Finite Group Databasebeta

← C5×#69418 #14280208

Subgroups — C5×#69418 #14280208

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C5×#95C211yesmaximal, characteristic
2C2×C5×C3⋊#95C211yesmaximal, characteristic
3C2×C5×C3⋊#95C211yesmaximal, characteristic
4C2×C5×C3⋊#95C211yesmaximal, characteristic
5C2×C5×C3⋊#95C211yesmaximal, characteristic
6C2×C5×C3⋊#95C211yesmaximal, characteristic
7C2×C5×C3⋊#95C211yesmaximal, characteristic
8C5×#1443—31nomaximal, Hall
9C23×C3×C4×C5C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C5×Dic3C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C3×C5×#95—22no—
17C5×C3⋊#95—22no—
18C5×C3⋊#95—22no—
19C5×C3⋊#95—22no—
20C5×C3⋊#95—22no—
21C5×C3⋊#95—22no—
22C5×C3⋊#95C414yescomplemented
23#69418C511yesmaximal, characteristic, direct product factor, Hall
24C2×C5×#95—31no—
25C2×C5×#95—31no—
26C2×C5×#95—31no—
27C2×C5×#95—31no—
28C2×C5×#95—31no—
29C2×C5×#95—31no—
30C2×C5×#95D311yescharacteristic
31C24×C3×C5C2311yescharacteristic
32C22×C3×C4×C5—21no—
33C22×C3×C4×C5—21no—
34C22×C3×C4×C5—21no—
35C22×C3×C4×C5—21no—
36C22×C3×C4×C5—21no—
37C22×C3×C4×C5—21no—
38C22×C3×C4×C5—21no—
39C22×C3×C4×C5—21no—
40C22×C3×C4×C5—21no—
41C22×C3×C4×C5—21no—
42C22×C3×C4×C5—21no—
43C22×C3×C4×C5—21no—
44C22×C3×C4×C5—21no—
45C22×C3×C4×C5—21no—
46C22×C3×C4×C5—21no—
47C22×C3×C4×C5—21no—
48C22×C3×C4×C5—21no—
49C22×C3×C4×C5—21no—
50C22×C3×C4×C5C2×C412yes—
51C22×C3×C4×C5D412yes—
52C22×C3×C4×C5D412yes—
53C22×C5×Dic3—21no—
54C22×C5×Dic3—21no—
55C22×C5×Dic3—21no—
56C22×C5×Dic3—21no—
57C22×C5×Dic3—21no—
58C22×C5×Dic3—21no—
59C22×C5×Dic3—21no—
60C22×C5×Dic3—21no—
61C22×C5×Dic3—21no—
62C22×C5×Dic3—21no—
63C22×C5×Dic3—21no—
64C22×C5×Dic3—21no—
65C22×C5×Dic3—21no—
66C22×C5×Dic3—21no—
67C22×C5×Dic3—21no—
68C22×C5×Dic3—21no—
69C22×C5×Dic3—21no—
70C22×C5×Dic3—21no—
71C22×C5×Dic3—21no—
72C22×C5×Dic3—21no—
73C22×C5×Dic3—21no—
74C22×C5×Dic3—21no—
75C22×C5×Dic3—21no—
76C22×C5×Dic3—21no—
77C22×C5×Dic3C2×C412yes—
78C22×C5×Dic3C2×C412yes—
79C22×C5×Dic3D412yes—
80C22×C5×Dic3Q812yes—
81C2×C3×#95C2×C511yescharacteristic
82C2×C3⋊#95C2×C511yescharacteristic
83C2×C3⋊#95C2×C511yescharacteristic
84C2×C3⋊#95C2×C511yescharacteristic
85C2×C3⋊#95C2×C511yescharacteristic
86C2×C3⋊#95C2×C511yescharacteristic
87C2×C3⋊#95C2×C511yescharacteristic
88C23×C4×C5—31no—
89C23×C4×C5—31no—
90C23×C4×C5—31no—
91C23×C4×C5—31no—
92C23×C4×C5C2×D311yescharacteristic
93C23×C4×C5C2×D311yescharacteristic
94C23×C4×C5C2×D311yescharacteristic
95C5×#95—22no—
96C5×#95—34no—
97C5×#95—62no—
98C5×#95—62no—
99C5×#95—62no—
100C5×#95—62no—
101C5×#95—62no—
102#1443—31noSylow
103C23×C3×C5C22×C411yescharacteristic
104C23×C3×C5C2×D411yescharacteristic
105C23×C3×C5C2×D411yescharacteristic
106C23×C3×C5C2×D411yescharacteristic
