Finite Group Databasebeta

← C2×#11749174 #14411945

Subgroups — C2×#11749174 #14411945

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6819C211yesmaximal, characteristic
2C2×#91532C212yesmaximal, complemented
3C2×C5×#834C211yesmaximal, characteristic, complemented
4C2×C3×#3966C211yesmaximal, characteristic, complemented
5C2×#90997C212yesmaximal, complemented
6#11749174C218yesmaximal, direct product factor
7C2×#65029—31nomaximal, Hall
8C22×C3×C5×D4C2211yescharacteristic
9C22×#1220C411yescharacteristic, complemented
10C22×#1220C2211yescharacteristic
11C23×Dic15C411yescharacteristic, complemented
12C23×Dic15C2211yescharacteristic
13C2×#6819—22no—
14C2×#6819—24no—
15C2×#6819—22no—
16C2×#6819C414yescomplemented
17C2×#6819C2214yes—
18C22×C4×D15C411yescharacteristic, complemented
19C22×Dic30C411yescharacteristic, complemented
20C2×C5×#217C2212yes—
21C2×C3×C22⋊Dic5C2212yes—
22C2×#6669—22no—
23#91532—24no—
24#91532C2218yescomplemented
25C2×Dic3×Dic5—22no—
26C5×#834C2214yescomplemented
27C3×#3966C2214yescomplemented
28#90997C2218yescomplemented
29C2×#4740—51nomaximal, Hall
30C22×#711—31no—
31C2×#4023—32no—
32C2×C5×#99—31no—
33C2×#3966D311yescharacteristic, complemented
34C2×#3938—32no—
35#65029—38no—
36C24×C3×C5C2×C411yescharacteristic
37C24×C3×C5C2311yescharacteristic
38C23×D15C2×C411yescharacteristic
39C2×C3×C5×D4—22no—
40C2×C3×C5×D4—22no—
41C2×C3×C5×D4C2×C412yes—
42C2×C3×C5×D4C2312yes—
43C22×C3×C4×C5C2×C411yescharacteristic
44C2×#1220—22no—
45C2×#1220—22no—
46C2×#1220—22no—
47C2×#1220—22no—
48C2×#1220C2×C412yes—
49C2×#1220C2×C414yescomplemented
50C2×#1220C2312yes—
51C22×Dic15—22no—
52C22×Dic15—21no—
53C22×Dic15—21no—
54C22×Dic15C2×C411yescharacteristic
55C22×Dic15C2×C411yescharacteristic
56C22×Dic15C2×C411yescharacteristic
57C22×Dic15C2×C412yes—
58C22×Dic15C2×C414yescomplemented
59C22×Dic15D412yes—
60C22×Dic15D414yes—
61C22×Dic15D412yes—
62C22×Dic15C2312yes—
63#6819—28no—
64#6819—28no—
65#6819—28no—
66#6819—28no—
67C2×C4×D15—22no—
68C2×C4×D15—21no—
69C2×C4×D15—21no—
70C2×C4×D15C2×C414yescomplemented
71C2×Dic30—22no—
72C2×Dic30—22no—
73C2×Dic30C2×C414yescomplemented
74C22×C5×Dic3—22no—
75C22×C3×Dic5—22no—
76C5×#217—22no—
77C5×#217C2314yes—
78C3×C22⋊Dic5—22no—
79C3×C22⋊Dic5C2314yes—
80#6669—28no—
81Dic3×Dic5—28no—
82C22×#237—51no—
83C2×#877—52no—
84C2×C3×#99—51no—
85C2×#834D511yescharacteristic, complemented
86C2×#806—52no—
87#4740—58no—
88C22×C5×D4C2×D311yescharacteristic
89C22×C22⋊D5—31no—
90C22×C22⋊D5—31no—
91C23×Dic5—31no—
92C23×Dic5—31no—
93C2×#711—34no—
94C2×#711—34no—
95C2×#711—64no—
96C2×#711—62no—
97C2×#711—62no—
98C22×C4×D5—31no—
99C22×Dic10—31no—
100C2×C5×C22⋊C4—32no—
101C2×C22⋊Dic5C2×D312yes—
102C2×#683—62no—
103C2×C4×Dic5—62no—
104#4023—38no—
105#4023—64no—
