Finite Group Databasebeta

← C2×#11754176 #14480155

Subgroups — C2×#11754176 #14480155

Order 1920.

2336 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
1C2×#91813C211yesmaximal, characteristic
2C22×C4×C5×Dic3C211yesmaximal, characteristic
3C2×C3×#4070C211yesmaximal, characteristic
4C2×#91575C212yesmaximal
5C2×#91529C212yesmaximal
6C2×#91469C211yesmaximal, characteristic, complemented
7C2×#91389C211yesmaximal, characteristic, complemented
8C2×#91379C212yesmaximal, complemented
9C2×#91340C211yesmaximal, characteristic, complemented
10C2×Dic3×Dic10C211yesmaximal, characteristic, complemented
11#11754176C2116yesmaximal, direct product factor
12C2×#91324C212yesmaximal, complemented
13C2×#65804—31nomaximal, Hall
14C23×C3×C4×C5C2211yescharacteristic
15C22×Dic30C2211yescharacteristic
16C23×C5×Dic3C2211yescharacteristic
17C23×C5×Dic3C2211yescharacteristic
18C22×C3×Dic10C2211yescharacteristic
19C22×#1204C2212yes—
20C2×#6719C2212yes—
21C2×C4⋊Dic15C2211yescharacteristic
22#91813C2218yes—
23C2×#6712C2212yes—
24C2×C4×C5×Dic3C2211yescharacteristic
25C2×C4×C5×Dic3C2211yescharacteristic
26C2×C4×C5×Dic3C2211yescharacteristic
27C2×C4×C5×Dic3C2218yes—
28C2×C4×C5×Dic3C2211yescharacteristic
29C2×C3×C22⋊Dic5C2212yes—
30C2×C3×C4⋊Dic5C2211yescharacteristic
31C3×#4070C2218yes—
32C2×C3×#683C2212yes—
33#91575C22116yes—
34C2×Dic3⋊Dic5C2212yes—
35C2×Dic3⋊Dic5C2212yes—
36C2×Dic3⋊Dic5C2212yes—
37C2×#6669C2212yes—
38C2×#6668C2212yes—
39#91529C22116yes—
40C2×Dic3×Dic5C2212yes—
41C2×Dic3×Dic5C2212yes—
42#91469C2218yescomplemented
43#91389C2218yescomplemented
44#91379C22116yescomplemented
45#91340C2218yescomplemented
46Dic3×Dic10C2218yescomplemented
47#91324C22116yescomplemented
48C2×#5622—51nomaximal, Hall
49C22×C42×C5—31no—
50C2×#4072—32no—
51C2×#4070—31no—
52C2×#4070—32no—
53C2×#4070D311yescharacteristic
54#65804—316no—
55C2×#4016—32no—
56C2×#4015—31no—
57C2×#4015—31no—
58C2×C4×Dic10—31no—
59C2×C4×Dic10—32no—
60C2×C4×Dic10—31no—
61C24×C3×C5C2311yescharacteristic
62C22×C3×C4×C5—24no—
63C22×C3×C4×C5C2311yescharacteristic
64C22×C3×C4×C5C2314yes—
65C22×C3×C4×C5C2311yescharacteristic
66C22×Dic15C2312yes—
67C22×Dic15C2312yes—
68C2×Dic30—24no—
69C2×Dic30C2314yes—
70C22×C5×Dic3—24no—
71C22×C5×Dic3Q818yescomplemented
72C22×C5×Dic3C2311yescharacteristic
73C22×C5×Dic3C2314yes—
74C22×C5×Dic3C2311yescharacteristic
75C22×C5×Dic3C2311yescharacteristic
76C22×C5×Dic3C2314yes—
77C22×C5×Dic3C2311yescharacteristic
78C22×C3×Dic5C2312yes—
79C22×C3×Dic5C2312yes—
80C2×C3×Dic10—24no—
81C2×C3×Dic10C2314yes—
82C2×#1204—28no—
83C2×#1204C2318yes—
84#6719C2318yes—
85C4⋊Dic15C2314yes—
86#6712C2318yes—
87C4×C5×Dic3C2314yes—
88C4×C5×Dic3C2314yes—
89C4×C5×Dic3C2314yes—
90C4×C5×Dic3C2314yes—
