Finite Group Databasebeta

← C2×#11755218 #14481428

Subgroups — C2×#11755218 #14481428

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91835C211yesmaximal, characteristic, complemented
2C2×C5×Q8×Dic3C211yesmaximal, characteristic, complemented
3C2×C3×#4093C211yesmaximal, characteristic, complemented
4#11755218C2116yesmaximal, direct product factor
5C2×#91468C211yesmaximal, characteristic, complemented
6C2×#91465C211yesmaximal, characteristic
7C2×#91430C212yesmaximal, complemented
8C2×Dic3×D20C211yesmaximal, characteristic, complemented
9C2×#91413C212yesmaximal, complemented
10C2×#91386C211yesmaximal, characteristic, complemented
11C2×#91363C212yesmaximal, complemented
12C2×#91353C212yesmaximal, complemented
13C2×#65916—31nomaximal, Hall
14C22×C3×C5×Q8C2211yescharacteristic
15C22×C4×D15C2211yescharacteristic
16C22×C3×D20C2211yescharacteristic
17C22×#1204C2212yes—
18C22×#1202C2212yes—
19C22×D5×Dic3C2212yes—
20#91835C2218yescomplemented
21C2×#6714C2212yes—
22C2×C4⋊Dic15C2211yescharacteristic
23C2×#6712C2212yes—
24C5×Q8×Dic3C2218yescomplemented
25C2×C5×C4⋊Dic3C2211yescharacteristic
26C2×C5×C4⋊Dic3C2212yes—
27C2×C4×C5×Dic3C2212yes—
28C2×C4×C5×Dic3C2211yescharacteristic
29C3×#4093C2218yescomplemented
30C2×C3×#685C2212yes—
31C2×C3×#685C2212yes—
32C2×C3×C4×Dic5C2211yescharacteristic
33C2×#6669C2211yescharacteristic
34C2×#6669C2211yescharacteristic
35C2×#6668C2212yes—
36C2×#6667C2211yescharacteristic
37C2×#6667C2211yescharacteristic
38C2×#6665C2212yes—
39C2×#6665C2212yes—
40#91468C2218yescomplemented
41#91465C2218yes—
42#91430C22116yescomplemented
43Dic3×D20C2218yescomplemented
44#91413C22116yescomplemented
45#91386C2218yescomplemented
46#91363C22116yescomplemented
47#91353C22116yescomplemented
48C2×#5682—51nomaximal, Hall
49C2×C4×C5×Q8—31no—
50C2×#4093D311yescharacteristic, complemented
51C2×#4092—31no—
52#65916—316no—
53C2×#4042—32no—
54C2×#4041—31no—
55C2×#4040—32no—
56C2×#4034—31no—
57C2×#4022—32no—
58C2×#4021—32no—
59C2×C4×D20—31no—
60C2×#4018—31no—
61C23×D15C2311yescharacteristic
62C23×C3×D5C2312yes—
63C2×C3×C5×Q8—24no—
64C2×C3×C5×Q8C2314yes—
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2311yescharacteristic
67C22×Dic15C2312yes—
68C22×Dic15C2311yescharacteristic
69C2×C4×D15—24no—
70C2×C4×D15C2314yes—
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2311yescharacteristic
73C22×C5×Dic3C2312yes—
74C22×C3×Dic5C2311yescharacteristic
75C22×C3×Dic5C2311yescharacteristic
76C2×C3×D20—24no—
77C2×C3×D20C2314yes—
78C2×#1204—44no—
79C2×#1204C2318yes—
80C2×#1202—44no—
81C2×#1202C2318yes—
82C2×D5×Dic3—44no—
83C2×D5×Dic3C2318yes—
84#6714C2318yes—
85C4⋊Dic15C2314yes—
86#6712C2318yes—
87C5×C4⋊Dic3C2318yes—
88C5×C4⋊Dic3C2314yes—
89C4×C5×Dic3C2314yes—
90C4×C5×Dic3C2318yes—
