Finite Group Databasebeta

← C5×#83446 #14436075

Subgroups — C5×#83446 #14436075

Order 1920.

744 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×#541C211yesmaximal, characteristic, complemented
2C5×#5523C211yesmaximal, characteristic
3C5×#5090C211yesmaximal, characteristic, complemented
4C5×#5083C211yesmaximal, characteristic, complemented
5C5×#5066C211yesmaximal, characteristic, complemented
6C5×#5063C211yesmaximal, characteristic, complemented
7C5×#5047C211yesmaximal, characteristic
8C5×#5047C211yesmaximal, characteristic
9C5×#5044C211yesmaximal, characteristic, complemented
10C5×#5043C211yesmaximal, characteristic, complemented
11C5×#5030C211yesmaximal, characteristic, complemented
12C4×C5×#216C211yesmaximal, characteristic, complemented
13C5×#5026C211yesmaximal, characteristic, complemented
14C4×C5×#215C211yesmaximal, characteristic, complemented
15C5×#5000C211yesmaximal, characteristic, complemented
16C5×#3120—31nomaximal, Hall
17C2×C5×#235C2211yescharacteristic
18C3×C5×C4⋊Q8C2211yescharacteristic
19C3×C5×#126—21no—
20C3×C5×#126—21no—
21C3×C5×#125—21no—
22C3×C5×#125—21no—
23C3×C5×#125C2211yescharacteristic
24C3×C5×C22⋊Q8C2211yescharacteristic
25C3×C5×C22⋊Q8C2211yescharacteristic
26C3×C4×C5×Q8C2211yescharacteristic
27C3×C4×C5×Q8C2211yescharacteristic
28C3×C5×#117C2211yescharacteristic
29C2×C5×#216C2211yescharacteristic
30C2×C5×#216C2211yescharacteristic
31C2×C5×#215C2211yescharacteristic
32C2×C5×#215C2211yescharacteristic
33C2×C5×C4⋊Dic3C2211yescharacteristic
34C5×#892—21no—
35C5×D3×C4⋊C4—21no—
36C5×#67⋊C4—21no—
37C5×#67⋊C4—21no—
38C4×C5×D12C2211yescharacteristic
39C4×C5×D12C2211yescharacteristic
40C4×C5×Dic6C2211yescharacteristic
41C4×C5×Dic6C2211yescharacteristic
42C5×#835C2211yescharacteristic
43C5×#835C2211yescharacteristic
44C5×#835C2211yescharacteristic
45C5×#835C2211yescharacteristic
46C5×#830C2211yescharacteristic
47C5×#830C2211yescharacteristic
48C5×#810C2211yescharacteristic
49C5×#810C2211yescharacteristic
50C5×#809C2211yescharacteristic
51C5×#809C2211yescharacteristic
52C5×#808C2211yescharacteristic
53C5×#808C2211yescharacteristic
54C5×#807C2211yescharacteristic
55C5×#807C2211yescharacteristic
56C5×C4⋊(C3⋊C8)C2211yescharacteristic
57C5×C4⋊(C3⋊C8)C2211yescharacteristic
58C5×#803C2211yescharacteristic
59C4×C5×C3⋊C8C2211yescharacteristic
60#83446C511yesmaximal, characteristic, direct product factor, Hall
61C5×#541D311yescharacteristic, complemented
62C5×#520—31no—
63C5×#484—31no—
64C5×#483—31no—
65C5×#479—31no—
66C5×#478—31no—
67C5×#462—31no—
68C5×#461—31no—
69C5×#452—31no—
70C5×#452—31no—
71C5×#441—31no—
72C5×#440—31no—
73C4×C5×Q16—31no—
74C4×C5×SD16—31no—
75C5×#433—31no—
76C2×C3×C5×Q8C2311yescharacteristic
77C2×C3×C5×Q8C2311yescharacteristic
78C22×C3×C4×C5C2311yescharacteristic
79C2×C5×#67—21no—
80C22×C5×Dic3—21no—
81C5×#235—22no—
82C5×#235—22no—
83C2×C5×D12C2311yescharacteristic
84C2×C4×C5×D3—21no—
85C2×C4×C5×D3—21no—
