Finite Group Databasebeta

← C2×#11754539 #14480075

Subgroups — C2×#11754539 #14480075

Order 1920.

3456 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C5×#235C211yesmaximal, characteristic, complemented
2C22×#6771C211yesmaximal, characteristic, complemented
3C2×C4×#1220C211yesmaximal, characteristic, complemented
4C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
5C2×#91567C211yesmaximal, characteristic, complemented
6C2×#91565C211yesmaximal, characteristic, complemented
7C2×#91558C211yesmaximal, characteristic, complemented
8C2×#91525C211yesmaximal, characteristic, complemented
9C2×#91455C211yesmaximal, characteristic, complemented
10#11754539C2116yesmaximal, direct product factor
11C2×#91453C211yesmaximal, characteristic, complemented
12C2×C4×#1203C211yesmaximal, characteristic, complemented
13C2×C4×#1201C211yesmaximal, characteristic, complemented
14C2×#91416C211yesmaximal, characteristic, complemented
15C2×C4×D3×Dic5C211yesmaximal, characteristic, complemented
16C2×#91329C211yesmaximal, characteristic, complemented
17C2×#66166—31nomaximal, Hall
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C5×#67C2211yescharacteristic
23C2×C5×#235—28no—
24C2×C5×#235C2218yescomplemented
25C22×C5×D12C2211yescharacteristic
26C22×C4×C5×D3C2211yescharacteristic
27C22×C4×C5×D3C2211yescharacteristic
28C22×C5×Dic6C2211yescharacteristic
29C22×C3×C22⋊D5C2211yescharacteristic
30C22×C3×C4×D5C2211yescharacteristic
31C22×#1204C2211yescharacteristic
32C22×#1203C2211yescharacteristic
33C22×#1203C2211yescharacteristic
34C22×#1202C2211yescharacteristic
35C22×#1201C2211yescharacteristic
36C22×#1201C2211yescharacteristic
37C22×D3×Dic5C2211yescharacteristic
38C22×D3×Dic5C2211yescharacteristic
39C2×#6771—28no—
40C2×#6771C2218yescomplemented
41C2×#6719C2211yescharacteristic
42C4×#1220C2218yescomplemented
43C2×#6714C2211yescharacteristic
44C2×#6712C2211yescharacteristic
45C2×C4×Dic15C2211yescharacteristic
46C2×C3×C22⋊Dic5C2211yescharacteristic
47C3×C4×C22⋊D5C2218yescomplemented
48C2×C3×#685C2211yescharacteristic
49C2×C3×#683C2211yescharacteristic
50C2×C3×C4×Dic5C2211yescharacteristic
51#91567C2218yescomplemented
52#91565C2218yescomplemented
53#91558C2218yescomplemented
54C2×#6669C2211yescharacteristic
55C2×#6668C2211yescharacteristic
56C2×#6667C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×(C2×D3)⋊Dic5C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60C2×Dic3×Dic5C2211yescharacteristic
61C2×Dic3×Dic5C2211yescharacteristic
62#91525C2218yescomplemented
63#91455C2218yescomplemented
64#91453C2218yescomplemented
65C4×#1203C2218yescomplemented
66C4×#1201C2218yescomplemented
67#91416C2218yescomplemented
68C4×D3×Dic5C2218yescomplemented
69#91329C2218yescomplemented
70C2×#5548—51nomaximal, Hall
