Finite Group Databasebeta

← C2×#11747135 #14425652

Subgroups — C2×#11747135 #14425652

Order 1920.

1588 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#92049C211yesmaximal, characteristic
2C2×C5×#886C211yesmaximal, characteristic, complemented
3C2×#91542C211yesmaximal, characteristic, complemented
4C2×#91536C211yesmaximal, characteristic, complemented
5C2×#91090C211yesmaximal, characteristic, complemented
6C2×C3×#3938C211yesmaximal, characteristic, complemented
7C2×#90996C211yesmaximal, characteristic, complemented
8#11747135C218yesmaximal, direct product factor
9C2×#65342—31nomaximal, Hall
10C22×#1220C2211yescharacteristic
11C22×C5×#67C2211yescharacteristic
12C23×C5×Dic3C2211yescharacteristic, complemented
13C22×C3×C22⋊D5C2211yescharacteristic
14#92049—22no—
15#92049—22no—
16#92049—22no—
17#92049C2214yes—
18C2×#6790—21no—
19C2×D3×C22⋊D5—21no—
20C2×D5×#67—21no—
21C2×#6782—21no—
22C2×#6780—21no—
23C2×#6779—21no—
24C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
25C2×#6719C2211yescharacteristic, complemented
26C2×C5×(C2×D3)⋊C4—21no—
27C2×C5×C4⋊Dic3—21no—
28C5×#886—22no—
29C5×#886C2214yescomplemented
30C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
31C2×#6669—21no—
32#91542—22no—
33#91542C2214yescomplemented
34C2×#6668—21no—
35C2×#6667—21no—
36#91536—22no—
37#91536C2214yescomplemented
38C2×#6665—21no—
39#91090C2214yescomplemented
40C3×#3938C2214yescomplemented
41#90996C2214yescomplemented
42C2×#4742—51nomaximal, Hall
43C2×#4144—31no—
44C2×C5×#123—31no—
45C2×#4075—31no—
46C2×#4075—31no—
47C2×#3966—31no—
48#65342—38no—
49C2×#3938—31no—
50C2×#3938D311yescharacteristic, complemented
51C24×C3×C5C2311yescharacteristic
52C23×D15D411yescharacteristic
53C23×C5×D3D411yescharacteristic
54C23×C3×D5D411yescharacteristic
55C22×D3×D5—21no—
56C22×C3×C4×C5—21no—
57C2×#1220—21no—
58C2×#1220—21no—
59C2×#1220—21no—
60C2×#1220—21no—
61C2×#1220D412yes—
62C2×#1220C2312yes—
63C22×Dic15—21no—
64C22×Dic15D411yescharacteristic
65C2×C5×#67—21no—
66C2×C5×#67—21no—
67C2×C5×#67—21no—
68C2×C5×#67—21no—
69C2×C5×#67D412yes—
70C2×C5×#67C2312yes—
71C22×C5×Dic3—21no—
72C22×C5×Dic3—21no—
73C22×C5×Dic3—21no—
74C22×C5×Dic3—21no—
75C22×C5×Dic3—21no—
76C22×C5×Dic3—21no—
77C22×C5×Dic3D411yescharacteristic
78C22×C5×Dic3C2312yescomplemented
79C2×C3×C22⋊D5—21no—
80C2×C3×C22⋊D5—21no—
81C2×C3×C22⋊D5—21no—
82C2×C3×C22⋊D5—21no—
83C2×C3×C22⋊D5D412yes—
84C2×C3×C22⋊D5C2312yes—
85C22×C3×Dic5—21no—
86C22×C3×Dic5D411yescharacteristic
87#6790—24no—
88#6790—24no—
89D3×C22⋊D5—24no—
90D3×C22⋊D5—24no—
91D5×#67—24no—
92D5×#67—24no—
93C2×#1204—21no—
94C2×#1203—21no—
95C2×#1202—21no—
96C2×#1201—21no—
97C2×#1200—21no—
98#6782—24no—
99#6782—24no—
100C2×D3×Dic5—21no—
