Finite Group Databasebeta

← #14484648

Subgroups — #14484648

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
1#11756326C211yesmaximal, characteristic, complemented
2C5×#5579C211yesmaximal, characteristic, complemented
3C3×C4×Q8×D5C211yesmaximal, characteristic, complemented
4#11755225C212yesmaximal, complemented
5#11755180C212yesmaximal, complemented
6#11753707C214yesmaximal, complemented
7#11753705C212yesmaximal, complemented
8#11753457C214yesmaximal, complemented
9D3×#4033C212yesmaximal, complemented
10C4×#6772C211yesmaximal, characteristic
11C4×#6772C212yesmaximal
12#11752583C212yesmaximal, complemented
13D12×Dic10C211yesmaximal, characteristic, complemented
14#11752506C211yesmaximal, characteristic, complemented
15#11752498C212yesmaximal, complemented
16#11752473C211yesmaximal, characteristic, complemented
17#11752463C212yesmaximal, complemented
18#10618824—31nomaximal, Hall
19C2×C3×Q8×D5C2211yescharacteristic
20C2×#6772C2211yescharacteristic
21C2×D3×Dic10C2212yes—
22C3×C4×C5×Q8C2211yescharacteristic
23#91833C2212yes—
24#91778C2214yes—
25#91776C2212yes—
26#91759C2212yes—
27#91758C2211yescharacteristic
28C4×Dic30C2212yes—
29C4×Dic30C2211yescharacteristic
30C5×#946C2212yes—
31C5×#896C2214yes—
32C5×D3×C4⋊C4C2212yes—
33C4×C5×D12C2211yescharacteristic
34C4×C5×D12C2212yes—
35C5×#870C2212yes—
36C5×#869C2211yescharacteristic
37C3×Q8×Dic5C2211yescharacteristic
38C3×D5×C4⋊C4C2211yescharacteristic
39C3×D5×C4⋊C4C2212yes—
40C3×#4033C2211yescharacteristic
41C3×#4033C2212yes—
42C3×C42×D5C2212yes—
43C3×C42×D5C2211yescharacteristic
44C3×C4×Dic10C2212yes—
45C3×C4×Dic10C2211yescharacteristic
46#91470C2212yes—
47#91468C2212yes—
48#91468C2212yes—
49#91440C2214yes—
50#91440C2212yes—
51C4×#1201C2212yes—
52C4×#1201C2214yes—
53#91436C2214yes—
54#91417C2214yes—
55Dic5×D12C2212yes—
56Dic5×D12C2211yescharacteristic
57#91410C2214yes—
58D3×#683C2214yes—
59#91398C2214yes—
60#91398C2212yes—
61C4×D3×Dic5C2212yes—
62C4×D3×Dic5C2214yes—
63#91388C2212yes—
64#91382C2214yes—
65#91365C2212yes—
66#91360C2212yes—
67#91359C2212yes—
68#91358C2211yescharacteristic
69#91358C2212yes—
70#91352C2214yes—
71#91349C2214yes—
72#91349C2214yes—
73#91339C2214yes—
74#91333C2211yescharacteristic
75#91333C2212yes—
76#91333C2212yes—
77Dic5×Dic6C2212yes—
78#91331C2212yes—
79#91329C2214yes—
80#91327C2214yes—
81#91325C2214yes—
82#91323C2214yes—
83#91323C2214yes—
84Q8×#235—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×D5D311yescharacteristic, complemented
95#65901—31no—
96#65873—32no—
