Finite Group Databasebeta

← C2×#11753162 #14495220

Subgroups — C2×#11753162 #14495220

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×#91772C211yesmaximal, characteristic, complemented
2C2×C5×#883C211yesmaximal, characteristic, complemented
3C2×C3×#4028C211yesmaximal, characteristic, complemented
4C2×#91567C211yesmaximal, characteristic, complemented
5C2×#91564C211yesmaximal, characteristic, complemented
6C2×#91563C211yesmaximal, characteristic, complemented
7C2×#91548C211yesmaximal, characteristic, complemented
8C2×#91465C211yesmaximal, characteristic, complemented
9C2×#91461C211yesmaximal, characteristic, complemented
10C2×#91456C211yesmaximal, characteristic, complemented
11C2×#91454C211yesmaximal, characteristic, complemented
12C2×#91409C211yesmaximal, characteristic, complemented
13C2×#91408C211yesmaximal, characteristic, complemented
14C2×#91362C211yesmaximal, characteristic, complemented
15C2×#91361C211yesmaximal, characteristic, complemented
16#11753162C2116yesmaximal, direct product factor
17C2×#66000—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic, complemented
21C22×C5×#67C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic, complemented
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×D20C2211yescharacteristic
25C22×C3×D20C2211yescharacteristic
26C22×#1203C2211yescharacteristic, complemented
27C22×#1202C2211yescharacteristic
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic, complemented
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C22×#1201C2211yescharacteristic, complemented
33C22×D5×Dic3C2211yescharacteristic, complemented
34C2×C3×C5×C22⋊C4C2211yescharacteristic
35C2×#6719C2211yescharacteristic
36C2×#6714C2211yescharacteristic, complemented
37C2×C4⋊Dic15C2211yescharacteristic, complemented
38C2×#6712C2211yescharacteristic, complemented
39#91772C2218yescomplemented
40C2×C5×#217C2211yescharacteristic
41C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C2×C5×C4⋊Dic3C2211yescharacteristic, complemented
43C2×C5×Dic3⋊C4C2211yescharacteristic, complemented
44C5×#883C2218yescomplemented
45C2×C3×#685C2211yescharacteristic
46C2×C3×#685C2211yescharacteristic
47C3×#4028C2218yescomplemented
48#91567C2218yescomplemented
49#91564C2218yescomplemented
50#91563C2218yescomplemented
51#91548C2218yescomplemented
52C2×Dic3⋊Dic5C2211yescharacteristic, complemented
53C2×#6669C2211yescharacteristic, complemented
54C2×#6665C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56C2×#6665C2211yescharacteristic
57C2×#6665C2211yescharacteristic
58C2×#6665C2211yescharacteristic, complemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91465C2218yescomplemented
61#91461C2218yescomplemented
62#91456C2218yescomplemented
63#91454C2218yescomplemented
64#91409C2218yescomplemented
65#91408C2218yescomplemented
66#91362C2218yescomplemented
67#91361C2218yescomplemented
68C2×#5595—51nomaximal, Hall
69C2×C5×#123—31no—
70C2×#4086—31no—
71C2×#4083—31no—
72C2×#4076—31no—
73C2×#4076—31no—
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×#4028D311yescharacteristic, complemented
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C23×C3×D5—42no—
89C23×C3×D5—42no—
90C23×C3×D5—42no—
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C23×C3×D5C2311yescharacteristic
94C23×C3×D5C2314yes—
95C22×C3×C4×C5C2311yescharacteristic
96C22×C3×C4×C5C2311yescharacteristic
97C2×#1220—42no—
98C2×#1220C2314yes—
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C2×C4×D15—42no—
103C2×C4×D15C2314yescomplemented
104C2×C5×#67—42no—
