Finite Group Databasebeta

← C2×#11754311 #14480076

Subgroups — C2×#11754311 #14480076

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×C3×#709C211yesmaximal, characteristic, complemented
2C22×#6771C211yesmaximal, characteristic, complemented
3C2×C4×#1220C211yesmaximal, characteristic, complemented
4C2×C4×C5×#67C211yesmaximal, characteristic, complemented
5C2×#91567C211yesmaximal, characteristic, complemented
6C2×#91550C211yesmaximal, characteristic, complemented
7C2×#91549C211yesmaximal, characteristic, complemented
8C2×#91534C211yesmaximal, characteristic, complemented
9C2×C4×#1202C211yesmaximal, characteristic, complemented
10C2×C4×#1201C211yesmaximal, characteristic, complemented
11C2×#91409C211yesmaximal, characteristic, complemented
12#11754311C2116yesmaximal, direct product factor
13C2×#91408C211yesmaximal, characteristic, complemented
14C2×C4×D5×Dic3C211yesmaximal, characteristic, complemented
15C2×#91327C211yesmaximal, characteristic, complemented
16C2×#91326C211yesmaximal, characteristic, complemented
17C2×#65882—31nomaximal, Hall
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C22×C5×#67C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C22⋊D5C2211yescharacteristic
25C2×C3×#709—28no—
26C2×C3×#709C2218yescomplemented
27C22×C3×D20C2211yescharacteristic
28C22×C3×C4×D5C2211yescharacteristic
29C22×C3×C4×D5C2211yescharacteristic
30C22×C3×Dic10C2211yescharacteristic
31C22×#1204C2211yescharacteristic
32C22×#1203C2211yescharacteristic
33C22×#1202C2211yescharacteristic
34C22×#1202C2211yescharacteristic
35C22×#1201C2211yescharacteristic
36C22×#1201C2211yescharacteristic
37C22×D5×Dic3C2211yescharacteristic
38C22×D5×Dic3C2211yescharacteristic
39C2×#6771—28no—
40C2×#6771C2218yescomplemented
41C2×#6719C2211yescharacteristic
42C4×#1220C2218yescomplemented
43C2×#6714C2211yescharacteristic
44C2×#6712C2211yescharacteristic
45C2×C4×Dic15C2211yescharacteristic
46C2×C5×#217C2211yescharacteristic
47C4×C5×#67C2218yescomplemented
48C2×C5×(C2×D3)⋊C4C2211yescharacteristic
49C2×C5×Dic3⋊C4C2211yescharacteristic
50C2×C4×C5×Dic3C2211yescharacteristic
51#91567C2218yescomplemented
52#91550C2218yescomplemented
53#91549C2218yescomplemented
54C2×Dic3⋊Dic5C2211yescharacteristic
55C2×#6669C2211yescharacteristic
56C2×#6667C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×#6665C2211yescharacteristic
59C2×#6665C2211yescharacteristic
60#91534C2218yescomplemented
61C2×Dic3×Dic5C2211yescharacteristic
62C2×Dic3×Dic5C2211yescharacteristic
63C4×#1202C2218yescomplemented
64C4×#1201C2218yescomplemented
65#91409C2218yescomplemented
66#91408C2218yescomplemented
67C4×D5×Dic3C2218yescomplemented
68#91327C2218yescomplemented
69#91326C2218yescomplemented
70C2×#5832—51nomaximal, Hall
