Finite Group Databasebeta

← C4×D5⋊#99 #13033338

Subgroups — C4×D5⋊#99 #13033338

Order 1280.

2242 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D4×D5C211yesmaximal, characteristic
2C2×D5⋊#99C212yesmaximal
3C2×C4×C22⋊AGL(1,𝔽5)C212yesmaximal, complemented
4C4×#4011C212yesmaximal, complemented
5#10604305C212yesmaximal, complemented
6#10604216C212yesmaximal, complemented
7#10604214C212yesmaximal, complemented
8C4×#3999C212yesmaximal, complemented
9C22×D4×D5C2211yescharacteristic
10C23×C4×D5C411yescharacteristic, complemented
11C23×C4×D5C2211yescharacteristic
12C22×C22⋊AGL(1,𝔽5)C2214yes—
13C22×C4×AGL(1,𝔽5)—22no—
14C2×C4×C5×D4C411yescharacteristic, complemented
15C2×D4×Dic5C411yescharacteristic, complemented
16C2×C4×C22⋊D5C411yescharacteristic, complemented
17C2×C4×C22⋊D5C2211yescharacteristic
18C4×D4×D5—22no—
19C4×D4×D5—22no—
20C4×D4×D5—22no—
21C4×D4×D5—22no—
22C2×#4039C2211yescharacteristic
23C2×D5×C4⋊C4C411yescharacteristic, complemented
24C2×#4027C411yescharacteristic, complemented
25C2×#4027C2211yescharacteristic
26C2×D5×C22⋊C4C411yescharacteristic, complemented
27C2×D5×C22⋊C4C2211yescharacteristic
28C2×C4×D20C2211yescharacteristic
29C2×C42×D5C411yescharacteristic, complemented
30C2×#4011C2214yes—
31D5⋊#99C4116yesdirect product factor
32C4×C22⋊AGL(1,𝔽5)—22no—
33C4×C22⋊AGL(1,𝔽5)—22no—
34C4×C22⋊AGL(1,𝔽5)C2214yescomplemented
35C4×C22⋊AGL(1,𝔽5)C2214yescomplemented
36C2×(C2×AGL(1,𝔽5))⋊C4—22no—
37C2×#3999C2214yes—
38#64917C2214yescomplemented
39#64917C2214yescomplemented
40C2×C4×#99—51nomaximal, Sylow
41C24×D5C2×C411yescharacteristic
42C24×D5C2311yescharacteristic
43C23×AGL(1,𝔽5)—24no—
44C22×C5×D4C2×C411yescharacteristic
45C23×C4×C5C2×C411yescharacteristic
46C23×C4×C5C2×C411yescharacteristic, complemented
47C22×C22⋊D5C2×C411yescharacteristic
48C22×C22⋊D5C2311yescharacteristic
49C23×Dic5C2×C411yescharacteristic
50C23×Dic5C2×C411yescharacteristic, complemented
51C2×D4×D5—22no—
52C2×D4×D5—22no—
53C2×D4×D5—24no—
54C2×D4×D5C2×C418yes—
55C22×D20C2311yescharacteristic
56C22×C4×D5—21no—
57C22×C4×D5—21no—
58C22×C4×D5—21no—
59C22×C4×D5—21no—
60C22×C4×D5—44no—
61C22×C4×D5—44no—
62C22×C4×D5C2×C411yescharacteristic
63C22×C4×D5C2×C411yescharacteristic
64C22×C4×D5C2×C411yescharacteristic
65C22×C4×D5C2×C411yescharacteristic
66C22×C4×D5C2×C411yescharacteristic
67C22×C4×D5C2×C411yescharacteristic, complemented
68C22×C4×D5C2×C411yescharacteristic, complemented
69C22×C4×D5D412yes—
