Finite Group Databasebeta

← C4×#66266 #13043842

Subgroups — C4×#66266 #13043842

Order 1280.

3698 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#66266C212yesmaximal
2C4×D5×#41C211yesmaximal, characteristic
3#10617208C212yesmaximal, complemented
4C4×Q8×AGL(1,𝔽5)C212yesmaximal, complemented
5#10617172C216yesmaximal, complemented
6C4×D4×AGL(1,𝔽5)C216yesmaximal, complemented
7#10617127C216yesmaximal, complemented
8C4×#4130C213yesmaximal, complemented
9C2×C4×C4⋊AGL(1,𝔽5)C213yesmaximal, complemented
10C2×D5×#41C2211yescharacteristic
11#66266C4132yesdirect product factor
12C2×Q8×AGL(1,𝔽5)C2214yes—
13C2×D4×AGL(1,𝔽5)C22112yes—
14C2×#4130C2216yes—
15C22×C4⋊AGL(1,𝔽5)C2216yes—
16C22×C4×AGL(1,𝔽5)C2216yes—
17C4×C5×#41C411yescharacteristic, complemented
18#41×Dic5C411yescharacteristic, complemented
19C4×#713C411yescharacteristic, complemented
20C4×#713C411yescharacteristic, complemented
21C4×Q8×D5C2211yescharacteristic
22C4×Q8×D5C2211yescharacteristic
23C4×D4×D5C2213yes—
24C4×D4×D5C2213yes—
25C4×#711C413yescomplemented
26C4×#711C413yescomplemented
27#65856C413yescomplemented
28D5×#117C2213yes—
29C4×#709C413yescomplemented
30C2×C42×D5C2213yes—
31C4×C22⋊AGL(1,𝔽5)C2216yes—
32C4×C22⋊AGL(1,𝔽5)C2216yes—
33C2×(C2×AGL(1,𝔽5))⋊C4C2216yes—
34C4⋊C4×AGL(1,𝔽5)C22112yes—
35C4⋊C4×AGL(1,𝔽5)C22112yes—
36C22⋊C4×AGL(1,𝔽5)C22124yes—
37C4×C4⋊AGL(1,𝔽5)C2216yes—
38C4×C4⋊AGL(1,𝔽5)C2216yes—
39C4×C4⋊AGL(1,𝔽5)C2216yes—
40C4×C4⋊AGL(1,𝔽5)C2216yes—
41C4×C4⋊AGL(1,𝔽5)C2213yes—
42C4×C4⋊AGL(1,𝔽5)C2211yescharacteristic
43#65686C2216yes—
44C42×AGL(1,𝔽5)C2216yes—
45C4×#520—51nomaximal, Sylow
46C23×AGL(1,𝔽5)C23112yes—
47C2×C5×#41C2×C411yescharacteristic
48D5×#41C2×C4116yes—
49C2×#713C2×C411yescharacteristic
50C2×Q8×D5C2311yescharacteristic
51C2×#711C2×C413yes—
52C2×D4×D5C2313yes—
53C2×#709C2×C413yes—
54C22×C4×D5C2313yes—
55C22×C4×D5C2313yes—
56C22×C4×D5C2313yes—
57C2×C22⋊AGL(1,𝔽5)C23112yes—
58Q8×AGL(1,𝔽5)C2×C4132yescomplemented
59D4×AGL(1,𝔽5)C2×C4196yescomplemented
60#4130C2×C4148yescomplemented
61C2×C4⋊AGL(1,𝔽5)C2×C4148yescomplemented
62C2×C4⋊AGL(1,𝔽5)C2316yes—
63C2×C4⋊AGL(1,𝔽5)C2312yes—
64C2×C4⋊AGL(1,𝔽5)C23112yes—
65C2×C4×AGL(1,𝔽5)—412no—
66C2×C4×AGL(1,𝔽5)C2312yes—
67C2×C4×AGL(1,𝔽5)C2316yes—
68C2×C4×AGL(1,𝔽5)C23112yes—
69C2×C4×AGL(1,𝔽5)C23112yes—
70C2×C4×AGL(1,𝔽5)C23112yes—
71C4×C5×Q8C2×C411yescharacteristic, complemented
72C4×C5×Q8C2×C411yescharacteristic, complemented
73C4×C5×D4C2×C413yescomplemented
74C4×C5×D4C2×C413yescomplemented
75C5×#117C2×C413yescomplemented
76C2×C42×C5C2×C413yescomplemented
77Q8×Dic5C2×C411yescharacteristic, complemented