97D4×Dic10—31no—
98C4×#711—31no—
99C4×#711—32no—
100#65845—32no—
101C2×#4033—32no—
102C2×C3×C5×Q8C2311yescharacteristic
103C2×Dic30C2312yes—
104C2×Dic30C2311yescharacteristic
105C2×C5×D12C2311yescharacteristic
106C2×C4×C5×D3C2312yes—
107C2×C4×C5×D3C2314yes—
108C2×C5×Dic6C2312yes—
109C3×Q8×D5—24no—
110C2×C3×C4×D5C2311yescharacteristic
111C2×C3×C4×D5C2312yes—
112C2×C3×C4×D5C2312yes—
113C2×C3×C4×D5C2311yescharacteristic
114C2×C3×C4×D5C2311yescharacteristic
115C2×C3×Dic10C2312yes—
116C2×C3×Dic10C2311yescharacteristic
117C2×#1204C2314yes—
118C2×#1204C2314yes—
119C2×#1201C2312yes—
120C2×D3×Dic5C2314yes—
121C2×D3×Dic5C2312yes—
122C2×D3×Dic5C2312yes—
123#6772Q818yescomplemented
124D3×Dic10—28no—
125C3×C5×C4⋊C4C2311yescharacteristic
126C3×C5×C4⋊C4C2312yes—
127C3×C42×C5C2311yescharacteristic
128C3×C42×C5C2312yes—
129C4⋊Dic15C2311yescharacteristic
130C4⋊Dic15C2312yes—
131C4⋊Dic15C2312yes—
132#6712C2312yes—
133#6712C2314yes—
134#6712C2314yes—
135#6712C2314yes—
136C4×Dic15C2312yes—
137C4×Dic15C2314yes—
138C5×(C2×D3)⋊C4C2314yes—
139C5×(C2×D3)⋊C4C2312yes—
140C5×C4⋊Dic3C2312yes—
141C5×C4⋊Dic3C2312yes—
142C5×C4⋊Dic3C2311yescharacteristic
143C5×Dic3⋊C4C2314yes—
144C5×Dic3⋊C4C2314yes—
145C3×C4⋊Dic5C2312yes—
146C3×C4⋊Dic5C2311yescharacteristic
147C3×#683C2312yes—
148C3×#683C2312yes—
149C3×#683C2312yes—
150C3×C4×Dic5C2311yescharacteristic
151C3×C4×Dic5C2312yes—
152C3×C4×Dic5C2312yes—
153C3×C4×Dic5C2311yescharacteristic
154C3×C4×Dic5C2312yes—
155C3×C4×Dic5C2311yescharacteristic
156Dic3⋊Dic5C2314yes—
157#6669C2314yes—
158#6669C2312yes—
159#6669C2314yes—
160#6668C2314yes—
161#6668C2314yes—
162(C2×D3)⋊Dic5C2312yes—
163(C2×D3)⋊Dic5C2314yes—
164#6665C2312yes—
165#6665C2314yes—
166Dic3×Dic5C2312yes—
167Dic3×Dic5C2314yes—
168Dic3×Dic5C2312yes—
169Dic3×Dic5C2314yes—
170C2×C3×C4×Q8—51no—
171Q8×#67—52no—
172#5579—52no—
173#5579D511yescharacteristic, complemented
174#5578—52no—
175#5578—54no—
176Q8×D12—51no—
177C4×D3×Q8—52no—
178#5567—51no—
179#5567—52no—
180Q8×Dic6—51no—
181#5511—54no—
182#5511—52no—
183C4×#235—51no—
184C4×#235—52no—
185#5470—52no—
186#5470—51no—
187C2×Q8×D5C2×D311yescharacteristic
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—32no—
200Q8×Dic5C2×D311yescharacteristic
201#4090—32no—
202#4090—34no—
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—32no—
211C2×C4×Dic5—34no—
212#4043—32no—
213#4042—34no—
214#4042—34no—
215#4038—32no—
216#4038—31no—
217D5×C4⋊C4C2×D311yescharacteristic
218D5×C4⋊C4C2×D312yes—
219#4036—32no—
220#4035—34no—
221#4035—34no—
