Finite Group Databasebeta

← C2×#11753080 #14483018

Subgroups — C2×#11753080 #14483018

Order 1920.

3472 conjugacy classes of subgroups.

The subgroup lattice has 1024 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6780C211yesmaximal, characteristic, complemented
2C22×#6771C211yesmaximal, characteristic, complemented
3C2×#91770C211yesmaximal, characteristic, complemented
4C2×C5×#884C211yesmaximal, characteristic, complemented
5C2×C3×#4030C211yesmaximal, characteristic, complemented
6C2×#91571C211yesmaximal, characteristic, complemented
7C2×#91567C211yesmaximal, characteristic, complemented
8C2×#91567C211yesmaximal, characteristic, complemented
9C2×#91463C211yesmaximal, characteristic, complemented
10C2×#91461C211yesmaximal, characteristic, complemented
11C2×#91441C211yesmaximal, characteristic, complemented
12C2×#91440C211yesmaximal, characteristic, complemented
13C2×#91416C211yesmaximal, characteristic, complemented
14C2×#91409C211yesmaximal, characteristic, complemented
15C2×#91325C211yesmaximal, characteristic, complemented
16#11753080C2116yesmaximal, direct product factor
17C2×#65933—31nomaximal, Hall
18C22×#1220C2211yescharacteristic
19C23×Dic15C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C22×C5×D12C2211yescharacteristic
24C22×C4×C5×D3C2211yescharacteristic
25C22×C3×C22⋊D5C2211yescharacteristic
26C22×C3×C22⋊D5C2211yescharacteristic
27C22×C3×D20C2211yescharacteristic
28C22×C3×C4×D5C2211yescharacteristic
29C22×#1204C2211yescharacteristic
30C22×#1203C2211yescharacteristic
31C22×#1203C2211yescharacteristic
32C22×#1202C2211yescharacteristic
33C22×#1202C2211yescharacteristic
34C22×#1201C2211yescharacteristic
35C22×#1201C2211yescharacteristic
36C22×#1201C2211yescharacteristic
37C22×#1201C2211yescharacteristic
38C22×D3×Dic5C2211yescharacteristic
39C2×#6780—28no—
40C2×#6780C2218yescomplemented
41C22×D5×Dic3C2211yescharacteristic
42C2×#6771—28no—
43C2×#6771C2218yescomplemented
44C2×C3×C5×C22⋊C4C2211yescharacteristic
45C2×#6714C2211yescharacteristic
46C2×#6712C2211yescharacteristic
47C2×C4×Dic15C2211yescharacteristic
48#91770C2218yescomplemented
49C2×C5×(C2×D3)⋊C4C2211yescharacteristic
50C2×C5×Dic3⋊C4C2211yescharacteristic
51C5×#884C2218yescomplemented
52C2×C3×#685C2211yescharacteristic
53C2×C3×#683C2211yescharacteristic
54C3×#4030C2218yescomplemented
55#91571C2218yescomplemented
56#91567C2218yescomplemented
57#91567C2218yescomplemented
58C2×#6669C2211yescharacteristic
59C2×(C2×D3)⋊Dic5C2211yescharacteristic
60C2×#6665C2211yescharacteristic
61C2×Dic3×Dic5C2211yescharacteristic
62C2×Dic3×Dic5C2211yescharacteristic
63#91463C2218yescomplemented
64#91461C2218yescomplemented
65#91441C2218yescomplemented
66#91440C2218yescomplemented
67#91416C2218yescomplemented
68#91409C2218yescomplemented
69#91325C2218yescomplemented