91C3×#685C2318yes—
92C3×#685C2318yes—
93C3×C4×Dic5C2314yes—
94#6669C2314yes—
95#6669C2314yes—
96#6668C2318yes—
97#6667C2314yes—
98#6667C2314yes—
99#6665C2318yes—
100#6665C2318yes—
101C2×C3×#124—51no—
102C2×#946—51no—
103C2×Q8×Dic3D511yescharacteristic, complemented
104C2×#938—51no—
105C2×D4×Dic3—51no—
106#5682—516no—
107C2×#886—52no—
108C2×#885—52no—
109C2×#879—52no—
110C2×#878—52no—
111C2×#872—51no—
112C2×#869—51no—
113C22×C5×Q8C2×D311yescharacteristic
114C22×D20—32no—
115C22×D20C2×D311yescharacteristic
116C22×C4×D5—31no—
117C22×C4×D5—32no—
118C22×Dic10—32no—
119C4×C5×Q8—38no—
120C2×C5×C4⋊C4—31no—
121C2×C5×C4⋊C4—32no—
122C2×C42×C5—31no—
123C2×C42×C5—32no—
124#4093C2×D318yescomplemented
125#4092—38no—
126C2×#685—32no—
127C2×#685—32no—
128C2×#685—32no—
129C2×#685—31no—
130C2×#685—31no—
131C2×#685C2×D312yes—
132C2×#685C2×D312yes—
133C2×C4⋊Dic5—31no—
134C2×#683—32no—
135C2×#683—31no—
136C2×#683—31no—
137C2×#683—32no—
138C2×C4×Dic5C2×D311yescharacteristic
139#4042—316no—
140#4041—38no—
141#4040—316no—
142#4034—38no—
143#4022—316no—
144#4021—316no—
145C4×D20—38no—
146#4018—38no—
147C2×#542—151noSylow
148C23×C3×C5C2411yescharacteristic
149C22×D15—22no—
150C22×D15—22no—
151C22×D15—22no—
152C22×D15C2412yes—
153C22×C3×D5—24no—
154C22×C3×D5—24no—
155C22×C3×D5—24no—
156C22×C3×D5C2414yes—
157C3×C5×Q8—28no—
158C2×C3×C4×C5—24no—
159C2×C3×C4×C5#4114yes—
160C2×C3×C4×C5C2414yes—
161C2×C3×C4×C5C2412yes—
162C2×Dic15—22no—
163C2×Dic15—24no—
164C2×Dic15C2412yes—
165C2×Dic15C2414yes—
166C4×D15—28no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3—24no—
169C2×C5×Dic3—22no—
170C2×C5×Dic3C2412yes—
171C2×C5×Dic3C2414yes—
172C2×C5×Dic3C2412yes—
173C2×C3×Dic5—22no—
174C2×C3×Dic5—22no—
175C2×C3×Dic5C2412yes—
176C2×C3×Dic5C2412yes—
177C3×D20—28no—
178#1204—48no—
179#1202—48no—
180D5×Dic3—48no—
181C22×C3×Q8C2×D511yescharacteristic
182C22×C3×D4—51no—
183C22×#67—52no—
184C23×Dic3—52no—
185C22×C4×D3—51no—
186C22×Dic6—52no—
187C3×#124—58no—
188C2×C3×C22⋊C4—52no—
189C2×C3×C22⋊C4—52no—
190C2×C3×C42—51no—
191C2×#217—52no—
192C2×#217—52no—
193#946—58no—
194Q8×Dic3C2×D518yescomplemented
195#938—58no—
196D4×Dic3—58no—
197C2×(C2×D3)⋊C4—52no—
198C2×(C2×D3)⋊C4—51no—
199C2×(C2×D3)⋊C4—51no—
200C2×C4⋊Dic3—51no—
201C2×C4⋊Dic3—52no—
202C2×C4⋊Dic3C2×D511yescharacteristic
203C2×C4⋊Dic3C2×D512yes—
204C2×Dic3⋊C4—52no—
205C2×Dic3⋊C4—51no—
206C2×Dic3⋊C4—51no—
207C2×C4×Dic3C2×D511yescharacteristic
208C2×C4×Dic3C2×D512yes—
209#886—516no—
210#885—516no—
211#879—516no—
212#878—516no—
213#872—58no—
214#869—58no—
215C23×D5—31no—
216C23×D5C22×D312yes—
217C2×C5×Q8—24no—
218C2×C5×Q8C22×D314yes—
219C22×C4×C5—31no—
220C22×C4×C5—32no—
221C22×C4×C5—31no—
222C22×C4×C5C22×D312yes—
223C22×C4×C5C22×D311yescharacteristic
