Finite Group Databasebeta

← C2×#11753223 #14480433

Subgroups — C2×#11753223 #14480433

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×#6765C211yesmaximal, characteristic, complemented
3C2×#91774C211yesmaximal, characteristic, complemented
4C2×C5×#884C211yesmaximal, characteristic, complemented
5C2×C3×#4028C211yesmaximal, characteristic, complemented
6C2×#91567C211yesmaximal, characteristic, complemented
7C2×#91563C211yesmaximal, characteristic, complemented
8C2×#91549C211yesmaximal, characteristic, complemented
9C2×#91475C211yesmaximal, characteristic, complemented
10C2×#91474C211yesmaximal, characteristic, complemented
11C2×#91463C211yesmaximal, characteristic, complemented
12C2×#91462C211yesmaximal, characteristic, complemented
13C2×#91454C211yesmaximal, characteristic, complemented
14C2×#91409C211yesmaximal, characteristic, complemented
15C2×#91394C211yesmaximal, characteristic, complemented
16#11753223C2116yesmaximal, direct product factor
17C2×#65941—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic, complemented
24C22×C5×D12C2211yescharacteristic, complemented
25C22×C4×C5×D3C2211yescharacteristic, 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, complemented
34C22×#1201C2211yescharacteristic
35C22×#1201C2211yescharacteristic
36C22×#1201C2211yescharacteristic, complemented
37C22×#1201C2211yescharacteristic, complemented
38C22×#1201C2211yescharacteristic, complemented
39C22×D5×Dic3C2211yescharacteristic
40C22×D5×Dic3C2211yescharacteristic, complemented
41C2×#6765—28no—
42C2×#6765C2218yescomplemented
43C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
44C2×#6719C2211yescharacteristic, complemented
45C2×#6714C2211yescharacteristic, complemented
46C2×#6714C2211yescharacteristic, complemented
47C2×C4×Dic15C2211yescharacteristic, complemented
48#91774C2218yescomplemented
49C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
51C5×#884C2218yescomplemented
52C2×C3×#685C2211yescharacteristic
53C2×C3×#685C2211yescharacteristic, complemented
54C3×#4028C2218yescomplemented
55#91567C2218yescomplemented
56#91563C2218yescomplemented
57#91549C2218yescomplemented
58C2×Dic3⋊Dic5C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
60C2×#6665C2211yescharacteristic
61C2×#6665C2211yescharacteristic, complemented
62C2×Dic3×Dic5C2211yescharacteristic, complemented
63#91475C2218yescomplemented
64#91474C2218yescomplemented
65#91463C2218yescomplemented
66#91462C2218yescomplemented
67#91454C2218yescomplemented
68#91409C2218yescomplemented
69#91394C2218yescomplemented
70C2×#5592—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#121—31no—
74C2×#4086—31no—
75C2×#4086—31no—
76C2×#4084—31no—
77C2×#4083—31no—
78C2×#4083—31no—
79C2×#4076—31no—
80#65941—316no—
81C2×#4041—31no—
82C2×#4038—31no—
83C2×#4031—31no—
84C2×#4031—31no—
85C2×#4028—31no—
86C2×#4028D311yescharacteristic, complemented
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
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×#1220C2314yes—
