Finite Group Databasebeta

← C2×#11755056 #14482604

Subgroups — C2×#11755056 #14482604

Order 1920.

3800 conjugacy classes of subgroups.

The subgroup lattice has 1040 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6790C211yesmaximal, characteristic, complemented
2C22×#6782C211yesmaximal, characteristic, complemented
3C2×#91826C211yesmaximal, characteristic, complemented
4C2×C5×#938C211yesmaximal, characteristic, complemented
5C2×C3×#4085C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91561C211yesmaximal, characteristic, complemented
8C2×#91555C211yesmaximal, characteristic, complemented
9C2×#91552C211yesmaximal, characteristic, complemented
10C2×#91534C211yesmaximal, characteristic, complemented
11C2×#91533C211yesmaximal, characteristic, complemented
12#11755056C2116yesmaximal, direct product factor
13C2×D3×#685C211yesmaximal, characteristic, complemented
14C2×#91446C211yesmaximal, characteristic, complemented
15C2×#91419C211yesmaximal, characteristic, complemented
16C2×#91356C211yesmaximal, characteristic, complemented
17C2×#65944—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic, complemented
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×C22⋊D5C2211yescharacteristic, complemented
28C23×C3×Dic5C2211yescharacteristic, complemented
29C2×#6790—28no—
30C2×#6790C2218yescomplemented
31C22×#1204C2211yescharacteristic, complemented
32C22×#1203C2211yescharacteristic
33C22×#1202C2211yescharacteristic
34C22×#1200C2211yescharacteristic
35C22×#1200C2211yescharacteristic, complemented
36C22×#1200C2211yescharacteristic, complemented
37C2×#6782—28no—
38C2×#6782C2218yescomplemented
39C22×D3×Dic5C2211yescharacteristic, complemented
40C2×#6719C2211yescharacteristic, complemented
41#91826C2218yescomplemented
42C2×#6714C2211yescharacteristic
43C2×#6714C2211yescharacteristic, complemented
44C2×C5×#217C2211yescharacteristic, complemented
45C2×C5×#217C2211yescharacteristic, complemented
46C5×#938C2218yescomplemented
47C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
48C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
49C3×#4085C2218yescomplemented
50C2×C3×#685C2211yescharacteristic, complemented
51C2×C3×#683C2211yescharacteristic, complemented
52#91577C2218yescomplemented
53#91561C2218yescomplemented
54#91555C2218yescomplemented
55#91552C2218yescomplemented
56C2×#6669C2211yescharacteristic, complemented
57C2×#6668C2211yescharacteristic, complemented
58C2×#6667C2211yescharacteristic
59C2×#6667C2211yescharacteristic
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63#91534C2218yescomplemented
64#91533C2218yescomplemented
65C2×Dic3×Dic5C2211yescharacteristic, complemented
66D3×#685C2218yescomplemented
67#91446C2218yescomplemented
68#91419C2218yescomplemented
69#91356C2218yescomplemented
70C2×#5612—51nomaximal, Hall
71C22×#711—31no—
72C22×D4×D5—31no—
73C2×C5×#121—31no—
74C2×#4085D311yescharacteristic, complemented
75C2×#4083—31no—
76C2×#4083—31no—
77C2×#4081—31no—
78C2×C4×C22⋊D5—31no—
79C22×#685—31no—
80#65944—316no—
81C2×#4042—31no—
82C2×#4040—31no—
83C2×#4031—31no—
84C2×#4030—31no—
