Finite Group Databasebeta

← D3×#65852 #14481222

Subgroups — D3×#65852 #14481222

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756277C211yesmaximal, characteristic, complemented
2C5×D3×#117C211yesmaximal, characteristic
3C3×#65852C211yesmaximal, characteristic, complemented
4D3×#4070C212yesmaximal
5#11754195C212yesmaximal, complemented
6#11753830C214yesmaximal, complemented
7D3×#4035C214yesmaximal, complemented
8#11753192C214yesmaximal, complemented
9D3×#4025C214yesmaximal
10D3×#4016C211yesmaximal, characteristic, complemented
11D3×#4015C211yesmaximal, characteristic, complemented
12C4×D3×Dic10C212yesmaximal, complemented
13#11752512C212yesmaximal, complemented
14#11752492C211yesmaximal, characteristic, complemented
15#11752479C211yesmaximal, characteristic, complemented
16C2×#65852—31nomaximal, Hall
17C22×C4×C5×D3C2211yescharacteristic
18C2×D3×Dic10C2212yes—
19C3×C5×#117C2211yescharacteristic
20#91813C2212yes—
21#91778C2214yescomplemented
22#91768C2214yes—
23#91759C2211yescharacteristic, complemented
24#91758C2211yescharacteristic, complemented
25C4×Dic30C2212yescomplemented
26C5×#926C2211yescharacteristic
27C5×#892C2212yes—
28C5×D3×C4⋊C4C2212yes—
29C5×D3×C22⋊C4C2212yes—
30C5×#877C2212yes—
31C5×#872C2211yescharacteristic
32C5×#872C2211yescharacteristic
33C42×C5×D3C2211yescharacteristic
34C42×C5×D3C2211yescharacteristic
35C3×#4070C2212yes—
36C3×#4035C2214yescomplemented
37C3×#4025C2214yes—
38C3×#4016C2211yescharacteristic, complemented
39C3×#4015C2211yescharacteristic, complemented
40C3×C4×Dic10C2212yescomplemented
41#91575C2214yes—
42D3×C22⋊Dic5C2214yes—
43#91531C2214yes—
44#91530C2214yes—
45#91469C2214yescomplemented
46C4×#1204C2214yescomplemented
47D3×C4⋊Dic5C2214yes—
48D3×C4⋊Dic5C2212yes—
49D3×#683C2214yes—
50D3×#683C2214yes—
51D3×#683C2214yes—
52C4×D3×Dic5C2214yes—
53#91389C2212yescomplemented
54#91382C2214yescomplemented
55#91381C2212yescomplemented
56#91379C2214yescomplemented
57#91378C2214yescomplemented
58#91372C2214yes—
59#91369C2212yes—
60#91367C2214yes—
61#91365C2212yes—
62#91352C2214yes—
63#91342C2214yes—
64#91341C2214yes—
65#91340C2212yescomplemented
66#91339C2214yescomplemented
67#91336C2214yescomplemented
68#91335C2214yescomplemented
69#91334C2214yescomplemented
70Dic3×Dic10C2212yescomplemented
71#91324C2214yescomplemented
72D3×#541—51nomaximal, Hall
73C2×C5×#117—31no—
74C2×#4070—32no—
75#65852—32no—
76#65852—34no—
77#65852—34no—
78#65852—31no—
79#65852—31no—
80#65852—32no—
81#65852—31no—
82#65852D311yescharacteristic, direct product factor
83C2×#4035—34no—
84C2×#4025—34no—
85C2×#4016—31no—
86C2×#4015—31no—
87C2×C4×Dic10—32no—
88C23×C5×D3C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C2×Dic30C2312yes—
91C22×C5×Dic3C2311yescharacteristic
92C2×C4×C5×D3—24no—
93C2×C4×C5×D3C2312yes—
94C2×C4×C5×D3C2311yescharacteristic