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C2×Dic30—24no—
110C2×Dic30C2314yescomplemented
111C2×C5×#67—24no—
112C2×C5×#67—42no—
113C2×C5×#67C2314yes—
114C2×C5×#67C2314yescomplemented
115C22×C5×Dic3C2311yescharacteristic
116C22×C5×Dic3C2311yescharacteristic
117C2×C5×D12—42no—
118C2×C5×D12C2314yescomplemented
119C2×C4×C5×D3—24no—
120C2×C4×C5×D3C2314yescomplemented
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—42no—
133C2×#1202C2314yes—
134C2×#1202C2314yescomplemented
135C2×#1201—24no—
136C2×#1201—24no—
137C2×#1201—24no—
138C2×#1201—42no—
139C2×#1201—42no—
140C2×#1201C2314yes—
141C2×#1201C2314yes—
142C2×#1201C2314yescomplemented
143C2×#1201C2314yescomplemented
144C2×#1201C2314yescomplemented
145C2×D5×Dic3—24no—
146C2×D5×Dic3D418yescomplemented
147C2×D5×Dic3C2314yes—
148C2×D5×Dic3C2314yescomplemented
149#6765—232no—
150C3×C5×C22⋊C4C2314yescomplemented
151#6719C2314yescomplemented
152#6714C2314yescomplemented
153#6714C2314yescomplemented
154C4×Dic15C2314yescomplemented
155C5×(C2×D3)⋊C4C2314yescomplemented
156C5×Dic3⋊C4C2314yescomplemented
157C3×#685C2314yes—
158C3×#685C2314yescomplemented
159Dic3⋊Dic5C2314yescomplemented
160(C2×D3)⋊Dic5C2314yescomplemented
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×#885—51no—
176C2×#884—51no—
177C2×#884D511yescharacteristic, complemented
178C2×#882—51no—
179C2×#877—51no—
180C24×D5—31no—
181C24×D5C2×D311yescharacteristic
182C22×C5×D4—31no—
183C22×C5×D4—31no—
184C22×C5×D4—31no—
185C23×C4×C5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—31no—
190C22×C22⋊D5—31no—
191C22×C22⋊D5—31no—
192C22×C22⋊D5—31no—
193C22×C22⋊D5C2×D311yescharacteristic, complemented
194C2×D4×D5—38no—
195C2×D4×D5—68no—
196C2×#709—38no—
197C2×#709—68no—
198C22×D20—31no—
199C22×D20—31no—
200C22×D20C2×D311yescharacteristic
201C22×D20C2×D311yescharacteristic, complemented
202C22×C4×D5—31no—
203C22×C4×D5—31no—
204C22×Dic10—31no—
205C5×#121—38no—
206C2×C5×C4⋊C4—31no—
207C2×C5×C22⋊C4—31no—
208C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
209C2×C22⋊Dic5—31no—
210C2×C22⋊Dic5—31no—
211#4086—38no—
212#4086—38no—
213#4084—38no—
214#4083—38no—
215#4083—38no—
216#4076—38no—
217C2×#685—31no—
218C2×#685—31no—
219C2×#685—31no—
220C2×#685—31no—
221C2×#685C2×D311yescharacteristic
222C2×#685C2×D311yescharacteristic, complemented
223C2×C4⋊Dic5—31no—
224C2×C4×Dic5—31no—
225C2×C4×Dic5—31no—
226#4041—38no—
227#4038—38no—
228#4031—38no—
229#4031—38no—
230#4028—38no—
231#4028C2×D318yescomplemented
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×D15C2412yes—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3—22no—
247C22×C5×D3—22no—
248C22×C5×D3C2412yes—
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—
275C2×Dic15—22no—
276C2×Dic15—22no—
277C2×Dic15C2×D414yes—
278C2×Dic15C2412yes—
279C2×Dic15C2412yes—
280C2×Dic15C2412yes—
281Dic30—28no—
282C5×#67—28no—
283C5×#67—44no—
284C2×C5×Dic3—22no—
285C2×C5×Dic3C2×D414yes—
286C2×C5×Dic3C2412yes—
287C2×C5×Dic3C2412yes—
288C5×D12—44no—
