Finite Group Databasebeta

← C2×#11754817 #14482716

Subgroups — C2×#11754817 #14482716

Order 1920.

3264 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6819C211yesmaximal, characteristic, complemented
2C22×#6779C211yesmaximal, characteristic, complemented
3C2×C5×#935C211yesmaximal, characteristic, complemented
4C2×C3×#4085C211yesmaximal, characteristic, complemented
5C2×#91576C211yesmaximal, characteristic, complemented
6C2×#91562C211yesmaximal, characteristic, complemented
7C2×#91559C211yesmaximal, characteristic, complemented
8C2×#91552C211yesmaximal, characteristic, complemented
9C22×#6668C211yesmaximal, characteristic, complemented
10C2×#91537C211yesmaximal, characteristic, complemented
11C2×#91533C211yesmaximal, characteristic, complemented
12#11754817C2116yesmaximal, direct product factor
13C2×#91431C211yesmaximal, characteristic, complemented
14C2×#91404C211yesmaximal, characteristic, complemented
15C2×#91354C211yesmaximal, characteristic, complemented
16C2×#91328C211yesmaximal, characteristic, complemented
17C2×#65989—31nomaximal, Hall
18C22×C3×C5×D4C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C23×Dic15C2211yescharacteristic
22C23×Dic15C2211yescharacteristic
23C2×#6819—28no—
24C2×#6819C2218yescomplemented
25C22×C4×D15C2211yescharacteristic
26C22×Dic30C2211yescharacteristic
27C23×C5×Dic3C2211yescharacteristic
28C22×C3×C22⋊D5C2211yescharacteristic
29C22×C3×C22⋊D5C2211yescharacteristic
30C23×C3×Dic5C2211yescharacteristic
31C22×#1204C2211yescharacteristic
32C22×#1202C2211yescharacteristic
33C22×#1200C2211yescharacteristic
34C22×#1200C2211yescharacteristic
35C2×#6779—28no—
36C2×#6779C2218yescomplemented
37C22×D5×Dic3C2211yescharacteristic
38C2×C5×#217C2211yescharacteristic
39C2×C5×#217C2211yescharacteristic
40C2×C5×#217C2211yescharacteristic
41C5×#935C2218yescomplemented
42C2×C5×Dic3⋊C4C2211yescharacteristic
43C2×C5×Dic3⋊C4C2211yescharacteristic
44C2×C3×C22⋊Dic5C2211yescharacteristic
45C3×#4085C2218yescomplemented
46C2×C3×#685C2211yescharacteristic
47C2×C3×#683C2211yescharacteristic
48#91576C2218yescomplemented
49#91562C2218yescomplemented
50#91559C2218yescomplemented
51#91552C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic
53C2×Dic3⋊Dic5C2211yescharacteristic
54C2×#6669C2211yescharacteristic
55C2×#6668C2211yescharacteristic
56C2×#6668C2211yescharacteristic
57C2×#6668C2211yescharacteristic
58C2×#6668C2211yescharacteristic
59C2×#6668C2218yescomplemented
60C2×#6667C2211yescharacteristic
61#91537C2218yescomplemented
62C2×#6665C2211yescharacteristic
63C2×#6665C2211yescharacteristic
64#91533C2218yescomplemented
