Finite Group Databasebeta

← C2×#11747129 #14411941

Subgroups — C2×#11747129 #14411941

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×#6782C211yesmaximal, characteristic
2C2×C3×#4023C211yesmaximal, characteristic, complemented
3C2×#91528C211yesmaximal, characteristic, complemented
4C2×#91090C211yesmaximal, characteristic, complemented
5C2×C5×#806C211yesmaximal, characteristic, complemented
6C2×#90997C211yesmaximal, characteristic, complemented
7C2×#90996C211yesmaximal, characteristic, complemented
8#11747129C218yesmaximal, direct product factor
9C2×#65029—31nomaximal, Hall
10C22×#1220C2211yescharacteristic
11C22×C5×#67C2211yescharacteristic
12C23×C3×Dic5C2211yescharacteristic
13C22×#1204C411yescharacteristic, complemented
14C22×#1203C411yescharacteristic, complemented
15C22×#1200C411yescharacteristic, complemented
16C2×#6782—21no—
17C2×#6782—22no—
18C2×#6782—21no—
19C2×#6782—22no—
20C2×#6782—21no—
21C2×#6782—21no—
22C2×#6782C414yescomplemented
23C2×#6782C2214yes—
24C22×D3×Dic5C411yescharacteristic, complemented
25C2×C3×C5×C22⋊C4C2211yescharacteristic
26C2×#6719C2211yescharacteristic
27C2×C5×#217C2211yescharacteristic
28C2×C3×C22⋊Dic5C2211yescharacteristic
29C2×C3×#683—21no—
30C2×C3×C4×Dic5—21no—
31C3×#4023—22no—
32C3×#4023C2214yescomplemented
33C2×#6668—21no—
34#91528—22no—
35#91528C2214yescomplemented
36C2×Dic3×Dic5—21no—
37#91090C2214yescomplemented
38C5×#806C2214yescomplemented
39#90997C2214yescomplemented
40#90996C2214yescomplemented
41C2×#5006—51nomaximal, Hall
42C22×#711—31no—
43C2×#4023—31no—
44C2×#4023D311yescharacteristic, complemented
45C2×C5×#99—31no—
46C2×#3966—31no—
47C2×#3938—31no—
48C2×#3938—31no—
49#65029—38no—
50C24×C3×C5C2311yescharacteristic
51C23×D15C2×C411yescharacteristic
52C23×C5×D3C2×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
62C2×C5×#67—21no—
63C2×C5×#67—21no—
64C2×C5×#67—21no—
65C2×C5×#67—21no—
66C2×C5×#67C2×C412yes—
67C2×C5×#67C2312yes—
68C22×C5×Dic3—21no—
69C22×C5×Dic3C2×C411yescharacteristic
70C22×C3×Dic5—21no—
71C22×C3×Dic5C2×C411yescharacteristic
72C22×C3×Dic5C2×C412yes—
73C22×C3×Dic5C2×C411yescharacteristic
74C22×C3×Dic5D411yescharacteristic
75C22×C3×Dic5D412yes—
76C22×C3×Dic5D411yescharacteristic
77C22×C3×Dic5D412yes—
78C22×C3×Dic5D411yescharacteristic
79C22×C3×Dic5D411yescharacteristic
80C22×C3×Dic5C2312yes—
81C2×#1204—22no—
82C2×#1204—21no—
83C2×#1204—21no—
84C2×#1204C2×C414yescomplemented
85C2×#1203—22no—
86C2×#1203—21no—
87C2×#1203—21no—
88C2×#1203C2×C414yescomplemented
89C2×#1200—22no—
90C2×#1200—21no—
91C2×#1200—21no—
92C2×#1200C2×C414yescomplemented
93#6782—24no—
94#6782—24no—
95#6782—24no—
96#6782—24no—
97#6782—24no—
98#6782—24no—
99#6782—24no—
100#6782—24no—