91C3×C22⋊Dic5C2318yes—
92C3×C4⋊Dic5C2314yes—
93C3×#683C2318yes—
94Dic3⋊Dic5C2318yes—
95Dic3⋊Dic5C2318yes—
96Dic3⋊Dic5C2318yes—
97#6669C2318yes—
98#6668C2318yes—
99Dic3×Dic5C2318yes—
100Dic3×Dic5C2318yes—
101C2×C3×C22⋊Q8—51no—
102C2×Q8×Dic3—51no—
103C2×#944—51no—
104C2×#924—51no—
105C22×C4×Dic3D511yescharacteristic
106#5622—516no—
107C2×#889—52no—
108C2×#888—51no—
109C2×#887—52no—
110C2×#887—51no—
111C2×#878—52no—
112C2×#877—52no—
113C23×C4×C5—31no—
114C23×C4×C5—31no—
115C23×C4×C5C2×D311yescharacteristic
116C22×Dic10—31no—
117C22×Dic10—32no—
118C22×Dic10C2×D311yescharacteristic
119C2×C42×C5—31no—
120C2×C42×C5—31no—
121C2×C42×C5—31no—
122C2×C42×C5—31no—
123C2×C42×C5—38no—
124C2×C22⋊Dic5—32no—
125C2×C22⋊Dic5C2×D312yes—
126#4072—316no—
127C2×C4⋊Dic5—31no—
128C2×C4⋊Dic5—32no—
129C2×C4⋊Dic5—32no—
130C2×C4⋊Dic5—32no—
131C2×C4⋊Dic5C2×D311yescharacteristic
132#4070—38no—
133#4070—316no—
134#4070C2×D318yes—
135C2×#683—32no—
136C2×#683—32no—
137C2×#683—32no—
138C2×#683C2×D312yes—
139C2×C4×Dic5—32no—
140C2×C4×Dic5—32no—
141#4016—316no—
142#4015—38no—
143#4015—38no—
144C4×Dic10—38no—
145C4×Dic10—38no—
146C4×Dic10—316no—
147C2×#533—151noSylow
148C23×C3×C5—22no—
149C23×C3×C5—22no—
150C23×C3×C5C2×Q814yes—
151C23×C3×C5C2412yes—
152C23×C3×C5C2411yescharacteristic
153C2×C3×C4×C5—22no—
154C2×C3×C4×C5—28no—
155C2×C3×C4×C5#4114yes—
156C2×C3×C4×C5C2412yes—
157C2×C3×C4×C5C2412yes—
158C2×Dic15—24no—
159C2×Dic15—24no—
160C2×Dic15C2414yes—
161C2×Dic15C2414yes—
162Dic30—28no—
163C2×C5×Dic3—22no—
164C2×C5×Dic3—28no—
165C2×C5×Dic3C2×Q814yes—
166C2×C5×Dic3C2×Q814yes—
167C2×C5×Dic3C2×Q8116yescomplemented
168C2×C5×Dic3#4114yes—
169C2×C5×Dic3C2412yes—
170C2×C5×Dic3C2412yes—
171C2×C5×Dic3C2412yes—
172C2×C5×Dic3C2412yes—
173C2×C3×Dic5—24no—
174C2×C3×Dic5—24no—
175C2×C3×Dic5C2414yes—
176C2×C3×Dic5C2414yes—
177C3×Dic10—28no—
178#1204—216no—
179C22×C3×Q8—51no—
180C23×C3×C4C2×D511yescharacteristic
181C23×Dic3C2×D511yescharacteristic
182C23×Dic3C2×D511yescharacteristic
183C22×Dic6—51no—
184C22×Dic6—52no—
185C3×C22⋊Q8—58no—
186C2×C3×C4⋊C4—51no—
187C2×C3×C4⋊C4—52no—
188C2×C3×C22⋊C4—52no—
189C2×#217—52no—
190Q8×Dic3—58no—
191#944—58no—
192C2×C4⋊Dic3—51no—
193C2×C4⋊Dic3—52no—
194#924—58no—
195C2×Dic3⋊C4—52no—
196C2×Dic3⋊C4—52no—
197C2×Dic3⋊C4—52no—
198C2×Dic3⋊C4—52no—
199C2×Dic3⋊C4—52no—
200C2×C4×Dic3—52no—
201C2×C4×Dic3—52no—
202C2×C4×Dic3C2×D511yescharacteristic
203C2×C4×Dic3C2×D511yescharacteristic
204C2×C4×Dic3C2×D511yescharacteristic
205C2×C4×Dic3C2×D511yescharacteristic
206C2×C4×Dic3C2×D518yes—
207#889—516no—
208#888—58no—
209#887—516no—
210#887—58no—
211#878—516no—
212#877—516no—
213C24×C5C22×D311yescharacteristic
214C22×C4×C5—24no—
215C22×C4×C5—38no—
