Finite Group Databasebeta

← #14484649

Subgroups — #14484649

Order 1920.

2136 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×Q8×D15C211yesmaximal, characteristic, complemented
2C5×#5579C211yesmaximal, characteristic, complemented
3C3×#65901C211yesmaximal, characteristic, complemented
4#11755181C212yesmaximal, complemented
5#11755169C212yesmaximal, complemented
6#11753715C212yesmaximal, complemented
7#11753473C214yesmaximal, complemented
8#11753460C214yesmaximal, complemented
9D3×#4033C212yesmaximal, complemented
10#11752627C212yesmaximal, complemented
11#11752558C211yesmaximal, characteristic, complemented
12C4×#6768C211yesmaximal, characteristic
13C4×#6768C212yesmaximal
14#11752484C211yesmaximal, characteristic, complemented
15#11752473C211yesmaximal, characteristic, complemented
16#11752471C212yesmaximal, complemented
17#11752469C212yesmaximal, complemented
18#10618824—31nomaximal, Hall
19C2×Q8×D15C2211yescharacteristic
20C2×#6768C2211yescharacteristic
21C2×D3×Dic10C2212yes—
22C3×C4×C5×Q8C2211yescharacteristic
23Q8×Dic15C2211yescharacteristic
24C4⋊C4×D15C2212yes—
25C4⋊C4×D15C2211yescharacteristic
26#91776C2211yescharacteristic
27#91776C2212yes—
28C42×D15C2212yes—
29C42×D15C2211yescharacteristic
30C4×Dic30C2212yes—
31C4×Dic30C2211yescharacteristic
32C5×#946C2212yes—
33C5×#896C2214yes—
34C5×D3×C4⋊C4C2212yes—
35C4×C5×D12C2211yescharacteristic
36C4×C5×D12C2212yes—
37C5×#870C2212yes—
38C5×#869C2211yescharacteristic
39C3×#4090C2212yes—
40C3×#4035C2214yes—
41C3×#4033C2212yes—
42C3×#4016C2212yes—
43C3×#4015C2211yescharacteristic
44C3×C4×Dic10C2212yes—
45C3×C4×Dic10C2211yescharacteristic
46#91470C2212yes—
47#91470C2212yes—
48#91468C2212yes—
49C4×#1203C2214yes—
50C4×#1203C2212yes—
51#91436C2214yes—
52#91435C2212yes—
53#91435C2211yescharacteristic
54#91432C2214yes—
55#91417C2214yes—
56#91406C2212yes—
57#91406C2214yes—
58#91400C2214yes—
59#91400C2212yes—
60D3×#683C2214yes—
61C4×D3×Dic5C2212yes—
62C4×D3×Dic5C2214yes—
63#91390C2212yes—
64#91384C2212yes—
65#91383C2212yes—
66#91378C2214yes—
67#91377C2214yes—
68#91377C2214yes—
69#91369C2212yes—
70#91352C2214yes—
71#91347C2211yescharacteristic
72#91347C2212yes—
73#91344C2212yes—
74#91334C2214yes—
75#91333C2212yes—
76#91331C2211yescharacteristic
77#91331C2212yes—
78#91331C2212yes—
79#91329C2214yes—
80#91328C2214yes—
81#91325C2214yes—
82#91325C2214yes—
83#91323C2214yes—
84#87015—51nomaximal, Hall
85C5×#554—31no—
86#66062—31no—
87#66056—31no—
88#66022—32no—
89#66019—32no—
90#65970—34no—
91#65966—32no—
92#65956—32no—
93#65956—34no—
94C4×Q8×D5—31no—
95#65901D311yescharacteristic, complemented
96#65873—32no—
97D4×Dic10—31no—
