Finite Group Databasebeta

← C2×C3×#65246 #14320767

Subgroups — C2×C3×#65246 #14320767

Order 1920.

2720 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C3×C22⋊D5C211yesmaximal, characteristic
2C22×C3×C5×C22⋊C4C211yesmaximal, characteristic, complemented
3C22×C3×C22⋊Dic5C211yesmaximal, characteristic, complemented
4C22×C3×#685C211yesmaximal, characteristic, complemented
5C22×C3×#685C211yesmaximal, characteristic, complemented
6C22×C3×#683C211yesmaximal, characteristic, complemented
7C22×C3×C4×Dic5C211yesmaximal, characteristic, complemented
8C3×#65246C218yesmaximal, direct product factor
9C2×#65246C311yesmaximal, characteristic, direct product factor, Hall
10C25×C3×C5C2211yescharacteristic
11C24×C3×D5C2211yescharacteristic
12C23×C3×C4×C5C2211yescharacteristic
13C23×C3×C4×C5C2211yescharacteristic
14C22×C3×C22⋊D5—24no—
15C22×C3×C22⋊D5—24no—
16C22×C3×C22⋊D5C418yescomplemented
17C22×C3×C22⋊D5C2214yes—
18C23×C3×Dic5C2211yescharacteristic
19C23×C3×Dic5C2211yescharacteristic
20C23×C3×Dic5C2211yescharacteristic
21C2×C3×C5×C22⋊C4—24no—
22C2×C3×C5×C22⋊C4C2214yescomplemented
23C2×C3×C22⋊Dic5—24no—
24C2×C3×C22⋊Dic5C2214yescomplemented
25C2×C3×#685—24no—
26C2×C3×#685—24no—
27C2×C3×#685C2214yescomplemented
28C2×C3×#685C2214yescomplemented
29C2×C3×#683—24no—
30C2×C3×#683C2214yescomplemented
31C2×C3×C4×Dic5—24no—
32C2×C3×C4×Dic5C2214yescomplemented
33C2×C3×#390—51nomaximal, Hall
34C23×C22⋊D5C2×C311yescharacteristic
35C22×C5×C22⋊C4C2×C311yescharacteristic, complemented
36C22×C22⋊Dic5C2×C311yescharacteristic, complemented
37C22×#685C2×C311yescharacteristic, complemented
38C22×#685C2×C311yescharacteristic, complemented
39C22×#683C2×C311yescharacteristic, complemented
40C22×C4×Dic5C2×C311yescharacteristic, complemented
41#65246C2×C318yesdirect product factor
42C24×C3×C5—22no—
43C24×C3×C5—22no—
44C24×C3×C5—22no—
45C24×C3×C5—22no—
46C24×C3×C5—22no—
47C24×C3×C5—22no—
48C24×C3×C5C2×C414yes—
49C24×C3×C5C2312yes—
50C24×C3×C5C2311yescharacteristic
51C23×C3×D5—22no—
52C23×C3×D5—22no—
53C23×C3×D5—22no—
54C23×C3×D5—22no—
55C23×C3×D5—22no—
56C23×C3×D5—22no—
57C23×C3×D5C2×C414yes—
58C23×C3×D5C2312yes—
59C22×C3×C4×C5—22no—
60C22×C3×C4×C5—22no—
61C22×C3×C4×C5—22no—
62C22×C3×C4×C5—22no—
63C22×C3×C4×C5—22no—
64C22×C3×C4×C5D414yescomplemented
65C22×C3×C4×C5C2312yes—
66C22×C3×C4×C5C2312yes—
67C2×C3×C22⋊D5—232no—
68C2×C3×C22⋊D5—28no—
69C2×C3×C22⋊D5—28no—
70C2×C3×C22⋊D5C2×C4116yescomplemented
71C22×C3×Dic5—22no—
72C22×C3×Dic5—22no—
73C22×C3×Dic5—22no—
74C22×C3×Dic5—22no—
75C22×C3×Dic5—22no—
76C22×C3×Dic5C2×C414yes—
77C22×C3×Dic5D414yes—
78C22×C3×Dic5D414yes—
79C22×C3×Dic5D414yescomplemented
80C22×C3×Dic5C2312yes—
81C22×C3×Dic5C2312yes—
