Finite Group Databasebeta

← C2×#11752965 #14481457

Subgroups — C2×#11752965 #14481457

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×#91767C211yesmaximal, characteristic, complemented
2C2×C5×#879C211yesmaximal, characteristic, complemented
3C2×C3×#4030C211yesmaximal, characteristic
4C2×#91559C211yesmaximal, characteristic, complemented
5C2×#91537C211yesmaximal, characteristic, complemented
6C2×#91534C211yesmaximal, characteristic, complemented
7C2×#91534C211yesmaximal, characteristic, complemented
8C2×#91422C211yesmaximal, characteristic, complemented
9C2×#91407C211yesmaximal, characteristic, complemented
10C2×#91364C211yesmaximal, characteristic, complemented
11C2×#91361C211yesmaximal, characteristic, complemented
12C2×#91358C211yesmaximal, characteristic, complemented
13C2×#91349C211yesmaximal, characteristic, complemented
14C2×#91328C211yesmaximal, characteristic, complemented
15C2×#91324C211yesmaximal, characteristic, complemented
16#11752965C2116yesmaximal, direct product factor
17C2×#66044—31nomaximal, Hall
18C23×Dic15C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C3×C22⋊D5C2211yescharacteristic
21C22×C3×C22⋊D5C2211yescharacteristic
22C22×C3×D20C2211yescharacteristic
23C22×C3×C4×D5C2211yescharacteristic
24C22×#1204C2211yescharacteristic
25C22×#1204C2211yescharacteristic
26C22×D5×Dic3C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×C4⋊Dic15C2211yescharacteristic
30C2×#6712C2211yescharacteristic
31C2×#6712C2211yescharacteristic
32#91767C2218yescomplemented
33C2×C5×#217C2211yescharacteristic
34C2×C5×#217C2211yescharacteristic
35C2×C5×C4⋊Dic3C2211yescharacteristic
36C2×C5×Dic3⋊C4C2211yescharacteristic
37C2×C5×Dic3⋊C4C2211yescharacteristic
38C2×C4×C5×Dic3C2211yescharacteristic
39C5×#879C2218yescomplemented
40C2×C3×#685C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C3×#4030C2218yes—
43#91559C2218yescomplemented
44C2×Dic3⋊Dic5C2211yescharacteristic
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×#6668C2211yescharacteristic
47#91537C2218yescomplemented
48C2×#6665C2211yescharacteristic
49C2×#6665C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×#6665C2211yescharacteristic
53C2×#6665C2211yescharacteristic
54C2×#6665C2211yescharacteristic
55#91534C2218yescomplemented
56#91534C2218yescomplemented
57C2×Dic3×Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91422C2218yescomplemented
61#91407C2218yescomplemented
62#91364C2218yescomplemented
63#91361C2218yescomplemented
64#91358C2218yescomplemented
65#91349C2218yescomplemented
66#91328C2218yescomplemented
67#91324C2218yescomplemented
68C2×#5603—51nomaximal, Hall
69C2×C5×#126—31no—
70#66044—316no—
71C2×#4044—31no—
72C2×#4043—31no—
73C2×#4042—31no—
74C2×#4040—31no—
75C2×#4038—31no—
76C2×#4034—31no—
77C2×#4032—31no—
78C2×#4031—31no—
79C2×#4031—31no—
80C2×#4030D311yescharacteristic
81C2×#4027—31no—
82C2×#4024—31no—
83C2×#4021—31no—
84C2×C4×Dic10—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C3×D5C2311yescharacteristic
87C23×C3×D5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C22×Dic15—42no—
