Finite Group Databasebeta

← C2×#11752832 #14480601

Subgroups — C2×#11752832 #14480601

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6779C211yesmaximal, characteristic, complemented
2C22×#6766C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×#878C211yesmaximal, characteristic, complemented
5C2×C3×#4030C211yesmaximal, characteristic, complemented
6C2×#91569C211yesmaximal, characteristic, complemented
7C2×#91550C211yesmaximal, characteristic, complemented
8C2×#91550C211yesmaximal, characteristic, complemented
9C2×#91459C211yesmaximal, characteristic, complemented
10C2×#91450C211yesmaximal, characteristic, complemented
11C2×#91430C211yesmaximal, characteristic, complemented
12C2×#91424C211yesmaximal, characteristic, complemented
13C2×#91409C211yesmaximal, characteristic, complemented
14C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C2×#91377C211yesmaximal, characteristic, complemented
16#11752832C2116yesmaximal, direct product factor
17C2×#65963—31nomaximal, Hall
18C22×#1220C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C23×C5×Dic3C2211yescharacteristic
23C22×C5×Dic6C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×D20C2211yescharacteristic
27C22×C3×C4×D5C2211yescharacteristic
28C22×#1204C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic
31C22×#1202C2211yescharacteristic
32C22×#1202C2211yescharacteristic
33C22×#1200C2211yescharacteristic
34C2×#6779—28no—
35C2×#6779C2218yescomplemented
36C22×D5×Dic3C2211yescharacteristic
37C22×D5×Dic3C2211yescharacteristic
38C22×D5×Dic3C2211yescharacteristic
39C2×#6766—28no—
40C2×#6766C2218yescomplemented
41C2×C3×C5×C22⋊C4C2211yescharacteristic
42C2×#6714C2211yescharacteristic
43C2×#6712C2211yescharacteristic
44#91773C2218yescomplemented
45C2×C5×#217C2211yescharacteristic
46C2×C5×C4⋊Dic3C2211yescharacteristic
47C2×C5×Dic3⋊C4C2211yescharacteristic
48C2×C5×Dic3⋊C4C2211yescharacteristic
49C5×#878C2218yescomplemented
50C2×C3×#685C2211yescharacteristic
51C2×C3×#683C2211yescharacteristic
52C3×#4030C2218yescomplemented
53#91569C2218yescomplemented
54#91550C2218yescomplemented
55#91550C2218yescomplemented
56C2×Dic3⋊Dic5C2211yescharacteristic
57C2×#6669C2211yescharacteristic
58C2×#6669C2211yescharacteristic
59C2×#6667C2211yescharacteristic
60C2×#6667C2211yescharacteristic
61C2×#6667C2211yescharacteristic
62C2×#6665C2211yescharacteristic
63#91459C2218yescomplemented
64#91450C2218yescomplemented
65#91430C2218yescomplemented
66#91424C2218yescomplemented
67#91409C2218yescomplemented
68D5×Dic3⋊C4C2218yescomplemented
69#91377C2218yescomplemented
70C2×#5597—51nomaximal, Hall
71C22×#713—31no—
72C22×#709—31no—
73C2×C5×C22⋊Q8—31no—
74C2×#4092—31no—
75C2×#4076—31no—
76#65963—316no—
77C2×#4042—31no—
78C2×#4042—31no—
79C2×#4041—31no—
80C2×#4041—31no—
81C2×#4041—31no—
82C2×D5×C4⋊C4—31no—
83C2×#4030—31no—
84C2×#4030—31no—
85C2×#4030—31no—
86C2×#4030D311yescharacteristic, complemented
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C2×#1220—24no—
95C2×#1220—42no—