78Q8×Dic5C2×C411yescharacteristic, complemented
79D4×Dic5C2×C413yescomplemented
80D4×Dic5C2×C413yescomplemented
81C4×C22⋊D5C2×C416yescomplemented
82C4×C22⋊D5C2×C416yescomplemented
83#4072C2×C413yescomplemented
84C2×C4×Dic5C2×C413yescomplemented
85C2×C4×Dic5C2×C413yescomplemented
86C2×C4×Dic5C2×C413yescomplemented
87#4039C2×C413yescomplemented
88#4039C2×C413yescomplemented
89#4038C2×C413yescomplemented
90#4038C2×C413yescomplemented
91D5×C4⋊C4C2313yes—
92D5×C4⋊C4C2313yes—
93#4033C2×C413yescomplemented
94#4033C2×C413yescomplemented
95#4027C2×C416yescomplemented
96#4027C2×C416yescomplemented
97D5×C22⋊C4C2316yes—
98#4023C2×C416yescomplemented
99C4×D20C2×C413yescomplemented
100C4×D20C2×C413yescomplemented
101#4018C2×C416yescomplemented
102C42×D5C2×C413yescomplemented
103C42×D5C2×C413yescomplemented
104C42×D5C2×C413yescomplemented
105C42×D5C2×C413yescomplemented
106C42×D5C2311yescharacteristic
107C42×D5C2313yes—
108C42×D5C2313yes—
109C42×D5C2313yes—
110C4×Dic10C2×C413yescomplemented
111C4×Dic10C2×C413yescomplemented
112(C2×AGL(1,𝔽5))⋊C4C2312yes—
113(C2×AGL(1,𝔽5))⋊C4C2316yes—
114(C2×AGL(1,𝔽5))⋊C4C23112yes—
115(C2×AGL(1,𝔽5))⋊C4C23112yes—
116C2×#520—52no—
117C2×C4×#41—51no—
118#2276—52no—
119#2275—56no—
120#2274—56no—
121C42×Q8—52no—
122C42×D4—56no—
123C4×#117—53no—
124C2×C4×C4⋊C4—53no—
125C23×D5C2413yes—
126C22×AGL(1,𝔽5)—412no—
127C22×AGL(1,𝔽5)—412no—
128C22×AGL(1,𝔽5)C22×C4148yes—
129C22×AGL(1,𝔽5)C2414yes—
130C22×AGL(1,𝔽5)C24112yes—
131C5×#41C4218yescomplemented
132C2×C5×Q8C22×C411yescharacteristic
133C2×C5×D4C22×C413yes—
134C22×C4×C5C22×C413yes—
135C22×C4×C5C22×C413yes—
136C22×C4×C5C22×C413yes—
137C2×C22⋊D5C22×C416yes—
138C22×Dic5C22×C413yes—
139C22×Dic5C22×C413yes—
140C22×Dic5C22×C413yes—
141#713C4218yescomplemented
142Q8×D5C22×C418yes—
143#711C42124yescomplemented
144D4×D5C22×C4124yes—
145#709C42124yescomplemented
146C2×D20C22×C413yes—
147C2×C4×D5—26no—
148C2×C4×D5—26no—
149C2×C4×D5—46no—
150C2×C4×D5C22×C413yes—
151C2×C4×D5C22×C413yes—
152C2×C4×D5C22×C413yes—
153C2×C4×D5C22×C413yes—
154C2×C4×D5C22×C413yes—
155C2×C4×D5C22×C413yes—
156C2×C4×D5C22×C4124yes—
157C2×C4×D5C2413yes—
158C2×C4×D5C2413yes—
159C2×C4×D5C2411yescharacteristic
160C2×C4×D5C2413yes—
161C2×C4×D5C2411yescharacteristic
162C2×C4×D5C2411yescharacteristic
163C2×Dic10C22×C413yes—
164C22⋊AGL(1,𝔽5)C22×C4148yes—
165C4⋊AGL(1,𝔽5)C22×C4124yes—
166C4⋊AGL(1,𝔽5)C22×C4148yes—
167C4⋊AGL(1,𝔽5)C22×C418yes—
168C4×AGL(1,𝔽5)—212no—
169C4×AGL(1,𝔽5)—24no—
170C4×AGL(1,𝔽5)—412no—
171C4×AGL(1,𝔽5)—412no—
172C4×AGL(1,𝔽5)C22×C4148yes—
173C5×C4⋊C4C22×C413yes—
