Finite Group Databasebeta

← C2×#11753010 #14484091

Subgroups — C2×#11753010 #14484091

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91767C211yesmaximal, characteristic, complemented
2C2×C5×#885C211yesmaximal, characteristic
3C2×C3×#4025C211yesmaximal, characteristic, complemented
4C2×#67⋊Dic5C211yesmaximal, characteristic
5C2×#91532C211yesmaximal, characteristic, complemented
6C2×#91530C211yesmaximal, characteristic, complemented
7C2×#91525C211yesmaximal, characteristic
8C2×#91432C211yesmaximal, characteristic, complemented
9C2×#91398C211yesmaximal, characteristic, complemented
10C2×#91342C211yesmaximal, characteristic, complemented
11C2×#91341C211yesmaximal, characteristic, complemented
12C2×#91340C211yesmaximal, characteristic, complemented
13C2×Dic5×Dic6C211yesmaximal, characteristic, complemented
14C2×#91329C211yesmaximal, characteristic, complemented
15C2×#91324C211yesmaximal, characteristic, complemented
16#11753010C2116yesmaximal, direct product factor
17C2×#66005—31nomaximal, Hall
18C23×Dic15C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C22×C5×Dic6C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C2×C3×C5×C22⋊C4C2211yescharacteristic
25C2×#6719C2211yescharacteristic
26C2×C4⋊Dic15C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C2×#6712C2211yescharacteristic
29#91767C2218yescomplemented
30C2×C5×#217C2211yescharacteristic
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C4×C5×Dic3C2211yescharacteristic
34C5×#885C2218yes—
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×C22⋊Dic5C2211yescharacteristic
37C2×C3×C4⋊Dic5C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×C4×Dic5C2211yescharacteristic
41C3×#4025C2218yescomplemented
42#67⋊Dic5C2218yes—
43C2×Dic3⋊Dic5C2211yescharacteristic
44C2×Dic3⋊Dic5C2211yescharacteristic
45C2×#6669C2211yescharacteristic
46C2×#6669C2211yescharacteristic
47C2×#6669C2211yescharacteristic
48C2×#6668C2211yescharacteristic
49C2×(C2×D3)⋊Dic5C2211yescharacteristic
50C2×(C2×D3)⋊Dic5C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52#91532C2218yescomplemented
53#91530C2218yescomplemented
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56C2×Dic3×Dic5C2211yescharacteristic
57C2×Dic3×Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59#91525C2218yes—
60#91432C2218yescomplemented
61#91398C2218yescomplemented
62#91342C2218yescomplemented
63#91341C2218yescomplemented
64#91340C2218yescomplemented
65Dic5×Dic6C2218yescomplemented
66#91329C2218yescomplemented
67#91324C2218yescomplemented