86C2×C4×C5×D3—21no—
87C2×C5×Dic6C2311yescharacteristic
88C3×C5×C4⋊C4—21no—
89C3×C5×C4⋊C4—21no—
90C3×C5×C4⋊C4—21no—
91C3×C5×C4⋊C4—21no—
92C3×C5×C4⋊C4—21no—
93C3×C5×C4⋊C4—21no—
94C3×C5×C4⋊C4—21no—
95C3×C5×C4⋊C4—21no—
96C3×C5×C4⋊C4D411yescharacteristic
97C3×C5×C4⋊C4D411yescharacteristic
98C3×C5×C4⋊C4C2311yescharacteristic
99C3×C5×C4⋊C4C2311yescharacteristic
100C3×C5×C22⋊C4—21no—
101C3×C5×C22⋊C4—21no—
102C3×C5×C22⋊C4D411yescharacteristic
103C3×C5×C22⋊C4D411yescharacteristic
104C3×C42×C5—21no—
105C3×C42×C5—21no—
106C3×C42×C5C2311yescharacteristic
107C3×C42×C5C2311yescharacteristic
108C5×#216—22no—
109C5×#216—22no—
110C5×#215—22no—
111C5×#215—22no—
112C5×(C2×D3)⋊C4—21no—
113C5×(C2×D3)⋊C4—21no—
114C5×C4⋊Dic3—21no—
115C5×C4⋊Dic3C2311yescharacteristic
116C5×C4⋊Dic3C2311yescharacteristic
117C5×Dic3⋊C4—21no—
118C5×Dic3⋊C4—21no—
119C4×C5×Dic3—21no—
120C4×C5×Dic3—21no—
121C2×C5×C3⋊C8C2311yescharacteristic
122C2×C5×C3⋊C8C2311yescharacteristic
123C2×C5×C3⋊C8C2311yescharacteristic
124C2×C5×C3⋊C8C2311yescharacteristic
125C3×#541C2×C511yescharacteristic, complemented
126#5523C2×C511yescharacteristic
127#5090C2×C511yescharacteristic, complemented
128#5083C2×C511yescharacteristic, complemented
129#5066C2×C511yescharacteristic, complemented
130#5063C2×C511yescharacteristic, complemented
131#5047C2×C511yescharacteristic
132#5047C2×C511yescharacteristic
133#5044C2×C511yescharacteristic, complemented
134#5043C2×C511yescharacteristic, complemented
135#5030C2×C511yescharacteristic, complemented
136C4×#216C2×C511yescharacteristic, complemented
137#5026C2×C511yescharacteristic, complemented
138C4×#215C2×C511yescharacteristic, complemented
139#5000C2×C511yescharacteristic, complemented
140C2×C5×#41—31no—
141C2×C5×Q16—31no—
142C2×C5×Q16—31no—
143C2×C5×SD16—31no—
144C2×C5×SD16—31no—
145C5×C4⋊Q8C2×D311yescharacteristic
146C5×#126—21no—
147C5×#126—21no—
148C5×#125—21no—
149C5×#125—21no—
150C5×#125C2×D311yescharacteristic
151C5×C22⋊Q8C2×D311yescharacteristic
152C5×C22⋊Q8C2×D311yescharacteristic
153C4×C5×Q8—31no—
154C4×C5×Q8—31no—
155C4×C5×Q8C2×D311yescharacteristic
156C4×C5×Q8C2×D311yescharacteristic
157C4×C5×D4—31no—
158C4×C5×D4—31no—
159C4×C5×D4—61no—
160C4×C5×D4—61no—
161C5×#117—61no—
162C5×#117C2×D311yescharacteristic
163C2×C5×C4⋊C4—31no—
164C2×C5×C4⋊C4—61no—
165C5×#107—31no—
166C5×#107—31no—
167C5×#106—31no—
168C5×#106—31no—
169C5×C4⋊C8—31no—
170C5×C4⋊C8—31no—
171C5×#103—31no—
172C5×#103—31no—
173C5×#103—31no—
174C5×#103—31no—
175C5×#103—31no—
176C5×#103—31no—
177C5×#102—31no—
178C5×#102—31no—
179C5×C22⋊C8—31no—
180C5×C22⋊C8—31no—
181C5×#97—31no—
182C4×C5×C8—31no—
183#3120—31noSylow
184C23×C3×C5C2×D411yescharacteristic
185C22×C5×D3—21no—
186C3×C5×Q8—21no—
187C3×C5×Q8—21no—
188C3×C5×Q8—21no—
189C3×C5×Q8—21no—
190C2×C3×C4×C5—21no—
191C2×C3×C4×C5—21no—
192C2×C3×C4×C5—21no—
193C2×C3×C4×C5—21no—
194C2×C3×C4×C5—21no—
195C2×C3×C4×C5—21no—
196C2×C3×C4×C5C2×D411yescharacteristic