71C22×#709—31no—
72C22×#709D311yescharacteristic, complemented
73C2×C4×C5×D4—31no—
74C2×#4086—31no—
75C2×#4084—31no—
76C2×C4×C22⋊D5—31no—
77C2×C4×C22⋊D5—31no—
78#65882—316no—
79C2×#4041—31no—
80C2×#4034—31no—
81C2×#4031—31no—
82C2×#4031—31no—
83C2×#4030—31no—
84C2×#4030—31no—
85C2×C4×D20—31no—
86C2×C42×D5—31no—
87C24×C3×C5C2311yescharacteristic
88C23×D15C2311yescharacteristic
89C23×C5×D3C2311yescharacteristic
90C23×C3×D5C2311yescharacteristic
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×#67C2314yes—
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2311yescharacteristic
108C2×C4×C5×D3—24no—
109C2×C4×C5×D3C2314yes—
110C2×C3×C22⋊D5—24no—
111C2×C3×C22⋊D5—24no—
112C2×C3×C22⋊D5C2314yes—
113C2×C3×C22⋊D5C2314yes—
114C22×C3×Dic5C2311yescharacteristic
115C22×C3×Dic5C2311yescharacteristic
116C3×#709—232no—
117C2×C3×D20—24no—
118C2×C3×D20C2314yes—
119C2×C3×C4×D5—24no—
120C2×C3×C4×D5D418yescomplemented
121C2×C3×C4×D5C2314yes—
122C2×C3×C4×D5C2314yes—
123C2×C3×Dic10—24no—
124C2×C3×Dic10C2314yes—
125C2×#1204—24no—
126C2×#1204C2314yes—
127C2×#1203—24no—
128C2×#1203C2314yes—
129C2×#1202—24no—
130C2×#1202—24no—
131C2×#1202C2314yes—
132C2×#1202C2314yes—
133C2×#1201—24no—
134C2×#1201—24no—
135C2×#1201C2314yes—
136C2×#1201C2314yes—
137C2×D5×Dic3—24no—
138C2×D5×Dic3—24no—
139C2×D5×Dic3C2314yes—
140C2×D5×Dic3C2314yes—
141#6771—232no—
142#6719C2314yes—
143#6714C2314yes—
144#6712C2314yes—
145C4×Dic15C2314yes—
146C5×#217C2314yes—
147C5×(C2×D3)⋊C4C2314yes—
148C5×Dic3⋊C4C2314yes—
149C4×C5×Dic3C2314yes—
150Dic3⋊Dic5C2314yes—
151#6669C2314yes—
152#6667C2314yes—
153(C2×D3)⋊Dic5C2314yes—
154#6665C2314yes—
155#6665C2314yes—
156Dic3×Dic5C2314yes—
157Dic3×Dic5C2314yes—
158C22×C3×#41—51no—
159C22×#235—51no—
160#5832—516no—
161C2×#947—51no—
162C2×#944—51no—
163C2×#940—51no—
164C2×#939—51no—
165C2×#939—51no—
166C2×#939—51no—
167C2×#939—51no—
168C2×#936—51no—
169C2×C4×#67—51no—
170C2×C4×#67—51no—
171C2×C4×#67—51no—
172C2×C4×#67D511yescharacteristic, complemented
173C22×C4×Dic3—51no—
174C22×C5×D4—31no—
175C23×C4×C5—31no—
176C23×C4×C5C2×D311yescharacteristic
177C22×C22⋊D5—31no—
178C22×C22⋊D5—31no—
179C22×C22⋊D5—31no—
180C22×C22⋊D5—31no—
181C22×C22⋊D5C2×D311yescharacteristic
182C22×C22⋊D5C2×D311yescharacteristic
183C2×#709—28no—
184C2×#709—38no—
185C2×#709—68no—
186C2×#709C2×D318yescomplemented
187C22×D20—31no—
188C22×D20—31no—
189C22×D20C2×D311yescharacteristic
190C22×C4×D5—31no—
191C22×C4×D5—31no—
192C22×C4×D5—31no—
193C22×C4×D5C2×D311yescharacteristic
194C22×C4×D5C2×D311yescharacteristic
195C22×Dic10—31no—
196C22×Dic10C2×D311yescharacteristic
197C4×C5×D4—38no—
198C2×C5×C4⋊C4—31no—
199C2×C5×C22⋊C4—31no—
200C2×C5×C22⋊C4—31no—
201C2×C42×C5—31no—
202C2×C22⋊Dic5—31no—