68C2×#5702—51nomaximal, Hall
69C2×C5×#124—31no—
70C2×Q8×Dic5—31no—
71C2×#4090—31no—
72C2×#4082—31no—
73C2×D4×Dic5—31no—
74#66005—316no—
75C2×#4025—31no—
76C2×#4025—31no—
77C2×#4025—31no—
78C2×#4025D311yescharacteristic, complemented
79C2×#4024—31no—
80C2×#4024—31no—
81C2×#4023—31no—
82C2×#4023—31no—
83C2×C4×Dic10—31no—
84C2×C4×Dic10—31no—
85C24×C3×C5C2311yescharacteristic
86C23×C5×D3C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×Dic15—24no—
90C22×Dic15C2314yes—
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×Dic30—24no—
96C2×Dic30C2314yes—
97C2×C5×#67—24no—
98C2×C5×#67C2314yes—
99C22×C5×Dic3C2311yescharacteristic
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C2×C5×Dic6—24no—
103C2×C5×Dic6C2314yes—
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×#1204—24no—
109C2×#1204C2314yes—
110C2×D3×Dic5—24no—
111C2×D3×Dic5C2314yes—
112C3×C5×C22⋊C4C2314yes—
113#6719C2314yes—
114C4⋊Dic15C2314yes—
115#6712C2314yes—
116#6712C2314yes—
117C5×#217C2314yes—
118C5×(C2×D3)⋊C4C2314yes—
119C5×(C2×D3)⋊C4C2314yes—
120C4×C5×Dic3C2314yes—
121C3×C22⋊Dic5C2314yes—
122C3×C22⋊Dic5C2314yes—
123C3×C4⋊Dic5C2314yes—
124C3×#683C2314yes—
125C3×#683C2314yes—
126C3×C4×Dic5C2314yes—
127Dic3⋊Dic5C2314yes—
128Dic3⋊Dic5C2314yes—
129#6669C2314yes—
130#6669C2314yes—
131#6669C2314yes—
132#6668C2314yes—
133(C2×D3)⋊Dic5C2314yes—
134(C2×D3)⋊Dic5C2314yes—
135(C2×D3)⋊Dic5C2314yes—
136Dic3×Dic5C2314yes—
137Dic3×Dic5C2314yes—
138Dic3×Dic5C2314yes—
139Dic3×Dic5C2314yes—
140Dic3×Dic5C2314yes—
141C2×C3×#126—51no—
142#5702—516no—
143C2×#898—51no—
144C2×#898—51no—
145C2×#896—51no—
146C2×#888—51no—
147C2×#887—51no—
148C2×#887—51no—
149C2×#885—51no—
150C2×#885D511yescharacteristic
151C2×#67⋊C4—51no—
152C2×#879—51no—
153C2×#878—51no—
154C2×#877—51no—
155C2×#872—51no—
156C2×C4×Dic6—51no—
157C22×C5×Q8—31no—
158C22×C5×D4—31no—
159C23×Dic5—31no—
160C23×Dic5—31no—
161C22×Dic10—31no—
162C22×Dic10—31no—
163C5×#124—38no—
164C2×C5×C22⋊C4—31no—
165C2×C5×C22⋊C4—31no—
166C2×C5×C22⋊C4—31no—
167C2×C5×C22⋊C4C2×D311yescharacteristic
168C2×C42×C5—31no—
169C2×C22⋊Dic5—31no—
170C2×C22⋊Dic5—31no—
171C2×C22⋊Dic5—31no—
172C2×C22⋊Dic5—31no—
173C2×C22⋊Dic5C2×D311yescharacteristic
174C2×C22⋊Dic5C2×D311yescharacteristic
175Q8×Dic5—38no—
176#4090—38no—
177#4082—38no—
178D4×Dic5—38no—
179C2×C4⋊Dic5—31no—
180C2×C4⋊Dic5—31no—
181C2×C4⋊Dic5—31no—
182C2×C4⋊Dic5C2×D311yescharacteristic
183C2×#683—31no—
184C2×#683—31no—
185C2×#683—31no—
186C2×#683—31no—
187C2×#683—31no—
188C2×#683—31no—
189C2×#683C2×D311yescharacteristic
