Finite Group Databasebeta

← C2×#11752858 #14482761

Subgroups — C2×#11752858 #14482761

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×#6782C211yesmaximal, characteristic, complemented
2C22×#6769C211yesmaximal, characteristic, complemented
3C2×#91773C211yesmaximal, characteristic, complemented
4C2×C5×#883C211yesmaximal, characteristic, complemented
5C2×C3×#4024C211yesmaximal, characteristic, complemented
6C2×#91562C211yesmaximal, characteristic, complemented
7C2×#91558C211yesmaximal, characteristic, complemented
8C2×#91552C211yesmaximal, characteristic, complemented
9C2×#91437C211yesmaximal, characteristic, complemented
10C2×#91433C211yesmaximal, characteristic, complemented
11C2×#91427C211yesmaximal, characteristic, complemented
12C2×#91419C211yesmaximal, characteristic, complemented
13C2×#91406C211yesmaximal, characteristic, complemented
14C2×D3×#683C211yesmaximal, characteristic, complemented
15C2×#91327C211yesmaximal, characteristic, complemented
16#11752858C2116yesmaximal, direct product factor
17C2×#65989—31nomaximal, Hall
18C22×#1220C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C22×C4×D15C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C4×C5×D3C2211yescharacteristic
24C23×C3×Dic5C2211yescharacteristic
25C22×C3×Dic10C2211yescharacteristic
26C22×#1204C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1203C2211yescharacteristic
29C22×#1200C2211yescharacteristic
30C22×#1200C2211yescharacteristic
31C22×#1200C2211yescharacteristic
32C2×#6782—28no—
33C2×#6782C2218yescomplemented
34C22×D3×Dic5C2211yescharacteristic
35C22×D3×Dic5C2211yescharacteristic
36C2×#6769—28no—
37C2×#6769C2218yescomplemented
38C2×C3×C5×C22⋊C4C2211yescharacteristic
39C2×#6714C2211yescharacteristic
40C2×#6712C2211yescharacteristic
41#91773C2218yescomplemented
42C2×C5×#217C2211yescharacteristic
43C2×C5×(C2×D3)⋊C4C2211yescharacteristic
44C2×C5×C4⋊Dic3C2211yescharacteristic
45C2×C5×Dic3⋊C4C2211yescharacteristic
46C5×#883C2218yescomplemented
47C2×C3×C22⋊Dic5C2211yescharacteristic
48C2×C3×C4⋊Dic5C2211yescharacteristic
49C2×C3×#683C2211yescharacteristic
50C2×C3×#683C2211yescharacteristic
51C3×#4024C2218yescomplemented
52#91562C2218yescomplemented
53#91558C2218yescomplemented
54#91552C2218yescomplemented
55C2×Dic3⋊Dic5C2211yescharacteristic
56C2×#6669C2211yescharacteristic
57C2×#6669C2211yescharacteristic
58C2×#6668C2211yescharacteristic
59C2×#6667C2211yescharacteristic
60C2×#6667C2211yescharacteristic
61C2×#6667C2211yescharacteristic
62C2×Dic3×Dic5C2211yescharacteristic
63#91437C2218yescomplemented
64#91433C2218yescomplemented
65#91427C2218yescomplemented
66#91419C2218yescomplemented
67#91406C2218yescomplemented
68D3×#683C2218yescomplemented
69#91327C2218yescomplemented
70C2×#5631—51nomaximal, Hall
71C22×#711—31no—
72C22×#709—31no—
73C2×C5×#123—31no—
74C2×#4085—31no—
