Finite Group Databasebeta

← C2×#11753397 #14479028

Subgroups — C2×#11753397 #14479028

Order 1920.

2976 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×Dic6C211yesmaximal, characteristic
2C2×#91776C211yesmaximal, characteristic, complemented
3C2×C5×#887C211yesmaximal, characteristic, complemented
4C2×C3×#4038C211yesmaximal, characteristic
5C2×C4×#1204C212yesmaximal, complemented
6C2×#91394C212yesmaximal
7C2×#91393C212yesmaximal
8C2×#91357C211yesmaximal, characteristic
9C2×#91344C211yesmaximal, characteristic, complemented
10C2×#91340C211yesmaximal, characteristic, complemented
11C2×#91323C212yesmaximal, complemented
12#11753397C2116yesmaximal, direct product factor
13C2×#65906—31nomaximal, Hall
14C22×Dic30C2211yescharacteristic
15C22×C5×Dic6C2211yescharacteristic
16C22×C3×C4×D5C2211yescharacteristic
17C22×#1204C2212yes—
18C22×D5×Dic3C2212yes—
19C2×D5×Dic6C4116yescomplemented
20C2×D5×Dic6C2218yes—
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×#6712C2212yes—
23C2×C4×Dic15C2212yes—
24C2×C4×Dic15C2211yescharacteristic
25#91776C2218yescomplemented
26C2×C5×Dic3⋊C4C2212yes—
27C2×C4×C5×Dic3C2212yes—
28C2×C4×C5×Dic3C2211yescharacteristic
29C5×#887C2218yescomplemented
30C2×C3×#685C2212yes—
31C2×C3×C4⋊Dic5C2211yescharacteristic
32C2×C3×C4×Dic5C2212yes—
33C3×#4038C2218yes—
34C2×Dic3⋊Dic5C2212yes—
35C2×#6669C2212yes—
36C2×#6668C2211yescharacteristic
37C2×#6668C2211yescharacteristic
38C2×#6665C2211yescharacteristic
39C2×#6665C2211yescharacteristic
40C2×Dic3×Dic5C2212yes—
41C2×Dic3×Dic5C2212yes—
42C4×#1204C22116yescomplemented
43#91394C22116yes—
44#91393C22116yes—
45#91357C2218yes—
46#91344C2218yescomplemented
47#91340C2218yescomplemented
48#91323C22116yescomplemented
49C2×#5516—51nomaximal, Hall
50C22×Q8×D5—31no—
51C2×C4×C5×Q8—31no—
52C2×Q8×Dic5—31no—
53#65906—316no—
54C2×#4038—32no—
55C2×#4038D311yescharacteristic
56C2×#4033—32no—
57C2×#4033—31no—
58C2×#4018—32no—
59C2×#4018—31no—
60C2×C4×Dic10—31no—
61C2×C4×Dic10—32no—
62C23×C3×D5C2311yescharacteristic
63C22×C3×C4×C5C2312yes—
64C22×C3×C4×C5C2311yescharacteristic
65C22×Dic15C2311yescharacteristic
66C22×Dic15C2311yescharacteristic
67C22×Dic15C2312yes—
68C2×Dic30C2×C418yes—
69C2×Dic30C2314yes—
70C22×C5×Dic3C2311yescharacteristic
71C22×C5×Dic3C2311yescharacteristic
72C22×C5×Dic3C2312yes—
73C2×C5×Dic6C2×C418yes—
74C2×C5×Dic6C2314yes—
75C22×C3×Dic5C2312yes—
76C22×C3×Dic5C2311yescharacteristic
77C2×C3×C4×D5C2×C418yes—
78C2×C3×C4×D5C2314yes—
79C2×#1204C2×C4116yes—
80C2×#1204C2318yes—
81C2×D5×Dic3C2×C4116yes—
82C2×D5×Dic3C2318yes—
83D5×Dic6C2×C4164yescomplemented
84C3×C5×C4⋊C4C2314yes—
85#6712C2318yes—
86C4×Dic15C2318yes—
87C4×Dic15C2314yes—
