Finite Group Databasebeta

← C2×#11753224 #14480428

Subgroups — C2×#11753224 #14480428

Order 1920.

3792 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D5×#67C211yesmaximal, characteristic, complemented
2C22×#6766C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×#885C211yesmaximal, characteristic, complemented
5C2×C3×#4028C211yesmaximal, characteristic, complemented
6C2×#91567C211yesmaximal, characteristic, complemented
7C2×#91564C211yesmaximal, characteristic, complemented
8C2×#91550C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×#91474C211yesmaximal, characteristic, complemented
11C2×#91461C211yesmaximal, characteristic, complemented
12C2×#91458C211yesmaximal, characteristic, complemented
13C2×#91455C211yesmaximal, characteristic, complemented
14C2×#91408C211yesmaximal, characteristic, complemented
15C2×#91393C211yesmaximal, characteristic, complemented
16#11753224C2116yesmaximal, direct product factor
17C2×#66008—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic, complemented
23C22×C4×D15C2211yescharacteristic, complemented
24C22×C5×#67C2211yescharacteristic
25C22×C5×Dic6C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic, complemented
27C22×C3×D20C2211yescharacteristic
28C22×C3×D20C2211yescharacteristic, complemented
29C2×D5×#67—28no—
30C2×D5×#67C2218yescomplemented
31C22×#1203C2211yescharacteristic, complemented
32C22×#1202C2211yescharacteristic
33C22×#1202C2211yescharacteristic
34C22×#1202C2211yescharacteristic, complemented
35C22×#1202C2211yescharacteristic, complemented
36C22×#1202C2211yescharacteristic, complemented
37C22×#1201C2211yescharacteristic
38C22×#1201C2211yescharacteristic, complemented
39C22×D5×Dic3C2211yescharacteristic
40C22×D5×Dic3C2211yescharacteristic, complemented
41C2×#6766—28no—
42C2×#6766C2218yescomplemented
43C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
44C2×#6714C2211yescharacteristic, complemented
45C2×#6712C2211yescharacteristic, complemented
46#91773C2218yescomplemented
47C2×C5×#217C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C4×C5×Dic3C2211yescharacteristic, complemented
51C5×#885C2218yescomplemented
52C2×C3×#685C2211yescharacteristic
53C2×C3×#685C2211yescharacteristic, complemented
54C3×#4028C2218yescomplemented
55#91567C2218yescomplemented
56#91564C2218yescomplemented
57#91550C2218yescomplemented
58C2×#6669C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×#6665C2211yescharacteristic
61C2×#6665C2211yescharacteristic, complemented
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63#91476C2218yescomplemented
64#91474C2218yescomplemented
65#91461C2218yescomplemented
66#91458C2218yescomplemented
67#91455C2218yescomplemented
68#91408C2218yescomplemented
69#91393C2218yescomplemented
70C2×#5592—51nomaximal, Hall
71C22×#713—31no—
72C22×D4×D5—31no—
73C2×C5×#124—31no—
74C2×#4093—31no—
75C2×#4086—31no—
76#66008—316no—
77C2×#4030—31no—
78C2×#4030—31no—
79C2×#4030—31no—
80C2×#4030—31no—
81C2×#4028—31no—
82C2×#4028—31no—
83C2×#4028—31no—
84C2×#4028D311yescharacteristic, complemented
85C2×#4020—31no—
86C2×#4018—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5—24no—
92C23×C3×D5—42no—
93C23×C3×D5—42no—
94C23×C3×D5C2311yescharacteristic
