Finite Group Databasebeta

← C2×C3×#65295 #14411919

Subgroups — C2×C3×#65295 #14411919

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#709C211yesmaximal, characteristic
2C2×C3×C5×#117C211yesmaximal, characteristic, complemented
3C2×C3×#4072C211yesmaximal, characteristic, complemented
4C3×#65295C218yesmaximal, direct product factor
5C2×C3×#3938C214yesmaximal, complemented
6C2×#65295C311yesmaximal, characteristic, direct product factor, Hall
7C23×C3×C4×C5C2211yescharacteristic
8C22×C3×C22⋊D5C2212yes—
9C2×C3×#709—21no—
10C2×C3×#709—21no—
11C2×C3×#709—22no—
12C2×C3×#709—21no—
13C2×C3×#709—21no—
14C2×C3×#709—22no—
15C2×C3×#709C414yescomplemented
16C2×C3×#709C2214yes—
17C22×C3×D20C411yescharacteristic, complemented
18C22×C3×C4×D5C412yescomplemented
19C22×C3×Dic10C411yescharacteristic, complemented
20C3×C5×#117—22no—
21C3×C5×#117C2214yescomplemented
22C2×C3×C5×C4⋊C4—21no—
23C2×C3×C5×C22⋊C4C2212yes—
24C2×C3×C42×C5—21no—
25C2×C3×C22⋊Dic5C2212yes—
26C3×#4072—22no—
27C3×#4072C2214yescomplemented
28C2×C3×C4⋊Dic5—21no—
29C2×C3×C4×Dic5—21no—
30C3×#3938C22116yescomplemented
31C2×C3×#410—51nomaximal, Hall
32C22×#709C2×C311yescharacteristic
33C2×C5×#117C2×C311yescharacteristic, complemented
34C2×#4072C2×C311yescharacteristic, complemented
35#65295C2×C318yesdirect product factor
36C2×#3938C2×C314yescomplemented
37C24×C3×C5C2311yescharacteristic
38C23×C3×D5C2×C412yes—
39C22×C3×C4×C5—22no—
40C22×C3×C4×C5C2×C411yescharacteristic
41C22×C3×C4×C5C2×C411yescharacteristic
42C22×C3×C4×C5C2×C412yes—
43C22×C3×C4×C5D411yescharacteristic
44C22×C3×C4×C5D411yescharacteristic
45C22×C3×C4×C5D412yes—
46C22×C3×C4×C5D411yescharacteristic
47C22×C3×C4×C5D411yescharacteristic
48C22×C3×C4×C5D412yes—
49C22×C3×C4×C5C2312yes—
50C2×C3×C22⋊D5—22no—
51C2×C3×C22⋊D5—22no—
52C2×C3×C22⋊D5—22no—
53C2×C3×C22⋊D5—22no—
54C2×C3×C22⋊D5C2×C414yes—
55C2×C3×C22⋊D5C2314yes—
56C22×C3×Dic5—22no—
57C22×C3×Dic5C2×C412yes—
58C3×#709—24no—
59C3×#709—24no—
60C3×#709—24no—
61C3×#709—24no—
62C3×#709—24no—
63C3×#709—24no—
64C3×#709—24no—
65C3×#709—24no—
66C2×C3×D20—22no—
67C2×C3×D20—21no—
68C2×C3×D20—21no—
69C2×C3×D20C2×C414yescomplemented
70C2×C3×C4×D5—24no—
71C2×C3×C4×D5—22no—
72C2×C3×C4×D5—22no—
73C2×C3×C4×D5C2×C418yescomplemented
74C2×C3×Dic10—22no—
75C2×C3×Dic10—21no—
76C2×C3×Dic10—21no—
77C2×C3×Dic10C2×C414yescomplemented
78C3×C5×C4⋊C4—24no—
79C3×C5×C22⋊C4—22no—
80C3×C5×C22⋊C4C2314yes—
