Finite Group Databasebeta

← C5×#26151 #11948871

Subgroups — C5×#26151 #11948871

Order 1280.

854 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#485C211yesmaximal, characteristic, complemented
2C2×C5×#428C211yesmaximal, characteristic, complemented
3C5×#2417C211yesmaximal, characteristic
4C5×#2354C211yesmaximal, characteristic
5C5×#2095C211yesmaximal, characteristic, complemented
6C5×#2083C211yesmaximal, characteristic, complemented
7C5×#2075C211yesmaximal, characteristic, complemented
8C5×#2036C211yesmaximal, characteristic, complemented
9C5×#1927C211yesmaximal, characteristic, complemented
10C5×#1920C211yesmaximal, characteristic, complemented
11C5×#1894C211yesmaximal, characteristic, complemented
12C5×#1873C211yesmaximal, characteristic, complemented
13C5×#1870C211yesmaximal, characteristic
14C5×#1854C211yesmaximal, characteristic, complemented
15C5×#1852C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C2×C5×C22⋊Q8C2211yescharacteristic
18C2×C5×C22⋊Q8C2211yescharacteristic
19C2×C4×C5×D4C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C5×#485—24no—
24C5×#428—24no—
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#107C2211yescharacteristic
28C2×C5×#107C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×#106C2211yescharacteristic
31C2×C5×#103C2211yescharacteristic
32C2×C5×#103C2211yescharacteristic
33C2×C5×#103C2211yescharacteristic
34C2×C5×#103C2211yescharacteristic
35C2×C5×C22⋊C8C2211yescharacteristic
36C2×C5×C22⋊C8C2211yescharacteristic
37C2×C5×C22⋊C8C2211yescharacteristic
38C5×#398—21no—
39C5×#396—21no—
40C5×#391C2211yescharacteristic
41C5×#390—21no—
42C5×#389C2211yescharacteristic
43C5×#388—21no—
44C5×#388—21no—
45C5×#386—21no—
46C5×#384C2211yescharacteristic
47C5×#380—21no—
48C5×#380C2211yescharacteristic
49C5×#380C2211yescharacteristic
50C5×#380C2211yescharacteristic
51C4×C5×C4⋊C4—21no—
52C4×C5×C4⋊C4C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#336C2211yescharacteristic
60C5×#336C2211yescharacteristic
61#26151C511yesmaximal, characteristic, direct product factor, Sylow
62C22×C5×Q8C2311yescharacteristic
63C22×C5×D4D411yescharacteristic
64C23×C4×C5—21no—
65C23×C4×C5C2311yescharacteristic
66C23×C4×C5C2311yescharacteristic
67C2×C5×M16—22no—
68C2×C5×M16—22no—
69C2×C5×M16—22no—
70C22×C5×C8C2311yescharacteristic
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C5×C22⋊Q8—22no—
75C5×C22⋊Q8—22no—
76C5×C22⋊Q8—22no—
77C5×C22⋊Q8—41no—
78C4×C5×D4—22no—
79C4×C5×D4—22no—
80C5×#117—22no—
81C5×#117—22no—
82C5×#117—41no—
83C5×#117—41no—
84C2×C5×C4⋊C4—22no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—21no—
88C2×C5×C4⋊C4—21no—
89C2×C5×C4⋊C4—21no—
90C2×C5×C4⋊C4—21no—
91C2×C5×C4⋊C4—41no—
92C2×C5×C4⋊C4D411yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C4⋊C4C2311yescharacteristic
98C2×C5×C4⋊C4C2311yescharacteristic
99C2×C5×C4⋊C4C2311yescharacteristic
