Finite Group Databasebeta

← C2×#11753460 #14480175

Subgroups — C2×#11753460 #14480175

Order 1920.

2336 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91776C211yesmaximal, characteristic, complemented
2C2×C5×#896C211yesmaximal, characteristic
3C2×C3×#4035C211yesmaximal, characteristic, complemented
4C2×#91436C211yesmaximal, characteristic
5C2×#91432C211yesmaximal, characteristic
6C2×#91400C211yesmaximal, characteristic
7C2×#91400C211yesmaximal, characteristic
8C2×C4×D3×Dic5C211yesmaximal, characteristic
9C2×#91378C211yesmaximal, characteristic, complemented
10C2×#91352C211yesmaximal, characteristic
11C2×#91344C211yesmaximal, characteristic, complemented
12C2×#91329C211yesmaximal, characteristic, complemented
13C2×#91328C211yesmaximal, characteristic, complemented
14C2×#91325C211yesmaximal, characteristic, complemented
15C2×#91325C211yesmaximal, characteristic, complemented
16#11753460C2116yesmaximal, direct product factor
17C2×#65956—31nomaximal, Hall
18C22×Dic30C2211yescharacteristic
19C22×C4×C5×D3C2211yescharacteristic
20C22×C5×Dic6C2211yescharacteristic
21C22×#1204C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C2×C4×Dic15C2211yescharacteristic
29C2×C4×Dic15C2211yescharacteristic
30C2×C4×Dic15C2211yescharacteristic
31#91776C2218yescomplemented
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C5×Dic3⋊C4C2211yescharacteristic
36C5×#896C2218yes—
37C2×C3×C4⋊Dic5C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C3×#4035C2218yescomplemented
44C2×Dic3⋊Dic5C2211yescharacteristic
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×#6669C2211yescharacteristic
47C2×#6669C2211yescharacteristic
48C2×#6668C2211yescharacteristic
49C2×#6668C2211yescharacteristic
50C2×(C2×D3)⋊Dic5C2211yescharacteristic
51C2×(C2×D3)⋊Dic5C2211yescharacteristic
52C2×Dic3×Dic5C2211yescharacteristic
53C2×Dic3×Dic5C2211yescharacteristic
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91436C2218yes—
57#91432C2218yes—
58#91400C2218yes—
59#91400C2218yes—
60C4×D3×Dic5C2218yes—
61#91378C2218yescomplemented
62#91352C2218yes—
63#91344C2218yescomplemented
64#91329C2218yescomplemented
65#91328C2218yescomplemented
66#91325C2218yescomplemented
67#91325C2218yescomplemented
68C2×#5688—51nomaximal, Hall
69C2×C5×C22⋊Q8—31no—
70C2×Q8×Dic5—31no—
71C2×#4090—31no—
72C2×#4070—31no—
73C22×C4×Dic5—31no—
74#65956—316no—
75C2×#4035—31no—
76C2×#4035D311yescharacteristic, complemented
77C2×#4034—31no—
78C2×#4033—31no—
79C2×#4033—31no—
80C2×#4033—31no—
81C2×#4024—31no—
82C2×#4024—31no—
83C2×#4023—31no—
84C2×#4023—31no—
85C23×C5×D3C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C2×Dic30—24no—
94C2×Dic30C2314yes—
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C5×Dic3C2311yescharacteristic
98C2×C4×C5×D3—24no—
99C2×C4×C5×D3C2314yes—
100C2×C5×Dic6—24no—
101C2×C5×Dic6C2314yes—
