Finite Group Databasebeta

← C2×#11752979 #14481364

Subgroups — C2×#11752979 #14481364

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#91774C211yesmaximal, characteristic, complemented
2C2×C5×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×C3×#4025C211yesmaximal, characteristic, complemented
4C2×#91575C211yesmaximal, characteristic, complemented
5C2×#91557C211yesmaximal, characteristic
6C2×#91542C211yesmaximal, characteristic, complemented
7C2×#91525C211yesmaximal, characteristic, complemented
8C2×C4×#1204C211yesmaximal, characteristic, complemented
9C2×#91429C211yesmaximal, characteristic, complemented
10C2×#91403C211yesmaximal, characteristic, complemented
11C2×#91367C211yesmaximal, characteristic, complemented
12C2×#91365C211yesmaximal, characteristic, complemented
13C2×#91351C211yesmaximal, characteristic, complemented
14C2×#91350C211yesmaximal, characteristic, complemented
15C2×#91328C211yesmaximal, characteristic, complemented
16#11752979C2116yesmaximal, direct product factor
17C2×#65895—31nomaximal, Hall
18C22×#1220C2211yescharacteristic
19C22×Dic30C2211yescharacteristic
20C22×C5×#67C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C22×C4×C5×D3C2211yescharacteristic
23C22×#1204C2211yescharacteristic
24C22×#1204C2211yescharacteristic
25C22×#1203C2211yescharacteristic
26C22×#1200C2211yescharacteristic
27C2×C3×C5×C22⋊C4C2211yescharacteristic
28C2×#6719C2211yescharacteristic
29C2×#6714C2211yescharacteristic
30C2×#6714C2211yescharacteristic
31C2×C4×Dic15C2211yescharacteristic
32#91774C2218yescomplemented
33C2×C5×(C2×D3)⋊C4C2211yescharacteristic
34C2×C5×Dic3⋊C4C2211yescharacteristic
35C2×C4×C5×Dic3C2211yescharacteristic
36C5×#67⋊C4C2218yescomplemented
37C2×C3×C22⋊Dic5C2211yescharacteristic
38C2×C3×C22⋊Dic5C2211yescharacteristic
39C2×C3×C4⋊Dic5C2211yescharacteristic
40C2×C3×#683C2211yescharacteristic
41C2×C3×#683C2211yescharacteristic
42C2×C3×C4×Dic5C2211yescharacteristic
43C3×#4025C2218yescomplemented
44#91575C2218yescomplemented
45#91557C2218yes—
46C2×Dic3⋊Dic5C2211yescharacteristic
47C2×Dic3⋊Dic5C2211yescharacteristic
48C2×#6669C2211yescharacteristic
49#91542C2218yescomplemented
50C2×#6668C2211yescharacteristic
51C2×#6668C2211yescharacteristic
52C2×#6668C2211yescharacteristic
53C2×#6667C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×(C2×D3)⋊Dic5C2211yescharacteristic
56C2×(C2×D3)⋊Dic5C2211yescharacteristic