70C22×C4×D5D412yes—
71C22×C4×D5D412yes—
72C22×C4×D5D412yes—
73C22×C4×D5C2311yescharacteristic
74C22×C4×D5C2311yescharacteristic
75C2×C22⋊AGL(1,𝔽5)—24no—
76C2×C22⋊AGL(1,𝔽5)—28no—
77C2×C22⋊AGL(1,𝔽5)C2×C4116yescomplemented
78C2×C22⋊AGL(1,𝔽5)C2318yes—
79C2×C4×AGL(1,𝔽5)—24no—
80C2×C4×AGL(1,𝔽5)—24no—
81C2×C4×AGL(1,𝔽5)—48no—
82C4×C5×D4—22no—
83C4×C5×D4—22no—
84C2×C5×C4⋊C4C2×C411yescharacteristic, complemented
85C2×C5×C22⋊C4C2×C411yescharacteristic
86C2×C5×C22⋊C4C2×C411yescharacteristic, complemented
87C2×C42×C5C2×C411yescharacteristic, complemented
88C2×C22⋊Dic5C2×C411yescharacteristic
89C2×C22⋊Dic5C2×C411yescharacteristic, complemented
90D4×Dic5—22no—
91D4×Dic5—22no—
92C4×C22⋊D5—22no—
93C4×C22⋊D5—22no—
94C4×C22⋊D5—22no—
95C4×C22⋊D5—22no—
96C2×#685C2×C411yescharacteristic, complemented
97C2×#685C2×C411yescharacteristic, complemented
98C2×#685C2311yescharacteristic
99C2×#685C2311yescharacteristic
100C2×C4⋊Dic5C2×C411yescharacteristic, complemented
101C2×#683C2×C411yescharacteristic, complemented
102C2×#683C2×C411yescharacteristic, complemented
103C2×C4×Dic5C2×C411yescharacteristic, complemented
104C2×C4×Dic5C2×C411yescharacteristic, complemented
105C2×C4×Dic5C2×C411yescharacteristic, complemented
106#4039—22no—
107#4039—22no—
108D5×C4⋊C4—22no—
109D5×C4⋊C4—22no—
110#4027—22no—
111#4027—22no—
112#4027—22no—
113#4027—22no—
114D5×C22⋊C4—22no—
115D5×C22⋊C4—22no—
116D5×C22⋊C4—22no—
117D5×C22⋊C4—22no—
118C4×D20—22no—
119C4×D20—22no—
120C42×D5—21no—
121C42×D5—21no—
122C42×D5—21no—
123C42×D5—21no—
124#4011C2×C4116yescomplemented
125(C2×AGL(1,𝔽5))⋊C4—24no—
126(C2×AGL(1,𝔽5))⋊C4—24no—
127#3999C2×C4116yescomplemented
128C22×C4×D4—51no—
129C22×#99—52no—
130C2×C4×C22⋊C4—52no—
131C4×#99—52no—
132C4×#99—52no—
133C4×#99—52no—
134C4×#99—52no—
135C2×#342—52no—
136C24×C5C22×C411yescharacteristic
137C24×C5C22×C411yescharacteristic
138C23×D5—21no—
139C23×D5—21no—
140C23×D5—22no—
141C23×D5—42no—
142C23×D5—42no—
143C23×D5—42no—
144C23×D5—42no—
145C23×D5C4214yescomplemented
146C23×D5C22×C411yescharacteristic
147C23×D5C22×C411yescharacteristic
148C23×D5C22×C414yes—
149C23×D5C2×D412yes—
150C23×D5C2×D412yes—
151C23×D5#4114yes—
152C23×D5C2411yescharacteristic
153C22×AGL(1,𝔽5)—216no—
154C22×AGL(1,𝔽5)—28no—
155C22×AGL(1,𝔽5)—48no—
156C22×AGL(1,𝔽5)—48no—
157C2×C5×D4—22no—
158C2×C5×D4—22no—
159C2×C5×D4C4214yescomplemented
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—42no—
163C22×C4×C5—42no—