105C2×C5×#67C2314yes—
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C2×C4×C5×D3—42no—
110C2×C4×C5×D3C2314yescomplemented
111C2×C3×C22⋊D5—42no—
112C2×C3×C22⋊D5C2314yes—
113C22×C3×Dic5C2311yescharacteristic
114C2×C3×D20—42no—
115C2×C3×D20—42no—
116C2×C3×D20C2314yes—
117C2×C3×D20C2314yes—
118C2×#1203—42no—
119C2×#1203C2314yescomplemented
120C2×#1202—42no—
121C2×#1202—42no—
122C2×#1202—42no—
123C2×#1202C2314yes—
124C2×#1202C2314yes—
125C2×#1202C2314yescomplemented
126C2×#1201—42no—
127C2×#1201—42no—
128C2×#1201—42no—
129C2×#1201C2314yes—
130C2×#1201C2314yes—
131C2×#1201C2314yescomplemented
132C2×D5×Dic3—42no—
133C2×D5×Dic3C2314yescomplemented
134C3×C5×C22⋊C4C2314yes—
135#6719C2314yes—
136#6714C2314yescomplemented
137C4⋊Dic15C2314yescomplemented
138#6712C2314yescomplemented
139C5×#217C2314yes—
140C5×(C2×D3)⋊C4C2314yescomplemented
141C5×C4⋊Dic3C2314yescomplemented
142C5×Dic3⋊C4C2314yescomplemented
143C3×#685C2314yes—
144C3×#685C2314yes—
145Dic3⋊Dic5C2314yescomplemented
146#6669C2314yescomplemented
147#6665C2314yes—
148#6665C2314yes—
149#6665C2314yes—
150#6665C2314yes—
151#6665C2314yescomplemented
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×#938—51no—
161C2×#935—51no—
162#5595—516no—
163C2×#884—51no—
164C2×#884—51no—
165C2×#883—51no—
166C2×#883D511yescharacteristic, complemented
167C2×#879—51no—
168C2×#879—51no—
169C24×D5C2×D311yescharacteristic
170C22×C5×D4—31no—
171C23×C4×C5—31no—
172C22×C22⋊D5—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5—31no—
177C22×C22⋊D5C2×D311yescharacteristic
178C22×D20—31no—
179C22×D20—31no—
180C22×D20—31no—
181C22×D20C2×D311yescharacteristic
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⋊C4C2×D311yescharacteristic
191C2×C22⋊Dic5—31no—
192#4086—38no—
193#4083—38no—
194#4076—38no—
195#4076—38no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685C2×D311yescharacteristic
203C2×#685C2×D311yescharacteristic
204C2×C4⋊Dic5—31no—
205C2×C4⋊Dic5—31no—
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#4028C2×D318yescomplemented
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×D15C2412yes—
229C22×C5×D3—22no—
230C22×C5×D3—22no—
231C22×C5×D3—22no—
232C22×C5×D3C2412yes—
233C22×C3×D5—22no—
234C22×C3×D5—22no—
235C22×C3×D5—22no—
236C22×C3×D5—22no—
237C22×C3×D5—22no—
238C22×C3×D5—22no—
239C22×C3×D5—22no—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—44no—
243C22×C3×D5—44no—
244C22×C3×D5—44no—
245C22×C3×D5—416no—
246C22×C3×D5C2412yes—
247C22×C3×D5C2412yes—
248C22×C3×D5C2412yes—
249C2×C3×C4×C5—22no—
250C2×C3×C4×C5—22no—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253#1220—44no—
254C2×Dic15—22no—
255C2×Dic15—22no—
256C2×Dic15—22no—
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C4×D15—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—
268C4×C5×D3—44no—
269C3×C22⋊D5—44no—
270C2×C3×Dic5—22no—
271C2×C3×Dic5C2412yes—
272C3×D20—44no—
273C3×D20—44no—
274#1203—44no—
275#1202—44no—
276#1202—44no—
277#1202—44no—
278#1201—44no—
279#1201—44no—
280#1201—44no—
281D5×Dic3—44no—
282C25×C3—51no—
283C22×C3×D4—51no—
284C22×C3×D4—51no—
285C22×C3×D4—51no—
286C22×#67—51no—
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×C4×D3—51no—
297C22×C4×D3C2×D511yescharacteristic, complemented
298C3×#120—58no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4—51no—
301C2×C3×C22⋊C4C2×D511yescharacteristic
302#953—58no—
303#953—58no—
304C2×#217—51no—
305C2×#217—51no—
306C2×#217—51no—
307C2×#217—51no—
308C2×#217—51no—
309C2×#217—51no—
310C2×#217C2×D511yescharacteristic
311#940—58no—
312#939—58no—