98C4×#711—31no—
99C4×#711—32no—
100#65845—32no—
101C2×#4033—32no—
102C2×C3×C5×Q8C2311yescharacteristic
103Q8×D15—24no—
104C2×C4×D15C2312yes—
105C2×C4×D15C2311yescharacteristic
106C2×C4×D15C2311yescharacteristic
107C2×C4×D15C2312yes—
108C2×C4×D15C2311yescharacteristic
109C2×Dic30C2312yes—
110C2×Dic30C2311yescharacteristic
111C2×C5×D12C2311yescharacteristic
112C2×C4×C5×D3C2312yes—
113C2×C4×C5×D3C2314yes—
114C2×C5×Dic6C2312yes—
115C2×C3×Dic10C2312yes—
116C2×C3×Dic10C2311yescharacteristic
117C2×#1204C2314yes—
118C2×#1204C2314yes—
119C2×#1203C2312yes—
120C2×D3×Dic5C2314yes—
121C2×D3×Dic5C2312yes—
122C2×D3×Dic5C2312yes—
123#6768Q818yescomplemented
124D3×Dic10—28no—
125C3×C5×C4⋊C4C2311yescharacteristic
126C3×C5×C4⋊C4C2312yes—
127C3×C42×C5C2311yescharacteristic
128C3×C42×C5C2312yes—
129C4⋊Dic15C2312yes—
130C4⋊Dic15C2311yescharacteristic
131#6712C2312yes—
132#6712C2312yes—
133#6712C2312yes—
134C4×Dic15C2312yes—
135C4×Dic15C2311yescharacteristic
136C4×Dic15C2311yescharacteristic
137C4×Dic15C2312yes—
138C4×Dic15C2312yes—
139C4×Dic15C2311yescharacteristic
140C5×(C2×D3)⋊C4C2314yes—
141C5×(C2×D3)⋊C4C2312yes—
142C5×C4⋊Dic3C2312yes—
143C5×C4⋊Dic3C2312yes—
144C5×C4⋊Dic3C2311yescharacteristic
145C5×Dic3⋊C4C2314yes—
146C5×Dic3⋊C4C2314yes—
147C3×C4⋊Dic5C2311yescharacteristic
148C3×C4⋊Dic5C2312yes—
149C3×C4⋊Dic5C2312yes—
150C3×#683C2314yes—
151C3×#683C2314yes—
152C3×#683C2312yes—
153C3×#683C2314yes—
154C3×C4×Dic5C2312yes—
155C3×C4×Dic5C2314yes—
156Dic3⋊Dic5C2314yes—
157#6669C2314yes—
158#6669C2314yes—
159#6668C2314yes—
160#6668C2314yes—
161#6668C2312yes—
162#6667C2312yes—
163#6667C2314yes—
164(C2×D3)⋊Dic5C2314yes—
165(C2×D3)⋊Dic5C2312yes—
166Dic3×Dic5C2312yes—
167Dic3×Dic5C2314yes—
168Dic3×Dic5C2312yes—
169Dic3×Dic5C2314yes—
170C3×#557—51no—
171#5728—52no—
172#5728—51no—
173#5727—52no—
174#5727—51no—
175#5690—54no—
176#5690—52no—
177#5688—54no—
178#5688—52no—
179#5579—52no—
180#5579D511yescharacteristic, complemented
181C4×#239—52no—
182C4×#239—51no—
183C4×D3×Q8—51no—
184C4×D3×Q8—52no—
185#5569—52no—
186Q8×Dic6—51no—
187C2×Q8×D5—31no—
188C2×#711—31no—
189C22×Dic10—32no—
190C5×C4⋊Q8—31no—
191C5×#125—32no—
192C5×C22⋊Q8—32no—
193C5×C22⋊Q8—34no—
194C4×C5×Q8C2×D311yescharacteristic
195C4×C5×D4—31no—
196C4×C5×D4—32no—
197C2×C5×C4⋊C4—32no—
198#4092—32no—
199Q8×Dic5—31no—
200Q8×Dic5—32no—
201#4090—34no—
202#4090C2×D312yes—
203D4×Dic5—32no—
204D4×Dic5—31no—
205C4×C22⋊D5—32no—
206C4×C22⋊D5—34no—
207#4070—32no—
208#4070—34no—
209C2×#683—34no—
210C2×C4×Dic5—34no—
211C2×C4×Dic5—32no—
212#4043—32no—
213#4042—34no—
214#4042—34no—
215#4038—32no—
216#4038—31no—
217D5×C4⋊C4—31no—
218D5×C4⋊C4—32no—
