Finite Group Databasebeta

← C2×#11753238 #14482617

Subgroups — C2×#11753238 #14482617

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×D5×#67C211yesmaximal, characteristic, complemented
2C22×#6773C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×#885C211yesmaximal, characteristic, complemented
5C2×C3×D5×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#91564C211yesmaximal, characteristic, complemented
7C2×#91562C211yesmaximal, characteristic, complemented
8C2×#91557C211yesmaximal, characteristic, complemented
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×#91473C211yesmaximal, characteristic, complemented
11C2×#91448C211yesmaximal, characteristic, complemented
12C2×#91447C211yesmaximal, characteristic, complemented
13C2×C4×#1202C211yesmaximal, characteristic, complemented
14C2×#91421C211yesmaximal, characteristic, complemented
15C2×#91395C211yesmaximal, characteristic, complemented
16#11753238C2116yesmaximal, direct product factor
17C2×#66010—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×C4×D5C2211yescharacteristic, complemented
27C22×C3×C4×D5C2211yescharacteristic, complemented
28C2×D5×#67—28no—
29C2×D5×#67C2218yescomplemented
30C22×#1203C2211yescharacteristic, complemented
31C22×#1202C2211yescharacteristic
32C22×#1202C2211yescharacteristic
33C22×#1202C2211yescharacteristic, complemented
34C22×#1201C2211yescharacteristic
35C22×#1200C2211yescharacteristic, complemented
36C22×#1200C2211yescharacteristic, complemented
37C22×D5×Dic3C2211yescharacteristic
38C2×#6773—28no—
39C2×#6773C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6714C2211yescharacteristic, complemented
42C2×#6712C2211yescharacteristic, complemented
43#91773C2218yescomplemented
44C2×C5×#217C2211yescharacteristic, complemented
45C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C4×C5×Dic3C2211yescharacteristic, complemented
48C5×#885C2218yescomplemented
49C2×C3×C22⋊Dic5C2211yescharacteristic, complemented
50C2×C3×#685C2211yescharacteristic
51C2×C3×#685C2211yescharacteristic
52C3×D5×C22⋊C4C2218yescomplemented
53#91564C2218yescomplemented
54#91562C2218yescomplemented
55#91557C2218yescomplemented
56C2×Dic3⋊Dic5C2211yescharacteristic, complemented
57C2×Dic3⋊Dic5C2211yescharacteristic, complemented
58C2×#6668C2211yescharacteristic, complemented
59C2×#6667C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
61C2×#6665C2211yescharacteristic
62C2×#6665C2211yescharacteristic, complemented
63#91476C2218yescomplemented
64#91473C2218yescomplemented
65#91448C2218yescomplemented
66#91447C2218yescomplemented
67C4×#1202C2218yescomplemented
68#91421C2218yescomplemented
69#91395C2218yescomplemented
70C2×#5490—51nomaximal, Hall
71C22×#713—31no—
72C22×D4×D5—31no—
73C2×C5×#124—31no—
74C2×#4092—31no—
75C2×#4084—31no—
76#66010—316no—
77C2×#4030—31no—
78C2×#4030—31no—
79C2×#4029—31no—
80C2×#4029—31no—
81C2×#4028—31no—
82C2×#4028—31no—
83C2×D5×C22⋊C4—31no—
84C2×D5×C22⋊C4D311yescharacteristic, complemented
85C2×C4×D20—31no—
86C2×C4×D20—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5—24no—
92C23×C3×D5—24no—
93C23×C3×D5—42no—