313#939—58no—
314#938—58no—
315#938—58no—
316#935—58no—
317C2×(C2×D3)⋊C4—51no—
318C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
319C2×C4⋊Dic3—51no—
320C2×C4⋊Dic3C2×D511yescharacteristic, complemented
321C2×Dic3⋊C4—51no—
322C2×Dic3⋊C4—51no—
323C2×Dic3⋊C4—51no—
324C2×Dic3⋊C4C2×D511yescharacteristic, complemented
325C2×C4×Dic3—51no—
326#884—58no—
327#884—58no—
328#883—58no—
329#883C2×D518yescomplemented
330#879—58no—
331#879—58no—
332C24×C5—31no—
333C24×C5C22×D311yescharacteristic
334C23×D5—31no—
335C23×D5—42no—
336C23×D5—42no—
337C23×D5—42no—
338C23×D5C22×D311yescharacteristic
339C23×D5C22×D311yescharacteristic
340C23×D5C22×D311yescharacteristic
341C23×D5C22×D314yes—
342C2×C5×D4—34no—
343C2×C5×D4—122no—
344C22×C4×C5—31no—
345C22×C4×C5—31no—
346C22×C4×C5—31no—
347C22×C4×C5—34no—
348C22×C4×C5—122no—
349C22×C4×C5C22×D311yescharacteristic
350C22×C4×C5C22×D311yescharacteristic
351C2×C22⋊D5—34no—
352C2×C22⋊D5—34no—
353C2×C22⋊D5—34no—
354C2×C22⋊D5—34no—
355C2×C22⋊D5—34no—
356C2×C22⋊D5—42no—
357C2×C22⋊D5—122no—
358C2×C22⋊D5—122no—
359C2×C22⋊D5—122no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5C22×D314yes—
363C22×Dic5—31no—
364C22×Dic5—31no—
365C22×Dic5—31no—
366C22×Dic5C22×D311yescharacteristic
367C2×D20—34no—
368C2×D20—34no—
369C2×D20—34no—
370C2×D20—42no—
371C2×D20—42no—
372C2×D20—122no—
373C2×D20—122no—
374C2×D20—122no—
375C2×D20C22×D314yes—
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⋊C4C22×D314yes—
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×D314yes—
395C4⋊Dic5—34no—
396C4⋊Dic5—34no—
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—151no—
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—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—44no—
428C2×C5×D3—22no—
429C2×C5×D3—22no—
430C2×C5×D3—22no—
431C2×C5×D3—44no—
432C2×C3×D5—22no—
433C2×C3×D5—22no—
434C2×C3×D5—22no—
435C2×C3×D5—22no—
436C2×C3×D5—22no—
437C2×C3×D5—22no—
438C2×C3×D5—22no—
439C2×C3×D5—22no—
440C2×C3×D5—22no—
441C2×C3×D5—416no—
442C2×C3×D5—44no—
443C2×C3×D5—44no—
444C2×C3×D5—44no—
445C3×C4×C5—22no—
446C3×C4×C5—22no—
447Dic15—22no—
448Dic15—22no—
449Dic15—22no—
450C3×Dic5—22no—
451C5×Dic3—22no—
452C5×Dic3—22no—
453C5×Dic3—22no—
454C24×C3—51no—
455C24×C3—51no—
456C24×C3—51no—
457C24×C3—54no—
458C24×C3—202no—
459C24×C3—202no—
460C24×C3—202no—
461C24×C3C22×D511yescharacteristic
462C23×D3—51no—
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—51no—
471C22×C3×C4C22×D511yescharacteristic
472C22×C3×C4C22×D511yescharacteristic
473C2×#67—42no—
474C2×#67—54no—
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×#67—202no—
488C2×#67C22×D514yes—
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⋊C4C22×D514yes—
506#217—54no—
507#217—54no—
508#217—54no—
509#217—54no—
510#217—54no—
511#217—54no—
512#217C22×D514yes—
513(C2×D3)⋊C4—54no—
514(C2×D3)⋊C4C22×D514yescomplemented
515C4⋊Dic3—54no—
516C4⋊Dic3C22×D514yescomplemented
517Dic3⋊C4—54no—
518Dic3⋊C4—54no—
519Dic3⋊C4—54no—
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—22no—
538C22×D5—22no—
539C22×D5—22no—
540C22×D5—32no—
541C22×D5—44no—
542C22×D5—44no—
543C22×D5—44no—
544C22×D5—416no—
545C22×D5—62no—
546C22×D5—62no—
547C22×D5—62no—
548C22×D5C23×D312yes—
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—62no—
558C2×C4×C5—62no—
559C2×C4×C5—62no—
560C2×C4×C5—124no—
561C2×C4×C5C23×D312yes—
562C2×C4×C5C23×D312yes—
563C22⋊D5—44no—
564C22⋊D5—124no—
565C22⋊D5—124no—
566C22⋊D5—124no—
567C22⋊D5—124no—
568C22⋊D5—124no—
569C2×Dic5—22no—
570C2×Dic5—32no—
571C2×Dic5—32no—
572C2×Dic5—32no—
