Finite Group Databasebeta

← C2×#11754284 #14479081

Subgroups — C2×#11754284 #14479081

Order 1920.

3280 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6779C211yesmaximal, characteristic
2C2×C4×#1220C211yesmaximal, characteristic, complemented
3C22×C5×Dic3⋊C4C211yesmaximal, characteristic, complemented
4C2×C3×C4×C22⋊D5C211yesmaximal, characteristic, complemented
5C2×#91556C211yesmaximal, characteristic, complemented
6C2×Dic3×C22⋊D5C211yesmaximal, characteristic, complemented
7C2×#91529C211yesmaximal, characteristic, complemented
8C2×#91444C211yesmaximal, characteristic, complemented
9C2×#91404C211yesmaximal, characteristic, complemented
10C2×#91402C211yesmaximal, characteristic, complemented
11C2×#91396C211yesmaximal, characteristic, complemented
12#11754284C2116yesmaximal, direct product factor
13C2×#91394C211yesmaximal, characteristic, complemented
14C2×D5×Dic3⋊C4C211yesmaximal, characteristic, complemented
15C2×#91325C211yesmaximal, characteristic, complemented
16C2×#91323C211yesmaximal, characteristic, complemented
17C2×#65838—31nomaximal, Hall
18C23×C3×C4×C5C2211yescharacteristic
19C22×#1220C2211yescharacteristic
20C22×C4×D15C2211yescharacteristic
21C23×C5×Dic3C2211yescharacteristic
22C23×C5×Dic3C2211yescharacteristic
23C22×C3×C22⋊D5C2211yescharacteristic
24C22×C3×C4×D5C2211yescharacteristic
25C22×#1204C2211yescharacteristic
26C22×#1202C2211yescharacteristic
27C22×#1200C2211yescharacteristic
28C22×#1200C2211yescharacteristic
29C2×#6779C4116yescomplemented
30C2×#6779C2218yes—
31C22×D5×Dic3C2211yescharacteristic
32C22×D5×Dic3C2211yescharacteristic
33C2×#6719C2211yescharacteristic
34C4×#1220C2218yescomplemented
35C2×#6714C2211yescharacteristic
36C2×#6712C2211yescharacteristic
37C2×C4×Dic15C2211yescharacteristic
38C2×C5×Dic3⋊C4C2211yescharacteristic
39C2×C5×Dic3⋊C4C2211yescharacteristic
40C2×C5×Dic3⋊C4C2211yescharacteristic
41C2×C5×Dic3⋊C4C2211yescharacteristic
42C2×C5×Dic3⋊C4C2218yescomplemented
43C2×C3×C22⋊Dic5C2211yescharacteristic
44C3×C4×C22⋊D5C2218yescomplemented
45C2×C3×#685C2211yescharacteristic
46C2×C3×#683C2211yescharacteristic
47C2×C3×C4×Dic5C2211yescharacteristic
48#91556C2218yescomplemented
49Dic3×C22⋊D5C2218yescomplemented
50C2×Dic3⋊Dic5C2211yescharacteristic
51C2×Dic3⋊Dic5C2211yescharacteristic
52C2×#6669C2211yescharacteristic
53C2×#6668C2211yescharacteristic
54C2×#6667C2211yescharacteristic
55C2×#6665C2211yescharacteristic
56#91529C2218yescomplemented
57C2×Dic3×Dic5C2211yescharacteristic
58C2×Dic3×Dic5C2211yescharacteristic
59C2×Dic3×Dic5C2211yescharacteristic
60C2×Dic3×Dic5C2211yescharacteristic
61#91444C2218yescomplemented
62#91404C2218yescomplemented
