Finite Group Databasebeta

← C2×#11754376 #14482728

Subgroups — C2×#11754376 #14482728

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×#6817C211yesmaximal, characteristic, complemented
2C22×#6782C211yesmaximal, characteristic, complemented
3C2×C5×#929C211yesmaximal, characteristic, complemented
4C22×C3×#683C211yesmaximal, characteristic, complemented
5C2×#91566C211yesmaximal, characteristic, complemented
6C2×#91552C211yesmaximal, characteristic, complemented
7C2×#91546C211yesmaximal, characteristic, complemented
8C2×#91433C211yesmaximal, characteristic, complemented
9#11754376C2116yesmaximal, direct product factor
10C2×#91432C211yesmaximal, characteristic, complemented
11C2×#91420C211yesmaximal, characteristic, complemented
12C2×#91406C211yesmaximal, characteristic, complemented
13C2×#91404C211yesmaximal, characteristic, complemented
14C2×#91377C211yesmaximal, characteristic, complemented
15C2×#91355C211yesmaximal, characteristic, complemented
16C2×#91328C211yesmaximal, characteristic, complemented
17C2×#65989—31nomaximal, Hall
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C2×#6817—28no—
22C2×#6817C2218yescomplemented
23C22×D60C2211yescharacteristic
24C22×C4×D15C2211yescharacteristic
25C22×C4×D15C2211yescharacteristic
26C22×Dic30C2211yescharacteristic
27C22×C5×#67C2211yescharacteristic
28C23×C3×Dic5C2211yescharacteristic
29C23×C3×Dic5C2211yescharacteristic
30C22×#1204C2211yescharacteristic
31C22×#1203C2211yescharacteristic
32C22×#1203C2211yescharacteristic
33C22×#1200C2211yescharacteristic
34C22×#1200C2211yescharacteristic
35C2×#6782—28no—
36C2×#6782C2218yescomplemented
37C22×D3×Dic5C2211yescharacteristic
38C2×C5×#217C2211yescharacteristic
39C5×#929C2218yescomplemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic
41C2×C5×(C2×D3)⋊C4C2211yescharacteristic
42C2×C5×Dic3⋊C4C2211yescharacteristic
43C2×C5×Dic3⋊C4C2211yescharacteristic
44C2×C3×#683C2211yescharacteristic
45C2×C3×#683C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic
47C2×C3×#683C2211yescharacteristic
48C2×C3×#683C2218yescomplemented
49#91566C2218yescomplemented
50#91552C2218yescomplemented
51#91546C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic
53C2×Dic3⋊Dic5C2211yescharacteristic
54C2×#6669C2211yescharacteristic
55C2×#6668C2211yescharacteristic
56C2×#6667C2211yescharacteristic
57C2×#6667C2211yescharacteristic
58C2×#6667C2211yescharacteristic
59C2×#6667C2211yescharacteristic
60C2×(C2×D3)⋊Dic5C2211yescharacteristic
61C2×Dic3×Dic5C2211yescharacteristic
62#91433C2218yescomplemented
63#91432C2218yescomplemented
64#91420C2218yescomplemented
65#91406C2218yescomplemented
66#91404C2218yescomplemented
67#91377C2218yescomplemented
68#91355C2218yescomplemented
69#91328C2218yescomplemented
70C2×#5507—51nomaximal, Hall
71C22×#711—31no—
72C22×#709—31no—
73C2×C5×#123—31no—
74C2×#4085—31no—
75C22×#683D311yescharacteristic, complemented
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
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C22×C3×C4×C5—24no—
92C22×C3×C4×C5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2314yes—
95C2×#1220—24no—
96C2×#1220D418yescomplemented
97C2×#1220C2314yes—
98C2×#1220C2314yes—