57C2×(C2×D3)⋊Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59#91525C2218yescomplemented
60C4×#1204C2218yescomplemented
61#91429C2218yescomplemented
62#91403C2218yescomplemented
63#91367C2218yescomplemented
64#91365C2218yescomplemented
65#91351C2218yescomplemented
66#91350C2218yescomplemented
67#91328C2218yescomplemented
68C2×#5710—51nomaximal, Hall
69C2×C4×C5×D4—31no—
70C2×#4084—31no—
71C2×#4082—31no—
72C2×#4075—31no—
73C2×#4075—31no—
74C2×#4070—31no—
75C2×#4070—31no—
76#65895—316no—
77C2×#4043—31no—
78C2×#4034—31no—
79C2×#4031—31no—
80C2×#4031—31no—
81C2×#4025—31no—
82C2×#4025D311yescharacteristic, complemented
83C2×#4018—31no—
84C2×C4×Dic10—31no—
85C24×C3×C5C2311yescharacteristic
86C23×D15C2311yescharacteristic
87C23×C5×D3C2311yescharacteristic
88C22×C3×C4×C5C2311yescharacteristic
89C22×C3×C4×C5C2311yescharacteristic
90C2×#1220—42no—
91C2×#1220C2314yes—
92C22×Dic15C2311yescharacteristic
93C22×Dic15C2311yescharacteristic
94C22×Dic15C2311yescharacteristic
95C2×Dic30—42no—
96C2×Dic30C2314yes—
97C2×C5×#67—24no—
98C2×C5×#67C2314yes—
99C22×C5×Dic3—42no—
100C22×C5×Dic3C2311yescharacteristic
101C22×C5×Dic3C2311yescharacteristic
102C22×C5×Dic3C2314yes—
103C22×C5×Dic3C2311yescharacteristic
104C2×C4×C5×D3—42no—
105C2×C4×C5×D3C2314yes—
106C22×C3×Dic5C2311yescharacteristic
107C22×C3×Dic5C2311yescharacteristic
108C22×C3×Dic5C2311yescharacteristic
109C22×C3×Dic5C2311yescharacteristic
110C2×#1204—24no—
111C2×#1204—42no—
112C2×#1204C2314yes—
113C2×#1204C2314yes—
114C2×#1203—42no—
115C2×#1203C2314yes—
116C2×#1200—24no—
117C2×#1200C2314yes—
118C3×C5×C22⋊C4C2314yes—
119#6719C2314yes—
120#6714C2314yes—
121#6714C2314yes—
122C4×Dic15C2314yes—
123C5×(C2×D3)⋊C4C2314yes—
124C5×Dic3⋊C4C2314yes—
125C4×C5×Dic3C2314yes—
126C3×C22⋊Dic5C2314yes—
127C3×C22⋊Dic5C2314yes—
128C3×C4⋊Dic5C2314yes—
129C3×#683C2314yes—
130C3×#683C2314yes—
131C3×C4×Dic5C2314yes—
132Dic3⋊Dic5C2314yes—
133Dic3⋊Dic5C2314yes—
134#6669C2314yes—
135#6668C2314yes—
136#6668C2314yes—
137#6668C2314yes—
138#6667C2314yes—
139#6667C2314yes—
140(C2×D3)⋊Dic5C2314yes—
141(C2×D3)⋊Dic5C2314yes—
142(C2×D3)⋊Dic5C2314yes—
143Dic3×Dic5C2314yes—
144C2×C3×#126—51no—
145#5710—516no—
146C2×#898—51no—
147C2×#897—51no—
148C2×#896—51no—
149C2×#894—51no—
150C2×#892—51no—
151C2×#888—51no—
152C2×#886—51no—
153C2×#885—51no—
154C2×#885—51no—
155C2×#884—51no—
156C2×#67⋊C4D511yescharacteristic, complemented
157C2×#878—51no—
158C2×#875—51no—
159C2×C4×Dic6—51no—
