Finite Group Databasebeta

← C2×#11753462 #14481783

Subgroups — C2×#11753462 #14481783

Order 1920.

2160 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×#91777C211yesmaximal, characteristic, complemented
2C2×C5×#896C211yesmaximal, characteristic
3C2×C3×#4035C211yesmaximal, characteristic, complemented
4C2×#91432C211yesmaximal, characteristic
5C2×#91417C211yesmaximal, characteristic
6C2×#91400C211yesmaximal, characteristic
7C2×D3×#683C211yesmaximal, characteristic
8C2×#91398C211yesmaximal, characteristic
9C2×#91382C211yesmaximal, characteristic, complemented
10C2×#91376C211yesmaximal, characteristic, complemented
11C2×#91365C211yesmaximal, characteristic
12C2×#91339C211yesmaximal, characteristic, complemented
13C2×#91334C211yesmaximal, characteristic, complemented
14C2×#91329C211yesmaximal, characteristic, complemented
15C2×#91328C211yesmaximal, characteristic, complemented
16#11753462C2116yesmaximal, direct product factor
17C2×#65957—31nomaximal, Hall
18C22×Dic30C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C4×C5×D3C2211yescharacteristic
21C22×C5×Dic6C2211yescharacteristic
22C22×#1204C2211yescharacteristic
23C22×D3×Dic5C2211yescharacteristic
24C22×D3×Dic5C2211yescharacteristic
25C2×C3×C5×C4⋊C4C2211yescharacteristic
26C2×C4⋊Dic15C2211yescharacteristic
27C2×#6712C2211yescharacteristic
28C2×#6712C2211yescharacteristic
29C2×C4×Dic15C2211yescharacteristic
30#91777C2218yescomplemented
31C2×C5×(C2×D3)⋊C4C2211yescharacteristic
32C2×C5×(C2×D3)⋊C4C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C5×#896C2218yes—
36C2×C3×C4⋊Dic5C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×C4×Dic5C2211yescharacteristic
42C3×#4035C2218yescomplemented
43C2×Dic3⋊Dic5C2211yescharacteristic
44C2×#6669C2211yescharacteristic
45C2×#6669C2211yescharacteristic
46C2×#6669C2211yescharacteristic
47C2×#6668C2211yescharacteristic
48C2×#6668C2211yescharacteristic
49C2×#6668C2211yescharacteristic
50C2×#6668C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×(C2×D3)⋊Dic5C2211yescharacteristic
53C2×(C2×D3)⋊Dic5C2211yescharacteristic
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91432C2218yes—
57#91417C2218yes—
58#91400C2218yes—
59D3×#683C2218yes—
60#91398C2218yes—
61#91382C2218yescomplemented
62#91376C2218yescomplemented
63#91365C2218yes—
64#91339C2218yescomplemented
65#91334C2218yescomplemented
66#91329C2218yescomplemented
67#91328C2218yescomplemented
68C2×#5689—51nomaximal, Hall
69C2×C5×C22⋊Q8—31no—
70C2×#4090—31no—
71C2×#4090—31no—
72C2×#4070—31no—
73C22×#683—31no—
74#65957—316no—
75C2×#4035—31no—
76C2×#4035—31no—
77C2×#4035—31no—
78C2×#4035D311yescharacteristic, complemented
79C2×#4034—31no—
80C2×#4034—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—42no—
