Finite Group Databasebeta

← C2×#11754685 #14495211

Subgroups — C2×#11754685 #14495211

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×#91819C211yesmaximal, characteristic, complemented
2C2×C5×#929C211yesmaximal, characteristic, complemented
3C2×C3×#4076C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91567C211yesmaximal, characteristic, complemented
6C2×#91550C211yesmaximal, characteristic, complemented
7C2×#91533C211yesmaximal, characteristic, complemented
8#11754685C2116yesmaximal, direct product factor
9C2×#91476C211yesmaximal, characteristic, complemented
10C2×#91474C211yesmaximal, characteristic, complemented
11C2×#91459C211yesmaximal, characteristic, complemented
12C2×#91438C211yesmaximal, characteristic, complemented
13C2×#91414C211yesmaximal, characteristic, complemented
14C2×#91409C211yesmaximal, characteristic, complemented
15C2×#91362C211yesmaximal, characteristic, complemented
16C2×#91345C211yesmaximal, characteristic, complemented
17C2×#66000—31nomaximal, Hall
18C23×D3×D5C2211yescharacteristic
19C23×C3×C4×C5C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×#1220C2211yescharacteristic, complemented
22C22×D60C2211yescharacteristic
23C22×C5×#67C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic, complemented
26C22×C3×D20C2211yescharacteristic
27C22×#1203C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1202C2211yescharacteristic, complemented
31C22×#1201C2211yescharacteristic
32C22×#1200C2211yescharacteristic, complemented
33C22×D5×Dic3C2211yescharacteristic, complemented
34#91819C2218yescomplemented
35C2×#6714C2211yescharacteristic
36C2×#6714C2211yescharacteristic, complemented
37C2×C4⋊Dic15C2211yescharacteristic, complemented
38C2×C5×#217C2211yescharacteristic, complemented
39C5×#929C2218yescomplemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic
41C2×C5×(C2×D3)⋊C4C2211yescharacteristic
42C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
43C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
44C3×#4076C2218yescomplemented
45C2×C3×#685C2211yescharacteristic
46C2×C3×#685C2211yescharacteristic, complemented
47C2×C3×C4⋊Dic5C2211yescharacteristic, complemented
48#91577C2218yescomplemented
49#91567C2218yescomplemented
50#91550C2218yescomplemented
51C2×#6669C2211yescharacteristic, complemented
52C2×#6668C2211yescharacteristic, complemented
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58#91533C2218yescomplemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91476C2218yescomplemented
61#91474C2218yescomplemented
62#91459C2218yescomplemented
63#91438C2218yescomplemented
64#91414C2218yescomplemented
65#91409C2218yescomplemented
66#91362C2218yescomplemented
67#91345C2218yescomplemented
68C2×#5620—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4086—31no—
71C2×#4083—31no—
72C2×#4076—31no—
73C2×#4076D311yescharacteristic, complemented
74#66000—316no—
75C2×#4044—31no—
76C2×#4044—31no—
77C2×#4041—31no—
78C2×#4041—31no—
79C2×#4030—31no—
80C2×#4030—31no—
81C2×#4029—31no—
82C2×#4029—31no—
83C2×#4028—31no—
84C2×#4028—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C5×D3C2311yescharacteristic