101#6780—24no—
102#6780—24no—
103#6779—24no—
104#6779—24no—
105C2×D5×Dic3—21no—
106C3×C5×C22⋊C4—21no—
107C3×C5×C22⋊C4C2312yescomplemented
108#6719—21no—
109#6719C2312yescomplemented
110C5×(C2×D3)⋊C4—24no—
111C5×C4⋊Dic3—24no—
112C3×C22⋊Dic5—21no—
113C3×C22⋊Dic5C2312yescomplemented
114#6669—24no—
115#6668—24no—
116#6667—24no—
117#6665—24no—
118C2×#1004—51no—
119C2×#935—51no—
120C2×#886—51no—
121C2×#886D511yescharacteristic, complemented
122C2×C3×#99—51no—
123C2×#806—51no—
124C2×#806—51no—
125#4742—58no—
126C22×C5×D4—31no—
127C23×C4×C5—31no—
128C22×C22⋊D5—31no—
129C22×C22⋊D5—61no—
130C22×C22⋊D5C2×D311yescharacteristic
131#4144—34no—
132#4144—62no—
133#4144—62no—
134#4144—62no—
135C2×#711—61no—
136C2×#711—61no—
137C2×D4×D5—61no—
138C2×D4×D5—61no—
139C2×#709—61no—
140C5×#123—34no—
141C5×#123—62no—
142C2×C5×C4⋊C4—61no—
143C2×C5×C22⋊C4—61no—
144C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
145C2×C22⋊Dic5—31no—
146C2×C22⋊Dic5C2×D311yescharacteristic, complemented
147#4075—34no—
148#4075—34no—
149#4075—62no—
150#4075—62no—
151C2×#685—61no—
152C2×#685—61no—
153C2×#683—61no—
154C2×#683—61no—
155#3966—34no—
156#3938—34no—
157#3938C2×D314yescomplemented
158C2×#458—151noSylow
159C23×C3×C5—42no—
160C23×C3×C5C2×D411yescharacteristic
161C23×C3×C5C2×D411yescharacteristic
162C23×C3×C5C2×D411yescharacteristic
163C23×C3×C5C2×D411yescharacteristic
164C23×C3×C5C2×D411yescharacteristic
165C23×C3×C5C2×D411yescharacteristic
166C23×C3×C5C2411yescharacteristic
167C22×D15—21no—
168C22×D15—21no—
169C22×D15—42no—
170C22×D15C2×D412yes—
171C22×C5×D3—21no—
172C22×C5×D3—21no—
173C22×C5×D3—42no—
174C22×C5×D3C2×D412yes—
175C22×C3×D5—21no—
176C22×C3×D5—21no—
177C22×C3×D5—42no—
178C22×C3×D5C2×D412yes—
179C2×D3×D5—24no—
180C2×D3×D5—82no—
181C2×C3×C4×C5—22no—
182C2×C3×C4×C5—42no—
183#1220—22no—
184#1220—22no—
185#1220—22no—
186#1220—22no—
187C2×Dic15—21no—
188C2×Dic15—21no—
189C2×Dic15—22no—
190C2×Dic15—42no—
191C2×Dic15C2×D412yes—
192C5×#67—22no—
193C5×#67—22no—
194C5×#67—22no—
195C5×#67—22no—
196C2×C5×Dic3—21no—
197C2×C5×Dic3—21no—
198C2×C5×Dic3—22no—
199C2×C5×Dic3—22no—
200C2×C5×Dic3—22no—
201C2×C5×Dic3—41no—
202C2×C5×Dic3—41no—
203C2×C5×Dic3—41no—
204C2×C5×Dic3—41no—
205C2×C5×Dic3C2×D412yes—
206C3×C22⋊D5—22no—
207C3×C22⋊D5—22no—
208C3×C22⋊D5—22no—
209C3×C22⋊D5—22no—
210C2×C3×Dic5—21no—
211C2×C3×Dic5—21no—
212C2×C3×Dic5—22no—
213C2×C3×Dic5—42no—
214C2×C3×Dic5C2×D412yes—
215#1204—24no—
216#1203—24no—
217#1202—24no—
218#1201—24no—
219#1200—24no—
220D3×Dic5—24no—
221D5×Dic3—24no—
222C22×C3×D4—51no—
223C22×#67—51no—
224C22×#67—101no—
225C22×#67C2×D511yescharacteristic
226C23×Dic3C2×D511yescharacteristic, complemented
227#1004—54no—
228#1004—102no—
229#1004—102no—