96C2×#1220C2314yes—
97C2×#1220C2314yes—
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C2×D60—42no—
101C2×D60C2314yes—
102C2×C4×D15—24no—
103C2×C4×D15C2314yes—
104C22×C5×Dic3—24no—
105C22×C5×Dic3C2314yes—
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C2×C5×Dic6—24no—
111C2×C5×Dic6C2314yes—
112C2×C3×C22⋊D5—24no—
113C2×C3×C22⋊D5—42no—
114C2×C3×C22⋊D5C2314yes—
115C2×C3×C22⋊D5C2314yes—
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C2×C3×D20—24no—
119C2×C3×D20C2314yes—
120C2×C3×C4×D5—42no—
121C2×C3×C4×D5C2314yes—
122C2×#1204—24no—
123C2×#1204C2314yes—
124C2×#1202—24no—
125C2×#1202—24no—
126C2×#1202—24no—
127C2×#1202—42no—
128C2×#1202C2314yes—
129C2×#1202C2314yes—
130C2×#1202C2314yes—
131C2×#1202C2314yes—
132C2×#1200—24no—
133C2×#1200C2314yes—
134#6779—232no—
135C2×D5×Dic3—24no—
136C2×D5×Dic3—42no—
137C2×D5×Dic3D418yescomplemented
138C2×D5×Dic3C2314yes—
139C2×D5×Dic3C2314yes—
140C2×D5×Dic3C2314yes—
141#6766—232no—
142C3×C5×C22⋊C4C2314yes—
143#6714C2314yes—
144#6712C2314yes—
145C5×#217C2314yes—
146C5×C4⋊Dic3C2314yes—
147C5×Dic3⋊C4C2314yes—
148C5×Dic3⋊C4C2314yes—
149C3×#685C2314yes—
150C3×#683C2314yes—
151Dic3⋊Dic5C2314yes—
152#6669C2314yes—
153#6669C2314yes—
154#6667C2314yes—
155#6667C2314yes—
156#6667C2314yes—
157#6665C2314yes—
158C22×#237—51no—
159C22×#237—51no—
160C2×C3×#121—51no—
161C2×#939—51no—
162C2×#939—51no—
163C2×#939—51no—
164C2×#939—51no—
165C2×#930—51no—
166C22×Dic3⋊C4—51no—
167#5597—516no—
168C2×#896—51no—
169C2×#896—51no—
170C2×#884—51no—
171C2×#884—51no—
172C2×#878—51no—
173C2×#878D511yescharacteristic, complemented
174C22×C5×Q8—31no—
175C23×C4×C5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5C2×D311yescharacteristic
179C22×C22⋊D5C2×D311yescharacteristic
180C2×#713—38no—
181C2×#713—68no—
182C2×#709—38no—
183C2×#709—68no—
184C22×D20—31no—
185C22×D20—31no—
186C22×D20—31no—
187C22×D20—31no—
188C22×D20—31no—
189C22×D20C2×D311yescharacteristic
190C22×C4×D5—31no—
191C22×C4×D5—31no—
192C22×C4×D5—31no—
193C22×C4×D5—31no—
194C22×C4×D5—31no—
195C22×C4×D5C2×D311yescharacteristic
196C22×Dic10—31no—
197C5×C22⋊Q8—38no—
198C2×C5×C4⋊C4—31no—
199C2×C5×C4⋊C4—31no—
200C2×C5×C4⋊C4—31no—
201C2×C5×C22⋊C4—31no—
202C2×C5×C22⋊C4C2×D311yescharacteristic
203#4092—38no—
204#4076—38no—
205C2×#685—31no—
206C2×#685—31no—
207C2×#685—31no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685C2×D311yescharacteristic
211C2×C4⋊Dic5—31no—
212C2×#683—31no—
213C2×#683—31no—
214C2×#683—31no—
215C2×#683C2×D311yescharacteristic
216#4042—38no—
217#4042—38no—
218#4041—38no—
219#4041—38no—
220#4041—38no—
221D5×C4⋊C4—38no—
222#4030—38no—
223#4030—38no—
224#4030—38no—
225#4030C2×D318yescomplemented
226C2×#537—151noSylow
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5—22no—
230C23×C3×C5C2412yes—
231C23×C3×C5C2411yescharacteristic
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—22no—
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15C2412yes—
239C22×D15C2412yes—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—22no—