65C2×Dic3×Dic5C2211yescharacteristic
66#91431C2218yescomplemented
67#91404C2218yescomplemented
68#91354C2218yescomplemented
69#91328C2218yescomplemented
70C2×#5611—51nomaximal, Hall
71C22×#711—31no—
72C22×#709—31no—
73C2×C5×#123—31no—
74C2×#4085D311yescharacteristic, complemented
75C22×#683—31no—
76#65989—316no—
77C2×#4042—31no—
78C2×#4040—31no—
79C2×D5×C4⋊C4—31no—
80C2×#4034—31no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4029—31no—
84C2×#4027—31no—
85C2×#4027—31no—
86C2×#4024—31no—
87C24×C3×C5C2311yescharacteristic
88C24×C3×C5C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C2×C3×C5×D4—24no—
92C2×C3×C5×D4C2314yes—
93C22×C3×C4×C5C2311yescharacteristic
94C2×#1220—24no—
95C2×#1220D418yescomplemented
96C2×#1220C2314yes—
97C2×#1220C2314yes—
98C22×Dic15—24no—
99C22×Dic15—24no—
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C22×Dic15C2314yes—
103C22×Dic15C2314yes—
104C22×Dic15C2311yescharacteristic
105#6819—232no—
106C2×C4×D15—24no—
107C2×C4×D15C2314yes—
108C2×Dic30—24no—
109C2×Dic30C2314yes—
110C22×C5×Dic3—24no—
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2311yescharacteristic
114C22×C5×Dic3C2311yescharacteristic
115C22×C5×Dic3C2314yes—
116C2×C3×C22⋊D5—24no—
117C2×C3×C22⋊D5—24no—
118C2×C3×C22⋊D5C2314yes—
119C2×C3×C22⋊D5C2314yes—
120C22×C3×Dic5—24no—
121C22×C3×Dic5C2314yes—
122C22×C3×Dic5C2311yescharacteristic
123C22×C3×Dic5C2311yescharacteristic
124C22×C3×Dic5C2311yescharacteristic
125C2×#1204—24no—
126C2×#1204C2314yes—
127C2×#1202—24no—
128C2×#1202C2314yes—
129C2×#1200—24no—
130C2×#1200—24no—
131C2×#1200C2314yes—
132C2×#1200C2314yes—
133#6779—232no—
134C2×D5×Dic3—24no—
135C2×D5×Dic3C2314yes—
136C5×#217C2314yes—
137C5×#217C2314yes—
138C5×#217C2314yes—
139C5×Dic3⋊C4C2314yes—
140C5×Dic3⋊C4C2314yes—
141C3×C22⋊Dic5C2314yes—
142C3×#685C2314yes—
143C3×#683C2314yes—
144Dic3⋊Dic5C2314yes—
145Dic3⋊Dic5C2314yes—
146#6669C2314yes—
147#6668C2314yes—
148#6668C2314yes—
149#6668C2314yes—
150#6668C2314yes—
151#6667C2314yes—
152#6665C2314yes—
153#6665C2314yes—
154Dic3×Dic5C2314yes—
155C22×#237—51no—
156C22×#237—51no—
157C2×C3×#121—51no—
158C2×#938—51no—
159C2×#935—51no—
160C2×#935D511yescharacteristic, complemented
161C2×D4×Dic3—51no—
162C2×C4×#67—51no—
163C22×C4⋊Dic3—51no—
164#5611—516no—
165C2×D3×C4⋊C4—51no—
166C2×#888—51no—
167C2×#883—51no—
168C2×#883—51no—
169C2×#878—51no—
170C2×#878—51no—
171C22×C5×D4C2×D311yescharacteristic
172C23×C4×C5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5C2×D311yescharacteristic
176C22×C22⋊D5C2×D311yescharacteristic
177C23×Dic5—31no—
178C23×Dic5—31no—
179C23×Dic5C2×D311yescharacteristic
180C2×#711—38no—
181C2×#711—68no—