203C2×C22⋊Dic5—31no—
204#4086—38no—
205#4084—38no—
206C4×C22⋊D5—38no—
207C4×C22⋊D5—38no—
208C2×#685—31no—
209C2×#685—31no—
210C2×#685—31no—
211C2×#685—31no—
212C2×C4⋊Dic5—31no—
213C2×#683—31no—
214C2×#683—31no—
215C2×C4×Dic5—31no—
216C2×C4×Dic5—31no—
217C2×C4×Dic5—31no—
218#4041—38no—
219#4034—38no—
220#4031—38no—
221#4031—38no—
222#4030—38no—
223#4030—38no—
224C4×D20—38no—
225C42×D5—38no—
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×D3C2412yes—
240C22×C3×D5—22no—
241C22×C3×D5—22no—
242C22×C3×D5—22no—
243C22×C3×D5—22no—
244C22×C3×D5—22no—
245C22×C3×D5C2×D414yes—
246C22×C3×D5C2412yes—
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—
262C2×C5×Dic3—22no—
263C2×C5×Dic3—22no—
264C2×C5×Dic3#4114yescomplemented
265C2×C5×Dic3C2412yes—
266C2×C5×Dic3C2412yes—
267C2×C5×Dic3C2412yes—
268C4×C5×D3—28no—
269C3×C22⋊D5—28no—
270C3×C22⋊D5—28no—
271C2×C3×Dic5—22no—
272C2×C3×Dic5C2×D414yes—
273C2×C3×Dic5C2412yes—
274C2×C3×Dic5C2412yes—
275C3×D20—28no—
276C3×C4×D5—28no—
277C3×C4×D5C2×D4116yescomplemented
278C3×Dic10—28no—
279#1204—28no—
280#1203—28no—
281#1202—28no—
282#1202—28no—
283#1201—28no—
284#1201—28no—
285D5×Dic3—28no—
286D5×Dic3—28no—
287C2×C3×#41—58no—
288C2×C3×#41—108no—
289C22×C3×Q8—51no—
290C22×C3×D4—51no—
291C22×C3×D4—51no—
292C22×C3×D4—51no—
293C23×C3×C4—51no—
294C23×C3×C4—51no—
295C23×C3×C4C2×D511yescharacteristic
296C22×#67—51no—
297C22×#67—51no—
298C22×#67—51no—
299C22×#67—51no—
300C22×#67—51no—
301C22×#67C2×D511yescharacteristic
302C23×Dic3—51no—
303C23×Dic3—51no—
304C2×#235—58no—
305C2×#235—108no—
306C22×D12—51no—
307C22×C4×D3—51no—
308C22×C4×D3C2×D511yescharacteristic
309C22×Dic6—51no—
310C2×#217—51no—
311C2×#217—51no—
312C2×#217—51no—
313C2×#217C2×D511yescharacteristic
314#947—58no—
315#944—58no—
316#940—58no—
317#939—58no—
318#939—58no—
319#939—58no—
320#939—58no—
321#936—58no—
322C4×#67—58no—
323C4×#67—58no—
324C4×#67—58no—
325C4×#67C2×D518yescomplemented
326C2×(C2×D3)⋊C4—51no—
327C2×(C2×D3)⋊C4—51no—
328C2×(C2×D3)⋊C4—51no—
329C2×(C2×D3)⋊C4C2×D511yescharacteristic
330C2×Dic3⋊C4—51no—
331C2×Dic3⋊C4—51no—
332C2×Dic3⋊C4—51no—
333C2×Dic3⋊C4C2×D511yescharacteristic
334C2×C4×Dic3—51no—
335C2×C4×Dic3—51no—
336C2×C4×Dic3—51no—
337C2×C4×Dic3—58no—
338C2×C4×Dic3C2×D511yescharacteristic
339C24×C5—31no—
340C24×C5C22×D311yescharacteristic
341C23×D5—31no—
342C23×D5C22×D311yescharacteristic
343C23×D5C22×D311yescharacteristic
344C2×C5×D4—34no—
345C2×C5×D4—64no—
346C22×C4×C5—24no—
347C22×C4×C5—31no—
348C22×C4×C5—31no—
349C22×C4×C5—31no—
350C22×C4×C5—34no—
351C22×C4×C5—64no—
352C22×C4×C5C22×D311yescharacteristic
353C22×C4×C5C22×D314yes—
354C22×C4×C5C22×D311yescharacteristic
355C2×C22⋊D5—24no—
356C2×C22⋊D5—24no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—34no—