94C23×C3×D5C2314yes—
95C23×C3×D5C2311yescharacteristic
96C23×C3×D5C2311yescharacteristic
97C22×D3×D5—24no—
98C22×D3×D5—24no—
99C22×D3×D5—42no—
100C22×D3×D5C2314yes—
101C22×C3×C4×C5C2311yescharacteristic
102C22×C3×C4×C5C2311yescharacteristic
103C2×#1220—24no—
104C2×#1220—42no—
105C2×#1220C2314yes—
106C2×#1220C2314yescomplemented
107C22×Dic15C2311yescharacteristic
108C22×Dic15C2311yescharacteristic
109C2×D60—24no—
110C2×D60C2314yescomplemented
111C2×C4×D15—42no—
112C2×C4×D15C2314yescomplemented
113C2×C5×#67—24no—
114C2×C5×#67C2314yes—
115C22×C5×Dic3C2311yescharacteristic
116C22×C5×Dic3C2311yescharacteristic
117C22×C5×Dic3C2311yescharacteristic
118C2×C5×Dic6—24no—
119C2×C5×Dic6C2314yescomplemented
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5—42no—
124C2×C3×C4×D5C2314yescomplemented
125C2×C3×C4×D5C2314yescomplemented
126D5×#67—232no—
127C2×#1203—42no—
128C2×#1203C2314yescomplemented
129C2×#1202—24no—
130C2×#1202—24no—
131C2×#1202D418yescomplemented
132C2×#1202C2314yes—
133C2×#1202C2314yes—
134C2×#1202C2314yescomplemented
135C2×#1201—24no—
136C2×#1201C2314yes—
137C2×#1200—24no—
138C2×#1200—24no—
139C2×#1200C2314yescomplemented
140C2×#1200C2314yescomplemented
141C2×D5×Dic3—24no—
142C2×D5×Dic3C2314yes—
143#6773—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6714C2314yescomplemented
146#6712C2314yescomplemented
147C5×#217C2314yescomplemented
148C5×(C2×D3)⋊C4C2314yescomplemented
149C5×(C2×D3)⋊C4C2314yescomplemented
150C4×C5×Dic3C2314yescomplemented
151C3×C22⋊Dic5C2314yescomplemented
152C3×#685C2314yes—
153C3×#685C2314yes—
154Dic3⋊Dic5C2314yescomplemented
155Dic3⋊Dic5C2314yescomplemented
156#6668C2314yescomplemented
157#6667C2314yescomplemented
158(C2×D3)⋊Dic5C2314yescomplemented
159#6665C2314yes—
160#6665C2314yescomplemented
161C23×#67—51no—
162C22×#235—51no—
163C22×C3×C22⋊C4—51no—
164C2×#953—51no—
165C2×#930—51no—
166C2×#929—51no—
167C2×C4×#67—51no—
168C2×#885D511yescharacteristic, complemented
169#5490—516no—
170C2×#884—51no—
171C2×#884—51no—
172C2×#883—51no—
173C2×#882—51no—
174C2×#67⋊C4—51no—
175C2×D3×C22⋊C4—51no—
176C2×#878—51no—
177C24×D5—31no—
178C24×D5C2×D311yescharacteristic
179C22×C5×Q8—31no—
180C22×C5×D4—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C2×#713—38no—
186C2×#713—68no—
187C2×D4×D5—38no—
188C2×D4×D5—68no—
189C22×D20—31no—
190C22×D20—31no—
191C22×D20—31no—
192C22×D20—31no—
193C22×C4×D5—31no—
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5C2×D311yescharacteristic, complemented
198C22×C4×D5C2×D311yescharacteristic, complemented
199C5×#124—38no—
200C2×C5×C22⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4—31no—
203C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
204C2×C42×C5—31no—
205C2×C22⋊Dic5—31no—
206C2×C22⋊Dic5C2×D311yescharacteristic, complemented
207#4092—38no—
208#4084—38no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685C2×D311yescharacteristic
214C2×#685C2×D311yescharacteristic
215C2×C4⋊Dic5—31no—
216C2×C4⋊Dic5—31no—
217C2×#683—31no—
218C2×#683—31no—
219#4030—38no—
220#4030—38no—
221#4029—38no—
222#4029—38no—
223#4028—38no—
224#4028—38no—