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×#4024D311yescharacteristic, complemented
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×D15C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C2×#1220—24no—
94C2×#1220—24no—
95C2×#1220C2314yes—
96C2×#1220C2314yes—
97C22×Dic15C2311yescharacteristic
98C22×Dic15C2311yescharacteristic
99C2×D60—24no—
100C2×D60C2314yes—
101C2×C4×D15—24no—
102C2×C4×D15C2314yes—
103C2×C5×#67—24no—
104C2×C5×#67C2314yes—
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C2×C4×C5×D3—24no—
109C2×C4×C5×D3C2314yes—
110C22×C3×Dic5—24no—
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C22×C3×Dic5C2311yescharacteristic
114C22×C3×Dic5C2314yes—
115C22×C3×Dic5C2311yescharacteristic
116C2×C3×Dic10—24no—
117C2×C3×Dic10C2314yes—
118C2×#1204—24no—
119C2×#1204C2314yes—
120C2×#1203—24no—
121C2×#1203D418yescomplemented
122C2×#1203C2314yes—
123C2×#1203C2314yes—
124C2×#1200—24no—
125C2×#1200—24no—
126C2×#1200—24no—
127C2×#1200C2314yes—
128C2×#1200C2314yes—
129C2×#1200C2314yes—
130#6782—232no—
131C2×D3×Dic5—24no—
132C2×D3×Dic5—24no—
133C2×D3×Dic5C2314yes—
134C2×D3×Dic5C2314yes—
135#6769—232no—
136C3×C5×C22⋊C4C2314yes—
137#6714C2314yes—
138#6712C2314yes—
139C5×#217C2314yes—
140C5×(C2×D3)⋊C4C2314yes—
141C5×C4⋊Dic3C2314yes—
142C5×Dic3⋊C4C2314yes—
143C3×C22⋊Dic5C2314yes—
144C3×C4⋊Dic5C2314yes—
145C3×#683C2314yes—
146C3×#683C2314yes—
147Dic3⋊Dic5C2314yes—
148#6669C2314yes—
149#6669C2314yes—
150#6668C2314yes—
151#6667C2314yes—
152#6667C2314yes—
153#6667C2314yes—
154Dic3×Dic5C2314yes—
155C22×#239—51no—
156C22×#235—51no—
157C2×C3×C22⋊Q8—51no—
158C2×#944—51no—
159C2×C4×#67—51no—
160#5631—516no—
161C2×#897—51no—
162C2×#894—51no—
163C2×#894—51no—
164C2×#893—51no—
165C2×D3×C4⋊C4—51no—
166C2×D3×C4⋊C4—51no—
167C2×#884—51no—
168C2×#884—51no—
169C2×#883—51no—
170C2×#883D511yescharacteristic, complemented
171C22×C5×D4—31no—
172C23×C4×C5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
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×Dic10C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
197C2×C22⋊Dic5C2×D311yescharacteristic
198#4085—38no—
199C2×#685—31no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×C4⋊Dic5—31no—
204C2×C4⋊Dic5C2×D311yescharacteristic
205C2×#683—31no—
206C2×#683—31no—
207C2×#683—31no—
208C2×#683—31no—
209C2×#683—38no—
210C2×#683C2×D311yescharacteristic
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#4024C2×D318yescomplemented
223C2×#547—151noSylow
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5—22no—
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×D3C2×D414yes—
240C22×C5×D3C2412yes—
241C2×C3×C4×C5—22no—
242C2×C3×C4×C5—22no—
243C2×C3×C4×C5C2412yes—
244C2×C3×C4×C5C2412yes—
245#1220—28no—
246#1220—28no—
247C2×Dic15—22no—
248C2×Dic15#4114yescomplemented
249C2×Dic15C2412yes—
250C2×Dic15C2412yes—
251D60—28no—
252C4×D15—28no—
253C5×#67—28no—
254C2×C5×Dic3—22no—
255C2×C5×Dic3—22no—