219#4036—32no—
220#4035—34no—
221#4035—34no—
222#4035C2×D314yes—
223#4034—32no—
224#4034—32no—
225#4034—34no—
226#4034—32no—
227#4033—32no—
228#4033—32no—
229#4033—31no—
230#4033—31no—
231#4033—32no—
232#4033—34no—
233#4033—34no—
234#4033—32no—
235#4033—34no—
236#4033C2×D312yes—
237#4027—34no—
238#4027—32no—
239#4024—34no—
240#4024—34no—
241#4024—34no—
242#4023—34no—
243#4023—32no—
244C42×D5—31no—
245C42×D5—32no—
246#4016C2×D312yes—
247#4015C2×D311yescharacteristic
248C4×Dic10—31no—
249C4×Dic10—32no—
250C4×Dic10C2×D311yescharacteristic
251C4×Dic10C2×D312yes—
252Q8×#41—151noSylow
253C22×D15C2411yescharacteristic
254C22×C5×D3C2412yes—
255C3×C5×Q8—22no—
256C2×C3×C4×C5C2412yes—
257C2×C3×C4×C5C2412yes—
258C2×C3×C4×C5C2411yescharacteristic
259C2×C3×C4×C5C2411yescharacteristic
260C2×C3×C4×C5C2411yescharacteristic
261C2×Dic15C2411yescharacteristic
262C2×Dic15C2412yes—
263C2×Dic15C2411yescharacteristic
264C2×Dic15C2411yescharacteristic
265C2×Dic15C2412yes—
266C4×D15—22no—
267C4×D15—24no—
268C4×D15—41no—
269C4×D15—42no—
270C4×D15C2×Q814yescomplemented
271Dic30—24no—
272Dic30#4114yescomplemented
273C2×C5×Dic3C2414yes—
274C2×C5×Dic3C2412yes—
275C5×D12C2×Q814yescomplemented
276C4×C5×D3—24no—
277C4×C5×D3—44no—
278C5×Dic6—42no—
279C2×C3×Dic5C2414yes—
280C2×C3×Dic5C2412yes—
281C2×C3×Dic5C2412yes—
282C3×Dic10—24no—
283C3×Dic10C2×Q814yescomplemented
284#1204—28no—
285#1204—44no—
286#1203C2×Q818yescomplemented
287D3×Dic5—28no—
288D3×Dic5—42no—
289D3×Dic5C2×Q818yescomplemented
290C2×#239—51no—
291C2×D3×Q8—51no—
292C2×D3×Q8—52no—
293C3×C4⋊Q8—52no—
294C3×C4⋊Q8—51no—
295C3×#125—54no—
296C3×#125—52no—
297C3×C4×Q8—52no—
298C3×C4×Q8—51no—
299C3×C4×Q8—52no—
300C3×C4×Q8C2×D511yescharacteristic
301#946—52no—
302#946—52no—
303#946C2×D512yes—
304Q8×Dic3—51no—
305Q8×Dic3—52no—
306Q8×Dic3—52no—
307Q8×Dic3—51no—
308#897—52no—
309#897—54no—
310#896—54no—
311#896—54no—
312#896—54no—
313#896—54no—
314#896—54no—
315#896C2×D514yes—
316#893—51no—
317#893—52no—
318#893—52no—
319#893—54no—
320#892—52no—
321#892—54no—
322#892—51no—
323#892—52no—
324D3×C4⋊C4—54no—
325D3×C4⋊C4—52no—
326D3×C4⋊C4—51no—
327D3×C4⋊C4C2×D512yes—
328#890—52no—
329#890—54no—
330#888—54no—
331#888—52no—
332#888—52no—
333#888—54no—
334#887—52no—
335#887—52no—
336#887—51no—
337#887—54no—
338#887—54no—
339C4×D12—54no—
340C4×D12—52no—
341C4×D12C2×D512yes—
342C4×D12C2×D511yescharacteristic
343C42×D3—54no—
344C42×D3—52no—
345C42×D3—52no—
346C42×D3—51no—
347#870—54no—
348#870C2×D512yes—
349#869—52no—
350#869C2×D511yescharacteristic
351C4×Dic6—52no—
352C4×Dic6—51no—
353C4×Dic6—52no—
354C4×Dic6—54no—
355C2×C5×Q8—32no—
356C2×C5×Q8C22×D311yescharacteristic
