Finite Group Databasebeta

← C2×#11747130 #14411943

Subgroups — C2×#11747130 #14411943

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6779C211yesmaximal, characteristic
2C2×C5×#877C211yesmaximal, characteristic, complemented
3C2×#91529C211yesmaximal, characteristic, complemented
4C2×#91090C211yesmaximal, characteristic, complemented
5C2×C3×#3938C211yesmaximal, characteristic, complemented
6C2×#90997C211yesmaximal, characteristic, complemented
7C2×#90995C211yesmaximal, characteristic, complemented
8#11747130C218yesmaximal, direct product factor
9C2×#65295—31nomaximal, Hall
10C22×#1220C2211yescharacteristic
11C23×C5×Dic3C2211yescharacteristic
12C22×C3×C22⋊D5C2211yescharacteristic
13C22×#1204C411yescharacteristic, complemented
14C22×#1202C411yescharacteristic, complemented
15C22×#1200C411yescharacteristic, complemented
16C2×#6779—21no—
17C2×#6779—22no—
18C2×#6779—21no—
19C2×#6779—22no—
20C2×#6779—21no—
21C2×#6779—21no—
22C2×#6779C414yescomplemented
23C2×#6779C2214yes—
24C22×D5×Dic3C411yescharacteristic, complemented
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C2×C5×Dic3⋊C4—21no—
29C2×C4×C5×Dic3—21no—
30C5×#877—22no—
31C5×#877C2214yescomplemented
32C2×C3×C22⋊Dic5C2211yescharacteristic
33C2×Dic3⋊Dic5—21no—
34#91529—22no—
35#91529C2214yescomplemented
36C2×Dic3×Dic5—21no—
37#91090C2214yescomplemented
38C3×#3938C2214yescomplemented
39#90997C2214yescomplemented
40#90995C2214yescomplemented
41C2×#4740—51nomaximal, Hall
42C22×#709—31no—
43C2×C5×#117—31no—
44C2×#4072—31no—
45#65295—38no—
46C2×#3938—31no—
47C2×#3938—31no—
48C2×#3938—31no—
49C2×#3938D311yescharacteristic, complemented
50C24×C3×C5C2311yescharacteristic
51C23×D15C2×C411yescharacteristic
52C23×C3×D5C2×C411yescharacteristic
53C22×C3×C4×C5—21no—
54C2×#1220—21no—
55C2×#1220—21no—
56C2×#1220—21no—
57C2×#1220—21no—
58C2×#1220C2×C412yes—
59C2×#1220C2312yes—
60C22×Dic15—21no—
61C22×Dic15C2×C411yescharacteristic
62C22×C5×Dic3—21no—
63C22×C5×Dic3C2×C411yescharacteristic
64C22×C5×Dic3C2×C412yes—
65C22×C5×Dic3C2×C411yescharacteristic
66C22×C5×Dic3D411yescharacteristic
67C22×C5×Dic3D412yes—
68C22×C5×Dic3D411yescharacteristic
69C22×C5×Dic3D412yes—
70C22×C5×Dic3D411yescharacteristic
71C22×C5×Dic3D411yescharacteristic
72C22×C5×Dic3C2312yes—
73C2×C3×C22⋊D5—21no—
74C2×C3×C22⋊D5—21no—
75C2×C3×C22⋊D5—21no—
76C2×C3×C22⋊D5—21no—
77C2×C3×C22⋊D5C2×C412yes—
78C2×C3×C22⋊D5C2312yes—
79C22×C3×Dic5—21no—
80C22×C3×Dic5C2×C411yescharacteristic
81C2×#1204—22no—
82C2×#1204—21no—
83C2×#1204—21no—
84C2×#1204C2×C414yescomplemented
85C2×#1202—22no—
86C2×#1202—21no—
87C2×#1202—21no—
88C2×#1202C2×C414yescomplemented
89C2×#1200—22no—
90C2×#1200—21no—
91C2×#1200—21no—
92C2×#1200C2×C414yescomplemented