63#91402C2218yescomplemented
64#91396C2218yescomplemented
65#91394C2218yescomplemented
66D5×Dic3⋊C4C2218yescomplemented
67#91325C2218yescomplemented
68#91323C2218yescomplemented
69C2×#5546—51nomaximal, Hall
70C22×#709—31no—
71C22×C5×C4⋊C4—31no—
72C2×C4×C22⋊D5—31no—
73C2×C4×C22⋊D5—31no—
74C2×C4×C22⋊D5—31no—
75C2×C4×C22⋊D5D311yescharacteristic, complemented
76C2×#4072—31no—
77#65838—316no—
78C2×#4039—31no—
79C2×#4039—31no—
80C2×#4038—31no—
81C2×#4038—31no—
82C2×D5×C4⋊C4—31no—
83C2×D5×C4⋊C4—31no—
84C2×#4033—31no—
85C2×#4033—31no—
86C24×C3×C5C2311yescharacteristic
87C23×D15C2311yescharacteristic
88C23×C3×D5C2311yescharacteristic
89C22×C3×C4×C5—42no—
90C22×C3×C4×C5C2311yescharacteristic
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2314yes—
93C2×#1220C2×C418yescomplemented
94C2×#1220C2314yes—
95C22×Dic15C2311yescharacteristic
96C22×Dic15C2311yescharacteristic
97C22×Dic15C2311yescharacteristic
98C2×C4×D15—42no—
99C2×C4×D15C2314yes—
100C22×C5×Dic3—42no—
101C22×C5×Dic3C2×C418yescomplemented
102C22×C5×Dic3C2311yescharacteristic
103C22×C5×Dic3C2311yescharacteristic
104C22×C5×Dic3C2314yes—
105C22×C5×Dic3C2311yescharacteristic
106C22×C5×Dic3C2311yescharacteristic
107C22×C5×Dic3C2314yes—
108C2×C3×C22⋊D5C2×C418yescomplemented
109C2×C3×C22⋊D5C2314yes—
110C22×C3×Dic5C2311yescharacteristic
111C22×C3×Dic5C2311yescharacteristic
112C22×C3×Dic5C2311yescharacteristic
113C2×C3×C4×D5—42no—
114C2×C3×C4×D5C2314yes—
115C2×#1204C2×C418yescomplemented
116C2×#1204C2314yes—
117C2×#1202C2×C418yescomplemented
118C2×#1202C2314yes—
119C2×#1200—42no—
120C2×#1200C2×C418yescomplemented
121C2×#1200C2314yes—
122C2×#1200C2314yes—
123#6779C2×C4164yescomplemented
124C2×D5×Dic3—42no—
125C2×D5×Dic3C2×C418yescomplemented
126C2×D5×Dic3C2314yes—
127C2×D5×Dic3C2314yes—
128#6719C2314yes—
129#6714C2314yes—
130#6712C2314yes—
131C4×Dic15C2314yes—
132C5×Dic3⋊C4C2314yes—
133C5×Dic3⋊C4C2314yes—
134C5×Dic3⋊C4C2314yes—
135C5×Dic3⋊C4C2314yes—
136C3×C22⋊Dic5C2314yes—
137C3×#685C2314yes—
138C3×#683C2314yes—
139C3×C4×Dic5C2314yes—
140Dic3⋊Dic5C2314yes—
141Dic3⋊Dic5C2314yes—
142#6669C2314yes—
143#6668C2314yes—
144#6667C2314yes—
145#6665C2314yes—
146Dic3×Dic5C2314yes—
147Dic3×Dic5C2314yes—
148Dic3×Dic5C2314yes—
149Dic3×Dic5C2314yes—
150C22×#237—51no—
151C2×C3×C4×D4—51no—
152C2×D4×Dic3—51no—
153C2×C4×#67—51no—
154C2×C4×#67—51no—
155C22×Dic3⋊C4—51no—
156C22×Dic3⋊C4D511yescharacteristic, complemented
157#5546—516no—
158C2×D3×C4⋊C4—51no—
159C2×#887—51no—
160C2×#67⋊C4—51no—
161C2×#67⋊C4—51no—
162C2×#877—51no—
163C2×#877—51no—
164C2×#872—51no—
165C2×C4×Dic6—51no—
166C23×C4×C5—31no—
167C23×C4×C5—31no—
168C23×C4×C5C2×D311yescharacteristic