289C4×C5×D3—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—44no—
298#1201—28no—
299#1201—28no—
300#1201—28no—
301#1201—44no—
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—51no—
315C22×#67—51no—
316C22×#67—58no—
317C22×#67—51no—
318C22×#67—51no—
319C22×#67—108no—
320C22×#67C2×D511yescharacteristic
321C22×#67C2×D511yescharacteristic, complemented
322C23×Dic3—51no—
323C23×Dic3—51no—
324C2×#237—58no—
325C2×#237—108no—
326C22×D12—51no—
327C22×D12C2×D511yescharacteristic, complemented
328C22×C4×D3C2×D511yescharacteristic, complemented
329C22×Dic6—51no—
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×#217—51no—
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)⋊C4—51no—
346C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
347C2×Dic3⋊C4—51no—
348C2×Dic3⋊C4C2×D511yescharacteristic, complemented
349C2×C4×Dic3—51no—
350C2×C4×Dic3—51no—
351#885—58no—
352#885—58no—
353#884—58no—
354#884C2×D518yescomplemented
355#882—58no—
356#877—58no—
357C24×C5—31no—
358C24×C5—31no—
359C24×C5C22×D311yescharacteristic
360C23×D5—24no—
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×D4—34no—
373C2×C5×D4—34no—
374C2×C5×D4—34no—
375C2×C5×D4—64no—
376C2×C5×D4—122no—
377C2×C5×D4—122no—
378C22×C4×C5—31no—
379C22×C4×C5—31no—
380C22×C4×C5—34no—
381C22×C4×C5—64no—
382C22×C4×C5C22×D311yescharacteristic
383C22×C4×C5C22×D311yescharacteristic
384C2×C22⋊D5—34no—
385C2×C22⋊D5—34no—
386C2×C22⋊D5—34no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—34no—
390C2×C22⋊D5—34no—
391C2×C22⋊D5—42no—
392C2×C22⋊D5—64no—
393C2×C22⋊D5—64no—
394C2×C22⋊D5—64no—
395C2×C22⋊D5—64no—
396C2×C22⋊D5—122no—
397C2×C22⋊D5—122no—
398C2×C22⋊D5—122no—
399C2×C22⋊D5C22×D314yescomplemented
400C22×Dic5—31no—
401C22×Dic5—31no—
402C22×Dic5—31no—
403C22×Dic5C22×D311yescharacteristic
404D4×D5—632no—
405#709—632no—
406C2×D20—24no—
407C2×D20—34no—
408C2×D20—34no—
409C2×D20—42no—
410C2×D20—64no—
411C2×D20—122no—
412C2×D20C22×D314yes—
413C2×D20C22×D314yescomplemented
414C2×C4×D5—38no—
415C2×C4×D5—34no—
416C2×C4×D5—34no—
417C2×C4×D5—64no—
418C2×Dic10—34no—
419C2×Dic10—64no—
420C5×C4⋊C4—34no—
421C5×C22⋊C4—34no—
422C5×C22⋊C4C22×D314yescomplemented
423C22⋊Dic5—34no—
424C22⋊Dic5—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685C22×D314yes—
430#685C22×D314yescomplemented
431C4⋊Dic5—34no—
432C4×Dic5—34no—
433C4×Dic5—34no—
434C22×#41—151no—
435C23×D4—151no—
436#535—1516no—
437C2×#127—151no—
438C2×#127—151no—
439C2×#124—151no—
440C2×#124—151no—
441C2×#121—31no—
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—44no—
462C2×C5×D3—22no—
463C2×C5×D3—22no—
464C2×C5×D3—22no—
465C2×C5×D3—22no—
466C2×C5×D3—22no—
467C2×C5×D3—22no—
468C2×C5×D3—44no—
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—
487Dic15—22no—
488Dic15C22×D414yes—
489C3×Dic5—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—54no—
502C23×D3—104no—
503C23×D3—202no—
504C23×D3—202no—
505C23×D3C22×D511yescharacteristic
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—42no—