82C22×C3×Dic5C2312yes—
83C3×C5×C22⋊C4—28no—
84C3×C22⋊Dic5—28no—
85C3×#685—28no—
86C3×#685—28no—
87C3×#683—28no—
88C3×C4×Dic5—28no—
89C23×C3×D4—51no—
90C22×C3×C4⋊C4—51no—
91C22×C3×C22⋊C4—51no—
92C22×C3×C22⋊C4—51no—
93C22×C3×C22⋊C4—51no—
94C22×C3×C22⋊C4D511yescharacteristic, complemented
95C22×C3×C42—51no—
96C3×#390—58no—
97C25×C5C22×C311yescharacteristic
98C24×D5C22×C311yescharacteristic
99C23×C4×C5C22×C311yescharacteristic
100C23×C4×C5C22×C311yescharacteristic
101C22×C22⋊D5—24no—
102C22×C22⋊D5—24no—
103C22×C22⋊D5C3×C418yescomplemented
104C22×C22⋊D5C22×C314yes—
105C23×Dic5C22×C311yescharacteristic
106C23×Dic5C22×C311yescharacteristic
107C23×Dic5C22×C311yescharacteristic
108C2×C5×C22⋊C4—24no—
109C2×C5×C22⋊C4C22×C314yescomplemented
110C2×C22⋊Dic5—24no—
111C2×C22⋊Dic5C22×C314yescomplemented
112C2×#685—24no—
113C2×#685—24no—
114C2×#685C22×C314yescomplemented
115C2×#685C22×C314yescomplemented
116C2×#683—24no—
117C2×#683C22×C314yescomplemented
118C2×C4×Dic5—24no—
119C2×C4×Dic5C22×C314yescomplemented
120C2×#390—51noSylow
121C23×C3×C5—28no—
122C23×C3×C5—28no—
123C23×C3×C5—28no—
124C23×C3×C5—22no—
125C23×C3×C5—22no—
126C23×C3×C5—22no—
127C23×C3×C5—22no—
128C23×C3×C5—22no—
129C23×C3×C5—22no—
130C23×C3×C5—44no—
131C23×C3×C5—44no—
132C23×C3×C5—44no—
133C23×C3×C5—44no—
134C23×C3×C5C22×C414yes—
135C23×C3×C5C22×C412yes—
136C23×C3×C5C2×D412yes—
137C23×C3×C5C2×D412yes—
138C23×C3×C5C2×D412yes—
139C23×C3×C5C2×D412yes—
140C23×C3×C5#4112yes—
141C23×C3×C5#4112yes—
142C23×C3×C5C2411yescharacteristic
143C22×C3×D5—28no—
144C22×C3×D5—28no—
145C22×C3×D5—28no—
146C22×C3×D5—22no—
147C22×C3×D5—22no—
148C22×C3×D5—22no—
149C22×C3×D5—22no—
150C22×C3×D5—22no—
151C22×C3×D5—22no—
152C22×C3×D5—44no—
153C22×C3×D5—44no—
154C22×C3×D5—44no—
155C22×C3×D5—44no—
156C22×C3×D5C22×C414yes—
157C2×C3×C4×C5—28no—
158C2×C3×C4×C5—22no—
159C2×C3×C4×C5—22no—
160C2×C3×C4×C5—22no—
161C2×C3×C4×C5—22no—
162C2×C3×C4×C5—22no—
163C2×C3×C4×C5—44no—
164C2×C3×C4×C5C2×D414yescomplemented
165C3×C22⋊D5—232no—
166C2×C3×Dic5—28no—
167C2×C3×Dic5—22no—
168C2×C3×Dic5—22no—
169C2×C3×Dic5—22no—
170C2×C3×Dic5—22no—
171C2×C3×Dic5—22no—
172C2×C3×Dic5—44no—
173C2×C3×Dic5C22⋊C4116yescomplemented
174C2×C3×Dic5C22×C414yes—
175C2×C3×Dic5C2×D414yes—
176C2×C3×Dic5C2×D414yes—
177C2×C3×Dic5C2×D414yescomplemented
178C25×C3—51no—
179C25×C3C2×D511yescharacteristic
180C22×C3×D4—58no—
181C22×C3×D4—54no—
182C22×C3×D4—104no—
183C22×C3×D4—104no—
184C23×C3×C4—51no—
185C23×C3×C4—51no—
186C23×C3×C4—51no—
187C23×C3×C4C2×D511yescharacteristic
188C23×C3×C4C2×D511yescharacteristic
189C2×C3×C4⋊C4—54no—
190C2×C3×C4⋊C4—104no—
191C2×C3×C22⋊C4—24no—
192C2×C3×C22⋊C4—54no—
193C2×C3×C22⋊C4—54no—
194C2×C3×C22⋊C4—54no—
195C2×C3×C22⋊C4—104no—