106C5×#99—34no—
107#3966C2×D314yescomplemented
108#3938—38no—
109C2×#410—151noSylow
110C23×C3×C5—21no—
111C23×C3×C5—21no—
112C23×C3×C5—42no—
113C23×C3×C5—42no—
114C23×C3×C5C22×C411yescharacteristic
115C23×C3×C5C22×C412yes—
116C23×C3×C5C22×C411yescharacteristic
117C23×C3×C5C2×D412yes—
118C23×C3×C5C2×D412yes—
119C23×C3×C5C2411yescharacteristic
120C22×D15—21no—
121C22×D15—21no—
122C22×D15—42no—
123C22×D15C22×C412yes—
124C3×C5×D4—24no—
125C3×C5×D4—24no—
126C2×C3×C4×C5—21no—
127C2×C3×C4×C5—21no—
128C2×C3×C4×C5C22×C412yes—
129#1220—24no—
130#1220—24no—
131#1220—28no—
132C2×Dic15—21no—
133C2×Dic15—21no—
134C2×Dic15—24no—
135C2×Dic15—24no—
136C2×Dic15C22⋊C412yes—
137C2×Dic15C22⋊C412yes—
138C2×Dic15C22⋊C412yes—
139C2×Dic15C22⋊C411yescharacteristic
140C2×Dic15C22⋊C411yescharacteristic
141C2×Dic15C22⋊C414yes—
142C2×Dic15C22⋊C414yes—
143C2×Dic15C22×C412yes—
144C2×Dic15C22×C412yes—
145C2×Dic15C22×C412yes—
146C2×Dic15C2×D414yes—
147C2×Dic15C2×D414yes—
148C4×D15—24no—
149C4×D15—24no—
150Dic30—28no—
151C2×C5×Dic3—24no—
152C2×C5×Dic3—44no—
153C2×C3×Dic5—24no—
154C2×C3×Dic5—44no—
155C22×C3×D4C2×D511yescharacteristic
156C22×#67—51no—
157C22×#67—51no—
158C23×Dic3—51no—
159C23×Dic3—51no—
160C2×#237—54no—
161C2×#237—54no—
162C2×#237—104no—
163C2×#237—102no—
164C2×#237—102no—
165C22×C4×D3—51no—
166C22×Dic6—51no—
167C2×C3×C22⋊C4—52no—
168C2×#217C2×D512yes—
169C2×Dic3⋊C4—102no—
170C2×C4×Dic3—102no—
171#877—58no—
172#877—104no—
173C3×#99—54no—
174#834C2×D514yescomplemented
175#806—58no—
176C24×C5C4×D311yescharacteristic
177C24×C5C22×D311yescharacteristic
178C23×D5—31no—
179C2×C5×D4—22no—
180C2×C5×D4—22no—
181C2×C5×D4C4×D312yes—
182C2×C5×D4C22×D312yes—
183C22×C4×C5—62no—
184C22×C4×C5C4×D311yescharacteristic
185C2×C22⋊D5—32no—
186C2×C22⋊D5—34no—
187C2×C22⋊D5—32no—
188C2×C22⋊D5—62no—
189C2×C22⋊D5—62no—
190C2×C22⋊D5—62no—
191C2×C22⋊D5—62no—
192C22×Dic5—22no—
193C22×Dic5—31no—
194C22×Dic5—31no—
195C22×Dic5—32no—
196C22×Dic5—34no—
197C22×Dic5—32no—
198C22×Dic5—32no—
199C22×Dic5—32no—
200C22×Dic5—31no—
201C22×Dic5—34no—
202C22×Dic5—62no—
203C22×Dic5—61no—
204C22×Dic5—61no—
205#711—68no—
206#711—68no—
207#711—68no—
208#711—68no—
209C2×C4×D5—34no—
210C2×C4×D5—62no—
211C2×C4×D5—61no—
212C2×C4×D5—61no—
213C2×Dic10—34no—
214C2×Dic10—62no—
215C2×Dic10—62no—
216C5×C22⋊C4—34no—
217C5×C22⋊C4—62no—
218C22⋊Dic5—22no—
219C22⋊Dic5C22×D314yes—
220#683—68no—
221C4×Dic5—68no—
222C22×#41—151no—
223C2×#117—152no—
224#410—158no—
225C2×#99—31no—
226C2×#99—51no—
227C2×#99—152no—
228C22×C3×C5—24no—
229C22×C3×C5—22no—
230C22×C3×C5—22no—
231C22×C3×C5—41no—
232C22×C3×C5—42no—
233C22×C3×C5—41no—
234C22×C3×C5—42no—
235C22×C3×C5—42no—
236C22×C3×C5—42no—
237C22×C3×C5C2×C22⋊C411yescharacteristic
238C22×C3×C5C2×C22⋊C412yes—