182C2×#709—38no—
183C2×#709—68no—
184C22×D20—31no—
185C22×C4×D5—31no—
186C22×C4×D5—31no—
187C22×C4×D5—31no—
188C22×C4×D5—31no—
189C22×Dic10—31no—
190C22×Dic10—31no—
191C5×#123—38no—
192C2×C5×C4⋊C4—31no—
193C2×C5×C4⋊C4—31no—
194C2×C5×C22⋊C4—31no—
195C2×C5×C22⋊C4—31no—
196C2×C5×C22⋊C4—31no—
197C2×C22⋊Dic5C2×D311yescharacteristic
198#4085C2×D318yescomplemented
199C2×#685—31no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685C2×D311yescharacteristic
203C2×C4⋊Dic5—31no—
204C2×C4⋊Dic5—31no—
205C2×#683—31no—
206C2×#683—31no—
207C2×#683—31no—
208C2×#683—31no—
209C2×#683—31no—
210C2×#683—38no—
211C2×#683C2×D311yescharacteristic
212C2×C4×Dic5—31no—
213#4042—38no—
214#4040—38no—
215D5×C4⋊C4—38no—
216#4034—38no—
217#4032—38no—
218#4030—38no—
219#4029—38no—
220#4027—38no—
221#4027—38no—
222#4024—38no—
223C2×#547—151noSylow
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5—22no—
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5C2×D414yes—
230C23×C3×C5C2412yes—
231C23×C3×C5C2412yes—
232C23×C3×C5C2411yescharacteristic
233C22×D15—22no—
234C22×D15—22no—
235C22×D15C2×D414yes—
236C22×D15C2412yes—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5C2412yes—
241C3×C5×D4—28no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5C2412yes—
244#1220—28no—
245#1220C2×D4116yescomplemented
246C2×Dic15—22no—
247C2×Dic15—22no—
248C2×Dic15—28no—
249C2×Dic15—28no—
250C2×Dic15C2×D414yes—
251C2×Dic15C2412yes—
252C2×Dic15C2412yes—
253C2×Dic15C2412yes—
254C4×D15—28no—
255Dic30—28no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3—28no—
258C2×C5×Dic3—22no—
259C2×C5×Dic3—22no—
260C2×C5×Dic3—22no—
261C2×C5×Dic3C2412yes—
262C2×C5×Dic3C2412yes—
263C2×C5×Dic3C2412yes—
264C2×C5×Dic3C2412yes—
265C3×C22⋊D5—28no—
266C3×C22⋊D5—28no—
267C2×C3×Dic5—22no—
268C2×C3×Dic5—22no—
269C2×C3×Dic5—28no—
270C2×C3×Dic5#4114yescomplemented
271C2×C3×Dic5C2412yes—
272C2×C3×Dic5C2412yes—
273C2×C3×Dic5C2412yes—
274#1204—28no—
275#1202—28no—
276#1200—28no—
277#1200—28no—
278D5×Dic3—28no—
279C22×C3×D4—51no—
280C22×C3×D4—51no—
281C22×C3×D4C2×D511yescharacteristic
282C23×C3×C4—51no—
283C22×#67—51no—
284C22×#67—51no—
285C22×#67—51no—
286C23×Dic3—51no—
287C23×Dic3—51no—
288C23×Dic3—51no—
289C23×Dic3C2×D511yescharacteristic
290C2×#237—58no—
291C2×#237—58no—
292C2×#237—108no—
293C2×#237—108no—
294C22×C4×D3—51no—
295C22×C4×D3—51no—
296C22×C4×D3—51no—
297C22×Dic6—51no—
298C22×Dic6—51no—
299C3×#121—58no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×C3×C22⋊C4—51no—
303C2×#217—51no—
304C2×#217—51no—
305C2×#217C2×D511yescharacteristic
306C2×#217C2×D511yescharacteristic
307C2×#217C2×D511yescharacteristic
