Finite Group Databasebeta

← C2×#11748446 #14431645

Subgroups — C2×#11748446 #14431645

Order 1920.

832 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91815C211yesmaximal, characteristic
2C2×C3×#4070C211yesmaximal, characteristic
3C2×C5×#830C211yesmaximal, characteristic
4C2×#90990C211yesmaximal, characteristic, complemented
5C2×#90987C211yesmaximal, characteristic, complemented
6#11748446C218yesmaximal, direct product factor
7C2×#90971C211yesmaximal, characteristic, complemented
8C2×#90971C211yesmaximal, characteristic, complemented
9C2×#65012—31nomaximal, Hall
10C23×C3×C4×C5C2211yescharacteristic
11C22×C3×Dic10C2211yescharacteristic
12C2×#6719—21no—
13#91815—22no—
14#91815C2214yes—
15C2×C4⋊Dic15C2211yescharacteristic
16C2×C4⋊Dic15C2211yescharacteristic
17C2×C4×Dic15—21no—
18C22×C5×C3⋊C8C2211yescharacteristic
19C22×C5×C3⋊C8C2211yescharacteristic
20C2×C3×C22⋊Dic5—21no—
21C2×C3×C4⋊Dic5C2211yescharacteristic
22C3×#4070—22no—
23C3×#4070C2214yes—
24C2×C3×#683—21no—
25C5×#830C2214yes—
26#90990C2214yescomplemented
27#90987C2214yescomplemented
28#90971C2214yescomplemented
29#90971C2214yescomplemented
30C2×#5045—51nomaximal, Hall
31C2×#4072—31no—
32C2×#4070D311yescharacteristic
33C2×C5×C22⋊C8—31no—
34C2×#3950—31no—
35C2×#3949—31no—
36C2×#3948—31no—
37C2×#3948—31no—
38#65012—38no—
39C24×C3×C5D411yescharacteristic
40C22×C3×C4×C5—22no—
41C22×C3×C4×C5—22no—
42C22×C3×C4×C5D411yescharacteristic
43C22×C3×C4×C5D412yes—
44C22×C3×C4×C5C2312yes—
45C22×C3×C4×C5C2311yescharacteristic
46C22×Dic15—21no—
47C22×Dic15—21no—
48C22×C3×Dic5—21no—
49C22×C3×Dic5—21no—
50C2×C3×Dic10—22no—
51C2×C3×Dic10—22no—
52C2×C3×Dic10—21no—
53C2×C3×Dic10C2312yes—
54#6719—24no—
55C4⋊Dic15—21no—
56C4⋊Dic15—21no—
57C4⋊Dic15C2312yes—
58C4⋊Dic15C2312yes—
59C4×Dic15—24no—
60C2×C5×C3⋊C8—22no—
61C2×C5×C3⋊C8—22no—
62C2×C5×C3⋊C8C2312yes—
63C2×C5×C3⋊C8C2312yes—
64C3×C22⋊Dic5—24no—
65C3×C4⋊Dic5—21no—
66C3×C4⋊Dic5C2312yes—
67C3×#683—24no—
68C2×C3×C22⋊Q8—51no—
69C2×#926—51no—
70C2×#835—51no—
71C2×#835—51no—
72C2×#830D511yescharacteristic
73#5045—58no—
74C2×#808—51no—
75C2×#807—51no—
76C23×C4×C5C2×D311yescharacteristic
77C22×Dic10C2×D311yescharacteristic
78C22×C5×C8—31no—
79C22×C5×C8—31no—
80C2×C22⋊Dic5—21no—
81C2×C22⋊Dic5—61no—
82#4072—34no—
83#4072—62no—
84C2×C4⋊Dic5—31no—
85C2×C4⋊Dic5—31no—
86C2×C4⋊Dic5C2×D311yescharacteristic
87#4070—22no—
88#4070C2×D314yes—
89C2×#683—21no—
90C2×C4×Dic5—61no—
91C5×C22⋊C8—34no—
92#3950—34no—
93#3949—34no—
94#3948—34no—
95#3948—34no—
96C2×#485—151noSylow
97C23×C3×C5—22no—
98C23×C3×C5—22no—
99C23×C3×C5—22no—