225D5×C22⋊C4—38no—
226D5×C22⋊C4C2×D318yescomplemented
227C4×D20—38no—
228C4×D20—38no—
229C2×#546—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5C2412yes—
234C23×C3×C5C2411yescharacteristic
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15—22no—
239C22×D15—22no—
240C22×D15C2×D414yes—
241C22×D15C2412yes—
242C22×D15C2412yes—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3—22no—
246C22×C5×D3C2412yes—
247C22×C3×D5—22no—
248C22×C3×D5—22no—
249C22×C3×D5—22no—
250C22×C3×D5—22no—
251C22×C3×D5—28no—
252C22×C3×D5—28no—
253C22×C3×D5—44no—
254C22×C3×D5—416no—
255C22×C3×D5C2×D414yes—
256C22×C3×D5#4114yescomplemented
257C22×C3×D5C2412yes—
258C22×C3×D5C2412yes—
259C2×D3×D5—28no—
260C2×D3×D5—28no—
261C2×D3×D5—44no—
262C2×D3×D5—416no—
263C2×C3×C4×C5—22no—
264C2×C3×C4×C5—22no—
265C2×C3×C4×C5C2412yes—
266C2×C3×C4×C5C2412yes—
267#1220—28no—
268#1220—44no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273D60—28no—
274C4×D15—44no—
275C5×#67—28no—
276C2×C5×Dic3—22no—
277C2×C5×Dic3—22no—
278C2×C5×Dic3C2×D414yes—
279C2×C5×Dic3C2412yes—
280C2×C5×Dic3C2412yes—
281C2×C5×Dic3C2412yes—
282C5×Dic6—28no—
283C2×C3×Dic5—22no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5C2412yes—
286C2×C3×Dic5C2412yes—
287C3×C4×D5—28no—
288C3×C4×D5—44no—
289#1203—44no—
290#1202—28no—
291#1202—28no—
292#1202C2×D4116yescomplemented
293#1201—28no—
294#1200—28no—
295#1200—28no—
296D5×Dic3—28no—
297C25×C3—51no—
298C24×D3—51no—
299C23×C3×C4—51no—
300C23×C3×C4—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—58no—
305C22×#67—51no—
306C22×#67—51no—
307C22×#67—51no—
308C22×#67—108no—
309C22×#67C2×D511yescharacteristic
310C23×Dic3—51no—
311C2×#235—58no—
312C2×#235—108no—
313C22×D12—51no—
314C22×D12—51no—
315C22×C4×D3—51no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×Dic6C2×D511yescharacteristic, complemented
319C2×C3×C22⋊C4—51no—
320C2×C3×C22⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4—58no—
323C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
324#953—58no—
325C2×#217—51no—
326C2×#217—51no—
327C2×#217C2×D511yescharacteristic, complemented
328#930—58no—
329#929—58no—
330C4×#67—58no—
331C2×(C2×D3)⋊C4—51no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
335C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
336C2×C4⋊Dic3—51no—
337C2×Dic3⋊C4—51no—
338C2×Dic3⋊C4—51no—
339C2×Dic3⋊C4—51no—
340C2×C4×Dic3C2×D511yescharacteristic, complemented
341#885C2×D518yescomplemented
342#884—58no—
343#884—58no—
344#883—58no—
345#882—58no—
346#67⋊C4—58no—
347D3×C22⋊C4—58no—
348#878—58no—
349C24×C5—31no—
350C24×C5C22×D311yescharacteristic
351C23×D5—24no—
352C23×D5—24no—
353C23×D5—31no—
354C23×D5—31no—
355C23×D5—34no—
356C23×D5—42no—
357C23×D5—64no—
358C23×D5—64no—
359C23×D5—122no—
360C23×D5C22×D314yes—
361C23×D5C22×D311yescharacteristic
362C23×D5C22×D311yescharacteristic
363C2×C5×Q8—34no—
364C2×C5×Q8—64no—
365C2×C5×D4—34no—
366C2×C5×D4—64no—
367C22×C4×C5—31no—
368C22×C4×C5—31no—
369C22×C4×C5—31no—
370C22×C4×C5C22×D311yescharacteristic
371C22×C4×C5C22×D311yescharacteristic
372C2×C22⋊D5—34no—
373C2×C22⋊D5—34no—
374C2×C22⋊D5—34no—