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4—21no—
105C2×C5×C22⋊C4—21no—
106C2×C5×C22⋊C4—21no—
107C2×C5×C22⋊C4D411yescharacteristic
108C2×C5×C22⋊C4D411yescharacteristic
109C2×C42×C5—21no—
110C2×C42×C5—21no—
111C2×C42×C5—21no—
112C2×C42×C5C2311yescharacteristic
113C5×#107—22no—
114C5×#107—22no—
115C5×#107—22no—
116C5×#107—41no—
117C5×#106—22no—
118C5×#106D414yescomplemented
119C5×#103—22no—
120C5×#103—22no—
121C5×#103—22no—
122C5×#103—41no—
123C5×C22⋊C8—22no—
124C5×C22⋊C8—22no—
125C5×C22⋊C8—22no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C5×#95—21no—
131C5×#95—21no—
132C5×#95—21no—
133C2×#485C2×C511yescharacteristic, complemented
134C2×#428C2×C511yescharacteristic, complemented
135#2417C2×C511yescharacteristic
136#2354C2×C511yescharacteristic
137#2095C2×C511yescharacteristic, complemented
138#2083C2×C511yescharacteristic, complemented
139#2075C2×C511yescharacteristic, complemented
140#2036C2×C511yescharacteristic, complemented
141#1927C2×C511yescharacteristic, complemented
142#1920C2×C511yescharacteristic, complemented
143#1894C2×C511yescharacteristic, complemented
144#1873C2×C511yescharacteristic, complemented
145#1870C2×C511yescharacteristic
146#1854C2×C511yescharacteristic, complemented
147#1852C2×C511yescharacteristic, complemented
148C24×C5C2×D411yescharacteristic
149C24×C5C2×D411yescharacteristic
150C2×C5×Q8—21no—
151C2×C5×Q8—21no—
152C2×C5×Q8—21no—
153C2×C5×Q8—21no—
154C2×C5×Q8—21no—
155C2×C5×Q8—21no—
156C2×C5×D4—22no—
157C2×C5×D4—22no—
158C2×C5×D4—41no—
159C22×C4×C5—21no—
160C22×C4×C5—21no—
161C22×C4×C5—21no—
162C22×C4×C5—21no—
163C22×C4×C5—21no—
164C22×C4×C5—21no—
165C22×C4×C5—21no—
166C22×C4×C5—21no—
167C22×C4×C5—21no—
168C22×C4×C5—21no—
169C22×C4×C5—21no—
170C22×C4×C5—21no—
171C22×C4×C5—21no—
172C22×C4×C5—21no—
173C22×C4×C5—21no—
174C22×C4×C5—21no—
175C22×C4×C5—21no—
176C22×C4×C5—21no—
177C22×C4×C5—42no—
178C22×C4×C5—42no—
179C22×C4×C5—81no—
180C22×C4×C5C2×D411yescharacteristic
181C22×C4×C5C2×D411yescharacteristic
182C22×C4×C5C2×D411yescharacteristic
183C22×C4×C5C2×D411yescharacteristic
184C22×C4×C5#4112yes—
185C22×C4×C5#4112yes—
186C22×C4×C5C2411yescharacteristic
187C5×M16—28no—
188C2×C5×C8—21no—
189C2×C5×C8—21no—
190C2×C5×C8—21no—
191C2×C5×C8—21no—
192C2×C5×C8—21no—
193C2×C5×C8—21no—
194C2×C5×C8—21no—
195C2×C5×C8—21no—
196C2×C5×C8—21no—
197C2×C5×C8—21no—
198C2×C5×C8C2×D412yes—
199C2×C5×C8#4112yes—
200C5×C4⋊C4—22no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—21no—
207C5×C4⋊C4—21no—
208C5×C4⋊C4—21no—
209C5×C4⋊C4—21no—
210C5×C4⋊C4—21no—
211C5×C4⋊C4—21no—
212C5×C4⋊C4—21no—
213C5×C4⋊C4—42no—
214C5×C4⋊C4—42no—
215C5×C4⋊C4—42no—
216C5×C4⋊C4—42no—
217C5×C4⋊C4—81no—
218C5×C4⋊C4—81no—
219C5×C4⋊C4C2×D412yes—
220C5×C4⋊C4C2×D412yes—
221C5×C22⋊C4—22no—
222C5×C22⋊C4—22no—
223C5×C22⋊C4—42no—
224C5×C22⋊C4—42no—
225C5×C22⋊C4—42no—
226C5×C22⋊C4—42no—
227C5×C22⋊C4—81no—
228C5×C22⋊C4—81no—
229C5×C22⋊C4—81no—
230C42×C5—21no—