100C23×C3×C5C2×D412yes—
101C23×C3×C5C2×D411yescharacteristic
102C2×C3×C4×C5—22no—
103C2×C3×C4×C5—24no—
104C2×C3×C4×C5—22no—
105C2×C3×C4×C5—22no—
106C2×C3×C4×C5C2×D412yes—
107C2×C3×C4×C5C2×D411yescharacteristic
108C2×C3×C4×C5#4112yes—
109C2×C3×C4×C5#4112yes—
110C2×C3×C4×C5C2411yescharacteristic
111C2×Dic15—22no—
112C2×Dic15—22no—
113C2×Dic15—42no—
114C2×Dic15—42no—
115C2×C3×Dic5—22no—
116C2×C3×Dic5—22no—
117C2×C3×Dic5—42no—
118C2×C3×Dic5—42no—
119C3×Dic10—22no—
120C3×Dic10—22no—
121C3×Dic10—42no—
122C5×C3⋊C8—22no—
123C5×C3⋊C8—22no—
124C22×C3×Q8—51no—
125C23×C3×C4C2×D511yescharacteristic
126C3×C22⋊Q8—54no—
127C3×C22⋊Q8—102no—
128C2×C3×C4⋊C4—51no—
129C2×C3×C4⋊C4—101no—
130C2×C3×C22⋊C4—101no—
131C2×#217—101no—
132#926—54no—
133#926—102no—
134C2×C4⋊Dic3—51no—
135C2×C4⋊Dic3—51no—
136C2×C4×Dic3—101no—
137C22×C3⋊C8C2×D511yescharacteristic
138C22×C3⋊C8C2×D511yescharacteristic
139#835—54no—
140#835—54no—
141#830C2×D514yes—
142#808—54no—
143#807—54no—
144C24×C5#6711yescharacteristic
145C22×C4×C5—22no—
146C22×C4×C5—22no—
147C22×C4×C5#6711yescharacteristic
148C22×C4×C5#6712yes—
149C22×C4×C5C22×D312yes—
150C22×C4×C5C22×D311yescharacteristic
151C22×Dic5—21no—
152C22×Dic5—21no—
153C22×Dic5—61no—
154C22×Dic5—61no—
155C2×Dic10—22no—
156C2×Dic10—22no—
157C2×Dic10—21no—
158C2×Dic10C22×D312yes—
159C2×C5×C8—32no—
160C2×C5×C8—32no—
161C2×C5×C8—62no—
162C2×C5×C8—62no—
163C22⋊Dic5—24no—
164C22⋊Dic5—64no—
165C4⋊Dic5—21no—
166C4⋊Dic5—32no—
167C4⋊Dic5—32no—
168C4⋊Dic5—61no—
169C4⋊Dic5—61no—
170C4⋊Dic5C22×D312yes—
171#683—24no—
172C4×Dic5—64no—
173C2×C22⋊Q8—51no—
174C2×#117—151no—
175#485—158no—
176C2×#107—151no—
177C2×#106—151no—
178C2×#103—151no—
179C2×#103—151no—
180C2×C22⋊C8—31no—
181C22×C3×C5—22no—
182C22×C3×C5—22no—
183C22×C3×C5—22no—
184C22×C3×C5—44no—
185C22×C3×C5#12312yes—
186C22×C3×C5#13512yes—
187C22×C3×C5#13712yes—
188C22×C3×C5C22×D411yescharacteristic
189C3×C4×C5—22no—
190C3×C4×C5#12312yes—
191C3×C4×C5C2×#4111yescharacteristic
192C3×C4×C5C2×#4111yescharacteristic
193Dic15—42no—
194Dic15—42no—
195C3×Dic5—42no—
196C3×Dic5—42no—
197C24×C3D2011yescharacteristic
198C2×C3×Q8—52no—
199C2×C3×Q8—101no—
200C2×C3×Q8—102no—
201C2×C3×Q8—102no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—101no—
205C22×C3×C4—101no—
206C22×C3×C4D2011yescharacteristic
207C22×C3×C4D2012yes—
208C22×C3×C4C22×D512yes—
209C22×C3×C4C22×D511yescharacteristic
210C22×Dic3—101no—
211C22×Dic3—101no—
212C3×C4⋊C4—52no—
213C3×C4⋊C4—104no—
214C3×C4⋊C4—101no—
215C3×C22⋊C4—104no—
216#217—104no—
217C4⋊Dic3—52no—
218C4⋊Dic3—52no—
219C4⋊Dic3—101no—
220C4⋊Dic3—101no—