160C22×C5×D4—31no—
161C23×C4×C5—31no—
162C23×C4×C5—31no—
163C22×C22⋊D5—31no—
164C22×C22⋊D5—31no—
165C22×C4×D5—31no—
166C22×Dic10—31no—
167C22×Dic10—31no—
168C22×Dic10—31no—
169C4×C5×D4—38no—
170C2×C5×C4⋊C4—31no—
171C2×C5×C22⋊C4—31no—
172C2×C5×C22⋊C4C2×D311yescharacteristic
173C2×C42×C5—31no—
174C2×C22⋊Dic5—31no—
175C2×C22⋊Dic5—31no—
176C2×C22⋊Dic5—31no—
177C2×C22⋊Dic5—31no—
178C2×C22⋊Dic5C2×D311yescharacteristic
179C2×C22⋊Dic5C2×D311yescharacteristic
180#4084—38no—
181#4082—38no—
182#4075—38no—
183#4075—38no—
184C2×#685—31no—
185C2×#685—31no—
186C2×#685—31no—
187C2×#685—31no—
188C2×C4⋊Dic5—31no—
189C2×C4⋊Dic5—31no—
190C2×C4⋊Dic5C2×D311yescharacteristic
191#4070—38no—
192#4070—38no—
193C2×#683—31no—
194C2×#683—31no—
195C2×#683—31no—
196C2×#683—31no—
197C2×#683C2×D311yescharacteristic
198C2×#683C2×D311yescharacteristic
199C2×C4×Dic5—31no—
200C2×C4×Dic5—31no—
201C2×C4×Dic5C2×D311yescharacteristic
202#4043—38no—
203#4034—38no—
204#4031—38no—
205#4031—38no—
206#4025—38no—
207#4025C2×D318yescomplemented
208#4018—38no—
209C4×Dic10—38no—
210C2×#542—151noSylow
211C23×C3×C5—22no—
212C23×C3×C5—22no—
213C23×C3×C5—22no—
214C23×C3×C5C2412yes—
215C23×C3×C5C2411yescharacteristic
216C22×D15—22no—
217C22×D15—22no—
218C22×D15—22no—
219C22×D15C2412yes—
220C22×C5×D3—22no—
221C22×C5×D3—22no—
222C22×C5×D3—22no—
223C22×C5×D3C2412yes—
224C2×C3×C4×C5—22no—
225C2×C3×C4×C5—22no—
226C2×C3×C4×C5C2412yes—
227C2×C3×C4×C5C2412yes—
228#1220—44no—
229C2×Dic15—22no—
230C2×Dic15—22no—
231C2×Dic15—22no—
232C2×Dic15C2412yes—
233C2×Dic15C2412yes—
234C2×Dic15C2412yes—
235Dic30—44no—
236C5×#67—28no—
237C2×C5×Dic3—22no—
238C2×C5×Dic3—22no—
239C2×C5×Dic3—44no—
240C2×C5×Dic3#4114yes—
241C2×C5×Dic3C2412yes—
242C2×C5×Dic3C2412yes—
243C2×C5×Dic3C2412yes—
244C4×C5×D3—44no—
245C2×C3×Dic5—22no—
246C2×C3×Dic5—22no—
247C2×C3×Dic5—22no—
248C2×C3×Dic5—22no—
249C2×C3×Dic5C2412yes—
250C2×C3×Dic5C2412yes—
251C2×C3×Dic5C2412yes—
252C2×C3×Dic5C2412yes—
253#1204—28no—
254#1204—44no—
255#1203—44no—
256#1200—28no—
257C22×#67—51no—
258C22×#67C2×D511yescharacteristic
259C23×Dic3C2×D511yescharacteristic
260C22×D12—51no—
261C22×C4×D3—51no—
262C22×C4×D3C2×D511yescharacteristic
263C22×Dic6—51no—
264C22×Dic6—51no—
265C22×Dic6—51no—
266C3×#126—58no—
267C2×C3×C4⋊C4—51no—
268C2×C3×C4⋊C4—51no—
269C2×C3×C4⋊C4—51no—
270C2×C3×C22⋊C4—51no—
271C2×C3×C22⋊C4—51no—
272C2×C3×C22⋊C4C2×D511yescharacteristic
273C2×C3×C42—51no—
274C2×#217—51no—