239C22×C3×C5C2×C22⋊C411yescharacteristic
240C22×C3×C5C23×C411yescharacteristic
241C22×C3×C5C22×D412yes—
242C2×D15—22no—
243C2×D15—42no—
244C2×D15—42no—
245C2×D15—42no—
246C3×C4×C5—22no—
247Dic15—22no—
248Dic15C2×C22⋊C414yes—
249Dic15C2×C22⋊C412yes—
250Dic15C2×C22⋊C412yes—
251C3×Dic5—44no—
252C5×Dic3—44no—
253C24×C3C4×D511yescharacteristic
254C24×C3C22×D511yescharacteristic
255C23×D3—51no—
256C2×C3×D4—22no—
257C2×C3×D4—22no—
258C2×C3×D4C4×D512yes—
259C2×C3×D4C22×D512yes—
260C22×C3×C4—102no—
261C22×C3×C4C4×D511yescharacteristic
262C2×#67—52no—
263C2×#67—54no—
264C2×#67—52no—
265C2×#67—102no—
266C2×#67—102no—
267C2×#67—102no—
268C2×#67—102no—
269C22×Dic3—22no—
270C22×Dic3—51no—
271C22×Dic3—51no—
272C22×Dic3—52no—
273C22×Dic3—54no—
274C22×Dic3—52no—
275C22×Dic3—52no—
276C22×Dic3—52no—
277C22×Dic3—51no—
278C22×Dic3—54no—
279C22×Dic3—102no—
280C22×Dic3—101no—
281C22×Dic3—101no—
282#237—108no—
283#237—108no—
284#237—108no—
285#237—108no—
286C2×C4×D3—54no—
287C2×C4×D3—102no—
288C2×C4×D3—101no—
289C2×C4×D3—101no—
290C2×Dic6—54no—
291C2×Dic6—102no—
292C2×Dic6—102no—
293C3×C22⋊C4—54no—
294C3×C22⋊C4—102no—
295#217—22no—
296#217C22×D514yes—
297Dic3⋊C4—108no—
298C4×Dic3—108no—
299C23×C5—21no—
300C23×C5—21no—
301C23×C5—42no—
302C23×C5—42no—
303C23×C5C2×C4×D311yescharacteristic
304C23×C5C2×C4×D312yes—
305C23×C5C2×C4×D311yescharacteristic
306C23×C5D3×D412yes—
307C23×C5D3×D412yes—
308C23×C5C23×D311yescharacteristic
309C22×D5—32no—
310C22×D5—61no—
311C22×D5—61no—
312C22×D5—122no—
313C5×D4—24no—
314C5×D4—24no—
315C2×C4×C5—21no—
316C2×C4×C5—21no—
317C2×C4×C5—64no—
318C2×C4×C5—124no—
319C2×C4×C5C2×C4×D312yes—
320C22⋊D5—68no—
321C22⋊D5—64no—
322C22⋊D5—64no—
323C2×Dic5—24no—
324C2×Dic5—32no—
325C2×Dic5—32no—
326C2×Dic5—32no—
327C2×Dic5—31no—
328C2×Dic5—31no—
329C2×Dic5—34no—
330C2×Dic5—34no—
331C2×Dic5—32no—
332C2×Dic5—32no—
333C2×Dic5—34no—
334C2×Dic5—34no—
335C2×Dic5—32no—
336C2×Dic5—44no—
337C2×Dic5—64no—
338C2×Dic5—64no—
339C2×Dic5—61no—
340C2×Dic5—61no—
341C4×D5—64no—
342C4×D5—64no—
343Dic10—68no—
344C2×#41—154no—
345C2×#41—154no—
346C2×#41—302no—
347C2×#41—302no—
348C2×#41—304no—
349C22×Q8—151no—
350C22×D4—151no—
351C22×D4—151no—
352C22×D4D3×D511yescharacteristic
353C23×C4—151no—
354C23×C4—151no—
355C23×C4—151no—
356#117—158no—
357#117—304no—
358C2×C4⋊C4—302no—
359C2×C22⋊C4—32no—
360C2×C22⋊C4—52no—
361C2×C42—302no—
362#99—34no—
363#99—54no—
364#99—158no—
365C2×C3×C5—22no—
366C2×C3×C5—21no—
367C2×C3×C5—21no—
368C2×C3×C5—22no—
369C2×C3×C5—42no—
370C2×C3×C5#41012yescomplemented
371C2×C3×C5C22×C22⋊C411yescharacteristic
372D15—42no—
373C23×C3—21no—
374C23×C3—21no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3C2×C4×D511yescharacteristic
378C23×C3C2×C4×D512yes—
379C23×C3C2×C4×D511yescharacteristic