169C22×C22⋊D5—31no—
170C22×C22⋊D5C2×D311yescharacteristic
171C2×#709—316no—
172C2×#709—38no—
173C22×D20—31no—
174C22×C4×D5—31no—
175C22×C4×D5—31no—
176C22×C4×D5—31no—
177C22×C4×D5—31no—
178C22×C4×D5—31no—
179C22×C4×D5C2×D311yescharacteristic
180C22×Dic10—31no—
181C2×C5×C4⋊C4—31no—
182C2×C5×C4⋊C4—31no—
183C2×C5×C4⋊C4—31no—
184C2×C5×C4⋊C4—31no—
185C2×C5×C4⋊C4—38no—
186C2×C22⋊Dic5—31no—
187C2×C22⋊Dic5C2×D311yescharacteristic
188C4×C22⋊D5—38no—
189C4×C22⋊D5—38no—
190C4×C22⋊D5—38no—
191C4×C22⋊D5C2×D318yescomplemented
192C2×#685—31no—
193C2×#685—31no—
194C2×#685—31no—
195C2×#685C2×D311yescharacteristic
196#4072—38no—
197C2×C4⋊Dic5—31no—
198C2×C4⋊Dic5—31no—
199C2×#683—31no—
200C2×#683—31no—
201C2×#683—31no—
202C2×#683C2×D311yescharacteristic
203C2×C4×Dic5—31no—
204C2×C4×Dic5—31no—
205C2×C4×Dic5—31no—
206C2×C4×Dic5—31no—
207C2×C4×Dic5—31no—
208C2×C4×Dic5C2×D311yescharacteristic
209#4039—38no—
210#4039—38no—
211#4038—38no—
212#4038—38no—
213D5×C4⋊C4—38no—
214D5×C4⋊C4—38no—
215#4033—38no—
216#4033—38no—
217C2×#520—151noSylow
218C23×C3×C5—22no—
219C23×C3×C5—22no—
220C23×C3×C5C22×C414yes—
221C23×C3×C5C2412yes—
222C23×C3×C5C2411yescharacteristic
223C22×D15—22no—
224C22×D15—22no—
225C22×D15C22×C414yes—
226C22×D15C2412yes—
227C22×C3×D5—22no—
228C22×C3×D5—22no—
229C22×C3×D5C22×C414yes—
230C22×C3×D5C2412yes—
231C2×C3×C4×C5—22no—
232C2×C3×C4×C5—22no—
233C2×C3×C4×C5—44no—
234C2×C3×C4×C5C2412yes—
235C2×C3×C4×C5C2412yes—
236#1220C22×C4116yescomplemented
237C2×Dic15—22no—
238C2×Dic15—22no—
239C2×Dic15C22×C414yes—
240C2×Dic15C2412yes—
241C2×Dic15C2412yes—
242C2×Dic15C2412yes—
243C4×D15—44no—
244C2×C5×Dic3—22no—
245C2×C5×Dic3—22no—
246C2×C5×Dic3—44no—
247C2×C5×Dic3C22×C414yes—
248C2×C5×Dic3C22×C414yes—
249C2×C5×Dic3C22×C4116yescomplemented
250C2×C5×Dic3C2412yes—
251C2×C5×Dic3C2412yes—
252C2×C5×Dic3C2412yes—
253C2×C5×Dic3C2412yes—
254C3×C22⋊D5C22×C4116yescomplemented
255C2×C3×Dic5—22no—
256C2×C3×Dic5—22no—
257C2×C3×Dic5C22×C414yes—
258C2×C3×Dic5C2412yes—
259C2×C3×Dic5C2412yes—
260C2×C3×Dic5C2412yes—
261C3×C4×D5—44no—
262#1204C22×C4116yescomplemented
263#1202C22×C4116yescomplemented
264#1200—44no—
265#1200C22×C4116yescomplemented
266D5×Dic3—44no—
267D5×Dic3C22×C4116yescomplemented
268C22×C3×D4—51no—
269C23×C3×C4—51no—
270C23×C3×C4C2×D511yescharacteristic
271C22×#67—51no—
272C22×#67—51no—
273C23×Dic3—51no—
274C23×Dic3—51no—
275C23×Dic3C2×D511yescharacteristic
276C23×Dic3C2×D511yescharacteristic
277C2×#237—516no—
278C2×#237—58no—
279C22×C4×D3—51no—
280C22×C4×D3—51no—
281C22×C4×D3—51no—
282C22×Dic6—51no—
283C3×C4×D4—58no—
284C2×C3×C4⋊C4—51no—
285C2×C3×C22⋊C4—51no—
286C2×C3×C22⋊C4—51no—
287C2×C3×C42—51no—
288C2×#217—51no—
