Finite Group Databasebeta

← C2×#11756728 #14514388

Subgroups — C2×#11756728 #14514388

Order 1920.

726 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 726 conjugacy classes of subgroups — too many to draw. Only its 92 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×A4×Dic5C211yesmaximal, characteristic
2#11756728C214yesmaximal, direct product factor
3C2×A4⋊#170C212yesmaximal, complemented
4C2×#65798—31nomaximal, Hall
5C23×C5×A4C411yescharacteristic
6C2×#6762—41nomaximal
7C2×A4×Dic5C412yes—
8C2×A4×Dic5C411yescharacteristic
9C2×A4×Dic5C2211yescharacteristic
10C2×A4×Dic5C2212yes—
11A4⋊#170C2214yescomplemented
12C2×#5409—51nomaximal, Hall
13C24×Dic5D311yescharacteristic
14C22×#704—31no—
15C22×#704—31no—
16#65798—34no—
17#65798—34no—
18C2×C22⋊#170—32no—
19C2×C22⋊#170—32no—
20C22×C5×A4—22no—
21C22×C5×A4C2×C412yes—
22C22×C5×A4C2×C411yescharacteristic
23C22×C3×Dic5—41no—
24#6762—44no—
25C2×C3⋊#170—42no—
26A4×Dic5C2×C411yescharacteristic
27A4×Dic5C2×C412yes—
28A4×Dic5C2311yescharacteristic
29C22×C4×A4—51no—
30#5409—54no—
31C2×A4⋊C8—52no—
32C25×C5Dic311yescharacteristic
33C23×Dic5—31no—
34C23×Dic5—31no—
35C23×Dic5—32no—
36C23×Dic5—31no—
37C23×Dic5—31no—
38C23×Dic5—32no—
39C23×Dic5Dic312yes—
40C23×Dic5Dic311yescharacteristic
41C23×Dic5C2×D311yescharacteristic
42C23×Dic5C2×D312yes—
43C2×#704—34no—
44C2×#704—34no—
45C2×#704—61no—
46C2×#704—61no—
47C2×#704—62no—
48C2×#704—62no—
49C2×#704—61no—
50C2×#704—61no—
51C22×#170—32no—
52C22×#170—32no—
53C22⋊#170—38no—
54C22⋊#170—34no—
55C22⋊#170—34no—
56C2×#407—151noSylow
57C23×C3×C5—41no—
58C2×C5×A4—22no—
59C2×C5×A4M1612yescomplemented
60C2×C5×A4C22×C411yescharacteristic
61C2×C3×Dic5—41no—
62C2×C3×Dic5—42no—
63C2×C3×Dic5—41no—
64C2×C3×Dic5—42no—
65C3⋊#170—44no—
66C23×A4AGL(1,𝔽5)11yescharacteristic
67C2×C4×A4—51no—
68C2×C4×A4—52no—
69C2×C4×A4—52no—
70C2×C4×A4—51no—
71C2×#208—201no—
72A4⋊C8—54no—
73C24×C5—22no—
74C24×C5—31no—
75C24×C5—31no—
76C24×C5—32no—
77C24×C5—62no—
78C24×C5C2×Dic312yes—
79C24×C5C2×Dic311yescharacteristic
80C22×Dic5—31no—
81C22×Dic5—31no—
82C22×Dic5—32no—
83C22×Dic5—31no—
84C22×Dic5—32no—
85C22×Dic5—31no—
86C22×Dic5—32no—
87C22×Dic5—32no—
88C22×Dic5—31no—
89C22×Dic5—31no—
90C22×Dic5—32no—
91C22×Dic5—32no—
92C22×Dic5—32no—
93C22×Dic5—32no—
94C22×Dic5—31no—
95C22×Dic5—32no—
96C22×Dic5—31no—
97C22×Dic5—32no—
98C22×Dic5—31no—
99C22×Dic5—32no—
100C22×Dic5—61no—
101C22×Dic5—62no—
102C22×Dic5—61no—
103C22×Dic5—61no—
104C22×Dic5—62no—
105C22×Dic5C2×Dic311yescharacteristic
106C22×Dic5C2×Dic312yes—
107C22×Dic5S411yescharacteristic
108C22×Dic5C22×D311yescharacteristic
109#704—64no—
110#704—64no—
111#704—64no—
112#704—64no—
113C2×#170—34no—
114C2×#170—34no—
115C2×#170—62no—
116C2×#170—62no—
117C2×#170—62no—
118C2×#170—62no—
119C24×C4—51no—
120C22×M16—151no—
121C22×M16—151no—
122#407—154no—
123#407—154no—
124C2×C22⋊C8—152no—
125C2×C22⋊C8—152no—