573C2×Dic5—62no—
574C2×Dic5—62no—
575C2×Dic5—62no—
576C2×Dic5C23×D312yes—
577D20—44no—
578D20—44no—
579D20—124no—
580D20—124no—
581D20—124no—
582C4×D5—124no—
583C4×D5—124no—
584C25—51no—
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—31no—
598C23×C4—151no—
599C23×C4—151no—
600#127—158no—
601#126—158no—
602#126—158no—
603#123—38no—
604#123—158no—
605#123—158no—
606#121—158no—
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—31no—
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—151no—
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⋊C4D3×D511yescharacteristic
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—
640C3×D5—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—52no—
650C23×C3—102no—
651C23×C3—102no—
652C23×C3—102no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3—102no—
656C23×C3—102no—
657C23×C3—102no—
658C23×C3—102no—
659C23×C3—204no—
660C23×C3—204no—
661C23×C3—204no—
662C23×C3—2016no—
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—204no—
674C3×D4—204no—
675C3×D4—204no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—52no—
679C2×C3×C4—102no—
680C2×C3×C4C23×D512yes—
681C2×C3×C4C23×D512yes—
682#67—44no—
683#67—204no—
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—44no—
710C22×C5—62no—
711C22×C5—62no—
712C22×C5—62no—
713C22×C5—124no—
714C22×C5#100412yes—
715C22×C5#100412yes—
716C22×C5#100412yes—
717C22×C5C24×D311yescharacteristic
718C2×D5—22no—
719C2×D5—22no—
720C2×D5—22no—
721C2×D5—22no—
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—416no—
728C2×D5—44no—
729C2×D5—44no—
730C2×D5—44no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—124no—
735C4×C5—22no—
736C4×C5—22no—
737C4×C5—62no—
738C4×C5—62no—
739C4×C5—62no—
740Dic5—22no—
741Dic5—62no—
742Dic5—62no—
743Dic5—62no—
744C24—31no—
745C24—51no—
746C24—51no—
747C24—51no—
748C24—54no—
749C24—151no—
750C24—202no—
751C24—202no—
752C24—202no—
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—34no—
782C22×C4—51no—
783C22×C4—122no—
784C22×C4—154no—
785C22×C4—151no—
786C22×C4—151no—
787C22×C4—151no—
788C22×C4—154no—
789C22×C4—602no—
790C22×C4—602no—
791C22×C4C2×D3×D511yescharacteristic
792C22×C4C2×D3×D511yescharacteristic
793C4⋊C4—34no—
794C4⋊C4—34no—
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—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4C2×D3×D514yes—
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—102no—
824C22×C3—102no—
825C22×C3—102no—
826C22×C3—2016no—
827C22×C3—204no—
828C22×C3—204no—
829C22×C3—204no—
830C22×C3#414412yes—
831C22×C3#414912yes—
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—22no—
844C3×C4—102no—
845Dic3—22no—
846Dic3—22no—
847Dic3—22no—
848Dic3—102no—
849Dic3—102no—
850Dic3—102no—
851C2×C5—42no—
852C2×C5—122no—
853C2×C5#559514yescomplemented
854C2×C5C2×#100411yescharacteristic
855C2×C5C2×#100411yescharacteristic
856C2×C5C2×#100411yescharacteristic
857D5—42no—
858D5—42no—
859D5—42no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—52no—
866C23—52no—
867C23—52no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—102no—
872C23—102no—
873C23—102no—
874C23—102no—
875C23—102no—
876C23—102no—
877C23—102no—
878C23—102no—
879C23—102no—
880C23—152no—
881C23—204no—
882C23—204no—
883C23—204no—
884C23—2016no—
885C23—302no—
886C23—302no—
887C23—302no—
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—52no—
908C2×C4—62no—
909C2×C4—62no—
910C2×C4—62no—
911C2×C4—102no—
912C2×C4—124no—
913C2×C4—152no—
914C2×C4—152no—
915C2×C4—152no—
916C2×C4—302no—