256C2×C5×Dic3—22no—
257C2×C5×Dic3C2412yes—
258C2×C5×Dic3C2412yes—
259C2×C5×Dic3C2412yes—
260C4×C5×D3—28no—
261C2×C3×Dic5—22no—
262C2×C3×Dic5—22no—
263C2×C3×Dic5—22no—
264C2×C3×Dic5—28no—
265C2×C3×Dic5C2×D414yes—
266C2×C3×Dic5C2412yes—
267C2×C3×Dic5C2412yes—
268C2×C3×Dic5C2412yes—
269C2×C3×Dic5C2412yes—
270C3×Dic10—28no—
271#1204—28no—
272#1203—28no—
273#1203C2×D4116yescomplemented
274#1200—28no—
275#1200—28no—
276#1200—28no—
277D3×Dic5—28no—
278D3×Dic5—28no—
279C22×C3×Q8—51no—
280C23×C3×C4—51no—
281C22×#67—51no—
282C22×#67—51no—
283C22×#67C2×D511yescharacteristic
284C2×#239—58no—
285C2×#239—108no—
286C2×#235—58no—
287C2×#235—108no—
288C22×D12—51no—
289C22×D12—51no—
290C22×D12—51no—
291C22×C4×D3—51no—
292C22×C4×D3—51no—
293C22×C4×D3—51no—
294C22×C4×D3—51no—
295C22×C4×D3—51no—
296C22×C4×D3—51no—
297C22×C4×D3C2×D511yescharacteristic
298C22×Dic6—51no—
299C3×C22⋊Q8—58no—
300C2×C3×C4⋊C4—51no—
301C2×C3×C4⋊C4—51no—
302C2×C3×C4⋊C4—51no—
303C2×C3×C22⋊C4—51no—
304C2×C3×C22⋊C4C2×D511yescharacteristic
305C2×#217C2×D511yescharacteristic
306#944—58no—
307C4×#67—58no—
308C2×(C2×D3)⋊C4—51no—
309C2×(C2×D3)⋊C4—51no—
310C2×(C2×D3)⋊C4—51no—
311C2×(C2×D3)⋊C4—51no—
312C2×(C2×D3)⋊C4C2×D511yescharacteristic
313C2×C4⋊Dic3—51no—
314C2×C4⋊Dic3C2×D511yescharacteristic
315C2×Dic3⋊C4—51no—
316C2×Dic3⋊C4—51no—
317C2×Dic3⋊C4—51no—
318C2×Dic3⋊C4—51no—
319C2×Dic3⋊C4C2×D511yescharacteristic
320C2×C4×Dic3—51no—
321#897—58no—
322#894—58no—
323#894—58no—
324#893—58no—
325D3×C4⋊C4—58no—
326D3×C4⋊C4—58no—
327#884—58no—
328#884—58no—
329#883—58no—
330#883C2×D518yescomplemented
331C24×C5—31no—
332C24×C5C22×D311yescharacteristic
333C23×D5—31no—
334C23×D5—31no—
335C2×C5×D4—34no—
336C2×C5×D4—64no—
337C22×C4×C5—31no—
338C22×C4×C5—31no—
339C22×C4×C5—31no—
340C22×C4×C5—34no—
341C22×C4×C5—64no—
342C22×C4×C5C22×D311yescharacteristic
343C22×C4×C5C22×D311yescharacteristic
344C2×C22⋊D5—34no—
345C2×C22⋊D5—34no—
346C2×C22⋊D5—38no—
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—31no—
354C22×Dic5—31no—
355C22×Dic5—34no—
356C22×Dic5—34no—
357C22×Dic5—64no—
358C22×Dic5—64no—
359C22×Dic5C22×D311yescharacteristic
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—24no—
377C2×Dic10—34no—
378C2×Dic10—64no—
379C2×Dic10C22×D314yes—
380C5×C4⋊C4—34no—
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C5×C22⋊C4C22×D314yes—
385C22⋊Dic5C22×D314yes—
386#685—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390C4⋊Dic5—34no—
391C4⋊Dic5C22×D314yes—
392#683—34no—
393#683—34no—
394#683—34no—
395#683—34no—
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—51no—
408C2×C22⋊Q8—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×C4×D4—151no—
412C2×C4×D4—151no—
413C22×C4⋊C4—151no—
414C22×C4⋊C4—151no—
415C22×C3×C5—22no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—44no—
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—28no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3C22×D414yes—
