Finite Group Databasebeta

← C2×#11753239 #14482599

Subgroups — C2×#11753239 #14482599

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×#6766C211yesmaximal, characteristic, complemented
3C2×#91772C211yesmaximal, characteristic, complemented
4C2×C5×#885C211yesmaximal, characteristic, complemented
5C2×C3×#4028C211yesmaximal, characteristic, complemented
6C2×#91549C211yesmaximal, characteristic, complemented
7C2×D5×#217C211yesmaximal, characteristic, complemented
8C2×#91533C211yesmaximal, characteristic, complemented
9C2×#91474C211yesmaximal, characteristic, complemented
10C2×#91473C211yesmaximal, characteristic, complemented
11C2×Dic3×D20C211yesmaximal, characteristic, complemented
12C2×#91421C211yesmaximal, characteristic, complemented
13C2×#91414C211yesmaximal, characteristic, complemented
14C2×#91408C211yesmaximal, characteristic, complemented
15C2×#91395C211yesmaximal, characteristic, complemented
16#11753239C2116yesmaximal, direct product factor
17C2×#66010—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C23×D3×D5C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C22×C5×Dic6C2211yescharacteristic, complemented
24C22×C3×C22⋊D5C2211yescharacteristic, complemented
25C22×C3×D20C2211yescharacteristic
26C22×C3×D20C2211yescharacteristic, complemented
27C2×D5×#67—28no—
28C2×D5×#67C2218yescomplemented
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic, complemented
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic, complemented
33C22×#1200C2211yescharacteristic, complemented
34C22×D5×Dic3C2211yescharacteristic
35C22×D5×Dic3C2211yescharacteristic, complemented
36C22×D5×Dic3C2211yescharacteristic, complemented
37C22×D5×Dic3C2211yescharacteristic, complemented
38C2×#6766—28no—
39C2×#6766C2218yescomplemented
40C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
41C2×#6719C2211yescharacteristic, complemented
42C2×#6714C2211yescharacteristic, complemented
43C2×C4⋊Dic15C2211yescharacteristic, complemented
44C2×#6712C2211yescharacteristic, complemented
45#91772C2218yescomplemented
46C2×C5×#217C2211yescharacteristic, complemented
47C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C4×C5×Dic3C2211yescharacteristic, complemented
50C5×#885C2218yescomplemented
51C2×C3×#685C2211yescharacteristic
52C2×C3×#685C2211yescharacteristic, complemented
53C3×#4028C2218yescomplemented
54#91549C2218yescomplemented
55D5×#217C2218yescomplemented
56C2×Dic3⋊Dic5C2211yescharacteristic, complemented
57C2×#6668C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
59C2×#6665C2211yescharacteristic
60C2×#6665C2211yescharacteristic
61C2×#6665C2211yescharacteristic, complemented
62#91533C2218yescomplemented
63#91474C2218yescomplemented
64#91473C2218yescomplemented
65Dic3×D20C2218yescomplemented
66#91421C2218yescomplemented
67#91414C2218yescomplemented
68#91408C2218yescomplemented
69#91395C2218yescomplemented
70C2×#5591—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×#4028D311yescharacteristic, complemented
83C2×D5×C22⋊C4—31no—
84C2×D5×C22⋊C4—31no—
85C2×C4×D20—31no—
