Finite Group Databasebeta

← C2×#11752786 #14481243

Subgroups — C2×#11752786 #14481243

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91768C211yesmaximal, characteristic
2C2×C5×#878C211yesmaximal, characteristic
3C2×C3×#4025C211yesmaximal, characteristic
4C2×#91575C211yesmaximal, characteristic
5C2×#91530C211yesmaximal, characteristic
6C2×#91530C211yesmaximal, characteristic
7C2×#91529C211yesmaximal, characteristic
8C2×#91388C211yesmaximal, characteristic, complemented
9C2×#91382C211yesmaximal, characteristic, complemented
10C2×#91346C211yesmaximal, characteristic, complemented
11C2×#91344C211yesmaximal, characteristic, complemented
12C2×#91343C211yesmaximal, characteristic, complemented
13C2×#91335C211yesmaximal, characteristic, complemented
14C2×#91329C211yesmaximal, characteristic, complemented
15C2×#91323C211yesmaximal, characteristic, complemented
16#11752786C2116yesmaximal, direct product factor
17C2×#65959—31nomaximal, Hall
18C23×C5×Dic3C2211yescharacteristic
19C22×C5×Dic6C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C2×C3×C5×C22⋊C4C2211yescharacteristic
22C2×#6719C2211yescharacteristic
23C2×#6719C2211yescharacteristic
24C2×C4⋊Dic15C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28#91768C2218yes—
29C2×C5×#217C2211yescharacteristic
30C2×C5×C4⋊Dic3C2211yescharacteristic
31C2×C5×Dic3⋊C4C2211yescharacteristic
32C2×C5×Dic3⋊C4C2211yescharacteristic
33C5×#878C2218yes—
34C2×C3×C22⋊Dic5C2211yescharacteristic
35C2×C3×C22⋊Dic5C2211yescharacteristic
36C2×C3×C4⋊Dic5C2211yescharacteristic
37C2×C3×#683C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×C4×Dic5C2211yescharacteristic
40C3×#4025C2218yes—
41#91575C2218yes—
42C2×Dic3⋊Dic5C2211yescharacteristic
43C2×Dic3⋊Dic5C2211yescharacteristic
44C2×Dic3⋊Dic5C2211yescharacteristic
45C2×Dic3⋊Dic5C2211yescharacteristic
46C2×Dic3⋊Dic5C2211yescharacteristic
47C2×#6669C2211yescharacteristic
48C2×#6669C2211yescharacteristic
49C2×#6669C2211yescharacteristic
50C2×#6668C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×#6668C2211yescharacteristic
53#91530C2218yes—
54#91530C2218yes—
55#91529C2218yes—
56C2×Dic3×Dic5C2211yescharacteristic
57C2×Dic3×Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60#91388C2218yescomplemented
61#91382C2218yescomplemented
62#91346C2218yescomplemented
63#91344C2218yescomplemented
64#91343C2218yescomplemented
65#91335C2218yescomplemented
66#91329C2218yescomplemented
67#91323C2218yescomplemented
68C2×#5701—51nomaximal, Hall
69C2×C5×C22⋊Q8—31no—
70C2×Q8×Dic5—31no—
71C2×#4090—31no—
72C2×#4072—31no—
73C2×#4070—31no—
74#65959—316no—
75C2×#4036—31no—
76C2×#4036—31no—
77C2×#4036—31no—
78C2×#4035—31no—
79C2×#4035—31no—
80C2×#4033—31no—
81C2×#4025—31no—
82C2×#4025—31no—
83C2×#4025—31no—
84C2×#4025D311yescharacteristic