216C22×C4×C5—31no—
217C22×C4×C5—31no—
218C22×C4×C5—31no—
219C22×C4×C5—34no—
220C22×C4×C5—31no—
221C22×C4×C5—34no—
222C22×C4×C5—64no—
223C22×C4×C5C22×D311yescharacteristic
224C22×C4×C5C22×D314yes—
225C22×C4×C5C22×D311yescharacteristic
226C22×Dic5—32no—
227C22×Dic5—32no—
228C22×Dic5C22×D312yes—
229C22×Dic5C22×D312yes—
230C2×Dic10—24no—
231C2×Dic10—34no—
232C2×Dic10—38no—
233C2×Dic10—68no—
234C2×Dic10—64no—
235C2×Dic10C22×D314yes—
236C42×C5—34no—
237C42×C5—34no—
238C42×C5—34no—
239C42×C5—34no—
240C22⋊Dic5—38no—
241C22⋊Dic5C22×D318yes—
242C4⋊Dic5—34no—
243C4⋊Dic5—38no—
244C4⋊Dic5—38no—
245C4⋊Dic5—38no—
246C4⋊Dic5C22×D314yes—
247#683—38no—
248#683—38no—
249#683—38no—
250#683C22×D318yes—
251C4×Dic5—38no—
252C4×Dic5—38no—
253#533—1516no—
254C2×C4⋊Q8—151no—
255C2×C4⋊Q8—151no—
256C2×#125—152no—
257C2×C22⋊Q8—51no—
258C2×C22⋊Q8—152no—
259C2×C22⋊Q8—151no—
260C2×C4×Q8—152no—
261C2×C4×Q8—151no—
262C2×C4×Q8—151no—
263C2×#117—152no—
264C22×C42—31no—
265C22×C3×C5—28no—
266C22×C3×C5—22no—
267C22×C3×C5—22no—
268C22×C3×C5C22×Q814yes—
269C22×C3×C5C22×Q812yes—
270C22×C3×C5C2×#4112yes—
271C22×C3×C5C2×#4112yes—
272C22×C3×C5C2511yescharacteristic
273C3×C4×C5—22no—
274C3×C4×C5C2×#4114yes—
275Dic15—24no—
276Dic15—24no—
277C3×Dic5—24no—
278C3×Dic5—24no—
279C5×Dic3—22no—
280C5×Dic3C22×Q814yes—
281C5×Dic3C22×Q814yes—
282C5×Dic3C2×#4114yes—
283C24×C3C22×D511yescharacteristic
284C2×C3×Q8—54no—
285C2×C3×Q8—104no—
286C22×C3×C4—24no—
287C22×C3×C4—52no—
288C22×C3×C4—52no—
289C22×C3×C4C22×D511yescharacteristic
290C22×C3×C4C22×D514yes—
291C22×C3×C4C22×D511yescharacteristic
292C22×Dic3—24no—
293C22×Dic3—52no—
294C22×Dic3—52no—
295C22×Dic3Dic1018yescomplemented
296C22×Dic3C22×D514yes—
297C22×Dic3C22×D511yescharacteristic
298C22×Dic3C22×D511yescharacteristic
299C22×Dic3C22×D511yescharacteristic
300C22×Dic3C22×D514yes—
301C22×Dic3C22×D511yescharacteristic
302C2×Dic6—54no—
303C2×Dic6—58no—
304C2×Dic6—104no—
305C2×Dic6—108no—
306C3×C4⋊C4—58no—
307C3×C4⋊C4—54no—
308C3×C22⋊C4—58no—
309#217—58no—
310C4⋊Dic3—54no—
311C4⋊Dic3—58no—
312Dic3⋊C4—58no—
313Dic3⋊C4—58no—
314Dic3⋊C4—58no—
315Dic3⋊C4—58no—
316Dic3⋊C4—58no—
317C4×Dic3—58no—
318C4×Dic3—58no—
319C4×Dic3C22×D514yes—
320C4×Dic3C22×D514yes—
321C4×Dic3C22×D514yes—
322C4×Dic3C22×D514yes—
323C23×C5—22no—
324C23×C5—22no—
325C23×C5D3×Q814yes—
326C23×C5C23×D312yes—
327C23×C5C23×D311yescharacteristic
328C2×C4×C5—22no—
329C2×C4×C5—28no—
330C2×C4×C5—34no—
331C2×C4×C5—34no—
332C2×C4×C5—316no—
333C2×C4×C5—34no—
334C2×C4×C5—32no—
335C2×C4×C5—32no—
336C2×C4×C5—32no—
337C2×C4×C5—32no—
338C2×C4×C5—68no—
339C2×C4×C5—62no—
340C2×C4×C5#23714yes—
341C2×C4×C5C23×D312yes—
342C2×C4×C5C23×D312yes—
343C2×Dic5—24no—
344C2×Dic5—24no—
345C2×Dic5—34no—