86C2×C4×D20—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C3×D5—24no—
91C23×C3×D5—24no—
92C23×C3×D5—42no—
93C23×C3×D5C2311yescharacteristic
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×#1220C2314yes—
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2311yescharacteristic
107C22×Dic15C2311yescharacteristic
108C2×C4×D15—24no—
109C2×C4×D15C2314yescomplemented
110C2×C5×#67—24no—
111C2×C5×#67C2314yes—
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2311yescharacteristic
114C22×C5×Dic3C2311yescharacteristic
115C2×C5×Dic6—24no—
116C2×C5×Dic6C2314yescomplemented
117C2×C3×C22⋊D5—42no—
118C2×C3×C22⋊D5C2314yescomplemented
119C22×C3×Dic5C2311yescharacteristic
120C2×C3×D20—24no—
121C2×C3×D20—24no—
122C2×C3×D20C2314yes—
123C2×C3×D20C2314yescomplemented
124D5×#67—232no—
125C2×#1202—24no—
126C2×#1202D418yescomplemented
127C2×#1202C2314yes—
128C2×#1202C2314yescomplemented
129C2×#1201—24no—
130C2×#1201—42no—
131C2×#1201C2314yes—
132C2×#1201C2314yescomplemented
133C2×#1200—42no—
134C2×#1200C2314yescomplemented
135C2×D5×Dic3—24no—
136C2×D5×Dic3—24no—
137C2×D5×Dic3—24no—
138C2×D5×Dic3—42no—
139C2×D5×Dic3C2314yes—
140C2×D5×Dic3C2314yescomplemented
141C2×D5×Dic3C2314yescomplemented
142C2×D5×Dic3C2314yescomplemented
143#6766—232no—
144C3×C5×C22⋊C4C2314yescomplemented
145#6719C2314yescomplemented
146#6714C2314yescomplemented
147C4⋊Dic15C2314yescomplemented
148#6712C2314yescomplemented
149C5×#217C2314yescomplemented
150C5×(C2×D3)⋊C4C2314yescomplemented
151C5×(C2×D3)⋊C4C2314yescomplemented
152C4×C5×Dic3C2314yescomplemented
153C3×#685C2314yes—
154C3×#685C2314yescomplemented
155Dic3⋊Dic5C2314yescomplemented
156#6668C2314yescomplemented
157(C2×D3)⋊Dic5C2314yescomplemented
158#6665C2314yes—
159#6665C2314yes—
160#6665C2314yescomplemented
161C23×#67—51no—
162C22×#237—51no—
163C2×C3×#120—51no—
164C22×#217—51no—
165C2×#939—51no—
166C2×#939—51no—
167C2×#938—51no—
168C2×#937—51no—
169C2×D4×Dic3—51no—
170#5591—516no—
171C2×#886—51no—
172C2×#885D511yescharacteristic, complemented
173C2×#883—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⋊D5C2×D311yescharacteristic, complemented
185C2×#713—38no—
186C2×#713—68no—
187C2×D4×D5—38no—
188C2×D4×D5—68no—
189C22×D20—31no—
190C22×D20—31no—
191C22×D20C2×D311yescharacteristic
192C22×D20C2×D311yescharacteristic, complemented
193C22×C4×D5—31no—
194C22×C4×D5—31no—
195C22×C4×D5—31no—
196C22×C4×D5—31no—
197C22×C4×D5—31no—
198C22×C4×D5—31no—
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⋊Dic5—31no—
207#4092—38no—
208#4084—38no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×#685—31no—
213C2×#685C2×D311yescharacteristic
214C2×#685C2×D311yescharacteristic, complemented
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#4028C2×D318yescomplemented
225D5×C22⋊C4—38no—
226D5×C22⋊C4—38no—
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×D15C2×D414yes—
238C22×D15C2412yes—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3C2412yes—
243C22×C3×D5—22no—
244C22×C3×D5—22no—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5—22no—
