Finite Group Databasebeta

← C2×#11755124 #14479035

Subgroups — C2×#11755124 #14479035

Order 1920.

2976 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q8×D15C211yesmaximal, characteristic
2C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×Q8×Dic5C211yesmaximal, characteristic, complemented
4#11755124C2116yesmaximal, direct product factor
5C2×#91386C213yesmaximal
6C2×#91347C213yesmaximal
7C2×#91340C213yesmaximal, complemented
8C2×#91333C213yesmaximal, complemented
9C2×#65906—31nomaximal, Hall
10C22×C3×C5×Q8C2211yescharacteristic
11C2×Q8×D15C4116yescomplemented
12C2×Q8×D15C2218yes—
13C22×C4×D15C2213yes—
14C22×Dic30C2213yes—
15C5×Q8×Dic3C2218yescomplemented
16C2×C5×C4⋊Dic3C2213yes—
17C2×C4×C5×Dic3C2213yes—
18C3×Q8×Dic5C2218yescomplemented
19C2×C3×C4⋊Dic5C2213yes—
20C2×C3×C4×Dic5C2213yes—
21C2×#6669C2213yes—
22C2×#6669C2213yes—
23C2×#6667C2211yescharacteristic
24C2×#6667C2213yes—
25C2×Dic3×Dic5C2216yes—
26#91386C22124yes—
27#91347C22124yes—
28#91340C22124yescomplemented
29#91333C22124yescomplemented
30C2×#5572—51nomaximal, Hall
31C22×Q8×D5—31no—
32C2×C4×C5×Q8—31no—
33C2×Q8×Dic5D311yescharacteristic, complemented
34#65906—316no—
35C2×#4038—33no—
36C2×#4033—33no—
37C2×#4018—33no—
38C2×C4×Dic10—33no—
39C23×D15C2311yescharacteristic
40C2×C3×C5×Q8C2×C418yes—
41C2×C3×C5×Q8C2314yes—
42C22×C3×C4×C5C2313yes—
43C22×Dic15C2313yes—
44Q8×D15C2×C4164yescomplemented
45C2×C4×D15C2×C4124yes—
46C2×C4×D15C23112yes—
47C2×Dic30C2×C4124yes—
48C2×Dic30C23112yes—
49C22×C5×Dic3C2311yescharacteristic
50C22×C5×Dic3C2313yes—
51C22×C3×Dic5C2313yes—
52C22×C3×Dic5C2311yescharacteristic
53C5×C4⋊Dic3C23112yes—
54C4×C5×Dic3C23112yes—
55C3×C4⋊Dic5C23112yes—
56C3×C4×Dic5C23112yes—
57#6669C23112yes—
58#6669C23112yes—
59#6667C23112yes—
60#6667C2314yes—
61Dic3×Dic5C23124yes—
62C22×D3×Q8—51no—
63C2×C3×C4×Q8—51no—
64C2×Q8×Dic3D511yescharacteristic, complemented
65#5572—516no—
66C2×#892—53no—
67C2×#887—53no—
68C2×#872—53no—
69C2×C4×Dic6—53no—
70C22×C5×Q8C2×D311yescharacteristic
71C2×Q8×D5—316no—
72C2×Q8×D5—38no—
73C22×C4×D5—33no—
74C22×Dic10—33no—
75C4×C5×Q8—38no—
76C2×C5×C4⋊C4—33no—
77C2×C42×C5—33no—
78Q8×Dic5C2×D318yescomplemented
79C2×#685—31no—
80C2×#685—33no—
81C2×C4⋊Dic5C2×D313yes—
82C2×#683—33no—
83C2×#683—33no—
84C2×C4×Dic5—36no—
85C2×C4×Dic5C2×D313yes—
86#4038—324no—
87#4033—324no—
88#4018—324no—
89C4×Dic10—324no—
90C2×#519—151noSylow
91C23×C3×C5C2411yescharacteristic
92C22×D15—22no—
93C22×D15—22no—
94C22×D15C22×C414yes—
95C22×D15C2412yes—
96C3×C5×Q8C22×C4116yes—
97C2×C3×C4×C5C22×C4112yes—
98C2×C3×C4×C5C2416yes—
99C2×Dic15C22×C4112yes—
100C2×Dic15C2416yes—
101C4×D15C22×C4148yes—
102Dic30C22×C4148yes—
103C2×C5×Dic3—22no—
104C2×C5×Dic3—26no—
105C2×C5×Dic3C2416yes—
106C2×C5×Dic3C2412yes—
107C2×C3×Dic5—26no—
108C2×C3×Dic5—22no—
109C2×C3×Dic5C2416yes—
110C2×C3×Dic5C2412yes—
111C22×C3×Q8C2×D511yescharacteristic
112C2×D3×Q8—516no—
113C2×D3×Q8—58no—
114C22×C4×D3—53no—
115C22×Dic6—53no—
116C3×C4×Q8—58no—
117C2×C3×C4⋊C4—53no—
118C2×C3×C42—53no—
119Q8×Dic3C2×D518yescomplemented
