Finite Group Databasebeta

← C2×A4×#683 #14514175

Subgroups — C2×A4×#683 #14514175

Order 1920.

1136 conjugacy classes of subgroups; only the 171 normal subgroups are shown.

normal subgroups only

This group has 1136 conjugacy classes of subgroups — too many to draw. Only its 171 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×A4×Dic5C211yesmaximal, characteristic
3C22×A4×Dic5C211yesmaximal, characteristic
4A4×#683C214yesmaximal, direct product factor
5C23×#683C311yesmaximal, characteristic, complemented, Hall
6C23×C5×A4C2211yescharacteristic
7C2×C4×C5×A4—22no—
8C2×C4×C5×A4C2212yes—
9C2×A4×Dic5—22no—
10C2×A4×Dic5C414yescomplemented
11C2×A4×Dic5C2212yes—
12C2×A4×Dic5C2212yes—
13C2×C3×#683—41nomaximal
14C2×A4×C4⋊C4—51nomaximal, Hall
15C24×C4×C5C2×C311yescharacteristic
16C24×Dic5C2×C311yescharacteristic
17C24×Dic5C2×C311yescharacteristic
18C22×#683—31no—
19C22×#683—31no—
20C22×#683—31no—
21C22×#683—34no—
22C22×#683—31no—
23C22×#683C2×C314yescomplemented
24C22×C5×A4C2×C412yes—
25C22×C5×A4D412yes—
26C22×C5×A4Q812yes—
27C22×C5×A4C2311yescharacteristic
28C22×C3×C4×C5—41no—
29C22×C3×Dic5—41no—
30C22×C3×Dic5—41no—
31C4×C5×A4—22no—
32A4×Dic5—22no—
33A4×Dic5C2×C414yescomplemented
34C3×#683—44no—
35C22×C4×A4—51no—
36C22×C4×A4—51no—
37C22×C4×A4D511yescharacteristic
38A4×C4⋊C4—54no—
39C25×C5C22×C311yescharacteristic
40C23×C4×C5—22no—
41C23×C4×C5—31no—
42C23×C4×C5—31no—
43C23×C4×C5—32no—
44C23×C4×C5—62no—
45C23×C4×C5C22×C312yes—
46C23×Dic5—22no—
47C23×Dic5—31no—
48C23×Dic5—31no—
49C23×Dic5—32no—
50C23×Dic5—34no—
51C23×Dic5—31no—
52C23×Dic5—31no—
53C23×Dic5—32no—
54C23×Dic5—62no—
55C23×Dic5C3×C414yescomplemented
56C23×Dic5C22×C312yes—
57C23×Dic5C22×C312yes—
58C2×#683—32no—
59C2×#683—34no—
60C2×#683—34no—
61C2×#683—34no—
62C2×#683—31no—
63C2×#683—31no—
64C2×#683—31no—
65C2×#683—34no—
66C2×#683—34no—
67C2×#683—34no—
68C2×#683—34no—
69C2×#683—34no—
70C2×#683A411yescharacteristic, direct product factor
71C23×C4⋊C4—51noSylow
72C23×C3×C5—41no—
73C2×C5×A4C4⋊C414yescomplemented
74C2×C5×A4C22×C411yescharacteristic
75C2×C5×A4C2×D411yescharacteristic
76C2×C5×A4C2×Q811yescharacteristic
77C2×C3×C4×C5—42no—
78C2×C3×C4×C5—82no—
79C2×C3×Dic5—44no—
80C2×C3×Dic5—42no—
81C2×C3×Dic5—42no—
82C2×C3×Dic5—82no—
83C23×A4C2×D511yescharacteristic
84C2×C4×A4—22no—
85C2×C4×A4—54no—
86C2×C4×A4—52no—
87C2×C4×A4—52no—
88C2×C4×A4—102no—
89C2×C4×A4C2×D512yes—
90C2×C3×C4⋊C4—201no—
91C24×C5—31no—
92C24×C5—32no—
93C24×C5—32no—
94C24×C5—32no—
95C24×C5—31no—
96C24×C5C2×C3×C412yes—
97C24×C5C3×D412yes—
98C24×C5C3×Q812yes—
99C24×C5C23×C311yescharacteristic
100C22×C4×C5—22no—
101C22×C4×C5—32no—
102C22×C4×C5—31no—
103C22×C4×C5—32no—
104C22×C4×C5—32no—
105C22×C4×C5—32no—
106C22×C4×C5—62no—
107C22×C4×C5—62no—