196C2×C3×C22⋊C4—104no—
197C2×C3×C22⋊C4—104no—
198C2×C3×C22⋊C4C2×D514yescomplemented
199C2×C3×C42—54no—
200C2×C3×C42—104no—
201C24×C5—22no—
202C24×C5—22no—
203C24×C5—22no—
204C24×C5—22no—
205C24×C5—22no—
206C24×C5—22no—
207C24×C5C2×C3×C414yes—
208C24×C5C23×C312yes—
209C24×C5C23×C311yescharacteristic
210C23×D5—22no—
211C23×D5—22no—
212C23×D5—22no—
213C23×D5—22no—
214C23×D5—22no—
215C23×D5—22no—
216C23×D5C2×C3×C414yes—
217C23×D5C23×C312yes—
218C22×C4×C5—22no—
219C22×C4×C5—22no—
220C22×C4×C5—22no—
221C22×C4×C5—22no—
222C22×C4×C5—22no—
223C22×C4×C5C3×D414yescomplemented
224C22×C4×C5C23×C312yes—
225C22×C4×C5C23×C312yes—
226C2×C22⋊D5—232no—
227C2×C22⋊D5—28no—
228C2×C22⋊D5—28no—
229C2×C22⋊D5C2×C3×C4116yescomplemented
230C22×Dic5—22no—
231C22×Dic5—22no—
232C22×Dic5—22no—
233C22×Dic5—22no—
234C22×Dic5—22no—
235C22×Dic5C2×C3×C414yes—
236C22×Dic5C3×D414yes—
237C22×Dic5C3×D414yes—
238C22×Dic5C3×D414yescomplemented
239C22×Dic5C23×C312yes—
240C22×Dic5C23×C312yes—
241C22×Dic5C23×C312yes—
242C5×C22⋊C4—28no—
243C22⋊Dic5—28no—
244#685—28no—
245#685—28no—
246#683—28no—
247C4×Dic5—28no—
248C23×D4—51no—
249C22×C4⋊C4—51no—
250C22×C22⋊C4—51no—
251C22×C22⋊C4—51no—
252C22×C22⋊C4—51no—
253C22×C22⋊C4C3×D511yescharacteristic, complemented
254C22×C42—51no—
255#390—58no—
256C22×C3×C5—24no—
257C22×C3×C5—24no—
258C22×C3×C5—24no—
259C22×C3×C5—42no—
260C22×C3×C5—42no—
261C22×C3×C5—42no—
262C22×C3×C5—42no—
263C22×C3×C5—416no—
264C22×C3×C5C2×C22⋊C414yes—
265C22×C3×C5C4×D414yes—
266C22×C3×C5C4×D414yes—
267C22×C3×C5#12114yes—
268C22×C3×C5#12114yes—
269C22×C3×C5#12414yes—
270C22×C3×C5#12714yes—
271C22×C3×C5C23×C411yescharacteristic
272C22×C3×C5C22×D411yescharacteristic
273C22×C3×C5C22×D411yescharacteristic
274C22×C3×C5C22×D411yescharacteristic
275C22×C3×C5C22×D411yescharacteristic
276C22×C3×C5C2×#4111yescharacteristic
277C22×C3×C5C2×#4111yescharacteristic
278C2×C3×D5—24no—
279C2×C3×D5—24no—
280C2×C3×D5—24no—
281C2×C3×D5—42no—
282C2×C3×D5—42no—
283C2×C3×D5—42no—
284C2×C3×D5—42no—
285C2×C3×D5—416no—
286C3×C4×C5—24no—
287C3×C4×C5—42no—
288C3×Dic5—24no—
289C3×Dic5—42no—
290C3×Dic5C2×C22⋊C418yescomplemented
291C24×C3—22no—
292C24×C3—22no—
293C24×C3—22no—
294C24×C3—22no—
295C24×C3—22no—
296C24×C3—22no—
297C24×C3—54no—
298C24×C3—52no—
299C24×C3—102no—
300C24×C3—102no—
301C24×C3—102no—
302C24×C3—102no—
303C24×C3—102no—
304C24×C3—102no—
305C24×C3C4×D514yes—
306C24×C3C22×D512yes—
307C24×C3C22×D511yescharacteristic
308C2×C3×D4—516no—
309C2×C3×D4—108no—
310C2×C3×D4—108no—
311C2×C3×D4—1032no—
312C22×C3×C4—22no—
313C22×C3×C4—22no—
314C22×C3×C4—22no—
315C22×C3×C4—22no—
316C22×C3×C4—22no—
317C22×C3×C4—54no—
318C22×C3×C4—54no—
319C22×C3×C4—54no—
320C22×C3×C4—52no—
