Finite Group Databasebeta

← C2×C5×SL(2,ℤ/4)⋊C4 #14511217

Subgroups — C2×C5×SL(2,ℤ/4)⋊C4 #14511217

Order 1920.

998 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 998 conjugacy classes of subgroups — too many to draw. Only its 152 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
1C22×C4×C5×A4C211yesmaximal, characteristic
2C22×C5×SL(2,ℤ/4)C211yesmaximal, characteristic
3C22×C5×SL(2,ℤ/4)C211yesmaximal, characteristic
4C5×SL(2,ℤ/4)⋊C4C214yesmaximal, direct product factor
5C2×C5×#385—31nomaximal, Hall
6C23×C5×A4C2211yescharacteristic
7C2×C4×C5×A4—22no—
8C2×C4×C5×A4C2212yes—
9C2×C5×SL(2,ℤ/4)—22no—
10C2×C5×SL(2,ℤ/4)C414yescomplemented
11C2×C5×SL(2,ℤ/4)C2212yes—
12C2×C5×SL(2,ℤ/4)C2212yes—
13C2×C5×Dic3⋊C4—41nomaximal
14C2×SL(2,ℤ/4)⋊C4C511yesmaximal, characteristic, direct product factor, Hall
15C24×C4×C5D311yescharacteristic
16C22×C5×C4⋊C4—31no—
17C22×C5×C4⋊C4—31no—
18C22×C5×C22⋊C4—31no—
19C22×C5×C22⋊C4—31no—
20C5×#385—34no—
21C5×#385—34no—
22C2×C5×#95—31no—
23C2×C5×#95—31no—
24C22×C5×A4C2×C412yes—
25C22×C5×A4D412yes—
26C22×C5×A4Q812yes—
27C22×C5×A4C2311yescharacteristic
28C22×C3×C4×C5—41no—
29C22×C5×Dic3—41no—
30C22×C5×Dic3—41no—
31C4×C5×A4—22no—
32C5×SL(2,ℤ/4)—22no—
33C5×SL(2,ℤ/4)C2×C414yescomplemented
34C5×Dic3⋊C4—44no—
35C22×C4×A4C2×C511yescharacteristic
36C22×SL(2,ℤ/4)C2×C511yescharacteristic
37C22×SL(2,ℤ/4)C2×C511yescharacteristic
38SL(2,ℤ/4)⋊C4C2×C514yesdirect product factor
39C25×C5C2×D311yescharacteristic
40C23×C4×C5—22no—
41C23×C4×C5—31no—
42C23×C4×C5—31no—
43C23×C4×C5—31no—
44C23×C4×C5—31no—
45C23×C4×C5—32no—
46C23×C4×C5—31no—
47C23×C4×C5—31no—
48C23×C4×C5—62no—
49C23×C4×C5C2×D312yes—
50C2×C5×C4⋊C4—34no—
51C2×C5×C4⋊C4—34no—
52C2×C5×C4⋊C4—64no—
53C2×C5×C4⋊C4—61no—
54C2×C5×C4⋊C4—62no—
55C2×C5×C4⋊C4—61no—
56C2×C5×C22⋊C4—32no—
57C2×C5×C22⋊C4—34no—
58C2×C5×C22⋊C4—34no—
59C2×C5×C22⋊C4—32no—
60C2×C5×C22⋊C4—32no—
61C2×C5×C22⋊C4—32no—
62C2×C5×C22⋊C4—62no—
63C2×C5×C22⋊C4—62no—
64C5×#95—34no—
65C5×#95—34no—
66C2×#385—31noSylow
67C23×C3×C5—41no—
68C2×C5×A4C4⋊C414yescomplemented
69C2×C5×A4C22×C411yescharacteristic
70C2×C5×A4C2×D411yescharacteristic
71C2×C5×A4C2×Q811yescharacteristic
72C2×C3×C4×C5—42no—
73C2×C3×C4×C5—82no—
74C2×C5×Dic3—42no—
75C2×C5×Dic3—44no—
76C2×C5×Dic3—42no—
77C2×C5×Dic3—82no—
78C23×A4C22×C511yescharacteristic
79C2×C4×A4—22no—
80C2×C4×A4C22×C512yes—
81C2×SL(2,ℤ/4)—22no—
82C2×SL(2,ℤ/4)C4×C514yescomplemented
83C2×SL(2,ℤ/4)C22×C512yes—
84C2×SL(2,ℤ/4)C22×C512yes—
85C2×Dic3⋊C4—41no—
86C24×C5—31no—
87C24×C5—31no—
88C24×C5—32no—
89C24×C5—32no—
90C24×C5—32no—
91C24×C5Dic612yes—
92C24×C5C4×D312yes—
93C24×C5#6712yes—
94C24×C5C22×D311yescharacteristic
95C22×C4×C5—22no—
96C22×C4×C5—32no—
97C22×C4×C5—32no—
98C22×C4×C5—32no—
99C22×C4×C5—34no—
100C22×C4×C5—34no—
101C22×C4×C5—34no—
102C22×C4×C5—31no—
103C22×C4×C5—32no—
104C22×C4×C5—32no—
105C22×C4×C5—32no—
106C22×C4×C5—32no—
107C22×C4×C5—62no—
108C22×C4×C5—62no—
109C22×C4×C5—61no—
110C22×C4×C5—62no—
111C22×C4×C5—64no—
112C22×C4×C5—62no—
113C22×C4×C5—61no—
114C22×C4×C5—62no—
115C22×C4×C5—62no—
116C22×C4×C5—61no—
117C22×C4×C5—64no—
118C22×C4×C5—62no—
119C22×C4×C5—62no—
120C22×C4×C5—62no—
121C22×C4×C5—62no—
122C22×C4×C5—61no—
123C22×C4×C5—62no—
124C22×C4×C5—62no—
125C22×C4×C5—61no—
126C22×C4×C5S411yescharacteristic