357C2×C5×D4—31no—
358C22×C4×C5—32no—
359C22×C4×C5—34no—
360C2×C22⋊D5—32no—
361C22×Dic5—32no—
362C22×Dic5—34no—
363C22×Dic5—32no—
364Q8×D5—64no—
365#711—38no—
366C2×C4×D5—31no—
367C2×C4×D5—32no—
368C2×C4×D5—31no—
369C2×C4×D5—31no—
370C2×C4×D5—32no—
371C2×Dic10—31no—
372C2×Dic10—32no—
373C2×Dic10—34no—
374C2×Dic10—34no—
375C2×Dic10—68no—
376C2×Dic10C22×D312yes—
377C2×Dic10C22×D311yescharacteristic
378C5×C4⋊C4—34no—
379C5×C4⋊C4—32no—
380C5×C4⋊C4—31no—
381C5×C4⋊C4—32no—
382C5×C4⋊C4—34no—
383C5×C4⋊C4C22×D311yescharacteristic
384C5×C4⋊C4C22×D312yes—
385C5×C22⋊C4—34no—
386C5×C22⋊C4—32no—
387C42×C5C22×D312yes—
388C42×C5C22×D311yescharacteristic
389C22⋊Dic5—34no—
390C22⋊Dic5—32no—
391#685—32no—
392#685—34no—
393C4⋊Dic5—32no—
394C4⋊Dic5—31no—
395C4⋊Dic5—34no—
396C4⋊Dic5C22×D312yes—
397C4⋊Dic5C22×D311yescharacteristic
398C4⋊Dic5C22×D312yes—
399#683—32no—
400#683—32no—
401#683—32no—
402#683—32no—
403#683—34no—
404#683—34no—
405#683—34no—
406#683—34no—
407#683C22×D314yes—
408#683C22×D312yes—
409#683C22×D314yes—
410#683C22×D314yes—
411C4×Dic5—32no—
412C4×Dic5—31no—
413C4×Dic5—32no—
414C4×Dic5—31no—
415C4×Dic5—32no—
416C4×Dic5—31no—
417C4×Dic5—32no—
418C4×Dic5—34no—
419C4×Dic5—34no—
420C4×Dic5—32no—
421C4×Dic5C22×D312yes—
422C4×Dic5C22×D314yes—
423Q82—151no—
424#557—51no—
425#557—152no—
426#554—31no—
427#554—152no—
428#554—152no—
429#554—154no—
430D4×Q8—151no—
431D4×Q8—152no—
432#533—154no—
433#533—152no—
434#533—152no—
435#533—151no—
436C4×#41—151no—
437C4×#41—152no—
438C2×C4×Q8—152no—
439C2×C4×Q8—151no—
440C22×C3×C5C2511yescharacteristic
441C2×D15—21no—
442C2×D15—21no—
443C2×D15C22×Q812yes—
444C2×C5×D3—22no—
445C2×C5×D3—22no—
446C2×C5×D3C22×Q814yes—
447C3×C4×C5—22no—
448C3×C4×C5—21no—
449C3×C4×C5—22no—
450C3×C4×C5C22×Q812yes—
451C3×C4×C5C2×#4112yes—
452Dic15—21no—
453Dic15—21no—
454Dic15—22no—
455Dic15C22×Q812yes—
456Dic15C2×#4114yes—
457C3×Dic5—24no—
458C3×Dic5—22no—
459C3×Dic5C22×Q814yes—
460C5×Dic3—22no—
461C5×Dic3—24no—
462C2×C3×Q8—51no—
463C2×C3×Q8—52no—
464C2×C3×Q8C22×D511yescharacteristic
465#239—58no—
466D3×Q8—108no—
467D3×Q8—104no—
468C2×D12—52no—
469C2×D12C22×D511yescharacteristic
470C2×C4×D3—52no—
471C2×C4×D3—51no—
472C2×C4×D3—54no—
473C2×C4×D3—51no—
474C2×C4×D3—52no—
475C2×C4×D3—52no—
476C2×C4×D3—52no—
477C2×C4×D3—51no—
478C2×C4×D3C22×D512yes—
479C2×C4×D3C22×D514yes—
480C2×Dic6—51no—
481C2×Dic6—52no—
482C2×Dic6—54no—
483C2×Dic6—54no—
484C2×Dic6C22×D512yes—
485C3×C4⋊C4—54no—
486C3×C4⋊C4—54no—
487C3×C4⋊C4—52no—
488C3×C4⋊C4—54no—
489C3×C4⋊C4—52no—
490C3×C4⋊C4—51no—
491C3×C4⋊C4—52no—
492C3×C4⋊C4C22×D511yescharacteristic
493C3×C4⋊C4C22×D512yes—
494C3×C42—52no—