70C2×#5599—51nomaximal, Hall
71C22×#711—31no—
72C22×#709—31no—
73C2×C5×#121—31no—
74C2×#4086—31no—
75C2×#4086—31no—
76C2×#4086—31no—
77C2×#4085—31no—
78C2×#4085—31no—
79C2×C4×C22⋊D5—31no—
80#65933—316no—
81C2×#4041—31no—
82C2×#4033—31no—
83C2×#4030—31no—
84C2×#4030D311yescharacteristic, complemented
85C2×#4027—31no—
86C2×#4027—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C23×C3×D5C2311yescharacteristic
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2311yescharacteristic
95C2×#1220—24no—
96C2×#1220C2314yes—
97C22×Dic15—24no—
98C22×Dic15C2314yes—
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C22×Dic15C2311yescharacteristic
102C2×C4×D15—24no—
103C2×C4×D15C2314yes—
104C2×C5×#67—24no—
105C2×C5×#67—42no—
106C2×C5×#67C2314yes—
107C2×C5×#67C2314yes—
108C22×C5×Dic3C2311yescharacteristic
109C22×C5×Dic3C2311yescharacteristic
110C2×C5×D12—42no—
111C2×C5×D12C2314yes—
112C2×C4×C5×D3—24no—
113C2×C4×C5×D3C2314yes—
114C2×C3×C22⋊D5—24no—
115C2×C3×C22⋊D5—42no—
116C2×C3×C22⋊D5C2314yes—
117C2×C3×C22⋊D5C2314yes—
118C22×C3×Dic5C2311yescharacteristic
119C22×C3×Dic5C2311yescharacteristic
120C2×C3×D20—42no—
121C2×C3×D20C2314yes—
122C2×C3×C4×D5—24no—
123C2×C3×C4×D5C2314yes—
124C2×#1204D418yescomplemented
125C2×#1204C2314yes—
126C2×#1203—24no—
127C2×#1203—42no—
128C2×#1203C2314yes—
129C2×#1203C2314yes—
130C2×#1202—24no—
131C2×#1202—42no—
132C2×#1202C2314yes—
133C2×#1202C2314yes—
134C2×#1201—24no—
135C2×#1201—24no—
136C2×#1201—24no—
137C2×#1201—24no—
138C2×#1201C2314yes—
139C2×#1201C2314yes—
140C2×#1201C2314yes—
141C2×#1201C2314yes—
142C2×D3×Dic5—24no—
143C2×D3×Dic5C2314yes—
144#6780—232no—
145C2×D5×Dic3—24no—
146C2×D5×Dic3C2314yes—
147#6771—232no—
148C3×C5×C22⋊C4C2314yes—
149#6714C2314yes—
150#6712C2314yes—
151C4×Dic15C2314yes—
152C5×(C2×D3)⋊C4C2314yes—
153C5×Dic3⋊C4C2314yes—
154C3×#685C2314yes—
155C3×#683C2314yes—
156#6669C2314yes—
157(C2×D3)⋊Dic5C2314yes—
158#6665C2314yes—
159Dic3×Dic5C2314yes—
160Dic3×Dic5C2314yes—
161C22×#237—51no—
162C22×#235—51no—
163C2×C3×#121—51no—
164C2×#940—51no—
165C2×#940—51no—
166C2×#940—51no—
167C2×#939—51no—
168C2×#939—51no—
169C2×C4×#67—51no—
170#5599—516no—
171C2×#895—51no—
172C2×#887—51no—
173C2×#884—51no—
174C2×#884D511yescharacteristic, complemented
175C2×#67⋊C4—51no—
176C2×#67⋊C4—51no—
177C22×C5×D4—31no—
178C22×C5×D4—31no—
179C22×C5×D4—31no—
180C23×C4×C5—31no—
181C22×C22⋊D5—31no—
182C22×C22⋊D5—31no—
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5C2×D311yescharacteristic
189C22×C22⋊D5C2×D311yescharacteristic
190C23×Dic5—31no—
191C23×Dic5—31no—
192C2×#711—38no—
193C2×#711—68no—
194C2×#709—38no—
195C2×#709—68no—
196C22×D20—31no—
197C22×D20—31no—
198C22×D20C2×D311yescharacteristic
199C22×C4×D5—31no—
200C22×C4×D5—31no—
201C22×C4×D5C2×D311yescharacteristic
202C22×Dic10—31no—