85C2×#4027—31no—
86C2×D5×C22⋊C4—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15—24no—
90C23×D15—24no—
91C23×D15—42no—
92C23×D15C2314yes—
93C23×D15C2311yescharacteristic
94C23×D15C2311yescharacteristic
95C23×C5×D3C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C22×D3×D5—24no—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5C2314yes—
101C2×C3×C5×D4—42no—
102C2×C3×C5×D4C2314yescomplemented
103C22×C3×C4×C5C2311yescharacteristic
104C2×#1220—24no—
105C2×#1220—24no—
106C2×#1220C2314yes—
107C2×#1220C2314yescomplemented
108C22×Dic15C2311yescharacteristic
109C22×Dic15C2311yescharacteristic
110C2×C5×#67—24no—
111C2×C5×#67—24no—
112C2×C5×#67C2314yes—
113C2×C5×#67C2314yescomplemented
114C22×C5×Dic3C2311yescharacteristic
115C22×C5×Dic3C2311yescharacteristic
116C22×C5×Dic3C2311yescharacteristic
117C2×C4×C5×D3—42no—
118C2×C4×C5×D3C2314yescomplemented
119C2×C3×C22⋊D5—24no—
120C2×C3×C22⋊D5—42no—
121C2×C3×C22⋊D5C2314yes—
122C2×C3×C22⋊D5C2314yescomplemented
123C22×C3×Dic5—24no—
124C22×C3×Dic5C2311yescharacteristic
125C22×C3×Dic5C2311yescharacteristic
126C22×C3×Dic5C2311yescharacteristic
127C22×C3×Dic5C2314yescomplemented
128#6790—232no—
129C2×#1204—24no—
130C2×#1204C2314yescomplemented
131C2×#1203D418yescomplemented
132C2×#1203C2314yes—
133C2×#1202—24no—
134C2×#1202C2314yes—
135C2×#1200—24no—
136C2×#1200—24no—
137C2×#1200—42no—
138C2×#1200C2314yes—
139C2×#1200C2314yescomplemented
140C2×#1200C2314yescomplemented
141#6782—232no—
142C2×D3×Dic5—24no—
143C2×D3×Dic5C2314yescomplemented
144#6719C2314yescomplemented
145#6714C2314yes—
146#6714C2314yescomplemented
147C5×#217C2314yescomplemented
148C5×#217C2314yescomplemented
149C5×C4⋊Dic3C2314yescomplemented
150C3×C22⋊Dic5C2314yescomplemented
151C3×#685C2314yescomplemented
152C3×#683C2314yescomplemented
153#6669C2314yescomplemented
154#6668C2314yescomplemented
155#6667C2314yes—
156#6667C2314yes—
157(C2×D3)⋊Dic5C2314yescomplemented
158#6665C2314yescomplemented
159#6665C2314yescomplemented
160Dic3×Dic5C2314yescomplemented
161C22×D3×D4—51no—
162C22×#235—51no—
163C2×C3×#121—51no—
164C2×#938—51no—
165C2×#938D511yescharacteristic, complemented
166C2×#937—51no—
167C2×#937—51no—
168C2×#936—51no—
169C2×C4×#67—51no—
170#5612—516no—
171C2×#897—51no—
172C2×#893—51no—
173C2×#883—51no—
174C2×#883—51no—
175C2×D3×C22⋊C4—51no—
176C2×D3×C22⋊C4—51no—
177C24×D5—31no—
178C24×D5—31no—
179C22×C5×D4—31no—
180C22×C5×D4—31no—
181C22×C5×D4C2×D311yescharacteristic, complemented
182C23×C4×C5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5C2×D311yescharacteristic
187C22×C22⋊D5C2×D311yescharacteristic, complemented
188C23×Dic5—31no—
189C23×Dic5C2×D311yescharacteristic, complemented
190C2×#711—38no—
191C2×#711—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×Dic10—31no—
199C5×#121—38no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C22⋊Dic5—31no—
204C2×C22⋊Dic5—31no—
205C2×C22⋊Dic5C2×D311yescharacteristic, complemented
206#4085C2×D318yescomplemented
207#4083—38no—
208#4083—38no—
209#4081—38no—
210C4×C22⋊D5—38no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685—38no—