289C2×#217—51no—
290D4×Dic3—58no—
291C4×#67—58no—
292C4×#67—58no—
293C2×(C2×D3)⋊C4—51no—
294C2×(C2×D3)⋊C4—51no—
295C2×C4⋊Dic3—51no—
296C2×Dic3⋊C4—51no—
297C2×Dic3⋊C4—51no—
298C2×Dic3⋊C4—51no—
299C2×Dic3⋊C4—51no—
300C2×Dic3⋊C4—58no—
301C2×Dic3⋊C4C2×D511yescharacteristic
302C2×Dic3⋊C4C2×D511yescharacteristic
303C2×Dic3⋊C4C2×D511yescharacteristic
304C2×Dic3⋊C4C2×D511yescharacteristic
305C2×Dic3⋊C4C2×D518yescomplemented
306C2×C4×Dic3—51no—
307C2×C4×Dic3—51no—
308C2×C4×Dic3—51no—
309C2×C4×Dic3—51no—
310C2×C4×Dic3—51no—
311D3×C4⋊C4—58no—
312#887—58no—
313#67⋊C4—58no—
314#67⋊C4—58no—
315#877—58no—
316#877—58no—
317#872—58no—
318C4×Dic6—58no—
319C24×C5C22×D311yescharacteristic
320C23×D5—31no—
321C23×D5C22×D311yescharacteristic
322C22×C4×C5—38no—
323C22×C4×C5—31no—
324C22×C4×C5—31no—
325C22×C4×C5—34no—
326C22×C4×C5—31no—
327C22×C4×C5—31no—
328C22×C4×C5—34no—
329C22×C4×C5—42no—
330C22×C4×C5—122no—
331C22×C4×C5C22×D311yescharacteristic
332C22×C4×C5C22×D311yescharacteristic
333C22×C4×C5C22×D314yes—
334C2×C22⋊D5—38no—
335C2×C22⋊D5—34no—
336C2×C22⋊D5C4×D318yescomplemented
337C2×C22⋊D5C22×D314yes—
338C22×Dic5—31no—
339C22×Dic5—31no—
340C22×Dic5—31no—
341C22×Dic5C22×D311yescharacteristic
342C22×Dic5C22×D311yescharacteristic
343C22×Dic5C22×D311yescharacteristic
344#709—364no—
345C2×D20—38no—
346C2×D20—34no—
347C2×C4×D5—38no—
348C2×C4×D5—34no—
349C2×C4×D5—38no—
350C2×C4×D5—34no—
351C2×C4×D5—34no—
352C2×C4×D5—34no—
353C2×C4×D5—34no—
354C2×C4×D5—42no—
355C2×C4×D5—122no—
356C2×C4×D5—122no—
357C2×C4×D5—122no—
358C2×C4×D5C22×D314yes—
359C2×Dic10—38no—
360C2×Dic10—34no—
361C5×C4⋊C4—34no—
362C5×C4⋊C4—34no—
363C5×C4⋊C4—34no—
364C5×C4⋊C4—34no—
365C22⋊Dic5—34no—
366C22⋊Dic5C22×D314yes—
367#685—34no—
368#685—34no—
369#685—34no—
370#685C22×D314yes—
371C4⋊Dic5—34no—
372C4⋊Dic5—34no—
373#683—34no—
374#683—34no—
375#683—34no—
376#683C22×D314yes—
377C4×Dic5—34no—
378C4×Dic5—34no—
379C4×Dic5—34no—
380C4×Dic5—34no—
381C4×Dic5—34no—
382C4×Dic5C22×D314yes—
383C22×#41—151no—
384#520—1516no—
385C2×C4×Q8—151no—
386C2×C4×Q8—151no—
387C2×C4×D4—51no—
388C2×C4×D4—151no—
389C2×C4×D4—151no—
390C2×C4×D4—151no—
391C2×C4×D4—151no—
392C2×C4×D4—151no—
393C2×#117—151no—
394C2×#117—151no—
395C2×#117—151no—
396C22×C4⋊C4—31no—
397C22×C4⋊C4—151no—
398C22×C4⋊C4—151no—
399C22×C3×C5—28no—
400C22×C3×C5—22no—
401C22×C3×C5—22no—
402C22×C3×C5C23×C414yes—
403C22×C3×C5C23×C412yes—
404C22×C3×C5H(5,𝔽2)12yes—
405C22×C3×C52−1+412yes—
406C22×C3×C5C2511yescharacteristic
407C2×D15—28no—
408C2×D15—22no—
409C2×D15—22no—
410C2×D15C23×C414yes—
411C2×C3×D5—28no—
412C2×C3×D5—22no—
413C2×C3×D5—22no—
414C2×C3×D5C23×C414yes—
415C3×C4×C5—22no—
416C3×C4×C5—22no—