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—1032no—
527C2×#67—104no—
528C2×#67—104no—
529C2×#67—104no—
530C2×#67—104no—
531C2×#67—104no—
532C2×#67—202no—
533C2×#67—202no—
534C2×#67—202no—
535C2×#67C22×D514yes—
536C2×#67C22×D514yescomplemented
537C22×Dic3—51no—
538C22×Dic3—58no—
539C22×Dic3—54no—
540C22×Dic3—51no—
541C22×Dic3—51no—
542C22×Dic3—54no—
543C22×Dic3—104no—
544C22×Dic3C22×D511yescharacteristic
545C22×Dic3C22×D511yescharacteristic
546#237—1032no—
547C2×D12—42no—
548C2×D12—54no—
549C2×D12—202no—
550C2×D12C22×D514yescomplemented
551C2×C4×D3—24no—
552C2×C4×D3C22×D514yescomplemented
553C2×Dic6—54no—
554C2×Dic6—104no—
555C3×C22⋊C4—54no—
556C3×C22⋊C4—54no—
557C3×C22⋊C4C22×D514yescomplemented
558#217—54no—
559#217—54no—
560#217—54no—
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4C22×D514yescomplemented
565Dic3⋊C4—54no—
566Dic3⋊C4C22×D514yescomplemented
567C4×Dic3—54no—
568C4×Dic3—54no—
569C23×C5—22no—
570C23×C5—22no—
571C23×C5—22no—
572C23×C5—32no—
573C23×C5—32no—
574C23×C5—62no—
575C23×C5—62no—
576C23×C5—62no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5—62no—
580C23×C5C23×D312yes—
581C23×C5C23×D311yescharacteristic
582C22×D5—22no—
583C22×D5—22no—
584C22×D5—22no—
585C22×D5—22no—
586C22×D5—22no—
587C22×D5—22no—
588C22×D5—22no—
589C22×D5—22no—
590C22×D5—28no—
591C22×D5—32no—
592C22×D5—44no—
593C22×D5—44no—
594C22×D5—416no—
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×D4—68no—
607C5×D4—124no—
608C5×D4—124no—
609C2×C4×C5—22no—
610C2×C4×C5—22no—
611C2×C4×C5—34no—
612C2×C4×C5—32no—
613C2×C4×C5—32no—
614C2×C4×C5—68no—
615C2×C4×C5—62no—
616C2×C4×C5C23×D312yes—
617C2×C4×C5C23×D312yes—
618C22⋊D5—44no—
619C22⋊D5—68no—
620C22⋊D5—68no—
621C22⋊D5—68no—
622C22⋊D5—68no—
623C22⋊D5—124no—
624C22⋊D5—124no—
625C22⋊D5—124no—
626C2×Dic5—22no—
627C2×Dic5—34no—
628C2×Dic5—32no—
629C2×Dic5—32no—
630C2×Dic5—32no—
631C2×Dic5—62no—
632C2×Dic5—62no—
633C2×Dic5C23×D312yes—
634D20—28no—
635D20—44no—
636D20—68no—
637D20—124no—
638C4×D5—316no—
639C4×D5—68no—
640Dic10—68no—
641C25—51no—
642C25—151no—
643C2×#41—158no—
644C2×#41—308no—
645C22×Q8—151no—
646C22×D4—31no—
647C22×D4—31no—
648C22×D4—31no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—51no—
652C22×D4—151no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—158no—
656C22×D4—151no—
657C22×D4—151no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—151no—
662C22×D4—308no—
663C23×C4—31no—
664C23×C4—151no—
665C23×C4—151no—
666#127—158no—
667#127—158no—
668#124—158no—
669#124—158no—
670#121—38no—
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—31no—
680C2×C4⋊C4—151no—
681C2×C22⋊C4—31no—
682C2×C22⋊C4—51no—
683C2×C22⋊C4—51no—
684C2×C22⋊C4—151no—
685C2×C22⋊C4—151no—
686C2×C22⋊C4—151no—
687C2×C22⋊C4—151no—
688C2×C22⋊C4—151no—
689C2×C22⋊C4—151no—
690C2×C22⋊C4D3×D511yescharacteristic, complemented
691C2×C42—151no—
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—
699C3×D5—24no—
700C3×D5—42no—
701C3×D5—42no—
