Finite Group Databasebeta

← C2×#11753299 #14495264

Subgroups — C2×#11753299 #14495264

Order 1920.

2816 conjugacy classes of subgroups.

The subgroup lattice has 992 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91774C211yesmaximal, characteristic, complemented
2C2×C5×#885C211yesmaximal, characteristic, complemented
3C2×C3×#4028C211yesmaximal, characteristic, complemented
4C2×#91577C211yesmaximal, characteristic, complemented
5C2×#91564C211yesmaximal, characteristic, complemented
6C2×#91563C211yesmaximal, characteristic, complemented
7C2×#91534C211yesmaximal, characteristic, complemented
8C2×#91474C211yesmaximal, characteristic, complemented
9C2×#91474C211yesmaximal, characteristic, complemented
10C2×#91464C211yesmaximal, characteristic, complemented
11C2×#91462C211yesmaximal, characteristic, complemented
12C2×#91455C211yesmaximal, characteristic, complemented
13C2×#91368C211yesmaximal, characteristic, complemented
14C2×#91364C211yesmaximal, characteristic, complemented
15C2×#91353C211yesmaximal, characteristic, complemented
16#11753299C2116yesmaximal, direct product factor
17C2×#66017—31nomaximal, Hall
18C24×C3×D5C2211yescharacteristic, complemented
19C23×D3×D5C2211yescharacteristic, complemented
20C22×#1220C2211yescharacteristic
21C22×Dic30C2211yescharacteristic, complemented
22C22×C5×#67C2211yescharacteristic
23C22×C5×Dic6C2211yescharacteristic, complemented
24C22×C3×C22⋊D5C2211yescharacteristic
25C22×C3×D20C2211yescharacteristic
26C22×C3×D20C2211yescharacteristic
27C22×#1204C2211yescharacteristic, complemented
28C22×#1202C2211yescharacteristic
29C22×#1202C2211yescharacteristic
30C22×#1201C2211yescharacteristic
31C22×#1201C2211yescharacteristic
32C2×C3×C5×C22⋊C4C2211yescharacteristic, complemented
33C2×#6719C2211yescharacteristic, complemented
34C2×#6714C2211yescharacteristic, complemented
35C2×#6714C2211yescharacteristic, complemented
36C2×C4×Dic15C2211yescharacteristic, complemented
37#91774C2218yescomplemented
38C2×C5×#217C2211yescharacteristic, complemented
39C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C5×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C4×C5×Dic3C2211yescharacteristic, complemented
42C5×#885C2218yescomplemented
43C2×C3×#685C2211yescharacteristic, complemented
44C2×C3×#685C2211yescharacteristic, complemented
45C3×#4028C2218yescomplemented
46#91577C2218yescomplemented
47#91564C2218yescomplemented
48#91563C2218yescomplemented
49C2×#6667C2211yescharacteristic, complemented
50C2×(C2×D3)⋊Dic5C2211yescharacteristic, complemented
51C2×#6665C2211yescharacteristic, complemented
52C2×#6665C2211yescharacteristic, complemented
53C2×#6665C2211yescharacteristic, complemented
54C2×#6665C2211yescharacteristic, complemented
55C2×#6665C2211yescharacteristic, complemented
56C2×#6665C2211yescharacteristic, complemented
57C2×#6665C2211yescharacteristic, complemented
58#91534C2218yescomplemented
59C2×Dic3×Dic5C2211yescharacteristic, complemented