190C2×#683C2×D311yescharacteristic
191C2×C4×Dic5—31no—
192C2×C4×Dic5—31no—
193C2×C4×Dic5—31no—
194C2×C4×Dic5—31no—
195C2×C4×Dic5—31no—
196C2×C4×Dic5C2×D311yescharacteristic
197#4025—38no—
198#4025—38no—
199#4025—38no—
200#4025C2×D318yescomplemented
201#4024—38no—
202#4024—38no—
203#4023—38no—
204#4023—38no—
205C4×Dic10—38no—
206C4×Dic10—38no—
207C2×#556—151noSylow
208C23×C3×C5—22no—
209C23×C3×C5—22no—
210C23×C3×C5—22no—
211C23×C3×C5C2412yes—
212C23×C3×C5C2411yescharacteristic
213C22×C5×D3—22no—
214C22×C5×D3—22no—
215C22×C5×D3—22no—
216C22×C5×D3C2412yes—
217C2×C3×C4×C5—22no—
218C2×C3×C4×C5—22no—
219C2×C3×C4×C5C2412yes—
220C2×C3×C4×C5C2412yes—
221C2×Dic15—22no—
222C2×Dic15—22no—
223C2×Dic15—22no—
224C2×Dic15—28no—
225C2×Dic15#4114yes—
226C2×Dic15C2412yes—
227C2×Dic15C2412yes—
228C2×Dic15C2412yes—
229C2×Dic15C2412yes—
230Dic30—28no—
231C5×#67—28no—
232C2×C5×Dic3—22no—
233C2×C5×Dic3—22no—
234C2×C5×Dic3#4114yes—
235C2×C5×Dic3C2412yes—
236C2×C5×Dic3C2412yes—
237C2×C5×Dic3C2412yes—
238C5×Dic6—28no—
239C2×C3×Dic5—22no—
240C2×C3×Dic5—22no—
241C2×C3×Dic5—22no—
242C2×C3×Dic5—22no—
243C2×C3×Dic5C2412yes—
244C2×C3×Dic5C2412yes—
245C2×C3×Dic5C2412yes—
246C2×C3×Dic5C2412yes—
247#1204—28no—
248D3×Dic5—28no—
249C22×#67C2×D511yescharacteristic
250C23×Dic3—51no—
251C22×C4×D3—51no—
252C22×Dic6—51no—
253C22×Dic6—51no—
254C22×Dic6C2×D511yescharacteristic
255C3×#126—58no—
256C2×C3×C4⋊C4—51no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C4⋊C4—51no—
259C2×C3×C22⋊C4—51no—
260C2×C3×C22⋊C4—51no—
261C2×C3×C22⋊C4C2×D511yescharacteristic
262C2×C3×C42—51no—
263C2×#217—51no—
264C2×#217C2×D511yescharacteristic
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4—51no—
267C2×(C2×D3)⋊C4—51no—
268C2×(C2×D3)⋊C4C2×D511yescharacteristic
269C2×(C2×D3)⋊C4C2×D511yescharacteristic
270C2×C4⋊Dic3—51no—
271C2×C4⋊Dic3—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C2×C4×Dic3—51no—
283C2×C4×Dic3—51no—
284C2×C4×Dic3C2×D511yescharacteristic
285#898—58no—
286#898—58no—
287#896—58no—
288#888—58no—
289#887—58no—
290#887—58no—
291#885—58no—
292#885C2×D518yes—
293#67⋊C4—58no—
294#879—58no—
295#878—58no—
296#877—58no—
297#872—58no—
298C4×Dic6—58no—
299C24×C5—31no—
300C24×C5C22×D311yescharacteristic
301C2×C5×Q8—34no—
302C2×C5×Q8—64no—
303C2×C5×D4—34no—
304C2×C5×D4—64no—
305C22×C4×C5—31no—
306C22×C4×C5—31no—
307C22×C4×C5—31no—
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×Dic5—31no—
311C22×Dic5—31no—
312C22×Dic5—31no—
313C22×Dic5—31no—
314C22×Dic5—34no—
315C22×Dic5—34no—
316C22×Dic5—64no—
