Finite Group Databasebeta

← C2×#11756927 #14514641

Subgroups — C2×#11756927 #14514641

Order 1920.

1694 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 1694 conjugacy classes of subgroups — too many to draw. Only its 63 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×C5×C22⋊A4C211yesmaximal, characteristic
2#11756927C212yesmaximal, direct product factor
3C2×#65536—31nomaximal, Hall
4C2×C5×C22⋊A4C412yescomplemented
5C2×C5×C22⋊A4C2211yescharacteristic
6C2×A4⋊Dic5—43nomaximal
7C2×#5936—51nomaximal, Hall
8C26×C5D311yescharacteristic
9C22×C22⋊Dic5—33no—
10C22×C22⋊Dic5—33no—
11#65536—36no—
12#65536—32no—
13C5×C22⋊A4C2×C411yescharacteristic, complemented
14C22×C5×A4—43no—
15C22×C5×A4—81no—
16A4⋊Dic5—46no—
17C22×C22⋊A4D511yescharacteristic
18#5936—52no—
19C25×C5—33no—
20C25×C5—33no—
21C25×C5—36no—
22C25×C5—61no—
23C25×C5—62no—
24C25×C5—61no—
25C25×C5Dic312yescomplemented
26C25×C5C2×D311yescharacteristic
27C23×Dic5—33no—
28C23×Dic5—31no—
29C2×C22⋊Dic5—36no—
30C2×C22⋊Dic5—36no—
31C2×C22⋊Dic5—36no—
32C2×C22⋊Dic5—36no—
33C2×C22⋊Dic5—63no—
34C2×C22⋊Dic5—66no—
35C2×C22⋊Dic5—63no—
36C2×C22⋊Dic5—66no—
37C2×C22⋊Dic5—63no—
38C2×C22⋊Dic5—63no—
39C2×#379—151noSylow
40C2×C5×A4—46no—
41C2×C5×A4—43no—
42C2×C5×A4—82no—
43C2×C5×A4—81no—
44C2×Dic15—161no—
45C2×C22⋊A4Dic512yescomplemented
46C2×C22⋊A4C2×D511yescharacteristic
47C2×SL(2,ℤ/4)—203no—
48C24×C5—21no—
49C24×C5—31no—
50C24×C5—33no—
51C24×C5—33no—
52C24×C5—36no—
53C24×C5—33no—
54C24×C5—36no—
55C24×C5—36no—
56C24×C5—36no—
57C24×C5—33no—
58C24×C5—33no—
59C24×C5—36no—
60C24×C5—33no—
61C24×C5—36no—
62C24×C5—62no—
63C24×C5—61no—
64C24×C5—62no—
65C24×C5—61no—
66C24×C5—62no—
67C24×C5—61no—
68C24×C5—63no—
69C24×C5—66no—
70C24×C5—612no—
71C24×C5—63no—
72C24×C5—63no—
73C24×C5—612no—
74C24×C5—66no—
75C24×C5—66no—
76C24×C5—63no—
77C24×C5—63no—
78C24×C5—66no—
79C24×C5—66no—
80C24×C5—62no—
81C24×C5C2×Dic311yescharacteristic, complemented
82C24×C5S413yes—
83C22×Dic5—36no—
84C22×Dic5—32no—
85C22×Dic5—612no—
86C22×Dic5—63no—
87C22×Dic5—63no—
88C22×Dic5—63no—
89C22×Dic5—63no—
90C22⋊Dic5—66no—
91C22⋊Dic5—612no—
92C22⋊Dic5—66no—
93C22⋊Dic5—66no—
94C22⋊Dic5—66no—
95C22⋊Dic5—66no—
96C22⋊Dic5—66no—
97C26D1511yescharacteristic
98C22×C22⋊C4—153no—
99C22×C22⋊C4—153no—
100#379—156no—
101#379—152no—
102C22×C3×C5—161no—
103C5×A4—43no—
104C5×A4—81no—
105Dic15—162no—
106C22⋊A4C2×Dic511yescharacteristic, complemented
107C22×A4—43no—
108C22×A4—81no—
109SL(2,ℤ/4)—206no—
110C23×C5—22no—
111C23×C5—21no—
112C23×C5—31no—
113C23×C5—36no—
114C23×C5—33no—
115C23×C5—32no—
116C23×C5—33no—
117C23×C5—33no—
118C23×C5—36no—
119C23×C5—36no—
120C23×C5—33no—
121C23×C5—33no—
122C23×C5—33no—
123C23×C5—36no—
124C23×C5—33no—
125C23×C5—36no—
126C23×C5—36no—