93#6779—24no—
94#6779—24no—
95#6779—24no—
96#6779—24no—
97#6779—24no—
98#6779—24no—
99#6779—24no—
100#6779—24no—
101C2×D5×Dic3—22no—
102C2×D5×Dic3—21no—
103C2×D5×Dic3—21no—
104C2×D5×Dic3C2×C414yescomplemented
105C3×C5×C22⋊C4—21no—
106C3×C5×C22⋊C4C2312yes—
107#6719—21no—
108#6719C2312yes—
109C5×#217—21no—
110C5×#217C2312yes—
111C5×Dic3⋊C4—24no—
112C4×C5×Dic3—24no—
113C3×C22⋊Dic5—21no—
114C3×C22⋊Dic5C2312yes—
115Dic3⋊Dic5—24no—
116Dic3×Dic5—24no—
117C22×#237—51no—
118C2×#877—51no—
119C2×#877D511yescharacteristic, complemented
120C2×C3×#99—51no—
121C2×#834—51no—
122C2×#806—51no—
123C2×#806—51no—
124#4740—58no—
125C23×C4×C5—31no—
126C22×C22⋊D5—31no—
127C22×C22⋊D5C2×D311yescharacteristic
128C2×#709—34no—
129C2×#709—34no—
130C2×#709—61no—
131C2×#709—61no—
132C2×#709—62no—
133C2×#709—61no—
134C2×#709—61no—
135C2×#709—62no—
136C22×D20—31no—
137C22×C4×D5—31no—
138C22×C4×D5—31no—
139C22×Dic10—31no—
140C5×#117—34no—
141C5×#117—62no—
142C2×C5×C4⋊C4—61no—
143C2×C5×C22⋊C4—31no—
144C2×C5×C22⋊C4C2×D311yescharacteristic
145C2×C42×C5—61no—
146C2×C22⋊Dic5—31no—
147C2×C22⋊Dic5C2×D311yescharacteristic
148#4072—34no—
149#4072—62no—
150C2×C4⋊Dic5—61no—
151C2×C4×Dic5—61no—
152#3938—34no—
153#3938—34no—
154#3938—34no—
155#3938C2×D314yescomplemented
156C2×#410—151noSylow
157C23×C3×C5—42no—
158C23×C3×C5C22×C411yescharacteristic
159C23×C3×C5C22×C411yescharacteristic
160C23×C3×C5C2×D411yescharacteristic
161C23×C3×C5C2×D411yescharacteristic
162C23×C3×C5C2×D411yescharacteristic
163C23×C3×C5C2×D411yescharacteristic
164C23×C3×C5C2411yescharacteristic
165C22×D15—21no—
166C22×D15—21no—
167C22×D15—42no—
168C22×D15C22×C412yes—
169C22×C3×D5—21no—
170C22×C3×D5—21no—
171C22×C3×D5—42no—
172C22×C3×D5C22×C412yes—
173C2×C3×C4×C5—22no—
174C2×C3×C4×C5—42no—
175#1220—22no—
176#1220—22no—
177#1220—22no—
178#1220—22no—
179C2×Dic15—21no—
180C2×Dic15—21no—
181C2×Dic15—22no—
182C2×Dic15—42no—
183C2×Dic15C22×C412yes—
184C2×C5×Dic3—22no—
185C2×C5×Dic3—42no—
186C2×C5×Dic3C22⋊C412yes—
187C2×C5×Dic3C22⋊C411yescharacteristic
188C2×C5×Dic3C22⋊C411yescharacteristic
189C2×C5×Dic3C22⋊C412yes—
190C2×C5×Dic3C22⋊C412yes—
191C2×C5×Dic3C22⋊C412yes—
192C2×C5×Dic3C22⋊C412yes—
193C2×C5×Dic3C22⋊C412yes—
194C2×C5×Dic3C22⋊C411yescharacteristic
195C2×C5×Dic3C22⋊C411yescharacteristic
196C2×C5×Dic3C22×C412yes—
197C2×C5×Dic3C22×C412yes—
198C2×C5×Dic3C2×D412yes—
199C2×C5×Dic3C2×D412yes—
200C2×C5×Dic3C2×D412yes—
201C2×C5×Dic3C2×D412yes—
202C3×C22⋊D5—22no—
203C3×C22⋊D5—22no—
204C3×C22⋊D5—22no—
205C3×C22⋊D5—22no—
206C2×C3×Dic5—21no—
207C2×C3×Dic5—21no—
208C2×C3×Dic5—22no—
209C2×C3×Dic5—42no—
210C2×C3×Dic5C22×C412yes—
211#1204—24no—
212#1204—24no—
213#1202—24no—
214#1202—24no—
