Finite Group Databasebeta

← C2×A4×#677 #14514133

Subgroups — C2×A4×#677 #14514133

Order 1920.

800 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 99 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×A4×D20C211yesmaximal, characteristic
2C2×A4×Dic10C211yesmaximal, characteristic, complemented
3C2×C5×C8×A4C211yesmaximal, characteristic, complemented
4A4×#677C214yesmaximal, direct product factor
5C23×#677C311yesmaximal, characteristic, complemented, Hall
6C22×D5×A4—21no—
7C2×C4×C5×A4C2211yescharacteristic
8C2×A4×Dic5—21no—
9A4×D20—21no—
10A4×D20C2212yes—
11A4×Dic10—21no—
12A4×Dic10C2212yescomplemented
13C2×C3×#677—41nomaximal
14C5×C8×A4C2212yescomplemented
15C2×A4×SD16—51nomaximal, Hall
16C23×D20C2×C311yescharacteristic
17C23×Dic10C2×C311yescharacteristic, complemented
18C23×C5×C8C2×C311yescharacteristic, complemented
19C22×#677—31no—
20C22×#677—31no—
21C22×#677—31no—
22C22×#677—34no—
23C22×#677—31no—
24C22×#677C2×C314yescomplemented
25C22×C5×A4D411yescharacteristic
26C2×D5×A4—22no—
27C2×D5×A4—42no—
28C2×C3×D20—41no—
29C2×C3×Dic10—41no—
30C4×C5×A4D411yescharacteristic
31C4×C5×A4C2311yescharacteristic
32A4×Dic5—22no—
33C2×C3×C5×C8—41no—
34C3×#677—44no—
35C2×Q8×A4—51no—
36C2×D4×A4—51no—
37A4×SD16—54no—
38C2×C8×A4D511yescharacteristic, complemented
39C24×D5—21no—
40C23×C4×C5C22×C311yescharacteristic
41C23×Dic5—21no—
42C22×D20—21no—
43C22×D20—31no—
44C22×D20—31no—
45C22×D20—32no—
46C22×D20—61no—
47C22×D20—61no—
48C22×D20C22×C312yes—
49C22×Dic10—21no—
50C22×Dic10—31no—
51C22×Dic10—31no—
52C22×Dic10—32no—
53C22×Dic10—61no—
54C22×Dic10—61no—
55C22×Dic10C22×C312yescomplemented
56C22×C5×C8—31no—
57C22×C5×C8—31no—
58C22×C5×C8—32no—
59C22×C5×C8C22×C312yescomplemented
60C2×#677—32no—
61C2×#677—34no—
62C2×#677—34no—
63C2×#677—34no—
64C2×#677—31no—
65C2×#677—31no—
66C2×#677—31no—
67C2×#677—34no—
68C2×#677—34no—
69C2×#677—34no—
70C2×#677—34no—
71C2×#677—34no—
72C2×#677A411yescharacteristic, direct product factor
73C23×SD16—51noSylow
74C22×C3×D5—81no—
75C2×C5×A4SD1612yescomplemented
76C2×C5×A4C2×D411yescharacteristic
77D5×A4—42no—
78C2×C3×C4×C5—41no—
79C2×C3×Dic5—81no—
80C3×D20—42no—
81C3×D20—81no—
82C3×Dic10—42no—
83C3×Dic10—81no—
84C3×C5×C8—42no—
85C23×A4—101no—
86Q8×A4—52no—
87Q8×A4—101no—
88D4×A4—52no—
89D4×A4—101no—
90C2×C4×A4—101no—
91C2×C4×A4C2×D511yescharacteristic
92C2×C3×SD16—201no—
93C8×A4C2×D512yescomplemented
94C24×C5C3×D411yescharacteristic
95C23×D5—22no—
96C23×D5—42no—
97C23×D5—61no—
98C23×D5—62no—
99C23×D5—61no—
100C23×D5—122no—
101C22×C4×C5—31no—
102C22×C4×C5—31no—
103C22×C4×C5—31no—
104C22×C4×C5—31no—
105C22×C4×C5C3×D411yescharacteristic
106C22×C4×C5C23×C311yescharacteristic