164C22×C4×C5C22⋊C412yes—
165C22×C4×C5C22⋊C412yes—
166C22×C4×C5C22×C411yescharacteristic
167C22×C4×C5C22×C411yescharacteristic
168C22×C4×C5C22×C411yescharacteristic
169C22×C4×C5C22×C411yescharacteristic
170C22×C4×C5C22×C411yescharacteristic
171C2×C22⋊D5—22no—
172C2×C22⋊D5—22no—
173C2×C22⋊D5—22no—
174C2×C22⋊D5—22no—
175C2×C22⋊D5C4214yescomplemented
176C2×C22⋊D5C22×C414yes—
177C22×Dic5—21no—
178C22×Dic5—21no—
179C22×Dic5—42no—
180C22×Dic5—42no—
181C22×Dic5C22⋊C412yes—
182C22×Dic5C22⋊C412yes—
183C22×Dic5C22×C411yescharacteristic
184C22×Dic5C22×C411yescharacteristic
185C22×Dic5C22×C411yescharacteristic
186C22×Dic5C22×C411yescharacteristic
187C22×Dic5C22×C411yescharacteristic
188D4×D5—216no—
189D4×D5—216no—
190C2×D20—22no—
191C2×D20—22no—
192C2×D20C22×C414yes—
193C2×C4×D5—21no—
194C2×C4×D5—21no—
195C2×C4×D5—22no—
196C2×C4×D5—28no—
197C2×C4×D5—24no—
198C2×C4×D5—21no—
199C2×C4×D5—21no—
200C2×C4×D5—21no—
201C2×C4×D5—21no—
202C2×C4×D5—21no—
203C2×C4×D5—21no—
204C2×C4×D5—21no—
205C2×C4×D5—21no—
206C2×C4×D5—44no—
207C2×C4×D5—42no—
208C2×C4×D5—44no—
209C2×C4×D5—42no—
210C2×C4×D5—42no—
211C2×C4×D5—44no—
212C2×C4×D5—44no—
213C2×C4×D5—44no—
214C2×C4×D5—44no—
215C2×C4×D5—44no—
216C2×C4×D5—42no—
217C2×C4×D5—42no—
218C2×C4×D5—42no—
219C2×C4×D5—42no—
220C2×C4×D5C4214yescomplemented
221C2×C4×D5C22⋊C411yescharacteristic
222C2×C4×D5C22⋊C411yescharacteristic
223C2×C4×D5C22⋊C411yescharacteristic
224C2×C4×D5C22⋊C412yes—
225C2×C4×D5C22⋊C412yes—
226C2×C4×D5C22⋊C411yescharacteristic
227C2×C4×D5C2×D412yes—
228C2×C4×D5C2×D412yes—
229C2×C4×D5C2×D412yes—
230C2×C4×D5C2×D412yes—
231C22⋊AGL(1,𝔽5)—216no—
232C22⋊AGL(1,𝔽5)—28no—
233C22⋊AGL(1,𝔽5)C22×C4116yescomplemented
234C4×AGL(1,𝔽5)—48no—
235C4×AGL(1,𝔽5)—48no—
236C5×C4⋊C4—22no—
237C5×C22⋊C4—22no—
238C5×C22⋊C4—22no—
239C42×C5—21no—
240C42×C5—21no—
241C22⋊Dic5—22no—
242C22⋊Dic5—22no—
243#685—22no—
244#685—22no—
245#685—22no—
246#685—22no—
247C4⋊Dic5—22no—
248#683—22no—
249#683—22no—
250C4×Dic5—21no—
251C4×Dic5—21no—
252C4×Dic5—21no—
253C4×Dic5—21no—
254C4×Dic5—21no—
255C4×Dic5—21no—
256C23×D4—51no—
257C24×C4—51no—
258C24×C4—51no—
259C2×C4×D4—51no—
260C2×C4×D4—51no—
261C2×C4×D4—51no—
262C2×C4×D4—51no—
263C2×C4×D4—51no—
264C2×C4×D4—51no—
265C2×C4×D4—51no—
266C2×C4×D4—102no—
267C2×C4×D4—102no—
268C2×C4×D4—102no—
269C2×C4×D4—102no—
270C2×C4×D4AGL(1,𝔽5)11yescharacteristic, complemented
271C22×C4⋊C4—51no—
272C22×C22⋊C4—54no—
273C22×C22⋊C4—51no—
274C22×C22⋊C4—51no—
275C22×C42—51no—
