Finite Group Databasebeta

← C2×#10614839 #12269383

Subgroups — C2×#10614839 #12269383

Order 1280.

3158 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#126C211yesmaximal, characteristic, complemented
2C22×#4040C211yesmaximal, characteristic, complemented
3#10614839C2116yesmaximal, direct product factor
4C2×#65283C211yesmaximal, characteristic, complemented
5C2×#65269C211yesmaximal, characteristic, complemented
6C2×#65277C211yesmaximal, characteristic, complemented
7C2×#65279C211yesmaximal, characteristic, complemented
8C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
9C2×#65249C211yesmaximal, characteristic
10C2×#65245C211yesmaximal, characteristic, complemented
11C2×#65250C211yesmaximal, characteristic, complemented
12C2×#65246C211yesmaximal, characteristic, complemented
13C2×#65246C211yesmaximal, characteristic, complemented
14C2×#65234C211yesmaximal, characteristic, complemented
15C2×#65229C211yesmaximal, characteristic, complemented
16C2×C4×#685C211yesmaximal, characteristic, complemented
17C23×C22⋊D5C2211yescharacteristic
18C23×C22⋊D5C2211yescharacteristic
19C23×D20C2211yescharacteristic
20C23×C4×D5C2211yescharacteristic
21C2×C5×#126—28no—
22C2×C5×#126C2218yescomplemented
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C4⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C5×C22⋊C4C2211yescharacteristic
29C22×C42×C5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×#685C2211yescharacteristic
33C22×#685C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×#685C2211yescharacteristic
40C22×#685C2211yescharacteristic
41C22×C4⋊Dic5C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×#683C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4040—28no—
49C2×#4040C2218yescomplemented
50C2×#3963C2211yescharacteristic
51C2×#3963C2211yescharacteristic
52C2×#3963C2211yescharacteristic
53C2×#3963C2211yescharacteristic
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56#65283C2218yescomplemented
57#65279C2218yescomplemented
58#65277C2218yescomplemented
59#65269C2218yescomplemented
60C4⋊C4×Dic5C2218yescomplemented
61#65250C2218yescomplemented
62#65249C2218yes—
63#65246C2218yescomplemented
64#65246C2218yescomplemented
65#65245C2218yescomplemented
66#65234C2218yescomplemented
67#65229C2218yescomplemented
68C4×#685C2218yescomplemented
69C2×#2554—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C24×D5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C23×C4×C5C2311yescharacteristic
74C23×C4×C5C2311yescharacteristic
75C23×C4×C5C2311yescharacteristic
76C23×C4×C5C2311yescharacteristic
77C23×C4×C5C2311yescharacteristic
78C23×C4×C5C2311yescharacteristic
79C22×C22⋊D5—24no—
80C22×C22⋊D5—24no—
81C22×C22⋊D5—24no—
82C22×C22⋊D5—42no—
83C22×C22⋊D5—42no—
84C22×C22⋊D5—42no—
85C22×C22⋊D5C2314yes—
86C22×C22⋊D5C2314yes—
87C23×Dic5C2311yescharacteristic
88C23×Dic5C2311yescharacteristic
89C23×Dic5C2311yescharacteristic
90C23×Dic5C2311yescharacteristic
91C23×Dic5C2311yescharacteristic