203C5×#121—38no—
204C2×C5×C4⋊C4—31no—
205C2×C5×C22⋊C4—31no—
206C2×C5×C22⋊C4C2×D311yescharacteristic
207C2×C22⋊Dic5—31no—
208#4086—38no—
209#4086—38no—
210#4086—38no—
211#4085—38no—
212#4085—38no—
213C4×C22⋊D5—38no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685C2×D311yescharacteristic
217C2×#683—31no—
218C2×#683—31no—
219C2×#683C2×D311yescharacteristic
220C2×C4×Dic5—31no—
221C2×C4×Dic5—31no—
222C2×C4×Dic5—31no—
223#4041—38no—
224#4033—38no—
225#4030—38no—
226#4030C2×D318yescomplemented
227#4027—38no—
228#4027—38no—
229C2×#550—151noSylow
230C23×C3×C5—22no—
231C23×C3×C5—22no—
232C23×C3×C5—22no—
233C23×C3×C5C2412yes—
234C23×C3×C5C2411yescharacteristic
235C22×D15—22no—
236C22×D15—22no—
237C22×D15—22no—
238C22×D15C2412yes—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3—22no—
242C22×C5×D3—22no—
243C22×C5×D3—22no—
244C22×C5×D3—22no—
245C22×C5×D3C2412yes—
246C22×C5×D3C2412yes—
247C22×C3×D5—22no—
248C22×C3×D5—22no—
249C22×C3×D5—22no—
250C22×C3×D5—22no—
251C22×C3×D5—22no—
252C22×C3×D5—22no—
253C22×C3×D5C2412yes—
254C22×C3×D5C2412yes—
255C2×C3×C4×C5—22no—
256C2×C3×C4×C5—22no—
257C2×C3×C4×C5C2412yes—
258C2×C3×C4×C5C2412yes—
259#1220—28no—
260C2×Dic15—22no—
261C2×Dic15—28no—
262C2×Dic15C2×D414yes—
263C2×Dic15#4114yescomplemented
264C2×Dic15C2412yes—
265C2×Dic15C2412yes—
266C2×Dic15C2412yes—
267C4×D15—28no—
268C5×#67—28no—
269C5×#67—44no—
270C2×C5×Dic3—22no—
271C2×C5×Dic3C2×D414yes—
272C2×C5×Dic3C2412yes—
273C2×C5×Dic3C2412yes—
274C5×D12—44no—
275C4×C5×D3—28no—
276C3×C22⋊D5—28no—
277C3×C22⋊D5—44no—
278C2×C3×Dic5—22no—
279C2×C3×Dic5C2×D414yes—
280C2×C3×Dic5C2412yes—
281C2×C3×Dic5C2412yes—
282C3×D20—44no—
283C3×C4×D5—28no—
284#1204C2×D4116yescomplemented
285#1203—28no—
286#1203—44no—
287#1202—28no—
288#1202—44no—
289#1201—28no—
290#1201—28no—
291#1201—28no—
292#1201—28no—
293D3×Dic5—28no—
294D5×Dic3—28no—
295C22×C3×D4—51no—
296C22×C3×D4—51no—
297C22×C3×D4—51no—
298C23×C3×C4—51no—
299C22×#67—51no—
300C22×#67—51no—
301C22×#67—51no—
302C22×#67—51no—
303C22×#67—51no—
304C22×#67—51no—
305C22×#67—51no—
306C22×#67C2×D511yescharacteristic
307C22×#67C2×D511yescharacteristic
308C23×Dic3—51no—
309C23×Dic3—51no—
310C2×#237—58no—
311C2×#237—108no—
312C2×#235—58no—
313C2×#235—108no—
314C22×D12—51no—
315C22×D12—51no—
316C22×D12C2×D511yescharacteristic
317C22×C4×D3—51no—
318C22×C4×D3—51no—
319C22×C4×D3C2×D511yescharacteristic
320C22×Dic6—51no—
321C3×#121—58no—
322C2×C3×C4⋊C4—51no—
323C2×C3×C22⋊C4—51no—
324C2×C3×C22⋊C4C2×D511yescharacteristic
325C2×#217—51no—
326#940—58no—
327#940—58no—
328#940—58no—
329#939—58no—
330#939—58no—
331C4×#67—58no—
332C2×(C2×D3)⋊C4—51no—
333C2×(C2×D3)⋊C4—51no—
334C2×(C2×D3)⋊C4C2×D511yescharacteristic
335C2×Dic3⋊C4—51no—
336C2×Dic3⋊C4—51no—
337C2×Dic3⋊C4C2×D511yescharacteristic
338C2×C4×Dic3—51no—
339C2×C4×Dic3—51no—
