Finite Group Databasebeta

← C2×#11752598 #14481369

Subgroups — C2×#11752598 #14481369

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91765C211yesmaximal, characteristic, complemented
2C2×C4×C5×Dic6C211yesmaximal, characteristic, complemented
3C2×C3×#4021C211yesmaximal, characteristic, complemented
4C2×#91455C211yesmaximal, characteristic, complemented
5C2×#91430C211yesmaximal, characteristic, complemented
6C2×#91421C211yesmaximal, characteristic, complemented
7C2×#91411C211yesmaximal, characteristic, complemented
8C2×#91409C211yesmaximal, characteristic
9C2×#91407C211yesmaximal, characteristic, complemented
10C2×#91395C211yesmaximal, characteristic, complemented
11C2×#91393C211yesmaximal, characteristic, complemented
12C2×#91363C211yesmaximal, characteristic, complemented
13C2×#91356C211yesmaximal, characteristic, complemented
14C2×#91353C211yesmaximal, characteristic, complemented
15C2×#91327C211yesmaximal, characteristic, complemented
16#11752598C2116yesmaximal, direct product factor
17C2×#65916—31nomaximal, Hall
18C22×C5×Dic6C2211yescharacteristic
19C22×C3×D20C2211yescharacteristic
20C22×C3×Dic10C2211yescharacteristic
21C22×#1204C2211yescharacteristic
22C22×#1202C2211yescharacteristic
23C22×#1202C2211yescharacteristic
24C22×#1200C2211yescharacteristic
25C22×D5×Dic3C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C2×C3×C42×C5C2211yescharacteristic
28C2×#6714C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32C2×#6712C2211yescharacteristic
33C2×#6712C2211yescharacteristic
34#91765C2218yescomplemented
35C2×C5×C4⋊Dic3C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C2×C5×Dic3⋊C4C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic
39C2×C4×C5×Dic3C2211yescharacteristic
40C4×C5×Dic6C2218yescomplemented
41C2×C3×#685C2211yescharacteristic
42C2×C3×#685C2211yescharacteristic
43C2×C3×#685C2211yescharacteristic
44C2×C3×#685C2211yescharacteristic
45C3×#4021C2218yescomplemented
46C2×Dic3⋊Dic5C2211yescharacteristic
47C2×#6669C2211yescharacteristic
48C2×#6669C2211yescharacteristic
49C2×#6668C2211yescharacteristic
50C2×#6667C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×#6665C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91455C2218yescomplemented
57#91430C2218yescomplemented
58#91421C2218yescomplemented
59#91411C2218yescomplemented
60#91409C2218yes—
61#91407C2218yescomplemented
62#91395C2218yescomplemented
63#91393C2218yescomplemented
64#91363C2218yescomplemented
65#91356C2218yescomplemented
66#91353C2218yescomplemented
67#91327C2218yescomplemented
68C2×#5669—51nomaximal, Hall
69C2×C4×C5×Q8—31no—
70C2×#4093—31no—
71C2×#4092—31no—
72#65916—316no—
73C2×#4042—31no—
74C2×#4042—31no—
75C2×#4041—31no—
76C2×#4040—31no—
77C2×#4040—31no—
78C2×#4034—31no—
79C2×#4022—31no—
80C2×#4022—31no—
81C2×#4021—31no—
82C2×#4021D311yescharacteristic, complemented
83C2×C4×D20—31no—
84C2×#4018—31no—
85C23×D15C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×C3×C4×C5C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C2×C5×Dic6—24no—
99C2×C5×Dic6C2314yes—
100C22×C3×Dic5C2311yescharacteristic