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101#6817—232no—
102C2×D60—24no—
103C2×D60C2314yes—
104C2×C4×D15—24no—
105C2×C4×D15—24no—
106C2×C4×D15C2314yes—
107C2×C4×D15C2314yes—
108C2×Dic30—24no—
109C2×Dic30C2314yes—
110C2×C5×#67—24no—
111C2×C5×#67C2314yes—
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2311yescharacteristic
114C22×C5×Dic3C2311yescharacteristic
115C22×C3×Dic5—24no—
116C22×C3×Dic5—24no—
117C22×C3×Dic5C2311yescharacteristic
118C22×C3×Dic5C2314yes—
119C22×C3×Dic5C2311yescharacteristic
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2314yes—
122C22×C3×Dic5C2311yescharacteristic
123C2×#1204—24no—
124C2×#1204C2314yes—
125C2×#1203—24no—
126C2×#1203—24no—
127C2×#1203C2314yes—
128C2×#1203C2314yes—
129C2×#1200—24no—
130C2×#1200—24no—
131C2×#1200C2314yes—
132C2×#1200C2314yes—
133#6782—232no—
134C2×D3×Dic5—24no—
135C2×D3×Dic5C2314yes—
136C5×#217C2314yes—
137C5×(C2×D3)⋊C4C2314yes—
138C5×(C2×D3)⋊C4C2314yes—
139C5×Dic3⋊C4C2314yes—
140C5×Dic3⋊C4C2314yes—
141C3×#683C2314yes—
142C3×#683C2314yes—
143C3×#683C2314yes—
144C3×#683C2314yes—
145Dic3⋊Dic5C2314yes—
146Dic3⋊Dic5C2314yes—
147#6669C2314yes—
148#6668C2314yes—
149#6667C2314yes—
150#6667C2314yes—
151#6667C2314yes—
152#6667C2314yes—
153(C2×D3)⋊Dic5C2314yes—
154Dic3×Dic5C2314yes—
155C22×#235—51no—
156C22×#235—51no—
157C22×C3×C4⋊C4—51no—
158C2×#930—51no—
159C2×#929—51no—
160C2×#929D511yescharacteristic, complemented
161C2×C4×#67—51no—
162C2×#896—51no—
163C2×#896—51no—
164#5507—516no—
165C2×#895—51no—
166C2×#894—51no—
167C2×#894—51no—
168C2×#893—51no—
169C2×D3×C4⋊C4—51no—
170C2×#888—51no—
171C22×C5×D4—31no—
172C23×C4×C5C2×D311yescharacteristic
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C23×Dic5—31no—
178C23×Dic5C2×D311yescharacteristic
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⋊Dic5—31no—
198#4085—38no—
199C2×#685—31no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×C4⋊Dic5—31no—
204C2×C4⋊Dic5—31no—
205C2×#683—31no—
206C2×#683—31no—
207C2×#683C2×D311yescharacteristic
208C2×#683C2×D311yescharacteristic
209C2×#683C2×D311yescharacteristic
210C2×#683C2×D311yescharacteristic
211C2×#683C2×D318yescomplemented
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×C5C2×D414yes—
227C23×C3×C5C2412yes—
228C23×C3×C5C2411yescharacteristic
229C22×D15—22no—
230C22×D15—22no—
231C22×D15—22no—
232C22×D15—22no—
233C22×D15—22no—
234C22×D15C2×D414yes—
235C22×D15C2412yes—
236C22×D15C2412yes—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3—22no—
240C22×C5×D3C2412yes—
241C2×C3×C4×C5—22no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5—28no—
244C2×C3×C4×C5C2412yes—
245C2×C3×C4×C5C2412yes—
246#1220—28no—
247#1220C2×D4116yescomplemented
248C2×Dic15—22no—
249C2×Dic15C2×D414yes—
250C2×Dic15C2412yes—
251C2×Dic15C2412yes—
252D60—28no—
253C4×D15—28no—
254C4×D15—28no—
255Dic30—28no—
256C5×#67—28no—
257C2×C5×Dic3—22no—
258C2×C5×Dic3—22no—
259C2×C5×Dic3—22no—
260C2×C5×Dic3C2412yes—
261C2×C5×Dic3C2412yes—
262C2×C5×Dic3C2412yes—
263C2×C3×Dic5—22no—
264C2×C3×Dic5—28no—
265C2×C3×Dic5—22no—
266C2×C3×Dic5—22no—
267C2×C3×Dic5—28no—
268C2×C3×Dic5#4114yescomplemented
269C2×C3×Dic5C2412yes—
270C2×C3×Dic5C2412yes—
271C2×C3×Dic5C2412yes—