71C22×C5×#41—31no—
72C22×#709—31no—
73#66166—316no—
74C2×#4093—31no—
75C2×#4090—31no—
76C2×#4086—31no—
77C2×#4085—31no—
78C2×#4085—31no—
79C2×#4085—31no—
80C2×#4085—31no—
81C2×#4082—31no—
82C2×C4×C22⋊D5—31no—
83C2×C4×C22⋊D5—31no—
84C2×C4×C22⋊D5—31no—
85C2×C4×C22⋊D5D311yescharacteristic, complemented
86C22×C4×Dic5—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C5×D3C2311yescharacteristic
91C23×C3×D5C2311yescharacteristic
92C22×C3×C4×C5—24no—
93C22×C3×C4×C5C2311yescharacteristic
94C22×C3×C4×C5C2314yes—
95C22×C3×C4×C5C2311yescharacteristic
96C2×#1220—24no—
97C2×#1220C2314yes—
98C22×Dic15C2311yescharacteristic
99C22×Dic15C2311yescharacteristic
100C22×Dic15C2311yescharacteristic
101C2×C4×D15—24no—
102C2×C4×D15C2314yes—
103C2×C5×#67—24no—
104C2×C5×#67—24no—
105C2×C5×#67C2314yes—
106C2×C5×#67C2314yes—
107C22×C5×Dic3C2311yescharacteristic
108C22×C5×Dic3C2311yescharacteristic
109C5×#235—232no—
110C2×C5×D12—24no—
111C2×C5×D12C2314yes—
112C2×C4×C5×D3—24no—
113C2×C4×C5×D3D418yescomplemented
114C2×C4×C5×D3C2314yes—
115C2×C4×C5×D3C2314yes—
116C2×C5×Dic6—24no—
117C2×C5×Dic6C2314yes—
118C2×C3×C22⋊D5—24no—
119C2×C3×C22⋊D5C2314yes—
120C22×C3×Dic5C2311yescharacteristic
121C22×C3×Dic5C2311yescharacteristic
122C22×C3×Dic5C2311yescharacteristic
123C2×C3×C4×D5—24no—
124C2×C3×C4×D5C2314yes—
125C2×#1204—24no—
126C2×#1204C2314yes—
127C2×#1203—24no—
128C2×#1203—24no—
129C2×#1203C2314yes—
130C2×#1203C2314yes—
131C2×#1202—24no—
132C2×#1202C2314yes—
133C2×#1201—24no—
134C2×#1201—24no—
135C2×#1201C2314yes—
136C2×#1201C2314yes—
137C2×D3×Dic5—24no—
138C2×D3×Dic5—24no—
139C2×D3×Dic5C2314yes—
140C2×D3×Dic5C2314yes—
141#6771—232no—
142#6719C2314yes—
143#6714C2314yes—
144#6712C2314yes—
145C4×Dic15C2314yes—
146C3×C22⋊Dic5C2314yes—
147C3×#685C2314yes—
148C3×#683C2314yes—
149C3×C4×Dic5C2314yes—
150#6669C2314yes—
151#6668C2314yes—
152#6667C2314yes—
153(C2×D3)⋊Dic5C2314yes—
154(C2×D3)⋊Dic5C2314yes—
155#6665C2314yes—
156Dic3×Dic5C2314yes—
157Dic3×Dic5C2314yes—
158C22×#235—51no—
159C22×#235D511yescharacteristic, complemented
160C2×C3×C4×D4—51no—
161C2×#940—51no—
162C2×#938—51no—
163C2×C4×#67—51no—
164C2×C4×#67—51no—
165#5548—516no—
166C2×#895—51no—
167C2×#888—51no—
168C2×#885—51no—
169C2×#885—51no—
170C2×#884—51no—
171C2×#884—51no—
172C2×C4×D12—51no—
173C2×C42×D3—51no—
174C2×C5×#41—38no—
175C2×C5×#41—68no—
176C22×C5×Q8—31no—
177C22×C5×D4—31no—
178C22×C5×D4—31no—
179C22×C5×D4—31no—
180C23×C4×C5—31no—
181C23×C4×C5—31no—
182C23×C4×C5C2×D311yescharacteristic
183C22×C22⋊D5—31no—
184C22×C22⋊D5—31no—
185C22×C22⋊D5—31no—
186C22×C22⋊D5—31no—
187C22×C22⋊D5—31no—
188C22×C22⋊D5C2×D311yescharacteristic
189C23×Dic5—31no—
190C23×Dic5—31no—
191C2×#709—38no—
192C2×#709—68no—
193C22×D20—31no—
194C22×C4×D5—31no—
195C22×C4×D5C2×D311yescharacteristic
