Finite Group Databasebeta

← C5×#69428 #14280054

Subgroups — C5×#69428 #14280054

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
2C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
3C22×C5×(C2×D3)⋊C4C211yesmaximal, characteristic
4C22×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×C5×#95C211yesmaximal, characteristic, complemented
6C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
7C2×C5×C3⋊#95C211yesmaximal, characteristic, complemented
8C5×#1439—31nomaximal, Hall
9C24×C5×D3C2211yescharacteristic
10C23×C3×C4×C5C2211yescharacteristic
11C23×C3×C4×C5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C5×Dic3C2211yescharacteristic
14C23×C5×Dic3C2211yescharacteristic
15C23×C5×Dic3C2211yescharacteristic
16C2×C5×(C2×D3)⋊C4—22no—
17C2×C5×(C2×D3)⋊C4—22no—
18C2×C5×(C2×D3)⋊C4—22no—
19C2×C5×(C2×D3)⋊C4—22no—
20C2×C5×(C2×D3)⋊C4—22no—
21C2×C5×(C2×D3)⋊C4—22no—
22C2×C5×(C2×D3)⋊C4—22no—
23C2×C5×(C2×D3)⋊C4—22no—
24C2×C5×(C2×D3)⋊C4C414yescomplemented
25C2×C5×Dic3⋊C4—22no—
26C2×C5×Dic3⋊C4—22no—
27C2×C5×Dic3⋊C4—22no—
28C3×C5×#95—22no—
29C5×C3⋊#95—22no—
30C5×C3⋊#95—22no—
31#69428C511yesmaximal, characteristic, direct product factor, Hall
32C22×C5×C4⋊C4—31no—
33C22×C5×C22⋊C4—31no—
34C22×C5×C22⋊C4—31no—
35C22×C5×C22⋊C4—31no—
36C2×C5×#95—31no—
37C2×C5×#95—31no—
38C2×C5×#95D311yescharacteristic, complemented
39C24×C3×C5C2311yescharacteristic
40C23×C5×D3—21no—
41C23×C5×D3—21no—
42C23×C5×D3—21no—
43C23×C5×D3—21no—
44C23×C5×D3—21no—
45C23×C5×D3—21no—
46C23×C5×D3—21no—
47C23×C5×D3—21no—
48C23×C5×D3—21no—
49C23×C5×D3—21no—
50C23×C5×D3—21no—
51C23×C5×D3—21no—
52C23×C5×D3C2×C412yes—
53C23×C5×D3D412yes—
54C23×C5×D3Q812yes—
55C22×C3×C4×C5—21no—
56C22×C3×C4×C5—21no—
57C22×C3×C4×C5—21no—
58C22×C3×C4×C5—21no—
59C22×C3×C4×C5—21no—
60C22×C3×C4×C5—21no—
61C22×C3×C4×C5—21no—
62C22×C3×C4×C5—21no—
63C22×C3×C4×C5—21no—
64C22×C3×C4×C5—21no—
65C22×C3×C4×C5—21no—
66C22×C3×C4×C5—21no—
67C22×C3×C4×C5—21no—
68C22×C3×C4×C5—21no—
69C22×C3×C4×C5—21no—
70C22×C3×C4×C5—21no—
71C22×C3×C4×C5—21no—
72C22×C3×C4×C5—21no—
73C22×C3×C4×C5C2×C412yes—
74C22×C3×C4×C5D412yes—
75C22×C3×C4×C5D412yes—
76C22×C5×Dic3—21no—
77C22×C5×Dic3—21no—
78C22×C5×Dic3—21no—
79C22×C5×Dic3—21no—
80C22×C5×Dic3—21no—
81C22×C5×Dic3—21no—
82C22×C5×Dic3—21no—
83C22×C5×Dic3—21no—
84C22×C5×Dic3—21no—
85C22×C5×Dic3—21no—
86C22×C5×Dic3—21no—
87C22×C5×Dic3—21no—
88C22×C5×Dic3—21no—
89C22×C5×Dic3—21no—
90C22×C5×Dic3—21no—
91C22×C5×Dic3—21no—
92C22×C5×Dic3C2×C412yes—
93C22×C5×Dic3D412yes—
94C22×C5×Dic3D412yes—
95C22×C5×Dic3D412yes—
96C22×C5×Dic3D412yes—
97C5×(C2×D3)⋊C4—28no—
98C5×(C2×D3)⋊C4—28no—
99C5×(C2×D3)⋊C4—28no—
100C5×Dic3⋊C4—28no—
101C22×(C2×D3)⋊C4C2×C511yescharacteristic
102C22×(C2×D3)⋊C4C2×C511yescharacteristic
103C22×(C2×D3)⋊C4C2×C511yescharacteristic
104C22×Dic3⋊C4C2×C511yescharacteristic, complemented
105C2×C3×#95C2×C511yescharacteristic, complemented
106C2×C3⋊#95C2×C511yescharacteristic, complemented
107C2×C3⋊#95C2×C511yescharacteristic, complemented
108C25×C5—31no—
109C23×C4×C5—31no—
110C23×C4×C5—31no—
111C23×C4×C5—31no—
112C23×C4×C5C2×D311yescharacteristic