272C2×C3×Dic5C2412yes—
273#1204—28no—
274#1203—28no—
275#1203—28no—
276#1200—28no—
277#1200—28no—
278D3×Dic5—28no—
279C23×C3×C4—51no—
280C23×C3×C4—51no—
281C23×C3×C4C2×D511yescharacteristic
282C22×#67—51no—
283C22×#67—51no—
284C22×#67C2×D511yescharacteristic
285C2×#235—58no—
286C2×#235—58no—
287C2×#235—108no—
288C2×#235—108no—
289C22×D12—51no—
290C22×D12—51no—
291C22×D12—51no—
292C22×C4×D3—51no—
293C22×C4×D3—51no—
294C22×C4×D3—51no—
295C22×C4×D3—51no—
296C22×C4×D3—51no—
297C22×Dic6—51no—
298C22×Dic6—51no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C4⋊C4—51no—
302C2×C3×C4⋊C4—51no—
303C2×C3×C4⋊C4—58no—
304C2×#217C2×D511yescharacteristic
305#930—58no—
306#929—58no—
307#929C2×D518yescomplemented
308C4×#67—58no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×(C2×D3)⋊C4—51no—
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4C2×D511yescharacteristic
315C2×(C2×D3)⋊C4C2×D511yescharacteristic
316C2×C4⋊Dic3—51no—
317C2×Dic3⋊C4—51no—
318C2×Dic3⋊C4—51no—
319C2×Dic3⋊C4—51no—
320C2×Dic3⋊C4C2×D511yescharacteristic
321C2×Dic3⋊C4C2×D511yescharacteristic
322C2×C4×Dic3—51no—
323#896—58no—
324#896—58no—
325#895—58no—
326#894—58no—
327#894—58no—
328#893—58no—
329D3×C4⋊C4—58no—
330#888—58no—
331C24×C5—31no—
332C24×C5C22×D311yescharacteristic
333C23×D5—31no—
334C23×D5—31no—
335C2×C5×D4—34no—
336C2×C5×D4—64no—
337C22×C4×C5—24no—
338C22×C4×C5—31no—
339C22×C4×C5—31no—
340C22×C4×C5—31no—
341C22×C4×C5C22×D311yescharacteristic
342C22×C4×C5C22×D311yescharacteristic
343C22×C4×C5C22×D314yes—
344C2×C22⋊D5—38no—
345C2×C22⋊D5—34no—
346C2×C22⋊D5—34no—
347C2×C22⋊D5—34no—
348C2×C22⋊D5—34no—
349C2×C22⋊D5—64no—
350C2×C22⋊D5—64no—
351C2×C22⋊D5—64no—
352C22×Dic5—24no—
353C22×Dic5—24no—
354C22×Dic5—31no—
355C22×Dic5—31no—
356C22×Dic5—34no—
357C22×Dic5—64no—
358C22×Dic5C22×D311yescharacteristic
359C22×Dic5C22×D311yescharacteristic
360C22×Dic5C22×D311yescharacteristic
361C22×Dic5C22×D314yes—
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⋊Dic5—34no—
386#685—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390C4⋊Dic5—34no—
391C4⋊Dic5—34no—
392#683—34no—
393#683—34no—
394#683C22×D314yes—
395#683C22×D314yes—
396#683C22×D314yes—
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—151no—
410C2×#121—151no—
411C2×C4×D4—151no—
412C2×C4×D4—151no—
413C22×C4⋊C4—51no—
414C22×C4⋊C4—151no—
415C22×C3×C5—28no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5C22×D414yes—
419C22×C3×C5C22×D412yes—
420C22×C3×C5C2×#4112yes—
421C22×C3×C52−1+412yes—
422C22×C3×C5C2511yescharacteristic
423C2×D15—28no—
424C2×D15—22no—
425C2×D15—22no—
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—44no—
430C2×D15C22×D414yes—
431C2×C5×D3—22no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—44no—
435C3×C4×C5—22no—
436C3×C4×C5—22no—
437Dic15—22no—
438Dic15C22×D414yes—
439C3×Dic5—22no—
440C3×Dic5—22no—
441C3×Dic5—22no—
442C3×Dic5C2×#4114yescomplemented
443C5×Dic3—22no—
444C5×Dic3—22no—
445C5×Dic3—22no—
446C24×C3C22×D511yescharacteristic
447C23×D3—51no—
448C23×D3—51no—
449C23×D3C22×D511yescharacteristic
450C22×C3×C4—24no—
451C22×C3×C4—51no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4—54no—
456C22×C3×C4—54no—
457C22×C3×C4—104no—
458C22×C3×C4—104no—
