Finite Group Databasebeta

← C2×#11751072 #14431463

Subgroups — C2×#11751072 #14431463

Order 1920.

920 conjugacy classes of subgroups.

The subgroup lattice has 352 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C5×C4⋊C4C211yesmaximal, characteristic
2C2×#91813C211yesmaximal, characteristic
3C2×#91114C211yesmaximal, characteristic
4#11751072C218yesmaximal, direct product factor
5C2×#91094C212yesmaximal, complemented
6C2×#91092C212yesmaximal, complemented
7C2×#65260—31nomaximal, Hall
8C23×C3×C4×C5—21no—
9C23×C3×C4×C5C2211yescharacteristic
10C22×Dic30C2211yescharacteristic
11C2×C3×C5×C4⋊C4—21no—
12C2×C3×C5×C4⋊C4—22no—
13C2×C3×C5×C4⋊C4C2212yes—
14C2×C3×C5×C4⋊C4C2214yes—
15C2×#6719—21no—
16C2×C4⋊Dic15C2211yescharacteristic
17#91813—22no—
18#91813C2214yes—
19C2×#6712—21no—
20C22×C3⋊#168C2212yes—
21#91114C2214yes—
22#91094C2218yescomplemented
23#91092C2218yescomplemented
24C2×#4971—51nomaximal, Hall
25C22×C5×C4⋊C4D311yescharacteristic
26C2×#4070—31no—
27C2×C22⋊#168—31no—
28#65260—38no—
29C2×#3942—32no—
30C2×#3940—32no—
31C24×C3×C5D411yescharacteristic
32C22×C3×C4×C5—24no—
33C22×C3×C4×C5—24no—
34C22×C3×C4×C5—22no—
35C22×C3×C4×C5—44no—
36C22×C3×C4×C5D411yescharacteristic
37C22×C3×C4×C5D412yes—
38C22×C3×C4×C5C2312yes—
39C22×C3×C4×C5C2311yescharacteristic
40C22×Dic15—21no—
41C22×Dic15—21no—
42C2×Dic30—24no—
43C2×Dic30—21no—
44C2×Dic30C2312yes—
45C3×C5×C4⋊C4—24no—
46C3×C5×C4⋊C4—22no—
47C3×C5×C4⋊C4C2314yes—
48#6719—24no—
49C4⋊Dic15—21no—
50C4⋊Dic15C2312yes—
51#6712—24no—
52C2×C3⋊#168—24no—
53C2×C3⋊#168C2314yes—
54C22×C3×C4⋊C4D511yescharacteristic
55C2×#924—51no—
56C2×#830—51no—
57#4971—58no—
58C2×#810—52no—
59C2×#808—52no—
60C23×C4×C5—21no—
61C23×C4×C5C2×D311yescharacteristic
62C22×Dic10—31no—
63C2×C5×C4⋊C4—21no—
64C2×C5×C4⋊C4—22no—
65C2×C5×C4⋊C4C2×D312yes—
66C2×C5×C4⋊C4C2×D314yes—
67C2×C22⋊Dic5—61no—
68C2×C4⋊Dic5—31no—
69#4070—34no—
70#4070—62no—
71C2×#683—61no—
72C22×#168—32no—
73C22⋊#168—34no—
74#3942—38no—
75#3940—38no—
76C2×#483—151noSylow
77C23×C3×C5—22no—
78C23×C3×C5—22no—
79C23×C3×C5SD1614yes—
80C23×C3×C5C2×D412yes—
81C23×C3×C5C2×D411yescharacteristic
82C2×C3×C4×C5—22no—
83C2×C3×C4×C5—24no—
84C2×C3×C4×C5—24no—
85C2×C3×C4×C5—24no—
86C2×C3×C4×C5—48no—
87C2×C3×C4×C5—44no—
88C2×C3×C4×C5C2×D412yes—
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5#4114yes—
91C2×C3×C4×C5C2411yescharacteristic
92C2×Dic15—22no—
93C2×Dic15—22no—
94C2×Dic15—42no—
95C2×Dic15—42no—
96Dic30—24no—
97Dic30—42no—
98C3⋊#168—24no—
99C23×C3×C4—21no—
100C23×C3×C4C2×D511yescharacteristic
101C22×Dic6—51no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4C2×D512yes—
105C2×C3×C4⋊C4C2×D514yes—
106C2×#217—101no—
107C2×C4⋊Dic3—51no—
108#924—54no—
109#924—102no—
110C2×Dic3⋊C4—101no—
111C22×C3⋊C8—52no—
112#830—54no—
113#810—58no—
114#808—58no—
115C24×C5#6711yescharacteristic
116C22×C4×C5—24no—
117C22×C4×C5—24no—
118C22×C4×C5—22no—