113C23×C4×C5C2×D311yescharacteristic
114C23×C4×C5C2×D311yescharacteristic
115C2×C5×C4⋊C4—62no—
116C2×C5×C4⋊C4—62no—
117C2×C5×C4⋊C4—62no—
118C2×C5×C22⋊C4—34no—
119C2×C5×C22⋊C4—62no—
120C2×C5×C22⋊C4—62no—
121C2×C5×C22⋊C4—62no—
122C2×C5×C22⋊C4—62no—
123C2×C5×C22⋊C4—62no—
124C2×C5×C22⋊C4—62no—
125C2×C5×C22⋊C4—62no—
126C2×C5×C22⋊C4—62no—
127C5×#95—22no—
128C5×#95—62no—
129C5×#95—62no—
130#1439—31noSylow
131C23×C3×C5C22×C411yescharacteristic
132C23×C3×C5C2×D411yescharacteristic
133C23×C3×C5C2×D411yescharacteristic
134C23×C3×C5C2×D411yescharacteristic
135C23×C3×C5C2×D411yescharacteristic
136C23×C3×C5C2×D411yescharacteristic
137C23×C3×C5C2×D411yescharacteristic
138C23×C3×C5C2×D411yescharacteristic
139C23×C3×C5C2×Q811yescharacteristic
140C23×C3×C5#4111yescharacteristic
141C23×C3×C5#4111yescharacteristic
142C23×C3×C5#4111yescharacteristic
143C23×C3×C5#4111yescharacteristic
144C23×C3×C5#4111yescharacteristic
145C23×C3×C5#4111yescharacteristic
146C22×C5×D3—22no—
147C22×C5×D3—22no—
148C22×C5×D3—22no—
149C22×C5×D3—22no—
150C22×C5×D3—22no—
151C22×C5×D3—22no—
152C22×C5×D3—22no—
153C22×C5×D3—22no—
154C22×C5×D3—22no—
155C22×C5×D3—22no—
156C22×C5×D3—22no—
157C22×C5×D3—22no—
158C22×C5×D3—22no—
159C22×C5×D3—22no—
160C22×C5×D3—22no—
161C22×C5×D3—22no—
162C22×C5×D3—22no—
163C22×C5×D3—22no—
164C22×C5×D3—41no—
165C22×C5×D3—41no—
166C22×C5×D3—41no—
167C22×C5×D3—41no—
168C22×C5×D3—41no—
169C22×C5×D3—41no—
170C22×C5×D3—41no—
171C22×C5×D3—41no—
172C22×C5×D3—41no—
173C22×C5×D3—41no—
174C22×C5×D3—41no—
175C22×C5×D3—41no—
176C22×C5×D3—41no—
177C22×C5×D3—41no—
178C22×C5×D3—41no—
179C22×C5×D3—41no—
180C22×C5×D3C4⋊C414yescomplemented
181C2×C3×C4×C5—22no—
182C2×C3×C4×C5—22no—
183C2×C3×C4×C5—22no—
184C2×C3×C4×C5—22no—
185C2×C3×C4×C5—22no—
186C2×C3×C4×C5—22no—
187C2×C3×C4×C5—22no—
188C2×C3×C4×C5—22no—
189C2×C3×C4×C5—22no—
190C2×C3×C4×C5—41no—
191C2×C3×C4×C5—41no—
192C2×C3×C4×C5—41no—
193C2×C3×C4×C5—41no—
194C2×C3×C4×C5—41no—
195C2×C3×C4×C5—41no—
196C2×C3×C4×C5—41no—
197C2×C3×C4×C5—41no—
198C2×C3×C4×C5—41no—
199C2×C3×C4×C5—41no—
200C2×C3×C4×C5—41no—
201C2×C3×C4×C5—41no—
202C2×C5×Dic3—22no—
203C2×C5×Dic3—22no—
204C2×C5×Dic3—22no—
205C2×C5×Dic3—22no—
206C2×C5×Dic3—22no—
207C2×C5×Dic3—22no—
208C2×C5×Dic3—22no—
209C2×C5×Dic3—22no—
210C2×C5×Dic3—22no—
211C2×C5×Dic3—22no—
212C2×C5×Dic3—22no—
213C2×C5×Dic3—22no—
214C2×C5×Dic3—41no—
215C2×C5×Dic3—41no—
216C2×C5×Dic3—41no—
217C2×C5×Dic3—41no—
218C2×C5×Dic3—41no—
219C2×C5×Dic3—41no—
220C2×C5×Dic3—41no—
221C2×C5×Dic3—41no—
222C2×C5×Dic3C22⋊C414yescomplemented
223C24×D3C22×C511yescharacteristic
224C23×C3×C4C22×C511yescharacteristic
225C23×C3×C4C22×C511yescharacteristic
226C23×C3×C4C22×C511yescharacteristic
227C23×Dic3C22×C511yescharacteristic
228C23×Dic3C22×C511yescharacteristic
229C23×Dic3C22×C511yescharacteristic
230C2×(C2×D3)⋊C4—22no—
231C2×(C2×D3)⋊C4—22no—
232C2×(C2×D3)⋊C4—22no—
233C2×(C2×D3)⋊C4—22no—
234C2×(C2×D3)⋊C4—22no—
235C2×(C2×D3)⋊C4—22no—
236C2×(C2×D3)⋊C4—22no—
237C2×(C2×D3)⋊C4—22no—
238C2×(C2×D3)⋊C4C4×C514yescomplemented
239C2×Dic3⋊C4—22no—
240C2×Dic3⋊C4—22no—
241C2×Dic3⋊C4—22no—
242C3×#95—22no—
243C3⋊#95—22no—