435C3×C4×C5—22no—
436C3×C4×C5—22no—
437Dic15—22no—
438Dic15C2×#4114yescomplemented
439C3×Dic5—22no—
440C3×Dic5—22no—
441C3×Dic5—22no—
442C3×Dic5C22×D414yes—
443C5×Dic3—22no—
444C5×Dic3—22no—
445C5×Dic3—22no—
446C24×C3C22×D511yescharacteristic
447C23×D3—51no—
448C23×D3—51no—
449C23×D3C22×D511yescharacteristic
450C2×C3×Q8—54no—
451C2×C3×Q8—104no—
452C22×C3×C4—51no—
453C22×C3×C4—51no—
454C22×C3×C4—51no—
455C22×C3×C4—51no—
456C22×C3×C4—54no—
457C22×C3×C4—104no—
458C22×C3×C4C22×D511yescharacteristic
459C22×C3×C4C22×D511yescharacteristic
460C2×#67—24no—
461C2×#67—54no—
462C2×#67—54no—
463C2×#67—104no—
464C2×#67—104no—
465C2×#67C22×D514yes—
466C22×Dic3—51no—
467C22×Dic3—51no—
468C22×Dic3C22×D511yescharacteristic
469C22×Dic3C22×D511yescharacteristic
470C22×Dic3C22×D511yescharacteristic
471#239—1032no—
472#235—1032no—
473C2×D12—58no—
474C2×D12—54no—
475C2×D12—54no—
476C2×D12—54no—
477C2×D12—104no—
478C2×D12—104no—
479C2×C4×D3—24no—
480C2×C4×D3—54no—
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×C4×D3—104no—
492C2×C4×D3C22×D514yes—
493C2×Dic6—54no—
494C2×Dic6—104no—
495C3×C4⋊C4—54no—
496C3×C4⋊C4—54no—
497C3×C4⋊C4—54no—
498C3×C22⋊C4—54no—
499C3×C22⋊C4C22×D514yes—
500#217C22×D514yes—
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—
506C4⋊Dic3—54no—
507C4⋊Dic3C22×D514yes—
508Dic3⋊C4—54no—
509Dic3⋊C4—54no—
510Dic3⋊C4—54no—
511Dic3⋊C4—54no—
512Dic3⋊C4C22×D514yes—
513C4×Dic3—54no—
514C23×C5—22no—
515C23×C5—22no—
516C23×C5—22no—
517C23×C5—34no—
518C23×C5—32no—
519C23×C5—62no—
520C23×C5—62no—
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—32no—
535C2×C4×C5—32no—
536C2×C4×C5—32no—
537C2×C4×C5—68no—
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—34no—
552C2×Dic5—32no—
553C2×Dic5—32no—
554C2×Dic5—68no—
555C2×Dic5—68no—
556C2×Dic5—62no—
557C2×Dic5D3×D414yes—
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—28no—
568Dic10—68no—
569C2×#41—158no—
570C2×#41—158no—
571C2×#41—308no—
572C2×#41—308no—
573C22×Q8—51no—
574C22×Q8—151no—
575C22×D4—31no—
576C22×D4—151no—
577C22×D4—151no—
578C22×D4—151no—
579C22×D4—151no—
580C22×D4—151no—
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—58no—
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—158no—
606C2×C4⋊C4—158no—
607C2×C4⋊C4—151no—
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—51no—
615C2×C22⋊C4—151no—
616C2×C22⋊C4—151no—
617C2×C22⋊C4—151no—
618C2×C22⋊C4—151no—
619C2×C22⋊C4D3×D511yescharacteristic
620C2×C42—151no—
621C2×C3×C5—42no—
622C2×C3×C5#54714yescomplemented
623C2×C3×C5C23×D411yescharacteristic
624C2×C3×C5C22×#4111yescharacteristic
625C2×C3×C5C2×2−1+411yescharacteristic
626D15—24no—
627D15—42no—
628C5×D3—24no—
629C23×C3—22no—
630C23×C3—22no—
631C23×C3—22no—
632C23×C3C23×D512yes—
633C23×C3C23×D511yescharacteristic
634C22×D3—22no—
635C22×D3—22no—
636C22×D3—54no—
637C22×D3—52no—
638C22×D3—52no—