321C22×C3×C4—54no—
322C22×C3×C4—52no—
323C22×C3×C4—52no—
324C22×C3×C4—102no—
325C22×C3×C4—102no—
326C22×C3×C4—102no—
327C22×C3×C4—102no—
328C22×C3×C4—102no—
329C22×C3×C4C22⋊D514yescomplemented
330C22×C3×C4C22×D512yes—
331C22×C3×C4C22×D512yes—
332C3×C4⋊C4—108no—
333C3×C22⋊C4—28no—
334C3×C22⋊C4—108no—
335C3×C22⋊C4—108no—
336C3×C22⋊C4—108no—
337C3×C42—108no—
338C23×C5—28no—
339C23×C5—28no—
340C23×C5—28no—
341C23×C5—22no—
342C23×C5—22no—
343C23×C5—22no—
344C23×C5—22no—
345C23×C5—22no—
346C23×C5—22no—
347C23×C5—44no—
348C23×C5—44no—
349C23×C5—44no—
350C23×C5—44no—
351C23×C5C22×C3×C414yes—
352C23×C5C22×C3×C412yes—
353C23×C5C2×C3×D412yes—
354C23×C5C2×C3×D412yes—
355C23×C5C2×C3×D412yes—
356C23×C5C2×C3×D412yes—
357C23×C5C3×#4112yes—
358C23×C5C3×#4112yes—
359C23×C5C24×C311yescharacteristic
360C22×D5—28no—
361C22×D5—28no—
362C22×D5—28no—
363C22×D5—22no—
364C22×D5—22no—
365C22×D5—22no—
366C22×D5—22no—
367C22×D5—22no—
368C22×D5—22no—
369C22×D5—44no—
370C22×D5—44no—
371C22×D5—44no—
372C22×D5—44no—
373C22×D5C22×C3×C414yes—
374C2×C4×C5—28no—
375C2×C4×C5—22no—
376C2×C4×C5—22no—
377C2×C4×C5—22no—
378C2×C4×C5—22no—
379C2×C4×C5—22no—
380C2×C4×C5—44no—
381C2×C4×C5C2×C3×D414yescomplemented
382C22⋊D5—232no—
383C2×Dic5—28no—
384C2×Dic5—22no—
385C2×Dic5—22no—
386C2×Dic5—22no—
387C2×Dic5—22no—
388C2×Dic5—22no—
389C2×Dic5—44no—
390C2×Dic5C3×C22⋊C4116yescomplemented
391C2×Dic5C22×C3×C414yes—
392C2×Dic5C2×C3×D414yes—
393C2×Dic5C2×C3×D414yes—
394C2×Dic5C2×C3×D414yescomplemented
395C25—51no—
396C25C2×C3×D511yescharacteristic
397C22×D4—58no—
398C22×D4—54no—
399C22×D4—104no—
400C22×D4—104no—
401C23×C4—51no—
402C23×C4—51no—
403C23×C4—51no—
404C23×C4C2×C3×D511yescharacteristic
405C23×C4C2×C3×D511yescharacteristic
406C2×C4⋊C4—54no—
407C2×C4⋊C4—104no—
408C2×C22⋊C4—24no—
409C2×C22⋊C4—54no—
410C2×C22⋊C4—54no—
411C2×C22⋊C4—54no—
412C2×C22⋊C4—104no—
413C2×C22⋊C4—104no—
414C2×C22⋊C4—104no—
415C2×C22⋊C4C2×C3×D514yescomplemented
416C2×C42—54no—
417C2×C42—104no—
418C2×C3×C5—44no—
419C2×C3×C5#39018yescomplemented
420C2×C3×C5C22×C22⋊C411yescharacteristic
421C2×C3×C5C2×C4×D411yescharacteristic
422C2×C3×C5C2×C4×D411yescharacteristic
423C2×C3×C5C2×#12111yescharacteristic
424C2×C3×C5C2×#12111yescharacteristic
425C2×C3×C5C2×#12411yescharacteristic
426C2×C3×C5C2×#12711yescharacteristic
427C3×D5—44no—
428C23×C3—22no—
429C23×C3—22no—
430C23×C3—22no—
431C23×C3—22no—
432C23×C3—22no—
433C23×C3—22no—
434C23×C3—28no—
435C23×C3—28no—
436C23×C3—28no—
437C23×C3—44no—
438C23×C3—44no—
439C23×C3—44no—
440C23×C3—44no—
441C23×C3—54no—
442C23×C3—102no—
443C23×C3—102no—
444C23×C3—102no—
445C23×C3—102no—
446C23×C3—102no—
447C23×C3—102no—
448C23×C3—108no—
449C23×C3—108no—
