Finite Group Databasebeta

← C2×#11755051 #14480420

Subgroups — C2×#11755051 #14480420

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×#6790C211yesmaximal, characteristic, complemented
2C22×#6779C211yesmaximal, characteristic, complemented
3C2×#91826C211yesmaximal, characteristic, complemented
4C2×C5×#939C211yesmaximal, characteristic, complemented
5C2×C3×#4086C211yesmaximal, characteristic, complemented
6C2×#91577C211yesmaximal, characteristic, complemented
7C2×#91572C211yesmaximal, characteristic, complemented
8C2×#91569C211yesmaximal, characteristic, complemented
9C2×#91567C211yesmaximal, characteristic, complemented
10C2×#91549C211yesmaximal, characteristic, complemented
11C2×#91534C211yesmaximal, characteristic, complemented
12#11755051C2116yesmaximal, direct product factor
13C2×#91474C211yesmaximal, characteristic, complemented
14C2×#91409C211yesmaximal, characteristic, complemented
15C2×#91402C211yesmaximal, characteristic, complemented
16C2×#91350C211yesmaximal, characteristic, complemented
17C2×#65941—31nomaximal, Hall
18C24×D15C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×C3×C5×D4C2211yescharacteristic, complemented
21C22×#1220C2211yescharacteristic
22C22×#1220C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic, complemented
25C23×C5×Dic3C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×C22⋊D5C2211yescharacteristic, complemented
28C22×C3×C22⋊D5C2211yescharacteristic, complemented
29C22×C3×C22⋊D5C2211yescharacteristic, complemented
30C22×C3×D20C2211yescharacteristic, complemented
31C2×#6790—28no—
32C2×#6790C2218yescomplemented
33C22×#1204C2211yescharacteristic, complemented
34C22×#1203C2211yescharacteristic
35C22×#1202C2211yescharacteristic
36C22×#1202C2211yescharacteristic
37C22×#1202C2211yescharacteristic, complemented
38C22×#1201C2211yescharacteristic, complemented
39C22×#1200C2211yescharacteristic
40C2×#6779—28no—
41C2×#6779C2218yescomplemented
42C22×D5×Dic3C2211yescharacteristic, complemented
43C2×#6719C2211yescharacteristic, complemented
44#91826C2218yescomplemented
45C2×#6714C2211yescharacteristic
46C2×#6714C2211yescharacteristic, complemented
47C2×C5×#217C2211yescharacteristic, complemented
48C5×#939C2218yescomplemented
49C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
51C3×#4086C2218yescomplemented
52C2×C3×C4×Dic5C2211yescharacteristic, complemented
53#91577C2218yescomplemented
54#91572C2218yescomplemented
55#91569C2218yescomplemented
56#91567C2218yescomplemented
57#91549C2218yescomplemented
58C2×Dic3⋊Dic5C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic
60C2×#6667C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
62C2×#6665C2211yescharacteristic, complemented
63C2×#6665C2211yescharacteristic, complemented
64#91534C2218yescomplemented
65C2×Dic3×Dic5C2211yescharacteristic, complemented
66#91474C2218yescomplemented
67#91409C2218yescomplemented
68#91402C2218yescomplemented
69#91350C2218yescomplemented
70C2×#5715—51nomaximal, Hall
71C22×D4×D5—31no—
72C22×#709—31no—
73C2×C5×#121—31no—
74C2×#4086—31no—
75C2×#4086D311yescharacteristic, complemented
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×#4028—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15—24no—