702C5×D3—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—22no—
729C22×D3—22no—
730C22×D3—22no—
731C22×D3—52no—
732C22×D3—108no—
733C22×D3—102no—
734C22×D3—102no—
735C22×D3—102no—
736C22×D3—204no—
737C22×D3—204no—
738C22×D3—2016no—
739C22×D3C23×D512yes—
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—44no—
752#67—108no—
753#67—108no—
754#67—108no—
755#67—108no—
756#67—108no—
757#67—204no—
758#67—204no—
759#67—204no—
760C2×Dic3—22no—
761C2×Dic3—54no—
762C2×Dic3—52no—
763C2×Dic3—516no—
764C2×Dic3—52no—
765C2×Dic3—52no—
766C2×Dic3—102no—
767C2×Dic3—102no—
768C2×Dic3—108no—
769C2×Dic3D4×D514yes—
770C2×Dic3C23×D512yes—
771C2×Dic3C23×D512yes—
772D12—44no—
773D12—204no—
774C4×D3—28no—
775Dic6—108no—
776C22×C5—22no—
777C22×C5—22no—
778C22×C5—22no—
779C22×C5—44no—
780C22×C5—62no—
781C22×C5—62no—
782C22×C5—62no—
783C22×C5—62no—
784C22×C5—62no—
785C22×C5—62no—
786C22×C5—124no—
787C22×C5—124no—
788C22×C5C2×D3×D412yes—
789C22×C5#100412yes—
790C22×C5#100412yes—
791C22×C5C24×D311yescharacteristic
792C2×D5—22no—
793C2×D5—22no—
794C2×D5—28no—
795C2×D5—22no—
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—22no—
799C2×D5—22no—
800C2×D5—22no—
801C2×D5—416no—
802C2×D5—44no—
803C2×D5—44no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—1216no—
808C2×D5—124no—
809C2×D5C2×D3×D414yes—
810C4×C5—22no—
811C4×C5—22no—
812C4×C5—34no—
813C4×C5—62no—
814Dic5—22no—
815Dic5—34no—
816Dic5—62no—
817Dic5—62no—
818C24—31no—
819C24—31no—
820C24—51no—
821C24—51no—
822C24—51no—
823C24—54no—
824C24—104no—
825C24—154no—
826C24—151no—
827C24—202no—
828C24—202no—
829C24—304no—
830C24—602no—
831C24—602no—
832C24C2×D3×D511yescharacteristic
833#41—3032no—
834C2×Q8—154no—
835C2×Q8—304no—
836C2×D4—34no—
837C2×D4—34no—
838C2×D4—34no—
839C2×D4—54no—
840C2×D4—54no—
841C2×D4—54no—
842C2×D4—64no—
843C2×D4—104no—
844C2×D4—122no—
845C2×D4—122no—
846C2×D4—154no—
847C2×D4—154no—
848C2×D4—154no—
849C2×D4—154no—
850C2×D4—154no—
851C2×D4—154no—
852C2×D4—154no—
853C2×D4—154no—
854C2×D4—154no—
855C2×D4—202no—
856C2×D4—202no—
857C2×D4—304no—
858C2×D4—3032no—
859C2×D4—304no—
860C2×D4—304no—
861C2×D4—304no—
862C2×D4—304no—
863C2×D4—602no—
864C2×D4—602no—
865C2×D4—602no—
866C2×D4—602no—
867C22×C4—31no—
868C22×C4—31no—
869C22×C4—34no—
870C22×C4—51no—
871C22×C4—64no—
872C22×C4—154no—
873C22×C4—158no—
874C22×C4—154no—
875C22×C4—151no—
876C22×C4—151no—
877C22×C4—151no—
878C22×C4—304no—
879C22×C4C2×D3×D511yescharacteristic
880C22×C4C2×D3×D511yescharacteristic
881C4⋊C4—34no—
882C4⋊C4—154no—
883C22⋊C4—34no—
884C22⋊C4—54no—
885C22⋊C4—54no—
886C22⋊C4—154no—
887C22⋊C4—154no—
888C22⋊C4—154no—
889C22⋊C4—154no—
890C22⋊C4—154no—
891C22⋊C4—154no—
892C22⋊C4C2×D3×D514yescomplemented
893C42—154no—
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#414412yes—
915C22×C3#414912yes—
916C22×C3C24×D511yescharacteristic
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—44no—
924C2×D3—44no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—102no—
928C2×D3—2016no—
929C2×D3—204no—
930C3×C4—22no—