495C3×C42—54no—
496C3×C42C22×D511yescharacteristic
497C3×C42C22×D512yes—
498(C2×D3)⋊C4—52no—
499(C2×D3)⋊C4—54no—
500(C2×D3)⋊C4—52no—
501(C2×D3)⋊C4—54no—
502(C2×D3)⋊C4C22×D512yes—
503(C2×D3)⋊C4C22×D514yes—
504C4⋊Dic3—51no—
505C4⋊Dic3—52no—
506C4⋊Dic3—54no—
507C4⋊Dic3—54no—
508C4⋊Dic3—52no—
509C4⋊Dic3C22×D512yes—
510C4⋊Dic3C22×D512yes—
511C4⋊Dic3C22×D511yescharacteristic
512Dic3⋊C4—52no—
513Dic3⋊C4—52no—
514Dic3⋊C4—52no—
515Dic3⋊C4—54no—
516Dic3⋊C4—54no—
517Dic3⋊C4—54no—
518Dic3⋊C4C22×D514yes—
519Dic3⋊C4C22×D514yes—
520C4×Dic3—52no—
521C4×Dic3—51no—
522C4×Dic3—52no—
523C4×Dic3—51no—
524C4×Dic3—51no—
525C4×Dic3—52no—
526C4×Dic3—54no—
527C4×Dic3—52no—
528C4×Dic3—52no—
529C4×Dic3—54no—
530C23×C5—32no—
531C22×D5—31no—
532C5×Q8—22no—
533C5×Q8—122no—
534C5×D4—34no—
535C2×C4×C5—34no—
536C2×C4×C5—32no—
537C2×C4×C5—64no—
538C2×C4×C5—124no—
539C2×C4×C5C23×D312yes—
540C2×C4×C5C23×D311yescharacteristic
541C2×C4×C5C23×D312yes—
542C2×C4×C5C23×D311yescharacteristic
543C2×C4×C5C23×D311yescharacteristic
544C22⋊D5—38no—
545C2×Dic5—31no—
546C2×Dic5—32no—
547C2×Dic5—38no—
548C2×Dic5—31no—
549C2×Dic5—32no—
550C2×Dic5—31no—
551C2×Dic5—68no—
552C2×Dic5—122no—
553C2×Dic5C23×D312yes—
554C2×Dic5C23×D314yes—
555C2×Dic5C23×D312yes—
556C4×D5—34no—
557C4×D5—64no—
558C4×D5—62no—
559C4×D5—122no—
560C4×D5—121no—
561Dic10—24no—
562Dic10—34no—
563Dic10—68no—
564Dic10—64no—
565Dic10—124no—
566Dic10D3×Q814yescomplemented
567C2×#41—151no—
568C22×Q8—152no—
569C22×Q8—151no—
570C4⋊Q8—31no—
571C4⋊Q8—52no—
572C4⋊Q8—51no—
573C4⋊Q8—152no—
574C4⋊Q8—154no—
575C4⋊Q8—152no—
576C4⋊Q8—152no—
577C4⋊Q8—154no—
578#125—32no—
579#125—54no—
580#125—52no—
581#125—154no—
582#125—154no—
583#125—152no—
584C22⋊Q8—32no—
585C22⋊Q8—34no—
586C22⋊Q8—154no—
587C22⋊Q8—154no—
588C22⋊Q8—154no—
589C22⋊Q8—154no—
590C22⋊Q8—154no—
591C22⋊Q8—152no—
592C22⋊Q8—154no—
593C22⋊Q8—152no—
594C22⋊Q8—152no—
595C4×Q8—52no—
596C4×Q8—52no—
597C4×Q8—51no—
598C4×Q8—152no—
599C4×Q8—154no—
600C4×Q8—154no—
601C4×Q8—154no—
602C4×Q8—152no—
603C4×Q8—151no—
604C4×Q8—152no—
605C4×Q8—152no—
606C4×Q8—151no—
607C4×Q8—151no—
608C4×Q8—152no—
609C4×Q8—151no—
610C4×Q8—152no—
611C4×Q8D3×D511yescharacteristic
612C4×D4—31no—
613C4×D4—32no—
614C4×D4—152no—
615C4×D4—154no—
616C4×D4—154no—
617C4×D4—152no—
618C4×D4—152no—
619C4×D4—151no—
620#117—152no—
621#117—154no—
622#117—151no—
623#117—152no—
624C2×C4⋊C4—32no—
625C2×C4⋊C4—154no—
626C2×C4⋊C4—152no—
627C2×C4⋊C4—151no—
628C2×C42—154no—
629C2×C42—152no—
630C2×C42—151no—
631C2×C42—152no—
632C2×C3×C5C23×Q811yescharacteristic
633C2×C3×C5C22×#4111yescharacteristic
634C2×C3×C5#58511yescharacteristic
635D15—22no—
636C5×D3—24no—