174C5×C4⋊C4C22×C413yes—
175C5×C22⋊C4C22×C416yes—
176C42×C5C22×C411yescharacteristic
177C42×C5C22×C413yes—
178C42×C5C22×C413yes—
179C42×C5C22×C413yes—
180C22⋊Dic5C22×C416yes—
181#685C22×C416yes—
182#685C22×C416yes—
183C4⋊Dic5C22×C413yes—
184C4⋊Dic5C22×C413yes—
185#683C22×C416yes—
186#683C22×C416yes—
187C4×Dic5C22×C413yes—
188C4×Dic5C22×C413yes—
189C4×Dic5C22×C411yescharacteristic
190C4×Dic5C22×C411yescharacteristic
191C4×Dic5C22×C411yescharacteristic
192C4×Dic5C22×C413yes—
193C4×Dic5C22×C413yes—
194C4×Dic5C22×C413yes—
195C4×Dic5C22×C413yes—
196C4×Dic5C22×C413yes—
197C4×Dic5C22×C413yes—
198C4×Dic5C22×C413yes—
199C22×#41—51no—
200#520—532no—
201C4×#41—51no—
202C4×#41—51no—
203C4×#41—51no—
204C4×#41—53no—
205C4×#41—53no—
206C4×#41—53no—
207C4×#41—53no—
208C4×#41AGL(1,𝔽5)11yescharacteristic, complemented
209C2×C4×Q8—54no—
210C2×C4×Q8—51no—
211C2×C4×Q8—51no—
212C2×C4×D4—512no—
213C2×C4×D4—53no—
214C2×C4×D4—53no—
215C2×#117—56no—
216C2×#117—53no—
217C22×C4⋊C4—56no—
218C22×C42—53no—
219C22×C42—56no—
220C4×C4⋊C4—53no—
221C4×C4⋊C4—56no—
222C4×C4⋊C4—56no—
223C4×C4⋊C4—56no—
224C4×C4⋊C4—51no—
225C4×C4⋊C4—56no—
226C4×C4⋊C4—512no—
227C4×C4⋊C4—512no—
228C4×C22⋊C4—524no—
229C4×C22⋊C4—56no—
230C4×C22⋊C4—56no—
231#376—56no—
232C2×#95—56no—
233C43—56no—
234C23×C5C23×C413yes—
235C22×D5—23no—
236C22×D5—23no—
237C22×D5—26no—
238C22×D5C23×C4112yes—
239C22×D5C23×C413yes—
240C22×D5C2511yescharacteristic
241C2×AGL(1,𝔽5)—212no—
242C2×AGL(1,𝔽5)—24no—
243C2×AGL(1,𝔽5)—24no—
244C2×AGL(1,𝔽5)—212no—
245C2×AGL(1,𝔽5)—448no—
246C2×AGL(1,𝔽5)C23×C418yes—
247C2×AGL(1,𝔽5)C23×C4124yes—
248C5×Q8C2×C4214yescomplemented
249C5×D4C2×C42112yescomplemented
250C2×C4×C5—26no—
251C2×C4×C5—43no—
252C2×C4×C5C2×C42112yescomplemented
253C2×C4×C5C23×C411yescharacteristic
254C2×C4×C5C23×C413yes—
255C2×C4×C5C23×C413yes—
256C2×C4×C5C23×C411yescharacteristic
257C2×C4×C5C23×C413yes—
258C2×C4×C5C23×C411yescharacteristic
259C22⋊D5C2×C42124yescomplemented
260C2×Dic5—26no—
261C2×Dic5—43no—
262C2×Dic5C2×C42112yescomplemented
263C2×Dic5C23×C411yescharacteristic
264C2×Dic5C23×C413yes—
265C2×Dic5C23×C413yes—
266C2×Dic5C23×C411yescharacteristic
267C2×Dic5C23×C411yescharacteristic
268C2×Dic5C23×C413yes—
269D20C2×C42112yescomplemented
270C4×D5—23no—
271C4×D5—23no—
272C4×D5—26no—
273C4×D5—22no—
274C4×D5—26no—
275C4×D5—26no—
276C4×D5—43no—
277C4×D5—43no—
278C4×D5C2×C42112yescomplemented
279C4×D5C2×C42112yescomplemented
280C4×D5C23×C4112yes—
281C4×D5C23×C414yes—
282C4×D5H(5,𝔽2)12yes—
283C4×D52−1+412yes—
284Dic10C2×C42112yescomplemented
285C2×#41—516no—
286C2×#41—51no—
287C2×#41—53no—