95C23×C3×D5C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C23×C3×D5C2314yes—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5C2314yes—
102C22×C3×C4×C5C2311yescharacteristic
103C22×C3×C4×C5C2311yescharacteristic
104C2×#1220—24no—
105C2×#1220—42no—
106C2×#1220C2314yes—
107C2×#1220C2314yescomplemented
108C22×Dic15C2311yescharacteristic
109C22×Dic15C2311yescharacteristic
110C2×D60—42no—
111C2×D60C2314yescomplemented
112C2×C4×D15—24no—
113C2×C4×D15C2314yescomplemented
114C2×C5×#67—24no—
115C2×C5×#67C2314yes—
116C22×C5×Dic3C2311yescharacteristic
117C22×C5×Dic3C2311yescharacteristic
118C22×C5×Dic3C2311yescharacteristic
119C2×C5×Dic6—24no—
120C2×C5×Dic6C2314yescomplemented
121C2×C3×C22⋊D5—42no—
122C2×C3×C22⋊D5C2314yescomplemented
123C22×C3×Dic5C2311yescharacteristic
124C2×C3×D20—24no—
125C2×C3×D20—42no—
126C2×C3×D20C2314yes—
127C2×C3×D20C2314yescomplemented
128D5×#67—232no—
129C2×#1203—42no—
130C2×#1203C2314yescomplemented
131C2×#1202—24no—
132C2×#1202—24no—
133C2×#1202—24no—
134C2×#1202—42no—
135C2×#1202—42no—
136C2×#1202C2314yes—
137C2×#1202C2314yes—
138C2×#1202C2314yescomplemented
139C2×#1202C2314yescomplemented
140C2×#1202C2314yescomplemented
141C2×#1201—24no—
142C2×#1201—42no—
143C2×#1201C2314yes—
144C2×#1201C2314yescomplemented
145C2×D5×Dic3—24no—
146C2×D5×Dic3D418yescomplemented
147C2×D5×Dic3C2314yes—
148C2×D5×Dic3C2314yescomplemented
149#6766—232no—
150C3×C5×C22⋊C4C2314yescomplemented
151#6714C2314yescomplemented
152#6712C2314yescomplemented
153C5×#217C2314yescomplemented
154C5×(C2×D3)⋊C4C2314yescomplemented
155C5×(C2×D3)⋊C4C2314yescomplemented
156C4×C5×Dic3C2314yescomplemented
157C3×#685C2314yes—
158C3×#685C2314yescomplemented
159#6669C2314yescomplemented
160#6667C2314yescomplemented
161#6665C2314yes—
162#6665C2314yescomplemented
163Dic3×Dic5C2314yescomplemented
164C23×#67—51no—
165C22×#237—51no—
166C2×C3×#120—51no—
167C2×#953—51no—
168C2×#940—51no—
169C2×#940—51no—
170C2×#939—51no—
171C2×#939—51no—
172C2×#937—51no—
173#5592—516no—
174C2×#885—51no—
175C2×#885D511yescharacteristic, complemented
176C2×#884—51no—
177C2×#884—51no—
178C2×#882—51no—
179C2×#877—51no—
180C24×D5—31no—
181C24×D5C2×D311yescharacteristic
182C22×C5×Q8—31no—
183C22×C5×D4—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5C2×D311yescharacteristic, complemented
190C2×#713—38no—
191C2×#713—68no—
192C2×D4×D5—38no—
193C2×D4×D5—68no—
194C22×D20—31no—
195C22×D20—31no—
196C22×D20—31no—
197C22×D20—31no—
198C22×D20—31no—
199C22×D20—31no—
200C22×D20C2×D311yescharacteristic
201C22×D20C2×D311yescharacteristic, complemented
202C22×C4×D5—31no—
203C22×C4×D5—31no—
204C22×C4×D5—31no—
205C5×#124—38no—
206C2×C5×C22⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4—31no—
209C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
210C2×C42×C5—31no—
211#4093—38no—
212#4086—38no—
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685—31no—
217C2×#685C2×D311yescharacteristic
218C2×#685C2×D311yescharacteristic, complemented
219C2×#683—31no—
220C2×#683—31no—
221C2×C4×Dic5—31no—
222#4030—38no—
223#4030—38no—
224#4030—38no—
225#4030—38no—
226#4028—38no—
227#4028—38no—
228#4028—38no—
229#4028C2×D318yescomplemented
230#4020—38no—
231#4018—38no—