637C22×D3—51no—
638C22×D3C23×D512yes—
639C3×Q8—22no—
640C3×Q8—54no—
641C3×Q8—104no—
642C2×C3×C4—52no—
643C2×C3×C4—54no—
644C2×C3×C4—52no—
645C2×C3×C4C23×D512yes—
646C2×C3×C4C23×D511yescharacteristic
647C2×C3×C4C23×D512yes—
648C2×C3×C4C23×D511yescharacteristic
649C2×C3×C4C23×D511yescharacteristic
650C2×Dic3—51no—
651C2×Dic3—52no—
652C2×Dic3—51no—
653C2×Dic3—51no—
654C2×Dic3—52no—
655C2×Dic3C23×D512yes—
656C2×Dic3C23×D514yes—
657D12—58no—
658D12Q8×D514yescomplemented
659C4×D3—24no—
660C4×D3—44no—
661C4×D3—58no—
662C4×D3—54no—
663C4×D3—104no—
664C4×D3—108no—
665C4×D3—102no—
666C4×D3—202no—
667C4×D3—201no—
668C4×D3—202no—
669Dic6—42no—
670Dic6—54no—
671Dic6—108no—
672Dic6—104no—
673Dic6—204no—
674C22×C5—34no—
675C22×C5—62no—
676C22×C5—62no—
677C22×C5C24×D311yescharacteristic
678C2×D5—32no—
679C2×D5—61no—
680C2×D5—61no—
681C4×C5—22no—
682C4×C5—22no—
683C4×C5—21no—
684C4×C5—62no—
685C4×C5—64no—
686C4×C5C2×D3×Q812yes—
687C4×C5D3×#4112yes—
688Dic5—24no—
689Dic5—22no—
690Dic5—32no—
691Dic5—34no—
692Dic5—61no—
693Dic5—62no—
694Dic5—61no—
695Dic5C2×D3×Q814yes—
696#41—158no—
697C2×Q8—32no—
698C2×Q8—51no—
699C2×Q8—52no—
700C2×Q8—154no—
701C2×Q8—154no—
702C2×Q8—151no—
703C2×Q8—152no—
704C2×Q8—308no—
705C2×Q8—304no—
706C2×Q8C2×D3×D511yescharacteristic
707C2×D4—31no—
708C2×D4—152no—
709C22×C4—32no—
710C22×C4—34no—
711C22×C4—152no—
712C22×C4—154no—
713C22×C4—152no—
714C22×C4—151no—
715C22×C4—152no—
716C22×C4—151no—
717C22×C4—151no—
718C22×C4—152no—
719C4⋊C4—34no—
720C4⋊C4—32no—
721C4⋊C4—31no—
722C4⋊C4—32no—
723C4⋊C4—34no—
724C4⋊C4—54no—
725C4⋊C4—52no—
726C4⋊C4—51no—
727C4⋊C4—54no—
728C4⋊C4—52no—
729C4⋊C4—54no—
730C4⋊C4—52no—
731C4⋊C4—154no—
732C4⋊C4—154no—
733C4⋊C4—152no—
734C4⋊C4—154no—
735C4⋊C4—154no—
736C4⋊C4—154no—
737C4⋊C4—152no—
738C4⋊C4—152no—
739C4⋊C4—152no—
740C4⋊C4—152no—
741C4⋊C4—151no—
742C4⋊C4C2×D3×D511yescharacteristic
743C4⋊C4C2×D3×D512yes—
744C22⋊C4—32no—
745C22⋊C4—34no—
746C22⋊C4—152no—
747C22⋊C4—154no—
748C22⋊C4—152no—
749C22⋊C4—154no—
750C42—54no—
751C42—52no—
752C42—152no—
753C42—154no—
754C42—152no—
755C42—154no—
756C42—152no—
757C42—151no—
758C42—152no—
759C42—151no—
760C42—151no—
761C42—152no—
762C42C2×D3×D512yes—
763C42C2×D3×D511yescharacteristic
764C3×C5Q8×#4111yescharacteristic, complemented, Hall
765C22×C3C24×D511yescharacteristic
766C2×D3—22no—
767C2×D3—22no—
768C2×D3—52no—
769C2×D3—101no—
770C2×D3—101no—
771C2×D3C2×Q8×D514yes—
772C3×C4—22no—
773C3×C4—21no—
774C3×C4—22no—
775C3×C4—54no—
776C3×C4—104no—
777C3×C4—102no—
778C3×C4C2×Q8×D512yes—
779C3×C4D5×#4112yes—
780Dic3—22no—
781Dic3—24no—
782Dic3—52no—
783Dic3—54no—
784Dic3—101no—
785Dic3—102no—
786Dic3—101no—