340C2×C4×Dic3—51no—
341#895—58no—
342#887—58no—
343#884—58no—
344#884C2×D518yescomplemented
345#67⋊C4—58no—
346#67⋊C4—58no—
347C24×C5—31no—
348C24×C5—31no—
349C24×C5C22×D311yescharacteristic
350C23×D5—31no—
351C23×D5C22×D311yescharacteristic
352C23×D5C22×D311yescharacteristic
353C2×C5×D4—34no—
354C2×C5×D4—34no—
355C2×C5×D4—34no—
356C2×C5×D4—64no—
357C2×C5×D4—122no—
358C2×C5×D4—122no—
359C22×C4×C5—31no—
360C22×C4×C5—31no—
361C22×C4×C5—34no—
362C22×C4×C5—64no—
363C22×C4×C5C22×D311yescharacteristic
364C22×C4×C5C22×D311yescharacteristic
365C2×C22⋊D5—24no—
366C2×C22⋊D5—34no—
367C2×C22⋊D5—34no—
368C2×C22⋊D5—34no—
369C2×C22⋊D5—34no—
370C2×C22⋊D5—34no—
371C2×C22⋊D5—34no—
372C2×C22⋊D5—34no—
373C2×C22⋊D5—42no—
374C2×C22⋊D5—64no—
375C2×C22⋊D5—64no—
376C2×C22⋊D5—64no—
377C2×C22⋊D5—64no—
378C2×C22⋊D5—64no—
379C2×C22⋊D5—64no—
380C2×C22⋊D5—122no—
381C2×C22⋊D5C22×D314yes—
382C2×C22⋊D5C22×D314yes—
383C22×Dic5—31no—
384C22×Dic5—31no—
385C22×Dic5—31no—
386C22×Dic5—34no—
387C22×Dic5—34no—
388C22×Dic5—64no—
389C22×Dic5—64no—
390C22×Dic5C22×D311yescharacteristic
391C22×Dic5C22×D311yescharacteristic
392#711—632no—
393#709—632no—
394C2×D20—34no—
395C2×D20—34no—
396C2×D20—42no—
397C2×D20—64no—
398C2×D20—122no—
399C2×D20C22×D314yes—
400C2×C4×D5—24no—
401C2×C4×D5—34no—
402C2×C4×D5—34no—
403C2×C4×D5—64no—
404C2×C4×D5—64no—
405C2×C4×D5C22×D314yes—
406C2×Dic10—38no—
407C2×Dic10—34no—
408C5×C4⋊C4—34no—
409C5×C22⋊C4—34no—
410C5×C22⋊C4C22×D314yes—
411C22⋊Dic5—34no—
412#685—34no—
413#685—34no—
414#685C22×D314yes—
415#683—34no—
416#683—34no—
417#683C22×D314yes—
418C4×Dic5—34no—
419C4×Dic5—34no—
420C4×Dic5—34no—
421C22×#41—151no—
422C22×#41—151no—
423#550—1516no—
424C2×#127—151no—
425C2×#127—151no—
426C2×#127—151no—
427C2×#121—31no—
428C2×#121—51no—
429C2×#121—151no—
430C2×#121—151no—
431C2×#121—151no—
432C2×#121—151no—
433C2×C4×Q8—151no—
434C2×C4×D4—151no—
435C2×C4×D4—151no—
436C2×C4×D4—151no—
437C22×C3×C5—22no—
438C22×C3×C5—22no—
439C22×C3×C5—22no—
440C22×C3×C5—44no—
441C22×C3×C5C22×D412yes—
442C22×C3×C5C2×#4112yes—
443C22×C3×C5H(5,𝔽2)12yes—
444C22×C3×C5C2511yescharacteristic
445C2×D15—22no—
446C2×D15—22no—
447C2×D15—22no—
448C2×D15—44no—
449C2×C5×D3—22no—
450C2×C5×D3—22no—
451C2×C5×D3—22no—
452C2×C5×D3—22no—
453C2×C5×D3—22no—
454C2×C5×D3—22no—
455C2×C5×D3—44no—
456C2×C5×D3—44no—
457C2×C3×D5—22no—
458C2×C3×D5—22no—
459C2×C3×D5—22no—
460C2×C3×D5—22no—
461C2×C3×D5—22no—
462C2×C3×D5—22no—
463C2×C3×D5—44no—
464C2×C3×D5—44no—
465C3×C4×C5—22no—
466C3×C4×C5—22no—
467Dic15—22no—
468Dic15C22×D414yes—
469Dic15C2×#4114yescomplemented
470C3×Dic5—22no—
471C3×Dic5C22×D414yes—
472C5×Dic3—22no—
473C5×Dic3C22×D414yes—
474C24×C3—51no—
475C24×C3—51no—
476C24×C3C22×D511yescharacteristic
477C23×D3—51no—
478C23×D3C22×D511yescharacteristic
479C23×D3C22×D511yescharacteristic