417Dic15—22no—
418Dic15—22no—
419Dic15C23×C414yes—
420C3×Dic5—22no—
421C3×Dic5—22no—
422C3×Dic5C23×C414yes—
423C5×Dic3—22no—
424C5×Dic3—22no—
425C5×Dic3C23×C414yes—
426C5×Dic3C23×C414yes—
427C24×C3—51no—
428C24×C3C22×D511yescharacteristic
429C23×D3—51no—
430C2×C3×D4—58no—
431C2×C3×D4—54no—
432C22×C3×C4—42no—
433C22×C3×C4—51no—
434C22×C3×C4—51no—
435C22×C3×C4—51no—
436C22×C3×C4—54no—
437C22×C3×C4—202no—
438C22×C3×C4C22×D511yescharacteristic
439C22×C3×C4C22×D511yescharacteristic
440C22×C3×C4C22×D514yes—
441C2×#67—58no—
442C2×#67—54no—
443C2×#67—58no—
444C2×#67—54no—
445C22×Dic3—42no—
446C22×Dic3—51no—
447C22×Dic3—58no—
448C22×Dic3—54no—
449C22×Dic3—51no—
450C22×Dic3—51no—
451C22×Dic3—54no—
452C22×Dic3—202no—
453C22×Dic3C4×D518yescomplemented
454C22×Dic3C22×D511yescharacteristic
455C22×Dic3C22×D511yescharacteristic
456C22×Dic3C22×D514yes—
457C22×Dic3C22×D511yescharacteristic
458C22×Dic3C22×D511yescharacteristic
459C22×Dic3C22×D514yes—
460#237—564no—
461C2×C4×D3—58no—
462C2×C4×D3—54no—
463C2×C4×D3—54no—
464C2×C4×D3—54no—
465C2×C4×D3—202no—
466C2×C4×D3—202no—
467C2×Dic6—58no—
468C2×Dic6—54no—
469C3×C4⋊C4—54no—
470C3×C22⋊C4—54no—
471C3×C22⋊C4—54no—
472C3×C42—54no—
473#217—54no—
474#217—54no—
475(C2×D3)⋊C4—54no—
476(C2×D3)⋊C4—54no—
477C4⋊Dic3—54no—
478Dic3⋊C4—54no—
479Dic3⋊C4—54no—
480Dic3⋊C4—54no—
481Dic3⋊C4—54no—
482Dic3⋊C4C22×D514yes—
483Dic3⋊C4C22×D514yes—
484Dic3⋊C4C22×D514yes—
485Dic3⋊C4C22×D514yes—
486C4×Dic3—54no—
487C4×Dic3—54no—
488C4×Dic3—54no—
489C4×Dic3—54no—
490C4×Dic3—54no—
491C23×C5—22no—
492C23×C5—22no—
493C23×C5C2×C4×D314yes—
494C23×C5C23×D312yes—
495C23×C5C23×D311yescharacteristic
496C22×D5—22no—
497C22×D5—22no—
498C22×D5—34no—
499C22×D5—32no—
500C22×D5—62no—
501C22×D5—62no—
502C22×D5C2×C4×D314yes—
503C22×D5C23×D312yes—
504C2×C4×C5—22no—
505C2×C4×C5—22no—
506C2×C4×C5—34no—
507C2×C4×C5—34no—
508C2×C4×C5—316no—
509C2×C4×C5—32no—
510C2×C4×C5—32no—
511C2×C4×C5—32no—
512C2×C4×C5—32no—
513C2×C4×C5—44no—
514C2×C4×C5—62no—
515C2×C4×C5—62no—
516C2×C4×C5—124no—
517C2×C4×C5C23×D312yes—
518C2×C4×C5C23×D312yes—
519C22⋊D5—316no—
520C22⋊D5C2×C4×D3116yescomplemented
521C2×Dic5—22no—
522C2×Dic5—22no—
523C2×Dic5—34no—
524C2×Dic5—32no—
525C2×Dic5—32no—
526C2×Dic5—32no—
527C2×Dic5—62no—
528C2×Dic5—62no—
529C2×Dic5C2×C4×D314yes—
530C2×Dic5C23×D312yes—
531C2×Dic5C23×D312yes—
532C2×Dic5C23×D312yes—
533D20—316no—
534C4×D5—316no—
535C4×D5—316no—
536C4×D5—44no—
537C4×D5—124no—
538C4×D5—124no—
539C4×D5—124no—
540Dic10—316no—
541C2×#41—158no—
542C2×#41—1516no—
543C22×Q8—151no—
544C22×D4—51no—
545C22×D4—151no—
546C22×D4—151no—
547C23×C4—31no—
548C23×C4—31no—
549C23×C4—51no—
550C23×C4—151no—
