Finite Group Databasebeta

← C2×#11753352 #14481286

Subgroups — C2×#11753352 #14481286

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×#91778C211yesmaximal, characteristic, complemented
2C2×C5×#890C211yesmaximal, characteristic, complemented
3C2×C3×#4042C211yesmaximal, characteristic
4C2×#91366C211yesmaximal, characteristic
5C2×#91363C211yesmaximal, characteristic
6C2×#91361C211yesmaximal, characteristic
7C2×#91361C211yesmaximal, characteristic
8C2×#91358C211yesmaximal, characteristic
9C2×#91349C211yesmaximal, characteristic
10C2×#91343C211yesmaximal, characteristic, complemented
11C2×#91335C211yesmaximal, characteristic, complemented
12C2×#91335C211yesmaximal, characteristic, complemented
13C2×#91331C211yesmaximal, characteristic, complemented
14C2×#91327C211yesmaximal, characteristic, complemented
15C2×#91324C211yesmaximal, characteristic, complemented
16#11753352C2116yesmaximal, direct product factor
17C2×#66030—31nomaximal, Hall
18C22×C3×C4×D5C2211yescharacteristic
19C22×C3×Dic10C2211yescharacteristic
20C22×#1204C2211yescharacteristic
21C2×C3×C5×C4⋊C4C2211yescharacteristic
22C2×C4⋊Dic15C2211yescharacteristic
23C2×#6712C2211yescharacteristic
24C2×#6712C2211yescharacteristic
25C2×#6712C2211yescharacteristic
26C2×#6712C2211yescharacteristic
27C2×C4×Dic15C2211yescharacteristic
28#91778C2218yescomplemented
29C2×C5×C4⋊Dic3C2211yescharacteristic
30C2×C5×C4⋊Dic3C2211yescharacteristic
31C2×C5×C4⋊Dic3C2211yescharacteristic
32C2×C5×Dic3⋊C4C2211yescharacteristic
33C2×C5×Dic3⋊C4C2211yescharacteristic
34C2×C4×C5×Dic3C2211yescharacteristic
35C5×#890C2218yescomplemented
36C2×C3×#685C2211yescharacteristic
37C2×C3×#685C2211yescharacteristic
38C2×C3×#683C2211yescharacteristic
39C2×C3×#683C2211yescharacteristic
40C3×#4042C2218yes—
41C2×Dic3⋊Dic5C2211yescharacteristic
42C2×Dic3⋊Dic5C2211yescharacteristic
43C2×Dic3⋊Dic5C2211yescharacteristic
44C2×#6669C2211yescharacteristic
45C2×#6668C2211yescharacteristic
46C2×#6668C2211yescharacteristic
47C2×#6668C2211yescharacteristic
48C2×#6665C2211yescharacteristic
49C2×#6665C2211yescharacteristic
50C2×#6665C2211yescharacteristic
51C2×#6665C2211yescharacteristic
52C2×Dic3×Dic5C2211yescharacteristic
53C2×Dic3×Dic5C2211yescharacteristic
54C2×Dic3×Dic5C2211yescharacteristic
55C2×Dic3×Dic5C2211yescharacteristic
56#91366C2218yes—
57#91363C2218yes—
58#91361C2218yes—
59#91361C2218yes—
60#91358C2218yes—
61#91349C2218yes—
62#91343C2218yescomplemented
63#91335C2218yescomplemented
64#91335C2218yescomplemented
65#91331C2218yescomplemented
66#91327C2218yescomplemented
67#91324C2218yescomplemented
68C2×#5625—51nomaximal, Hall
69C2×C5×#125—31no—
70#66030—316no—
71C2×#4044—31no—
72C2×#4044—31no—
73C2×#4044—31no—
74C2×#4042—31no—
75C2×#4042D311yescharacteristic