218C2×#685C2×D311yescharacteristic, complemented
219C2×#683—31no—
220C2×#683—31no—
221C2×#683C2×D311yescharacteristic, complemented
222C2×C4×Dic5—31no—
223#4042—38no—
224#4040—38no—
225#4031—38no—
226#4030—38no—
227#4027—38no—
228D5×C22⋊C4—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5C2412yes—
237C23×C3×C5C2412yes—
238C23×C3×C5C2411yescharacteristic
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—22no—
243C22×D15—28no—
244C22×D15—28no—
245C22×D15—44no—
246C22×D15—416no—
247C22×D15C2×D414yes—
248C22×D15#4114yescomplemented
249C22×D15C2412yes—
250C22×D15C2412yes—
251C22×C5×D3—22no—
252C22×C5×D3—22no—
253C22×C5×D3C2×D414yes—
254C22×C5×D3C2412yes—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5—22no—
258C22×C3×D5C2412yes—
259C2×D3×D5—28no—
260C2×D3×D5—28no—
261C2×D3×D5—44no—
262C2×D3×D5—416no—
263C3×C5×D4—44no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266#1220—28no—
267#1220—28no—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15C2412yes—
271C2×Dic15C2412yes—
272C5×#67—28no—
273C5×#67—28no—
274C2×C5×Dic3—22no—
275C2×C5×Dic3—22no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3C2412yes—
278C2×C5×Dic3C2412yes—
279C2×C5×Dic3C2412yes—
280C4×C5×D3—44no—
281C3×C22⋊D5—28no—
282C3×C22⋊D5—44no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5—28no—
286C2×C3×Dic5C2×D414yes—
287C2×C3×Dic5C2412yes—
288C2×C3×Dic5C2412yes—
289C2×C3×Dic5C2412yes—
290#1204—28no—
291#1203C2×D4116yescomplemented
292#1202—28no—
293#1200—28no—
294#1200—28no—
295#1200—44no—
296D3×Dic5—28no—
297C24×D3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4C2×D511yescharacteristic, complemented
302C23×C3×C4—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C22×#67C2×D511yescharacteristic
307C22×#67C2×D511yescharacteristic, complemented
308C2×D3×D4—58no—
309C2×D3×D4—108no—
310C2×#235—58no—
311C2×#235—108no—
312C22×D12—51no—
313C22×C4×D3—51no—
314C22×C4×D3—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3C2×D511yescharacteristic, complemented
318C22×Dic6—51no—
319C3×#121—58no—
320C2×C3×C4⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—51no—
323C2×#217—51no—
324C2×#217—51no—
325C2×#217—51no—
326C2×#217C2×D511yescharacteristic, complemented
327C2×#217C2×D511yescharacteristic, complemented
328#938—58no—
329#938C2×D518yescomplemented
330#937—58no—
331#937—58no—
332#936—58no—
333C4×#67—58no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4—51no—
336C2×(C2×D3)⋊C4—51no—
337C2×(C2×D3)⋊C4—51no—
338C2×(C2×D3)⋊C4—51no—
339C2×C4⋊Dic3—51no—
340C2×C4⋊Dic3C2×D511yescharacteristic, complemented
341C2×Dic3⋊C4—51no—
342C2×C4×Dic3—51no—
343#897—58no—
344#893—58no—
345#883—58no—
346#883—58no—
347D3×C22⋊C4—58no—
348D3×C22⋊C4—58no—
349C24×C5—31no—
350C24×C5C22×D311yescharacteristic
351C24×C5C22×D311yescharacteristic
352C23×D5—31no—
353C23×D5—31no—
354C23×D5—34no—
355C23×D5—34no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—64no—
360C23×D5—122no—
361C23×D5—122no—
362C23×D5C22×D311yescharacteristic
363C2×C5×D4—34no—
364C2×C5×D4—34no—
365C2×C5×D4—42no—
366C2×C5×D4—64no—
367C2×C5×D4—64no—