197C2×C3×C4×C5C2×D411yescharacteristic
198C2×C3×C4×C5C2×D411yescharacteristic
199C2×C3×C4×C5C2×D411yescharacteristic
200C2×C3×C4×C5C2×D411yescharacteristic
201C2×C3×C4×C5C2411yescharacteristic
202C5×#67—24no—
203C2×C5×Dic3—21no—
204C2×C5×Dic3—21no—
205C2×C5×Dic3—21no—
206C2×C5×Dic3—81no—
207C5×D12—21no—
208C5×D12#4112yes—
209C4×C5×D3—24no—
210C4×C5×D3—81no—
211C4×C5×D3—81no—
212C5×Dic6—21no—
213C5×Dic6#4112yes—
214C5×C3⋊C8—21no—
215C5×C3⋊C8—21no—
216C5×C3⋊C8—21no—
217C5×C3⋊C8—21no—
218C2×#235C22×C511yescharacteristic
219C3×C4⋊Q8C22×C511yescharacteristic
220C3×#126—21no—
221C3×#126—21no—
222C3×#125—21no—
223C3×#125—21no—
224C3×#125C22×C511yescharacteristic
225C3×C22⋊Q8C22×C511yescharacteristic
226C3×C22⋊Q8C22×C511yescharacteristic
227C3×C4×Q8C22×C511yescharacteristic
228C3×C4×Q8C22×C511yescharacteristic
229C3×#117C22×C511yescharacteristic
230C2×#216C22×C511yescharacteristic
231C2×#216C22×C511yescharacteristic
232C2×#215C22×C511yescharacteristic
233C2×#215C22×C511yescharacteristic
234C2×C4⋊Dic3C22×C511yescharacteristic
235#892—21no—
236D3×C4⋊C4—21no—
237#67⋊C4—21no—
238#67⋊C4—21no—
239C4×D12C22×C511yescharacteristic
240C4×D12C22×C511yescharacteristic
241C4×Dic6C22×C511yescharacteristic
242C4×Dic6C22×C511yescharacteristic
243#835C22×C511yescharacteristic
244#835C22×C511yescharacteristic
245#835C22×C511yescharacteristic
246#835C22×C511yescharacteristic
247#830C22×C511yescharacteristic
248#830C22×C511yescharacteristic
249#810C22×C511yescharacteristic
250#810C22×C511yescharacteristic
251#809C22×C511yescharacteristic
252#809C22×C511yescharacteristic
253#808C22×C511yescharacteristic
254#808C22×C511yescharacteristic
255#807C22×C511yescharacteristic
256#807C22×C511yescharacteristic
257C4⋊(C3⋊C8)C22×C511yescharacteristic
258C4⋊(C3⋊C8)C22×C511yescharacteristic
259#803C22×C511yescharacteristic
260C4×C3⋊C8C22×C511yescharacteristic
261C5×#41—62no—
262C5×#41—62no—
263C2×C5×Q8—31no—
264C2×C5×Q8C22×D311yescharacteristic
265C2×C5×Q8C22×D311yescharacteristic
266C2×C5×D4—31no—
267C2×C5×D4—61no—
268C22×C4×C5—61no—
269C22×C4×C5—61no—
270C22×C4×C5—61no—
271C22×C4×C5—61no—
272C22×C4×C5C22×D311yescharacteristic
273C5×Q16—62no—
274C5×Q16—62no—
275C5×SD16—62no—
276C5×SD16—62no—
277C2×C5×C8—31no—
278C2×C5×C8—31no—
279C2×C5×C8—31no—
280C2×C5×C8—31no—
281C5×C4⋊C4—21no—
282C5×C4⋊C4—21no—
283C5×C4⋊C4—21no—
284C5×C4⋊C4—21no—
285C5×C4⋊C4—21no—
286C5×C4⋊C4—21no—
287C5×C4⋊C4—21no—
288C5×C4⋊C4—21no—
289C5×C4⋊C4—31no—
290C5×C4⋊C4—31no—
291C5×C4⋊C4—61no—
292C5×C4⋊C4—61no—
293C5×C4⋊C4—61no—
294C5×C4⋊C4#6711yescharacteristic
295C5×C4⋊C4#6711yescharacteristic
296C5×C4⋊C4C22×D311yescharacteristic
297C5×C4⋊C4C22×D311yescharacteristic
298C5×C22⋊C4—21no—
299C5×C22⋊C4—21no—
300C5×C22⋊C4—61no—
301C5×C22⋊C4—61no—
302C5×C22⋊C4#6711yescharacteristic
303C5×C22⋊C4#6711yescharacteristic
304C42×C5—21no—
305C42×C5—21no—
306C42×C5—61no—
307C42×C5—61no—
308C42×C5C22×D311yescharacteristic