119C22×C4×C5—44no—
120C22×C4×C5#6711yescharacteristic
121C22×C4×C5#6712yes—
122C22×C4×C5C22×D312yes—
123C22×C4×C5C22×D311yescharacteristic
124C22×Dic5—61no—
125C22×Dic5—61no—
126C2×Dic10—32no—
127C2×Dic10—64no—
128C2×Dic10—61no—
129C5×C4⋊C4—24no—
130C5×C4⋊C4—22no—
131C5×C4⋊C4C22×D314yes—
132C22⋊Dic5—64no—
133C4⋊Dic5—32no—
134C4⋊Dic5—61no—
135#683—64no—
136C2×#168—34no—
137C2×#168—64no—
138C2×C22⋊Q8—151no—
139C22×C4⋊C4D1511yescharacteristic
140#483—158no—
141C2×#106—152no—
142C2×#103—152no—
143C2×C22⋊C8—151no—
144C22×C3×C5—22no—
145C22×C3×C5—22no—
146C22×C3×C5—28no—
147C22×C3×C5#12312yes—
148C22×C3×C5C2×SD1614yes—
149C22×C3×C5C2×SD1612yes—
150C22×C3×C5#13712yes—
151C22×C3×C5C22×D411yescharacteristic
152C3×C4×C5—22no—
153C3×C4×C5—44no—
154C3×C4×C5#12312yes—
155C3×C4×C5C2×#4112yes—
156Dic15—42no—
157Dic15—42no—
158C24×C3C22⋊D511yescharacteristic
159C22×C3×C4—24no—
160C22×C3×C4—24no—
161C22×C3×C4—22no—
162C22×C3×C4—44no—
163C22×C3×C4C22⋊D511yescharacteristic
164C22×C3×C4C22⋊D512yes—
165C22×C3×C4C22×D512yes—
166C22×C3×C4C22×D511yescharacteristic
167C22×Dic3—101no—
168C22×Dic3—101no—
169C2×Dic6—52no—
170C2×Dic6—104no—
171C2×Dic6—101no—
172C3×C4⋊C4—24no—
173C3×C4⋊C4—22no—
174C3×C4⋊C4C22×D514yes—
175#217—104no—
176C4⋊Dic3—52no—
177C4⋊Dic3—101no—
178Dic3⋊C4—104no—
179C2×C3⋊C8—54no—
180C2×C3⋊C8—104no—
181C23×C5—22no—
182C23×C5—22no—
183C23×C5#21414yes—
184C23×C5C2×#6712yes—
185C23×C5C2×#6711yescharacteristic
186C2×C4×C5—22no—
187C2×C4×C5—24no—
188C2×C4×C5—24no—
189C2×C4×C5—24no—
190C2×C4×C5—48no—
191C2×C4×C5—44no—
192C2×C4×C5#23514yes—
193C2×C4×C5C2×#6712yes—
194C2×C4×C5C2×#6711yescharacteristic
195C2×C4×C5C23×D311yescharacteristic
196C2×Dic5—62no—
197C2×Dic5—62no—
198C2×Dic5—122no—
199C2×Dic5—122no—
200Dic10—64no—
201Dic10—122no—
202#168—64no—
203C22×Q8—151no—
204C23×C4—21no—
205C23×C4C2×D1511yescharacteristic
206C22×C8—152no—
207C22⋊Q8—154no—
208C22⋊Q8—302no—
209C2×C4⋊C4—22no—
210C2×C4⋊C4—21no—
211C2×C4⋊C4—151no—
212C2×C4⋊C4—301no—
213C2×C4⋊C4C2×D1512yes—
214C2×C4⋊C4C2×D1514yes—
215C2×C22⋊C4—301no—
216#106—158no—
217#103—158no—
218C22⋊C8—154no—
219C2×C3×C5—24no—
220C2×C3×C5#48314yescomplemented
221C2×C3×C5C2×#12311yescharacteristic
222C2×C3×C5C22×SD1611yescharacteristic
223C2×C3×C5C2×#13711yescharacteristic
224C23×C3—22no—
225C23×C3—22no—
226C23×C3#68714yes—
227C23×C3C2×C22⋊D512yes—
228C23×C3C2×C22⋊D511yescharacteristic
229C2×C3×C4—22no—
230C2×C3×C4—24no—
231C2×C3×C4—24no—
232C2×C3×C4—24no—
233C2×C3×C4—48no—
234C2×C3×C4—44no—
235C2×C3×C4#70914yes—
236C2×C3×C4C2×C22⋊D512yes—
237C2×C3×C4C2×C22⋊D511yescharacteristic
238C2×C3×C4C23×D511yescharacteristic
239C2×Dic3—102no—
240C2×Dic3—102no—
241C2×Dic3—202no—
242C2×Dic3—202no—
243Dic6—104no—
244Dic6—202no—
245C3⋊C8—104no—
246C22×C5—28no—
247C22×C5—22no—
248C22×C5—22no—
249C22×C5#92912yes—
250C22×C5C2×#21414yes—
251C22×C5C2×#21412yes—
252C22×C5#94212yes—