368C2×C5×D4C22×D314yescomplemented
369C22×C4×C5—31no—
370C22×C4×C5—31no—
371C22×C4×C5—31no—
372C22×C4×C5—34no—
373C22×C4×C5—122no—
374C22×C4×C5C22×D311yescharacteristic
375C2×C22⋊D5—24no—
376C2×C22⋊D5—34no—
377C2×C22⋊D5—34no—
378C2×C22⋊D5—38no—
379C2×C22⋊D5—34no—
380C2×C22⋊D5—42no—
381C2×C22⋊D5—64no—
382C2×C22⋊D5—64no—
383C2×C22⋊D5C22×D314yes—
384C2×C22⋊D5C22×D314yescomplemented
385C22×Dic5—24no—
386C22×Dic5—31no—
387C22×Dic5—31no—
388C22×Dic5—34no—
389C22×Dic5—64no—
390C22×Dic5C22×D311yescharacteristic
391C22×Dic5C22×D311yescharacteristic
392C22×Dic5C22×D311yescharacteristic
393C22×Dic5C22×D314yescomplemented
394#711—632no—
395D4×D5—632no—
396C2×D20—34no—
397C2×D20—64no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—34no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×Dic10—34no—
405C2×Dic10—64no—
406C5×C4⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C22⋊Dic5—34no—
410C22⋊Dic5—34no—
411C22⋊Dic5C22×D314yescomplemented
412#685—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685—34no—
418#685C22×D314yescomplemented
419#683—34no—
420#683—34no—
421#683C22×D314yescomplemented
422C4×Dic5—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—151no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—31no—
431C2×#121—51no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—22no—
443C22×C3×C5—22no—
444C22×C3×C5—22no—
445C22×C3×C5—44no—
446C22×C3×C5—44no—
447C22×C3×C5C22×D412yes—
448C22×C3×C5C2×#4112yes—
449C22×C3×C5H(5,𝔽2)12yes—
450C22×C3×C5C2511yescharacteristic
451C2×D15—28no—
452C2×D15—28no—
453C2×D15—22no—
454C2×D15—22no—
455C2×D15—22no—
456C2×D15—22no—
457C2×D15—416no—
458C2×D15C22×D414yes—
459C2×D15C2×#4114yescomplemented
460C2×C5×D3—28no—
461C2×C5×D3—22no—
462C2×C5×D3—22no—
463C2×C5×D3C22×D414yes—
464C2×C3×D5—22no—
465C2×C3×D5—22no—
466C2×C3×D5—22no—
467C2×C3×D5—44no—
468D3×D5—416no—
469C3×C4×C5—22no—
470Dic15—22no—
471Dic15—22no—
472C3×Dic5—22no—
473C3×Dic5—22no—
474C3×Dic5C22×D414yes—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3—22no—
478C24×C3—51no—
479C24×C3C22×D511yescharacteristic
480C24×C3C22×D511yescharacteristic
481C23×D3—51no—
482C23×D3—51no—
483C23×D3—54no—
484C23×D3—54no—
485C23×D3—104no—
486C23×D3—104no—
487C23×D3—104no—
488C23×D3—104no—
489C23×D3—202no—
490C23×D3—202no—
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—42no—
493C2×C3×D4—54no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C2×C3×D4—202no—
497C2×C3×D4C22×D514yescomplemented
498C22×C3×C4—51no—
499C22×C3×C4—51no—
500C22×C3×C4—51no—
501C22×C3×C4—54no—
502C22×C3×C4—104no—
503C22×C3×C4C22×D511yescharacteristic
504C2×#67—24no—
505C2×#67—24no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—54no—
509C2×#67—104no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67C22×D514yes—
513C2×#67C22×D514yescomplemented
514C22×Dic3—51no—
515C22×Dic3—51no—
516C22×Dic3C22×D511yescharacteristic
517C22×Dic3C22×D511yescharacteristic
518C22×Dic3C22×D511yescharacteristic
519D3×D4—1032no—
520#235—1032no—
521C2×D12—58no—
522C2×D12—54no—
523C2×C4×D3—42no—
524C2×C4×D3—54no—
525C2×C4×D3—54no—
526C2×C4×D3—54no—