480C2×C3×D4—54no—
481C2×C3×D4—54no—
482C2×C3×D4—54no—
483C2×C3×D4—104no—
484C2×C3×D4—202no—
485C2×C3×D4—202no—
486C22×C3×C4—51no—
487C22×C3×C4—51no—
488C22×C3×C4—54no—
489C22×C3×C4—104no—
490C22×C3×C4C22×D511yescharacteristic
491C22×C3×C4C22×D511yescharacteristic
492C2×#67—24no—
493C2×#67—42no—
494C2×#67—54no—
495C2×#67—54no—
496C2×#67—54no—
497C2×#67—54no—
498C2×#67—54no—
499C2×#67—54no—
500C2×#67—54no—
501C2×#67—104no—
502C2×#67—104no—
503C2×#67—104no—
504C2×#67—104no—
505C2×#67—104no—
506C2×#67—104no—
507C2×#67—202no—
508C2×#67C22×D514yes—
509C2×#67C22×D514yes—
510C22×Dic3—51no—
511C22×Dic3—51no—
512C22×Dic3—54no—
513C22×Dic3—51no—
514C22×Dic3—54no—
515C22×Dic3—104no—
516C22×Dic3—104no—
517C22×Dic3C22×D511yescharacteristic
518C22×Dic3C22×D511yescharacteristic
519#237—1032no—
520#235—1032no—
521C2×D12—42no—
522C2×D12—54no—
523C2×D12—54no—
524C2×D12—104no—
525C2×D12—202no—
526C2×D12C22×D514yes—
527C2×C4×D3—24no—
528C2×C4×D3—54no—
529C2×C4×D3—54no—
530C2×C4×D3—104no—
531C2×C4×D3—104no—
532C2×C4×D3C22×D514yes—
533C2×Dic6—58no—
534C2×Dic6—54no—
535C3×C4⋊C4—54no—
536C3×C22⋊C4—54no—
537C3×C22⋊C4C22×D514yes—
538#217—54no—
539(C2×D3)⋊C4—54no—
540(C2×D3)⋊C4—54no—
541(C2×D3)⋊C4C22×D514yes—
542Dic3⋊C4—54no—
543Dic3⋊C4—54no—
544Dic3⋊C4C22×D514yes—
545C4×Dic3—54no—
546C4×Dic3—54no—
547C4×Dic3—54no—
548C23×C5—22no—
549C23×C5—22no—
550C23×C5—22no—
551C23×C5—32no—
552C23×C5—32no—
553C23×C5—62no—
554C23×C5—62no—
555C23×C5—62no—
556C23×C5—62no—
557C23×C5—62no—
558C23×C5—62no—
559C23×C5C23×D312yes—
560C23×C5C23×D311yescharacteristic
561C22×D5—22no—
562C22×D5—22no—
563C22×D5—22no—
564C22×D5—22no—
565C22×D5—22no—
566C22×D5—22no—
567C22×D5—32no—
568C22×D5—62no—
569C22×D5—62no—
570C22×D5—62no—
571C22×D5C23×D312yes—
572C22×D5C23×D312yes—
573C5×D4—68no—
574C5×D4—124no—
575C5×D4—124no—
576C2×C4×C5—22no—
577C2×C4×C5—22no—
578C2×C4×C5—34no—
579C2×C4×C5—32no—
580C2×C4×C5—32no—
581C2×C4×C5—68no—
582C2×C4×C5—62no—
583C2×C4×C5C23×D312yes—
584C2×C4×C5C23×D312yes—
585C22⋊D5—28no—
586C22⋊D5—44no—
587C22⋊D5—68no—
588C22⋊D5—68no—
589C22⋊D5—68no—
590C22⋊D5—68no—
591C22⋊D5—68no—
592C22⋊D5—68no—
593C22⋊D5—124no—
594C2×Dic5—22no—
595C2×Dic5—34no—
596C2×Dic5—34no—
597C2×Dic5—32no—
598C2×Dic5—32no—
599C2×Dic5—32no—
600C2×Dic5—68no—
601C2×Dic5—62no—
602C2×Dic5—68no—
603C2×Dic5D3×D414yes—
604C2×Dic5C23×D312yes—
605C2×Dic5C23×D312yes—
606D20—44no—
607D20—68no—
608D20—124no—
609C4×D5—28no—
610C4×D5—68no—
611C4×D5—68no—
612Dic10—316no—
613C2×#41—158no—
614C2×#41—158no—
615C2×#41—308no—
616C2×#41—308no—
617C22×Q8—151no—
618C22×D4—31no—
619C22×D4—31no—
620C22×D4—31no—
621C22×D4—51no—
622C22×D4—51no—
623C22×D4—51no—
624C22×D4—151no—
625C22×D4—151no—
626C22×D4—151no—
627C22×D4—151no—
628C22×D4—151no—
629C22×D4—151no—
630C22×D4—151no—
631C22×D4—151no—
632C22×D4—151no—