76C2×#4038—31no—
77C2×#4036—31no—
78C2×#4035—31no—
79C2×#4035—31no—
80C2×#4035—31no—
81C2×#4034—31no—
82C2×#4033—31no—
83C2×#4022—31no—
84C2×C4×Dic10—31no—
85C23×C3×D5C2311yescharacteristic
86C22×C3×C4×C5C2311yescharacteristic
87C22×C3×C4×C5C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×Dic15C2311yescharacteristic
90C22×Dic15C2311yescharacteristic
91C22×Dic15C2311yescharacteristic
92C22×Dic15C2311yescharacteristic
93C22×C5×Dic3C2311yescharacteristic
94C22×C5×Dic3C2311yescharacteristic
95C22×C5×Dic3C2311yescharacteristic
96C22×C5×Dic3C2311yescharacteristic
97C22×C3×Dic5C2311yescharacteristic
98C22×C3×Dic5C2311yescharacteristic
99C22×C3×Dic5C2311yescharacteristic
100C2×C3×C4×D5—24no—
101C2×C3×C4×D5C2314yes—
102C2×C3×Dic10—24no—
103C2×C3×Dic10C2314yes—
104C2×#1204—24no—
105C2×#1204C2314yes—
106C3×C5×C4⋊C4C2314yes—
107C4⋊Dic15C2314yes—
108#6712C2314yes—
109#6712C2314yes—
110#6712C2314yes—
111#6712C2314yes—
112C4×Dic15C2314yes—
113C5×C4⋊Dic3C2314yes—
114C5×C4⋊Dic3C2314yes—
115C5×C4⋊Dic3C2314yes—
116C5×Dic3⋊C4C2314yes—
117C5×Dic3⋊C4C2314yes—
118C4×C5×Dic3C2314yes—
119C3×#685C2314yes—
120C3×#685C2314yes—
121C3×#683C2314yes—
122C3×#683C2314yes—
123Dic3⋊Dic5C2314yes—
124Dic3⋊Dic5C2314yes—
125Dic3⋊Dic5C2314yes—
126#6669C2314yes—
127#6668C2314yes—
128#6668C2314yes—
129#6668C2314yes—
130#6665C2314yes—
131#6665C2314yes—
132#6665C2314yes—
133#6665C2314yes—
134Dic3×Dic5C2314yes—
135Dic3×Dic5C2314yes—
136Dic3×Dic5C2314yes—
137Dic3×Dic5C2314yes—
138C2×C3×C22⋊Q8—51no—
139C2×Q8×Dic3—51no—
140C2×#944—51no—
141C2×#926—51no—
142C2×#924—51no—
143#5625—516no—
144C2×#890—51no—
145C2×#890—51no—
146C2×#890D511yescharacteristic, complemented
147C2×#889—51no—
148C2×#889—51no—
149C2×#887—51no—
150C2×#879—51no—
151C2×#879—51no—
152C2×#879—51no—
153C2×#879—51no—
154C22×C4×D5C2×D311yescharacteristic
155C22×Dic10—31no—
156C22×Dic10C2×D311yescharacteristic
157C5×#125—38no—
158C2×C5×C4⋊C4—31no—
159C2×C5×C4⋊C4—31no—
160C2×C5×C4⋊C4—31no—
161C2×C5×C4⋊C4—31no—
162C2×C5×C4⋊C4—31no—
163C2×C5×C4⋊C4C2×D311yescharacteristic
164C2×C42×C5—31no—
165C2×#685—31no—
166C2×#685—31no—
167C2×#685—31no—
168C2×#685—31no—
169C2×#685C2×D311yescharacteristic
170C2×#685C2×D311yescharacteristic
171C2×C4⋊Dic5—31no—
172C2×C4⋊Dic5—31no—
173C2×C4⋊Dic5—31no—
174C2×C4⋊Dic5—31no—
175C2×#683—31no—
176C2×#683—31no—
177C2×#683—31no—
178C2×#683—31no—
179C2×#683—31no—
180C2×#683—31no—
181C2×#683—31no—
182C2×#683—31no—
183C2×#683C2×D311yescharacteristic
184C2×#683C2×D311yescharacteristic
185C2×C4×Dic5—31no—
186C2×C4×Dic5—31no—
187C2×C4×Dic5—31no—
188C2×C4×Dic5—31no—
189C2×C4×Dic5—31no—
190#4044—38no—
191#4044—38no—
192#4044—38no—
193#4042—38no—
194#4042C2×D318yes—
195#4038—38no—
196#4036—38no—
197#4035—38no—
198#4035—38no—
199#4035—38no—
200#4034—38no—