120C2×(C2×D3)⋊C4—51no—
121C2×(C2×D3)⋊C4—53no—
122C2×C4⋊Dic3C2×D513yes—
123C2×Dic3⋊C4—53no—
124C2×Dic3⋊C4—53no—
125C2×C4×Dic3—56no—
126C2×C4×Dic3C2×D513yes—
127#892—524no—
128#887—524no—
129#872—524no—
130C4×Dic6—524no—
131C23×D5—31no—
132C2×C5×Q8C4×D318yes—
133C2×C5×Q8C22×D314yes—
134C22×C4×C5—31no—
135C22×C4×C5—33no—
136C22×C4×C5C22×D313yes—
137C22×Dic5—33no—
138C22×Dic5C22×D313yes—
139C22×Dic5C22×D311yescharacteristic
140Q8×D5—364no—
141C2×C4×D5—324no—
142C2×C4×D5—312no—
143C2×Dic10—324no—
144C2×Dic10—312no—
145C5×C4⋊C4—312no—
146C42×C5—312no—
147#685—34no—
148#685—312no—
149C4⋊Dic5C22×D3112yes—
150#683—312no—
151#683—312no—
152C4×Dic5—324no—
153C4×Dic5C22×D3112yes—
154C23×Q8—151no—
155#519—1516no—
156C2×C4×Q8—31no—
157C2×C4×Q8—51no—
158C2×C4×Q8—153no—
159C2×C4×Q8—153no—
160C2×#117—153no—
161C2×#117—153no—
162C22×C3×C5C23×C412yes—
163C22×C3×C52−1+412yes—
164C22×C3×C52−1+412yes—
165C22×C3×C5C2511yescharacteristic
166C2×D15—28no—
167C2×D15—22no—
168C2×D15—22no—
169C2×D15C23×C414yes—
170C3×C4×C5C23×C4112yes—
171Dic15C23×C4112yes—
172C3×Dic5—26no—
173C3×Dic5—22no—
174C5×Dic3—22no—
175C5×Dic3—26no—
176C23×D3—51no—
177C2×C3×Q8C4×D518yes—
178C2×C3×Q8C22×D514yes—
179C22×C3×C4—53no—
180C22×C3×C4—51no—
181C22×C3×C4C22×D513yes—
182C22×Dic3—53no—
183C22×Dic3C22×D513yes—
184C22×Dic3C22×D511yescharacteristic
185D3×Q8—564no—
186C2×C4×D3—524no—
187C2×C4×D3—512no—
188C2×Dic6—524no—
189C2×Dic6—512no—
190C3×C4⋊C4—512no—
191C3×C42—512no—
192(C2×D3)⋊C4—54no—
193(C2×D3)⋊C4—512no—
194C4⋊Dic3C22×D5112yes—
195Dic3⋊C4—512no—
196Dic3⋊C4—512no—
197C4×Dic3—524no—
198C4×Dic3C22×D5112yes—
199C23×C5C23×D311yescharacteristic
200C22×D5—34no—
201C22×D5—32no—
202C22×D5—62no—
203C22×D5—62no—
204C5×Q8C2×C4×D3116yes—
205C2×C4×C5—36no—
206C2×C4×C5—32no—
207C2×C4×C5—66no—
208C2×C4×C5—62no—
209C2×C4×C5C2×C4×D3112yes—
210C2×C4×C5C23×D316yes—
211C2×Dic5—22no—
212C2×Dic5—26no—
213C2×Dic5—312no—
214C2×Dic5—36no—
215C2×Dic5C23×D316yes—
216C2×Dic5C23×D312yes—
217C4×D5—348no—
218Dic10—348no—
219C22×Q8—1516no—
220C22×Q8—158no—
221C22×Q8—153no—
222C22×Q8D3×D511yescharacteristic
223C23×C4—153no—
224C4×Q8—38no—
225C4×Q8—58no—
226C4×Q8—1524no—
227C4×Q8—1524no—
228#117—1524no—
229#117—1524no—
230C2×C4⋊C4—33no—
231C2×C4⋊C4—53no—
232C2×C4⋊C4—153no—
233C2×C4⋊C4—153no—
234C2×C22⋊C4—151no—
235C2×C22⋊C4—153no—
236C2×C42—33no—
237C2×C42—53no—
238C2×C42—156no—
239C2×C3×C5#51914yescomplemented
240C2×C3×C5C24×C411yescharacteristic
241C2×C3×C5C2×2−1+411yescharacteristic
242C2×C3×C5C2×2−1+411yescharacteristic
243D15—24no—
244C23×C3C23×D511yescharacteristic
245C22×D3—54no—
246C22×D3—52no—
247C22×D3—102no—
248C22×D3—102no—
249C3×Q8C2×C4×D5116yes—
250C2×C3×C4—56no—
251C2×C3×C4—52no—
252C2×C3×C4—106no—
253C2×C3×C4—102no—
254C2×C3×C4C2×C4×D5112yes—
255C2×C3×C4C23×D516yes—
256C2×Dic3—22no—
257C2×Dic3—26no—
258C2×Dic3—512no—
259C2×Dic3—56no—
260C2×Dic3C23×D516yes—
261C2×Dic3C23×D512yes—
262C4×D3—548no—
263Dic6—548no—
264C22×C5C22×C4×D312yes—
265C22×C5#100712yes—
266C22×C5#101012yes—
267C22×C5C24×D311yescharacteristic