308#938—58no—
309#935—58no—
310#935C2×D518yescomplemented
311D4×Dic3—58no—
312C4×#67—58no—
313C2×(C2×D3)⋊C4—51no—
314C2×C4⋊Dic3—51no—
315C2×C4⋊Dic3—51no—
316C2×C4⋊Dic3—51no—
317C2×C4⋊Dic3—51no—
318C2×C4⋊Dic3—58no—
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4—51no—
321C2×Dic3⋊C4—51no—
322C2×Dic3⋊C4C2×D511yescharacteristic
323C2×Dic3⋊C4C2×D511yescharacteristic
324C2×C4×Dic3—51no—
325D3×C4⋊C4—58no—
326#888—58no—
327#883—58no—
328#883—58no—
329#878—58no—
330#878—58no—
331C24×C5C22×D311yescharacteristic
332C24×C5C22×D311yescharacteristic
333C23×D5—31no—
334C23×D5C22×D311yescharacteristic
335C2×C5×D4—24no—
336C2×C5×D4C22×D314yes—
337C22×C4×C5—31no—
338C22×C4×C5—31no—
339C22×C4×C5—31no—
340C22×C4×C5—31no—
341C22×C4×C5—34no—
342C22×C4×C5—64no—
343C22×C4×C5C22×D311yescharacteristic
344C2×C22⋊D5—24no—
345C2×C22⋊D5—24no—
346C2×C22⋊D5—38no—
347C2×C22⋊D5—34no—
348C2×C22⋊D5—34no—
349C2×C22⋊D5—64no—
350C2×C22⋊D5C22×D314yes—
351C2×C22⋊D5C22×D314yes—
352C22×Dic5—24no—
353C22×Dic5—31no—
354C22×Dic5—31no—
355C22×Dic5—31no—
356C22×Dic5—34no—
357C22×Dic5—34no—
358C22×Dic5—64no—
359C22×Dic5—64no—
360C22×Dic5C22×D311yescharacteristic
361C22×Dic5C22×D311yescharacteristic
362C22×Dic5C22×D314yes—
363C22×Dic5C22×D311yescharacteristic
364#711—632no—
365#709—632no—
366C2×D20—34no—
367C2×D20—64no—
368C2×C4×D5—34no—
369C2×C4×D5—34no—
370C2×C4×D5—34no—
371C2×C4×D5—34no—
372C2×C4×D5—64no—
373C2×C4×D5—64no—
374C2×C4×D5—64no—
375C2×C4×D5—64no—
376C2×Dic10—34no—
377C2×Dic10—34no—
378C2×Dic10—64no—
379C2×Dic10—64no—
380C5×C4⋊C4—34no—
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C5×C22⋊C4—34no—
385C22⋊Dic5C22×D314yes—
386#685—34no—
387#685—34no—
388#685—34no—
389#685C22×D314yes—
390C4⋊Dic5—34no—
391C4⋊Dic5—34no—
392#683—34no—
393#683—34no—
394#683—34no—
395#683—34no—
396#683—34no—
397#683C22×D314yes—
398C4×Dic5—34no—
399C22×#41—151no—
400C22×#41—151no—
401#547—1516no—
402C2×C4⋊Q8—151no—
403C2×#123—31no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×C22⋊Q8—151no—
408C2×C22⋊Q8—151no—
409C2×#121—51no—
410C2×#121—151no—
411C2×C4×D4—151no—
412C2×C4×D4—151no—
413C22×C4⋊C4—151no—
414C22×C4⋊C4—151no—
415C22×C3×C5—28no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—22no—
421C22×C3×C5—44no—
422C22×C3×C5C22×D414yes—
423C22×C3×C5C22×D412yes—
424C22×C3×C5C2×#4112yes—
425C22×C3×C52−1+412yes—
426C22×C3×C5C2511yescharacteristic
427C2×D15—28no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15C22×D414yes—
431C2×C3×D5—22no—
432C2×C3×D5—22no—
433C2×C3×D5—22no—
434C2×C3×D5—44no—
435C3×C4×C5—22no—
436Dic15—22no—
437Dic15—22no—
438Dic15C22×D414yes—
439C3×Dic5—22no—