375C2×C22⋊D5—34no—
376C2×C22⋊D5—64no—
377C2×C22⋊D5—64no—
378C2×C22⋊D5—122no—
379C2×C22⋊D5—122no—
380C22×Dic5—31no—
381C22×Dic5—31no—
382C22×Dic5C22×D311yescharacteristic
383C22×Dic5C22×D311yescharacteristic
384#713—632no—
385D4×D5—632no—
386C2×D20—38no—
387C2×D20—34no—
388C2×D20—34no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—64no—
392C2×D20—64no—
393C2×D20—64no—
394C2×C4×D5—24no—
395C2×C4×D5—34no—
396C2×C4×D5—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—42no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—122no—
404C2×C4×D5C22×D314yescomplemented
405C2×C4×D5C22×D314yescomplemented
406C5×C22⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C5×C22⋊C4C22×D314yescomplemented
410C42×C5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5C22×D314yescomplemented
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685C22×D314yes—
418#685C22×D314yes—
419C4⋊Dic5—34no—
420C4⋊Dic5—34no—
421#683—34no—
422#683—34no—
423C22×#41—151no—
424C23×D4—151no—
425#546—1516no—
426C2×#124—31no—
427C2×#123—151no—
428C2×#123—151no—
429C2×C22⋊Q8—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×#120—151no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—51no—
438C22×C22⋊C4—151no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—44no—
443C22×C3×C5C22×D412yes—
444C22×C3×C5C2×#4112yes—
445C22×C3×C5H(5,𝔽2)12yes—
446C22×C3×C5C2511yescharacteristic
447C2×D15—28no—
448C2×D15—22no—
449C2×D15—22no—
450C2×D15—22no—
451C2×D15—22no—
452C2×D15—22no—
453C2×D15—44no—
454C2×D15C22×D414yes—
455C2×C5×D3—22no—
456C2×C5×D3—22no—
457C2×C5×D3—22no—
458C2×C5×D3—44no—
459C2×C3×D5—28no—
460C2×C3×D5—28no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—22no—
465C2×C3×D5—416no—
466C2×C3×D5C22×D414yes—
467C2×C3×D5C2×#4114yescomplemented
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472Dic15—22no—
473C3×Dic5—22no—
474C3×Dic5—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3—54no—
481C24×C3—104no—
482C24×C3—104no—
483C24×C3—202no—
484C24×C3C22×D511yescharacteristic
485C23×D3—51no—
486C23×D3—51no—
487C23×D3—54no—
488C23×D3—104no—
489C23×D3—104no—
490C23×D3—202no—
491C23×D3C22×D511yescharacteristic
492C22×C3×C4—51no—
493C22×C3×C4—51no—
494C22×C3×C4—54no—
495C22×C3×C4—54no—
496C22×C3×C4—104no—
497C22×C3×C4—202no—
498C22×C3×C4C22×D511yescharacteristic
499C22×C3×C4C22×D511yescharacteristic
500C2×#67—24no—
501C2×#67—54no—
502C2×#67—54no—
503C2×#67—54no—
504C2×#67—58no—
505C2×#67—54no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—104no—
509C2×#67—104no—
510C2×#67—1032no—
511C2×#67—104no—
512C2×#67—104no—
513C2×#67—202no—
514C2×#67C22×D514yes—
515C22×Dic3—51no—
516C22×Dic3—51no—
517C22×Dic3—54no—
518C22×Dic3—104no—
519C22×Dic3C22×D511yescharacteristic
520C22×Dic3C22×D511yescharacteristic
521C22×Dic3C22×D511yescharacteristic
522#235—1032no—
523C2×D12—54no—
524C2×D12—54no—
525C2×D12—104no—
526C2×D12—202no—
527C2×C4×D3—54no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×Dic6—24no—
534C2×Dic6C22×D514yescomplemented
535C3×C22⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4—54no—
538C3×C22⋊C4C22×D514yescomplemented
