Finite Group Databasebeta

← C2×#11756597 #14510129

Subgroups — C2×#11756597 #14510129

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×2−1+4C211yesmaximal, characteristic, complemented
2C2×#92101C211yesmaximal, characteristic, complemented
3#11756597C2116yesmaximal, direct product factor
4C2×#91840C213yesmaximal, complemented
5C2×#91839C213yesmaximal, complemented
6C2×#91837C211yesmaximal, characteristic, complemented
7C22×#6718C213yesmaximal, complemented
8C2×#91831C213yesmaximal, complemented
9C2×#66172—31nomaximal, Hall
10C3×C5×2−1+4—24no—
11C3×C5×2−1+4C2218yescomplemented
12C2×C3×C5×#41—23no—
13C2×C3×C5×#41C2213yes—
14C2×C3×C5×#41C2211yescharacteristic
15C22×C3×C5×Q8—21no—
16C22×C3×C5×Q8C2213yes—
17#92101—24no—
18#92101C2218yescomplemented
19C2×Q8×D15—21no—
20C2×#6819—23no—
21C2×#6817C2213yes—
22C22×Dic30C2213yes—
23#91840C22124yescomplemented
24#91839C22124yescomplemented
25#91837C2218yescomplemented
26C2×#6718C2216yes—
27C2×#6718C2213yes—
28C2×#6718C22124yescomplemented
29#91831C22124yescomplemented
30C2×#6717C2213yes—
31C2×#6716C2213yes—
32C2×#6715C2211yescharacteristic
33C2×#6710C2213yes—
34C22×C3⋊#168C2213yes—
35C2×#5838—51nomaximal, Hall
36C2×C5×2−1+4D311yescharacteristic, complemented
37C2×#4150—31no—
38#66172—316no—
39C2×#4097—33no—
40C2×#4096—33no—
41C2×#4094—31no—
42C22×#689—33no—
43C2×#4088—33no—
44C3×C5×#41—224no—
45C3×C5×#41—26no—
46C3×C5×#41D414yes—
47C3×C5×#41C23112yes—
48C3×C5×#41C2314yes—
49C2×C3×C5×Q8—28no—
50C2×C3×C5×Q8—23no—
51C2×C3×C5×Q8—26no—
52C2×C3×C5×Q8D411yescharacteristic
53C2×C3×C5×Q8C2313yes—
54C2×C3×C5×Q8C23112yes—
55C2×C3×C5×D4—23no—
56C2×C3×C5×D4D413yes—
57C2×C3×C5×D4C2311yescharacteristic
58C22×C3×C4×C5—23no—
59C22×C3×C4×C5—23no—
60C22×C3×C4×C5C2313yes—
61C2×#1220—23no—
62C22×Dic15—23no—
63Q8×D15—28no—
64#6819—224no—
65#6817—26no—
66#6817C23112yes—
67C2×D60C2311yescharacteristic
68C2×C4×D15—23no—
69C2×Dic30—23no—
70C2×Dic30—26no—
71C2×Dic30C2313yes—
72C2×Dic30C23112yes—
73#6718C23124yes—
74#6718C23112yes—
75#6717C23112yes—
76#6716C23112yes—
77#6715C2314yes—
78#6710C23112yes—
79C2×C3⋊#168C2311yescharacteristic
80C2×C3⋊#168C2313yes—
81C2×C3⋊#168C23112yes—
82C2×C3×2−1+4D511yescharacteristic, complemented
83C2×#1010—51no—
84#5838—516no—
85C2×#951—53no—
86C2×#950—53no—
87C2×#948—51no—
88C22×#216—53no—
89C2×#942—53no—
90C5×2−1+4—24no—
91C5×2−1+4C2×D318yescomplemented
92C2×C5×#41—23no—
93C2×C5×#41C2×D313yes—
94C2×C5×#41C2×D311yescharacteristic
95C22×C5×Q8—21no—
96C22×C5×Q8C2×D313yes—
97#4150—38no—
98#4150—64no—
99C2×Q8×D5—61no—
100C2×#711—63no—
101C2×#709—33no—
102C22×Dic10—33no—
103#4097—324no—
104#4096—324no—
105#4094—38no—
106C2×#689—36no—
107C2×#689—33no—
108C2×#689—324no—
109#4088—324no—
110C2×#688—33no—
111C2×#687—33no—
112C2×#686—31no—
113C2×#681—33no—