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C2×#1204—24no—
107C2×#1204—24no—
108C2×#1204C2314yes—
109C2×#1204C2314yes—
110C2×D3×Dic5—24no—
111C2×D3×Dic5Q818yescomplemented
112C2×D3×Dic5C2314yes—
113C2×D3×Dic5C2314yes—
114C3×C5×C4⋊C4C2314yes—
115#6712C2314yes—
116#6712C2314yes—
117C4×Dic15C2314yes—
118C4×Dic15C2314yes—
119C4×Dic15C2314yes—
120C5×(C2×D3)⋊C4C2314yes—
121C5×(C2×D3)⋊C4C2314yes—
122C5×Dic3⋊C4C2314yes—
123C5×Dic3⋊C4C2314yes—
124C3×C4⋊Dic5C2314yes—
125C3×#683C2314yes—
126C3×#683C2314yes—
127C3×#683C2314yes—
128C3×#683C2314yes—
129C3×C4×Dic5C2314yes—
130Dic3⋊Dic5C2314yes—
131Dic3⋊Dic5C2314yes—
132#6669C2314yes—
133#6669C2314yes—
134#6668C2314yes—
135#6668C2314yes—
136(C2×D3)⋊Dic5C2314yes—
137(C2×D3)⋊Dic5C2314yes—
138Dic3×Dic5C2314yes—
139Dic3×Dic5C2314yes—
140Dic3×Dic5C2314yes—
141Dic3×Dic5C2314yes—
142C2×C3×#125—51no—
143#5688—516no—
144C2×#896—51no—
145C2×#896—51no—
146C2×#896—51no—
147C2×#896D511yescharacteristic
148C2×#892—51no—
149C2×#892—51no—
150C2×#888—51no—
151C2×#888—51no—
152C2×#887—51no—
153C2×#887—51no—
154C2×#887—51no—
155C2×#887—51no—
156C2×C42×D3—51no—
157C2×#870—51no—
158C22×C5×Q8—31no—
159C23×C4×C5—31no—
160C23×Dic5—31no—
161C23×Dic5—31no—
162C22×Dic10—31no—
163C22×Dic10—31no—
164C22×Dic10—31no—
165C5×C22⋊Q8—38no—
166C2×C5×C4⋊C4—31no—
167C2×C5×C4⋊C4—31no—
168C2×C5×C4⋊C4C2×D311yescharacteristic
169C2×C5×C22⋊C4—31no—
170C2×C5×C22⋊C4—31no—
171C2×C22⋊Dic5—31no—
172C2×C22⋊Dic5—31no—
173Q8×Dic5—38no—
174#4090—38no—
175C2×C4⋊Dic5—31no—
176C2×C4⋊Dic5—31no—
177C2×C4⋊Dic5C2×D311yescharacteristic
178#4070—38no—
179C2×#683—31no—
180C2×#683—31no—
181C2×#683—31no—
182C2×#683—31no—
183C2×#683—31no—
184C2×#683—31no—
185C2×#683C2×D311yescharacteristic
186C2×#683C2×D311yescharacteristic
187C2×#683C2×D311yescharacteristic
188C2×#683C2×D311yescharacteristic
189C2×C4×Dic5—31no—
190C2×C4×Dic5—31no—
191C2×C4×Dic5—31no—
192C2×C4×Dic5—31no—
193C2×C4×Dic5—31no—
194C2×C4×Dic5—31no—
195C2×C4×Dic5—31no—
196C2×C4×Dic5—38no—
197C2×C4×Dic5C2×D311yescharacteristic
198#4035—38no—
199#4035C2×D318yescomplemented
200#4034—38no—
201#4033—38no—
202#4033—38no—
203#4033—38no—
204#4024—38no—
205#4024—38no—
206#4023—38no—
207#4023—38no—
208C2×#533—151noSylow
209C23×C3×C5C2411yescharacteristic
210C22×C5×D3—22no—
211C22×C5×D3—22no—
212C22×C5×D3C2×Q814yes—
213C22×C5×D3C2412yes—
214C2×C3×C4×C5—22no—
215C2×C3×C4×C5—22no—
216C2×C3×C4×C5—22no—
217C2×C3×C4×C5C2412yes—
218C2×C3×C4×C5C2412yes—
219C2×C3×C4×C5C2412yes—
220C2×Dic15—22no—
221C2×Dic15—22no—
222C2×Dic15C2×Q814yes—
223C2×Dic15#4114yes—
224C2×Dic15C2412yes—
225C2×Dic15C2412yes—
226C2×Dic15C2412yes—
227C2×Dic15C2412yes—
228Dic30—28no—
229C2×C5×Dic3—22no—
230C2×C5×Dic3—22no—
231C2×C5×Dic3#4114yes—
232C2×C5×Dic3C2412yes—
233C2×C5×Dic3C2412yes—
234C2×C5×Dic3C2412yes—
235C4×C5×D3—28no—
236C5×Dic6—28no—