92C23×Dic5C2311yescharacteristic
93C22×D20—24no—
94C22×D20—24no—
95C22×D20—42no—
96C22×D20C2314yes—
97C22×C4×D5—24no—
98C22×C4×D5—24no—
99C22×C4×D5—42no—
100C22×C4×D5C2314yes—
101C5×#126—232no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4—24no—
104C2×C5×C4⋊C4D418yescomplemented
105C2×C5×C4⋊C4C2314yes—
106C2×C5×C4⋊C4C2314yes—
107C2×C5×C4⋊C4C2314yes—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4—24no—
110C2×C5×C22⋊C4—24no—
111C2×C5×C22⋊C4C2314yes—
112C2×C5×C22⋊C4C2314yes—
113C2×C5×C22⋊C4C2314yes—
114C2×C42×C5—24no—
115C2×C42×C5C2314yes—
116C2×C22⋊Dic5—24no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5C2314yes—
119C2×C22⋊Dic5C2314yes—
120C2×#685—24no—
121C2×#685—24no—
122C2×#685—24no—
123C2×#685—24no—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—42no—
128C2×#685—42no—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×#685C2314yes—
135C2×#685C2314yes—
136C2×#685C2314yes—
137C2×#685C2314yes—
138C2×C4⋊Dic5—24no—
139C2×C4⋊Dic5C2314yes—
140C2×#683—24no—
141C2×#683—42no—
142C2×#683—42no—
143C2×#683C2314yes—
144C2×#683C2314yes—
145C2×#683C2314yes—
146C2×C4×Dic5—24no—
147C2×C4×Dic5—42no—
148C2×C4×Dic5—42no—
149C2×C4×Dic5C2314yes—
150C2×C4×Dic5C2314yes—
151C2×C4×Dic5C2314yes—
152#4040—232no—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126D511yescharacteristic, complemented
160C22×#123—51no—
161#2554—516no—
162C2×#398—51no—
163C2×#396—51no—
164C2×#394—51no—
165C2×#392—51no—
166C2×#390—51no—
167C2×#390—51no—
168C2×#390—51no—
169C2×#388—51no—
170C2×#388—51no—
171C2×#388—51no—
172C2×#386—51no—
173C2×C4×C4⋊C4—51no—
174C2×C4×C22⋊C4—51no—
175C24×C5—22no—
176C24×C5—22no—
177C24×C5—22no—
178C24×C5—22no—
179C24×C5—22no—
180C24×C5—22no—
181C24×C5—22no—
182C24×C5C2412yes—
183C24×C5C2411yescharacteristic
184C23×D5—22no—
185C23×D5—22no—
186C23×D5—22no—
187C23×D5—22no—
188C23×D5—22no—
189C23×D5—22no—
190C23×D5—22no—
191C23×D5—22no—
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5#4114yes—
198C23×D5C2412yes—
199C23×D5C2412yes—
200C22×C4×C5—22no—
201C22×C4×C5—22no—
202C22×C4×C5—22no—
203C22×C4×C5—22no—
204C22×C4×C5—22no—
205C22×C4×C5—22no—
206C22×C4×C5—22no—
207C22×C4×C5—22no—
208C22×C4×C5—22no—
209C22×C4×C5—22no—
210C22×C4×C5—22no—
211C22×C4×C5—22no—
212C22×C4×C5—22no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5C2×D414yes—
216C22×C4×C5C2×D414yes—
217C22×C4×C5C2×D414yes—
218C22×C4×C5C2412yes—
219C22×C4×C5C2412yes—
220C22×C4×C5C2412yes—
221C22×C4×C5C2412yes—
222C22×C4×C5C2412yes—
223C22×C4×C5C2412yes—
224C2×C22⋊D5—28no—
225C2×C22⋊D5—28no—
226C2×C22⋊D5—28no—
227C2×C22⋊D5—44no—
228C2×C22⋊D5—44no—
229C2×C22⋊D5—44no—
230C2×C22⋊D5—416no—
231C2×C22⋊D5—416no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5—22no—
236C22×Dic5—22no—
237C22×Dic5—22no—
238C22×Dic5—22no—
239C22×Dic5—22no—
240C22×Dic5—22no—
241C22×Dic5—22no—
242C22×Dic5—22no—
243C22×Dic5—22no—
244C22×Dic5—22no—
245C22×Dic5—22no—
246C22×Dic5—22no—
247C22×Dic5#4114yes—
248C22×Dic5#4114yes—