101C2×D3×Dic5—22no—
102C2×D3×Dic5—21no—
103C2×D3×Dic5—21no—
104C2×D3×Dic5C2×C414yescomplemented
105C3×C5×C22⋊C4—21no—
106C3×C5×C22⋊C4C2312yes—
107#6719—21no—
108#6719C2312yes—
109C5×#217—21no—
110C5×#217C2312yes—
111C3×C22⋊Dic5—21no—
112C3×C22⋊Dic5C2312yes—
113C3×#683—24no—
114C3×C4×Dic5—24no—
115#6668—24no—
116Dic3×Dic5—24no—
117C22×#235—51no—
118C2×C3×#117—51no—
119C2×#926—51no—
120#5006—58no—
121C2×#806—51no—
122C2×#806—51no—
123C2×#806—51no—
124C2×#806D511yescharacteristic, complemented
125C22×C5×D4—31no—
126C22×C22⋊D5—31no—
127C22×C22⋊D5—31no—
128C23×Dic5—31no—
129C23×Dic5C2×D311yescharacteristic
130C2×#711—34no—
131C2×#711—34no—
132C2×#711—62no—
133C2×#711—61no—
134C2×#711—61no—
135C2×#711—62no—
136C2×#711—61no—
137C2×#711—61no—
138C22×C4×D5—31no—
139C22×Dic10—31no—
140C2×C5×C22⋊C4—31no—
141C2×C5×C22⋊C4C2×D311yescharacteristic
142C2×C22⋊Dic5—31no—
143C2×C22⋊Dic5C2×D311yescharacteristic
144C2×#683—21no—
145C2×#683—61no—
146C2×C4×Dic5—21no—
147C2×C4×Dic5—61no—
148#4023—22no—
149#4023—34no—
150#4023—62no—
151#4023C2×D314yescomplemented
152C5×#99—34no—
153#3966—34no—
154#3938—34no—
155#3938—34no—
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×C5×D3—21no—
170C22×C5×D3—21no—
171C22×C5×D3—42no—
172C22×C5×D3C22×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—
184C5×#67—22no—
185C5×#67—22no—
186C5×#67—22no—
187C5×#67—22no—
188C2×C5×Dic3—21no—
189C2×C5×Dic3—21no—
190C2×C5×Dic3—22no—
191C2×C5×Dic3—42no—
192C2×C5×Dic3C22×C412yes—
193C2×C3×Dic5—22no—
194C2×C3×Dic5—42no—
195C2×C3×Dic5C22⋊C412yes—
196C2×C3×Dic5C22⋊C411yescharacteristic
197C2×C3×Dic5C22⋊C411yescharacteristic
198C2×C3×Dic5C22⋊C412yes—
199C2×C3×Dic5C22⋊C412yes—
200C2×C3×Dic5C22⋊C412yes—
201C2×C3×Dic5C22⋊C412yes—
202C2×C3×Dic5C22⋊C412yes—
203C2×C3×Dic5C22⋊C411yescharacteristic
204C2×C3×Dic5C22⋊C411yescharacteristic
205C2×C3×Dic5C22×C412yes—
206C2×C3×Dic5C22×C412yes—
207C2×C3×Dic5C2×D412yes—
208C2×C3×Dic5C2×D412yes—
209C2×C3×Dic5C2×D412yes—
210C2×C3×Dic5C2×D412yes—
211#1204—24no—
212#1204—24no—
213#1203—24no—
214#1203—24no—
215#1200—24no—
216#1200—24no—
217D3×Dic5—24no—
218D3×Dic5—24no—
219C23×C3×C4—51no—
220C22×#67—51no—
221C22×#67C2×D511yescharacteristic
222C2×#235—54no—
223C2×#235—54no—
224C2×#235—101no—
225C2×#235—101no—
226C2×#235—102no—
227C2×#235—101no—
228C2×#235—101no—
229C2×#235—102no—
230C22×D12—51no—
231C22×C4×D3—51no—
232C22×C4×D3—51no—
233C22×Dic6—51no—
234C3×#117—54no—
235C3×#117—102no—
236C2×C3×C4⋊C4—101no—
237C2×C3×C22⋊C4—51no—
238C2×C3×C22⋊C4C2×D511yescharacteristic
239C2×C3×C42—101no—
240C2×#217—51no—
241C2×#217C2×D511yescharacteristic
242#926—54no—
243#926—102no—
244C2×C4⋊Dic3—101no—
245C2×C4×Dic3—101no—
246#806—54no—
247#806—54no—
248#806—54no—