244C22×C3×D5—22no—
245C22×C3×D5C2×D414yes—
246C22×C3×D5C2412yes—
247C22×C3×D5C2412yes—
248C2×C3×C4×C5—22no—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5C2412yes—
251C2×C3×C4×C5C2412yes—
252#1220—28no—
253#1220—44no—
254C2×Dic15—22no—
255C2×Dic15C2×D414yes—
256C2×Dic15C2412yes—
257C2×Dic15C2412yes—
258D60—44no—
259C4×D15—28no—
260C2×C5×Dic3—22no—
261C2×C5×Dic3—22no—
262C2×C5×Dic3—22no—
263C2×C5×Dic3—28no—
264C2×C5×Dic3C2×D414yes—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C2×C5×Dic3C2412yes—
268C2×C5×Dic3C2412yes—
269C5×Dic6—28no—
270C3×C22⋊D5—28no—
271C3×C22⋊D5—44no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5—22no—
274C2×C3×Dic5C2412yes—
275C2×C3×Dic5C2412yes—
276C3×D20—28no—
277C3×C4×D5—44no—
278#1204—28no—
279#1202—28no—
280#1202—28no—
281#1202—28no—
282#1202—44no—
283#1200—28no—
284D5×Dic3—28no—
285D5×Dic3—44no—
286D5×Dic3C2×D4116yescomplemented
287C22×C3×D4—51no—
288C22×C3×D4—51no—
289C22×C3×D4—51no—
290C23×C3×C4—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67—51no—
294C22×#67—51no—
295C22×#67—51no—
296C22×#67—51no—
297C23×Dic3—51no—
298C23×Dic3—51no—
299C23×Dic3—51no—
300C23×Dic3C2×D511yescharacteristic
301C2×#237—58no—
302C2×#237—58no—
303C2×#237—108no—
304C2×#237—108no—
305C22×D12—51no—
306C22×C4×D3—51no—
307C22×C4×D3—51no—
308C22×Dic6—51no—
309C22×Dic6C2×D511yescharacteristic
310C3×#121—58no—
311C2×C3×C4⋊C4—51no—
312C2×C3×C22⋊C4—51no—
313C2×C3×C22⋊C4C2×D511yescharacteristic
314C2×#217—51no—
315C2×#217C2×D511yescharacteristic
316#939—58no—
317#939—58no—
318#939—58no—
319#939—58no—
320#930—58no—
321C2×(C2×D3)⋊C4—51no—
322C2×(C2×D3)⋊C4—51no—
323C2×(C2×D3)⋊C4—51no—
324C2×(C2×D3)⋊C4—51no—
325C2×C4⋊Dic3C2×D511yescharacteristic
326C2×Dic3⋊C4—51no—
327C2×Dic3⋊C4—51no—
328C2×Dic3⋊C4—51no—
329C2×Dic3⋊C4—51no—
330C2×Dic3⋊C4—58no—
331C2×Dic3⋊C4C2×D511yescharacteristic
332C2×Dic3⋊C4C2×D511yescharacteristic
333#896—58no—
334#896—58no—
335#884—58no—
336#884—58no—
337#878—58no—
338#878C2×D518yescomplemented
339C24×C5C22×D311yescharacteristic
340C23×D5—31no—
341C23×D5—31no—
342C23×D5C22×D311yescharacteristic
343C23×D5C22×D311yescharacteristic
344C2×C5×Q8—34no—
345C2×C5×Q8—64no—
346C22×C4×C5—31no—
347C22×C4×C5—31no—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5—34no—
351C22×C4×C5—64no—
352C22×C4×C5C22×D311yescharacteristic
353C22×C4×C5C22×D311yescharacteristic
354C2×C22⋊D5—24no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—42no—
358C2×C22⋊D5—64no—
359C2×C22⋊D5—122no—
360C2×C22⋊D5C22×D314yes—
361C2×C22⋊D5C22×D314yes—
362C22×Dic5—31no—
363C22×Dic5—31no—
364C22×Dic5C22×D311yescharacteristic
365C22×Dic5C22×D311yescharacteristic
366#713—632no—
367#709—632no—
368C2×D20—24no—
369C2×D20—34no—
370C2×D20—34no—
371C2×D20—34no—
372C2×D20—34no—
373C2×D20—34no—
374C2×D20—64no—
375C2×D20—64no—
376C2×D20—64no—
377C2×D20—122no—
378C2×D20—122no—
379C2×D20C22×D314yes—
380C2×C4×D5—38no—
381C2×C4×D5—34no—
382C2×C4×D5—34no—
383C2×C4×D5—34no—
384C2×C4×D5—34no—
385C2×C4×D5—34no—
386C2×C4×D5—42no—