230#1004—102no—
231C2×#237—101no—
232C2×#237—101no—
233C2×D3×D4—101no—
234C2×D3×D4—101no—
235C2×#235—101no—
236C2×C3×C22⋊C4—51no—
237C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
238C2×#217—51no—
239C2×#217—101no—
240#935—54no—
241#935—102no—
242C2×(C2×D3)⋊C4—21no—
243C2×(C2×D3)⋊C4—101no—
244C2×C4⋊Dic3—21no—
245C2×C4⋊Dic3—101no—
246C2×Dic3⋊C4—101no—
247#886—22no—
248#886—54no—
249#886—102no—
250#886C2×D514yescomplemented
251C3×#99—54no—
252#806—54no—
253#806—54no—
254C24×C5—31no—
255C24×C5C22×D311yescharacteristic
256C23×D5—31no—
257C23×D5—61no—
258C23×D5D1211yescharacteristic
259C2×C5×D4—32no—
260C2×C5×D4—32no—
261C2×C5×D4—61no—
262C2×C5×D4—61no—
263C2×C5×D4—61no—
264C2×C5×D4—61no—
265C22×C4×C5—21no—
266C22×C4×C5—31no—
267C22×C4×C5—32no—
268C22×C4×C5—61no—
269C22×C4×C5—61no—
270C22×C4×C5—61no—
271C22×C4×C5—61no—
272C22×C4×C5—61no—
273C22×C4×C5—61no—
274C2×C22⋊D5—21no—
275C2×C22⋊D5—21no—
276C2×C22⋊D5—21no—
277C2×C22⋊D5—21no—
278C2×C22⋊D5—32no—
279C2×C22⋊D5—32no—
280C2×C22⋊D5—61no—
281C2×C22⋊D5—64no—
282C2×C22⋊D5—64no—
283C2×C22⋊D5—61no—
284C2×C22⋊D5—61no—
285C2×C22⋊D5—61no—
286C2×C22⋊D5—61no—
287C2×C22⋊D5—61no—
288C2×C22⋊D5D1212yes—
289C2×C22⋊D5C22×D312yes—
290C22×Dic5—21no—
291C22×Dic5—31no—
292C22×Dic5—61no—
293C22×Dic5—61no—
294C22×Dic5D1211yescharacteristic
295#711—64no—
296#711—64no—
297#711—64no—
298#711—64no—
299D4×D5—64no—
300D4×D5—64no—
301D4×D5—64no—
302D4×D5—64no—
303#709—64no—
304#709—64no—
305C2×D20—61no—
306C2×C4×D5—61no—
307C2×C4×D5—61no—
308C2×Dic10—61no—
309C5×C4⋊C4—64no—
310C5×C22⋊C4—21no—
311C5×C22⋊C4—64no—
312C5×C22⋊C4C22×D312yescomplemented
313C22⋊Dic5—21no—
314C22⋊Dic5—32no—
315C22⋊Dic5—61no—
316C22⋊Dic5C22×D312yescomplemented
317#685—64no—
318#685—64no—
319#683—64no—
320#683—64no—
321C2×H(5,𝔽2)—151no—
322C2×#123—31no—
323C2×#123—151no—
324C2×#123—151no—
325#458—158no—
326C2×#99—51no—
327C2×#99—151no—
328C2×#99—151no—
329C22×C3×C5—22no—
330C22×C3×C5—22no—
331C22×C3×C5—22no—
332C22×C3×C5—41no—
333C22×C3×C5—41no—
334C22×C3×C5—41no—
335C22×C3×C5—41no—
336C22×C3×C5#12011yescharacteristic
337C22×C3×C5#12011yescharacteristic
338C22×C3×C5#12011yescharacteristic
339C22×C3×C5#12011yescharacteristic
340C22×C3×C5C22×D411yescharacteristic
341C22×C3×C5C22×D411yescharacteristic
342C22×C3×C5C22×D411yescharacteristic
343C2×D15—22no—
344C2×D15—42no—
345C2×D15—42no—
346C2×D15—81no—
347C2×C5×D3—22no—
348C2×C5×D3—42no—
349C2×C5×D3—42no—
350C2×C5×D3—81no—
351C2×C3×D5—22no—
352C2×C3×D5—42no—
353C2×C3×D5—42no—
354C2×C3×D5—81no—
355D3×D5—84no—
356C3×C4×C5—42no—
357Dic15—22no—
358Dic15—42no—
359C3×Dic5—22no—
360C3×Dic5—42no—
361C5×Dic3—22no—
362C5×Dic3—42no—
363C24×C3—51no—
364C24×C3C22×D511yescharacteristic
365C23×D3—51no—