787C2×C5—64no—
788C2×C5C22×D3×Q811yescharacteristic
789C2×C5C2×D3×#4111yescharacteristic
790C2×C5#596811yescharacteristic
791D5—62no—
792C23—32no—
793C23—151no—
794Q8—22no—
795Q8—54no—
796Q8—104no—
797Q8—122no—
798Q8—154no—
799Q8—304no—
800Q8—308no—
801Q8—604no—
802D4—34no—
803D4—158no—
804C2×C4—32no—
805C2×C4—34no—
806C2×C4—52no—
807C2×C4—52no—
808C2×C4—54no—
809C2×C4—64no—
810C2×C4—124no—
811C2×C4—158no—
812C2×C4—151no—
813C2×C4—152no—
814C2×C4—154no—
815C2×C4—151no—
816C2×C4—152no—
817C2×C4—151no—
818C2×C4—304no—
819C2×C4—308no—
820C2×C4—302no—
821C2×C4—602no—
822C2×C4—601no—
823C2×C4—602no—
824C2×C4C22×D3×D512yes—
825C2×C4C22×D3×D512yes—
826C2×C4C22×D3×D511yescharacteristic
827C2×C4C22×D3×D511yescharacteristic
828C2×C4C22×D3×D511yescharacteristic
829C2×C3C22×Q8×D511yescharacteristic
830C2×C3C2×D5×#4111yescharacteristic
831C2×C3#6628511yescharacteristic
832D3—24no—
833D3—102no—
834C5#8701511yescharacteristic, complemented, Sylow
835C22—34no—
836C22—62no—
837C22—62no—
838C22—152no—
839C22—301no—
840C22—301no—
841C22C23×D3×D511yescharacteristic
842C4—22no—
843C4—21no—
844C4—22no—
845C4—54no—
846C4—64no—
847C4—62no—
848C4—102no—
849C4—104no—
850C4—154no—
851C4—152no—
852C4—301no—
853C4—302no—
854C4—301no—
855C4#9201612yes—
856C4D3×Q8×D512yes—
857C3#1061882411yescharacteristic, complemented, Sylow
858C2—64no—
859C2—302no—
860C2C2×#9201611yescharacteristic
861C2C2×D3×Q8×D511yescharacteristic
862C2#1175706411yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC2×#6768C22
hypercenterC4×Q8D3×D5
hypocenterC3×C5Q8×#41
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. C4×Q8×D15C2semidirect
2. C5×#5579C2semidirect
3. C3×#65901C2semidirect
4. #11755181C2semidirect
5. #11755169C2semidirect
6. #11753715C2semidirect
7. #11753473C2semidirect
8. #11753460C2semidirect
9. D3×#4033C2semidirect
10. #11752627C2semidirect
11. #11752558C2semidirect
14. #11752484C2semidirect
15. #11752473C2semidirect
16. #11752471C2semidirect
17. #11752469C2semidirect
95. #65901D3semidirect
123. #6768Q8semidirect
180. #5579D5semidirect
270. C4×D15C2×Q8semidirect
272. Dic30#41semidirect
275. C5×D12C2×Q8semidirect
283. C3×Dic10C2×Q8semidirect
286. #1203C2×Q8semidirect
289. D3×Dic5C2×Q8semidirect
566. Dic10D3×Q8semidirect
658. D12Q8×D5semidirect
764. C3×C5Q8×#41semidirect
834. C5#87015semidirect
857. C3#10618824semidirect

Maximal subgroups

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

subgroupindex
C4×Q8×D152
C5×#55792
C3×#659012
#117551812
#117551692
#117537152
#117534732
#117534602
D3×#40332
#117526272
#117525582
C4×#67682
#117524842
#117524732
#117524712
#117524692
#106188243
#870155