215#1200—24no—
216#1200—24no—
217D5×Dic3—24no—
218D5×Dic3—24no—
219C22×C3×D4—51no—
220C22×#67—51no—
221C22×#67—51no—
222C23×Dic3—51no—
223C23×Dic3C2×D511yescharacteristic
224C2×#237—54no—
225C2×#237—54no—
226C2×#237—102no—
227C2×#237—101no—
228C2×#237—101no—
229C2×#237—102no—
230C2×#237—101no—
231C2×#237—101no—
232C22×C4×D3—51no—
233C22×Dic6—51no—
234C2×C3×C22⋊C4—51no—
235C2×C3×C22⋊C4C2×D511yescharacteristic
236C2×#217—51no—
237C2×#217C2×D511yescharacteristic
238C2×Dic3⋊C4—21no—
239C2×Dic3⋊C4—101no—
240C2×C4×Dic3—21no—
241C2×C4×Dic3—101no—
242#877—22no—
243#877—54no—
244#877—102no—
245#877C2×D514yescomplemented
246C3×#99—54no—
247#834—54no—
248#806—54no—
249#806—54no—
250C24×C5C22×D311yescharacteristic
251C23×D5—31no—
252C23×D5C4×D311yescharacteristic
253C22×C4×C5—21no—
254C22×C4×C5—31no—
255C22×C4×C5—31no—
256C22×C4×C5—32no—
257C22×C4×C5—31no—
258C22×C4×C5—31no—
259C22×C4×C5—32no—
260C22×C4×C5—31no—
261C22×C4×C5—31no—
262C22×C4×C5—32no—
263C22×C4×C5—32no—
264C22×C4×C5—61no—
265C2×C22⋊D5—21no—
266C2×C22⋊D5—21no—
267C2×C22⋊D5—21no—
268C2×C22⋊D5—21no—
269C2×C22⋊D5—32no—
270C2×C22⋊D5—32no—
271C2×C22⋊D5—61no—
272C2×C22⋊D5—61no—
273C2×C22⋊D5—61no—
274C2×C22⋊D5—61no—
275C2×C22⋊D5C4×D312yes—
276C2×C22⋊D5C22×D312yes—
277C22×Dic5—21no—
278C22×Dic5—31no—
279C22×Dic5—61no—
280C22×Dic5C4×D311yescharacteristic
281#709—64no—
282#709—64no—
283#709—64no—
284#709—64no—
285#709—64no—
286#709—64no—
287#709—64no—
288#709—64no—
289C2×D20—34no—
290C2×D20—62no—
291C2×D20—61no—
292C2×D20—61no—
293C2×C4×D5—34no—
294C2×C4×D5—34no—
295C2×C4×D5—62no—
296C2×C4×D5—61no—
297C2×C4×D5—61no—
298C2×C4×D5—62no—
299C2×C4×D5—61no—
300C2×C4×D5—61no—
301C2×Dic10—34no—
302C2×Dic10—62no—
303C2×Dic10—61no—
304C2×Dic10—61no—
305C5×C4⋊C4—64no—
306C5×C22⋊C4—21no—
307C5×C22⋊C4—32no—
308C5×C22⋊C4—61no—
309C5×C22⋊C4C22×D312yes—
310C42×C5—64no—
311C22⋊Dic5—21no—
312C22⋊Dic5—32no—
313C22⋊Dic5—61no—
314C22⋊Dic5C22×D312yes—
315C4⋊Dic5—64no—
316C4×Dic5—64no—
317C22×#41—151no—
318C2×#117—31no—
319C2×#117—151no—
320#410—158no—
321C2×#99—51no—
322C2×#99—151no—
323C2×#99—151no—
324C2×#99—151no—
325C22×C3×C5—22no—
326C22×C3×C5—22no—
327C22×C3×C5—22no—
328C22×C3×C5—41no—
329C22×C3×C5—41no—
330C22×C3×C5—41no—
331C22×C3×C5—41no—
332C22×C3×C5C2×C22⋊C411yescharacteristic
333C22×C3×C5C2×C22⋊C411yescharacteristic
334C22×C3×C5C2×C22⋊C411yescharacteristic
335C22×C3×C5C2×C22⋊C411yescharacteristic
336C22×C3×C5C23×C411yescharacteristic
337C22×C3×C5C22×D411yescharacteristic
338C22×C3×C5C22×D411yescharacteristic
339C2×D15—22no—
340C2×D15—42no—
341C2×D15—42no—
342C2×D15—42no—
343C2×C3×D5—22no—
344C2×C3×D5—42no—
345C2×C3×D5—42no—
346C2×C3×D5—42no—
347C3×C4×C5—42no—
348Dic15—22no—