95C2×C4×C5×D3C2312yes—
96C2×C4×C5×D3C2311yescharacteristic
97C2×C4×C5×D3C2311yescharacteristic
98C2×C4×C5×D3C2311yescharacteristic
99C2×C3×Dic10C2312yes—
100C2×#1204C2314yes—
101C2×D3×Dic5C2314yes—
102C2×D3×Dic5C2314yes—
103D3×Dic10—28no—
104C3×C5×C4⋊C4C2312yes—
105C3×C5×C22⋊C4C2312yes—
106C3×C42×C5C2311yescharacteristic
107C3×C42×C5C2311yescharacteristic
108#6719C2314yes—
109C4⋊Dic15C2314yes—
110C4⋊Dic15C2312yes—
111#6712C2314yes—
112#6712C2314yes—
113#6712C2314yes—
114C4×Dic15C2314yes—
115C5×#217C2312yes—
116C5×(C2×D3)⋊C4C2312yes—
117C5×(C2×D3)⋊C4C2312yes—
118C5×C4⋊Dic3C2312yes—
119C5×Dic3⋊C4C2312yes—
120C5×Dic3⋊C4C2312yes—
121C4×C5×Dic3C2311yescharacteristic
122C4×C5×Dic3C2311yescharacteristic
123C4×C5×Dic3C2312yes—
124C4×C5×Dic3C2312yes—
125C3×C22⋊Dic5C2314yes—
126C3×C4⋊Dic5C2314yes—
127C3×C4⋊Dic5C2312yes—
128C3×#683C2314yes—
129C3×#683C2314yes—
130C3×#683C2314yes—
131C3×C4×Dic5C2314yes—
132Dic3⋊Dic5C2314yes—
133Dic3⋊Dic5C2314yes—
134Dic3⋊Dic5C2314yes—
135#6669C2314yes—
136#6669C2314yes—
137#6669C2314yes—
138#6668C2314yes—
139#6668C2314yes—
140#6668C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143Dic3×Dic5C2314yes—
144Dic3×Dic5C2314yes—
145C3×#541—51no—
146#5731—51no—
147D3×C4⋊Q8—51no—
148D3×#126—54no—
149#5701—54no—
150#5698—51no—
151#5696—54no—
152D3×#125—54no—
153D3×#125—51no—
154D3×C22⋊Q8—52no—
155#5625—52no—
156#5583—52no—
157C4×D3×Q8—52no—
158D3×#117D511yescharacteristic
159#5518—51no—
160C23×C4×C5—31no—
161C22×Dic10—32no—
162C5×#117—31no—
163C5×#117—32no—
164C5×#117—32no—
165C5×#117—31no—
166C5×#117—31no—
167C5×#117C2×D311yescharacteristic
168C2×C5×C4⋊C4—32no—
169C2×C5×C22⋊C4—32no—
170C2×C42×C5—31no—
171C2×C42×C5—31no—
172C2×C22⋊Dic5—34no—
173C2×C4⋊Dic5—32no—
174C2×C4⋊Dic5—34no—
175#4070—32no—
176#4070—32no—
177#4070—34no—
178#4070—32no—
179#4070—34no—
180#4070C2×D312yes—
181C2×#683—34no—
182C2×#683—34no—
183C2×#683—34no—
184C2×C4×Dic5—34no—
185#4035—34no—
186#4035—34no—
187#4035—34no—
188#4035—34no—
189#4035—34no—
190#4035—34no—
191#4035—34no—
192#4035C2×D314yescomplemented
193#4025—34no—
194#4025—34no—
195#4025—34no—
196#4025—34no—
197#4025—34no—
198#4025—34no—
199#4025—34no—
200#4025C2×D314yes—
201#4016—31no—
202#4016—32no—
203#4016—34no—
204#4016C2×D311yescharacteristic, complemented
205#4015—32no—
206#4015—31no—
207#4015—34no—
208#4015C2×D311yescharacteristic, complemented
209C4×Dic10—32no—
210C4×Dic10—32no—
211C4×Dic10—32no—
212C4×Dic10—34no—
213C4×Dic10—34no—
214C4×Dic10C2×D312yescomplemented
215C2×#541—151noSylow
216C23×C3×C5C2411yescharacteristic
217C22×C5×D3—22no—
218C22×C5×D3—24no—
219C22×C5×D3C2411yescharacteristic
220C22×C5×D3C2411yescharacteristic
221C2×C3×C4×C5—22no—
222C2×C3×C4×C5C2412yes—
223C2×C3×C4×C5C2411yescharacteristic
224C2×C3×C4×C5C2412yes—
225C2×C3×C4×C5C2411yescharacteristic
226C2×Dic15C2414yes—