248C22×C3×D5—22no—
249C22×C3×D5—22no—
250C22×C3×D5—28no—
251C22×C3×D5—28no—
252C22×C3×D5—44no—
253C22×C3×D5—416no—
254C22×C3×D5C2×D414yes—
255C22×C3×D5#4114yescomplemented
256C22×C3×D5C2412yes—
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—
268C2×Dic15—22no—
269C2×Dic15—22no—
270C2×Dic15—22no—
271C2×Dic15C2412yes—
272C2×Dic15C2412yes—
273C2×Dic15C2412yes—
274C4×D15—28no—
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—
283C3×C22⋊D5—44no—
284C2×C3×Dic5—22no—
285C2×C3×Dic5C2412yes—
286C3×D20—28no—
287C3×D20—28no—
288#1202—28no—
289#1202C2×D4116yescomplemented
290#1201—28no—
291#1201—44no—
292#1200—44no—
293D5×Dic3—28no—
294D5×Dic3—28no—
295D5×Dic3—28no—
296D5×Dic3—44no—
297C25×C3—51no—
298C24×D3—51no—
299C22×C3×D4—51no—
300C22×C3×D4—51no—
301C22×C3×D4—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—58no—
306C22×#67—51no—
307C22×#67—51no—
308C22×#67—108no—
309C22×#67C2×D511yescharacteristic
310C23×Dic3—51no—
311C23×Dic3—51no—
312C23×Dic3—51no—
313C23×Dic3—51no—
314C2×#237—58no—
315C2×#237—108no—
316C22×C4×D3—51no—
317C22×C4×D3—51no—
318C22×Dic6C2×D511yescharacteristic, complemented
319C3×#120—58no—
320C2×C3×C22⋊C4—51no—
321C2×C3×C22⋊C4—51no—
322C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
323C2×#217—51no—
324C2×#217—51no—
325C2×#217—51no—
326C2×#217—51no—
327C2×#217—58no—
328C2×#217C2×D511yescharacteristic, complemented
329#939—58no—
330#939—58no—
331#938—58no—
332#937—58no—
333D4×Dic3—58no—
334C2×(C2×D3)⋊C4—51no—
335C2×(C2×D3)⋊C4—51no—
336C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
337C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
338C2×C4⋊Dic3—51no—
339C2×C4⋊Dic3—51no—
340C2×Dic3⋊C4—51no—
341C2×Dic3⋊C4—51no—
342C2×C4×Dic3C2×D511yescharacteristic, complemented
343#886—58no—
344#885C2×D518yescomplemented
345#883—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—34no—
355C23×D5—42no—
356C23×D5—64no—
357C23×D5—64no—
358C23×D5—122no—
359C23×D5C22×D311yescharacteristic
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—42no—
376C2×C22⋊D5—64no—
377C2×C22⋊D5—64no—
378C2×C22⋊D5—122no—
379C2×C22⋊D5C22×D314yescomplemented
380C22×Dic5—31no—
381C22×Dic5—31no—
382C22×Dic5—31no—
383C22×Dic5C22×D311yescharacteristic
384#713—632no—
385D4×D5—632no—
386C2×D20—24no—
387C2×D20—24no—
388C2×D20—38no—
389C2×D20—34no—
390C2×D20—34no—
391C2×D20—64no—
392C2×D20C22×D314yes—
393C2×D20C22×D314yescomplemented
394C2×C4×D5—34no—
395C2×C4×D5—34no—
396C2×C4×D5—34no—
397C2×C4×D5—34no—
398C2×C4×D5—34no—
399C2×C4×D5—34no—
400C2×C4×D5—64no—
401C2×C4×D5—64no—
402C2×C4×D5—64no—
403C2×C4×D5—64no—
404C2×C4×D5—122no—
405C2×C4×D5—122no—
406C5×C22⋊C4—34no—
407C5×C22⋊C4—34no—
408C5×C22⋊C4—34no—
409C5×C22⋊C4C22×D314yescomplemented
410C42×C5—34no—
411C22⋊Dic5—34no—
412C22⋊Dic5—34no—
413#685—34no—
414#685—34no—
415#685—34no—
416#685—34no—
417#685C22×D314yes—
418#685C22×D314yescomplemented
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—51no—
434C2×#120—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C22⋊C4—151no—
438C22×C22⋊C4—151no—