89C23×C3×D5C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
91C22×D3×D5—42no—
92C22×D3×D5—42no—
93C22×D3×D5—42no—
94C22×D3×D5C2314yes—
95C22×C3×C4×C5—42no—
96C22×C3×C4×C5C2311yescharacteristic
97C22×C3×C4×C5C2311yescharacteristic
98C22×C3×C4×C5C2314yescomplemented
99C2×#1220—42no—
100C2×#1220—42no—
101C2×#1220C2314yes—
102C2×#1220C2314yescomplemented
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C2×D60—42no—
106C2×D60C2314yes—
107C2×C5×#67—42no—
108C2×C5×#67C2314yes—
109C22×C5×Dic3C2311yescharacteristic
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C2×C3×C22⋊D5—42no—
113C2×C3×C22⋊D5—42no—
114C2×C3×C22⋊D5C2314yes—
115C2×C3×C22⋊D5C2314yescomplemented
116C22×C3×Dic5C2311yescharacteristic
117C22×C3×Dic5C2311yescharacteristic
118C2×C3×D20—42no—
119C2×C3×D20C2314yes—
120C2×#1203—42no—
121C2×#1203C2314yes—
122C2×#1202—42no—
123C2×#1202—42no—
124C2×#1202—42no—
125C2×#1202C2314yes—
126C2×#1202C2314yes—
127C2×#1202C2314yescomplemented
128C2×#1201—42no—
129C2×#1201C2314yes—
130C2×#1200—42no—
131C2×#1200C2314yescomplemented
132C2×D5×Dic3—42no—
133C2×D5×Dic3C2314yescomplemented
134#6714C2314yes—
135#6714C2314yescomplemented
136C4⋊Dic15C2314yescomplemented
137C5×#217C2314yescomplemented
138C5×(C2×D3)⋊C4C2314yes—
139C5×(C2×D3)⋊C4C2314yes—
140C5×Dic3⋊C4C2314yescomplemented
141C5×Dic3⋊C4C2314yescomplemented
142C3×#685C2314yes—
143C3×#685C2314yescomplemented
144C3×C4⋊Dic5C2314yescomplemented
145#6669C2314yescomplemented
146#6668C2314yescomplemented
147#6667C2314yes—
148#6667C2314yes—
149(C2×D3)⋊Dic5C2314yes—
150#6665C2314yes—
151#6665C2314yes—
152Dic3×Dic5C2314yescomplemented
153C2×C3×#121—51no—
154C2×#940—51no—
155C2×#939—51no—
156C2×#939—51no—
157C2×#938—51no—
158C2×#937—51no—
159C2×#937—51no—
160C2×#930—51no—
161C2×#929D511yescharacteristic, complemented
162#5620—516no—
163C2×#898—51no—
164C2×#894—51no—
165C2×#886—51no—
166C2×#884—51no—
167C2×#882—51no—
168C2×#879—51no—
169C24×D5—31no—
170C22×C5×D4—31no—
171C23×C4×C5C2×D311yescharacteristic, complemented
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5C2×D311yescharacteristic
177C22×C22⋊D5C2×D311yescharacteristic, complemented
178C22×D20—31no—
179C22×D20—31no—
180C22×D20—31no—
181C22×D20—31no—
182C22×D20C2×D311yescharacteristic
183C22×C4×D5—31no—
184C22×C4×D5—31no—
185C5×#123—38no—
186C2×C5×C4⋊C4—31no—
187C2×C5×C4⋊C4—31no—
188C2×C5×C22⋊C4—31no—
189C2×C5×C22⋊C4—31no—
190C2×C5×C22⋊C4—31no—
191C2×C22⋊Dic5—31no—
192#4086—38no—
193#4083—38no—
194#4076—38no—
195#4076C2×D318yescomplemented
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685C2×D311yescharacteristic
203C2×#685C2×D311yescharacteristic, complemented
204C2×C4⋊Dic5—31no—
205C2×C4⋊Dic5C2×D311yescharacteristic, complemented
206C2×#683—31no—
207C2×#683—31no—
208C2×C4×Dic5—31no—
209#4044—38no—
210#4044—38no—
211#4041—38no—
212#4041—38no—
213#4030—38no—
214#4030—38no—
215#4029—38no—
216#4029—38no—
217#4028—38no—
218#4028—38no—
219C2×#560—151noSylow
220C23×C3×C5—22no—
221C23×C3×C5—22no—
222C23×C3×C5—22no—
223C23×C3×C5C2412yes—
224C23×C3×C5C2411yescharacteristic
225C22×D15—22no—
226C22×D15—22no—
227C22×D15—22no—
228C22×D15—22no—