221C4×Dic3—104no—
222C2×C3⋊C8—22no—
223C2×C3⋊C8—22no—
224C2×C3⋊C8C22×D512yes—
225C2×C3⋊C8C22×D512yes—
226C23×C5—22no—
227C23×C5—22no—
228C23×C5—22no—
229C23×C5C2×#6712yes—
230C23×C5C2×#6711yescharacteristic
231C2×C4×C5—22no—
232C2×C4×C5—24no—
233C2×C4×C5—22no—
234C2×C4×C5—22no—
235C2×C4×C5#23712yes—
236C2×C4×C5#23712yes—
237C2×C4×C5C2×#6712yes—
238C2×C4×C5C2×#6711yescharacteristic
239C2×C4×C5C23×D311yescharacteristic
240C2×Dic5—22no—
241C2×Dic5—22no—
242C2×Dic5—42no—
243C2×Dic5—42no—
244C2×Dic5—62no—
245C2×Dic5—62no—
246C2×Dic5—122no—
247C2×Dic5—122no—
248Dic10—22no—
249Dic10—22no—
250Dic10—42no—
251C5×C8—62no—
252C5×C8—62no—
253C22×Q8—51no—
254C23×C4D3×D511yescharacteristic
255C22×C8—31no—
256C22×C8—31no—
257C22⋊Q8—54no—
258C22⋊Q8—102no—
259#117—154no—
260#117—302no—
261C2×C4⋊C4—51no—
262C2×C4⋊C4—101no—
263C2×C4⋊C4—151no—
264C2×C4⋊C4—151no—
265C2×C22⋊C4—101no—
266C2×C22⋊C4—301no—
267C2×C42—301no—
268#107—154no—
269#106—154no—
270#103—154no—
271#103—154no—
272C22⋊C8—34no—
273C2×C3×C5—42no—
274C2×C3×C5#48514yescomplemented
275C2×C3×C5C2×#12311yescharacteristic
276C2×C3×C5C2×#13511yescharacteristic
277C2×C3×C5C2×#13711yescharacteristic
278C23×C3—22no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3C2×D2012yes—
282C23×C3C2×D2011yescharacteristic
283C3×Q8—102no—
284C3×Q8—102no—
285C3×Q8—202no—
286C2×C3×C4—22no—
287C2×C3×C4—22no—
288C2×C3×C4—22no—
289C2×C3×C4—24no—
290C2×C3×C4—102no—
291C2×C3×C4—102no—
292C2×C3×C4—202no—
293C2×C3×C4—202no—
294C2×C3×C4C2×D2012yes—
295C2×C3×C4C2×D2011yescharacteristic
296C2×C3×C4#71112yes—
297C2×C3×C4#71112yes—
298C2×C3×C4C23×D511yescharacteristic
299C2×Dic3—102no—
300C2×Dic3—102no—
301C2×Dic3—202no—
302C2×Dic3—202no—
303C3⋊C8—22no—
304C3⋊C8—22no—
305C22×C5—22no—
306C22×C5—22no—
307C22×C5—22no—
308C22×C5—44no—
309C22×C5#93512yes—
310C22×C5#94212yes—
311C22×C5#95012yes—
312C22×C5C22×#6711yescharacteristic
313C4×C5—22no—
314C4×C5#93512yes—
315C4×C5C2×#23711yescharacteristic
316C4×C5C2×#23711yescharacteristic
317Dic5—42no—
318Dic5—42no—
319Dic5—122no—
320Dic5—122no—
321C24#120211yescharacteristic
322C2×Q8—52no—
323C2×Q8—101no—
324C2×Q8—102no—
325C2×Q8—102no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—101no—
329C22×C4—101no—
330C22×C4—301no—
331C22×C4—301no—
332C22×C4#120212yes—
333C22×C4#120211yescharacteristic
334C22×C4C2×D3×D512yes—
335C22×C4C2×D3×D511yescharacteristic
336C2×C8—32no—
337C2×C8—32no—
338C2×C8—62no—
339C2×C8—62no—
340C4⋊C4—52no—
341C4⋊C4—101no—
342C4⋊C4—104no—
343C4⋊C4—152no—
344C4⋊C4—152no—
345C4⋊C4—301no—
346C4⋊C4—301no—
347C22⋊C4—104no—