107C22×Dic5—22no—
108C22×Dic5—61no—
109C22×Dic5—62no—
110C22×Dic5—61no—
111C2×D20—32no—
112C2×D20—31no—
113C2×D20—32no—
114C2×D20—32no—
115C2×D20—32no—
116C2×D20—61no—
117C2×D20—61no—
118C2×D20—61no—
119C2×D20—61no—
120C2×D20—64no—
121C2×D20—62no—
122C2×D20—61no—
123C2×D20—61no—
124C2×D20—62no—
125C2×D20C2×A411yescharacteristic
126C2×Dic10—32no—
127C2×Dic10—31no—
128C2×Dic10—32no—
129C2×Dic10—32no—
130C2×Dic10—32no—
131C2×Dic10—61no—
132C2×Dic10—61no—
133C2×Dic10—61no—
134C2×Dic10—64no—
135C2×Dic10—61no—
136C2×Dic10—62no—
137C2×Dic10—61no—
138C2×Dic10—61no—
139C2×Dic10—62no—
140C2×Dic10C2×A411yescharacteristic, complemented
141C2×C5×C8—32no—
142C2×C5×C8—31no—
143C2×C5×C8—32no—
144C2×C5×C8—32no—
145C2×C5×C8—32no—
146C2×C5×C8C2×A411yescharacteristic, complemented
147#677—38no—
148#677—34no—
149#677—34no—
150#677—34no—
151#677C2×A414yesdirect product factor
152C23×Q8—51no—
153C23×D4—51no—
154C22×SD16—54no—
155C22×SD16—151no—
156C22×SD16—151no—
157C22×SD16—154no—
158C22×SD16—151no—
159C22×SD16—151no—
160C23×C8C3×D511yescharacteristic, complemented
161C22×C3×C5—41no—
162C2×C3×D5—82no—
163C2×C3×D5—162no—
164C5×A4C2×SD1611yescharacteristic, complemented
165C3×C4×C5—41no—
166C3×C4×C5—41no—
167C3×Dic5—82no—
168C22×A4—102no—
169C22×A4—202no—
170C22×A4D2011yescharacteristic
171C2×C3×Q8—201no—
172C2×C3×D4—201no—
173C4×A4—102no—
174C4×A4D2011yescharacteristic
175C4×A4C22×D511yescharacteristic
176C3×SD16—204no—
177C2×C3×C8—41no—
178C23×C5—31no—
179C23×C5—32no—
180C23×C5—31no—
181C23×C5C3×SD1612yescomplemented
182C23×C5C2×C3×D411yescharacteristic
183C22×D5—21no—
184C22×D5—42no—
185C22×D5—62no—
186C22×D5—62no—
187C22×D5—62no—
188C22×D5—61no—
189C22×D5—62no—
190C22×D5—122no—
191C22×D5—122no—
192C22×D5—124no—
193C22×D5—124no—
194C22×D5—122no—
195C22×D5—122no—
196C22×D5—122no—
197C2×C4×C5—32no—
198C2×C4×C5—31no—
199C2×C4×C5—31no—
200C2×C4×C5—31no—
201C2×C4×C5—31no—
202C2×C4×C5—31no—
203C2×C4×C5—31no—
204C2×C4×C5—31no—
205C2×C4×C5C22×A411yescharacteristic
206C2×Dic5—21no—
207C2×Dic5—62no—
208C2×Dic5—62no—
209C2×Dic5—62no—
210C2×Dic5—61no—
211C2×Dic5—62no—
212D20—21no—
213D20—32no—
214D20—62no—
215D20—62no—
216D20—62no—
217D20—62no—
218D20—61no—
219D20C22×A412yes—
220Dic10—21no—
221Dic10—32no—
222Dic10—62no—
223Dic10—62no—
224Dic10—62no—
225Dic10—61no—
226Dic10—62no—
227Dic10C22×A412yescomplemented
228C5×C8—32no—
229C5×C8C22×A412yescomplemented
230C25—101no—
231C22×Q8—52no—
232C22×Q8—101no—
233C22×Q8—151no—
234C22×Q8—151no—
235C22×Q8—152no—
236C22×Q8—301no—
237C22×Q8—301no—
238C22×D4—52no—
239C22×D4—101no—
240C22×D4—151no—
241C22×D4—151no—
242C22×D4—152no—
243C22×D4—301no—
244C22×D4—301no—