224C22×Dic5—32no—
225C22×Dic5—31no—
226C22×Dic5C22×D311yescharacteristic
227C22×Dic5C22×D311yescharacteristic
228C2×D20—24no—
229C2×D20—38no—
230C2×D20—124no—
231C2×D20C22×D314yes—
232C2×C4×D5—34no—
233C2×C4×D5—38no—
234C2×C4×D5—64no—
235C2×C4×D5—124no—
236C2×Dic10—38no—
237C2×Dic10—124no—
238C5×C4⋊C4—34no—
239C5×C4⋊C4—38no—
240C42×C5—34no—
241C42×C5—38no—
242#685—38no—
243#685—38no—
244#685—38no—
245#685—34no—
246#685—34no—
247#685C22×D318yes—
248#685C22×D318yes—
249C4⋊Dic5—34no—
250#683—38no—
251#683—38no—
252#683—34no—
253#683—34no—
254C4×Dic5C22×D314yes—
255#542—1516no—
256C2×C4⋊Q8—151no—
257C2×#126—152no—
258C2×#124—51no—
259C2×#124—152no—
260C2×#123—152no—
261C2×C22⋊Q8—152no—
262C2×C22⋊Q8—151no—
263C2×#121—151no—
264C2×C4×Q8—31no—
265C2×C4×D4—151no—
266C2×#117—151no—
267C22×C3×C5C2×#4112yes—
268C22×C3×C5H(5,𝔽2)12yes—
269C22×C3×C52−1+412yes—
270C22×C3×C5C2511yescharacteristic
271C2×D15—22no—
272C2×D15—22no—
273C2×D15—22no—
274C2×D15—44no—
275C2×C3×D5—24no—
276C2×C3×D5—24no—
277C2×C3×D5—24no—
278C2×C3×D5—48no—
279C3×C4×C5—24no—
280C3×C4×C5C2×#4114yes—
281Dic15—22no—
282Dic15—24no—
283C3×Dic5—22no—
284C3×Dic5—22no—
285C5×Dic3—22no—
286C5×Dic3—24no—
287C5×Dic3—22no—
288C24×C3—52no—
289C23×D3—51no—
290C2×C3×Q8—24no—
291C2×C3×Q8C22×D514yes—
292C2×C3×D4—54no—
293C2×C3×D4—104no—
294C22×C3×C4—51no—
295C22×C3×C4—51no—
296C22×C3×C4C22×D512yes—
297C22×C3×C4C22×D511yescharacteristic
298C2×#67—58no—
299C2×#67—204no—
300C22×Dic3—51no—
301C22×Dic3—52no—
302C22×Dic3—58no—
303C22×Dic3—204no—
304C22×Dic3C22×D511yescharacteristic
305C22×Dic3C22×D511yescharacteristic
306C22×Dic3C22×D512yes—
307C2×C4×D3—54no—
308C2×C4×D3—104no—
309C2×Dic6—58no—
310C2×Dic6—204no—
311C3×C22⋊C4—58no—
312C3×C22⋊C4—58no—
313C3×C42—54no—
314#217—58no—
315#217—58no—
316(C2×D3)⋊C4—58no—
317(C2×D3)⋊C4—54no—
318(C2×D3)⋊C4—54no—
319C4⋊Dic3—54no—
320C4⋊Dic3—58no—
321C4⋊Dic3C22×D514yes—
322C4⋊Dic3C22×D518yes—
323Dic3⋊C4—58no—
324Dic3⋊C4—54no—
325Dic3⋊C4—54no—
326C4×Dic3C22×D514yes—
327C4×Dic3C22×D518yes—
328C23×C5C23×D311yescharacteristic
329C22×D5—24no—
330C22×D5—24no—
331C22×D5—24no—
332C22×D5—32no—
333C22×D5—62no—
334C22×D5—62no—
335C22×D5—62no—
336C22×D5C23×D314yes—
337C5×Q8—28no—
338C2×C4×C5—24no—
339C2×C4×C5—32no—
340C2×C4×C5—34no—
341C2×C4×C5—32no—
342C2×C4×C5—64no—
343C2×C4×C5—62no—
344C2×C4×C5—62no—
345C2×C4×C5#23714yes—
346C2×C4×C5C23×D314yes—
347C2×C4×C5C23×D312yes—
348C2×Dic5—22no—
349C2×Dic5—22no—
350C2×Dic5—32no—
351C2×Dic5—34no—
352C2×Dic5—62no—
353C2×Dic5—64no—
354C2×Dic5C23×D312yes—
355C2×Dic5C23×D312yes—
356D20—28no—
357D20—128no—
358C4×D5—68no—
359C4×D5—128no—
360Dic10—128no—
361C22×Q8—152no—
362C22×Q8D3×D511yescharacteristic
363C22×D4—51no—
364C22×D4—152no—
365C23×C4—152no—
366C23×C4—151no—