366C23×D3—101no—
367C23×D3C22⋊D511yescharacteristic
368C2×C3×D4—52no—
369C2×C3×D4—52no—
370C2×C3×D4—101no—
371C2×C3×D4—101no—
372C2×C3×D4—101no—
373C2×C3×D4—101no—
374C22×C3×C4—21no—
375C22×C3×C4—51no—
376C22×C3×C4—101no—
377C2×#67—21no—
378C2×#67—21no—
379C2×#67—21no—
380C2×#67—21no—
381C2×#67—52no—
382C2×#67—52no—
383C2×#67—101no—
384C2×#67—104no—
385C2×#67—104no—
386C2×#67—101no—
387C2×#67—101no—
388C2×#67—101no—
389C2×#67—101no—
390C2×#67—101no—
391C2×#67C22⋊D512yes—
392C2×#67C22×D512yes—
393C22×Dic3—21no—
394C22×Dic3—21no—
395C22×Dic3—21no—
396C22×Dic3—21no—
397C22×Dic3—21no—
398C22×Dic3—21no—
399C22×Dic3—51no—
400C22×Dic3—101no—
401C22×Dic3—101no—
402C22×Dic3C22⋊D511yescharacteristic
403C22×Dic3C22×D512yescomplemented
404#237—104no—
405#237—104no—
406#237—104no—
407#237—104no—
408D3×D4—104no—
409D3×D4—104no—
410D3×D4—104no—
411D3×D4—104no—
412#235—104no—
413#235—104no—
414C2×D12—101no—
415C2×C4×D3—101no—
416C2×C4×D3—101no—
417C2×Dic6—101no—
418C3×C22⋊C4—21no—
419C3×C22⋊C4—52no—
420C3×C22⋊C4—101no—
421C3×C22⋊C4C22×D512yescomplemented
422#217—52no—
423#217—104no—
424#217—101no—
425(C2×D3)⋊C4—24no—
426(C2×D3)⋊C4—104no—
427C4⋊Dic3—24no—
428C4⋊Dic3—104no—
429Dic3⋊C4—104no—
430C23×C5—32no—
431C23×C5—42no—
432C23×C5—61no—
433C23×C5—61no—
434C23×C5—122no—
435C23×C5C2×D1211yescharacteristic
436C23×C5C2×D1211yescharacteristic
437C23×C5D3×D411yescharacteristic
438C23×C5D3×D411yescharacteristic
439C23×C5D3×D411yescharacteristic
440C23×C5D3×D411yescharacteristic
441C23×C5C23×D311yescharacteristic
442C22×D5—21no—
443C22×D5—21no—
444C22×D5—32no—
445C22×D5—42no—
446C22×D5—64no—
447C22×D5—61no—
448C22×D5—61no—
449C22×D5—122no—
450C22×D5—242no—
451C22×D5C2×D1212yes—
452C5×D4—62no—
453C5×D4—62no—
454C5×D4—62no—
455C5×D4—62no—
456C2×C4×C5—22no—
457C2×C4×C5—32no—
458C2×C4×C5—42no—
459C2×C4×C5—61no—
460C2×C4×C5—61no—
461C2×C4×C5—62no—
462C2×C4×C5—62no—
463C2×C4×C5—62no—
464C2×C4×C5—121no—
465C2×C4×C5—121no—
466C2×C4×C5—121no—
467C2×C4×C5—121no—
468C22⋊D5—22no—
469C22⋊D5—22no—
470C22⋊D5—22no—
471C22⋊D5—22no—
472C22⋊D5—64no—
473C22⋊D5—64no—
474C22⋊D5—62no—
475C22⋊D5—62no—
476C22⋊D5—62no—
477C22⋊D5—62no—
478C2×Dic5—21no—
479C2×Dic5—21no—
480C2×Dic5—22no—
481C2×Dic5—32no—
482C2×Dic5—42no—
483C2×Dic5—64no—
484C2×Dic5—61no—
485C2×Dic5—61no—
486C2×Dic5—62no—
487C2×Dic5—122no—
488C2×Dic5C2×D1212yes—
489D20—64no—
490C4×D5—64no—
491C4×D5—64no—
492Dic10—64no—
493H(5,𝔽2)—154no—
494H(5,𝔽2)—302no—
495H(5,𝔽2)—302no—
496H(5,𝔽2)—302no—
497C2×#41—301no—
498C2×#41—301no—
499C2×#41—301no—
500C22×D4—31no—
501C22×D4—51no—
502C22×D4—151no—
503C22×D4—301no—
504C22×D4—301no—
505C22×D4—301no—
506C23×C4—31no—
507#123—34no—
508#123—62no—
509#123—154no—
510#123—154no—