94C2×Dic30—42no—
95C2×Dic30C2314yes—
96C2×Dic30C2314yes—
97C22×C5×Dic3C2311yescharacteristic
98C22×C5×Dic3C2311yescharacteristic
99C22×C5×Dic3C2311yescharacteristic
100C2×C4×C5×D3—42no—
101C2×C4×C5×D3C2314yes—
102C2×C5×Dic6—42no—
103C2×C5×Dic6C2314yes—
104C22×C3×Dic5C2311yescharacteristic
105C22×C3×Dic5C2311yescharacteristic
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C2×#1204—42no—
109C2×#1204C2314yes—
110C2×D3×Dic5—42no—
111C2×D3×Dic5Q818yescomplemented
112C2×D3×Dic5C2314yes—
113C2×D3×Dic5C2314yes—
114C3×C5×C4⋊C4C2314yes—
115C4⋊Dic15C2314yes—
116#6712C2314yes—
117#6712C2314yes—
118C4×Dic15C2314yes—
119C5×(C2×D3)⋊C4C2314yes—
120C5×(C2×D3)⋊C4C2314yes—
121C5×Dic3⋊C4C2314yes—
122C5×Dic3⋊C4C2314yes—
123C3×C4⋊Dic5C2314yes—
124C3×#683C2314yes—
125C3×#683C2314yes—
126C3×#683C2314yes—
127C3×#683C2314yes—
128C3×C4×Dic5C2314yes—
129Dic3⋊Dic5C2314yes—
130#6669C2314yes—
131#6669C2314yes—
132#6669C2314yes—
133#6668C2314yes—
134#6668C2314yes—
135#6668C2314yes—
136#6668C2314yes—
137#6668C2314yes—
138(C2×D3)⋊Dic5C2314yes—
139(C2×D3)⋊Dic5C2314yes—
140Dic3×Dic5C2314yes—
141Dic3×Dic5C2314yes—
142C2×C3×#125—51no—
143#5689—516no—
144C2×#897—51no—
145C2×#897—51no—
146C2×#896—51no—
147C2×#896D511yescharacteristic
148C2×#892—51no—
149C2×D3×C4⋊C4—51no—
150C2×#890—51no—
151C2×#889—51no—
152C2×#889—51no—
153C2×#888—51no—
154C2×#888—51no—
155C2×#888—51no—
156C2×#872—51no—
157C2×#869—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—
173#4090—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×#683—31no—
186C2×#683—31no—
187C2×#683—31no—
188C2×#683—31no—
189C2×#683—38no—
190C2×#683C2×D311yescharacteristic
191C2×#683C2×D311yescharacteristic
192C2×#683C2×D311yescharacteristic
193C2×#683C2×D311yescharacteristic
194C2×C4×Dic5—31no—
195C2×C4×Dic5—31no—
196C2×C4×Dic5—31no—
197C2×C4×Dic5C2×D311yescharacteristic
198#4035—38no—
199#4035—38no—
200#4035—38no—
201#4035C2×D318yescomplemented
202#4034—38no—
203#4034—38no—
204#4024—38no—
205#4024—38no—
206#4023—38no—
207#4023—38no—
208C2×#544—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×Dic15—22no—
223C2×Dic15C2×Q814yes—
224C2×Dic15C2412yes—
225C2×Dic15C2412yes—
226C2×Dic15C2412yes—
227C2×Dic15C2412yes—
228Dic30—44no—
229Dic30—44no—
230C2×C5×Dic3—22no—
231C2×C5×Dic3—22no—
232C2×C5×Dic3—22no—
233C2×C5×Dic3C2412yes—
234C2×C5×Dic3C2412yes—
235C2×C5×Dic3C2412yes—
236C4×C5×D3—44no—
237C5×Dic6—44no—
238C2×C3×Dic5—22no—
239C2×C3×Dic5—22no—
240C2×C3×Dic5—22no—
241C2×C3×Dic5C2×Q814yes—
242C2×C3×Dic5C2412yes—
243C2×C3×Dic5C2412yes—
244C2×C3×Dic5C2412yes—
245C2×C3×Dic5C2412yes—
246#1204—44no—
247D3×Dic5—44no—
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×C4⋊Dic3—51no—
271C2×C4⋊Dic3—51no—
