3—21no—
110C2×C5×Dic3—42no—
111C5×D12—41no—
112C4×C5×D3—41no—
113C4×C5×D3—41no—
114C5×Dic6—41no—
115C3×C5×C8—42no—
116C5×C3⋊C8—42no—
117C2×C3×#41C22×C511yescharacteristic
118C2×#235C4×C511yescharacteristic
119C2×C3×M16—21no—
120#947C22×C511yescharacteristic
121#944C22×C511yescharacteristic
122#940C4×C511yescharacteristic
123#939—21no—
124#939—21no—
125#936C4×C511yescharacteristic
126C4×#67—21no—
127C4×#67—21no—
128C2×C4×Dic3C4×C511yescharacteristic
129C2×#208—21no—
130C3×#101C22×C512yes—
131C3×#100—21no—
132#836C22×C512yes—
133#833—21no—
134C5×#41—41no—
135C5×#41—41no—
136C5×#41—121no—
137C5×#41—121no—
138C2×C5×Q8—31no—
139C2×C5×Q8C22×D311yescharacteristic
140C2×C5×D4—31no—
141C2×C5×D4—61no—
142C2×C5×D4—61no—
143C2×C5×D4—61no—
144C2×C5×D4C4×D311yescharacteristic
145C2×C5×D4D1211yescharacteristic
146C2×C5×D4#6711yescharacteristic
147C22×C4×C5—61no—
148C22×C4×C5—61no—
149C22×C4×C5C4×D311yescharacteristic
150C22×C4×C5D1211yescharacteristic
151C22×C4×C5#6711yescharacteristic
152C5×M16—22no—
153C5×M16—41no—
154C5×M16—62no—
155C5×M16—121no—
156C2×C5×C8—41no—
157C2×C5×C8—121no—
158C5×C4⋊C4—61no—
159C5×C4⋊C4—61no—
160C5×C22⋊C4—61no—
161C5×C22⋊C4—61no—
162C5×C22⋊C4—61no—
163C5×C22⋊C4—61no—
164C42×C5—31no—
165C42×C5—31no—
166C42×C5—61no—
167#532—31no—
168#413—31no—
169#413C5×D311yescharacteristic, complemented
170#356—32no—
171#355—32no—
172C22×C3×C5—21no—
173C22×C3×C5—21no—
174C22×C3×C5—21no—
175C22×C3×C5—41no—
176C22×C3×C5—41no—
177C22×C3×C5—41no—
178C22×C3×C5C2×C22⋊C411yescharacteristic
179C2×C5×D3—41no—
180C2×C5×D3—41no—
181C2×C5×D3—41no—
182C3×C4×C5—21no—
183C3×C4×C5—21no—
184C3×C4×C5—21no—
185C3×C4×C5#9911yescharacteristic
186C3×C4×C5#9911yescharacteristic
187C5×Dic3—22no—
188C5×Dic3—41no—
189C5×Dic3—41no—
190C3×#41—41no—
191C3×#41—41no—
192C2×C3×Q8C23×C511yescharacteristic
193C2×C3×D4C2×C4×C511yescharacteristic
194C2×C3×D4C5×D411yescharacteristic
195C2×C3×D4C5×D411yescharacteristic
196C22×C3×C4C2×C4×C511yescharacteristic
197C22×C3×C4C5×D411yescharacteristic
198C22×C3×C4C5×D411yescharacteristic
199C2×#67—21no—
200C2×#67—21no—
201C2×#67—21no—
202C22×Dic3—21no—
203#235—41no—
204#235—41no—
205C2×D12C2×C4×C511yescharacteristic
206C2×C4×D3—21no—
207C2×Dic6C2×C4×C511yescharacteristic
208C3×M16—22no—
209C3×M16—41no—
210C2×C3×C8—41no—
211#217—21no—
212#217—21no—
213(C2×D3)⋊C4—21no—
214(C2×D3)⋊C4—21no—
215Dic3⋊C4—21no—
216Dic3⋊C4—21no—
217C4×Dic3—21no—
218C4×Dic3C2×C4×C511yescharacteristic
219C4×Dic3C2×C4×C511yescharacteristic
220#208—22no—
221#208—41no—
222C2×C3⋊C8—41no—
223C23×C5—61no—
224C23×C5(C2×D3)⋊C411yescharacteristic
225C23×C5(C2×D3)⋊C411yescharacteristic