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C22×Dic15C2314yes—
96C2×Dic30—42no—
97C2×Dic30C2314yes—
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C2×C3×C22⋊D5—24no—
103C2×C3×C22⋊D5—42no—
104C2×C3×C22⋊D5C2314yes—
105C2×C3×C22⋊D5C2314yes—
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×C3×D20—42no—
109C2×C3×D20C2314yes—
110C2×C3×C4×D5—24no—
111C2×C3×C4×D5C2314yes—
112C2×#1204—24no—
113C2×#1204—42no—
114C2×#1204C2314yes—
115C2×#1204C2314yes—
116C2×D5×Dic3—42no—
117C2×D5×Dic3C2314yes—
118C3×C5×C22⋊C4C2314yes—
119#6719C2314yes—
120C4⋊Dic15C2314yes—
121#6712C2314yes—
122#6712C2314yes—
123C5×#217C2314yes—
124C5×#217C2314yes—
125C5×C4⋊Dic3C2314yes—
126C5×Dic3⋊C4C2314yes—
127C5×Dic3⋊C4C2314yes—
128C4×C5×Dic3C2314yes—
129C3×#685C2314yes—
130C3×#683C2314yes—
131Dic3⋊Dic5C2314yes—
132Dic3⋊Dic5C2314yes—
133#6668C2314yes—
134#6665C2314yes—
135#6665C2314yes—
136#6665C2314yes—
137#6665C2314yes—
138#6665C2314yes—
139#6665C2314yes—
140#6665C2314yes—
141Dic3×Dic5C2314yes—
142Dic3×Dic5C2314yes—
143Dic3×Dic5C2314yes—
144C2×C3×#121—51no—
145C2×#936—51no—
146C2×#936—51no—
147C2×#936—51no—
148C2×#935—51no—
149C2×#935—51no—
150C2×D4×Dic3—51no—
151C2×#926—51no—
152C2×#924—51no—
153#5603—516no—
154C2×#888—51no—
155C2×#887—51no—
156C2×#879—51no—
157C2×#879D511yescharacteristic, complemented
158C2×#878—51no—
159C2×#878—51no—
160C22×C22⋊D5C2×D311yescharacteristic
161C22×C22⋊D5C2×D311yescharacteristic
162C23×Dic5—31no—
163C22×D20C2×D311yescharacteristic
164C22×C4×D5—31no—
165C22×C4×D5C2×D311yescharacteristic
166C22×Dic10—31no—
167C22×Dic10—31no—
168C22×Dic10—31no—
169C5×#126—38no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C4⋊C4—31no—
172C2×C5×C4⋊C4—31no—
173C2×C5×C22⋊C4—31no—
174C2×C5×C22⋊C4—31no—
175C2×C5×C22⋊C4C2×D311yescharacteristic
176C2×C42×C5—31no—
177C2×C22⋊Dic5—31no—
178C2×#685—31no—
179C2×#685—31no—
180C2×#685—31no—
181C2×#685—31no—
182C2×#685—31no—
183C2×#685—31no—
184C2×#685—31no—
185C2×#685C2×D311yescharacteristic
186C2×C4⋊Dic5—31no—
187C2×C4⋊Dic5—31no—
188C2×C4⋊Dic5—31no—
189C2×#683—31no—
190C2×#683—31no—
191C2×#683—31no—
192C2×#683C2×D311yescharacteristic
193C2×C4×Dic5—31no—
194C2×C4×Dic5—31no—
195C2×C4×Dic5—31no—
196#4044—38no—
197#4043—38no—
198#4042—38no—
199#4040—38no—
200#4038—38no—
201#4034—38no—
202#4032—38no—
203#4031—38no—
204#4031—38no—
205#4030C2×D318yes—
206#4027—38no—
207#4024—38no—
208#4021—38no—
209C4×Dic10—38no—
210C2×#542—151noSylow
211C23×C3×C5—22no—
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5C2412yes—
215C23×C3×C5C2411yescharacteristic
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×C5C2412yes—
227C2×C3×C4×C5C2412yes—
228C2×Dic15—22no—
229C2×Dic15—22no—
230C2×Dic15—22no—
231C2×Dic15—22no—
232C2×Dic15—44no—
233C2×Dic15C2412yes—
234C2×Dic15C2412yes—
235C2×Dic15C2412yes—
236C2×Dic15C2412yes—
237Dic30—44no—
238C2×C5×Dic3—22no—
239C2×C5×Dic3—22no—
240C2×C5×Dic3—22no—
241C2×C5×Dic3—22no—
242C2×C5×Dic3C2412yes—
243C2×C5×Dic3C2412yes—
244C2×C5×Dic3C2412yes—
245C2×C5×Dic3C2412yes—