85C24×C3×C5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×Dic15C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×C5×Dic3—24no—
93C22×C5×Dic3C2314yes—
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
102C22×C3×Dic5C2311yescharacteristic
103C22×C3×Dic5C2311yescharacteristic
104C2×#1204—24no—
105C2×#1204C2314yes—
106C3×C5×C22⋊C4C2314yes—
107#6719C2314yes—
108#6719C2314yes—
109C4⋊Dic15C2314yes—
110#6712C2314yes—
111#6712C2314yes—
112C4×Dic15C2314yes—
113C5×#217C2314yes—
114C5×C4⋊Dic3C2314yes—
115C5×Dic3⋊C4C2314yes—
116C5×Dic3⋊C4C2314yes—
117C3×C22⋊Dic5C2314yes—
118C3×C22⋊Dic5C2314yes—
119C3×C4⋊Dic5C2314yes—
120C3×#683C2314yes—
121C3×#683C2314yes—
122C3×C4×Dic5C2314yes—
123Dic3⋊Dic5C2314yes—
124Dic3⋊Dic5C2314yes—
125Dic3⋊Dic5C2314yes—
126Dic3⋊Dic5C2314yes—
127Dic3⋊Dic5C2314yes—
128#6669C2314yes—
129#6669C2314yes—
130#6669C2314yes—
131#6668C2314yes—
132#6668C2314yes—
133#6668C2314yes—
134Dic3×Dic5C2314yes—
135Dic3×Dic5C2314yes—
136Dic3×Dic5C2314yes—
137Dic3×Dic5C2314yes—
138C2×C3×#126—51no—
139#5701—516no—
140C2×#890—51no—
141C2×#889—51no—
142C2×#889—51no—
143C2×#889—51no—
144C2×#888—51no—
145C2×#887—51no—
146C2×#879—51no—
147C2×#879—51no—
148C2×#879—51no—
149C2×#878—51no—
150C2×#878D511yescharacteristic
151C2×#877—51no—
152C2×#870—51no—
153C2×C4×Dic6—51no—
154C22×C5×Q8—31no—
155C23×C4×C5—31no—
156C22×Dic10—31no—
157C5×C22⋊Q8—38no—
158C2×C5×C4⋊C4—31no—
159C2×C5×C4⋊C4—31no—
160C2×C5×C4⋊C4—31no—
161C2×C5×C22⋊C4—31no—
162C2×C5×C22⋊C4C2×D311yescharacteristic
163C2×C22⋊Dic5—31no—
164C2×C22⋊Dic5—31no—
165C2×C22⋊Dic5C2×D311yescharacteristic
166C2×C22⋊Dic5C2×D311yescharacteristic
167Q8×Dic5—38no—
168#4090—38no—
169#4072—38no—
170C2×C4⋊Dic5—31no—
171C2×C4⋊Dic5—31no—
172C2×C4⋊Dic5—31no—
173C2×C4⋊Dic5—31no—
174C2×C4⋊Dic5—31no—
175C2×C4⋊Dic5—31no—
176C2×C4⋊Dic5C2×D311yescharacteristic
177#4070—38no—
178C2×#683—31no—
179C2×#683—31no—
180C2×#683—31no—
181C2×#683—31no—
182C2×#683—31no—
183C2×#683—31no—
184C2×#683—31no—
185C2×#683—31no—
186C2×#683C2×D311yescharacteristic
187C2×#683C2×D311yescharacteristic
188C2×C4×Dic5—31no—
189C2×C4×Dic5—31no—
190C2×C4×Dic5—31no—
191C2×C4×Dic5—31no—
192C2×C4×Dic5—31no—
193C2×C4×Dic5C2×D311yescharacteristic
194#4036—38no—
195#4036—38no—
196#4036—38no—
197#4035—38no—
198#4035—38no—
199#4033—38no—
200#4025—38no—
201#4025—38no—
202#4025—38no—
203#4025C2×D318yes—
204C2×#541—151noSylow
205C23×C3×C5—22no—
206C23×C3×C5—22no—
207C23×C3×C5—22no—
208C23×C3×C5C2412yes—
209C23×C3×C5C2411yescharacteristic
210C2×C3×C4×C5—22no—
211C2×C3×C4×C5—22no—
212C2×C3×C4×C5C2412yes—
213C2×C3×C4×C5C2412yes—
214C2×Dic15—22no—
215C2×Dic15—22no—
216C2×Dic15—22no—
217C2×Dic15—22no—
218C2×Dic15C2412yes—
219C2×Dic15C2412yes—
220C2×Dic15C2412yes—
221C2×Dic15C2412yes—
222C2×C5×Dic3—22no—
223C2×C5×Dic3—22no—