245C23×C4—101no—
246C23×C4C2×C3×D511yescharacteristic
247C2×SD16—51no—
248C2×SD16—154no—
249C2×SD16—154no—
250C2×SD16—151no—
251C2×SD16—151no—
252C2×SD16—154no—
253C2×SD16—154no—
254C2×SD16—152no—
255C2×SD16—154no—
256C2×SD16—154no—
257C2×SD16—154no—
258C2×SD16—154no—
259C2×SD16—151no—
260C22×C8—31no—
261C22×C8—31no—
262C22×C8—32no—
263C22×C8C2×C3×D512yescomplemented
264C2×C3×C5—41no—
265C2×C3×C5—42no—
266C3×D5—162no—
267C23×C3—401no—
268C2×A4—202no—
269C2×A4#67712yesdirect product factor
270C2×A4C2×D2011yescharacteristic
271C3×Q8—202no—
272C3×Q8—401no—
273C3×D4—202no—
274C3×D4—401no—
275C2×C3×C4—41no—
276C2×C3×C4—401no—
277C3×C8—42no—
278C22×C5—32no—
279C22×C5—31no—
280C22×C5—32no—
281C22×C5—31no—
282C22×C5—31no—
283C22×C5—32no—
284C22×C5—32no—
285C22×C5C2×C3×SD1611yescharacteristic, complemented
286C22×C5D4×A411yescharacteristic
287C2×D5—22no—
288C2×D5—42no—
289C2×D5—62no—
290C2×D5—122no—
291C2×D5—122no—
292C2×D5—124no—
293C2×D5—124no—
294C2×D5—122no—
295C2×D5—122no—
296C2×D5—122no—
297C4×C5—31no—
298C4×C5—31no—
299C4×C5D4×A411yescharacteristic
300C4×C5C23×A411yescharacteristic
301Dic5—22no—
302Dic5—62no—
303C24—102no—
304C24—202no—
305C24—301no—
306C24—302no—
307C24—301no—
308C24—602no—
309C24C3×D2011yescharacteristic
310C2×Q8—51no—
311C2×Q8—152no—
312C2×Q8—152no—
313C2×Q8—152no—
314C2×Q8—152no—
315C2×Q8—151no—
316C2×Q8—301no—
317C2×Q8—301no—
318C2×Q8—301no—
319C2×Q8—302no—
320C2×Q8—301no—
321C2×Q8—302no—
322C2×Q8—301no—
323C2×Q8—304no—
324C2×Q8—301no—
325C2×D4—51no—
326C2×D4—152no—
327C2×D4—152no—
328C2×D4—152no—
329C2×D4—152no—
330C2×D4—151no—
331C2×D4—301no—
332C2×D4—301no—
333C2×D4—301no—
334C2×D4—301no—
335C2×D4—304no—
336C2×D4—301no—
337C2×D4—302no—
338C2×D4—301no—
339C2×D4—302no—
340C22×C4—31no—
341C22×C4—31no—
342C22×C4—31no—
343C22×C4—31no—
344C22×C4—102no—
345C22×C4—301no—
346C22×C4—302no—
347C22×C4—301no—
348C22×C4C3×D2011yescharacteristic
349C22×C4C22×C3×D511yescharacteristic
350SD16—54no—
351SD16—154no—
352SD16—154no—
353SD16—158no—
354SD16—154no—
355C2×C8—32no—
356C2×C8—31no—
357C2×C8—32no—
358C2×C8—32no—
359C2×C8—32no—
360C2×C8D5×A411yescharacteristic, complemented
361C3×C5—41noHall
362C22×C3—41no—
363C22×C3—402no—
364C22×C3—802no—
365A4C2×#67711yescharacteristic, direct product factor
366C3×C4—41no—
367C3×C4—41no—
368C3×C4—402no—
369C2×C5—32no—
370C2×C5—31no—
371C2×C5—31no—
372C2×C5A4×SD1612yescomplemented
373C2×C5C2×D4×A411yescharacteristic
374D5—42no—
375D5—122no—
376C23—31no—
377C23—32no—
378C23—31no—
379C23—101no—
380C23—202no—
381C23—302no—
382C23—302no—
383C23—302no—
384C23—302no—
385C23—301no—
386C23—602no—
387C23—602no—
388C23—602no—
389C23—604no—