227C2×Dic15C2414yes—
228Dic30—24no—
229C2×C5×Dic3—22no—
230C2×C5×Dic3C2412yes—
231C2×C5×Dic3C2411yescharacteristic
232C2×C5×Dic3C2412yes—
233C2×C5×Dic3C2411yescharacteristic
234C4×C5×D3—22no—
235C4×C5×D3—24no—
236C4×C5×D3—24no—
237C4×C5×D3—22no—
238C4×C5×D3—22no—
239C4×C5×D3#4114yes—
240C2×C3×Dic5C2414yes—
241C2×C3×Dic5C2414yes—
242C3×Dic10—24no—
243#1204—28no—
244D3×Dic5—28no—
245D3×Dic5—28no—
246C2×D3×Q8—52no—
247C22×C4×D3C2×D511yescharacteristic
248C3×C4⋊Q8—51no—
249C3×#126—54no—
250C3×#125—54no—
251C3×#125—51no—
252C3×C22⋊Q8—52no—
253C3×C4×Q8—52no—
254C3×#117C2×D511yescharacteristic
255#946—52no—
256Q8×Dic3—52no—
257#944—52no—
258#926C2×D511yescharacteristic
259#924—52no—
260#898—54no—
261#898—54no—
262#898—54no—
263#897—52no—
264#896—54no—
265#892C2×D512yes—
266D3×C4⋊C4—54no—
267D3×C4⋊C4—54no—
268D3×C4⋊C4—54no—
269D3×C4⋊C4—54no—
270D3×C4⋊C4—52no—
271D3×C4⋊C4C2×D512yes—
272#890—54no—
273#890—54no—
274#890—52no—
275#889—54no—
276#889—54no—
277#889—54no—
278#889—54no—
279#889—54no—
280#888—54no—
281#887—54no—
282#887—52no—
283D3×C22⋊C4—54no—
284D3×C22⋊C4C2×D512yes—
285#879—54no—
286#879—54no—
287#879—54no—
288#878—54no—
289#877C2×D512yes—
290#876—54no—
291#872C2×D511yescharacteristic
292#872C2×D511yescharacteristic
293C42×D3—54no—
294C42×D3C2×D511yescharacteristic
295C42×D3C2×D511yescharacteristic
296#870—51no—
297#870—54no—
298#869—51no—
299C4×Dic6—52no—
300C4×Dic6—54no—
301C24×C5—31no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5—32no—
305C22×C4×C5—32no—
306C22×C4×C5—31no—
307C22×C4×C5—31no—
308C22×C4×C5—31no—
309C22×C4×C5—64no—
310C22×C4×C5C22×D311yescharacteristic
311C22×Dic5—34no—
312C22×Dic5—34no—
313C2×Dic10—32no—
314C2×Dic10—34no—
315C2×Dic10—68no—
316C2×Dic10C22×D312yes—
317C5×C4⋊C4—32no—
318C5×C4⋊C4—32no—
319C5×C4⋊C4—32no—
320C5×C4⋊C4C22×D312yes—
321C5×C22⋊C4—32no—
322C5×C22⋊C4—32no—
323C5×C22⋊C4—32no—
324C5×C22⋊C4C22×D312yes—
325C42×C5—32no—
326C42×C5—31no—
327C42×C5—32no—
328C42×C5—31no—
329C42×C5C22×D311yescharacteristic
330C42×C5C22×D311yescharacteristic
331C22⋊Dic5—34no—
332C22⋊Dic5—34no—
333C22⋊Dic5—34no—
334C22⋊Dic5C22×D314yes—
335C4⋊Dic5—32no—
336C4⋊Dic5—34no—
337C4⋊Dic5—34no—
338C4⋊Dic5—34no—
339C4⋊Dic5—34no—
340C4⋊Dic5C22×D312yes—
341C4⋊Dic5C22×D314yes—
342#683—34no—
343#683—34no—
344#683—34no—
345#683—34no—
346#683—34no—
347#683—34no—
348#683—34no—
349#683—34no—
350#683—34no—
351#683C22×D314yes—
352#683C22×D314yes—
353#683C22×D314yes—
354C4×Dic5—34no—
355C4×Dic5—34no—
356C4×Dic5—34no—
357C4×Dic5C22×D314yes—
358#541—51no—
359#541—152no—
360#541—152no—
361#541—154no—
362#541—151no—
363#541—154no—
364#541—151no—
365#541—151no—
366C2×C4⋊Q8—151no—
367C2×#126—154no—
368C2×#125—151no—
369C2×#125—154no—
370C2×C22⋊Q8—152no—
371C2×C4×Q8—152no—
372C2×#117—31no—
373C22×C3×C5—21no—
374C22×C3×C5—22no—
375C22×C3×C5C2511yescharacteristic
