Finite Group Databasebeta

← C2×#11750818 #14417933

Subgroups — C2×#11750818 #14417933

Order 1920.

928 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
1C2×#91793C211yesmaximal, characteristic
2C2×#91790C212yesmaximal, complemented
3C2×C3×C5×#97C211yesmaximal, characteristic, complemented
4C2×#91103C211yesmaximal, characteristic, complemented
5C2×#91089C212yesmaximal, complemented
6#11750818C218yesmaximal, direct product factor
7C2×#65006—31nomaximal, Hall
8C2×#6817C2212yes—
9C22×C3×C5×C8C2211yescharacteristic
10C22×C3×C5×C8C2211yescharacteristic
11C2×C3×C42×C5C2211yescharacteristic
12C2×#6710C2212yes—
13C2×Dic60C411yescharacteristic, complemented
14#91793C414yescomplemented
15#91793C2214yes—
16C2×D120C411yescharacteristic, complemented
17C2×#6706C412yescomplemented
18#91790—24no—
19#91790C2218yescomplemented
20C2×#6705—22no—
21C2×C8×D15—22no—
22C3×C5×#97C2214yescomplemented
23#91103C2214yescomplemented
24#91089C2218yescomplemented
25C2×#4717—51nomaximal, Hall
26C2×#4050—31no—
27C2×#4047—32no—
28C2×C5×#97D311yescharacteristic, complemented
29C2×#3951—31no—
30C2×#3937—32no—
31#65006—38no—
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5C2311yescharacteristic
34C2×#1220—22no—
35#6817—22no—
36#6817—22no—
37#6817C2×C414yes—
38#6817C2314yes—
39C2×D60C2×C412yes—
40C2×C4×D15—22no—
41C2×Dic30C2×C412yes—
42C2×C3×C5×C8C2×C411yescharacteristic
43C2×C3×C5×C8C2×C411yescharacteristic
44C2×C3×C5×C8C2×C412yes—
45C2×C3×C5×C8D412yes—
46C2×C3×C5×C8D412yes—
47C2×C3×C5×C8C2312yes—
48C2×C3×C5×C8C2312yes—
49C3×C42×C5—21no—
50C3×C42×C5C2312yes—
51#6710—22no—
52#6710C2314yes—
53C2×C3⋊#168—22no—
54Dic60C2×C414yescomplemented
55D120C2×C414yescomplemented
56#6706C2×C418yescomplemented
57#6705—28no—
58C8×D15—28no—
59C2×#904—51no—
60C2×#901—52no—
61C2×C3×#97D511yescharacteristic, complemented
62C2×#819—51no—
63C2×#805—52no—
64#4717—58no—
65C2×#709—32no—
66C22×C5×C8C2×D311yescharacteristic
67C22×C5×C8C2×D311yescharacteristic
68C2×C42×C5C2×D311yescharacteristic
69C2×#681—32no—
70C2×Dic20—31no—
71#4050—34no—
72#4050—34no—
73C2×D40—31no—
74C2×#677—32no—
75#4047—38no—
76#4047—64no—
77C2×#676—62no—
78C2×C8×D5—62no—
79C5×#97C2×D314yescomplemented
80#3951—34no—
81#3937—38no—
82C2×#444—151noSylow
83C23×C3×C5#4111yescharacteristic
84C22×D15—22no—
85C2×C3×C4×C5—22no—
86C2×C3×C4×C5—42no—
87C2×C3×C4×C5C22×C411yescharacteristic
88C2×C3×C4×C5C22×C411yescharacteristic
89C2×C3×C4×C5C2×D411yescharacteristic
90C2×C3×C4×C5C2×D411yescharacteristic
91C2×C3×C4×C5#4111yescharacteristic
92C2×C3×C4×C5C2411yescharacteristic
93#1220—24no—
94#1220—24no—
95C2×Dic15—22no—
96D60—22no—
97D60C22×C414yes—
98C4×D15—24no—
99C4×D15—24no—
100Dic30—22no—
101Dic30C22×C414yes—
102C3×C5×C8C22×C412yes—
103C3×C5×C8C22×C412yes—
104C3×C5×C8C2×D414yes—
105C3⋊#168—24no—
106C2×#235—52no—
107C22×C3×C8C2×D511yescharacteristic
108C22×C3×C8C2×D511yescharacteristic
109C2×C3×C42C2×D511yescharacteristic
110C2×#208—52no—
111C2×Dic12—51no—
112#904—54no—
113#904—54no—
114C2×D24—51no—
115C2×#204—52no—
116#901—58no—
117#901—104no—
118C2×ΓL(1,𝔽25)—102no—
119C2×D3×C8—102no—
120C3×#97C2×D514yescomplemented
121#819—54no—
122#805—58no—
123C22×C4×C5—21no—
124C22×C4×C5C22×D311yescharacteristic
125C2×C22⋊D5—62no—
126#709—34no—
127#709—34no—
128#709—62no—
129#709—62no—