108C22×C4×C5—64no—
109C22×C4×C5—64no—
110C22×C4×C5—62no—
111C22×C4×C5—62no—
112C22×C4×C5—62no—
113C22×C4×C5C2×A411yescharacteristic
114C22×Dic5—22no—
115C22×Dic5—34no—
116C22×Dic5—38no—
117C22×Dic5—32no—
118C22×Dic5—31no—
119C22×Dic5—34no—
120C22×Dic5—34no—
121C22×Dic5—32no—
122C22×Dic5—32no—
123C22×Dic5—34no—
124C22×Dic5—38no—
125C22×Dic5—34no—
126C22×Dic5—32no—
127C22×Dic5—32no—
128C22×Dic5—31no—
129C22×Dic5—32no—
130C22×Dic5—32no—
131C22×Dic5—32no—
132C22×Dic5—62no—
133C22×Dic5—62no—
134C22×Dic5—64no—
135C22×Dic5—64no—
136C22×Dic5—62no—
137C22×Dic5—62no—
138C22×Dic5—62no—
139C22×Dic5C2×C3×C414yescomplemented
140C22×Dic5C2×A411yescharacteristic
141C22×Dic5C2×A411yescharacteristic
142#683—38no—
143#683—34no—
144#683—34no—
145#683—34no—
146#683C2×A414yesdirect product factor
147C24×C4—51no—
148C24×C4—51no—
149C24×C4C3×D511yescharacteristic
150C22×C4⋊C4—54no—
151C22×C4⋊C4—151no—
152C22×C4⋊C4—154no—
153C22×C4⋊C4—151no—
154C22×C4⋊C4—151no—
155C22×C4⋊C4—151no—
156C22×C3×C5—42no—
157C22×C3×C5—42no—
158C22×C3×C5—42no—
159C22×C3×C5—41no—
160C5×A4C2×C4⋊C411yescharacteristic, complemented
161C3×C4×C5—82no—
162C3×Dic5—44no—
163C3×Dic5—82no—
164C22×A4Dic1012yes—
165C22×A4C4×D512yes—
166C22×A4C22⋊D512yes—
167C22×A4C22×D511yescharacteristic
168C22×C3×C4—41no—
169C22×C3×C4—201no—
170C22×C3×C4—201no—
171C4×A4—22no—
172C4×A4—54no—
173C4×A4—102no—
174C3×C4⋊C4—204no—
175C23×C5—32no—
176C23×C5—31no—
177C23×C5—32no—
178C23×C5—31no—
179C23×C5—34no—
180C23×C5—34no—
181C23×C5—32no—
182C23×C5—34no—
183C23×C5—31no—
184C23×C5—32no—
185C23×C5—32no—
186C23×C5—32no—
187C23×C5—38no—
188C23×C5—32no—
189C23×C5—32no—
190C23×C5—32no—
191C23×C5—32no—
192C23×C5—32no—
193C23×C5—32no—
194C23×C5—31no—
195C23×C5—31no—
196C23×C5C3×C4⋊C414yescomplemented
197C23×C5C22×C3×C411yescharacteristic
198C23×C5C2×C3×D411yescharacteristic
199C23×C5C2×C3×Q811yescharacteristic
200C23×C5C22×A411yescharacteristic
201C2×C4×C5—22no—
202C2×C4×C5—32no—
203C2×C4×C5—62no—
204C2×C4×C5—62no—
205C2×C4×C5—64no—
206C2×C4×C5—64no—
207C2×C4×C5—62no—
208C2×C4×C5—62no—
209C2×C4×C5—62no—
210C2×C4×C5C22×A412yes—
211C2×Dic5—22no—
212C2×Dic5—34no—
213C2×Dic5—38no—
214C2×Dic5—34no—
215C2×Dic5—32no—
216C2×Dic5—34no—
217C2×Dic5—38no—
218C2×Dic5—34no—
219C2×Dic5—34no—
220C2×Dic5—32no—
221C2×Dic5—62no—
222C2×Dic5—62no—
223C2×Dic5—64no—
224C2×Dic5—64no—
225C2×Dic5—62no—
226C2×Dic5—62no—
227C2×Dic5—62no—
228C2×Dic5C4×A414yescomplemented
229C2×Dic5C22×A412yes—
230C2×Dic5C22×A412yes—
231C25C2×C3×D511yescharacteristic
232C23×C4—22no—
233C23×C4—31no—
234C23×C4—31no—
235C23×C4—32no—
236C23×C4—54no—
237C23×C4—52no—
238C23×C4—52no—
239C23×C4—62no—
240C23×C4—102no—
241C23×C4—151no—
242C23×C4—151no—
243C23×C4—152no—
244C23×C4—151no—
245C23×C4—154no—