376C2×C5×D3—21no—
377C2×C5×D3—22no—
378C2×C5×D3—44no—
379C2×C5×D3C2×#4112yes—
380C2×C5×D32−1+414yes—
381C3×C4×C5—21no—
382C3×C4×C5—22no—
383C3×C4×C5—22no—
384C3×C4×C5C2×#4112yes—
385Dic15—24no—
386Dic15—24no—
387C3×Dic5—24no—
388C3×Dic5—24no—
389C5×Dic3—21no—
390C5×Dic3—22no—
391C5×Dic3—22no—
392C5×Dic3C2×#4112yes—
393C23×D3C22×D511yescharacteristic
394C2×C3×Q8—52no—
395C22×C3×C4C22×D511yescharacteristic
396C22×Dic3C22×D511yescharacteristic
397D3×Q8—108no—
398C2×C4×D3—24no—
399C2×C4×D3—54no—
400C2×C4×D3—54no—
401C2×C4×D3C22×D512yes—
402C2×C4×D3C22×D512yes—
403C2×C4×D3C22×D511yescharacteristic
404C2×C4×D3C22×D511yescharacteristic
405C2×C4×D3C22×D511yescharacteristic
406C2×C4×D3C22×D511yescharacteristic
407C2×Dic6—52no—
408C2×Dic6—54no—
409C3×C4⋊C4—54no—
410C3×C4⋊C4—54no—
411C3×C4⋊C4—54no—
412C3×C4⋊C4—52no—
413C3×C4⋊C4—54no—
414C3×C4⋊C4C22×D512yes—
415C3×C22⋊C4—54no—
416C3×C22⋊C4C22×D512yes—
417C3×C42—54no—
418C3×C42C22×D511yescharacteristic
419C3×C42C22×D511yescharacteristic
420#217—54no—
421#217C22×D512yes—
422(C2×D3)⋊C4—54no—
423(C2×D3)⋊C4—54no—
424(C2×D3)⋊C4C22×D512yes—
425(C2×D3)⋊C4C22×D512yes—
426C4⋊Dic3—52no—
427C4⋊Dic3—54no—
428C4⋊Dic3—54no—
429C4⋊Dic3—54no—
430C4⋊Dic3—54no—
431C4⋊Dic3C22×D512yes—
432Dic3⋊C4—54no—
433Dic3⋊C4—54no—
434Dic3⋊C4—54no—
435Dic3⋊C4—54no—
436Dic3⋊C4—54no—
437Dic3⋊C4—54no—
438Dic3⋊C4—54no—
439Dic3⋊C4—54no—
440Dic3⋊C4—54no—
441Dic3⋊C4C22×D512yes—
442Dic3⋊C4C22×D512yes—
443C4×Dic3—54no—
444C4×Dic3—54no—
445C4×Dic3—54no—
446C4×Dic3C22×D512yes—
447C4×Dic3C22×D511yescharacteristic
448C4×Dic3C22×D511yescharacteristic
449C4×Dic3C22×D512yes—
450C23×C5—31no—
451C23×C5—31no—
452C23×C5—62no—
453C23×C5—64no—
454C23×C5C23×D311yescharacteristic
455C2×C4×C5—22no—
456C2×C4×C5—31no—
457C2×C4×C5—34no—
458C2×C4×C5—32no—
459C2×C4×C5—31no—
460C2×C4×C5—32no—
461C2×C4×C5—62no—
462C2×C4×C5—64no—
463C2×C4×C5—64no—
464C2×C4×C5—62no—
465C2×C4×C5—62no—
466C2×C4×C5—62no—
467C2×C4×C5C23×D312yes—
468C2×C4×C5C23×D311yescharacteristic
469C2×C4×C5C23×D312yes—
470C2×C4×C5C23×D311yescharacteristic
471C2×Dic5—34no—
472C2×Dic5—34no—
473C2×Dic5—68no—
474C2×Dic5—68no—
475C2×Dic5C23×D314yes—
476C2×Dic5C23×D314yes—
477Dic10—24no—
478Dic10—68no—
479Dic10—64no—
480C22×Q8—152no—
481C23×C4—31no—
482C4⋊Q8—51no—
483C4⋊Q8—154no—
484C4⋊Q8—152no—
485C4⋊Q8—151no—
486#126—54no—
487#126—154no—
488#126—154no—
489#126—154no—
490#126—154no—
491#126—154no—
492#126—154no—
493#126—154no—
494#125—54no—
495#125—51no—
496#125—154no—
497#125—152no—
498#125—154no—
499#125—154no—
500#125—154no—
501#125—154no—
502#125—154no—
503#125—154no—
504#125—154no—
505#125—151no—
506C22⋊Q8—52no—
507C22⋊Q8—154no—
508C22⋊Q8—154no—
509C22⋊Q8—152no—
510C22⋊Q8—152no—
511C22⋊Q8—152no—
512C4×Q8—52no—
513C4×Q8—154no—
514C4×Q8—152no—
515C4×Q8—154no—
516C4×Q8—152no—
517C4×Q8—152no—
518#117—31no—