288C2×#41—53no—
289C2×#41C2×AGL(1,𝔽5)11yescharacteristic
290C22×Q8—51no—
291C22×D4—53no—
292C23×C4—53no—
293C23×C4—512no—
294C23×C4—53no—
295C23×C4—53no—
296C4×Q8—532no—
297C4×Q8—51no—
298C4×Q8—51no—
299C4×Q8—53no—
300C4×Q8—53no—
301C4×Q8—53no—
302C4×Q8—53no—
303C4×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
304C4×Q8C2×AGL(1,𝔽5)11yescharacteristic, complemented
305C4×D4—596no—
306C4×D4—53no—
307C4×D4—53no—
308C4×D4—56no—
309C4×D4—56no—
310C4×D4—53no—
311C4×D4—53no—
312C4×D4—56no—
313C4×D4—56no—
314C4×D4—53no—
315C4×D4—53no—
316C4×D4C2×AGL(1,𝔽5)13yescomplemented
317C4×D4C2×AGL(1,𝔽5)13yescomplemented
318#117—548no—
319#117—53no—
320#117—53no—
321#117—53no—
322#117—56no—
323#117—56no—
324#117C2×AGL(1,𝔽5)13yescomplemented
325C2×C4⋊C4—56no—
326C2×C4⋊C4—512no—
327C2×C4⋊C4—548no—
328C2×C4⋊C4—52no—
329C2×C4⋊C4—53no—
330C2×C4⋊C4—53no—
331C2×C22⋊C4—512no—
332C2×C22⋊C4—56no—
333C2×C42—512no—
334C2×C42—53no—
335C2×C42—53no—
336C2×C42—53no—
337C2×C42—53no—
338C2×C42—53no—
339C2×C42—53no—
340C2×C42—53no—
341C2×C42—53no—
342C2×C42—53no—
343C2×C42—53no—
344C2×C42—51no—
345C2×C42—52no—
346C2×C42—56no—
347C2×C42—512no—
348C2×C42—512no—
349C2×C42—2012no—
350C2×C42C2×AGL(1,𝔽5)13yescomplemented
351#95—56no—
352#95—512no—
353#95—52no—
354#95—512no—
355C22×C5—23no—
356C22×C5—23no—
357C22×C5C22×C4216yes—
358C22×C5C24×C411yescharacteristic
359C2×D5—23no—
360C2×D5—23no—
361C2×D5—212no—
362C2×D5—212no—
363C2×D5C22×C4216yes—
364C2×D5C24×C412yes—
365C2×D5C2×H(5,𝔽2)11yescharacteristic
366C2×D5C2×2−1+411yescharacteristic
367C2×D5#58512yes—
368AGL(1,𝔽5)—224no—
369AGL(1,𝔽5)—28no—
370C4×C5—23no—
371C4×C5—21no—
372C4×C5—23no—
373C4×C5C22×C4216yes—
374C4×C5C22×C4212yes—
375C4×C5#52012yescomplemented
376Dic5—23no—
377Dic5—21no—
378Dic5—23no—
379Dic5C22×C4216yes—
380Dic5C22×C4212yes—
381Dic5#52012yescomplemented
382C24—53no—
383#41—58no—
384#41—524no—
385#41—524no—
386#41C4×AGL(1,𝔽5)18yescomplemented
387C2×Q8—58no—
388C2×Q8—53no—
389C2×Q8C22×AGL(1,𝔽5)11yescharacteristic
390C2×D4—56no—
391C2×D4—524no—
392C2×D4—53no—
393C2×D4C22×AGL(1,𝔽5)13yes—
394C22×C4—53no—
395C22×C4—524no—
396C22×C4—53no—
397C22×C4—51no—
398C22×C4—53no—
399C22×C4—53no—
400C22×C4—51no—
401C22×C4—54no—
402C22×C4—512no—
403C22×C4—53no—
404C22×C4—548no—
405C22×C4—53no—
406C22×C4—51no—
407C22×C4—53no—
408C22×C4—53no—
409C22×C4—53no—
410C22×C4—53no—
411C22×C4—53no—
412C22×C4—53no—
413C22×C4—106no—
414C22×C4—106no—
415C22×C4—206no—
416C22×C4—2012no—
417C22×C4—2012no—
418C22×C4C22×AGL(1,𝔽5)13yes—
419C22×C4C22×AGL(1,𝔽5)13yes—
420C22×C4C22×AGL(1,𝔽5)13yes—
421C4⋊C4—524no—