440C3×Dic5—22no—
441C3×Dic5C2×#4114yescomplemented
442C5×Dic3—22no—
443C5×Dic3—22no—
444C5×Dic3—22no—
445C5×Dic3—22no—
446C24×C3—51no—
447C24×C3C22×D511yescharacteristic
448C24×C3C22×D511yescharacteristic
449C23×D3—51no—
450C2×C3×D4—24no—
451C2×C3×D4—54no—
452C2×C3×D4—54no—
453C2×C3×D4—104no—
454C2×C3×D4—104no—
455C2×C3×D4C22×D514yes—
456C22×C3×C4—51no—
457C22×C3×C4—51no—
458C22×C3×C4—51no—
459C22×C3×C4—54no—
460C22×C3×C4—104no—
461C22×C3×C4C22×D511yescharacteristic
462C2×#67—58no—
463C2×#67—54no—
464C2×#67—54no—
465C2×#67—54no—
466C2×#67—104no—
467C2×#67—104no—
468C22×Dic3—24no—
469C22×Dic3—51no—
470C22×Dic3—54no—
471C22×Dic3—51no—
472C22×Dic3—51no—
473C22×Dic3—54no—
474C22×Dic3—54no—
475C22×Dic3—104no—
476C22×Dic3—104no—
477C22×Dic3—104no—
478C22×Dic3C22×D511yescharacteristic
479C22×Dic3C22×D511yescharacteristic
480C22×Dic3C22×D511yescharacteristic
481C22×Dic3C22×D511yescharacteristic
482C22×Dic3C22×D514yes—
483#237—1032no—
484#237—1032no—
485C2×C4×D3—54no—
486C2×C4×D3—54no—
487C2×C4×D3—54no—
488C2×C4×D3—104no—
489C2×C4×D3—104no—
490C2×C4×D3—104no—
491C2×Dic6—54no—
492C2×Dic6—54no—
493C2×Dic6—104no—
494C2×Dic6—104no—
495C3×C4⋊C4—54no—
496C3×C22⋊C4—54no—
497C3×C22⋊C4—54no—
498#217—54no—
499#217—54no—
500#217C22×D514yes—
501#217C22×D514yes—
502#217C22×D514yes—
503(C2×D3)⋊C4—54no—
504C4⋊Dic3—54no—
505C4⋊Dic3—54no—
506C4⋊Dic3—54no—
507C4⋊Dic3—54no—
508Dic3⋊C4—54no—
509Dic3⋊C4—54no—
510Dic3⋊C4—54no—
511Dic3⋊C4C22×D514yes—
512Dic3⋊C4C22×D514yes—
513C4×Dic3—54no—
514C23×C5—22no—
515C23×C5—22no—
516C23×C5—22no—
517C23×C5—22no—
518C23×C5—22no—
519C23×C5D3×D414yes—
520C23×C5C23×D312yes—
521C23×C5C23×D312yes—
522C23×C5C23×D311yescharacteristic
523C22×D5—22no—
524C22×D5—22no—
525C22×D5—22no—
526C22×D5—34no—
527C22×D5—32no—
528C22×D5—62no—
529C22×D5—62no—
530C22×D5C23×D312yes—
531C5×D4—28no—
532C2×C4×C5—22no—
533C2×C4×C5—32no—
534C2×C4×C5—32no—
535C2×C4×C5—32no—
536C2×C4×C5—32no—
537C2×C4×C5—62no—
538C2×C4×C5—62no—
539C2×C4×C5—68no—
540C2×C4×C5—62no—
541C2×C4×C5—62no—
542C2×C4×C5C23×D312yes—
543C22⋊D5—28no—
544C22⋊D5—28no—
545C22⋊D5—316no—
546C22⋊D5—68no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—28no—
550C2×Dic5—34no—
551C2×Dic5—32no—
552C2×Dic5—32no—
553C2×Dic5—32no—
554C2×Dic5—68no—
555C2×Dic5—62no—
556C2×Dic5—62no—
557C2×Dic5—68no—
558C2×Dic5#23714yescomplemented
559C2×Dic5C23×D312yes—
560C2×Dic5C23×D312yes—
561C2×Dic5C23×D312yes—
562D20—68no—
563C4×D5—68no—
564C4×D5—68no—
565C4×D5—68no—
566C4×D5—68no—
567Dic10—68no—
568Dic10—68no—
569C2×#41—158no—
570C2×#41—158no—
571C2×#41—308no—
572C2×#41—308no—
573C22×Q8—151no—
574C22×Q8—151no—
575C22×D4—51no—
576C22×D4—51no—