633C23×C4—31no—
634C23×C4—51no—
635C23×C4—151no—
636C23×C4—151no—
637C23×C4—151no—
638C23×C4—151no—
639#127—158no—
640#127—158no—
641#127—158no—
642#121—38no—
643#121—58no—
644#121—158no—
645#121—158no—
646#121—158no—
647#121—158no—
648C4×Q8—158no—
649C4×D4—158no—
650C4×D4—158no—
651C4×D4—158no—
652C2×C4⋊C4—31no—
653C2×C4⋊C4—51no—
654C2×C4⋊C4—151no—
655C2×C4⋊C4—151no—
656C2×C22⋊C4—31no—
657C2×C22⋊C4—51no—
658C2×C22⋊C4—151no—
659C2×C22⋊C4—151no—
660C2×C22⋊C4—151no—
661C2×C22⋊C4D3×D511yescharacteristic
662C2×C42—151no—
663C2×C42—151no—
664C2×C42—151no—
665C2×C3×C5—42no—
666C2×C3×C5#55014yescomplemented
667C2×C3×C5C23×D411yescharacteristic
668C2×C3×C5C22×#4111yescharacteristic
669C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
670D15—42no—
671C3×D5—42no—
672C3×D5—42no—
673C5×D3—42no—
674C5×D3—42no—
675C23×C3—22no—
676C23×C3—22no—
677C23×C3—22no—
678C23×C3—52no—
679C23×C3—52no—
680C23×C3—102no—
681C23×C3—102no—
682C23×C3—102no—
683C23×C3—102no—
684C23×C3—102no—
685C23×C3—102no—
686C23×C3C23×D512yes—
687C23×C3C23×D511yescharacteristic
688C22×D3—22no—
689C22×D3—22no—
690C22×D3—22no—
691C22×D3—22no—
692C22×D3—22no—
693C22×D3—22no—
694C22×D3—52no—
695C22×D3—102no—
696C22×D3—102no—
697C22×D3—102no—
698C22×D3C23×D512yes—
699C22×D3C23×D512yes—
700C3×D4—108no—
701C3×D4—204no—
702C3×D4—204no—
703C2×C3×C4—22no—
704C2×C3×C4—22no—
705C2×C3×C4—54no—
706C2×C3×C4—52no—
707C2×C3×C4—52no—
708C2×C3×C4—108no—
709C2×C3×C4—102no—
710C2×C3×C4C23×D512yes—
711C2×C3×C4C23×D512yes—
712#67—28no—
713#67—44no—
714#67—108no—
715#67—108no—
716#67—108no—
717#67—108no—
718#67—108no—
719#67—108no—
720#67—204no—
721C2×Dic3—22no—
722C2×Dic3—54no—
723C2×Dic3—54no—
724C2×Dic3—52no—
725C2×Dic3—52no—
726C2×Dic3—52no—
727C2×Dic3—108no—
728C2×Dic3—102no—
729C2×Dic3—108no—
730C2×Dic3D4×D514yes—
731C2×Dic3C23×D512yes—
732C2×Dic3C23×D512yes—
733D12—44no—
734D12—108no—
735D12—204no—
736C4×D3—28no—
737C4×D3—108no—
738C4×D3—108no—
739Dic6—516no—
740C22×C5—22no—
741C22×C5—22no—
742C22×C5—22no—
743C22×C5—44no—
744C22×C5—62no—
745C22×C5—62no—
746C22×C5—62no—
747C22×C5—62no—
748C22×C5—62no—
749C22×C5—62no—
750C22×C5—124no—
751C22×C5—124no—
752C22×C5C2×D3×D412yes—
753C22×C5#100412yes—
754C22×C5D3×#4112yes—
755C22×C5C24×D311yescharacteristic
756C2×D5—22no—
757C2×D5—22no—
758C2×D5—22no—
759C2×D5—22no—
760C2×D5—22no—
761C2×D5—22no—
762C2×D5—44no—
763C2×D5—44no—
764C2×D5—62no—
765C2×D5—62no—
766C2×D5—62no—
767C2×D5—124no—
768C4×C5—22no—
769C4×C5—22no—
770C4×C5—34no—
771C4×C5—62no—
772Dic5—22no—
773Dic5—34no—
774Dic5—34no—
775Dic5—62no—
776Dic5C2×D3×D414yes—
777C24—31no—
778C24—31no—
779C24—51no—
780C24—51no—
781C24—151no—
782C24C2×D3×D511yescharacteristic
783#41—3032no—
784#41—3032no—
785C2×Q8—154no—
786C2×Q8—158no—
787C2×D4—34no—
788C2×D4—34no—
789C2×D4—34no—