360C2×C22⋊D5—34no—
361C2×C22⋊D5—64no—
362C2×C22⋊D5—64no—
363C2×C22⋊D5—64no—
364C2×C22⋊D5—64no—
365C2×C22⋊D5C22×D314yes—
366C2×C22⋊D5C22×D314yes—
367C22×Dic5—31no—
368C22×Dic5—31no—
369C22×Dic5—31no—
370C22×Dic5C22×D311yescharacteristic
371C22×Dic5C22×D311yescharacteristic
372#709—232no—
373#709—632no—
374C2×D20—24no—
375C2×D20—34no—
376C2×D20—34no—
377C2×D20—64no—
378C2×D20—64no—
379C2×D20C22×D314yes—
380C2×C4×D5—24no—
381C2×C4×D5—34no—
382C2×C4×D5—34no—
383C2×C4×D5—34no—
384C2×C4×D5—64no—
385C2×C4×D5—64no—
386C2×C4×D5—64no—
387C2×C4×D5#6718yescomplemented
388C2×C4×D5C22×D314yes—
389C2×C4×D5C22×D314yes—
390C2×Dic10—24no—
391C2×Dic10—34no—
392C2×Dic10—64no—
393C2×Dic10C22×D314yes—
394C5×C4⋊C4—34no—
395C5×C22⋊C4—34no—
396C5×C22⋊C4—34no—
397C42×C5—34no—
398C22⋊Dic5—34no—
399C22⋊Dic5—34no—
400#685—34no—
401#685—34no—
402#685—34no—
403#685—34no—
404C4⋊Dic5—34no—
405#683—34no—
406#683—34no—
407C4×Dic5—34no—
408C4×Dic5—34no—
409C4×Dic5—34no—
410C22×#41—51no—
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—31no—
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—22no—
439C2×C5×D3—22no—
440C2×C5×D3—22no—
441C2×C5×D3—44no—
442C2×C3×D5—28no—
443C2×C3×D5—22no—
444C2×C3×D5—22no—
445C2×C3×D5—22no—
446C2×C3×D5—22no—
447C2×C3×D5—22no—
448C2×C3×D5—44no—
449C2×C3×D5C22×D414yes—
450C3×C4×C5—22no—
451C3×C4×C5C22×D414yes—
452Dic15—22no—
453Dic15—22no—
454Dic15C2×#4114yescomplemented
455C3×Dic5—22no—
456C3×Dic5C22×D414yes—
457C5×Dic3—22no—
458C5×Dic3—22no—
459C5×Dic3C2×#4114yescomplemented
460C24×C3—51no—
461C24×C3—51no—
462C24×C3C22×D511yescharacteristic
463C23×D3—51no—
464C23×D3C22×D511yescharacteristic
465C3×#41—1032no—
466C2×C3×Q8—54no—
467C2×C3×Q8—104no—
468C2×C3×D4—54no—
469C2×C3×D4—54no—
470C2×C3×D4—54no—
471C2×C3×D4—104no—
472C2×C3×D4—104no—
473C2×C3×D4—104no—
474C22×C3×C4—24no—
475C22×C3×C4—51no—
476C22×C3×C4—58no—
477C22×C3×C4—54no—
478C22×C3×C4—51no—
479C22×C3×C4—54no—
480C22×C3×C4—104no—
481C22×C3×C4C22×D511yescharacteristic
482C22×C3×C4C22×D514yes—
483C22×C3×C4C22×D511yescharacteristic
484C2×#67—24no—
485C2×#67—54no—
486C2×#67—54no—
487C2×#67—54no—
488C2×#67—54no—
489C2×#67—54no—
490C2×#67—104no—
491C2×#67—104no—
492C2×#67—104no—
493C2×#67—104no—
494C2×#67—104no—
495C2×#67C22×D514yes—
496C22×Dic3—51no—
497C22×Dic3—51no—
498C22×Dic3—51no—
499C22×Dic3—54no—
500C22×Dic3—54no—
501C22×Dic3—104no—
502C22×Dic3—104no—
503C22×Dic3C22×D511yescharacteristic
504C22×Dic3C22×D511yescharacteristic
505C22×Dic3C22×D511yescharacteristic
506#235—1032no—
507C2×D12—54no—
508C2×D12—104no—
509C2×C4×D3—24no—
510C2×C4×D3—54no—
511C2×C4×D3—104no—
512C2×C4×D3C22×D514yes—
513C2×Dic6—54no—
514C2×Dic6—104no—
515#217—54no—
516#217—54no—
517#217—54no—
