Finite Group Databasebeta

← C5×#22712 #11945432

Subgroups — C5×#22712 #11945432

Order 1280.

898 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C5×#435C211yesmaximal, characteristic
2C5×#2354C211yesmaximal, characteristic
3C5×#2352C211yesmaximal, characteristic
4C5×#1949C211yesmaximal, characteristic, complemented
5C5×#1947C211yesmaximal, characteristic, complemented
6C5×#1854C211yesmaximal, characteristic, complemented
7C5×#1854C211yesmaximal, characteristic, complemented
8C5×#1854C211yesmaximal, characteristic, complemented
9C5×#1852C211yesmaximal, characteristic, complemented
10C5×#1836C211yesmaximal, characteristic, complemented
11C5×#1809C211yesmaximal, characteristic, complemented
12C5×#1808C211yesmaximal, characteristic, complemented
13C5×#1776C211yesmaximal, characteristic, complemented
14C5×#1736C211yesmaximal, characteristic, complemented
15C5×#1735C211yesmaximal, characteristic, complemented
16C22×C5×M16C2211yescharacteristic
17C23×C5×C8C2211yescharacteristic
18C2×C4×C5×D4C2211yescharacteristic
19C2×C5×#117C2211yescharacteristic
20C2×C5×#117C2211yescharacteristic
21C2×C5×#117C2211yescharacteristic
22C22×C5×C4⋊C4C2211yescharacteristic
23C5×#435C418yescomplemented
24C2×C5×#107C2211yescharacteristic
25C2×C5×#107C2211yescharacteristic
26C2×C5×#107C2211yescharacteristic
27C2×C5×#107C2211yescharacteristic
28C2×C5×#106C2211yescharacteristic
29C2×C5×#106C2211yescharacteristic
30C2×C5×C4⋊C8C2211yescharacteristic
31C2×C5×C22⋊C8C2211yescharacteristic
32C2×C5×C22⋊C8C2211yescharacteristic
33C2×C5×#97C2211yescharacteristic
34C5×#390—21no—
35C5×#388—21no—
36C5×#388—21no—
37C5×#388—21no—
38C5×#387—21no—
39C5×#386—21no—
40C5×#384C2211yescharacteristic
41C5×#382C2211yescharacteristic
42C5×#380C2211yescharacteristic
43C5×#380C2211yescharacteristic
44C5×#380C2211yescharacteristic
45C5×#380C2211yescharacteristic
46C4×C5×C4⋊C4—21no—
47C4×C5×C4⋊C4C2211yescharacteristic
48C4×C5×C4⋊C4C2211yescharacteristic
49C4×C5×C22⋊C4—21no—
50C5×#340C2211yescharacteristic
51C5×#340C2211yescharacteristic
52C5×#340C2211yescharacteristic
53C5×#340C2211yescharacteristic
54C5×#340C2211yescharacteristic
55C5×#340C2211yescharacteristic
56C5×#340C2211yescharacteristic
57C5×#340C2211yescharacteristic
58C5×#340C2211yescharacteristic
59C5×#340C2211yescharacteristic
60#22712C511yesmaximal, characteristic, direct product factor, Sylow
61C22×C5×D4D411yescharacteristic
62C23×C4×C5—21no—
63C23×C4×C5C2311yescharacteristic
64C23×C4×C5C2311yescharacteristic
65C2×C5×M16—41no—
66C2×C5×M16—41no—
67C2×C5×M16C2×C414yes—
68C22×C5×C8—41no—
69C22×C5×C8—41no—
70C22×C5×C8C2×C414yescomplemented
71C22×C5×C8C2311yescharacteristic
72C22×C5×C8C2311yescharacteristic
73C22×C5×C8C2311yescharacteristic
74C22×C5×C8C2311yescharacteristic
75C4×C5×D4C2×C414yes—
76C4×C5×D4Q814yes—
77C5×#117—22no—
78C5×#117—22no—
79C5×#117—22no—
80C5×#117—41no—
81C5×#117—41no—
82C5×#117—41no—
83C2×C5×C4⋊C4—22no—
84C2×C5×C4⋊C4—21no—
85C2×C5×C4⋊C4—21no—
86C2×C5×C4⋊C4—21no—
87C2×C5×C4⋊C4—41no—
88C2×C5×C4⋊C4D411yescharacteristic