309C42×C5C22×D311yescharacteristic
310#541C5×D311yescharacteristic, complemented
311#520—31no—
312#484—31no—
313#483—31no—
314#479—31no—
315#478—31no—
316#462—31no—
317#461—31no—
318#452—31no—
319#452—31no—
320#441—31no—
321#440—31no—
322C4×Q16—31no—
323C4×SD16—31no—
324#433—31no—
325C22×C3×C5—21no—
326C22×C3×C5—21no—
327C22×C3×C5—21no—
328C22×C3×C5C22×D411yescharacteristic
329C2×C5×D3—22no—
330C2×C5×D3—41no—
331C2×C5×D3—41no—
332C3×C4×C5—21no—
333C3×C4×C5—21no—
334C3×C4×C5—21no—
335C3×C4×C5—21no—
336C3×C4×C5—21no—
337C3×C4×C5—41no—
338C3×C4×C5—41no—
339C3×C4×C5—41no—
340C3×C4×C5—41no—
341C3×C4×C5C2×#4111yescharacteristic
342C3×C4×C5C2×#4111yescharacteristic
343C5×Dic3—22no—
344C5×Dic3—41no—
345C5×Dic3—41no—
346C2×C3×Q8C23×C511yescharacteristic
347C2×C3×Q8C23×C511yescharacteristic
348C22×C3×C4C23×C511yescharacteristic
349C2×#67—21no—
350C22×Dic3—21no—
351#235—22no—
352#235—22no—
353C2×D12C23×C511yescharacteristic
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3—21no—
357C2×Dic6C23×C511yescharacteristic
358C3×C4⋊C4—21no—
359C3×C4⋊C4—21no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—21no—
363C3×C4⋊C4—21no—
364C3×C4⋊C4—21no—
365C3×C4⋊C4—21no—
366C3×C4⋊C4C5×D411yescharacteristic
367C3×C4⋊C4C5×D411yescharacteristic
368C3×C4⋊C4C23×C511yescharacteristic
369C3×C4⋊C4C23×C511yescharacteristic
370C3×C22⋊C4—21no—
371C3×C22⋊C4—21no—
372C3×C22⋊C4C5×D411yescharacteristic
373C3×C22⋊C4C5×D411yescharacteristic
374C3×C42—21no—
375C3×C42—21no—
376C3×C42C23×C511yescharacteristic
377C3×C42C23×C511yescharacteristic
378#216—22no—
379#216—22no—
380#215—22no—
381#215—22no—
382(C2×D3)⋊C4—21no—
383(C2×D3)⋊C4—21no—
384C4⋊Dic3—21no—
385C4⋊Dic3C23×C511yescharacteristic
386C4⋊Dic3C23×C511yescharacteristic
387Dic3⋊C4—21no—
388Dic3⋊C4—21no—
389C4×Dic3—21no—
390C4×Dic3—21no—
391C2×C3⋊C8C23×C511yescharacteristic
392C2×C3⋊C8C23×C511yescharacteristic
393C2×C3⋊C8C23×C511yescharacteristic
394C2×C3⋊C8C23×C511yescharacteristic
395C23×C5—61no—
396C23×C5C2×#6711yescharacteristic
397C5×Q8—21no—
398C5×Q8—21no—
399C5×Q8—21no—
400C5×Q8—21no—
401C5×Q8—32no—
402C5×Q8—61no—
403C5×D4—32no—
404C5×D4—64no—
405C5×D4—61no—
406C2×C4×C5—21no—
407C2×C4×C5—21no—
408C2×C4×C5—21no—
409C2×C4×C5—21no—
410C2×C4×C5—21no—
411C2×C4×C5—21no—
412C2×C4×C5—64no—
413C2×C4×C5—61no—
414C2×C4×C5—61no—
415C2×C4×C5—61no—
416C2×C4×C5—241no—
417C2×C4×C5—241no—
418C2×C4×C5—241no—
419C2×C4×C5C2×#6711yescharacteristic
420C2×C4×C5C2×#6711yescharacteristic
421C2×C4×C5C2×#6711yescharacteristic
422C2×C4×C5C2×#6711yescharacteristic
423C2×C4×C5C2×#6711yescharacteristic
424C2×C4×C5C23×D311yescharacteristic
425C5×C8—61no—
426C5×C8—61no—
427C5×C8—61no—
428C5×C8—61no—
429C2×#41—31no—
430C2×Q16—31no—
431C2×Q16—31no—
432C2×SD16—31no—
433C2×SD16—31no—
434C4⋊Q8C2×C5×D311yescharacteristic
435#126—21no—
436#126—21no—
437#125—21no—
438#125—21no—
439#125C2×C5×D311yescharacteristic
440C22⋊Q8C2×C5×D311yescharacteristic