246C3×C22⋊D5—28no—
247C3×C22⋊D5—44no—
248C2×C3×Dic5—22no—
249C2×C3×Dic5#4114yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C3×D20—44no—
253C3×C4×D5—28no—
254#1204—28no—
255#1204—44no—
256D5×Dic3—44no—
257C22×C3×D4—51no—
258C22×C3×D4—51no—
259C22×C3×D4—51no—
260C23×C3×C4—51no—
261C23×Dic3—51no—
262C23×Dic3—51no—
263C22×Dic6—51no—
264C22×Dic6—51no—
265C22×Dic6—51no—
266C3×#121—58no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C22⋊C4—51no—
269C2×C3×C22⋊C4C2×D511yescharacteristic
270C2×#217—51no—
271C2×#217—51no—
272C2×#217—51no—
273C2×#217—51no—
274C2×#217—51no—
275C2×#217—51no—
276C2×#217—51no—
277C2×#217—51no—
278C2×#217C2×D511yescharacteristic
279C2×#217C2×D511yescharacteristic
280#936—58no—
281#936—58no—
282#936—58no—
283#935—58no—
284#935—58no—
285D4×Dic3—58no—
286#926—58no—
287C2×C4⋊Dic3—51no—
288C2×C4⋊Dic3—51no—
289C2×C4⋊Dic3C2×D511yescharacteristic
290#924—58no—
291C2×Dic3⋊C4—51no—
292C2×Dic3⋊C4—51no—
293C2×Dic3⋊C4—51no—
294C2×Dic3⋊C4—51no—
295C2×Dic3⋊C4C2×D511yescharacteristic
296C2×Dic3⋊C4C2×D511yescharacteristic
297C2×C4×Dic3—51no—
298C2×C4×Dic3—51no—
299C2×C4×Dic3—51no—
300C2×C4×Dic3C2×D511yescharacteristic
301#888—58no—
302#887—58no—
303#879—58no—
304#879C2×D518yescomplemented
305#878—58no—
306#878—58no—
307C24×C5C22×D311yescharacteristic
308C23×D5C22×D311yescharacteristic
309C23×D5C22×D311yescharacteristic
310C22×C4×C5—31no—
311C22×C4×C5—31no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5C22×D311yescharacteristic
315C22×C4×C5C22×D311yescharacteristic
316C2×C22⋊D5—24no—
317C2×C22⋊D5—42no—
318C2×C22⋊D5C22×D314yes—
319C2×C22⋊D5C22×D314yes—
320C22×Dic5—31no—
321C22×Dic5—31no—
322C22×Dic5—31no—
323C22×Dic5—31no—
324C22×Dic5—34no—
325C22×Dic5—122no—
326C22×Dic5C22×D311yescharacteristic
327C22×Dic5C22×D311yescharacteristic
328C2×D20—42no—
329C2×D20C22×D314yes—
330C2×C4×D5—24no—
331C2×C4×D5—34no—
332C2×C4×D5—122no—
333C2×C4×D5C22×D314yes—
334C2×Dic10—34no—
335C2×Dic10—34no—
336C2×Dic10—34no—
337C2×Dic10—64no—
338C2×Dic10—122no—
339C2×Dic10—122no—
340C5×C4⋊C4—34no—
341C5×C4⋊C4—34no—
342C5×C4⋊C4—34no—
343C5×C22⋊C4—34no—
344C5×C22⋊C4—34no—
345C5×C22⋊C4C22×D314yes—
346C42×C5—34no—
347C22⋊Dic5—34no—
348#685—34no—
349#685—34no—
350#685—34no—
351#685—34no—
352#685—34no—
353#685—34no—
354#685—34no—
355#685C22×D314yes—
356C4⋊Dic5—34no—
357C4⋊Dic5—34no—
358C4⋊Dic5—34no—
359#683—34no—
360#683—34no—
361#683—34no—
362#683C22×D314yes—
363C4×Dic5—34no—
364C4×Dic5—34no—
365C4×Dic5—34no—
366#542—1516no—
367C2×C4⋊Q8—151no—
368C2×#126—31no—
369C2×#126—151no—
370C2×#124—151no—
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—51no—
379C2×C4×Q8—151no—
380C2×C4×D4—151no—
381C2×#117—151no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—22no—
385C22×C3×C5—44no—
386C22×C3×C5C2×#4112yes—
387C22×C3×C5H(5,𝔽2)12yes—
388C22×C3×C52−1+412yes—
389C22×C3×C5C2511yescharacteristic
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—
400Dic15—22no—
401Dic15—22no—
402Dic15—22no—
403Dic15—22no—
404C3×Dic5—22no—
405C3×Dic5C2×#4114yes—
406C5×Dic3—22no—
407C5×Dic3—22no—