201#4033—38no—
202#4022—38no—
203C4×Dic10—38no—
204C2×#541—151noSylow
205C23×C3×C5C2411yescharacteristic
206C22×C3×D5—22no—
207C22×C3×D5—22no—
208C22×C3×D5—22no—
209C22×C3×D5C2412yes—
210C2×C3×C4×C5—22no—
211C2×C3×C4×C5—22no—
212C2×C3×C4×C5—22no—
213C2×C3×C4×C5C2412yes—
214C2×C3×C4×C5C2412yes—
215C2×C3×C4×C5C2412yes—
216C2×Dic15—22no—
217C2×Dic15—22no—
218C2×Dic15—22no—
219C2×Dic15—22no—
220C2×Dic15C2412yes—
221C2×Dic15C2412yes—
222C2×Dic15C2412yes—
223C2×Dic15C2412yes—
224C2×C5×Dic3—22no—
225C2×C5×Dic3—22no—
226C2×C5×Dic3—22no—
227C2×C5×Dic3—22no—
228C2×C5×Dic3C2412yes—
229C2×C5×Dic3C2412yes—
230C2×C5×Dic3C2412yes—
231C2×C5×Dic3C2412yes—
232C2×C3×Dic5—22no—
233C2×C3×Dic5—22no—
234C2×C3×Dic5#4114yes—
235C2×C3×Dic5C2412yes—
236C2×C3×Dic5C2412yes—
237C2×C3×Dic5C2412yes—
238C3×C4×D5—28no—
239C3×Dic10—28no—
240#1204—28no—
241C22×C3×Q8—51no—
242C23×C3×C4—51no—
243C22×Dic6—51no—
244C3×C22⋊Q8—58no—
245C2×C3×C4⋊C4—51no—
246C2×C3×C4⋊C4—51no—
247C2×C3×C4⋊C4C2×D511yescharacteristic
248C2×C3×C22⋊C4—51no—
249C2×C3×C22⋊C4—51no—
250C2×#217—51no—
251C2×#217—51no—
252C2×#217—51no—
253C2×#217—51no—
254Q8×Dic3—58no—
255#944—58no—
256#926—58no—
257C2×C4⋊Dic3—51no—
258C2×C4⋊Dic3—51no—
259C2×C4⋊Dic3—51no—
260C2×C4⋊Dic3—51no—
261C2×C4⋊Dic3C2×D511yescharacteristic
262C2×C4⋊Dic3C2×D511yescharacteristic
263C2×C4⋊Dic3C2×D511yescharacteristic
264#924—58no—
265C2×Dic3⋊C4—51no—
266C2×Dic3⋊C4—51no—
267C2×Dic3⋊C4—51no—
268C2×Dic3⋊C4—51no—
269C2×Dic3⋊C4—51no—
270C2×Dic3⋊C4—51no—
271C2×Dic3⋊C4—51no—
272C2×Dic3⋊C4—51no—
273C2×Dic3⋊C4C2×D511yescharacteristic
274C2×Dic3⋊C4C2×D511yescharacteristic
275C2×C4×Dic3—51no—
276C2×C4×Dic3—51no—
277C2×C4×Dic3—51no—
278C2×C4×Dic3—51no—
279C2×C4×Dic3—51no—
280C2×C4×Dic3C2×D511yescharacteristic
281#890—58no—
282#890—58no—
283#890C2×D518yescomplemented
284#889—58no—
285#889—58no—
286#887—58no—
287#879—58no—
288#879—58no—
289#879—58no—
290#879—58no—
291C23×D5C22×D311yescharacteristic
292C22×C4×C5—31no—
293C22×C4×C5—31no—
294C22×C4×C5—31no—
295C22×C4×C5—31no—
296C22×C4×C5C22×D311yescharacteristic
297C22×C4×C5C22×D311yescharacteristic
298C22×C4×C5C22×D311yescharacteristic
299C22×Dic5—31no—
300C22×Dic5—31no—
301C22×Dic5—31no—
302C22×Dic5—31no—
303C22×Dic5C22×D311yescharacteristic
304C22×Dic5C22×D311yescharacteristic
305C22×Dic5C22×D311yescharacteristic
306C2×C4×D5—24no—
307C2×C4×D5C22×D314yes—
308C2×Dic10—24no—
309C2×Dic10—34no—
310C2×Dic10—64no—
311C2×Dic10C22×D314yes—
312C5×C4⋊C4—34no—
313C5×C4⋊C4—34no—
314C5×C4⋊C4—34no—
315C5×C4⋊C4—34no—
316C5×C4⋊C4—34no—
317C5×C4⋊C4C22×D314yes—
318C42×C5—34no—
319#685—34no—
320#685—34no—
321#685—34no—
322#685—34no—
323#685C22×D314yes—
324#685C22×D314yes—
325C4⋊Dic5—34no—
326C4⋊Dic5—34no—
327C4⋊Dic5—34no—
328C4⋊Dic5—34no—
329#683—34no—
330#683—34no—