244C3⋊#95—22no—
245C24×C5—32no—
246C24×C5—32no—
247C24×C5—32no—
248C24×C5—61no—
249C24×C5—61no—
250C24×C5—61no—
251C24×C5—61no—
252C24×C5—61no—
253C24×C5—61no—
254C24×C5—61no—
255C24×C5—61no—
256C24×C5—61no—
257C24×C5—61no—
258C24×C5—61no—
259C24×C5—61no—
260C24×C5C22×D311yescharacteristic
261C22×C4×C5—21no—
262C22×C4×C5—21no—
263C22×C4×C5—21no—
264C22×C4×C5—21no—
265C22×C4×C5—21no—
266C22×C4×C5—21no—
267C22×C4×C5—21no—
268C22×C4×C5—21no—
269C22×C4×C5—21no—
270C22×C4×C5—21no—
271C22×C4×C5—21no—
272C22×C4×C5—21no—
273C22×C4×C5—21no—
274C22×C4×C5—21no—
275C22×C4×C5—21no—
276C22×C4×C5—21no—
277C22×C4×C5—21no—
278C22×C4×C5—21no—
279C22×C4×C5—32no—
280C22×C4×C5—32no—
281C22×C4×C5—32no—
282C22×C4×C5—32no—
283C22×C4×C5—32no—
284C22×C4×C5—61no—
285C22×C4×C5—61no—
286C22×C4×C5—61no—
287C22×C4×C5—61no—
288C22×C4×C5—61no—
289C22×C4×C5—61no—
290C22×C4×C5—61no—
291C22×C4×C5—61no—
292C22×C4×C5—61no—
293C22×C4×C5—61no—
294C22×C4×C5—61no—
295C22×C4×C5—61no—
296C22×C4×C5—61no—
297C22×C4×C5—61no—
298C22×C4×C5—61no—
299C22×C4×C5—61no—
300C22×C4×C5C4×D312yes—
301C22×C4×C5D1212yes—
302C22×C4×C5#6712yes—
303C5×C4⋊C4—68no—
304C5×C22⋊C4—68no—
305C5×C22⋊C4—68no—
306C5×C22⋊C4—68no—
307C22×C4⋊C4—31no—
308C22×C22⋊C4—31no—
309C22×C22⋊C4—31no—
310C22×C22⋊C4—31no—
311C2×#95—31no—
312C2×#95—31no—
313C2×#95C5×D311yescharacteristic, complemented
314C22×C3×C5C2×C22⋊C411yescharacteristic
315C22×C3×C5C2×C4⋊C411yescharacteristic
316C22×C3×C5#11711yescharacteristic
317C22×C3×C5C4×D411yescharacteristic
318C22×C3×C5C4×D411yescharacteristic
319C22×C3×C5C4×D411yescharacteristic
320C22×C3×C5C4×D411yescharacteristic
321C22×C3×C5#12011yescharacteristic
322C22×C3×C5#12011yescharacteristic
323C22×C3×C5#12011yescharacteristic
324C22×C3×C5#12111yescharacteristic
325C22×C3×C5#12111yescharacteristic
326C22×C3×C5#12111yescharacteristic
327C22×C3×C5#12111yescharacteristic
328C22×C3×C5#12111yescharacteristic
329C22×C3×C5#12111yescharacteristic
330C22×C3×C5#12111yescharacteristic
331C22×C3×C5#12111yescharacteristic
332C22×C3×C5C22⋊Q811yescharacteristic
333C22×C3×C5C22⋊Q811yescharacteristic
334C22×C3×C5C22⋊Q811yescharacteristic
335C22×C3×C5C22⋊Q811yescharacteristic
336C22×C3×C5C22⋊Q811yescharacteristic
337C22×C3×C5C22⋊Q811yescharacteristic
338C22×C3×C5#12311yescharacteristic
339C22×C3×C5#12311yescharacteristic
340C22×C3×C5#12311yescharacteristic
341C22×C3×C5#12311yescharacteristic
342C22×C3×C5#12311yescharacteristic
343C22×C3×C5#12411yescharacteristic
344C22×C3×C5#12411yescharacteristic
345C22×C3×C5#12411yescharacteristic
346C22×C3×C5#12611yescharacteristic
347C22×C3×C5#12611yescharacteristic
348C22×C3×C5#12711yescharacteristic
349C2×C5×D3—24no—
350C2×C5×D3—24no—
351C2×C5×D3—24no—
352C2×C5×D3—42no—
353C2×C5×D3—42no—
354C2×C5×D3—42no—
355C2×C5×D3—42no—
356C2×C5×D3—42no—
357C2×C5×D3—42no—
358C2×C5×D3—42no—
359C2×C5×D3—42no—
360C2×C5×D3—42no—
361C2×C5×D3—42no—
362C2×C5×D3—42no—
363C2×C5×D3—42no—
364C3×C4×C5—42no—
365C3×C4×C5—42no—
366C3×C4×C5—42no—
367C5×Dic3—24no—
368C5×Dic3—42no—
369C5×Dic3—42no—
370C24×C3C23×C511yescharacteristic
371C23×D3—21no—
372C23×D3—21no—