439C22×C3×C5—22no—
440C22×C3×C5—22no—
441C22×C3×C5—22no—
442C22×C3×C5—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×D15C22×D414yes—
451C2×C5×D3—22no—
452C2×C5×D3—22no—
453C2×C5×D3—22no—
454C2×C5×D3—44no—
455C2×C3×D5—28no—
456C2×C3×D5—28no—
457C2×C3×D5—22no—
458C2×C3×D5—22no—
459C2×C3×D5—22no—
460C2×C3×D5—22no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—22no—
464C2×C3×D5—416no—
465C2×C3×D5—44no—
466C2×C3×D5C22×D414yes—
467C2×C3×D5C2×#4114yescomplemented
468D3×D5—416no—
469C3×C4×C5—22no—
470C3×C4×C5—22no—
471Dic15—22no—
472Dic15—22no—
473Dic15—22no—
474C3×Dic5—22no—
475C5×Dic3—22no—
476C5×Dic3—22no—
477C5×Dic3C22×D414yes—
478C24×C3—51no—
479C24×C3—51no—
480C24×C3—51no—
481C24×C3—54no—
482C24×C3—104no—
483C24×C3—104no—
484C24×C3—202no—
485C24×C3C22×D511yescharacteristic
486C23×D3—51no—
487C23×D3—54no—
488C23×D3—104no—
489C23×D3—104no—
490C23×D3—202no—
491C23×D3C22×D511yescharacteristic
492C2×C3×D4—54no—
493C2×C3×D4—54no—
494C2×C3×D4—54no—
495C2×C3×D4—104no—
496C2×C3×D4—104no—
497C2×C3×D4—202no—
498C22×C3×C4—51no—
499C22×C3×C4C22×D511yescharacteristic
500C22×C3×C4C22×D511yescharacteristic
501C2×#67—24no—
502C2×#67—54no—
503C2×#67—54no—
504C2×#67—54no—
505C2×#67—58no—
506C2×#67—54no—
507C2×#67—54no—
508C2×#67—104no—
509C2×#67—1032no—
510C2×#67—104no—
511C2×#67—104no—
512C2×#67—202no—
513C2×#67C22×D514yes—
514C22×Dic3—51no—
515C22×Dic3—51no—
516C22×Dic3—51no—
517C22×Dic3—54no—
518C22×Dic3—54no—
519C22×Dic3—54no—
520C22×Dic3—54no—
521C22×Dic3—104no—
522C22×Dic3—104no—
523C22×Dic3—104no—
524C22×Dic3—202no—
525C22×Dic3C22×D511yescharacteristic
526C22×Dic3C22×D511yescharacteristic
527C22×Dic3C22×D511yescharacteristic
528#237—1032no—
529C2×C4×D3—54no—
530C2×C4×D3—54no—
531C2×C4×D3—104no—
532C2×C4×D3—202no—
533C2×Dic6—24no—
534C2×Dic6C22×D514yescomplemented
535C3×C22⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4C22×D514yescomplemented
538#217—54no—
539#217—54no—
540#217—54no—
541#217—54no—
542#217C22×D514yescomplemented
543(C2×D3)⋊C4—54no—
544(C2×D3)⋊C4—54no—
545(C2×D3)⋊C4C22×D514yescomplemented
546(C2×D3)⋊C4C22×D514yescomplemented
547C4⋊Dic3—54no—
548C4⋊Dic3—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—22no—
566C22×D5—22no—
567C22×D5—22no—
568C22×D5—28no—
569C22×D5—28no—
570C22×D5—34no—
571C22×D5—32no—
572C22×D5—44no—
573C22×D5—416no—
574C22×D5—68no—
575C22×D5—62no—
576C22×D5—62no—
577C22×D5—68no—
578C22×D5—124no—
579C22×D5—1216no—
580C22×D5D3×D414yes—
581C22×D5#23714yescomplemented
582C22×D5C23×D312yes—
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—44no—
598C22⋊D5—68no—
599C22⋊D5—68no—
600C22⋊D5—124no—
601C2×Dic5—22no—
602C2×Dic5—32no—
603C2×Dic5—32no—
604C2×Dic5—32no—
605C2×Dic5—62no—
606C2×Dic5—62no—
607C2×Dic5—62no—
608C2×Dic5C23×D312yes—
609D20—28no—
610D20—28no—
611D20—316no—
612D20—68no—
613C4×D5—68no—
614C4×D5—68no—
615C4×D5—68no—
616C4×D5—68no—
617C4×D5—124no—
618C4×D5—124no—
619C25—51no—
620C25—151no—
621C2×#41—158no—
622C2×#41—308no—
623C22×Q8—31no—
624C22×D4—31no—
625C22×D4—51no—
626C22×D4—51no—