527C2×C4×D3—54no—
528C2×C4×D3—104no—
529C2×C4×D3—104no—
530C2×C4×D3—104no—
531C2×C4×D3—202no—
532C2×C4×D3C22×D514yescomplemented
533C2×Dic6—54no—
534C2×Dic6—104no—
535C3×C4⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538#217—54no—
539#217—54no—
540#217—54no—
541#217C22×D514yescomplemented
542#217C22×D514yescomplemented
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4—54no—
546(C2×D3)⋊C4—54no—
547(C2×D3)⋊C4—54no—
548C4⋊Dic3—54no—
549C4⋊Dic3C22×D514yescomplemented
550Dic3⋊C4—54no—
551C4×Dic3—54no—
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—22no—
556C23×C5—22no—
557C23×C5—22no—
558C23×C5—34no—
559C23×C5—32no—
560C23×C5—62no—
561C23×C5—62no—
562C23×C5C23×D312yes—
563C23×C5C23×D312yes—
564C23×C5C23×D311yescharacteristic
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—34no—
569C22×D5—34no—
570C22×D5—32no—
571C22×D5—32no—
572C22×D5—68no—
573C22×D5—68no—
574C22×D5—68no—
575C22×D5—68no—
576C22×D5—62no—
577C22×D5—62no—
578C22×D5—62no—
579C22×D5—62no—
580C22×D5—124no—
581C22×D5—1216no—
582C22×D5—124no—
583C22×D5—1216no—
584C22×D5C23×D312yes—
585C5×D4—44no—
586C5×D4—68no—
587C5×D4—68no—
588C2×C4×C5—22no—
589C2×C4×C5—32no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—62no—
593C2×C4×C5—62no—
594C2×C4×C5—62no—
595C2×C4×C5—124no—
596C2×C4×C5C23×D312yes—
597C22⋊D5—28no—
598C22⋊D5—316no—
599C22⋊D5—44no—
600C22⋊D5—68no—
601C22⋊D5—68no—
602C2×Dic5—22no—
603C2×Dic5—22no—
604C2×Dic5—28no—
605C2×Dic5—32no—
606C2×Dic5—32no—
607C2×Dic5—68no—
608C2×Dic5—62no—
609C2×Dic5—62no—
610C2×Dic5D3×D414yes—
611C2×Dic5C23×D312yes—
612C2×Dic5C23×D312yes—
613C2×Dic5C23×D312yes—
614D20—68no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618Dic10—68no—
619C25—151no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—151no—
624C22×D4—31no—
625C22×D4—31no—
626C22×D4—51no—
627C22×D4—51no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—158no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—308no—
634C22×D4D3×D511yescharacteristic, complemented
635C23×C4—31no—
636C23×C4—51no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—158no—
642#123—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—38no—
646#121—58no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—51no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—51no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—158no—
661C2×C22⋊C4—158no—
662C2×C22⋊C4—151no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4—151no—
670C2×C42—151no—
671C2×C3×C5—42no—
672C2×C3×C5—42no—
673C2×C3×C5#54614yescomplemented
674C2×C3×C5C23×D411yescharacteristic
675C2×C3×C5C22×#4111yescharacteristic
676C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
677D15—24no—
678D15—24no—
679C3×D5—42no—
680C5×D3—24no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—22no—
686C23×C3—22no—
687C23×C3—52no—
688C23×C3—102no—
689C23×C3—102no—
690C23×C3—102no—
691C23×C3C23×D512yes—
692C23×C3C23×D512yes—
693C23×C3C23×D511yescharacteristic
694C22×D3—22no—
695C22×D3—22no—
696C22×D3—54no—
697C22×D3—54no—
698C22×D3—52no—
699C22×D3—52no—
700C22×D3—108no—
701C22×D3—108no—