222#4035—34no—
223#4034—34no—
224#4034—32no—
225#4034—32no—
226#4034—32no—
227#4033—32no—
228#4033—32no—
229#4033—34no—
230#4033—32no—
231#4033—32no—
232#4033—34no—
233#4033—31no—
234#4033—34no—
235#4033C2×D311yescharacteristic
236#4033C2×D312yes—
237#4027—34no—
238#4027—32no—
239#4024—34no—
240#4024—34no—
241#4024—34no—
242#4023—32no—
243#4023—34no—
244C42×D5C2×D311yescharacteristic
245C42×D5C2×D312yes—
246#4016—32no—
247#4015—31no—
248C4×Dic10—31no—
249C4×Dic10—32no—
250C4×Dic10C2×D311yescharacteristic
251C4×Dic10C2×D312yes—
252Q8×#41—151noSylow
253C22×C5×D3C2412yes—
254C22×C3×D5C2411yescharacteristic
255C3×C5×Q8—22no—
256C2×C3×C4×C5C2412yes—
257C2×C3×C4×C5C2411yescharacteristic
258C2×C3×C4×C5C2412yes—
259C2×C3×C4×C5C2411yescharacteristic
260C2×C3×C4×C5C2411yescharacteristic
261C2×Dic15C2412yes—
262C2×Dic15C2414yes—
263C2×Dic15C2412yes—
264Dic30—24no—
265Dic30C2×Q814yescomplemented
266C2×C5×Dic3C2412yes—
267C2×C5×Dic3C2414yes—
268C5×D12C2×Q814yescomplemented
269C4×C5×D3—24no—
270C4×C5×D3—44no—
271C5×Dic6—42no—
272C2×C3×Dic5C2411yescharacteristic
273C2×C3×Dic5C2412yes—
274C2×C3×Dic5C2411yescharacteristic
275C2×C3×Dic5C2411yescharacteristic
276C2×C3×Dic5C2412yes—
277C3×C4×D5—22no—
278C3×C4×D5—24no—
279C3×C4×D5—41no—
280C3×C4×D5—42no—
281C3×C4×D5C2×Q814yescomplemented
282C3×Dic10—24no—
283C3×Dic10#4114yescomplemented
284#1204—28no—
285#1204—44no—
286#1201C2×Q818yescomplemented
287D3×Dic5—28no—
288D3×Dic5—42no—
289D3×Dic5C2×Q818yescomplemented
290C22×C3×Q8—51no—
291C2×D3×Q8—52no—
292C2×#235—51no—
293C3×C4×Q8—51no—
294C3×C4×Q8—51no—
295C3×C4×Q8—52no—
296C3×C4×Q8—51no—
297C3×C4×Q8—52no—
298C3×C4×Q8C2×D511yescharacteristic
299C2×C3×C4⋊C4—52no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C42—52no—
302C2×C3×C42—51no—
303#946—54no—
304#946C2×D512yes—
305Q8×Dic3—52no—
306#944—52no—
307#944—54no—
308C4×#67—54no—
309C4×#67—52no—
310C4×#67—52no—
311C4×#67—54no—
312#926—51no—
313#926—52no—
314#924—52no—
315#924—52no—
316#924—54no—
317#924—54no—
318#897—52no—
319#897—54no—
320#896—54no—
321#896—54no—
322#896C2×D514yes—
323D3×C4⋊C4—54no—
324D3×C4⋊C4C2×D512yes—
325#889—54no—
326#889—54no—
327#889—54no—
328#888—54no—
329#888—52no—
330#887—52no—
331#887—54no—
332C4×D12—52no—
333C4×D12—51no—
334C4×D12C2×D511yescharacteristic
335C4×D12C2×D512yes—
336#872—52no—
337#872—54no—
338C42×D3—54no—
339C42×D3—52no—
340#870—52no—
341#870—52no—
342#870C2×D512yes—
343#869—51no—
344#869—52no—
345#869—52no—
346#869C2×D511yescharacteristic
347C4×Dic6—52no—
348C4×Dic6—51no—
