Finite Group Databasebeta

← C2×#11754984 #14495223

Subgroups — C2×#11754984 #14495223

Order 1920.

2688 conjugacy classes of subgroups.

The subgroup lattice has 984 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91828C211yesmaximal, characteristic, complemented
2C2×C5×#938C211yesmaximal, characteristic, complemented
3C2×C3×#4083C211yesmaximal, characteristic, complemented
4C2×#91571C211yesmaximal, characteristic, complemented
5C2×#91567C211yesmaximal, characteristic, complemented
6C2×#91564C211yesmaximal, characteristic, complemented
7C2×#91563C211yesmaximal, characteristic, complemented
8C2×#91557C211yesmaximal, characteristic, complemented
9C2×#91537C211yesmaximal, characteristic, complemented
10C2×#91533C211yesmaximal, characteristic, complemented
11C2×#91530C211yesmaximal, characteristic, complemented
12#11754984C2116yesmaximal, direct product factor
13C2×#91454C211yesmaximal, characteristic, complemented
14C2×#91452C211yesmaximal, characteristic, complemented
15C2×#91361C211yesmaximal, characteristic, complemented
16C2×#91356C211yesmaximal, characteristic, complemented
17C2×#65954—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C22×C3×C5×D4C2211yescharacteristic
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C23×Dic15C2211yescharacteristic, complemented
23C22×C5×#67C2211yescharacteristic
24C22×C5×#67C2211yescharacteristic, complemented
25C22×C4×C5×D3C2211yescharacteristic, complemented
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×C22⋊D5C2211yescharacteristic
28C22×#1203C2211yescharacteristic, complemented
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic
33C22×#1200C2211yescharacteristic, complemented
34C2×#6719C2211yescharacteristic
35#91828C2218yescomplemented
36C2×#6714C2211yescharacteristic, complemented
37C2×#6712C2211yescharacteristic, complemented
38C2×C5×#217C2211yescharacteristic
39C2×C5×#217C2211yescharacteristic, complemented
40C5×#938C2218yescomplemented
41C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C3×C22⋊Dic5C2211yescharacteristic
43C3×#4083C2218yescomplemented
44C2×C3×#685C2211yescharacteristic
45C2×C3×#685C2211yescharacteristic
46#91571C2218yescomplemented
47#91567C2218yescomplemented
48#91564C2218yescomplemented
49#91563C2218yescomplemented
50#91557C2218yescomplemented
51C2×Dic3⋊Dic5C2211yescharacteristic, complemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6669C2211yescharacteristic, complemented
54C2×#6668C2211yescharacteristic, complemented
55C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
56#91537C2218yescomplemented
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60C2×#6665C2211yescharacteristic
61#91533C2218yescomplemented
62#91530C2218yescomplemented
63C2×Dic3×Dic5C2211yescharacteristic, complemented
64#91454C2218yescomplemented
65#91452C2218yescomplemented
66#91361C2218yescomplemented
67#91356C2218yescomplemented
68C2×#5595—51nomaximal, Hall
69C2×C5×#121—31no—
70C2×#4086—31no—
71C2×#4085—31no—
72C2×#4085—31no—
73C2×#4084—31no—
74C2×#4083—31no—
75C2×#4083D311yescharacteristic, complemented
76C2×#4076—31no—
77C2×#4075—31no—
78#65954—316no—
79C2×#4044—31no—
80C2×#4040—31no—
81C2×#4032—31no—
82C2×#4030—31no—
83C2×#4028—31no—
84C2×#4025—31no—
85C24×C3×C5C2311yescharacteristic
86C24×C3×C5C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5—42no—
90C23×C3×D5—42no—
91C23×C3×D5—42no—
92C23×C3×D5C2311yescharacteristic
93C23×C3×D5C2311yescharacteristic
94C23×C3×D5C2314yes—
95C2×C3×C5×D4—42no—
96C2×C3×C5×D4C2314yes—
97C22×C3×C4×C5C2311yescharacteristic
98C2×#1220—42no—
99C2×#1220—42no—
100C2×#1220C2314yes—
101C2×#1220C2314yescomplemented
102C22×Dic15—42no—