196C22×Dic10—31no—
197C2×C22⋊Dic5—31no—
198C2×C22⋊Dic5—31no—
199C2×C22⋊Dic5—31no—
200C2×C22⋊Dic5C2×D311yescharacteristic
201#4093—38no—
202#4090—38no—
203#4086—38no—
204#4085—38no—
205#4085—38no—
206#4085—38no—
207#4085—38no—
208#4082—38no—
209C4×C22⋊D5—38no—
210C4×C22⋊D5—38no—
211C4×C22⋊D5—38no—
212C4×C22⋊D5C2×D318yescomplemented
213C2×#685—31no—
214C2×#685—31no—
215C2×#685—31no—
216C2×#685C2×D311yescharacteristic
217C2×#683—31no—
218C2×#683—31no—
219C2×#683—31no—
220C2×#683C2×D311yescharacteristic
221C2×C4×Dic5—31no—
222C2×C4×Dic5—31no—
223C2×C4×Dic5—31no—
224C2×C4×Dic5—38no—
225C2×C4×Dic5C2×D311yescharacteristic
226C2×#532—151noSylow
227C23×C3×C5—22no—
228C23×C3×C5—22no—
229C23×C3×C5—22no—
230C23×C3×C5C2412yes—
231C23×C3×C5C2411yescharacteristic
232C22×D15—22no—
233C22×D15—22no—
234C22×D15—22no—
235C22×D15C2412yes—
236C22×C5×D3—22no—
237C22×C5×D3—22no—
238C22×C5×D3—22no—
239C22×C5×D3—22no—
240C22×C5×D3—22no—
241C22×C5×D3C2×D414yes—
242C22×C5×D3C2412yes—
243C22×C5×D3C2412yes—
244C22×C3×D5—22no—
245C22×C3×D5—22no—
246C22×C3×D5—22no—
247C22×C3×D5C2412yes—
248C2×C3×C4×C5—22no—
249C2×C3×C4×C5—28no—
250C2×C3×C4×C5C2×D414yes—
251C2×C3×C4×C5C2412yes—
252C2×C3×C4×C5C2412yes—
253#1220—28no—
254C2×Dic15—22no—
255C2×Dic15—22no—
256C2×Dic15#4114yescomplemented
257C2×Dic15C2412yes—
258C2×Dic15C2412yes—
259C2×Dic15C2412yes—
260C4×D15—28no—
261C5×#67—28no—
262C5×#67—28no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3C2×D414yes—
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C5×D12—28no—
268C4×C5×D3—28no—
269C4×C5×D3C2×D4116yescomplemented
270C5×Dic6—28no—
271C3×C22⋊D5—28no—
272C2×C3×Dic5—22no—
273C2×C3×Dic5—22no—
274C2×C3×Dic5#4114yescomplemented
275C2×C3×Dic5C2412yes—
276C2×C3×Dic5C2412yes—
277C2×C3×Dic5C2412yes—
278C3×C4×D5—28no—
279#1204—28no—
280#1203—28no—
281#1203—28no—
282#1202—28no—
283#1201—28no—
284#1201—28no—
285D3×Dic5—28no—
286D3×Dic5—28no—
287C22×C3×D4—51no—
288C23×C3×C4—51no—
289C23×C3×C4C2×D511yescharacteristic
290C22×#67—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67—51no—
294C22×#67C2×D511yescharacteristic
295C22×#67C2×D511yescharacteristic
296C2×#235—28no—
297C2×#235—58no—
298C2×#235—108no—
299C2×#235C2×D518yescomplemented
300C22×D12—51no—
301C22×D12—51no—
302C22×D12C2×D511yescharacteristic
303C22×C4×D3—51no—
304C22×C4×D3—51no—
305C22×C4×D3—51no—
306C22×C4×D3C2×D511yescharacteristic
307C22×C4×D3C2×D511yescharacteristic
308C22×Dic6—51no—
309C22×Dic6C2×D511yescharacteristic
310C3×C4×D4—58no—
311C2×C3×C4⋊C4—51no—
312C2×C3×C22⋊C4—51no—
313C2×C3×C22⋊C4—51no—
314C2×C3×C42—51no—
315C2×#217—51no—
316C2×#217—51no—
317#940—58no—
318#938—58no—
319C4×#67—58no—
320C4×#67—58no—
321C2×(C2×D3)⋊C4—51no—
322C2×(C2×D3)⋊C4—51no—
323C2×(C2×D3)⋊C4—51no—