459C22×C3×C4C22×D511yescharacteristic
460C22×C3×C4C22×D511yescharacteristic
461C22×C3×C4C22×D514yes—
462C2×#67—24no—
463C2×#67—58no—
464C2×#67—54no—
465C2×#67—54no—
466C2×#67—104no—
467C2×#67C22×D514yes—
468C22×Dic3—51no—
469C22×Dic3—51no—
470C22×Dic3C22×D511yescharacteristic
471C22×Dic3C22×D511yescharacteristic
472C22×Dic3C22×D511yescharacteristic
473#235—1032no—
474#235—1032no—
475C2×D12—54no—
476C2×D12—54no—
477C2×D12—54no—
478C2×D12—104no—
479C2×D12—104no—
480C2×D12—104no—
481C2×C4×D3—54no—
482C2×C4×D3—54no—
483C2×C4×D3—54no—
484C2×C4×D3—54no—
485C2×C4×D3—54no—
486C2×C4×D3—104no—
487C2×C4×D3—104no—
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×C4⋊C4—54no—
497C3×C4⋊C4—54no—
498C3×C4⋊C4—54no—
499#217C22×D514yes—
500(C2×D3)⋊C4—54no—
501(C2×D3)⋊C4—54no—
502(C2×D3)⋊C4—54no—
503(C2×D3)⋊C4—54no—
504(C2×D3)⋊C4—54no—
505(C2×D3)⋊C4C22×D514yes—
506(C2×D3)⋊C4C22×D514yes—
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—32no—
517C23×C5—62no—
518C23×C5—62no—
519C23×C5—62no—
520C23×C5D3×D414yes—
521C23×C5C23×D312yes—
522C23×C5C23×D311yescharacteristic
523C22×D5—34no—
524C22×D5—32no—
525C22×D5—32no—
526C22×D5—62no—
527C22×D5—62no—
528C22×D5—62no—
529C22×D5—62no—
530C22×D5—62no—
531C5×D4—68no—
532C2×C4×C5—22no—
533C2×C4×C5—22no—
534C2×C4×C5—28no—
535C2×C4×C5—32no—
536C2×C4×C5—32no—
537C2×C4×C5—32no—
538C2×C4×C5—62no—
539C2×C4×C5—62no—
540C2×C4×C5—62no—
541C2×C4×C5C23×D312yes—
542C2×C4×C5C23×D312yes—
543C22⋊D5—316no—
544C22⋊D5—68no—
545C22⋊D5—68no—
546C22⋊D5—68no—
547C2×Dic5—22no—
548C2×Dic5—22no—
549C2×Dic5—22no—
550C2×Dic5—28no—
551C2×Dic5—28no—
552C2×Dic5—34no—
553C2×Dic5—32no—
554C2×Dic5—32no—
555C2×Dic5—68no—
556C2×Dic5—62no—
557C2×Dic5#23514yescomplemented
558C2×Dic5C23×D312yes—
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—31no—
576C22×D4—151no—
577C22×D4—151no—
578C22×D4—151no—
579C22×D4—151no—
580C22×D4—151no—
581C23×C4—51no—
582C23×C4—51no—
583C23×C4—151no—
584C23×C4—151no—
585C23×C4—151no—
586C23×C4—151no—
587C23×C4—151no—
588C23×C4D3×D511yescharacteristic
589C4⋊Q8—158no—
590#123—38no—
591#123—158no—
592#123—158no—
593#123—158no—
594C22⋊Q8—158no—
595C22⋊Q8—158no—
596#121—158no—
597#121—158no—
598C4×D4—158no—
599C4×D4—158no—
600C2×C4⋊C4—31no—
601C2×C4⋊C4—31no—
602C2×C4⋊C4—51no—
603C2×C4⋊C4—51no—
604C2×C4⋊C4—51no—
605C2×C4⋊C4—51no—
606C2×C4⋊C4—58no—
607C2×C4⋊C4—158no—
608C2×C4⋊C4—151no—
609C2×C4⋊C4—151no—
610C2×C4⋊C4—151no—
611C2×C4⋊C4—151no—
612C2×C22⋊C4—31no—
613C2×C22⋊C4—31no—
614C2×C22⋊C4—31no—
615C2×C22⋊C4—151no—
616C2×C22⋊C4—151no—
617C2×C22⋊C4—151no—
618C2×C22⋊C4—151no—
619C2×C22⋊C4—151no—
620C2×C42—151no—
621C2×C3×C5—24no—
622C2×C3×C5#54714yescomplemented
623C2×C3×C5C23×D411yescharacteristic
624C2×C3×C5C22×#4111yescharacteristic
625C2×C3×C5C2×2−1+411yescharacteristic
626D15—24no—
627D15—42no—
628C5×D3—42no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3D4×D514yes—
632C23×C3C23×D512yes—
633C23×C3C23×D511yescharacteristic
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—22no—
637C22×D3—54no—
638C22×D3—52no—
639C22×D3—52no—
640C22×D3—102no—
641C22×D3—102no—
642C22×D3—102no—
643C22×D3—102no—
644C22×D3—102no—
645C22×D3C23×D512yes—
646C2×C3×C4—22no—
647C2×C3×C4—22no—