229C22×D15—22no—
230C22×D15—22no—
231C22×D15C2412yes—
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×D5C2412yes—
244C22×C3×D5C2412yes—
245C2×D3×D5—44no—
246C2×D3×D5—44no—
247C2×D3×D5—44no—
248C2×D3×D5—416no—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5—44no—
252C2×C3×C4×C5C2412yes—
253C2×C3×C4×C5C2412yes—
254#1220—44no—
255#1220—44no—
256C2×Dic15—22no—
257C2×Dic15—22no—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260D60—44no—
261C5×#67—44no—
262C2×C5×Dic3—22no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3—22no—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C2×C5×Dic3C2412yes—
268C3×C22⋊D5—44no—
269C3×C22⋊D5—44no—
270C2×C3×Dic5—22no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5C2412yes—
273C2×C3×Dic5C2412yes—
274C3×D20—44no—
275#1203—44no—
276#1202—44no—
277#1202—44no—
278#1202—44no—
279#1201—44no—
280#1200—44no—
281D5×Dic3—44no—
282C24×D3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4—51no—
286C23×C3×C4C2×D511yescharacteristic, complemented
287C22×#67—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67C2×D511yescharacteristic
294C23×Dic3—51no—
295C22×D12—51no—
296C22×D12—51no—
297C22×C4×D3—51no—
298C3×#121—58no—
299C2×C3×C4⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4—51no—
302C2×#217—51no—
303C2×#217—51no—
304C2×#217C2×D511yescharacteristic, complemented
305#940—58no—
306#939—58no—
307#939—58no—
308#938—58no—
309#937—58no—
310#937—58no—
311#930—58no—
312#929C2×D518yescomplemented
313C2×(C2×D3)⋊C4—51no—
314C2×(C2×D3)⋊C4—51no—
315C2×(C2×D3)⋊C4—51no—
316C2×(C2×D3)⋊C4—51no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4C2×D511yescharacteristic
319C2×(C2×D3)⋊C4C2×D511yescharacteristic
320C2×C4⋊Dic3—51no—
321C2×C4⋊Dic3—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4C2×D511yescharacteristic, complemented
324C2×Dic3⋊C4C2×D511yescharacteristic, complemented
325C2×C4×Dic3—51no—
326#898—58no—
327#894—58no—
328#886—58no—
329#884—58no—
330#882—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5C22×D311yescharacteristic
334C23×D5—31no—
335C23×D5—31no—
336C23×D5—34no—
337C23×D5—122no—
338C23×D5—122no—
339C23×D5—122no—
340C23×D5C22×D311yescharacteristic
341C23×D5C22×D311yescharacteristic
342C2×C5×D4—34no—
343C2×C5×D4—122no—
344C22×C4×C5—31no—
345C22×C4×C5—31no—
346C22×C4×C5—31no—
347C22×C4×C5—42no—
348C22×C4×C5C22×D311yescharacteristic
349C22×C4×C5C22×D311yescharacteristic
350C22×C4×C5C22×D314yescomplemented
351C2×C22⋊D5—34no—
352C2×C22⋊D5—34no—
353C2×C22⋊D5—34no—
354C2×C22⋊D5—34no—
355C2×C22⋊D5—42no—
356C2×C22⋊D5—42no—
357C2×C22⋊D5—122no—
358C2×C22⋊D5—122no—
359C2×C22⋊D5—122no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5C22×D314yes—
362C2×C22⋊D5C22×D314yescomplemented
363C22×Dic5—31no—
364C22×Dic5—31no—
365C22×Dic5C22×D311yescharacteristic
366C22×Dic5C22×D311yescharacteristic
367C2×D20—34no—
368C2×D20—34no—
369C2×D20—34no—
370C2×D20—34no—
371C2×D20—42no—
372C2×D20—122no—
373C2×D20—122no—
374C2×D20—122no—
375C2×D20—122no—
376C2×D20C22×D314yes—
377C2×C4×D5—34no—
378C2×C4×D5—34no—
379C2×C4×D5—122no—
380C2×C4×D5—122no—
381C5×C4⋊C4—34no—
382C5×C4⋊C4—34no—