226C23×C5(C2×D3)⋊C411yescharacteristic
227C5×Q8—41no—
228C5×Q8—121no—
229C5×D4—41no—
230C5×D4—41no—
231C5×D4—41no—
232C5×D4—121no—
233C5×D4—122no—
234C5×D4—122no—
235C5×D4—122no—
236C2×C4×C5—21no—
237C2×C4×C5—21no—
238C2×C4×C5—21no—
239C2×C4×C5—21no—
240C2×C4×C5—21no—
241C2×C4×C5—21no—
242C2×C4×C5—61no—
243C2×C4×C5—61no—
244C2×C4×C5—61no—
245C2×C4×C5—122no—
246C2×C4×C5—121no—
247C2×C4×C5—121no—
248C2×C4×C5(C2×D3)⋊C411yescharacteristic
249C2×C4×C5C2×C4×D311yescharacteristic
250C2×C4×C5C2×D1211yescharacteristic
251C2×C4×C5C2×#6711yescharacteristic
252C5×C8—42no—
253C5×C8—122no—
254C2×#41—31no—
255C2×#41C2×C5×D311yescharacteristic
256C2×M16—21no—
257C2×M16—61no—
258C4⋊Q8—31no—
259#127—31no—
260#124—31no—
261#124—31no—
262#121—61no—
263#121—61no—
264C4×D4—61no—
265C4×D4—61no—
266C2×C42—31no—
267#101—32no—
268#101C2×C5×D312yes—
269#100—21no—
270#100—61no—
271C2×C3×C5—21no—
272C2×C3×C5—41no—
273C2×C3×C5—41no—
274C2×C3×C5—41no—
275C2×C3×C5C2×#9911yescharacteristic
276C5×D3—81no—
277C23×C3C5×C22⋊C411yescharacteristic
278C23×C3C5×C22⋊C411yescharacteristic
279C23×C3C5×C22⋊C411yescharacteristic
280C22×D3—21no—
281C3×Q8—41no—
282C3×D4—41no—
283C3×D4—41no—
284C3×D4—41no—
285C2×C3×C4—21no—
286C2×C3×C4—21no—
287C2×C3×C4—21no—
288C2×C3×C4—21no—
289C2×C3×C4—21no—
290C2×C3×C4—21no—
291C2×C3×C4C5×C22⋊C411yescharacteristic
292C2×C3×C4C22×C4×C511yescharacteristic
293C2×C3×C4C2×C5×D411yescharacteristic
294C2×C3×C4C2×C5×D411yescharacteristic
295#67—42no—
296#67—42no—
297#67—42no—
298C2×Dic3—21no—
299C2×Dic3—21no—
300C2×Dic3—21no—
301C2×Dic3—42no—
302D12—41no—
303C4×D3—41no—
304C4×D3—41no—
305Dic6—41no—
306C3×C8—42no—
307C3⋊C8—42no—
308C22×C5—21no—
309C22×C5—21no—
310C22×C5—21no—
311C22×C5—41no—
312C22×C5—41no—
313C22×C5—41no—
314C22×C5—121no—
315C22×C5—121no—
316C22×C5—121no—
317C22×C5C2×(C2×D3)⋊C411yescharacteristic
318C4×C5—21no—
319C4×C5—21no—
320C4×C5—21no—
321C4×C5—62no—
322C4×C5—121no—
323C4×C5—121no—
324C4×C5#80611yescharacteristic
325C4×C5#80611yescharacteristic
326#41—41no—
327#41—41no—
328#41—121no—
329#41—121no—
330C2×Q8—31no—
331C2×Q8C22×C5×D311yescharacteristic
332C2×D4—31no—
333C2×D4—61no—
334C2×D4—61no—
335C2×D4—61no—
336C2×D4C4×C5×D311yescharacteristic
337C2×D4C5×D1211yescharacteristic
338C2×D4C5×#6711yescharacteristic
339C22×C4—61no—
340C22×C4—61no—
341C22×C4C4×C5×D311yescharacteristic
342C22×C4C5×D1211yescharacteristic
343C22×C4C5×#6711yescharacteristic
344M16—22no—
345M16—41no—
346M16—62no—
347M16—121no—
348C2×C8—41no—
349C2×C8—121no—
350C4⋊C4—61no—
351C4⋊C4—61no—
352C22⋊C4—61no—
353C22⋊C4—61no—
354C22⋊C4—61no—
355C22⋊C4—61no—
356C42—31no—
357C42—31no—
358C42—61no—