249#806C2×D514yescomplemented
250C24×C5—31no—
251C24×C5C22×D311yescharacteristic
252C23×D5—31no—
253C2×C5×D4—32no—
254C2×C5×D4—32no—
255C2×C5×D4—61no—
256C2×C5×D4—61no—
257C2×C5×D4—61no—
258C2×C5×D4—61no—
259C22×C4×C5—21no—
260C22×C4×C5—31no—
261C22×C4×C5—61no—
262C2×C22⋊D5—32no—
263C2×C22⋊D5—32no—
264C2×C22⋊D5—34no—
265C2×C22⋊D5—61no—
266C2×C22⋊D5—61no—
267C2×C22⋊D5—61no—
268C2×C22⋊D5—61no—
269C2×C22⋊D5—62no—
270C2×C22⋊D5—61no—
271C2×C22⋊D5—61no—
272C22×Dic5—21no—
273C22×Dic5—31no—
274C22×Dic5—34no—
275C22×Dic5—62no—
276C22×Dic5—61no—
277C22×Dic5—61no—
278C22×Dic5—61no—
279C22×Dic5C4×D311yescharacteristic
280C22×Dic5C4×D311yescharacteristic
281C22×Dic5C4×D312yes—
282C22×Dic5D1212yes—
283C22×Dic5D1211yescharacteristic
284C22×Dic5D1211yescharacteristic
285C22×Dic5#6712yes—
286C22×Dic5#6711yescharacteristic
287C22×Dic5#6711yescharacteristic
288C22×Dic5C22×D312yes—
289#711—64no—
290#711—64no—
291#711—64no—
292#711—64no—
293#711—64no—
294#711—64no—
295#711—64no—
296#711—64no—
297C2×C4×D5—34no—
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×C22⋊C4—21no—
306C5×C22⋊C4—32no—
307C5×C22⋊C4—61no—
308C5×C22⋊C4C22×D312yes—
309C22⋊Dic5—21no—
310C22⋊Dic5—32no—
311C22⋊Dic5—61no—
312C22⋊Dic5C22×D312yes—
313#683—24no—
314#683—64no—
315C4×Dic5—24no—
316C4×Dic5—64no—
317C22×#41—151no—
318C2×#117—51no—
319C2×#117—151no—
320#410—158no—
321C2×#99—31no—
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×C5×D3—22no—
344C2×C5×D3—42no—
345C2×C5×D3—42no—
346C2×C5×D3—42no—
347C3×C4×C5—42no—
348Dic15—22no—
349Dic15—42no—
350C3×Dic5—42no—
351C3×Dic5C2×C22⋊C412yes—
352C3×Dic5C2×C22⋊C412yes—
353C3×Dic5C2×C22⋊C412yes—
354C3×Dic5C2×C22⋊C412yes—
355C5×Dic3—22no—
356C5×Dic3—42no—
357C24×C3C22×D511yescharacteristic
358C23×D3—51no—
359C23×D3C4×D511yescharacteristic
360C22×C3×C4—21no—
361C22×C3×C4—51no—
362C22×C3×C4—51no—
363C22×C3×C4—52no—
364C22×C3×C4—51no—
365C22×C3×C4—51no—
366C22×C3×C4—52no—
367C22×C3×C4—51no—
368C22×C3×C4—51no—
369C22×C3×C4—52no—
370C22×C3×C4—52no—
371C22×C3×C4—101no—
372C2×#67—21no—
373C2×#67—21no—
374C2×#67—21no—
375C2×#67—21no—
376C2×#67—52no—
377C2×#67—52no—
378C2×#67—101no—
379C2×#67—101no—
380C2×#67—101no—
381C2×#67—101no—
382C2×#67C4×D512yes—
383C2×#67C22×D512yes—
384C22×Dic3—21no—
385C22×Dic3—51no—
386C22×Dic3—101no—
387C22×Dic3C4×D511yescharacteristic
388#235—104no—
389#235—104no—
390#235—104no—
391#235—104no—
392#235—104no—
393#235—104no—
394#235—104no—
395#235—104no—
396C2×D12—54no—
397C2×D12—102no—
398C2×D12—101no—
399C2×D12—101no—
400C2×C4×D3—54no—
401C2×C4×D3—54no—
402C2×C4×D3—102no—
403C2×C4×D3—101no—
404C2×C4×D3—101no—
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×C4⋊C4—104no—
413C3×C22⋊C4—21no—
414C3×C22⋊C4—52no—