89C2×C5×C4⋊C4C2311yescharacteristic
90C2×C5×C4⋊C4C2311yescharacteristic
91C2×C5×C4⋊C4C2311yescharacteristic
92C2×C5×C4⋊C4C2311yescharacteristic
93C2×C5×C4⋊C4C2311yescharacteristic
94C2×C5×C4⋊C4C2311yescharacteristic
95C2×C5×C4⋊C4C2311yescharacteristic
96C2×C5×C4⋊C4C2311yescharacteristic
97C2×C5×C22⋊C4—21no—
98C2×C5×C22⋊C4—21no—
99C2×C5×C22⋊C4—21no—
100C2×C5×C22⋊C4—21no—
101C2×C5×C22⋊C4—21no—
102C2×C5×C22⋊C4—21no—
103C2×C5×C22⋊C4—21no—
104C2×C5×C22⋊C4D411yescharacteristic
105C2×C5×C22⋊C4D411yescharacteristic
106C2×C42×C5—21no—
107C2×C42×C5—21no—
108C2×C42×C5—21no—
109C2×C42×C5—21no—
110C2×C42×C5—21no—
111C2×C42×C5C2311yescharacteristic
112C5×#107—22no—
113C5×#107—41no—
114C5×#107—41no—
115C5×#107—41no—
116C5×#106—22no—
117C5×#106—41no—
118C5×C4⋊C8C2×C414yescomplemented
119C5×C22⋊C8C2×C414yes—
120C5×C22⋊C8C2×C414yescomplemented
121C5×#97C2×C414yescomplemented
122C5×#95—21no—
123C5×#95—21no—
124C5×#95—21no—
125C5×#95—21no—
126C5×#95—21no—
127C5×#95—21no—
128C5×#95—21no—
129C5×#95—21no—
130C2×#435C2×C511yescharacteristic
131#2354C2×C511yescharacteristic
132#2352C2×C511yescharacteristic
133#1949C2×C511yescharacteristic, complemented
134#1947C2×C511yescharacteristic, complemented
135#1854C2×C511yescharacteristic, complemented
136#1854C2×C511yescharacteristic, complemented
137#1854C2×C511yescharacteristic, complemented
138#1852C2×C511yescharacteristic, complemented
139#1836C2×C511yescharacteristic, complemented
140#1809C2×C511yescharacteristic, complemented
141#1808C2×C511yescharacteristic, complemented
142#1776C2×C511yescharacteristic, complemented
143#1736C2×C511yescharacteristic, complemented
144#1735C2×C511yescharacteristic, complemented
145C24×C5C2×D411yescharacteristic
146C24×C5C2×D411yescharacteristic
147C2×C5×D4—41no—
148C2×C5×D4—41no—
149C2×C5×D4C4⋊C414yes—
150C22×C4×C5—21no—
151C22×C4×C5—21no—
152C22×C4×C5—21no—
153C22×C4×C5—21no—
154C22×C4×C5—21no—
155C22×C4×C5—21no—
156C22×C4×C5—21no—
157C22×C4×C5—21no—
158C22×C4×C5—21no—
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—42no—
167C22×C4×C5—42no—
168C22×C4×C5—81no—
169C22×C4×C5C22×C412yes—
170C22×C4×C5C22×C412yes—
171C22×C4×C5C2×D411yescharacteristic
172C22×C4×C5C2×D411yescharacteristic
173C22×C4×C5C2×D411yescharacteristic
174C22×C4×C5C2×D411yescharacteristic
175C22×C4×C5C2×Q812yes—
176C22×C4×C5C2×Q812yes—
177C22×C4×C5C2411yescharacteristic
178C5×M16—44no—
179C2×C5×C8—21no—
180C2×C5×C8—21no—
181C2×C5×C8—21no—
182C2×C5×C8—21no—
183C2×C5×C8—21no—
184C2×C5×C8—21no—
185C2×C5×C8—21no—
186C2×C5×C8—21no—
187C2×C5×C8—44no—
188C2×C5×C8C22×C412yes—
189C2×C5×C8C22×C412yes—
190C2×C5×C8C22×C412yes—
191C2×C5×C8C22×C412yes—
192C5×C4⋊C4—21no—
193C5×C4⋊C4—21no—
194C5×C4⋊C4—21no—
195C5×C4⋊C4—21no—
196C5×C4⋊C4—21no—
197C5×C4⋊C4—21no—
198C5×C4⋊C4—21no—
199C5×C4⋊C4—21no—
200C5×C4⋊C4—21no—
201C5×C4⋊C4—21no—
202C5×C4⋊C4—21no—
203C5×C4⋊C4—21no—
204C5×C4⋊C4—21no—
205C5×C4⋊C4—21no—
206C5×C4⋊C4—42no—
207C5×C4⋊C4—42no—
208C5×C4⋊C4—81no—
209C5×C4⋊C4C4⋊C414yes—
210C5×C4⋊C4#4112yes—
211C5×C4⋊C4#4112yes—
212C5×C22⋊C4—42no—
213C5×C22⋊C4—42no—
