Finite Group Databasebeta

← C2×C5×#5838 #14510127

Subgroups — C2×C5×#5838 #14510127

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×2−1+4C211yesmaximal, characteristic, complemented
2C2×C5×#1010C211yesmaximal, characteristic, complemented
3C5×#5838C2116yesmaximal, direct product factor
4C2×C5×#951C213yesmaximal, complemented
5C2×C5×#950C213yesmaximal, complemented
6C2×C5×#948C211yesmaximal, characteristic, complemented
7C22×C5×#216C213yesmaximal, complemented
8C2×C5×#942C213yesmaximal, complemented
9C2×C5×#578—31nomaximal, Hall
10C3×C5×2−1+4—24no—
11C3×C5×2−1+4C2218yescomplemented
12C2×C3×C5×#41—23no—
13C2×C3×C5×#41C2213yes—
14C2×C3×C5×#41C2211yescharacteristic
15C22×C3×C5×Q8—21no—
16C22×C3×C5×Q8C2213yes—
17C5×#1010—24no—
18C5×#1010C2218yescomplemented
19C2×C5×D3×Q8—21no—
20C2×C5×#237—23no—
21C2×C5×#235C2213yes—
22C22×C5×Dic6C2213yes—
23C5×#951C22124yescomplemented
24C5×#950C22124yescomplemented
25C5×#948C2218yescomplemented
26C2×C5×#216C2216yes—
27C2×C5×#216C2213yes—
28C2×C5×#216C22124yescomplemented
29C5×#942C22124yescomplemented
30C2×C5×#215C2213yes—
31C2×C5×#214C2213yes—
32C2×C5×#213C2211yescharacteristic
33C2×C5×#208C2213yes—
34C22×C5×C3⋊C8C2213yes—
35C2×#5838C511yesmaximal, characteristic, direct product factor, Hall
36C2×C5×2−1+4—31no—
37C2×C5×2−1+4D311yescharacteristic, complemented
38C5×#578—316no—
39C2×C5×#137—33no—
40C2×C5×#137—33no—
41C2×C5×#135—33no—
42C22×C5×Q16—33no—
43C2×C5×#131—31no—
44C3×C5×#41—224no—
45C3×C5×#41—26no—
46C3×C5×#41D414yes—
47C3×C5×#41C23112yes—
48C3×C5×#41C2314yes—
49C2×C3×C5×Q8—28no—
50C2×C3×C5×Q8—23no—
51C2×C3×C5×Q8—26no—
52C2×C3×C5×Q8D411yescharacteristic
53C2×C3×C5×Q8C2313yes—
54C2×C3×C5×Q8C23112yes—
55C2×C3×C5×D4—23no—
56C2×C3×C5×D4D413yes—
57C2×C3×C5×D4C2311yescharacteristic
58C22×C3×C4×C5—23no—
59C22×C3×C4×C5—23no—
60C22×C3×C4×C5C2313yes—
61C2×C5×#67—23no—
62C22×C5×Dic3—23no—
63C5×D3×Q8—28no—
64C5×#237—224no—
65C5×#235—26no—
66C5×#235C23112yes—
67C2×C5×D12C2311yescharacteristic
68C2×C4×C5×D3—23no—
69C2×C5×Dic6—23no—
70C2×C5×Dic6—26no—
71C2×C5×Dic6C2313yes—
72C2×C5×Dic6C23112yes—
73C5×#216C23124yes—
74C5×#216C23112yes—
75C5×#215C23112yes—
76C5×#214C23112yes—
77C5×#213C2314yes—
78C5×#208C23112yes—
79C2×C5×C3⋊C8C2311yescharacteristic
80C2×C5×C3⋊C8C2313yes—
81C2×C5×C3⋊C8C23112yes—
82C2×C3×2−1+4C2×C511yescharacteristic, complemented
83C2×#1010C2×C511yescharacteristic, complemented
84#5838C2×C5116yesdirect product factor