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—202no—
927C2×C3#6600014yescomplemented
928C2×C3C2×#414411yescharacteristic
929C2×C3C2×#414911yescharacteristic
930C2×C3C2×#414911yescharacteristic
931D3—42no—
932D3—202no—
933C5C2×#559511yescharacteristic, 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—102no—
948C22—102no—
949C22—102no—
950C22—124no—
951C22—2016no—
952C22—204no—
953C22—204no—
954C22—204no—
955C22—302no—
956C22—302no—
957C22—302no—
958C22—604no—
959C22#9201712yes—
960C22#9202512yes—
961C22#9202612yes—
962C22C23×D3×D511yescharacteristic
963C4—22no—
964C4—22no—
965C4—62no—
966C4—62no—
967C4—62no—
968C4—102no—
969C4—302no—
970C4—302no—
971C4—302no—
972C3C2×#6600011yescharacteristic, complemented, Sylow
973C2—42no—
974C2—122no—
975C2—202no—
976C2—202no—
977C2—202no—
978C2—602no—
979C2#1175316214yesdirect product factor
980C2C2×#9201711yescharacteristic
981C2C2×#9202511yescharacteristic
982C2C2×#9202611yescharacteristic
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×#560
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. C2×#91772C2semidirect
2. C2×C5×#883C2semidirect
3. C2×C3×#4028C2semidirect
4. C2×#91567C2semidirect
5. C2×#91564C2semidirect
6. C2×#91563C2semidirect
7. C2×#91548C2semidirect
8. C2×#91465C2semidirect
9. C2×#91461C2semidirect
10. C2×#91456C2semidirect
11. C2×#91454C2semidirect
12. C2×#91409C2semidirect
13. C2×#91408C2semidirect
14. C2×#91362C2semidirect
15. C2×#91361C2semidirect
16. #11753162C2direct (N × H)
20. C22×C4×D15C22semidirect
22. C22×C4×C5×D3C22semidirect
26. C22×#1203C22semidirect
29. C22×#1202C22semidirect
32. C22×#1201C22semidirect
33. C22×D5×Dic3C22semidirect
36. C2×#6714C22semidirect
37. C2×C4⋊Dic15C22semidirect
38. C2×#6712C22semidirect
39. #91772C22semidirect
41. C2×C5×(C2×D3)⋊C4C22semidirect
42. C2×C5×C4⋊Dic3C22semidirect
43. C2×C5×Dic3⋊C4C22semidirect
44. C5×#883C22semidirect
47. C3×#4028C22semidirect
48. #91567C22semidirect
49. #91564C22semidirect
50. #91563C22semidirect
51. #91548C22semidirect
52. C2×Dic3⋊Dic5C22semidirect
53. C2×#6669C22semidirect
58. C2×#6665C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91465C22semidirect
61. #91461C22semidirect
62. #91456C22semidirect
63. #91454C22semidirect
64. #91409C22semidirect
65. #91408C22semidirect
66. #91362C22semidirect
67. #91361C22semidirect
84. C2×#4028D3semidirect
103. C2×C4×D15C23semidirect
110. C2×C4×C5×D3C23semidirect
119. C2×#1203C23semidirect
125. C2×#1202C23semidirect
131. C2×#1201C23semidirect
133. C2×D5×Dic3C23semidirect
136. #6714C23semidirect
137. C4⋊Dic15C23semidirect
138. #6712C23semidirect
140. C5×(C2×D3)⋊C4C23semidirect
141. C5×C4⋊Dic3C23semidirect
142. C5×Dic3⋊C4C23semidirect
145. Dic3⋊Dic5C23semidirect
146. #6669C23semidirect
151. #6665C23semidirect
152. Dic3×Dic5C23semidirect
166. C2×#883D5semidirect
218. #4028C2×D3semidirect
297. C22×C4×D3C2×D5semidirect
318. C2×(C2×D3)⋊C4C2×D5semidirect
320. C2×C4⋊Dic3C2×D5semidirect
324. C2×Dic3⋊C4C2×D5semidirect
329. #883C2×D5semidirect
502. C2×C4×D3C22×D5semidirect
514. (C2×D3)⋊C4C22×D5semidirect
516. C4⋊Dic3C22×D5semidirect
520. Dic3⋊C4C22×D5semidirect
635. C2×C3×C5#560semidirect
812. C3×C5C2×#560semidirect
853. C2×C5#5595semidirect
927. C2×C3#66000semidirect
933. C5C2×#5595semidirect
972. C3C2×#66000semidirect
979. C2#11753162direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917722
C2×C5×#8832
C2×C3×#40282
C2×#915672
C2×#915642
C2×#915632
C2×#915482
C2×#914652
C2×#914612
C2×#914562
C2×#914542
C2×#914092
C2×#914082
C2×#913622
C2×#913612
#117531622
C2×#660003
C2×#55955