551C23×C4—151no—
552C23×C4—151no—
553C23×C4—151no—
554C23×C4—151no—
555C23×C4D3×D511yescharacteristic
556C4×Q8—158no—
557C4×Q8—158no—
558C4×D4—58no—
559C4×D4—158no—
560C4×D4—158no—
561C4×D4—158no—
562C4×D4—158no—
563C4×D4—158no—
564#117—158no—
565#117—158no—
566#117—158no—
567C2×C4⋊C4—31no—
568C2×C4⋊C4—31no—
569C2×C4⋊C4—31no—
570C2×C4⋊C4—31no—
571C2×C4⋊C4—38no—
572C2×C4⋊C4—51no—
573C2×C4⋊C4—158no—
574C2×C4⋊C4—158no—
575C2×C4⋊C4—151no—
576C2×C4⋊C4—151no—
577C2×C4⋊C4—151no—
578C2×C4⋊C4—151no—
579C2×C4⋊C4—151no—
580C2×C22⋊C4—51no—
581C2×C22⋊C4—51no—
582C2×C22⋊C4—151no—
583C2×C22⋊C4—151no—
584C2×C22⋊C4—151no—
585C2×C22⋊C4—151no—
586C2×C42—51no—
587C2×C42—151no—
588C2×C42—151no—
589C2×C42—151no—
590C2×C42—151no—
591C2×C42—151no—
592C2×C3×C5—24no—
593C2×C3×C5#52014yescomplemented
594C2×C3×C5C24×C411yescharacteristic
595C2×C3×C5C2×H(5,𝔽2)11yescharacteristic
596C2×C3×C5C2×2−1+411yescharacteristic
597D15—24no—
598C3×D5—24no—
599C23×C3—22no—
600C23×C3—22no—
601C23×C3—54no—
602C23×C3—52no—
603C23×C3—102no—
604C23×C3—102no—
605C23×C3C2×C4×D514yes—
606C23×C3C23×D512yes—
607C23×C3C23×D511yescharacteristic
608C22×D3—54no—
609C22×D3—52no—
610C22×D3—102no—
611C22×D3—102no—
612C3×D4—516no—
613C2×C3×C4—22no—
614C2×C3×C4—22no—
615C2×C3×C4—44no—
616C2×C3×C4—54no—
617C2×C3×C4—52no—
618C2×C3×C4—52no—
619C2×C3×C4—52no—
620C2×C3×C4—102no—
621C2×C3×C4—102no—
622C2×C3×C4—204no—
623C2×C3×C4C23×D512yes—
624C2×C3×C4C23×D512yes—
625#67—516no—
626#67—516no—
627C2×Dic3—22no—
628C2×Dic3—22no—
629C2×Dic3—44no—
630C2×Dic3—54no—
631C2×Dic3—52no—
632C2×Dic3—516no—
633C2×Dic3—52no—
634C2×Dic3—52no—
635C2×Dic3—102no—
636C2×Dic3—102no—
637C2×Dic3—204no—
638C2×Dic3C2×C4×D514yes—
639C2×Dic3C2×C4×D514yes—
640C2×Dic3C2×C4×D5116yescomplemented
641C2×Dic3C23×D512yes—
642C2×Dic3C23×D512yes—
643C2×Dic3C23×D512yes—
644C2×Dic3C23×D512yes—
645C4×D3—516no—
646C4×D3—204no—
647C4×D3—204no—
648Dic6—516no—
649C22×C5—22no—
650C22×C5—22no—
651C22×C5—28no—
652C22×C5C22×C4×D314yes—
653C22×C5C22×C4×D312yes—
654C22×C5#100412yes—
655C22×C5#101012yes—
656C22×C5C24×D311yescharacteristic
657C2×D5—22no—
658C2×D5—22no—
659C2×D5—28no—
660C2×D5—34no—
661C2×D5—62no—
662C2×D5—62no—
663C2×D5—68no—
664C2×D5C22×C4×D314yes—
665C4×C5—22no—
666C4×C5—22no—
667C4×C5—34no—
668C4×C5—34no—
669C4×C5—62no—
670C4×C5—62no—
671Dic5—22no—
672Dic5—22no—
673Dic5—34no—
674Dic5—62no—
675Dic5—62no—
676Dic5C22×C4×D314yes—
677C24—51no—
678C24—151no—
679C24C2×D3×D511yescharacteristic
680#41—1564no—
681C2×Q8—154no—
682C2×Q8—158no—
683C2×D4—58no—
684C2×D4—54no—
685C2×D4—154no—
686C2×D4—158no—
687C2×D4—158no—
688C2×D4—154no—
689C22×C4—38no—
690C22×C4—34no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—34no—