511#123—302no—
512#123—302no—
513C2×C4⋊C4—61no—
514C2×C4⋊C4—301no—
515C2×C4⋊C4—301no—
516C2×C22⋊C4—51no—
517C2×C22⋊C4—61no—
518C2×C22⋊C4—151no—
519C2×C22⋊C4—301no—
520C2×C22⋊C4—301no—
521C2×C22⋊C4D3×D511yescharacteristic, complemented
522#99—54no—
523#99—154no—
524#99—154no—
525C2×C3×C5—21no—
526C2×C3×C5—21no—
527C2×C3×C5—21no—
528C2×C3×C5—21no—
529C2×C3×C5—21no—
530C2×C3×C5—21no—
531C2×C3×C5#45812yescomplemented
532C2×C3×C5C2×#12011yescharacteristic
533D15—42no—
534C3×D5—42no—
535C5×D3—42no—
536C23×C3—42no—
537C23×C3—52no—
538C23×C3—101no—
539C23×C3—101no—
540C23×C3—202no—
541C23×C3D4×D511yescharacteristic
542C23×C3D4×D511yescharacteristic
543C23×C3D4×D511yescharacteristic
544C23×C3D4×D511yescharacteristic
545C23×C3C2×C22⋊D511yescharacteristic
546C23×C3C2×C22⋊D511yescharacteristic
547C23×C3C23×D511yescharacteristic
548C22×D3—21no—
549C22×D3—21no—
550C22×D3—42no—
551C22×D3—52no—
552C22×D3—104no—
553C22×D3—101no—
554C22×D3—101no—
555C22×D3—202no—
556C22×D3—402no—
557C22×D3C2×C22⋊D512yes—
558C3×D4—102no—
559C3×D4—102no—
560C3×D4—102no—
561C3×D4—102no—
562C2×C3×C4—22no—
563C2×C3×C4—42no—
564C2×C3×C4—52no—
565C2×C3×C4—101no—
566C2×C3×C4—101no—
567C2×C3×C4—102no—
568C2×C3×C4—202no—
569#67—22no—
570#67—22no—
571#67—22no—
572#67—22no—
573#67—104no—
574#67—104no—
575#67—102no—
576#67—102no—
577#67—102no—
578#67—102no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—22no—
582C2×Dic3—22no—
583C2×Dic3—22no—
584C2×Dic3—41no—
585C2×Dic3—41no—
586C2×Dic3—41no—
587C2×Dic3—41no—
588C2×Dic3—52no—
589C2×Dic3—104no—
590C2×Dic3—101no—
591C2×Dic3—101no—
592C2×Dic3—102no—
593C2×Dic3—202no—
594C2×Dic3C2×C22⋊D512yes—
595D12—104no—
596C4×D3—104no—
597C4×D3—104no—
598Dic6—104no—
599C22×C5—22no—
600C22×C5—22no—
601C22×C5—22no—
602C22×C5—41no—
603C22×C5—41no—
604C22×C5—41no—
605C22×C5—41no—
606C22×C5—62no—
607C22×C5—122no—
608C22×C5—122no—
609C22×C5—241no—
610C22×C5#88211yescharacteristic
611C22×C5#88211yescharacteristic
612C22×C5#88211yescharacteristic
613C22×C5#88211yescharacteristic
614C22×C5C22×D1211yescharacteristic
615C22×C5C2×D3×D411yescharacteristic
616C22×C5C2×D3×D411yescharacteristic
617C2×D5—22no—
618C2×D5—42no—
619C2×D5—42no—
620C2×D5—62no—
621C2×D5—81no—
622C2×D5—122no—
623C2×D5—122no—
624C2×D5—244no—
625C2×D5—241no—
626C4×C5—42no—
627C4×C5—62no—
628C4×C5—122no—
629Dic5—22no—
630Dic5—42no—
631Dic5—62no—
632Dic5—122no—
633C24—31no—
634C24—51no—
635C24—151no—
636C24—301no—
637C24C2×D3×D511yescharacteristic
638#41—304no—
639#41—304no—
640#41—304no—
641#41—304no—
642#41—304no—
643#41—304no—
644C2×Q8—301no—
645C2×D4—32no—
646C2×D4—32no—
647C2×D4—52no—
648C2×D4—52no—
649C2×D4—61no—
650C2×D4—61no—
651C2×D4—61no—
652C2×D4—61no—
653C2×D4—101no—