373C23×D3—21no—
374C23×D3—21no—
375C23×D3—21no—
376C23×D3—21no—
377C23×D3—21no—
378C23×D3—21no—
379C23×D3—21no—
380C23×D3—21no—
381C23×D3—21no—
382C23×D3—21no—
383C23×D3C2×C4×C512yes—
384C23×D3C5×D412yes—
385C23×D3C5×Q812yes—
386C22×C3×C4—21no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—21no—
391C22×C3×C4—21no—
392C22×C3×C4—21no—
393C22×C3×C4—21no—
394C22×C3×C4—21no—
395C22×C3×C4—21no—
396C22×C3×C4—21no—
397C22×C3×C4—21no—
398C22×C3×C4—21no—
399C22×C3×C4—21no—
400C22×C3×C4—21no—
401C22×C3×C4—21no—
402C22×C3×C4—21no—
403C22×C3×C4—21no—
404C22×C3×C4C2×C4×C512yes—
405C22×C3×C4C5×D412yes—
406C22×C3×C4C5×D412yes—
407C22×Dic3—21no—
408C22×Dic3—21no—
409C22×Dic3—21no—
410C22×Dic3—21no—
411C22×Dic3—21no—
412C22×Dic3—21no—
413C22×Dic3—21no—
414C22×Dic3—21no—
415C22×Dic3—21no—
416C22×Dic3—21no—
417C22×Dic3—21no—
418C22×Dic3—21no—
419C22×Dic3—21no—
420C22×Dic3—21no—
421C22×Dic3—21no—
422C22×Dic3—21no—
423C22×Dic3C2×C4×C512yes—
424C22×Dic3C5×D412yes—
425C22×Dic3C5×D412yes—
426C22×Dic3C5×D412yes—
427C22×Dic3C5×D412yes—
428(C2×D3)⋊C4—28no—
429(C2×D3)⋊C4—28no—
430(C2×D3)⋊C4—28no—
431Dic3⋊C4—28no—
432C23×C5—34no—
433C23×C5—62no—
434C23×C5—62no—
435C23×C5—62no—
436C23×C5—62no—
437C23×C5—62no—
438C23×C5—62no—
439C23×C5—62no—
440C23×C5—62no—
441C23×C5—62no—
442C23×C5—62no—
443C23×C5—62no—
444C23×C5—62no—
445C23×C5—62no—
446C23×C5—62no—
447C23×C5—62no—
448C23×C5—62no—
449C23×C5—62no—
450C23×C5—62no—
451C23×C5—121no—
452C23×C5—121no—
453C23×C5—121no—
454C23×C5—121no—
455C23×C5—121no—
456C23×C5—121no—
457C23×C5—121no—
458C23×C5—121no—
459C23×C5—121no—
460C23×C5—121no—
461C23×C5—121no—
462C23×C5—121no—
463C23×C5—121no—
464C23×C5—121no—
465C23×C5—121no—
466C23×C5—121no—
467C23×C5C2×C4×D311yescharacteristic
468C23×C5C2×D1211yescharacteristic
469C23×C5#23511yescharacteristic
470C23×C5#23511yescharacteristic
471C23×C5#23511yescharacteristic
472C23×C5#23511yescharacteristic
473C23×C5D3×D411yescharacteristic
474C23×C5D3×D411yescharacteristic
475C23×C5D3×D411yescharacteristic
476C23×C5D3×D411yescharacteristic
477C23×C5D3×D411yescharacteristic
478C23×C5#23711yescharacteristic
479C23×C5D3×Q811yescharacteristic
480C23×C5#23911yescharacteristic
481C23×C5C2×#6711yescharacteristic
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—22no—
487C2×C4×C5—22no—
488C2×C4×C5—22no—
489C2×C4×C5—22no—
490C2×C4×C5—22no—
491C2×C4×C5—34no—
492C2×C4×C5—41no—
493C2×C4×C5—41no—
494C2×C4×C5—41no—
495C2×C4×C5—41no—
496C2×C4×C5—41no—
497C2×C4×C5—41no—
498C2×C4×C5—41no—
499C2×C4×C5—41no—
500C2×C4×C5—41no—
501C2×C4×C5—41no—
502C2×C4×C5—41no—
503C2×C4×C5—41no—
504C2×C4×C5—62no—
505C2×C4×C5—62no—
506C2×C4×C5—62no—
507C2×C4×C5—62no—
508C2×C4×C5—62no—
509C2×C4×C5—62no—
510C2×C4×C5—62no—
511C2×C4×C5—62no—
512C2×C4×C5—62no—
513C2×C4×C5—62no—
514C2×C4×C5—62no—
515C2×C4×C5—62no—
516C2×C4×C5—121no—
517C2×C4×C5—121no—
518C2×C4×C5—121no—
519C2×C4×C5—121no—
520C2×C4×C5—121no—
521C2×C4×C5—121no—
522C2×C4×C5—121no—
523C2×C4×C5—121no—
524C25—31no—
525C23×C4—31no—
526C23×C4—31no—
527C23×C4—31no—
528C23×C4C2×C5×D311yescharacteristic
529C23×C4C2×C5×D311yescharacteristic