331#683—34no—
332#683—34no—
333#683—34no—
334#683—34no—
335#683—34no—
336#683—34no—
337#683C22×D314yes—
338#683C22×D314yes—
339C4×Dic5—34no—
340C4×Dic5—34no—
341C4×Dic5—34no—
342C4×Dic5—34no—
343C4×Dic5—34no—
344#541—1516no—
345C2×C4⋊Q8—151no—
346C2×#126—151no—
347C2×#126—151no—
348C2×#126—151no—
349C2×#126—151no—
350C2×#125—31no—
351C2×#125—151no—
352C2×#125—151no—
353C2×#125—151no—
354C2×#125—151no—
355C2×C22⋊Q8—51no—
356C2×C22⋊Q8—151no—
357C2×C4×Q8—151no—
358C2×C4×Q8—151no—
359C2×#117—151no—
360C22×C3×C5C2×#4112yes—
361C22×C3×C52−1+412yes—
362C22×C3×C52−1+412yes—
363C22×C3×C5C2511yescharacteristic
364C2×C3×D5—22no—
365C2×C3×D5—22no—
366C2×C3×D5—22no—
367C2×C3×D5—44no—
368C3×C4×C5—22no—
369C3×C4×C5—22no—
370C3×C4×C5—22no—
371Dic15—22no—
372Dic15—22no—
373Dic15—22no—
374Dic15—22no—
375C3×Dic5—22no—
376C3×Dic5—22no—
377C3×Dic5C2×#4114yes—
378C5×Dic3—22no—
379C5×Dic3—22no—
380C5×Dic3—22no—
381C5×Dic3—22no—
382C24×C3—51no—
383C2×C3×Q8—54no—
384C2×C3×Q8—104no—
385C22×C3×C4—51no—
386C22×C3×C4—51no—
387C22×C3×C4—51no—
388C22×C3×C4—54no—
389C22×C3×C4—104no—
390C22×C3×C4C22×D511yescharacteristic
391C22×C3×C4C22×D511yescharacteristic
392C22×C3×C4C22×D511yescharacteristic
393C22×Dic3—51no—
394C22×Dic3—51no—
395C22×Dic3—51no—
396C22×Dic3—51no—
397C22×Dic3C22×D511yescharacteristic
398C22×Dic3C22×D511yescharacteristic
399C22×Dic3C22×D511yescharacteristic
400C22×Dic3C22×D511yescharacteristic
401C2×Dic6—54no—
402C2×Dic6—104no—
403C3×C4⋊C4—54no—
404C3×C4⋊C4—54no—
405C3×C4⋊C4C22×D514yes—
406C3×C22⋊C4—54no—
407C3×C22⋊C4—54no—
408#217—54no—
409#217—54no—
410#217—54no—
411#217—54no—
412C4⋊Dic3—54no—
413C4⋊Dic3—54no—
414C4⋊Dic3—54no—
415C4⋊Dic3—54no—
416C4⋊Dic3C22×D514yes—
417C4⋊Dic3C22×D514yes—
418C4⋊Dic3C22×D514yes—
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⋊C4C22×D514yes—
428Dic3⋊C4C22×D514yes—
429C4×Dic3—54no—
430C4×Dic3—54no—
431C4×Dic3—54no—
432C4×Dic3—54no—
433C4×Dic3—54no—
434C4×Dic3C22×D514yes—
435C23×C5C23×D311yescharacteristic
436C22×D5—22no—
437C22×D5—22no—
438C22×D5—22no—
439C22×D5C23×D312yes—
440C2×C4×C5—22no—
441C2×C4×C5—22no—
442C2×C4×C5—22no—
443C2×C4×C5—32no—
444C2×C4×C5—32no—
445C2×C4×C5—32no—
446C2×C4×C5—32no—
447C2×C4×C5—62no—
448C2×C4×C5—62no—
449C2×C4×C5—62no—
450C2×C4×C5—62no—
451C2×C4×C5C23×D312yes—
452C2×C4×C5C23×D312yes—
453C2×C4×C5C23×D312yes—
454C2×Dic5—22no—
455C2×Dic5—22no—
456C2×Dic5—32no—
457C2×Dic5—32no—
458C2×Dic5—32no—
459C2×Dic5—32no—
460C2×Dic5—62no—
461C2×Dic5—62no—
462C2×Dic5—62no—
463C2×Dic5—62no—
464C2×Dic5#23714yes—
465C2×Dic5C23×D312yes—
466C2×Dic5C23×D312yes—
467C2×Dic5C23×D312yes—
468C4×D5—28no—
469Dic10—28no—
470Dic10—68no—
471C22×Q8—51no—
472C22×Q8—151no—
473C23×C4—51no—
474C4⋊Q8—158no—
475#126—158no—
476#126—158no—
477#126—158no—
478#126—158no—