81C3×C42×C5—24no—
82C3×C22⋊Dic5—22no—
83C3×C22⋊Dic5C2314yes—
84C3×C4⋊Dic5—24no—
85C3×C4×Dic5—24no—
86C22×C3×#41—51no—
87C2×C3×#117—51no—
88C2×C3×#117D511yescharacteristic, complemented
89C3×#410—58no—
90C2×C3×#99—54no—
91C23×C4×C5C22×C311yescharacteristic
92C22×C22⋊D5C22×C312yes—
93C2×#709—21no—
94C2×#709—21no—
95C2×#709—22no—
96C2×#709—21no—
97C2×#709—21no—
98C2×#709—22no—
99C2×#709C3×C414yescomplemented
100C2×#709C22×C314yes—
101C22×D20C3×C411yescharacteristic, complemented
102C22×C4×D5C3×C412yescomplemented
103C22×Dic10C3×C411yescharacteristic, complemented
104C5×#117—22no—
105C5×#117C22×C314yescomplemented
106C2×C5×C4⋊C4—21no—
107C2×C5×C22⋊C4C22×C312yes—
108C2×C42×C5—21no—
109C2×C22⋊Dic5C22×C312yes—
110#4072—22no—
111#4072C22×C314yescomplemented
112C2×C4⋊Dic5—21no—
113C2×C4×Dic5—21no—
114#3938C22×C3116yescomplemented
115C2×#410—51noSylow
116C23×C3×C5—42no—
117C23×C3×C5C22×C411yescharacteristic
118C23×C3×C5C22×C411yescharacteristic
119C23×C3×C5C2×D411yescharacteristic
120C23×C3×C5C2×D411yescharacteristic
121C23×C3×C5C2×D411yescharacteristic
122C23×C3×C5C2×D411yescharacteristic
123C23×C3×C5C2411yescharacteristic
124C22×C3×D5—22no—
125C22×C3×D5—22no—
126C22×C3×D5—44no—
127C22×C3×D5C22×C414yes—
128C2×C3×C4×C5—24no—
129C2×C3×C4×C5—44no—
130C2×C3×C4×C5C22⋊C412yes—
131C2×C3×C4×C5C22⋊C411yescharacteristic
132C2×C3×C4×C5C22⋊C411yescharacteristic
133C2×C3×C4×C5C22⋊C412yes—
134C2×C3×C4×C5C22⋊C411yescharacteristic
135C2×C3×C4×C5C22⋊C412yes—
136C2×C3×C4×C5C22⋊C412yes—
137C2×C3×C4×C5C22⋊C412yes—
138C2×C3×C4×C5C22⋊C412yes—
139C2×C3×C4×C5C22⋊C411yescharacteristic
140C2×C3×C4×C5C22×C412yes—
141C2×C3×C4×C5C22×C412yes—
142C2×C3×C4×C5C2×D412yes—
143C2×C3×C4×C5C2×D412yes—
144C2×C3×C4×C5C2×D412yes—
145C2×C3×C4×C5C2×D412yes—
146C3×C22⋊D5—24no—
147C3×C22⋊D5—24no—
148C3×C22⋊D5—24no—
149C3×C22⋊D5—24no—
150C2×C3×Dic5—22no—
151C2×C3×Dic5—22no—
152C2×C3×Dic5—24no—
153C2×C3×Dic5—44no—
154C2×C3×Dic5C22×C414yes—
155C3×D20—24no—
156C3×D20—24no—
157C3×C4×D5—28no—
158C3×C4×D5—28no—
159C3×Dic10—24no—
160C3×Dic10—24no—
161C2×C3×#41—54no—
162C2×C3×#41—54no—
163C2×C3×#41—101no—
164C2×C3×#41—102no—
165C2×C3×#41—101no—
166C2×C3×#41—101no—
167C2×C3×#41—102no—
168C2×C3×#41—101no—
169C22×C3×Q8—51no—
170C22×C3×D4—52no—
171C22×C3×D4—51no—
172C23×C3×C4—52no—
173C23×C3×C4C2×D511yescharacteristic
174C3×#117—22no—
175C3×#117—54no—
176C3×#117—102no—