107C23×C3×C5C2×Q811yescharacteristic
108C23×C3×C5#4111yescharacteristic
109C23×C3×C5#4111yescharacteristic
110C23×C3×C5#4111yescharacteristic
111C23×C3×C5#4111yescharacteristic
112C23×C3×C5#4111yescharacteristic
113C23×C3×C5#4111yescharacteristic
114C23×C3×C5#4111yescharacteristic
115C23×C3×C5#4111yescharacteristic
116C23×C3×C5#4111yescharacteristic
117C23×C3×C5#4111yescharacteristic
118C2×C3×C4×C5—22no—
119C2×C3×C4×C5—22no—
120C2×C3×C4×C5—22no—
121C2×C3×C4×C5—22no—
122C2×C3×C4×C5—22no—
123C2×C3×C4×C5—22no—
124C2×C3×C4×C5—22no—
125C2×C3×C4×C5—22no—
126C2×C3×C4×C5—22no—
127C2×C3×C4×C5—41no—
128C2×C3×C4×C5—41no—
129C2×C3×C4×C5—41no—
130C2×C3×C4×C5—41no—
131C2×C3×C4×C5—41no—
132C2×C3×C4×C5—41no—
133C2×C3×C4×C5—41no—
134C2×C3×C4×C5—41no—
135C2×C3×C4×C5—41no—
136C2×C3×C4×C5—41no—
137C2×C3×C4×C5—41no—
138C2×C3×C4×C5—41no—
139C2×C5×Dic3—22no—
140C2×C5×Dic3—22no—
141C2×C5×Dic3—22no—
142C2×C5×Dic3—22no—
143C2×C5×Dic3—22no—
144C2×C5×Dic3—22no—
145C2×C5×Dic3—22no—
146C2×C5×Dic3—22no—
147C2×C5×Dic3—22no—
148C2×C5×Dic3—22no—
149C2×C5×Dic3—22no—
150C2×C5×Dic3—22no—
151C2×C5×Dic3—41no—
152C2×C5×Dic3—41no—
153C2×C5×Dic3—41no—
154C2×C5×Dic3—41no—
155C2×C5×Dic3—41no—
156C2×C5×Dic3—41no—
157C2×C5×Dic3—41no—
158C2×C5×Dic3—41no—
159C2×C5×Dic3—41no—
160C2×C5×Dic3—41no—
161C2×C5×Dic3—41no—
162C2×C5×Dic3—41no—
163C2×C5×Dic3—41no—
164C2×C5×Dic3—41no—
165C2×C5×Dic3—41no—
166C2×C5×Dic3—41no—
167C23×C3×C4C22×C511yescharacteristic
168C23×C3×C4C22×C511yescharacteristic
169C23×C3×C4C22×C511yescharacteristic
170C23×Dic3C22×C511yescharacteristic
171C23×Dic3C22×C511yescharacteristic
172C23×Dic3C22×C511yescharacteristic
173C23×Dic3C22×C511yescharacteristic
174C3×#95—22no—
175C3⋊#95—22no—
176C3⋊#95—22no—
177C3⋊#95—22no—
178C3⋊#95—22no—
179C3⋊#95—22no—
180C3⋊#95C4×C514yescomplemented
181C24×C5C22×D311yescharacteristic
182C22×C4×C5—21no—
183C22×C4×C5—21no—
184C22×C4×C5—21no—
185C22×C4×C5—21no—
186C22×C4×C5—21no—
187C22×C4×C5—21no—
188C22×C4×C5—21no—
189C22×C4×C5—21no—
190C22×C4×C5—21no—
191C22×C4×C5—21no—
192C22×C4×C5—21no—
193C22×C4×C5—21no—
194C22×C4×C5—21no—
195C22×C4×C5—21no—
196C22×C4×C5—21no—
197C22×C4×C5—21no—
198C22×C4×C5—21no—
199C22×C4×C5—21no—
200C22×C4×C5—32no—
201C22×C4×C5—32no—
202C22×C4×C5—32no—
203C22×C4×C5—32no—
204C22×C4×C5—61no—
205C22×C4×C5—61no—
206C22×C4×C5—61no—
207C22×C4×C5—61no—
208C22×C4×C5—61no—
209C22×C4×C5—61no—
210C22×C4×C5—61no—
211C22×C4×C5—61no—
212C22×C4×C5—61no—
213C22×C4×C5—61no—
214C22×C4×C5—61no—
215C22×C4×C5—61no—
216C22×C4×C5—61no—
217C22×C4×C5—61no—
218C22×C4×C5—61no—
219C22×C4×C5—61no—
220C22×C4×C5—61no—
221C22×C4×C5—61no—
222C22×C4×C5—61no—
223C22×C4×C5—61no—
224C22×C4×C5—61no—
225C22×C4×C5—61no—
226C22×C4×C5—61no—
227C22×C4×C5—61no—
228C22×C4×C5C4×D312yes—