790C2×D4—54no—
791C2×D4—54no—
792C2×D4—54no—
793C2×D4—64no—
794C2×D4—104no—
795C2×D4—122no—
796C2×D4—122no—
797C2×D4—154no—
798C2×D4—154no—
799C2×D4—154no—
800C2×D4—154no—
801C2×D4—154no—
802C2×D4—154no—
803C2×D4—154no—
804C2×D4—154no—
805C2×D4—154no—
806C2×D4—202no—
807C2×D4—202no—
808C2×D4—304no—
809C2×D4—304no—
810C2×D4—304no—
811C2×D4—304no—
812C2×D4—304no—
813C2×D4—304no—
814C2×D4—304no—
815C2×D4—602no—
816C2×D4—602no—
817C22×C4—31no—
818C22×C4—31no—
819C22×C4—34no—
820C22×C4—51no—
821C22×C4—51no—
822C22×C4—54no—
823C22×C4—64no—
824C22×C4—104no—
825C22×C4—154no—
826C22×C4—154no—
827C22×C4—151no—
828C22×C4—151no—
829C22×C4—154no—
830C22×C4—151no—
831C22×C4—154no—
832C22×C4—304no—
833C22×C4—304no—
834C22×C4—304no—
835C22×C4—304no—
836C22×C4C2×D3×D511yescharacteristic
837C22×C4C2×D3×D511yescharacteristic
838C4⋊C4—34no—
839C4⋊C4—54no—
840C4⋊C4—154no—
841C4⋊C4—154no—
842C22⋊C4—34no—
843C22⋊C4—54no—
844C22⋊C4—154no—
845C22⋊C4—154no—
846C22⋊C4—154no—
847C22⋊C4C2×D3×D514yes—
848C42—154no—
849C42—154no—
850C42—154no—
851C3×C5C2×#55011yescharacteristic, complemented, Hall
852C22×C3—22no—
853C22×C3—22no—
854C22×C3—22no—
855C22×C3—44no—
856C22×C3—102no—
857C22×C3—102no—
858C22×C3—102no—
859C22×C3—102no—
860C22×C3—102no—
861C22×C3—102no—
862C22×C3—204no—
863C22×C3—204no—
864C22×C3C2×D4×D512yes—
865C22×C3#414412yes—
866C22×C3D5×#4112yes—
867C22×C3C24×D511yescharacteristic
868C2×D3—22no—
869C2×D3—22no—
870C2×D3—22no—
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—44no—
875C2×D3—44no—
876C2×D3—102no—
877C2×D3—102no—
878C2×D3—102no—
879C2×D3—204no—
880C3×C4—22no—
881C3×C4—22no—
882C3×C4—54no—
883C3×C4—102no—
884Dic3—22no—
885Dic3—54no—
886Dic3—54no—
887Dic3—102no—
888Dic3C2×D4×D514yes—
889C2×C5—42no—
890C2×C5—122no—
891C2×C5—122no—
892C2×C5#559914yescomplemented
893C2×C5C22×D3×D411yescharacteristic
894C2×C5C2×#100411yescharacteristic
895C2×C5C2×D3×#4111yescharacteristic
896D5—42no—
897D5—42no—
898D5—122no—
899C23—22no—
900C23—22no—
901C23—22no—
902C23—32no—
903C23—32no—
904C23—52no—
905C23—52no—
906C23—62no—
907C23—62no—
908C23—62no—
909C23—62no—
910C23—62no—
911C23—62no—
912C23—102no—
913C23—102no—
914C23—102no—
915C23—102no—
916C23—102no—
917C23—102no—
918C23—152no—
919C23—302no—
920C23—302no—
921C23—302no—
922C23C22×D3×D512yes—
923C23C22×D3×D511yescharacteristic
924Q8—1516no—
925D4—68no—
926D4—108no—
927D4—124no—
928D4—124no—
929D4—204no—
930D4—204no—
931D4—308no—
932D4—308no—
933D4—308no—
934D4—308no—
935D4—308no—
936D4—308no—
937D4—308no—
938D4—604no—
939D4—604no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—34no—
943C2×C4—32no—
944C2×C4—32no—
945C2×C4—54no—
946C2×C4—52no—
947C2×C4—52no—
948C2×C4—68no—
949C2×C4—62no—
950C2×C4—108no—
951C2×C4—102no—
952C2×C4—154no—
953C2×C4—154no—
954C2×C4—152no—
955C2×C4—152no—