539#217—54no—
540#217—54no—
541#217C22×D514yescomplemented
542(C2×D3)⋊C4—54no—
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4C22×D514yescomplemented
546(C2×D3)⋊C4C22×D514yescomplemented
547C4⋊Dic3—54no—
548Dic3⋊C4—54no—
549Dic3⋊C4—54no—
550Dic3⋊C4—54no—
551C4×Dic3C22×D514yescomplemented
552C23×C5—22no—
553C23×C5—22no—
554C23×C5—22no—
555C23×C5—32no—
556C23×C5—62no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5C23×D312yes—
560C23×C5C23×D311yescharacteristic
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—28no—
566C22×D5—28no—
567C22×D5—34no—
568C22×D5—32no—
569C22×D5—32no—
570C22×D5—44no—
571C22×D5—416no—
572C22×D5—68no—
573C22×D5—62no—
574C22×D5—62no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—62no—
578C22×D5—68no—
579C22×D5—124no—
580C22×D5—1216no—
581C22×D5#23514yescomplemented
582C22×D5D3×D414yes—
583C22×D5C23×D312yes—
584C22×D5C23×D312yes—
585C5×Q8—68no—
586C5×D4—68no—
587C2×C4×C5—22no—
588C2×C4×C5—22no—
589C2×C4×C5—34no—
590C2×C4×C5—32no—
591C2×C4×C5—32no—
592C2×C4×C5—32no—
593C2×C4×C5—62no—
594C2×C4×C5—62no—
595C2×C4×C5C23×D312yes—
596C2×C4×C5C23×D312yes—
597C22⋊D5—68no—
598C22⋊D5—68no—
599C22⋊D5—124no—
600C22⋊D5—124no—
601C2×Dic5—22no—
602C2×Dic5—22no—
603C2×Dic5—32no—
604C2×Dic5—32no—
605C2×Dic5—62no—
606C2×Dic5—62no—
607C2×Dic5C23×D312yes—
608C2×Dic5C23×D312yes—
609D20—316no—
610D20—68no—
611D20—68no—
612D20—68no—
613C4×D5—28no—
614C4×D5—44no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—68no—
618C4×D5—124no—
619C25—51no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—31no—
624C22×D4—31no—
625C22×D4—151no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—158no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—51no—
636C23×C4—51no—
637C23×C4—151no—
638C23×C4—151no—
639C23×C4—151no—
640C23×C4—151no—
641#124—38no—
642#123—158no—
643#123—158no—
644C22⋊Q8—158no—
645#121—158no—
646#121—158no—
647#121—158no—
648#120—158no—
649#120—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—151no—
653C2×C4⋊C4—151no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—31no—
658C2×C22⋊C4—31no—
659C2×C22⋊C4—51no—
660C2×C22⋊C4—51no—
661C2×C22⋊C4—51no—
662C2×C22⋊C4—58no—
663C2×C22⋊C4—158no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊C4D3×D511yescharacteristic, complemented
670C2×C42—31no—
671C2×C3×C5—42no—
672C2×C3×C5#54614yescomplemented
673C2×C3×C5C23×D411yescharacteristic
674C2×C3×C5C22×#4111yescharacteristic
675C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
676D15—24no—
677D15—42no—
678C3×D5—24no—
679C3×D5—24no—
680C5×D3—42no—
681C23×C3—22no—
682C23×C3—22no—
683C23×C3—22no—
684C23×C3—54no—
685C23×C3—54no—
686C23×C3—52no—
687C23×C3—52no—
688C23×C3—108no—
689C23×C3—108no—
690C23×C3—102no—
691C23×C3—102no—
692C23×C3—102no—
693C23×C3—102no—
694C23×C3—204no—
695C23×C3—2016no—
696C23×C3C23×D512yes—
697C23×C3C23×D511yescharacteristic
698C22×D3—22no—
699C22×D3—22no—
700C22×D3—22no—
701C22×D3—54no—
702C22×D3—52no—
703C22×D3—52no—
704C22×D3—108no—
705C22×D3—108no—
706C22×D3—102no—
707C22×D3—102no—
708C22×D3—102no—
709C22×D3—102no—
710C22×D3—102no—