127C5×C4⋊C4—68no—
128C5×C4⋊C4—64no—
129C5×C4⋊C4—64no—
130C5×C22⋊C4—38no—
131C5×C22⋊C4—34no—
132C5×C22⋊C4—34no—
133C5×C22⋊C4—64no—
134C5×C22⋊C4—62no—
135C5×C22⋊C4—62no—
136C24×C4C5×D311yescharacteristic
137C22×C4⋊C4—31no—
138C22×C4⋊C4—31no—
139C22×C22⋊C4—31no—
140C22×C22⋊C4—31no—
141#385—34no—
142#385—34no—
143C2×#95—31no—
144C2×#95—31no—
145C22×C3×C5—42no—
146C22×C3×C5—42no—
147C22×C3×C5—42no—
148C22×C3×C5—41no—
149C5×A4C2×C4⋊C411yescharacteristic, complemented
150C3×C4×C5—82no—
151C5×Dic3—44no—
152C5×Dic3—82no—
153C22×A4C2×C4×C512yes—
154C22×A4C5×D412yes—
155C22×A4C5×Q812yes—
156C22×A4C23×C511yescharacteristic
157C22×C3×C4—41no—
158C22×Dic3—41no—
159C22×Dic3—41no—
160C4×A4—22no—
161SL(2,ℤ/4)—22no—
162SL(2,ℤ/4)C2×C4×C514yescomplemented
163Dic3⋊C4—44no—
164C23×C5—32no—
165C23×C5—32no—
166C23×C5—32no—
167C23×C5—32no—
168C23×C5—32no—
169C23×C5—32no—
170C23×C5—31no—
171C23×C5—31no—
172C23×C5—32no—
173C23×C5—31no—
174C23×C5—32no—
175C23×C5—31no—
176C23×C5—32no—
177C23×C5—34no—
178C23×C5—34no—
179C23×C5—34no—
180C23×C5—31no—
181C23×C5—61no—
182C23×C5—61no—
183C23×C5—61no—
184C23×C5—64no—
185C23×C5Dic3⋊C414yescomplemented
186C23×C5C2×Dic611yescharacteristic
187C23×C5C2×C4×D311yescharacteristic
188C23×C5C2×#6711yescharacteristic
189C23×C5C2×S411yescharacteristic
190C2×C4×C5—22no—
191C2×C4×C5—34no—
192C2×C4×C5—34no—
193C2×C4×C5—34no—
194C2×C4×C5—32no—
195C2×C4×C5—62no—
196C2×C4×C5—62no—
197C2×C4×C5—64no—
198C2×C4×C5—62no—
199C2×C4×C5—62no—
200C2×C4×C5—68no—
201C2×C4×C5—62no—
202C2×C4×C5—64no—
203C2×C4×C5—64no—
204C2×C4×C5—64no—
205C2×C4×C5—62no—
206C2×C4×C5—62no—
207C2×C4×C5—62no—
208C2×C4×C5—62no—
209C2×C4×C5—62no—
210C2×C4×C5—62no—
211C2×C4×C5—62no—
212C2×C4×C5—62no—
213C2×C4×C5—62no—
214C2×C4×C5—124no—
215C2×C4×C5—122no—
216C2×C4×C5—122no—
217C2×C4×C5C2×S412yes—
218C25C2×C5×D311yescharacteristic
219C23×C4—22no—
220C23×C4—31no—
221C23×C4—31no—
222C23×C4—31no—
223C23×C4—31no—
224C23×C4—32no—
225C23×C4—31no—
226C23×C4—31no—
227C23×C4—62no—
228C23×C4C2×C5×D312yes—
229C2×C4⋊C4—34no—
230C2×C4⋊C4—34no—
231C2×C4⋊C4—64no—
232C2×C4⋊C4—61no—
233C2×C4⋊C4—62no—
234C2×C4⋊C4—61no—
235C2×C22⋊C4—34no—
236C2×C22⋊C4—32no—
237C2×C22⋊C4—34no—
238C2×C22⋊C4—32no—
239C2×C22⋊C4—32no—
240C2×C22⋊C4—32no—
241C2×C22⋊C4—62no—
242C2×C22⋊C4—62no—
243#95—34no—
244#95—34no—
245C2×C3×C5—41no—
246C2×C3×C5—41no—
247C2×C3×C5—44no—
248C2×C3×C5—41no—
249C23×C3—41no—
250C2×A4C5×C4⋊C414yescomplemented
251C2×A4C22×C4×C511yescharacteristic
252C2×A4C2×C5×D411yescharacteristic
253C2×A4C2×C5×Q811yescharacteristic
254C2×C3×C4—42no—
255C2×C3×C4—82no—
256C2×Dic3—42no—
257C2×Dic3—44no—
258C2×Dic3—42no—
259C2×Dic3—82no—
260C22×C5—34no—
261C22×C5—31no—
262C22×C5—31no—
263C22×C5—31no—
264C22×C5—31no—
265C22×C5—31no—
266C22×C5—32no—
267C22×C5—31no—
268C22×C5—31no—
269C22×C5—32no—
270C22×C5—34no—
271C22×C5—34no—
272C22×C5—34no—
273C22×C5—34no—
274C22×C5—31no—
275C22×C5—31no—
276C22×C5—32no—
277C22×C5—61no—
278C22×C5—62no—
279C22×C5—62no—
280C22×C5—62no—
281C22×C5C2×Dic3⋊C411yescharacteristic, complemented
282C22×C5A4⋊Q812yes—
283C22×C5C4×S412yes—
284C22×C5GL(2,ℤ/4)12yes—
285C22×C5C22×S411yescharacteristic
286C4×C5—22no—
287C4×C5—64no—
288C4×C5—64no—
289C4×C5—62no—
290C4×C5—122no—
291C4×C5—122no—
292C24—31no—
293C24—31no—
294C24—32no—