224C2×C5×Dic3—22no—
225C2×C5×Dic3—28no—
226C2×C5×Dic3#4114yes—
227C2×C5×Dic3C2412yes—
228C2×C5×Dic3C2412yes—
229C2×C5×Dic3C2412yes—
230C2×C5×Dic3C2412yes—
231C5×Dic6—28no—
232C2×C3×Dic5—22no—
233C2×C3×Dic5—22no—
234C2×C3×Dic5—22no—
235C2×C3×Dic5—22no—
236C2×C3×Dic5C2412yes—
237C2×C3×Dic5C2412yes—
238C2×C3×Dic5C2412yes—
239C2×C3×Dic5C2412yes—
240#1204—28no—
241C23×Dic3C2×D511yescharacteristic
242C22×Dic6—51no—
243C22×Dic6C2×D511yescharacteristic
244C3×#126—58no—
245C2×C3×C4⋊C4—51no—
246C2×C3×C4⋊C4—51no—
247C2×C3×C4⋊C4—51no—
248C2×C3×C22⋊C4—51no—
249C2×C3×C22⋊C4—51no—
250C2×C3×C22⋊C4C2×D511yescharacteristic
251C2×C3×C42—51no—
252C2×#217—51no—
253C2×#217—51no—
254C2×#217C2×D511yescharacteristic
255C2×C4⋊Dic3—51no—
256C2×C4⋊Dic3—51no—
257C2×C4⋊Dic3—51no—
258C2×C4⋊Dic3—51no—
259C2×C4⋊Dic3C2×D511yescharacteristic
260C2×Dic3⋊C4—51no—
261C2×Dic3⋊C4—51no—
262C2×Dic3⋊C4—51no—
263C2×Dic3⋊C4—51no—
264C2×Dic3⋊C4—51no—
265C2×Dic3⋊C4—51no—
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4C2×D511yescharacteristic
271C2×Dic3⋊C4C2×D511yescharacteristic
272C2×C4×Dic3—51no—
273C2×C4×Dic3—51no—
274C2×C4×Dic3—51no—
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277#890—58no—
278#889—58no—
279#889—58no—
280#889—58no—
281#888—58no—
282#887—58no—
283#879—58no—
284#879—58no—
285#879—58no—
286#878—58no—
287#878C2×D518yes—
288#877—58no—
289#870—58no—
290C4×Dic6—58no—
291C24×C5C22×D311yescharacteristic
292C2×C5×Q8—34no—
293C2×C5×Q8—64no—
294C22×C4×C5—31no—
295C22×C4×C5—31no—
296C22×C4×C5—31no—
297C22×C4×C5—31no—
298C22×C4×C5—34no—
299C22×C4×C5—64no—
300C22×C4×C5C22×D311yescharacteristic
301C22×C4×C5C22×D311yescharacteristic
302C22×Dic5—31no—
303C22×Dic5—31no—
304C22×Dic5—31no—
305C22×Dic5—31no—
306C22×Dic5C22×D311yescharacteristic
307C22×Dic5C22×D311yescharacteristic
308C22×Dic5C22×D311yescharacteristic
309C22×Dic5C22×D311yescharacteristic
310C2×Dic10—34no—
311C2×Dic10—64no—
312C5×C4⋊C4—34no—
313C5×C4⋊C4—34no—
314C5×C4⋊C4—34no—
315C5×C22⋊C4—34no—
316C5×C22⋊C4C22×D314yes—
317C22⋊Dic5—34no—
318C22⋊Dic5—34no—
319C22⋊Dic5C22×D314yes—
320C22⋊Dic5C22×D314yes—
321C4⋊Dic5—34no—
322C4⋊Dic5—34no—
323C4⋊Dic5—34no—
324C4⋊Dic5—34no—
325C4⋊Dic5—34no—
326C4⋊Dic5—34no—
327C4⋊Dic5C22×D314yes—
328#683—34no—
329#683—34no—
330#683—34no—
331#683—34no—
332#683—34no—
333#683—34no—
334#683—34no—
335#683—34no—
336#683C22×D314yes—
337#683C22×D314yes—
338C4×Dic5—34no—
339C4×Dic5—34no—
340C4×Dic5—34no—
341C4×Dic5—34no—
342C4×Dic5—34no—
343C4×Dic5C22×D314yes—
344#541—1516no—
345C2×C4⋊Q8—151no—
346C2×#126—51no—
347C2×#126—151no—
348C2×#126—151no—
349C2×#126—151no—
350C2×#125—151no—
351C2×#125—151no—
352C2×#125—151no—
353C2×#125—151no—
354C2×#125—151no—
355C2×C22⋊Q8—31no—
356C2×C22⋊Q8—151no—
357C2×C4×Q8—151no—
358C2×C4×Q8—151no—
359C2×#117—151no—