177C3×#117C2×D514yescomplemented
178C2×C3×C4⋊C4—21no—
179C2×C3×C4⋊C4—101no—
180C2×C3×C22⋊C4—52no—
181C2×C3×C22⋊C4C2×D512yes—
182C2×C3×C42—21no—
183C2×C3×C42—101no—
184C3×#99—516no—
185C24×C5C23×C311yescharacteristic
186C23×D5C2×C3×C412yes—
187C22×C4×C5—22no—
188C22×C4×C5C2×C3×C411yescharacteristic
189C22×C4×C5C2×C3×C411yescharacteristic
190C22×C4×C5C2×C3×C412yes—
191C22×C4×C5C3×D411yescharacteristic
192C22×C4×C5C3×D411yescharacteristic
193C22×C4×C5C3×D412yes—
194C22×C4×C5C3×D411yescharacteristic
195C22×C4×C5C3×D411yescharacteristic
196C22×C4×C5C3×D412yes—
197C22×C4×C5C23×C312yes—
198C2×C22⋊D5—22no—
199C2×C22⋊D5—22no—
200C2×C22⋊D5—22no—
201C2×C22⋊D5—22no—
202C2×C22⋊D5C2×C3×C414yes—
203C2×C22⋊D5C23×C314yes—
204C22×Dic5—22no—
205C22×Dic5C2×C3×C412yes—
206#709—24no—
207#709—24no—
208#709—24no—
209#709—24no—
210#709—24no—
211#709—24no—
212#709—24no—
213#709—24no—
214C2×D20—22no—
215C2×D20—21no—
216C2×D20—21no—
217C2×D20C2×C3×C414yescomplemented
218C2×C4×D5—24no—
219C2×C4×D5—22no—
220C2×C4×D5—22no—
221C2×C4×D5C2×C3×C418yescomplemented
222C2×Dic10—22no—
223C2×Dic10—21no—
224C2×Dic10—21no—
225C2×Dic10C2×C3×C414yescomplemented
226C5×C4⋊C4—24no—
227C5×C22⋊C4—22no—
228C5×C22⋊C4C23×C314yes—
229C42×C5—24no—
230C22⋊Dic5—22no—
231C22⋊Dic5C23×C314yes—
232C4⋊Dic5—24no—
233C4×Dic5—24no—
234C22×#41—51no—
235C2×#117—51no—
236C2×#117C3×D511yescharacteristic, complemented
237#410—58no—
238C2×#99—54no—
239C22×C3×C5—22no—
240C22×C3×C5—22no—
241C22×C3×C5—22no—
242C22×C3×C5—41no—
243C22×C3×C5—41no—
244C22×C3×C5—41no—
245C22×C3×C5—41no—
246C22×C3×C5C2×C22⋊C411yescharacteristic
247C22×C3×C5C2×C22⋊C411yescharacteristic
248C22×C3×C5C2×C22⋊C411yescharacteristic
249C22×C3×C5C2×C22⋊C411yescharacteristic
250C22×C3×C5C23×C411yescharacteristic
251C22×C3×C5C22×D411yescharacteristic
252C22×C3×C5C22×D411yescharacteristic
253C2×C3×D5—24no—
254C2×C3×D5—44no—
255C2×C3×D5—44no—
256C2×C3×D5—44no—
257C3×C4×C5—44no—
258C3×C4×C5C2×C22⋊C412yes—
259C3×C4×C5C2×C22⋊C412yes—
260C3×C4×C5C2×C22⋊C412yes—
261C3×C4×C5C2×C22⋊C412yes—
262C3×Dic5—24no—
263C3×Dic5—44no—
264C24×C3—52no—
265C24×C3C22×D511yescharacteristic
266C3×#41—104no—
267C3×#41—104no—
268C3×#41—104no—
269C3×#41—104no—
270C3×#41—104no—
271C3×#41—104no—
272C3×#41—104no—
273C3×#41—104no—
274C2×C3×Q8—54no—
275C2×C3×Q8—102no—
276C2×C3×Q8—101no—
277C2×C3×Q8—101no—
278C2×C3×D4—54no—
279C2×C3×D4—54no—
280C2×C3×D4—54no—
281C2×C3×D4—102no—