232C2×#535—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5C2412yes—
237C23×C3×C5C2411yescharacteristic
238C22×D15—22no—
239C22×D15—22no—
240C22×D15—22no—
241C22×D15—22no—
242C22×D15—22no—
243C22×D15—22no—
244C22×D15C2412yes—
245C22×D15C2412yes—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3—22no—
249C22×C5×D3C2412yes—
250C22×C3×D5—22no—
251C22×C3×D5—22no—
252C22×C3×D5—22no—
253C22×C3×D5—22no—
254C22×C3×D5—22no—
255C22×C3×D5—22no—
256C22×C3×D5—22no—
257C22×C3×D5—22no—
258C22×C3×D5—28no—
259C22×C3×D5—44no—
260C22×C3×D5—44no—
261C22×C3×D5—416no—
262C22×C3×D5C2×D414yes—
263C22×C3×D5C2412yes—
264C22×C3×D5C2412yes—
265C22×C3×D5C2412yes—
266C2×D3×D5—28no—
267C2×D3×D5—44no—
268C2×D3×D5—44no—
269C2×D3×D5—416no—
270C2×C3×C4×C5—22no—
271C2×C3×C4×C5—22no—
272C2×C3×C4×C5C2412yes—
273C2×C3×C4×C5C2412yes—
274#1220—28no—
275#1220—44no—
276C2×Dic15—22no—
277C2×Dic15C2×D414yes—
278C2×Dic15C2412yes—
279C2×Dic15C2412yes—
280D60—44no—
281C4×D15—28no—
282C5×#67—28no—
283C2×C5×Dic3—22no—
284C2×C5×Dic3—22no—
285C2×C5×Dic3C2×D414yes—
286C2×C5×Dic3C2412yes—
287C2×C5×Dic3C2412yes—
288C2×C5×Dic3C2412yes—
289C5×Dic6—28no—
290C3×C22⋊D5—44no—
291C2×C3×Dic5—22no—
292C2×C3×Dic5C2412yes—
293C3×D20—28no—
294C3×D20—44no—
295#1203—44no—
296#1202—28no—
297#1202—28no—
298#1202—28no—
299#1202—44no—
300#1202—44no—
301#1201—28no—
302#1201—44no—
303D5×Dic3—28no—
304D5×Dic3C2×D4116yescomplemented
305C25×C3—51no—
306C24×D3—51no—
307C22×C3×D4—51no—
308C22×C3×D4—51no—
309C22×C3×D4—51no—
310C22×#67—51no—
311C22×#67—51no—
312C22×#67—51no—
313C22×#67—51no—
314C22×#67—58no—
315C22×#67—51no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67—51no—
319C22×#67—51no—
320C22×#67—108no—
321C22×#67C2×D511yescharacteristic
322C23×Dic3—51no—
323C23×Dic3—51no—
324C2×#237—58no—
325C2×#237—108no—
326C22×D12—51no—
327C22×D12—51no—
328C22×C4×D3—51no—
329C22×Dic6C2×D511yescharacteristic, complemented
330C3×#120—58no—
331C2×C3×C22⋊C4—51no—
332C2×C3×C22⋊C4—51no—
333C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
334#953—58no—
335C2×#217—51no—
336C2×#217—51no—
337C2×#217C2×D511yescharacteristic, complemented
338#940—58no—
339#940—58no—
340#939—58no—
341#939—58no—
342#937—58no—
343C2×(C2×D3)⋊C4—51no—
344C2×(C2×D3)⋊C4—51no—
345C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
346C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
347C2×Dic3⋊C4—51no—
348C2×Dic3⋊C4—51no—
349C2×C4×Dic3—51no—
350C2×C4×Dic3C2×D511yescharacteristic, complemented
351#885—58no—
352#885C2×D518yescomplemented
353#884—58no—
354#884—58no—
355#882—58no—
356#877—58no—
357C24×C5—31no—
358C24×C5C22×D311yescharacteristic
359C23×D5—24no—
360C23×D5—31no—
361C23×D5—31no—
362C23×D5—34no—
363C23×D5—42no—
364C23×D5—42no—
365C23×D5—64no—
366C23×D5—122no—
367C23×D5—122no—
368C23×D5C22×D311yescharacteristic
369C23×D5C22×D311yescharacteristic
370C23×D5C22×D311yescharacteristic
371C23×D5C22×D314yes—
372C2×C5×Q8—34no—
373C2×C5×Q8—64no—
374C2×C5×D4—34no—
375C2×C5×D4—64no—
376C22×C4×C5—31no—
377C22×C4×C5—31no—
378C22×C4×C5—31no—
379C22×C4×C5C22×D311yescharacteristic
380C22×C4×C5C22×D311yescharacteristic
381C2×C22⋊D5—34no—
382C2×C22⋊D5—34no—
383C2×C22⋊D5—34no—
384C2×C22⋊D5—34no—
385C2×C22⋊D5—34no—
386C2×C22⋊D5—42no—
387C2×C22⋊D5—64no—