387C2×C4×D5—64no—
388C2×C4×D5—64no—
389C2×C4×D5—64no—
390C2×C4×D5—122no—
391C2×C4×D5C22×D314yes—
392C2×Dic10—34no—
393C2×Dic10—64no—
394C5×C4⋊C4—34no—
395C5×C4⋊C4—34no—
396C5×C4⋊C4—34no—
397C5×C22⋊C4—34no—
398C5×C22⋊C4C22×D314yes—
399#685—34no—
400#685—34no—
401#685—34no—
402#685—34no—
403#685—34no—
404#685C22×D314yes—
405C4⋊Dic5—34no—
406#683—34no—
407#683—34no—
408#683—34no—
409#683C22×D314yes—
410C22×#41—151no—
411C22×#41—151no—
412#537—1516no—
413C2×C22⋊Q8—31no—
414C2×C22⋊Q8—151no—
415C2×C22⋊Q8—151no—
416C2×C22⋊Q8—151no—
417C2×#121—51no—
418C2×#121—151no—
419C2×#121—151no—
420C2×#121—151no—
421C2×#121—151no—
422C2×#121—151no—
423C2×#121—151no—
424C2×#121—151no—
425C22×C4⋊C4—151no—
426C22×C3×C5—22no—
427C22×C3×C5—22no—
428C22×C3×C5—22no—
429C22×C3×C5—44no—
430C22×C3×C5C22×D412yes—
431C22×C3×C5H(5,𝔽2)12yes—
432C22×C3×C52−1+412yes—
433C22×C3×C5C2511yescharacteristic
434C2×D15—22no—
435C2×D15—22no—
436C2×D15—22no—
437C2×D15—22no—
438C2×D15—22no—
439C2×D15—22no—
440C2×D15—44no—
441C2×D15—44no—
442C2×C3×D5—28no—
443C2×C3×D5—22no—
444C2×C3×D5—22no—
445C2×C3×D5—22no—
446C2×C3×D5—22no—
447C2×C3×D5—22no—
448C2×C3×D5—44no—
449C2×C3×D5C22×D414yes—
450C3×C4×C5—22no—
451C3×C4×C5—22no—
452Dic15—22no—
453Dic15C22×D414yes—
454C3×Dic5—22no—
455C3×Dic5—22no—
456C5×Dic3—22no—
457C5×Dic3—22no—
458C5×Dic3—22no—
459C5×Dic3C22×D414yes—
460C24×C3—51no—
461C24×C3—51no—
462C24×C3C22×D511yescharacteristic
463C23×D3—51no—
464C23×D3—51no—
465C2×C3×D4—54no—
466C2×C3×D4—54no—
467C2×C3×D4—54no—
468C2×C3×D4—104no—
469C2×C3×D4—104no—
470C2×C3×D4—202no—
471C22×C3×C4—51no—
472C22×C3×C4—51no—
473C22×C3×C4—54no—
474C22×C3×C4—202no—
475C22×C3×C4C22×D511yescharacteristic
476C22×C3×C4C22×D511yescharacteristic
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—104no—
484C2×#67—104no—
485C2×#67—104no—
486C2×#67—104no—
487C2×#67—202no—
488C2×#67—202no—
489C22×Dic3—24no—
490C22×Dic3—51no—
491C22×Dic3—58no—
492C22×Dic3—54no—
493C22×Dic3—51no—
494C22×Dic3—54no—
495C22×Dic3—54no—
496C22×Dic3—104no—
497C22×Dic3—202no—
498C22×Dic3C22×D514yes—
499C22×Dic3C22×D511yescharacteristic
500C22×Dic3C22×D511yescharacteristic
501C22×Dic3C22×D511yescharacteristic
502C22×Dic3C22×D511yescharacteristic
503#237—1032no—
504#237—1032no—
505C2×D12—54no—
506C2×D12—202no—
507C2×C4×D3—54no—
508C2×C4×D3—54no—
509C2×C4×D3—104no—
510C2×C4×D3—104no—
511C2×Dic6—24no—
512C2×Dic6—54no—
513C2×Dic6—104no—
514C2×Dic6C22×D514yes—
515C3×C4⋊C4—54no—
516C3×C22⋊C4—54no—
517C3×C22⋊C4C22×D514yes—
518#217—54no—
519#217C22×D514yes—
520(C2×D3)⋊C4—54no—
521(C2×D3)⋊C4—54no—
522(C2×D3)⋊C4—54no—
523(C2×D3)⋊C4—54no—
524C4⋊Dic3C22×D514yes—
525Dic3⋊C4—54no—
526Dic3⋊C4—54no—
527Dic3⋊C4—54no—
528Dic3⋊C4—54no—
529Dic3⋊C4C22×D514yes—
530Dic3⋊C4C22×D514yes—
531C23×C5—22no—
532C23×C5—22no—
533C23×C5—22no—
534C23×C5C23×D312yes—
535C23×C5C23×D311yescharacteristic
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—22no—
539C22×D5—22no—
540C22×D5—22no—
541C22×D5—32no—
542C22×D5—32no—
543C22×D5—62no—