249C22×Dic5#4114yes—
250C22×Dic5C2412yes—
251C22×Dic5C2412yes—
252C22×Dic5C2412yes—
253C22×Dic5C2412yes—
254C22×Dic5C2412yes—
255C22×Dic5C2412yes—
256C2×D20—28no—
257C2×D20—28no—
258C2×D20—44no—
259C2×D20—416no—
260C2×C4×D5—28no—
261C2×C4×D5—28no—
262C2×C4×D5—44no—
263C2×C4×D5—416no—
264C5×C4⋊C4—28no—
265C5×C4⋊C4—28no—
266C5×C4⋊C4C2×D4116yescomplemented
267C5×C22⋊C4—28no—
268C5×C22⋊C4—28no—
269C5×C22⋊C4—28no—
270C42×C5—28no—
271C22⋊Dic5—28no—
272C22⋊Dic5—44no—
273#685—28no—
274#685—28no—
275#685—28no—
276#685—28no—
277#685—28no—
278#685—28no—
279#685—28no—
280#685—44no—
281#685—44no—
282C4⋊Dic5—28no—
283#683—28no—
284#683—44no—
285#683—44no—
286C4×Dic5—28no—
287C4×Dic5—44no—
288C4×Dic5—44no—
289C23×D4—51no—
290C23×D4—51no—
291C23×D4—51no—
292C24×C4—51no—
293C2×#126—28no—
294C2×#126C2×D518yescomplemented
295C2×#123—58no—
296C2×#123—108no—
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4C2×D511yescharacteristic
302C22×C4⋊C4C2×D511yescharacteristic
303C22×C4⋊C4C2×D511yescharacteristic
304C22×C22⋊C4—51no—
305C22×C22⋊C4—51no—
306C22×C22⋊C4—51no—
307C22×C22⋊C4—51no—
308C22×C22⋊C4—51no—
309C22×C22⋊C4—51no—
310C22×C22⋊C4—51no—
311C22×C22⋊C4—51no—
312C22×C22⋊C4—51no—
313C22×C22⋊C4—51no—
314C22×C22⋊C4—51no—
315C22×C22⋊C4C2×D511yescharacteristic
316C22×C22⋊C4C2×D511yescharacteristic
317C22×C22⋊C4C2×D511yescharacteristic
318C22×C42—51no—
319C22×C42—51no—
320C22×C42—51no—
321C22×C42C2×D511yescharacteristic
322#398—58no—
323#396—58no—
324#394—58no—
325#392—58no—
326#390—58no—
327#390—58no—
328#390—58no—
329#388—58no—
330#388—58no—
331#388—58no—
332#386—58no—
333C4×C4⋊C4—58no—
334C4×C22⋊C4—58no—
335C2×#95—51no—
336C2×#95—51no—
337C2×#95—51no—
338C2×#95—51no—
339C2×#95—51no—
340C2×#95—51no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—44no—
349C23×C5—44no—
350C23×C5—44no—
351C23×C5—44no—
352C23×C5—44no—
353C23×C5—44no—
354C23×C5—44no—
355C23×C5C22×D412yes—
356C23×C5C2×#4112yes—
357C23×C5C2×#4112yes—
358C23×C5C2×#4112yes—
359C23×C5C2×#4112yes—
360C23×C5H(5,𝔽2)12yes—
361C23×C5H(5,𝔽2)12yes—
362C23×C5C2511yescharacteristic
363C22×D5—28no—
364C22×D5—28no—
365C22×D5—28no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—22no—
370C22×D5—22no—
371C22×D5—22no—
372C22×D5—22no—
373C22×D5—22no—
374C22×D5—22no—
375C22×D5—22no—
376C22×D5—22no—
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—44no—
380C22×D5—44no—
381C22×D5—44no—
382C22×D5—44no—
383C22×D5—44no—
384C22×D5—44no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5C2×#4114yes—
391C2×C4×C5—28no—
392C2×C4×C5—28no—
393C2×C4×C5—28no—
394C2×C4×C5—22no—
395C2×C4×C5—22no—
396C2×C4×C5—22no—
397C2×C4×C5—22no—
398C2×C4×C5—22no—
399C2×C4×C5—22no—
400C2×C4×C5—22no—
401C2×C4×C5—22no—
402C2×C4×C5—22no—
403C2×C4×C5—22no—
404C2×C4×C5—22no—
405C2×C4×C5—22no—
406C2×C4×C5—22no—
407C2×C4×C5—22no—
408C2×C4×C5—22no—
409C2×C4×C5—44no—
410C2×C4×C5—44no—
411C2×C4×C5—44no—
412C2×C4×C5C22×D414yes—
413C2×C4×C5C22×D414yes—
414C2×C4×C5C22×D414yes—
415C22⋊D5—416no—