272C2×C4⋊Dic3—51no—
273C2×C4⋊Dic3—51no—
274C2×Dic3⋊C4—51no—
275C2×Dic3⋊C4—51no—
276C2×Dic3⋊C4—51no—
277C2×Dic3⋊C4—51no—
278C2×Dic3⋊C4—51no—
279C2×Dic3⋊C4—51no—
280C2×Dic3⋊C4C2×D511yescharacteristic
281C2×Dic3⋊C4C2×D511yescharacteristic
282C2×C4×Dic3—51no—
283C2×C4×Dic3—51no—
284C2×C4×Dic3—51no—
285#897—58no—
286#897—58no—
287#896—58no—
288#896C2×D518yes—
289#892—58no—
290D3×C4⋊C4—58no—
291#890—58no—
292#889—58no—
293#889—58no—
294#888—58no—
295#888—58no—
296#888—58no—
297#872—58no—
298#869—58no—
299C24×C5—31no—
300C2×C5×Q8—34no—
301C2×C5×Q8—122no—
302C22×C4×C5—31no—
303C22×C4×C5—31no—
304C22×C4×C5—31no—
305C22×C4×C5—34no—
306C22×C4×C5—122no—
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C22×C4×C5C22×D311yescharacteristic
310C22×Dic5—31no—
311C22×Dic5—38no—
312C22×Dic5—34no—
313C22×Dic5—31no—
314C22×Dic5—31no—
315C22×Dic5—31no—
316C22×Dic5—34no—
317C22×Dic5—122no—
318C22×Dic5C22×D311yescharacteristic
319C22×Dic5C22×D311yescharacteristic
320C22×Dic5C22×D311yescharacteristic
321C22×Dic5C22×D311yescharacteristic
322C2×Dic10—34no—
323C2×Dic10—34no—
324C2×Dic10—34no—
325C2×Dic10—122no—
326C2×Dic10—122no—
327C2×Dic10—122no—
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#683—34no—
345#683—34no—
346#683—34no—
347#683—34no—
348#683C22×D314yes—
349#683C22×D314yes—
350#683C22×D314yes—
351#683C22×D314yes—
352C4×Dic5—34no—
353C4×Dic5—34no—
354C4×Dic5—34no—
355C4×Dic5C22×D314yes—
356#544—1516no—
357C2×C4⋊Q8—151no—
358C2×C4⋊Q8—151no—
359C2×C4⋊Q8—151no—
360C2×C4⋊Q8—151no—
361C2×#125—51no—
362C2×#125—151no—
363C2×#125—151no—
364C2×#125—151no—
365C2×C22⋊Q8—31no—
366C2×C22⋊Q8—151no—
367C2×C22⋊Q8—151no—
368C2×C22⋊Q8—151no—
369C2×#117—151no—
370C2×#117—151no—
371C22×C4⋊C4—151no—
372C22×C3×C5C22×Q812yes—
373C22×C3×C5H(5,𝔽2)12yes—
374C22×C3×C52−1+412yes—
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—
385Dic15—22no—
386Dic15C22×Q814yes—
387C3×Dic5—22no—
388C3×Dic5—22no—
389C3×Dic5—22no—
390C3×Dic5C22×Q814yes—
391C5×Dic3—22no—
392C5×Dic3—22no—
393C5×Dic3—22no—
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—42no—
410C2×C4×D3—58no—
411C2×C4×D3—54no—
412C2×C4×D3—54no—
413C2×C4×D3—202no—
414C2×C4×D3C22×D514yes—
415C2×Dic6—42no—
416C2×Dic6—54no—
417C2×Dic6—54no—
418C2×Dic6—54no—
419C2×Dic6—202no—
420C2×Dic6—202no—
421C2×Dic6—202no—
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—
436C4⋊Dic3—54no—
437C4⋊Dic3—54no—
438C4⋊Dic3—54no—
439C4⋊Dic3—54no—
440Dic3⋊C4—54no—
441Dic3⋊C4—54no—
442Dic3⋊C4—54no—
443Dic3⋊C4—54no—
444Dic3⋊C4—54no—
445Dic3⋊C4—54no—
446Dic3⋊C4C22×D514yes—
447Dic3⋊C4C22×D514yes—
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—124no—
457C2×C4×C5—22no—
458C2×C4×C5—22no—
459C2×C4×C5—22no—
460C2×C4×C5—32no—
461C2×C4×C5—32no—