349Dic15—42no—
350C3×Dic5—22no—
351C3×Dic5—42no—
352C5×Dic3—42no—
353C5×Dic3C2×C22⋊C412yes—
354C5×Dic3C2×C22⋊C412yes—
355C5×Dic3C2×C22⋊C412yes—
356C5×Dic3C2×C22⋊C412yes—
357C24×C3—51no—
358C24×C3C22×D511yescharacteristic
359C23×D3—51no—
360C2×C3×D4—52no—
361C2×C3×D4—52no—
362C2×C3×D4—101no—
363C2×C3×D4—101no—
364C2×C3×D4—101no—
365C2×C3×D4—101no—
366C22×C3×C4—21no—
367C22×C3×C4—51no—
368C22×C3×C4—101no—
369C2×#67—52no—
370C2×#67—52no—
371C2×#67—54no—
372C2×#67—101no—
373C2×#67—101no—
374C2×#67—101no—
375C2×#67—101no—
376C2×#67—102no—
377C2×#67—101no—
378C2×#67—101no—
379C22×Dic3—21no—
380C22×Dic3—51no—
381C22×Dic3—54no—
382C22×Dic3—102no—
383C22×Dic3—101no—
384C22×Dic3—101no—
385C22×Dic3—101no—
386C22×Dic3C4×D511yescharacteristic
387C22×Dic3C4×D511yescharacteristic
388C22×Dic3C4×D512yes—
389C22×Dic3D2012yes—
390C22×Dic3D2011yescharacteristic
391C22×Dic3D2011yescharacteristic
392C22×Dic3C22⋊D512yes—
393C22×Dic3C22⋊D511yescharacteristic
394C22×Dic3C22⋊D511yescharacteristic
395C22×Dic3C22×D512yes—
396#237—104no—
397#237—104no—
398#237—104no—
399#237—104no—
400#237—104no—
401#237—104no—
402#237—104no—
403#237—104no—
404C2×C4×D3—54no—
405C2×C4×D3—102no—
406C2×C4×D3—101no—
407C2×C4×D3—101no—
408C2×Dic6—54no—
409C2×Dic6—102no—
410C2×Dic6—101no—
411C2×Dic6—101no—
412C3×C22⋊C4—21no—
413C3×C22⋊C4—52no—
414C3×C22⋊C4—101no—
415C3×C22⋊C4C22×D512yes—
416#217—21no—
417#217—52no—
418#217—101no—
419#217C22×D512yes—
420Dic3⋊C4—24no—
421Dic3⋊C4—104no—
422C4×Dic3—24no—
423C4×Dic3—104no—
424C23×C5—42no—
425C23×C5C2×C4×D311yescharacteristic
426C23×C5C2×C4×D311yescharacteristic
427C23×C5D3×D411yescharacteristic
428C23×C5D3×D411yescharacteristic
429C23×C5D3×D411yescharacteristic
430C23×C5D3×D411yescharacteristic
431C23×C5C23×D311yescharacteristic
432C22×D5—21no—
433C22×D5—21no—
434C22×D5—32no—
435C22×D5—42no—
436C22×D5—61no—
437C22×D5—61no—
438C22×D5—122no—
439C22×D5C2×C4×D312yes—
440C2×C4×C5—22no—
441C2×C4×C5—32no—
442C2×C4×C5—31no—
443C2×C4×C5—31no—
444C2×C4×C5—32no—
445C2×C4×C5—31no—
446C2×C4×C5—31no—
447C2×C4×C5—32no—
448C2×C4×C5—32no—
449C2×C4×C5—32no—
450C2×C4×C5—32no—
451C2×C4×C5—32no—
452C2×C4×C5—32no—
453C2×C4×C5—32no—
454C2×C4×C5—32no—
455C2×C4×C5—32no—
456C2×C4×C5—32no—
457C2×C4×C5—42no—
458C2×C4×C5—62no—
459C2×C4×C5—122no—
460C22⋊D5—22no—
461C22⋊D5—22no—
462C22⋊D5—22no—
463C22⋊D5—22no—
464C22⋊D5—62no—
465C22⋊D5—62no—
466C22⋊D5—62no—
467C22⋊D5—62no—
468C2×Dic5—21no—
469C2×Dic5—21no—
470C2×Dic5—22no—
471C2×Dic5—32no—
472C2×Dic5—42no—
473C2×Dic5—61no—
474C2×Dic5—61no—
475C2×Dic5—62no—
476C2×Dic5—122no—
477C2×Dic5C2×C4×D312yes—
478D20—64no—
479D20—64no—
480C4×D5—64no—
481C4×D5—64no—
482C4×D5—64no—
483C4×D5—64no—
484Dic10—64no—