360C22×C3×C5—22no—
361C22×C3×C5—22no—
362C22×C3×C5—22no—
363C22×C3×C5—44no—
364C22×C3×C5C2×#4112yes—
365C22×C3×C52−1+412yes—
366C22×C3×C52−1+412yes—
367C22×C3×C5C2511yescharacteristic
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370Dic15—22no—
371Dic15—22no—
372Dic15—22no—
373Dic15—22no—
374C3×Dic5—22no—
375C3×Dic5—22no—
376C3×Dic5—22no—
377C3×Dic5—22no—
378C5×Dic3—22no—
379C5×Dic3—22no—
380C5×Dic3—22no—
381C5×Dic3C2×#4114yes—
382C24×C3C22×D511yescharacteristic
383C22×C3×C4—51no—
384C22×C3×C4—51no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4C22×D511yescharacteristic
388C22×C3×C4C22×D511yescharacteristic
389C22×Dic3—24no—
390C22×Dic3—51no—
391C22×Dic3—51no—
392C22×Dic3—51no—
393C22×Dic3—51no—
394C22×Dic3C22×D514yes—
395C22×Dic3C22×D511yescharacteristic
396C22×Dic3C22×D511yescharacteristic
397C22×Dic3C22×D511yescharacteristic
398C22×Dic3C22×D511yescharacteristic
399C2×Dic6—24no—
400C2×Dic6—54no—
401C2×Dic6—104no—
402C2×Dic6C22×D514yes—
403C3×C4⋊C4—54no—
404C3×C4⋊C4—54no—
405C3×C4⋊C4—54no—
406C3×C22⋊C4—54no—
407C3×C22⋊C4—54no—
408C3×C22⋊C4C22×D514yes—
409C3×C42—54no—
410#217—54no—
411#217—54no—
412#217C22×D514yes—
413C4⋊Dic3—54no—
414C4⋊Dic3—54no—
415C4⋊Dic3—54no—
416C4⋊Dic3—54no—
417C4⋊Dic3C22×D514yes—
418Dic3⋊C4—54no—
419Dic3⋊C4—54no—
420Dic3⋊C4—54no—
421Dic3⋊C4—54no—
422Dic3⋊C4—54no—
423Dic3⋊C4—54no—
424Dic3⋊C4—54no—
425Dic3⋊C4—54no—
426Dic3⋊C4—54no—
427Dic3⋊C4—54no—
428Dic3⋊C4C22×D514yes—
429Dic3⋊C4C22×D514yes—
430C4×Dic3—54no—
431C4×Dic3—54no—
432C4×Dic3—54no—
433C4×Dic3—54no—
434C4×Dic3—54no—
435C23×C5—22no—
436C23×C5—22no—
437C23×C5—22no—
438C23×C5C23×D312yes—
439C23×C5C23×D311yescharacteristic
440C5×Q8—68no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—34no—
444C2×C4×C5—32no—
445C2×C4×C5—32no—
446C2×C4×C5—32no—
447C2×C4×C5—32no—
448C2×C4×C5—68no—
449C2×C4×C5—62no—
450C2×C4×C5—62no—
451C2×C4×C5—62no—
452C2×C4×C5C23×D312yes—
453C2×C4×C5C23×D312yes—
454C2×Dic5—22no—
455C2×Dic5—22no—
456C2×Dic5—22no—
457C2×Dic5—22no—
458C2×Dic5—32no—
459C2×Dic5—32no—
460C2×Dic5—32no—
461C2×Dic5—32no—
462C2×Dic5—62no—
463C2×Dic5—62no—
464C2×Dic5—62no—
465C2×Dic5—62no—
466C2×Dic5C23×D312yes—
467C2×Dic5C23×D312yes—
468C2×Dic5C23×D312yes—
469C2×Dic5C23×D312yes—
470Dic10—68no—
471C22×Q8—31no—
472C22×Q8—151no—
473C23×C4—31no—
474C4⋊Q8—158no—
475#126—58no—
476#126—158no—
477#126—158no—
478#126—158no—
479#125—158no—
480#125—158no—
481#125—158no—
482#125—158no—
483#125—158no—
484C22⋊Q8—38no—
485C22⋊Q8—158no—
486C4×Q8—158no—
487C4×Q8—158no—
488#117—158no—
489C2×C4⋊C4—31no—
490C2×C4⋊C4—31no—
491C2×C4⋊C4—31no—
492C2×C4⋊C4—51no—
493C2×C4⋊C4—51no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—151no—
496C2×C4⋊C4—151no—
497C2×C4⋊C4—151no—
498C2×C4⋊C4—151no—
499C2×C4⋊C4—151no—
500C2×C4⋊C4—151no—