380C23×C3D4×D512yes—
381C23×C3D4×D512yes—
382C23×C3C23×D511yescharacteristic
383C22×D3—52no—
384C22×D3—101no—
385C22×D3—101no—
386C22×D3—202no—
387C3×D4—24no—
388C3×D4—24no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—104no—
392C2×C3×C4—204no—
393C2×C3×C4C2×C4×D512yes—
394#67—108no—
395#67—104no—
396#67—104no—
397C2×Dic3—24no—
398C2×Dic3—44no—
399C2×Dic3—52no—
400C2×Dic3—52no—
401C2×Dic3—54no—
402C2×Dic3—54no—
403C2×Dic3—52no—
404C2×Dic3—52no—
405C2×Dic3—52no—
406C2×Dic3—51no—
407C2×Dic3—51no—
408C2×Dic3—54no—
409C2×Dic3—54no—
410C2×Dic3—52no—
411C2×Dic3—104no—
412C2×Dic3—104no—
413C2×Dic3—101no—
414C2×Dic3—101no—
415C4×D3—104no—
416C4×D3—104no—
417Dic6—108no—
418C22×C5—24no—
419C22×C5—22no—
420C22×C5—22no—
421C22×C5—41no—
422C22×C5—42no—
423C22×C5—41no—
424C22×C5—42no—
425C22×C5—42no—
426C22×C5—42no—
427C22×C5D3×C22⋊C411yescharacteristic
428C22×C5D3×C22⋊C412yes—
429C22×C5D3×C22⋊C411yescharacteristic
430C22×C5C22×C4×D311yescharacteristic
431C22×C5C2×D3×D412yes—
432C2×D5—62no—
433C2×D5—122no—
434C2×D5—122no—
435C2×D5—122no—
436C4×C5—22no—
437C4×C5—124no—
438Dic5—34no—
439Dic5—32no—
440Dic5—32no—
441Dic5—44no—
442Dic5—62no—
443C24—151no—
444C24#120011yescharacteristic
445C24C2×D3×D511yescharacteristic
446#41—308no—
447#41—308no—
448#41—308no—
449#41—308no—
450C2×Q8—154no—
451C2×Q8—302no—
452C2×Q8—302no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—154no—
456C2×D4—152no—
457C2×D4—152no—
458C2×D4—302no—
459C2×D4—302no—
460C2×D4—302no—
461C2×D4—302no—
462C2×D4#120012yes—
463C2×D4C2×D3×D512yes—
464C22×C4—62no—
465C22×C4—102no—
466C22×C4—151no—
467C22×C4—151no—
468C22×C4—152no—
469C22×C4—152no—
470C22×C4—152no—
471C22×C4—154no—
472C22×C4—152no—
473C22×C4—151no—
474C22×C4—154no—
475C22×C4—154no—
476C22×C4—302no—
477C22×C4—301no—
478C22×C4—301no—
479C22×C4—302no—
480C22×C4—301no—
481C22×C4—301no—
482C22×C4#120011yescharacteristic
483C4⋊C4—308no—
484C22⋊C4—34no—
485C22⋊C4—54no—
486C22⋊C4—62no—
487C22⋊C4—102no—
488C42—308no—
489C3×C5C2×#41011yescharacteristic, complemented, Hall
490C22×C3—24no—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—41no—
494C22×C3—42no—
495C22×C3—41no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—42no—
499C22×C3D5×C22⋊C411yescharacteristic
500C22×C3D5×C22⋊C412yes—
501C22×C3D5×C22⋊C411yescharacteristic
502C22×C3C22×C4×D511yescharacteristic
503C22×C3C2×D4×D512yes—
504C2×D3—102no—
505C2×D3—202no—
506C2×D3—202no—
507C2×D3—202no—
508C3×C4—22no—
509C3×C4—204no—
510Dic3—44no—
511Dic3—54no—
512Dic3—52no—
513Dic3—52no—
514Dic3—102no—
515C2×C5—22no—
516C2×C5—21no—
517C2×C5—21no—
518C2×C5—22no—
519C2×C5—42no—
520C2×C5#474012yescomplemented
521C2×C5C2×D3×C22⋊C411yescharacteristic
522D5—122no—
523C23—21no—
524C23—21no—
525C23—42no—
