Finite Group Databasebeta

← C2×#10614592 #12269375

Subgroups — C2×#10614592 #12269375

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×#123C211yesmaximal, characteristic, complemented
2C22×#4044C211yesmaximal, characteristic, complemented
3C2×#65512C211yesmaximal, characteristic
4C2×#65510C211yesmaximal, characteristic, complemented
5C2×#65502C211yesmaximal, characteristic, complemented
6C2×C4×C22⋊Dic5C211yesmaximal, characteristic, complemented
7#10614592C2116yesmaximal, direct product factor
8C2×#65272C211yesmaximal, characteristic, complemented
9C2×#65279C211yesmaximal, characteristic, complemented
10C2×C4⋊C4×Dic5C211yesmaximal, characteristic, complemented
11C2×#65237C211yesmaximal, characteristic, complemented
12C2×#65250C211yesmaximal, characteristic, complemented
13C2×#65246C211yesmaximal, characteristic, complemented
14C2×#65246C211yesmaximal, characteristic, complemented
15C2×#65234C211yesmaximal, characteristic, complemented
16C2×#65233C211yesmaximal, characteristic, complemented
17C23×C5×D4C2211yescharacteristic
18C24×C4×C5C2211yescharacteristic
19C23×C22⋊D5C2211yescharacteristic
20C23×C22⋊D5C2211yescharacteristic
21C2×C5×#123—28no—
22C2×C5×#123C2218yescomplemented
23C22×C5×C4⋊C4C2211yescharacteristic
24C22×C5×C4⋊C4C2211yescharacteristic
25C22×C5×C22⋊C4C2211yescharacteristic
26C22×C5×C22⋊C4C2211yescharacteristic
27C22×C5×C22⋊C4C2211yescharacteristic
28C22×C22⋊Dic5C2211yescharacteristic
29C22×C22⋊Dic5C2211yescharacteristic
30C22×C22⋊Dic5C2211yescharacteristic
31C22×C22⋊Dic5C2211yescharacteristic
32C22×C22⋊Dic5C2211yescharacteristic
33C22×C22⋊Dic5C2211yescharacteristic
34C22×#685C2211yescharacteristic
35C22×#685C2211yescharacteristic
36C22×#685C2211yescharacteristic
37C22×#685C2211yescharacteristic
38C22×#685C2211yescharacteristic
39C22×C4⋊Dic5C2211yescharacteristic
40C22×C4⋊Dic5C2211yescharacteristic
41C22×#683C2211yescharacteristic
42C22×#683C2211yescharacteristic
43C22×#683C2211yescharacteristic
44C22×C4×Dic5C2211yescharacteristic
45C22×C4×Dic5C2211yescharacteristic
46C22×C4×Dic5C2211yescharacteristic
47C22×C4×Dic5C2211yescharacteristic
48C2×#4044—28no—
49C2×#4044C2218yescomplemented
50#65512C2218yes—
51#65510C2218yescomplemented
52#65502C2218yescomplemented
53C4×C22⋊Dic5C2218yescomplemented
54C2×#3963C2211yescharacteristic
55C2×#3963C2211yescharacteristic
56C2×#3963C2211yescharacteristic
57C2×#3963C2211yescharacteristic
58C2×#3963C2211yescharacteristic
59C2×#3963C2211yescharacteristic
60#65279C2218yescomplemented
61#65272C2218yescomplemented
62C4⋊C4×Dic5C2218yescomplemented
63#65250C2218yescomplemented
64#65246C2218yescomplemented
65#65246C2218yescomplemented
66#65237C2218yescomplemented
67#65234C2218yescomplemented
68#65233C2218yescomplemented
69C2×#2554—51nomaximal, Sylow
70C25×C5C2311yescharacteristic
71C25×C5C2311yescharacteristic
72C24×D5C2311yescharacteristic
73C22×C5×D4—24no—
74C22×C5×D4—24no—
75C22×C5×D4—42no—
76C22×C5×D4C2314yes—
77C23×C4×C5—24no—
78C23×C4×C5—24no—
79C23×C4×C5—42no—
80C23×C4×C5C2311yescharacteristic
81C23×C4×C5C2311yescharacteristic
82C23×C4×C5C2314yes—
83C23×C4×C5C2311yescharacteristic