275C2×(C2×D3)⋊C4—51no—
276C2×(C2×D3)⋊C4—51no—
277C2×(C2×D3)⋊C4—51no—
278C2×(C2×D3)⋊C4—51no—
279C2×(C2×D3)⋊C4—51no—
280C2×(C2×D3)⋊C4—51no—
281C2×(C2×D3)⋊C4—51no—
282C2×(C2×D3)⋊C4C2×D511yescharacteristic
283C2×C4⋊Dic3—51no—
284C2×C4⋊Dic3—51no—
285C2×C4⋊Dic3—51no—
286C2×Dic3⋊C4—51no—
287C2×Dic3⋊C4—51no—
288C2×Dic3⋊C4—51no—
289C2×Dic3⋊C4C2×D511yescharacteristic
290C2×C4×Dic3—51no—
291C2×C4×Dic3—51no—
292C2×C4×Dic3C2×D511yescharacteristic
293#898—58no—
294#897—58no—
295#896—58no—
296#894—58no—
297#892—58no—
298#888—58no—
299#886—58no—
300#885—58no—
301#885—58no—
302#884—58no—
303#67⋊C4C2×D518yescomplemented
304#878—58no—
305#875—58no—
306C4×Dic6—58no—
307C24×C5—31no—
308C24×C5C22×D311yescharacteristic
309C23×D5—31no—
310C2×C5×D4—34no—
311C2×C5×D4—64no—
312C22×C4×C5—31no—
313C22×C4×C5—31no—
314C22×C4×C5—31no—
315C22×C4×C5—34no—
316C22×C4×C5—34no—
317C22×C4×C5—122no—
318C22×C4×C5—122no—
319C22×C4×C5C22×D311yescharacteristic
320C22×C4×C5C22×D311yescharacteristic
321C2×C22⋊D5—34no—
322C2×C22⋊D5—34no—
323C2×C22⋊D5—122no—
324C2×C22⋊D5—122no—
325C22×Dic5—31no—
326C22×Dic5—31no—
327C22×Dic5—31no—
328C22×Dic5C22×D311yescharacteristic
329C22×Dic5C22×D311yescharacteristic
330C22×Dic5C22×D311yescharacteristic
331C22×Dic5C22×D311yescharacteristic
332C2×C4×D5—34no—
333C2×C4×D5—64no—
334C2×Dic10—34no—
335C2×Dic10—34no—
336C2×Dic10—34no—
337C2×Dic10—64no—
338C2×Dic10—122no—
339C2×Dic10—122no—
340C5×C4⋊C4—34no—
341C5×C22⋊C4—34no—
342C5×C22⋊C4C22×D314yes—
343C42×C5—34no—
344C22⋊Dic5—34no—
345C22⋊Dic5—34no—
346C22⋊Dic5—34no—
347C22⋊Dic5—34no—
348C22⋊Dic5C22×D314yes—
349C22⋊Dic5C22×D314yes—
350#685—34no—
351#685—34no—
352#685—34no—
353#685—34no—
354C4⋊Dic5—34no—
355C4⋊Dic5—34no—
356C4⋊Dic5C22×D314yes—
357#683—34no—
358#683—34no—
359#683—34no—
360#683—34no—
361#683C22×D314yes—
362#683C22×D314yes—
363C4×Dic5—34no—
364C4×Dic5—34no—
365C4×Dic5C22×D314yes—
366#542—1516no—
367C2×C4⋊Q8—151no—
368C2×#126—51no—
369C2×#126—151no—
370C2×#124—151no—
371C2×#124—151no—
372C2×#124—151no—
373C2×#123—151no—
374C2×#123—151no—
375C2×C22⋊Q8—151no—
376C2×C22⋊Q8—151no—
377C2×C22⋊Q8—151no—
378C2×#121—151no—
379C2×C4×Q8—151no—
380C2×C4×D4—31no—
381C2×#117—151no—
382C22×C3×C5—22no—
383C22×C3×C5—22no—
384C22×C3×C5—22no—
385C22×C3×C5—44no—
386C22×C3×C5C2×#4112yes—
387C22×C3×C5H(5,𝔽2)12yes—
388C22×C3×C52−1+412yes—
389C22×C3×C5C2511yescharacteristic
390C2×D15—22no—
391C2×D15—22no—
392C2×D15—22no—
393C2×D15—44no—