711C22×D3—204no—
712C22×D3—2016no—
713C22×D3C23×D512yes—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—52no—
717C2×C3×C4—52no—
718C2×C3×C4—108no—
719C2×C3×C4—102no—
720C2×C3×C4—102no—
721C2×C3×C4—204no—
722C2×C3×C4C23×D512yes—
723C2×C3×C4C23×D512yes—
724#67—28no—
725#67—516no—
726#67—108no—
727#67—108no—
728#67—108no—
729#67—108no—
730#67—204no—
731C2×Dic3—22no—
732C2×Dic3—22no—
733C2×Dic3—52no—
734C2×Dic3—52no—
735C2×Dic3—102no—
736C2×Dic3—102no—
737C2×Dic3—108no—
738C2×Dic3D4×D514yes—
739C2×Dic3C23×D512yes—
740C2×Dic3C23×D512yes—
741C2×Dic3C23×D512yes—
742D12—108no—
743D12—204no—
744C4×D3—108no—
745C4×D3—108no—
746C4×D3—204no—
747Dic6—28no—
748C22×C5—22no—
749C22×C5—22no—
750C22×C5—22no—
751C22×C5—44no—
752C22×C5—62no—
753C22×C5—62no—
754C22×C5—62no—
755C22×C5—124no—
756C22×C5C2×#23512yes—
757C22×C5C2×D3×D412yes—
758C22×C5#100412yes—
759C22×C5C24×D311yescharacteristic
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—22no—
763C2×D5—22no—
764C2×D5—28no—
765C2×D5—28no—
766C2×D5—34no—
767C2×D5—416no—
768C2×D5—62no—
769C2×D5—62no—
770C2×D5—68no—
771C2×D5—62no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—1216no—
775C2×D5—124no—
776C2×D5C2×#23514yescomplemented
777C2×D5C2×D3×D414yes—
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—34no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—22no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—51no—
789C24—51no—
790C24—54no—
791C24—104no—
792C24—104no—
793C24—154no—
794C24—151no—
795C24—151no—
796C24—202no—
797C24—304no—
798C24—304no—
799C24—602no—
800C24C2×D3×D511yescharacteristic
801#41—3032no—
802C2×Q8—34no—
803C2×Q8—64no—
804C2×D4—34no—
805C2×D4—64no—
806C2×D4—154no—
807C2×D4—158no—
808C2×D4—154no—
809C2×D4—154no—
810C2×D4—154no—
811C2×D4—154no—
812C2×D4—154no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—304no—
816C2×D4—304no—
817C2×D4—304no—
818C2×D4—3032no—
819C2×D4—304no—
820C2×D4—304no—
821C2×D4—602no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—51no—
827C22×C4—51no—
828C22×C4—54no—
829C22×C4—54no—
830C22×C4—104no—
831C22×C4—154no—
832C22×C4—154no—
833C22×C4—154no—
834C22×C4—151no—
835C22×C4—151no—
836C22×C4—154no—
837C22×C4—202no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—304no—
841C22×C4—602no—
842C22×C4C2×D3×D511yescharacteristic
843C22×C4C2×D3×D511yescharacteristic
844C4⋊C4—154no—
845C4⋊C4—154no—
846C4⋊C4—154no—
847C4⋊C4—154no—
848C22⋊C4—34no—
849C22⋊C4—34no—
850C22⋊C4—34no—
851C22⋊C4—54no—
852C22⋊C4—54no—
853C22⋊C4—54no—
854C22⋊C4—154no—
855C22⋊C4—154no—
856C22⋊C4—154no—
857C22⋊C4—154no—
858C22⋊C4—154no—
859C22⋊C4C2×D3×D514yescomplemented
860C42—34no—
861C3×C5C2×#54611yescharacteristic, complemented, Hall
862C22×C3—22no—
863C22×C3—22no—
864C22×C3—22no—
865C22×C3—44no—
866C22×C3—54no—
867C22×C3—54no—
868C22×C3—108no—
869C22×C3—108no—
870C22×C3—102no—
871C22×C3—102no—
872C22×C3—102no—
873C22×C3—102no—
874C22×C3—2016no—
875C22×C3C2×D4×D512yes—
876C22×C3D5×#4112yes—
877C22×C3#414912yes—
878C22×C3C24×D511yescharacteristic
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—44no—
883C2×D3—54no—
884C2×D3—108no—