214C5×C22⋊C4—42no—
215C5×C22⋊C4—42no—
216C5×C22⋊C4—81no—
217C5×C22⋊C4—81no—
218C5×C22⋊C4—81no—
219C5×C22⋊C4C4⋊C414yes—
220C5×C22⋊C4C4⋊C414yes—
221C42×C5—42no—
222C42×C5—42no—
223C42×C5—42no—
224C42×C5—42no—
225C42×C5—81no—
226C42×C5C22×C412yes—
227C42×C5C2×Q812yes—
228C22×M16C22×C511yescharacteristic
229C23×C8C22×C511yescharacteristic
230C2×C4×D4C22×C511yescharacteristic
231C2×#117C22×C511yescharacteristic
232C2×#117C22×C511yescharacteristic
233C2×#117C22×C511yescharacteristic
234C22×C4⋊C4C22×C511yescharacteristic
235#435C4×C518yescomplemented
236C2×#107C22×C511yescharacteristic
237C2×#107C22×C511yescharacteristic
238C2×#107C22×C511yescharacteristic
239C2×#107C22×C511yescharacteristic
240C2×#106C22×C511yescharacteristic
241C2×#106C22×C511yescharacteristic
242C2×C4⋊C8C22×C511yescharacteristic
243C2×C22⋊C8C22×C511yescharacteristic
244C2×C22⋊C8C22×C511yescharacteristic
245C2×#97C22×C511yescharacteristic
246#390—21no—
247#388—21no—
248#388—21no—
249#388—21no—
250#387—21no—
251#386—21no—
252#384C22×C511yescharacteristic
253#382C22×C511yescharacteristic
254#380C22×C511yescharacteristic
255#380C22×C511yescharacteristic
256#380C22×C511yescharacteristic
257#380C22×C511yescharacteristic
258C4×C4⋊C4—21no—
259C4×C4⋊C4C22×C511yescharacteristic
260C4×C4⋊C4C22×C511yescharacteristic
261C4×C22⋊C4—21no—
262#340C22×C511yescharacteristic
263#340C22×C511yescharacteristic
264#340C22×C511yescharacteristic
265#340C22×C511yescharacteristic
266#340C22×C511yescharacteristic
267#340C22×C511yescharacteristic
268#340C22×C511yescharacteristic
269#340C22×C511yescharacteristic
270#340C22×C511yescharacteristic
271#340C22×C511yescharacteristic
272C23×C5—21no—
273C23×C5—21no—
274C23×C5—21no—
275C23×C5—21no—
276C23×C5—21no—
277C23×C5—21no—
278C23×C5—21no—
279C23×C5—21no—
280C23×C5—21no—
281C23×C5—21no—
282C23×C5—21no—
283C23×C5—21no—
284C23×C5C2×C4⋊C412yes—
285C23×C5C2×C4⋊C412yes—
286C23×C5C22×D411yescharacteristic
287C5×D4—44no—
288C2×C4×C5—21no—
289C2×C4×C5—21no—
290C2×C4×C5—21no—
291C2×C4×C5—21no—
292C2×C4×C5—21no—
293C2×C4×C5—21no—
294C2×C4×C5—21no—
295C2×C4×C5—21no—
296C2×C4×C5—22no—
297C2×C4×C5—22no—
298C2×C4×C5—22no—
299C2×C4×C5—22no—
300C2×C4×C5—22no—
301C2×C4×C5—22no—
302C2×C4×C5—22no—
303C2×C4×C5—22no—
304C2×C4×C5—22no—
305C2×C4×C5—22no—
306C2×C4×C5—41no—
307C2×C4×C5—41no—
308C2×C4×C5—41no—
309C2×C4×C5—41no—
310C2×C4×C5—41no—
311C2×C4×C5—41no—
312C2×C4×C5—41no—
313C2×C4×C5—41no—
314C2×C4×C5—41no—
315C2×C4×C5—41no—
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—84no—
329C2×C4×C5C2×C4⋊C412yes—
330C2×C4×C5C2×C4⋊C412yes—
331C2×C4×C5C2×C4⋊C412yes—
332C2×C4×C5C2×C4⋊C412yes—
333C2×C4×C5C23×C411yescharacteristic
334C2×C4×C5C22×Q811yescharacteristic
335C2×C4×C5C2×#4111yescharacteristic
336C2×C4×C5C2×#4111yescharacteristic
337C2×C4×C5H(5,𝔽2)11yescharacteristic
338C2×C4×C5H(5,𝔽2)11yescharacteristic
339C5×C8—22no—
340C5×C8—22no—
341C5×C8—22no—
342C5×C8—22no—
343C22×D4C5×D411yescharacteristic
344C23×C4—21no—
345C23×C4C23×C511yescharacteristic
346C23×C4C23×C511yescharacteristic
347C2×M16—41no—