415C3×C22⋊C4—101no—
416C3×C22⋊C4C22×D512yes—
417C3×C42—104no—
418#217—21no—
419#217—52no—
420#217—101no—
421#217C22×D512yes—
422C4⋊Dic3—104no—
423C4×Dic3—104no—
424C23×C5—32no—
425C23×C5—42no—
426C23×C5—61no—
427C23×C5—61no—
428C23×C5—122no—
429C23×C5C2×C4×D311yescharacteristic
430C23×C5C2×C4×D311yescharacteristic
431C23×C5C2×D1211yescharacteristic
432C23×C5C2×D1211yescharacteristic
433C23×C5C2×#6711yescharacteristic
434C23×C5C2×#6711yescharacteristic
435C23×C5C23×D311yescharacteristic
436C22×D5—32no—
437C22×D5—61no—
438C22×D5—61no—
439C22×D5—122no—
440C5×D4—62no—
441C5×D4—62no—
442C5×D4—62no—
443C5×D4—62no—
444C2×C4×C5—22no—
445C2×C4×C5—32no—
446C2×C4×C5—42no—
447C2×C4×C5—61no—
448C2×C4×C5—61no—
449C2×C4×C5—62no—
450C2×C4×C5—122no—
451C22⋊D5—62no—
452C22⋊D5—62no—
453C22⋊D5—62no—
454C22⋊D5—62no—
455C22⋊D5—64no—
456C22⋊D5—64no—
457C2×Dic5—22no—
458C2×Dic5—32no—
459C2×Dic5—42no—
460C2×Dic5—61no—
461C2×Dic5—61no—
462C2×Dic5—64no—
463C2×Dic5—64no—
464C2×Dic5—62no—
465C2×Dic5—122no—
466C2×Dic5(C2×D3)⋊C412yes—
467C2×Dic5(C2×D3)⋊C411yescharacteristic
468C2×Dic5(C2×D3)⋊C411yescharacteristic
469C2×Dic5(C2×D3)⋊C412yes—
470C2×Dic5(C2×D3)⋊C411yescharacteristic
471C2×Dic5(C2×D3)⋊C411yescharacteristic
472C2×Dic5(C2×D3)⋊C412yes—
473C2×Dic5(C2×D3)⋊C412yes—
474C2×Dic5(C2×D3)⋊C412yes—
475C2×Dic5(C2×D3)⋊C412yes—
476C2×Dic5C2×C4×D312yes—
477C2×Dic5C2×C4×D312yes—
478C2×Dic5C2×D1212yes—
479C2×Dic5C2×D1212yes—
480C2×Dic5C2×#6712yes—
481C2×Dic5C2×#6712yes—
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—31no—
496C22×D4—151no—
497C22×D4—151no—
498C23×C4—51no—
499C23×C4—151no—
500C23×C4—151no—
501#117—54no—
502#117—102no—
503#117—154no—
504#117—302no—
505C2×C4⋊C4—101no—
506C2×C4⋊C4—301no—
507C2×C22⋊C4—31no—
508C2×C22⋊C4—51no—
509C2×C22⋊C4—151no—
510C2×C22⋊C4D3×D511yescharacteristic
511C2×C42—101no—
512C2×C42—301no—
513#99—34no—
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—
526C5×D3—42no—
527C23×C3—42no—
528C23×C3C2×C4×D511yescharacteristic
529C23×C3C2×C4×D511yescharacteristic
530C23×C3D4×D511yescharacteristic
531C23×C3D4×D511yescharacteristic
532C23×C3D4×D511yescharacteristic
533C23×C3D4×D511yescharacteristic
534C23×C3C23×D511yescharacteristic
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—42no—
538C22×D3—52no—
539C22×D3—101no—
540C22×D3—101no—
541C22×D3—202no—
542C22×D3C2×C4×D512yes—
543C2×C3×C4—22no—
544C2×C3×C4—42no—
545C2×C3×C4—52no—
546C2×C3×C4—52no—
547C2×C3×C4—52no—
548C2×C3×C4—52no—
549C2×C3×C4—52no—
550C2×C3×C4—52no—
551C2×C3×C4—52no—
552C2×C3×C4—51no—
553C2×C3×C4—51no—
554C2×C3×C4—52no—
555C2×C3×C4—51no—
556C2×C3×C4—51no—
557C2×C3×C4—52no—
558C2×C3×C4—52no—
559C2×C3×C4—52no—
560C2×C3×C4—52no—
561C2×C3×C4—102no—
562C2×C3×C4—202no—