627C22×D4—51no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—158no—
631C22×D4—151no—
632C22×D4—151no—
633C22×D4—151no—
634C22×D4—308no—
635C23×C4—151no—
636C23×C4—151no—
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—58no—
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—158no—
662C2×C22⋊C4—158no—
663C2×C22⋊C4—151no—
664C2×C22⋊C4—151no—
665C2×C22⋊C4—151no—
666C2×C22⋊C4—151no—
667C2×C22⋊C4—151no—
668C2×C22⋊C4—151no—
669C2×C22⋊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—
677C3×D5—24no—
678C3×D5—24no—
679C3×D5—42no—
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—52no—
689C23×C3—108no—
690C23×C3—108no—
691C23×C3—102no—
692C23×C3—102no—
693C23×C3—102no—
694C23×C3—102no—
695C23×C3—102no—
696C23×C3—102no—
697C23×C3—102no—
698C23×C3—204no—
699C23×C3—2016no—
700C23×C3C23×D512yes—
701C23×C3C23×D511yescharacteristic
702C22×D3—22no—
703C22×D3—22no—
704C22×D3—22no—
705C22×D3—54no—
706C22×D3—52no—
707C22×D3—108no—
708C22×D3—108no—
709C22×D3—102no—
710C22×D3—102no—
711C22×D3—204no—
712C22×D3—2016no—
713C22×D3C23×D512yes—
714C3×D4—108no—
715C3×D4—108no—
716C3×D4—204no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—52no—
720C2×C3×C4—102no—
721C2×C3×C4C23×D512yes—
722C2×C3×C4C23×D512yes—
723#67—28no—
724#67—516no—
725#67—108no—
726#67—108no—
727#67—108no—
728#67—204no—
729C2×Dic3—22no—
730C2×Dic3—22no—
731C2×Dic3—52no—
732C2×Dic3—52no—
733C2×Dic3—52no—
734C2×Dic3—108no—
735C2×Dic3—102no—
736C2×Dic3—102no—
737C2×Dic3—102no—
738C2×Dic3—108no—
739C2×Dic3—108no—
740C2×Dic3—204no—
741C2×Dic3D4×D514yes—
742C2×Dic3C23×D512yes—
743C2×Dic3C23×D512yes—
744C2×Dic3C23×D512yes—
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×D3×D412yes—
757C22×C5C2×#23712yes—
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—22no—
767C2×D5—22no—
768C2×D5—22no—
769C2×D5—34no—
770C2×D5—416no—
771C2×D5—44no—
772C2×D5—62no—
773C2×D5—62no—
774C2×D5—68no—
775C2×D5—1216no—
776C2×D5C2×D3×D414yes—
777C2×D5C2×#23714yescomplemented
778C4×C5—22no—
779C4×C5—22no—
780C4×C5—34no—
781C4×C5—62no—
782C4×C5—62no—
783Dic5—22no—
784Dic5—62no—
785Dic5—62no—
786Dic5—62no—
787C24—31no—
788C24—51no—
789C24—51no—
790C24—51no—
791C24—54no—
792C24—104no—
793C24—104no—
794C24—154no—
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—54no—
806C2×D4—54no—
807C2×D4—54no—
808C2×D4—64no—
809C2×D4—104no—
810C2×D4—104no—
811C2×D4—154no—
812C2×D4—158no—
813C2×D4—154no—
814C2×D4—154no—
815C2×D4—154no—
816C2×D4—154no—
817C2×D4—202no—
818C2×D4—304no—
819C2×D4—3032no—
820C2×D4—304no—
821C2×D4—304no—
822C2×D4—602no—
823C22×C4—31no—
824C22×C4—31no—
825C22×C4—31no—
826C22×C4—51no—
827C22×C4—154no—
828C22×C4—154no—
829C22×C4—154no—
830C22×C4—154no—
831C22×C4—154no—
832C22×C4—151no—
833C22×C4—151no—
834C22×C4—151no—
835C22×C4—154no—
836C22×C4—304no—
837C22×C4—304no—
838C22×C4—304no—
839C22×C4—304no—
840C22×C4—602no—
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—154no—
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—102no—
875C22×C3—102no—
876C22×C3—102no—
877C22×C3—2016no—
878C22×C3—204no—
879C22×C3C2×D4×D512yes—