526C23—42no—
527C23—152no—
528C23—301no—
529C23—301no—
530C23—602no—
531C23C2×#120011yescharacteristic
532C23C2×#120012yes—
533C23C2×#120011yescharacteristic
534C23#679012yes—
535C23#679012yes—
536C23C22×D3×D511yescharacteristic
537Q8—308no—
538D4—24no—
539D4—24no—
540D4—308no—
541D4—304no—
542D4—304no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—64no—
546C2×C4—104no—
547C2×C4—124no—
548C2×C4—152no—
549C2×C4—152no—
550C2×C4—154no—
551C2×C4—154no—
552C2×C4—152no—
553C2×C4—152no—
554C2×C4—154no—
555C2×C4—154no—
556C2×C4—151no—
557C2×C4—151no—
558C2×C4—152no—
559C2×C4—152no—
560C2×C4—204no—
561C2×C4—304no—
562C2×C4—304no—
563C2×C4—304no—
564C2×C4—304no—
565C2×C4—301no—
566C2×C4—301no—
567C2×C4C2×#120012yes—
568C2×C3—22no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—22no—
572C2×C3—42no—
573C2×C3#6502912yescomplemented
574C2×C3C2×D5×C22⋊C411yescharacteristic
575D3—202no—
576C5C2×#474011yescharacteristic, complemented, Sylow
577C22—24no—
578C22—22no—
579C22—22no—
580C22—41no—
581C22—42no—
582C22—41no—
583C22—42no—
584C22—42no—
585C22—42no—
586C22—302no—
587C22—602no—
588C22—602no—
589C22—602no—
590C22#9156111yescharacteristic
591C22#9156112yes—
592C22#9156111yescharacteristic
593C22C22×#120011yescharacteristic
594C22C2×#679012yes—
595C4—22no—
596C4—124no—
597C4—152no—
598C4—152no—
599C4—154no—
600C4—204no—
601C4—302no—
602C3C2×#6502911yescharacteristic, complemented, Sylow
603C2—22no—
604C2—21no—
605C2—21no—
606C2—22no—
607C2—42no—
608C2—602no—
609C2#1174917412yesdirect product factor
610C2C2×#9156111yescharacteristic
subgroupG/H
centerC22#91561
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC22×C3×C5×D4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6819C2
cosocleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#410
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C2×#91532C2semidirect
3. C2×C5×#834C2semidirect
4. C2×C3×#3966C2semidirect
5. C2×#90997C2semidirect
6. #11749174C2direct (N × H)
9. C22×#1220C4semidirect
11. C23×Dic15C4semidirect
16. C2×#6819C4semidirect
18. C22×C4×D15C4semidirect
19. C22×Dic30C4semidirect
24. #91532C22semidirect
26. C5×#834C22semidirect
27. C3×#3966C22semidirect
28. #90997C22semidirect
33. C2×#3966D3semidirect
49. C2×#1220C2×C4semidirect
58. C22×Dic15C2×C4semidirect
70. C2×C4×D15C2×C4semidirect
73. C2×Dic30C2×C4semidirect
85. C2×#834D5semidirect
107. #3966C2×D3semidirect
174. #834C2×D5semidirect
370. C2×C3×C5#410semidirect
489. C3×C5C2×#410semidirect
520. C2×C5#4740semidirect
573. C2×C3#65029semidirect
576. C5C2×#4740semidirect
602. C3C2×#65029semidirect
609. C2#11749174direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68192
C2×#915322
C2×C5×#8342
C2×C3×#39662
C2×#909972
#117491742
C2×#650293
C2×#47405