563#67—22no—
564#67—22no—
565#67—22no—
566#67—22no—
567#67—102no—
568#67—102no—
569#67—102no—
570#67—102no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—22no—
574C2×Dic3—42no—
575C2×Dic3—52no—
576C2×Dic3—101no—
577C2×Dic3—101no—
578C2×Dic3—102no—
579C2×Dic3—202no—
580C2×Dic3C2×C4×D512yes—
581D12—104no—
582D12—104no—
583C4×D3—104no—
584C4×D3—104no—
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×C5—62no—
597C22×C5—122no—
598C22×C5—122no—
599C22×C5—122no—
600C22×C5C2×(C2×D3)⋊C411yescharacteristic
601C22×C5C2×(C2×D3)⋊C411yescharacteristic
602C22×C5C2×(C2×D3)⋊C411yescharacteristic
603C22×C5C2×(C2×D3)⋊C411yescharacteristic
604C22×C5C22×C4×D311yescharacteristic
605C22×C5C22×D1211yescharacteristic
606C22×C5C22×#6711yescharacteristic
607C2×D5—62no—
608C2×D5—122no—
609C2×D5—122no—
610C2×D5—122no—
611C4×C5—42no—
612C4×C5—62no—
613C4×C5—122no—
614Dic5—42no—
615Dic5—62no—
616Dic5—122no—
617Dic5C2×(C2×D3)⋊C412yes—
618Dic5C2×(C2×D3)⋊C412yes—
619Dic5C2×(C2×D3)⋊C412yes—
620Dic5C2×(C2×D3)⋊C412yes—
621C24—31no—
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—32no—
637C2×D4—32no—
638C2×D4—61no—
639C2×D4—61no—
640C2×D4—61no—
641C2×D4—61no—
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—51no—
655C22×C4—51no—
656C22×C4—52no—
657C22×C4—51no—
658C22×C4—51no—
659C22×C4—52no—
660C22×C4—51no—
661C22×C4—51no—
662C22×C4—52no—
663C22×C4—52no—
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—104no—
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—104no—
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×C3D5×C22⋊C411yescharacteristic
697C22×C3D5×C22⋊C411yescharacteristic
698C22×C3D5×C22⋊C411yescharacteristic
699C22×C3D5×C22⋊C411yescharacteristic
700C22×C3C22×C4×D511yescharacteristic
701C22×C3C2×D4×D511yescharacteristic
702C22×C3C2×D4×D511yescharacteristic
703C2×D3—22no—
704C2×D3—42no—
705C2×D3—42no—
706C2×D3—42no—
707C2×D3—102no—
708C2×D3—202no—
709C2×D3—202no—
710C2×D3—202no—
711C3×C4—42no—
712C3×C4—52no—
713C3×C4—52no—
714C3×C4—52no—
715C3×C4—52no—
716C3×C4—202no—
717Dic3—22no—
718Dic3—42no—
719Dic3—102no—
720Dic3—202no—
721C2×C5—21no—
722C2×C5—21no—
723C2×C5—21no—
724C2×C5—21no—
725C2×C5—21no—
726C2×C5—21no—
727C2×C5—122no—
728C2×C5#500612yescomplemented
729C2×C5C22×(C2×D3)⋊C411yescharacteristic
730D5—122no—
731C23—32no—
732C23—42no—
733C23—61no—
734C23—61no—
735C23—122no—
736C23—152no—
737C23—301no—
738C23—301no—
739C23—602no—
740C23C4×D3×D511yescharacteristic
741C23C4×D3×D511yescharacteristic
742C23D5×D1211yescharacteristic
743C23D5×D1211yescharacteristic
744C23D5×#6711yescharacteristic
745C23D5×#6711yescharacteristic
746C23C22×D3×D511yescharacteristic
747Q8—304no—
748Q8—304no—
749D4—62no—
750D4—62no—