348C2×M16—41no—
349C2×M16C2×C4×C514yes—
350C22×C8—41no—
351C22×C8—41no—
352C22×C8C2×C4×C514yescomplemented
353C22×C8C23×C511yescharacteristic
354C22×C8C23×C511yescharacteristic
355C22×C8C23×C511yescharacteristic
356C22×C8C23×C511yescharacteristic
357C4×D4C2×C4×C514yes—
358C4×D4C5×Q814yes—
359#117—22no—
360#117—22no—
361#117—22no—
362#117—41no—
363#117—41no—
364#117—41no—
365C2×C4⋊C4—22no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—41no—
370C2×C4⋊C4C5×D411yescharacteristic
371C2×C4⋊C4C23×C511yescharacteristic
372C2×C4⋊C4C23×C511yescharacteristic
373C2×C4⋊C4C23×C511yescharacteristic
374C2×C4⋊C4C23×C511yescharacteristic
375C2×C4⋊C4C23×C511yescharacteristic
376C2×C4⋊C4C23×C511yescharacteristic
377C2×C4⋊C4C23×C511yescharacteristic
378C2×C4⋊C4C23×C511yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4C5×D411yescharacteristic
387C2×C22⋊C4C5×D411yescharacteristic
388C2×C42—21no—
389C2×C42—21no—
390C2×C42—21no—
391C2×C42—21no—
392C2×C42—21no—
393C2×C42C23×C511yescharacteristic
394#107—22no—
395#107—41no—
396#107—41no—
397#107—41no—
398#106—22no—
399#106—41no—
400C4⋊C8C2×C4×C514yescomplemented
401C22⋊C8C2×C4×C514yes—
402C22⋊C8C2×C4×C514yescomplemented
403#97C2×C4×C514yescomplemented
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412C22×C5—22no—
413C22×C5—22no—
414C22×C5—22no—
415C22×C5—22no—
416C22×C5—22no—
417C22×C5—22no—
418C22×C5—41no—
419C22×C5—41no—
420C22×C5—41no—
421C22×C5—41no—
422C22×C5—41no—
423C22×C5—41no—
424C22×C5—41no—
425C22×C5—41no—
426C22×C5C22×C4⋊C411yescharacteristic
427C22×C5#54611yescharacteristic
428C22×C5#54611yescharacteristic
429C22×C5#57511yescharacteristic
430C22×C5#57511yescharacteristic
431C22×C5#57611yescharacteristic
432C22×C5#57811yescharacteristic
433C4×C5—22no—
434C4×C5—22no—
435C4×C5—22no—
436C4×C5—22no—
437C4×C5—42no—
438C4×C5—42no—
439C4×C5—81no—
440C4×C5—81no—
441C4×C5—81no—
442C4×C5—81no—
443C4×C5—81no—
444C4×C5—81no—
445C4×C5C4×#4111yescharacteristic
446C4×C5#51811yescharacteristic
447C4×C5#55411yescharacteristic
448C4×C5#55411yescharacteristic
449C24C2×C5×D411yescharacteristic
450C24C2×C5×D411yescharacteristic
451C2×D4—41no—
452C2×D4—41no—
453C2×D4C5×C4⋊C414yes—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4C22×C4×C512yes—
474C22×C4C22×C4×C512yes—
475C22×C4C2×C5×D411yescharacteristic
476C22×C4C2×C5×D411yescharacteristic
477C22×C4C2×C5×D411yescharacteristic
478C22×C4C2×C5×D411yescharacteristic
479C22×C4C2×C5×Q812yes—
480C22×C4C2×C5×Q812yes—
481C22×C4C24×C511yescharacteristic
482M16—44no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—44no—
492C2×C8C22×C4×C512yes—
493C2×C8C22×C4×C512yes—
494C2×C8C22×C4×C512yes—
495C2×C8C22×C4×C512yes—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—81no—
513C4⋊C4C5×C4⋊C414yes—
514C4⋊C4C5×#4112yes—
515C4⋊C4C5×#4112yes—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—81no—
521C22⋊C4—81no—
522C22⋊C4—81no—
523C22⋊C4C5×C4⋊C414yes—
524C22⋊C4C5×C4⋊C414yes—
525C42—42no—
526C42—42no—
527C42—42no—
528C42—42no—
529C42—81no—
530C42C22×C4×C512yes—
531C42C2×C5×Q812yes—
532C2×C5—42no—