654C2×D4—101no—
655C2×D4—101no—
656C2×D4—101no—
657C2×D4—152no—
658C2×D4—152no—
659C2×D4—301no—
660C2×D4—301no—
661C2×D4—304no—
662C2×D4—304no—
663C2×D4—304no—
664C2×D4—304no—
665C2×D4—304no—
666C2×D4—304no—
667C2×D4—301no—
668C2×D4—301no—
669C2×D4—301no—
670C2×D4—301no—
671C2×D4—301no—
672C22×C4—21no—
673C22×C4—31no—
674C22×C4—32no—
675C22×C4—51no—
676C22×C4—61no—
677C22×C4—61no—
678C22×C4—61no—
679C22×C4—61no—
680C22×C4—61no—
681C22×C4—61no—
682C22×C4—101no—
683C22×C4—151no—
684C22×C4—301no—
685C22×C4—301no—
686C22×C4—301no—
687C22×C4—301no—
688C4⋊C4—64no—
689C4⋊C4—304no—
690C4⋊C4—304no—
691C22⋊C4—21no—
692C22⋊C4—52no—
693C22⋊C4—64no—
694C22⋊C4—101no—
695C22⋊C4—152no—
696C22⋊C4—304no—
697C22⋊C4—304no—
698C22⋊C4—301no—
699C22⋊C4C2×D3×D512yescomplemented
700C3×C5C2×#45811yescharacteristic, complemented, Hall
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—41no—
705C22×C3—41no—
706C22×C3—41no—
707C22×C3—41no—
708C22×C3—102no—
709C22×C3—202no—
710C22×C3—202no—
711C22×C3—401no—
712C22×C3#408311yescharacteristic
713C22×C3#408311yescharacteristic
714C22×C3#408311yescharacteristic
715C22×C3#408311yescharacteristic
716C22×C3C2×D4×D511yescharacteristic
717C22×C3C2×D4×D511yescharacteristic
718C22×C3C22×C22⋊D511yescharacteristic
719C2×D3—22no—
720C2×D3—42no—
721C2×D3—42no—
722C2×D3—81no—
723C2×D3—102no—
724C2×D3—202no—
725C2×D3—202no—
726C2×D3—404no—
727C2×D3—401no—
728C3×C4—42no—
729C3×C4—102no—
730C3×C4—202no—
731Dic3—22no—
732Dic3—42no—
733Dic3—102no—
734Dic3—202no—
735C2×C5—21no—
736C2×C5—21no—
737C2×C5—21no—
738C2×C5—21no—
739C2×C5—21no—
740C2×C5—21no—
741C2×C5—122no—
742C2×C5#474212yescomplemented
743C2×C5C2×#88211yescharacteristic
744D5—42no—
745D5—122no—
746C23—32no—
747C23—42no—
748C23—52no—
749C23—61no—
750C23—61no—
751C23—101no—
752C23—101no—
753C23—122no—
754C23—152no—
755C23—202no—
756C23—304no—
757C23—301no—
758C23—301no—
759C23—602no—
760C23—1202no—
761C23D5×D1211yescharacteristic
762C23D5×D1211yescharacteristic
763C23#677711yescharacteristic
764C23#677711yescharacteristic
765C23D3×C22⋊D511yescharacteristic
766C23D3×C22⋊D511yescharacteristic
767C23C22×D3×D511yescharacteristic
768Q8—304no—
769D4—62no—
770D4—62no—
771D4—62no—
772D4—62no—
773D4—102no—
774D4—102no—
775D4—102no—
776D4—102no—
777D4—304no—
778D4—304no—
779D4—304no—
780D4—302no—
781D4—302no—
782D4—302no—
783D4—302no—
784C2×C4—22no—
785C2×C4—32no—
786C2×C4—42no—
787C2×C4—52no—
788C2×C4—61no—
789C2×C4—61no—
790C2×C4—62no—
791C2×C4—62no—
792C2×C4—62no—
793C2×C4—101no—
794C2×C4—101no—
795C2×C4—102no—
796C2×C4—121no—
797C2×C4—121no—
798C2×C4—121no—
799C2×C4—121no—
800C2×C4—152no—
801C2×C4—202no—
802C2×C4—304no—
803C2×C4—304no—
804C2×C4—304no—
805C2×C4—301no—