648C2×C3×C4—28no—
649C2×C3×C4—54no—
650C2×C3×C4—52no—
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×C4—108no—
658C2×C3×C4—102no—
659C2×C3×C4C23×D512yes—
660C2×C3×C4C23×D512yes—
661#67—28no—
662#67—516no—
663#67—108no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—22no—
667C2×Dic3—54no—
668C2×Dic3—52no—
669C2×Dic3—52no—
670C2×Dic3—102no—
671C2×Dic3C23×D512yes—
672C2×Dic3C23×D512yes—
673C2×Dic3C23×D512yes—
674D12—108no—
675D12—108no—
676D12—108no—
677C4×D3—108no—
678C4×D3—108no—
679C4×D3—108no—
680C4×D3—108no—
681C4×D3—108no—
682Dic6—108no—
683Dic6—108no—
684C22×C5—22no—
685C22×C5—22no—
686C22×C5—28no—
687C22×C5—62no—
688C22×C5—62no—
689C22×C5—62no—
690C22×C5—124no—
691C22×C5C2×#23512yes—
692C22×C5C2×D3×D414yes—
693C22×C5C2×D3×D412yes—
694C22×C5#100712yes—
695C22×C5C24×D311yescharacteristic
696C2×D5—34no—
697C2×D5—62no—
698C2×D5—62no—
699C2×D5—68no—
700C2×D5—62no—
701C2×D5—62no—
702C2×D5—62no—
703C2×D5—124no—
704C4×C5—22no—
705C4×C5—22no—
706C4×C5—62no—
707C4×C5—62no—
708C4×C5—62no—
709Dic5—22no—
710Dic5—22no—
711Dic5—22no—
712Dic5—34no—
713Dic5—62no—
714Dic5C2×#23514yescomplemented
715C24—31no—
716C24—151no—
717C24—151no—
718C24C2×D3×D511yescharacteristic
719#41—3032no—
720#41—3032no—
721C2×Q8—154no—
722C2×Q8—154no—
723C2×Q8—304no—
724C2×Q8—304no—
725C2×D4—34no—
726C2×D4—64no—
727C2×D4—154no—
728C2×D4—154no—
729C2×D4—158no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—304no—
734C2×D4—304no—
735C2×D4—304no—
736C2×D4—304no—
737C22×C4—24no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—31no—
741C22×C4—51no—
742C22×C4—54no—
743C22×C4—54no—
744C22×C4—51no—
745C22×C4—51no—
746C22×C4—51no—
747C22×C4—104no—
748C22×C4—104no—
749C22×C4—154no—
750C22×C4—154no—
751C22×C4—154no—
752C22×C4—151no—
753C22×C4—151no—
754C22×C4—154no—
755C22×C4—154no—
756C22×C4—304no—
757C22×C4—304no—
758C22×C4—304no—
759C22×C4—304no—
760C22×C4—304no—
761C22×C4C2×D3×D514yes—
762C22×C4C2×D3×D511yescharacteristic
763C22×C4C2×D3×D511yescharacteristic
764C4⋊C4—34no—
765C4⋊C4—34no—
766C4⋊C4—54no—
767C4⋊C4—54no—
768C4⋊C4—54no—
769C4⋊C4—54no—
770C4⋊C4—154no—
771C4⋊C4—154no—
772C4⋊C4—154no—
773C4⋊C4—154no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—34no—
777C22⋊C4—154no—
778C22⋊C4—154no—
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×C3C2×D4×D514yes—
788C22×C3C2×D4×D512yes—
789C22×C3D5×#4112yes—
790C22×C3#415012yes—
791C22×C3C24×D511yescharacteristic
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—44no—
796C2×D3—54no—
797C2×D3—108no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—102no—
803C2×D3—204no—
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—54no—
807C3×C4—102no—
808C3×C4—102no—
809C3×C4—102no—
810Dic3—22no—
811Dic3—22no—
812Dic3—22no—
813Dic3—54no—
814Dic3—102no—
815C2×C5—24no—
816C2×C5—122no—
817C2×C5#550714yescomplemented
818C2×C5C22×#23511yescharacteristic
819C2×C5C22×D3×D411yescharacteristic
820C2×C5C2×#100711yescharacteristic
821D5—64no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—32no—
826C23—62no—
827C23—62no—
828C23—62no—
829C23—154no—
830C23—152no—
831C23—152no—
832C23—302no—
833C23—302no—
834C23—302no—
835C23—302no—
836C23—302no—
837C23#679014yes—
838C23C22×D3×D512yes—