127C23×C5—36no—
128C23×C5—36no—
129C23×C5—36no—
130C23×C5—33no—
131C23×C5—33no—
132C23×C5—36no—
133C23×C5—61no—
134C23×C5—62no—
135C23×C5—61no—
136C23×C5—612no—
137C23×C5—612no—
138C23×C5—66no—
139C23×C5—66no—
140C23×C5—66no—
141C23×C5—612no—
142C23×C5—66no—
143C23×C5—63no—
144C23×C5—66no—
145C23×C5—63no—
146C23×C5—66no—
147C23×C5—63no—
148C23×C5—66no—
149C23×C5—612no—
150C23×C5—66no—
151C23×C5—612no—
152C23×C5—66no—
153C23×C5—63no—
154C23×C5—66no—
155C23×C5—63no—
156C23×C5—612no—
157C23×C5—66no—
158C23×C5—62no—
159C23×C5—61no—
160C23×C5—66no—
161C23×C5—66no—
162C23×C5—66no—
163C23×C5—66no—
164C23×C5—61no—
165C23×C5SL(2,ℤ/4)16yescomplemented
166C23×C5C2×S413yes—
167C2×Dic5—612no—
168C2×Dic5—66no—
169C2×Dic5—66no—
170C2×Dic5—126no—
171C2×Dic5—126no—
172C2×Dic5—123no—
173C2×Dic5—121no—
174C25—33no—
175C25—36no—
176C25—33no—
177C25—61no—
178C25—62no—
179C25—61no—
180C25Dic1512yescomplemented
181C25C2×D1511yescharacteristic
182C23×C4—153no—
183C23×C4—151no—
184C2×C22⋊C4—156no—
185C2×C22⋊C4—156no—
186C2×C22⋊C4—156no—
187C2×C22⋊C4—156no—
188C2×C22⋊C4—303no—
189C2×C22⋊C4—306no—
190C2×C22⋊C4—303no—
191C2×C22⋊C4—306no—
192C2×C22⋊C4—303no—
193C2×C22⋊C4—303no—
194C2×C3×C5—162no—
195C2×C3×C5—161no—
196C2×A4—46no—
197C2×A4—43no—
198C2×A4—82no—
199C2×A4—81no—
200C2×Dic3—801no—
201C22×C5—21no—
202C22×C5—36no—
203C22×C5—33no—
204C22×C5—33no—
205C22×C5—36no—
206C22×C5—31no—
207C22×C5—36no—
208C22×C5—36no—
209C22×C5—36no—
210C22×C5—33no—
211C22×C5—33no—
212C22×C5—33no—
213C22×C5—36no—
214C22×C5—33no—
215C22×C5—63no—
216C22×C5—63no—
217C22×C5—66no—
218C22×C5—612no—
219C22×C5—63no—
220C22×C5—612no—
221C22×C5—66no—
222C22×C5—66no—
223C22×C5—63no—
224C22×C5—63no—
225C22×C5—66no—
226C22×C5—66no—
227C22×C5—62no—
228C22×C5—61no—
229C22×C5—62no—
230C22×C5—62no—
231C22×C5—62no—
232C22×C5—61no—
233C22×C5—61no—
234C22×C5C2×SL(2,ℤ/4)13yescomplemented
235C22×C5#102011yescharacteristic
236Dic5—126no—
237Dic5—122no—
238C24—21no—
239C24—31no—
240C24—33no—
241C24—33no—
242C24—36no—
243C24—33no—
244C24—36no—
245C24—36no—
246C24—36no—
247C24—33no—
248C24—33no—
249C24—36no—
250C24—33no—
251C24—36no—
252C24—62no—
253C24—61no—
254C24—62no—
255C24—61no—
256C24—62no—
257C24—61no—
258C24—63no—
259C24—66no—
260C24—612no—
261C24—63no—
262C24—63no—
263C24—612no—
264C24—66no—
265C24—66no—
266C24—63no—
267C24—63no—
268C24—66no—
269C24—66no—
270C24—62no—
271C24C2×Dic1511yescharacteristic, complemented
272C24C5⋊S413yes—
273C22×C4—156no—
274C22×C4—152no—
275C22×C4—3012no—
276C22×C4—303no—
277C22×C4—303no—
278C22×C4—303no—
279C22×C4—303no—
280C22⋊C4—306no—
281C22⋊C4—3012no—
282C22⋊C4—306no—
283C22⋊C4—306no—
284C22⋊C4—306no—
285C22⋊C4—306no—
286C22⋊C4—306no—
287C3×C5—161noHall
288C22×C3—161no—