751D4—62no—
752D4—62no—
753D4—304no—
754D4—304no—
755D4—302no—
756D4—302no—
757D4—302no—
758D4—302no—
759C2×C4—22no—
760C2×C4—32no—
761C2×C4—42no—
762C2×C4—52no—
763C2×C4—52no—
764C2×C4—52no—
765C2×C4—52no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—51no—
769C2×C4—51no—
770C2×C4—51no—
771C2×C4—51no—
772C2×C4—52no—
773C2×C4—52no—
774C2×C4—52no—
775C2×C4—52no—
776C2×C4—52no—
777C2×C4—52no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—62no—
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#6502912yescomplemented
800C2×C3C2×D5×C22⋊C411yescharacteristic
801D3—42no—
802D3—202no—
803C5C2×#500611yescharacteristic, complemented, Sylow
804C22—22no—
805C22—22no—
806C22—22no—
807C22—41no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—62no—
812C22—122no—
813C22—122no—
814C22—122no—
815C22—302no—
816C22—602no—
817C22—602no—
818C22—602no—
819C22D5×(C2×D3)⋊C411yescharacteristic
820C22D5×(C2×D3)⋊C411yescharacteristic
821C22D5×(C2×D3)⋊C411yescharacteristic
822C22D5×(C2×D3)⋊C411yescharacteristic
823C22C2×C4×D3×D511yescharacteristic
824C22C2×D5×D1211yescharacteristic
825C22C2×D5×#6711yescharacteristic
826C4—42no—
827C4—52no—
828C4—52no—
829C4—52no—
830C4—52no—
831C4—62no—
832C4—122no—
833C4—202no—
834C4—302no—
835C4—602no—
836C3C2×#6502911yescharacteristic, complemented, Sylow
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—21no—
843C2—122no—
844C2—602no—
845C2#1174712912yesdirect product factor
846C2C2×D5×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC22D5×(C2×D3)⋊C4
commutatorC22×C3×C5C23×C4
FrattiniC23C22×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×#6782C2
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×C3×#4023C2semidirect
3. C2×#91528C2semidirect
4. C2×#91090C2semidirect
5. C2×C5×#806C2semidirect
6. C2×#90997C2semidirect
7. C2×#90996C2semidirect
8. #11747129C2direct (N × H)
13. C22×#1204C4semidirect
14. C22×#1203C4semidirect
15. C22×#1200C4semidirect
22. C2×#6782C4semidirect
24. C22×D3×Dic5C4semidirect
32. C3×#4023C22semidirect
35. #91528C22semidirect
37. #91090C22semidirect
38. C5×#806C22semidirect
39. #90997C22semidirect
40. #90996C22semidirect
44. C2×#4023D3semidirect
84. C2×#1204C2×C4semidirect
88. C2×#1203C2×C4semidirect
92. C2×#1200C2×C4semidirect
104. C2×D3×Dic5C2×C4semidirect
124. C2×#806D5semidirect
151. #4023C2×D3semidirect
249. #806C2×D5semidirect
523. C2×C3×C5#410semidirect
688. C3×C5C2×#410semidirect
728. C2×C5#5006semidirect
799. C2×C3#65029semidirect
803. C5C2×#5006semidirect
836. C3C2×#65029semidirect
845. C2#11747129direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67822
C2×C3×#40232
C2×#915282
C2×#910902
C2×C5×#8062
C2×#909972
C2×#909962
#117471292
C2×#650293
C2×#50065