394C2×C5×D3—22no—
395C2×C5×D3—22no—
396C2×C5×D3—22no—
397C2×C5×D3—44no—
398C3×C4×C5—22no—
399C3×C4×C5—22no—
400Dic15—22no—
401Dic15—22no—
402Dic15—22no—
403C3×Dic5—22no—
404C3×Dic5—22no—
405C3×Dic5—22no—
406C3×Dic5—22no—
407C5×Dic3—22no—
408C5×Dic3—22no—
409C5×Dic3C2×#4114yes—
410C24×C3C22×D511yescharacteristic
411C23×D3—51no—
412C23×D3C22×D511yescharacteristic
413C22×C3×C4—51no—
414C22×C3×C4—51no—
415C22×C3×C4—51no—
416C22×C3×C4—51no—
417C22×C3×C4C22×D511yescharacteristic
418C22×C3×C4C22×D511yescharacteristic
419C2×#67—24no—
420C2×#67—54no—
421C2×#67—202no—
422C2×#67C22×D514yes—
423C22×Dic3—42no—
424C22×Dic3—51no—
425C22×Dic3—51no—
426C22×Dic3—51no—
427C22×Dic3C22×D511yescharacteristic
428C22×Dic3C22×D511yescharacteristic
429C22×Dic3C22×D514yes—
430C22×Dic3C22×D511yescharacteristic
431C2×D12—54no—
432C2×D12—202no—
433C2×C4×D3—42no—
434C2×C4×D3—54no—
435C2×C4×D3—104no—
436C2×C4×D3C22×D514yes—
437C2×Dic6—54no—
438C2×Dic6—54no—
439C2×Dic6—54no—
440C2×Dic6—104no—
441C2×Dic6—202no—
442C2×Dic6—202no—
443C3×C4⋊C4—54no—
444C3×C4⋊C4—54no—
445C3×C4⋊C4—54no—
446C3×C22⋊C4—54no—
447C3×C22⋊C4—54no—
448C3×C22⋊C4C22×D514yes—
449C3×C42—54no—
450#217—54no—
451(C2×D3)⋊C4—54no—
452(C2×D3)⋊C4—54no—
453(C2×D3)⋊C4—54no—
454(C2×D3)⋊C4—54no—
455(C2×D3)⋊C4—54no—
456(C2×D3)⋊C4—54no—
457(C2×D3)⋊C4—54no—
458(C2×D3)⋊C4C22×D514yes—
459C4⋊Dic3—54no—
460C4⋊Dic3—54no—
461C4⋊Dic3—54no—
462Dic3⋊C4—54no—
463Dic3⋊C4—54no—
464Dic3⋊C4—54no—
465Dic3⋊C4C22×D514yes—
466C4×Dic3—54no—
467C4×Dic3—54no—
468C4×Dic3C22×D514yes—
469C23×C5—22no—
470C23×C5—22no—
471C23×C5—22no—
472C23×C5—32no—
473C23×C5—62no—
474C23×C5—62no—
475C23×C5—62no—
476C23×C5C23×D312yes—
477C23×C5C23×D311yescharacteristic
478C22×D5—32no—
479C22×D5—62no—
480C22×D5—62no—
481C22×D5—62no—
482C5×D4—68no—
483C2×C4×C5—22no—
484C2×C4×C5—22no—
485C2×C4×C5—34no—
486C2×C4×C5—32no—
487C2×C4×C5—32no—
488C2×C4×C5—32no—
489C2×C4×C5—62no—
490C2×C4×C5—62no—
491C2×C4×C5—124no—
492C2×C4×C5—124no—
493C2×C4×C5C23×D312yes—
494C2×C4×C5C23×D312yes—
495C22⋊D5—124no—
496C22⋊D5—124no—
497C2×Dic5—22no—
498C2×Dic5—22no—
499C2×Dic5—22no—
500C2×Dic5—22no—
501C2×Dic5—32no—
502C2×Dic5—32no—
503C2×Dic5—32no—
504C2×Dic5—62no—
505C2×Dic5—62no—
506C2×Dic5—62no—
507C2×Dic5C23×D312yes—
508C2×Dic5C23×D312yes—
509C2×Dic5C23×D312yes—
510C2×Dic5C23×D312yes—
511C4×D5—68no—
512Dic10—68no—
513Dic10—124no—
514Dic10—124no—
515C22×Q8—151no—
516C22×Q8—151no—
517C22×Q8—151no—