416C22⋊D5—416no—
417C2×Dic5—28no—
418C2×Dic5—28no—
419C2×Dic5—28no—
420C2×Dic5—22no—
421C2×Dic5—22no—
422C2×Dic5—22no—
423C2×Dic5—22no—
424C2×Dic5—22no—
425C2×Dic5—22no—
426C2×Dic5—22no—
427C2×Dic5—22no—
428C2×Dic5—22no—
429C2×Dic5—22no—
430C2×Dic5—22no—
431C2×Dic5—22no—
432C2×Dic5—22no—
433C2×Dic5—22no—
434C2×Dic5—22no—
435C2×Dic5—44no—
436C2×Dic5—44no—
437C2×Dic5—44no—
438C2×Dic5C2×#4114yes—
439C2×Dic5C2×#4114yes—
440C2×Dic5C2×#4114yes—
441D20—416no—
442C4×D5—416no—
443C25—51no—
444C25—51no—
445C25C22×D511yescharacteristic
446C22×D4—54no—
447C22×D4—54no—
448C22×D4—54no—
449C22×D4—104no—
450C22×D4—104no—
451C22×D4—104no—
452C22×D4—104no—
453C22×D4—104no—
454C22×D4—202no—
455C22×D4—202no—
456C22×D4—202no—
457C22×D4—202no—
458C23×C4—51no—
459C23×C4—51no—
460C23×C4—51no—
461C23×C4—51no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—54no—
465C23×C4—104no—
466C23×C4—104no—
467C23×C4—202no—
468C23×C4C22×D511yescharacteristic
469C23×C4C22×D511yescharacteristic
470C23×C4C22×D511yescharacteristic
471C23×C4C22×D511yescharacteristic
472C23×C4C22×D511yescharacteristic
473C23×C4C22×D511yescharacteristic
474#126—232no—
475#123—1032no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—24no—
478C2×C4⋊C4—54no—
479C2×C4⋊C4—54no—
480C2×C4⋊C4—54no—
481C2×C4⋊C4—54no—
482C2×C4⋊C4—104no—
483C2×C4⋊C4—104no—
484C2×C4⋊C4—202no—
485C2×C4⋊C4—202no—
486C2×C4⋊C4C22⋊D518yescomplemented
487C2×C4⋊C4C22×D514yes—
488C2×C4⋊C4C22×D514yes—
489C2×C4⋊C4C22×D514yes—
490C2×C22⋊C4—24no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—24no—
493C2×C22⋊C4—54no—
494C2×C22⋊C4—54no—
495C2×C22⋊C4—54no—
496C2×C22⋊C4—54no—
497C2×C22⋊C4—54no—
498C2×C22⋊C4—54no—
499C2×C22⋊C4—54no—
500C2×C22⋊C4—54no—
501C2×C22⋊C4—54no—
502C2×C22⋊C4—54no—
503C2×C22⋊C4—54no—
504C2×C22⋊C4—104no—
505C2×C22⋊C4—104no—
506C2×C22⋊C4—104no—
507C2×C22⋊C4—104no—
508C2×C22⋊C4—104no—
509C2×C22⋊C4—104no—
510C2×C22⋊C4—104no—
511C2×C22⋊C4—104no—
512C2×C22⋊C4—202no—
513C2×C22⋊C4—202no—
514C2×C22⋊C4—202no—
515C2×C22⋊C4C22×D514yes—
516C2×C22⋊C4C22×D514yes—
517C2×C22⋊C4C22×D514yes—
518C2×C42—24no—
519C2×C42—54no—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—104no—
523C2×C42—202no—
524C2×C42—202no—
525C2×C42C22×D514yes—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532C22×C5—42no—
533C22×C5—42no—
534C22×C5—42no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—88no—
540C22×C5#52914yes—
541C22×C5#53214yes—
542C22×C5#53814yes—
543C22×C5#54614yes—
544C22×C5#55014yes—
545C22×C5#55114yes—
546C22×C5#55314yes—
547C22×C5C23×D411yescharacteristic
548C22×C5C22×#4111yescharacteristic
549C22×C5C22×#4111yescharacteristic
550C22×C5C22×#4111yescharacteristic
551C22×C5C22×#4111yescharacteristic
552C22×C5C2×H(5,𝔽2)11yescharacteristic
553C22×C5C2×H(5,𝔽2)11yescharacteristic
554C2×D5—24no—
555C2×D5—24no—
556C2×D5—24no—
557C2×D5—42no—
558C2×D5—42no—
559C2×D5—42no—
560C2×D5—42no—
561C2×D5—416no—
562C2×D5—42no—
563C2×D5—42no—
564C2×D5—42no—
565C2×D5—42no—
566C2×D5—42no—