367C4⋊Q8—158no—
368#126—1516no—
369#124—58no—
370#124—1516no—
371#123—1516no—
372C22⋊Q8—1516no—
373C22⋊Q8—158no—
374#121—158no—
375C4×Q8—38no—
376C4×D4—158no—
377#117—158no—
378C2×C4⋊C4—31no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4—151no—
381C2×C4⋊C4—151no—
382C2×C4⋊C4—152no—
383C2×C4⋊C4—151no—
384C2×C4⋊C4—152no—
385C2×C22⋊C4—52no—
386C2×C22⋊C4—52no—
387C2×C22⋊C4—151no—
388C2×C22⋊C4—151no—
389C2×C22⋊C4—152no—
390C2×C22⋊C4—152no—
391C2×C22⋊C4—152no—
392C2×C42—31no—
393C2×C42—32no—
394C2×C42—51no—
395C2×C3×C5#54214yescomplemented
396C2×C3×C5C22×#4111yescharacteristic
397C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
398C2×C3×C5C2×2−1+411yescharacteristic
399D15—42no—
400C3×D5—44no—
401C23×C3—54no—
402C23×C3—104no—
403C23×C3—104no—
404C23×C3—104no—
405C23×C3C23×D511yescharacteristic
406C22×D3—52no—
407C22×D3—102no—
408C22×D3—102no—
409C22×D3—102no—
410C3×Q8—28no—
411C3×D4—108no—
412C2×C3×C4—24no—
413C2×C3×C4—52no—
414C2×C3×C4—52no—
415C2×C3×C4—102no—
416C2×C3×C4—102no—
417C2×C3×C4#70914yes—
418C2×C3×C4C23×D514yes—
419C2×C3×C4C23×D512yes—
420#67—208no—
421C2×Dic3—22no—
422C2×Dic3—24no—
423C2×Dic3—22no—
424C2×Dic3—52no—
425C2×Dic3—54no—
426C2×Dic3—102no—
427C2×Dic3—104no—
428C2×Dic3—208no—
429C2×Dic3C23×D512yes—
430C2×Dic3C23×D512yes—
431C2×Dic3C23×D514yes—
432C4×D3—108no—
433Dic6—208no—
434C22×C5C2×#23712yes—
435C22×C5#100912yes—
436C22×C5#101012yes—
437C22×C5C24×D311yescharacteristic
438C2×D5—24no—
439C2×D5—24no—
440C2×D5—24no—
441C2×D5—48no—
442C2×D5—62no—
443C2×D5—62no—
444C2×D5—62no—
445C2×D5—124no—
446C4×C5—24no—
447C4×C5—64no—
448C4×C5—62no—
449C4×C5—62no—
450C4×C5C2×#23714yes—
451Dic5—22no—
452Dic5—22no—
453Dic5—62no—
454Dic5—64no—
455C24—52no—
456C24—151no—
457C2×Q8—24no—
458C2×Q8—158no—
459C2×Q8—604no—
460C2×Q8C2×D3×D514yes—
461C2×D4—54no—
462C2×D4—104no—
463C2×D4—158no—
464C2×D4—604no—
465C22×C4—31no—
466C22×C4—31no—
467C22×C4—32no—
468C22×C4—51no—
469C22×C4—51no—
470C22×C4—158no—
471C22×C4—151no—
472C22×C4—152no—
473C22×C4—154no—
474C22×C4—304no—
475C22×C4—604no—
476C22×C4C2×D3×D512yes—
477C22×C4C2×D3×D511yescharacteristic
478C4⋊C4—34no—
479C4⋊C4—38no—
480C4⋊C4—154no—
481C4⋊C4—154no—
482C4⋊C4—158no—
483C4⋊C4—154no—
484C4⋊C4—158no—
485C22⋊C4—58no—
486C22⋊C4—58no—
487C22⋊C4—154no—
488C22⋊C4—154no—
489C22⋊C4—158no—
490C22⋊C4—158no—
491C22⋊C4—158no—
492C42—34no—
493C42—38no—
494C42—54no—
495C3×C5C2×#54211yescharacteristic, complemented, Hall
496C22×C3—104no—
497C22×C3—104no—
498C22×C3—104no—
499C22×C3—208no—
500C22×C3C2×#70912yes—
501C22×C3#414712yes—
502C22×C3#414912yes—
503C22×C3C24×D511yescharacteristic
504C2×D3—102no—
505C2×D3—102no—
506C2×D3—102no—
507C2×D3—204no—
508C3×C4—24no—
509C3×C4—102no—
510C3×C4—102no—
511C3×C4C2×#70914yes—