422C4⋊C4—548no—
423C4⋊C4—58no—
424C4⋊C4—56no—
425C4⋊C4—56no—
426C4⋊C4—53no—
427C4⋊C4—53no—
428C4⋊C4C22×AGL(1,𝔽5)13yes—
429C4⋊C4C22×AGL(1,𝔽5)13yes—
430C22⋊C4—548no—
431C22⋊C4—56no—
432C22⋊C4—56no—
433C22⋊C4—56no—
434C22⋊C4C22×AGL(1,𝔽5)16yes—
435C42—548no—
436C42—51no—
437C42—51no—
438C42—53no—
439C42—53no—
440C42—53no—
441C42—53no—
442C42—53no—
443C42—53no—
444C42—53no—
445C42—53no—
446C42—51no—
447C42—53no—
448C42—1012no—
449C42—104no—
450C42—2012no—
451C42—2012no—
452C42C22×AGL(1,𝔽5)13yes—
453C42C22×AGL(1,𝔽5)13yes—
454C42C22×AGL(1,𝔽5)11yescharacteristic
455C42C22×AGL(1,𝔽5)13yes—
456C2×C5—26no—
457C2×C5C23×C4211yescharacteristic
458C2×C5C2×#52011yescharacteristic
459C2×C5#342811yescharacteristic
460D5—26no—
461D5C4×H(5,𝔽2)12yes—
462D5C4×2−1+412yes—
463C23—51no—
464C23—512no—
465C23—53no—
466C23—103no—
467C23—103no—
468C23—106no—
469C23C23×AGL(1,𝔽5)13yes—
470Q8—512no—
471Q8C2×C4×AGL(1,𝔽5)14yescomplemented
472D4—524no—
473D4—512no—
474D4C2×C4×AGL(1,𝔽5)112yescomplemented
475C2×C4—26no—
476C2×C4—43no—
477C2×C4—512no—
478C2×C4—51no—
479C2×C4—51no—
480C2×C4—53no—
481C2×C4—512no—
482C2×C4—54no—
483C2×C4—512no—
484C2×C4—512no—
485C2×C4—52no—
486C2×C4—52no—
487C2×C4—58no—
488C2×C4—524no—
489C2×C4—51no—
490C2×C4—53no—
491C2×C4—53no—
492C2×C4—106no—
493C2×C4—103no—
494C2×C4—106no—
495C2×C4—103no—
496C2×C4—102no—
497C2×C4—106no—
498C2×C4—1012no—
499C2×C4—104no—
500C2×C4—104no—
501C2×C4—1012no—
502C2×C4—106no—
503C2×C4—203no—
504C2×C4—203no—
505C2×C4—203no—
506C2×C4—2048no—
507C2×C4C2×C4×AGL(1,𝔽5)112yescomplemented
508C2×C4C23×AGL(1,𝔽5)11yescharacteristic
509C2×C4C23×AGL(1,𝔽5)13yes—
510C2×C4C23×AGL(1,𝔽5)13yes—
511C2×C4C23×AGL(1,𝔽5)11yescharacteristic
512C2×C4C23×AGL(1,𝔽5)13yes—
513C2×C4C23×AGL(1,𝔽5)11yescharacteristic
514C5C4×#52011yescharacteristic, complemented, Sylow
515C22—23no—
516C22—23no—
517C22—52no—
518C22—51no—
519C22—51no—
520C22—52no—
521C22—56no—
522C22—1012no—
523C22—1012no—
524C22—103no—
525C22—103no—
526C22C22×C4×AGL(1,𝔽5)16yes—
527C22C24×AGL(1,𝔽5)11yescharacteristic
528C4—23no—
529C4—21no—
530C4—23no—
531C4—52no—
532C4—56no—
533C4—52no—
534C4—1024no—
535C4—108no—
536C4—103no—
537C4—101no—
538C4—103no—
539C4C22×C4×AGL(1,𝔽5)12yes—
540C4C22×C4×AGL(1,𝔽5)16yes—
541C4#6626612yesdirect product factor
542C2—26no—
543C2—52no—
544C2—52no—
545C2—106no—
546C2C23×C4×AGL(1,𝔽5)11yescharacteristic
547C2C2×#6626611yescharacteristic
548C2#1061941211yescharacteristic
subgroupG/H
centerC2×C4C23×AGL(1,𝔽5)
commutatorC2×C5C23×C42
FrattiniC22C24×AGL(1,𝔽5)
FittingC4×C5×#41C4
socleC22×C5C24×C4
prime radicalC2×D5×#41C22