246C23×C4—152no—
247C23×C4—151no—
248C23×C4—302no—
249C23×C4C2×C3×D512yes—
250C2×C4⋊C4—51no—
251C2×C4⋊C4—154no—
252C2×C4⋊C4—154no—
253C2×C4⋊C4—151no—
254C2×C4⋊C4—151no—
255C2×C4⋊C4—154no—
256C2×C4⋊C4—154no—
257C2×C4⋊C4—152no—
258C2×C4⋊C4—154no—
259C2×C4⋊C4—151no—
260C2×C4⋊C4—154no—
261C2×C4⋊C4—154no—
262C2×C4⋊C4—154no—
263C2×C3×C5—41no—
264C2×C3×C5—41no—
265C2×C3×C5—41no—
266C2×C3×C5—44no—
267C23×C3—41no—
268C2×A4#68314yesdirect product factor
269C2×A4C2×Dic1011yescharacteristic
270C2×A4C2×C4×D511yescharacteristic
271C2×A4C2×C22⋊D511yescharacteristic
272C2×C3×C4—42no—
273C2×C3×C4—82no—
274C2×C3×C4—202no—
275C2×C3×C4—204no—
276C2×C3×C4—202no—
277C2×C3×C4—402no—
278C22×C5—34no—
279C22×C5—31no—
280C22×C5—31no—
281C22×C5—31no—
282C22×C5—34no—
283C22×C5—32no—
284C22×C5—34no—
285C22×C5—34no—
286C22×C5—32no—
287C22×C5—31no—
288C22×C5—31no—
289C22×C5—32no—
290C22×C5—31no—
291C22×C5—31no—
292C22×C5—32no—
293C22×C5—31no—
294C22×C5—31no—
295C22×C5—34no—
296C22×C5—34no—
297C22×C5—34no—
298C22×C5—34no—
299C22×C5C2×C3×C4⋊C411yescharacteristic, complemented
300C22×C5C2×C4×A412yes—
301C22×C5D4×A412yes—
302C22×C5Q8×A412yes—
303C22×C5C23×A411yescharacteristic
304C4×C5—22no—
305C4×C5—62no—
306Dic5—22no—
307Dic5—34no—
308Dic5—62no—
309Dic5C2×C4×A414yescomplemented
310C24—31no—
311C24—32no—
312C24—32no—
313C24—32no—
314C24—31no—
315C24C3×Dic1012yes—
316C24C3×C4×D512yes—
317C24C3×C22⋊D512yes—
318C24C22×C3×D511yescharacteristic
319C22×C4—22no—
320C22×C4—32no—
321C22×C4—31no—
322C22×C4—32no—
323C22×C4—32no—
324C22×C4—32no—
325C22×C4—51no—
326C22×C4—51no—
327C22×C4—54no—
328C22×C4—62no—
329C22×C4—62no—
330C22×C4—64no—
331C22×C4—64no—
332C22×C4—62no—
333C22×C4—62no—
334C22×C4—62no—
335C22×C4—102no—
336C22×C4—152no—
337C22×C4—152no—
338C22×C4—154no—
339C22×C4—154no—
340C22×C4—152no—
341C22×C4—152no—
342C22×C4—152no—
343C22×C4—158no—
344C22×C4—154no—
345C22×C4—151no—
346C22×C4—152no—
347C22×C4—158no—
348C22×C4—154no—
349C22×C4—154no—
350C22×C4—152no—
351C22×C4—151no—
352C22×C4—152no—
353C22×C4—302no—
354C22×C4—302no—
355C22×C4—304no—
356C22×C4—304no—
357C22×C4—302no—
358C22×C4—302no—
359C22×C4—302no—
360C22×C4D5×A411yescharacteristic
361C4⋊C4—54no—
362C4⋊C4—154no—
363C4⋊C4—154no—
364C4⋊C4—158no—
365C4⋊C4—154no—
366C3×C5—41noHall
367C22×C3—42no—
368C22×C3—42no—
369C22×C3—42no—
370C22×C3—41no—
371A4C2×#68311yescharacteristic, direct product factor
372C3×C4—82no—
373C3×C4—204no—
374C3×C4—402no—
375C2×C5—34no—
376C2×C5—31no—
377C2×C5—31no—
378C2×C5—31no—
379C2×C5—31no—
380C2×C5A4×C4⋊C414yescomplemented
381C2×C5C22×C4×A411yescharacteristic
382C2×C5C2×D4×A411yescharacteristic
383C2×C5C2×Q8×A411yescharacteristic
384C23—32no—
385C23—31no—
386C23—32no—
387C23—31no—
388C23—32no—
389C23—34no—