282C2×C3×D4—102no—
283C2×C3×D4—102no—
284C2×C3×D4—102no—
285C2×C3×D4—102no—
286C2×C3×D4—101no—
287C2×C3×D4—101no—
288C22×C3×C4—22no—
289C22×C3×C4—52no—
290C22×C3×C4—58no—
291C22×C3×C4—104no—
292C22×C3×C4—102no—
293C22×C3×C4—102no—
294C22×C3×C4—102no—
295C22×C3×C4C4×D511yescharacteristic
296C22×C3×C4C4×D512yes—
297C22×C3×C4C4×D511yescharacteristic
298C22×C3×C4D2011yescharacteristic
299C22×C3×C4D2012yes—
300C22×C3×C4D2011yescharacteristic
301C22×C3×C4C22⋊D511yescharacteristic
302C22×C3×C4C22⋊D512yes—
303C22×C3×C4C22⋊D511yescharacteristic
304C22×C3×C4C22×D512yes—
305C3×C4⋊C4—24no—
306C3×C4⋊C4—104no—
307C3×C22⋊C4—22no—
308C3×C22⋊C4—54no—
309C3×C22⋊C4—102no—
310C3×C22⋊C4C22×D514yes—
311C3×C42—24no—
312C3×C42—104no—
313C23×C5—42no—
314C23×C5C22×C3×C411yescharacteristic
315C23×C5C22×C3×C411yescharacteristic
316C23×C5C2×C3×D411yescharacteristic
317C23×C5C2×C3×D411yescharacteristic
318C23×C5C2×C3×D411yescharacteristic
319C23×C5C2×C3×D411yescharacteristic
320C23×C5C24×C311yescharacteristic
321C22×D5—22no—
322C22×D5—22no—
323C22×D5—44no—
324C22×D5C22×C3×C414yes—
325C2×C4×C5—24no—
326C2×C4×C5—44no—
327C2×C4×C5C3×C22⋊C412yes—
328C2×C4×C5C3×C22⋊C411yescharacteristic
329C2×C4×C5C3×C22⋊C411yescharacteristic
330C2×C4×C5C3×C22⋊C412yes—
331C2×C4×C5C3×C22⋊C411yescharacteristic
332C2×C4×C5C3×C22⋊C411yescharacteristic
333C2×C4×C5C3×C22⋊C412yes—
334C2×C4×C5C3×C22⋊C412yes—
335C2×C4×C5C3×C22⋊C412yes—
336C2×C4×C5C3×C22⋊C412yes—
337C2×C4×C5C22×C3×C412yes—
338C2×C4×C5C22×C3×C412yes—
339C2×C4×C5C2×C3×D412yes—
340C2×C4×C5C2×C3×D412yes—
341C2×C4×C5C2×C3×D412yes—
342C2×C4×C5C2×C3×D412yes—
343C22⋊D5—24no—
344C22⋊D5—24no—
345C22⋊D5—24no—
346C22⋊D5—24no—
347C2×Dic5—22no—
348C2×Dic5—22no—
349C2×Dic5—24no—
350C2×Dic5—44no—
351C2×Dic5C22×C3×C414yes—
352D20—24no—
353D20—24no—
354C4×D5—28no—
355C4×D5—28no—
356Dic10—24no—
357Dic10—24no—
358C2×#41—54no—
359C2×#41—54no—
360C2×#41—101no—
361C2×#41—101no—
362C2×#41—102no—
363C2×#41—101no—
364C2×#41—101no—
365C2×#41—102no—
366C22×Q8—51no—
367C22×D4—52no—
368C22×D4—51no—
369C23×C4—52no—
370C23×C4C2×C3×D511yescharacteristic
371#117—22no—
372#117—54no—
373#117—102no—
374#117C2×C3×D514yescomplemented
375C2×C4⋊C4—21no—
376C2×C4⋊C4—101no—
377C2×C22⋊C4—52no—
378C2×C22⋊C4C2×C3×D512yes—
379C2×C42—21no—
380C2×C42—101no—
381#99—516no—
382C2×C3×C5—21no—
383C2×C3×C5—21no—
384C2×C3×C5—21no—
385C2×C3×C5—21no—
386C2×C3×C5—21no—