324C2×(C2×D3)⋊C4—51no—
325C2×C4⋊Dic3—51no—
326C2×Dic3⋊C4—51no—
327C2×Dic3⋊C4—51no—
328C2×C4×Dic3—51no—
329C2×C4×Dic3—51no—
330C2×C4×Dic3—51no—
331#895—58no—
332#888—58no—
333#885—58no—
334#885—58no—
335#884—58no—
336#884—58no—
337C4×D12—58no—
338C42×D3—58no—
339C24×C5—31no—
340C24×C5—31no—
341C24×C5C22×D311yescharacteristic
342C23×D5—31no—
343C23×D5C22×D311yescharacteristic
344C5×#41—632no—
345C2×C5×Q8—34no—
346C2×C5×Q8—64no—
347C2×C5×D4—34no—
348C2×C5×D4—34no—
349C2×C5×D4—34no—
350C2×C5×D4—64no—
351C2×C5×D4—64no—
352C2×C5×D4—64no—
353C22×C4×C5—24no—
354C22×C4×C5—31no—
355C22×C4×C5—38no—
356C22×C4×C5—34no—
357C22×C4×C5—31no—
358C22×C4×C5—34no—
359C22×C4×C5—64no—
360C22×C4×C5C22×D311yescharacteristic
361C22×C4×C5C22×D314yes—
362C22×C4×C5C22×D311yescharacteristic
363C2×C22⋊D5—24no—
364C2×C22⋊D5—34no—
365C2×C22⋊D5—34no—
366C2×C22⋊D5—34no—
367C2×C22⋊D5—34no—
368C2×C22⋊D5—34no—
369C2×C22⋊D5—64no—
370C2×C22⋊D5—64no—
371C2×C22⋊D5—64no—
372C2×C22⋊D5—64no—
373C2×C22⋊D5—64no—
374C2×C22⋊D5C22×D314yes—
375C22×Dic5—31no—
376C22×Dic5—31no—
377C22×Dic5—31no—
378C22×Dic5—34no—
379C22×Dic5—34no—
380C22×Dic5—64no—
381C22×Dic5—64no—
382C22×Dic5C22×D311yescharacteristic
383C22×Dic5C22×D311yescharacteristic
384C22×Dic5C22×D311yescharacteristic
385#709—632no—
386C2×D20—34no—
387C2×D20—64no—
388C2×C4×D5—24no—
389C2×C4×D5—34no—
390C2×C4×D5—64no—
391C2×C4×D5C22×D314yes—
392C2×Dic10—34no—
393C2×Dic10—64no—
394C22⋊Dic5—34no—
395C22⋊Dic5—34no—
396C22⋊Dic5—34no—
397C22⋊Dic5C22×D314yes—
398#685—34no—
399#685—34no—
400#685—34no—
401#685C22×D314yes—
402#683—34no—
403#683—34no—
404#683—34no—
405#683C22×D314yes—
406C4×Dic5—34no—
407C4×Dic5—34no—
408C4×Dic5—34no—
409C4×Dic5C22×D314yes—
410C22×#41—31no—
411C22×#41—151no—
412#532—1516no—
413C2×C4⋊Q8—151no—
414C2×#127—151no—
415C2×#124—151no—
416C2×#124—151no—
417C2×#121—151no—
418C2×#121—151no—
419C2×#121—151no—
420C2×#121—151no—
421C2×C4×D4—51no—
422C2×C4×D4—151no—
423C2×C4×D4—151no—
424C2×C4×D4—151no—
425C22×C42—151no—
426C22×C3×C5—22no—
427C22×C3×C5—22no—
428C22×C3×C5—22no—
429C22×C3×C5—44no—
430C22×C3×C5C22×D412yes—
431C22×C3×C5C2×#4112yes—
432C22×C3×C5C2×#4112yes—
433C22×C3×C5C2511yescharacteristic
434C2×D15—22no—
435C2×D15—22no—
436C2×D15—22no—
437C2×D15—44no—
438C2×C5×D3—28no—
439C2×C5×D3—22no—
440C2×C5×D3—22no—
441C2×C5×D3—22no—
442C2×C5×D3—22no—
443C2×C5×D3—22no—
444C2×C5×D3—44no—
445C2×C5×D3C22×D414yes—
446C2×C3×D5—22no—
447C2×C3×D5—22no—
448C2×C3×D5—22no—
449C2×C3×D5—44no—
450C3×C4×C5—22no—
451C3×C4×C5C22×D414yes—
452Dic15—22no—
453Dic15—22no—
454Dic15C2×#4114yescomplemented
455C3×Dic5—22no—
456C3×Dic5—22no—
457C3×Dic5C2×#4114yescomplemented
458C5×Dic3—22no—
459C5×Dic3C22×D414yes—
460C24×C3—51no—
461C24×C3C22×D511yescharacteristic
462C23×D3—51no—