130C2×D20—32no—
131C2×C4×D5—62no—
132C2×Dic10—32no—
133C2×C5×C8C4×D311yescharacteristic
134C2×C5×C8C4×D311yescharacteristic
135C2×C5×C8C4×D312yes—
136C2×C5×C8D1212yes—
137C2×C5×C8D1212yes—
138C2×C5×C8C22×D312yes—
139C2×C5×C8C22×D312yes—
140C42×C5—21no—
141C42×C5C22×D312yes—
142#681—34no—
143#681—62no—
144C2×#168—62no—
145Dic20—34no—
146D40—34no—
147#677—38no—
148#676—68no—
149C8×D5—68no—
150C2×#135—151no—
151C2×#131—152no—
152#444—158no—
153C2×#108—151no—
154C2×#104—152no—
155C2×#97D1511yescharacteristic, complemented
156C22×C3×C5—22no—
157C22×C3×C5C4×D411yescharacteristic
158C22×C3×C5C4×D411yescharacteristic
159C22×C3×C5C2×#4111yescharacteristic
160C2×D15—24no—
161C2×D15—44no—
162C3×C4×C5—42no—
163C3×C4×C5C4×D411yescharacteristic
164C3×C4×C5C4×D411yescharacteristic
165C3×C4×C5C23×C411yescharacteristic
166C3×C4×C5C22×D411yescharacteristic
167Dic15—24no—
168C22×C3×C4—21no—
169C22×C3×C4C22×D511yescharacteristic
170C2×#67—102no—
171#235—54no—
172#235—54no—
173#235—102no—
174#235—102no—
175C2×D12—52no—
176C2×C4×D3—102no—
177C2×Dic6—52no—
178C2×C3×C8C4×D511yescharacteristic
179C2×C3×C8C4×D511yescharacteristic
180C2×C3×C8C4×D512yes—
181C2×C3×C8D2012yes—
182C2×C3×C8D2012yes—
183C2×C3×C8C22×D512yes—
184C2×C3×C8C22×D512yes—
185C3×C42—21no—
186C3×C42C22×D512yes—
187#208—54no—
188#208—102no—
189C2×C3⋊C8—102no—
190Dic12—54no—
191D24—54no—
192#204—58no—
193ΓL(1,𝔽25)—108no—
194D3×C8—108no—
195C23×C5#23511yescharacteristic
196C22×D5—62no—
197C2×C4×C5—22no—
198C2×C4×C5—42no—
199C2×C4×C5C2×C4×D311yescharacteristic
200C2×C4×C5C2×C4×D311yescharacteristic
201C2×C4×C5C2×D1211yescharacteristic
202C2×C4×C5C2×D1211yescharacteristic
203C2×C4×C5#23511yescharacteristic
204C2×C4×C5C23×D311yescharacteristic
205C22⋊D5—64no—
206C22⋊D5—64no—
207C2×Dic5—62no—
208D20—34no—
209D20—62no—
210C4×D5—64no—
211C4×D5—64no—
212Dic10—34no—
213Dic10—62no—
214C5×C8C2×C4×D312yes—
215C5×C8C2×C4×D312yes—
216C5×C8C2×D1214yes—
217#168—64no—
218C2×#41—152no—
219#135—154no—
220#135—154no—
221C2×Q16—151no—
222C2×SD16—152no—
223C2×D8—151no—
224#131—158no—
225#131—304no—
226C2×M16—152no—
227C2×M16—302no—
228C22×C8—302no—
229C22×C8C2×D1511yescharacteristic
230C22×C8C2×D1511yescharacteristic
231C2×C42C2×D1511yescharacteristic
232#108—154no—
233#104—158no—
234#97C2×D1514yescomplemented
235C2×C3×C5—21no—
236C2×C3×C5—21no—
237C2×C3×C5#44412yescomplemented
238C2×C3×C5C2×C4×D411yescharacteristic
239D15—44no—
240C23×C3#70911yescharacteristic
241C22×D3—102no—
242C2×C3×C4—22no—
243C2×C3×C4—42no—
244C2×C3×C4C2×C4×D511yescharacteristic
245C2×C3×C4C2×C4×D511yescharacteristic
246C2×C3×C4C2×D2011yescharacteristic
247C2×C3×C4C2×D2011yescharacteristic
248C2×C3×C4#70911yescharacteristic
249C2×C3×C4C23×D511yescharacteristic
250#67—104no—
251#67—104no—
252C2×Dic3—102no—
253D12—54no—
254D12—102no—
255C4×D3—104no—
256C4×D3—104no—
257Dic6—54no—
258Dic6—102no—
259C3×C8C2×C4×D512yes—
260C3×C8C2×C4×D512yes—
261C3×C8C2×D2014yes—
262C3⋊C8—104no—
263C22×C5—22no—
264C22×C5C4×D1211yescharacteristic
265C22×C5C4×D1211yescharacteristic
266C22×C5C2×#23511yescharacteristic
267C2×D5—64no—
268C2×D5—124no—
269C4×C5—42no—
270C4×C5C4×D1211yescharacteristic
271C4×C5C4×D1211yescharacteristic
272C4×C5C22×C4×D311yescharacteristic
273C4×C5C22×D1211yescharacteristic
274Dic5—64no—