88C5×Dic3⋊C4C2318yes—
89C4×C5×Dic3C2318yes—
90C4×C5×Dic3C2314yes—
91C3×#685C2318yes—
92C3×C4⋊Dic5C2314yes—
93C3×C4×Dic5C2318yes—
94Dic3⋊Dic5C2318yes—
95#6669C2318yes—
96#6668C2314yes—
97#6668C2314yes—
98#6665C2314yes—
99#6665C2314yes—
100Dic3×Dic5C2318yes—
101Dic3×Dic5C2318yes—
102C23×Dic6—51no—
103C2×C3×#117—51no—
104C2×#926—51no—
105#5516—516no—
106C2×#887—51no—
107C2×#887—51no—
108C2×#887—51no—
109C2×#887D511yescharacteristic, complemented
110C2×#877—52no—
111C2×#877—52no—
112C2×C4×Dic6—52no—
113C2×C4×Dic6—52no—
114C22×C5×Q8—31no—
115C2×Q8×D5—316no—
116C2×Q8×D5—38no—
117C22×C4×D5—32no—
118C22×C4×D5C2×D311yescharacteristic
119C22×Dic10—31no—
120C22×Dic10—32no—
121C4×C5×Q8—38no—
122C2×C5×C4⋊C4—32no—
123C2×C5×C4⋊C4C2×D311yescharacteristic
124C2×C42×C5—32no—
125C2×C42×C5—31no—
126Q8×Dic5—38no—
127C2×#685—31no—
128C2×#685—31no—
129C2×#685C2×D312yes—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5C2×D311yescharacteristic
132C2×#683—32no—
133C2×#683—31no—
134C2×#683—32no—
135C2×#683—31no—
136C2×C4×Dic5—32no—
137C2×C4×Dic5—31no—
138C2×C4×Dic5—32no—
139C2×C4×Dic5—32no—
140C2×C4×Dic5C2×D312yes—
141#4038—316no—
142#4038C2×D318yes—
143#4033—38no—
144#4033—316no—
145#4018—38no—
146#4018—316no—
147C4×Dic10—38no—
148C4×Dic10—316no—
149C2×#519—151noSylow
150C23×C3×C5C2411yescharacteristic
151C22×C3×D5—22no—
152C22×C3×D5—22no—
153C22×C3×D5C22×C414yes—
154C22×C3×D5C2412yes—
155C2×C3×C4×C5—24no—
156C2×C3×C4×C5C22×C414yes—
157C2×C3×C4×C5C2414yes—
158C2×C3×C4×C5C2412yes—
159C2×Dic15—22no—
160C2×Dic15—22no—
161C2×Dic15C22×C418yes—
162C2×Dic15C2412yes—
163C2×Dic15C2412yes—
164C2×Dic15C2414yes—
165Dic30C22×C4116yes—
166C2×C5×Dic3—22no—
167C2×C5×Dic3—22no—
168C2×C5×Dic3C22×C418yes—
169C2×C5×Dic3C2412yes—
170C2×C5×Dic3C2412yes—
171C2×C5×Dic3C2414yes—
172C5×Dic6C22×C4116yes—
173C2×C3×Dic5—24no—
174C2×C3×Dic5C22×C414yes—
175C2×C3×Dic5C2414yes—
176C2×C3×Dic5C2412yes—
177C3×C4×D5C22×C4116yes—
178#1204C22×C4132yes—
179D5×Dic3C22×C4132yes—
180C23×C3×C4—51no—
181C23×Dic3—52no—
182C22×Dic6—51no—
183C22×Dic6—52no—
184C22×Dic6—516no—
185C22×Dic6—58no—
186C22×Dic6C2×D511yescharacteristic
187C3×#117—58no—
188C2×C3×C4⋊C4—51no—
189C2×C3×C4⋊C4C2×D511yescharacteristic
190C2×C3×C22⋊C4—52no—
191C2×C3×C42—52no—
192C2×#217—51no—
193C2×#217—51no—
194#926—58no—
195C2×C4⋊Dic3—51no—
196C2×C4⋊Dic3—51no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×Dic3⋊C4C2×D512yes—
201C2×C4×Dic3—52no—
202C2×C4×Dic3—51no—
203C2×C4×Dic3—52no—
204C2×C4×Dic3—52no—
205C2×C4×Dic3C2×D512yes—
206C2×C4×Dic3C2×D511yescharacteristic
207#887—58no—
208#887—58no—
209#887—58no—
210#887C2×D518yescomplemented
211#877—516no—
212#877—516no—
213C4×Dic6—516no—
