Finite Group Databasebeta

← C2×C5×#5927 #14511429

Subgroups — C2×C5×#5927 #14511429

Order 1920.

1470 conjugacy classes of subgroups; only the 204 normal subgroups are shown.

normal subgroups only

This group has 1470 conjugacy classes of subgroups — too many to draw. Only its 204 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×2−1+4⋊C3C211yesmaximal, characteristic, complemented
2C5×#5927C218yesmaximal, direct product factor
3C2×C5×#985C211yesmaximal, characteristic, complemented
4C2×C5×#984C211yesmaximal, characteristic, complemented
5C2×C5×#983C212yesmaximal, complemented
6C22×C5×#226C212yesmaximal, complemented
7C2×C5×#578—31nomaximal, Hall
8C2×C5×#237—41nomaximal
9C5×2−1+4⋊C3C2214yescomplemented
10C2×C5×#41⋊C3C2211yescharacteristic
11C22×C5×SL(2,𝔽3)C2212yes—
12C5×#985C2214yescomplemented
13C5×#984C2214yescomplemented
14C5×#983C2218yescomplemented
15C2×C5×GL(2,𝔽3)C2211yescharacteristic
16C2×C5×#226C2211yescharacteristic
17C2×C5×#226C2212yes—
18C2×C5×#226C2218yescomplemented
19C2×#5927C511yesmaximal, characteristic, direct product factor, Hall
20C2×C5×2−1+4—31no—
21C2×C5×2−1+4D311yescharacteristic, complemented
22C5×#578—38no—
23C5×#578—38no—
24C2×C5×#137—31no—
25C2×C5×#137—32no—
26C2×C5×#137—31no—
27C2×C5×#137—32no—
28C2×C5×#135—32no—
29C2×C5×#135—31no—
30C22×C5×Q16—31no—
31C22×C5×Q16—32no—
32C2×C5×#131—31no—
33C2×C3×C5×D4—41no—
34C2×C5×#67—42no—
35C22×C5×Dic3—42no—
36C5×#237—48no—
37C2×C4×C5×D3—41no—
38C2×C5×Dic6—41no—
39C5×#41⋊C3C2312yes—
40C2×C5×SL(2,𝔽3)C2311yescharacteristic
41C2×C5×SL(2,𝔽3)C2314yes—
42C5×GL(2,𝔽3)C2312yes—
43C5×#226C2312yes—
44C5×#226C2314yes—
45C2×2−1+4⋊C3C2×C511yescharacteristic, complemented
46#5927C2×C518yesdirect product factor
47C2×#985C2×C511yescharacteristic, complemented
48C2×#984C2×C511yescharacteristic, complemented
49C2×#983C2×C512yescomplemented
50C22×#226C2×C512yescomplemented
51C5×2−1+4—34no—
52C5×2−1+4—38no—
53C5×2−1+4—64no—
54C5×2−1+4C2×D314yescomplemented
55C2×C5×#41—31no—
56C2×C5×#41—32no—
57C2×C5×#41—32no—
58C2×C5×#41—31no—
59C2×C5×#41—62no—
60C2×C5×#41—61no—
61C2×C5×#41C2×D311yescharacteristic
62C22×C5×Q8—31no—
63C22×C5×Q8—32no—
64C22×C5×Q8—31no—
65C22×C5×Q8—61no—
66C22×C5×Q8C2×D312yes—
67C5×#137—38no—
68C5×#137—38no—
69C5×#137—34no—
70C5×#137—316no—
71C5×#137—34no—
72C5×#137—38no—
73C5×#135—34no—
74C5×#135—316no—
75C5×#135—34no—
76C2×C5×Q16—32no—
77C2×C5×Q16—32no—
78C2×C5×Q16—32no—
79C2×C5×Q16—38no—
80C2×C5×Q16—38no—
81C2×C5×Q16—31no—
82C2×C5×Q16—32no—
83C2×C5×Q16—38no—
84C2×C5×SD16—32no—
85C2×C5×SD16—31no—
86C2×C5×SD16—32no—
87C2×C5×SD16—31no—
88C2×C5×D8—31no—
89C5×#131—38no—
90C2×C5×M16—32no—
91C2×C5×M16—31no—
92C22×C5×C8—32no—
93C22×C5×C8—31no—
94C2×#578—31noSylow
95C23×C3×C5—42no—
96C22×C5×D3—41no—
97C3×C5×D4—44no—
98C2×C3×C4×C5—41no—
99C5×#67—48no—
100C2×C5×Dic3—42no—
101C2×C5×Dic3—41no—
102C2×C5×Dic3—48no—
103C4×C5×D3—44no—
104C5×Dic6—44no—
105C5×SL(2,𝔽3)C2411yescharacteristic
106C2×#237—41no—
1072−1+4⋊C3C22×C514yescomplemented
108C2×#41⋊C3C22×C511yescharacteristic
109C22×SL(2,𝔽3)C22×C512yes—
110#985C22×C514yescomplemented
111#984C22×C514yescomplemented
112#983C22×C518yescomplemented