387C2×C3×C5—21no—
388C2×C3×C5#41012yescomplemented
389C2×C3×C5C22×C22⋊C411yescharacteristic
390C3×D5—44no—
391C23×C3—42no—
392C23×C3—54no—
393C23×C3—102no—
394C23×C3—102no—
395C23×C3—204no—
396C23×C3C2×C4×D511yescharacteristic
397C23×C3C2×C4×D511yescharacteristic
398C23×C3C2×D2011yescharacteristic
399C23×C3C2×D2011yescharacteristic
400C23×C3C2×C22⋊D511yescharacteristic
401C23×C3C2×C22⋊D511yescharacteristic
402C23×C3C23×D511yescharacteristic
403C3×Q8—104no—
404C3×Q8—104no—
405C3×D4—104no—
406C3×D4—104no—
407C3×D4—104no—
408C3×D4—104no—
409C3×D4—104no—
410C3×D4—104no—
411C2×C3×C4—24no—
412C2×C3×C4—44no—
413C2×C3×C4—54no—
414C2×C3×C4—102no—
415C2×C3×C4—102no—
416C2×C3×C4—108no—
417C2×C3×C4—108no—
418C2×C3×C4—104no—
419C2×C3×C4—204no—
420C2×C3×C4#68511yescharacteristic
421C2×C3×C4#68512yes—
422C2×C3×C4#68512yes—
423C2×C3×C4#68511yescharacteristic
424C2×C3×C4#68511yescharacteristic
425C2×C3×C4#68512yes—
426C2×C3×C4#68512yes—
427C2×C3×C4#68512yes—
428C2×C3×C4#68512yes—
429C2×C3×C4#68511yescharacteristic
430C2×C3×C4C2×C4×D512yes—
431C2×C3×C4C2×C4×D512yes—
432C2×C3×C4C2×D2012yes—
433C2×C3×C4C2×D2012yes—
434C2×C3×C4C2×C22⋊D512yes—
435C2×C3×C4C2×C22⋊D512yes—
436C22×C5—22no—
437C22×C5—22no—
438C22×C5—22no—
439C22×C5—41no—
440C22×C5—41no—
441C22×C5—41no—
442C22×C5—41no—
443C22×C5C2×C3×C22⋊C411yescharacteristic
444C22×C5C2×C3×C22⋊C411yescharacteristic
445C22×C5C2×C3×C22⋊C411yescharacteristic
446C22×C5C2×C3×C22⋊C411yescharacteristic
447C22×C5C23×C3×C411yescharacteristic
448C22×C5C22×C3×D411yescharacteristic
449C22×C5C22×C3×D411yescharacteristic
450C2×D5—24no—
451C2×D5—44no—
452C2×D5—44no—
453C2×D5—44no—
454C4×C5—44no—
455C4×C5C2×C3×C22⋊C412yes—
456C4×C5C2×C3×C22⋊C412yes—
457C4×C5C2×C3×C22⋊C412yes—
458C4×C5C2×C3×C22⋊C412yes—
459Dic5—24no—
460Dic5—44no—
461C24—52no—
462C24C22×C3×D511yescharacteristic
463#41—104no—
464#41—104no—
465#41—104no—
466#41—104no—
467#41—104no—
468#41—104no—
469#41—104no—
470#41—104no—
471C2×Q8—54no—
472C2×Q8—102no—
473C2×Q8—101no—
474C2×Q8—101no—
475C2×D4—54no—
476C2×D4—54no—
477C2×D4—54no—
478C2×D4—102no—
479C2×D4—102no—
480C2×D4—102no—
481C2×D4—102no—
482C2×D4—102no—
483C2×D4—101no—
484C2×D4—101no—
485C22×C4—22no—
486C22×C4—52no—
487C22×C4—58no—
488C22×C4—104no—
489C22×C4—102no—
490C22×C4—102no—
491C22×C4—102no—
492C22×C4C3×C4×D511yescharacteristic
493C22×C4C3×C4×D511yescharacteristic
494C22×C4C3×C4×D512yes—