388C2×C22⋊D5—64no—
389C2×C22⋊D5—122no—
390C2×C22⋊D5—122no—
391C2×C22⋊D5—122no—
392C2×C22⋊D5C22×D314yescomplemented
393C22×Dic5—31no—
394C22×Dic5—31no—
395C22×Dic5C22×D311yescharacteristic
396#713—632no—
397D4×D5—632no—
398C2×D20—24no—
399C2×D20—34no—
400C2×D20—34no—
401C2×D20—34no—
402C2×D20—34no—
403C2×D20—34no—
404C2×D20—34no—
405C2×D20—42no—
406C2×D20—64no—
407C2×D20—64no—
408C2×D20—64no—
409C2×D20—122no—
410C2×D20—122no—
411C2×D20—122no—
412C2×D20C22×D314yes—
413C2×D20C22×D314yescomplemented
414C2×C4×D5—38no—
415C2×C4×D5—34no—
416C2×C4×D5—34no—
417C2×C4×D5—34no—
418C2×C4×D5—64no—
419C2×C4×D5—64no—
420C5×C22⋊C4—34no—
421C5×C22⋊C4—34no—
422C5×C22⋊C4—34no—
423C5×C22⋊C4C22×D314yescomplemented
424C42×C5—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685C22×D314yes—
430#685C22×D314yescomplemented
431#683—34no—
432#683—34no—
433C4×Dic5—34no—
434C22×#41—151no—
435C23×D4—151no—
436#535—1516no—
437C2×#127—151no—
438C2×#127—151no—
439C2×#124—31no—
440C2×#124—151no—
441C2×#121—151no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#120—51no—
446C2×#120—151no—
447C2×#120—151no—
448C2×#120—151no—
449C2×#117—151no—
450C22×C3×C5—22no—
451C22×C3×C5—22no—
452C22×C3×C5—22no—
453C22×C3×C5—44no—
454C22×C3×C5C22×D412yes—
455C22×C3×C5H(5,𝔽2)12yes—
456C22×C3×C5H(5,𝔽2)12yes—
457C22×C3×C5C2511yescharacteristic
458C2×D15—22no—
459C2×D15—22no—
460C2×D15—22no—
461C2×D15—22no—
462C2×D15—22no—
463C2×D15—22no—
464C2×D15—44no—
465C2×D15—44no—
466C2×C5×D3—22no—
467C2×C5×D3—22no—
468C2×C5×D3—22no—
469C2×C5×D3—44no—
470C2×C3×D5—28no—
471C2×C3×D5—22no—
472C2×C3×D5—22no—
473C2×C3×D5—22no—
474C2×C3×D5—22no—
475C2×C3×D5—22no—
476C2×C3×D5—22no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—416no—
480C2×C3×D5—44no—
481C2×C3×D5—44no—
482C2×C3×D5C22×D414yes—
483D3×D5—416no—
484C3×C4×C5—22no—
485C3×C4×C5—22no—
486Dic15—22no—
487Dic15C22×D414yes—
488C3×Dic5—22no—
489C5×Dic3—22no—
490C5×Dic3—22no—
491C5×Dic3C22×D414yes—
492C24×C3—51no—
493C24×C3—51no—
494C24×C3—51no—
495C24×C3—54no—
496C24×C3—104no—
497C24×C3—202no—
498C24×C3—202no—
499C24×C3C22×D511yescharacteristic
500C23×D3—51no—
501C23×D3—51no—
502C23×D3—54no—
503C23×D3—104no—
504C23×D3—202no—
505C23×D3—202no—
506C23×D3C22×D511yescharacteristic
507C2×C3×D4—54no—
508C2×C3×D4—54no—
509C2×C3×D4—54no—
510C2×C3×D4—104no—
511C2×C3×D4—202no—
512C2×C3×D4—202no—
513C22×C3×C4—51no—
514C22×C3×C4C22×D511yescharacteristic
515C22×C3×C4C22×D511yescharacteristic
516C2×#67—24no—
517C2×#67—54no—
518C2×#67—54no—
519C2×#67—54no—
520C2×#67—54no—
521C2×#67—54no—
522C2×#67—54no—
523C2×#67—54no—
524C2×#67—54no—
525C2×#67—54no—
526C2×#67—104no—
527C2×#67—1032no—
528C2×#67—104no—
529C2×#67—104no—
530C2×#67—104no—
531C2×#67—104no—
532C2×#67—202no—
533C2×#67—202no—
534C2×#67—202no—
535C2×#67—202no—
536C2×#67C22×D514yes—
537C22×Dic3—51no—
538C22×Dic3—58no—
539C22×Dic3—54no—
540C22×Dic3—51no—
541C22×Dic3—54no—
542C22×Dic3—104no—
543C22×Dic3C22×D511yescharacteristic
544C22×Dic3C22×D511yescharacteristic
545C22×Dic3C22×D511yescharacteristic
546#237—1032no—
547C2×D12—54no—
548C2×D12—54no—
549C2×D12—202no—
550C2×D12—202no—
551C2×C4×D3—54no—
552C2×C4×D3—104no—
553C2×Dic6—24no—
554C2×Dic6C22×D514yescomplemented