567C2×D5—42no—
568C2×D5—42no—
569C2×D5—88no—
570C4×C5—24no—
571C4×C5—24no—
572C4×C5—24no—
573C4×C5—42no—
574C4×C5—42no—
575C4×C5—42no—
576Dic5—24no—
577Dic5—24no—
578Dic5—24no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—54no—
590C24—52no—
591C24—52no—
592C24—102no—
593C24—102no—
594C24—102no—
595C24—102no—
596C24—102no—
597C24—102no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24—102no—
604C24—102no—
605C24C23×D512yes—
606C24C23×D511yescharacteristic
607C2×D4—108no—
608C2×D4—108no—
609C2×D4—108no—
610C2×D4—108no—
611C2×D4—108no—
612C2×D4—204no—
613C2×D4—2016no—
614C2×D4—204no—
615C2×D4—204no—
616C2×D4—204no—
617C2×D4—2016no—
618C2×D4—2016no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—54no—
635C22×C4—54no—
636C22×C4—54no—
637C22×C4—52no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—52no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—108no—
644C22×C4—102no—
645C22×C4—102no—
646C22×C4—102no—
647C22×C4—102no—
648C22×C4—102no—
649C22×C4—102no—
650C22×C4—102no—
651C22×C4—102no—
652C22×C4—102no—
653C22×C4—102no—
654C22×C4—102no—
655C22×C4—102no—
656C22×C4—102no—
657C22×C4—102no—
658C22×C4—102no—
659C22×C4—108no—
660C22×C4—204no—
661C22×C4—2016no—
662C22×C4C2×C22⋊D514yes—
663C22×C4C2×C22⋊D514yes—
664C22×C4C2×C22⋊D514yes—
665C22×C4C23×D512yes—
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C4⋊C4—28no—
672C4⋊C4—28no—
673C4⋊C4—108no—
674C4⋊C4—108no—
675C4⋊C4—204no—
676C4⋊C4—204no—
677C4⋊C4C2×C22⋊D5116yescomplemented
678C22⋊C4—28no—
679C22⋊C4—28no—
680C22⋊C4—28no—
681C22⋊C4—108no—
682C22⋊C4—108no—
683C22⋊C4—108no—
684C22⋊C4—108no—
685C22⋊C4—108no—
686C22⋊C4—108no—
687C22⋊C4—108no—
688C22⋊C4—108no—
689C22⋊C4—204no—
690C22⋊C4—204no—
691C22⋊C4—204no—
692C42—28no—
693C42—108no—
694C42—204no—
695C42—204no—
696C2×C5—82no—
697C2×C5#255418yescomplemented
698C2×C5C2×#52911yescharacteristic
699C2×C5C2×#53211yescharacteristic
700C2×C5C2×#53811yescharacteristic
701C2×C5C2×#54611yescharacteristic
702C2×C5C2×#55011yescharacteristic
703C2×C5C2×#55111yescharacteristic
704C2×C5C2×#55311yescharacteristic
705D5—44no—
706D5—82no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—44no—
715C23—44no—
716C23—44no—
717C23—44no—
718C23—44no—
719C23—44no—
720C23—44no—
721C23—54no—
722C23—108no—
723C23—102no—
724C23—102no—
725C23—102no—
726C23—102no—
727C23—102no—
728C23—102no—
729C23—108no—
730C23—108no—
731C23—102no—
732C23—102no—
733C23—102no—
734C23—102no—
735C23—102no—
736C23—102no—
737C23—102no—
738C23—204no—
739C23—204no—
740C23—204no—
741C23—204no—
742C23—204no—
743C23—204no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23—204no—
749C23D5×#4112yes—
750C23D5×#4112yes—
751C23D5×#4112yes—
752C23D5×#4112yes—
753C23#414912yes—
754C23#414912yes—
755C23C22×C22⋊D512yes—
756C23C24×D511yescharacteristic
757D4—2016no—
758D4—2016no—
759D4—2016no—
760C2×C4—28no—
761C2×C4—28no—
762C2×C4—28no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—44no—
780C2×C4—44no—
781C2×C4—54no—