253C22×C5C22×#6711yescharacteristic
254C4×C5—22no—
255C4×C5—44no—
256C4×C5#92912yes—
257C4×C5C2×#23512yes—
258Dic5—122no—
259Dic5—122no—
260C24#122011yescharacteristic
261C2×Q8—152no—
262C2×Q8—301no—
263C2×Q8—304no—
264C22×C4—24no—
265C22×C4—24no—
266C22×C4—22no—
267C22×C4—44no—
268C22×C4—301no—
269C22×C4—301no—
270C22×C4#122012yes—
271C22×C4#122011yescharacteristic
272C22×C4C22×D1512yes—
273C22×C4C22×D1511yescharacteristic
274C2×C8—154no—
275C2×C8—304no—
276C4⋊C4—24no—
277C4⋊C4—22no—
278C4⋊C4—152no—
279C4⋊C4—301no—
280C4⋊C4—304no—
281C4⋊C4C22×D1514yes—
282C22⋊C4—304no—
283C3×C5C2×#48311yescharacteristic, complemented, Hall
284C22×C3—22no—
285C22×C3—22no—
286C22×C3—28no—
287C22×C3#407512yes—
288C22×C3C2×#68714yes—
289C22×C3C2×#68712yes—
290C22×C3#408812yes—
291C22×C3C22×C22⋊D511yescharacteristic
292C3×C4—22no—
293C3×C4—44no—
294C3×C4#407512yes—
295C3×C4C2×#70912yes—
296Dic3—202no—
297Dic3—202no—
298C2×C5—24no—
299C2×C5#497114yescomplemented
300C2×C5C2×#92911yescharacteristic
301C2×C5C22×#21411yescharacteristic
302C2×C5C2×#94211yescharacteristic
303C23—22no—
304C23—22no—
305C23#671614yes—
306C23C2×#122012yes—
307C23C2×#122011yescharacteristic
308Q8—304no—
309Q8—602no—
310C2×C4—22no—
311C2×C4—24no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—48no—
315C2×C4—44no—
316C2×C4—302no—
317C2×C4—302no—
318C2×C4—602no—
319C2×C4—602no—
320C2×C4#681714yes—
321C2×C4C2×#122012yes—
322C2×C4C2×#122011yescharacteristic
323C2×C4C23×D1511yescharacteristic
324C8—304no—
325C2×C3—24no—
326C2×C3#6526014yescomplemented
327C2×C3C2×#407511yescharacteristic
328C2×C3C22×#68711yescharacteristic
329C2×C3C2×#408811yescharacteristic
330C5C2×#497111yescharacteristic, complemented, Sylow
331C22—22no—
332C22—22no—
333C22—28no—
334C22#9181812yes—
335C22C2×#671614yes—
336C22C2×#671612yes—
337C22#9183112yes—
338C22C22×#122011yescharacteristic
339C4—22no—
340C4—44no—
341C4—602no—
342C4—602no—
343C4#9181812yes—
344C4C2×#681712yes—
345C3C2×#6526011yescharacteristic, complemented, Sylow
346C2—24no—
347C2#1175107214yesdirect product factor
348C2C2×#9181811yescharacteristic
349C2C22×#671611yescharacteristic
350C2C2×#9183111yescharacteristic
subgroupG/H
centerC23C2×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC22×C3×C5×C4⋊C4C2
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
hypercenterC22×C4⋊C4D15
hypocenterC3×C5C2×#483
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
4. #11751072C2direct (N × H)
5. C2×#91094C2semidirect
6. C2×#91092C2semidirect
22. #91094C22semidirect
23. #91092C22semidirect
220. C2×C3×C5#483semidirect
283. C3×C5C2×#483semidirect
299. C2×C5#4971semidirect
326. C2×C3#65260semidirect
330. C5C2×#4971semidirect
345. C3C2×#65260semidirect
347. C2#11751072direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C5×C4⋊C42
C2×#918132
C2×#911142
#117510722
C2×#910942
C2×#910922
C2×#652603
C2×#49715