408C5×Dic3—22no—
409C5×Dic3—22no—
410C24×C3—51no—
411C24×C3—51no—
412C24×C3C22×D511yescharacteristic
413C2×C3×D4—54no—
414C2×C3×D4—54no—
415C2×C3×D4—54no—
416C2×C3×D4—104no—
417C2×C3×D4—202no—
418C2×C3×D4—202no—
419C22×C3×C4—51no—
420C22×C3×C4—51no—
421C22×C3×C4—54no—
422C22×C3×C4—104no—
423C22×C3×C4C22×D511yescharacteristic
424C22×C3×C4C22×D511yescharacteristic
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3—51no—
428C22×Dic3—51no—
429C22×Dic3—54no—
430C22×Dic3—54no—
431C22×Dic3—202no—
432C22×Dic3—202no—
433C22×Dic3C22×D511yescharacteristic
434C22×Dic3C22×D511yescharacteristic
435C22×Dic3C22×D511yescharacteristic
436C22×Dic3C22×D511yescharacteristic
437C2×Dic6—54no—
438C2×Dic6—54no—
439C2×Dic6—54no—
440C2×Dic6—104no—
441C2×Dic6—202no—
442C2×Dic6—202no—
443C3×C4⋊C4—54no—
444C3×C22⋊C4—54no—
445C3×C22⋊C4C22×D514yes—
446#217—54no—
447#217—54no—
448#217—54no—
449#217—54no—
450#217—54no—
451#217—54no—
452#217—54no—
453#217—54no—
454#217C22×D514yes—
455#217C22×D514yes—
456C4⋊Dic3—54no—
457C4⋊Dic3—54no—
458C4⋊Dic3C22×D514yes—
459Dic3⋊C4—54no—
460Dic3⋊C4—54no—
461Dic3⋊C4—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4C22×D514yes—
464Dic3⋊C4C22×D514yes—
465C4×Dic3—54no—
466C4×Dic3—54no—
467C4×Dic3—54no—
468C4×Dic3C22×D514yes—
469C23×C5—22no—
470C23×C5—22no—
471C23×C5—22no—
472C23×C5C23×D312yes—
473C23×C5C23×D311yescharacteristic
474C22×D5—22no—
475C22×D5—22no—
476C22×D5—22no—
477C22×D5—22no—
478C22×D5—22no—
479C22×D5—22no—
480C22×D5C23×D312yes—
481C22×D5C23×D312yes—
482C2×C4×C5—22no—
483C2×C4×C5—22no—
484C2×C4×C5—32no—
485C2×C4×C5—32no—
486C2×C4×C5—32no—
487C2×C4×C5—32no—
488C2×C4×C5—62no—
489C2×C4×C5—62no—
490C2×C4×C5—62no—
491C2×C4×C5—62no—
492C2×C4×C5C23×D312yes—
493C2×C4×C5C23×D312yes—
494C22⋊D5—28no—
495C22⋊D5—44no—
496C2×Dic5—22no—
497C2×Dic5—32no—
498C2×Dic5—32no—
499C2×Dic5—32no—
500C2×Dic5—32no—
501C2×Dic5—62no—
502C2×Dic5—62no—
503C2×Dic5—62no—
504C2×Dic5—62no—
505C2×Dic5—124no—
506C2×Dic5#23714yes—
507C2×Dic5C23×D312yes—
508C2×Dic5C23×D312yes—
509D20—44no—
510C4×D5—28no—
511C4×D5—124no—
512Dic10—68no—
513Dic10—124no—
514Dic10—124no—
515C22×Q8—151no—
516C22×Q8—151no—
517C22×Q8—151no—
518C22×D4—51no—
519C22×D4—51no—
520C22×D4—51no—
521C23×C4—51no—
522C23×C4—151no—
523C23×C4—151no—
524C4⋊Q8—158no—
525#126—38no—
526#126—158no—
527#124—158no—
528#124—158no—
529#124—158no—
530#123—158no—
531#123—158no—
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8—158no—
535#121—58no—
536C4×Q8—158no—
537C4×D4—158no—
538#117—158no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—31no—
541C2×C4⋊C4—31no—
542C2×C4⋊C4—51no—
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—31no—
550C2×C22⋊C4—31no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—151no—
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⋊C4D3×D511yescharacteristic
561C2×C42—31no—
562C2×C42—151no—
563C2×C42—151no—
564C2×C42—151no—
565C2×C3×C5—42no—
566C2×C3×C5#54214yescomplemented
567C2×C3×C5C22×#4111yescharacteristic
568C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