931C3×C4—22no—
932C3×C4—102no—
933Dic3—22no—
934Dic3—54no—
935Dic3—102no—
936Dic3—102no—
937Dic3C2×D4×D514yes—
938C2×C5—42no—
939C2×C5—122no—
940C2×C5—122no—
941C2×C5#559214yescomplemented
942C2×C5C22×D3×D411yescharacteristic
943C2×C5C2×#100411yescharacteristic
944C2×C5C2×#100411yescharacteristic
945D5—24no—
946D5—42no—
947D5—42no—
948D5—122no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—32no—
953C23—32no—
954C23—54no—
955C23—52no—
956C23—52no—
957C23—52no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—62no—
962C23—62no—
963C23—62no—
964C23—108no—
965C23—102no—
966C23—102no—
967C23—102no—
968C23—102no—
969C23—102no—
970C23—102no—
971C23—102no—
972C23—102no—
973C23—152no—
974C23—204no—
975C23—204no—
976C23—2016no—
977C23—308no—
978C23—302no—
979C23—302no—
980C23—302no—
981C23—604no—
982C23—604no—
983C23—6016no—
984C23C22×D3×D512yes—
985C23C22×D3×D511yescharacteristic
986Q8—308no—
987D4—68no—
988D4—108no—
989D4—124no—
990D4—124no—
991D4—204no—
992D4—204no—
993D4—308no—
994D4—308no—
995D4—308no—
996D4—308no—
997D4—308no—
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—52no—
1008C2×C4—68no—
1009C2×C4—62no—
1010C2×C4—102no—
1011C2×C4—1516no—
1012C2×C4—154no—
1013C2×C4—152no—
1014C2×C4—152no—
1015C2×C4—152no—
1016C2×C4—308no—
1017C2×C4—302no—
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#6594114yescomplemented
1026C2×C3C22×D4×D511yescharacteristic
1027C2×C3C2×#414411yescharacteristic
1028C2×C3C2×#414911yescharacteristic
1029D3—42no—
1030D3—42no—
1031D3—202no—
1032C5C2×#559211yescharacteristic, complemented, Sylow
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—44no—
1037C22—54no—
1038C22—62no—
1039C22—62no—
1040C22—62no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—108no—
1045C22—102no—
1046C22—102no—
1047C22—102no—
1048C22—102no—
1049C22—102no—
1050C22—102no—
1051C22—102no—
1052C22—102no—
1053C22—124no—
1054C22—124no—
1055C22—2016no—
1056C22—204no—
1057C22—204no—
1058C22—302no—
1059C22—302no—
1060C22—302no—
1061C22—6016no—
1062C22—604no—
1063C22#9201712yes—
1064C22D3×D4×D512yes—
1065C22#9202512yes—
1066C22C23×D3×D511yescharacteristic
1067C4—22no—
1068C4—22no—
1069C4—34no—
1070C4—62no—
1071C4—102no—
1072C4—154no—
1073C4—302no—
1074C4—302no—
1075C3C2×#6594111yescharacteristic, complemented, Sylow
1076C2—42no—
1077C2—104no—
1078C2—122no—
1079C2—122no—
1080C2—202no—
1081C2—202no—
1082C2—602no—
1083C2#1175322314yesdirect product factor
1084C2C2×#9201711yescharacteristic
1085C2C2×D3×D4×D511yescharacteristic
1086C2C2×#9202511yescharacteristic
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×#6765C2semidirect
3. C2×#91774C2semidirect
4. C2×C5×#884C2semidirect
5. C2×C3×#4028C2semidirect
6. C2×#91567C2semidirect
7. C2×#91563C2semidirect
8. C2×#91549C2semidirect
9. C2×#91475C2semidirect
10. C2×#91474C2semidirect
11. C2×#91463C2semidirect
12. C2×#91462C2semidirect
13. C2×#91454C2semidirect
14. C2×#91409C2semidirect
15. C2×#91394C2semidirect
16. #11753223C2direct (N × H)