113C2×GL(2,𝔽3)C22×C511yescharacteristic
114C2×#226C22×C511yescharacteristic
115C2×#226C22×C512yes—
116C2×#226C22×C518yescomplemented
117C5×#41—34no—
118C5×#41—34no—
119C5×#41—32no—
120C5×#41—38no—
121C5×#41—38no—
122C5×#41—34no—
123C5×#41—64no—
124C5×#41—64no—
125C5×#41—62no—
126C5×#41—616no—
127C5×#41—68no—
128C5×#41C22×D312yes—
129C2×C5×Q8—31no—
130C2×C5×Q8—32no—
131C2×C5×Q8—34no—
132C2×C5×Q8—34no—
133C2×C5×Q8—32no—
134C2×C5×Q8—31no—
135C2×C5×Q8—38no—
136C2×C5×Q8—34no—
137C2×C5×Q8—62no—
138C2×C5×Q8—62no—
139C2×C5×Q8—64no—
140C2×C5×Q8—62no—
141C2×C5×Q8—68no—
142C2×C5×Q8—61no—
143C2×C5×Q8C22×D311yescharacteristic
144C2×C5×Q8C22×D314yes—
145C2×C5×D4—32no—
146C2×C5×D4—31no—
147C2×C5×D4—31no—
148C2×C5×D4—61no—
149C2×C5×D4—62no—
150C2×C5×D4S411yescharacteristic
151C22×C4×C5—32no—
152C22×C4×C5—31no—
153C22×C4×C5—61no—
154C22×C4×C5—62no—
155C22×C4×C5—61no—
156C22×C4×C5—62no—
157C22×C4×C5—61no—
158C5×Q16—38no—
159C5×Q16—32no—
160C5×Q16—38no—
161C5×Q16—38no—
162C5×Q16—34no—
163C5×Q16—32no—
164C5×Q16—34no—
165C5×SD16—38no—
166C5×SD16—34no—
167C5×SD16—38no—
168C5×SD16—32no—
169C5×SD16—32no—
170C5×D8—34no—
171C5×M16—38no—
172C5×M16—34no—
173C2×C5×C8—31no—
174C2×C5×C8—32no—
175C2×C5×C8—31no—
176C2×C5×C8—38no—
177C2×C5×C8—34no—
178C2×2−1+4—31no—
179C2×2−1+4C5×D311yescharacteristic, complemented
180#578—38no—
181#578—38no—
182C2×#137—31no—
183C2×#137—32no—
184C2×#137—31no—
185C2×#137—32no—
186C2×#135—32no—
187C2×#135—31no—
188C22×Q16—31no—
189C22×Q16—32no—
190C2×#131—31no—
191C22×C3×C5—44no—
192C22×C3×C5—41no—
193C22×C3×C5—84no—
194C2×C5×D3—42no—
195C2×C5×D3—82no—
196C3×C4×C5—42no—
197C5×Dic3—44no—
198C5×Dic3—42no—
199C2×C3×D4—41no—
200C2×#67—42no—
201C22×Dic3—42no—
202#237—48no—
203C2×C4×D3—41no—
204C2×Dic6—41no—
205#41⋊C3C23×C512yes—
206C2×SL(2,𝔽3)C23×C511yescharacteristic
207C2×SL(2,𝔽3)C23×C514yes—
208GL(2,𝔽3)C23×C512yes—
209#226C23×C512yes—
210#226C23×C514yes—
211C23×C5—31no—
212C23×C5—61no—
213C23×C5C2×S412yes—
214C5×Q8—31no—
215C5×Q8—34no—
216C5×Q8—34no—
217C5×Q8—34no—
218C5×Q8—32no—
219C5×Q8—62no—
220C5×Q8—62no—
221C5×Q8—61no—
222C5×Q8—68no—
223C5×Q8—64no—
224C5×Q8C23×D311yescharacteristic
225C5×D4—32no—
226C5×D4—38no—
227C5×D4—32no—
228C5×D4—61no—
229C5×D4—61no—
230C5×D4—64no—
231C5×D4—68no—
232C5×D4C2×S414yes—
233C2×C4×C5—34no—
234C2×C4×C5—34no—
235C2×C4×C5—31no—
236C2×C4×C5—32no—
237C2×C4×C5—32no—
238C2×C4×C5—32no—
239C2×C4×C5—64no—
240C2×C4×C5—68no—
241C2×C4×C5—64no—
242C2×C4×C5—68no—
243C2×C4×C5—62no—
244C2×C4×C5—61no—
245C2×C4×C5—64no—
246C2×C4×C5C2×S411yescharacteristic
247C5×C8—32no—
248C5×C8—34no—
249C5×C8—32no—
2502−1+4—34no—
2512−1+4—38no—
2522−1+4—64no—
2532−1+4C2×C5×D314yescomplemented
254C2×#41—31no—
255C2×#41—32no—
256C2×#41—32no—
257C2×#41—31no—
258C2×#41—62no—
259C2×#41—61no—
260C2×#41C2×C5×D311yescharacteristic
261C22×Q8—31no—
262C22×Q8—32no—
263C22×Q8—31no—
264C22×Q8—61no—
265C22×Q8C2×C5×D312yes—
266#137—38no—
267#137—38no—
268#137—34no—
269#137—316no—
270#137—34no—
271#137—38no—
272#135—34no—
273#135—316no—
274#135—34no—
275C2×Q16—32no—
276C2×Q16—32no—
277C2×Q16—32no—
278C2×Q16—38no—
279C2×Q16—38no—
280C2×Q16—31no—