317C22×Dic5—64no—
318C22×Dic5C22×D311yescharacteristic
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C2×Dic10—34no—
323C2×Dic10—34no—
324C2×Dic10—64no—
325C2×Dic10—64no—
326C5×C22⋊C4—34no—
327C5×C22⋊C4—34no—
328C5×C22⋊C4—34no—
329C5×C22⋊C4C22×D314yes—
330C42×C5—34no—
331C22⋊Dic5—34no—
332C22⋊Dic5—34no—
333C22⋊Dic5—34no—
334C22⋊Dic5—34no—
335C22⋊Dic5C22×D314yes—
336C22⋊Dic5C22×D314yes—
337C4⋊Dic5—34no—
338C4⋊Dic5—34no—
339C4⋊Dic5—34no—
340C4⋊Dic5C22×D314yes—
341#683—34no—
342#683—34no—
343#683—34no—
344#683—34no—
345#683—34no—
346#683—34no—
347#683C22×D314yes—
348#683C22×D314yes—
349C4×Dic5—34no—
350C4×Dic5—34no—
351C4×Dic5—34no—
352C4×Dic5—34no—
353C4×Dic5—34no—
354C4×Dic5C22×D314yes—
355#556—1516no—
356C2×C4⋊Q8—151no—
357C2×#126—51no—
358C2×#126—151no—
359C2×#126—151no—
360C2×#126—151no—
361C2×#124—31no—
362C2×#124—151no—
363C2×C22⋊Q8—151no—
364C2×C22⋊Q8—151no—
365C2×C4×Q8—151no—
366C2×C4×Q8—151no—
367C2×C4×Q8—151no—
368C2×C4×D4—151no—
369C2×#117—151no—
370C2×#117—151no—
371C22×C3×C5—22no—
372C22×C3×C5—22no—
373C22×C3×C5—22no—
374C22×C3×C5—44no—
375C22×C3×C5C2×#4112yes—
376C22×C3×C5C2×#4112yes—
377C22×C3×C52−1+412yes—
378C22×C3×C5C2511yescharacteristic
379C2×C5×D3—22no—
380C2×C5×D3—22no—
381C2×C5×D3—22no—
382C2×C5×D3—44no—
383C3×C4×C5—22no—
384C3×C4×C5—22no—
385Dic15—22no—
386Dic15—22no—
387Dic15—22no—
388Dic15C2×#4114yes—
389C3×Dic5—22no—
390C3×Dic5—22no—
391C3×Dic5—22no—
392C3×Dic5—22no—
393C5×Dic3—22no—
394C5×Dic3—22no—
395C5×Dic3C2×#4114yes—
396C24×C3C22×D511yescharacteristic
397C23×D3C22×D511yescharacteristic
398C22×C3×C4—51no—
399C22×C3×C4—51no—
400C22×C3×C4—51no—
401C22×C3×C4—51no—
402C22×C3×C4C22×D511yescharacteristic
403C22×C3×C4C22×D511yescharacteristic
404C2×#67—24no—
405C2×#67C22×D514yes—
406C22×Dic3—51no—
407C22×Dic3—54no—
408C22×Dic3—51no—
409C22×Dic3—51no—
410C22×Dic3—51no—
411C22×Dic3—104no—
412C22×Dic3C22×D511yescharacteristic
413C22×Dic3C22×D511yescharacteristic
414C22×Dic3C22×D511yescharacteristic
415C2×C4×D3—54no—
416C2×C4×D3—104no—
417C2×Dic6—24no—
418C2×Dic6—54no—
419C2×Dic6—54no—
420C2×Dic6—104no—
421C2×Dic6—104no—
422C2×Dic6C22×D514yes—
423C3×C4⋊C4—54no—
424C3×C4⋊C4—54no—
425C3×C4⋊C4—54no—
426C3×C22⋊C4—54no—
427C3×C22⋊C4—54no—
428C3×C22⋊C4C22×D514yes—
429C3×C42—54no—
430#217—54no—
431#217C22×D514yes—
432(C2×D3)⋊C4—54no—
433(C2×D3)⋊C4—54no—
434(C2×D3)⋊C4—54no—
435(C2×D3)⋊C4C22×D514yes—
436(C2×D3)⋊C4C22×D514yes—
437C4⋊Dic3—54no—
438C4⋊Dic3—54no—
439Dic3⋊C4—54no—
440Dic3⋊C4—54no—
441Dic3⋊C4—54no—
442Dic3⋊C4—54no—
443Dic3⋊C4—54no—