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C22×Dic15C2314yescomplemented
107C2×C5×#67—42no—
108C2×C5×#67—42no—
109C2×C5×#67C2314yes—
110C2×C5×#67C2314yescomplemented
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C22×C5×Dic3C2311yescharacteristic
114C2×C4×C5×D3—42no—
115C2×C4×C5×D3C2314yescomplemented
116C2×C3×C22⋊D5—42no—
117C2×C3×C22⋊D5—42no—
118C2×C3×C22⋊D5C2314yes—
119C2×C3×C22⋊D5C2314yes—
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C2×#1203—42no—
123C2×#1203C2314yescomplemented
124C2×#1202—42no—
125C2×#1202—42no—
126C2×#1202C2314yes—
127C2×#1202C2314yes—
128C2×#1201—42no—
129C2×#1201—42no—
130C2×#1201C2314yes—
131C2×#1201C2314yes—
132C2×#1200—42no—
133C2×#1200C2314yescomplemented
134#6719C2314yes—
135#6714C2314yescomplemented
136#6712C2314yescomplemented
137C5×#217C2314yes—
138C5×#217C2314yescomplemented
139C5×C4⋊Dic3C2314yescomplemented
140C3×C22⋊Dic5C2314yes—
141C3×#685C2314yes—
142C3×#685C2314yes—
143Dic3⋊Dic5C2314yescomplemented
144Dic3⋊Dic5C2314yescomplemented
145#6669C2314yescomplemented
146#6668C2314yescomplemented
147(C2×D3)⋊Dic5C2314yescomplemented
148#6665C2314yes—
149#6665C2314yes—
150#6665C2314yes—
151#6665C2314yes—
152Dic3×Dic5C2314yescomplemented
153C2×C3×#120—51no—
154C2×#953—51no—
155C2×#953—51no—
156C2×#940—51no—
157C2×#939—51no—
158C2×#939—51no—
159C2×#938—51no—
160C2×#938D511yescharacteristic, complemented
161C2×#935—51no—
162#5595—516no—
163C2×#884—51no—
164C2×#884—51no—
165C2×#883—51no—
166C2×#883—51no—
167C2×#879—51no—
168C2×#879—51no—
169C24×D5C2×D311yescharacteristic
170C22×C5×D4—31no—
171C22×C5×D4—31no—
172C22×C5×D4C2×D311yescharacteristic
173C23×C4×C5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5C2×D311yescharacteristic
180C22×C22⋊D5C2×D311yescharacteristic
181C23×Dic5—31no—
182C22×D20—31no—
183C22×D20—31no—
184C22×C4×D5—31no—
185C5×#121—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C22⋊C4—31no—
188C2×C5×C22⋊C4—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191C2×C22⋊Dic5C2×D311yescharacteristic
192#4086—38no—
193#4085—38no—
194#4085—38no—
195#4084—38no—
196#4083—38no—
197#4083C2×D318yescomplemented
198#4076—38no—
199#4075—38no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685C2×D311yescharacteristic
206C2×#685C2×D311yescharacteristic
207C2×C4⋊Dic5—31no—
208C2×C4⋊Dic5—31no—
209C2×#683—31no—
210C2×#683—31no—
211C2×#683—31no—
212C2×C4×Dic5—31no—
213#4044—38no—
214#4040—38no—
215#4032—38no—
216#4030—38no—
217#4028—38no—
218#4025—38no—
219C2×#560—151noSylow
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5—22no—
224C23×C3×C5—22no—
225C23×C3×C5—22no—
226C23×C3×C5C2412yes—
227C23×C3×C5C2412yes—
228C23×C3×C5C2411yescharacteristic
229C22×D15—22no—
230C22×D15—22no—
231C22×D15—22no—
232C22×D15C2412yes—
233C22×C5×D3—22no—
234C22×C5×D3—22no—
235C22×C5×D3—22no—
236C22×C5×D3C2412yes—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—44no—
244C22×C3×D5—44no—
245C22×C3×D5—44no—
246C22×C3×D5—416no—
247C22×C3×D5C2412yes—
248C22×C3×D5C2412yes—
249C3×C5×D4—44no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5C2412yes—
252#1220—44no—
253#1220—44no—
254C2×Dic15—22no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15—44no—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C2×Dic15C2412yes—
261C5×#67—44no—
262C5×#67—44no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3—22no—
266C2×C5×Dic3C2412yes—
267C2×C5×Dic3C2412yes—
268C2×C5×Dic3C2412yes—
269C4×C5×D3—44no—
270C3×C22⋊D5—44no—
271C3×C22⋊D5—44no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5—22no—
274C2×C3×Dic5C2412yes—
275C2×C3×Dic5C2412yes—
276#1203—44no—
277#1202—44no—
278#1202—44no—
279#1201—44no—
280#1201—44no—
281#1200—44no—