696C22×C4—42no—
697C22×C4—51no—
698C22×C4—51no—
699C22×C4—51no—
700C22×C4—54no—
701C22×C4—122no—
702C22×C4—154no—
703C22×C4—158no—
704C22×C4—154no—
705C22×C4—154no—
706C22×C4—158no—
707C22×C4—154no—
708C22×C4—151no—
709C22×C4—151no—
710C22×C4—151no—
711C22×C4—154no—
712C22×C4—202no—
713C22×C4—602no—
714C22×C4—602no—
715C22×C4—602no—
716C22×C4C2×D3×D511yescharacteristic
717C22×C4C2×D3×D511yescharacteristic
718C22×C4C2×D3×D514yes—
719C4⋊C4—34no—
720C4⋊C4—34no—
721C4⋊C4—34no—
722C4⋊C4—34no—
723C4⋊C4—54no—
724C4⋊C4—154no—
725C4⋊C4—154no—
726C4⋊C4—154no—
727C4⋊C4—154no—
728C4⋊C4—154no—
729C22⋊C4—54no—
730C22⋊C4—54no—
731C22⋊C4—154no—
732C22⋊C4—154no—
733C22⋊C4—154no—
734C22⋊C4—154no—
735C42—54no—
736C42—154no—
737C42—154no—
738C42—154no—
739C42—154no—
740C42—154no—
741C3×C5C2×#52011yescharacteristic, complemented, Hall
742C22×C3—28no—
743C22×C3—22no—
744C22×C3—22no—
745C22×C3—54no—
746C22×C3—108no—
747C22×C3—102no—
748C22×C3—102no—
749C22×C3C22×C4×D514yes—
750C22×C3C22×C4×D512yes—
751C22×C3#414412yes—
752C22×C3#414712yes—
753C22×C3C24×D511yescharacteristic
754C2×D3—54no—
755C2×D3—108no—
756C2×D3—102no—
757C2×D3—102no—
758C3×C4—22no—
759C3×C4—22no—
760C3×C4—54no—
761C3×C4—102no—
762C3×C4—102no—
763Dic3—22no—
764Dic3—22no—
765Dic3—54no—
766Dic3—102no—
767Dic3—102no—
768Dic3C22×C4×D514yes—
769Dic3C22×C4×D514yes—
770C2×C5—24no—
771C2×C5#554614yescomplemented
772C2×C5C23×C4×D311yescharacteristic
773C2×C5C2×#100411yescharacteristic
774C2×C5C2×#101011yescharacteristic
775D5—24no—
776D5—64no—
777C23—22no—
778C23—22no—
779C23—54no—
780C23—52no—
781C23—102no—
782C23—102no—
783C23—154no—
784C23—152no—
785C23—302no—
786C23—302no—
787C23C4×D3×D514yes—
788C23C22×D3×D512yes—
789C23C22×D3×D511yescharacteristic
790Q8—1516no—
791D4—516no—
792D4—1516no—
793D4—1516no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—34no—
797C2×C4—34no—
798C2×C4—316no—
799C2×C4—32no—
800C2×C4—32no—
801C2×C4—32no—
802C2×C4—32no—
803C2×C4—44no—
804C2×C4—54no—
805C2×C4—52no—
806C2×C4—52no—
807C2×C4—52no—
808C2×C4—62no—
809C2×C4—62no—
810C2×C4—102no—
811C2×C4—102no—
812C2×C4—124no—
813C2×C4—1516no—
814C2×C4—1516no—
815C2×C4—154no—
816C2×C4—152no—
817C2×C4—152no—
818C2×C4—152no—
819C2×C4—204no—
820C2×C4—302no—
821C2×C4—302no—
822C2×C4—604no—
823C2×C4—604no—
824C2×C4—604no—
825C2×C4C22×D3×D512yes—
826C2×C4C22×D3×D512yes—
827C2×C3—24no—
828C2×C3—104no—
829C2×C3#6583814yescomplemented
830C2×C3C23×C4×D511yescharacteristic
831C2×C3C2×#414411yescharacteristic
832C2×C3C2×#414711yescharacteristic
833D3—104no—
834C5C2×#554611yescharacteristic, complemented, Sylow
835C22—22no—
836C22—28no—
837C22—22no—