544C22×D5—62no—
545C22×D5—62no—
546C22×D5—62no—
547C22×D5—62no—
548C22×D5—62no—
549C22×D5D3×D414yes—
550C22×D5C23×D312yes—
551C22×D5C23×D312yes—
552C5×Q8—68no—
553C2×C4×C5—22no—
554C2×C4×C5—22no—
555C2×C4×C5—34no—
556C2×C4×C5—32no—
557C2×C4×C5—32no—
558C2×C4×C5—32no—
559C2×C4×C5—32no—
560C2×C4×C5—68no—
561C2×C4×C5—62no—
562C2×C4×C5—62no—
563C2×C4×C5—62no—
564C2×C4×C5C23×D312yes—
565C2×C4×C5C23×D312yes—
566C22⋊D5—28no—
567C22⋊D5—44no—
568C22⋊D5—68no—
569C22⋊D5—124no—
570C2×Dic5—22no—
571C2×Dic5—22no—
572C2×Dic5—34no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5C23×D312yes—
577C2×Dic5C23×D312yes—
578D20—28no—
579D20—68no—
580D20—68no—
581D20—68no—
582D20—124no—
583D20—124no—
584C4×D5—316no—
585C4×D5—44no—
586C4×D5—68no—
587C4×D5—68no—
588C4×D5—68no—
589C4×D5—124no—
590Dic10—68no—
591C2×#41—158no—
592C2×#41—158no—
593C2×#41—308no—
594C2×#41—308no—
595C22×Q8—31no—
596C22×Q8—151no—
597C22×D4—51no—
598C22×D4—51no—
599C22×D4—51no—
600C22×D4—151no—
601C22×D4—151no—
602C22×D4—151no—
603C22×D4—151no—
604C22×D4—151no—
605C22×D4—151no—
606C22×D4—151no—
607C23×C4—31no—
608C23×C4—51no—
609C23×C4—151no—
610C23×C4—151no—
611C23×C4—151no—
612C23×C4—151no—
613C23×C4—151no—
614C22⋊Q8—38no—
615C22⋊Q8—158no—
616C22⋊Q8—158no—
617C22⋊Q8—158no—
618#121—58no—
619#121—158no—
620#121—158no—
621#121—158no—
622#121—158no—
623#121—158no—
624#121—158no—
625#121—158no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—31no—
628C2×C4⋊C4—31no—
629C2×C4⋊C4—51no—
630C2×C4⋊C4—158no—
631C2×C4⋊C4—151no—
632C2×C4⋊C4—151no—
633C2×C4⋊C4—151no—
634C2×C4⋊C4—151no—
635C2×C22⋊C4—31no—
636C2×C22⋊C4—51no—
637C2×C22⋊C4—151no—
638C2×C22⋊C4—151no—
639C2×C22⋊C4—151no—
640C2×C22⋊C4—151no—
641C2×C22⋊C4—151no—
642C2×C22⋊C4D3×D511yescharacteristic
643C2×C3×C5—42no—
644C2×C3×C5#53714yescomplemented
645C2×C3×C5C23×D411yescharacteristic
646C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
647C2×C3×C5C2×2−1+411yescharacteristic
648D15—42no—
649D15—42no—
650C3×D5—24no—
651C3×D5—42no—
652C23×C3—22no—
653C23×C3—22no—
654C23×C3—22no—
655C23×C3—54no—
656C23×C3—52no—
657C23×C3—52no—
658C23×C3—102no—
659C23×C3—102no—
660C23×C3—102no—
661C23×C3—102no—
662C23×C3—102no—
663C23×C3C23×D512yes—
664C23×C3C23×D511yescharacteristic
665C22×D3—52no—
666C22×D3—52no—
667C22×D3—102no—
668C22×D3—102no—
669C22×D3—102no—
670C22×D3—102no—
671C22×D3—102no—
672C22×D3—102no—
673C3×D4—108no—
674C3×D4—108no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—204no—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—108no—
686#67—108no—
687#67—108no—
688#67—108no—
689#67—204no—
690#67—204no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—28no—
695C2×Dic3—54no—
696C2×Dic3—52no—
697C2×Dic3—516no—
698C2×Dic3—52no—
699C2×Dic3—108no—
700C2×Dic3—102no—
701C2×Dic3—204no—
702C2×Dic3D4×D514yes—
703C2×Dic3C23×D512yes—
704C2×Dic3C23×D512yes—
705C2×Dic3C23×D512yes—
706C2×Dic3C23×D512yes—
707D12—204no—
708C4×D3—108no—
709C4×D3—108no—
710Dic6—28no—
711Dic6—108no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—44no—