85C2×#951C2×C513yescomplemented
86C2×#950C2×C513yescomplemented
87C2×#948C2×C511yescharacteristic, complemented
88C22×#216C2×C513yescomplemented
89C2×#942C2×C513yescomplemented
90C5×2−1+4—24no—
91C5×2−1+4—38no—
92C5×2−1+4—64no—
93C5×2−1+4C2×D318yescomplemented
94C2×C5×#41—23no—
95C2×C5×#41—33no—
96C2×C5×#41—63no—
97C2×C5×#41C2×D313yes—
98C2×C5×#41C2×D311yescharacteristic
99C22×C5×Q8—21no—
100C22×C5×Q8—33no—
101C22×C5×Q8—61no—
102C22×C5×Q8C2×D313yes—
103C5×#137—324no—
104C5×#137—324no—
105C5×#135—324no—
106C2×C5×Q16—33no—
107C2×C5×Q16—36no—
108C2×C5×Q16—324no—
109C2×C5×SD16—33no—
110C2×C5×SD16—33no—
111C2×C5×D8—31no—
112C5×#131—38no—
113C2×C5×M16—33no—
114C22×C5×C8—33no—
115C2×#578—31noSylow
116C23×C3×C5—21no—
117C23×C3×C5C2×D413yes—
118C22×C5×D3—21no—
119C3×C5×Q8—23no—
120C3×C5×Q8—212no—
121C3×C5×Q8C2×D414yes—
122C3×C5×Q8C2416yes—
123C3×C5×D4—212no—
124C3×C5×D4—21no—
125C3×C5×D4C2×D4112yes—
126C3×C5×D4C2412yes—
127C2×C3×C4×C5—23no—
128C2×C3×C4×C5—212no—
129C2×C3×C4×C5—212no—
130C2×C3×C4×C5C2×D413yes—
131C2×C3×C4×C5C2×D416yes—
132C2×C3×C4×C5C2411yescharacteristic
133C2×C3×C4×C5C2416yes—
134C5×#67—212no—
135C2×C5×Dic3—23no—
136C2×C5×Dic3—212no—
137C5×D12—21no—
138C5×D12C2412yes—
139C4×C5×D3—212no—
140C5×Dic6—23no—
141C5×Dic6—212no—
142C5×Dic6C2416yes—
143C5×C3⋊C8C2412yes—
144C5×C3⋊C8C2416yes—
145C3×2−1+4—24no—
146C3×2−1+4C22×C518yescomplemented
147C2×C3×#41—23no—
148C2×C3×#41C22×C513yes—
149C2×C3×#41C22×C511yescharacteristic
150C22×C3×Q8—21no—
151C22×C3×Q8C22×C513yes—
152#1010—24no—
153#1010C22×C518yescomplemented
154C2×D3×Q8—21no—
155C2×#237—23no—
156C2×#235C22×C513yes—
157C22×Dic6C22×C513yes—
158#951C22×C5124yescomplemented
159#950C22×C5124yescomplemented
160#948C22×C518yescomplemented
161C2×#216C22×C516yes—
162C2×#216C22×C513yes—
163C2×#216C22×C5124yescomplemented
164#942C22×C5124yescomplemented
165C2×#215C22×C513yes—
166C2×#214C22×C513yes—
167C2×#213C22×C511yescharacteristic
168C2×#208C22×C513yes—
169C22×C3⋊C8C22×C513yes—
170C5×#41—224no—
171C5×#41—26no—
172C5×#41—312no—
173C5×#41—624no—
174C5×#41—66no—
175C5×#41#6714yes—
176C5×#41C22×D3112yes—
177C5×#41C22×D314yes—
178C2×C5×Q8—28no—
179C2×C5×Q8—23no—
180C2×C5×Q8—26no—
181C2×C5×Q8—33no—
182C2×C5×Q8—312no—
183C2×C5×Q8—68no—
184C2×C5×Q8—63no—
185C2×C5×Q8—66no—
186C2×C5×Q8#6711yescharacteristic
187C2×C5×Q8C22×D313yes—
188C2×C5×Q8C22×D3112yes—
189C2×C5×D4—23no—
190C2×C5×D4—31no—
191C2×C5×D4—63no—
192C2×C5×D4#6713yes—
193C2×C5×D4C22×D311yescharacteristic