577C22×D4—151no—
578C22×D4—151no—
579C22×D4—151no—
580C22×D4D3×D511yescharacteristic
581C23×C4—31no—
582C23×C4—51no—
583C23×C4—151no—
584C23×C4—151no—
585C23×C4—151no—
586C23×C4—151no—
587C23×C4—151no—
588C23×C4—151no—
589C4⋊Q8—158no—
590#123—38no—
591#123—158no—
592#123—158no—
593#123—158no—
594C22⋊Q8—158no—
595C22⋊Q8—158no—
596#121—58no—
597#121—158no—
598C4×D4—158no—
599C4×D4—158no—
600C2×C4⋊C4—31no—
601C2×C4⋊C4—31no—
602C2×C4⋊C4—51no—
603C2×C4⋊C4—158no—
604C2×C4⋊C4—151no—
605C2×C4⋊C4—151no—
606C2×C4⋊C4—151no—
607C2×C4⋊C4—151no—
608C2×C4⋊C4—151no—
609C2×C4⋊C4—158no—
610C2×C4⋊C4—151no—
611C2×C4⋊C4—151no—
612C2×C22⋊C4—31no—
613C2×C22⋊C4—31no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—51no—
616C2×C22⋊C4—51no—
617C2×C22⋊C4—151no—
618C2×C22⋊C4—151no—
619C2×C22⋊C4—151no—
620C2×C42—151no—
621C2×C3×C5—24no—
622C2×C3×C5—42no—
623C2×C3×C5#54714yescomplemented
624C2×C3×C5C23×D411yescharacteristic
625C2×C3×C5C22×#4111yescharacteristic
626C2×C3×C5C2×2−1+411yescharacteristic
627D15—24no—
628C3×D5—42no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—52no—
635C23×C3—102no—
636C23×C3—102no—
637C23×C3—102no—
638C23×C3D4×D514yes—
639C23×C3C23×D512yes—
640C23×C3C23×D512yes—
641C23×C3C23×D511yescharacteristic
642C22×D3—54no—
643C22×D3—52no—
644C22×D3—102no—
645C22×D3—102no—
646C3×D4—28no—
647C3×D4—108no—
648C3×D4—108no—
649C2×C3×C4—22no—
650C2×C3×C4—54no—
651C2×C3×C4—52no—
652C2×C3×C4—52no—
653C2×C3×C4—52no—
654C2×C3×C4—108no—
655C2×C3×C4—102no—
656C2×C3×C4—102no—
657C2×C3×C4C23×D512yes—
658#67—516no—
659#67—108no—
660#67—108no—
661C2×Dic3—22no—
662C2×Dic3—22no—
663C2×Dic3—28no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—54no—
667C2×Dic3—52no—
668C2×Dic3—52no—
669C2×Dic3—52no—
670C2×Dic3—108no—
671C2×Dic3—108no—
672C2×Dic3—102no—
673C2×Dic3—102no—
674C2×Dic3—108no—
675C2×Dic3C23×D512yes—
676C2×Dic3C23×D512yes—
677C2×Dic3C23×D512yes—
678C2×Dic3C23×D512yes—
679C4×D3—108no—
680C4×D3—108no—
681C4×D3—108no—
682Dic6—108no—
683Dic6—108no—
684C22×C5—22no—
685C22×C5—22no—
686C22×C5—28no—
687C22×C5—22no—
688C22×C5—22no—
689C22×C5—22no—
690C22×C5—44no—
691C22×C5C2×D3×D414yes—
692C22×C5C2×D3×D412yes—
693C22×C5C2×#23712yes—
694C22×C5#101012yes—
695C22×C5C24×D311yescharacteristic
696C2×D5—22no—
697C2×D5—22no—
698C2×D5—22no—
699C2×D5—34no—
700C2×D5—44no—
701C2×D5—62no—
702C2×D5—62no—
703C2×D5—68no—
704C4×C5—22no—
705C4×C5—62no—
706C4×C5—62no—
707C4×C5—62no—
708C4×C5—62no—
709Dic5—22no—
710Dic5—22no—
711Dic5—34no—
712Dic5—62no—
713Dic5—62no—
714Dic5C2×#23714yescomplemented
715C24—51no—
716C24—151no—
717C24C2×D3×D511yescharacteristic
718C24C2×D3×D511yescharacteristic