519#117—32no—
520#117—32no—
521#117—31no—
522#117—31no—
523#117D3×D511yescharacteristic
524C2×C4⋊C4—32no—
525C2×C4⋊C4—152no—
526C2×C4⋊C4—154no—
527C2×C4⋊C4—154no—
528C2×C4⋊C4—154no—
529C2×C4⋊C4—154no—
530C2×C22⋊C4—32no—
531C2×C22⋊C4—154no—
532C2×C42—31no—
533C2×C42—31no—
534C2×C42—154no—
535C2×C3×C5—41no—
536C2×C3×C5C22×#4111yescharacteristic
537C2×C3×C5C2×2−1+412yes—
538C5×D3—41no—
539C5×D3#54114yescomplemented
540C23×C3C23×D511yescharacteristic
541C22×D3—22no—
542C22×D3—24no—
543C22×D3C23×D511yescharacteristic
544C22×D3C23×D511yescharacteristic
545C3×Q8—104no—
546C2×C3×C4—22no—
547C2×C3×C4—54no—
548C2×C3×C4—54no—
549C2×C3×C4C23×D512yes—
550C2×C3×C4C23×D512yes—
551C2×C3×C4C23×D511yescharacteristic
552C2×C3×C4C23×D511yescharacteristic
553C2×Dic3—22no—
554C2×Dic3—54no—
555C2×Dic3—54no—
556C2×Dic3C23×D512yes—
557C2×Dic3C23×D512yes—
558C2×Dic3C23×D511yescharacteristic
559C2×Dic3C23×D511yescharacteristic
560C4×D3—22no—
561C4×D3—24no—
562C4×D3—24no—
563C4×D3—22no—
564C4×D3—22no—
565C4×D3—108no—
566C4×D3—108no—
567C4×D3#70914yes—
568Dic6—104no—
569Dic6—108no—
570C22×C5—21no—
571C22×C5—22no—
572C22×C5—32no—
573C22×C5—34no—
574C22×C5—61no—
575C22×C5—62no—
576C22×C5—124no—
577C22×C5C24×D311yescharacteristic
578C4×C5—21no—
579C4×C5—22no—
580C4×C5—22no—
581C4×C5—32no—
582C4×C5—61no—
583C4×C5—62no—
584C4×C5—62no—
585C4×C5D3×#4112yes—
586Dic5—24no—
587Dic5—24no—
588Dic5—64no—
589Dic5—64no—
590C24—31no—
591C2×Q8—52no—
592C2×Q8—154no—
593C2×Q8—152no—
594C2×Q8—308no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—32no—
598C22×C4—32no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—64no—
603C22×C4—154no—
604C22×C4—154no—
605C22×C4C2×D3×D511yescharacteristic
606C4⋊C4—32no—
607C4⋊C4—32no—
608C4⋊C4—32no—
609C4⋊C4—52no—
610C4⋊C4—54no—
611C4⋊C4—54no—
612C4⋊C4—54no—
613C4⋊C4—54no—
614C4⋊C4—154no—
615C4⋊C4—154no—
616C4⋊C4—154no—
617C4⋊C4—154no—
618C4⋊C4—154no—
619C4⋊C4—154no—
620C4⋊C4—154no—
621C4⋊C4—154no—
622C4⋊C4—154no—
623C4⋊C4—152no—
624C4⋊C4—154no—
625C4⋊C4—154no—
626C4⋊C4—154no—
627C4⋊C4—154no—
628C4⋊C4C2×D3×D512yes—
629C22⋊C4—32no—
630C22⋊C4—32no—
631C22⋊C4—32no—
632C22⋊C4—54no—
633C22⋊C4—154no—
634C22⋊C4—154no—
635C22⋊C4—154no—
636C22⋊C4C2×D3×D512yes—
637C42—32no—
638C42—31no—
639C42—32no—
640C42—31no—
641C42—54no—
642C42—154no—
643C42—154no—
644C42—154no—
645C42C2×D3×D511yescharacteristic
646C42C2×D3×D511yescharacteristic
647C3×C5C2×#54111yescharacteristic, complemented, Hall
648C22×C3—21no—
649C22×C3—22no—
650C22×C3C24×D511yescharacteristic
651C2×D3—21no—
652C2×D3—22no—
653C2×D3—44no—
654C2×D3C2×#70912yes—
655C2×D3#415014yes—
656C3×C4—21no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—104no—
660C3×C4—104no—
661C3×C4C2×#70912yes—
662Dic3—21no—
663Dic3—22no—
664Dic3—22no—
665Dic3—104no—
666Dic3—104no—
667Dic3C2×#70912yes—
668C2×C5—34no—