518#217C22×D514yes—
519(C2×D3)⋊C4—54no—
520(C2×D3)⋊C4—54no—
521(C2×D3)⋊C4—54no—
522(C2×D3)⋊C4C22×D514yes—
523Dic3⋊C4—54no—
524Dic3⋊C4—54no—
525Dic3⋊C4—54no—
526Dic3⋊C4C22×D514yes—
527C4×Dic3—54no—
528C4×Dic3—54no—
529C4×Dic3—54no—
530C4×Dic3C22×D514yes—
531C23×C5—22no—
532C23×C5—22no—
533C23×C5—22no—
534C23×C5—32no—
535C23×C5—62no—
536C23×C5—62no—
537C23×C5—62no—
538C23×C5C23×D312yes—
539C23×C5C23×D311yescharacteristic
540C22×D5—22no—
541C22×D5—22no—
542C22×D5—22no—
543C22×D5—22no—
544C22×D5—22no—
545C22×D5—32no—
546C22×D5—62no—
547C22×D5—62no—
548C22×D5—62no—
549C22×D5C2×#6714yes—
550C22×D5C23×D312yes—
551C22×D5C23×D312yes—
552C5×D4—68no—
553C2×C4×C5—22no—
554C2×C4×C5—28no—
555C2×C4×C5—34no—
556C2×C4×C5—32no—
557C2×C4×C5—32no—
558C2×C4×C5—32no—
559C2×C4×C5—62no—
560C2×C4×C5—62no—
561C2×C4×C5—68no—
562C2×C4×C5C2×#6714yes—
563C2×C4×C5C23×D312yes—
564C2×C4×C5C23×D312yes—
565C22⋊D5—28no—
566C22⋊D5—28no—
567C22⋊D5—68no—
568C22⋊D5—68no—
569C22⋊D5—68no—
570C22⋊D5—68no—
571C2×Dic5—22no—
572C2×Dic5—34no—
573C2×Dic5—32no—
574C2×Dic5—32no—
575C2×Dic5—32no—
576C2×Dic5—62no—
577C2×Dic5—62no—
578C2×Dic5C2×#6714yes—
579C2×Dic5C23×D312yes—
580C2×Dic5C23×D312yes—
581D20—28no—
582D20—68no—
583D20—68no—
584C4×D5—28no—
585C4×D5—68no—
586C4×D5—68no—
587C4×D5—68no—
588C4×D5C2×#67116yescomplemented
589Dic10—28no—
590Dic10—68no—
591C2×#41—58no—
592C2×#41—108no—
593C2×#41—158no—
594C2×#41—308no—
595C22×Q8—51no—
596C22×Q8—151no—
597C22×D4—31no—
598C22×D4—51no—
599C22×D4—51no—
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—51no—
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—38no—
623C4×D4—158no—
624C4×D4—158no—
625C4×D4—158no—
626C2×C4⋊C4—31no—
627C2×C4⋊C4—151no—
628C2×C4⋊C4—151no—
629C2×C4⋊C4—151no—
630C2×C22⋊C4—31no—
631C2×C22⋊C4—31no—
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—31no—
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—24no—
650C3×D5—42no—
651C5×D3—42no—
652C23×C3—22no—
653C23×C3—22no—
654C23×C3—22no—
655C23×C3—54no—
656C23×C3—52no—
657C23×C3—52no—
658C23×C3—102no—
659C23×C3—102no—
660C23×C3—102no—
661C23×C3—102no—
662C23×C3—102no—
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×Q8—108no—
674C3×D4—108no—
675C3×D4—108no—
676C3×D4—108no—
677C2×C3×C4—22no—
678C2×C3×C4—28no—
679C2×C3×C4—54no—
680C2×C3×C4—52no—
681C2×C3×C4—516no—
682C2×C3×C4—52no—
683C2×C3×C4—102no—
684C2×C3×C4—108no—
685C2×C3×C4D4×D514yes—
686C2×C3×C4C23×D512yes—
687C2×C3×C4C23×D512yes—
688#67—28no—
689#67—108no—
690#67—108no—
691#67—108no—
692#67—108no—
693#67—108no—
694C2×Dic3—22no—
695C2×Dic3—22no—
696C2×Dic3—54no—
697C2×Dic3—52no—
698C2×Dic3—52no—
699C2×Dic3—52no—
700C2×Dic3—108no—
701C2×Dic3—102no—
702C2×Dic3—102no—
703C2×Dic3—108no—
704C2×Dic3#70914yescomplemented