390C23—34no—
391C23—34no—
392C23—31no—
393C23—32no—
394C23—32no—
395C23—32no—
396C23—38no—
397C23—32no—
398C23—32no—
399C23—32no—
400C23—32no—
401C23—32no—
402C23—32no—
403C23—31no—
404C23—31no—
405C23C3×#68314yescomplemented
406C23C2×C3×Dic1011yescharacteristic
407C23C2×C3×C4×D511yescharacteristic
408C23C2×C3×C22⋊D511yescharacteristic
409C23C2×D5×A411yescharacteristic
410C2×C4—22no—
411C2×C4—32no—
412C2×C4—54no—
413C2×C4—52no—
414C2×C4—52no—
415C2×C4—62no—
416C2×C4—62no—
417C2×C4—64no—
418C2×C4—64no—
419C2×C4—62no—
420C2×C4—62no—
421C2×C4—62no—
422C2×C4—102no—
423C2×C4—154no—
424C2×C4—154no—
425C2×C4—158no—
426C2×C4—158no—
427C2×C4—154no—
428C2×C4—154no—
429C2×C4—152no—
430C2×C4—154no—
431C2×C4—152no—
432C2×C4—302no—
433C2×C4—302no—
434C2×C4—304no—
435C2×C4—304no—
436C2×C4—302no—
437C2×C4—302no—
438C2×C4—302no—
439C2×C4C2×D5×A412yes—
440C2×C3—41no—
441C2×C3—41no—
442C2×C3—41no—
443C2×C3—44no—
444C5C2×A4×C4⋊C411yescharacteristic, complemented, Sylow
445C22—34no—
446C22—31no—
447C22—31no—
448C22—31no—
449C22—34no—
450C22—32no—
451C22—34no—
452C22—34no—
453C22—31no—
454C22—32no—
455C22—31no—
456C22—31no—
457C22—32no—
458C22—31no—
459C22—31no—
460C22—32no—
461C22—31no—
462C22—34no—
463C22—34no—
464C22—34no—
465C22—34no—
466C22C2×C3×#68311yescharacteristic, complemented
467C22A4×Dic1012yes—
468C22C4×D5×A412yes—
469C22A4×C22⋊D512yes—
470C22C22×D5×A411yescharacteristic
471C4—22no—
472C4—54no—
473C4—62no—
474C4—102no—
475C4—154no—
476C4—302no—
477C3—41noSylow
478C2—31no—
479C2—34no—
480C2—31no—
481C2—31no—
482C2—31no—
483C2A4×#68314yesdirect product factor
484C2C2×A4×Dic1011yescharacteristic
485C2C2×C4×D5×A411yescharacteristic
486C2C2×A4×C22⋊D511yescharacteristic
subgroupG/H
centerC23C2×D5×A4
commutatorC23×C5C22×C3×C4
FrattiniC22C22×D5×A4
FittingC24×C4×C5C2×C3
socleC25×C5C22×C3
prime radicalC23×C5×A4C22
cosocleC24×C5C23×C3
hypercenterC22×C4D5×A4
hypocenterC22×C5C2×C3×C4⋊C4
LCSG ▷ C23×C5 ▷ C22×C5
UCSC1 ◁ C23 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. A4×#683C2direct (N × H)
5. C23×#683C3semidirect
10. C2×A4×Dic5C4semidirect
23. C22×#683C2×C3semidirect
33. A4×Dic5C2×C4semidirect
55. C23×Dic5C3×C4semidirect
70. C2×#683A4direct (N × H)
73. C2×C5×A4C4⋊C4semidirect
139. C22×Dic5C2×C3×C4semidirect
146. #683C2×A4direct (N × H)
160. C5×A4C2×C4⋊C4semidirect
196. C23×C5C3×C4⋊C4semidirect
228. C2×Dic5C4×A4semidirect
268. C2×A4#683direct (N × H)
299. C22×C5C2×C3×C4⋊C4semidirect
309. Dic5C2×C4×A4semidirect
371. A4C2×#683direct (N × H)
380. C2×C5A4×C4⋊C4semidirect
405. C23C3×#683semidirect
444. C5C2×A4×C4⋊C4semidirect
466. C22C2×C3×#683semidirect
483. C2A4×#683direct (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×A4×Dic52
A4×#6832
C23×#6833
C2×C3×#6834
C2×A4×C4⋊C45