390C23—602no—
391C23—602no—
392C23—604no—
393C23C3×#67712yescomplemented
394C23C2×C3×D2011yescharacteristic
395Q8—52no—
396Q8—101no—
397Q8—152no—
398Q8—302no—
399Q8—302no—
400Q8—302no—
401Q8—302no—
402Q8—301no—
403D4—52no—
404D4—101no—
405D4—152no—
406D4—302no—
407D4—302no—
408D4—302no—
409D4—302no—
410D4—301no—
411C2×C4—32no—
412C2×C4—31no—
413C2×C4—31no—
414C2×C4—31no—
415C2×C4—31no—
416C2×C4—31no—
417C2×C4—31no—
418C2×C4—31no—
419C2×C4—101no—
420C2×C4—302no—
421C2×C4—302no—
422C2×C4—302no—
423C2×C4—301no—
424C2×C4—302no—
425C2×C4C2×D5×A411yescharacteristic
426C8—32no—
427C8C2×D5×A412yescomplemented
428C2×C3—41no—
429C2×C3—42no—
430C2×C3—802no—
431C5C2×A4×SD1611yescharacteristic, complemented, Sylow
432C22—32no—
433C22—31no—
434C22—32no—
435C22—31no—
436C22—31no—
437C22—32no—
438C22—32no—
439C22—102no—
440C22—202no—
441C22—302no—
442C22—602no—
443C22—602no—
444C22—604no—
445C22—602no—
446C22—602no—
447C22—604no—
448C22—602no—
449C22C2×C3×#67711yescharacteristic, complemented
450C22A4×D2011yescharacteristic
451C4—31no—
452C4—31no—
453C4—102no—
454C4—302no—
455C4A4×D2011yescharacteristic
456C4C22×D5×A411yescharacteristic
457C3—41noSylow
458C2—31no—
459C2—32no—
460C2—31no—
461C2—202no—
462C2—602no—
463C2A4×#67712yesdirect product factor
464C2C2×A4×D2011yescharacteristic
subgroupG/H
centerC22A4×D20
commutator, cosocleC22×C4×C5C23×C3
FrattiniC4C22×D5×A4
FittingC23×C5×C8C2×C3
socleC24×C5C3×D4
prime radicalC2×A4×D20C2
hypercenterC2×C8D5×A4
hypocenterC22×C5C2×C3×SD16
LCSG ▷ C22×C4×C5 ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. C2×A4×Dic10C2semidirect
3. C2×C5×C8×A4C2semidirect
4. A4×#677C2direct (N × H)
5. C23×#677C3semidirect
12. A4×Dic10C22semidirect
14. C5×C8×A4C22semidirect
17. C23×Dic10C2×C3semidirect
18. C23×C5×C8C2×C3semidirect
24. C22×#677C2×C3semidirect
38. C2×C8×A4D5semidirect
55. C22×Dic10C22×C3semidirect
59. C22×C5×C8C22×C3semidirect
72. C2×#677A4direct (N × H)
75. C2×C5×A4SD16semidirect
93. C8×A4C2×D5semidirect
140. C2×Dic10C2×A4semidirect
146. C2×C5×C8C2×A4semidirect
151. #677C2×A4direct (N × H)
160. C23×C8C3×D5semidirect
164. C5×A4C2×SD16semidirect
181. C23×C5C3×SD16semidirect
227. Dic10C22×A4semidirect
229. C5×C8C22×A4semidirect
263. C22×C8C2×C3×D5semidirect
269. C2×A4#677direct (N × H)
285. C22×C5C2×C3×SD16semidirect
360. C2×C8D5×A4semidirect
365. A4C2×#677direct (N × H)
372. C2×C5A4×SD16semidirect
393. C23C3×#677semidirect
427. C8C2×D5×A4semidirect
431. C5C2×A4×SD16semidirect
449. C22C2×C3×#677semidirect
463. C2A4×#677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×A4×D202
C2×A4×Dic102
C2×C5×C8×A42
A4×#6772
C23×#6773
C2×C3×#6774
C2×A4×SD165