cosocleC22×D5C25
hypercenterC4×#41AGL(1,𝔽5)
hypocenterC5C4×#520
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
3. #10617208C2semidirect
4. C4×Q8×AGL(1,𝔽5)C2semidirect
5. #10617172C2semidirect
6. C4×D4×AGL(1,𝔽5)C2semidirect
7. #10617127C2semidirect
8. C4×#4130C2semidirect
9. C2×C4×C4⋊AGL(1,𝔽5)C2semidirect
11. #66266C4direct (N × H)
17. C4×C5×#41C4semidirect
18. #41×Dic5C4semidirect
19. C4×#713C4semidirect
20. C4×#713C4semidirect
25. C4×#711C4semidirect
26. C4×#711C4semidirect
27. #65856C4semidirect
29. C4×#709C4semidirect
58. Q8×AGL(1,𝔽5)C2×C4semidirect
59. D4×AGL(1,𝔽5)C2×C4semidirect
60. #4130C2×C4semidirect
61. C2×C4⋊AGL(1,𝔽5)C2×C4semidirect
71. C4×C5×Q8C2×C4semidirect
72. C4×C5×Q8C2×C4semidirect
73. C4×C5×D4C2×C4semidirect
74. C4×C5×D4C2×C4semidirect
75. C5×#117C2×C4semidirect
76. C2×C42×C5C2×C4semidirect
77. Q8×Dic5C2×C4semidirect
78. Q8×Dic5C2×C4semidirect
79. D4×Dic5C2×C4semidirect
80. D4×Dic5C2×C4semidirect
81. C4×C22⋊D5C2×C4semidirect
82. C4×C22⋊D5C2×C4semidirect
83. #4072C2×C4semidirect
84. C2×C4×Dic5C2×C4semidirect
85. C2×C4×Dic5C2×C4semidirect
86. C2×C4×Dic5C2×C4semidirect
87. #4039C2×C4semidirect
88. #4039C2×C4semidirect
89. #4038C2×C4semidirect
90. #4038C2×C4semidirect
93. #4033C2×C4semidirect
94. #4033C2×C4semidirect
95. #4027C2×C4semidirect
96. #4027C2×C4semidirect
98. #4023C2×C4semidirect
99. C4×D20C2×C4semidirect
100. C4×D20C2×C4semidirect
101. #4018C2×C4semidirect
102. C42×D5C2×C4semidirect
103. C42×D5C2×C4semidirect
104. C42×D5C2×C4semidirect
105. C42×D5C2×C4semidirect
110. C4×Dic10C2×C4semidirect
111. C4×Dic10C2×C4semidirect
131. C5×#41C42semidirect
141. #713C42semidirect
143. #711C42semidirect
145. #709C42semidirect
208. C4×#41AGL(1,𝔽5)semidirect
248. C5×Q8C2×C42semidirect
249. C5×D4C2×C42semidirect
252. C2×C4×C5C2×C42semidirect
259. C22⋊D5C2×C42semidirect
262. C2×Dic5C2×C42semidirect
269. D20C2×C42semidirect
278. C4×D5C2×C42semidirect
279. C4×D5C2×C42semidirect
284. Dic10C2×C42semidirect
303. C4×Q8C2×AGL(1,𝔽5)semidirect
304. C4×Q8C2×AGL(1,𝔽5)semidirect
316. C4×D4C2×AGL(1,𝔽5)semidirect
317. C4×D4C2×AGL(1,𝔽5)semidirect
324. #117C2×AGL(1,𝔽5)semidirect
350. C2×C42C2×AGL(1,𝔽5)semidirect
375. C4×C5#520semidirect
381. Dic5#520semidirect
386. #41C4×AGL(1,𝔽5)semidirect
471. Q8C2×C4×AGL(1,𝔽5)semidirect
474. D4C2×C4×AGL(1,𝔽5)semidirect
507. C2×C4C2×C4×AGL(1,𝔽5)semidirect
514. C5C4×#520semidirect
541. C4#66266direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#662662
C4×D5×#412
#106172082
C4×Q8×AGL(1,𝔽5)2
#106171722
C4×D4×AGL(1,𝔽5)2
#106171272
C4×#41302
C2×C4×C4⋊AGL(1,𝔽5)2
C4×#5205