462C2×C4×C5—32no—
463C2×C4×C5—62no—
464C2×C4×C5—62no—
465C2×C4×C5—62no—
466C2×C4×C5—124no—
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—32no—
475C2×Dic5—316no—
476C2×Dic5—32no—
477C2×Dic5—32no—
478C2×Dic5—32no—
479C2×Dic5—62no—
480C2×Dic5—62no—
481C2×Dic5—62no—
482C2×Dic5—124no—
483C2×Dic5D3×Q814yes—
484C2×Dic5C23×D312yes—
485C2×Dic5C23×D312yes—
486C2×Dic5C23×D312yes—
487C2×Dic5C23×D312yes—
488Dic10—124no—
489Dic10—124no—
490Dic10—124no—
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—
500C4⋊Q8—158no—
501C4⋊Q8—158no—
502#125—58no—
503#125—158no—
504#125—158no—
505#125—158no—
506C22⋊Q8—38no—
507C22⋊Q8—158no—
508C22⋊Q8—158no—
509C22⋊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—158no—
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⋊C4—151no—
528C2×C4⋊C4—151no—
529C2×C4⋊C4—151no—
530C2×C4⋊C4—151no—
531C2×C4⋊C4—151no—
532C2×C4⋊C4D3×D511yescharacteristic
533C2×C22⋊C4—31no—
534C2×C22⋊C4—31no—
535C2×C22⋊C4—151no—
536C2×C22⋊C4—151no—
537C2×C42—51no—
538C2×C42—151no—
539C2×C42—151no—
540C2×C42—151no—
541C2×C3×C5#54414yescomplemented
542C2×C3×C5C23×Q811yescharacteristic
543C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
544C2×C3×C5C2×2−1+411yescharacteristic
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—22no—
568C2×Dic3—54no—
569C2×Dic3—52no—
570C2×Dic3—52no—
571C2×Dic3—52no—
572C2×Dic3—52no—
573C2×Dic3—102no—
574C2×Dic3—102no—
575C2×Dic3—102no—
576C2×Dic3C23×D512yes—
577C2×Dic3C23×D512yes—
578C2×Dic3C23×D512yes—
579C4×D3—44no—
580C4×D3—516no—
581C4×D3—204no—
582Dic6—44no—
583Dic6—204no—
584Dic6—204no—
585Dic6—204no—
586C22×C5—34no—
587C22×C5—68no—
588C22×C5—62no—
589C22×C5—62no—
590C22×C5C2×D3×Q812yes—
591C22×C5#100912yes—
592C22×C5#101012yes—
593C22×C5C24×D311yescharacteristic
594C4×C5—22no—
595C4×C5—22no—
596C4×C5—22no—
597C4×C5—62no—
598C4×C5—62no—
599C4×C5—62no—
600Dic5—22no—
601Dic5—22no—
602Dic5—22no—
603Dic5—34no—
604Dic5—62no—
605Dic5—62no—
606Dic5—62no—
607Dic5C2×D3×Q814yes—
608C24—31no—
609C2×Q8—34no—
610C2×Q8—122no—
611C2×Q8—154no—
612C2×Q8—154no—
613C2×Q8—154no—
614C2×Q8—602no—
615C2×Q8—602no—
616C2×Q8—602no—
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—122no—
626C22×C4—154no—
627C22×C4—158no—
628C22×C4—154no—
629C22×C4—151no—
630C22×C4—151no—
631C22×C4—151no—
632C22×C4—151no—
633C22×C4—602no—
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⋊C4—154no—
653C4⋊C4—154no—
654C4⋊C4—154no—
655C4⋊C4—154no—
656C4⋊C4C2×D3×D514yes—
657C22⋊C4—34no—
658C22⋊C4—34no—
659C22⋊C4—154no—
660C22⋊C4—154no—
661C42—54no—
662C42—154no—
663C42—154no—
664C42—154no—
665C3×C5C2×#54411yescharacteristic, complemented, Hall
666C22×C3#414412yes—
667C22×C3C2×Q8×D512yes—
668C22×C3#415012yes—