84C23×C4×C5C2311yescharacteristic
85C23×C4×C5C2311yescharacteristic
86C22×C22⋊D5—24no—
87C22×C22⋊D5—24no—
88C22×C22⋊D5—24no—
89C22×C22⋊D5—42no—
90C22×C22⋊D5—42no—
91C22×C22⋊D5—42no—
92C22×C22⋊D5C2314yes—
93C22×C22⋊D5C2314yes—
94C23×Dic5C2311yescharacteristic
95C23×Dic5C2311yescharacteristic
96C23×Dic5C2311yescharacteristic
97C23×Dic5C2311yescharacteristic
98C23×Dic5C2311yescharacteristic
99C23×Dic5C2311yescharacteristic
100C23×Dic5C2311yescharacteristic
101C5×#123—232no—
102C2×C5×C4⋊C4—24no—
103C2×C5×C4⋊C4D418yescomplemented
104C2×C5×C4⋊C4C2314yes—
105C2×C5×C4⋊C4C2314yes—
106C2×C5×C22⋊C4—24no—
107C2×C5×C22⋊C4—24no—
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4C2314yes—
110C2×C5×C22⋊C4C2314yes—
111C2×C5×C22⋊C4C2314yes—
112C2×C22⋊Dic5—24no—
113C2×C22⋊Dic5—24no—
114C2×C22⋊Dic5—24no—
115C2×C22⋊Dic5—24no—
116C2×C22⋊Dic5—42no—
117C2×C22⋊Dic5—42no—
118C2×C22⋊Dic5C2314yes—
119C2×C22⋊Dic5C2314yes—
120C2×C22⋊Dic5C2314yes—
121C2×C22⋊Dic5C2314yes—
122C2×C22⋊Dic5C2314yes—
123C2×C22⋊Dic5C2314yes—
124C2×#685—24no—
125C2×#685—24no—
126C2×#685—24no—
127C2×#685—24no—
128C2×#685—42no—
129C2×#685C2314yes—
130C2×#685C2314yes—
131C2×#685C2314yes—
132C2×#685C2314yes—
133C2×#685C2314yes—
134C2×C4⋊Dic5—24no—
135C2×C4⋊Dic5—24no—
136C2×C4⋊Dic5C2314yes—
137C2×C4⋊Dic5C2314yes—
138C2×#683—24no—
139C2×#683—42no—
140C2×#683—42no—
141C2×#683C2314yes—
142C2×#683C2314yes—
143C2×#683C2314yes—
144C2×C4×Dic5—24no—
145C2×C4×Dic5—24no—
146C2×C4×Dic5—42no—
147C2×C4×Dic5—42no—
148C2×C4×Dic5C2314yes—
149C2×C4×Dic5C2314yes—
150C2×C4×Dic5C2314yes—
151C2×C4×Dic5C2314yes—
152#4044—232no—
153#3963C2314yes—
154#3963C2314yes—
155#3963C2314yes—
156#3963C2314yes—
157#3963C2314yes—
158#3963C2314yes—
159C22×#126—51no—
160C22×#123D511yescharacteristic, complemented
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×C5—22no—
183C24×C5—22no—
184C24×C5—22no—
185C24×C5—22no—
186C24×C5—22no—
187C24×C5—22no—
188C24×C5#4114yes—
189C24×C5C2412yes—
190C24×C5C2412yes—
191C24×C5C2411yescharacteristic
192C23×D5—22no—
193C23×D5—22no—
194C23×D5—22no—
195C23×D5—22no—
196C23×D5—22no—
197C23×D5—22no—
198C23×D5—22no—
199C23×D5C2412yes—
200C2×C5×D4—28no—
201C2×C5×D4—28no—
202C2×C5×D4—44no—
203C2×C5×D4—416no—
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—28no—
213C22×C4×C5—22no—
214C22×C4×C5—22no—
215C22×C4×C5—22no—
216C22×C4×C5—22no—
217C22×C4×C5—28no—
218C22×C4×C5—44no—
219C22×C4×C5—416no—
220C22×C4×C5C2×D414yes—
221C22×C4×C5C2×D414yes—
222C22×C4×C5C2×D414yes—
223C22×C4×C5C2412yes—
224C22×C4×C5C2412yes—
225C22×C4×C5C2412yes—
226C22×C4×C5C2412yes—
227C22×C4×C5C2412yes—
228C2×C22⋊D5—28no—
229C2×C22⋊D5—28no—
230C2×C22⋊D5—28no—
231C2×C22⋊D5—44no—
232C2×C22⋊D5—44no—
233C2×C22⋊D5—44no—
234C2×C22⋊D5—416no—
235C2×C22⋊D5—416no—
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—22no—
248C22×Dic5—22no—
249C22×Dic5—22no—
250C22×Dic5—22no—
251C22×Dic5—22no—
252C22×Dic5—22no—
253C22×Dic5—22no—
254C22×Dic5#4114yes—
255C22×Dic5#4114yes—
256C22×Dic5#4114yes—
257C22×Dic5C2412yes—
258C22×Dic5C2412yes—
259C22×Dic5C2412yes—
260C22×Dic5C2412yes—
261C22×Dic5C2412yes—
262C22×Dic5C2412yes—