383C5×C22⋊C4—34no—
384C5×C22⋊C4—34no—
385C5×C22⋊C4—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685C22×D314yes—
394#685C22×D314yescomplemented
395C4⋊Dic5—34no—
396C4⋊Dic5C22×D314yescomplemented
397#683—34no—
398#683—34no—
399C4×Dic5—34no—
400#560—1516no—
401C2×#127—151no—
402C2×#126—151no—
403C2×#126—151no—
404C2×#123—31no—
405C2×#123—151no—
406C2×#123—151no—
407C2×#121—51no—
408C2×#121—151no—
409C2×#121—151no—
410C2×#121—151no—
411C2×#121—151no—
412C2×#121—151no—
413C2×#120—151no—
414C2×#120—151no—
415C2×#120—151no—
416C22×C3×C5—22no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—44no—
420C22×C3×C5H(5,𝔽2)12yes—
421C22×C3×C5H(5,𝔽2)12yes—
422C22×C3×C5H(5,𝔽2)12yes—
423C22×C3×C5C2511yescharacteristic
424C2×D15—22no—
425C2×D15—22no—
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—22no—
429C2×D15—22no—
430C2×D15—44no—
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—44no—
443C2×C3×D5—44no—
444D3×D5—416no—
445C3×C4×C5—22no—
446C3×C4×C5—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×C3C22×D511yescharacteristic
457C23×D3—51no—
458C23×D3—51no—
459C23×D3—54no—
460C23×D3—202no—
461C23×D3—202no—
462C23×D3—202no—
463C23×D3C22×D511yescharacteristic
464C2×C3×D4—54no—
465C2×C3×D4—54no—
466C2×C3×D4—54no—
467C2×C3×D4—202no—
468C2×C3×D4—202no—
469C2×C3×D4—202no—
470C22×C3×C4—42no—
471C22×C3×C4—51no—
472C22×C3×C4—51no—
473C22×C3×C4C22×D511yescharacteristic
474C22×C3×C4C22×D511yescharacteristic
475C22×C3×C4C22×D514yescomplemented
476C2×#67—42no—
477C2×#67—54no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—202no—
484C2×#67—202no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67—202no—
488C2×#67—202no—
489C2×#67C22×D514yes—
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—54no—
499C2×D12—202no—
500C2×D12—202no—
501C2×C4×D3—54no—
502C2×C4×D3—202no—
503C3×C4⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4—54no—
506#217—54no—
507#217—54no—
508#217C22×D514yescomplemented
509(C2×D3)⋊C4—54no—
510(C2×D3)⋊C4—54no—
511(C2×D3)⋊C4—54no—
512(C2×D3)⋊C4—54no—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4C22×D514yes—
515(C2×D3)⋊C4C22×D514yes—
516C4⋊Dic3—54no—
517C4⋊Dic3—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4C22×D514yescomplemented
520Dic3⋊C4C22×D514yescomplemented
521C4×Dic3—54no—
522C23×C5—22no—
523C23×C5—22no—
524C23×C5—22no—
525C23×C5—32no—
526C23×C5—62no—
527C23×C5—62no—
528C23×C5—62no—
529C23×C5C23×D312yes—
530C23×C5C23×D311yescharacteristic
531C22×D5—22no—
532C22×D5—22no—
533C22×D5—22no—
534C22×D5—22no—
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—32no—
538C22×D5—32no—
539C22×D5—62no—
540C22×D5—62no—
541C22×D5—62no—
542C22×D5—62no—
543C22×D5—62no—
544C22×D5—62no—
545C22×D5—124no—
546C22×D5—124no—
547C22×D5—124no—
548C22×D5—1216no—
549C22×D5C23×D312yes—
550C22×D5C23×D312yes—
551C5×D4—124no—
552C2×C4×C5—22no—
553C2×C4×C5—22no—
554C2×C4×C5—32no—
555C2×C4×C5—32no—
556C2×C4×C5—32no—
557C2×C4×C5—44no—
558C2×C4×C5—62no—
559C2×C4×C5—62no—
560C2×C4×C5—62no—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—44no—
564C22⋊D5—44no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C2×Dic5—22no—