90C23×D15—42no—
91C23×D15—42no—
92C23×D15C2311yescharacteristic
93C23×D15C2311yescharacteristic
94C23×D15C2314yes—
95C23×C5×D3C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C23×C3×D5C2311yescharacteristic
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5—42no—
101C22×D3×D5C2314yes—
102C2×C3×C5×D4—42no—
103C2×C3×C5×D4C2314yescomplemented
104C22×C3×C4×C5C2311yescharacteristic
105C2×#1220—24no—
106C2×#1220—42no—
107C2×#1220C2314yes—
108C2×#1220C2314yescomplemented
109C22×Dic15C2311yescharacteristic
110C22×Dic15C2311yescharacteristic
111C2×C5×#67—24no—
112C2×C5×#67—42no—
113C2×C5×#67C2314yes—
114C2×C5×#67C2314yescomplemented
115C22×C5×Dic3—24no—
116C22×C5×Dic3C2311yescharacteristic
117C22×C5×Dic3C2311yescharacteristic
118C22×C5×Dic3C2311yescharacteristic
119C22×C5×Dic3C2314yescomplemented
120C2×C3×C22⋊D5—24no—
121C2×C3×C22⋊D5—24no—
122C2×C3×C22⋊D5—42no—
123C2×C3×C22⋊D5—42no—
124C2×C3×C22⋊D5C2314yes—
125C2×C3×C22⋊D5C2314yescomplemented
126C2×C3×C22⋊D5C2314yescomplemented
127C2×C3×C22⋊D5C2314yescomplemented
128C22×C3×Dic5C2311yescharacteristic
129C22×C3×Dic5C2311yescharacteristic
130C2×C3×D20—42no—
131C2×C3×D20C2314yescomplemented
132#6790—232no—
133C2×#1204—24no—
134C2×#1204C2314yescomplemented
135C2×#1203—24no—
136C2×#1203C2314yes—
137C2×#1202—24no—
138C2×#1202—24no—
139C2×#1202—42no—
140C2×#1202C2314yes—
141C2×#1202C2314yes—
142C2×#1202C2314yescomplemented
143C2×#1201—42no—
144C2×#1201C2314yescomplemented
145C2×#1200D418yescomplemented
146C2×#1200C2314yes—
147#6779—232no—
148C2×D5×Dic3—24no—
149C2×D5×Dic3C2314yescomplemented
150#6719C2314yescomplemented
151#6714C2314yes—
152#6714C2314yescomplemented
153C5×#217C2314yescomplemented
154C5×(C2×D3)⋊C4C2314yescomplemented
155C5×Dic3⋊C4C2314yescomplemented
156C3×C4×Dic5C2314yescomplemented
157Dic3⋊Dic5C2314yescomplemented
158#6667C2314yes—
159#6667C2314yescomplemented
160(C2×D3)⋊Dic5C2314yescomplemented
161#6665C2314yescomplemented
162#6665C2314yescomplemented
163Dic3×Dic5C2314yescomplemented
164C22×#237—51no—
165C22×D3×D4—51no—
166C2×C3×#127—51no—
167C2×#940—51no—
168C2×#939—51no—
169C2×#939—51no—
170C2×#939—51no—
171C2×#939D511yescharacteristic, complemented
172C2×#937—51no—
173C2×#937—51no—
174C2×#937—51no—
175C2×#937—51no—
176C2×#936—51no—
177#5715—516no—
178C2×#875—51no—
179C2×#872—51no—
180C24×D5—31no—
181C24×D5—31no—
182C22×C5×D4—31no—
183C22×C5×D4—31no—
184C22×C5×D4C2×D311yescharacteristic, complemented
185C23×C4×C5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5—31no—
189C22×C22⋊D5—31no—
190C22×C22⋊D5C2×D311yescharacteristic
191C22×C22⋊D5C2×D311yescharacteristic, complemented
192C22×C22⋊D5C2×D311yescharacteristic, complemented
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×D20—31no—
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⋊C4—31no—
209C2×C22⋊Dic5—31no—
210C2×C22⋊Dic5—31no—
211#4086—38no—
212#4086C2×D318yescomplemented
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×#685—31no—
222C2×#685—31no—
223C2×C4⋊Dic5—31no—
224C2×C4×Dic5—31no—
225C2×C4×Dic5C2×D311yescharacteristic, complemented
226#4041—38no—
227#4038—38no—
228#4031—38no—
229#4031—38no—