282C25×C3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4C2×D511yescharacteristic
286C22×#67—51no—
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67C2×D511yescharacteristic
293C22×#67C2×D511yescharacteristic, complemented
294C23×Dic3—51no—
295C22×D12—51no—
296C22×C4×D3—51no—
297C22×C4×D3C2×D511yescharacteristic, complemented
298C3×#120—58no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302#953—58no—
303#953—58no—
304C2×#217—51no—
305C2×#217—51no—
306C2×#217—51no—
307C2×#217—51no—
308C2×#217—51no—
309C2×#217C2×D511yescharacteristic
310C2×#217C2×D511yescharacteristic, complemented
311#940—58no—
312#939—58no—
313#939—58no—
314#938—58no—
315#938C2×D518yescomplemented
316#935—58no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4—51no—
319C2×C4⋊Dic3—51no—
320C2×C4⋊Dic3C2×D511yescharacteristic, complemented
321C2×Dic3⋊C4—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4—51no—
325C2×C4×Dic3—51no—
326#884—58no—
327#884—58no—
328#883—58no—
329#883—58no—
330#879—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5C22×D311yescharacteristic
334C24×C5C22×D311yescharacteristic
335C23×D5—31no—
336C23×D5—42no—
337C23×D5—42no—
338C23×D5—42no—
339C23×D5C22×D311yescharacteristic
340C23×D5C22×D311yescharacteristic
341C23×D5C22×D314yes—
342C2×C5×D4—34no—
343C2×C5×D4—34no—
344C2×C5×D4—42no—
345C2×C5×D4—122no—
346C2×C5×D4—122no—
347C2×C5×D4C22×D314yes—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5—31no—
351C22×C4×C5—34no—
352C22×C4×C5—122no—
353C22×C4×C5C22×D311yescharacteristic
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—34no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—42no—
360C2×C22⋊D5—42no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5—122no—
364C2×C22⋊D5—122no—
365C2×C22⋊D5—122no—
366C2×C22⋊D5C22×D314yes—
367C2×C22⋊D5C22×D314yes—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5—31no—
371C22×Dic5—34no—
372C22×Dic5—122no—
373C22×Dic5C22×D311yescharacteristic
374C22×Dic5C22×D311yescharacteristic
375C2×D20—34no—
376C2×D20—34no—
377C2×D20—122no—
378C2×D20—122no—
379C2×C4×D5—34no—
380C2×C4×D5—122no—
381C5×C4⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4—34no—
384C22⋊Dic5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5C22×D314yes—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685C22×D314yes—
393#685C22×D314yes—
394C4⋊Dic5—34no—
395C4⋊Dic5—34no—
396#683—34no—
397#683—34no—
398#683—34no—
399C4×Dic5—34no—
400#560—1516no—
401C2×#127—151no—
402C2×#126—151no—
403C2×#126—151no—
404C2×#123—151no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—31no—
408C2×#121—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—51no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—22no—
421C22×C3×C5—22no—
422C22×C3×C5—44no—
423C22×C3×C5—44no—
424C22×C3×C5H(5,𝔽2)12yes—
425C22×C3×C5H(5,𝔽2)12yes—
426C22×C3×C5H(5,𝔽2)12yes—
427C22×C3×C5C2511yescharacteristic
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—22no—
431C2×D15—44no—
432C2×C5×D3—22no—
433C2×C5×D3—22no—
434C2×C5×D3—22no—
435C2×C5×D3—44no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—22no—
442C2×C3×D5—416no—
443C2×C3×D5—44no—
444C2×C3×D5—44no—
445C3×C4×C5—22no—
446Dic15—22no—
447Dic15—22no—
448Dic15—22no—
449C3×Dic5—22no—
450C3×Dic5—22no—
451C5×Dic3—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3—54no—
457C24×C3—202no—
458C24×C3—202no—
459C24×C3—202no—
460C24×C3C22×D511yescharacteristic
461C24×C3C22×D511yescharacteristic
462C23×D3—51no—
463C23×D3C22×D511yescharacteristic
464C2×C3×D4—42no—
465C2×C3×D4—54no—
466C2×C3×D4—54no—
467C2×C3×D4—202no—
468C2×C3×D4—202no—
469C2×C3×D4C22×D514yes—
470C22×C3×C4—51no—
471C22×C3×C4—51no—
472C22×C3×C4C22×D511yescharacteristic