450C23×C3—108no—
451C23×C3—204no—
452C23×C3—204no—
453C23×C3—204no—
454C23×C3—204no—
455C23×C3C2×C4×D514yes—
456C23×C3C2×C4×D512yes—
457C23×C3#70912yes—
458C23×C3D4×D512yes—
459C23×C3D4×D512yes—
460C23×C3D4×D512yes—
461C23×C3#71112yes—
462C23×C3C2×C22⋊D512yes—
463C23×C3C23×D511yescharacteristic
464C3×D4—1032no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—28no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—44no—
472C2×C3×C4—54no—
473C2×C3×C4—54no—
474C2×C3×C4—54no—
475C2×C3×C4—516no—
476C2×C3×C4—54no—
477C2×C3×C4—102no—
478C2×C3×C4—102no—
479C2×C3×C4—108no—
480C2×C3×C4—102no—
481C2×C3×C4—102no—
482C2×C3×C4—102no—
483C2×C3×C4—204no—
484C2×C3×C4C2×C22⋊D514yescomplemented
485C22×C5—24no—
486C22×C5—24no—
487C22×C5—24no—
488C22×C5—416no—
489C22×C5—42no—
490C22×C5—42no—
491C22×C5—42no—
492C22×C5—42no—
493C22×C5C2×C3×C22⋊C414yes—
494C22×C5C3×C4×D414yes—
495C22×C5C3×C4×D414yes—
496C22×C5C3×#12114yes—
497C22×C5C3×#12114yes—
498C22×C5C3×#12414yes—
499C22×C5C3×#12714yes—
500C22×C5C23×C3×C411yescharacteristic
501C22×C5C22×C3×D411yescharacteristic
502C22×C5C22×C3×D411yescharacteristic
503C22×C5C22×C3×D411yescharacteristic
504C22×C5C22×C3×D411yescharacteristic
505C22×C5C2×C3×#4111yescharacteristic
506C22×C5C2×C3×#4111yescharacteristic
507C2×D5—24no—
508C2×D5—24no—
509C2×D5—24no—
510C2×D5—416no—
511C2×D5—42no—
512C2×D5—42no—
513C2×D5—42no—
514C2×D5—42no—
515C4×C5—24no—
516C4×C5—42no—
517Dic5—24no—
518Dic5—42no—
519Dic5C2×C3×C22⋊C418yescomplemented
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—54no—
527C24—52no—
528C24—102no—
529C24—102no—
530C24—102no—
531C24—102no—
532C24—102no—
533C24—102no—
534C24C3×C4×D514yes—
535C24C22×C3×D512yes—
536C24C22×C3×D511yescharacteristic
537C2×D4—516no—
538C2×D4—108no—
539C2×D4—108no—
540C2×D4—1032no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—54no—
547C22×C4—54no—
548C22×C4—54no—
549C22×C4—52no—
550C22×C4—54no—
551C22×C4—52no—
552C22×C4—52no—
553C22×C4—102no—
554C22×C4—102no—
555C22×C4—102no—
556C22×C4—102no—
557C22×C4—102no—
558C22×C4C3×C22⋊D514yescomplemented
559C22×C4C22×C3×D512yes—
560C22×C4C22×C3×D512yes—
561C4⋊C4—108no—
562C22⋊C4—28no—
563C22⋊C4—108no—
564C22⋊C4—108no—
565C22⋊C4—108no—
566C42—108no—
567C3×C5C2×#39011yescharacteristic, complemented, Hall
568C22×C3—24no—
569C22×C3—24no—
570C22×C3—24no—
571C22×C3—42no—
572C22×C3—42no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—416no—
576C22×C3—104no—
577C22×C3—104no—
578C22×C3—104no—
579C22×C3—202no—
580C22×C3—202no—
581C22×C3—202no—
582C22×C3—202no—
583C22×C3—2016no—
584C22×C3D5×C22⋊C414yes—
585C22×C3#402714yes—
586C22×C3#403014yes—
587C22×C3#403114yes—
588C22×C3C4×C22⋊D514yes—
589C22×C3#408514yes—