702C22×D3—108no—
703C22×D3—102no—
704C22×D3—102no—
705C22×D3—102no—
706C22×D3—102no—
707C22×D3—108no—
708C22×D3—204no—
709C22×D3—2016no—
710C22×D3—204no—
711C22×D3—2016no—
712C22×D3D4×D514yes—
713C22×D3C23×D512yes—
714C3×D4—44no—
715C3×D4—108no—
716C3×D4—204no—
717C2×C3×C4—22no—
718C2×C3×C4—54no—
719C2×C3×C4—52no—
720C2×C3×C4—52no—
721C2×C3×C4—52no—
722C2×C3×C4—108no—
723C2×C3×C4—102no—
724C2×C3×C4—102no—
725C2×C3×C4C23×D512yes—
726#67—28no—
727#67—28no—
728#67—108no—
729#67—108no—
730#67—108no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—22no—
734C2×Dic3—52no—
735C2×Dic3—52no—
736C2×Dic3—102no—
737C2×Dic3—102no—
738C2×Dic3C23×D512yes—
739C2×Dic3C23×D512yes—
740C2×Dic3C23×D512yes—
741D12—516no—
742C4×D3—44no—
743C4×D3—108no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—108no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—22no—
752C22×C5—22no—
753C22×C5—22no—
754C22×C5—34no—
755C22×C5—44no—
756C22×C5—44no—
757C22×C5—62no—
758C22×C5—62no—
759C22×C5—68no—
760C22×C5C2×D3×D412yes—
761C22×C5#100412yes—
762C22×C5D3×#4112yes—
763C22×C5C24×D311yescharacteristic
764C2×D5—22no—
765C2×D5—22no—
766C2×D5—22no—
767C2×D5—34no—
768C2×D5—34no—
769C2×D5—44no—
770C2×D5—62no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—68no—
775C2×D5—68no—
776C2×D5—1216no—
777C2×D5—1216no—
778C4×C5—22no—
779C4×C5—62no—
780C4×C5—62no—
781C4×C5—62no—
782Dic5—22no—
783Dic5—22no—
784Dic5—62no—
785Dic5—62no—
786Dic5C2×D3×D414yes—
787C24—31no—
788C24—51no—
789C24—154no—
790C24—151no—
791C24—151no—
792C24—154no—
793C24—304no—
794C24—304no—
795C24—304no—
796C24—304no—
797C24—602no—
798C24—602no—
799C24C2×D3×D511yescharacteristic
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—154no—
803C2×Q8—304no—
804C2×D4—34no—
805C2×D4—34no—
806C2×D4—42no—
807C2×D4—54no—
808C2×D4—54no—
809C2×D4—64no—
810C2×D4—64no—
811C2×D4—104no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—158no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—202no—
818C2×D4—304no—
819C2×D4—3032no—
820C2×D4—304no—
821C2×D4—304no—
822C2×D4C2×D3×D514yescomplemented
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—34no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—51no—
830C22×C4—51no—
831C22×C4—104no—
832C22×C4—122no—
833C22×C4—154no—
834C22×C4—154no—
835C22×C4—154no—
836C22×C4—154no—
837C22×C4—151no—
838C22×C4—151no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—304no—
842C22×C4—602no—
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—34no—
845C4⋊C4—54no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—54no—
851C22⋊C4—54no—
852C22⋊C4—154no—
853C22⋊C4—154no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4—154no—
860C42—154no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—22no—
866C22×C3—22no—
867C22×C3—22no—
868C22×C3—44no—
869C22×C3—44no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—102no—
873C22×C3—204no—
874C22×C3C2×D4×D512yes—
875C22×C3#414412yes—
876C22×C3D5×#4112yes—
877C22×C3C24×D511yescharacteristic
878C2×D3—28no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—54no—
882C2×D3—54no—
883C2×D3—108no—