214C4×Dic6—516no—
215C23×D5C22×D311yescharacteristic
216C2×C5×Q8—38no—
217C2×C5×Q8—34no—
218C22×C4×C5—32no—
219C22×C4×C5—31no—
220C22×C4×C5—31no—
221C22×C4×C5C22×D312yes—
222C22×C4×C5C22×D311yescharacteristic
223C22×Dic5—32no—
224C22×Dic5—31no—
225C22×Dic5—31no—
226C22×Dic5C22×D312yes—
227C22×Dic5C22×D311yescharacteristic
228Q8×D5—364no—
229C2×C4×D5—316no—
230C2×C4×D5—38no—
231C2×C4×D5C4×D318yes—
232C2×C4×D5C22×D314yes—
233C2×Dic10—38no—
234C2×Dic10—34no—
235C2×Dic10—316no—
236C2×Dic10—38no—
237C5×C4⋊C4—38no—
238C5×C4⋊C4C22×D314yes—
239C42×C5—38no—
240C42×C5—34no—
241#685—34no—
242#685—34no—
243#685C22×D318yes—
244C4⋊Dic5—38no—
245C4⋊Dic5C22×D314yes—
246#683—38no—
247#683—34no—
248#683—34no—
249#683—38no—
250C4×Dic5—38no—
251C4×Dic5—34no—
252C4×Dic5—38no—
253C4×Dic5—38no—
254C4×Dic5C22×D318yes—
255C23×Q8—151no—
256#519—1516no—
257C2×C4×Q8—31no—
258C2×C4×Q8—152no—
259C2×C4×Q8—151no—
260C2×C4×Q8—152no—
261C2×C4×Q8—151no—
262C2×C4×Q8—151no—
263C2×#117—51no—
264C2×#117—152no—
265C2×#117—151no—
266C2×#117—152no—
267C22×C3×C5C23×C412yes—
268C22×C3×C52−1+412yes—
269C22×C3×C52−1+412yes—
270C22×C3×C5C2511yescharacteristic
271C2×C3×D5—28no—
272C2×C3×D5—22no—
273C2×C3×D5—22no—
274C2×C3×D5C23×C414yes—
275C3×C4×C5—24no—
276C3×C4×C5C23×C414yes—
277Dic15—22no—
278Dic15—22no—
279Dic15C23×C418yes—
280C3×Dic5—24no—
281C3×Dic5C23×C414yes—
282C5×Dic3—22no—
283C5×Dic3—22no—
284C5×Dic3C23×C418yes—
285C24×C3—51no—
286C22×C3×C4—51no—
287C22×C3×C4—58no—
288C22×C3×C4—54no—
289C22×C3×C4—52no—
290C22×C3×C4C22×D512yes—
291C22×C3×C4C22×D511yescharacteristic
292C22×Dic3—52no—
293C22×Dic3—516no—
294C22×Dic3—58no—
295C22×Dic3—51no—
296C22×Dic3—51no—
297C22×Dic3C22×D511yescharacteristic
298C22×Dic3C22×D511yescharacteristic
299C22×Dic3C22×D512yes—
300C2×Dic6—58no—
301C2×Dic6—54no—
302C2×Dic6—516no—
303C2×Dic6—58no—
304C2×Dic6—564no—
305C2×Dic6C4×D518yes—
306C2×Dic6C22×D514yes—
307C3×C4⋊C4—54no—
308C3×C4⋊C4C22×D514yes—
309C3×C22⋊C4—58no—
310C3×C42—58no—
311#217—54no—
312#217—54no—
313C4⋊Dic3—54no—
314C4⋊Dic3—54no—
315Dic3⋊C4—58no—
316Dic3⋊C4—58no—
317Dic3⋊C4—58no—
318Dic3⋊C4C22×D518yes—
319C4×Dic3—58no—
320C4×Dic3—54no—
321C4×Dic3—58no—
322C4×Dic3—58no—
323C4×Dic3C22×D518yes—
324C4×Dic3C22×D514yes—
325C23×C5C23×D311yescharacteristic
326C22×D5—22no—
327C22×D5—22no—
328C22×D5C2×C4×D314yes—
329C22×D5C23×D312yes—
330C5×Q8—316no—
331C2×C4×C5—24no—
332C2×C4×C5—38no—
333C2×C4×C5—34no—
334C2×C4×C5—32no—
335C2×C4×C5—32no—
336C2×C4×C5—62no—
337C2×C4×C5—62no—
338C2×C4×C5C2×C4×D314yes—
339C2×C4×C5C23×D314yes—
340C2×C4×C5C23×D312yes—
341C2×Dic5—24no—
342C2×Dic5—38no—
343C2×Dic5—34no—
344C2×Dic5—32no—
345C2×Dic5—32no—
346C2×Dic5—62no—
347C2×Dic5—62no—