101C22×C3×Dic5C2311yescharacteristic
102C2×C3×D20—42no—
103C2×C3×D20C2314yes—
104C2×C3×Dic10—42no—
105C2×C3×Dic10C2314yes—
106C2×#1204—42no—
107C2×#1204C2314yes—
108C2×#1202—24no—
109C2×#1202—42no—
110C2×#1202C2314yes—
111C2×#1202C2314yes—
112C2×#1200—42no—
113C2×#1200C2314yes—
114C2×D5×Dic3—24no—
115C2×D5×Dic3—42no—
116C2×D5×Dic3C2314yes—
117C2×D5×Dic3C2314yes—
118C3×C42×C5C2314yes—
119#6714C2314yes—
120#6714C2314yes—
121#6714C2314yes—
122#6712C2314yes—
123#6712C2314yes—
124#6712C2314yes—
125C5×C4⋊Dic3C2314yes—
126C5×Dic3⋊C4C2314yes—
127C5×Dic3⋊C4C2314yes—
128C4×C5×Dic3C2314yes—
129C4×C5×Dic3C2314yes—
130C3×#685C2314yes—
131C3×#685C2314yes—
132C3×#685C2314yes—
133C3×#685C2314yes—
134Dic3⋊Dic5C2314yes—
135#6669C2314yes—
136#6669C2314yes—
137#6668C2314yes—
138#6667C2314yes—
139#6665C2314yes—
140#6665C2314yes—
141#6665C2314yes—
142#6665C2314yes—
143Dic3×Dic5C2314yes—
144C2×C3×#124—51no—
145C2×#946—51no—
146C2×#944—51no—
147C2×#939—51no—
148C2×#935—51no—
149#5669—516no—
150C2×#885—51no—
151C2×#885—51no—
152C2×#883—51no—
153C2×#67⋊C4—51no—
154C2×#879—51no—
155C2×#878—51no—
156C2×#878—51no—
157C2×#877—51no—
158C2×#876—51no—
159C2×C4×Dic6D511yescharacteristic, complemented
160C22×C5×Q8—31no—
161C22×D20—31no—
162C22×D20—31no—
163C22×D20C2×D311yescharacteristic
164C22×C4×D5—31no—
165C22×C4×D5—31no—
166C22×C4×D5—31no—
167C22×Dic10—31no—
168C22×Dic10C2×D311yescharacteristic
169C4×C5×Q8—38no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C4⋊C4—31no—
172C2×C5×C4⋊C4—31no—
173C2×C42×C5—31no—
174C2×C42×C5—31no—
175C2×C42×C5C2×D311yescharacteristic
176#4093—38no—
177#4092—38no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685C2×D311yescharacteristic
187C2×#685C2×D311yescharacteristic
188C2×#685C2×D311yescharacteristic
189C2×#685C2×D311yescharacteristic
190C2×C4⋊Dic5—31no—
191C2×#683—31no—
192C2×#683—31no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×C4×Dic5—31no—
198#4042—38no—
199#4042—38no—
200#4041—38no—
201#4040—38no—
202#4040—38no—
203#4034—38no—
204#4022—38no—
205#4022—38no—
206#4021—38no—
207#4021C2×D318yescomplemented
208C4×D20—38no—
209#4018—38no—
210C2×#542—151noSylow
211C23×C3×C5C2411yescharacteristic
212C22×D15—22no—
213C22×D15—22no—
214C22×D15—22no—
215C22×D15C2412yes—
216C22×C3×D5—22no—
217C22×C3×D5—22no—
218C22×C3×D5—22no—
219C22×C3×D5—22no—
220C22×C3×D5—22no—
221C22×C3×D5—22no—
222C22×C3×D5C2412yes—
223C22×C3×D5C2412yes—
224C2×C3×C4×C5—22no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5—22no—
227C2×C3×C4×C5C2412yes—
228C2×C3×C4×C5C2412yes—
229C2×C3×C4×C5C2412yes—
230C2×Dic15—22no—
231C2×Dic15—22no—
232C2×Dic15—22no—
233C2×Dic15C2412yes—
234C2×Dic15C2412yes—
235C2×Dic15C2412yes—
236C2×C5×Dic3—22no—
237C2×C5×Dic3—22no—
238C2×C5×Dic3—22no—
239C2×C5×Dic3#4114yes—
240C2×C5×Dic3C2412yes—
241C2×C5×Dic3C2412yes—
242C2×C5×Dic3C2412yes—
243C2×C5×Dic3C2412yes—
244C5×Dic6—28no—
245C2×C3×Dic5—22no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5C2412yes—
248C2×C3×Dic5C2412yes—
249C3×D20—44no—
250C3×Dic10—44no—
251#1204—44no—
252#1202—28no—
253#1202—44no—
254#1200—44no—
255D5×Dic3—28no—