276C22×C42—102no—
277C2×#99—54no—
278C2×#99—54no—
279C2×#99—516no—
280C4×C22⋊C4—54no—
281C4×C22⋊C4—54no—
282C4×C22⋊C4—102no—
283C4×C22⋊C4—102no—
284C2×#95—102no—
285#342—54no—
286#342—54no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—41no—
290C23×C5—41no—
291C23×C5—41no—
292C23×C5—41no—
293C23×C5C2×C4212yes—
294C23×C5C2×C4212yescomplemented
295C23×C5C2×C22⋊C412yes—
296C23×C5#11712yes—
297C23×C5C23×C411yescharacteristic
298C22×D5—22no—
299C22×D5—24no—
300C22×D5—22no—
301C22×D5—24no—
302C22×D5—21no—
303C22×D5—21no—
304C22×D5—24no—
305C22×D5—24no—
306C22×D5—48no—
307C22×D5—48no—
308C22×D5—42no—
309C22×D5—41no—
310C22×D5—42no—
311C22×D5—41no—
312C22×D5—42no—
313C22×D5—42no—
314C22×D5—48no—
315C22×D5—48no—
316C22×D5—42no—
317C22×D5—42no—
318C22×D5—41no—
319C22×D5—41no—
320C22×D5C2×C4212yes—
321C22×D5C2×C4212yescomplemented
322C22×D5C2×C22⋊C411yescharacteristic
323C22×D5C2×C22⋊C411yescharacteristic
324C22×D5#11712yes—
325C22×D5C4×D418yes—
326C22×D5C4×D418yes—
327C22×D5C23×C412yes—
328C22×D5C22×D412yes—
329C22×D5C2×#4112yes—
330C2×AGL(1,𝔽5)—216no—
331C2×AGL(1,𝔽5)—48no—
332C2×AGL(1,𝔽5)—48no—
333C2×AGL(1,𝔽5)—432no—
334C5×D4—28no—
335C2×C4×C5—21no—
336C2×C4×C5—21no—
337C2×C4×C5—22no—
338C2×C4×C5—24no—
339C2×C4×C5—21no—
340C2×C4×C5—21no—
341C2×C4×C5—42no—
342C2×C4×C5—41no—
343C2×C4×C5—42no—
344C2×C4×C5—42no—
345C2×C4×C5—41no—
346C2×C4×C5—41no—
347C2×C4×C5C2×C4212yescomplemented
348C2×C4×C5C2×C22⋊C411yescharacteristic
349C2×C4×C5C2×C22⋊C412yes—
350C2×C4×C5C2×C22⋊C411yescharacteristic
351C22⋊D5—28no—
352C22⋊D5—28no—
353C2×Dic5—21no—
354C2×Dic5—21no—
355C2×Dic5—22no—
356C2×Dic5—24no—
357C2×Dic5—21no—
358C2×Dic5—21no—
359C2×Dic5—42no—
360C2×Dic5—41no—
361C2×Dic5—42no—
362C2×Dic5—42no—
363C2×Dic5—41no—
364C2×Dic5—41no—
365C2×Dic5C2×C4212yescomplemented
366C2×Dic5C2×C22⋊C411yescharacteristic
367C2×Dic5C2×C22⋊C412yes—
368C2×Dic5C2×C22⋊C411yescharacteristic
369D20—28no—
370C4×D5—24no—
371C4×D5—24no—
372C4×D5—22no—
373C4×D5—24no—
374C4×D5—24no—
375C4×D5—22no—
376C4×D5—24no—
377C4×D5—22no—
378C4×D5—42no—
379C4×D5—42no—
380C4×D5—42no—
381C4×D5—42no—
382C4×D5—42no—
383C4×D5—42no—
384C4×D5—42no—
385C4×D5—42no—
386C4×D5—42no—
387C4×D5—42no—
388C4×D5—42no—
389C4×D5#9914yescomplemented
390C25—51no—
391C25—51no—
392C22×D4—51no—
393C22×D4—51no—
394C22×D4—58no—
395C22×D4—51no—
396C22×D4—102no—
397C22×D4—102no—
398C22×D4—104no—
399C22×D4C2×AGL(1,𝔽5)11yescharacteristic
400C23×C4—51no—