194C22×C4×C5—23no—
195C22×C4×C5—23no—
196C22×C4×C5—63no—
197C22×C4×C5—63no—
198C22×C4×C5C22×D313yes—
199C5×Q16—312no—
200C5×Q16—324no—
201C5×SD16—312no—
202C5×SD16—312no—
203C5×D8—34no—
204C5×M16—312no—
205C2×C5×C8—31no—
206C2×C5×C8—33no—
207C2×C5×C8—312no—
208C2×2−1+4—31no—
209C2×2−1+4C5×D311yescharacteristic, complemented
210#578—316no—
211C2×#137—33no—
212C2×#137—33no—
213C2×#135—33no—
214C22×Q16—33no—
215C2×#131—31no—
216C22×C3×C5—26no—
217C22×C3×C5—22no—
218C22×C3×C5—42no—
219C22×C3×C5C22×D416yes—
220C22×C3×C5C22×D411yescharacteristic
221C2×C5×D3—22no—
222C2×C5×D3—42no—
223C3×C4×C5—26no—
224C3×C4×C5C22×D411yescharacteristic
225C3×C4×C5C22×D416yes—
226C3×C4×C5C2511yescharacteristic
227C5×Dic3—26no—
228C3×#41—224no—
229C3×#41—26no—
230C3×#41C5×D414yes—
231C3×#41C23×C5112yes—
232C3×#41C23×C514yes—
233C2×C3×Q8—28no—
234C2×C3×Q8—23no—
235C2×C3×Q8—26no—
236C2×C3×Q8C5×D411yescharacteristic
237C2×C3×Q8C23×C513yes—
238C2×C3×Q8C23×C5112yes—
239C2×C3×D4—23no—
240C2×C3×D4C5×D413yes—
241C2×C3×D4C23×C511yescharacteristic
242C22×C3×C4—23no—
243C22×C3×C4—23no—
244C22×C3×C4C23×C513yes—
245C2×#67—23no—
246C22×Dic3—23no—
247D3×Q8—28no—
248#237—224no—
249#235—26no—
250#235C23×C5112yes—
251C2×D12C23×C511yescharacteristic
252C2×C4×D3—23no—
253C2×Dic6—23no—
254C2×Dic6—26no—
255C2×Dic6C23×C513yes—
256C2×Dic6C23×C5112yes—
257#216C23×C5124yes—
258#216C23×C5112yes—
259#215C23×C5112yes—
260#214C23×C5112yes—
261#213C23×C514yes—
262#208C23×C5112yes—
263C2×C3⋊C8C23×C511yescharacteristic
264C2×C3⋊C8C23×C513yes—
265C2×C3⋊C8C23×C5112yes—
266C23×C5—21no—
267C23×C5—61no—
268C23×C5C2×#6713yes—
269C5×Q8—212no—
270C5×Q8—23no—
271C5×Q8—36no—
272C5×Q8—612no—
273C5×Q8—63no—
274C5×Q8C2×#6714yes—
275C5×Q8C23×D316yes—
276C5×D4—212no—
277C5×D4—21no—
278C5×D4—32no—
279C5×D4—612no—
280C5×D4—61no—
281C5×D4C2×#67112yes—
282C5×D4C23×D312yes—
283C2×C4×C5—212no—
284C2×C4×C5—23no—
285C2×C4×C5—212no—
286C2×C4×C5—612no—
287C2×C4×C5—63no—
288C2×C4×C5—612no—
289C2×C4×C5C2×#6716yes—
290C2×C4×C5C2×#6713yes—
291C2×C4×C5C23×D316yes—
292C2×C4×C5C23×D311yescharacteristic
293C5×C8—32no—
294C5×C8—36no—
2952−1+4—24no—
2962−1+4—38no—
2972−1+4—64no—
2982−1+4C2×C5×D318yescomplemented
299C2×#41—23no—
300C2×#41—33no—
301C2×#41—63no—
302C2×#41C2×C5×D313yes—
303C2×#41C2×C5×D311yescharacteristic
304C22×Q8—21no—
305C22×Q8—33no—
306C22×Q8—61no—
307C22×Q8C2×C5×D313yes—
308#137—324no—
309#137—324no—
310#135—324no—
311C2×Q16—33no—