231C42×C5—21no—
232C42×C5—42no—
233C42×C5—42no—
234C42×C5—42no—
235C22×M16C22×C511yescharacteristic
236C2×C22⋊Q8C22×C511yescharacteristic
237C2×C22⋊Q8C22×C511yescharacteristic
238C2×C4×D4C22×C511yescharacteristic
239C2×#117C22×C511yescharacteristic
240C2×#117C22×C511yescharacteristic
241C22×C4⋊C4C22×C511yescharacteristic
242#485—24no—
243#428—24no—
244C2×#107C22×C511yescharacteristic
245C2×#107C22×C511yescharacteristic
246C2×#107C22×C511yescharacteristic
247C2×#107C22×C511yescharacteristic
248C2×#106C22×C511yescharacteristic
249C2×#106C22×C511yescharacteristic
250C2×#103C22×C511yescharacteristic
251C2×#103C22×C511yescharacteristic
252C2×#103C22×C511yescharacteristic
253C2×#103C22×C511yescharacteristic
254C2×C22⋊C8C22×C511yescharacteristic
255C2×C22⋊C8C22×C511yescharacteristic
256C2×C22⋊C8C22×C511yescharacteristic
257#398—21no—
258#396—21no—
259#391C22×C511yescharacteristic
260#390—21no—
261#389C22×C511yescharacteristic
262#388—21no—
263#388—21no—
264#386—21no—
265#384C22×C511yescharacteristic
266#380—21no—
267#380C22×C511yescharacteristic
268#380C22×C511yescharacteristic
269#380C22×C511yescharacteristic
270C4×C4⋊C4—21no—
271C4×C4⋊C4C22×C511yescharacteristic
272#340C22×C511yescharacteristic
273#340C22×C511yescharacteristic
274#340C22×C511yescharacteristic
275#340C22×C511yescharacteristic
276#340C22×C511yescharacteristic
277#340C22×C511yescharacteristic
278#336C22×C511yescharacteristic
279#336C22×C511yescharacteristic
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5—21no—
285C23×C5—21no—
286C23×C5—21no—
287C23×C5—21no—
288C23×C5—21no—
289C23×C5—21no—
290C23×C5—21no—
291C23×C5—21no—
292C23×C5—21no—
293C23×C5#12312yes—
294C23×C5C22×D411yescharacteristic
295C5×Q8—41no—
296C5×Q8—41no—
297C5×Q8—41no—
298C5×Q8—41no—
299C5×D4—44no—
300C2×C4×C5—21no—
301C2×C4×C5—21no—
302C2×C4×C5—21no—
303C2×C4×C5—21no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—22no—
307C2×C4×C5—22no—
308C2×C4×C5—21no—
309C2×C4×C5—21no—
310C2×C4×C5—22no—
311C2×C4×C5—21no—
312C2×C4×C5—22no—
313C2×C4×C5—21no—
314C2×C4×C5—21no—
315C2×C4×C5—21no—
316C2×C4×C5—41no—
317C2×C4×C5—41no—
318C2×C4×C5—41no—
319C2×C4×C5—41no—
320C2×C4×C5—41no—
321C2×C4×C5—41no—
322C2×C4×C5—41no—
323C2×C4×C5—41no—
324C2×C4×C5—41no—
325C2×C4×C5—41no—
326C2×C4×C5—41no—
327C2×C4×C5—41no—
328C2×C4×C5—41no—
329C2×C4×C5—41no—
330C2×C4×C5—41no—
331C2×C4×C5—41no—
332C2×C4×C5—41no—
333C2×C4×C5—41no—
334C2×C4×C5—41no—
335C2×C4×C5—41no—
336C2×C4×C5—41no—
337C2×C4×C5—41no—
338C2×C4×C5—41no—
339C2×C4×C5—41no—
340C2×C4×C5—41no—
341C2×C4×C5—41no—
342C2×C4×C5—84no—
343C2×C4×C5#12312yes—
344C2×C4×C5#13712yes—
345C2×C4×C5C22×D411yescharacteristic
346C2×C4×C5C2×#4111yescharacteristic
347C2×C4×C5C2×#4111yescharacteristic
348C2×C4×C5C2×#4111yescharacteristic
349C2×C4×C5H(5,𝔽2)11yescharacteristic
350C2×C4×C52−1+411yescharacteristic
351C5×C8—22no—
352C5×C8—22no—
353C5×C8—41no—
354C5×C8—41no—