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—22no—
684Dic3—54no—
685Dic3—102no—
686Dic3—102no—
687Dic3—102no—
688C2×C5—64no—
689C2×C5#568914yescomplemented
690C2×C5C22×D3×Q811yescharacteristic
691C2×C5C2×#100911yescharacteristic
692C2×C5C2×#101011yescharacteristic
693C23—34no—
694C23—32no—
695C23—62no—
696C23—62no—
697C23C22×D3×D511yescharacteristic
698Q8—124no—
699Q8—604no—
700Q8—604no—
701Q8—604no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—32no—
706C2×C4—32no—
707C2×C4—32no—
708C2×C4—54no—
709C2×C4—52no—
710C2×C4—52no—
711C2×C4—52no—
712C2×C4—52no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—62no—
716C2×C4—102no—
717C2×C4—102no—
718C2×C4—102no—
719C2×C4—124no—
720C2×C4—1516no—
721C2×C4—154no—
722C2×C4—152no—
723C2×C4—152no—
724C2×C4—152no—
725C2×C4—152no—
726C2×C4—302no—
727C2×C4—302no—
728C2×C4—302no—
729C2×C4—604no—
730C2×C4C22×D3×D512yes—
731C2×C4C22×D3×D512yes—
732C2×C4C22×D3×D512yes—
733C2×C3#6595714yescomplemented
734C2×C3C2×#414411yescharacteristic
735C2×C3C22×Q8×D511yescharacteristic
736C2×C3C2×#415011yescharacteristic
737D3—24no—
738C5C2×#568911yescharacteristic, complemented, Sylow
739C22—34no—
740C22—62no—
741C22—62no—
742C22—68no—
743C22#9200112yes—
744C22#9202712yes—
745C22D3×Q8×D512yes—
746C22C23×D3×D511yescharacteristic
747C4—22no—
748C4—22no—
749C4—22no—
750C4—54no—
751C4—62no—
752C4—62no—
753C4—62no—
754C4—102no—
755C4—102no—
756C4—102no—
757C4—154no—
758C4—302no—
759C4—302no—
760C4—302no—
761C3C2×#6595711yescharacteristic, complemented, Sylow
762C2—64no—
763C2#1175346214yesdirect product factor
764C2C2×#9200111yescharacteristic
765C2C2×#9202711yescharacteristic
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×#544
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×#91777C2semidirect
3. C2×C3×#4035C2semidirect
9. C2×#91382C2semidirect
10. C2×#91376C2semidirect
12. C2×#91339C2semidirect
13. C2×#91334C2semidirect
14. C2×#91329C2semidirect
15. C2×#91328C2semidirect
16. #11753462C2direct (N × H)
30. #91777C22semidirect
42. C3×#4035C22semidirect
61. #91382C22semidirect
62. #91376C22semidirect
64. #91339C22semidirect
65. #91334C22semidirect
66. #91329C22semidirect
67. #91328C22semidirect
78. C2×#4035D3semidirect
111. C2×D3×Dic5Q8semidirect
201. #4035C2×D3semidirect
248. D3×Dic5C2×Q8semidirect
541. C2×C3×C5#544semidirect
665. C3×C5C2×#544semidirect
689. C2×C5#5689semidirect
733. C2×C3#65957semidirect
738. C5C2×#5689semidirect
761. C3C2×#65957semidirect
763. C2#11753462direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917772
C2×C5×#8962
C2×C3×#40352
C2×#914322
C2×#914172
C2×#914002
C2×D3×#6832
C2×#913982
C2×#913822
C2×#913762
C2×#913652
C2×#913392
C2×#913342
C2×#913292
C2×#913282
#117534622
C2×#659573
C2×#56895