230#4028—38no—
231#4028—38no—
232C2×#535—151noSylow
233C23×C3×C5—22no—
234C23×C3×C5—22no—
235C23×C3×C5—22no—
236C23×C3×C5—22no—
237C23×C3×C5—22no—
238C23×C3×C5—22no—
239C23×C3×C5C2412yes—
240C23×C3×C5C2412yes—
241C23×C3×C5C2411yescharacteristic
242C22×D15—22no—
243C22×D15—22no—
244C22×D15—22no—
245C22×D15—22no—
246C22×D15—22no—
247C22×D15—28no—
248C22×D15—44no—
249C22×D15—44no—
250C22×D15—416no—
251C22×D15C2×D414yes—
252C22×D15C2412yes—
253C22×D15C2412yes—
254C22×C5×D3—22no—
255C22×C5×D3—22no—
256C22×C5×D3—22no—
257C22×C5×D3C2412yes—
258C22×C3×D5—22no—
259C22×C3×D5—22no—
260C22×C3×D5—22no—
261C22×C3×D5—22no—
262C22×C3×D5—22no—
263C22×C3×D5—22no—
264C22×C3×D5C2412yes—
265C22×C3×D5C2412yes—
266C2×D3×D5—28no—
267C2×D3×D5—44no—
268C2×D3×D5—44no—
269C2×D3×D5—416no—
270C3×C5×D4—44no—
271C2×C3×C4×C5—22no—
272C2×C3×C4×C5C2412yes—
273#1220—28no—
274#1220—44no—
275C2×Dic15—22no—
276C2×Dic15—22no—
277C2×Dic15C2412yes—
278C2×Dic15C2412yes—
279C5×#67—28no—
280C5×#67—44no—
281C2×C5×Dic3—22no—
282C2×C5×Dic3—22no—
283C2×C5×Dic3—28no—
284C2×C5×Dic3C2×D414yes—
285C2×C5×Dic3C2412yes—
286C2×C5×Dic3C2412yes—
287C2×C5×Dic3C2412yes—
288C3×C22⋊D5—28no—
289C3×C22⋊D5—28no—
290C3×C22⋊D5—44no—
291C3×C22⋊D5—44no—
292C2×C3×Dic5—22no—
293C2×C3×Dic5C2×D414yes—
294C2×C3×Dic5C2412yes—
295C2×C3×Dic5C2412yes—
296C3×D20—44no—
297#1204—28no—
298#1203—28no—
299#1202—28no—
300#1202—28no—
301#1202—44no—
302#1201—44no—
303#1200C2×D4116yescomplemented
304D5×Dic3—28no—
305C24×D3—51no—
306C24×D3—51no—
307C22×C3×D4—51no—
308C22×C3×D4—51no—
309C22×C3×D4—51no—
310C22×C3×D4—51no—
311C22×C3×D4—51no—
312C22×C3×D4C2×D511yescharacteristic, complemented
313C22×#67—51no—
314C22×#67—51no—
315C22×#67—51no—
316C22×#67—51no—
317C22×#67—51no—
318C22×#67—51no—
319C22×#67C2×D511yescharacteristic
320C22×#67C2×D511yescharacteristic, complemented
321C23×Dic3—51no—
322C23×Dic3C2×D511yescharacteristic, complemented
323C2×#237—58no—
324C2×#237—108no—
325C2×D3×D4—58no—
326C2×D3×D4—108no—
327C22×D12—51no—
328C22×C4×D3—51no—
329C22×Dic6—51no—
330C3×#127—58no—
331C2×C3×C42—51no—
332C2×#217—51no—
333C2×#217—51no—
334C2×#217—51no—
335C2×#217C2×D511yescharacteristic, complemented
336#940—58no—
337#939—58no—
338#939—58no—
339#939—58no—
340#939C2×D518yescomplemented
341#937—58no—
342#937—58no—
343#937—58no—
344#937—58no—
345#936—58no—
346C2×(C2×D3)⋊C4—51no—
347C2×(C2×D3)⋊C4—51no—
348C2×(C2×D3)⋊C4—51no—
349C2×(C2×D3)⋊C4—51no—
350C2×(C2×D3)⋊C4—51no—
351C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
352C2×Dic3⋊C4—51no—
353C2×Dic3⋊C4C2×D511yescharacteristic, complemented
354C2×C4×Dic3—51no—
355#875—58no—
356#872—58no—
357C24×C5—31no—
358C24×C5C22×D311yescharacteristic
359C24×C5C22×D311yescharacteristic
360C23×D5—31no—
361C23×D5—31no—
362C23×D5—34no—
363C23×D5—34no—
364C23×D5—64no—
365C23×D5—64no—
366C23×D5—122no—
367C23×D5—122no—
368C23×D5—122no—
369C23×D5—122no—
370C23×D5C22×D311yescharacteristic
371C23×D5C22×D311yescharacteristic
372C2×C5×D4—34no—
373C2×C5×D4—34no—
374C2×C5×D4—42no—
375C2×C5×D4—64no—
376C2×C5×D4—122no—
377C2×C5×D4C22×D314yescomplemented
378C22×C4×C5—31no—
379C22×C4×C5—31no—
380C22×C4×C5—31no—
381C22×C4×C5—34no—
382C22×C4×C5—64no—