530C23×C4C2×C5×D311yescharacteristic
531C2×C4⋊C4—62no—
532C2×C4⋊C4—62no—
533C2×C4⋊C4—62no—
534C2×C22⋊C4—34no—
535C2×C22⋊C4—62no—
536C2×C22⋊C4—62no—
537C2×C22⋊C4—62no—
538C2×C22⋊C4—62no—
539C2×C22⋊C4—62no—
540C2×C22⋊C4—62no—
541C2×C22⋊C4—62no—
542C2×C22⋊C4—62no—
543#95—22no—
544#95—62no—
545#95—62no—
546C2×C3×C5#38011yescharacteristic
547C2×C3×C5#38511yescharacteristic
548C2×C3×C5#38511yescharacteristic
549C2×C3×C5#38611yescharacteristic
550C2×C3×C5#38811yescharacteristic
551C2×C3×C5#38811yescharacteristic
552C2×C3×C5#39011yescharacteristic
553C2×C3×C5#39211yescharacteristic
554C2×C3×C5#39311yescharacteristic
555C2×C3×C5#39411yescharacteristic
556C2×C3×C5#39411yescharacteristic
557C2×C3×C5#39611yescharacteristic
558C2×C3×C5#39611yescharacteristic
559C2×C3×C5#39711yescharacteristic
560C2×C3×C5#39911yescharacteristic
561C5×D3—44no—
562C23×C3C22×C4×C511yescharacteristic
563C23×C3C2×C5×D411yescharacteristic
564C23×C3C2×C5×D411yescharacteristic
565C23×C3C2×C5×D411yescharacteristic
566C23×C3C2×C5×D411yescharacteristic
567C23×C3C2×C5×D411yescharacteristic
568C23×C3C2×C5×D411yescharacteristic
569C23×C3C2×C5×D411yescharacteristic
570C23×C3C2×C5×Q811yescharacteristic
571C23×C3C5×#4111yescharacteristic
572C23×C3C5×#4111yescharacteristic
573C23×C3C5×#4111yescharacteristic
574C23×C3C5×#4111yescharacteristic
575C23×C3C5×#4111yescharacteristic
576C23×C3C5×#4111yescharacteristic
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—22no—
581C22×D3—22no—
582C22×D3—22no—
583C22×D3—22no—
584C22×D3—22no—
585C22×D3—22no—
586C22×D3—22no—
587C22×D3—22no—
588C22×D3—22no—
589C22×D3—22no—
590C22×D3—22no—
591C22×D3—22no—
592C22×D3—22no—
593C22×D3—22no—
594C22×D3—22no—
595C22×D3—41no—
596C22×D3—41no—
597C22×D3—41no—
598C22×D3—41no—
599C22×D3—41no—
600C22×D3—41no—
601C22×D3—41no—
602C22×D3—41no—
603C22×D3—41no—
604C22×D3—41no—
605C22×D3—41no—
606C22×D3—41no—
607C22×D3—41no—
608C22×D3—41no—
609C22×D3—41no—
610C22×D3—41no—
611C22×D3C5×C4⋊C414yescomplemented
612C2×C3×C4—22no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—22no—
621C2×C3×C4—41no—
622C2×C3×C4—41no—
623C2×C3×C4—41no—
624C2×C3×C4—41no—
625C2×C3×C4—41no—
626C2×C3×C4—41no—
627C2×C3×C4—41no—
628C2×C3×C4—41no—
629C2×C3×C4—41no—
630C2×C3×C4—41no—
631C2×C3×C4—41no—
632C2×C3×C4—41no—
633C2×Dic3—22no—
634C2×Dic3—22no—
635C2×Dic3—22no—
636C2×Dic3—22no—
637C2×Dic3—22no—
638C2×Dic3—22no—
639C2×Dic3—22no—
640C2×Dic3—22no—
641C2×Dic3—22no—
642C2×Dic3—22no—
643C2×Dic3—22no—
644C2×Dic3—22no—
645C2×Dic3—41no—
646C2×Dic3—41no—
647C2×Dic3—41no—
648C2×Dic3—41no—
649C2×Dic3—41no—
650C2×Dic3—41no—
651C2×Dic3—41no—
652C2×Dic3—41no—
653C2×Dic3C5×C22⋊C414yescomplemented
654C22×C5—64no—
655C22×C5—64no—
656C22×C5—64no—
657C22×C5—122no—
658C22×C5—122no—
659C22×C5—122no—
660C22×C5—122no—
661C22×C5—122no—
662C22×C5—122no—
663C22×C5—122no—
664C22×C5—122no—
665C22×C5—122no—
666C22×C5—122no—
667C22×C5—122no—
668C22×C5—122no—
669C22×C5#87211yescharacteristic
670C22×C5C4×D1211yescharacteristic
671C22×C5#87511yescharacteristic
672C22×C5#87611yescharacteristic
673C22×C5D3×C22⋊C411yescharacteristic