21. C22×Dic30C22semidirect
23. C22×C5×#67C22semidirect
24. C22×C5×D12C22semidirect
25. C22×C4×C5×D3C22semidirect
26. C22×C3×C22⋊D5C22semidirect
28. C22×C3×D20C22semidirect
30. C2×D5×#67C22semidirect
31. C22×#1203C22semidirect
33. C22×#1202C22semidirect
36. C22×#1201C22semidirect
37. C22×#1201C22semidirect
38. C22×#1201C22semidirect
40. C22×D5×Dic3C22semidirect
42. C2×#6765C22semidirect
43. C2×C3×C5×C22⋊C4C22semidirect
44. C2×#6719C22semidirect
45. C2×#6714C22semidirect
46. C2×#6714C22semidirect
47. C2×C4×Dic15C22semidirect
48. #91774C22semidirect
49. C2×C5×(C2×D3)⋊C4C22semidirect
50. C2×C5×Dic3⋊C4C22semidirect
51. C5×#884C22semidirect
53. C2×C3×#685C22semidirect
54. C3×#4028C22semidirect
55. #91567C22semidirect
56. #91563C22semidirect
57. #91549C22semidirect
58. C2×Dic3⋊Dic5C22semidirect
59. C2×(C2×D3)⋊Dic5C22semidirect
61. C2×#6665C22semidirect
62. C2×Dic3×Dic5C22semidirect
63. #91475C22semidirect
64. #91474C22semidirect
65. #91463C22semidirect
66. #91462C22semidirect
67. #91454C22semidirect
68. #91409C22semidirect
69. #91394C22semidirect
86. C2×#4028D3semidirect
110. C2×Dic30C23semidirect
114. C2×C5×#67C23semidirect
118. C2×C5×D12C23semidirect
120. C2×C4×C5×D3C23semidirect
122. C2×C3×C22⋊D5C23semidirect
127. C2×C3×D20C23semidirect
130. C2×#1203C23semidirect
134. C2×#1202C23semidirect
142. C2×#1201C23semidirect
143. C2×#1201C23semidirect
144. C2×#1201C23semidirect
146. C2×D5×Dic3D4semidirect
148. C2×D5×Dic3C23semidirect
150. C3×C5×C22⋊C4C23semidirect
151. #6719C23semidirect
152. #6714C23semidirect
153. #6714C23semidirect
154. C4×Dic15C23semidirect
155. C5×(C2×D3)⋊C4C23semidirect
156. C5×Dic3⋊C4C23semidirect
158. C3×#685C23semidirect
159. Dic3⋊Dic5C23semidirect
160. (C2×D3)⋊Dic5C23semidirect
162. #6665C23semidirect
163. Dic3×Dic5C23semidirect
177. C2×#884D5semidirect
193. C22×C22⋊D5C2×D3semidirect
201. C22×D20C2×D3semidirect
208. C2×C5×C22⋊C4C2×D3semidirect
222. C2×#685C2×D3semidirect
231. #4028C2×D3semidirect
304. D5×Dic3C2×D4semidirect
321. C22×#67C2×D5semidirect
327. C22×D12C2×D5semidirect
328. C22×C4×D3C2×D5semidirect
333. C2×C3×C22⋊C4C2×D5semidirect
346. C2×(C2×D3)⋊C4C2×D5semidirect
348. C2×Dic3⋊C4C2×D5semidirect
354. #884C2×D5semidirect
399. C2×C22⋊D5C22×D3semidirect
413. C2×D20C22×D3semidirect
422. C5×C22⋊C4C22×D3semidirect
430. #685C22×D3semidirect
536. C2×#67C22×D5semidirect
550. C2×D12C22×D5semidirect
552. C2×C4×D3C22×D5semidirect
557. C3×C22⋊C4C22×D5semidirect
564. (C2×D3)⋊C4C22×D5semidirect
566. Dic3⋊C4C22×D5semidirect
690. C2×C22⋊C4D3×D5semidirect
694. C2×C3×C5#535semidirect
892. C22⋊C4C2×D3×D5semidirect
895. C3×C5C2×#535semidirect
941. C2×C5#5592semidirect
1025. C2×C3#65941semidirect
1032. C5C2×#5592semidirect
1075. C3C2×#65941semidirect
1083. C2#11753223direct (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×#67652
C2×#917742
C2×C5×#8842
C2×C3×#40282
C2×#915672
C2×#915632
C2×#915492
C2×#914752
C2×#914742
C2×#914632
C2×#914622
C2×#914542
C2×#914092
C2×#913942
#117532232
C2×#659413
C2×#55925