880C22×C3D5×#4112yes—
881C22×C3#414912yes—
882C22×C3C24×D511yescharacteristic
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—44no—
887C2×D3—54no—
888C2×D3—108no—
889C2×D3—102no—
890C2×D3—102no—
891C2×D3—2016no—
892C3×C4—22no—
893C3×C4—22no—
894C3×C4—102no—
895Dic3—22no—
896Dic3—22no—
897Dic3—102no—
898Dic3—102no—
899Dic3—102no—
900Dic3C2×D4×D514yes—
901C2×C5—42no—
902C2×C5—122no—
903C2×C5#559114yescomplemented
904C2×C5C22×D3×D411yescharacteristic
905C2×C5C22×#23711yescharacteristic
906C2×C5C2×#100411yescharacteristic
907D5—24no—
908D5—24no—
909D5—42no—
910D5—64no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—32no—
915C23—54no—
916C23—54no—
917C23—52no—
918C23—52no—
919C23—52no—
920C23—62no—
921C23—62no—
922C23—62no—
923C23—108no—
924C23—108no—
925C23—102no—
926C23—102no—
927C23—102no—
928C23—102no—
929C23—102no—
930C23—102no—
931C23—102no—
932C23—154no—
933C23—152no—
934C23—204no—
935C23—2016no—
936C23—308no—
937C23—308no—
938C23—302no—
939C23—302no—
940C23—604no—
941C23—6016no—
942C23C22×D3×D512yes—
943C23C22×D3×D511yescharacteristic
944Q8—68no—
945D4—68no—
946D4—108no—
947D4—108no—
948D4—1516no—
949D4—204no—
950D4—308no—
951D4—308no—
952D4—308no—
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—62no—
962C2×C4—62no—
963C2×C4—102no—
964C2×C4—152no—
965C2×C4—152no—
966C2×C4—152no—
967C2×C4—308no—
968C2×C4—308no—
969C2×C4—308no—
970C2×C4—308no—
971C2×C4—302no—
972C2×C4—302no—
973C2×C4—302no—
974C2×C4—604no—
975C2×C4—604no—
976C2×C4C22×D3×D512yes—
977C2×C4C22×D3×D512yes—
978C2×C3—42no—
979C2×C3—104no—
980C2×C3—104no—
981C2×C3—202no—
982C2×C3#6601014yescomplemented
983C2×C3C22×D4×D511yescharacteristic
984C2×C3C2×D5×#4111yescharacteristic
985C2×C3C2×#414911yescharacteristic
986D3—42no—
987D3—104no—
988C5C2×#559111yescharacteristic, 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—102no—
1005C22—102no—
1006C22—102no—
1007C22—124no—
1008C22—154no—
1009C22—2016no—
1010C22—204no—
1011C22—308no—
1012C22—302no—
1013C22—302no—
1014C22—6016no—
1015C22#9201712yes—
1016C22D3×D4×D512yes—
1017C22D5×#23712yes—
1018C22C23×D3×D511yescharacteristic
1019C4—22no—
1020C4—22no—
1021C4—34no—
1022C4—62no—
1023C4—62no—
1024C4—102no—
1025C4—302no—
1026C4—302no—
1027C4—302no—
1028C3C2×#6601011yescharacteristic, complemented, Sylow
1029C2—42no—
1030C2—104no—
1031C2—104no—
1032C2—122no—
1033C2—202no—
1034C2—304no—
1035C2#1175323914yesdirect product factor
1036C2C2×#9201711yescharacteristic
1037C2C2×D3×D4×D511yescharacteristic
1038C2C2×D5×#23711yescharacteristic
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×#6766C2semidirect
3. C2×#91772C2semidirect
4. C2×C5×#885C2semidirect
5. C2×C3×#4028C2semidirect
6. C2×#91549C2semidirect
7. C2×D5×#217C2semidirect
8. C2×#91533C2semidirect
9. C2×#91474C2semidirect
10. C2×#91473C2semidirect
11. C2×Dic3×D20C2semidirect
12. C2×#91421C2semidirect
13. C2×#91414C2semidirect
14. C2×#91408C2semidirect
15. C2×#91395C2semidirect
16. #11753239C2direct (N × H)
21. C22×C4×D15C22semidirect
23. C22×C5×Dic6C22semidirect