495C22×C4C3×D2011yescharacteristic
496C22×C4C3×D2011yescharacteristic
497C22×C4C3×D2012yes—
498C22×C4C3×C22⋊D511yescharacteristic
499C22×C4C3×C22⋊D511yescharacteristic
500C22×C4C3×C22⋊D512yes—
501C22×C4C22×C3×D512yes—
502C4⋊C4—24no—
503C4⋊C4—104no—
504C22⋊C4—22no—
505C22⋊C4—54no—
506C22⋊C4—102no—
507C22⋊C4C22×C3×D514yes—
508C42—24no—
509C42—104no—
510C3×C5C2×#41011yescharacteristic, complemented, Hall
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—104no—
519C22×C3—204no—
520C22×C3—204no—
521C22×C3—204no—
522C22×C3C2×#68511yescharacteristic
523C22×C3C2×#68511yescharacteristic
524C22×C3C2×#68511yescharacteristic
525C22×C3C2×#68511yescharacteristic
526C22×C3C22×C4×D511yescharacteristic
527C22×C3C22×D2011yescharacteristic
528C22×C3C22×C22⋊D511yescharacteristic
529C3×C4—44no—
530C3×C4—104no—
531C3×C4—204no—
532C3×C4C2×#68512yes—
533C3×C4C2×#68512yes—
534C3×C4C2×#68512yes—
535C3×C4C2×#68512yes—
536C2×C5—21no—
537C2×C5—21no—
538C2×C5—21no—
539C2×C5—21no—
540C2×C5—21no—
541C2×C5—21no—
542C2×C5C3×#41012yescomplemented
543C2×C5C22×C3×C22⋊C411yescharacteristic
544D5—44no—
545C23—42no—
546C23—54no—
547C23—102no—
548C23—102no—
549C23—204no—
550C23C2×C3×C4×D511yescharacteristic
551C23C2×C3×C4×D511yescharacteristic
552C23C2×C3×D2011yescharacteristic
553C23C2×C3×D2011yescharacteristic
554C23C2×C3×C22⋊D511yescharacteristic
555C23C2×C3×C22⋊D511yescharacteristic
556C23C23×C3×D511yescharacteristic
557Q8—104no—
558Q8—104no—
559D4—104no—
560D4—104no—
561D4—104no—
562D4—104no—
563D4—104no—
564D4—104no—
565C2×C4—24no—
566C2×C4—44no—
567C2×C4—54no—
568C2×C4—102no—
569C2×C4—102no—
570C2×C4—108no—
571C2×C4—108no—
572C2×C4—104no—
573C2×C4—204no—
574C2×C4C3×#68512yes—
575C2×C4C3×#68511yescharacteristic
576C2×C4C3×#68511yescharacteristic
577C2×C4C3×#68512yes—
578C2×C4C3×#68511yescharacteristic
579C2×C4C3×#68511yescharacteristic
580C2×C4C3×#68512yes—
581C2×C4C3×#68512yes—
582C2×C4C3×#68512yes—
583C2×C4C3×#68512yes—
584C2×C4C2×C3×C4×D512yes—
585C2×C4C2×C3×C4×D512yes—
586C2×C4C2×C3×D2012yes—
587C2×C4C2×C3×D2012yes—
588C2×C4C2×C3×C22⋊D512yes—
589C2×C4C2×C3×C22⋊D512yes—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—21no—
595C2×C3—21no—
596C2×C3—204no—
597C2×C3#6529512yesdirect product factor
598C2×C3C22×#68511yescharacteristic
599C5C2×C3×#41011yescharacteristic, complemented, Sylow
600C22—22no—
601C22—22no—