485Dic10—64no—
486C2×#41—154no—
487C2×#41—154no—
488C2×#41—301no—
489C2×#41—301no—
490C2×#41—302no—
491C2×#41—301no—
492C2×#41—301no—
493C2×#41—302no—
494C22×Q8—151no—
495C22×D4—51no—
496C22×D4—151no—
497C22×D4—151no—
498C23×C4—31no—
499C23×C4—151no—
500C23×C4—151no—
501#117—34no—
502#117—62no—
503#117—154no—
504#117—302no—
505C2×C4⋊C4—61no—
506C2×C4⋊C4—301no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—51no—
509C2×C22⋊C4—151no—
510C2×C22⋊C4D3×D511yescharacteristic
511C2×C42—61no—
512C2×C42—301no—
513#99—54no—
514#99—154no—
515#99—154no—
516#99—154no—
517C2×C3×C5—21no—
518C2×C3×C5—21no—
519C2×C3×C5—21no—
520C2×C3×C5—21no—
521C2×C3×C5—21no—
522C2×C3×C5—21no—
523C2×C3×C5#41012yescomplemented
524C2×C3×C5C22×C22⋊C411yescharacteristic
525D15—42no—
526C3×D5—42no—
527C23×C3—42no—
528C23×C3—52no—
529C23×C3—101no—
530C23×C3—101no—
531C23×C3—202no—
532C23×C3C2×C4×D511yescharacteristic
533C23×C3C2×C4×D511yescharacteristic
534C23×C3C2×D2011yescharacteristic
535C23×C3C2×D2011yescharacteristic
536C23×C3C2×C22⋊D511yescharacteristic
537C23×C3C2×C22⋊D511yescharacteristic
538C23×C3C23×D511yescharacteristic
539C22×D3—52no—
540C22×D3—101no—
541C22×D3—101no—
542C22×D3—202no—
543C3×D4—102no—
544C3×D4—102no—
545C3×D4—102no—
546C3×D4—102no—
547C2×C3×C4—22no—
548C2×C3×C4—42no—
549C2×C3×C4—52no—
550C2×C3×C4—101no—
551C2×C3×C4—101no—
552C2×C3×C4—102no—
553C2×C3×C4—202no—
554#67—102no—
555#67—102no—
556#67—102no—
557#67—102no—
558#67—104no—
559#67—104no—
560C2×Dic3—22no—
561C2×Dic3—42no—
562C2×Dic3—52no—
563C2×Dic3—101no—
564C2×Dic3—101no—
565C2×Dic3—104no—
566C2×Dic3—104no—
567C2×Dic3—102no—
568C2×Dic3—202no—
569C2×Dic3#68512yes—
570C2×Dic3#68511yescharacteristic
571C2×Dic3#68511yescharacteristic
572C2×Dic3#68512yes—
573C2×Dic3#68511yescharacteristic
574C2×Dic3#68511yescharacteristic
575C2×Dic3#68512yes—
576C2×Dic3#68512yes—
577C2×Dic3#68512yes—
578C2×Dic3#68512yes—
579C2×Dic3C2×C4×D512yes—
580C2×Dic3C2×C4×D512yes—
581C2×Dic3C2×D2012yes—
582C2×Dic3C2×D2012yes—
583C2×Dic3C2×C22⋊D512yes—
584C2×Dic3C2×C22⋊D512yes—
585C4×D3—104no—
586C4×D3—104no—
587Dic6—104no—
588Dic6—104no—
589C22×C5—22no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—41no—
593C22×C5—41no—
594C22×C5—41no—
595C22×C5—41no—
596C22×C5D3×C22⋊C411yescharacteristic
597C22×C5D3×C22⋊C411yescharacteristic
598C22×C5D3×C22⋊C411yescharacteristic
599C22×C5D3×C22⋊C411yescharacteristic
600C22×C5C22×C4×D311yescharacteristic
601C22×C5C2×D3×D411yescharacteristic
602C22×C5C2×D3×D411yescharacteristic
603C2×D5—22no—
604C2×D5—42no—
605C2×D5—42no—
606C2×D5—42no—
607C2×D5—62no—
608C2×D5—122no—
609C2×D5—122no—
610C2×D5—122no—
611C4×C5—32no—
612C4×C5—32no—
613C4×C5—32no—
614C4×C5—32no—
615C4×C5—42no—