383C22×C4×C5C22×D311yescharacteristic
384C2×C22⋊D5—24no—
385C2×C22⋊D5—24no—
386C2×C22⋊D5—34no—
387C2×C22⋊D5—34no—
388C2×C22⋊D5—34no—
389C2×C22⋊D5—34no—
390C2×C22⋊D5—42no—
391C2×C22⋊D5—42no—
392C2×C22⋊D5—64no—
393C2×C22⋊D5—64no—
394C2×C22⋊D5—122no—
395C2×C22⋊D5—122no—
396C2×C22⋊D5C22×D314yes—
397C2×C22⋊D5C22×D314yescomplemented
398C2×C22⋊D5C22×D314yescomplemented
399C2×C22⋊D5C22×D314yescomplemented
400C22×Dic5—31no—
401C22×Dic5—31no—
402C22×Dic5C22×D311yescharacteristic
403C22×Dic5C22×D311yescharacteristic
404D4×D5—632no—
405#709—632no—
406C2×D20—34no—
407C2×D20—34no—
408C2×D20—34no—
409C2×D20—42no—
410C2×D20—64no—
411C2×D20—64no—
412C2×D20—122no—
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⋊C4—34no—
423C22⋊Dic5—34no—
424C22⋊Dic5—34no—
425#685—34no—
426#685—34no—
427#685—34no—
428#685—34no—
429#685—34no—
430#685—34no—
431C4⋊Dic5—34no—
432C4×Dic5—34no—
433C4×Dic5C22×D314yescomplemented
434C22×#41—151no—
435C23×D4—151no—
436#535—1516no—
437C2×#127—51no—
438C2×#127—151no—
439C2×#124—151no—
440C2×#124—151no—
441C2×#121—31no—
442C2×#121—151no—
443C2×#121—151no—
444C2×#121—151no—
445C2×#120—151no—
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—22no—
454C22×C3×C5—22no—
455C22×C3×C5—22no—
456C22×C3×C5—44no—
457C22×C3×C5—44no—
458C22×C3×C5C22×D412yes—
459C22×C3×C5H(5,𝔽2)12yes—
460C22×C3×C5H(5,𝔽2)12yes—
461C22×C3×C5C2511yescharacteristic
462C2×D15—28no—
463C2×D15—22no—
464C2×D15—22no—
465C2×D15—22no—
466C2×D15—22no—
467C2×D15—22no—
468C2×D15—416no—
469C2×D15—44no—
470C2×D15C22×D414yes—
471C2×C5×D3—22no—
472C2×C5×D3—22no—
473C2×C5×D3—22no—
474C2×C5×D3—44no—
475C2×C3×D5—22no—
476C2×C3×D5—22no—
477C2×C3×D5—22no—
478C2×C3×D5—22no—
479C2×C3×D5—22no—
480C2×C3×D5—22no—
481C2×C3×D5—44no—
482C2×C3×D5—44no—
483D3×D5—416no—
484C3×C4×C5—22no—
485Dic15—22no—
486Dic15—22no—
487C3×Dic5—22no—
488C3×Dic5C22×D414yes—
489C5×Dic3—22no—
490C5×Dic3—22no—
491C5×Dic3C22×D414yes—
492C24×C3—51no—
493C24×C3—51no—
494C24×C3C22×D511yescharacteristic
495C24×C3C22×D511yescharacteristic
496C23×D3—51no—
497C23×D3—51no—
498C23×D3—54no—
499C23×D3—54no—
500C23×D3—104no—
501C23×D3—104no—
502C23×D3—202no—
503C23×D3—202no—
504C23×D3—202no—
505C23×D3—202no—
506C23×D3C22×D511yescharacteristic
507C2×C3×D4—42no—
508C2×C3×D4—54no—
509C2×C3×D4—54no—
510C2×C3×D4—54no—
511C2×C3×D4—54no—
512C2×C3×D4—54no—
513C2×C3×D4—104no—
514C2×C3×D4—104no—
515C2×C3×D4—202no—
516C2×C3×D4—202no—
517C2×C3×D4—202no—
518C2×C3×D4C22×D514yescomplemented
519C22×C3×C4—51no—
520C22×C3×C4—51no—
521C22×C3×C4C22×D511yescharacteristic
522C2×#67—24no—
523C2×#67—42no—
524C2×#67—54no—
525C2×#67—54no—
526C2×#67—54no—
527C2×#67—54no—
528C2×#67—54no—
529C2×#67—54no—
530C2×#67—104no—
531C2×#67—104no—
532C2×#67—104no—
533C2×#67—202no—
534C2×#67—202no—
535C2×#67—202no—
536C2×#67C22×D514yes—
537C2×#67C22×D514yescomplemented
538C22×Dic3—24no—
539C22×Dic3—51no—
540C22×Dic3—51no—
541C22×Dic3—54no—
542C22×Dic3—104no—
543C22×Dic3C22×D511yescharacteristic
544C22×Dic3C22×D511yescharacteristic
545C22×Dic3C22×D511yescharacteristic
546C22×Dic3C22×D514yescomplemented
547#237—1032no—
548D3×D4—1032no—
549C2×D12—54no—
550C2×D12—104no—
551C2×C4×D3—58no—