463C23×D3C22×D511yescharacteristic
464C23×D3C22×D511yescharacteristic
465C2×C3×D4—54no—
466C2×C3×D4—104no—
467C22×C3×C4—24no—
468C22×C3×C4—51no—
469C22×C3×C4—51no—
470C22×C3×C4—51no—
471C22×C3×C4—54no—
472C22×C3×C4—104no—
473C22×C3×C4C22×D511yescharacteristic
474C22×C3×C4C22×D514yes—
475C22×C3×C4C22×D511yescharacteristic
476C2×#67—24no—
477C2×#67—24no—
478C2×#67—54no—
479C2×#67—54no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—104no—
483C2×#67—104no—
484C2×#67—104no—
485C2×#67—104no—
486C2×#67C22×D514yes—
487C2×#67C22×D514yes—
488C22×Dic3—51no—
489C22×Dic3—51no—
490C22×Dic3—51no—
491C22×Dic3C22×D511yescharacteristic
492C22×Dic3C22×D511yescharacteristic
493#235—232no—
494#235—1032no—
495C2×D12—24no—
496C2×D12—54no—
497C2×D12—54no—
498C2×D12—104no—
499C2×D12—104no—
500C2×D12C22×D514yes—
501C2×C4×D3—24no—
502C2×C4×D3—54no—
503C2×C4×D3—54no—
504C2×C4×D3—54no—
505C2×C4×D3—104no—
506C2×C4×D3—104no—
507C2×C4×D3—104no—
508C2×C4×D3C22⋊D518yescomplemented
509C2×C4×D3C22×D514yes—
510C2×C4×D3C22×D514yes—
511C2×Dic6—24no—
512C2×Dic6—54no—
513C2×Dic6—104no—
514C2×Dic6C22×D514yes—
515C3×C4⋊C4—54no—
516C3×C22⋊C4—54no—
517C3×C22⋊C4—54no—
518C3×C42—54no—
519#217—54no—
520#217—54no—
521(C2×D3)⋊C4—54no—
522(C2×D3)⋊C4—54no—
523(C2×D3)⋊C4—54no—
524(C2×D3)⋊C4—54no—
525C4⋊Dic3—54no—
526Dic3⋊C4—54no—
527Dic3⋊C4—54no—
528C4×Dic3—54no—
529C4×Dic3—54no—
530C4×Dic3—54no—
531C23×C5—22no—
532C23×C5—22no—
533C23×C5—22no—
534C23×C5—34no—
535C23×C5—32no—
536C23×C5—32no—
537C23×C5—62no—
538C23×C5—62no—
539C23×C5—62no—
540C23×C5—62no—
541C23×C5—62no—
542C23×C5C23×D312yes—
543C23×C5C23×D311yescharacteristic
544C22×D5—22no—
545C22×D5—22no—
546C22×D5—22no—
547C22×D5—32no—
548C22×D5—62no—
549C22×D5—62no—
550C22×D5—62no—
551C22×D5C23×D312yes—
552C5×Q8—68no—
553C5×D4—68no—
554C5×D4—68no—
555C5×D4—68no—
556C2×C4×C5—22no—
557C2×C4×C5—28no—
558C2×C4×C5—34no—
559C2×C4×C5—32no—
560C2×C4×C5—316no—
561C2×C4×C5—32no—
562C2×C4×C5—62no—
563C2×C4×C5—68no—
564C2×C4×C5D3×D414yes—
565C2×C4×C5C23×D312yes—
566C2×C4×C5C23×D312yes—
567C22⋊D5—28no—
568C22⋊D5—68no—
569C22⋊D5—68no—
570C22⋊D5—68no—
571C22⋊D5—68no—
572C22⋊D5—68no—
573C2×Dic5—22no—
574C2×Dic5—22no—
575C2×Dic5—34no—
576C2×Dic5—32no—
577C2×Dic5—32no—
578C2×Dic5—32no—
579C2×Dic5—68no—
580C2×Dic5—62no—
581C2×Dic5—62no—
582C2×Dic5—68no—
583C2×Dic5#23514yescomplemented
584C2×Dic5C23×D312yes—
585C2×Dic5C23×D312yes—
586C2×Dic5C23×D312yes—
587D20—68no—
588C4×D5—28no—
589C4×D5—68no—
590Dic10—68no—
591C2×#41—38no—
592C2×#41—68no—
593C2×#41—158no—
594C2×#41—308no—
595C22×Q8—31no—
596C22×Q8—151no—
597C22×D4—31no—
598C22×D4—31no—
599C22×D4—31no—
600C22×D4—51no—
601C22×D4—151no—
602C22×D4—151no—
603C22×D4—151no—
604C22×D4—151no—
605C22×D4—151no—
606C22×D4—151no—
607C23×C4—31no—
608C23×C4—31no—