263C22×Dic5C2412yes—
264C5×C4⋊C4—28no—
265C5×C4⋊C4C2×D4116yescomplemented
266C5×C22⋊C4—28no—
267C5×C22⋊C4—28no—
268C5×C22⋊C4—28no—
269C22⋊Dic5—28no—
270C22⋊Dic5—28no—
271C22⋊Dic5—28no—
272C22⋊Dic5—28no—
273C22⋊Dic5—44no—
274C22⋊Dic5—44no—
275#685—28no—
276#685—28no—
277#685—28no—
278#685—28no—
279#685—44no—
280C4⋊Dic5—28no—
281C4⋊Dic5—28no—
282#683—28no—
283#683—44no—
284#683—44no—
285C4×Dic5—28no—
286C4×Dic5—28no—
287C4×Dic5—44no—
288C4×Dic5—44no—
289C23×D4—51no—
290C23×D4—51no—
291C23×D4C2×D511yescharacteristic
292C24×C4C2×D511yescharacteristic
293C2×#126—58no—
294C2×#126—108no—
295C2×#123—28no—
296C2×#123C2×D518yescomplemented
297C22×C4⋊C4—51no—
298C22×C4⋊C4—51no—
299C22×C4⋊C4—51no—
300C22×C4⋊C4—51no—
301C22×C4⋊C4—51no—
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×C42—51no—
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—28no—
342C23×C5—28no—
343C23×C5—28no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—22no—
348C23×C5—22no—
349C23×C5—22no—
350C23×C5—22no—
351C23×C5—22no—
352C23×C5—22no—
353C23×C5—22no—
354C23×C5—22no—
355C23×C5—22no—
356C23×C5—22no—
357C23×C5—44no—
358C23×C5—44no—
359C23×C5—44no—
360C23×C5—44no—
361C23×C5—44no—
362C23×C5—44no—
363C23×C5—44no—
364C23×C5—44no—
365C23×C5—44no—
366C23×C5—44no—
367C23×C5—44no—
368C23×C5C22×D412yes—
369C23×C5C2×#4114yes—
370C23×C5C2×#4112yes—
371C23×C5C2×#4112yes—
372C23×C5C2×#4112yes—
373C23×C5C2×#4112yes—
374C23×C5H(5,𝔽2)12yes—
375C23×C5H(5,𝔽2)12yes—
376C23×C5C2511yescharacteristic
377C22×D5—22no—
378C22×D5—22no—
379C22×D5—22no—
380C22×D5—22no—
381C22×D5—22no—
382C22×D5—22no—
383C22×D5—22no—
384C22×D5—44no—
385C22×D5—44no—
386C22×D5—44no—
387C22×D5—44no—
388C22×D5—44no—
389C22×D5—44no—
390C22×D5—44no—
391C5×D4—416no—
392C2×C4×C5—28no—
393C2×C4×C5—28no—
394C2×C4×C5—28no—
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—416no—
408C2×C4×C5—44no—
409C2×C4×C5—44no—
410C2×C4×C5C22×D414yes—
411C2×C4×C5C22×D414yes—
412C2×C4×C5C22×D414yes—
413C22⋊D5—416no—
414C22⋊D5—416no—
415C2×Dic5—28no—
416C2×Dic5—28no—
417C2×Dic5—28no—
418C2×Dic5—22no—
419C2×Dic5—22no—
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—22no—
436C2×Dic5—44no—
437C2×Dic5—44no—
438C2×Dic5—44no—
439C2×Dic5—44no—
440C2×Dic5C2×#4114yes—
441C2×Dic5C2×#4114yes—
442C2×Dic5C2×#4114yes—
443C25—51no—
444C25C22×D511yescharacteristic
445C25C22×D511yescharacteristic
446C22×D4—24no—
447C22×D4—24no—
448C22×D4—42no—
449C22×D4—54no—
450C22×D4—54no—
451C22×D4—104no—
452C22×D4—104no—
453C22×D4—104no—
454C22×D4—202no—
455C22×D4—202no—
456C22×D4—202no—
457C22×D4C22×D514yes—
458C23×C4—24no—
459C23×C4—24no—
460C23×C4—42no—
461C23×C4—51no—
462C23×C4—51no—
463C23×C4—51no—
464C23×C4—51no—
465C23×C4—51no—
466C23×C4—51no—
467C23×C4—51no—
468C23×C4C22×D511yescharacteristic
469C23×C4C22×D511yescharacteristic
470C23×C4C22×D514yes—
471C23×C4C22×D511yescharacteristic
472C23×C4C22×D511yescharacteristic
473C23×C4C22×D511yescharacteristic
474#126—1032no—
475#123—232no—
476C2×C4⋊C4—24no—
477C2×C4⋊C4—54no—
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—104no—
485C2×C4⋊C4—202no—
486C2×C4⋊C4—202no—
487C2×C4⋊C4C22⋊D518yescomplemented