229C22×C4×C5D1212yes—
230C22×C4×C5#6712yes—
231C2×#95—31no—
232C2×#95—31no—
233C2×#95—31no—
234C2×#95—31no—
235C2×#95—31no—
236C2×#95—31no—
237C2×#95C5×D311yescharacteristic
238C22×C3×C5#11711yescharacteristic
239C22×C3×C5#11711yescharacteristic
240C22×C3×C5#11711yescharacteristic
241C22×C3×C5C4×D411yescharacteristic
242C22×C3×C5C4×D411yescharacteristic
243C22×C3×C5C4×D411yescharacteristic
244C22×C3×C5C4×Q811yescharacteristic
245C22×C3×C5#12111yescharacteristic
246C22×C3×C5#12111yescharacteristic
247C22×C3×C5#12111yescharacteristic
248C22×C3×C5C22⋊Q811yescharacteristic
249C22×C3×C5C22⋊Q811yescharacteristic
250C22×C3×C5C22⋊Q811yescharacteristic
251C22×C3×C5#12311yescharacteristic
252C22×C3×C5#12311yescharacteristic
253C22×C3×C5#12311yescharacteristic
254C22×C3×C5#12311yescharacteristic
255C22×C3×C5#12311yescharacteristic
256C22×C3×C5#12311yescharacteristic
257C22×C3×C5#12411yescharacteristic
258C22×C3×C5#12411yescharacteristic
259C22×C3×C5#12411yescharacteristic
260C22×C3×C5#12511yescharacteristic
261C22×C3×C5#12511yescharacteristic
262C22×C3×C5#12511yescharacteristic
263C22×C3×C5#12611yescharacteristic
264C22×C3×C5#12611yescharacteristic
265C22×C3×C5#12611yescharacteristic
266C22×C3×C5#12611yescharacteristic
267C22×C3×C5#12611yescharacteristic
268C22×C3×C5#12611yescharacteristic
269C22×C3×C5#12611yescharacteristic
270C22×C3×C5#12611yescharacteristic
271C22×C3×C5#12611yescharacteristic
272C22×C3×C5#12611yescharacteristic
273C3×C4×C5—42no—
274C3×C4×C5—42no—
275C3×C4×C5—42no—
276C5×Dic3—42no—
277C5×Dic3—42no—
278C5×Dic3—42no—
279C5×Dic3—42no—
280C24×C3C23×C511yescharacteristic
281C22×C3×C4—21no—
282C22×C3×C4—21no—
283C22×C3×C4—21no—
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—21no—
292C22×C3×C4—21no—
293C22×C3×C4—21no—
294C22×C3×C4—21no—
295C22×C3×C4—21no—
296C22×C3×C4—21no—
297C22×C3×C4—21no—
298C22×C3×C4—21no—
299C22×C3×C4C2×C4×C512yes—
300C22×C3×C4C5×D412yes—
301C22×C3×C4C5×D412yes—
302C22×Dic3—21no—
303C22×Dic3—21no—
304C22×Dic3—21no—
305C22×Dic3—21no—
306C22×Dic3—21no—
307C22×Dic3—21no—
308C22×Dic3—21no—
309C22×Dic3—21no—
310C22×Dic3—21no—
311C22×Dic3—21no—
312C22×Dic3—21no—
313C22×Dic3—21no—
314C22×Dic3—21no—
315C22×Dic3—21no—
316C22×Dic3—21no—
317C22×Dic3—21no—
318C22×Dic3—21no—
319C22×Dic3—21no—
320C22×Dic3—21no—
321C22×Dic3—21no—
322C22×Dic3—21no—
323C22×Dic3—21no—
324C22×Dic3—21no—
325C22×Dic3—21no—
326C22×Dic3C2×C4×C512yes—
327C22×Dic3C2×C4×C512yes—
328C22×Dic3C5×D412yes—
329C22×Dic3C5×Q812yes—
330C23×C5C2×C4×D311yescharacteristic
331C23×C5C2×D1211yescharacteristic
332C23×C5#23511yescharacteristic
333C23×C5#23511yescharacteristic
334C23×C5#23511yescharacteristic
335C23×C5#23511yescharacteristic
336C23×C5D3×D411yescharacteristic
337C23×C5#23711yescharacteristic