295C24—32no—
296C24—32no—
297C24C5×Dic612yes—
298C24C4×C5×D312yes—
299C24C5×#6712yes—
300C24C22×C5×D311yescharacteristic
301C22×C4—22no—
302C22×C4—32no—
303C22×C4—32no—
304C22×C4—32no—
305C22×C4—34no—
306C22×C4—34no—
307C22×C4—34no—
308C22×C4—31no—
309C22×C4—32no—
310C22×C4—32no—
311C22×C4—32no—
312C22×C4—32no—
313C22×C4—62no—
314C22×C4—62no—
315C22×C4—61no—
316C22×C4—62no—
317C22×C4—64no—
318C22×C4—62no—
319C22×C4—61no—
320C22×C4—62no—
321C22×C4—62no—
322C22×C4—61no—
323C22×C4—64no—
324C22×C4—62no—
325C22×C4—62no—
326C22×C4—62no—
327C22×C4—62no—
328C22×C4—61no—
329C22×C4—62no—
330C22×C4—62no—
331C22×C4—61no—
332C22×C4C5×S411yescharacteristic
333C4⋊C4—68no—
334C4⋊C4—64no—
335C4⋊C4—64no—
336C22⋊C4—38no—
337C22⋊C4—34no—
338C22⋊C4—34no—
339C22⋊C4—64no—
340C22⋊C4—62no—
341C22⋊C4—62no—
342C3×C5—41noHall
343C22×C3—42no—
344C22×C3—42no—
345C22×C3—42no—
346C22×C3—41no—
347A4C2×C5×C4⋊C411yescharacteristic, complemented
348C3×C4—82no—
349Dic3—44no—
350Dic3—82no—
351C2×C5—31no—
352C2×C5—31no—
353C2×C5—31no—
354C2×C5—34no—
355C2×C5—31no—
356C2×C5SL(2,ℤ/4)⋊C414yesdirect product factor
357C2×C5C2×A4⋊Q811yescharacteristic
358C2×C5C2×C4×S411yescharacteristic
359C2×C5C2×GL(2,ℤ/4)11yescharacteristic
360C23—32no—
361C23—32no—
362C23—32no—
363C23—32no—
364C23—32no—
365C23—32no—
366C23—31no—
367C23—31no—
368C23—32no—
369C23—31no—
370C23—32no—
371C23—31no—
372C23—32no—
373C23—34no—
374C23—34no—
375C23—34no—
376C23—31no—
377C23—61no—
378C23—61no—
379C23—61no—
380C23—64no—
381C23C5×Dic3⋊C414yescomplemented
382C23C2×C5×Dic611yescharacteristic
383C23C2×C4×C5×D311yescharacteristic
384C23C2×C5×#6711yescharacteristic
385C23C2×C5×S411yescharacteristic
386C2×C4—22no—
387C2×C4—34no—
388C2×C4—34no—
389C2×C4—34no—
390C2×C4—32no—
391C2×C4—62no—
392C2×C4—62no—
393C2×C4—64no—
394C2×C4—62no—
395C2×C4—64no—
396C2×C4—62no—
397C2×C4—68no—
398C2×C4—62no—
399C2×C4—64no—
400C2×C4—64no—
401C2×C4—62no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—62no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—62no—
408C2×C4—62no—
409C2×C4—62no—
410C2×C4—124no—
411C2×C4—122no—
412C2×C4—122no—
413C2×C4C2×C5×S412yes—
414C2×C3—41no—
415C2×C3—41no—
416C2×C3—41no—
417C2×C3—44no—
418C5C2×SL(2,ℤ/4)⋊C411yescharacteristic, direct product factor, Sylow
419C22—34no—
420C22—31no—
421C22—31no—
422C22—31no—
423C22—31no—
424C22—31no—
425C22—32no—
426C22—31no—
427C22—31no—
428C22—32no—
429C22—31no—
430C22—31no—
431C22—32no—
432C22—34no—
433C22—34no—
434C22—34no—
435C22—34no—
436C22—61no—
437C22—62no—
438C22—62no—
439C22—62no—
440C22C2×C5×Dic3⋊C411yescharacteristic, complemented
441C22C5×A4⋊Q812yes—
442C22C4×C5×S412yes—
443C22C5×GL(2,ℤ/4)12yes—
444C22C22×C5×S411yescharacteristic
445C4—22no—
446C4—64no—
447C4—64no—
448C4—62no—
449C4—122no—
450C4—122no—
451C3—41noSylow
452C2—31no—
453C2—31no—
454C2—31no—
455C2—34no—
456C2—31no—
457C2C5×SL(2,ℤ/4)⋊C414yesdirect product factor
458C2C2×C5×A4⋊Q811yescharacteristic
459C2C2×C4×C5×S411yescharacteristic
460C2C2×C5×GL(2,ℤ/4)11yescharacteristic
subgroupG/H
centerC23×C5C2×S4
commutatorC2×A4C22×C4×C5
FrattiniC22C22×C5×S4
FittingC24×C4×C5D3
socleC25×C5C2×D3
prime radicalC23×C5×A4C22
cosocleC22×A4C23×C5
hypercenterC22×C4×C5S4
hypocenterA4C2×C5×C4⋊C4
LCSG ▷ C2×A4 ▷ A4
UCSC1 ◁ C23×C5 ◁ C22×C4×C5