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—54no—
519C2×C42—54no—
520C2×C42—54no—
521C2×C42—54no—
522C2×C42—104no—
523C2×C42—104no—
524C2×C42—202no—
525C2×C42—202no—
526#95—54no—
527#95—54no—
528#95—54no—
529#95—54no—
530#95—54no—
531#95—54no—
532C22×C5—24no—
533C22×C5—24no—
534C22×C5—24no—
535C22×C5—42no—
536C22×C5—42no—
537C22×C5—42no—
538C22×C5—42no—
539C22×C5—416no—
540C22×C5—42no—
541C22×C5—42no—
542C22×C5—42no—
543C22×C5—42no—
544C22×C5—42no—
545C22×C5—42no—
546C22×C5—42no—
547C22×C5—88no—
548C22×C5#52914yes—
549C22×C5#53214yes—
550C22×C5#53814yes—
551C22×C5#54614yes—
552C22×C5#55014yes—
553C22×C5#55114yes—
554C22×C5#55314yes—
555C22×C5C23×D411yescharacteristic
556C22×C5C22×#4111yescharacteristic
557C22×C5C22×#4111yescharacteristic
558C22×C5C22×#4111yescharacteristic
559C22×C5C22×#4111yescharacteristic
560C22×C5C2×H(5,𝔽2)11yescharacteristic
561C22×C5C2×H(5,𝔽2)11yescharacteristic
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—
575Dic5—24no—
576Dic5—24no—
577Dic5—24no—
578Dic5—42no—
579Dic5—42no—
580Dic5—42no—
581Dic5—42no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—52no—
596C24—102no—
597C24—102no—
598C24—102no—
599C24—102no—
600C24—102no—
601C24—102no—
602C24—102no—
603C24#71114yes—
604C24C23×D512yes—
605C24C23×D512yes—
606C24C23×D511yescharacteristic
607C2×D4—28no—
608C2×D4—28no—
609C2×D4—44no—
610C2×D4—416no—
611C2×D4—108no—
612C2×D4—108no—
613C2×D4—108no—
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—28no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—28no—
633C22×C4—44no—
634C22×C4—416no—
635C22×C4—54no—
636C22×C4—54no—
637C22×C4—54no—
638C22×C4—52no—
639C22×C4—52no—
640C22×C4—52no—
641C22×C4—52no—
642C22×C4—52no—
643C22×C4—52no—
644C22×C4—52no—
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—102no—
660C22×C4—102no—
661C22×C4—102no—
662C22×C4—102no—
663C22×C4C2×C22⋊D514yes—
664C22×C4C2×C22⋊D514yes—
665C22×C4C2×C22⋊D514yes—
666C22×C4C23×D512yes—
667C22×C4C23×D512yes—
668C22×C4C23×D512yes—
669C22×C4C23×D512yes—
670C22×C4C23×D512yes—
671C4⋊C4—28no—
672C4⋊C4—108no—
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—108no—
693C42—108no—
694C42—204no—
695C42—204no—
696C2×C5—44no—
697C2×C5—82no—
698C2×C5#255418yescomplemented
699C2×C5C2×#52911yescharacteristic
700C2×C5C2×#53211yescharacteristic
701C2×C5C2×#53811yescharacteristic
702C2×C5C2×#54611yescharacteristic
703C2×C5C2×#55011yescharacteristic
704C2×C5C2×#55111yescharacteristic
705C2×C5C2×#55311yescharacteristic
706D5—82no—
707C23—28no—
708C23—28no—
709C23—28no—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—22no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—44no—
724C23—44no—
725C23—44no—
726C23—44no—
727C23—44no—
728C23—44no—
729C23—44no—
730C23—44no—
731C23—44no—
732C23—44no—
733C23—44no—
734C23—102no—
735C23—102no—
736C23—102no—
737C23—102no—
738C23—102no—
739C23—102no—
740C23—102no—
741C23—204no—
742C23—204no—
743C23—204no—
744C23—204no—
745C23—204no—
746C23—204no—
747C23—204no—
748C23C2×#71114yes—
749C23C2×#71112yes—
750C23#414412yes—
751C23D5×#4112yes—
752C23D5×#4112yes—
753C23D5×#4112yes—
754C23#414912yes—