256D5×Dic3—44no—
257C22×C3×Q8—51no—
258C22×C3×D4—51no—
259C22×#67—51no—
260C22×#67—51no—
261C23×Dic3—51no—
262C23×Dic3—51no—
263C22×C4×D3—51no—
264C22×Dic6—51no—
265C22×Dic6C2×D511yescharacteristic
266C3×#124—58no—
267C2×C3×C22⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C22⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C42C2×D511yescharacteristic
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276#946—58no—
277#944—58no—
278#939—58no—
279#935—58no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4—51no—
283C2×(C2×D3)⋊C4—51no—
284C2×C4⋊Dic3—51no—
285C2×C4⋊Dic3C2×D511yescharacteristic
286C2×Dic3⋊C4—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4—51no—
290C2×Dic3⋊C4—51no—
291C2×Dic3⋊C4—51no—
292C2×Dic3⋊C4C2×D511yescharacteristic
293C2×Dic3⋊C4C2×D511yescharacteristic
294C2×C4×Dic3—51no—
295C2×C4×Dic3C2×D511yescharacteristic
296C2×C4×Dic3C2×D511yescharacteristic
297#885—58no—
298#885—58no—
299#883—58no—
300#67⋊C4—58no—
301#879—58no—
302#878—58no—
303#878—58no—
304#877—58no—
305#876—58no—
306C4×Dic6C2×D518yescomplemented
307C23×D5—31no—
308C23×D5C22×D311yescharacteristic
309C23×D5C22×D311yescharacteristic
310C2×C5×Q8—34no—
311C2×C5×Q8—64no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5—31no—
315C22×C4×C5—31no—
316C22×C4×C5C22×D311yescharacteristic
317C22×C4×C5C22×D311yescharacteristic
318C22×C4×C5C22×D311yescharacteristic
319C22×Dic5—31no—
320C22×Dic5—31no—
321C22×Dic5—31no—
322C22×Dic5C22×D311yescharacteristic
323C22×Dic5C22×D311yescharacteristic
324C2×D20—34no—
325C2×D20—34no—
326C2×D20—42no—
327C2×D20—64no—
328C2×D20—122no—
329C2×D20C22×D314yes—
330C2×C4×D5—34no—
331C2×C4×D5—34no—
332C2×C4×D5—34no—
333C2×C4×D5—64no—
334C2×C4×D5—122no—
335C2×C4×D5—122no—
336C2×Dic10—34no—
337C2×Dic10—42no—
338C2×Dic10—122no—
339C2×Dic10C22×D314yes—
340C5×C4⋊C4—34no—
341C5×C4⋊C4—34no—
342C5×C4⋊C4—34no—
343C42×C5—34no—
344C42×C5—34no—
345C42×C5C22×D314yes—
346#685—34no—
347#685—34no—
348#685—34no—
349#685—34no—
350#685—34no—
351#685—34no—
352#685—34no—
353#685—34no—
354#685C22×D314yes—
355#685C22×D314yes—
356#685C22×D314yes—
357#685C22×D314yes—
358C4⋊Dic5—34no—
359#683—34no—
360#683—34no—
361#683—34no—
362#683—34no—
363#683—34no—
364#683—34no—
365C4×Dic5—34no—
366#542—1516no—
367C2×C4⋊Q8—151no—
368C2×#126—151no—
369C2×#126—151no—
370C2×#124—51no—
371C2×#124—151no—
372C2×#124—151no—
373C2×#123—151no—
374C2×#123—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C22⋊Q8—151no—
378C2×#121—151no—
379C2×C4×Q8—31no—
380C2×C4×D4—151no—
381C2×#117—151no—
382C22×C3×C5C2×#4112yes—
383C22×C3×C5H(5,𝔽2)12yes—
384C22×C3×C52−1+412yes—
385C22×C3×C5C2511yescharacteristic
386C2×D15—22no—
387C2×D15—22no—
388C2×D15—22no—
389C2×D15—44no—
390C2×C3×D5—22no—
391C2×C3×D5—22no—
392C2×C3×D5—22no—
393C2×C3×D5—22no—
394C2×C3×D5—22no—
395C2×C3×D5—22no—
396C2×C3×D5—44no—
397C2×C3×D5—44no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400C3×C4×C5—22no—
401Dic15—22no—
402Dic15—22no—
403Dic15—22no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C5×Dic3—22no—
407C5×Dic3—22no—
408C5×Dic3—22no—