609C23×C4—51no—
610C23×C4—151no—
611C23×C4—151no—
612C23×C4—151no—
613C23×C4D3×D511yescharacteristic
614C4⋊Q8—158no—
615#127—158no—
616#124—158no—
617#124—158no—
618#121—158no—
619#121—158no—
620#121—158no—
621#121—158no—
622C4×D4—58no—
623C4×D4—158no—
624C4×D4—158no—
625C4×D4—158no—
626C2×C4⋊C4—51no—
627C2×C4⋊C4—151no—
628C2×C4⋊C4—151no—
629C2×C4⋊C4—151no—
630C2×C22⋊C4—51no—
631C2×C22⋊C4—51no—
632C2×C22⋊C4—151no—
633C2×C22⋊C4—151no—
634C2×C22⋊C4—151no—
635C2×C22⋊C4—151no—
636C2×C22⋊C4—151no—
637C2×C22⋊C4—151no—
638C2×C42—51no—
639C2×C42—158no—
640C2×C42—151no—
641C2×C42—151no—
642C2×C42—151no—
643C2×C3×C5—42no—
644C2×C3×C5#53214yescomplemented
645C2×C3×C5C23×D411yescharacteristic
646C2×C3×C5C22×#4111yescharacteristic
647C2×C3×C5C22×#4111yescharacteristic
648D15—42no—
649C3×D5—42no—
650C5×D3—24no—
651C5×D3—42no—
652C23×C3—22no—
653C23×C3—22no—
654C23×C3—22no—
655C23×C3—52no—
656C23×C3—102no—
657C23×C3—102no—
658C23×C3—102no—
659C23×C3C23×D512yes—
660C23×C3C23×D511yescharacteristic
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—52no—
667C22×D3—102no—
668C22×D3—102no—
669C22×D3—102no—
670C22×D3C2×C22⋊D514yes—
671C22×D3C23×D512yes—
672C22×D3C23×D512yes—
673C3×D4—108no—
674C2×C3×C4—22no—
675C2×C3×C4—28no—
676C2×C3×C4—54no—
677C2×C3×C4—52no—
678C2×C3×C4—52no—
679C2×C3×C4—52no—
680C2×C3×C4—102no—
681C2×C3×C4—102no—
682C2×C3×C4—108no—
683C2×C3×C4C2×C22⋊D514yes—
684C2×C3×C4C23×D512yes—
685C2×C3×C4C23×D512yes—
686#67—28no—
687#67—28no—
688#67—108no—
689#67—108no—
690#67—108no—
691#67—108no—
692C2×Dic3—22no—
693C2×Dic3—54no—
694C2×Dic3—52no—
695C2×Dic3—52no—
696C2×Dic3—52no—
697C2×Dic3—102no—
698C2×Dic3—102no—
699C2×Dic3C2×C22⋊D514yes—
700C2×Dic3C23×D512yes—
701C2×Dic3C23×D512yes—
702D12—28no—
703D12—108no—
704D12—108no—
705C4×D3—28no—
706C4×D3—108no—
707C4×D3—108no—
708C4×D3—108no—
709C4×D3C2×C22⋊D5116yescomplemented
710Dic6—28no—
711Dic6—108no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—34no—
716C22×C5—44no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—68no—
720C22×C5—62no—
721C22×C5—62no—
722C22×C5—62no—
723C22×C5—124no—
724C22×C5C2×#23512yes—
725C22×C5C2×D3×D412yes—
726C22×C5D3×#4112yes—
727C22×C5C24×D311yescharacteristic
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—44no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—62no—
735C2×D5—124no—
736C4×C5—22no—
737C4×C5—34no—
738C4×C5—62no—
739C4×C5C2×D3×D414yes—
740Dic5—22no—
741Dic5—22no—
742Dic5—34no—
743Dic5—62no—
744Dic5—62no—
745Dic5C2×#23514yescomplemented
746C24—31no—
747C24—31no—
748C24—51no—
749C24—151no—
750C24C2×D3×D511yescharacteristic
751#41—632no—
752#41—3032no—
753C2×Q8—34no—
754C2×Q8—64no—
755C2×Q8—154no—
756C2×Q8—304no—
757C2×D4—34no—
758C2×D4—34no—
759C2×D4—34no—
760C2×D4—54no—
761C2×D4—64no—