349C4×Dic6—52no—
350C4×Dic6—52no—
351C4×Dic6—52no—
352C4×Dic6—51no—
353C4×Dic6—54no—
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—24no—
365#711—38no—
366C2×C4×D5C22×D312yes—
367C2×C4×D5C22×D311yescharacteristic
368C2×C4×D5C22×D311yescharacteristic
369C2×C4×D5C22×D312yes—
370C2×C4×D5C22×D311yescharacteristic
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—32no—
390C22⋊Dic5—34no—
391#685—32no—
392#685—34no—
393C4⋊Dic5—32no—
394C4⋊Dic5—31no—
395C4⋊Dic5—32no—
396C4⋊Dic5—34no—
397C4⋊Dic5C22×D312yes—
398C4⋊Dic5C22×D311yescharacteristic
399#683—34no—
400#683—32no—
401#683—34no—
402#683—34no—
403#683—34no—
404#683—34no—
405#683—32no—
406#683—34no—
407#683—34no—
408#683C22×D312yes—
409#683C22×D312yes—
410#683C22×D312yes—
411C4×Dic5—32no—
412C4×Dic5—34no—
413C4×Dic5—32no—
414C4×Dic5—34no—
415C4×Dic5—34no—
416C4×Dic5—32no—
417C4×Dic5C22×D312yes—
418C4×Dic5C22×D311yescharacteristic
419C4×Dic5C22×D312yes—
420C4×Dic5C22×D311yescharacteristic
421C4×Dic5C22×D312yes—
422C4×Dic5C22×D311yescharacteristic
423Q82—151no—
424#557—152no—
425#557—151no—
426#554—31no—
427#554—152no—
428#554—154no—
429#554—152no—
430D4×Q8—151no—
431D4×Q8—152no—
432#533—152no—
433#533—151no—
434#533—152no—
435#533—154no—
436C4×#41—151no—
437C4×#41—152no—
438C2×C4×Q8—51no—
439C2×C4×Q8—152no—
440C22×C3×C5C2511yescharacteristic
441C2×C5×D3—22no—
442C2×C5×D3—22no—
443C2×C5×D3C22×Q814yes—
444C2×C3×D5—21no—
445C2×C3×D5—21no—
446C2×C3×D5C22×Q812yes—
447C3×C4×C5—22no—
448C3×C4×C5—21no—
449C3×C4×C5—22no—
450C3×C4×C5C22×Q812yes—
451C3×C4×C5C2×#4112yes—
452Dic15—24no—
453Dic15—22no—
454Dic15C22×Q814yes—
455C3×Dic5—21no—
456C3×Dic5—21no—
457C3×Dic5—22no—
458C3×Dic5C22×Q812yes—
459C3×Dic5C2×#4114yes—
460C5×Dic3—22no—
461C5×Dic3—24no—
462C2×C3×Q8—51no—
463C2×C3×Q8—52no—
464C2×C3×Q8—104no—
465C2×C3×Q8C22×D511yescharacteristic
466C22×C3×C4—51no—
467C22×C3×C4—52no—
468C22×C3×C4—51no—
469C22×C3×C4—51no—
470C22×C3×C4—52no—
471C2×#67—52no—
472D3×Q8—108no—
473#235—58no—
474C2×D12C22×D511yescharacteristic
475C2×C4×D3—52no—
476C2×C4×D3—54no—
477C2×C4×D3—52no—
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—52no—
486C3×C4⋊C4—52no—
487C3×C4⋊C4—52no—
488C3×C4⋊C4—51no—
489C3×C4⋊C4—52no—
490C3×C4⋊C4C22×D511yescharacteristic
491C3×C4⋊C4C22×D512yes—
492C3×C42—52no—
493C3×C42—51no—
494C3×C42—51no—
495C3×C42—52no—
496C3×C42—52no—
497C3×C42—51no—
498C3×C42C22×D511yescharacteristic
499C3×C42C22×D512yes—
500#217—54no—
501#217—52no—
502(C2×D3)⋊C4—54no—
503(C2×D3)⋊C4—52no—
504(C2×D3)⋊C4C22×D514yes—