473C2×#67—42no—
474C2×#67—42no—
475C2×#67—54no—
476C2×#67—54no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—202no—
482C2×#67—202no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67C22×D514yes—
488C2×#67C22×D514yescomplemented
489C22×Dic3—51no—
490C22×Dic3—51no—
491C22×Dic3—51no—
492C22×Dic3—54no—
493C22×Dic3—202no—
494C22×Dic3C22×D511yescharacteristic
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497C2×D12—54no—
498C2×D12—202no—
499C2×C4×D3—42no—
500C2×C4×D3—54no—
501C2×C4×D3—202no—
502C2×C4×D3C22×D514yescomplemented
503C3×C22⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4—54no—
506#217—54no—
507#217—54no—
508#217—54no—
509#217—54no—
510#217—54no—
511#217C22×D514yes—
512#217C22×D514yescomplemented
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4—54no—
515C4⋊Dic3—54no—
516C4⋊Dic3C22×D514yescomplemented
517Dic3⋊C4—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
520Dic3⋊C4—54no—
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—22no—
526C23×C5—22no—
527C23×C5—22no—
528C23×C5—32no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5—62no—
532C23×C5C23×D312yes—
533C23×C5C23×D312yes—
534C23×C5C23×D311yescharacteristic
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—22no—
539C22×D5—22no—
540C22×D5—22no—
541C22×D5—32no—
542C22×D5—44no—
543C22×D5—44no—
544C22×D5—44no—
545C22×D5—416no—
546C22×D5—62no—
547C22×D5—62no—
548C22×D5—62no—
549C22×D5C23×D312yes—
550C22×D5C23×D312yes—
551C5×D4—44no—
552C5×D4—124no—
553C5×D4—124no—
554C2×C4×C5—22no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—32no—
558C2×C4×C5—62no—
559C2×C4×C5—62no—
560C2×C4×C5—62no—
561C2×C4×C5—124no—
562C2×C4×C5C23×D312yes—
563C22⋊D5—44no—
564C22⋊D5—44no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C22⋊D5—124no—
570C2×Dic5—22no—
571C2×Dic5—22no—
572C2×Dic5—32no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—62no—
576C2×Dic5—62no—
577C2×Dic5—62no—
578C2×Dic5—124no—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—124no—
582D20—124no—
583C4×D5—124no—
584C25—51no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—51no—
588C22×D4—51no—
589C22×D4—151no—
590C22×D4—151no—
591C22×D4—151no—
592C22×D4—151no—
593C22×D4—151no—
594C22×D4—151no—
595C22×D4—151no—
596C22×D4D3×D511yescharacteristic
597C23×C4—31no—
598C23×C4—151no—
599C23×C4—151no—
600#127—158no—
601#126—158no—
602#126—158no—
603#123—158no—
604#123—158no—
605#123—158no—
606#121—38no—
607#121—158no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121—158no—
612#120—58no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—151no—
617C2×C4⋊C4—151no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—51no—
624C2×C22⋊C4—51no—
625C2×C22⋊C4—51no—
626C2×C22⋊C4—151no—
627C2×C22⋊C4—151no—
628C2×C22⋊C4—151no—
629C2×C22⋊C4—151no—
630C2×C22⋊C4—151no—
631C2×C22⋊C4—151no—
632C2×C22⋊C4—151no—
633C2×C42—151no—
634C2×C3×C5—42no—
635C2×C3×C5—42no—
636C2×C3×C5#56014yescomplemented
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
640D15—42no—
641C3×D5—42no—
642C3×D5—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—52no—
651C23×C3—52no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3—102no—
656C23×C3—102no—
657C23×C3—102no—
658C23×C3—204no—
659C23×C3—204no—
660C23×C3—204no—
661C23×C3—2016no—
662C23×C3C23×D512yes—
663C23×C3C23×D512yes—
664C23×C3C23×D511yescharacteristic
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—22no—
668C22×D3—52no—
669C22×D3—102no—
670C22×D3—102no—
671C22×D3—102no—
672C22×D3C23×D512yes—
673C3×D4—44no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—102no—
680C2×C3×C4—102no—
681C2×C3×C4C23×D512yes—
682#67—44no—
683#67—44no—
684#67—204no—
685#67—204no—