268C2×D5—34no—
269C2×D5—62no—
270C2×D5—62no—
271C2×D5—68no—
272C4×C5—66no—
273C4×C5—62no—
274C4×C5C22×C4×D3112yes—
275Dic5—22no—
276Dic5—26no—
277Dic5—312no—
278C24—151no—
279C2×Q8—1564no—
280C2×Q8—1524no—
281C2×Q8—1512no—
282C2×Q8#120018yes—
283C2×Q8C2×D3×D514yes—
284C22×C4—31no—
285C22×C4—33no—
286C22×C4—51no—
287C22×C4—53no—
288C22×C4—153no—
289C22×C4—1524no—
290C22×C4—1512no—
291C22×C4C2×D3×D513yes—
292C4⋊C4—312no—
293C4⋊C4—512no—
294C4⋊C4—1512no—
295C4⋊C4—1512no—
296C22⋊C4—154no—
297C22⋊C4—1512no—
298C42—312no—
299C42—512no—
300C42—1524no—
301C3×C5C2×#51911yescharacteristic, complemented, Hall
302C22×C3C22×C4×D512yes—
303C22×C3#414712yes—
304C22×C3#415012yes—
305C22×C3C24×D511yescharacteristic
306C2×D3—54no—
307C2×D3—108no—
308C2×D3—102no—
309C2×D3—102no—
310C3×C4—106no—
311C3×C4—102no—
312C3×C4C22×C4×D5112yes—
313Dic3—22no—
314Dic3—26no—
315Dic3—512no—
316C2×C5#557214yescomplemented
317C2×C5C23×C4×D311yescharacteristic
318C2×C5C2×#100711yescharacteristic
319C2×C5C2×#101011yescharacteristic
320D5—64no—
321C23—154no—
322C23—152no—
323C23—302no—
324C23—302no—
325C23C22×D3×D511yescharacteristic
326Q8—1548no—
327Q8C2×#1200116yes—
328C2×C4—32no—
329C2×C4—36no—
330C2×C4—52no—
331C2×C4—56no—
332C2×C4—62no—
333C2×C4—66no—
334C2×C4—106no—
335C2×C4—102no—
336C2×C4—1512no—
337C2×C4—156no—
338C2×C4—1548no—
339C2×C4C2×#1200112yes—
340C2×C4C22×D3×D516yes—
341C2×C3#6590614yescomplemented
342C2×C3C23×C4×D511yescharacteristic
343C2×C3C2×#414711yescharacteristic
344C2×C3C2×#415011yescharacteristic
345D3—104no—
346C5C2×#557211yescharacteristic, complemented, Sylow
347C22—154no—
348C22—308no—
349C22—302no—
350C22—302no—
351C22#9202812yes—
352C22#9203012yes—
353C22C22×#120012yes—
354C22C23×D3×D511yescharacteristic
355C4—62no—
356C4—66no—
357C4—106no—
358C4—102no—
359C4—1512no—
360C4C22×#1200112yes—
361C3C2×#6590611yescharacteristic, complemented, Sylow
362C2—304no—
363C2#1175512414yesdirect product factor
364C2C2×#9202811yescharacteristic
365C2C2×#9203011yescharacteristic
366C2C23×#120011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC23×D15C23
cosocleC22×C3×C5C25
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#519
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C5×Q8×Dic3C2semidirect
3. C2×C3×Q8×Dic5C2semidirect
4. #11755124C2direct (N × H)
7. C2×#91340C2semidirect
8. C2×#91333C2semidirect
11. C2×Q8×D15C4semidirect
15. C5×Q8×Dic3C22semidirect
18. C3×Q8×Dic5C22semidirect
28. #91340C22semidirect
29. #91333C22semidirect
33. C2×Q8×Dic5D3semidirect
44. Q8×D15C2×C4semidirect
64. C2×Q8×Dic3D5semidirect
78. Q8×Dic5C2×D3semidirect
119. Q8×Dic3C2×D5semidirect
239. C2×C3×C5#519semidirect
301. C3×C5C2×#519semidirect
316. C2×C5#5572semidirect
341. C2×C3#65906semidirect
346. C5C2×#5572semidirect
361. C3C2×#65906semidirect
363. C2#11755124direct (N × H)

Maximal subgroups

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

subgroupindex
C22×Q8×D152
C2×C5×Q8×Dic32
C2×C3×Q8×Dic52
#117551242
C2×#913862
C2×#913472
C2×#913402
C2×#913332
C2×#659063
C2×#55725