348C22⋊C4—304no—
349C42—304no—
350C3×C5C2×#48511yescharacteristic, complemented, Hall
351C22×C3—22no—
352C22×C3—22no—
353C22×C3—22no—
354C22×C3—44no—
355C22×C3#403212yes—
356C22×C3#405012yes—
357C22×C3#405512yes—
358C22×C3C22×D2011yescharacteristic
359C3×C4—22no—
360C3×C4—202no—
361C3×C4—202no—
362C3×C4#403212yes—
363C3×C4C2×#71111yescharacteristic
364C3×C4C2×#71111yescharacteristic
365Dic3—202no—
366Dic3—202no—
367C2×C5—42no—
368C2×C5#504514yescomplemented
369C2×C5C2×#93511yescharacteristic
370C2×C5C2×#94211yescharacteristic
371C2×C5C2×#95011yescharacteristic
372C23—22no—
373C23—22no—
374C23—22no—
375C23C2×#120212yes—
376C23C2×#120211yescharacteristic
377Q8—102no—
378Q8—102no—
379Q8—202no—
380C2×C4—22no—
381C2×C4—22no—
382C2×C4—22no—
383C2×C4—24no—
384C2×C4—102no—
385C2×C4—102no—
386C2×C4—202no—
387C2×C4—202no—
388C2×C4—302no—
389C2×C4—302no—
390C2×C4—602no—
391C2×C4—602no—
392C2×C4#678012yes—
393C2×C4#678012yes—
394C2×C4C2×#120212yes—
395C2×C4C2×#120211yescharacteristic
396C2×C4C22×D3×D511yescharacteristic
397C8—62no—
398C8—62no—
399C2×C3—42no—
400C2×C3#6501214yescomplemented
401C2×C3C2×#403211yescharacteristic
402C2×C3C2×#405011yescharacteristic
403C2×C3C2×#405511yescharacteristic
404C5C2×#504511yescharacteristic, complemented, Sylow
405C22—22no—
406C22—22no—
407C22—22no—
408C22—44no—
409C22#9131112yes—
410C22#9131512yes—
411C22#9153712yes—
412C22C22×#120211yescharacteristic
413C4—22no—
414C4—202no—
415C4—202no—
416C4—602no—
417C4—602no—
418C4#9153712yes—
419C4C2×#678011yescharacteristic
420C4C2×#678011yescharacteristic
421C3C2×#6501211yescharacteristic, complemented, Sylow
422C2—42no—
423C2#1174844614yesdirect product factor
424C2C2×#9131111yescharacteristic
425C2C2×#9131511yescharacteristic
426C2C2×#9153711yescharacteristic
subgroupG/H
centerC23C2×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C2×D4
prime radicalC24×C3×C5D4
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#485
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. C2×#90990C2semidirect
5. C2×#90987C2semidirect
6. #11748446C2direct (N × H)
7. C2×#90971C2semidirect
8. C2×#90971C2semidirect
26. #90990C22semidirect
27. #90987C22semidirect
28. #90971C22semidirect
29. #90971C22semidirect
274. C2×C3×C5#485semidirect
350. C3×C5C2×#485semidirect
368. C2×C5#5045semidirect
400. C2×C3#65012semidirect
404. C5C2×#5045semidirect
421. C3C2×#65012semidirect
423. C2#11748446direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918152
C2×C3×#40702
C2×C5×#8302
C2×#909902
C2×#909872
#117484462
C2×#909712
C2×#650123
C2×#50455