126C22×C3×C5—41no—
127C22×C3×C5—42no—
128C22×C3×C5—82no—
129C5×A4C2×M1611yescharacteristic, complemented
130C3×Dic5—41no—
131C3×Dic5—42no—
132C3×Dic5—41no—
133C22×A4—22no—
134C22×A4C2×AGL(1,𝔽5)12yes—
135C22×A4C2×AGL(1,𝔽5)11yescharacteristic
136C22×C3×C4—201no—
137C4×A4—51no—
138C4×A4—51no—
139C4×A4—52no—
140#208—204no—
141C2×C3⋊C8—202no—
142C23×C5—22no—
143C23×C5—31no—
144C23×C5—31no—
145C23×C5—32no—
146C23×C5—32no—
147C23×C5—34no—
148C23×C5—32no—
149C23×C5—32no—
150C23×C5—31no—
151C23×C5—62no—
152C23×C5—62no—
153C23×C5—62no—
154C23×C5—61no—
155C23×C5—64no—
156C23×C5—62no—
157C23×C5—64no—
158C23×C5#20812yescomplemented
159C23×C5SL(2,ℤ/4)11yescharacteristic
160C23×C5C22×Dic311yescharacteristic
161C2×Dic5—31no—
162C2×Dic5—32no—
163C2×Dic5—32no—
164C2×Dic5—31no—
165C2×Dic5—31no—
166C2×Dic5—32no—
167C2×Dic5—31no—
168C2×Dic5—32no—
169C2×Dic5—32no—
170C2×Dic5—32no—
171C2×Dic5—32no—
172C2×Dic5—31no—
173C2×Dic5—31no—
174C2×Dic5—32no—
175C2×Dic5—31no—
176C2×Dic5—32no—
177C2×Dic5—31no—
178C2×Dic5—61no—
179C2×Dic5—62no—
180C2×Dic5—61no—
181C2×Dic5—62no—
182C2×Dic5SL(2,ℤ/4)12yes—
183C2×Dic5SL(2,ℤ/4)11yescharacteristic
184C2×Dic5C2×S411yescharacteristic
185C2×Dic5C2×S412yes—
186#170—64no—
187#170—64no—
188C25ΓL(1,𝔽16)11yescharacteristic
189C23×C4—52no—
190C23×C4—51no—
191C23×C4—51no—
192C23×C4—52no—
193C23×C4—151no—
194C23×C4—151no—
195C23×C4—152no—
196C23×C4—151no—
197C23×C4—151no—
198C23×C4—152no—
199C2×M16—154no—
200C2×M16—154no—
201C2×M16—301no—
202C2×M16—301no—
203C2×M16—302no—
204C2×M16—302no—
205C2×M16—301no—
206C2×M16—301no—
207C22×C8—152no—
208C22×C8—152no—
209C22⋊C8—154no—
210C22⋊C8—154no—
211C22⋊C8—158no—
212C2×C3×C5—42no—
213C2×C3×C5—41no—
214C2×C3×C5—82no—
215C23×C3—41no—
216C2×A4—22no—
217C2×A4#70412yescomplemented
218C2×A4C22×AGL(1,𝔽5)11yescharacteristic
219C2×C3×C4—201no—
220C2×C3×C4—202no—
221C2×C3×C4—202no—
222C2×C3×C4—201no—
223C3⋊C8—204no—
224C22×C5—22no—
225C22×C5—32no—
226C22×C5—31no—
227C22×C5—32no—
228C22×C5—32no—
229C22×C5—31no—
230C22×C5—31no—
231C22×C5—34no—
232C22×C5—32no—
233C22×C5—62no—
234C22×C5—62no—
235C22×C5—64no—
236C22×C5—61no—
237C22×C5—62no—
238C22×C5—64no—
239C22×C5—62no—
240C22×C5C2×#20811yescharacteristic, complemented
241C22×C5C2×SL(2,ℤ/4)12yes—
242C22×C5C2×SL(2,ℤ/4)11yescharacteristic
243Dic5—31no—
244Dic5—31no—
245Dic5—32no—
246Dic5C2×SL(2,ℤ/4)11yescharacteristic
247Dic5C2×SL(2,ℤ/4)12yes—
248Dic5C22×S411yescharacteristic
249C24—22no—
250C24—31no—
251C24—31no—
252C24—32no—
253C24—62no—
254C24C2×ΓL(1,𝔽16)12yes—
255C24C2×ΓL(1,𝔽16)11yescharacteristic
256C22×C4—51no—
257C22×C4—51no—
258C22×C4—51no—
259C22×C4—52no—
260C22×C4—151no—
261C22×C4—152no—
262C22×C4—152no—
263C22×C4—152no—
264C22×C4—151no—
265C22×C4—151no—
266C22×C4—152no—
267C22×C4—151no—
268C22×C4—151no—
269C22×C4—151no—
270C22×C4—152no—
271C22×C4—151no—
272C22×C4—152no—
273C22×C4—152no—