60#91474C2218yescomplemented
61#91474C2218yescomplemented
62#91464C2218yescomplemented
63#91462C2218yescomplemented
64#91455C2218yescomplemented
65#91368C2218yescomplemented
66#91364C2218yescomplemented
67#91353C2218yescomplemented
68C2×#5594—51nomaximal, Hall
69C2×C5×#124—31no—
70C2×#4093—31no—
71C2×#4093—31no—
72C2×#4083—31no—
73C2×#4083—31no—
74#66017—316no—
75C2×#4031—31no—
76C2×#4031—31no—
77C2×#4031—31no—
78C2×#4031—31no—
79C2×#4028—31no—
80C2×#4028—31no—
81C2×#4028—31no—
82C2×#4028D311yescharacteristic, complemented
83C2×#4021—31no—
84C2×#4021—31no—
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×D5C2314yescomplemented
95C22×D3×D5—42no—
96C22×D3×D5—42no—
97C22×D3×D5—42no—
98C22×D3×D5C2314yescomplemented
99C22×C3×C4×C5C2311yescharacteristic
100C22×C3×C4×C5C2311yescharacteristic
101C2×#1220—42no—
102C2×#1220C2314yes—
103C22×Dic15C2311yescharacteristic
104C22×Dic15C2311yescharacteristic
105C22×Dic15C2311yescharacteristic
106C2×Dic30—42no—
107C2×Dic30C2314yescomplemented
108C2×C5×#67—42no—
109C2×C5×#67C2314yes—
110C22×C5×Dic3C2311yescharacteristic
111C22×C5×Dic3C2311yescharacteristic
112C22×C5×Dic3C2311yescharacteristic
113C2×C5×Dic6—42no—
114C2×C5×Dic6C2314yescomplemented
115C2×C3×C22⋊D5—42no—
116C2×C3×C22⋊D5C2314yes—
117C22×C3×Dic5C2311yescharacteristic
118C2×C3×D20—42no—
119C2×C3×D20—42no—
120C2×C3×D20C2314yes—
121C2×C3×D20C2314yes—
122C2×#1204—42no—
123C2×#1204C2314yescomplemented
124C2×#1202—42no—
125C2×#1202—42no—
126C2×#1202C2314yes—
127C2×#1202C2314yes—
128C2×#1201—42no—
129C2×#1201—42no—
130C2×#1201C2314yes—
131C2×#1201C2314yes—
132C3×C5×C22⋊C4C2314yescomplemented
133#6719C2314yescomplemented
134#6714C2314yescomplemented
135#6714C2314yescomplemented
136C4×Dic15C2314yescomplemented
137C5×#217C2314yescomplemented
138C5×(C2×D3)⋊C4C2314yescomplemented
139C5×(C2×D3)⋊C4C2314yescomplemented
140C4×C5×Dic3C2314yescomplemented
141C3×#685C2314yescomplemented
142C3×#685C2314yescomplemented
143#6667C2314yescomplemented
144(C2×D3)⋊Dic5C2314yescomplemented
145#6665C2314yescomplemented
146#6665C2314yescomplemented
147#6665C2314yescomplemented
148#6665C2314yescomplemented
149#6665C2314yescomplemented
150#6665C2314yescomplemented
151#6665C2314yescomplemented
152Dic3×Dic5C2314yescomplemented
153C2×C3×#120—51no—
154C2×#953—51no—
155C2×#953—51no—
156C2×#937—51no—
157C2×#937—51no—
158C2×#937—51no—
159C2×#936—51no—
160C2×#936—51no—
161C2×#936—51no—
162#5594—516no—
163C2×#885—51no—
164C2×#885—51no—
165C2×#885—51no—
166C2×#885—51no—
167C2×#885—51no—
168C2×#885D511yescharacteristic, complemented
169C24×D5—31no—
170C24×D5C2×D311yescharacteristic, complemented
171C22×C5×Q8—31no—
172C22×C5×D4—31no—
173C22×C22⋊D5—31no—
174C22×C22⋊D5—31no—
175C22×C22⋊D5—31no—
176C22×C22⋊D5C2×D311yescharacteristic
177C22×D20—31no—
178C22×D20—31no—
179C22×D20C2×D311yescharacteristic
180C22×D20C2×D311yescharacteristic
181C22×Dic10—31no—
182C22×Dic10—31no—
183C5×#124—38no—
184C2×C5×C22⋊C4—31no—
185C2×C5×C22⋊C4—31no—