505(C2×D3)⋊C4C22×D512yes—
506C4⋊Dic3—51no—
507C4⋊Dic3—52no—
508C4⋊Dic3—52no—
509C4⋊Dic3—54no—
510C4⋊Dic3—54no—
511C4⋊Dic3C22×D511yescharacteristic
512C4⋊Dic3C22×D512yes—
513C4⋊Dic3C22×D512yes—
514Dic3⋊C4—54no—
515Dic3⋊C4—54no—
516Dic3⋊C4—52no—
517Dic3⋊C4—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4—52no—
521Dic3⋊C4—54no—
522Dic3⋊C4C22×D514yes—
523Dic3⋊C4C22×D514yes—
524C4×Dic3—54no—
525C4×Dic3—52no—
526C4×Dic3—54no—
527C4×Dic3—52no—
528C4×Dic3—52no—
529C4×Dic3—54no—
530C23×C5—32no—
531C22×D5C23×D311yescharacteristic
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×D312yes—
541C2×C4×C5C23×D311yescharacteristic
542C2×C4×C5C23×D311yescharacteristic
543C2×C4×C5C23×D311yescharacteristic
544C22⋊D5—38no—
545C2×Dic5—32no—
546C2×Dic5—38no—
547C2×Dic5—32no—
548C2×Dic5—34no—
549C2×Dic5—68no—
550C2×Dic5—122no—
551C2×Dic5C23×D311yescharacteristic
552C2×Dic5C23×D312yes—
553C2×Dic5C23×D311yescharacteristic
554C2×Dic5C23×D312yes—
555C2×Dic5C23×D311yescharacteristic
556C4×D5—22no—
557C4×D5—24no—
558C4×D5—42no—
559C4×D5—41no—
560C4×D5D3×Q814yescomplemented
561Dic10—24no—
562Dic10—34no—
563Dic10—64no—
564Dic10—68no—
565Dic10—124no—
566Dic10#23514yescomplemented
567C2×#41—151no—
568C22×Q8—51no—
569C22×Q8—152no—
570C4⋊Q8—31no—
571C4⋊Q8—152no—
572C4⋊Q8—152no—
573C4⋊Q8—152no—
574C4⋊Q8—154no—
575C4⋊Q8—154no—
576C4⋊Q8—152no—
577C4⋊Q8—151no—
578#125—32no—
579#125—152no—
580#125—154no—
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—152no—
591C22⋊Q8—154no—
592C22⋊Q8—152no—
593C22⋊Q8—154no—
594C22⋊Q8—152no—
595C4×Q8—51no—
596C4×Q8—51no—
597C4×Q8—52no—
598C4×Q8—51no—
599C4×Q8—52no—
600C4×Q8—154no—
601C4×Q8—152no—
602C4×Q8—151no—
603C4×Q8—152no—
604C4×Q8—154no—
605C4×Q8—152no—
606C4×Q8—154no—
607C4×Q8—152no—
608C4×Q8—152no—
609C4×Q8—152no—
610C4×Q8—151no—
611C4×Q8D3×D511yescharacteristic
612C4×D4—31no—
613C4×D4—32no—
614C4×D4—152no—
615C4×D4—151no—
616C4×D4—154no—
617C4×D4—152no—
618C4×D4—152no—
619C4×D4—154no—
620#117—154no—
621#117—152no—
622#117—151no—
623#117—152no—
624C2×C4⋊C4—32no—
625C2×C4⋊C4—52no—
626C2×C4⋊C4—51no—
627C2×C4⋊C4—154no—
628C2×C42—51no—
629C2×C42—52no—
630C2×C42—152no—
631C2×C42—154no—
632C2×C3×C5C23×Q811yescharacteristic
633C2×C3×C5C22×#4111yescharacteristic
634C2×C3×C5#58511yescharacteristic
635C3×D5—22no—
636C5×D3—24no—
637C23×C3—51no—
638C22×D3C23×D512yes—
639C3×Q8—22no—
640C3×Q8—54no—
641C3×Q8—104no—
642C2×C3×C4—51no—
643C2×C3×C4—52no—
644C2×C3×C4—54no—
645C2×C3×C4—51no—
646C2×C3×C4—51no—
647C2×C3×C4—52no—
648C2×C3×C4—104no—
649C2×C3×C4—102no—