Complements

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

NH ≅ G/Ntype
4. C5×SL(2,ℤ/4)⋊C4C2direct (N × H)
10. C2×C5×SL(2,ℤ/4)C4semidirect
14. C2×SL(2,ℤ/4)⋊C4C5direct (N × H)
33. C5×SL(2,ℤ/4)C2×C4semidirect
38. SL(2,ℤ/4)⋊C4C2×C5direct (N × H)
68. C2×C5×A4C4⋊C4semidirect
82. C2×SL(2,ℤ/4)C4×C5semidirect
149. C5×A4C2×C4⋊C4semidirect
162. SL(2,ℤ/4)C2×C4×C5semidirect
185. C23×C5Dic3⋊C4semidirect
250. C2×A4C5×C4⋊C4semidirect
281. C22×C5C2×Dic3⋊C4semidirect
347. A4C2×C5×C4⋊C4semidirect
356. C2×C5SL(2,ℤ/4)⋊C4direct (N × H)
381. C23C5×Dic3⋊C4semidirect
418. C5C2×SL(2,ℤ/4)⋊C4direct (N × H)
440. C22C2×C5×Dic3⋊C4semidirect
457. C2C5×SL(2,ℤ/4)⋊C4direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C5×A42
C22×C5×SL(2,ℤ/4)2
C5×SL(2,ℤ/4)⋊C42
C2×C5×#3853
C2×C5×Dic3⋊C44
C2×SL(2,ℤ/4)⋊C45