885C2×D3—102no—
886C2×D3—102no—
887C2×D3—102no—
888C2×D3—102no—
889C2×D3—102no—
890C2×D3—2016no—
891C2×D3—204no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—102no—
895C3×C4—102no—
896Dic3—22no—
897Dic3—22no—
898Dic3—102no—
899Dic3—102no—
900Dic3C2×D4×D514yes—
901C2×C5—42no—
902C2×C5—122no—
903C2×C5#549014yescomplemented
904C2×C5C22×#23511yescharacteristic
905C2×C5C22×D3×D411yescharacteristic
906C2×C5C2×#100411yescharacteristic
907D5—24no—
908D5—24no—
909D5—64no—
910D5—122no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—32no—
915C23—54no—
916C23—54no—
917C23—52no—
918C23—52no—
919C23—62no—
920C23—62no—
921C23—62no—
922C23—108no—
923C23—108no—
924C23—102no—
925C23—102no—
926C23—102no—
927C23—102no—
928C23—154no—
929C23—152no—
930C23—152no—
931C23—204no—
932C23—2016no—
933C23—308no—
934C23—308no—
935C23—302no—
936C23—302no—
937C23—302no—
938C23—302no—
939C23—302no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—68no—
945D4—68no—
946D4—1516no—
947D4—308no—
948D4—308no—
949D4—308no—
950D4—308no—
951D4—308no—
952D4—604no—
953D4—604no—
954C2×C4—22no—
955C2×C4—22no—
956C2×C4—34no—
957C2×C4—32no—
958C2×C4—32no—
959C2×C4—32no—
960C2×C4—52no—
961C2×C4—52no—
962C2×C4—62no—
963C2×C4—62no—
964C2×C4—108no—
965C2×C4—102no—
966C2×C4—102no—
967C2×C4—152no—
968C2×C4—152no—
969C2×C4—204no—
970C2×C4—308no—
971C2×C4—308no—
972C2×C4—308no—
973C2×C4—302no—
974C2×C4—302no—
975C2×C4—604no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3—104no—
981C2×C3#6601014yescomplemented
982C2×C3C22×D4×D511yescharacteristic
983C2×C3C2×D5×#4111yescharacteristic
984C2×C3C2×#414911yescharacteristic
985D3—42no—
986D3—104no—
987D3—202no—
988C5C2×#549011yescharacteristic, complemented, Sylow
989C22—22no—
990C22—22no—
991C22—22no—
992C22—44no—
993C22—54no—
994C22—54no—
995C22—62no—
996C22—62no—
997C22—62no—
998C22—108no—
999C22—108no—
1000C22—102no—
1001C22—102no—
1002C22—102no—
1003C22—102no—
1004C22—124no—
1005C22—154no—
1006C22—2016no—
1007C22—308no—
1008C22—302no—
1009C22—302no—
1010C22—302no—
1011C22—302no—
1012C22—302no—
1013C22—6016no—
1014C22—604no—
1015C22D5×#23512yes—
1016C22D3×D4×D512yes—
1017C22#9202612yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—34no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—102no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6601011yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—104no—
1031C2—104no—
1032C2—122no—
1033C2—304no—
1034C2—602no—
1035C2#1175323814yesdirect product factor
1036C2C2×D5×#23511yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×#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×#546
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×#6773C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×#885C2semidirect
5. C2×C3×D5×C22⋊C4C2semidirect
6. C2×#91564C2semidirect
7. C2×#91562C2semidirect
8. C2×#91557C2semidirect
9. C2×#91476C2semidirect
10. C2×#91473C2semidirect
11. C2×#91448C2semidirect
12. C2×#91447C2semidirect
13. C2×C4×#1202C2semidirect
14. C2×#91421C2semidirect
15. C2×#91395C2semidirect
16. #11753238C2direct (N × H)