348C2×Dic5C2×C4×D314yes—
349C2×Dic5C23×D314yes—
350C2×Dic5C23×D312yes—
351C4×D5—332no—
352C4×D5C2×C4×D3116yes—
353Dic10—316no—
354Dic10—332no—
355C22×Q8—31no—
356C22×Q8—152no—
357C22×Q8—158no—
358C22×Q8—1516no—
359C22×Q8—151no—
360C23×C4—51no—
361C23×C4—152no—
362C4×Q8—38no—
363C4×Q8—1516no—
364C4×Q8—158no—
365C4×Q8—1516no—
366C4×Q8—158no—
367C4×Q8—158no—
368#117—58no—
369#117—1516no—
370#117—158no—
371#117—1516no—
372C2×C4⋊C4—32no—
373C2×C4⋊C4—51no—
374C2×C4⋊C4—152no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4—151no—
378C2×C4⋊C4—152no—
379C2×C4⋊C4D3×D511yescharacteristic
380C2×C22⋊C4—52no—
381C2×C22⋊C4—151no—
382C2×C22⋊C4—151no—
383C2×C42—32no—
384C2×C42—31no—
385C2×C42—52no—
386C2×C42—152no—
387C2×C42—152no—
388C2×C42—152no—
389C2×C42—151no—
390C2×C3×C5#51914yescomplemented
391C2×C3×C5C24×C411yescharacteristic
392C2×C3×C5C2×2−1+411yescharacteristic
393C2×C3×C5C2×2−1+411yescharacteristic
394C3×D5—24no—
395C23×C3—54no—
396C23×C3—52no—
397C23×C3—102no—
398C23×C3—102no—
399C23×C3C23×D511yescharacteristic
400C2×C3×C4—24no—
401C2×C3×C4—54no—
402C2×C3×C4—52no—
403C2×C3×C4—516no—
404C2×C3×C4—54no—
405C2×C3×C4—104no—
406C2×C3×C4C2×C4×D514yes—
407C2×C3×C4C23×D514yes—
408C2×C3×C4C23×D512yes—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—58no—
412C2×Dic3—54no—
413C2×Dic3—532no—
414C2×Dic3—52no—
415C2×Dic3—52no—
416C2×Dic3—102no—
417C2×Dic3—102no—
418C2×Dic3C2×C4×D518yes—
419C2×Dic3C23×D512yes—
420C2×Dic3C23×D512yes—
421C2×Dic3C23×D514yes—
422Dic6—516no—
423Dic6—532no—
424Dic6C2×C4×D5116yes—
425C22×C5C22×C4×D312yes—
426C22×C5#101012yes—
427C22×C5#101012yes—
428C22×C5C24×D311yescharacteristic
429C2×D5—22no—
430C2×D5—22no—
431C2×D5—28no—
432C2×D5C22×C4×D314yes—
433C4×C5—24no—
434C4×C5—38no—
435C4×C5—62no—
436C4×C5—62no—
437C4×C5C22×C4×D314yes—
438Dic5—24no—
439Dic5—38no—
440Dic5—62no—
441Dic5—62no—
442Dic5C22×C4×D314yes—
443C24—51no—
444C2×Q8—38no—
445C2×Q8—34no—
446C2×Q8—158no—
447C2×Q8—1516no—
448C2×Q8—1564no—
449C2×Q8—158no—
450C2×Q8—154no—
451C22×C4—32no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—51no—
455C22×C4—58no—
456C22×C4—54no—
457C22×C4—52no—
458C22×C4—158no—
459C22×C4—1516no—
460C22×C4—152no—
461C22×C4—151no—
462C22×C4—151no—
463C22×C4C2×D3×D512yes—
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—38no—
466C4⋊C4—54no—
467C4⋊C4—158no—
468C4⋊C4—154no—
469C4⋊C4—154no—
470C4⋊C4—158no—
471C4⋊C4—158no—
472C4⋊C4C2×D3×D514yes—
473C22⋊C4—58no—
474C22⋊C4—154no—
475C22⋊C4—154no—
476C42—38no—
477C42—34no—
478C42—58no—
479C42—158no—
480C42—158no—
481C42—158no—
482C42—154no—
483C3×C5C2×#51911yescharacteristic, complemented, Hall
484C22×C3—54no—
485C22×C3—108no—