570C2×Dic5—22no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—62no—
574C2×Dic5—62no—
575C2×Dic5C23×D312yes—
576C2×Dic5C23×D312yes—
577D20—44no—
578D20—124no—
579D20—124no—
580D20—124no—
581D20—124no—
582C4×D5—124no—
583C4×D5—124no—
584C25—151no—
585C22×D4—31no—
586C22×D4—51no—
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×D4—151no—
597C23×C4—151no—
598C23×C4—151no—
599C23×C4D3×D511yescharacteristic, complemented
600#127—158no—
601#126—158no—
602#126—158no—
603#123—38no—
604#123—158no—
605#123—158no—
606#121—58no—
607#121—158no—
608#121—158no—
609#121—158no—
610#121—158no—
611#121—158no—
612#120—158no—
613#120—158no—
614#120—158no—
615C2×C4⋊C4—31no—
616C2×C4⋊C4—31no—
617C2×C4⋊C4—51no—
618C2×C4⋊C4—151no—
619C2×C4⋊C4—151no—
620C2×C4⋊C4—151no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—31no—
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#56014yescomplemented
636C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
637C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
638C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
639D15—42no—
640D15—42no—
641C3×D5—42no—
642C3×D5—42no—
643C5×D3—42no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—52no—
648C23×C3—52no—
649C23×C3—102no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3C23×D512yes—
656C23×C3C23×D511yescharacteristic
657C22×D3—22no—
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—52no—
661C22×D3—52no—
662C22×D3—102no—
663C22×D3—102no—
664C22×D3—102no—
665C22×D3—102no—
666C22×D3—102no—
667C22×D3—102no—
668C22×D3—204no—
669C22×D3—204no—
670C22×D3—204no—
671C22×D3—2016no—
672C22×D3C23×D512yes—
673C3×D4—204no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—44no—
679C2×C3×C4—52no—
680C2×C3×C4—52no—
681C2×C3×C4—102no—
682C2×C3×C4—102no—
683C2×C3×C4C23×D512yes—
684C2×C3×C4C23×D512yes—
685#67—44no—
686#67—204no—
687#67—204no—
688#67—204no—
689#67—204no—
690#67—204no—
691#67—204no—
692C2×Dic3—22no—
693C2×Dic3—22no—
694C2×Dic3—22no—
695C2×Dic3—52no—
696C2×Dic3—52no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3—204no—
700C2×Dic3C23×D512yes—
701C2×Dic3C23×D512yes—
702C2×Dic3C23×D512yes—
703D12—204no—
704D12—204no—
705C4×D3—204no—
706C22×C5—22no—
707C22×C5—22no—
708C22×C5—22no—
709C22×C5—44no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—124no—
714C22×C5#100412yes—
715C22×C5#100412yes—
716C22×C5#100912yes—
717C22×C5C24×D311yescharacteristic
718C2×D5—22no—
719C2×D5—22no—
720C2×D5—22no—
721C2×D5—22no—
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—44no—
725C2×D5—44no—
726C2×D5—62no—
727C2×D5—62no—
728C2×D5—62no—
729C2×D5—62no—
730C2×D5—62no—
731C2×D5—62no—
732C2×D5—1216no—
733C2×D5—124no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—62no—
738C4×C5—62no—
739C4×C5—62no—
740Dic5—22no—
741Dic5—22no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—51no—
746C24—51no—
747C24—154no—
748C24—151no—
749C24—151no—
750C24—602no—
751C24—602no—
752C24—602no—
753C24C2×D3×D511yescharacteristic
754C2×D4—34no—
755C2×D4—54no—
756C2×D4—54no—
757C2×D4—54no—
758C2×D4—122no—
759C2×D4—154no—
760C2×D4—154no—
761C2×D4—154no—
762C2×D4—154no—