839C23C22×D3×D511yescharacteristic
840Q8—308no—
841Q8—308no—
842D4—68no—
843D4—1516no—
844D4—308no—
845D4—308no—
846D4—308no—
847D4—308no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—28no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—54no—
855C2×C4—52no—
856C2×C4—52no—
857C2×C4—52no—
858C2×C4—52no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—108no—
863C2×C4—102no—
864C2×C4—102no—
865C2×C4—102no—
866C2×C4—108no—
867C2×C4—154no—
868C2×C4—152no—
869C2×C4—152no—
870C2×C4—308no—
871C2×C4—308no—
872C2×C4—308no—
873C2×C4—308no—
874C2×C4—308no—
875C2×C4—302no—
876C2×C4C22×D3×D512yes—
877C2×C4C22×D3×D512yes—
878C2×C3—24no—
879C2×C3#6598914yescomplemented
880C2×C3C22×D4×D511yescharacteristic
881C2×C3C2×D5×#4111yescharacteristic
882C2×C3C2×#415011yescharacteristic
883D3—42no—
884D3—104no—
885D3—202no—
886C5C2×#550711yescharacteristic, complemented, Sylow
887C22—28no—
888C22—22no—
889C22—22no—
890C22—62no—
891C22—62no—
892C22—62no—
893C22—124no—
894C22—154no—
895C22—308no—
896C22—302no—
897C22—302no—
898C22—302no—
899C22—302no—
900C22—302no—
901C22—604no—
902C22#9200412yes—
903C22D5×#23512yes—
904C22C2×#679014yes—
905C22C2×#679012yes—
906C22C23×D3×D511yescharacteristic
907C4—22no—
908C4—22no—
909C4—54no—
910C4—62no—
911C4—62no—
912C4—62no—
913C4—102no—
914C4—102no—
915C4—102no—
916C4—154no—
917C4—302no—
918C3C2×#6598911yescharacteristic, complemented, Sylow
919C2—24no—
920C2—122no—
921C2—304no—
922C2—602no—
923C2#1175437614yesdirect product factor
924C2C2×#9200411yescharacteristic
925C2C2×D5×#23511yescharacteristic
926C2C22×#679011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#547
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#6817C2semidirect
2. C22×#6782C2semidirect
3. C2×C5×#929C2semidirect
4. C22×C3×#683C2semidirect
5. C2×#91566C2semidirect
6. C2×#91552C2semidirect
7. C2×#91546C2semidirect
8. C2×#91433C2semidirect
9. #11754376C2direct (N × H)
10. C2×#91432C2semidirect
11. C2×#91420C2semidirect
12. C2×#91406C2semidirect
13. C2×#91404C2semidirect
14. C2×#91377C2semidirect
15. C2×#91355C2semidirect
16. C2×#91328C2semidirect
22. C2×#6817C22semidirect
36. C2×#6782C22semidirect
39. C5×#929C22semidirect
48. C2×C3×#683C22semidirect
49. #91566C22semidirect
50. #91552C22semidirect
51. #91546C22semidirect
62. #91433C22semidirect
63. #91432C22semidirect
64. #91420C22semidirect
65. #91406C22semidirect
66. #91404C22semidirect
67. #91377C22semidirect
68. #91355C22semidirect
69. #91328C22semidirect
75. C22×#683D3semidirect
96. C2×#1220D4semidirect
160. C2×#929D5semidirect
211. C2×#683C2×D3semidirect
247. #1220C2×D4semidirect
268. C2×C3×Dic5#41semidirect
307. #929C2×D5semidirect
442. C3×Dic5C2×#41semidirect
557. C2×Dic5#235semidirect
622. C2×C3×C5#547semidirect
714. Dic5C2×#235semidirect
783. C3×C5C2×#547semidirect
817. C2×C5#5507semidirect
879. C2×C3#65989semidirect
886. C5C2×#5507semidirect
918. C3C2×#65989semidirect
923. C2#11754376direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#68172
C22×#67822
C2×C5×#9292
C22×C3×#6832
C2×#915662
C2×#915522
C2×#915462
C2×#914332
#117543762
C2×#914322
C2×#914202
C2×#914062
C2×#914042
C2×#913772
C2×#913552
C2×#913282
C2×#659893
C2×#55075