441C22⋊Q8C2×C5×D311yescharacteristic
442C4×Q8—31no—
443C4×Q8—31no—
444C4×Q8C2×C5×D311yescharacteristic
445C4×Q8C2×C5×D311yescharacteristic
446C4×D4—31no—
447C4×D4—31no—
448C4×D4—61no—
449C4×D4—61no—
450#117—61no—
451#117C2×C5×D311yescharacteristic
452C2×C4⋊C4—31no—
453C2×C4⋊C4—61no—
454#107—31no—
455#107—31no—
456#106—31no—
457#106—31no—
458C4⋊C8—31no—
459C4⋊C8—31no—
460#103—31no—
461#103—31no—
462#103—31no—
463#103—31no—
464#103—31no—
465#103—31no—
466#102—31no—
467#102—31no—
468C22⋊C8—31no—
469C22⋊C8—31no—
470#97—31no—
471C4×C8—31no—
472C2×C3×C5—41no—
473C2×C3×C5#52511yescharacteristic
474C2×C3×C5#57711yescharacteristic
475C2×C3×C5#57811yescharacteristic
476C5×D3—42no—
477C23×C3C2×C5×D411yescharacteristic
478C22×D3—21no—
479C3×Q8—21no—
480C3×Q8—21no—
481C3×Q8—21no—
482C3×Q8—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4C2×C5×D411yescharacteristic
490C2×C3×C4C2×C5×D411yescharacteristic
491C2×C3×C4C2×C5×D411yescharacteristic
492C2×C3×C4C2×C5×D411yescharacteristic
493C2×C3×C4C2×C5×D411yescharacteristic
494C2×C3×C4C24×C511yescharacteristic
495#67—24no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—81no—
500D12—21no—
501D12C5×#4112yes—
502C4×D3—24no—
503C4×D3—81no—
504C4×D3—81no—
505Dic6—21no—
506Dic6C5×#4112yes—
507C3⋊C8—21no—
508C3⋊C8—21no—
509C3⋊C8—21no—
510C3⋊C8—21no—
511C22×C5—21no—
512C22×C5—21no—
513C22×C5—21no—
514C22×C5—62no—
515C22×C5—121no—
516C22×C5—121no—
517C22×C5C22×#6711yescharacteristic
518C4×C5—21no—
519C4×C5—21no—
520C4×C5—21no—
521C4×C5—21no—
522C4×C5—21no—
523C4×C5—41no—
524C4×C5—41no—
525C4×C5—41no—
526C4×C5—41no—
527C4×C5—62no—
528C4×C5—121no—
529C4×C5—121no—
530C4×C5D3×#4111yescharacteristic
531C4×C5D3×#4111yescharacteristic
532#41—62no—
533#41—62no—
534C2×Q8—31no—
535C2×Q8C22×C5×D311yescharacteristic
536C2×Q8C22×C5×D311yescharacteristic
537C2×D4—31no—
538C2×D4—61no—
539C22×C4—61no—
540C22×C4—61no—
541C22×C4—61no—
542C22×C4—61no—
543C22×C4C22×C5×D311yescharacteristic
544Q16—62no—
545Q16—62no—
546SD16—62no—
547SD16—62no—
548C2×C8—31no—
549C2×C8—31no—
550C2×C8—31no—
551C2×C8—31no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—31no—
561C4⋊C4—31no—
562C4⋊C4—61no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4C5×#6711yescharacteristic
566C4⋊C4C5×#6711yescharacteristic
567C4⋊C4C22×C5×D311yescharacteristic
568C4⋊C4C22×C5×D311yescharacteristic
569C22⋊C4—21no—
570C22⋊C4—21no—
571C22⋊C4—61no—
572C22⋊C4—61no—
573C22⋊C4C5×#6711yescharacteristic
574C22⋊C4C5×#6711yescharacteristic
575C42—21no—
576C42—21no—
577C42—61no—
578C42—61no—
579C42C22×C5×D311yescharacteristic
580C42C22×C5×D311yescharacteristic
581C3×C5#312011yescharacteristic, complemented, Hall
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3C22×C5×D411yescharacteristic
586C2×D3—22no—
587C2×D3—41no—
588C2×D3—41no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—41no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4C2×C5×#4111yescharacteristic