674C22×C5#67⋊C411yescharacteristic
675C22×C5#88211yescharacteristic
676C22×C5#88211yescharacteristic
677C22×C5#88311yescharacteristic
678C22×C5#88411yescharacteristic
679C22×C5#88411yescharacteristic
680C22×C5#88411yescharacteristic
681C22×C5#88411yescharacteristic
682C22×C5#88411yescharacteristic
683C22×C5#88511yescharacteristic
684C22×C5#88511yescharacteristic
685C22×C5D3×C4⋊C411yescharacteristic
686C22×C5#89311yescharacteristic
687C22×C5#89411yescharacteristic
688C22×C5#89411yescharacteristic
689C22×C5#89411yescharacteristic
690C22×C5#89511yescharacteristic
691C22×C5#89611yescharacteristic
692C22×C5#89611yescharacteristic
693C22×C5#89611yescharacteristic
694C22×C5#89611yescharacteristic
695C22×C5#89711yescharacteristic
696C22×C5#89811yescharacteristic
697C22×C5C4×#6711yescharacteristic
698C22×C5#92911yescharacteristic
699C22×C5#93011yescharacteristic
700C22×C5#93711yescharacteristic
701C22×C5#93911yescharacteristic
702C22×C5#94011yescharacteristic
703C22×C5#94611yescharacteristic
704C4×C5—42no—
705C4×C5—42no—
706C4×C5—42no—
707C4×C5—64no—
708C4×C5—122no—
709C4×C5—122no—
710C24—32no—
711C24—32no—
712C24—32no—
713C24—61no—
714C24—61no—
715C24—61no—
716C24—61no—
717C24—61no—
718C24—61no—
719C24—61no—
720C24—61no—
721C24—61no—
722C24—61no—
723C24—61no—
724C24—61no—
725C24C22×C5×D311yescharacteristic
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—32no—
745C22×C4—32no—
746C22×C4—32no—
747C22×C4—32no—
748C22×C4—32no—
749C22×C4—61no—
750C22×C4—61no—
751C22×C4—61no—
752C22×C4—61no—
753C22×C4—61no—
754C22×C4—61no—
755C22×C4—61no—
756C22×C4—61no—
757C22×C4—61no—
758C22×C4—61no—
759C22×C4—61no—
760C22×C4—61no—
761C22×C4—61no—
762C22×C4—61no—
763C22×C4—61no—
764C22×C4—61no—
765C22×C4C4×C5×D312yes—
766C22×C4C5×D1212yes—
767C22×C4C5×#6712yes—
768C4⋊C4—68no—
769C22⋊C4—68no—
770C22⋊C4—68no—
771C22⋊C4—68no—
772C3×C5#143911yescharacteristic, complemented, Hall
773C22×C3C2×C5×C22⋊C411yescharacteristic
774C22×C3C2×C5×C4⋊C411yescharacteristic
775C22×C3C5×#11711yescharacteristic
776C22×C3C4×C5×D411yescharacteristic
777C22×C3C4×C5×D411yescharacteristic
778C22×C3C4×C5×D411yescharacteristic
779C22×C3C4×C5×D411yescharacteristic
780C22×C3C5×#12011yescharacteristic
781C22×C3C5×#12011yescharacteristic
782C22×C3C5×#12011yescharacteristic
783C22×C3C5×#12111yescharacteristic
784C22×C3C5×#12111yescharacteristic
785C22×C3C5×#12111yescharacteristic
786C22×C3C5×#12111yescharacteristic
787C22×C3C5×#12111yescharacteristic
788C22×C3C5×#12111yescharacteristic
789C22×C3C5×#12111yescharacteristic
790C22×C3C5×#12111yescharacteristic
791C22×C3C5×C22⋊Q811yescharacteristic
792C22×C3C5×C22⋊Q811yescharacteristic
793C22×C3C5×C22⋊Q811yescharacteristic
794C22×C3C5×C22⋊Q811yescharacteristic
795C22×C3C5×C22⋊Q811yescharacteristic
796C22×C3C5×C22⋊Q811yescharacteristic
797C22×C3C5×#12311yescharacteristic
798C22×C3C5×#12311yescharacteristic
799C22×C3C5×#12311yescharacteristic
800C22×C3C5×#12311yescharacteristic
801C22×C3C5×#12311yescharacteristic
802C22×C3C5×#12411yescharacteristic
803C22×C3C5×#12411yescharacteristic
804C22×C3C5×#12411yescharacteristic
805C22×C3C5×#12611yescharacteristic