762C2×D4—64no—
763C2×D4—64no—
764C2×D4—104no—
765C2×D4—154no—
766C2×D4—154no—
767C2×D4—154no—
768C2×D4—154no—
769C2×D4—154no—
770C2×D4—154no—
771C2×D4—304no—
772C2×D4—304no—
773C2×D4—304no—
774C2×D4—304no—
775C2×D4—304no—
776C2×D4—304no—
777C22×C4—24no—
778C22×C4—31no—
779C22×C4—38no—
780C22×C4—34no—
781C22×C4—31no—
782C22×C4—34no—
783C22×C4—51no—
784C22×C4—51no—
785C22×C4—51no—
786C22×C4—54no—
787C22×C4—64no—
788C22×C4—104no—
789C22×C4—154no—
790C22×C4—154no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4—154no—
795C22×C4—304no—
796C22×C4—304no—
797C22×C4—304no—
798C22×C4C2×D3×D511yescharacteristic
799C22×C4C2×D3×D514yes—
800C22×C4C2×D3×D511yescharacteristic
801C4⋊C4—54no—
802C4⋊C4—154no—
803C4⋊C4—154no—
804C4⋊C4—154no—
805C22⋊C4—54no—
806C22⋊C4—54no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C42—54no—
814C42—154no—
815C42—154no—
816C42—154no—
817C3×C5C2×#53211yescharacteristic, complemented, Hall
818C22×C3—22no—
819C22×C3—22no—
820C22×C3—22no—
821C22×C3—44no—
822C22×C3—102no—
823C22×C3—102no—
824C22×C3—102no—
825C22×C3—204no—
826C22×C3D5×#4112yes—
827C22×C3D5×#4112yes—
828C22×C3C22×C22⋊D512yes—
829C22×C3C24×D511yescharacteristic
830C2×D3—28no—
831C2×D3—22no—
832C2×D3—22no—
833C2×D3—22no—
834C2×D3—22no—
835C2×D3—22no—
836C2×D3—44no—
837C2×D3—102no—
838C2×D3—102no—
839C2×D3—102no—
840C2×D3—204no—
841C2×D3C22×C22⋊D514yes—
842C3×C4—22no—
843C3×C4—54no—
844C3×C4—102no—
845C3×C4—102no—
846C3×C4C22×C22⋊D514yes—
847Dic3—22no—
848Dic3—54no—
849Dic3—102no—
850Dic3—102no—
851Dic3C22×C22⋊D514yes—
852C2×C5—42no—
853C2×C5—64no—
854C2×C5—122no—
855C2×C5#554814yescomplemented
856C2×C5C22×#23511yescharacteristic
857C2×C5C22×D3×D411yescharacteristic
858C2×C5C2×D3×#4111yescharacteristic
859D5—42no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—34no—
865C23—32no—
866C23—32no—
867C23—52no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—62no—
872C23—62no—
873C23—102no—
874C23—102no—
875C23—102no—
876C23—152no—
877C23—302no—
878C23—302no—
879C23—302no—
880C23C22×D3×D512yes—
881C23C22×D3×D511yescharacteristic
882Q8—68no—
883Q8—308no—
884D4—68no—
885D4—68no—
886D4—68no—
887D4—108no—
888D4—308no—
889D4—308no—
890D4—308no—
891D4—308no—
892D4—308no—
893D4—308no—
894C2×C4—22no—
895C2×C4—28no—
896C2×C4—34no—
897C2×C4—32no—
898C2×C4—316no—
899C2×C4—32no—
900C2×C4—54no—
901C2×C4—52no—
902C2×C4—52no—
903C2×C4—52no—
904C2×C4—62no—
905C2×C4—68no—
906C2×C4—102no—
907C2×C4—102no—
908C2×C4—108no—
909C2×C4—154no—
910C2×C4—152no—
911C2×C4—152no—
912C2×C4—152no—
913C2×C4—308no—
914C2×C4—308no—
915C2×C4—302no—
916C2×C4—302no—
917C2×C4—308no—
918C2×C4D3×C22⋊D514yes—
919C2×C4C22×D3×D512yes—
920C2×C4C22×D3×D512yes—
921C2×C3—42no—
922C2×C3—202no—
923C2×C3#6616614yescomplemented
924C2×C3C2×D5×#4111yescharacteristic