275#41—154no—
276#41—154no—
277#41—302no—
278#41—302no—
279C2×Q8—152no—
280C2×D4—152no—
281C2×D4—302no—
282C22×C4—21no—
283C22×C4—302no—
284C22×C4C22×D1511yescharacteristic
285Q16—154no—
286SD16—158no—
287D8—154no—
288M16—154no—
289M16—302no—
290M16—308no—
291C2×C8—302no—
292C2×C8—308no—
293C2×C8C4×D1511yescharacteristic
294C2×C8C4×D1511yescharacteristic
295C2×C8C4×D1512yes—
296C2×C8D6012yes—
297C2×C8D6012yes—
298C2×C8C22×D1512yes—
299C2×C8C22×D1512yes—
300C42—21no—
301C42C22×D1512yes—
302C3×C5C2×#44411yescharacteristic, complemented, Hall
303C22×C3—22no—
304C22×C3C4×D2011yescharacteristic
305C22×C3C4×D2011yescharacteristic
306C22×C3C2×#70911yescharacteristic
307C2×D3—104no—
308C2×D3—204no—
309C3×C4—42no—
310C3×C4C4×D2011yescharacteristic
311C3×C4C4×D2011yescharacteristic
312C3×C4C22×C4×D511yescharacteristic
313C3×C4C22×D2011yescharacteristic
314Dic3—104no—
315C2×C5—21no—
316C2×C5—21no—
317C2×C5#471712yescomplemented
318C2×C5C2×C4×D1211yescharacteristic
319D5—124no—
320C23—302no—
321C23#681711yescharacteristic
322Q8—154no—
323Q8—302no—
324D4—154no—
325D4—304no—
326D4—304no—
327D4—302no—
328C2×C4—22no—
329C2×C4—42no—
330C2×C4—302no—
331C2×C4—304no—
332C2×C4—304no—
333C2×C4C2×C4×D1511yescharacteristic
334C2×C4C2×C4×D1511yescharacteristic
335C2×C4C2×D6011yescharacteristic
336C2×C4C2×D6011yescharacteristic
337C2×C4#681711yescharacteristic
338C2×C4C23×D1511yescharacteristic
339C8—304no—
340C8C2×C4×D1512yes—
341C8C2×C4×D1512yes—
342C8C2×D6014yes—
343C2×C3—21no—
344C2×C3—21no—
345C2×C3#6500612yescomplemented
346C2×C3C2×C4×D2011yescharacteristic
347D3—204no—
348C5C2×#471711yescharacteristic, complemented, Sylow
349C22—22no—
350C22—304no—
351C22—604no—
352C22C4×D6011yescharacteristic
353C22C4×D6011yescharacteristic
354C22C2×#681711yescharacteristic
355C4—42no—
356C4—304no—
357C4C4×D6011yescharacteristic
358C4C4×D6011yescharacteristic
359C4C22×C4×D1511yescharacteristic
360C4C22×D6011yescharacteristic
361C3C2×#6500611yescharacteristic, complemented, Sylow
362C2—21no—
363C2—21no—
364C2—604no—
365C2#1175081812yesdirect product factor
366C2C2×C4×D6011yescharacteristic
subgroupG/H
centerC2×C4C2×D60
commutatorC3×C4×C5C23×C4
FrattiniC2×C4C23×D15
FittingC2×C3×C5×#97C2
socleC22×C3×C5C4×D4
prime radicalC2×#91793C2
cosocleC2×C3×C4×C5C24
hypercenterC2×#97D15
hypocenterC3×C5C2×#444
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
2. C2×#91790C2semidirect
3. C2×C3×C5×#97C2semidirect
4. C2×#91103C2semidirect
5. C2×#91089C2semidirect
6. #11750818C2direct (N × H)
13. C2×Dic60C4semidirect
14. #91793C4semidirect
16. C2×D120C4semidirect
17. C2×#6706C4semidirect
19. #91790C22semidirect
22. C3×C5×#97C22semidirect
23. #91103C22semidirect
24. #91089C22semidirect
28. C2×C5×#97D3semidirect
54. Dic60C2×C4semidirect
55. D120C2×C4semidirect
56. #6706C2×C4semidirect
61. C2×C3×#97D5semidirect
79. C5×#97C2×D3semidirect
120. C3×#97C2×D5semidirect
155. C2×#97D15semidirect
234. #97C2×D15semidirect
237. C2×C3×C5#444semidirect
302. C3×C5C2×#444semidirect
317. C2×C5#4717semidirect
345. C2×C3#65006semidirect
348. C5C2×#4717semidirect
361. C3C2×#65006semidirect
365. C2#11750818direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917932
C2×#917902
C2×C3×C5×#972
C2×#911032
C2×#910892
#117508182
C2×#650063
C2×#47175