569C2×C3×C5C2×2−1+411yescharacteristic
570C3×D5—42no—
571C3×D5—42no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—52no—
576C23×C3—52no—
577C23×C3—102no—
578C23×C3—102no—
579C23×C3—102no—
580C23×C3—102no—
581C23×C3—102no—
582C23×C3—102no—
583C23×C3C23×D512yes—
584C23×C3C23×D511yescharacteristic
585C3×D4—108no—
586C3×D4—204no—
587C3×D4—204no—
588C2×C3×C4—22no—
589C2×C3×C4—22no—
590C2×C3×C4—54no—
591C2×C3×C4—52no—
592C2×C3×C4—52no—
593C2×C3×C4—108no—
594C2×C3×C4—102no—
595C2×C3×C4C23×D512yes—
596C2×C3×C4C23×D512yes—
597C2×Dic3—22no—
598C2×Dic3—22no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—52no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—102no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3—102no—
609C2×Dic3—204no—
610C2×Dic3—204no—
611C2×Dic3C23×D512yes—
612C2×Dic3C23×D512yes—
613C2×Dic3C23×D512yes—
614C2×Dic3C23×D512yes—
615Dic6—108no—
616Dic6—204no—
617Dic6—204no—
618C22×C5—22no—
619C22×C5—22no—
620C22×C5—22no—
621C22×C5—44no—
622C22×C5C2×#23712yes—
623C22×C5#100412yes—
624C22×C5#101012yes—
625C22×C5C24×D311yescharacteristic
626C2×D5—22no—
627C2×D5—22no—
628C2×D5—22no—
629C2×D5—22no—
630C2×D5—22no—
631C2×D5—22no—
632C2×D5—44no—
633C2×D5—44no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—62no—
637C4×C5—62no—
638C4×C5—62no—
639C4×C5—62no—
640Dic5—22no—
641Dic5—62no—
642Dic5—62no—
643Dic5—62no—
644Dic5—62no—
645Dic5C2×#23714yes—
646C24—51no—
647C24—51no—
648C24C2×D3×D511yescharacteristic
649C2×Q8—154no—
650C2×Q8—154no—
651C2×Q8—154no—
652C2×Q8—304no—
653C2×Q8—602no—
654C2×Q8—602no—
655C2×D4—54no—
656C2×D4—54no—
657C2×D4—54no—
658C2×D4—104no—
659C2×D4—202no—
660C2×D4—202no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—31no—
665C22×C4—51no—
666C22×C4—51no—
667C22×C4—54no—
668C22×C4—104no—
669C22×C4—154no—
670C22×C4—151no—
671C22×C4—151no—
672C22×C4—151no—
673C22×C4—151no—
674C22×C4—154no—
675C22×C4—602no—
676C22×C4—602no—
677C22×C4C2×D3×D511yescharacteristic
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—34no—
680C4⋊C4—34no—
681C4⋊C4—34no—
682C4⋊C4—54no—
683C4⋊C4—154no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4—154no—
687C4⋊C4—154no—
688C4⋊C4—154no—
689C22⋊C4—34no—
690C22⋊C4—34no—
691C22⋊C4—54no—
692C22⋊C4—154no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4—154no—
699C22⋊C4—154no—
700C22⋊C4C2×D3×D514yes—
701C42—34no—
702C42—154no—
703C42—154no—
704C42—154no—
705C3×C5C2×#54211yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—44no—
710C22×C3—102no—
711C22×C3—102no—
712C22×C3—102no—
713C22×C3—102no—
714C22×C3—102no—
715C22×C3—102no—
716C22×C3—204no—
717C22×C3—204no—
718C22×C3D5×#4112yes—
719C22×C3#414912yes—
720C22×C3#415012yes—
721C22×C3C24×D511yescharacteristic
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—54no—
725C3×C4—102no—
726Dic3—22no—
727Dic3—22no—
728Dic3—22no—
729Dic3—22no—
730Dic3—102no—
731Dic3—102no—
732Dic3—102no—
733Dic3—102no—
734C2×C5—42no—
735C2×C5#560314yescomplemented
736C2×C5C22×#23711yescharacteristic
737C2×C5C2×#100411yescharacteristic
738C2×C5C2×#101011yescharacteristic