281C2×Q16—32no—
282C2×Q16—38no—
283C2×SD16—32no—
284C2×SD16—31no—
285C2×SD16—32no—
286C2×SD16—31no—
287C2×D8—31no—
288#131—38no—
289C2×M16—32no—
290C2×M16—31no—
291C22×C8—32no—
292C22×C8—31no—
293C2×C3×C5—42no—
294C2×C3×C5—41no—
295C2×C3×C5—84no—
296C5×D3—82no—
297C23×C3—42no—
298C22×D3—41no—
299C3×D4—44no—
300C2×C3×C4—41no—
301#67—48no—
302C2×Dic3—42no—
303C2×Dic3—41no—
304C2×Dic3—48no—
305C4×D3—44no—
306Dic6—44no—
307SL(2,𝔽3)C24×C511yescharacteristic
308C22×C5—24no—
309C22×C5—32no—
310C22×C5—62no—
311C22×C5—62no—
312C22×C5—122no—
313C22×C5C22×S414yes—
314C22×C5C22×S411yescharacteristic
315C4×C5—31no—
316C4×C5—31no—
317C4×C5—34no—
318C4×C5—64no—
319C4×C5—62no—
320C4×C5C22×S412yes—
321#41—34no—
322#41—34no—
323#41—32no—
324#41—38no—
325#41—38no—
326#41—34no—
327#41—64no—
328#41—64no—
329#41—62no—
330#41—616no—
331#41—68no—
332#41C22×C5×D312yes—
333C2×Q8—31no—
334C2×Q8—32no—
335C2×Q8—34no—
336C2×Q8—34no—
337C2×Q8—32no—
338C2×Q8—31no—
339C2×Q8—38no—
340C2×Q8—34no—
341C2×Q8—62no—
342C2×Q8—62no—
343C2×Q8—64no—
344C2×Q8—62no—
345C2×Q8—68no—
346C2×Q8—61no—
347C2×Q8C22×C5×D311yescharacteristic
348C2×Q8C22×C5×D314yes—
349C2×D4—32no—
350C2×D4—31no—
351C2×D4—31no—
352C2×D4—61no—
353C2×D4—62no—
354C2×D4C5×S411yescharacteristic
355C22×C4—32no—
356C22×C4—31no—
357C22×C4—61no—
358C22×C4—62no—
359C22×C4—61no—
360C22×C4—62no—
361C22×C4—61no—
362Q16—38no—
363Q16—32no—
364Q16—38no—
365Q16—38no—
366Q16—34no—
367Q16—32no—
368Q16—34no—
369SD16—38no—
370SD16—34no—
371SD16—38no—
372SD16—32no—
373SD16—32no—
374D8—34no—
375M16—38no—
376M16—34no—
377C2×C8—31no—
378C2×C8—32no—
379C2×C8—31no—
380C2×C8—38no—
381C2×C8—34no—
382C3×C5—41noHall
383C22×C3—41no—
384C22×C3—44no—
385C22×C3—84no—
386C2×D3—42no—
387C2×D3—82no—
388C3×C4—42no—
389Dic3—44no—
390Dic3—42no—
391C2×C5—24no—
392C2×C5—62no—
393C2×C5—122no—
394C2×C5#592712yesdirect product factor
395C2×C5C23×S411yescharacteristic
396C23—31no—
397C23—61no—
398C23C2×C5×S412yes—
399Q8—31no—
400Q8—34no—
401Q8—34no—
402Q8—34no—
403Q8—32no—
404Q8—62no—
405Q8—62no—
406Q8—61no—
407Q8—68no—
408Q8—64no—
409Q8C23×C5×D311yescharacteristic
410D4—32no—
411D4—38no—
412D4—32no—
413D4—61no—
414D4—61no—
415D4—64no—
416D4—68no—
417D4C2×C5×S414yes—
418C2×C4—31no—
419C2×C4—34no—
420C2×C4—32no—
421C2×C4—34no—
422C2×C4—32no—
423C2×C4—32no—
424C2×C4—64no—
425C2×C4—68no—
426C2×C4—64no—
427C2×C4—62no—
428C2×C4—61no—
429C2×C4—68no—
430C2×C4—64no—
431C2×C4C2×C5×S411yescharacteristic
432C8—32no—
433C8—34no—
434C8—32no—
435C2×C3—42no—
436C2×C3—41no—
437C2×C3—84no—
438D3—82no—
439C5C2×#592711yescharacteristic, direct product factor, Sylow
440C22—24no—
441C22—32no—
442C22—62no—
443C22—62no—
444C22—122no—
445C22C22×C5×S414yes—
446C22C22×C5×S411yescharacteristic
447C4—31no—
448C4—31no—
449C4—34no—
450C4—64no—
451C4—62no—
452C4C22×C5×S412yes—
453C3—41noSylow
454C2—24no—
455C2—62no—
456C2—122no—
457C2C5×#592712yesdirect product factor
458C2C23×C5×S411yescharacteristic
subgroupG/H
center, socleC22×C5C22×S4
commutator, cosocle, hypocenterSL(2,𝔽3)C24×C5
FrattiniC2C23×C5×S4
FittingC2×C5×2−1+4D3
hypercenterC2×C5×D4S4
LCSG ▷ SL(2,𝔽3)
UCSC1 ◁ C22×C5 ◁ C2×C5×D4