716C22×C5C2×D3×D412yes—
717C22×C5#100412yes—
718C22×C5#101012yes—
719C22×C5C24×D311yescharacteristic
720C2×D5—22no—
721C2×D5—22no—
722C2×D5—28no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—22no—
726C2×D5—44no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—124no—
734C2×D5—124no—
735C2×D5C2×D3×D414yes—
736C4×C5—22no—
737C4×C5—22no—
738C4×C5—34no—
739C4×C5—62no—
740C4×C5—62no—
741C4×C5—62no—
742Dic5—22no—
743Dic5—22no—
744Dic5—34no—
745Dic5—62no—
746C24—51no—
747C24—51no—
748C24—151no—
749C24—151no—
750C24C2×D3×D511yescharacteristic
751#41—3032no—
752#41—3032no—
753C2×Q8—34no—
754C2×Q8—64no—
755C2×Q8—154no—
756C2×Q8—304no—
757C2×D4—54no—
758C2×D4—54no—
759C2×D4—54no—
760C2×D4—104no—
761C2×D4—104no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—154no—
768C2×D4—154no—
769C2×D4—202no—
770C2×D4—304no—
771C2×D4—304no—
772C2×D4—304no—
773C2×D4—304no—
774C2×D4—602no—
775C2×D4—602no—
776C2×D4—602no—
777C22×C4—31no—
778C22×C4—34no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—31no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—54no—
785C22×C4—64no—
786C22×C4—154no—
787C22×C4—154no—
788C22×C4—158no—
789C22×C4—154no—
790C22×C4—154no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—154no—
794C22×C4—202no—
795C22×C4—304no—
796C22×C4—304no—
797C22×C4—304no—
798C22×C4—602no—
799C22×C4C2×D3×D511yescharacteristic
800C22×C4C2×D3×D511yescharacteristic
801C4⋊C4—34no—
802C4⋊C4—34no—
803C4⋊C4—34no—
804C4⋊C4—54no—
805C4⋊C4—154no—
806C4⋊C4—154no—
807C4⋊C4—154no—
808C4⋊C4—154no—
809C22⋊C4—34no—
810C22⋊C4—54no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4—154no—
814C22⋊C4—154no—
815C22⋊C4—154no—
816C22⋊C4C2×D3×D514yes—
817C3×C5C2×#53711yescharacteristic, complemented, Hall
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—44no—
822C22×C3—54no—
823C22×C3—108no—
824C22×C3—102no—
825C22×C3—102no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—204no—
830C22×C3C2×D4×D512yes—
831C22×C3#414712yes—
832C22×C3#414912yes—
833C22×C3C24×D511yescharacteristic
834C2×D3—102no—
835C2×D3—102no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—102no—
840C2×D3—204no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—22no—
844C3×C4—102no—
845C3×C4—102no—
846Dic3—22no—
847Dic3—22no—
848Dic3—22no—
849Dic3—54no—
850Dic3—102no—
851Dic3C2×D4×D514yes—
852C2×C5—42no—
853C2×C5#559714yescomplemented
854C2×C5C22×D3×D411yescharacteristic
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#101011yescharacteristic
857D5—24no—
858D5—42no—
859D5—122no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—54no—
865C23—52no—
866C23—52no—
867C23—102no—
868C23—102no—
869C23—102no—
870C23—102no—
871C23—102no—
872C23—152no—
873C23—152no—
874C23—302no—
875C23—302no—
876C23—302no—
877C23—302no—
878C23—302no—
879C23—302no—
880C23C22×D3×D512yes—
881C23C22×D3×D511yescharacteristic
882Q8—68no—
883Q8—308no—
884D4—108no—
885D4—108no—
886D4—204no—
887D4—308no—
888D4—308no—
889D4—308no—
890D4—308no—
891D4—604no—