114C22×#168—33no—
115C2×#578—151noSylow
116C23×C3×C5—21no—
117C23×C3×C5C2×D413yes—
118C22×D15—21no—
119C3×C5×Q8—23no—
120C3×C5×Q8—212no—
121C3×C5×Q8C2×D414yes—
122C3×C5×Q8C2416yes—
123C3×C5×D4—212no—
124C3×C5×D4—21no—
125C3×C5×D4C2×D4112yes—
126C3×C5×D4C2412yes—
127C2×C3×C4×C5—23no—
128C2×C3×C4×C5—212no—
129C2×C3×C4×C5—212no—
130C2×C3×C4×C5C2×D413yes—
131C2×C3×C4×C5C2×D416yes—
132C2×C3×C4×C5C2411yescharacteristic
133C2×C3×C4×C5C2416yes—
134#1220—212no—
135C2×Dic15—23no—
136C2×Dic15—212no—
137D60—21no—
138D60C2412yes—
139C4×D15—212no—
140Dic30—23no—
141Dic30—212no—
142Dic30C2416yes—
143C3⋊#168C2412yes—
144C3⋊#168C2416yes—
145C3×2−1+4—24no—
146C3×2−1+4C2×D518yescomplemented
147C2×C3×#41—23no—
148C2×C3×#41C2×D513yes—
149C2×C3×#41C2×D511yescharacteristic
150C22×C3×Q8—21no—
151C22×C3×Q8C2×D513yes—
152#1010—58no—
153#1010—104no—
154C2×D3×Q8—101no—
155C2×#237—103no—
156C2×#235—53no—
157C22×Dic6—53no—
158#951—524no—
159#950—524no—
160#948—58no—
161C2×#216—56no—
162C2×#216—53no—
163C2×#216—524no—
164#942—524no—
165C2×#215—53no—
166C2×#214—53no—
167C2×#213—51no—
168C2×#208—53no—
169C22×C3⋊C8—53no—
170C5×#41—224no—
171C5×#41—26no—
172C5×#41#6714yes—
173C5×#41C22×D3112yes—
174C5×#41C22×D314yes—
175C2×C5×Q8—28no—
176C2×C5×Q8—23no—
177C2×C5×Q8—26no—
178C2×C5×Q8#6711yescharacteristic
179C2×C5×Q8C22×D313yes—
180C2×C5×Q8C22×D3112yes—
181C2×C5×D4—23no—
182C2×C5×D4#6713yes—
183C2×C5×D4C22×D311yescharacteristic
184C22×C4×C5—23no—
185C22×C4×C5—23no—
186C22×C4×C5C22×D313yes—
187C2×C22⋊D5—63no—
188C22×Dic5—63no—
189Q8×D5—68no—
190#711—624no—
191#709—312no—
192#709—66no—
193C2×D20—31no—
194C2×C4×D5—63no—
195C2×Dic10—312no—
196C2×Dic10—33no—
197C2×Dic10—63no—
198C2×Dic10—66no—
199#689—312no—
200#689—324no—
201#688—312no—
202#687—312no—
203#686—34no—
204#681—312no—
205C2×#168—312no—
206C2×#168—31no—
207C2×#168—33no—
208C2×2−1+4—151no—
209C2×2−1+4D1511yescharacteristic, complemented
210#578—1516no—
211C2×#137—153no—
212C2×#137—153no—
213C2×#135—153no—
214C22×Q16—153no—
215C2×#131—151no—
216C22×C3×C5—26no—
217C22×C3×C5—22no—
218C22×C3×C5—42no—
219C22×C3×C5C22×D416yes—
220C22×C3×C5C22×D411yescharacteristic
221C2×D15—22no—
222C2×D15—42no—
223C3×C4×C5—26no—
224C3×C4×C5C22×D411yescharacteristic
225C3×C4×C5C22×D416yes—
226C3×C4×C5C2511yescharacteristic
227Dic15—26no—
228C3×#41—224no—
229C3×#41—26no—
230C3×#41C22⋊D514yes—
231C3×#41C22×D5112yes—
232C3×#41C22×D514yes—
233C2×C3×Q8—28no—
234C2×C3×Q8—23no—
235C2×C3×Q8—26no—
236C2×C3×Q8C22⋊D511yescharacteristic
237C2×C3×Q8C22×D513yes—
238C2×C3×Q8C22×D5112yes—
239C2×C3×D4—23no—
240C2×C3×D4C22⋊D513yes—
241C2×C3×D4C22×D511yescharacteristic
242C22×C3×C4—23no—
243C22×C3×C4—23no—
244C22×C3×C4C22×D513yes—
245C2×#67—103no—
246C22×Dic3—103no—
247D3×Q8—108no—
248#237—1024no—
249#235—512no—
250#235—106no—