555C3×C22⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4C22×D514yescomplemented
558#217—54no—
559#217—54no—
560#217C22×D514yescomplemented
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4C22×D514yescomplemented
564(C2×D3)⋊C4C22×D514yescomplemented
565Dic3⋊C4—54no—
566Dic3⋊C4—54no—
567C4×Dic3—54no—
568C4×Dic3C22×D514yescomplemented
569C23×C5—22no—
570C23×C5—22no—
571C23×C5—22no—
572C23×C5—32no—
573C23×C5—62no—
574C23×C5—62no—
575C23×C5—62no—
576C23×C5C23×D312yes—
577C23×C5C23×D311yescharacteristic
578C22×D5—22no—
579C22×D5—22no—
580C22×D5—22no—
581C22×D5—22no—
582C22×D5—22no—
583C22×D5—22no—
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—28no—
587C22×D5—32no—
588C22×D5—32no—
589C22×D5—44no—
590C22×D5—44no—
591C22×D5—416no—
592C22×D5—62no—
593C22×D5—62no—
594C22×D5—62no—
595C22×D5—62no—
596C22×D5—62no—
597C22×D5—62no—
598C22×D5—68no—
599C22×D5—124no—
600C22×D5—124no—
601C22×D5—1216no—
602C22×D5D3×D414yes—
603C22×D5C23×D312yes—
604C22×D5C23×D312yes—
605C22×D5C23×D312yes—
606C5×Q8—68no—
607C5×D4—68no—
608C2×C4×C5—22no—
609C2×C4×C5—22no—
610C2×C4×C5—34no—
611C2×C4×C5—32no—
612C2×C4×C5—32no—
613C2×C4×C5—32no—
614C2×C4×C5—62no—
615C2×C4×C5—62no—
616C2×C4×C5C23×D312yes—
617C2×C4×C5C23×D312yes—
618C22⋊D5—44no—
619C22⋊D5—68no—
620C22⋊D5—68no—
621C22⋊D5—124no—
622C22⋊D5—124no—
623C22⋊D5—124no—
624C2×Dic5—22no—
625C2×Dic5—34no—
626C2×Dic5—32no—
627C2×Dic5—32no—
628C2×Dic5—62no—
629C2×Dic5C23×D312yes—
630D20—28no—
631D20—44no—
632D20—68no—
633D20—68no—
634D20—68no—
635D20—124no—
636D20—124no—
637D20—124no—
638C4×D5—316no—
639C4×D5—68no—
640C4×D5—68no—
641C25—51no—
642C25—151no—
643C2×#41—158no—
644C2×#41—308no—
645C22×Q8—31no—
646C22×D4—31no—
647C22×D4—51no—
648C22×D4—51no—
649C22×D4—51no—
650C22×D4—151no—
651C22×D4—151no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—158no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—151no—
662C22×D4—308no—
663C23×C4—151no—
664C23×C4—151no—
665C23×C4—151no—
666#127—158no—
667#127—158no—
668#124—38no—
669#124—158no—
670#121—158no—
671#121—158no—
672#121—158no—
673#121—158no—
674#120—58no—
675#120—158no—
676#120—158no—
677#120—158no—
678#117—158no—
679C2×C4⋊C4—151no—
680C2×C4⋊C4—151no—
681C2×C22⋊C4—31no—
682C2×C22⋊C4—31no—
683C2×C22⋊C4—31no—
684C2×C22⋊C4—51no—
685C2×C22⋊C4—51no—
686C2×C22⋊C4—151no—
687C2×C22⋊C4—151no—
688C2×C22⋊C4—151no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4D3×D511yescharacteristic, complemented
691C2×C42—31no—
692C2×C42—151no—
693C2×C3×C5—42no—
694C2×C3×C5#53514yescomplemented
695C2×C3×C5C23×D411yescharacteristic
696C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
697C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
698D15—42no—
699D15—42no—
700C3×D5—24no—
701C3×D5—42no—
702C3×D5—42no—
703C5×D3—42no—
704C23×C3—22no—
705C23×C3—22no—
706C23×C3—22no—
707C23×C3—54no—
708C23×C3—52no—
709C23×C3—52no—
710C23×C3—52no—
711C23×C3—108no—
712C23×C3—102no—
713C23×C3—102no—
714C23×C3—102no—
715C23×C3—102no—
716C23×C3—102no—
717C23×C3—102no—
718C23×C3—102no—
719C23×C3—102no—
720C23×C3—204no—
721C23×C3—204no—
722C23×C3—2016no—
723C23×C3C23×D512yes—
724C23×C3C23×D511yescharacteristic
725C22×D3—22no—
726C22×D3—22no—
727C22×D3—22no—
728C22×D3—52no—
729C22×D3—52no—