650C2×C3×C4—201no—
651C2×C3×C4—202no—
652C2×C3×C4C23×D512yes—
653C2×C3×C4C23×D512yes—
654C2×C3×C4C23×D511yescharacteristic
655C2×C3×C4C23×D511yescharacteristic
656C2×C3×C4C23×D511yescharacteristic
657#67—58no—
658C2×Dic3—52no—
659C2×Dic3—54no—
660C2×Dic3—52no—
661C2×Dic3C23×D514yes—
662C2×Dic3C23×D512yes—
663D12Q8×D514yescomplemented
664C4×D3—24no—
665C4×D3—44no—
666C4×D3—58no—
667C4×D3—108no—
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—21no—
679C2×D5—21no—
680C2×D5C2×D3×Q812yes—
681C4×C5—22no—
682C4×C5—22no—
683C4×C5—21no—
684C4×C5—62no—
685C4×C5—64no—
686C4×C5C2×#23512yes—
687C4×C5C2×D3×Q812yes—
688Dic5—21no—
689Dic5—22no—
690Dic5—21no—
691Dic5—34no—
692Dic5—64no—
693Dic5—62no—
694Dic5C2×#23514yes—
695Dic5C2×D3×Q812yes—
696#41—158no—
697C2×Q8—32no—
698C2×Q8—51no—
699C2×Q8—52no—
700C2×Q8—104no—
701C2×Q8—154no—
702C2×Q8—154no—
703C2×Q8—151no—
704C2×Q8—152no—
705C2×Q8—308no—
706C2×Q8C2×D3×D511yescharacteristic
707C2×D4—31no—
708C2×D4—152no—
709C22×C4—32no—
710C22×C4—34no—
711C22×C4—51no—
712C22×C4—52no—
713C22×C4—51no—
714C22×C4—51no—
715C22×C4—52no—
716C22×C4—152no—
717C22×C4—154no—
718C22×C4—152no—
719C4⋊C4—34no—
720C4⋊C4—32no—
721C4⋊C4—31no—
722C4⋊C4—32no—
723C4⋊C4—34no—
724C4⋊C4—52no—
725C4⋊C4—52no—
726C4⋊C4—52no—
727C4⋊C4—52no—
728C4⋊C4—51no—
729C4⋊C4—154no—
730C4⋊C4—154no—
731C4⋊C4—152no—
732C4⋊C4—154no—
733C4⋊C4—154no—
734C4⋊C4—154no—
735C4⋊C4—154no—
736C4⋊C4—154no—
737C4⋊C4—152no—
738C4⋊C4—152no—
739C4⋊C4—151no—
740C4⋊C4—154no—
741C4⋊C4—152no—
742C4⋊C4C2×D3×D511yescharacteristic
743C4⋊C4C2×D3×D512yes—
744C22⋊C4—32no—
745C22⋊C4—34no—
746C22⋊C4—152no—
747C22⋊C4—154no—
748C22⋊C4—154no—
749C22⋊C4—152no—
750C42—52no—
751C42—51no—
752C42—52no—
753C42—51no—
754C42—51no—
755C42—52no—
756C42—152no—
757C42—154no—
758C42—152no—
759C42—154no—
760C42—154no—
761C42—152no—
762C42C2×D3×D512yes—
763C42C2×D3×D511yescharacteristic
764C3×C5Q8×#4111yescharacteristic, complemented, Hall
765C22×C3—52no—
766C22×C3—101no—
767C22×C3—101no—
768C22×C3C24×D511yescharacteristic
769C2×D3—22no—
770C2×D3—22no—
771C2×D3C2×Q8×D514yes—
772C3×C4—22no—
773C3×C4—21no—
774C3×C4—22no—
775C3×C4—52no—
776C3×C4—54no—
777C3×C4—101no—
778C3×C4—102no—
779C3×C4—101no—
780C3×C4C2×Q8×D512yes—
781C3×C4D5×#4112yes—
782Dic3—22no—
783Dic3—24no—
784Dic3—54no—
785Dic3—104no—
786Dic3—102no—
787C2×C5—64no—
788C2×C5C22×#23511yescharacteristic
789C2×C5C22×D3×Q811yescharacteristic
790C2×C5#596411yescharacteristic
791D5—22no—
792C23—32no—
793C23—51no—
794Q8—22no—
795Q8—54no—