346C2×Dic5—34no—
347C2×Dic5—64no—
348C2×Dic5—64no—
349C2×Dic5C23×D314yes—
350C2×Dic5C23×D314yes—
351Dic10—28no—
352Dic10—616no—
353Dic10—68no—
354C22×Q8—51no—
355C22×Q8—152no—
356C22×Q8—151no—
357C23×C4—31no—
358C23×C4—31no—
359C23×C4D3×D511yescharacteristic
360C4⋊Q8—158no—
361C4⋊Q8—158no—
362#125—1516no—
363C22⋊Q8—58no—
364C22⋊Q8—1516no—
365C22⋊Q8—158no—
366C4×Q8—1516no—
367C4×Q8—158no—
368C4×Q8—158no—
369#117—1516no—
370C2×C4⋊C4—52no—
371C2×C4⋊C4—51no—
372C2×C4⋊C4—152no—
373C2×C4⋊C4—152no—
374C2×C4⋊C4—152no—
375C2×C4⋊C4—152no—
376C2×C4⋊C4—152no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—151no—
379C2×C22⋊C4—52no—
380C2×C22⋊C4—152no—
381C2×C42—31no—
382C2×C42—31no—
383C2×C42—31no—
384C2×C42—31no—
385C2×C42—38no—
386C2×C42—152no—
387C2×C42—152no—
388C2×C3×C5—24no—
389C2×C3×C5#53314yescomplemented
390C2×C3×C5C23×Q811yescharacteristic
391C2×C3×C5C22×#4111yescharacteristic
392C2×C3×C5C22×#4111yescharacteristic
393C23×C3—22no—
394C23×C3—22no—
395C23×C3C2×Dic1014yes—
396C23×C3C23×D512yes—
397C23×C3C23×D511yescharacteristic
398C3×Q8—108no—
399C2×C3×C4—22no—
400C2×C3×C4—28no—
401C2×C3×C4—54no—
402C2×C3×C4—54no—
403C2×C3×C4—104no—
404C2×C3×C4—104no—
405C2×C3×C4#70914yes—
406C2×C3×C4C23×D512yes—
407C2×C3×C4C23×D512yes—
408C2×Dic3—22no—
409C2×Dic3—28no—
410C2×Dic3—54no—
411C2×Dic3—54no—
412C2×Dic3—104no—
413C2×Dic3—104no—
414C2×Dic3C2×Dic1014yes—
415C2×Dic3C2×Dic1014yes—
416C2×Dic3C2×Dic10116yescomplemented
417C2×Dic3#70914yes—
418C2×Dic3C23×D512yes—
419C2×Dic3C23×D512yes—
420C2×Dic3C23×D512yes—
421C2×Dic3C23×D512yes—
422Dic6—108no—
423Dic6—1016no—
424C22×C5—22no—
425C22×C5—22no—
426C22×C5—28no—
427C22×C5C2×#23712yes—
428C22×C5C2×D3×Q814yes—
429C22×C5C2×D3×Q812yes—
430C22×C5D3×#4112yes—
431C22×C5C24×D311yescharacteristic
432C4×C5—22no—
433C4×C5—34no—
434C4×C5—34no—
435C4×C5—34no—
436C4×C5—62no—
437C4×C5C2×#23714yes—
438Dic5—24no—
439Dic5—24no—
440Dic5—64no—
441Dic5—64no—
442C24C2×D3×D511yescharacteristic
443C2×Q8—54no—
444C2×Q8—104no—
445C2×Q8—158no—
446C2×Q8—154no—
447C2×Q8—308no—
448C2×Q8—304no—
449C22×C4—24no—
450C22×C4—38no—
451C22×C4—34no—
452C22×C4—31no—
453C22×C4—31no—
454C22×C4—31no—
455C22×C4—34no—
456C22×C4—31no—
457C22×C4—52no—
458C22×C4—52no—
459C22×C4—64no—
460C22×C4—152no—
461C22×C4—152no—
462C22×C4C2×D3×D514yes—
463C22×C4C2×D3×D511yescharacteristic
464C22×C4C2×D3×D511yescharacteristic
465C4⋊C4—58no—
466C4⋊C4—54no—
467C4⋊C4—158no—
468C4⋊C4—158no—
469C4⋊C4—158no—
470C4⋊C4—158no—
471C4⋊C4—158no—
472C4⋊C4—158no—
473C4⋊C4—154no—
474C22⋊C4—58no—
475C22⋊C4—158no—
476C42—34no—
477C42—34no—
478C42—34no—
479C42—34no—
480C42—158no—
481C42—158no—
482C3×C5C2×#53311yescharacteristic, complemented, Hall
483C22×C3—28no—