884C2×D3—108no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—2016no—
890C2×D3—2016no—
891C2×D3C2×D4×D514yes—
892C3×C4—22no—
893C3×C4—54no—
894C3×C4—102no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—22no—
899Dic3—102no—
900Dic3—102no—
901C2×C5—42no—
902C2×C5—42no—
903C2×C5—64no—
904C2×C5#561214yescomplemented
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C2×#100411yescharacteristic
907C2×C5C2×D3×#4111yescharacteristic
908D5—42no—
909D5—64no—
910D5—64no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—34no—
918C23—32no—
919C23—52no—
920C23—62no—
921C23—62no—
922C23—102no—
923C23—102no—
924C23—102no—
925C23—154no—
926C23—154no—
927C23—152no—
928C23—152no—
929C23—308no—
930C23—308no—
931C23—308no—
932C23—308no—
933C23—302no—
934C23—302no—
935C23—302no—
936C23—302no—
937C23—604no—
938C23—6016no—
939C23—604no—
940C23—6016no—
941C23C22×D3×D512yes—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—308no—
945D4—44no—
946D4—68no—
947D4—68no—
948D4—108no—
949D4—1516no—
950D4—204no—
951D4—308no—
952D4—308no—
953D4—308no—
954C2×C4—22no—
955C2×C4—32no—
956C2×C4—32no—
957C2×C4—32no—
958C2×C4—54no—
959C2×C4—52no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—62no—
965C2×C4—108no—
966C2×C4—102no—
967C2×C4—102no—
968C2×C4—124no—
969C2×C4—152no—
970C2×C4—152no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—308no—
974C2×C4—302no—
975C2×C4—302no—
976C2×C4—604no—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—42no—
980C2×C3—202no—
981C2×C3#6594414yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×#414411yescharacteristic
984C2×C3C2×D5×#4111yescharacteristic
985D3—24no—
986D3—104no—
987D3—104no—
988C5C2×#561211yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—22no—
993C22—22no—
994C22—22no—
995C22—34no—
996C22—44no—
997C22—44no—
998C22—62no—
999C22—68no—
1000C22—62no—
1001C22—102no—
1002C22—102no—
1003C22—102no—
1004C22—154no—
1005C22—154no—
1006C22—204no—
1007C22—302no—
1008C22—302no—
1009C22—308no—
1010C22—308no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—6016no—
1015C22D3×D4×D512yes—
1016C22#9202412yes—
1017C22#9204912yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—54no—
1021C4—62no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6594411yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—42no—
1031C2—64no—
1032C2—202no—
1033C2—304no—
1034C2—304no—
1035C2#1175505614yesdirect product factor
1036C2C2×D3×D4×D511yescharacteristic
1037C2C2×#9202411yescharacteristic
1038C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#546
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#6790C2semidirect
2. C22×#6782C2semidirect
3. C2×#91826C2semidirect
4. C2×C5×#938C2semidirect
5. C2×C3×#4085C2semidirect
6. C2×#91577C2semidirect
7. C2×#91561C2semidirect
8. C2×#91555C2semidirect
9. C2×#91552C2semidirect
10. C2×#91534C2semidirect
11. C2×#91533C2semidirect
12. #11755056C2direct (N × H)
13. C2×D3×#685C2semidirect
14. C2×#91446C2semidirect
15. C2×#91419C2semidirect
16. C2×#91356C2semidirect
20. C22×C3×C5×D4C22semidirect
22. C22×#1220C22semidirect