Complements

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

NH ≅ G/Ntype
1. C2×C5×2−1+4⋊C3C2semidirect
2. C5×#5927C2direct (N × H)
3. C2×C5×#985C2semidirect
4. C2×C5×#984C2semidirect
5. C2×C5×#983C2semidirect
6. C22×C5×#226C2semidirect
9. C5×2−1+4⋊C3C22semidirect
12. C5×#985C22semidirect
13. C5×#984C22semidirect
14. C5×#983C22semidirect
18. C2×C5×#226C22semidirect
19. C2×#5927C5direct (N × H)
21. C2×C5×2−1+4D3semidirect
45. C2×2−1+4⋊C3C2×C5semidirect
46. #5927C2×C5direct (N × H)
47. C2×#985C2×C5semidirect
48. C2×#984C2×C5semidirect
49. C2×#983C2×C5semidirect
50. C22×#226C2×C5semidirect
54. C5×2−1+4C2×D3semidirect
107. 2−1+4⋊C3C22×C5semidirect
110. #985C22×C5semidirect
111. #984C22×C5semidirect
112. #983C22×C5semidirect
116. C2×#226C22×C5semidirect
179. C2×2−1+4C5×D3semidirect
253. 2−1+4C2×C5×D3semidirect
394. C2×C5#5927direct (N × H)
439. C5C2×#5927direct (N × H)
457. C2C5×#5927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×2−1+4⋊C32
C5×#59272
C2×C5×#9852
C2×C5×#9842
C2×C5×#9832
C22×C5×#2262
C2×C5×#5783
C2×C5×#2374
C2×#59275