479#125—38no—
480#125—158no—
481#125—158no—
482#125—158no—
483#125—158no—
484C22⋊Q8—58no—
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—31no—
493C2×C4⋊C4—31no—
494C2×C4⋊C4—51no—
495C2×C4⋊C4—51no—
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⋊C4D3×D511yescharacteristic
509C2×C22⋊C4—51no—
510C2×C22⋊C4—51no—
511C2×C22⋊C4—151no—
512C2×C22⋊C4—151no—
513C2×C22⋊C4—151no—
514C2×C22⋊C4—151no—
515C2×C42—31no—
516C2×C42—151no—
517C2×C42—151no—
518C2×C42—151no—
519C2×C42—151no—
520C2×C42—151no—
521C2×C3×C5#54114yescomplemented
522C2×C3×C5C22×#4111yescharacteristic
523C2×C3×C5C2×2−1+411yescharacteristic
524C2×C3×C5C2×2−1+411yescharacteristic
525C3×D5—42no—
526C23×C3—52no—
527C23×C3—102no—
528C23×C3—102no—
529C23×C3—102no—
530C23×C3C23×D511yescharacteristic
531C3×Q8—108no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—54no—
536C2×C3×C4—52no—
537C2×C3×C4—52no—
538C2×C3×C4—52no—
539C2×C3×C4—108no—
540C2×C3×C4—102no—
541C2×C3×C4—102no—
542C2×C3×C4C23×D512yes—
543C2×C3×C4C23×D512yes—
544C2×C3×C4C23×D512yes—
545C2×Dic3—22no—
546C2×Dic3—22no—
547C2×Dic3—22no—
548C2×Dic3—22no—
549C2×Dic3—52no—
550C2×Dic3—52no—
551C2×Dic3—52no—
552C2×Dic3—52no—
553C2×Dic3—102no—
554C2×Dic3—102no—
555C2×Dic3—102no—
556C2×Dic3—102no—
557C2×Dic3C23×D512yes—
558C2×Dic3C23×D512yes—
559C2×Dic3C23×D512yes—
560C2×Dic3C23×D512yes—
561Dic6—108no—
562C22×C5C2×#23712yes—
563C22×C5#100712yes—
564C22×C5#101012yes—
565C22×C5C24×D311yescharacteristic
566C2×D5—22no—
567C2×D5—22no—
568C2×D5—22no—
569C2×D5—44no—
570C4×C5—22no—
571C4×C5—22no—
572C4×C5—22no—
573C4×C5—62no—
574C4×C5—62no—
575C4×C5—62no—
576C4×C5—62no—
577Dic5—22no—
578Dic5—22no—
579Dic5—62no—
580Dic5—62no—
581Dic5—62no—
582Dic5—62no—
583Dic5C2×#23714yes—
584C24—51no—
585C2×Q8—54no—
586C2×Q8—104no—
587C2×Q8—154no—
588C2×Q8—304no—
589C22×C4—31no—
590C22×C4—31no—
591C22×C4—31no—
592C22×C4—31no—
593C22×C4—51no—
594C22×C4—51no—
595C22×C4—51no—
596C22×C4—54no—
597C22×C4—104no—
598C22×C4—151no—
599C22×C4—151no—
600C22×C4—151no—
601C22×C4—151no—
602C22×C4C2×D3×D511yescharacteristic
603C22×C4C2×D3×D511yescharacteristic
604C22×C4C2×D3×D511yescharacteristic
605C4⋊C4—34no—
606C4⋊C4—34no—
607C4⋊C4—34no—
608C4⋊C4—34no—
609C4⋊C4—34no—
610C4⋊C4—54no—
611C4⋊C4—54no—
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⋊C4C2×D3×D514yes—
625C22⋊C4—54no—
626C22⋊C4—54no—
627C22⋊C4—154no—
628C22⋊C4—154no—
629C22⋊C4—154no—
630C22⋊C4—154no—
631C42—34no—
632C42—154no—
633C42—154no—
634C42—154no—
635C42—154no—
636C42—154no—
637C3×C5C2×#54111yescharacteristic, complemented, Hall
638C22×C3—102no—
639C22×C3—102no—
640C22×C3—102no—
641C22×C3—204no—
642C22×C3#414712yes—
643C22×C3D5×#4112yes—
644C22×C3#415012yes—
645C22×C3C24×D511yescharacteristic
646C3×C4—22no—
647C3×C4—22no—