409C5×Dic3C2×#4114yes—
410C24×C3—51no—
411C24×C3—51no—
412C23×D3—51no—
413C2×C3×Q8—54no—
414C2×C3×Q8—202no—
415C2×C3×D4—54no—
416C2×C3×D4—202no—
417C22×C3×C4—51no—
418C22×C3×C4—51no—
419C22×C3×C4C22×D511yescharacteristic
420C22×C3×C4C22×D511yescharacteristic
421C22×C3×C4C22×D511yescharacteristic
422C2×#67—54no—
423C2×#67—54no—
424C2×#67—104no—
425C2×#67—202no—
426C22×Dic3—51no—
427C22×Dic3—51no—
428C22×Dic3—51no—
429C22×Dic3—54no—
430C22×Dic3—54no—
431C22×Dic3—104no—
432C22×Dic3—202no—
433C22×Dic3C22×D511yescharacteristic
434C22×Dic3C22×D511yescharacteristic
435C22×Dic3C22×D511yescharacteristic
436C22×Dic3C22×D511yescharacteristic
437C2×C4×D3—54no—
438C2×C4×D3—202no—
439C2×Dic6—24no—
440C2×Dic6—54no—
441C2×Dic6—202no—
442C2×Dic6C22×D514yes—
443C3×C22⋊C4—54no—
444C3×C22⋊C4—54no—
445C3×C22⋊C4—54no—
446C3×C22⋊C4—54no—
447C3×C42C22×D514yes—
448#217—54no—
449#217—54no—
450#217—54no—
451#217—54no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—54no—
456C4⋊Dic3—54no—
457C4⋊Dic3C22×D514yes—
458Dic3⋊C4—54no—
459Dic3⋊C4—54no—
460Dic3⋊C4—54no—
461Dic3⋊C4—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4—54no—
464Dic3⋊C4C22×D514yes—
465Dic3⋊C4C22×D514yes—
466C4×Dic3—54no—
467C4×Dic3C22×D514yes—
468C4×Dic3C22×D514yes—
469C23×C5C23×D311yescharacteristic
470C22×D5—22no—
471C22×D5—22no—
472C22×D5—22no—
473C22×D5—22no—
474C22×D5—22no—
475C22×D5—22no—
476C22×D5—32no—
477C22×D5—62no—
478C22×D5—62no—
479C22×D5—62no—
480C22×D5C23×D312yes—
481C22×D5C23×D312yes—
482C5×Q8—68no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—22no—
486C2×C4×C5—34no—
487C2×C4×C5—32no—
488C2×C4×C5—32no—
489C2×C4×C5—32no—
490C2×C4×C5—32no—
491C2×C4×C5—62no—
492C2×C4×C5—62no—
493C2×C4×C5—62no—
494C2×C4×C5C23×D312yes—
495C2×C4×C5C23×D312yes—
496C2×C4×C5C23×D312yes—
497C2×Dic5—22no—
498C2×Dic5—22no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—32no—
502C2×Dic5—62no—
503C2×Dic5—62no—
504C2×Dic5—62no—
505C2×Dic5C23×D312yes—
506C2×Dic5C23×D312yes—
507D20—44no—
508D20—68no—
509D20—124no—
510C4×D5—68no—
511C4×D5—124no—
512C4×D5—124no—
513Dic10—44no—
514Dic10—124no—
515C22×Q8—31no—
516C22×Q8—51no—
517C22×Q8—151no—
518C22×D4—51no—
519C22×D4—151no—
520C22×D4—151no—
521C23×C4—151no—
522C23×C4—151no—
523C23×C4—151no—
524C4⋊Q8—158no—
525#126—158no—
526#126—158no—
527#124—58no—
528#124—158no—
529#124—158no—
530#123—158no—
531#123—158no—
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8—158no—
535#121—158no—
536C4×Q8—38no—
537C4×D4—158no—
538#117—158no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—151no—
543C2×C4⋊C4—151no—
544C2×C4⋊C4—151no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—151no—
548C2×C4⋊C4—151no—
549C2×C22⋊C4—51no—
550C2×C22⋊C4—51no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—51no—
553C2×C22⋊C4—151no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4—151no—
561C2×C42—31no—
562C2×C42—31no—
563C2×C42—151no—
564C2×C42D3×D511yescharacteristic
565C2×C3×C5#54214yescomplemented
566C2×C3×C5C22×#4111yescharacteristic
567C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
568C2×C3×C5C2×2−1+411yescharacteristic