484C22×C3—22no—
485C22×C3—22no—
486C22×C3C22×Dic1014yes—
487C22×C3C22×Dic1012yes—
488C22×C3C2×#70912yes—
489C22×C3C2×#70912yes—
490C22×C3C24×D511yescharacteristic
491C3×C4—22no—
492C3×C4—104no—
493C3×C4—104no—
494C3×C4C2×#70914yes—
495Dic3—22no—
496Dic3—104no—
497Dic3—104no—
498Dic3C22×Dic1014yes—
499Dic3C22×Dic1014yes—
500Dic3C2×#70914yes—
501C2×C5—24no—
502C2×C5#562214yescomplemented
503C2×C5C22×#23711yescharacteristic
504C2×C5C22×D3×Q811yescharacteristic
505C2×C5C2×D3×#4111yescharacteristic
506C23—22no—
507C23—22no—
508C23D3×Dic1014yes—
509C23C22×D3×D512yes—
510C23C22×D3×D511yescharacteristic
511Q8—108no—
512Q8—3016no—
513Q8—308no—
514C2×C4—22no—
515C2×C4—28no—
516C2×C4—34no—
517C2×C4—34no—
518C2×C4—316no—
519C2×C4—34no—
520C2×C4—32no—
521C2×C4—32no—
522C2×C4—32no—
523C2×C4—32no—
524C2×C4—54no—
525C2×C4—54no—
526C2×C4—68no—
527C2×C4—62no—
528C2×C4—104no—
529C2×C4—104no—
530C2×C4—154no—
531C2×C4—154no—
532C2×C4—304no—
533C2×C4—304no—
534C2×C4#677914yes—
535C2×C4C22×D3×D512yes—
536C2×C4C22×D3×D512yes—
537C2×C3—24no—
538C2×C3#6580414yescomplemented
539C2×C3C23×Dic1011yescharacteristic
540C2×C3C22×#70911yescharacteristic
541C2×C3C22×#70911yescharacteristic
542C5C2×#562211yescharacteristic, complemented, Sylow
543C22—22no—
544C22—28no—
545C22—22no—
546C22C2×D3×Dic1014yes—
547C22C2×D3×Dic1012yes—
548C22D3×#70912yes—
549C22C2×#677912yes—
550C22C23×D3×D511yescharacteristic
551C4—22no—
552C4—34no—
553C4—34no—
554C4—34no—
555C4—62no—
556C4—104no—
557C4—104no—
558C4—304no—
559C4—304no—
560C4C2×#677914yes—
561C3C2×#6580411yescharacteristic, complemented, Sylow
562C2—24no—
563C2#1175417614yesdirect product factor
564C2C22×D3×Dic1011yescharacteristic
565C2C2×D3×#70911yescharacteristic
566C2C22×#677911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#533
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
6. C2×#91469C2semidirect
7. C2×#91389C2semidirect
8. C2×#91379C2semidirect
9. C2×#91340C2semidirect
10. C2×Dic3×Dic10C2semidirect
11. #11754176C2direct (N × H)
12. C2×#91324C2semidirect
42. #91469C22semidirect
43. #91389C22semidirect
44. #91379C22semidirect
45. #91340C22semidirect
46. Dic3×Dic10C22semidirect
47. #91324C22semidirect
71. C22×C5×Dic3Q8semidirect
167. C2×C5×Dic3C2×Q8semidirect
295. C22×Dic3Dic10semidirect
389. C2×C3×C5#533semidirect
416. C2×Dic3C2×Dic10semidirect
482. C3×C5C2×#533semidirect
502. C2×C5#5622semidirect
538. C2×C3#65804semidirect
542. C5C2×#5622semidirect
561. C3C2×#65804semidirect
563. C2#11754176direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918132
C22×C4×C5×Dic32
C2×C3×#40702
C2×#915752
C2×#915292
C2×#914692
C2×#913892
C2×#913792
C2×#913402
C2×Dic3×Dic102
#117541762
C2×#913242
C2×#658043
C2×#56225