359C3×C5#213211yescharacteristic, complemented, Hall
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—21no—
363C22×C3—41no—
364C22×C3—41no—
365C22×C3—41no—
366C22×C3C2×C5×C22⋊C411yescharacteristic
367C2×D3—41no—
368C2×D3—41no—
369C2×D3—41no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4C5×#9911yescharacteristic
374C3×C4C5×#9911yescharacteristic
375Dic3—22no—
376Dic3—41no—
377Dic3—41no—
378C2×C5—21no—
379C2×C5—41no—
380C2×C5—41no—
381C2×C5—41no—
382C2×C5—241no—
383C2×C5C2×#80611yescharacteristic
384C23—61no—
385C23C5×(C2×D3)⋊C411yescharacteristic
386C23C5×(C2×D3)⋊C411yescharacteristic
387C23C5×(C2×D3)⋊C411yescharacteristic
388Q8—41no—
389Q8—121no—
390D4—41no—
391D4—41no—
392D4—41no—
393D4—121no—
394D4—122no—
395D4—122no—
396D4—122no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—61no—
404C2×C4—61no—
405C2×C4—61no—
406C2×C4—122no—
407C2×C4—121no—
408C2×C4—121no—
409C2×C4C5×(C2×D3)⋊C411yescharacteristic
410C2×C4C2×C4×C5×D311yescharacteristic
411C2×C4C2×C5×D1211yescharacteristic
412C2×C4C2×C5×#6711yescharacteristic
413C8—42no—
414C8—122no—
415C2×C3—21no—
416C2×C3—41no—
417C2×C3—41no—
418C2×C3—41no—
419C2×C3C2×C5×#9911yescharacteristic
420D3—81no—
421C5#7014811yescharacteristic, direct product factor, Sylow
422C22—21no—
423C22—21no—
424C22—21no—
425C22—41no—
426C22—41no—
427C22—41no—
428C22—121no—
429C22—121no—
430C22—121no—
431C22C2×C5×(C2×D3)⋊C411yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—62no—
436C4—121no—
437C4—121no—
438C4C5×#80611yescharacteristic
439C4C5×#80611yescharacteristic
440C3C5×#213211yescharacteristic, complemented, Sylow
441C2—21no—
442C2—41no—
443C2—41no—
444C2—41no—
445C2—241no—
446C2C2×C5×#80611yescharacteristic
subgroupG/H
centerC4×C5#806
commutatorC2×C3×C4C22×C4×C5
FrattiniC2×Q8C22×C5×D3
FittingC3×C5×#413C2
socleC2×C3×C5C2×#99
prime radicalC5×#5832C2
cosocleC2×C3×Q8C23×C5
hypercenterC5×#413D3
hypocenterC3C5×#2132
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C2×C3 ▷ C3
UCSC1 ◁ C4×C5 ◁ C2×C4×C5 ◁ C2×C5×#41 ◁ C5×#413

Complements

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

NH ≅ G/Ntype
2. C3×C5×#413C2semidirect
3. C5×#5237C2semidirect
4. C5×#4478C2semidirect
5. C5×#4477C2semidirect
24. #70148C5direct (N × H)
27. C5×#413D3semidirect
64. C3×#413C2×C5semidirect
65. #5237C2×C5semidirect
66. #4478C2×C5semidirect
67. #4477C2×C5semidirect
169. #413C5×D3semidirect
359. C3×C5#2132semidirect
421. C5#70148direct (N × H)
440. C3C5×#2132semidirect

Maximal subgroups

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

subgroupindex
C5×#58322
C3×C5×#4132
C5×#52372
C5×#44782
C5×#44772
C5×#21323
#701485