289A4—43no—
290A4—81no—
291Dic3—802no—
292C2×C5—33no—
293C2×C5—33no—
294C2×C5—36no—
295C2×C5—61no—
296C2×C5—62no—
297C2×C5—61no—
298C2×C5#593612yescomplemented
299C2×C5C2×#102011yescharacteristic
300C23—22no—
301C23—21no—
302C23—31no—
303C23—36no—
304C23—33no—
305C23—32no—
306C23—33no—
307C23—33no—
308C23—36no—
309C23—36no—
310C23—33no—
311C23—33no—
312C23—33no—
313C23—36no—
314C23—33no—
315C23—36no—
316C23—36no—
317C23—36no—
318C23—36no—
319C23—36no—
320C23—33no—
321C23—33no—
322C23—36no—
323C23—61no—
324C23—62no—
325C23—61no—
326C23—612no—
327C23—612no—
328C23—66no—
329C23—66no—
330C23—66no—
331C23—612no—
332C23—66no—
333C23—63no—
334C23—66no—
335C23—63no—
336C23—66no—
337C23—63no—
338C23—66no—
339C23—612no—
340C23—66no—
341C23—612no—
342C23—66no—
343C23—63no—
344C23—66no—
345C23—63no—
346C23—612no—
347C23—66no—
348C23—62no—
349C23—61no—
350C23—66no—
351C23—66no—
352C23—66no—
353C23—66no—
354C23—61no—
355C23A4⋊Dic516yescomplemented
356C23C2×C5⋊S413yes—
357C2×C4—3012no—
358C2×C4—306no—
359C2×C4—306no—
360C2×C4—606no—
361C2×C4—606no—
362C2×C4—603no—
363C2×C4—601no—
364C2×C3—162no—
365C2×C3—161no—
366C5C2×#593611yescharacteristic, complemented, Sylow
367C22—21no—
368C22—36no—
369C22—33no—
370C22—33no—
371C22—36no—
372C22—31no—
373C22—36no—
374C22—36no—
375C22—36no—
376C22—33no—
377C22—33no—
378C22—33no—
379C22—36no—
380C22—33no—
381C22—63no—
382C22—63no—
383C22—66no—
384C22—612no—
385C22—63no—
386C22—612no—
387C22—66no—
388C22—66no—
389C22—63no—
390C22—63no—
391C22—66no—
392C22—66no—
393C22—62no—
394C22—61no—
395C22—62no—
396C22—62no—
397C22—62no—
398C22—61no—
399C22—61no—
400C22C2×A4⋊Dic513yescomplemented
401C22C5⋊#102011yescharacteristic
402C4—606no—
403C4—602no—
404C3—161noSylow
405C2—33no—
406C2—33no—
407C2—36no—
408C2—61no—
409C2—62no—
410C2—61no—
411C2#1175692712yesdirect product factor
412C2C2×C5⋊#102011yescharacteristic
subgroupG/H
center, hypercenterC22C5⋊#1020
commutator, hypocenterC5×C22⋊A4C2×C4
FrattiniC2C2×C5⋊#1020
Fitting, socleC26×C5D3
prime radicalC22×C5×C22⋊A4C2
cosocleC2×C5×C22⋊A4C22
LCSG ▷ C5×C22⋊A4
UCSC1 ◁ C22

Complements

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

NH ≅ G/Ntype
2. #11756927C2direct (N × H)
4. C2×C5×C22⋊A4C4semidirect
13. C5×C22⋊A4C2×C4semidirect
25. C25×C5Dic3semidirect
45. C2×C22⋊A4Dic5semidirect
81. C24×C5C2×Dic3semidirect
106. C22⋊A4C2×Dic5semidirect
165. C23×C5SL(2,ℤ/4)semidirect
180. C25Dic15semidirect
234. C22×C5C2×SL(2,ℤ/4)semidirect
271. C24C2×Dic15semidirect
298. C2×C5#5936semidirect
355. C23A4⋊Dic5semidirect
366. C5C2×#5936semidirect
400. C22C2×A4⋊Dic5semidirect
411. C2#11756927direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×C22⋊A42
#117569272
C2×#655363
C2×A4⋊Dic54
C2×#59365