355C22×Q8C23×C511yescharacteristic
356C22×D4C5×D411yescharacteristic
357C23×C4—21no—
358C23×C4C23×C511yescharacteristic
359C23×C4C23×C511yescharacteristic
360C2×M16—22no—
361C2×M16—22no—
362C2×M16—22no—
363C22×C8C23×C511yescharacteristic
364C22×C8C23×C511yescharacteristic
365C22×C8C23×C511yescharacteristic
366C22×C8C23×C511yescharacteristic
367C22⋊Q8—22no—
368C22⋊Q8—22no—
369C22⋊Q8—22no—
370C22⋊Q8—41no—
371C4×D4—22no—
372C4×D4—22no—
373#117—22no—
374#117—22no—
375#117—41no—
376#117—41no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4C5×D411yescharacteristic
386C2×C4⋊C4C23×C511yescharacteristic
387C2×C4⋊C4C23×C511yescharacteristic
388C2×C4⋊C4C23×C511yescharacteristic
389C2×C4⋊C4C23×C511yescharacteristic
390C2×C4⋊C4C23×C511yescharacteristic
391C2×C4⋊C4C23×C511yescharacteristic
392C2×C4⋊C4C23×C511yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4C5×D411yescharacteristic
401C2×C22⋊C4C5×D411yescharacteristic
402C2×C42—21no—
403C2×C42—21no—
404C2×C42—21no—
405C2×C42C23×C511yescharacteristic
406#107—22no—
407#107—22no—
408#107—22no—
409#107—41no—
410#106—22no—
411#106C5×D414yescomplemented
412#103—22no—
413#103—22no—
414#103—22no—
415#103—41no—
416C22⋊C8—22no—
417C22⋊C8—22no—
418C22⋊C8—22no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424#95—21no—
425#95—21no—
426C22×C5—22no—
427C22×C5—22no—
428C22×C5—22no—
429C22×C5—41no—
430C22×C5—41no—
431C22×C5—41no—
432C22×C5—41no—
433C22×C5—41no—
434C22×C5—41no—
435C22×C5—41no—
436C22×C5—41no—
437C22×C5—41no—
438C22×C5—41no—
439C22×C5—41no—
440C22×C5C2×#12311yescharacteristic
441C22×C5D4211yescharacteristic
442C22×C5#54711yescharacteristic
443C22×C5C2×#13711yescharacteristic
444C22×C5#57511yescharacteristic
445C22×C5#57611yescharacteristic
446C22×C5#57811yescharacteristic
447C4×C5—22no—
448C4×C5—22no—
449C4×C5—41no—
450C4×C5—41no—
451C4×C5—42no—
452C4×C5—42no—
453C4×C5—81no—
454C4×C5—81no—
455C4×C5—81no—
456C4×C5—81no—
457C4×C5—81no—
458C4×C5—81no—
459C4×C5#52511yescharacteristic
460C4×C5#53911yescharacteristic
461C4×C5#54811yescharacteristic
462C4×C5#55311yescharacteristic
463C24C2×C5×D411yescharacteristic
464C24C2×C5×D411yescharacteristic
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—41no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—81no—
495C22×C4C2×C5×D411yescharacteristic
496C22×C4C2×C5×D411yescharacteristic
497C22×C4C2×C5×D411yescharacteristic
498C22×C4C2×C5×D411yescharacteristic
499C22×C4C5×#4112yes—
500C22×C4C5×#4112yes—
501C22×C4C24×C511yescharacteristic
502M16—28no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8C2×C5×D412yes—
514C2×C8C5×#4112yes—
515C4⋊C4—22no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—42no—
530C4⋊C4—42no—
531C4⋊C4—42no—
532C4⋊C4—81no—
533C4⋊C4—81no—
534C4⋊C4C2×C5×D412yes—
535C4⋊C4C2×C5×D412yes—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—42no—
539C22⋊C4—42no—
540C22⋊C4—42no—
541C22⋊C4—42no—