237C2×C3×Dic5—22no—
238C2×C3×Dic5—22no—
239C2×C3×Dic5—22no—
240C2×C3×Dic5C2×Q814yes—
241C2×C3×Dic5C2412yes—
242C2×C3×Dic5C2412yes—
243C2×C3×Dic5C2412yes—
244C2×C3×Dic5C2412yes—
245#1204—28no—
246#1204—28no—
247D3×Dic5—28no—
248D3×Dic5C2×Q8116yescomplemented
249C22×C4×D3—51no—
250C22×C4×D3—51no—
251C22×C4×D3C2×D511yescharacteristic
252C22×Dic6—51no—
253C22×Dic6—51no—
254C22×Dic6—51no—
255C22×Dic6C2×D511yescharacteristic
256C3×#125—58no—
257C2×C3×C4⋊C4—51no—
258C2×C3×C4⋊C4—51no—
259C2×C3×C4⋊C4—51no—
260C2×C3×C4⋊C4—51no—
261C2×C3×C4⋊C4—51no—
262C2×C3×C4⋊C4C2×D511yescharacteristic
263C2×C3×C42—51no—
264C2×(C2×D3)⋊C4—51no—
265C2×(C2×D3)⋊C4—51no—
266C2×(C2×D3)⋊C4C2×D511yescharacteristic
267C2×(C2×D3)⋊C4C2×D511yescharacteristic
268C2×C4⋊Dic3—51no—
269C2×C4⋊Dic3—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4—51no—
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4—51no—
276C2×Dic3⋊C4C2×D511yescharacteristic
277C2×Dic3⋊C4C2×D511yescharacteristic
278C2×C4×Dic3—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3—51no—
281C2×C4×Dic3—51no—
282C2×C4×Dic3—51no—
283C2×C4×Dic3—51no—
284C2×C4×Dic3—51no—
285#896—58no—
286#896—58no—
287#896—58no—
288#896C2×D518yes—
289#892—58no—
290#892—58no—
291#888—58no—
292#888—58no—
293#887—58no—
294#887—58no—
295#887—58no—
296#887—58no—
297C42×D3—58no—
298#870—58no—
299C24×C5—31no—
300C2×C5×Q8—34no—
301C2×C5×Q8—64no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5—34no—
306C22×C4×C5—64no—
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×Dic5—31no—
311C22×Dic5—31no—
312C22×Dic5—38no—
313C22×Dic5—34no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5—34no—
317C22×Dic5—64no—
318C22×Dic5C22×D311yescharacteristic
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C2×Dic10—34no—
323C2×Dic10—34no—
324C2×Dic10—34no—
325C2×Dic10—64no—
326C2×Dic10—64no—
327C2×Dic10—64no—
328C5×C4⋊C4—34no—
329C5×C4⋊C4—34no—
330C5×C4⋊C4C22×D314yes—
331C5×C22⋊C4—34no—
332C5×C22⋊C4—34no—
333C22⋊Dic5—34no—
334C22⋊Dic5—34no—
335C4⋊Dic5—34no—
336C4⋊Dic5—34no—
337C4⋊Dic5C22×D314yes—
338#683—34no—
339#683—34no—
340#683—34no—
341#683—34no—
342#683—34no—
343#683—34no—
344#683C22×D314yes—
345#683C22×D314yes—
346#683C22×D314yes—
347#683C22×D314yes—
348C4×Dic5—34no—
349C4×Dic5—34no—
350C4×Dic5—34no—
351C4×Dic5—34no—
352C4×Dic5—34no—
353C4×Dic5—34no—
354C4×Dic5—34no—
355C4×Dic5C22×D314yes—
356#533—1516no—
357C2×C4⋊Q8—151no—
358C2×C4⋊Q8—151no—
359C2×#125—51no—
360C2×#125—151no—
361C2×C22⋊Q8—31no—
362C2×C22⋊Q8—151no—
363C2×C22⋊Q8—151no—
364C2×C22⋊Q8—151no—
365C2×C4×Q8—151no—
366C2×C4×Q8—151no—
367C2×C4×Q8—151no—
368C2×C4×Q8—151no—
369C2×#117—151no—
370C2×#117—151no—
371C22×C42—151no—
372C22×C3×C5C22×Q812yes—
373C22×C3×C5C2×#4112yes—
374C22×C3×C5C2×#4112yes—
375C22×C3×C5C2511yescharacteristic
376C2×C5×D3—28no—
377C2×C5×D3—22no—
378C2×C5×D3—22no—