782C2×C4—54no—
783C2×C4—54no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—108no—
791C2×C4—108no—
792C2×C4—108no—
793C2×C4—102no—
794C2×C4—102no—
795C2×C4—102no—
796C2×C4—102no—
797C2×C4—102no—
798C2×C4—102no—
799C2×C4—102no—
800C2×C4—102no—
801C2×C4—102no—
802C2×C4—2016no—
803C2×C4—204no—
804C2×C4—204no—
805C2×C4—204no—
806C2×C4C22×C22⋊D514yes—
807C2×C4C22×C22⋊D514yes—
808C2×C4C22×C22⋊D514yes—
809C5C2×#255411yescharacteristic, complemented, Sylow
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—88no—
818C22—104no—
819C22—104no—
820C22—104no—
821C22—202no—
822C22—202no—
823C22—2016no—
824C22—202no—
825C22—202no—
826C22—202no—
827C22—202no—
828C22—202no—
829C22—202no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—408no—
834C22#6603814yes—
835C22#6603914yes—
836C22#6604014yes—
837C22#6604314yes—
838C22#6616314yes—
839C22#6616614yes—
840C22#6616814yes—
841C22C2×D5×#4111yescharacteristic
842C22C2×D5×#4111yescharacteristic
843C22C2×D5×#4111yescharacteristic
844C22C2×D5×#4111yescharacteristic
845C22C2×#414911yescharacteristic
846C22C2×#414911yescharacteristic
847C22C23×C22⋊D511yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—104no—
855C4—104no—
856C4—104no—
857C4—202no—
858C4—202no—
859C4—202no—
860C2—82no—
861C2—204no—
862C2—402no—
863C2#1061483918yesdirect product factor
864C2C2×#6604011yescharacteristic
865C2C2×#6604311yescharacteristic
866C2C2×#6603811yescharacteristic
867C2C2×#6603911yescharacteristic
868C2C2×#6616611yescharacteristic
869C2C2×#6616311yescharacteristic
870C2C2×#6616811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#126C2
socleC24×C5C24
prime radicalC2×#65249C2
hypercenterC22×#126D5
hypocenterC5C2×#2554
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C5×#126C2semidirect
2. C22×#4040C2semidirect
3. #10614839C2direct (N × H)
4. C2×#65283C2semidirect
5. C2×#65269C2semidirect
6. C2×#65277C2semidirect
7. C2×#65279C2semidirect
8. C2×C4⋊C4×Dic5C2semidirect
10. C2×#65245C2semidirect
11. C2×#65250C2semidirect
12. C2×#65246C2semidirect
13. C2×#65246C2semidirect
14. C2×#65234C2semidirect
15. C2×#65229C2semidirect
16. C2×C4×#685C2semidirect
22. C2×C5×#126C22semidirect
49. C2×#4040C22semidirect
56. #65283C22semidirect
57. #65279C22semidirect
58. #65277C22semidirect
59. #65269C22semidirect
60. C4⋊C4×Dic5C22semidirect
61. #65250C22semidirect
63. #65246C22semidirect
64. #65246C22semidirect
65. #65245C22semidirect
66. #65234C22semidirect
67. #65229C22semidirect
68. C4×#685C22semidirect
104. C2×C5×C4⋊C4D4semidirect
159. C22×#126D5semidirect
266. C5×C4⋊C4C2×D4semidirect
294. C2×#126C2×D5semidirect
486. C2×C4⋊C4C22⋊D5semidirect
677. C4⋊C4C2×C22⋊D5semidirect
697. C2×C5#2554semidirect
809. C5C2×#2554semidirect
863. C2#10614839direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1262
C22×#40402
#106148392
C2×#652832
C2×#652692
C2×#652772
C2×#652792
C2×C4⋊C4×Dic52
C2×#652492
C2×#652452
C2×#652502
C2×#652462
C2×#652342
C2×#652292
C2×C4×#6852
C2×#25545