401C23×C4—52no—
402C23×C4—51no—
403C23×C4—51no—
404C23×C4—52no—
405C23×C4—52no—
406C23×C4—52no—
407C23×C4—51no—
408C23×C4—51no—
409C23×C4—51no—
410C23×C4—51no—
411C23×C4—51no—
412C23×C4—51no—
413C23×C4—51no—
414C23×C4—51no—
415C23×C4—101no—
416C23×C4—101no—
417C23×C4—101no—
418C23×C4—101no—
419C23×C4—104no—
420C23×C4—204no—
421C23×C4—204no—
422C23×C4C2×AGL(1,𝔽5)11yescharacteristic
423C23×C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
424C4×D4—22no—
425C4×D4—22no—
426C4×D4—102no—
427C4×D4—102no—
428C4×D4—102no—
429C4×D4—102no—
430C4×D4—102no—
431C4×D4—102no—
432C4×D4—102no—
433C4×D4—102no—
434C4×D4—102no—
435C4×D4—102no—
436C4×D4—102no—
437C4×D4—102no—
438C4×D4—102no—
439C4×D4—102no—
440C2×C4⋊C4—51no—
441C2×C4⋊C4—51no—
442C2×C4⋊C4—51no—
443C2×C4⋊C4—102no—
444C2×C4⋊C4—102no—
445C2×C4⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
446C2×C22⋊C4—516no—
447C2×C22⋊C4—58no—
448C2×C22⋊C4—51no—
449C2×C22⋊C4—51no—
450C2×C22⋊C4—51no—
451C2×C22⋊C4—51no—
452C2×C22⋊C4—51no—
453C2×C22⋊C4—51no—
454C2×C22⋊C4—102no—
455C2×C22⋊C4—102no—
456C2×C22⋊C4—102no—
457C2×C22⋊C4—102no—
458C2×C22⋊C4—108no—
459C2×C22⋊C4—104no—
460C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic
461C2×C22⋊C4C2×AGL(1,𝔽5)11yescharacteristic, complemented
462C2×C42—51no—
463C2×C42—51no—
464C2×C42—51no—
465C2×C42—101no—
466C2×C42—101no—
467C2×C42—101no—
468C2×C42—101no—
469C2×C42—104no—
470C2×C42—104no—
471C2×C42—208no—
472C2×C42C2×AGL(1,𝔽5)11yescharacteristic, complemented
473#99—516no—
474#99—516no—
475#95—104no—
476#95—104no—
477C22×C5—21no—
478C22×C5—22no—
479C22×C5—21no—
480C22×C5—22no—
481C22×C5—22no—
482C22×C5—42no—
483C22×C5—42no—
484C22×C5—42no—
485C22×C5—42no—
486C22×C5—41no—
487C22×C5—41no—
488C22×C5C4×C22⋊C414yes—
489C22×C5C22×C4211yescharacteristic
490C22×C5C22×C22⋊C411yescharacteristic
491C22×C5C2×#11711yescharacteristic
492C2×D5—21no—
493C2×D5—22no—
494C2×D5—21no—
495C2×D5—22no—
496C2×D5—216no—
497C2×D5—24no—
498C2×D5—24no—
499C2×D5—22no—
500C2×D5—48no—
501C2×D5—42no—
502C2×D5—42no—
503C2×D5—48no—
504C2×D5—42no—
505C2×D5—41no—
506C2×D5—41no—
507C2×D5—48no—
508C2×D5—42no—
509C2×D5C4×C22⋊C412yes—
510C2×D5C4×C22⋊C412yes—
511C2×D5C2×#9912yes—
512C2×D5#41012yes—
513C2×D5C2×C4×D414yes—
514AGL(1,𝔽5)—416no—
515C4×C5—21no—
516C4×C5—22no—
517C4×C5—22no—
518C4×C5—41no—
519C4×C5—41no—
520C4×C5C2×#9912yescomplemented
521Dic5—21no—
522Dic5—22no—
523Dic5—22no—
524Dic5—41no—
525Dic5—41no—