444Dic3⋊C4—54no—
445Dic3⋊C4—54no—
446C4×Dic3—54no—
447C4×Dic3—54no—
448C4×Dic3—54no—
449C4×Dic3—54no—
450C4×Dic3—54no—
451C4×Dic3C22×D514yes—
452C23×C5—22no—
453C23×C5—22no—
454C23×C5—22no—
455C23×C5—32no—
456C23×C5—62no—
457C23×C5—62no—
458C23×C5—62no—
459C23×C5C23×D312yes—
460C23×C5C23×D311yescharacteristic
461C5×Q8—68no—
462C5×D4—68no—
463C2×C4×C5—22no—
464C2×C4×C5—22no—
465C2×C4×C5—34no—
466C2×C4×C5—32no—
467C2×C4×C5—32no—
468C2×C4×C5—32no—
469C2×C4×C5—62no—
470C2×C4×C5—62no—
471C2×C4×C5C23×D312yes—
472C2×C4×C5C23×D312yes—
473C2×Dic5—22no—
474C2×Dic5—22no—
475C2×Dic5—22no—
476C2×Dic5—22no—
477C2×Dic5—34no—
478C2×Dic5—32no—
479C2×Dic5—32no—
480C2×Dic5—32no—
481C2×Dic5—32no—
482C2×Dic5—68no—
483C2×Dic5—68no—
484C2×Dic5—62no—
485C2×Dic5—62no—
486C2×Dic5—62no—
487C2×Dic5C23×D312yes—
488C2×Dic5C23×D312yes—
489C2×Dic5C23×D312yes—
490C2×Dic5C23×D312yes—
491Dic10—68no—
492Dic10—68no—
493C22×Q8—31no—
494C22×Q8—151no—
495C22×Q8—151no—
496C22×D4—31no—
497C23×C4—151no—
498C23×C4—151no—
499C4⋊Q8—158no—
500#126—58no—
501#126—158no—
502#126—158no—
503#126—158no—
504#124—38no—
505#124—158no—
506C22⋊Q8—158no—
507C22⋊Q8—158no—
508C4×Q8—158no—
509C4×Q8—158no—
510C4×Q8—158no—
511C4×D4—158no—
512#117—158no—
513#117—158no—
514C2×C4⋊C4—51no—
515C2×C4⋊C4—51no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—151no—
518C2×C4⋊C4—151no—
519C2×C4⋊C4—151no—
520C2×C4⋊C4—151no—
521C2×C4⋊C4—151no—
522C2×C4⋊C4—151no—
523C2×C4⋊C4—151no—
524C2×C4⋊C4—151no—
525C2×C4⋊C4—151no—
526C2×C22⋊C4—31no—
527C2×C22⋊C4—31no—
528C2×C22⋊C4—31no—
529C2×C22⋊C4—51no—
530C2×C22⋊C4—51no—
531C2×C22⋊C4—151no—
532C2×C22⋊C4—151no—
533C2×C22⋊C4—151no—
534C2×C22⋊C4—151no—
535C2×C22⋊C4D3×D511yescharacteristic
536C2×C42—31no—
537C2×C42—51no—
538C2×C42—151no—
539C2×C42—151no—
540C2×C42—151no—
541C2×C42—151no—
542C2×C42—151no—
543C2×C3×C5—42no—
544C2×C3×C5#55614yescomplemented
545C2×C3×C5C22×#4111yescharacteristic
546C2×C3×C5C22×#4111yescharacteristic
547C2×C3×C5C2×2−1+411yescharacteristic
548C5×D3—42no—
549C23×C3—22no—
550C23×C3—22no—
551C23×C3—22no—
552C23×C3C23×D512yes—
553C23×C3C23×D511yescharacteristic
554C22×D3—22no—
555C22×D3—22no—
556C22×D3—22no—
557C22×D3C23×D512yes—
558C2×C3×C4—22no—
559C2×C3×C4—22no—
560C2×C3×C4—52no—
561C2×C3×C4—52no—
562C2×C3×C4—52no—
563C2×C3×C4—52no—
564C2×C3×C4—102no—
565C2×C3×C4—102no—
566C2×C3×C4—102no—
567C2×C3×C4—102no—
568C2×C3×C4C23×D512yes—
569C2×C3×C4C23×D512yes—
570#67—28no—
571C2×Dic3—22no—
572C2×Dic3—22no—
573C2×Dic3—54no—
574C2×Dic3—52no—
575C2×Dic3—52no—
576C2×Dic3—52no—