552C2×C4×D3—54no—
553C2×Dic6—54no—
554C2×Dic6—104no—
555C3×C42—54no—
556#217—54no—
557#217—54no—
558#217—54no—
559#217C22×D514yescomplemented
560(C2×D3)⋊C4—54no—
561(C2×D3)⋊C4—54no—
562(C2×D3)⋊C4—54no—
563(C2×D3)⋊C4—54no—
564(C2×D3)⋊C4—54no—
565(C2×D3)⋊C4C22×D514yescomplemented
566Dic3⋊C4—54no—
567Dic3⋊C4C22×D514yescomplemented
568C4×Dic3—54no—
569C23×C5—22no—
570C23×C5—22no—
571C23×C5—22no—
572C23×C5—22no—
573C23×C5—22no—
574C23×C5—22no—
575C23×C5—32no—
576C23×C5—62no—
577C23×C5—62no—
578C23×C5—62no—
579C23×C5C23×D312yes—
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—34no—
589C22×D5—32no—
590C22×D5—32no—
591C22×D5—68no—
592C22×D5—68no—
593C22×D5—62no—
594C22×D5—62no—
595C22×D5—62no—
596C22×D5—62no—
597C22×D5—62no—
598C22×D5—124no—
599C22×D5—124no—
600C22×D5—1216no—
601C22×D5—124no—
602C22×D5—124no—
603C22×D5—1216no—
604C22×D5C23×D312yes—
605C22×D5C23×D312yes—
606C5×D4—44no—
607C5×D4—68no—
608C5×D4—124no—
609C2×C4×C5—22no—
610C2×C4×C5—34no—
611C2×C4×C5—32no—
612C2×C4×C5—32no—
613C2×C4×C5—32no—
614C2×C4×C5—68no—
615C2×C4×C5—62no—
616C2×C4×C5—62no—
617C2×C4×C5C23×D312yes—
618C22⋊D5—28no—
619C22⋊D5—28no—
620C22⋊D5—44no—
621C22⋊D5—44no—
622C22⋊D5—68no—
623C22⋊D5—68no—
624C22⋊D5—124no—
625C22⋊D5—124no—
626C2×Dic5—22no—
627C2×Dic5—32no—
628C2×Dic5—32no—
629C2×Dic5—62no—
630C2×Dic5—62no—
631C2×Dic5D3×D414yes—
632C2×Dic5C23×D312yes—
633C2×Dic5C23×D312yes—
634D20—44no—
635D20—68no—
636D20—68no—
637D20—124no—
638C4×D5—316no—
639C4×D5—68no—
640Dic10—68no—
641C25—151no—
642C25—151no—
643C2×#41—158no—
644C2×#41—308no—
645C22×Q8—151no—
646C22×D4—31no—
647C22×D4—31no—
648C22×D4—51no—
649C22×D4—51no—
650C22×D4—51no—
651C22×D4—51no—
652C22×D4—51no—
653C22×D4—151no—
654C22×D4—151no—
655C22×D4—151no—
656C22×D4—151no—
657C22×D4—158no—
658C22×D4—151no—
659C22×D4—151no—
660C22×D4—151no—
661C22×D4—308no—
662C22×D4D3×D511yescharacteristic, complemented
663C23×C4—31no—
664C23×C4—151no—
665C23×C4—151no—
666#127—58no—
667#127—158no—
668#124—158no—
669#124—158no—
670#121—38no—
671#121—158no—
672#121—158no—
673#121—158no—
674#120—158no—
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—31no—
683C2×C22⋊C4—151no—
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⋊C4—151no—
691C2×C42—51no—
692C2×C42—151no—
693C2×C3×C5—42no—
694C2×C3×C5—42no—
695C2×C3×C5#53514yescomplemented
696C2×C3×C5C23×D411yescharacteristic
697C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
698C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
699D15—24no—
700D15—42no—
701C3×D5—42no—
702C3×D5—42no—
703C5×D3—42no—
704C23×C3—22no—
705C23×C3—22no—
706C23×C3—22no—
707C23×C3—22no—
708C23×C3—22no—
709C23×C3—22no—
710C23×C3—52no—
711C23×C3—52no—
712C23×C3—102no—
713C23×C3—102no—
714C23×C3—102no—
715C23×C3—102no—
716C23×C3—102no—
717C23×C3—102no—
718C23×C3C23×D512yes—
719C23×C3C23×D512yes—
720C23×C3C23×D511yescharacteristic
721C22×D3—22no—
722C22×D3—22no—
723C22×D3—22no—
724C22×D3—54no—
725C22×D3—52no—
726C22×D3—52no—
727C22×D3—108no—
728C22×D3—108no—
729C22×D3—102no—
730C22×D3—102no—
731C22×D3—102no—
732C22×D3—102no—
733C22×D3—102no—
734C22×D3—204no—
735C22×D3—204no—
736C22×D3—2016no—
737C22×D3—204no—
738C22×D3—204no—