526Dic5C2×#9912yescomplemented
527C24—52no—
528C24—51no—
529C24—54no—
530C24—54no—
531C24—52no—
532C24—51no—
533C24—54no—
534C24—51no—
535C24—101no—
536C24—101no—
537C24—102no—
538C24—202no—
539C24—202no—
540C24—202no—
541C24—202no—
542C24C22×AGL(1,𝔽5)11yescharacteristic
543C24C22×AGL(1,𝔽5)11yescharacteristic
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—54no—
547C2×D4—54no—
548C2×D4—54no—
549C2×D4—102no—
550C2×D4—102no—
551C2×D4—1016no—
552C2×D4—1016no—
553C2×D4—102no—
554C2×D4—102no—
555C2×D4—102no—
556C2×D4—102no—
557C2×D4C4×AGL(1,𝔽5)14yescomplemented
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—51no—
563C22×C4—52no—
564C22×C4—51no—
565C22×C4—51no—
566C22×C4—52no—
567C22×C4—51no—
568C22×C4—54no—
569C22×C4—52no—
570C22×C4—51no—
571C22×C4—51no—
572C22×C4—52no—
573C22×C4—52no—
574C22×C4—51no—
575C22×C4—52no—
576C22×C4—52no—
577C22×C4—52no—
578C22×C4—51no—
579C22×C4—51no—
580C22×C4—108no—
581C22×C4—104no—
582C22×C4—101no—
583C22×C4—101no—
584C22×C4—101no—
585C22×C4—101no—
586C22×C4—102no—
587C22×C4—101no—
588C22×C4—101no—
589C22×C4—101no—
590C22×C4—101no—
591C22×C4—101no—
592C22×C4—101no—
593C22×C4—108no—
594C22×C4—1016no—
595C22×C4—101no—
596C22×C4—101no—
597C22×C4—202no—
598C22×C4—204no—
599C22×C4—202no—
600C22×C4—204no—
601C22×C4—204no—
602C22×C4—202no—
603C22×C4—204no—
604C22×C4—202no—
605C22×C4—204no—
606C22×C4—204no—
607C22×C4—204no—
608C22×C4—202no—
609C22×C4—202no—
610C22×C4—202no—
611C22×C4—202no—
612C22×C4—202no—
613C22×C4—208no—
614C22×C4—208no—
615C22×C4C22⋊AGL(1,𝔽5)12yes—
616C22×C4C22⋊AGL(1,𝔽5)12yes—
617C22×C4C22×AGL(1,𝔽5)11yescharacteristic
618C22×C4C22×AGL(1,𝔽5)11yescharacteristic
619C22×C4C22×AGL(1,𝔽5)11yescharacteristic
620C22×C4C22×AGL(1,𝔽5)11yescharacteristic
621C22×C4C22×AGL(1,𝔽5)11yescharacteristic
622C4⋊C4—22no—
623C4⋊C4—102no—
624C4⋊C4—102no—
625C4⋊C4—102no—
626C22⋊C4—22no—
627C22⋊C4—22no—
628C22⋊C4—516no—
629C22⋊C4—102no—
630C22⋊C4—102no—
631C22⋊C4—102no—
632C22⋊C4—102no—
633C22⋊C4—108no—
634C22⋊C4—1016no—
635C22⋊C4—102no—
636C22⋊C4—102no—
637C42—21no—
638C42—21no—
639C42—101no—
640C42—101no—
641C42—101no—
642C42—101no—
643C42—101no—
644C42—101no—
645C42—208no—
646C42—208no—
647C2×C5—21no—
648C2×C5—21no—
649C2×C5—24no—
650C2×C5—42no—
651C2×C5C2×C4×C22⋊C411yescharacteristic
652C2×C5C22×#9911yescharacteristic
653C2×C5C2×#41011yescharacteristic
654D5—24no—
655D5—22no—
656D5—42no—
657D5C4×#9914yescomplemented
658C23—21no—