669C2×C5—41no—
670C2×C5—121no—
671C2×C5C2×D3×#4111yescharacteristic
672C2×C5D3×2−1+412yes—
673C23—31no—
674C23—31no—
675C23—62no—
676C23—64no—
677C23C22×D3×D511yescharacteristic
678Q8—104no—
679Q8—308no—
680Q8—304no—
681C2×C4—22no—
682C2×C4—31no—
683C2×C4—34no—
684C2×C4—32no—
685C2×C4—32no—
686C2×C4—31no—
687C2×C4—54no—
688C2×C4—54no—
689C2×C4—62no—
690C2×C4—62no—
691C2×C4—64no—
692C2×C4—64no—
693C2×C4—62no—
694C2×C4—62no—
695C2×C4—154no—
696C2×C4—154no—
697C2×C4—308no—
698C2×C4—308no—
699C2×C4C22×D3×D512yes—
700C2×C4C22×D3×D512yes—
701C2×C4C22×D3×D511yescharacteristic
702C2×C4C22×D3×D511yescharacteristic
703C2×C3—41no—
704C2×C3C22×#70911yescharacteristic
705C2×C3C2×#415012yes—
706D3—41no—
707D3#6585214yesdirect product factor
708C5D3×#54111yescharacteristic, complemented, Sylow
709C22—22no—
710C22—21no—
711C22—34no—
712C22—32no—
713C22—62no—
714C22—61no—
715C22—124no—
716C22C23×D3×D511yescharacteristic
717C4—22no—
718C4—22no—
719C4—21no—
720C4—32no—
721C4—62no—
722C4—62no—
723C4—61no—
724C4—104no—
725C4—104no—
726C4—304no—
727C4—304no—
728C4D3×#70912yes—
729C3C2×#6585211yescharacteristic, complemented, Sylow
730C2—34no—
731C2—41no—
732C2—121no—
733C2C2×D3×#70911yescharacteristic
734C2D3×#415012yes—
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C5×#117C22
prime radicalC23×C5×D3C23
hypercenter#117D3×D5
hypocenterC3×C5C2×#541
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #11756277C2semidirect
3. C3×#65852C2semidirect
5. #11754195C2semidirect
6. #11753830C2semidirect
7. D3×#4035C2semidirect
8. #11753192C2semidirect
10. D3×#4016C2semidirect
11. D3×#4015C2semidirect
12. C4×D3×Dic10C2semidirect
13. #11752512C2semidirect
14. #11752492C2semidirect
15. #11752479C2semidirect
21. #91778C22semidirect
23. #91759C22semidirect
24. #91758C22semidirect
25. C4×Dic30C22semidirect
36. C3×#4035C22semidirect
38. C3×#4016C22semidirect
39. C3×#4015C22semidirect
40. C3×C4×Dic10C22semidirect
45. #91469C22semidirect
46. C4×#1204C22semidirect
53. #91389C22semidirect
54. #91382C22semidirect
55. #91381C22semidirect
56. #91379C22semidirect
57. #91378C22semidirect
65. #91340C22semidirect
66. #91339C22semidirect
67. #91336C22semidirect
68. #91335C22semidirect
69. #91334C22semidirect
70. Dic3×Dic10C22semidirect
71. #91324C22semidirect
82. #65852D3direct (N × H)
192. #4035C2×D3semidirect
204. #4016C2×D3semidirect
208. #4015C2×D3semidirect
214. C4×Dic10C2×D3semidirect
539. C5×D3#541semidirect
647. C3×C5C2×#541semidirect
707. D3#65852direct (N × H)
708. C5D3×#541semidirect
729. C3C2×#65852semidirect

Maximal subgroups

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

subgroupindex
#117562772
C5×D3×#1172
C3×#658522
D3×#40702
#117541952
#117538302
D3×#40352
#117531922
D3×#40252
D3×#40162
D3×#40152
C4×D3×Dic102
#117525122
#117524922
#117524792
C2×#658523
D3×#5415