569D15—42no—
570C3×D5—42no—
571C3×D5—42no—
572C23×C3—52no—
573C23×C3—52no—
574C23×C3—102no—
575C23×C3—102no—
576C23×C3—102no—
577C23×C3—102no—
578C23×C3—102no—
579C23×C3—102no—
580C23×C3C23×D511yescharacteristic
581C22×D3—52no—
582C22×D3—102no—
583C22×D3—102no—
584C22×D3—102no—
585C3×Q8—204no—
586C3×D4—204no—
587C2×C3×C4—22no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—52no—
591C2×C3×C4—52no—
592C2×C3×C4—102no—
593C2×C3×C4—102no—
594C2×C3×C4C23×D512yes—
595C2×C3×C4C23×D512yes—
596C2×C3×C4C23×D512yes—
597#67—108no—
598#67—204no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—22no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—102no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3—108no—
609C2×Dic3—204no—
610C2×Dic3#70914yes—
611C2×Dic3C23×D512yes—
612C2×Dic3C23×D512yes—
613C2×Dic3C23×D512yes—
614C2×Dic3C23×D512yes—
615C4×D3—204no—
616Dic6—28no—
617Dic6—204no—
618C22×C5#100412yes—
619C22×C5D3×#4112yes—
620C22×C5#101012yes—
621C22×C5C24×D311yescharacteristic
622C2×D5—22no—
623C2×D5—22no—
624C2×D5—22no—
625C2×D5—22no—
626C2×D5—22no—
627C2×D5—22no—
628C2×D5—44no—
629C2×D5—44no—
630C2×D5—62no—
631C2×D5—62no—
632C2×D5—62no—
633C2×D5—124no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—22no—
637C4×C5—34no—
638C4×C5—62no—
639C4×C5—62no—
640C4×C5—62no—
641Dic5—22no—
642Dic5—22no—
643Dic5—62no—
644Dic5—62no—
645Dic5—62no—
646C24—51no—
647C24—51no—
648C24—151no—
649C2×Q8—34no—
650C2×Q8—54no—
651C2×Q8—64no—
652C2×Q8—154no—
653C2×Q8—202no—
654C2×Q8—602no—
655C2×D4—54no—
656C2×D4—154no—
657C2×D4—154no—
658C2×D4—202no—
659C2×D4—304no—
660C2×D4—602no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—51no—
666C22×C4—51no—
667C22×C4—154no—
668C22×C4—154no—
669C22×C4—154no—
670C22×C4—151no—
671C22×C4—151no—
672C22×C4—151no—
673C22×C4—304no—
674C22×C4—602no—
675C22×C4—602no—
676C22×C4C2×D3×D511yescharacteristic
677C22×C4C2×D3×D511yescharacteristic
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—34no—
680C4⋊C4—34no—
681C4⋊C4—34no—
682C4⋊C4—154no—
683C4⋊C4—154no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4—154no—
687C4⋊C4—154no—
688C4⋊C4—154no—
689C22⋊C4—54no—
690C22⋊C4—54no—
691C22⋊C4—54no—
692C22⋊C4—54no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4—154no—
699C22⋊C4—154no—
700C22⋊C4—154no—
701C42—34no—
702C42—34no—
703C42—154no—
704C42C2×D3×D514yes—
705C3×C5C2×#54211yescharacteristic, complemented, Hall
706C22×C3—102no—
707C22×C3—102no—
708C22×C3—102no—
709C22×C3—102no—
710C22×C3—102no—
711C22×C3—102no—
712C22×C3—204no—
713C22×C3—204no—
714C22×C3C2×#70912yes—
715C22×C3#414712yes—
716C22×C3#414912yes—
717C22×C3C24×D511yescharacteristic
718C2×D3—102no—
719C2×D3—102no—
720C2×D3—102no—
721C2×D3—204no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—22no—
725C3×C4—102no—
726C3×C4—102no—
727Dic3—22no—
728Dic3—22no—
729Dic3—22no—
730Dic3—102no—
731Dic3—102no—
732Dic3—102no—
733Dic3C2×#70914yes—
734C2×C5#566914yescomplemented
735C2×C5C2×#100411yescharacteristic
736C2×C5C2×D3×#4111yescharacteristic
737C2×C5C2×#101011yescharacteristic
738D5—42no—
739D5—42no—
740D5—122no—