659C23—21no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—51no—
665C23—52no—
666C23—52no—
667C23—52no—
668C23—51no—
669C23—58no—
670C23—52no—
671C23—52no—
672C23—58no—
673C23—52no—
674C23—104no—
675C23—102no—
676C23—104no—
677C23—102no—
678C23—104no—
679C23—104no—
680C23—101no—
681C23—101no—
682C23—201no—
683C23—202no—
684C23—201no—
685C23—202no—
686C23—201no—
687C23—201no—
688C23—202no—
689C23—202no—
690C23—208no—
691C23—208no—
692C23—208no—
693C23—202no—
694C23—208no—
695C23—202no—
696C23C2×C4×AGL(1,𝔽5)12yes—
697C23C2×C4×AGL(1,𝔽5)12yescomplemented
698C23#413012yes—
699C23C2×C22⋊AGL(1,𝔽5)12yes—
700C23C23×AGL(1,𝔽5)11yescharacteristic
701D4—28no—
702D4—108no—
703D4—108no—
704D4—108no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—24no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—51no—
718C2×C4—54no—
719C2×C4—52no—
720C2×C4—51no—
721C2×C4—52no—
722C2×C4—104no—
723C2×C4—102no—
724C2×C4—102no—
725C2×C4—104no—
726C2×C4—104no—
727C2×C4—104no—
728C2×C4—102no—
729C2×C4—104no—
730C2×C4—101no—
731C2×C4—101no—
732C2×C4—104no—
733C2×C4—102no—
734C2×C4—1016no—
735C2×C4—101no—
736C2×C4—101no—
737C2×C4—202no—
738C2×C4—202no—
739C2×C4—202no—
740C2×C4—202no—
741C2×C4—202no—
742C2×C4—202no—
743C2×C4—202no—
744C2×C4—202no—
745C2×C4—202no—
746C2×C4—202no—
747C2×C4—202no—
748C2×C4—202no—
749C2×C4—201no—
750C2×C4—202no—
751C2×C4—208no—
752C2×C4—2032no—
753C2×C4—208no—
754C2×C4—202no—
755C2×C4—201no—
756C2×C4—201no—
757C2×C4C2×C4×AGL(1,𝔽5)12yescomplemented
758C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
759C2×C4C2×C22⋊AGL(1,𝔽5)12yes—
760C2×C4C2×C22⋊AGL(1,𝔽5)11yescharacteristic
761C5C2×C4×#9911yescharacteristic, complemented, Sylow
762C22—21no—
763C22—22no—
764C22—21no—
765C22—22no—
766C22—22no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—41no—
772C22—41no—
773C22—52no—
774C22—52no—
775C22—52no—
776C22—54no—
777C22—52no—
778C22—1016no—
779C22—104no—
780C22—104no—
781C22—102no—
782C22—101no—
783C22—102no—
784C22—101no—
785C22—102no—
786C22—202no—
787C22—202no—
788C22—208no—
789C22—202no—
790C22—202no—
791C22—208no—
792C22—208no—
793C22—201no—
794C22—201no—
795C22C4×C22⋊AGL(1,𝔽5)14yes—
796C22C22×C4×AGL(1,𝔽5)11yescharacteristic
797C22C2×#413011yescharacteristic
798C22C22×C22⋊AGL(1,𝔽5)11yescharacteristic
799C4—22no—
800C4—21no—
801C4—22no—
802C4—41no—
803C4—41no—
804C4—52no—
805C4—102no—
806C4—101no—
807C4—102no—
808C4—2016no—
809C4—201no—
810C4—201no—
811C4D5⋊#9912yesdirect product factor