599C3×C4C2×C5×#4111yescharacteristic
600Dic3—22no—
601Dic3—41no—
602Dic3—41no—
603C2×C5—41no—
604C2×C5—122no—
605C2×C5#582811yescharacteristic
606C2×C5#583711yescharacteristic
607C2×C5#583811yescharacteristic
608C23—61no—
609C23C2×C5×#6711yescharacteristic
610Q8—21no—
611Q8—21no—
612Q8—21no—
613Q8—21no—
614Q8—32no—
615Q8—61no—
616D4—32no—
617D4—64no—
618D4—61no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—64no—
626C2×C4—61no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—241no—
630C2×C4—241no—
631C2×C4—241no—
632C2×C4C2×C5×#6711yescharacteristic
633C2×C4C2×C5×#6711yescharacteristic
634C2×C4C2×C5×#6711yescharacteristic
635C2×C4C2×C5×#6711yescharacteristic
636C2×C4C2×C5×#6711yescharacteristic
637C2×C4C23×C5×D311yescharacteristic
638C8—61no—
639C8—61no—
640C8—61no—
641C8—61no—
642C2×C3—41no—
643C2×C3C5×#52511yescharacteristic
644C2×C3C5×#57711yescharacteristic
645C2×C3C5×#57811yescharacteristic
646D3—42no—
647C5#8344611yescharacteristic, direct product factor, Sylow
648C22—21no—
649C22—21no—
650C22—21no—
651C22—62no—
652C22—121no—
653C22—121no—
654C22C22×C5×#6711yescharacteristic
655C4—21no—
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—41no—
661C4—41no—
662C4—41no—
663C4—41no—
664C4—62no—
665C4—121no—
666C4—121no—
667C4C5×D3×#4111yescharacteristic
668C4C5×D3×#4111yescharacteristic
669C3C5×#312011yescharacteristic, complemented, Sylow
670C2—41no—
671C2—122no—
672C2C5×#582811yescharacteristic
673C2C5×#583711yescharacteristic
674C2C5×#583811yescharacteristic
subgroupG/H
centerC22×C5C22×#67
commutator, cosocleC2×C3×C4C24×C5
FrattiniC2×C4C23×C5×D3
FittingC3×C5×#541C2
socleC22×C3×C5C22×D4
prime radicalC2×C5×#235C22
hypercenterC5×#541D3
hypocenterC3C5×#3120
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C5 ◁ C5×#117 ◁ C5×#541

Complements

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

NH ≅ G/Ntype
1. C3×C5×#541C2semidirect
3. C5×#5090C2semidirect
4. C5×#5083C2semidirect
5. C5×#5066C2semidirect
6. C5×#5063C2semidirect
9. C5×#5044C2semidirect
10. C5×#5043C2semidirect
11. C5×#5030C2semidirect
12. C4×C5×#216C2semidirect
13. C5×#5026C2semidirect
14. C4×C5×#215C2semidirect
15. C5×#5000C2semidirect
60. #83446C5direct (N × H)
61. C5×#541D3semidirect
125. C3×#541C2×C5semidirect
127. #5090C2×C5semidirect
128. #5083C2×C5semidirect
129. #5066C2×C5semidirect
130. #5063C2×C5semidirect
133. #5044C2×C5semidirect
134. #5043C2×C5semidirect
135. #5030C2×C5semidirect
136. C4×#216C2×C5semidirect
137. #5026C2×C5semidirect
138. C4×#215C2×C5semidirect
139. #5000C2×C5semidirect
310. #541C5×D3semidirect
581. C3×C5#3120semidirect
647. C5#83446direct (N × H)
669. C3C5×#3120semidirect

Maximal subgroups

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

subgroupindex
C3×C5×#5412
C5×#55232
C5×#50902
C5×#50832
C5×#50662
C5×#50632
C5×#50472
C5×#50442
C5×#50432
C5×#50302
C4×C5×#2162
C5×#50262
C4×C5×#2152
C5×#50002
C5×#31203
#834465