186C2×C5×C22⋊C4—31no—
187C2×C5×C22⋊C4C2×D311yescharacteristic, complemented
188C2×C42×C5—31no—
189C2×C22⋊Dic5—31no—
190C2×C22⋊Dic5—31no—
191#4093—38no—
192#4093—38no—
193#4083—38no—
194#4083—38no—
195C2×#685—31no—
196C2×#685—31no—
197C2×#685—31no—
198C2×#685—31no—
199C2×#685—31no—
200C2×#685—31no—
201C2×#685—31no—
202C2×#685—31no—
203C2×#685—31no—
204C2×#685—31no—
205C2×#685C2×D311yescharacteristic, complemented
206C2×#685C2×D311yescharacteristic, complemented
207C2×C4×Dic5—31no—
208C2×C4×Dic5—31no—
209#4031—38no—
210#4031—38no—
211#4031—38no—
212#4031—38no—
213#4028—38no—
214#4028—38no—
215#4028—38no—
216#4028C2×D318yescomplemented
217#4021—38no—
218#4021—38no—
219C2×H(3,𝔽4)—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×D3×D5—44no—
250C2×D3×D5—44no—
251C2×D3×D5—44no—
252C2×D3×D5—416no—
253C2×C3×C4×C5—22no—
254C2×C3×C4×C5—22no—
255C2×C3×C4×C5C2412yes—
256C2×C3×C4×C5C2412yes—
257#1220—44no—
258C2×Dic15—22no—
259C2×Dic15—22no—
260C2×Dic15—22no—
261C2×Dic15C2412yes—
262C2×Dic15C2412yes—
263C2×Dic15C2412yes—
264Dic30—44no—
265C5×#67—44no—
266C2×C5×Dic3—22no—
267C2×C5×Dic3—22no—
268C2×C5×Dic3—22no—
269C2×C5×Dic3C2412yes—
270C2×C5×Dic3C2412yes—
271C2×C5×Dic3C2412yes—
272C5×Dic6—44no—
273C3×C22⋊D5—44no—
274C2×C3×Dic5—22no—
275C2×C3×Dic5C2412yes—
276C3×D20—44no—
277C3×D20—44no—
278#1204—44no—
279#1202—44no—
280#1202—44no—
281#1201—44no—
282#1201—44no—
283C25×C3—51no—
284C24×D3—51no—
285C22×C3×D4—51no—
286C22×C3×D4—51no—
287C22×C3×D4—51no—
288C22×#67—51no—
289C22×#67—51no—
290C22×#67—51no—
291C22×#67—51no—
292C22×#67—51no—
293C22×#67C2×D511yescharacteristic
294C22×Dic6—51no—
295C22×Dic6—51no—
296C22×Dic6C2×D511yescharacteristic, complemented
297C3×#120—58no—
298C2×C3×C22⋊C4—51no—
299C2×C3×C22⋊C4—51no—
300C2×C3×C22⋊C4C2×D511yescharacteristic, complemented
301#953—58no—
302#953—58no—
303C2×#217—51no—
304C2×#217—51no—
305C2×#217—51no—
306C2×#217—51no—
307C2×#217—51no—
308C2×#217—51no—
309C2×#217—51no—
310C2×#217—51no—
311C2×#217C2×D511yescharacteristic, complemented
312#937—58no—
313#937—58no—
314#937—58no—
315#936—58no—
316#936—58no—
317#936—58no—
318C2×(C2×D3)⋊C4—51no—
319C2×(C2×D3)⋊C4—51no—
320C2×(C2×D3)⋊C4—51no—
321C2×(C2×D3)⋊C4—51no—
322C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
323C2×(C2×D3)⋊C4C2×D511yescharacteristic, complemented
324C2×C4×Dic3—51no—
325C2×C4×Dic3—51no—
326C2×C4×Dic3C2×D511yescharacteristic, complemented
327#885—58no—
328#885—58no—
329#885—58no—
330#885—58no—
331#885—58no—
332#885C2×D518yescomplemented
333C24×C5—31no—
334C24×C5C22×D311yescharacteristic
335C23×D5—31no—
336C23×D5—34no—
337C23×D5—42no—
338C23×D5—42no—
339C23×D5—42no—
340C23×D5—122no—
341C23×D5—122no—
342C23×D5—122no—
343C23×D5C22×D311yescharacteristic
344C23×D5C22×D311yescharacteristic
345C23×D5C22×D311yescharacteristic
346C23×D5C22×D314yescomplemented
347C2×C5×Q8—34no—
348C2×C5×Q8—122no—
349C2×C5×D4—34no—
350C2×C5×D4—122no—
351C22×C4×C5—31no—
352C22×C4×C5—31no—
353C22×C4×C5—31no—