486C22×C3—102no—
487C22×C3—102no—
488C22×C3C22×C4×D512yes—
489C22×C3#414712yes—
490C22×C3#415012yes—
491C22×C3C24×D511yescharacteristic
492C3×C4—24no—
493C3×C4—54no—
494C3×C4—104no—
495C3×C4C22×C4×D514yes—
496Dic3—22no—
497Dic3—22no—
498Dic3—58no—
499Dic3—102no—
500Dic3—102no—
501Dic3C22×C4×D518yes—
502C2×C5#551614yescomplemented
503C2×C5C23×C4×D311yescharacteristic
504C2×C5C2×#101011yescharacteristic
505C2×C5C2×#101011yescharacteristic
506D5—24no—
507C23—54no—
508C23—52no—
509C23—102no—
510C23—102no—
511C23C22×D3×D511yescharacteristic
512Q8—316no—
513Q8—1532no—
514Q8—1516no—
515C2×C4—24no—
516C2×C4—38no—
517C2×C4—34no—
518C2×C4—32no—
519C2×C4—32no—
520C2×C4—54no—
521C2×C4—52no—
522C2×C4—516no—
523C2×C4—54no—
524C2×C4—62no—
525C2×C4—62no—
526C2×C4—104no—
527C2×C4—1532no—
528C2×C4—158no—
529C2×C4—154no—
530C2×C4—152no—
531C2×C4—152no—
532C2×C4—302no—
533C2×C4—302no—
534C2×C4C4×D3×D514yes—
535C2×C4C22×D3×D514yes—
536C2×C4C22×D3×D512yes—
537C2×C3—104no—
538C2×C3#6590614yescomplemented
539C2×C3C23×C4×D511yescharacteristic
540C2×C3C2×#414711yescharacteristic
541C2×C3C2×#415011yescharacteristic
542C5C2×#551611yescharacteristic, complemented, Sylow
543C22—54no—
544C22—108no—
545C22—102no—
546C22—102no—
547C22C2×C4×D3×D512yes—
548C22#9202012yes—
549C22#9202812yes—
550C22C23×D3×D511yescharacteristic
551C4—24no—
552C4—38no—
553C4—54no—
554C4—62no—
555C4—62no—
556C4—104no—
557C4—158no—
558C4—302no—
559C4—302no—
560C4C2×C4×D3×D514yes—
561C3C2×#6590611yescharacteristic, complemented, Sylow
562C2—104no—
563C2#1175339714yesdirect product factor
564C2C22×C4×D3×D511yescharacteristic
565C2C2×#9202011yescharacteristic
566C2C2×#9202811yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
cosocleC22×C3×C5C25
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#519
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#91776C2semidirect
3. C2×C5×#887C2semidirect
5. C2×C4×#1204C2semidirect
9. C2×#91344C2semidirect
10. C2×#91340C2semidirect
11. C2×#91323C2semidirect
12. #11753397C2direct (N × H)
19. C2×D5×Dic6C4semidirect
25. #91776C22semidirect
29. C5×#887C22semidirect
42. C4×#1204C22semidirect
46. #91344C22semidirect
47. #91340C22semidirect
48. #91323C22semidirect
83. D5×Dic6C2×C4semidirect
109. C2×#887D5semidirect
210. #887C2×D5semidirect
390. C2×C3×C5#519semidirect
483. C3×C5C2×#519semidirect
502. C2×C5#5516semidirect
538. C2×C3#65906semidirect
542. C5C2×#5516semidirect
561. C3C2×#65906semidirect
563. C2#11753397direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×Dic62
C2×#917762
C2×C5×#8872
C2×C3×#40382
C2×C4×#12042
C2×#913942
C2×#913932
C2×#913572
C2×#913442
C2×#913402
C2×#913232
#117533972
C2×#659063
C2×#55165