705C2×Dic3C23×D512yes—
706C2×Dic3C23×D512yes—
707C2×Dic3C23×D512yes—
708D12—108no—
709C4×D3—28no—
710C4×D3—108no—
711Dic6—108no—
712C22×C5—22no—
713C22×C5—22no—
714C22×C5—22no—
715C22×C5—44no—
716C22×C5—62no—
717C22×C5—62no—
718C22×C5—62no—
719C22×C5—124no—
720C22×C5D3×#4112yes—
721C22×C5D3×#4112yes—
722C22×C5C22×#6712yes—
723C22×C5C24×D311yescharacteristic
724C2×D5—22no—
725C2×D5—22no—
726C2×D5—28no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—44no—
731C2×D5—62no—
732C2×D5—62no—
733C2×D5—62no—
734C2×D5—124no—
735C2×D5C22×#6714yes—
736C4×C5—22no—
737C4×C5—34no—
738C4×C5—62no—
739C4×C5—62no—
740C4×C5C22×#6714yes—
741Dic5—22no—
742Dic5—34no—
743Dic5—62no—
744Dic5—62no—
745Dic5C22×#6714yes—
746C24—31no—
747C24—51no—
748C24—51no—
749C24—151no—
750C24C2×D3×D511yescharacteristic
751#41—1032no—
752#41—3032no—
753C2×Q8—54no—
754C2×Q8—104no—
755C2×Q8—154no—
756C2×Q8—304no—
757C2×D4—34no—
758C2×D4—54no—
759C2×D4—54no—
760C2×D4—54no—
761C2×D4—64no—
762C2×D4—104no—
763C2×D4—104no—
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—31no—
780C22×C4—31no—
781C22×C4—34no—
782C22×C4—51no—
783C22×C4—58no—
784C22×C4—54no—
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—34no—
802C4⋊C4—154no—
803C4⋊C4—154no—
804C4⋊C4—154no—
805C22⋊C4—34no—
806C22⋊C4—34no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C42—34no—
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—54no—
823C22×C3—108no—
824C22×C3—102no—
825C22×C3—102no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—204no—
830C22×C3C2×#70912yes—
831C22×C3C2×D4×D512yes—
832C22×C3D5×#4112yes—
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—54no—
844C3×C4—102no—
845C3×C4C2×D4×D514yes—
846Dic3—22no—
847Dic3—22no—
848Dic3—54no—
849Dic3—102no—
850Dic3—102no—
851Dic3C2×#70914yescomplemented
852C2×C5—42no—
853C2×C5—122no—
854C2×C5#583214yescomplemented
855C2×C5C2×D3×#4111yescharacteristic
856C2×C5C2×D3×#4111yescharacteristic
857C2×C5C23×#6711yescharacteristic
858D5—24no—
859D5—42no—
860D5—122no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—32no—
865C23—54no—
866C23—52no—
867C23—52no—
868C23—62no—
869C23—62no—
870C23—62no—
871C23—102no—
872C23—102no—
873C23—102no—
874C23—102no—
875C23—102no—
876C23—152no—
877C23—302no—
878C23—302no—
879C23—302no—
880C23C22×D3×D512yes—
881C23C22×D3×D511yescharacteristic
882Q8—108no—
883Q8—308no—
884D4—68no—
885D4—108no—
886D4—108no—
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—32no—
899C2×C4—32no—
900C2×C4—54no—
901C2×C4—52no—
902C2×C4—516no—
903C2×C4—52no—
904C2×C4—62no—
905C2×C4—62no—
906C2×C4—68no—
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×C4D5×#6714yes—
919C2×C4C22×D3×D512yes—
920C2×C4C22×D3×D512yes—
921C2×C3—42no—