338C23×C5#23711yescharacteristic
339C23×C5#23711yescharacteristic
340C23×C5#23711yescharacteristic
341C23×C5#23711yescharacteristic
342C23×C5D3×Q811yescharacteristic
343C23×C5#23911yescharacteristic
344C23×C5C2×#6711yescharacteristic
345C2×C4×C5—22no—
346C2×C4×C5—22no—
347C2×C4×C5—22no—
348C2×C4×C5—22no—
349C2×C4×C5—22no—
350C2×C4×C5—22no—
351C2×C4×C5—22no—
352C2×C4×C5—22no—
353C2×C4×C5—22no—
354C2×C4×C5—41no—
355C2×C4×C5—41no—
356C2×C4×C5—41no—
357C2×C4×C5—41no—
358C2×C4×C5—41no—
359C2×C4×C5—41no—
360C2×C4×C5—41no—
361C2×C4×C5—41no—
362C2×C4×C5—41no—
363C2×C4×C5—41no—
364C2×C4×C5—41no—
365C2×C4×C5—41no—
366C2×C4×C5—62no—
367C2×C4×C5—62no—
368C2×C4×C5—62no—
369C2×C4×C5—62no—
370C2×C4×C5—62no—
371C2×C4×C5—62no—
372C2×C4×C5—62no—
373C2×C4×C5—62no—
374C2×C4×C5—62no—
375C2×C4×C5—62no—
376C2×C4×C5—62no—
377C2×C4×C5—62no—
378C2×C4×C5—121no—
379C2×C4×C5—121no—
380C2×C4×C5—121no—
381C2×C4×C5—121no—
382C2×C4×C5—121no—
383C2×C4×C5—121no—
384C2×C4×C5—121no—
385C2×C4×C5—121no—
386C2×C4×C5—121no—
387C2×C4×C5—121no—
388C2×C4×C5—121no—
389C2×C4×C5—121no—
390C2×C4×C5—121no—
391C2×C4×C5—121no—
392C2×C4×C5—121no—
393C2×C4×C5—121no—
394C23×C4—31no—
395C23×C4—31no—
396C23×C4—31no—
397C23×C4—31no—
398C23×C4C2×C5×D311yescharacteristic
399C23×C4C2×C5×D311yescharacteristic
400C23×C4C2×C5×D311yescharacteristic
401#95—22no—
402#95—34no—
403#95—62no—
404#95—62no—
405#95—62no—
406#95—62no—
407#95—62no—
408C2×C3×C5#38311yescharacteristic
409C2×C3×C5#38711yescharacteristic
410C2×C3×C5#38711yescharacteristic
411C2×C3×C5#38711yescharacteristic
412C2×C3×C5#38811yescharacteristic
413C2×C3×C5#38811yescharacteristic
414C2×C3×C5#38811yescharacteristic
415C2×C3×C5#39611yescharacteristic
416C2×C3×C5#39711yescharacteristic
417C2×C3×C5#39711yescharacteristic
418C2×C3×C5#39711yescharacteristic
419C2×C3×C5#40011yescharacteristic
420C2×C3×C5#40011yescharacteristic
421C2×C3×C5#40011yescharacteristic
422C2×C3×C5#40111yescharacteristic
423C23×C3C22×C4×C511yescharacteristic
424C23×C3C2×C5×D411yescharacteristic
425C23×C3C2×C5×D411yescharacteristic
426C23×C3C2×C5×D411yescharacteristic
427C23×C3C2×C5×Q811yescharacteristic
428C23×C3C5×#4111yescharacteristic
429C23×C3C5×#4111yescharacteristic
430C23×C3C5×#4111yescharacteristic
431C23×C3C5×#4111yescharacteristic
432C23×C3C5×#4111yescharacteristic
433C23×C3C5×#4111yescharacteristic
434C23×C3C5×#4111yescharacteristic
435C23×C3C5×#4111yescharacteristic
436C23×C3C5×#4111yescharacteristic
437C23×C3C5×#4111yescharacteristic
438C2×C3×C4—22no—
439C2×C3×C4—22no—
440C2×C3×C4—22no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—22no—
444C2×C3×C4—22no—
445C2×C3×C4—22no—
446C2×C3×C4—22no—
