Finite Group Databasebeta

← C2×#11751576 #14512994

Subgroups — C2×#11751576 #14512994

Order 1920.

534 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 71 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×#91948C211yesmaximal, characteristic
2C2×C5×A4⋊Q8C211yesmaximal, characteristic
3C2×A4×#168C211yesmaximal, characteristic
4#11751576C214yesmaximal, direct product factor
5C2×#65340—31nomaximal, Hall
6C2×C4×C5×A4C2211yescharacteristic
7C2×A4⋊Dic5—21no—
8#91948—21no—
9#91948C2212yes—
10C2×C5×SL(2,ℤ/4)—21no—
11C5×A4⋊Q8—21no—
12C5×A4⋊Q8C2212yes—
13C2×#6663—41nomaximal
14A4×#168C2212yes—
15C2×#5398—51nomaximal, Hall
16C2×C5×C22⋊Q8—31no—
17C22×#689—31no—
18C2×#4070—31no—
19C23×#168D311yescharacteristic
20C2×#3967—31no—
21#65340—34no—
22#65340—34no—
23C2×#3942—31no—
24C2×#3939—31no—
25C22×C5×A4D411yescharacteristic
26C2×Dic30—41no—
27C2×C5×Dic6—41no—
28C4×C5×A4D411yescharacteristic
29C4×C5×A4C2311yescharacteristic
30A4⋊Dic5—22no—
31C5×SL(2,ℤ/4)—22no—
32C2×C3×#168—41no—
33#6663—44no—
34C2×A4⋊Q8—51no—
35C2×A4⋊Q8D511yescharacteristic
36C2×C8×A4—51no—
37#5398—54no—
38C22×C5×Q8—31no—
39C23×C4×C5C2×D311yescharacteristic
40C22×Dic10—31no—
41C5×C22⋊Q8—32no—
42C5×C22⋊Q8—32no—
43C5×C22⋊Q8—61no—
44C5×C22⋊Q8—61no—
45C2×C5×C4⋊C4—31no—
46C2×C5×C4⋊C4—61no—
47C2×C5×C22⋊C4—61no—
48C2×C22⋊Dic5—61no—
49C2×#689—34no—
50C2×#689—61no—
51C2×#689—62no—
52C2×#689—61no—
53C2×C4⋊Dic5—31no—
54#4070—32no—
55#4070—32no—
56#4070—61no—
57#4070—61no—
58C2×#683—61no—
59C22×#168—31no—
60C22×#168—32no—
61C22×#168—31no—
62C22×#168C2×D312yes—
63#3967—34no—
64#3942—34no—
65#3939—34no—
66C2×#467—151noSylow
67C2×C5×A4Q1612yescomplemented
68C2×C5×A4C2×D411yescharacteristic
69C2×C3×C4×C5—41no—
70C2×Dic15—81no—
71Dic30—42no—
72Dic30—81no—
73C2×C5×Dic3—81no—
74C5×Dic6—42no—
75C5×Dic6—81no—
76C3×#168—42no—
77C2×C4×A4C2×D511yescharacteristic
78C2×SL(2,ℤ/4)—21no—
79C2×SL(2,ℤ/4)—101no—
80A4⋊Q8—21no—
81A4⋊Q8—52no—
82A4⋊Q8—101no—
83A4⋊Q8C2×D512yes—
84C2×Dic12—201no—
85C8×A4—52no—
86C24×C5D1211yescharacteristic
87C2×C5×Q8—32no—
88C2×C5×Q8—61no—
89C2×C5×Q8—61no—
90C2×C5×Q8—61no—
91C2×C5×Q8—61no—
92C2×C5×Q8—61no—
93C22×C4×C5—31no—
94C22×C4×C5—31no—
95C22×C4×C5—31no—
96C22×C4×C5—31no—
97C22×C4×C5—61no—
98C22×C4×C5—61no—
99C22×C4×C5D1211yescharacteristic
100C22×C4×C5C22×D311yescharacteristic
101C22×Dic5—61no—
102C22×Dic5—61no—
103C2×Dic10—32no—
104C2×Dic10—61no—
105C2×Dic10—61no—
106C2×Dic10—61no—
107C2×Dic10—61no—
108C2×Dic10—61no—
109C5×C4⋊C4—32no—
110C5×C4⋊C4—61no—
111C5×C4⋊C4—62no—
112C5×C4⋊C4—62no—
113C5×C22⋊C4—62no—
114C5×C22⋊C4—62no—
115C22⋊Dic5—62no—
116C22⋊Dic5—62no—
117#689—64no—