812C2—21no—
813C2—21no—
814C2—24no—
815C2—42no—
816C2—54no—
817C2—104no—
818C2—102no—
819C2—202no—
820C2C2×C4×C22⋊AGL(1,𝔽5)11yescharacteristic
821C2C2×D5⋊#9911yescharacteristic
822C2D5⋊#41011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊AGL(1,𝔽5)
commutatorC22×C5C22×C42
FrattiniC23C23×AGL(1,𝔽5)
FittingC2×C4×C5×D4C4
socleC22×C5C22×C22⋊C4
prime radicalC22×D4×D5C22
cosocleC23×D5C24
hypercenterC2×C4×D4AGL(1,𝔽5)
hypocenterC5C2×C4×#99
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊AGL(1,𝔽5)C2semidirect
4. C4×#4011C2semidirect
5. #10604305C2semidirect
6. #10604216C2semidirect
7. #10604214C2semidirect
8. C4×#3999C2semidirect
10. C23×C4×D5C4semidirect
14. C2×C4×C5×D4C4semidirect
15. C2×D4×Dic5C4semidirect
16. C2×C4×C22⋊D5C4semidirect
23. C2×D5×C4⋊C4C4semidirect
24. C2×#4027C4semidirect
26. C2×D5×C22⋊C4C4semidirect
29. C2×C42×D5C4semidirect
31. D5⋊#99C4direct (N × H)
34. C4×C22⋊AGL(1,𝔽5)C22semidirect
35. C4×C22⋊AGL(1,𝔽5)C22semidirect
38. #64917C22semidirect
39. #64917C22semidirect
46. C23×C4×C5C2×C4semidirect
50. C23×Dic5C2×C4semidirect
67. C22×C4×D5C2×C4semidirect
68. C22×C4×D5C2×C4semidirect
77. C2×C22⋊AGL(1,𝔽5)C2×C4semidirect
84. C2×C5×C4⋊C4C2×C4semidirect
86. C2×C5×C22⋊C4C2×C4semidirect
87. C2×C42×C5C2×C4semidirect
89. C2×C22⋊Dic5C2×C4semidirect
96. C2×#685C2×C4semidirect
97. C2×#685C2×C4semidirect
100. C2×C4⋊Dic5C2×C4semidirect
101. C2×#683C2×C4semidirect
102. C2×#683C2×C4semidirect
103. C2×C4×Dic5C2×C4semidirect
104. C2×C4×Dic5C2×C4semidirect
105. C2×C4×Dic5C2×C4semidirect
124. #4011C2×C4semidirect
127. #3999C2×C4semidirect
145. C23×D5C42semidirect
159. C2×C5×D4C42semidirect
175. C2×C22⋊D5C42semidirect
220. C2×C4×D5C42semidirect
233. C22⋊AGL(1,𝔽5)C22×C4semidirect
270. C2×C4×D4AGL(1,𝔽5)semidirect
294. C23×C5C2×C42semidirect
321. C22×D5C2×C42semidirect
347. C2×C4×C5C2×C42semidirect
365. C2×Dic5C2×C42semidirect
389. C4×D5#99semidirect
423. C23×C4C2×AGL(1,𝔽5)semidirect
445. C2×C4⋊C4C2×AGL(1,𝔽5)semidirect
461. C2×C22⋊C4C2×AGL(1,𝔽5)semidirect
472. C2×C42C2×AGL(1,𝔽5)semidirect
520. C4×C5C2×#99semidirect
526. Dic5C2×#99semidirect
557. C2×D4C4×AGL(1,𝔽5)semidirect
657. D5C4×#99semidirect
697. C23C2×C4×AGL(1,𝔽5)semidirect
757. C2×C4C2×C4×AGL(1,𝔽5)semidirect
761. C5C2×C4×#99semidirect
811. C4D5⋊#99direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×D52
C2×D5⋊#992
C2×C4×C22⋊AGL(1,𝔽5)2
C4×#40112
#106043052
#106042162
#106042142
C4×#39992
C2×C4×#995