577C2×Dic3—52no—
578C2×Dic3—108no—
579C2×Dic3—102no—
580C2×Dic3—102no—
581C2×Dic3—102no—
582C2×Dic3#71114yes—
583C2×Dic3C23×D512yes—
584C2×Dic3C23×D512yes—
585C2×Dic3C23×D512yes—
586C4×D3—108no—
587Dic6—28no—
588Dic6—108no—
589Dic6—108no—
590C22×C5—22no—
591C22×C5—22no—
592C22×C5—22no—
593C22×C5—44no—
594C22×C5—62no—
595C22×C5—62no—
596C22×C5—62no—
597C22×C5—124no—
598C22×C5D3×#4112yes—
599C22×C5D3×#4112yes—
600C22×C5#101012yes—
601C22×C5C24×D311yescharacteristic
602C4×C5—22no—
603C4×C5—22no—
604C4×C5—34no—
605C4×C5—62no—
606C4×C5—62no—
607Dic5—22no—
608Dic5—22no—
609Dic5—22no—
610Dic5—22no—
611Dic5—34no—
612Dic5—62no—
613Dic5—62no—
614Dic5—62no—
615C24—31no—
616C24C2×D3×D511yescharacteristic
617C2×Q8—34no—
618C2×Q8—64no—
619C2×Q8—154no—
620C2×Q8—154no—
621C2×Q8—304no—
622C2×Q8—304no—
623C2×D4—34no—
624C2×D4—64no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—51no—
629C22×C4—51no—
630C22×C4—51no—
631C22×C4—51no—
632C22×C4—154no—
633C22×C4—151no—
634C22×C4—154no—
635C22×C4—151no—
636C22×C4—151no—
637C22×C4—151no—
638C22×C4—304no—
639C22×C4—304no—
640C22×C4C2×D3×D511yescharacteristic
641C22×C4C2×D3×D511yescharacteristic
642C4⋊C4—54no—
643C4⋊C4—54no—
644C4⋊C4—54no—
645C4⋊C4—154no—
646C4⋊C4—154no—
647C4⋊C4—154no—
648C4⋊C4—154no—
649C4⋊C4—154no—
650C4⋊C4—154no—
651C4⋊C4—154no—
652C4⋊C4—154no—
653C4⋊C4—154no—
654C22⋊C4—34no—
655C22⋊C4—34no—
656C22⋊C4—34no—
657C22⋊C4—54no—
658C22⋊C4—54no—
659C22⋊C4—154no—
660C22⋊C4—154no—
661C22⋊C4—154no—
662C22⋊C4—154no—
663C22⋊C4C2×D3×D514yes—
664C42—34no—
665C42—54no—
666C42—154no—
667C42—154no—
668C42—154no—
669C42—154no—
670C42—154no—
671C3×C5C2×#55611yescharacteristic, complemented, Hall
672C22×C3—22no—
673C22×C3—22no—
674C22×C3—22no—
675C22×C3—44no—
676C22×C3C2×#71112yes—
677C22×C3D5×#4112yes—
678C22×C3#415012yes—
679C22×C3C24×D511yescharacteristic
680C2×D3—22no—
681C2×D3—22no—
682C2×D3—22no—
683C2×D3—44no—
684C3×C4—22no—
685C3×C4—22no—
686C3×C4—102no—
687C3×C4—102no—
688C3×C4—102no—
689C3×C4—102no—
690Dic3—22no—
691Dic3—22no—
692Dic3—54no—
693Dic3—102no—
694Dic3—102no—
695Dic3—102no—
696Dic3C2×#71114yes—
697C2×C5—42no—
698C2×C5—122no—
699C2×C5#570214yescomplemented
700C2×C5C2×D3×#4111yescharacteristic
701C2×C5C2×D3×#4111yescharacteristic
702C2×C5C2×#101011yescharacteristic
703C23—22no—
704C23—22no—
705C23—22no—
706C23—32no—
707C23—62no—
708C23—62no—
709C23—62no—
710C23C22×D3×D512yes—
711C23C22×D3×D511yescharacteristic
712Q8—68no—
713Q8—308no—
714Q8—308no—
715D4—68no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—34no—