892D4—604no—
893D4—604no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—34no—
897C2×C4—32no—
898C2×C4—32no—
899C2×C4—32no—
900C2×C4—32no—
901C2×C4—52no—
902C2×C4—52no—
903C2×C4—68no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—62no—
907C2×C4—102no—
908C2×C4—102no—
909C2×C4—1516no—
910C2×C4—154no—
911C2×C4—152no—
912C2×C4—152no—
913C2×C4—204no—
914C2×C4—308no—
915C2×C4—308no—
916C2×C4—308no—
917C2×C4—302no—
918C2×C4—604no—
919C2×C4C22×D3×D512yes—
920C2×C4C22×D3×D512yes—
921C2×C3—42no—
922C2×C3—104no—
923C2×C3—202no—
924C2×C3#6596314yescomplemented
925C2×C3C22×D4×D511yescharacteristic
926C2×C3C2×#414711yescharacteristic
927C2×C3C2×#414911yescharacteristic
928D3—202no—
929D3—202no—
930C5C2×#559711yescharacteristic, complemented, Sylow
931C22—22no—
932C22—22no—
933C22—22no—
934C22—44no—
935C22—54no—
936C22—108no—
937C22—102no—
938C22—102no—
939C22—102no—
940C22—102no—
941C22—102no—
942C22—204no—
943C22—302no—
944C22—302no—
945C22—302no—
946C22—302no—
947C22—302no—
948C22—302no—
949C22—604no—
950C22—604no—
951C22#9200012yes—
952C22D3×D4×D512yes—
953C22#9202612yes—
954C22C23×D3×D511yescharacteristic
955C4—22no—
956C4—22no—
957C4—34no—
958C4—62no—
959C4—62no—
960C4—62no—
961C4—102no—
962C4—102no—
963C4—154no—
964C4—302no—
965C3C2×#6596311yescharacteristic, complemented, Sylow
966C2—42no—
967C2—104no—
968C2—202no—
969C2—602no—
970C2—602no—
971C2#1175283214yesdirect product factor
972C2C2×#9200011yescharacteristic
973C2C2×D3×D4×D511yescharacteristic
974C2C2×#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×#537
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×#6779C2semidirect
2. C22×#6766C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×#878C2semidirect
5. C2×C3×#4030C2semidirect
6. C2×#91569C2semidirect
7. C2×#91550C2semidirect
8. C2×#91550C2semidirect
9. C2×#91459C2semidirect
10. C2×#91450C2semidirect
11. C2×#91430C2semidirect
12. C2×#91424C2semidirect
13. C2×#91409C2semidirect
14. C2×D5×Dic3⋊C4C2semidirect
15. C2×#91377C2semidirect
16. #11752832C2direct (N × H)
35. C2×#6779C22semidirect
40. C2×#6766C22semidirect
44. #91773C22semidirect
49. C5×#878C22semidirect
52. C3×#4030C22semidirect
53. #91569C22semidirect
54. #91550C22semidirect
55. #91550C22semidirect
63. #91459C22semidirect
64. #91450C22semidirect
65. #91430C22semidirect
66. #91424C22semidirect
67. #91409C22semidirect
68. D5×Dic3⋊C4C22semidirect
69. #91377C22semidirect
86. C2×#4030D3semidirect
137. C2×D5×Dic3D4semidirect
173. C2×#878D5semidirect
225. #4030C2×D3semidirect
286. D5×Dic3C2×D4semidirect
338. #878C2×D5semidirect
644. C2×C3×C5#537semidirect
817. C3×C5C2×#537semidirect
853. C2×C5#5597semidirect
924. C2×C3#65963semidirect
930. C5C2×#5597semidirect
965. C3C2×#65963semidirect
971. C2#11752832direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67792
C22×#67662
C2×#917732
C2×C5×#8782
C2×C3×#40302
C2×#915692
C2×#915502
C2×#914592
C2×#914502
C2×#914302
C2×#914242
C2×#914092
C2×D5×Dic3⋊C42
C2×#913772
#117528322
C2×#659633
C2×#55975