354C22×C4×C5C22×D311yescharacteristic
355C22×C4×C5C22×D311yescharacteristic
356C2×C22⋊D5—34no—
357C2×C22⋊D5—34no—
358C2×C22⋊D5—34no—
359C2×C22⋊D5—42no—
360C2×C22⋊D5—122no—
361C2×C22⋊D5—122no—
362C2×C22⋊D5—122no—
363C2×C22⋊D5C22×D314yes—
364C22×Dic5—31no—
365C22×Dic5—31no—
366C22×Dic5—31no—
367C22×Dic5C22×D311yescharacteristic
368C2×D20—34no—
369C2×D20—34no—
370C2×D20—42no—
371C2×D20—42no—
372C2×D20—122no—
373C2×D20—122no—
374C2×D20C22×D314yes—
375C2×D20C22×D314yes—
376C2×Dic10—34no—
377C2×Dic10—34no—
378C2×Dic10—122no—
379C2×Dic10—122no—
380C5×C22⋊C4—34no—
381C5×C22⋊C4—34no—
382C5×C22⋊C4—34no—
383C5×C22⋊C4C22×D314yescomplemented
384C42×C5—34no—
385C22⋊Dic5—34no—
386C22⋊Dic5—34no—
387#685—34no—
388#685—34no—
389#685—34no—
390#685—34no—
391#685—34no—
392#685—34no—
393#685—34no—
394#685—34no—
395#685—34no—
396#685—34no—
397#685C22×D314yescomplemented
398#685C22×D314yescomplemented
399C4×Dic5—34no—
400C4×Dic5—34no—
401H(3,𝔽4)—1516no—
402C2×#124—31no—
403C2×#124—151no—
404C2×#124—151no—
405C2×#124—151no—
406C2×#124—151no—
407C2×#124—151no—
408C2×#124—151no—
409C2×#124—151no—
410C2×#124—151no—
411C2×#120—51no—
412C2×#120—151no—
413C2×#120—151no—
414C2×#120—151no—
415C2×#120—151no—
416C2×#120—151no—
417C22×C3×C5—22no—
418C22×C3×C5—22no—
419C22×C3×C5—22no—
420C22×C3×C5—44no—
421C22×C3×C5H(5,𝔽2)12yes—
422C22×C3×C5H(5,𝔽2)12yes—
423C22×C3×C5H(5,𝔽2)12yes—
424C22×C3×C5C2511yescharacteristic
425C2×D15—22no—
426C2×D15—22no—
427C2×D15—22no—
428C2×D15—44no—
429C2×C5×D3—22no—
430C2×C5×D3—22no—
431C2×C5×D3—22no—
432C2×C5×D3—44no—
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—22no—
442C2×C3×D5—416no—
443C2×C3×D5—44no—
444C2×C3×D5—44no—
445C2×C3×D5—44no—
446D3×D5—416no—
447C3×C4×C5—22no—
448C3×C4×C5—22no—
449Dic15—22no—
450Dic15—22no—
451Dic15—22no—
452C3×Dic5—22no—
453C5×Dic3—22no—
454C5×Dic3—22no—
455C5×Dic3—22no—
456C24×C3—51no—
457C24×C3—51no—
458C24×C3—51no—
459C24×C3—54no—
460C24×C3—202no—
461C24×C3—202no—
462C24×C3—202no—
463C24×C3C22×D511yescharacteristic
464C23×D3—51no—
465C23×D3—54no—
466C23×D3—202no—
467C23×D3—202no—
468C23×D3—202no—
469C23×D3C22×D511yescharacteristic
470C2×C3×D4—54no—
471C2×C3×D4—54no—
472C2×C3×D4—54no—
473C2×C3×D4—202no—
474C2×C3×D4—202no—
475C2×C3×D4—202no—
476C22×C3×C4—51no—
477C22×C3×C4C22×D511yescharacteristic
478C22×C3×C4C22×D511yescharacteristic
479C2×#67—42no—
480C2×#67—54no—
481C2×#67—54no—
482C2×#67—54no—
483C2×#67—54no—
484C2×#67—54no—
485C2×#67—202no—
486C2×#67—202no—
487C2×#67—202no—
488C2×#67—202no—
489C2×#67—202no—
490C2×#67C22×D514yes—
491C22×Dic3—51no—
492C22×Dic3—51no—
493C22×Dic3—51no—
494C22×Dic3C22×D511yescharacteristic
495C22×Dic3C22×D511yescharacteristic
496C22×Dic3C22×D511yescharacteristic
497C2×Dic6—42no—
498C2×Dic6—54no—
499C2×Dic6—54no—
500C2×Dic6—202no—
501C2×Dic6—202no—
502C2×Dic6C22×D514yescomplemented
503C3×C22⋊C4—54no—
504C3×C22⋊C4—54no—
505C3×C22⋊C4C22×D514yescomplemented
506#217—54no—
507#217—54no—
508#217—54no—
509#217—54no—
510#217—54no—