763C2×D4—154no—
764C2×D4—154no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—202no—
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×D4—602no—
778C22×C4—31no—
779C22×C4—31no—
780C22×C4—31no—
781C22×C4—42no—
782C22×C4—51no—
783C22×C4—51no—
784C22×C4—154no—
785C22×C4—154no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—602no—
789C22×C4—602no—
790C22×C4C2×D3×D511yescharacteristic
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D514yescomplemented
793C4⋊C4—34no—
794C4⋊C4—34no—
795C4⋊C4—54no—
796C4⋊C4—154no—
797C4⋊C4—154no—
798C4⋊C4—154no—
799C22⋊C4—34no—
800C22⋊C4—34no—
801C22⋊C4—34no—
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—44no—
817C22×C3—102no—
818C22×C3—102no—
819C22×C3—102no—
820C22×C3—102no—
821C22×C3—102no—
822C22×C3—102no—
823C22×C3—204no—
824C22×C3—204no—
825C22×C3#414412yes—
826C22×C3#414912yes—
827C22×C3#414912yes—
828C22×C3C24×D511yescharacteristic
829C2×D3—22no—
830C2×D3—22no—
831C2×D3—22no—
832C2×D3—44no—
833C2×D3—102no—
834C2×D3—102no—
835C2×D3—102no—
836C2×D3—102no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—2016no—
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—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5#562014yescomplemented
854C2×C5C2×#100411yescharacteristic
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100911yescharacteristic
857D5—42no—
858D5—42no—
859D5—122no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—52no—
866C23—52no—
867C23—62no—
868C23—62no—
869C23—62no—
870C23—102no—
871C23—102no—
872C23—102no—
873C23—102no—
874C23—102no—
875C23—102no—
876C23—152no—
877C23—152no—
878C23—302no—
879C23—302no—
880C23—302no—
881C23—302no—
882C23—302no—
883C23—302no—
884C23—604no—
885C23—604no—
886C23—604no—
887C23—6016no—
888C23C22×D3×D512yes—
889C23C22×D3×D511yescharacteristic
890D4—124no—
891D4—204no—
892D4—204no—
893D4—204no—
894D4—604no—
895D4—604no—
896D4—604no—
897D4—604no—
898D4—604no—
899D4—604no—
900D4—604no—
901D4—604no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—32no—
905C2×C4—32no—
906C2×C4—32no—
907C2×C4—44no—
908C2×C4—52no—
909C2×C4—52no—
910C2×C4—62no—
911C2×C4—62no—
912C2×C4—62no—
913C2×C4—102no—
914C2×C4—102no—
915C2×C4—152no—
916C2×C4—152no—
917C2×C4—302no—
918C2×C4—302no—
919C2×C4—604no—
920C2×C4—604no—
921C2×C4C22×D3×D512yes—
922C2×C4C22×D3×D512yes—
923C2×C3—42no—
924C2×C3—202no—
925C2×C3—202no—
926C2×C3#6600014yescomplemented
927C2×C3C2×#414411yescharacteristic
928C2×C3C2×#414911yescharacteristic
929C2×C3C2×#414911yescharacteristic
930D3—42no—
931D3—202no—
932D3—202no—
933C5C2×#562011yescharacteristic, complemented, Sylow
934C22—22no—
935C22—22no—
936C22—22no—
937C22—44no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—102no—
942C22—102no—
943C22—102no—
944C22—102no—
945C22—102no—
946C22—102no—
947C22—124no—
948C22—204no—
949C22—204no—
950C22—302no—
951C22—302no—
952C22—302no—
953C22—302no—
954C22—302no—
955C22—302no—
956C22—6016no—
957C22—604no—
958C22—604no—
959C22#9201712yes—
960C22#9201912yes—
961C22#9204912yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—62no—
967C4—62no—
968C4—102no—
969C4—102no—
970C4—302no—