925C2×C3C2×D5×#4111yescharacteristic
926C2×C3C23×C22⋊D511yescharacteristic
927D3—24no—
928D3—42no—
929D3—202no—
930C5C2×#554811yescharacteristic, complemented, Sylow
931C22—22no—
932C22—22no—
933C22—22no—
934C22—34no—
935C22—44no—
936C22—68no—
937C22—62no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—102no—
943C22—102no—
944C22—102no—
945C22—124no—
946C22—204no—
947C22—302no—
948C22—302no—
949C22—302no—
950C22—604no—
951C22D5×#23512yes—
952C22#9201612yes—
953C22C2×D3×C22⋊D512yes—
954C22C23×D3×D511yescharacteristic
955C4—22no—
956C4—34no—
957C4—54no—
958C4—62no—
959C4—102no—
960C4—102no—
961C4—154no—
962C4—302no—
963C4—302no—
964C4C2×D3×C22⋊D514yes—
965C3C2×#6616611yescharacteristic, complemented, Sylow
966C2—42no—
967C2—64no—
968C2—122no—
969C2—202no—
970C2—602no—
971C2#1175453914yesdirect product factor
972C2C2×D5×#23511yescharacteristic
973C2C2×#9201611yescharacteristic
974C2C22×D3×C22⋊D511yescharacteristic
subgroupG/H
centerC22×C4C2×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#532
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×C5×#235C2semidirect
2. C22×#6771C2semidirect
3. C2×C4×#1220C2semidirect
4. C2×C3×C4×C22⋊D5C2semidirect
5. C2×#91567C2semidirect
6. C2×#91565C2semidirect
7. C2×#91558C2semidirect
8. C2×#91525C2semidirect
9. C2×#91455C2semidirect
10. #11754539C2direct (N × H)
11. C2×#91453C2semidirect
12. C2×C4×#1203C2semidirect
13. C2×C4×#1201C2semidirect
14. C2×#91416C2semidirect
15. C2×C4×D3×Dic5C2semidirect
16. C2×#91329C2semidirect
24. C2×C5×#235C22semidirect
40. C2×#6771C22semidirect
42. C4×#1220C22semidirect
47. C3×C4×C22⋊D5C22semidirect
51. #91567C22semidirect
52. #91565C22semidirect
53. #91558C22semidirect
62. #91525C22semidirect
63. #91455C22semidirect
64. #91453C22semidirect
65. C4×#1203C22semidirect
66. C4×#1201C22semidirect
67. #91416C22semidirect
68. C4×D3×Dic5C22semidirect
69. #91329C22semidirect
85. C2×C4×C22⋊D5D3semidirect
113. C2×C4×C5×D3D4semidirect
159. C22×#235D5semidirect
212. C4×C22⋊D5C2×D3semidirect
256. C2×Dic15#41semidirect
269. C4×C5×D3C2×D4semidirect
274. C2×C3×Dic5#41semidirect
299. C2×#235C2×D5semidirect
454. Dic15C2×#41semidirect
457. C3×Dic5C2×#41semidirect
508. C2×C4×D3C22⋊D5semidirect
583. C2×Dic5#235semidirect
644. C2×C3×C5#532semidirect
709. C4×D3C2×C22⋊D5semidirect
745. Dic5C2×#235semidirect
817. C3×C5C2×#532semidirect
855. C2×C5#5548semidirect
923. C2×C3#66166semidirect
930. C5C2×#5548semidirect
965. C3C2×#66166semidirect
971. C2#11754539direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C5×#2352
C22×#67712
C2×C4×#12202
C2×C3×C4×C22⋊D52
C2×#915672
C2×#915652
C2×#915582
C2×#915252
C2×#914552
#117545392
C2×#914532
C2×C4×#12032
C2×C4×#12012
C2×#914162
C2×C4×D3×Dic52
C2×#913292
C2×#661663
C2×#55485