379C2×C5×D3C22×Q814yes—
380C3×C4×C5—22no—
381C3×C4×C5—22no—
382C3×C4×C5—22no—
383Dic15—22no—
384Dic15—22no—
385Dic15C22×Q814yes—
386Dic15C2×#4114yes—
387C3×Dic5—22no—
388C3×Dic5—22no—
389C3×Dic5—22no—
390C3×Dic5C22×Q814yes—
391C5×Dic3—22no—
392C5×Dic3—22no—
393C5×Dic3C2×#4114yes—
394C23×D3C22×D511yescharacteristic
395C22×C3×C4—51no—
396C22×C3×C4—51no—
397C22×C3×C4—51no—
398C22×C3×C4—51no—
399C22×C3×C4C22×D511yescharacteristic
400C22×C3×C4C22×D511yescharacteristic
401C22×C3×C4C22×D511yescharacteristic
402C22×Dic3—51no—
403C22×Dic3—51no—
404C22×Dic3—51no—
405C22×Dic3—51no—
406C22×Dic3C22×D511yescharacteristic
407C22×Dic3C22×D511yescharacteristic
408C22×Dic3C22×D511yescharacteristic
409C2×C4×D3—24no—
410C2×C4×D3—58no—
411C2×C4×D3—54no—
412C2×C4×D3—54no—
413C2×C4×D3—104no—
414C2×C4×D3C22×D514yes—
415C2×Dic6—24no—
416C2×Dic6—54no—
417C2×Dic6—54no—
418C2×Dic6—54no—
419C2×Dic6—104no—
420C2×Dic6—104no—
421C2×Dic6—104no—
422C2×Dic6C22×D514yes—
423C3×C4⋊C4—54no—
424C3×C4⋊C4—54no—
425C3×C4⋊C4—54no—
426C3×C4⋊C4—54no—
427C3×C4⋊C4—54no—
428C3×C4⋊C4C22×D514yes—
429C3×C42—54no—
430(C2×D3)⋊C4—54no—
431(C2×D3)⋊C4—54no—
432(C2×D3)⋊C4C22×D514yes—
433(C2×D3)⋊C4C22×D514yes—
434C4⋊Dic3—54no—
435C4⋊Dic3—54no—
436Dic3⋊C4—54no—
437Dic3⋊C4—54no—
438Dic3⋊C4—54no—
439Dic3⋊C4—54no—
440Dic3⋊C4—54no—
441Dic3⋊C4—54no—
442Dic3⋊C4C22×D514yes—
443Dic3⋊C4C22×D514yes—
444C4×Dic3—54no—
445C4×Dic3—54no—
446C4×Dic3—54no—
447C4×Dic3—54no—
448C4×Dic3—54no—
449C4×Dic3—54no—
450C4×Dic3—54no—
451C23×C5—34no—
452C23×C5—32no—
453C23×C5—62no—
454C23×C5—62no—
455C23×C5C23×D311yescharacteristic
456C5×Q8—68no—
457C2×C4×C5—22no—
458C2×C4×C5—22no—
459C2×C4×C5—22no—
460C2×C4×C5—34no—
461C2×C4×C5—32no—
462C2×C4×C5—32no—
463C2×C4×C5—32no—
464C2×C4×C5—68no—
465C2×C4×C5—62no—
466C2×C4×C5—62no—
467C2×C4×C5C23×D312yes—
468C2×C4×C5C23×D312yes—
469C2×C4×C5C23×D312yes—
470C2×Dic5—22no—
471C2×Dic5—22no—
472C2×Dic5—22no—
473C2×Dic5—34no—
474C2×Dic5—34no—
475C2×Dic5—32no—
476C2×Dic5—32no—
477C2×Dic5—316no—
478C2×Dic5—32no—
479C2×Dic5—32no—
480C2×Dic5—68no—
481C2×Dic5—62no—
482C2×Dic5—62no—
483C2×Dic5D3×Q814yes—
484C2×Dic5C23×D312yes—
485C2×Dic5C23×D312yes—
486C2×Dic5C23×D312yes—
487C2×Dic5C23×D312yes—
488Dic10—68no—
489Dic10—68no—
490Dic10—68no—
491C22×Q8—31no—
492C22×Q8—151no—
493C22×Q8—151no—
494C22×Q8—151no—
495C23×C4—31no—
496C23×C4—151no—
497C23×C4—151no—
498C4⋊Q8—158no—
499C4⋊Q8—158no—
500#125—58no—
501#125—158no—
502C22⋊Q8—38no—
503C22⋊Q8—158no—
504C22⋊Q8—158no—
505C22⋊Q8—158no—
506C4×Q8—158no—
507C4×Q8—158no—
508C4×Q8—158no—
509C4×Q8—158no—
510#117—158no—
511#117—158no—
512C2×C4⋊C4—31no—
513C2×C4⋊C4—31no—
514C2×C4⋊C4—51no—
515C2×C4⋊C4—51no—
516C2×C4⋊C4—51no—
517C2×C4⋊C4—51no—
518C2×C4⋊C4—51no—
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×C4⋊C4—151no—
527C2×C4⋊C4D3×D511yescharacteristic