511#217—54no—
512#217—54no—
513#217—54no—
514#217C22×D514yescomplemented
515(C2×D3)⋊C4—54no—
516(C2×D3)⋊C4—54no—
517(C2×D3)⋊C4—54no—
518(C2×D3)⋊C4—54no—
519(C2×D3)⋊C4C22×D514yescomplemented
520(C2×D3)⋊C4C22×D514yescomplemented
521C4×Dic3—54no—
522C4×Dic3—54no—
523C4×Dic3C22×D514yescomplemented
524C23×C5—22no—
525C23×C5—22no—
526C23×C5—22no—
527C23×C5—32no—
528C23×C5—62no—
529C23×C5—62no—
530C23×C5—62no—
531C23×C5C23×D312yes—
532C23×C5C23×D311yescharacteristic
533C22×D5—22no—
534C22×D5—22no—
535C22×D5—22no—
536C22×D5—22no—
537C22×D5—22no—
538C22×D5—22no—
539C22×D5—22no—
540C22×D5—22no—
541C22×D5—22no—
542C22×D5—32no—
543C22×D5—44no—
544C22×D5—44no—
545C22×D5—44no—
546C22×D5—416no—
547C22×D5—62no—
548C22×D5—62no—
549C22×D5—62no—
550C22×D5—124no—
551C22×D5—124no—
552C22×D5—124no—
553C22×D5—1216no—
554C22×D5C23×D312yes—
555C22×D5C23×D312yes—
556C22×D5C23×D312yes—
557C5×Q8—124no—
558C5×D4—124no—
559C2×C4×C5—22no—
560C2×C4×C5—22no—
561C2×C4×C5—32no—
562C2×C4×C5—32no—
563C2×C4×C5—32no—
564C2×C4×C5—62no—
565C2×C4×C5—62no—
566C2×C4×C5—62no—
567C2×C4×C5C23×D312yes—
568C2×C4×C5C23×D312yes—
569C22⋊D5—44no—
570C22⋊D5—124no—
571C22⋊D5—124no—
572C22⋊D5—124no—
573C2×Dic5—22no—
574C2×Dic5—32no—
575C2×Dic5—32no—
576C2×Dic5—32no—
577C2×Dic5—62no—
578C2×Dic5—62no—
579C2×Dic5—62no—
580C2×Dic5C23×D312yes—
581D20—44no—
582D20—44no—
583D20—124no—
584D20—124no—
585Dic10—124no—
586Dic10—124no—
587C25—51no—
588C25—151no—
589C22×Q8—31no—
590C22×Q8—151no—
591C22×Q8—151no—
592C22×D4—31no—
593C22×D4—51no—
594C22×D4—51no—
595C22×D4—51no—
596C22×D4—151no—
597C22×D4—151no—
598C22×D4—151no—
599C22×D4—151no—
600C22×D4—151no—
601#124—38no—
602#124—158no—
603#124—158no—
604#124—158no—
605#124—158no—
606#124—158no—
607#124—158no—
608#124—158no—
609#124—158no—
610#120—58no—
611#120—158no—
612#120—158no—
613#120—158no—
614#120—158no—
615#120—158no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—51no—
620C2×C22⋊C4—51no—
621C2×C22⋊C4—151no—
622C2×C22⋊C4—151no—
623C2×C22⋊C4—151no—
624C2×C22⋊C4—151no—
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⋊C4—151no—
633C2×C22⋊C4D3×D511yescharacteristic, complemented
634C2×C42—31no—
635C2×C42—151no—
636C2×C42—151no—
637C2×C3×C5—42no—
638C2×C3×C5H(3,𝔽4)14yescomplemented
639C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
640C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
641C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
642D15—42no—
643C3×D5—42no—
644C3×D5—42no—
645C3×D5—42no—
646C5×D3—42no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—22no—
650C23×C3—52no—
651C23×C3—52no—
652C23×C3—52no—
653C23×C3—102no—
654C23×C3—102no—
655C23×C3—102no—
656C23×C3—102no—
657C23×C3—102no—
658C23×C3—102no—
659C23×C3—102no—
660C23×C3—102no—
661C23×C3—102no—
662C23×C3—204no—
663C23×C3—204no—
664C23×C3—204no—
665C23×C3—2016no—
666C23×C3C23×D512yes—
667C23×C3C23×D511yescharacteristic
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—22no—
671C22×D3—52no—
672C22×D3—102no—