602C22—22no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—104no—
608C22—204no—
609C22—204no—
610C22—204no—
611C22C2×C3×#68511yescharacteristic
612C22C2×C3×#68511yescharacteristic
613C22C2×C3×#68511yescharacteristic
614C22C2×C3×#68511yescharacteristic
615C22C22×C3×C4×D511yescharacteristic
616C22C22×C3×D2011yescharacteristic
617C22C22×C3×C22⋊D511yescharacteristic
618C4—44no—
619C4—104no—
620C4—204no—
621C4C2×C3×#68512yes—
622C4C2×C3×#68512yes—
623C4C2×C3×#68512yes—
624C4C2×C3×#68512yes—
625C3C2×#6529511yescharacteristic, direct product factor, Sylow
626C2—21no—
627C2—21no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—204no—
633C2C3×#6529512yesdirect product factor
634C2C22×C3×#68511yescharacteristic
subgroupG/H
centerC2×C3×C4#685
commutatorC22×C5C23×C3×C4
FrattiniC23C23×C3×D5
FittingC2×C3×C5×#117C2
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×C3×#709C2
cosocleC23×C5C24×C3
hypercenterC2×C3×#117D5
hypocenterC5C2×C3×#410
LCSG ▷ C22×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C2×C3×C4 ◁ C23×C3×C4 ◁ C2×C3×#117

Complements

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

NH ≅ G/Ntype
2. C2×C3×C5×#117C2semidirect
3. C2×C3×#4072C2semidirect
4. C3×#65295C2direct (N × H)
5. C2×C3×#3938C2semidirect
6. C2×#65295C3direct (N × H)
15. C2×C3×#709C4semidirect
17. C22×C3×D20C4semidirect
18. C22×C3×C4×D5C4semidirect
19. C22×C3×Dic10C4semidirect
21. C3×C5×#117C22semidirect
27. C3×#4072C22semidirect
30. C3×#3938C22semidirect
33. C2×C5×#117C2×C3semidirect
34. C2×#4072C2×C3semidirect
35. #65295C2×C3direct (N × H)
36. C2×#3938C2×C3semidirect
69. C2×C3×D20C2×C4semidirect
73. C2×C3×C4×D5C2×C4semidirect
77. C2×C3×Dic10C2×C4semidirect
88. C2×C3×#117D5semidirect
99. C2×#709C3×C4semidirect
101. C22×D20C3×C4semidirect
102. C22×C4×D5C3×C4semidirect
103. C22×Dic10C3×C4semidirect
105. C5×#117C22×C3semidirect
111. #4072C22×C3semidirect
114. #3938C22×C3semidirect
177. C3×#117C2×D5semidirect
217. C2×D20C2×C3×C4semidirect
221. C2×C4×D5C2×C3×C4semidirect
225. C2×Dic10C2×C3×C4semidirect
236. C2×#117C3×D5semidirect
374. #117C2×C3×D5semidirect
388. C2×C3×C5#410semidirect
510. C3×C5C2×#410semidirect
542. C2×C5C3×#410semidirect
597. C2×C3#65295direct (N × H)
599. C5C2×C3×#410semidirect
625. C3C2×#65295direct (N × H)
633. C2C3×#65295direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C2×C3×C5×#1172
C2×C3×#40722
C3×#652952
C2×C3×#39382
C2×#652953
C2×C3×#4105