719C2×C4—32no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—52no—
723C2×C4—52no—
724C2×C4—52no—
725C2×C4—52no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—102no—
729C2×C4—102no—
730C2×C4—102no—
731C2×C4—102no—
732C2×C4—154no—
733C2×C4—152no—
734C2×C4—152no—
735C2×C4—152no—
736C2×C4—152no—
737C2×C4—308no—
738C2×C4—308no—
739C2×C4—302no—
740C2×C4—302no—
741C2×C4—302no—
742C2×C4C22×D3×D512yes—
743C2×C4C22×D3×D512yes—
744C2×C3—42no—
745C2×C3#6600514yescomplemented
746C2×C3C22×#71111yescharacteristic
747C2×C3C2×D5×#4111yescharacteristic
748C2×C3C2×#415011yescharacteristic
749D3—42no—
750C5C2×#570211yescharacteristic, complemented, Sylow
751C22—22no—
752C22—22no—
753C22—22no—
754C22—44no—
755C22—62no—
756C22—62no—
757C22—62no—
758C22—124no—
759C22#9200112yes—
760C22D3×#71112yes—
761C22#9202412yes—
762C22C23×D3×D511yescharacteristic
763C4—22no—
764C4—22no—
765C4—34no—
766C4—62no—
767C4—62no—
768C4—102no—
769C4—102no—
770C4—102no—
771C4—102no—
772C4—154no—
773C4—302no—
774C4—302no—
775C4—302no—
776C3C2×#6600511yescharacteristic, complemented, Sylow
777C2—42no—
778C2—122no—
779C2#1175301014yesdirect product factor
780C2C2×#9200111yescharacteristic
781C2C2×D3×#71111yescharacteristic
782C2C2×#9202411yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC22×C5×#67C22
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#556
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
3. C2×C3×#4025C2semidirect
5. C2×#91532C2semidirect
6. C2×#91530C2semidirect
8. C2×#91432C2semidirect
9. C2×#91398C2semidirect
10. C2×#91342C2semidirect
11. C2×#91341C2semidirect
12. C2×#91340C2semidirect
13. C2×Dic5×Dic6C2semidirect
14. C2×#91329C2semidirect
15. C2×#91324C2semidirect
16. #11753010C2direct (N × H)
29. #91767C22semidirect
41. C3×#4025C22semidirect
52. #91532C22semidirect
53. #91530C22semidirect
60. #91432C22semidirect
61. #91398C22semidirect
62. #91342C22semidirect
63. #91341C22semidirect
64. #91340C22semidirect
65. Dic5×Dic6C22semidirect
66. #91329C22semidirect
67. #91324C22semidirect
78. C2×#4025D3semidirect
200. #4025C2×D3semidirect
544. C2×C3×C5#556semidirect
671. C3×C5C2×#556semidirect
699. C2×C5#5702semidirect
745. C2×C3#66005semidirect
750. C5C2×#5702semidirect
776. C3C2×#66005semidirect
779. C2#11753010direct (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×#8852
C2×C3×#40252
C2×#67⋊Dic52
C2×#915322
C2×#915302
C2×#915252
C2×#914322
C2×#913982
C2×#913422
C2×#913412
C2×#913402
C2×Dic5×Dic62
C2×#913292
C2×#913242
#117530102
C2×#660053
C2×#57025