730C22×D3—108no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—102no—
736C22×D3—102no—
737C22×D3—204no—
738C22×D3—204no—
739C22×D3—2016no—
740C22×D3C23×D512yes—
741C3×D4—108no—
742C3×D4—204no—
743C3×D4—204no—
744C2×C3×C4—22no—
745C2×C3×C4—22no—
746C2×C3×C4—52no—
747C2×C3×C4—102no—
748C2×C3×C4C23×D512yes—
749C2×C3×C4C23×D512yes—
750#67—28no—
751#67—108no—
752#67—108no—
753#67—108no—
754#67—108no—
755#67—108no—
756#67—204no—
757#67—204no—
758#67—204no—
759#67—204no—
760C2×Dic3—22no—
761C2×Dic3—22no—
762C2×Dic3—54no—
763C2×Dic3—52no—
764C2×Dic3—516no—
765C2×Dic3—52no—
766C2×Dic3—108no—
767C2×Dic3—102no—
768C2×Dic3D4×D514yes—
769C2×Dic3C23×D512yes—
770C2×Dic3C23×D512yes—
771C2×Dic3C23×D512yes—
772D12—204no—
773D12—204no—
774C4×D3—108no—
775Dic6—28no—
776C22×C5—22no—
777C22×C5—22no—
778C22×C5—22no—
779C22×C5—44no—
780C22×C5—62no—
781C22×C5—62no—
782C22×C5—62no—
783C22×C5—124no—
784C22×C5C2×D3×D412yes—
785C22×C5#100412yes—
786C22×C5#100412yes—
787C22×C5C24×D311yescharacteristic
788C2×D5—22no—
789C2×D5—22no—
790C2×D5—28no—
791C2×D5—22no—
792C2×D5—22no—
793C2×D5—22no—
794C2×D5—22no—
795C2×D5—22no—
796C2×D5—22no—
797C2×D5—416no—
798C2×D5—44no—
799C2×D5—44no—
800C2×D5—62no—
801C2×D5—62no—
802C2×D5—62no—
803C2×D5—62no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—1216no—
807C2×D5—124no—
808C2×D5—124no—
809C2×D5C2×D3×D414yes—
810C4×C5—22no—
811C4×C5—22no—
812C4×C5—34no—
813C4×C5—62no—
814C4×C5—62no—
815Dic5—22no—
816Dic5—34no—
817Dic5—62no—
818C24—31no—
819C24—51no—
820C24—51no—
821C24—51no—
822C24—54no—
823C24—104no—
824C24—154no—
825C24—151no—
826C24—151no—
827C24—202no—
828C24—202no—
829C24—304no—
830C24—602no—
831C24—602no—
832C24C2×D3×D511yescharacteristic
833#41—3032no—
834C2×Q8—34no—
835C2×Q8—64no—
836C2×D4—34no—
837C2×D4—54no—
838C2×D4—54no—
839C2×D4—54no—
840C2×D4—64no—
841C2×D4—104no—
842C2×D4—154no—
843C2×D4—154no—
844C2×D4—154no—
845C2×D4—154no—
846C2×D4—154no—
847C2×D4—154no—
848C2×D4—154no—
849C2×D4—154no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—202no—
854C2×D4—202no—
855C2×D4—304no—
856C2×D4—304no—
857C2×D4—304no—
858C2×D4—3032no—
859C2×D4—304no—
860C2×D4—304no—
861C2×D4—602no—
862C2×D4—602no—
863C2×D4—602no—
864C2×D4—602no—
865C2×D4—602no—
866C2×D4—602no—
867C22×C4—31no—
868C22×C4—31no—
869C22×C4—31no—
870C22×C4—51no—
871C22×C4—154no—
872C22×C4—158no—
873C22×C4—154no—
874C22×C4—151no—
875C22×C4—151no—
876C22×C4—154no—
877C22×C4—304no—
878C22×C4—304no—
879C22×C4C2×D3×D511yescharacteristic
880C22×C4C2×D3×D511yescharacteristic
881C4⋊C4—154no—
882C4⋊C4—154no—
883C22⋊C4—34no—
884C22⋊C4—34no—
885C22⋊C4—34no—
886C22⋊C4—54no—
887C22⋊C4—54no—
888C22⋊C4—154no—
889C22⋊C4—154no—
890C22⋊C4—154no—
891C22⋊C4—154no—
892C22⋊C4C2×D3×D514yescomplemented
893C42—34no—
894C42—154no—
895C3×C5C2×#53511yescharacteristic, complemented, Hall
896C22×C3—22no—
897C22×C3—22no—
898C22×C3—22no—
899C22×C3—44no—
900C22×C3—54no—
901C22×C3—108no—
902C22×C3—102no—
903C22×C3—102no—
904C22×C3—102no—
905C22×C3—102no—
906C22×C3—102no—
907C22×C3—102no—
908C22×C3—102no—
909C22×C3—102no—
910C22×C3—2016no—
911C22×C3—204no—
912C22×C3—204no—
913C22×C3C2×D4×D512yes—
914C22×C3#414912yes—
915C22×C3#414912yes—
916C22×C3C24×D511yescharacteristic