796Q8—104no—
797Q8—122no—
798Q8—154no—
799Q8—308no—
800Q8—304no—
801Q8—604no—
802D4—34no—
803D4—158no—
804C2×C4—32no—
805C2×C4—34no—
806C2×C4—51no—
807C2×C4—52no—
808C2×C4—54no—
809C2×C4—51no—
810C2×C4—52no—
811C2×C4—51no—
812C2×C4—64no—
813C2×C4—104no—
814C2×C4—102no—
815C2×C4—124no—
816C2×C4—158no—
817C2×C4—152no—
818C2×C4—152no—
819C2×C4—154no—
820C2×C4—202no—
821C2×C4—201no—
822C2×C4—308no—
823C2×C4—602no—
824C2×C4C22×D3×D512yes—
825C2×C4C22×D3×D512yes—
826C2×C4C22×D3×D511yescharacteristic
827C2×C4C22×D3×D511yescharacteristic
828C2×C4C22×D3×D511yescharacteristic
829C2×C3—102no—
830C2×C3C22×Q8×D511yescharacteristic
831C2×C3C2×D5×#4111yescharacteristic
832C2×C3#6628511yescharacteristic
833D3—24no—
834C5Q8×#23511yescharacteristic, complemented, Sylow
835C22—34no—
836C22—52no—
837C22—62no—
838C22—62no—
839C22—101no—
840C22—101no—
841C22C23×D3×D511yescharacteristic
842C4—22no—
843C4—21no—
844C4—22no—
845C4—54no—
846C4—52no—
847C4—64no—
848C4—62no—
849C4—101no—
850C4—102no—
851C4—101no—
852C4—154no—
853C4—302no—
854C4—304no—
855C4D5×#23512yes—
856C4D3×Q8×D512yes—
857C3#1061882411yescharacteristic, complemented, Sylow
858C2—64no—
859C2—102no—
860C2C2×D5×#23511yescharacteristic
861C2C2×D3×Q8×D511yescharacteristic
862C2#1175705911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D3×D5
commutator, socle, cosocleC22×C3×C5C25
FittingC3×C4×C5×Q8C22
prime radicalC2×#6772C22
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. #11756326C2semidirect
2. C5×#5579C2semidirect
3. C3×C4×Q8×D5C2semidirect
4. #11755225C2semidirect
5. #11755180C2semidirect
6. #11753707C2semidirect
7. #11753705C2semidirect
8. #11753457C2semidirect
9. D3×#4033C2semidirect
12. #11752583C2semidirect
13. D12×Dic10C2semidirect
14. #11752506C2semidirect
15. #11752498C2semidirect
16. #11752473C2semidirect
17. #11752463C2semidirect
94. C4×Q8×D5D3semidirect
123. #6772Q8semidirect
173. #5579D5semidirect
265. Dic30C2×Q8semidirect
268. C5×D12C2×Q8semidirect
281. C3×C4×D5C2×Q8semidirect
283. C3×Dic10#41semidirect
286. #1201C2×Q8semidirect
289. D3×Dic5C2×Q8semidirect
560. C4×D5D3×Q8semidirect
566. Dic10#235semidirect
663. D12Q8×D5semidirect
764. C3×C5Q8×#41semidirect
834. C5Q8×#235semidirect
857. C3#10618824semidirect

Maximal subgroups

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

subgroupindex
#117563262
C5×#55792
C3×C4×Q8×D52
#117552252
#117551802
#117537072
#117537052
#117534572
D3×#40332
C4×#67722
#117525832
D12×Dic102
#117525062
#117524982
#117524732
#117524632
#106188243
Q8×#2355