922C2×C3—104no—
923C2×C3—202no—
924C2×C3#6588214yescomplemented
925C2×C3C22×#70911yescharacteristic
926C2×C3C22×D4×D511yescharacteristic
927C2×C3C2×D5×#4111yescharacteristic
928D3—42no—
929D3—202no—
930C5C2×#583211yescharacteristic, complemented, Sylow
931C22—22no—
932C22—22no—
933C22—22no—
934C22—44no—
935C22—54no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—108no—
940C22—102no—
941C22—102no—
942C22—102no—
943C22—102no—
944C22—102no—
945C22—124no—
946C22—204no—
947C22—302no—
948C22—302no—
949C22—302no—
950C22—604no—
951C22D3×#70912yes—
952C22#9201612yes—
953C22C2×D5×#6712yes—
954C22C23×D3×D511yescharacteristic
955C4—22no—
956C4—34no—
957C4—54no—
958C4—62no—
959C4—62no—
960C4—102no—
961C4—154no—
962C4—302no—
963C4—302no—
964C4C2×D5×#6714yes—
965C3C2×#6588211yescharacteristic, complemented, Sylow
966C2—42no—
967C2—104no—
968C2—122no—
969C2—202no—
970C2—602no—
971C2#1175431114yesdirect product factor
972C2C2×D3×#70911yescharacteristic
973C2C2×#9201611yescharacteristic
974C2C22×D5×#6711yescharacteristic
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×C3×#709C2semidirect
2. C22×#6771C2semidirect
3. C2×C4×#1220C2semidirect
4. C2×C4×C5×#67C2semidirect
5. C2×#91567C2semidirect
6. C2×#91550C2semidirect
7. C2×#91549C2semidirect
8. C2×#91534C2semidirect
9. C2×C4×#1202C2semidirect
10. C2×C4×#1201C2semidirect
11. C2×#91409C2semidirect
12. #11754311C2direct (N × H)
13. C2×#91408C2semidirect
14. C2×C4×D5×Dic3C2semidirect
15. C2×#91327C2semidirect
16. C2×#91326C2semidirect
26. C2×C3×#709C22semidirect
40. C2×#6771C22semidirect
42. C4×#1220C22semidirect
47. C4×C5×#67C22semidirect
51. #91567C22semidirect
52. #91550C22semidirect
53. #91549C22semidirect
60. #91534C22semidirect
63. C4×#1202C22semidirect
64. C4×#1201C22semidirect
65. #91409C22semidirect
66. #91408C22semidirect
67. C4×D5×Dic3C22semidirect
68. #91327C22semidirect
69. #91326C22semidirect
72. C22×#709D3semidirect
120. C2×C3×C4×D5D4semidirect
172. C2×C4×#67D5semidirect
186. C2×#709C2×D3semidirect
256. C2×Dic15#41semidirect
264. C2×C5×Dic3#41semidirect
277. C3×C4×D5C2×D4semidirect
325. C4×#67C2×D5semidirect
387. C2×C4×D5#67semidirect
454. Dic15C2×#41semidirect
459. C5×Dic3C2×#41semidirect
588. C4×D5C2×#67semidirect
644. C2×C3×C5#532semidirect
704. C2×Dic3#709semidirect
817. C3×C5C2×#532semidirect
851. Dic3C2×#709semidirect
854. C2×C5#5832semidirect
924. C2×C3#65882semidirect
930. C5C2×#5832semidirect
965. C3C2×#65882semidirect
971. C2#11754311direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#7092
C22×#67712
C2×C4×#12202
C2×C4×C5×#672
C2×#915672
C2×#915502
C2×#915492
C2×#915342
C2×C4×#12022
C2×C4×#12012
C2×#914092
#117543112
C2×#914082
C2×C4×D5×Dic32
C2×#913272
C2×#913262
C2×#658823
C2×#58325