739C22×D3—2016no—
740C22×D3C23×D512yes—
741C3×D4—44no—
742C3×D4—108no—
743C3×D4—108no—
744C3×D4—204no—
745C3×D4—204no—
746C3×D4—204no—
747C2×C3×C4—22no—
748C2×C3×C4—54no—
749C2×C3×C4—52no—
750C2×C3×C4—52no—
751C2×C3×C4—102no—
752C2×C3×C4C23×D512yes—
753#67—28no—
754#67—44no—
755#67—108no—
756#67—108no—
757#67—108no—
758#67—204no—
759#67—204no—
760#67—204no—
761C2×Dic3—22no—
762C2×Dic3—22no—
763C2×Dic3—28no—
764C2×Dic3—52no—
765C2×Dic3—52no—
766C2×Dic3—102no—
767C2×Dic3—102no—
768C2×Dic3—108no—
769C2×Dic3D4×D514yes—
770C2×Dic3C23×D512yes—
771C2×Dic3C23×D512yes—
772C2×Dic3C23×D512yes—
773D12—108no—
774C4×D3—516no—
775Dic6—108no—
776C22×C5—22no—
777C22×C5—22no—
778C22×C5—22no—
779C22×C5—22no—
780C22×C5—22no—
781C22×C5—22no—
782C22×C5—44no—
783C22×C5—44no—
784C22×C5—62no—
785C22×C5—62no—
786C22×C5—62no—
787C22×C5—124no—
788C22×C5C2×D3×D412yes—
789C22×C5#100412yes—
790C22×C5#100412yes—
791C22×C5C24×D311yescharacteristic
792C2×D5—22no—
793C2×D5—22no—
794C2×D5—22no—
795C2×D5—22no—
796C2×D5—22no—
797C2×D5—22no—
798C2×D5—34no—
799C2×D5—44no—
800C2×D5—44no—
801C2×D5—62no—
802C2×D5—62no—
803C2×D5—68no—
804C2×D5—62no—
805C2×D5—62no—
806C2×D5—62no—
807C2×D5—1216no—
808C2×D5—1216no—
809C2×D5—124no—
810C4×C5—22no—
811C4×C5—34no—
812C4×C5—62no—
813C4×C5—62no—
814Dic5—22no—
815Dic5—62no—
816Dic5—62no—
817Dic5C2×D3×D414yes—
818C24—31no—
819C24—51no—
820C24—51no—
821C24—154no—
822C24—151no—
823C24—151no—
824C24—154no—
825C24—304no—
826C24—304no—
827C24—602no—
828C24—602no—
829C24—602no—
830C24—602no—
831C24C2×D3×D511yescharacteristic
832C24C2×D3×D511yescharacteristic
833#41—3032no—
834C2×Q8—154no—
835C2×Q8—304no—
836C2×D4—34no—
837C2×D4—34no—
838C2×D4—42no—
839C2×D4—54no—
840C2×D4—54no—
841C2×D4—54no—
842C2×D4—54no—
843C2×D4—54no—
844C2×D4—64no—
845C2×D4—104no—
846C2×D4—104no—
847C2×D4—122no—
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—202no—
858C2×D4—304no—
859C2×D4—304no—
860C2×D4—304no—
861C2×D4—3032no—
862C2×D4—304no—
863C2×D4—602no—
864C2×D4—602no—
865C2×D4—602no—
866C2×D4C2×D3×D514yescomplemented
867C22×C4—31no—
868C22×C4—34no—
869C22×C4—31no—
870C22×C4—31no—
871C22×C4—51no—
872C22×C4—51no—
873C22×C4—64no—
874C22×C4—154no—
875C22×C4—158no—
876C22×C4—154no—
877C22×C4—151no—
878C22×C4—151no—
879C22×C4—304no—
880C22×C4C2×D3×D511yescharacteristic
881C4⋊C4—34no—
882C4⋊C4—154no—
883C22⋊C4—34no—
884C22⋊C4—34no—
885C22⋊C4—154no—
886C22⋊C4—154no—
887C22⋊C4—154no—
888C22⋊C4—154no—
889C22⋊C4—154no—
890C22⋊C4—154no—
891C22⋊C4—154no—
892C22⋊C4—154no—
893C42—54no—
894C42—154no—
895C3×C5C2×#53511yescharacteristic, complemented, Hall
896C22×C3—22no—
897C22×C3—22no—
898C22×C3—22no—
899C22×C3—22no—
900C22×C3—22no—
901C22×C3—22no—
902C22×C3—44no—
903C22×C3—44no—
904C22×C3—102no—
905C22×C3—102no—
906C22×C3—102no—
907C22×C3—102no—
908C22×C3—102no—
909C22×C3—102no—
910C22×C3—204no—
911C22×C3—204no—
912C22×C3C2×D4×D512yes—
913C22×C3#414412yes—
914C22×C3#414912yes—
915C22×C3C24×D511yescharacteristic
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—44no—
920C2×D3—54no—
921C2×D3—108no—
922C2×D3—102no—
923C2×D3—102no—
924C2×D3—102no—
925C2×D3—102no—
926C2×D3—102no—
927C2×D3—2016no—
928C2×D3—2016no—
929C2×D3—204no—