24. C22×C3×C22⋊D5C22semidirect
26. C22×C3×D20C22semidirect
28. C2×D5×#67C22semidirect
30. C22×#1202C22semidirect
32. C22×#1201C22semidirect
33. C22×#1200C22semidirect
35. C22×D5×Dic3C22semidirect
36. C22×D5×Dic3C22semidirect
37. C22×D5×Dic3C22semidirect
39. C2×#6766C22semidirect
40. C2×C3×C5×C22⋊C4C22semidirect
41. C2×#6719C22semidirect
42. C2×#6714C22semidirect
43. C2×C4⋊Dic15C22semidirect
44. C2×#6712C22semidirect
45. #91772C22semidirect
46. C2×C5×#217C22semidirect
47. C2×C5×(C2×D3)⋊C4C22semidirect
48. C2×C5×(C2×D3)⋊C4C22semidirect
49. C2×C4×C5×Dic3C22semidirect
50. C5×#885C22semidirect
52. C2×C3×#685C22semidirect
53. C3×#4028C22semidirect
54. #91549C22semidirect
55. D5×#217C22semidirect
56. C2×Dic3⋊Dic5C22semidirect
57. C2×#6668C22semidirect
58. C2×(C2×D3)⋊Dic5C22semidirect
61. C2×#6665C22semidirect
62. #91533C22semidirect
63. #91474C22semidirect
64. #91473C22semidirect
65. Dic3×D20C22semidirect
66. #91421C22semidirect
67. #91414C22semidirect
68. #91408C22semidirect
69. #91395C22semidirect
82. C2×#4028D3semidirect
109. C2×C4×D15C23semidirect
116. C2×C5×Dic6C23semidirect
118. C2×C3×C22⋊D5C23semidirect
123. C2×C3×D20C23semidirect
126. C2×#1202D4semidirect
128. C2×#1202C23semidirect
132. C2×#1201C23semidirect
134. C2×#1200C23semidirect
140. C2×D5×Dic3C23semidirect
141. C2×D5×Dic3C23semidirect
142. C2×D5×Dic3C23semidirect
144. C3×C5×C22⋊C4C23semidirect
145. #6719C23semidirect
146. #6714C23semidirect
147. C4⋊Dic15C23semidirect
148. #6712C23semidirect
149. C5×#217C23semidirect
150. C5×(C2×D3)⋊C4C23semidirect
151. C5×(C2×D3)⋊C4C23semidirect
152. C4×C5×Dic3C23semidirect
154. C3×#685C23semidirect
155. Dic3⋊Dic5C23semidirect
156. #6668C23semidirect
157. (C2×D3)⋊Dic5C23semidirect
160. #6665C23semidirect
172. C2×#885D5semidirect
184. C22×C22⋊D5C2×D3semidirect
192. C22×D20C2×D3semidirect
203. C2×C5×C22⋊C4C2×D3semidirect
214. C2×#685C2×D3semidirect
224. #4028C2×D3semidirect
255. C22×C3×D5#41semidirect
289. #1202C2×D4semidirect
318. C22×Dic6C2×D5semidirect
322. C2×C3×C22⋊C4C2×D5semidirect
328. C2×#217C2×D5semidirect
336. C2×(C2×D3)⋊C4C2×D5semidirect
337. C2×(C2×D3)⋊C4C2×D5semidirect
342. C2×C4×Dic3C2×D5semidirect
344. #885C2×D5semidirect
379. C2×C22⋊D5C22×D3semidirect
393. C2×D20C22×D3semidirect
409. C5×C22⋊C4C22×D3semidirect
418. #685C22×D3semidirect
467. C2×C3×D5C2×#41semidirect
534. C2×Dic6C22×D5semidirect
537. C3×C22⋊C4C22×D5semidirect
542. #217C22×D5semidirect
545. (C2×D3)⋊C4C22×D5semidirect
546. (C2×D3)⋊C4C22×D5semidirect
551. C4×Dic3C22×D5semidirect
581. C22×D5#237semidirect
669. C2×C22⋊C4D3×D5semidirect
672. C2×C3×C5#546semidirect
777. C2×D5C2×#237semidirect
859. C22⋊C4C2×D3×D5semidirect
861. C3×C5C2×#546semidirect
903. C2×C5#5591semidirect
982. C2×C3#66010semidirect
988. C5C2×#5591semidirect
1028. C3C2×#66010semidirect
1035. C2#11753239direct (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×#917722
C2×C5×#8852
C2×C3×#40282
C2×#915492
C2×D5×#2172
C2×#915332
C2×#914742
C2×#914732
C2×Dic3×D202
C2×#914212
C2×#914142
C2×#914082
C2×#913952
#117532392
C2×#660103
C2×#55915