447C2×C3×C4—41no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—41no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×Dic3—22no—
460C2×Dic3—22no—
461C2×Dic3—22no—
462C2×Dic3—22no—
463C2×Dic3—22no—
464C2×Dic3—22no—
465C2×Dic3—22no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—22no—
469C2×Dic3—22no—
470C2×Dic3—22no—
471C2×Dic3—41no—
472C2×Dic3—41no—
473C2×Dic3—41no—
474C2×Dic3—41no—
475C2×Dic3—41no—
476C2×Dic3—41no—
477C2×Dic3—41no—
478C2×Dic3—41no—
479C2×Dic3—41no—
480C2×Dic3—41no—
481C2×Dic3—41no—
482C2×Dic3—41no—
483C2×Dic3—41no—
484C2×Dic3—41no—
485C2×Dic3—41no—
486C2×Dic3—41no—
487C22×C5#87211yescharacteristic
488C22×C5C4×D1211yescharacteristic
489C22×C5#87511yescharacteristic
490C22×C5#87611yescharacteristic
491C22×C5#87711yescharacteristic
492C22×C5#87911yescharacteristic
493C22×C5#87911yescharacteristic
494C22×C5#87911yescharacteristic
495C22×C5#87911yescharacteristic
496C22×C5#87911yescharacteristic
497C22×C5#67⋊C411yescharacteristic
498C22×C5#88311yescharacteristic
499C22×C5#88311yescharacteristic
500C22×C5#88511yescharacteristic
501C22×C5#88611yescharacteristic
502C22×C5#88611yescharacteristic
503C22×C5#88711yescharacteristic
504C22×C5#88911yescharacteristic
505C22×C5#88911yescharacteristic
506C22×C5#88911yescharacteristic
507C22×C5#89211yescharacteristic
508C22×C5#89511yescharacteristic
509C22×C5#89611yescharacteristic
510C22×C5#89711yescharacteristic
511C22×C5#89811yescharacteristic
512C22×C5#89811yescharacteristic
513C22×C5#89811yescharacteristic
514C22×C5#89811yescharacteristic
515C22×C5C4×#6711yescharacteristic
516C22×C5#92911yescharacteristic
517C22×C5#93011yescharacteristic
518C22×C5#93511yescharacteristic
519C22×C5#93611yescharacteristic
520C22×C5#93911yescharacteristic
521C22×C5#94611yescharacteristic
522C4×C5—42no—
523C4×C5—42no—
524C4×C5—42no—
525C4×C5—122no—
526C4×C5—122no—
527C4×C5—122no—
528C4×C5—122no—
529C24C22×C5×D311yescharacteristic
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—32no—
549C22×C4—32no—
550C22×C4—32no—
551C22×C4—32no—
552C22×C4—61no—
553C22×C4—61no—
554C22×C4—61no—
555C22×C4—61no—
556C22×C4—61no—
557C22×C4—61no—
558C22×C4—61no—
559C22×C4—61no—
560C22×C4—61no—
561C22×C4—61no—
562C22×C4—61no—
563C22×C4—61no—
564C22×C4—61no—
565C22×C4—61no—
566C22×C4—61no—
567C22×C4—61no—
568C22×C4—61no—
569C22×C4—61no—
570C22×C4—61no—
571C22×C4—61no—
572C22×C4—61no—
573C22×C4—61no—
574C22×C4—61no—
575C22×C4—61no—
576C22×C4C4×C5×D312yes—
577C22×C4C5×D1212yes—
578C22×C4C5×#6712yes—
579C3×C5#144311yescharacteristic, complemented, Hall
580C22×C3C5×#11711yescharacteristic
581C22×C3C5×#11711yescharacteristic
582C22×C3C5×#11711yescharacteristic
583C22×C3C4×C5×D411yescharacteristic
584C22×C3C4×C5×D411yescharacteristic
585C22×C3C4×C5×D411yescharacteristic
586C22×C3C4×C5×Q811yescharacteristic