590C22×C3#408614yes—
591C22×C3C22×C4×D511yescharacteristic
592C22×C3C2×#70911yescharacteristic
593C22×C3C2×D4×D511yescharacteristic
594C22×C3C2×D4×D511yescharacteristic
595C22×C3C2×D4×D511yescharacteristic
596C22×C3C2×#71111yescharacteristic
597C22×C3C22×C22⋊D511yescharacteristic
598C3×C4—24no—
599C3×C4—42no—
600C3×C4—58no—
601C3×C4—104no—
602C3×C4—202no—
603C2×C5—44no—
604C2×C5C3×#39018yescomplemented
605C2×C5C22×C3×C22⋊C411yescharacteristic
606C2×C5C2×C3×C4×D411yescharacteristic
607C2×C5C2×C3×C4×D411yescharacteristic
608C2×C5C2×C3×#12111yescharacteristic
609C2×C5C2×C3×#12111yescharacteristic
610C2×C5C2×C3×#12411yescharacteristic
611C2×C5C2×C3×#12711yescharacteristic
612D5—44no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—28no—
620C23—28no—
621C23—28no—
622C23—44no—
623C23—44no—
624C23—44no—
625C23—44no—
626C23—54no—
627C23—102no—
628C23—102no—
629C23—102no—
630C23—102no—
631C23—102no—
632C23—102no—
633C23—108no—
634C23—108no—
635C23—108no—
636C23—204no—
637C23—204no—
638C23—204no—
639C23—204no—
640C23C2×C3×C4×D514yes—
641C23C2×C3×C4×D512yes—
642C23C3×#70912yes—
643C23C3×D4×D512yes—
644C23C3×D4×D512yes—
645C23C3×D4×D512yes—
646C23C3×#71112yes—
647C23C2×C3×C22⋊D512yes—
648C23C23×C3×D511yescharacteristic
649D4—1032no—
650C2×C4—28no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—44no—
657C2×C4—54no—
658C2×C4—54no—
659C2×C4—54no—
660C2×C4—516no—
661C2×C4—54no—
662C2×C4—102no—
663C2×C4—102no—
664C2×C4—108no—
665C2×C4—102no—
666C2×C4—102no—
667C2×C4—102no—
668C2×C4—204no—
669C2×C4C2×C3×C22⋊D514yescomplemented
670C2×C3—44no—
671C2×C3—204no—
672C2×C3#6524618yesdirect product factor
673C2×C3C2×D5×C22⋊C411yescharacteristic
674C2×C3C2×#402711yescharacteristic
675C2×C3C2×#403011yescharacteristic
676C2×C3C2×#403111yescharacteristic
677C2×C3C2×C4×C22⋊D511yescharacteristic
678C2×C3C2×#408511yescharacteristic
679C2×C3C2×#408611yescharacteristic
680C5C2×C3×#39011yescharacteristic, complemented, Sylow
681C22—24no—
682C22—24no—
683C22—24no—
684C22—42no—
685C22—42no—
686C22—416no—
687C22—42no—
688C22—42no—
689C22—104no—
690C22—104no—
691C22—104no—
692C22—202no—
693C22—202no—
694C22—2016no—
695C22—202no—
696C22—202no—
697C22C3×D5×C22⋊C414yes—
698C22C3×#402714yes—
699C22C3×#403014yes—
700C22C3×#403114yes—
701C22C3×C4×C22⋊D514yes—
702C22C3×#408514yes—
703C22C3×#408614yes—
704C22C22×C3×C4×D511yescharacteristic
705C22C2×C3×#70911yescharacteristic
706C22C2×C3×D4×D511yescharacteristic
707C22C2×C3×D4×D511yescharacteristic
708C22C2×C3×D4×D511yescharacteristic
709C22C2×C3×#71111yescharacteristic
710C22C22×C3×C22⋊D511yescharacteristic
711C4—24no—
712C4—42no—
713C4—58no—
714C4—104no—
715C4—202no—
716C3C2×#6524611yescharacteristic, direct product factor, Sylow