806C22×C3C5×#12611yescharacteristic
807C22×C3C5×#12711yescharacteristic
808C2×D3—24no—
809C2×D3—24no—
810C2×D3—24no—
811C2×D3—42no—
812C2×D3—42no—
813C2×D3—42no—
814C2×D3—42no—
815C2×D3—42no—
816C2×D3—42no—
817C2×D3—42no—
818C2×D3—42no—
819C2×D3—42no—
820C2×D3—42no—
821C2×D3—42no—
822C2×D3—42no—
823C3×C4—42no—
824C3×C4—42no—
825C3×C4—42no—
826Dic3—24no—
827Dic3—42no—
828Dic3—42no—
829C2×C5—124no—
830C2×C5#466511yescharacteristic
831C2×C5#466711yescharacteristic
832C2×C5#466811yescharacteristic
833C2×C5#466911yescharacteristic
834C2×C5#467211yescharacteristic
835C2×C5#467311yescharacteristic
836C2×C5#467511yescharacteristic
837C2×C5#467611yescharacteristic
838C2×C5#494011yescharacteristic
839C2×C5#495711yescharacteristic
840C2×C5#495911yescharacteristic
841C2×C5#496011yescharacteristic
842C2×C5#498911yescharacteristic
843C2×C5#499311yescharacteristic
844C2×C5#499411yescharacteristic
845C23—34no—
846C23—62no—
847C23—62no—
848C23—62no—
849C23—62no—
850C23—62no—
851C23—62no—
852C23—62no—
853C23—62no—
854C23—62no—
855C23—62no—
856C23—62no—
857C23—62no—
858C23—62no—
859C23—62no—
860C23—62no—
861C23—62no—
862C23—62no—
863C23—62no—
864C23—121no—
865C23—121no—
866C23—121no—
867C23—121no—
868C23—121no—
869C23—121no—
870C23—121no—
871C23—121no—
872C23—121no—
873C23—121no—
874C23—121no—
875C23—121no—
876C23—121no—
877C23—121no—
878C23—121no—
879C23—121no—
880C23C2×C4×C5×D311yescharacteristic
881C23C2×C5×D1211yescharacteristic
882C23C5×#23511yescharacteristic
883C23C5×#23511yescharacteristic
884C23C5×#23511yescharacteristic
885C23C5×#23511yescharacteristic
886C23C5×D3×D411yescharacteristic
887C23C5×D3×D411yescharacteristic
888C23C5×D3×D411yescharacteristic
889C23C5×D3×D411yescharacteristic
890C23C5×D3×D411yescharacteristic
891C23C5×#23711yescharacteristic
892C23C5×D3×Q811yescharacteristic
893C23C5×#23911yescharacteristic
894C23C2×C5×#6711yescharacteristic
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—34no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—41no—
914C2×C4—41no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—62no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—62no—
922C2×C4—62no—
923C2×C4—62no—
924C2×C4—62no—
925C2×C4—62no—
926C2×C4—62no—
927C2×C4—62no—
928C2×C4—62no—
929C2×C4—121no—
930C2×C4—121no—
931C2×C4—121no—
932C2×C4—121no—
933C2×C4—121no—
934C2×C4—121no—
935C2×C4—121no—
936C2×C4—121no—
937C2×C3C5×#38011yescharacteristic
938C2×C3C5×#38511yescharacteristic
939C2×C3C5×#38511yescharacteristic
940C2×C3C5×#38611yescharacteristic
941C2×C3C5×#38811yescharacteristic
942C2×C3C5×#38811yescharacteristic
943C2×C3C5×#39011yescharacteristic
944C2×C3C5×#39211yescharacteristic
945C2×C3C5×#39311yescharacteristic
946C2×C3C5×#39411yescharacteristic
947C2×C3C5×#39411yescharacteristic
948C2×C3C5×#39611yescharacteristic
949C2×C3C5×#39611yescharacteristic
950C2×C3C5×#39711yescharacteristic
951C2×C3C5×#39911yescharacteristic
952D3—44no—
953C5#6942811yescharacteristic, direct product factor, Sylow
954C22—64no—
955C22—64no—
956C22—64no—
957C22—122no—
958C22—122no—
959C22—122no—
960C22—122no—