930C3×C4—22no—
931C3×C4—54no—
932C3×C4—102no—
933Dic3—22no—
934Dic3—22no—
935Dic3—102no—
936Dic3—102no—
937Dic3C2×D4×D514yes—
938C2×C5—42no—
939C2×C5—42no—
940C2×C5—122no—
941C2×C5#571514yescomplemented
942C2×C5C22×D3×D411yescharacteristic
943C2×C5C2×#100411yescharacteristic
944C2×C5C2×#100411yescharacteristic
945D5—42no—
946D5—42no—
947D5—64no—
948D5—122no—
949C23—22no—
950C23—22no—
951C23—22no—
952C23—22no—
953C23—22no—
954C23—22no—
955C23—32no—
956C23—52no—
957C23—52no—
958C23—62no—
959C23—62no—
960C23—62no—
961C23—102no—
962C23—102no—
963C23—102no—
964C23—102no—
965C23—102no—
966C23—102no—
967C23—154no—
968C23—152no—
969C23—152no—
970C23—308no—
971C23—308no—
972C23—302no—
973C23—302no—
974C23—302no—
975C23—302no—
976C23—302no—
977C23—604no—
978C23—604no—
979C23—6016no—
980C23—604no—
981C23—604no—
982C23—6016no—
983C23C22×D3×D512yes—
984C23C22×D3×D512yes—
985C23C22×D3×D511yescharacteristic
986Q8—308no—
987D4—44no—
988D4—68no—
989D4—108no—
990D4—108no—
991D4—124no—
992D4—204no—
993D4—204no—
994D4—204no—
995D4—308no—
996D4—308no—
997D4—308no—
998D4—308no—
999D4—604no—
1000D4—604no—
1001D4—604no—
1002C2×C4—22no—
1003C2×C4—34no—
1004C2×C4—32no—
1005C2×C4—32no—
1006C2×C4—32no—
1007C2×C4—54no—
1008C2×C4—52no—
1009C2×C4—52no—
1010C2×C4—68no—
1011C2×C4—62no—
1012C2×C4—62no—
1013C2×C4—102no—
1014C2×C4—1516no—
1015C2×C4—152no—
1016C2×C4—152no—
1017C2×C4—308no—
1018C2×C4—302no—
1019C2×C4—302no—
1020C2×C4C22×D3×D512yes—
1021C2×C3—42no—
1022C2×C3—42no—
1023C2×C3—202no—
1024C2×C3—202no—
1025C2×C3#6594114yescomplemented
1026C2×C3C22×D4×D511yescharacteristic
1027C2×C3C2×#414411yescharacteristic
1028C2×C3C2×#414911yescharacteristic
1029D3—42no—
1030D3—104no—
1031D3—202no—
1032C5C2×#571511yescharacteristic, complemented, Sylow
1033C22—22no—
1034C22—22no—
1035C22—22no—
1036C22—22no—
1037C22—22no—
1038C22—22no—
1039C22—44no—
1040C22—44no—
1041C22—62no—
1042C22—62no—
1043C22—62no—
1044C22—102no—
1045C22—102no—
1046C22—102no—
1047C22—102no—
1048C22—102no—
1049C22—102no—
1050C22—124no—
1051C22—154no—
1052C22—204no—
1053C22—204no—
1054C22—302no—
1055C22—308no—
1056C22—302no—
1057C22—302no—
1058C22—302no—
1059C22—302no—
1060C22—6016no—
1061C22—6016no—
1062C22—604no—
1063C22D3×D4×D512yes—
1064C22#9202612yes—
1065C22#9204912yes—
1066C22C23×D3×D511yescharacteristic
1067C4—22no—
1068C4—34no—
1069C4—54no—
1070C4—62no—
1071C4—62no—
1072C4—102no—
1073C4—302no—
1074C4—302no—
1075C3C2×#6594111yescharacteristic, complemented, Sylow
1076C2—42no—
1077C2—42no—
1078C2—122no—
1079C2—202no—
1080C2—202no—
1081C2—304no—
1082C2—602no—
1083C2#1175505114yesdirect product factor
1084C2C2×D3×D4×D511yescharacteristic
1085C2C2×#9202611yescharacteristic
1086C2C2×#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×#535
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×#6779C2semidirect
3. C2×#91826C2semidirect
4. C2×C5×#939C2semidirect
5. C2×C3×#4086C2semidirect
6. C2×#91577C2semidirect
7. C2×#91572C2semidirect
8. C2×#91569C2semidirect
9. C2×#91567C2semidirect
10. C2×#91549C2semidirect
11. C2×#91534C2semidirect
12. #11755051C2direct (N × H)
13. C2×#91474C2semidirect
14. C2×#91409C2semidirect
15. C2×#91402C2semidirect