956C2×C4—152no—
957C2×C4—308no—
958C2×C4—308no—
959C2×C4—308no—
960C2×C4—308no—
961C2×C4—302no—
962C2×C4C22×D3×D512yes—
963C2×C4C22×D3×D512yes—
964C2×C3—42no—
965C2×C3—202no—
966C2×C3—202no—
967C2×C3#6593314yescomplemented
968C2×C3C22×D4×D511yescharacteristic
969C2×C3C2×#414411yescharacteristic
970C2×C3C2×D5×#4111yescharacteristic
971D3—42no—
972D3—42no—
973D3—202no—
974C5C2×#559911yescharacteristic, complemented, Sylow
975C22—22no—
976C22—22no—
977C22—22no—
978C22—44no—
979C22—62no—
980C22—62no—
981C22—62no—
982C22—62no—
983C22—62no—
984C22—62no—
985C22—102no—
986C22—102no—
987C22—102no—
988C22—102no—
989C22—102no—
990C22—102no—
991C22—124no—
992C22—124no—
993C22—204no—
994C22—204no—
995C22—302no—
996C22—302no—
997C22—302no—
998C22—604no—
999C22#9201612yes—
1000C22D3×D4×D512yes—
1001C22#9202512yes—
1002C22C23×D3×D511yescharacteristic
1003C4—22no—
1004C4—22no—
1005C4—34no—
1006C4—54no—
1007C4—62no—
1008C4—102no—
1009C4—154no—
1010C4—154no—
1011C4—302no—
1012C3C2×#6593311yescharacteristic, complemented, Sylow
1013C2—42no—
1014C2—122no—
1015C2—122no—
1016C2—202no—
1017C2—202no—
1018C2—602no—
1019C2#1175308014yesdirect product factor
1020C2C2×#9201611yescharacteristic
1021C2C2×D3×D4×D511yescharacteristic
1022C2C2×#9202511yescharacteristic
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×#550
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×#6780C2semidirect
2. C22×#6771C2semidirect
3. C2×#91770C2semidirect
4. C2×C5×#884C2semidirect
5. C2×C3×#4030C2semidirect
6. C2×#91571C2semidirect
7. C2×#91567C2semidirect
8. C2×#91567C2semidirect
9. C2×#91463C2semidirect
10. C2×#91461C2semidirect
11. C2×#91441C2semidirect
12. C2×#91440C2semidirect
13. C2×#91416C2semidirect
14. C2×#91409C2semidirect
15. C2×#91325C2semidirect
16. #11753080C2direct (N × H)
40. C2×#6780C22semidirect
43. C2×#6771C22semidirect
48. #91770C22semidirect
51. C5×#884C22semidirect
54. C3×#4030C22semidirect
55. #91571C22semidirect
56. #91567C22semidirect
57. #91567C22semidirect
63. #91463C22semidirect
64. #91461C22semidirect
65. #91441C22semidirect
66. #91440C22semidirect
67. #91416C22semidirect
68. #91409C22semidirect
69. #91325C22semidirect
84. C2×#4030D3semidirect
124. C2×#1204D4semidirect
174. C2×#884D5semidirect
226. #4030C2×D3semidirect
263. C2×Dic15#41semidirect
284. #1204C2×D4semidirect
344. #884C2×D5semidirect
469. Dic15C2×#41semidirect
666. C2×C3×C5#550semidirect
851. C3×C5C2×#550semidirect
892. C2×C5#5599semidirect
967. C2×C3#65933semidirect
974. C5C2×#5599semidirect
1012. C3C2×#65933semidirect
1019. C2#11753080direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67802
C22×#67712
C2×#917702
C2×C5×#8842
C2×C3×#40302
C2×#915712
C2×#915672
C2×#914632
C2×#914612
C2×#914412
C2×#914402
C2×#914162
C2×#914092
C2×#913252
#117530802
C2×#659333
C2×#55995