961C22—122no—
962C22—122no—
963C22—122no—
964C22—122no—
965C22—122no—
966C22—122no—
967C22—122no—
968C22—122no—
969C22C5×#87211yescharacteristic
970C22C4×C5×D1211yescharacteristic
971C22C5×#87511yescharacteristic
972C22C5×#87611yescharacteristic
973C22C5×D3×C22⋊C411yescharacteristic
974C22C5×#67⋊C411yescharacteristic
975C22C5×#88211yescharacteristic
976C22C5×#88211yescharacteristic
977C22C5×#88311yescharacteristic
978C22C5×#88411yescharacteristic
979C22C5×#88411yescharacteristic
980C22C5×#88411yescharacteristic
981C22C5×#88411yescharacteristic
982C22C5×#88411yescharacteristic
983C22C5×#88511yescharacteristic
984C22C5×#88511yescharacteristic
985C22C5×D3×C4⋊C411yescharacteristic
986C22C5×#89311yescharacteristic
987C22C5×#89411yescharacteristic
988C22C5×#89411yescharacteristic
989C22C5×#89411yescharacteristic
990C22C5×#89511yescharacteristic
991C22C5×#89611yescharacteristic
992C22C5×#89611yescharacteristic
993C22C5×#89611yescharacteristic
994C22C5×#89611yescharacteristic
995C22C5×#89711yescharacteristic
996C22C5×#89811yescharacteristic
997C22C4×C5×#6711yescharacteristic
998C22C5×#92911yescharacteristic
999C22C5×#93011yescharacteristic
1000C22C5×#93711yescharacteristic
1001C22C5×#93911yescharacteristic
1002C22C5×#94011yescharacteristic
1003C22C5×#94611yescharacteristic
1004C4—42no—
1005C4—42no—
1006C4—42no—
1007C4—64no—
1008C4—122no—
1009C4—122no—
1010C3C5×#143911yescharacteristic, complemented, Sylow
1011C2—124no—
1012C2C5×#466511yescharacteristic
1013C2C5×#466711yescharacteristic
1014C2C5×#466811yescharacteristic
1015C2C5×#466911yescharacteristic
1016C2C5×#467211yescharacteristic
1017C2C5×#467311yescharacteristic
1018C2C5×#467511yescharacteristic
1019C2C5×#467611yescharacteristic
1020C2C5×#494011yescharacteristic
1021C2C5×#495711yescharacteristic
1022C2C5×#495911yescharacteristic
1023C2C5×#496011yescharacteristic
1024C2C5×#498911yescharacteristic
1025C2C5×#499311yescharacteristic
1026C2C5×#499411yescharacteristic
subgroupG/H
centerC24×C5C22×D3
commutatorC23×C3C22×C4×C5
FrattiniC24C22×C5×D3
FittingC2×C3×C5×#95C2
socleC24×C3×C5C23
prime radicalC24×C5×D3C22
cosocleC24×C3C23×C5
hypercenterC2×C5×#95D3
hypocenterC3C5×#1439
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24×C5 ◁ C2×C5×#95

Complements

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

NH ≅ G/Ntype
4. C22×C5×Dic3⋊C4C2semidirect
5. C2×C3×C5×#95C2semidirect
6. C2×C5×C3⋊#95C2semidirect
7. C2×C5×C3⋊#95C2semidirect
24. C2×C5×(C2×D3)⋊C4C4semidirect
31. #69428C5direct (N × H)
38. C2×C5×#95D3semidirect
104. C22×Dic3⋊C4C2×C5semidirect
105. C2×C3×#95C2×C5semidirect
106. C2×C3⋊#95C2×C5semidirect
107. C2×C3⋊#95C2×C5semidirect
180. C22×C5×D3C4⋊C4semidirect
222. C2×C5×Dic3C22⋊C4semidirect
238. C2×(C2×D3)⋊C4C4×C5semidirect
313. C2×#95C5×D3semidirect
611. C22×D3C5×C4⋊C4semidirect
653. C2×Dic3C5×C22⋊C4semidirect
772. C3×C5#1439semidirect
953. C5#69428direct (N × H)
1010. C3C5×#1439semidirect

Maximal subgroups

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

subgroupindex
C22×C5×(C2×D3)⋊C42
C22×C5×Dic3⋊C42
C2×C3×C5×#952
C2×C5×C3⋊#952
C5×#14393
#694285