501C2×C4⋊C4—151no—
502C2×C4⋊C4—151no—
503C2×C4⋊C4—151no—
504C2×C4⋊C4—151no—
505C2×C4⋊C4—151no—
506C2×C4⋊C4—151no—
507C2×C4⋊C4—151no—
508C2×C4⋊C4—151no—
509C2×C22⋊C4—31no—
510C2×C22⋊C4—51no—
511C2×C22⋊C4—51no—
512C2×C22⋊C4—151no—
513C2×C22⋊C4—151no—
514C2×C22⋊C4D3×D511yescharacteristic
515C2×C42—51no—
516C2×C42—151no—
517C2×C42—151no—
518C2×C42—151no—
519C2×C42—151no—
520C2×C42—151no—
521C2×C3×C5—42no—
522C2×C3×C5#54114yescomplemented
523C2×C3×C5C22×#4111yescharacteristic
524C2×C3×C5C2×2−1+411yescharacteristic
525C2×C3×C5C2×2−1+411yescharacteristic
526C23×C3—22no—
527C23×C3—22no—
528C23×C3—22no—
529C23×C3C23×D512yes—
530C23×C3C23×D511yescharacteristic
531C2×C3×C4—22no—
532C2×C3×C4—22no—
533C2×C3×C4—52no—
534C2×C3×C4—52no—
535C2×C3×C4—52no—
536C2×C3×C4—52no—
537C2×C3×C4—102no—
538C2×C3×C4—102no—
539C2×C3×C4—102no—
540C2×C3×C4—102no—
541C2×C3×C4C23×D512yes—
542C2×C3×C4C23×D512yes—
543C2×Dic3—22no—
544C2×Dic3—22no—
545C2×Dic3—22no—
546C2×Dic3—28no—
547C2×Dic3—52no—
548C2×Dic3—52no—
549C2×Dic3—52no—
550C2×Dic3—52no—
551C2×Dic3—102no—
552C2×Dic3—102no—
553C2×Dic3—102no—
554C2×Dic3—102no—
555C2×Dic3#71114yes—
556C2×Dic3C23×D512yes—
557C2×Dic3C23×D512yes—
558C2×Dic3C23×D512yes—
559C2×Dic3C23×D512yes—
560Dic6—28no—
561Dic6—108no—
562C22×C5—22no—
563C22×C5—22no—
564C22×C5—22no—
565C22×C5—44no—
566C22×C5D3×#4112yes—
567C22×C5#101012yes—
568C22×C5#101012yes—
569C22×C5C24×D311yescharacteristic
570C4×C5—22no—
571C4×C5—22no—
572C4×C5—34no—
573C4×C5—62no—
574C4×C5—62no—
575C4×C5—62no—
576Dic5—22no—
577Dic5—22no—
578Dic5—22no—
579Dic5—22no—
580Dic5—62no—
581Dic5—62no—
582Dic5—62no—
583Dic5—62no—
584C24C2×D3×D511yescharacteristic
585C2×Q8—34no—
586C2×Q8—64no—
587C2×Q8—154no—
588C2×Q8—304no—
589C22×C4—31no—
590C22×C4—34no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—31no—
594C22×C4—51no—
595C22×C4—51no—
596C22×C4—51no—
597C22×C4—51no—
598C22×C4—64no—
599C22×C4—151no—
600C22×C4—151no—
601C22×C4—151no—
602C22×C4—151no—
603C22×C4C2×D3×D511yescharacteristic
604C22×C4C2×D3×D511yescharacteristic
605C4⋊C4—34no—
606C4⋊C4—34no—
607C4⋊C4—34no—
608C4⋊C4—54no—
609C4⋊C4—54no—
610C4⋊C4—54no—
611C4⋊C4—154no—
612C4⋊C4—154no—
613C4⋊C4—154no—
614C4⋊C4—154no—
615C4⋊C4—154no—
616C4⋊C4—154no—
617C4⋊C4—154no—
618C4⋊C4—154no—
619C4⋊C4—154no—
620C4⋊C4—154no—
621C4⋊C4—154no—
622C4⋊C4—154no—
623C4⋊C4—154no—
624C4⋊C4—154no—
625C22⋊C4—34no—
626C22⋊C4—54no—
627C22⋊C4—54no—
628C22⋊C4—154no—
629C22⋊C4—154no—
630C22⋊C4C2×D3×D514yes—
631C42—54no—
632C42—154no—
633C42—154no—
634C42—154no—
635C42—154no—
636C42—154no—
637C3×C5C2×#54111yescharacteristic, complemented, Hall
638C22×C3—22no—
639C22×C3—22no—
640C22×C3—22no—
641C22×C3—44no—
642C22×C3C2×#71112yes—
643C22×C3#414712yes—
644C22×C3#415012yes—
645C22×C3C24×D511yescharacteristic