673C22×D3—102no—
674C22×D3—102no—
675C22×D3—204no—
676C22×D3—204no—
677C22×D3—204no—
678C22×D3—2016no—
679C22×D3C23×D512yes—
680C3×D4—204no—
681C3×D4—204no—
682C3×D4—204no—
683C2×C3×C4—22no—
684C2×C3×C4—22no—
685C2×C3×C4—52no—
686C2×C3×C4—102no—
687C2×C3×C4C23×D512yes—
688C2×C3×C4C23×D512yes—
689#67—44no—
690#67—204no—
691#67—204no—
692#67—204no—
693#67—204no—
694#67—204no—
695C2×Dic3—22no—
696C2×Dic3—22no—
697C2×Dic3—22no—
698C2×Dic3—52no—
699C2×Dic3—52no—
700C2×Dic3—52no—
701C2×Dic3—102no—
702C2×Dic3—102no—
703C2×Dic3—102no—
704C2×Dic3C23×D512yes—
705C2×Dic3C23×D512yes—
706C2×Dic3C23×D512yes—
707Dic6—44no—
708Dic6—204no—
709Dic6—204no—
710C22×C5—22no—
711C22×C5—22no—
712C22×C5—22no—
713C22×C5—44no—
714C22×C5—62no—
715C22×C5—62no—
716C22×C5—62no—
717C22×C5—124no—
718C22×C5#100412yes—
719C22×C5#100412yes—
720C22×C5#100412yes—
721C22×C5C24×D311yescharacteristic
722C2×D5—22no—
723C2×D5—22no—
724C2×D5—22no—
725C2×D5—22no—
726C2×D5—22no—
727C2×D5—22no—
728C2×D5—22no—
729C2×D5—22no—
730C2×D5—22no—
731C2×D5—416no—
732C2×D5—44no—
733C2×D5—44no—
734C2×D5—44no—
735C2×D5—62no—
736C2×D5—62no—
737C2×D5—62no—
738C2×D5—1216no—
739C2×D5—124no—
740C4×C5—22no—
741C4×C5—22no—
742C4×C5—62no—
743C4×C5—62no—
744C4×C5—62no—
745Dic5—22no—
746Dic5—62no—
747Dic5—62no—
748Dic5—62no—
749C24—31no—
750C24—51no—
751C24—51no—
752C24—51no—
753C24—54no—
754C24—154no—
755C24—151no—
756C24—202no—
757C24—202no—
758C24—202no—
759C24—602no—
760C24—602no—
761C24—602no—
762C24C2×D3×D511yescharacteristic
763C2×Q8—34no—
764C2×Q8—122no—
765C2×Q8—154no—
766C2×Q8—154no—
767C2×Q8—602no—
768C2×Q8—602no—
769C2×D4—34no—
770C2×D4—54no—
771C2×D4—54no—
772C2×D4—54no—
773C2×D4—122no—
774C2×D4—154no—
775C2×D4—154no—
776C2×D4—154no—
777C2×D4—154no—
778C2×D4—154no—
779C2×D4—202no—
780C2×D4—202no—
781C2×D4—202no—
782C2×D4—602no—
783C2×D4—602no—
784C2×D4—602no—
785C2×D4—602no—
786C2×D4—602no—
787C22×C4—31no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—51no—
791C22×C4—151no—
792C22×C4—151no—
793C22×C4—151no—
794C22×C4C2×D3×D511yescharacteristic
795C22×C4C2×D3×D511yescharacteristic
796C22⋊C4—34no—
797C22⋊C4—34no—
798C22⋊C4—34no—
799C22⋊C4—54no—
800C22⋊C4—54no—
801C22⋊C4—154no—
802C22⋊C4—154no—
803C22⋊C4—154no—
804C22⋊C4—154no—
805C22⋊C4—154no—
806C22⋊C4—154no—
807C22⋊C4—154no—
808C22⋊C4—154no—
809C22⋊C4—154no—
810C22⋊C4—154no—
811C22⋊C4—154no—
812C22⋊C4—154no—
813C22⋊C4C2×D3×D514yescomplemented
814C42—34no—
815C42—154no—
816C42—154no—
817C3×C5C2×H(3,𝔽4)11yescharacteristic, 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—102no—
826C22×C3—102no—
827C22×C3—102no—
828C22×C3—102no—
829C22×C3—102no—
830C22×C3—102no—
831C22×C3—2016no—
832C22×C3—204no—
833C22×C3—204no—
834C22×C3—204no—
835C22×C3#414412yes—
836C22×C3#414912yes—
837C22×C3#414912yes—
838C22×C3C24×D511yescharacteristic
839C2×D3—22no—
840C2×D3—22no—
841C2×D3—22no—
842C2×D3—44no—
843C2×D3—102no—
844C2×D3—102no—
845C2×D3—102no—
846C2×D3—2016no—
847C2×D3—204no—
848C3×C4—22no—