118#689—64no—
119C4⋊Dic5—32no—
120C4⋊Dic5—61no—
121#683—62no—
122#683—62no—
123C2×#168—31no—
124C2×#168—32no—
125C2×#168—32no—
126C2×#168—32no—
127C2×#168—61no—
128C2×#168S411yescharacteristic
129C22×Q16—151no—
130C23×C8—51no—
131C2×C22⋊Q8—31no—
132C2×C22⋊Q8—151no—
133#467—154no—
134#467—154no—
135C2×#107—151no—
136C2×#103—151no—
137C2×#103—151no—
138C22×C3×C5—41no—
139C5×A4C2×Q1611yescharacteristic, complemented
140C3×C4×C5—41no—
141C3×C4×C5—41no—
142Dic15—82no—
143C5×Dic3—82no—
144C22×A4C22⋊D511yescharacteristic
145C2×Dic6—41no—
146C2×Dic6—201no—
147C4×A4C22⋊D511yescharacteristic
148C4×A4C22×D511yescharacteristic
149SL(2,ℤ/4)—22no—
150SL(2,ℤ/4)—102no—
151C2×C3×C8—201no—
152Dic12—204no—
153C23×C5—31no—
154C23×C5—31no—
155C23×C5—32no—
156C23×C5Dic1212yescomplemented
157C23×C5C2×D1211yescharacteristic
158C5×Q8—62no—
159C5×Q8—62no—
160C5×Q8—121no—
161C5×Q8—121no—
162C2×C4×C5—31no—
163C2×C4×C5—31no—
164C2×C4×C5—31no—
165C2×C4×C5—31no—
166C2×C4×C5—31no—
167C2×C4×C5—31no—
168C2×C4×C5—31no—
169C2×C4×C5—61no—
170C2×C4×C5—62no—
171C2×C4×C5—62no—
172C2×C4×C5—122no—
173C2×C4×C5—121no—
174C2×C4×C5—121no—
175C2×C4×C5C2×S411yescharacteristic
176C2×Dic5—62no—
177C2×Dic5—62no—
178C2×Dic5—121no—
179C2×Dic5—122no—
180C2×Dic5—121no—
181Dic10—62no—
182Dic10—62no—
183Dic10—121no—
184Dic10—121no—
185#168—32no—
186#168C2×S412yes—
187C22×Q8—31no—
188C22×Q8—151no—
189C23×C4D3×D511yescharacteristic
190C2×Q16—154no—
191C2×Q16—301no—
192C2×Q16—302no—
193C2×Q16—301no—
194C22×C8—52no—
195C22×C8—151no—
196C22×C8—151no—
197C22×C8—152no—
198C22⋊Q8—32no—
199C22⋊Q8—32no—
200C22⋊Q8—61no—
201C22⋊Q8—61no—
202C22⋊Q8—152no—
203C22⋊Q8—152no—
204C22⋊Q8—301no—
205C22⋊Q8—301no—
206C2×C4⋊C4—31no—
207C2×C4⋊C4—61no—
208C2×C4⋊C4—151no—
209C2×C4⋊C4—301no—
210C2×C22⋊C4—61no—
211C2×C22⋊C4—301no—
212#107—154no—
213#103—154no—
214#103—154no—
215C2×C3×C5—42no—
216C2×C3×C5—41no—
217C2×A4#68912yescomplemented
218C2×A4C2×C22⋊D511yescharacteristic
219C2×C3×C4—41no—
220C2×Dic3—81no—
221C2×Dic3—401no—
222Dic6—42no—
223Dic6—81no—
224Dic6—202no—
225Dic6—401no—
226C3×C8—202no—
227C22×C5—32no—
228C22×C5—31no—
229C22×C5—32no—
230C22×C5—32no—
231C22×C5—31no—
232C22×C5—31no—
233C22×C5—61no—
234C22×C5C2×Dic1211yescharacteristic, complemented
235C22×C5C4⋊S411yescharacteristic
236C4×C5—31no—
237C4×C5—31no—
238C4×C5—122no—
239C4×C5—122no—
240C4×C5C4⋊S411yescharacteristic
241C4×C5C22×S411yescharacteristic
242Dic5—122no—
243Dic5—122no—
244C24#120311yescharacteristic
245C2×Q8—32no—
246C2×Q8—61no—
247C2×Q8—61no—
248C2×Q8—61no—
249C2×Q8—61no—
250C2×Q8—61no—
251C2×Q8—152no—
252C2×Q8—301no—
253C2×Q8—301no—