528C2×C22⋊C4—31no—
529C2×C22⋊C4—31no—
530C2×C22⋊C4—151no—
531C2×C22⋊C4—151no—
532C2×C42—51no—
533C2×C42—158no—
534C2×C42—151no—
535C2×C42—151no—
536C2×C42—151no—
537C2×C42—151no—
538C2×C42—151no—
539C2×C42—151no—
540C2×C42—151no—
541C2×C3×C5#53314yescomplemented
542C2×C3×C5C23×Q811yescharacteristic
543C2×C3×C5C22×#4111yescharacteristic
544C2×C3×C5C22×#4111yescharacteristic
545C5×D3—24no—
546C23×C3C23×D511yescharacteristic
547C22×D3—22no—
548C22×D3—22no—
549C22×D3Q8×D514yes—
550C22×D3C23×D512yes—
551C2×C3×C4—22no—
552C2×C3×C4—22no—
553C2×C3×C4—22no—
554C2×C3×C4—54no—
555C2×C3×C4—52no—
556C2×C3×C4—52no—
557C2×C3×C4—52no—
558C2×C3×C4—52no—
559C2×C3×C4—102no—
560C2×C3×C4—102no—
561C2×C3×C4—102no—
562C2×C3×C4C23×D512yes—
563C2×C3×C4C23×D512yes—
564C2×C3×C4C23×D512yes—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—54no—
568C2×Dic3—54no—
569C2×Dic3—52no—
570C2×Dic3—52no—
571C2×Dic3—52no—
572C2×Dic3—52no—
573C2×Dic3—102no—
574C2×Dic3—102no—
575C2×Dic3#71114yes—
576C2×Dic3C23×D512yes—
577C2×Dic3C23×D512yes—
578C2×Dic3C23×D512yes—
579C4×D3—28no—
580C4×D3—516no—
581C4×D3—108no—
582Dic6—28no—
583Dic6—108no—
584Dic6—108no—
585Dic6—108no—
586C22×C5—34no—
587C22×C5—68no—
588C22×C5—62no—
589C22×C5—62no—
590C22×C5C2×D3×Q812yes—
591C22×C5D3×#4112yes—
592C22×C5D3×#4112yes—
593C22×C5C24×D311yescharacteristic
594C4×C5—22no—
595C4×C5—22no—
596C4×C5—22no—
597C4×C5—34no—
598C4×C5—62no—
599C4×C5—62no—
600Dic5—22no—
601Dic5—22no—
602Dic5—22no—
603Dic5—34no—
604Dic5—34no—
605Dic5—62no—
606Dic5—62no—
607Dic5C2×D3×Q814yes—
608C24—31no—
609C2×Q8—34no—
610C2×Q8—64no—
611C2×Q8—154no—
612C2×Q8—154no—
613C2×Q8—154no—
614C2×Q8—304no—
615C2×Q8—304no—
616C2×Q8—304no—
617C22×C4—31no—
618C22×C4—31no—
619C22×C4—31no—
620C22×C4—34no—
621C22×C4—51no—
622C22×C4—51no—
623C22×C4—51no—
624C22×C4—51no—
625C22×C4—64no—
626C22×C4—154no—
627C22×C4—158no—
628C22×C4—154no—
629C22×C4—151no—
630C22×C4—151no—
631C22×C4—151no—
632C22×C4—151no—
633C22×C4—304no—
634C22×C4C2×D3×D511yescharacteristic
635C22×C4C2×D3×D511yescharacteristic
636C22×C4C2×D3×D511yescharacteristic
637C4⋊C4—34no—
638C4⋊C4—34no—
639C4⋊C4—54no—
640C4⋊C4—54no—
641C4⋊C4—54no—
642C4⋊C4—54no—
643C4⋊C4—54no—
644C4⋊C4—154no—
645C4⋊C4—154no—
646C4⋊C4—154no—
647C4⋊C4—154no—
648C4⋊C4—154no—
649C4⋊C4—154no—
650C4⋊C4—154no—
651C4⋊C4—154no—
652C4⋊C4C2×D3×D514yes—
653C22⋊C4—34no—
654C22⋊C4—34no—
655C22⋊C4—154no—
656C22⋊C4—154no—
657C42—54no—
658C42—154no—
659C42—154no—
660C42—154no—
661C42—154no—
662C42—154no—
663C42—154no—
664C42—154no—
665C3×C5C2×#53311yescharacteristic, complemented, Hall
666C22×C3C2×#71112yes—
667C22×C3C2×Q8×D512yes—
668C22×C3D5×#4112yes—
669C22×C3C24×D511yescharacteristic
670C2×D3—28no—
671C2×D3—22no—
672C2×D3—22no—
673C2×D3C2×Q8×D514yes—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—54no—
678C3×C4—102no—
679C3×C4—102no—