719#41—3032no—
720#41—3032no—
721C2×Q8—154no—
722C2×Q8—154no—
723C2×Q8—304no—
724C2×Q8—304no—
725C2×D4—24no—
726C2×D4—54no—
727C2×D4—54no—
728C2×D4—104no—
729C2×D4—104no—
730C2×D4—154no—
731C2×D4—158no—
732C2×D4—154no—
733C2×D4—154no—
734C2×D4—304no—
735C2×D4—304no—
736C2×D4C2×D3×D514yes—
737C22×C4—34no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—31no—
742C22×C4—51no—
743C22×C4—54no—
744C22×C4—51no—
745C22×C4—51no—
746C22×C4—64no—
747C22×C4—104no—
748C22×C4—154no—
749C22×C4—154no—
750C22×C4—154no—
751C22×C4—151no—
752C22×C4—154no—
753C22×C4—154no—
754C22×C4—151no—
755C22×C4—151no—
756C22×C4—154no—
757C22×C4—304no—
758C22×C4—304no—
759C22×C4—304no—
760C22×C4—304no—
761C22×C4—304no—
762C22×C4—304no—
763C22×C4C2×D3×D511yescharacteristic
764C4⋊C4—34no—
765C4⋊C4—34no—
766C4⋊C4—54no—
767C4⋊C4—154no—
768C4⋊C4—154no—
769C4⋊C4—154no—
770C4⋊C4—154no—
771C4⋊C4—154no—
772C4⋊C4—154no—
773C4⋊C4—154no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—54no—
778C22⋊C4—54no—
779C22⋊C4—154no—
780C22⋊C4—154no—
781C22⋊C4—154no—
782C42—154no—
783C3×C5C2×#54711yescharacteristic, complemented, Hall
784C22×C3—28no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—22no—
788C22×C3—22no—
789C22×C3—22no—
790C22×C3—44no—
791C22×C3—102no—
792C22×C3—102no—
793C22×C3—102no—
794C22×C3—204no—
795C22×C3C2×D4×D514yes—
796C22×C3C2×D4×D512yes—
797C22×C3D5×#4112yes—
798C22×C3#415012yes—
799C22×C3C24×D511yescharacteristic
800C2×D3—54no—
801C2×D3—108no—
802C2×D3—102no—
803C2×D3—102no—
804C3×C4—22no—
805C3×C4—54no—
806C3×C4—102no—
807C3×C4—102no—
808Dic3—22no—
809Dic3—22no—
810Dic3—22no—
811Dic3—22no—
812Dic3—54no—
813Dic3—102no—
814Dic3—102no—
815C2×C5—24no—
816C2×C5—42no—
817C2×C5#561114yescomplemented
818C2×C5C22×D3×D411yescharacteristic
819C2×C5C22×#23711yescharacteristic
820C2×C5C2×#101011yescharacteristic
821D5—42no—
822D5—64no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—22no—
827C23—22no—
828C23—52no—
829C23—102no—
830C23—102no—
831C23—102no—
832C23—154no—
833C23—152no—
834C23—302no—
835C23—302no—
836C23#679014yes—
837C23C22×D3×D512yes—
838C23C22×D3×D512yes—
839C23C22×D3×D511yescharacteristic
840Q8—308no—
841Q8—308no—
842D4—28no—
843D4—108no—
844D4—108no—
845D4—1516no—
846D4—308no—
847D4—308no—
848C2×C4—22no—
849C2×C4—32no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—54no—
854C2×C4—52no—
855C2×C4—52no—
856C2×C4—52no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—68no—
862C2×C4—108no—
863C2×C4—102no—
864C2×C4—102no—
865C2×C4—154no—
866C2×C4—152no—
867C2×C4—152no—
868C2×C4—152no—
869C2×C4—308no—
870C2×C4—308no—
871C2×C4—308no—
872C2×C4—308no—