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—44no—
921C2×D3—102no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—2016no—
928C2×D3—204no—
929C2×D3—204no—
930C3×C4—22no—
931C3×C4—22no—
932C3×C4—102no—
933Dic3—22no—
934Dic3—22no—
935Dic3—54no—
936Dic3—102no—
937Dic3C2×D4×D514yes—
938C2×C5—42no—
939C2×C5—122no—
940C2×C5#559214yescomplemented
941C2×C5C22×D3×D411yescharacteristic
942C2×C5C2×#100411yescharacteristic
943C2×C5C2×#100411yescharacteristic
944D5—24no—
945D5—42no—
946D5—42no—
947D5—122no—
948D5—122no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—32no—
953C23—54no—
954C23—52no—
955C23—52no—
956C23—52no—
957C23—62no—
958C23—62no—
959C23—62no—
960C23—108no—
961C23—102no—
962C23—102no—
963C23—102no—
964C23—102no—
965C23—102no—
966C23—102no—
967C23—102no—
968C23—102no—
969C23—152no—
970C23—152no—
971C23—204no—
972C23—204no—
973C23—2016no—
974C23—308no—
975C23—302no—
976C23—302no—
977C23—302no—
978C23—302no—
979C23—302no—
980C23—302no—
981C23—604no—
982C23—604no—
983C23—6016no—
984C23C22×D3×D512yes—
985C23C22×D3×D511yescharacteristic
986Q8—68no—
987D4—68no—
988D4—108no—
989D4—204no—
990D4—204no—
991D4—308no—
992D4—308no—
993D4—308no—
994D4—308no—
995D4—308no—
996D4—604no—
997D4—604no—
998D4—604no—
999D4—604no—
1000D4—604no—
1001D4—604no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—34no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—32no—
1008C2×C4—52no—
1009C2×C4—62no—
1010C2×C4—62no—
1011C2×C4—102no—
1012C2×C4—1516no—
1013C2×C4—154no—
1014C2×C4—152no—
1015C2×C4—152no—
1016C2×C4—308no—
1017C2×C4—308no—
1018C2×C4—302no—
1019C2×C4C22×D3×D512yes—
1020C2×C4C22×D3×D512yes—
1021C2×C3—42no—
1022C2×C3—104no—
1023C2×C3—202no—
1024C2×C3—202no—
1025C2×C3#6600814yescomplemented
1026C2×C3C22×D4×D511yescharacteristic
1027C2×C3C2×#414911yescharacteristic
1028C2×C3C2×#414911yescharacteristic
1029D3—42no—
1030D3—202no—
1031D3—202no—
1032C5C2×#559211yescharacteristic, complemented, Sylow
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—44no—
1037C22—54no—
1038C22—62no—
1039C22—62no—
1040C22—62no—
1041C22—108no—
1042C22—102no—
1043C22—102no—
1044C22—102no—
1045C22—102no—
1046C22—102no—
1047C22—102no—
1048C22—102no—
1049C22—102no—
1050C22—124no—
1051C22—2016no—
1052C22—204no—
1053C22—204no—
1054C22—302no—
1055C22—302no—
1056C22—302no—
1057C22—302no—
1058C22—302no—
1059C22—302no—
1060C22—6016no—
1061C22—604no—
1062C22—604no—
1063C22#9201712yes—
1064C22D3×D4×D512yes—
1065C22#9202612yes—
1066C22C23×D3×D511yescharacteristic
1067C4—22no—
1068C4—22no—
1069C4—34no—
1070C4—62no—
1071C4—62no—
1072C4—102no—
1073C4—154no—
1074C4—302no—
1075C3C2×#6600811yescharacteristic, complemented, Sylow
1076C2—42no—
1077C2—104no—
1078C2—122no—
1079C2—202no—
1080C2—202no—
1081C2—602no—
1082C2—602no—
1083C2#1175322414yesdirect product factor
1084C2C2×#9201711yescharacteristic
1085C2C2×D3×D4×D511yescharacteristic
1086C2C2×#9202611yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#535
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×D5×#67C2semidirect
2. C22×#6766C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×#885C2semidirect
5. C2×C3×#4028C2semidirect
6. C2×#91567C2semidirect
7. C2×#91564C2semidirect
8. C2×#91550C2semidirect