648C3×C4—22no—
649C3×C4—54no—
650C3×C4—102no—
651C3×C4—102no—
652Dic3—22no—
653Dic3—22no—
654Dic3—22no—
655Dic3—22no—
656Dic3—102no—
657Dic3—102no—
658Dic3—102no—
659Dic3—102no—
660C2×C5#562514yescomplemented
661C2×C5C22×#23711yescharacteristic
662C2×C5C2×#100711yescharacteristic
663C2×C5C2×#101011yescharacteristic
664D5—42no—
665C23—52no—
666C23—102no—
667C23—102no—
668C23—102no—
669C23C22×D3×D511yescharacteristic
670Q8—108no—
671Q8—308no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—32no—
676C2×C4—32no—
677C2×C4—32no—
678C2×C4—32no—
679C2×C4—54no—
680C2×C4—52no—
681C2×C4—52no—
682C2×C4—52no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—62no—
687C2×C4—108no—
688C2×C4—102no—
689C2×C4—102no—
690C2×C4—152no—
691C2×C4—152no—
692C2×C4—152no—
693C2×C4—152no—
694C2×C4—302no—
695C2×C4—302no—
696C2×C4—302no—
697C2×C4—302no—
698C2×C4C22×D3×D512yes—
699C2×C4C22×D3×D512yes—
700C2×C4C22×D3×D512yes—
701C2×C3—202no—
702C2×C3#6603014yescomplemented
703C2×C3C2×#414711yescharacteristic
704C2×C3C2×D5×#4111yescharacteristic
705C2×C3C2×#415011yescharacteristic
706C5C2×#562511yescharacteristic, complemented, Sylow
707C22—102no—
708C22—102no—
709C22—102no—
710C22—204no—
711C22#9200012yes—
712C22D5×#23712yes—
713C22#9203012yes—
714C22C23×D3×D511yescharacteristic
715C4—22no—
716C4—22no—
717C4—22no—
718C4—54no—
719C4—62no—
720C4—62no—
721C4—62no—
722C4—62no—
723C4—102no—
724C4—102no—
725C4—302no—
726C4—302no—
727C4—302no—
728C4—302no—
729C3C2×#6603011yescharacteristic, complemented, Sylow
730C2—202no—
731C2#1175335214yesdirect product factor
732C2C2×#9200011yescharacteristic
733C2C2×D5×#23711yescharacteristic
734C2C2×#9203011yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C4⋊C4C22
socleC23×C3×C5C24
prime radicalC23×C3×D5C23
hypercenterC2×C4⋊C4D3×D5
hypocenterC3×C5C2×#541
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×#91778C2semidirect
2. C2×C5×#890C2semidirect
10. C2×#91343C2semidirect
11. C2×#91335C2semidirect
12. C2×#91335C2semidirect
13. C2×#91331C2semidirect
14. C2×#91327C2semidirect
15. C2×#91324C2semidirect
16. #11753352C2direct (N × H)
28. #91778C22semidirect
35. C5×#890C22semidirect
62. #91343C22semidirect
63. #91335C22semidirect
64. #91335C22semidirect
65. #91331C22semidirect
66. #91327C22semidirect
67. #91324C22semidirect
146. C2×#890D5semidirect
283. #890C2×D5semidirect
521. C2×C3×C5#541semidirect
637. C3×C5C2×#541semidirect
660. C2×C5#5625semidirect
702. C2×C3#66030semidirect
706. C5C2×#5625semidirect
729. C3C2×#66030semidirect
731. C2#11753352direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917782
C2×C5×#8902
C2×C3×#40422
C2×#913662
C2×#913632
C2×#913612
C2×#913582
C2×#913492
C2×#913432
C2×#913352
C2×#913312
C2×#913272
C2×#913242
#117533522
C2×#660303
C2×#56255