739D5—42no—
740D5—42no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—52no—
745C23—52no—
746C23—102no—
747C23—102no—
748C23—102no—
749C23—102no—
750C23—102no—
751C23—102no—
752C23C22×D3×D512yes—
753C23C22×D3×D511yescharacteristic
754Q8—308no—
755Q8—604no—
756Q8—604no—
757D4—108no—
758D4—204no—
759D4—204no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—32no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—54no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—62no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—62no—
773C2×C4—108no—
774C2×C4—102no—
775C2×C4—152no—
776C2×C4—152no—
777C2×C4—152no—
778C2×C4—152no—
779C2×C4—302no—
780C2×C4—302no—
781C2×C4—302no—
782C2×C4—302no—
783C2×C4—604no—
784C2×C4—604no—
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D512yes—
787C2×C3—42no—
788C2×C3—202no—
789C2×C3—202no—
790C2×C3#6604414yescomplemented
791C2×C3C2×D5×#4111yescharacteristic
792C2×C3C2×#414911yescharacteristic
793C2×C3C2×#415011yescharacteristic
794C5C2×#560311yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—44no—
799C22—102no—
800C22—102no—
801C22—102no—
802C22—102no—
803C22—102no—
804C22—102no—
805C22—204no—
806C22—204no—
807C22#9200112yes—
808C22D5×#23712yes—
809C22#9202612yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—22no—
813C4—54no—
814C4—62no—
815C4—62no—
816C4—62no—
817C4—62no—
818C4—102no—
819C4—302no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6604411yescharacteristic, complemented, Sylow
824C2—42no—
825C2—202no—
826C2—202no—
827C2#1175296514yesdirect product factor
828C2C2×#9200111yescharacteristic
829C2C2×D5×#23711yescharacteristic
830C2C2×#9202611yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC2×C3×#4030C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#542
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×#91767C2semidirect
2. C2×C5×#879C2semidirect
4. C2×#91559C2semidirect
5. C2×#91537C2semidirect
6. C2×#91534C2semidirect
7. C2×#91534C2semidirect
8. C2×#91422C2semidirect
9. C2×#91407C2semidirect
10. C2×#91364C2semidirect
11. C2×#91361C2semidirect
12. C2×#91358C2semidirect
13. C2×#91349C2semidirect
14. C2×#91328C2semidirect
15. C2×#91324C2semidirect
16. #11752965C2direct (N × H)
32. #91767C22semidirect
39. C5×#879C22semidirect
43. #91559C22semidirect
47. #91537C22semidirect
55. #91534C22semidirect
56. #91534C22semidirect
60. #91422C22semidirect
61. #91407C22semidirect
62. #91364C22semidirect
63. #91361C22semidirect
64. #91358C22semidirect
65. #91349C22semidirect
66. #91328C22semidirect
67. #91324C22semidirect
157. C2×#879D5semidirect
304. #879C2×D5semidirect
566. C2×C3×C5#542semidirect
705. C3×C5C2×#542semidirect
735. C2×C5#5603semidirect
790. C2×C3#66044semidirect
794. C5C2×#5603semidirect
823. C3C2×#66044semidirect
827. C2#11752965direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917672
C2×C5×#8792
C2×C3×#40302
C2×#915592
C2×#915372
C2×#915342
C2×#914222
C2×#914072
C2×#913642
C2×#913612
C2×#913582
C2×#913492
C2×#913282
C2×#913242
#117529652
C2×#660443
C2×#56035