251C2×D12—51no—
252C2×C4×D3—103no—
253C2×Dic6—53no—
254C2×Dic6—512no—
255C2×Dic6—103no—
256C2×Dic6—106no—
257#216—524no—
258#216—512no—
259#215—512no—
260#214—512no—
261#213—54no—
262#208—512no—
263C2×C3⋊C8—51no—
264C2×C3⋊C8—53no—
265C2×C3⋊C8—512no—
266C23×C5—21no—
267C23×C5C2×#6713yes—
268C22×D5—61no—
269C5×Q8—23no—
270C5×Q8—212no—
271C5×Q8C2×#6714yes—
272C5×Q8C23×D316yes—
273C5×D4—212no—
274C5×D4—21no—
275C5×D4C2×#67112yes—
276C5×D4C23×D312yes—
277C2×C4×C5—23no—
278C2×C4×C5—212no—
279C2×C4×C5—212no—
280C2×C4×C5C2×#6713yes—
281C2×C4×C5C2×#6716yes—
282C2×C4×C5C23×D311yescharacteristic
283C2×C4×C5C23×D316yes—
284C22⋊D5—612no—
285C2×Dic5—63no—
286C2×Dic5—612no—
287D20—32no—
288D20—61no—
289C4×D5—612no—
290Dic10—36no—
291Dic10—63no—
292Dic10—612no—
293#168—32no—
294#168—36no—
2952−1+4—24no—
2962−1+4—158no—
2972−1+4—304no—
2982−1+4C2×D1518yescomplemented
299C2×#41—23no—
300C2×#41—153no—
301C2×#41—303no—
302C2×#41C2×D1513yes—
303C2×#41C2×D1511yescharacteristic
304C22×Q8—21no—
305C22×Q8—153no—
306C22×Q8—301no—
307C22×Q8C2×D1513yes—
308#137—1524no—
309#137—1524no—
310#135—1524no—
311C2×Q16—153no—
312C2×Q16—156no—
313C2×Q16—1524no—
314C2×SD16—153no—
315C2×SD16—153no—
316C2×D8—151no—
317#131—158no—
318C2×M16—153no—
319C22×C8—153no—
320C2×C3×C5—26no—
321C2×C3×C5—42no—
322C2×C3×C5#57812yescomplemented
323C2×C3×C5C23×D411yescharacteristic
324D15—42no—
325C23×C3—21no—
326C23×C3C2×C22⋊D513yes—
327C22×D3—101no—
328C3×Q8—23no—
329C3×Q8—212no—
330C3×Q8C2×C22⋊D514yes—
331C3×Q8C23×D516yes—
332C3×D4—212no—
333C3×D4—21no—
334C3×D4C2×C22⋊D5112yes—
335C3×D4C23×D512yes—
336C2×C3×C4—23no—
337C2×C3×C4—212no—
338C2×C3×C4—212no—
339C2×C3×C4C2×C22⋊D513yes—
340C2×C3×C4C2×C22⋊D516yes—
341C2×C3×C4C23×D511yescharacteristic
342C2×C3×C4C23×D516yes—
343#67—1012no—
344C2×Dic3—103no—
345C2×Dic3—1012no—
346D12—52no—
347D12—101no—
348C4×D3—1012no—
349Dic6—56no—
350Dic6—103no—
351Dic6—1012no—
352C3⋊C8—52no—
353C3⋊C8—56no—
354C22×C5—26no—
355C22×C5—22no—
356C22×C5—42no—
357C22×C5C22×#6716yes—
358C22×C5C22×#6711yescharacteristic
359C2×D5—62no—
360C2×D5—122no—
361C4×C5—26no—
362C4×C5C22×#6711yescharacteristic
363C4×C5C22×#6716yes—
364C4×C5C24×D311yescharacteristic
365Dic5—66no—
366#41—224no—
367#41—26no—
368#41—1512no—
369#41—3024no—
370#41—306no—
371#41#122014yes—
372#41C22×D15112yes—
373#41C22×D1514yes—
374C2×Q8—28no—
375C2×Q8—23no—
376C2×Q8—26no—
377C2×Q8—153no—
378C2×Q8—1512no—
379C2×Q8—308no—
380C2×Q8—303no—
381C2×Q8—306no—
382C2×Q8#122011yescharacteristic
383C2×Q8C22×D1513yes—
384C2×Q8C22×D15112yes—
385C2×D4—23no—
386C2×D4—151no—
387C2×D4—303no—
388C2×D4#122013yes—
389C2×D4C22×D1511yescharacteristic
390C22×C4—23no—
391C22×C4—23no—
392C22×C4—303no—
393C22×C4—303no—
394C22×C4C22×D1513yes—
395Q16—1512no—
396Q16—1524no—
397SD16—1512no—