806C2×C4—301no—
807C2×C4—302no—
808C2×C4—602no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—202no—
816C2×C3#6534212yescomplemented
817C2×C3C2×#408311yescharacteristic
818D3—42no—
819D3—202no—
820C5C2×#474211yescharacteristic, complemented, Sylow
821C22—22no—
822C22—22no—
823C22—22no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—62no—
829C22—102no—
830C22—122no—
831C22—122no—
832C22—202no—
833C22—202no—
834C22—241no—
835C22—302no—
836C22—401no—
837C22—602no—
838C22—602no—
839C22—1201no—
840C22—1204no—
841C22#9147511yescharacteristic
842C22#9147511yescharacteristic
843C22#9147511yescharacteristic
844C22#9147511yescharacteristic
845C22C2×D5×D1211yescharacteristic
846C22C2×#677711yescharacteristic
847C22C2×D3×C22⋊D511yescharacteristic
848C4—42no—
849C4—62no—
850C4—102no—
851C4—122no—
852C4—202no—
853C4—302no—
854C4—602no—
855C3C2×#6534211yescharacteristic, complemented, Sylow
856C2—21no—
857C2—21no—
858C2—21no—
859C2—21no—
860C2—21no—
861C2—21no—
862C2—122no—
863C2—202no—
864C2—602no—
865C2#1174713512yesdirect product factor
866C2C2×#9147511yescharacteristic
subgroupG/H
centerC22#91475
commutator, cosocleC23×C3×C5C24
FrattiniC23C22×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5#120
prime radicalC2×#92049C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#458
LCSG ▷ C23×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#886C2semidirect
3. C2×#91542C2semidirect
4. C2×#91536C2semidirect
5. C2×#91090C2semidirect
6. C2×C3×#3938C2semidirect
7. C2×#90996C2semidirect
8. #11747135C2direct (N × H)
12. C23×C5×Dic3C22semidirect
24. C2×C3×C5×C22⋊C4C22semidirect
25. C2×#6719C22semidirect
29. C5×#886C22semidirect
30. C2×C3×C22⋊Dic5C22semidirect
33. #91542C22semidirect
37. #91536C22semidirect
39. #91090C22semidirect
40. C3×#3938C22semidirect
41. #90996C22semidirect
50. C2×#3938D3semidirect
78. C22×C5×Dic3C23semidirect
107. C3×C5×C22⋊C4C23semidirect
109. #6719C23semidirect
113. C3×C22⋊Dic5C23semidirect
121. C2×#886D5semidirect
144. C2×C5×C22⋊C4C2×D3semidirect
146. C2×C22⋊Dic5C2×D3semidirect
157. #3938C2×D3semidirect
226. C23×Dic3C2×D5semidirect
237. C2×C3×C22⋊C4C2×D5semidirect
250. #886C2×D5semidirect
312. C5×C22⋊C4C22×D3semidirect
316. C22⋊Dic5C22×D3semidirect
403. C22×Dic3C22×D5semidirect
421. C3×C22⋊C4C22×D5semidirect
521. C2×C22⋊C4D3×D5semidirect
531. C2×C3×C5#458semidirect
699. C22⋊C4C2×D3×D5semidirect
700. C3×C5C2×#458semidirect
742. C2×C5#4742semidirect
816. C2×C3#65342semidirect
820. C5C2×#4742semidirect
855. C3C2×#65342semidirect
865. C2#11747135direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#920492
C2×C5×#8862
C2×#915422
C2×#915362
C2×#910902
C2×C3×#39382
C2×#909962
#117471352
C2×#653423
C2×#47425