21. C22×#1220C22semidirect
22. C22×D60C22semidirect
23. C22×C4×D15C22semidirect
25. C22×C5×Dic6C22semidirect
26. C22×C3×C4×D5C22semidirect
27. C22×C3×C4×D5C22semidirect
29. C2×D5×#67C22semidirect
30. C22×#1203C22semidirect
33. C22×#1202C22semidirect
35. C22×#1200C22semidirect
36. C22×#1200C22semidirect
39. C2×#6773C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6714C22semidirect
42. C2×#6712C22semidirect
43. #91773C22semidirect
44. C2×C5×#217C22semidirect
45. C2×C5×(C2×D3)⋊C4C22semidirect
46. C2×C5×(C2×D3)⋊C4C22semidirect
47. C2×C4×C5×Dic3C22semidirect
48. C5×#885C22semidirect
49. C2×C3×C22⋊Dic5C22semidirect
52. C3×D5×C22⋊C4C22semidirect
53. #91564C22semidirect
54. #91562C22semidirect
55. #91557C22semidirect
56. C2×Dic3⋊Dic5C22semidirect
57. C2×Dic3⋊Dic5C22semidirect
58. C2×#6668C22semidirect
59. C2×#6667C22semidirect
60. C2×(C2×D3)⋊Dic5C22semidirect
62. C2×#6665C22semidirect
63. #91476C22semidirect
64. #91473C22semidirect
65. #91448C22semidirect
66. #91447C22semidirect
67. C4×#1202C22semidirect
68. #91421C22semidirect
69. #91395C22semidirect
84. C2×D5×C22⋊C4D3semidirect
106. C2×#1220C23semidirect
110. C2×D60C23semidirect
112. C2×C4×D15C23semidirect
119. C2×C5×Dic6C23semidirect
124. C2×C3×C4×D5C23semidirect
125. C2×C3×C4×D5C23semidirect
128. C2×#1203C23semidirect
131. C2×#1202D4semidirect
134. C2×#1202C23semidirect
139. C2×#1200C23semidirect
140. C2×#1200C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6714C23semidirect
146. #6712C23semidirect
147. C5×#217C23semidirect
148. C5×(C2×D3)⋊C4C23semidirect
149. C5×(C2×D3)⋊C4C23semidirect
150. C4×C5×Dic3C23semidirect
151. C3×C22⋊Dic5C23semidirect
154. Dic3⋊Dic5C23semidirect
155. Dic3⋊Dic5C23semidirect
156. #6668C23semidirect
157. #6667C23semidirect
158. (C2×D3)⋊Dic5C23semidirect
160. #6665C23semidirect
168. C2×#885D5semidirect
197. C22×C4×D5C2×D3semidirect
198. C22×C4×D5C2×D3semidirect
203. C2×C5×C22⋊C4C2×D3semidirect
206. C2×C22⋊Dic5C2×D3semidirect
226. D5×C22⋊C4C2×D3semidirect
256. C22×C3×D5#41semidirect
292. #1202C2×D4semidirect
318. C22×Dic6C2×D5semidirect
323. C2×C3×C22⋊C4C2×D5semidirect
327. C2×#217C2×D5semidirect
334. C2×(C2×D3)⋊C4C2×D5semidirect
335. C2×(C2×D3)⋊C4C2×D5semidirect
340. C2×C4×Dic3C2×D5semidirect
341. #885C2×D5semidirect
404. C2×C4×D5C22×D3semidirect
405. C2×C4×D5C22×D3semidirect
409. C5×C22⋊C4C22×D3semidirect
412. C22⋊Dic5C22×D3semidirect
467. C2×C3×D5C2×#41semidirect
534. C2×Dic6C22×D5semidirect
538. C3×C22⋊C4C22×D5semidirect
541. #217C22×D5semidirect
545. (C2×D3)⋊C4C22×D5semidirect
546. (C2×D3)⋊C4C22×D5semidirect
551. C4×Dic3C22×D5semidirect
581. C22×D5#235semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
776. C2×D5C2×#235semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5490semidirect
981. C2×C3#66010semidirect
988. C5C2×#5490semidirect
1028. C3C2×#66010semidirect
1035. C2#11753238direct (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×#67732
C2×#917732
C2×C5×#8852
C2×C3×D5×C22⋊C42
C2×#915642
C2×#915622
C2×#915572
C2×#914762
C2×#914732
C2×#914482
C2×#914472
C2×C4×#12022
C2×#914212
C2×#913952
#117532382
C2×#660103
C2×#54905