741C23—52no—
742C23—52no—
743C23—102no—
744C23—102no—
745C23—102no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—152no—
750C23—302no—
751C23—302no—
752C23—302no—
753C23C22×D3×D511yescharacteristic
754Q8—68no—
755Q8—204no—
756Q8—604no—
757D4—204no—
758D4—308no—
759D4—604no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—34no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—32no—
768C2×C4—52no—
769C2×C4—52no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—152no—
776C2×C4—152no—
777C2×C4—152no—
778C2×C4—308no—
779C2×C4—302no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—604no—
783C2×C4—604no—
784C2×C4C22×D3×D512yes—
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D512yes—
787C2×C3—202no—
788C2×C3—202no—
789C2×C3#6591614yescomplemented
790C2×C3C22×#70911yescharacteristic
791C2×C3C2×#414711yescharacteristic
792C2×C3C2×#414911yescharacteristic
793D3—202no—
794C5C2×#566911yescharacteristic, complemented, Sylow
795C22—102no—
796C22—102no—
797C22—102no—
798C22—102no—
799C22—102no—
800C22—102no—
801C22—204no—
802C22—204no—
803C22—302no—
804C22—302no—
805C22—302no—
806C22—604no—
807C22#9200012yes—
808C22D3×#70912yes—
809C22#9201712yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—22no—
813C4—22no—
814C4—34no—
815C4—62no—
816C4—62no—
817C4—62no—
818C4—102no—
819C4—102no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6591611yescharacteristic, complemented, Sylow
824C2—202no—
825C2—202no—
826C2—602no—
827C2#1175259814yesdirect product factor
828C2C2×#9200011yescharacteristic
829C2C2×D3×#70911yescharacteristic
830C2C2×#9201711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C42×C5C22
socleC23×C3×C5C24
prime radicalC2×#91409C2
hypercenterC2×C42D3×D5
hypocenterC3×C5C2×#542
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#91765C2semidirect
2. C2×C4×C5×Dic6C2semidirect
3. C2×C3×#4021C2semidirect
4. C2×#91455C2semidirect
5. C2×#91430C2semidirect
6. C2×#91421C2semidirect
7. C2×#91411C2semidirect
9. C2×#91407C2semidirect
10. C2×#91395C2semidirect
11. C2×#91393C2semidirect
12. C2×#91363C2semidirect
13. C2×#91356C2semidirect
14. C2×#91353C2semidirect
15. C2×#91327C2semidirect
16. #11752598C2direct (N × H)
34. #91765C22semidirect
40. C4×C5×Dic6C22semidirect
45. C3×#4021C22semidirect
56. #91455C22semidirect
57. #91430C22semidirect
58. #91421C22semidirect
59. #91411C22semidirect
61. #91407C22semidirect
62. #91395C22semidirect
63. #91393C22semidirect
64. #91363C22semidirect
65. #91356C22semidirect
66. #91353C22semidirect
67. #91327C22semidirect
82. C2×#4021D3semidirect
159. C2×C4×Dic6D5semidirect
207. #4021C2×D3semidirect
306. C4×Dic6C2×D5semidirect
565. C2×C3×C5#542semidirect
705. C3×C5C2×#542semidirect
734. C2×C5#5669semidirect
789. C2×C3#65916semidirect
794. C5C2×#5669semidirect
823. C3C2×#65916semidirect
827. C2#11752598direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917652
C2×C4×C5×Dic62
C2×C3×#40212
C2×#914552
C2×#914302
C2×#914212
C2×#914112
C2×#914092
C2×#914072
C2×#913952
C2×#913932
C2×#913632
C2×#913562
C2×#913532
C2×#913272
#117525982
C2×#659163
C2×#56695