873C2×C4—308no—
874C2×C4—302no—
875C2×C4—302no—
876C2×C4—308no—
877C2×C4C22×D3×D512yes—
878C2×C3—24no—
879C2×C3—42no—
880C2×C3—202no—
881C2×C3#6598914yescomplemented
882C2×C3C22×D4×D511yescharacteristic
883C2×C3C2×D5×#4111yescharacteristic
884C2×C3C2×#415011yescharacteristic
885D3—104no—
886C5C2×#561111yescharacteristic, complemented, Sylow
887C22—28no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—44no—
894C22—102no—
895C22—102no—
896C22—102no—
897C22—154no—
898C22—204no—
899C22—308no—
900C22—302no—
901C22—302no—
902C22#9202012yes—
903C22D5×#23712yes—
904C22C2×#679014yes—
905C22C2×#679012yes—
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—54no—
909C4—62no—
910C4—62no—
911C4—62no—
912C4—62no—
913C4—102no—
914C4—102no—
915C4—154no—
916C4—302no—
917C4—302no—
918C3C2×#6598911yescharacteristic, complemented, Sylow
919C2—24no—
920C2—42no—
921C2—202no—
922C2—304no—
923C2#1175481714yesdirect product factor
924C2C2×#9202011yescharacteristic
925C2C2×D5×#23711yescharacteristic
926C2C22×#679011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#547
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×#6819C2semidirect
2. C22×#6779C2semidirect
3. C2×C5×#935C2semidirect
4. C2×C3×#4085C2semidirect
5. C2×#91576C2semidirect
6. C2×#91562C2semidirect
7. C2×#91559C2semidirect
8. C2×#91552C2semidirect
9. C22×#6668C2semidirect
10. C2×#91537C2semidirect
11. C2×#91533C2semidirect
12. #11754817C2direct (N × H)
13. C2×#91431C2semidirect
14. C2×#91404C2semidirect
15. C2×#91354C2semidirect
16. C2×#91328C2semidirect
24. C2×#6819C22semidirect
36. C2×#6779C22semidirect
41. C5×#935C22semidirect
45. C3×#4085C22semidirect
48. #91576C22semidirect
49. #91562C22semidirect
50. #91559C22semidirect
51. #91552C22semidirect
59. C2×#6668C22semidirect
61. #91537C22semidirect
64. #91533C22semidirect
66. #91431C22semidirect
67. #91404C22semidirect
68. #91354C22semidirect
69. #91328C22semidirect
74. C2×#4085D3semidirect
95. C2×#1220D4semidirect
160. C2×#935D5semidirect
198. #4085C2×D3semidirect
245. #1220C2×D4semidirect
270. C2×C3×Dic5#41semidirect
310. #935C2×D5semidirect
441. C3×Dic5C2×#41semidirect
558. C2×Dic5#237semidirect
623. C2×C3×C5#547semidirect
714. Dic5C2×#237semidirect
783. C3×C5C2×#547semidirect
817. C2×C5#5611semidirect
881. C2×C3#65989semidirect
886. C5C2×#5611semidirect
918. C3C2×#65989semidirect
923. C2#11754817direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68192
C22×#67792
C2×C5×#9352
C2×C3×#40852
C2×#915762
C2×#915622
C2×#915592
C2×#915522
C22×#66682
C2×#915372
C2×#915332
#117548172
C2×#914312
C2×#914042
C2×#913542
C2×#913282
C2×#659893
C2×#56115