398SD16—1512no—
399D8—154no—
400M16—1512no—
401C2×C8—151no—
402C2×C8—153no—
403C2×C8—1512no—
404C3×C5C2×#57811yescharacteristic, complemented, Hall
405C22×C3—26no—
406C22×C3—22no—
407C22×C3—42no—
408C22×C3C22×C22⋊D516yes—
409C22×C3C22×C22⋊D511yescharacteristic
410C2×D3—102no—
411C2×D3—202no—
412C3×C4—26no—
413C3×C4C22×C22⋊D511yescharacteristic
414C3×C4C22×C22⋊D516yes—
415C3×C4C24×D511yescharacteristic
416Dic3—106no—
417C2×C5—26no—
418C2×C5—42no—
419C2×C5#583812yescomplemented
420C2×C5C23×#6711yescharacteristic
421D5—122no—
422C23—21no—
423C23—301no—
424C23C2×#122013yes—
425Q8—212no—
426Q8—23no—
427Q8—156no—
428Q8—3012no—
429Q8—303no—
430Q8C2×#122014yes—
431Q8C23×D1516yes—
432D4—212no—
433D4—21no—
434D4—152no—
435D4—3012no—
436D4—301no—
437D4C2×#1220112yes—
438D4C23×D1512yes—
439C2×C4—212no—
440C2×C4—23no—
441C2×C4—212no—
442C2×C4—3012no—
443C2×C4—303no—
444C2×C4—3012no—
445C2×C4C2×#122016yes—
446C2×C4C2×#122013yes—
447C2×C4C23×D1516yes—
448C2×C4C23×D1511yescharacteristic
449C8—152no—
450C8—156no—
451C2×C3—26no—
452C2×C3—42no—
453C2×C3#6617212yescomplemented
454C2×C3C23×C22⋊D511yescharacteristic
455D3—202no—
456C5C2×#583811yescharacteristic, complemented, Sylow
457C22—26no—
458C22—22no—
459C22—42no—
460C22—302no—
461C22—602no—
462C22C22×#122016yes—
463C22C22×#122011yescharacteristic
464C4—26no—
465C4—306no—
466C4C22×#122016yes—
467C4C22×#122011yescharacteristic
468C4C24×D1511yescharacteristic
469C3C2×#6617211yescharacteristic, complemented, Sylow
470C2—26no—
471C2—42no—
472C2—602no—
473C2#1175659712yesdirect product factor
474C2C23×#122011yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC3×C4×C5C25
FrattiniC4C24×D15
FittingC2×C3×C5×2−1+4C2
socleC22×C3×C5C22×D4
hypercenterC2×2−1+4D15
hypocenterC3×C5C2×#578
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×#41 ◁ C2×2−1+4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C5×2−1+4C2semidirect
2. C2×#92101C2semidirect
3. #11756597C2direct (N × H)
4. C2×#91840C2semidirect
5. C2×#91839C2semidirect
6. C2×#91837C2semidirect
7. C22×#6718C2semidirect
8. C2×#91831C2semidirect
11. C3×C5×2−1+4C22semidirect
18. #92101C22semidirect
23. #91840C22semidirect
24. #91839C22semidirect
25. #91837C22semidirect
28. C2×#6718C22semidirect
29. #91831C22semidirect
36. C2×C5×2−1+4D3semidirect
82. C2×C3×2−1+4D5semidirect
91. C5×2−1+4C2×D3semidirect
146. C3×2−1+4C2×D5semidirect
209. C2×2−1+4D15semidirect
298. 2−1+4C2×D15semidirect
322. C2×C3×C5#578semidirect
404. C3×C5C2×#578semidirect
419. C2×C5#5838semidirect
453. C2×C3#66172semidirect
456. C5C2×#5838semidirect
469. C3C2×#66172semidirect
473. C2#11756597direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×C5×2−1+42
C2×#921012
#117565972
C2×#918402
C2×#918392
C2×#918372
C22×#67182
C2×#918312
C2×#661723
C2×#58385