971C4—302no—
972C3C2×#6600011yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—202no—
976C2—202no—
977C2—602no—
978C2—602no—
979C2#1175468514yesdirect product factor
980C2C2×#9201711yescharacteristic
981C2C2×#9201911yescharacteristic
982C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#560
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. C2×#91819C2semidirect
2. C2×C5×#929C2semidirect
3. C2×C3×#4076C2semidirect
4. C2×#91577C2semidirect
5. C2×#91567C2semidirect
6. C2×#91550C2semidirect
7. C2×#91533C2semidirect
8. #11754685C2direct (N × H)
9. C2×#91476C2semidirect
10. C2×#91474C2semidirect
11. C2×#91459C2semidirect
12. C2×#91438C2semidirect
13. C2×#91414C2semidirect
14. C2×#91409C2semidirect
15. C2×#91362C2semidirect
16. C2×#91345C2semidirect
19. C23×C3×C4×C5C22semidirect
21. C22×#1220C22semidirect
25. C22×C3×C22⋊D5C22semidirect
30. C22×#1202C22semidirect
32. C22×#1200C22semidirect
33. C22×D5×Dic3C22semidirect
34. #91819C22semidirect
36. C2×#6714C22semidirect
37. C2×C4⋊Dic15C22semidirect
38. C2×C5×#217C22semidirect
39. C5×#929C22semidirect
42. C2×C5×Dic3⋊C4C22semidirect
43. C2×C5×Dic3⋊C4C22semidirect
44. C3×#4076C22semidirect
46. C2×C3×#685C22semidirect
47. C2×C3×C4⋊Dic5C22semidirect
48. #91577C22semidirect
49. #91567C22semidirect
50. #91550C22semidirect
51. C2×#6669C22semidirect
52. C2×#6668C22semidirect
58. #91533C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91476C22semidirect
61. #91474C22semidirect
62. #91459C22semidirect
63. #91438C22semidirect
64. #91414C22semidirect
65. #91409C22semidirect
66. #91362C22semidirect
67. #91345C22semidirect
73. C2×#4076D3semidirect
98. C22×C3×C4×C5C23semidirect
102. C2×#1220C23semidirect
115. C2×C3×C22⋊D5C23semidirect
127. C2×#1202C23semidirect
131. C2×#1200C23semidirect
133. C2×D5×Dic3C23semidirect
135. #6714C23semidirect
136. C4⋊Dic15C23semidirect
137. C5×#217C23semidirect
140. C5×Dic3⋊C4C23semidirect
141. C5×Dic3⋊C4C23semidirect
143. C3×#685C23semidirect
144. C3×C4⋊Dic5C23semidirect
145. #6669C23semidirect
146. #6668C23semidirect
152. Dic3×Dic5C23semidirect
161. C2×#929D5semidirect
171. C23×C4×C5C2×D3semidirect
177. C22×C22⋊D5C2×D3semidirect
195. #4076C2×D3semidirect
203. C2×#685C2×D3semidirect
205. C2×C4⋊Dic5C2×D3semidirect
286. C23×C3×C4C2×D5semidirect
304. C2×#217C2×D5semidirect
312. #929C2×D5semidirect
323. C2×Dic3⋊C4C2×D5semidirect
324. C2×Dic3⋊C4C2×D5semidirect
350. C22×C4×C5C22×D3semidirect
362. C2×C22⋊D5C22×D3semidirect
394. #685C22×D3semidirect
396. C4⋊Dic5C22×D3semidirect
475. C22×C3×C4C22×D5semidirect
508. #217C22×D5semidirect
519. Dic3⋊C4C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
599. C23×C4D3×D5semidirect
635. C2×C3×C5#560semidirect
792. C22×C4C2×D3×D5semidirect
812. C3×C5C2×#560semidirect
853. C2×C5#5620semidirect
926. C2×C3#66000semidirect
933. C5C2×#5620semidirect
972. C3C2×#66000semidirect
979. C2#11754685direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#918192
C2×C5×#9292
C2×C3×#40762
C2×#915772
C2×#915672
C2×#915502
C2×#915332
#117546852
C2×#914762
C2×#914742
C2×#914592
C2×#914382
C2×#914142
C2×#914092
C2×#913622
C2×#913452
C2×#660003
C2×#56205