587C22×C3C5×#12111yescharacteristic
588C22×C3C5×#12111yescharacteristic
589C22×C3C5×#12111yescharacteristic
590C22×C3C5×C22⋊Q811yescharacteristic
591C22×C3C5×C22⋊Q811yescharacteristic
592C22×C3C5×C22⋊Q811yescharacteristic
593C22×C3C5×#12311yescharacteristic
594C22×C3C5×#12311yescharacteristic
595C22×C3C5×#12311yescharacteristic
596C22×C3C5×#12311yescharacteristic
597C22×C3C5×#12311yescharacteristic
598C22×C3C5×#12311yescharacteristic
599C22×C3C5×#12411yescharacteristic
600C22×C3C5×#12411yescharacteristic
601C22×C3C5×#12411yescharacteristic
602C22×C3C5×#12511yescharacteristic
603C22×C3C5×#12511yescharacteristic
604C22×C3C5×#12511yescharacteristic
605C22×C3C5×#12611yescharacteristic
606C22×C3C5×#12611yescharacteristic
607C22×C3C5×#12611yescharacteristic
608C22×C3C5×#12611yescharacteristic
609C22×C3C5×#12611yescharacteristic
610C22×C3C5×#12611yescharacteristic
611C22×C3C5×#12611yescharacteristic
612C22×C3C5×#12611yescharacteristic
613C22×C3C5×#12611yescharacteristic
614C22×C3C5×#12611yescharacteristic
615C3×C4—42no—
616C3×C4—42no—
617C3×C4—42no—
618Dic3—42no—
619Dic3—42no—
620Dic3—42no—
621Dic3—42no—
622C2×C5#465111yescharacteristic
623C2×C5#465211yescharacteristic
624C2×C5#465311yescharacteristic
625C2×C5#465811yescharacteristic
626C2×C5#465911yescharacteristic
627C2×C5C3⋊#40111yescharacteristic
628C2×C5#467011yescharacteristic
629C2×C5#467411yescharacteristic
630C2×C5#494011yescharacteristic
631C2×C5#494511yescharacteristic
632C2×C5#495211yescharacteristic
633C2×C5#495311yescharacteristic
634C2×C5#497811yescharacteristic
635C2×C5#498511yescharacteristic
636C2×C5#499411yescharacteristic
637C23C2×C4×C5×D311yescharacteristic
638C23C2×C5×D1211yescharacteristic
639C23C5×#23511yescharacteristic
640C23C5×#23511yescharacteristic
641C23C5×#23511yescharacteristic
642C23C5×#23511yescharacteristic
643C23C5×D3×D411yescharacteristic
644C23C5×#23711yescharacteristic
645C23C5×#23711yescharacteristic
646C23C5×#23711yescharacteristic
647C23C5×#23711yescharacteristic
648C23C5×#23711yescharacteristic
649C23C5×D3×Q811yescharacteristic
650C23C5×#23911yescharacteristic
651C23C2×C5×#6711yescharacteristic
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—62no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—121no—
688C2×C4—121no—
689C2×C4—121no—
690C2×C4—121no—
691C2×C4—121no—
692C2×C4—121no—
693C2×C4—121no—
694C2×C4—121no—
695C2×C4—121no—
696C2×C4—121no—
697C2×C4—121no—
698C2×C4—121no—
699C2×C4—121no—
700C2×C4—121no—
701C2×C3C5×#38311yescharacteristic
702C2×C3C5×#38711yescharacteristic
703C2×C3C5×#38711yescharacteristic
704C2×C3C5×#38711yescharacteristic
705C2×C3C5×#38811yescharacteristic
706C2×C3C5×#38811yescharacteristic
707C2×C3C5×#38811yescharacteristic