312C2×Q16—36no—
313C2×Q16—324no—
314C2×SD16—33no—
315C2×SD16—33no—
316C2×D8—31no—
317#131—38no—
318C2×M16—33no—
319C22×C8—33no—
320C2×C3×C5—26no—
321C2×C3×C5—42no—
322C2×C3×C5#57812yescomplemented
323C2×C3×C5C23×D411yescharacteristic
324C5×D3—42no—
325C23×C3—21no—
326C23×C3C2×C5×D413yes—
327C22×D3—21no—
328C3×Q8—23no—
329C3×Q8—212no—
330C3×Q8C2×C5×D414yes—
331C3×Q8C24×C516yes—
332C3×D4—212no—
333C3×D4—21no—
334C3×D4C2×C5×D4112yes—
335C3×D4C24×C512yes—
336C2×C3×C4—23no—
337C2×C3×C4—212no—
338C2×C3×C4—212no—
339C2×C3×C4C2×C5×D413yes—
340C2×C3×C4C2×C5×D416yes—
341C2×C3×C4C24×C511yescharacteristic
342C2×C3×C4C24×C516yes—
343#67—212no—
344C2×Dic3—23no—
345C2×Dic3—212no—
346D12—21no—
347D12C24×C512yes—
348C4×D3—212no—
349Dic6—23no—
350Dic6—212no—
351Dic6C24×C516yes—
352C3⋊C8C24×C512yes—
353C3⋊C8C24×C516yes—
354C22×C5—26no—
355C22×C5—22no—
356C22×C5—42no—
357C22×C5—62no—
358C22×C5—122no—
359C22×C5C22×#6716yes—
360C22×C5C22×#6711yescharacteristic
361C4×C5—26no—
362C4×C5—66no—
363C4×C5C22×#6716yes—
364C4×C5C22×#6711yescharacteristic
365C4×C5C24×D311yescharacteristic
366#41—224no—
367#41—26no—
368#41—312no—
369#41—624no—
370#41—66no—
371#41C5×#6714yes—
372#41C22×C5×D3112yes—
373#41C22×C5×D314yes—
374C2×Q8—28no—
375C2×Q8—23no—
376C2×Q8—26no—
377C2×Q8—33no—
378C2×Q8—312no—
379C2×Q8—68no—
380C2×Q8—63no—
381C2×Q8—66no—
382C2×Q8C5×#6711yescharacteristic
383C2×Q8C22×C5×D313yes—
384C2×Q8C22×C5×D3112yes—
385C2×D4—23no—
386C2×D4—31no—
387C2×D4—63no—
388C2×D4C5×#6713yes—
389C2×D4C22×C5×D311yescharacteristic
390C22×C4—23no—
391C22×C4—23no—
392C22×C4—63no—
393C22×C4—63no—
394C22×C4C22×C5×D313yes—
395Q16—312no—
396Q16—324no—
397SD16—312no—
398SD16—312no—
399D8—34no—
400M16—312no—
401C2×C8—31no—
402C2×C8—33no—
403C2×C8—312no—
404C3×C5C2×#57811yescharacteristic, complemented, Hall
405C22×C3—26no—
406C22×C3—22no—
407C22×C3—42no—
408C22×C3C22×C5×D416yes—
409C22×C3C22×C5×D411yescharacteristic
410C2×D3—22no—
411C2×D3—42no—
412C3×C4—26no—
413C3×C4C22×C5×D411yescharacteristic
414C3×C4C22×C5×D416yes—
415C3×C4C25×C511yescharacteristic
416Dic3—26no—
417C2×C5—26no—
418C2×C5—42no—
419C2×C5—122no—
420C2×C5#583812yesdirect product factor
421C2×C5C23×#6711yescharacteristic
422C23—21no—
423C23—61no—
424C23C2×C5×#6713yes—
425Q8—212no—
426Q8—23no—
427Q8—36no—
428Q8—612no—
429Q8—63no—
430Q8C2×C5×#6714yes—
431Q8C23×C5×D316yes—
432D4—212no—
433D4—21no—
434D4—32no—
435D4—612no—
436D4—61no—
437D4C2×C5×#67112yes—
438D4C23×C5×D312yes—