686#67—204no—
687#67—204no—
688#67—204no—
689#67—204no—
690C2×Dic3—22no—
691C2×Dic3—22no—
692C2×Dic3—22no—
693C2×Dic3—52no—
694C2×Dic3—52no—
695C2×Dic3—52no—
696C2×Dic3—102no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3—204no—
700C2×Dic3C23×D512yes—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—204no—
704C4×D3—44no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—22no—
710C22×C5—22no—
711C22×C5—22no—
712C22×C5—44no—
713C22×C5—44no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—124no—
718C22×C5#100412yes—
719C22×C5#100412yes—
720C22×C5#100412yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—416no—
729C2×D5—44no—
730C2×D5—44no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—62no—
737C4×C5—62no—
738C4×C5—62no—
739Dic5—22no—
740Dic5—22no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—51no—
746C24—51no—
747C24—54no—
748C24—151no—
749C24—202no—
750C24—202no—
751C24—202no—
752C24C2×D3×D511yescharacteristic
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—34no—
756C2×D4—42no—
757C2×D4—54no—
758C2×D4—54no—
759C2×D4—122no—
760C2×D4—122no—
761C2×D4—154no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—154no—
768C2×D4—202no—
769C2×D4—202no—
770C2×D4—602no—
771C2×D4—602no—
772C2×D4—602no—
773C2×D4—602no—
774C2×D4—602no—
775C2×D4—602no—
776C2×D4—602no—
777C2×D4C2×D3×D514yes—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—34no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—122no—
785C22×C4—154no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—151no—
789C22×C4—154no—
790C22×C4—602no—
791C22×C4—602no—
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—154no—
795C4⋊C4—154no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—54no—
802C22⋊C4—54no—
803C22⋊C4—54no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C42—154no—
812C3×C5C2×#56011yescharacteristic, complemented, Hall
813C22×C3—22no—
814C22×C3—22no—
815C22×C3—22no—
816C22×C3—22no—
817C22×C3—22no—
818C22×C3—22no—
819C22×C3—44no—
820C22×C3—44no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—102no—
824C22×C3—102no—
825C22×C3—102no—
826C22×C3—102no—
827C22×C3—2016no—
828C22×C3—204no—
829C22×C3—204no—
830C22×C3#414412yes—
831C22×C3#414412yes—
832C22×C3#414912yes—
833C22×C3C24×D511yescharacteristic
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—22no—
837C2×D3—44no—
838C2×D3—102no—
839C2×D3—102no—
840C2×D3—102no—
841C2×D3—204no—
842C3×C4—22no—
843C3×C4—102no—
844C3×C4—102no—
845Dic3—22no—
846Dic3—22no—
847Dic3—22no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—42no—
853C2×C5—122no—
854C2×C5#559514yescomplemented
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100411yescharacteristic
857C2×C5C2×#100411yescharacteristic
858D5—42no—
859D5—42no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23—22no—
867C23—32no—
868C23—52no—
869C23—52no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—102no—
874C23—102no—
875C23—102no—
876C23—102no—
877C23—102no—
878C23—102no—
879C23—152no—
880C23—204no—
881C23—204no—
882C23—204no—
883C23—2016no—
884C23—302no—
885C23—302no—
886C23—302no—
887C23C22×D3×D512yes—
888C23C22×D3×D512yes—
889C23C22×D3×D511yescharacteristic
890D4—44no—
891D4—124no—
892D4—124no—
893D4—204no—
894D4—204no—
895D4—604no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—32no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—52no—
907C2×C4—52no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—102no—
912C2×C4—102no—
913C2×C4—124no—
914C2×C4—152no—
915C2×C4—152no—
916C2×C4—152no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—302no—
920C2×C4—604no—
921C2×C4—604no—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—42no—