533C2×C5—42no—
534C2×C5#234911yescharacteristic
535C2×C5#291111yescharacteristic
536C2×C5#291311yescharacteristic
537C2×C5#330911yescharacteristic
538C2×C5#331311yescharacteristic
539C2×C5#331511yescharacteristic
540C2×C5#331911yescharacteristic
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23C2×C5×C4⋊C412yes—
554C23C2×C5×C4⋊C412yes—
555C23C22×C5×D411yescharacteristic
556D4—44no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—84no—
598C2×C4C2×C5×C4⋊C412yes—
599C2×C4C2×C5×C4⋊C412yes—
600C2×C4C2×C5×C4⋊C412yes—
601C2×C4C2×C5×C4⋊C412yes—
602C2×C4C23×C4×C511yescharacteristic
603C2×C4C22×C5×Q811yescharacteristic
604C2×C4C2×C5×#4111yescharacteristic
605C2×C4C2×C5×#4111yescharacteristic
606C2×C4C5×H(5,𝔽2)11yescharacteristic
607C2×C4C5×H(5,𝔽2)11yescharacteristic
608C8—22no—
609C8—22no—
610C8—22no—
611C8—22no—
612C5#2271211yescharacteristic, direct product factor, Sylow
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22C22×C5×C4⋊C411yescharacteristic
628C22C5×#54611yescharacteristic
629C22C5×#54611yescharacteristic
630C22C5×#57511yescharacteristic
631C22C5×#57511yescharacteristic
632C22C5×#57611yescharacteristic
633C22C5×#57811yescharacteristic
634C4—22no—
635C4—22no—
636C4—22no—
637C4—22no—
638C4—42no—
639C4—42no—
640C4—81no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—81no—
645C4—81no—
646C4C4×C5×#4111yescharacteristic
647C4C5×#51811yescharacteristic
648C4C5×#55411yescharacteristic
649C4C5×#55411yescharacteristic
650C2—42no—
651C2—42no—
652C2C5×#234911yescharacteristic
653C2C5×#291111yescharacteristic
654C2C5×#291311yescharacteristic
655C2C5×#330911yescharacteristic
656C2C5×#331311yescharacteristic
657C2C5×#331511yescharacteristic
658C2C5×#331911yescharacteristic
subgroupG/H
center, socleC23×C5C22×D4
commutatorC2×C4C23×C4×C5
Frattini, cosocleC22×C4C24×C5
prime radicalC22×C5×D4D4
LCSG ▷ C2×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
4. C5×#1949C2semidirect
5. C5×#1947C2semidirect
6. C5×#1854C2semidirect
7. C5×#1854C2semidirect
8. C5×#1854C2semidirect
9. C5×#1852C2semidirect
10. C5×#1836C2semidirect
11. C5×#1809C2semidirect
12. C5×#1808C2semidirect
13. C5×#1776C2semidirect
14. C5×#1736C2semidirect
15. C5×#1735C2semidirect
23. C5×#435C4semidirect
60. #22712C5direct (N × H)
70. C22×C5×C8C2×C4semidirect
118. C5×C4⋊C8C2×C4semidirect
120. C5×C22⋊C8C2×C4semidirect
121. C5×#97C2×C4semidirect
133. #1949C2×C5semidirect
134. #1947C2×C5semidirect
135. #1854C2×C5semidirect
136. #1854C2×C5semidirect
137. #1854C2×C5semidirect
138. #1852C2×C5semidirect
139. #1836C2×C5semidirect
140. #1809C2×C5semidirect
141. #1808C2×C5semidirect
142. #1776C2×C5semidirect
143. #1736C2×C5semidirect
144. #1735C2×C5semidirect
235. #435C4×C5semidirect
352. C22×C8C2×C4×C5semidirect
400. C4⋊C8C2×C4×C5semidirect
402. C22⋊C8C2×C4×C5semidirect
403. #97C2×C4×C5semidirect
612. C5#22712direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C5×#4352
C5×#23542
C5×#23522
C5×#19492
C5×#19472
C5×#18542
C5×#18522
C5×#18362
C5×#18092
C5×#18082
C5×#17762
C5×#17362
C5×#17352
#227125