16. C2×#91350C2semidirect
20. C22×C3×C5×D4C22semidirect
22. C22×#1220C22semidirect
24. C22×C5×#67C22semidirect
25. C23×C5×Dic3C22semidirect
27. C22×C3×C22⋊D5C22semidirect
28. C22×C3×C22⋊D5C22semidirect
29. C22×C3×C22⋊D5C22semidirect
30. C22×C3×D20C22semidirect
32. C2×#6790C22semidirect
33. C22×#1204C22semidirect
37. C22×#1202C22semidirect
38. C22×#1201C22semidirect
41. C2×#6779C22semidirect
42. C22×D5×Dic3C22semidirect
43. C2×#6719C22semidirect
44. #91826C22semidirect
46. C2×#6714C22semidirect
47. C2×C5×#217C22semidirect
48. C5×#939C22semidirect
49. C2×C5×(C2×D3)⋊C4C22semidirect
50. C2×C5×Dic3⋊C4C22semidirect
51. C3×#4086C22semidirect
52. C2×C3×C4×Dic5C22semidirect
53. #91577C22semidirect
54. #91572C22semidirect
55. #91569C22semidirect
56. #91567C22semidirect
57. #91549C22semidirect
58. C2×Dic3⋊Dic5C22semidirect
60. C2×#6667C22semidirect
61. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×#6665C22semidirect
63. C2×#6665C22semidirect
64. #91534C22semidirect
65. C2×Dic3×Dic5C22semidirect
66. #91474C22semidirect
67. #91409C22semidirect
68. #91402C22semidirect
69. #91350C22semidirect
75. C2×#4086D3semidirect
103. C2×C3×C5×D4C23semidirect
108. C2×#1220C23semidirect
114. C2×C5×#67C23semidirect
119. C22×C5×Dic3C23semidirect
125. C2×C3×C22⋊D5C23semidirect
126. C2×C3×C22⋊D5C23semidirect
127. C2×C3×C22⋊D5C23semidirect
131. C2×C3×D20C23semidirect
134. C2×#1204C23semidirect
142. C2×#1202C23semidirect
144. C2×#1201C23semidirect
145. C2×#1200D4semidirect
149. C2×D5×Dic3C23semidirect
150. #6719C23semidirect
152. #6714C23semidirect
153. C5×#217C23semidirect
154. C5×(C2×D3)⋊C4C23semidirect
155. C5×Dic3⋊C4C23semidirect
156. C3×C4×Dic5C23semidirect
157. Dic3⋊Dic5C23semidirect
159. #6667C23semidirect
160. (C2×D3)⋊Dic5C23semidirect
161. #6665C23semidirect
162. #6665C23semidirect
163. Dic3×Dic5C23semidirect
171. C2×#939D5semidirect
184. C22×C5×D4C2×D3semidirect
191. C22×C22⋊D5C2×D3semidirect
192. C22×C22⋊D5C2×D3semidirect
193. C22×C22⋊D5C2×D3semidirect
201. C22×D20C2×D3semidirect
212. #4086C2×D3semidirect
225. C2×C4×Dic5C2×D3semidirect
303. #1200C2×D4semidirect
312. C22×C3×D4C2×D5semidirect
320. C22×#67C2×D5semidirect
322. C23×Dic3C2×D5semidirect
335. C2×#217C2×D5semidirect
340. #939C2×D5semidirect
351. C2×(C2×D3)⋊C4C2×D5semidirect
353. C2×Dic3⋊C4C2×D5semidirect
377. C2×C5×D4C22×D3semidirect
397. C2×C22⋊D5C22×D3semidirect
398. C2×C22⋊D5C22×D3semidirect
399. C2×C22⋊D5C22×D3semidirect
413. C2×D20C22×D3semidirect
433. C4×Dic5C22×D3semidirect
518. C2×C3×D4C22×D5semidirect
537. C2×#67C22×D5semidirect
546. C22×Dic3C22×D5semidirect
559. #217C22×D5semidirect
565. (C2×D3)⋊C4C22×D5semidirect
567. Dic3⋊C4C22×D5semidirect
662. C22×D4D3×D5semidirect
695. C2×C3×C5#535semidirect
866. C2×D4C2×D3×D5semidirect
895. C3×C5C2×#535semidirect
941. C2×C5#5715semidirect
1025. C2×C3#65941semidirect
1032. C5C2×#5715semidirect
1075. C3C2×#65941semidirect
1083. C2#11755051direct (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×#67792
C2×#918262
C2×C5×#9392
C2×C3×#40862
C2×#915772
C2×#915722
C2×#915692
C2×#915672
C2×#915492
C2×#915342
#117550512
C2×#914742
C2×#914092
C2×#914022
C2×#913502
C2×#659413
C2×#57155