639C22×D3—102no—
640C22×D3—102no—
641C22×D3—102no—
642C22×D3—102no—
643C22×D3—102no—
644C22×D3D4×D514yes—
645C22×D3C23×D512yes—
646C3×Q8—108no—
647C2×C3×C4—22no—
648C2×C3×C4—22no—
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—102no—
658C2×C3×C4C23×D512yes—
659C2×C3×C4C23×D512yes—
660#67—28no—
661#67—108no—
662#67—108no—
663C2×Dic3—22no—
664C2×Dic3—22no—
665C2×Dic3—22no—
666C2×Dic3—54no—
667C2×Dic3—52no—
668C2×Dic3—52no—
669C2×Dic3—102no—
670C2×Dic3C23×D512yes—
671C2×Dic3C23×D512yes—
672C2×Dic3C23×D512yes—
673D12—516no—
674D12—108no—
675D12—108no—
676C4×D3—28no—
677C4×D3—108no—
678C4×D3—108no—
679C4×D3—108no—
680C4×D3—108no—
681C4×D3—108no—
682C4×D3—108no—
683Dic6—108no—
684C22×C5—22no—
685C22×C5—22no—
686C22×C5—22no—
687C22×C5—34no—
688C22×C5—44no—
689C22×C5—62no—
690C22×C5—62no—
691C22×C5—68no—
692C22×C5C2×D3×D412yes—
693C22×C5#100712yes—
694C22×C5D3×#4112yes—
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×D3×D414yes—
715C24—31no—
716C24—151no—
717C24—151no—
718C24C2×D3×D511yescharacteristic
719#41—3032no—
720#41—3032no—
721C2×Q8—54no—
722C2×Q8—104no—
723C2×Q8—154no—
724C2×Q8—304no—
725C2×D4—34no—
726C2×D4—64no—
727C2×D4—154no—
728C2×D4—158no—
729C2×D4—154no—
730C2×D4—154no—
731C2×D4—154no—
732C2×D4—154no—
733C2×D4—304no—
734C2×D4—304no—
735C2×D4—304no—
736C2×D4—304no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—31no—
740C22×C4—34no—
741C22×C4—51no—
742C22×C4—54no—
743C22×C4—51no—
744C22×C4—51no—
745C22×C4—51no—
746C22×C4—64no—
747C22×C4—104no—
748C22×C4—154no—
749C22×C4—154no—
750C22×C4—154no—
751C22×C4—154no—
752C22×C4—154no—
753C22×C4—151no—
754C22×C4—151no—
755C22×C4—154no—
756C22×C4—304no—
757C22×C4—304no—
758C22×C4—304no—
759C22×C4—304no—
760C22×C4—304no—
761C22×C4—304no—
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—154no—
770C4⋊C4—154no—
771C4⋊C4—154no—
772C4⋊C4—154no—
773C4⋊C4—154no—
774C22⋊C4—34no—
775C22⋊C4—34no—
776C22⋊C4—54no—
777C22⋊C4—154no—
778C22⋊C4—154no—
779C22⋊C4—154no—
780C22⋊C4—154no—
781C22⋊C4C2×D3×D514yes—
782C42—154no—
783C3×C5C2×#54711yescharacteristic, complemented, Hall
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—22no—
787C22×C3—44no—
788C22×C3C2×D4×D512yes—
789C22×C3D5×#4112yes—
790C22×C3#415012yes—
791C22×C3C24×D511yescharacteristic
792C2×D3—28no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—54no—
796C2×D3—108no—
797C2×D3—102no—
798C2×D3—102no—
799C2×D3—102no—
800C2×D3—102no—
801C2×D3—102no—
802C2×D3—204no—
803C2×D3C2×D4×D514yes—
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—42no—
816C2×C5—64no—
817C2×C5#563114yescomplemented
818C2×C5C22×D3×D411yescharacteristic
819C2×C5C2×#100711yescharacteristic
820C2×C5C2×D3×#4111yescharacteristic
821D5—64no—
822D5—122no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—34no—
827C23—32no—
828C23—62no—
829C23—62no—
830C23—154no—
831C23—152no—
832C23—152no—
833C23—302no—
834C23—302no—