708C2×C3C5×#39611yescharacteristic
709C2×C3C5×#39711yescharacteristic
710C2×C3C5×#39711yescharacteristic
711C2×C3C5×#39711yescharacteristic
712C2×C3C5×#40011yescharacteristic
713C2×C3C5×#40011yescharacteristic
714C2×C3C5×#40011yescharacteristic
715C2×C3C5×#40111yescharacteristic
716C5#6941811yescharacteristic, direct product factor, Sylow
717C22C5×#87211yescharacteristic
718C22C4×C5×D1211yescharacteristic
719C22C5×#87511yescharacteristic
720C22C5×#87611yescharacteristic
721C22C5×#87711yescharacteristic
722C22C5×#87911yescharacteristic
723C22C5×#87911yescharacteristic
724C22C5×#87911yescharacteristic
725C22C5×#87911yescharacteristic
726C22C5×#87911yescharacteristic
727C22C5×#67⋊C411yescharacteristic
728C22C5×#88311yescharacteristic
729C22C5×#88311yescharacteristic
730C22C5×#88511yescharacteristic
731C22C5×#88611yescharacteristic
732C22C5×#88611yescharacteristic
733C22C5×#88711yescharacteristic
734C22C5×#88911yescharacteristic
735C22C5×#88911yescharacteristic
736C22C5×#88911yescharacteristic
737C22C5×#89211yescharacteristic
738C22C5×#89511yescharacteristic
739C22C5×#89611yescharacteristic
740C22C5×#89711yescharacteristic
741C22C5×#89811yescharacteristic
742C22C5×#89811yescharacteristic
743C22C5×#89811yescharacteristic
744C22C5×#89811yescharacteristic
745C22C4×C5×#6711yescharacteristic
746C22C5×#92911yescharacteristic
747C22C5×#93011yescharacteristic
748C22C5×#93511yescharacteristic
749C22C5×#93611yescharacteristic
750C22C5×#93911yescharacteristic
751C22C5×#94611yescharacteristic
752C4—42no—
753C4—42no—
754C4—42no—
755C4—122no—
756C4—122no—
757C4—122no—
758C4—122no—
759C3C5×#144311yescharacteristic, complemented, Sylow
760C2C5×#465111yescharacteristic
761C2C5×#465211yescharacteristic
762C2C5×#465311yescharacteristic
763C2C5×#465811yescharacteristic
764C2C5×#465911yescharacteristic
765C2C5×C3⋊#40111yescharacteristic
766C2C5×#467011yescharacteristic
767C2C5×#467411yescharacteristic
768C2C5×#494011yescharacteristic
769C2C5×#494511yescharacteristic
770C2C5×#495211yescharacteristic
771C2C5×#495311yescharacteristic
772C2C5×#497811yescharacteristic
773C2C5×#498511yescharacteristic
774C2C5×#499411yescharacteristic
subgroupG/H
centerC24×C5C22×D3
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC2×C3×C5×#95C2
socle, prime radicalC24×C3×C5C23
cosocleC24×C3C23×C5
hypercenterC2×C5×#95D3
hypocenterC3C5×#1443
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C2×C5×#95

Complements

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

NH ≅ G/Ntype
22. C5×C3⋊#95C4semidirect
23. #69418C5direct (N × H)
180. C3⋊#95C4×C5semidirect
579. C3×C5#1443semidirect
716. C5#69418direct (N × H)
759. C3C5×#1443semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C5×#952
C2×C5×C3⋊#952
C5×#14433
#694185