925C2×C3—202no—
926C2×C3—202no—
927C2×C3#6595414yescomplemented
928C2×C3C2×#414411yescharacteristic
929C2×C3C2×#414411yescharacteristic
930C2×C3C2×#414911yescharacteristic
931D3—42no—
932D3—202no—
933C5C2×#559511yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—22no—
938C22—22no—
939C22—22no—
940C22—44no—
941C22—44no—
942C22—62no—
943C22—62no—
944C22—62no—
945C22—102no—
946C22—102no—
947C22—102no—
948C22—102no—
949C22—102no—
950C22—102no—
951C22—124no—
952C22—2016no—
953C22—204no—
954C22—204no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—604no—
959C22#9202512yes—
960C22#9202612yes—
961C22#9204912yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—62no—
965C4—62no—
966C4—62no—
967C4—102no—
968C4—102no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6595411yescharacteristic, complemented, Sylow
973C2—42no—
974C2—42no—
975C2—122no—
976C2—202no—
977C2—202no—
978C2—602no—
979C2#1175498414yesdirect product factor
980C2C2×#9202511yescharacteristic
981C2C2×#9202611yescharacteristic
982C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC22×C3×C5×D4C22
socleC23×C3×C5C24
hypercenterC22×D4D3×D5
hypocenterC3×C5C2×#560
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. C2×#91828C2semidirect
2. C2×C5×#938C2semidirect
3. C2×C3×#4083C2semidirect
4. C2×#91571C2semidirect
5. C2×#91567C2semidirect
6. C2×#91564C2semidirect
7. C2×#91563C2semidirect
8. C2×#91557C2semidirect
9. C2×#91537C2semidirect
10. C2×#91533C2semidirect
11. C2×#91530C2semidirect
12. #11754984C2direct (N × H)
13. C2×#91454C2semidirect
14. C2×#91452C2semidirect
15. C2×#91361C2semidirect
16. C2×#91356C2semidirect
21. C22×#1220C22semidirect
22. C23×Dic15C22semidirect
24. C22×C5×#67C22semidirect
25. C22×C4×C5×D3C22semidirect
28. C22×#1203C22semidirect
33. C22×#1200C22semidirect
35. #91828C22semidirect
36. C2×#6714C22semidirect
37. C2×#6712C22semidirect
39. C2×C5×#217C22semidirect
40. C5×#938C22semidirect
41. C2×C5×C4⋊Dic3C22semidirect
43. C3×#4083C22semidirect
46. #91571C22semidirect
47. #91567C22semidirect
48. #91564C22semidirect
49. #91563C22semidirect
50. #91557C22semidirect
51. C2×Dic3⋊Dic5C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6669C22semidirect
54. C2×#6668C22semidirect
55. C2×(C2×D3)⋊Dic5C22semidirect
56. #91537C22semidirect
61. #91533C22semidirect
62. #91530C22semidirect
63. C2×Dic3×Dic5C22semidirect
64. #91454C22semidirect
65. #91452C22semidirect
66. #91361C22semidirect
67. #91356C22semidirect
75. C2×#4083D3semidirect
101. C2×#1220C23semidirect
106. C22×Dic15C23semidirect
110. C2×C5×#67C23semidirect
115. C2×C4×C5×D3C23semidirect
123. C2×#1203C23semidirect
133. C2×#1200C23semidirect
135. #6714C23semidirect
136. #6712C23semidirect
138. C5×#217C23semidirect
139. C5×C4⋊Dic3C23semidirect
143. Dic3⋊Dic5C23semidirect
144. Dic3⋊Dic5C23semidirect
145. #6669C23semidirect
146. #6668C23semidirect
147. (C2×D3)⋊Dic5C23semidirect
152. Dic3×Dic5C23semidirect
160. C2×#938D5semidirect
197. #4083C2×D3semidirect
293. C22×#67C2×D5semidirect
297. C22×C4×D3C2×D5semidirect
310. C2×#217C2×D5semidirect
315. #938C2×D5semidirect
320. C2×C4⋊Dic3C2×D5semidirect
488. C2×#67C22×D5semidirect
502. C2×C4×D3C22×D5semidirect
512. #217C22×D5semidirect
516. C4⋊Dic3C22×D5semidirect
636. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
854. C2×C5#5595semidirect
927. C2×C3#65954semidirect
933. C5C2×#5595semidirect
972. C3C2×#65954semidirect
979. C2#11754984direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918282
C2×C5×#9382
C2×C3×#40832
C2×#915712
C2×#915672
C2×#915642
C2×#915632
C2×#915572
C2×#915372
C2×#915332
C2×#915302
#117549842
C2×#914542
C2×#914522
C2×#913612
C2×#913562
C2×#659543
C2×#55955