542C22⋊C4—81no—
543C22⋊C4—81no—
544C22⋊C4—81no—
545C42—21no—
546C42—21no—
547C42—42no—
548C42—42no—
549C42—42no—
550C2×C5—42no—
551C2×C5—81no—
552C2×C5#244311yescharacteristic
553C2×C5#309511yescharacteristic
554C2×C5#309811yescharacteristic
555C2×C5#326811yescharacteristic
556C2×C5#327611yescharacteristic
557C2×C5#334911yescharacteristic
558C2×C5#335711yescharacteristic
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—21no—
570C23—21no—
571C23—21no—
572C23C5×#12312yes—
573C23C22×C5×D411yescharacteristic
574Q8—41no—
575Q8—41no—
576Q8—41no—
577Q8—41no—
578D4—44no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—84no—
622C2×C4C5×#12312yes—
623C2×C4C5×#13712yes—
624C2×C4C22×C5×D411yescharacteristic
625C2×C4C2×C5×#4111yescharacteristic
626C2×C4C2×C5×#4111yescharacteristic
627C2×C4C2×C5×#4111yescharacteristic
628C2×C4C5×H(5,𝔽2)11yescharacteristic
629C2×C4C5×2−1+411yescharacteristic
630C8—22no—
631C8—22no—
632C8—41no—
633C8—41no—
634C5#2615111yescharacteristic, direct product factor, Sylow
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C2×C5×#12311yescharacteristic
650C22C5×D4211yescharacteristic
651C22C5×#54711yescharacteristic
652C22C2×C5×#13711yescharacteristic
653C22C5×#57511yescharacteristic
654C22C5×#57611yescharacteristic
655C22C5×#57811yescharacteristic
656C4—22no—
657C4—22no—
658C4—42no—
659C4—42no—
660C4—41no—
661C4—41no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4C5×#52511yescharacteristic
669C4C5×#53911yescharacteristic
670C4C5×#54811yescharacteristic
671C4C5×#55311yescharacteristic
672C2—42no—
673C2—81no—
674C2C5×#244311yescharacteristic
675C2C5×#309511yescharacteristic
676C2C5×#309811yescharacteristic
677C2C5×#326811yescharacteristic
678C2C5×#327611yescharacteristic
679C2C5×#334911yescharacteristic
680C2C5×#335711yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutator, Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C5 ◁ C2×C4×C5×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C5×#485C2semidirect
2. C2×C5×#428C2semidirect
5. C5×#2095C2semidirect
6. C5×#2083C2semidirect
7. C5×#2075C2semidirect
8. C5×#2036C2semidirect
9. C5×#1927C2semidirect
10. C5×#1920C2semidirect
11. C5×#1894C2semidirect
12. C5×#1873C2semidirect
14. C5×#1854C2semidirect
15. C5×#1852C2semidirect
61. #26151C5direct (N × H)
118. C5×#106D4semidirect
133. C2×#485C2×C5semidirect
134. C2×#428C2×C5semidirect
137. #2095C2×C5semidirect
138. #2083C2×C5semidirect
139. #2075C2×C5semidirect
140. #2036C2×C5semidirect
141. #1927C2×C5semidirect
142. #1920C2×C5semidirect
143. #1894C2×C5semidirect
144. #1873C2×C5semidirect
146. #1854C2×C5semidirect
147. #1852C2×C5semidirect
411. #106C5×D4semidirect
634. C5#26151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4852
C2×C5×#4282
C5×#24172
C5×#23542
C5×#20952
C5×#20832
C5×#20752
C5×#20362
C5×#19272
C5×#19202
C5×#18942
C5×#18732
C5×#18702
C5×#18542
C5×#18522
#261515