616C4×C5—122no—
617Dic5—22no—
618Dic5—42no—
619Dic5—62no—
620Dic5—122no—
621C24—51no—
622C24—151no—
623C24C2×D3×D511yescharacteristic
624#41—304no—
625#41—304no—
626#41—304no—
627#41—304no—
628#41—304no—
629#41—304no—
630#41—304no—
631#41—304no—
632C2×Q8—154no—
633C2×Q8—302no—
634C2×Q8—301no—
635C2×Q8—301no—
636C2×D4—52no—
637C2×D4—52no—
638C2×D4—101no—
639C2×D4—101no—
640C2×D4—101no—
641C2×D4—101no—
642C2×D4—154no—
643C2×D4—152no—
644C2×D4—152no—
645C2×D4—302no—
646C2×D4—301no—
647C2×D4—301no—
648C2×D4—301no—
649C2×D4—301no—
650C2×D4—301no—
651C2×D4—301no—
652C22×C4—21no—
653C22×C4—31no—
654C22×C4—31no—
655C22×C4—32no—
656C22×C4—31no—
657C22×C4—31no—
658C22×C4—32no—
659C22×C4—31no—
660C22×C4—31no—
661C22×C4—32no—
662C22×C4—32no—
663C22×C4—51no—
664C22×C4—61no—
665C22×C4—101no—
666C22×C4—154no—
667C22×C4—154no—
668C22×C4—151no—
669C22×C4—302no—
670C22×C4—301no—
671C22×C4—301no—
672C22×C4—302no—
673C22×C4—301no—
674C22×C4—301no—
675C22×C4—301no—
676C4⋊C4—64no—
677C4⋊C4—304no—
678C22⋊C4—21no—
679C22⋊C4—32no—
680C22⋊C4—52no—
681C22⋊C4—61no—
682C22⋊C4—101no—
683C22⋊C4—152no—
684C22⋊C4—301no—
685C22⋊C4C2×D3×D512yes—
686C42—64no—
687C42—304no—
688C3×C5C2×#41011yescharacteristic, complemented, Hall
689C22×C3—22no—
690C22×C3—22no—
691C22×C3—22no—
692C22×C3—41no—
693C22×C3—41no—
694C22×C3—41no—
695C22×C3—41no—
696C22×C3—102no—
697C22×C3—202no—
698C22×C3—202no—
699C22×C3—202no—
700C22×C3C2×#68511yescharacteristic
701C22×C3C2×#68511yescharacteristic
702C22×C3C2×#68511yescharacteristic
703C22×C3C2×#68511yescharacteristic
704C22×C3C22×C4×D511yescharacteristic
705C22×C3C22×D2011yescharacteristic
706C22×C3C22×C22⋊D511yescharacteristic
707C2×D3—102no—
708C2×D3—202no—
709C2×D3—202no—
710C2×D3—202no—
711C3×C4—42no—
712C3×C4—102no—
713C3×C4—202no—
714Dic3—42no—
715Dic3—102no—
716Dic3—202no—
717Dic3C2×#68512yes—
718Dic3C2×#68512yes—
719Dic3C2×#68512yes—
720Dic3C2×#68512yes—
721C2×C5—21no—
722C2×C5—21no—
723C2×C5—21no—
724C2×C5—21no—
725C2×C5—21no—
726C2×C5—21no—
727C2×C5#474012yescomplemented
728C2×C5C2×D3×C22⋊C411yescharacteristic
729D5—42no—
730D5—122no—
731C23—42no—
732C23—52no—
733C23—101no—
734C23—101no—
735C23—152no—
736C23—202no—
737C23—301no—
738C23—301no—
739C23—602no—
740C23C4×D3×D511yescharacteristic
741C23C4×D3×D511yescharacteristic
742C23D3×D2011yescharacteristic
743C23D3×D2011yescharacteristic
744C23D3×C22⋊D511yescharacteristic
745C23D3×C22⋊D511yescharacteristic
746C23C22×D3×D511yescharacteristic
747Q8—304no—
748Q8—304no—
749D4—102no—
750D4—102no—
751D4—102no—
752D4—102no—
753D4—304no—
754D4—304no—
755D4—302no—
756D4—302no—
757D4—302no—
758D4—302no—
759C2×C4—22no—
760C2×C4—32no—