439C2×C4—23no—
440C2×C4—212no—
441C2×C4—212no—
442C2×C4—63no—
443C2×C4—612no—
444C2×C4—612no—
445C2×C4C2×C5×#6713yes—
446C2×C4C2×C5×#6716yes—
447C2×C4C23×C5×D311yescharacteristic
448C2×C4C23×C5×D316yes—
449C8—32no—
450C8—36no—
451C2×C3—26no—
452C2×C3—42no—
453C2×C3C5×#57812yescomplemented
454C2×C3C23×C5×D411yescharacteristic
455D3—42no—
456C5C2×#583811yescharacteristic, direct product factor, Sylow
457C22—26no—
458C22—22no—
459C22—42no—
460C22—62no—
461C22—122no—
462C22C22×C5×#6716yes—
463C22C22×C5×#6711yescharacteristic
464C4—26no—
465C4—66no—
466C4C22×C5×#6716yes—
467C4C22×C5×#6711yescharacteristic
468C4C24×C5×D311yescharacteristic
469C3C2×C5×#57811yescharacteristic, complemented, Sylow
470C2—26no—
471C2—42no—
472C2—122no—
473C2C5×#583812yesdirect product factor
474C2C23×C5×#6711yescharacteristic
subgroupG/H
centerC22×C5C22×#67
commutator, cosocleC3×C4C25×C5
FrattiniC4C24×C5×D3
FittingC2×C3×C5×2−1+4C2
socleC22×C3×C5C22×D4
hypercenterC2×C5×2−1+4D3
hypocenterC3C2×C5×#578
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C2×C5×#41 ◁ C2×C5×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×2−1+4C2semidirect
2. C2×C5×#1010C2semidirect
3. C5×#5838C2direct (N × H)
4. C2×C5×#951C2semidirect
5. C2×C5×#950C2semidirect
6. C2×C5×#948C2semidirect
7. C22×C5×#216C2semidirect
8. C2×C5×#942C2semidirect
11. C3×C5×2−1+4C22semidirect
18. C5×#1010C22semidirect
23. C5×#951C22semidirect
24. C5×#950C22semidirect
25. C5×#948C22semidirect
28. C2×C5×#216C22semidirect
29. C5×#942C22semidirect
35. C2×#5838C5direct (N × H)
37. C2×C5×2−1+4D3semidirect
82. C2×C3×2−1+4C2×C5semidirect
83. C2×#1010C2×C5semidirect
84. #5838C2×C5direct (N × H)
85. C2×#951C2×C5semidirect
86. C2×#950C2×C5semidirect
87. C2×#948C2×C5semidirect
88. C22×#216C2×C5semidirect
89. C2×#942C2×C5semidirect
93. C5×2−1+4C2×D3semidirect
146. C3×2−1+4C22×C5semidirect
153. #1010C22×C5semidirect
158. #951C22×C5semidirect
159. #950C22×C5semidirect
160. #948C22×C5semidirect
163. C2×#216C22×C5semidirect
164. #942C22×C5semidirect
209. C2×2−1+4C5×D3semidirect
298. 2−1+4C2×C5×D3semidirect
322. C2×C3×C5#578semidirect
404. C3×C5C2×#578semidirect
420. C2×C5#5838direct (N × H)
453. C2×C3C5×#578semidirect
456. C5C2×#5838direct (N × H)
469. C3C2×C5×#578semidirect
473. C2C5×#5838direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×2−1+42
C2×C5×#10102
C5×#58382
C2×C5×#9512
C2×C5×#9502
C2×C5×#9482
C22×C5×#2162
C2×C5×#9422
C2×C5×#5783
C2×#58385