254C2×Q8—301no—
255C2×Q8—301no—
256C2×Q8—301no—
257C22×C4—31no—
258C22×C4—31no—
259C22×C4—31no—
260C22×C4—31no—
261C22×C4—61no—
262C22×C4—61no—
263C22×C4—301no—
264C22×C4—301no—
265C22×C4#120311yescharacteristic
266C22×C4C2×D3×D511yescharacteristic
267Q16—304no—
268Q16—304no—
269C2×C8—51no—
270C2×C8—152no—
271C2×C8—152no—
272C2×C8—151no—
273C2×C8—152no—
274C2×C8—301no—
275C4⋊C4—32no—
276C4⋊C4—61no—
277C4⋊C4—62no—
278C4⋊C4—62no—
279C4⋊C4—152no—
280C4⋊C4—301no—
281C4⋊C4—302no—
282C4⋊C4—302no—
283C22⋊C4—62no—
284C22⋊C4—62no—
285C22⋊C4—302no—
286C22⋊C4—302no—
287C3×C5—41noHall
288C22×C3—41no—
289A4C2×#68911yescharacteristic, complemented
290C3×C4—41no—
291C3×C4—41no—
292Dic3—82no—
293Dic3—402no—
294C2×C5—31no—
295C2×C5—31no—
296C2×C5—32no—
297C2×C5#539812yescomplemented
298C2×C5C2×C4⋊S411yescharacteristic
299C23—31no—
300C23—31no—
301C23—32no—
302C23#666312yescomplemented
303C23C2×#120311yescharacteristic
304Q8—62no—
305Q8—62no—
306Q8—121no—
307Q8—121no—
308Q8—302no—
309Q8—302no—
310Q8—601no—
311Q8—601no—
312C2×C4—31no—
313C2×C4—31no—
314C2×C4—31no—
315C2×C4—31no—
316C2×C4—31no—
317C2×C4—31no—
318C2×C4—31no—
319C2×C4—61no—
320C2×C4—62no—
321C2×C4—62no—
322C2×C4—121no—
323C2×C4—122no—
324C2×C4—121no—
325C2×C4—302no—
326C2×C4—302no—
327C2×C4—601no—
328C2×C4—602no—
329C2×C4—601no—
330C2×C4D5×S411yescharacteristic
331C8—52no—
332C8—152no—
333C2×C3—42no—
334C2×C3—41no—
335C5C2×#539811yescharacteristic, complemented, Sylow
336C22—32no—
337C22—31no—
338C22—32no—
339C22—32no—
340C22—31no—
341C22—31no—
342C22—61no—
343C22C2×#666311yescharacteristic, complemented
344C22#9190211yescharacteristic
345C4—31no—
346C4—31no—
347C4—122no—
348C4—122no—
349C4—602no—
350C4—602no—
351C4#9190211yescharacteristic
352C4C2×D5×S411yescharacteristic
353C3—41noSylow
354C2—31no—
355C2—31no—
356C2—32no—
357C2#1175157612yesdirect product factor
358C2C2×#9190211yescharacteristic
subgroupG/H
centerC22#91902
commutator, cosocleC4×C5×A4C23
FrattiniC4C2×D5×S4
FittingC23×C4×C5C2×D3
socleC24×C5D12
prime radicalC22×C5×A4D4
hypercenterC2×C4D5×S4
hypocenterC5×A4C2×Q16
LCSG ▷ C4×C5×A4 ▷ C2×C5×A4 ▷ C5×A4
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
4. #11751576C2direct (N × H)
67. C2×C5×A4Q16semidirect
139. C5×A4C2×Q16semidirect
156. C23×C5Dic12semidirect
217. C2×A4#689semidirect
234. C22×C5C2×Dic12semidirect
289. A4C2×#689semidirect
297. C2×C5#5398semidirect
302. C23#6663semidirect
335. C5C2×#5398semidirect
343. C22C2×#6663semidirect
357. C2#11751576direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#919482
C2×C5×A4⋊Q82
C2×A4×#1682
#117515762
C2×#653403
C2×#66634
C2×#53985