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—102no—
649C3×C4—102no—
650C3×C4—102no—
651C3×C4—102no—
652Dic3—22no—
653Dic3—22no—
654Dic3—22no—
655Dic3—102no—
656Dic3—102no—
657Dic3—102no—
658Dic3—102no—
659Dic3C2×#71114yes—
660C2×C5—42no—
661C2×C5#570114yescomplemented
662C2×C5C2×D3×#4111yescharacteristic
663C2×C5C2×#101011yescharacteristic
664C2×C5C2×#101011yescharacteristic
665C23—22no—
666C23—22no—
667C23—22no—
668C23C22×D3×D512yes—
669C23C22×D3×D511yescharacteristic
670Q8—68no—
671Q8—308no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—34no—
675C2×C4—32no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—32no—
679C2×C4—52no—
680C2×C4—52no—
681C2×C4—52no—
682C2×C4—52no—
683C2×C4—68no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—102no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—102no—
691C2×C4—152no—
692C2×C4—152no—
693C2×C4—152no—
694C2×C4—152no—
695C2×C4—302no—
696C2×C4—302no—
697C2×C4—302no—
698C2×C4—302no—
699C2×C4C22×D3×D512yes—
700C2×C4C22×D3×D512yes—
701C2×C3—42no—
702C2×C3#6595914yescomplemented
703C2×C3C22×#71111yescharacteristic
704C2×C3C2×#414711yescharacteristic
705C2×C3C2×#415011yescharacteristic
706C5C2×#570111yescharacteristic, complemented, Sylow
707C22—22no—
708C22—22no—
709C22—22no—
710C22—44no—
711C22#9200012yes—
712C22#9202012yes—
713C22D3×#71112yes—
714C22C23×D3×D511yescharacteristic
715C4—22no—
716C4—22no—
717C4—34no—
718C4—62no—
719C4—62no—
720C4—62no—
721C4—102no—
722C4—102no—
723C4—102no—
724C4—102no—
725C4—302no—
726C4—302no—
727C4—302no—
728C4—302no—
729C3C2×#6595911yescharacteristic, complemented, Sylow
730C2—42no—
731C2#1175278614yesdirect product factor
732C2C2×#9200011yescharacteristic
733C2C2×#9202011yescharacteristic
734C2C2×D3×#71111yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC24×C3×C5C23
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#541
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
8. C2×#91388C2semidirect
9. C2×#91382C2semidirect
10. C2×#91346C2semidirect
11. C2×#91344C2semidirect
12. C2×#91343C2semidirect
13. C2×#91335C2semidirect
14. C2×#91329C2semidirect
15. C2×#91323C2semidirect
16. #11752786C2direct (N × H)
60. #91388C22semidirect
61. #91382C22semidirect
62. #91346C22semidirect
63. #91344C22semidirect
64. #91343C22semidirect
65. #91335C22semidirect
66. #91329C22semidirect
67. #91323C22semidirect
522. C2×C3×C5#541semidirect
637. C3×C5C2×#541semidirect
661. C2×C5#5701semidirect
702. C2×C3#65959semidirect
706. C5C2×#5701semidirect
729. C3C2×#65959semidirect
731. C2#11752786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917682
C2×C5×#8782
C2×C3×#40252
C2×#915752
C2×#915302
C2×#915292
C2×#913882
C2×#913822
C2×#913462
C2×#913442
C2×#913432
C2×#913352
C2×#913292
C2×#913232
#117527862
C2×#659593
C2×#57015