24. C22×C5×#67C22semidirect
25. C22×C4×C5×D3C22semidirect
27. C22×C3×C22⋊D5C22semidirect
28. C23×C3×Dic5C22semidirect
30. C2×#6790C22semidirect
31. C22×#1204C22semidirect
35. C22×#1200C22semidirect
36. C22×#1200C22semidirect
38. C2×#6782C22semidirect
39. C22×D3×Dic5C22semidirect
40. C2×#6719C22semidirect
41. #91826C22semidirect
43. C2×#6714C22semidirect
44. C2×C5×#217C22semidirect
45. C2×C5×#217C22semidirect
46. C5×#938C22semidirect
47. C2×C5×C4⋊Dic3C22semidirect
48. C2×C3×C22⋊Dic5C22semidirect
49. C3×#4085C22semidirect
50. C2×C3×#685C22semidirect
51. C2×C3×#683C22semidirect
52. #91577C22semidirect
53. #91561C22semidirect
54. #91555C22semidirect
55. #91552C22semidirect
56. C2×#6669C22semidirect
57. C2×#6668C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
61. C2×#6665C22semidirect
62. C2×#6665C22semidirect
63. #91534C22semidirect
64. #91533C22semidirect
65. C2×Dic3×Dic5C22semidirect
66. D3×#685C22semidirect
67. #91446C22semidirect
68. #91419C22semidirect
69. #91356C22semidirect
74. C2×#4085D3semidirect
102. C2×C3×C5×D4C23semidirect
107. C2×#1220C23semidirect
113. C2×C5×#67C23semidirect
118. C2×C4×C5×D3C23semidirect
122. C2×C3×C22⋊D5C23semidirect
127. C22×C3×Dic5C23semidirect
130. C2×#1204C23semidirect
131. C2×#1203D4semidirect
139. C2×#1200C23semidirect
140. C2×#1200C23semidirect
143. C2×D3×Dic5C23semidirect
144. #6719C23semidirect
146. #6714C23semidirect
147. C5×#217C23semidirect
148. C5×#217C23semidirect
149. C5×C4⋊Dic3C23semidirect
150. C3×C22⋊Dic5C23semidirect
151. C3×#685C23semidirect
152. C3×#683C23semidirect
153. #6669C23semidirect
154. #6668C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
158. #6665C23semidirect
159. #6665C23semidirect
160. Dic3×Dic5C23semidirect
165. C2×#938D5semidirect
181. C22×C5×D4C2×D3semidirect
187. C22×C22⋊D5C2×D3semidirect
189. C23×Dic5C2×D3semidirect
205. C2×C22⋊Dic5C2×D3semidirect
206. #4085C2×D3semidirect
218. C2×#685C2×D3semidirect
221. C2×#683C2×D3semidirect
248. C22×D15#41semidirect
291. #1203C2×D4semidirect
301. C22×C3×D4C2×D5semidirect
307. C22×#67C2×D5semidirect
317. C22×C4×D3C2×D5semidirect
326. C2×#217C2×D5semidirect
327. C2×#217C2×D5semidirect
329. #938C2×D5semidirect
340. C2×C4⋊Dic3C2×D5semidirect
368. C2×C5×D4C22×D3semidirect
384. C2×C22⋊D5C22×D3semidirect
393. C22×Dic5C22×D3semidirect
411. C22⋊Dic5C22×D3semidirect
418. #685C22×D3semidirect
421. #683C22×D3semidirect
459. C2×D15C2×#41semidirect
497. C2×C3×D4C22×D5semidirect
513. C2×#67C22×D5semidirect
532. C2×C4×D3C22×D5semidirect
541. #217C22×D5semidirect
542. #217C22×D5semidirect
549. C4⋊Dic3C22×D5semidirect
634. C22×D4D3×D5semidirect
673. C2×C3×C5#546semidirect
822. C2×D4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
904. C2×C5#5612semidirect
981. C2×C3#65944semidirect
988. C5C2×#5612semidirect
1028. C3C2×#65944semidirect
1035. C2#11755056direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67902
C22×#67822
C2×#918262
C2×C5×#9382
C2×C3×#40852
C2×#915772
C2×#915612
C2×#915552
C2×#915522
C2×#915342
C2×#915332
#117550562
C2×D3×#6852
C2×#914462
C2×#914192
C2×#913562
C2×#659443
C2×#56125