274C22×C4—152no—
275C22×C4—152no—
276C22×C4—152no—
277C22×C4—152no—
278C22×C4—151no—
279C22×C4—151no—
280C22×C4—301no—
281C22×C4—301no—
282C22×C4—302no—
283C22×C4—302no—
284C22×C4—301no—
285M16—304no—
286M16—304no—
287M16—304no—
288M16—304no—
289C2×C8—154no—
290C2×C8—154no—
291C2×C8—302no—
292C2×C8—302no—
293C2×C8—302no—
294C2×C8—302no—
295C3×C5—41noHall
296C22×C3—42no—
297C22×C3—41no—
298C22×C3—82no—
299A4C2×#70411yescharacteristic, complemented
300C3×C4—201no—
301C3×C4—201no—
302C3×C4—202no—
303C2×C5—22no—
304C2×C5—31no—
305C2×C5—31no—
306C2×C5—32no—
307C2×C5—62no—
308C2×C5#540912yescomplemented
309C2×C5C22×SL(2,ℤ/4)11yescharacteristic
310C23—22no—
311C23—31no—
312C23—31no—
313C23—32no—
314C23—32no—
315C23—34no—
316C23—32no—
317C23—32no—
318C23—31no—
319C23—62no—
320C23—62no—
321C23—62no—
322C23—61no—
323C23—64no—
324C23—62no—
325C23—64no—
326C23#676212yescomplemented
327C23A4⋊AGL(1,𝔽5)11yescharacteristic
328C23C22×ΓL(1,𝔽16)11yescharacteristic
329C2×C4—52no—
330C2×C4—52no—
331C2×C4—51no—
332C2×C4—51no—
333C2×C4—151no—
334C2×C4—151no—
335C2×C4—151no—
336C2×C4—152no—
337C2×C4—152no—
338C2×C4—151no—
339C2×C4—152no—
340C2×C4—152no—
341C2×C4—152no—
342C2×C4—152no—
343C2×C4—152no—
344C2×C4—152no—
345C2×C4—151no—
346C2×C4—151no—
347C2×C4—151no—
348C2×C4—151no—
349C2×C4—152no—
350C2×C4—301no—
351C2×C4—302no—
352C2×C4—301no—
353C2×C4—302no—
354C8—304no—
355C8—304no—
356C2×C3—41no—
357C2×C3—42no—
358C2×C3—82no—
359C5C2×#540911yescharacteristic, complemented, Sylow
360C22—22no—
361C22—32no—
362C22—31no—
363C22—31no—
364C22—31no—
365C22—32no—
366C22—32no—
367C22—34no—
368C22—32no—
369C22—62no—
370C22—62no—
371C22—64no—
372C22—61no—
373C22—62no—
374C22—64no—
375C22—62no—
376C22C2×#676211yescharacteristic, complemented
377C22C2×A4⋊AGL(1,𝔽5)12yes—
378C22C2×A4⋊AGL(1,𝔽5)11yescharacteristic
379C4—51no—
380C4—52no—
381C4—51no—
382C4—151no—
383C4—151no—
384C4—152no—
385C3—41noSylow
386C2—22no—
387C2—31no—
388C2—31no—
389C2—32no—
390C2—62no—
391C2#1175672812yesdirect product factor
392C2C22×A4⋊AGL(1,𝔽5)11yescharacteristic
subgroupG/H
centerC22C2×A4⋊AGL(1,𝔽5)
commutatorC2×C5×A4C22×C4
FrattiniC2C22×A4⋊AGL(1,𝔽5)
FittingC25×C5Dic3
socleC24×C5C2×Dic3
prime radicalC23×C5×A4C4
cosocleA4×Dic5C23
hypercenterC23A4⋊AGL(1,𝔽5)
hypocenterC5×A4C2×M16
LCSG ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11756728C2direct (N × H)
3. C2×A4⋊#170C2semidirect
11. A4⋊#170C22semidirect
59. C2×C5×A4M16semidirect
129. C5×A4C2×M16semidirect
158. C23×C5#208semidirect
217. C2×A4#704semidirect
240. C22×C5C2×#208semidirect
299. A4C2×#704semidirect
308. C2×C5#5409semidirect
326. C23#6762semidirect
359. C5C2×#5409semidirect
376. C22C2×#6762semidirect
391. C2#11756728direct (N × H)

Maximal subgroups

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

subgroupindex
C22×A4×Dic52
#117567282
C2×A4⋊#1702
C2×#657983
C2×#67624
C2×#54095