755C23C22×C22⋊D512yes—
756C23C24×D511yescharacteristic
757D4—416no—
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—416no—
776C2×C4—44no—
777C2×C4—44no—
778C2×C4—54no—
779C2×C4—54no—
780C2×C4—54no—
781C2×C4—108no—
782C2×C4—108no—
783C2×C4—108no—
784C2×C4—102no—
785C2×C4—102no—
786C2×C4—102no—
787C2×C4—102no—
788C2×C4—102no—
789C2×C4—102no—
790C2×C4—102no—
791C2×C4—102no—
792C2×C4—102no—
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—204no—
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—24no—
811C22—24no—
812C22—24no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—416no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—88no—
826C22—202no—
827C22—202no—
828C22—202no—
829C22—202no—
830C22—202no—
831C22—202no—
832C22—202no—
833C22—408no—
834C22#6598314yes—
835C22#6599114yes—
836C22#6599214yes—
837C22#6599514yes—
838C22#6614014yes—
839C22#6616614yes—
840C22#6616814yes—
841C22C22×#71111yescharacteristic
842C22C2×#414411yescharacteristic
843C22C2×D5×#4111yescharacteristic
844C22C2×D5×#4111yescharacteristic
845C22C2×D5×#4111yescharacteristic
846C22C2×#414911yescharacteristic
847C22C23×C22⋊D511yescharacteristic
848C4—24no—
849C4—24no—
850C4—24no—
851C4—42no—
852C4—42no—
853C4—104no—
854C4—104no—
855C4—104no—
856C4—202no—
857C4—202no—
858C4—202no—
859C4—202no—
860C2—44no—
861C2—82no—
862C2—402no—
863C2#1061459218yesdirect product factor
864C2C2×#6598311yescharacteristic
865C2C2×#6599511yescharacteristic
866C2C2×#6599111yescharacteristic
867C2C2×#6599211yescharacteristic
868C2C2×#6614011yescharacteristic
869C2C2×#6616611yescharacteristic
870C2C2×#6616811yescharacteristic
subgroupG/H
centerC24C23×D5
commutator, cosocleC23×C5C25
FrattiniC23C24×D5
FittingC22×C5×#123C2
socleC24×C5C24
prime radicalC2×#65512C2
hypercenterC22×#123D5
hypocenterC5C2×#2554
LCSG ▷ C23×C5 ▷ C5
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C5×#123C2semidirect
2. C22×#4044C2semidirect
4. C2×#65510C2semidirect
5. C2×#65502C2semidirect
6. C2×C4×C22⋊Dic5C2semidirect
7. #10614592C2direct (N × H)
8. C2×#65272C2semidirect
9. C2×#65279C2semidirect
10. C2×C4⋊C4×Dic5C2semidirect
11. C2×#65237C2semidirect
12. C2×#65250C2semidirect
13. C2×#65246C2semidirect
14. C2×#65246C2semidirect
15. C2×#65234C2semidirect
16. C2×#65233C2semidirect
22. C2×C5×#123C22semidirect
49. C2×#4044C22semidirect
51. #65510C22semidirect
52. #65502C22semidirect
53. C4×C22⋊Dic5C22semidirect
60. #65279C22semidirect
61. #65272C22semidirect
62. C4⋊C4×Dic5C22semidirect
63. #65250C22semidirect
64. #65246C22semidirect
65. #65246C22semidirect
66. #65237C22semidirect
67. #65234C22semidirect
68. #65233C22semidirect
103. C2×C5×C4⋊C4D4semidirect
160. C22×#123D5semidirect
265. C5×C4⋊C4C2×D4semidirect
296. C2×#123C2×D5semidirect
487. C2×C4⋊C4C22⋊D5semidirect
677. C4⋊C4C2×C22⋊D5semidirect
698. C2×C5#2554semidirect
809. C5C2×#2554semidirect
863. C2#10614592direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#1232
C22×#40442
C2×#655122
C2×#655102
C2×#655022
C2×C4×C22⋊Dic52
#106145922
C2×#652722
C2×#652792
C2×C4⋊C4×Dic52
C2×#652372
C2×#652502
C2×#652462
C2×#652342
C2×#652332
C2×#25545