680C3×C4—102no—
681Dic3—22no—
682Dic3—22no—
683Dic3—54no—
684Dic3—54no—
685Dic3—102no—
686Dic3—102no—
687Dic3C2×#71114yes—
688C2×C5—64no—
689C2×C5#568814yescomplemented
690C2×C5C22×D3×Q811yescharacteristic
691C2×C5C2×D3×#4111yescharacteristic
692C2×C5C2×D3×#4111yescharacteristic
693C23—34no—
694C23—32no—
695C23—62no—
696C23—62no—
697C23C22×D3×D511yescharacteristic
698Q8—68no—
699Q8—308no—
700Q8—308no—
701Q8—308no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—34no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—32no—
709C2×C4—54no—
710C2×C4—52no—
711C2×C4—52no—
712C2×C4—52no—
713C2×C4—52no—
714C2×C4—68no—
715C2×C4—62no—
716C2×C4—62no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—102no—
720C2×C4—1516no—
721C2×C4—154no—
722C2×C4—154no—
723C2×C4—152no—
724C2×C4—152no—
725C2×C4—152no—
726C2×C4—152no—
727C2×C4—308no—
728C2×C4—302no—
729C2×C4—302no—
730C2×C4C22×D3×D512yes—
731C2×C4C22×D3×D512yes—
732C2×C4C22×D3×D512yes—
733C2×C3#6595614yescomplemented
734C2×C3C22×#71111yescharacteristic
735C2×C3C22×Q8×D511yescharacteristic
736C2×C3C2×D5×#4111yescharacteristic
737D3—24no—
738C5C2×#568811yescharacteristic, complemented, Sylow
739C22—34no—
740C22—62no—
741C22—62no—
742C22—68no—
743C22#9201612yes—
744C22D3×#71112yes—
745C22D3×Q8×D512yes—
746C22C23×D3×D511yescharacteristic
747C4—22no—
748C4—22no—
749C4—22no—
750C4—34no—
751C4—54no—
752C4—62no—
753C4—62no—
754C4—102no—
755C4—102no—
756C4—102no—
757C4—154no—
758C4—154no—
759C4—302no—
760C4—302no—
761C3C2×#6595611yescharacteristic, complemented, Sylow
762C2—64no—
763C2#1175346014yesdirect product factor
764C2C2×#9201611yescharacteristic
765C2C2×D3×#71111yescharacteristic
766C2C2×D3×Q8×D511yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC23×C5×D3C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#533
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#91776C2semidirect
3. C2×C3×#4035C2semidirect
9. C2×#91378C2semidirect
11. C2×#91344C2semidirect
12. C2×#91329C2semidirect
13. C2×#91328C2semidirect
14. C2×#91325C2semidirect
15. C2×#91325C2semidirect
16. #11753460C2direct (N × H)
31. #91776C22semidirect
43. C3×#4035C22semidirect
61. #91378C22semidirect
63. #91344C22semidirect
64. #91329C22semidirect
65. #91328C22semidirect
66. #91325C22semidirect
67. #91325C22semidirect
76. C2×#4035D3semidirect
111. C2×D3×Dic5Q8semidirect
199. #4035C2×D3semidirect
248. D3×Dic5C2×Q8semidirect
541. C2×C3×C5#533semidirect
665. C3×C5C2×#533semidirect
689. C2×C5#5688semidirect
733. C2×C3#65956semidirect
738. C5C2×#5688semidirect
761. C3C2×#65956semidirect
763. C2#11753460direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917762
C2×C5×#8962
C2×C3×#40352
C2×#914362
C2×#914322
C2×#914002
C2×C4×D3×Dic52
C2×#913782
C2×#913522
C2×#913442
C2×#913292
C2×#913282
C2×#913252
#117534602
C2×#659563
C2×#56885