835C23—302no—
836C23—302no—
837C23—302no—
838C23C22×D3×D512yes—
839C23C22×D3×D511yescharacteristic
840Q8—108no—
841Q8—308no—
842D4—68no—
843D4—1516no—
844D4—308no—
845D4—308no—
846D4—308no—
847D4—308no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—54no—
854C2×C4—52no—
855C2×C4—52no—
856C2×C4—52no—
857C2×C4—52no—
858C2×C4—68no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—108no—
863C2×C4—102no—
864C2×C4—102no—
865C2×C4—102no—
866C2×C4—154no—
867C2×C4—152no—
868C2×C4—152no—
869C2×C4—308no—
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—42no—
879C2×C3#6598914yescomplemented
880C2×C3C22×D4×D511yescharacteristic
881C2×C3C2×D5×#4111yescharacteristic
882C2×C3C2×#415011yescharacteristic
883D3—24no—
884D3—104no—
885D3—202no—
886C5C2×#563111yescharacteristic, complemented, Sylow
887C22—22no—
888C22—22no—
889C22—22no—
890C22—34no—
891C22—44no—
892C22—68no—
893C22—62no—
894C22—62no—
895C22—154no—
896C22—308no—
897C22—302no—
898C22—302no—
899C22—302no—
900C22—302no—
901C22—302no—
902C22—604no—
903C22#9200412yes—
904C22D3×D4×D512yes—
905C22#9202412yes—
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—42no—
920C2—64no—
921C2—304no—
922C2—602no—
923C2#1175285814yesdirect product factor
924C2C2×#9200411yescharacteristic
925C2C2×D3×D4×D511yescharacteristic
926C2C2×#9202411yescharacteristic
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×#547
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×#6782C2semidirect
2. C22×#6769C2semidirect
3. C2×#91773C2semidirect
4. C2×C5×#883C2semidirect
5. C2×C3×#4024C2semidirect
6. C2×#91562C2semidirect
7. C2×#91558C2semidirect
8. C2×#91552C2semidirect
9. C2×#91437C2semidirect
10. C2×#91433C2semidirect
11. C2×#91427C2semidirect
12. C2×#91419C2semidirect
13. C2×#91406C2semidirect
14. C2×D3×#683C2semidirect
15. C2×#91327C2semidirect
16. #11752858C2direct (N × H)
33. C2×#6782C22semidirect
37. C2×#6769C22semidirect
41. #91773C22semidirect
46. C5×#883C22semidirect
51. C3×#4024C22semidirect
52. #91562C22semidirect
53. #91558C22semidirect
54. #91552C22semidirect
63. #91437C22semidirect
64. #91433C22semidirect
65. #91427C22semidirect
66. #91419C22semidirect
67. #91406C22semidirect
68. D3×#683C22semidirect
69. #91327C22semidirect
86. C2×#4024D3semidirect
121. C2×#1203D4semidirect
170. C2×#883D5semidirect
222. #4024C2×D3semidirect
248. C2×Dic15#41semidirect
273. #1203C2×D4semidirect
330. #883C2×D5semidirect
438. Dic15C2×#41semidirect
622. C2×C3×C5#547semidirect
783. C3×C5C2×#547semidirect
817. C2×C5#5631semidirect
879. C2×C3#65989semidirect
886. C5C2×#5631semidirect
918. C3C2×#65989semidirect
923. C2#11752858direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67822
C22×#67692
C2×#917732
C2×C5×#8832
C2×C3×#40242
C2×#915622
C2×#915582
C2×#915522
C2×#914372
C2×#914332
C2×#914272
C2×#914192
C2×#914062
C2×D3×#6832
C2×#913272
#117528582
C2×#659893
C2×#56315