512Dic3—22no—
513Dic3—24no—
514Dic3—22no—
515Dic3—102no—
516Dic3—104no—
517C2×C5#568214yescomplemented
518C2×C5C22×#23711yescharacteristic
519C2×C5C2×#100911yescharacteristic
520C2×C5C2×#101011yescharacteristic
521D5—44no—
522D5—122no—
523C23—54no—
524C23—104no—
525C23—104no—
526C23—104no—
527C23—152no—
528C23—302no—
529C23—302no—
530C23—302no—
531C23C22×D3×D511yescharacteristic
532Q8—28no—
533Q8—608no—
534D4—108no—
535D4—608no—
536C2×C4—24no—
537C2×C4—32no—
538C2×C4—32no—
539C2×C4—34no—
540C2×C4—52no—
541C2×C4—52no—
542C2×C4—62no—
543C2×C4—62no—
544C2×C4—64no—
545C2×C4—102no—
546C2×C4—102no—
547C2×C4—152no—
548C2×C4—154no—
549C2×C4—304no—
550C2×C4—302no—
551C2×C4—308no—
552C2×C4—608no—
553C2×C4#677914yes—
554C2×C4C22×D3×D514yes—
555C2×C4C22×D3×D512yes—
556C2×C3—204no—
557C2×C3#6591614yescomplemented
558C2×C3C22×#70911yescharacteristic
559C2×C3C2×#414711yescharacteristic
560C2×C3C2×#414911yescharacteristic
561D3—202no—
562C5C2×#568211yescharacteristic, complemented, Sylow
563C22—104no—
564C22—104no—
565C22—104no—
566C22—208no—
567C22—302no—
568C22—302no—
569C22—302no—
570C22—604no—
571C22#9202812yes—
572C22#9203512yes—
573C22C2×#677912yes—
574C22C23×D3×D511yescharacteristic
575C4—24no—
576C4—62no—
577C4—62no—
578C4—64no—
579C4—102no—
580C4—102no—
581C4—302no—
582C4—304no—
583C4C2×#677914yes—
584C3C2×#6591611yescharacteristic, complemented, Sylow
585C2—204no—
586C2—602no—
587C2#1175521814yesdirect product factor
588C2C2×#9202811yescharacteristic
589C2C2×#9203511yescharacteristic
590C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×Q8C22
socleC23×C3×C5C24
prime radicalC2×#91465C2
hypercenterC22×Q8D3×D5
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×#91835C2semidirect
2. C2×C5×Q8×Dic3C2semidirect
3. C2×C3×#4093C2semidirect
4. #11755218C2direct (N × H)
5. C2×#91468C2semidirect
7. C2×#91430C2semidirect
8. C2×Dic3×D20C2semidirect
9. C2×#91413C2semidirect
10. C2×#91386C2semidirect
11. C2×#91363C2semidirect
12. C2×#91353C2semidirect
20. #91835C22semidirect
24. C5×Q8×Dic3C22semidirect
29. C3×#4093C22semidirect
40. #91468C22semidirect
42. #91430C22semidirect
43. Dic3×D20C22semidirect
44. #91413C22semidirect
45. #91386C22semidirect
46. #91363C22semidirect
47. #91353C22semidirect
50. C2×#4093D3semidirect
103. C2×Q8×Dic3D5semidirect
124. #4093C2×D3semidirect
194. Q8×Dic3C2×D5semidirect
395. C2×C3×C5#542semidirect
495. C3×C5C2×#542semidirect
517. C2×C5#5682semidirect
557. C2×C3#65916semidirect
562. C5C2×#5682semidirect
584. C3C2×#65916semidirect
587. C2#11755218direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918352
C2×C5×Q8×Dic32
C2×C3×#40932
#117552182
C2×#914682
C2×#914652
C2×#914302
C2×Dic3×D202
C2×#914132
C2×#913862
C2×#913632
C2×#913532
C2×#659163
C2×#56825