518C22×D4—31no—
519C22×D4—151no—
520C22×D4—151no—
521C23×C4—31no—
522C23×C4—31no—
523C23×C4—151no—
524C4⋊Q8—158no—
525#126—58no—
526#126—158no—
527#124—158no—
528#124—158no—
529#124—158no—
530#123—158no—
531#123—158no—
532C22⋊Q8—158no—
533C22⋊Q8—158no—
534C22⋊Q8—158no—
535#121—158no—
536C4×Q8—158no—
537C4×D4—38no—
538#117—158no—
539C2×C4⋊C4—31no—
540C2×C4⋊C4—51no—
541C2×C4⋊C4—51no—
542C2×C4⋊C4—51no—
543C2×C4⋊C4—151no—
544C2×C4⋊C4—151no—
545C2×C4⋊C4—151no—
546C2×C4⋊C4—151no—
547C2×C4⋊C4—151no—
548C2×C4⋊C4—151no—
549C2×C22⋊C4—31no—
550C2×C22⋊C4—51no—
551C2×C22⋊C4—51no—
552C2×C22⋊C4—151no—
553C2×C22⋊C4—151no—
554C2×C22⋊C4—151no—
555C2×C22⋊C4—151no—
556C2×C22⋊C4—151no—
557C2×C22⋊C4—151no—
558C2×C22⋊C4—151no—
559C2×C22⋊C4—151no—
560C2×C22⋊C4D3×D511yescharacteristic
561C2×C42—31no—
562C2×C42—51no—
563C2×C42—151no—
564C2×C42—151no—
565C2×C3×C5—42no—
566C2×C3×C5#54214yescomplemented
567C2×C3×C5C22×#4111yescharacteristic
568C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
569C2×C3×C5C2×2−1+411yescharacteristic
570D15—42no—
571C5×D3—42no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3C23×D512yes—
576C23×C3C23×D511yescharacteristic
577C22×D3—22no—
578C22×D3—22no—
579C22×D3—22no—
580C22×D3—52no—
581C22×D3—102no—
582C22×D3—102no—
583C22×D3—102no—
584C22×D3C23×D512yes—
585C2×C3×C4—22no—
586C2×C3×C4—22no—
587C2×C3×C4—52no—
588C2×C3×C4—52no—
589C2×C3×C4—52no—
590C2×C3×C4—52no—
591C2×C3×C4—102no—
592C2×C3×C4—102no—
593C2×C3×C4—102no—
594C2×C3×C4—102no—
595C2×C3×C4C23×D512yes—
596C2×C3×C4C23×D512yes—
597#67—28no—
598#67—204no—
599C2×Dic3—22no—
600C2×Dic3—22no—
601C2×Dic3—44no—
602C2×Dic3—52no—
603C2×Dic3—52no—
604C2×Dic3—52no—
605C2×Dic3—102no—
606C2×Dic3—102no—
607C2×Dic3—102no—
608C2×Dic3#70914yes—
609C2×Dic3C23×D512yes—
610C2×Dic3C23×D512yes—
611C2×Dic3C23×D512yes—
612D12—204no—
613C4×D3—44no—
614C4×D3—108no—
615Dic6—108no—
616Dic6—204no—
617Dic6—204no—
618C22×C5—22no—
619C22×C5—22no—
620C22×C5—22no—
621C22×C5—44no—
622C22×C5—62no—
623C22×C5—62no—
624C22×C5—62no—
625C22×C5—124no—
626C22×C5D3×#4112yes—
627C22×C5#100912yes—
628C22×C5#101012yes—
629C22×C5C24×D311yescharacteristic
630C2×D5—62no—
631C2×D5—62no—
632C2×D5—62no—
633C2×D5—124no—
634C4×C5—22no—
635C4×C5—22no—
636C4×C5—34no—
637C4×C5—62no—
638C4×C5—62no—
639Dic5—22no—
640Dic5—22no—
641Dic5—22no—
642Dic5—22no—
643Dic5—62no—
644Dic5—62no—
645Dic5—62no—
646C24—31no—
647C24—151no—
648C24C2×D3×D511yescharacteristic