761C2×C4—32no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—31no—
767C2×C4—31no—
768C2×C4—31no—
769C2×C4—31no—
770C2×C4—32no—
771C2×C4—32no—
772C2×C4—32no—
773C2×C4—32no—
774C2×C4—32no—
775C2×C4—32no—
776C2×C4—42no—
777C2×C4—52no—
778C2×C4—62no—
779C2×C4—101no—
780C2×C4—101no—
781C2×C4—102no—
782C2×C4—122no—
783C2×C4—152no—
784C2×C4—202no—
785C2×C4—304no—
786C2×C4—304no—
787C2×C4—304no—
788C2×C4—304no—
789C2×C4—301no—
790C2×C4—301no—
791C2×C4—302no—
792C2×C4—602no—
793C2×C3—21no—
794C2×C3—21no—
795C2×C3—21no—
796C2×C3—21no—
797C2×C3—21no—
798C2×C3—21no—
799C2×C3—202no—
800C2×C3#6529512yescomplemented
801C2×C3C22×#68511yescharacteristic
802D3—202no—
803C5C2×#474011yescharacteristic, complemented, Sylow
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—102no—
812C22—202no—
813C22—202no—
814C22—202no—
815C22—302no—
816C22—602no—
817C22—602no—
818C22—602no—
819C22D3×#68511yescharacteristic
820C22D3×#68511yescharacteristic
821C22D3×#68511yescharacteristic
822C22D3×#68511yescharacteristic
823C22C2×C4×D3×D511yescharacteristic
824C22C2×D3×D2011yescharacteristic
825C22C2×D3×C22⋊D511yescharacteristic
826C4—32no—
827C4—32no—
828C4—32no—
829C4—32no—
830C4—42no—
831C4—102no—
832C4—122no—
833C4—202no—
834C4—302no—
835C4—602no—
836C3C2×#6529511yescharacteristic, complemented, Sylow
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—21no—
843C2—202no—
844C2—602no—
845C2#1174713012yesdirect product factor
846C2C2×D3×#68511yescharacteristic
subgroupG/H
centerC22D3×#685
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6779C2
cosocleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#410
LCSG ▷ C22×C3×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C5×#877C2semidirect
3. C2×#91529C2semidirect
4. C2×#91090C2semidirect
5. C2×C3×#3938C2semidirect
6. C2×#90997C2semidirect
7. C2×#90995C2semidirect
8. #11747130C2direct (N × H)
13. C22×#1204C4semidirect
14. C22×#1202C4semidirect
15. C22×#1200C4semidirect
22. C2×#6779C4semidirect
24. C22×D5×Dic3C4semidirect
31. C5×#877C22semidirect
35. #91529C22semidirect
37. #91090C22semidirect
38. C3×#3938C22semidirect
39. #90997C22semidirect
40. #90995C22semidirect
49. C2×#3938D3semidirect
84. C2×#1204C2×C4semidirect
88. C2×#1202C2×C4semidirect
92. C2×#1200C2×C4semidirect
104. C2×D5×Dic3C2×C4semidirect
119. C2×#877D5semidirect
155. #3938C2×D3semidirect
245. #877C2×D5semidirect
523. C2×C3×C5#410semidirect
688. C3×C5C2×#410semidirect
727. C2×C5#4740semidirect
800. C2×C3#65295semidirect
803. C5C2×#4740semidirect
836. C3C2×#65295semidirect
845. C2#11747130direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67792
C2×C5×#8772
C2×#915292
C2×#910902
C2×C3×#39382
C2×#909972
C2×#909952
#117471302
C2×#652953
C2×#47405