849C3×C4—22no—
850C3×C4—102no—
851Dic3—22no—
852Dic3—22no—
853Dic3—22no—
854Dic3—102no—
855Dic3—102no—
856Dic3—102no—
857C2×C5—42no—
858C2×C5—122no—
859C2×C5#559414yescomplemented
860C2×C5C2×#100411yescharacteristic
861C2×C5C2×#100411yescharacteristic
862C2×C5C2×#100411yescharacteristic
863D5—42no—
864D5—42no—
865D5—42no—
866D5—122no—
867C23—22no—
868C23—22no—
869C23—22no—
870C23—32no—
871C23—52no—
872C23—52no—
873C23—52no—
874C23—62no—
875C23—62no—
876C23—62no—
877C23—102no—
878C23—102no—
879C23—102no—
880C23—102no—
881C23—102no—
882C23—102no—
883C23—102no—
884C23—102no—
885C23—102no—
886C23—152no—
887C23—204no—
888C23—204no—
889C23—204no—
890C23—2016no—
891C23—302no—
892C23—302no—
893C23—302no—
894C23—604no—
895C23—604no—
896C23—604no—
897C23—6016no—
898C23C22×D3×D512yes—
899C23C22×D3×D511yescharacteristic
900Q8—124no—
901Q8—604no—
902Q8—604no—
903D4—124no—
904D4—204no—
905D4—204no—
906D4—204no—
907D4—604no—
908D4—604no—
909D4—604no—
910D4—604no—
911D4—604no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—32no—
915C2×C4—32no—
916C2×C4—32no—
917C2×C4—52no—
918C2×C4—62no—
919C2×C4—62no—
920C2×C4—62no—
921C2×C4—102no—
922C2×C4—152no—
923C2×C4—152no—
924C2×C4—152no—
925C2×C4—302no—
926C2×C4—302no—
927C2×C4—302no—
928C2×C4C22×D3×D512yes—
929C2×C4C22×D3×D512yes—
930C2×C3—42no—
931C2×C3—202no—
932C2×C3—202no—
933C2×C3—202no—
934C2×C3#6601714yescomplemented
935C2×C3C2×#414411yescharacteristic
936C2×C3C2×#414911yescharacteristic
937C2×C3C2×#414911yescharacteristic
938D3—42no—
939D3—202no—
940C5C2×#559411yescharacteristic, complemented, Sylow
941C22—22no—
942C22—22no—
943C22—22no—
944C22—44no—
945C22—62no—
946C22—62no—
947C22—62no—
948C22—102no—
949C22—102no—
950C22—102no—
951C22—102no—
952C22—102no—
953C22—102no—
954C22—102no—
955C22—102no—
956C22—102no—
957C22—124no—
958C22—2016no—
959C22—204no—
960C22—204no—
961C22—204no—
962C22—302no—
963C22—302no—
964C22—302no—
965C22—6016no—
966C22—604no—
967C22#9201712yes—
968C22#9202512yes—
969C22#9202612yes—
970C22C23×D3×D511yescharacteristic
971C4—22no—
972C4—22no—
973C4—62no—
974C4—62no—
975C4—62no—
976C4—102no—
977C4—302no—
978C4—302no—
979C4—302no—
980C3C2×#6601711yescharacteristic, complemented, Sylow
981C2—42no—
982C2—122no—
983C2—202no—
984C2—202no—
985C2—202no—
986C2—602no—
987C2#1175329914yesdirect product factor
988C2C2×#9201711yescharacteristic
989C2C2×#9202511yescharacteristic
990C2C2×#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×H(3,𝔽4)
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×#91774C2semidirect
2. C2×C5×#885C2semidirect
3. C2×C3×#4028C2semidirect
4. C2×#91577C2semidirect
5. C2×#91564C2semidirect
6. C2×#91563C2semidirect
7. C2×#91534C2semidirect
8. C2×#91474C2semidirect
9. C2×#91474C2semidirect
10. C2×#91464C2semidirect
11. C2×#91462C2semidirect
12. C2×#91455C2semidirect
13. C2×#91368C2semidirect
14. C2×#91364C2semidirect
15. C2×#91353C2semidirect
16. #11753299C2direct (N × H)
18. C24×C3×D5C22semidirect