649C2×Q8—154no—
650C2×Q8—154no—
651C2×Q8—154no—
652C2×Q8—304no—
653C2×Q8—602no—
654C2×Q8—602no—
655C2×D4—34no—
656C2×D4—64no—
657C2×D4—154no—
658C2×D4—154no—
659C2×D4—602no—
660C2×D4—602no—
661C22×C4—31no—
662C22×C4—31no—
663C22×C4—31no—
664C22×C4—34no—
665C22×C4—34no—
666C22×C4—51no—
667C22×C4—51no—
668C22×C4—51no—
669C22×C4—51no—
670C22×C4—122no—
671C22×C4—122no—
672C22×C4—154no—
673C22×C4—151no—
674C22×C4—151no—
675C22×C4—151no—
676C22×C4—304no—
677C22×C4C2×D3×D511yescharacteristic
678C22×C4C2×D3×D511yescharacteristic
679C4⋊C4—34no—
680C4⋊C4—54no—
681C4⋊C4—54no—
682C4⋊C4—54no—
683C4⋊C4—154no—
684C4⋊C4—154no—
685C4⋊C4—154no—
686C4⋊C4—154no—
687C4⋊C4—154no—
688C4⋊C4—154no—
689C22⋊C4—34no—
690C22⋊C4—54no—
691C22⋊C4—54no—
692C22⋊C4—154no—
693C22⋊C4—154no—
694C22⋊C4—154no—
695C22⋊C4—154no—
696C22⋊C4—154no—
697C22⋊C4—154no—
698C22⋊C4—154no—
699C22⋊C4—154no—
700C22⋊C4C2×D3×D514yes—
701C42—34no—
702C42—54no—
703C42—154no—
704C42—154no—
705C3×C5C2×#54211yescharacteristic, complemented, Hall
706C22×C3—22no—
707C22×C3—22no—
708C22×C3—22no—
709C22×C3—44no—
710C22×C3C2×#70912yes—
711C22×C3#414412yes—
712C22×C3#415012yes—
713C22×C3C24×D511yescharacteristic
714C2×D3—22no—
715C2×D3—22no—
716C2×D3—22no—
717C2×D3—44no—
718C2×D3—102no—
719C2×D3—102no—
720C2×D3—102no—
721C2×D3—204no—
722C3×C4—22no—
723C3×C4—22no—
724C3×C4—102no—
725C3×C4—102no—
726C3×C4—102no—
727C3×C4—102no—
728Dic3—22no—
729Dic3—22no—
730Dic3—102no—
731Dic3—102no—
732Dic3—102no—
733Dic3C2×#70914yes—
734C2×C5—42no—
735C2×C5—122no—
736C2×C5#571014yescomplemented
737C2×C5C2×D3×#4111yescharacteristic
738C2×C5C2×#100911yescharacteristic
739C2×C5C2×#101011yescharacteristic
740D5—122no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—32no—
745C23—62no—
746C23—62no—
747C23—62no—
748C23—152no—
749C23—302no—
750C23—302no—
751C23—302no—
752C23C22×D3×D512yes—
753C23C22×D3×D511yescharacteristic
754Q8—308no—
755Q8—604no—
756Q8—604no—
757D4—68no—
758D4—604no—
759D4—604no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—34no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—52no—
767C2×C4—52no—
768C2×C4—52no—
769C2×C4—52no—
770C2×C4—62no—
771C2×C4—62no—
772C2×C4—102no—
773C2×C4—102no—
774C2×C4—102no—
775C2×C4—102no—
776C2×C4—124no—
777C2×C4—124no—
778C2×C4—152no—
779C2×C4—152no—
780C2×C4—152no—
781C2×C4—308no—
782C2×C4—302no—
783C2×C4—302no—
784C2×C4—302no—
785C2×C4C22×D3×D512yes—
786C2×C4C22×D3×D512yes—