717C2—44no—
718C2—204no—
719C2C3×#6524618yesdirect product factor
720C2C2×C3×D5×C22⋊C411yescharacteristic
721C2C2×C3×#402711yescharacteristic
722C2C2×C3×#403011yescharacteristic
723C2C2×C3×#403111yescharacteristic
724C2C2×C3×C4×C22⋊D511yescharacteristic
725C2C2×C3×#408511yescharacteristic
726C2C2×C3×#408611yescharacteristic
subgroupG/H
centerC24×C3C22×D5
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC22×C3×C5×C22⋊C4C2
socleC24×C3×C5C23
prime radicalC23×C3×C22⋊D5C2
cosocleC23×C5C24×C3
hypercenterC22×C3×C22⋊C4D5
hypocenterC5C2×C3×#390
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C24×C3 ◁ C22×C3×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C3×C5×C22⋊C4C2semidirect
3. C22×C3×C22⋊Dic5C2semidirect
4. C22×C3×#685C2semidirect
5. C22×C3×#685C2semidirect
6. C22×C3×#683C2semidirect
7. C22×C3×C4×Dic5C2semidirect
8. C3×#65246C2direct (N × H)
9. C2×#65246C3direct (N × H)
16. C22×C3×C22⋊D5C4semidirect
22. C2×C3×C5×C22⋊C4C22semidirect
24. C2×C3×C22⋊Dic5C22semidirect
27. C2×C3×#685C22semidirect
28. C2×C3×#685C22semidirect
30. C2×C3×#683C22semidirect
32. C2×C3×C4×Dic5C22semidirect
35. C22×C5×C22⋊C4C2×C3semidirect
36. C22×C22⋊Dic5C2×C3semidirect
37. C22×#685C2×C3semidirect
38. C22×#685C2×C3semidirect
39. C22×#683C2×C3semidirect
40. C22×C4×Dic5C2×C3semidirect
41. #65246C2×C3direct (N × H)
64. C22×C3×C4×C5D4semidirect
70. C2×C3×C22⋊D5C2×C4semidirect
79. C22×C3×Dic5D4semidirect
94. C22×C3×C22⋊C4D5semidirect
103. C22×C22⋊D5C3×C4semidirect
109. C2×C5×C22⋊C4C22×C3semidirect
111. C2×C22⋊Dic5C22×C3semidirect
114. C2×#685C22×C3semidirect
115. C2×#685C22×C3semidirect
117. C2×#683C22×C3semidirect
119. C2×C4×Dic5C22×C3semidirect
164. C2×C3×C4×C5C2×D4semidirect
173. C2×C3×Dic5C22⋊C4semidirect
177. C2×C3×Dic5C2×D4semidirect
198. C2×C3×C22⋊C4C2×D5semidirect
223. C22×C4×C5C3×D4semidirect
229. C2×C22⋊D5C2×C3×C4semidirect
238. C22×Dic5C3×D4semidirect
253. C22×C22⋊C4C3×D5semidirect
290. C3×Dic5C2×C22⋊C4semidirect
329. C22×C3×C4C22⋊D5semidirect
381. C2×C4×C5C2×C3×D4semidirect
390. C2×Dic5C3×C22⋊C4semidirect
394. C2×Dic5C2×C3×D4semidirect
415. C2×C22⋊C4C2×C3×D5semidirect
419. C2×C3×C5#390semidirect
484. C2×C3×C4C2×C22⋊D5semidirect
519. Dic5C2×C3×C22⋊C4semidirect
558. C22×C4C3×C22⋊D5semidirect
567. C3×C5C2×#390semidirect
604. C2×C5C3×#390semidirect
669. C2×C4C2×C3×C22⋊D5semidirect
672. C2×C3#65246direct (N × H)
680. C5C2×C3×#390semidirect
716. C3C2×#65246direct (N × H)
719. C2C3×#65246direct (N × H)

Maximal subgroups

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

subgroupindex
C23×C3×C22⋊D52
C22×C3×C5×C22⋊C42
C22×C3×C22⋊Dic52
C22×C3×#6852
C22×C3×#6832
C22×C3×C4×Dic52
C3×#652462
C2×#652463
C2×C3×#3905