19. C23×D3×D5C22semidirect
21. C22×Dic30C22semidirect
23. C22×C5×Dic6C22semidirect
27. C22×#1204C22semidirect
32. C2×C3×C5×C22⋊C4C22semidirect
33. C2×#6719C22semidirect
34. C2×#6714C22semidirect
35. C2×#6714C22semidirect
36. C2×C4×Dic15C22semidirect
37. #91774C22semidirect
38. C2×C5×#217C22semidirect
39. C2×C5×(C2×D3)⋊C4C22semidirect
40. C2×C5×(C2×D3)⋊C4C22semidirect
41. C2×C4×C5×Dic3C22semidirect
42. C5×#885C22semidirect
43. C2×C3×#685C22semidirect
44. C2×C3×#685C22semidirect
45. C3×#4028C22semidirect
46. #91577C22semidirect
47. #91564C22semidirect
48. #91563C22semidirect
49. C2×#6667C22semidirect
50. C2×(C2×D3)⋊Dic5C22semidirect
51. C2×#6665C22semidirect
52. C2×#6665C22semidirect
53. C2×#6665C22semidirect
54. C2×#6665C22semidirect
55. C2×#6665C22semidirect
56. C2×#6665C22semidirect
57. C2×#6665C22semidirect
58. #91534C22semidirect
59. C2×Dic3×Dic5C22semidirect
60. #91474C22semidirect
61. #91474C22semidirect
62. #91464C22semidirect
63. #91462C22semidirect
64. #91455C22semidirect
65. #91368C22semidirect
66. #91364C22semidirect
67. #91353C22semidirect
82. C2×#4028D3semidirect
94. C23×C3×D5C23semidirect
98. C22×D3×D5C23semidirect
107. C2×Dic30C23semidirect
114. C2×C5×Dic6C23semidirect
123. C2×#1204C23semidirect
132. C3×C5×C22⋊C4C23semidirect
133. #6719C23semidirect
134. #6714C23semidirect
135. #6714C23semidirect
136. C4×Dic15C23semidirect
137. C5×#217C23semidirect
138. C5×(C2×D3)⋊C4C23semidirect
139. C5×(C2×D3)⋊C4C23semidirect
140. C4×C5×Dic3C23semidirect
141. C3×#685C23semidirect
142. C3×#685C23semidirect
143. #6667C23semidirect
144. (C2×D3)⋊Dic5C23semidirect
145. #6665C23semidirect
146. #6665C23semidirect
147. #6665C23semidirect
148. #6665C23semidirect
149. #6665C23semidirect
150. #6665C23semidirect
151. #6665C23semidirect
152. Dic3×Dic5C23semidirect
168. C2×#885D5semidirect
170. C24×D5C2×D3semidirect
187. C2×C5×C22⋊C4C2×D3semidirect
205. C2×#685C2×D3semidirect
206. C2×#685C2×D3semidirect
216. #4028C2×D3semidirect
296. C22×Dic6C2×D5semidirect
300. C2×C3×C22⋊C4C2×D5semidirect
311. C2×#217C2×D5semidirect
322. C2×(C2×D3)⋊C4C2×D5semidirect
323. C2×(C2×D3)⋊C4C2×D5semidirect
326. C2×C4×Dic3C2×D5semidirect
332. #885C2×D5semidirect
346. C23×D5C22×D3semidirect
383. C5×C22⋊C4C22×D3semidirect
397. #685C22×D3semidirect
398. #685C22×D3semidirect
502. C2×Dic6C22×D5semidirect
505. C3×C22⋊C4C22×D5semidirect
514. #217C22×D5semidirect
519. (C2×D3)⋊C4C22×D5semidirect
520. (C2×D3)⋊C4C22×D5semidirect
523. C4×Dic3C22×D5semidirect
633. C2×C22⋊C4D3×D5semidirect
638. C2×C3×C5H(3,𝔽4)semidirect
813. C22⋊C4C2×D3×D5semidirect
817. C3×C5C2×H(3,𝔽4)semidirect
859. C2×C5#5594semidirect
934. C2×C3#66017semidirect
940. C5C2×#5594semidirect
980. C3C2×#66017semidirect
987. C2#11753299direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917742
C2×C5×#8852
C2×C3×#40282
C2×#915772
C2×#915642
C2×#915632
C2×#915342
C2×#914742
C2×#914642
C2×#914622
C2×#914552
C2×#913682
C2×#913642
C2×#913532
#117532992
C2×#660173
C2×#55945