9. C2×#91476C2semidirect
10. C2×#91474C2semidirect
11. C2×#91461C2semidirect
12. C2×#91458C2semidirect
13. C2×#91455C2semidirect
14. C2×#91408C2semidirect
15. C2×#91393C2semidirect
16. #11753224C2direct (N × H)
21. C22×#1220C22semidirect
22. C22×D60C22semidirect
23. C22×C4×D15C22semidirect
25. C22×C5×Dic6C22semidirect
26. C22×C3×C22⋊D5C22semidirect
28. C22×C3×D20C22semidirect
30. C2×D5×#67C22semidirect
31. C22×#1203C22semidirect
34. C22×#1202C22semidirect
35. C22×#1202C22semidirect
36. C22×#1202C22semidirect
38. C22×#1201C22semidirect
40. C22×D5×Dic3C22semidirect
42. C2×#6766C22semidirect
43. C2×C3×C5×C22⋊C4C22semidirect
44. C2×#6714C22semidirect
45. C2×#6712C22semidirect
46. #91773C22semidirect
47. C2×C5×#217C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C2×C5×(C2×D3)⋊C4C22semidirect
50. C2×C4×C5×Dic3C22semidirect
51. C5×#885C22semidirect
53. C2×C3×#685C22semidirect
54. C3×#4028C22semidirect
55. #91567C22semidirect
56. #91564C22semidirect
57. #91550C22semidirect
58. C2×#6669C22semidirect
59. C2×#6667C22semidirect
61. C2×#6665C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. #91476C22semidirect
64. #91474C22semidirect
65. #91461C22semidirect
66. #91458C22semidirect
67. #91455C22semidirect
68. #91408C22semidirect
69. #91393C22semidirect
84. C2×#4028D3semidirect
107. C2×#1220C23semidirect
111. C2×D60C23semidirect
113. C2×C4×D15C23semidirect
120. C2×C5×Dic6C23semidirect
122. C2×C3×C22⋊D5C23semidirect
127. C2×C3×D20C23semidirect
130. C2×#1203C23semidirect
138. C2×#1202C23semidirect
139. C2×#1202C23semidirect
140. C2×#1202C23semidirect
144. C2×#1201C23semidirect
146. C2×D5×Dic3D4semidirect
148. C2×D5×Dic3C23semidirect
150. C3×C5×C22⋊C4C23semidirect
151. #6714C23semidirect
152. #6712C23semidirect
153. C5×#217C23semidirect
154. C5×(C2×D3)⋊C4C23semidirect
155. C5×(C2×D3)⋊C4C23semidirect
156. C4×C5×Dic3C23semidirect
158. C3×#685C23semidirect
159. #6669C23semidirect
160. #6667C23semidirect
162. #6665C23semidirect
163. Dic3×Dic5C23semidirect
175. C2×#885D5semidirect
189. C22×C22⋊D5C2×D3semidirect
201. C22×D20C2×D3semidirect
209. C2×C5×C22⋊C4C2×D3semidirect
218. C2×#685C2×D3semidirect
229. #4028C2×D3semidirect
304. D5×Dic3C2×D4semidirect
329. C22×Dic6C2×D5semidirect
333. C2×C3×C22⋊C4C2×D5semidirect
337. C2×#217C2×D5semidirect
345. C2×(C2×D3)⋊C4C2×D5semidirect
346. C2×(C2×D3)⋊C4C2×D5semidirect
350. C2×C4×Dic3C2×D5semidirect
352. #885C2×D5semidirect
392. C2×C22⋊D5C22×D3semidirect
413. C2×D20C22×D3semidirect
423. C5×C22⋊C4C22×D3semidirect
430. #685C22×D3semidirect
554. C2×Dic6C22×D5semidirect
557. C3×C22⋊C4C22×D5semidirect
560. #217C22×D5semidirect
563. (C2×D3)⋊C4C22×D5semidirect
564. (C2×D3)⋊C4C22×D5semidirect
568. C4×Dic3C22×D5semidirect
690. C2×C22⋊C4D3×D5semidirect
694. C2×C3×C5#535semidirect
892. C22⋊C4C2×D3×D5semidirect
895. C3×C5C2×#535semidirect
940. C2×C5#5592semidirect
1025. C2×C3#66008semidirect
1032. C5C2×#5592semidirect
1075. C3C2×#66008semidirect
1083. C2#11753224direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D5×#672
C22×#67662
C2×#917732
C2×C5×#8852
C2×C3×#40282
C2×#915672
C2×#915642
C2×#915502
C2×#914762
C2×#914742
C2×#914612
C2×#914582
C2×#914552
C2×#914082
C2×#913932
#117532242
C2×#660083
C2×#55925