787C2×C3—42no—
788C2×C3#6589514yescomplemented
789C2×C3C22×#70911yescharacteristic
790C2×C3C2×#414411yescharacteristic
791C2×C3C2×#415011yescharacteristic
792D3—42no—
793D3—202no—
794C5C2×#571011yescharacteristic, complemented, Sylow
795C22—22no—
796C22—22no—
797C22—22no—
798C22—44no—
799C22—62no—
800C22—62no—
801C22—62no—
802C22—124no—
803C22—302no—
804C22—302no—
805C22—302no—
806C22—604no—
807C22D3×#70912yes—
808C22#9202012yes—
809C22#9202712yes—
810C22C23×D3×D511yescharacteristic
811C4—22no—
812C4—22no—
813C4—34no—
814C4—62no—
815C4—62no—
816C4—102no—
817C4—102no—
818C4—102no—
819C4—102no—
820C4—302no—
821C4—302no—
822C4—302no—
823C3C2×#6589511yescharacteristic, complemented, Sylow
824C2—42no—
825C2—122no—
826C2—602no—
827C2#1175297914yesdirect product factor
828C2C2×D3×#70911yescharacteristic
829C2C2×#9202011yescharacteristic
830C2C2×#9202711yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutator, cosocleC22×C3×C5C25
FrattiniC22C23×D3×D5
FittingC2×C3×C5×C22⋊C4C22
socleC23×C3×C5C24
prime radicalC2×#91557C2
hypercenterC2×C22⋊C4D3×D5
hypocenterC3×C5C2×#542
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×#91774C2semidirect
2. C2×C5×#67⋊C4C2semidirect
3. C2×C3×#4025C2semidirect
4. C2×#91575C2semidirect
6. C2×#91542C2semidirect
7. C2×#91525C2semidirect
8. C2×C4×#1204C2semidirect
9. C2×#91429C2semidirect
10. C2×#91403C2semidirect
11. C2×#91367C2semidirect
12. C2×#91365C2semidirect
13. C2×#91351C2semidirect
14. C2×#91350C2semidirect
15. C2×#91328C2semidirect
16. #11752979C2direct (N × H)
32. #91774C22semidirect
36. C5×#67⋊C4C22semidirect
43. C3×#4025C22semidirect
44. #91575C22semidirect
49. #91542C22semidirect
59. #91525C22semidirect
60. C4×#1204C22semidirect
61. #91429C22semidirect
62. #91403C22semidirect
63. #91367C22semidirect
64. #91365C22semidirect
65. #91351C22semidirect
66. #91350C22semidirect
67. #91328C22semidirect
82. C2×#4025D3semidirect
156. C2×#67⋊C4D5semidirect
207. #4025C2×D3semidirect
303. #67⋊C4C2×D5semidirect
566. C2×C3×C5#542semidirect
705. C3×C5C2×#542semidirect
736. C2×C5#5710semidirect
788. C2×C3#65895semidirect
794. C5C2×#5710semidirect
823. C3C2×#65895semidirect
827. C2#11752979direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#917742
C2×C5×#67⋊C42
C2×C3×#40252
C2×#915752
C2×#915572
C2×#915422
C2×#915252
C2×C4×#12042
C2×#914292
C2×#914032
C2×#913672
C2×#913652
C2×#913512
C2×#913502
C2×#913282
#117529792
C2×#658953
C2×#57105