838C22—54no—
839C22—102no—
840C22—108no—
841C22—102no—
842C22—154no—
843C22—302no—
844C22—308no—
845C22—302no—
846C22#9200012yes—
847C22C2×C4×D3×D514yes—
848C22C2×C4×D3×D512yes—
849C22#9204912yes—
850C22C23×D3×D511yescharacteristic
851C4—22no—
852C4—22no—
853C4—34no—
854C4—34no—
855C4—54no—
856C4—62no—
857C4—62no—
858C4—102no—
859C4—102no—
860C4—154no—
861C4—302no—
862C4—302no—
863C3C2×#6583811yescharacteristic, complemented, Sylow
864C2—24no—
865C2—104no—
866C2—304no—
867C2#1175428414yesdirect product factor
868C2C2×#9200011yescharacteristic
869C2C22×C4×D3×D511yescharacteristic
870C2C2×#9204911yescharacteristic
subgroupG/H
centerC23C22×D3×D5
commutatorC2×C3×C5C24×C4
FrattiniC22C23×D3×D5
FittingC23×C3×C4×C5C22
socleC23×C3×C5C24
prime radicalC22×#6779C2
cosocleC22×C3×C5C25
hypercenterC23×C4D3×D5
hypocenterC3×C5C2×#520
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#1220C2semidirect
3. C22×C5×Dic3⋊C4C2semidirect
4. C2×C3×C4×C22⋊D5C2semidirect
5. C2×#91556C2semidirect
6. C2×Dic3×C22⋊D5C2semidirect
7. C2×#91529C2semidirect
8. C2×#91444C2semidirect
9. C2×#91404C2semidirect
10. C2×#91402C2semidirect
11. C2×#91396C2semidirect
12. #11754284C2direct (N × H)
13. C2×#91394C2semidirect
14. C2×D5×Dic3⋊C4C2semidirect
15. C2×#91325C2semidirect
16. C2×#91323C2semidirect
29. C2×#6779C4semidirect
34. C4×#1220C22semidirect
42. C2×C5×Dic3⋊C4C22semidirect
44. C3×C4×C22⋊D5C22semidirect
48. #91556C22semidirect
49. Dic3×C22⋊D5C22semidirect
56. #91529C22semidirect
61. #91444C22semidirect
62. #91404C22semidirect
63. #91402C22semidirect
64. #91396C22semidirect
65. #91394C22semidirect
66. D5×Dic3⋊C4C22semidirect
67. #91325C22semidirect
68. #91323C22semidirect
75. C2×C4×C22⋊D5D3semidirect
93. C2×#1220C2×C4semidirect
101. C22×C5×Dic3C2×C4semidirect
108. C2×C3×C22⋊D5C2×C4semidirect
115. C2×#1204C2×C4semidirect
117. C2×#1202C2×C4semidirect
120. C2×#1200C2×C4semidirect
123. #6779C2×C4semidirect
125. C2×D5×Dic3C2×C4semidirect
156. C22×Dic3⋊C4D5semidirect
191. C4×C22⋊D5C2×D3semidirect
236. #1220C22×C4semidirect
249. C2×C5×Dic3C22×C4semidirect
254. C3×C22⋊D5C22×C4semidirect
262. #1204C22×C4semidirect
263. #1202C22×C4semidirect
265. #1200C22×C4semidirect
267. D5×Dic3C22×C4semidirect
305. C2×Dic3⋊C4C2×D5semidirect
336. C2×C22⋊D5C4×D3semidirect
453. C22×Dic3C4×D5semidirect
520. C22⋊D5C2×C4×D3semidirect
593. C2×C3×C5#520semidirect
640. C2×Dic3C2×C4×D5semidirect
741. C3×C5C2×#520semidirect
771. C2×C5#5546semidirect
829. C2×C3#65838semidirect
834. C5C2×#5546semidirect
863. C3C2×#65838semidirect
867. C2#11754284direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#67792
C2×C4×#12202
C22×C5×Dic3⋊C42
C2×C3×C4×C22⋊D52
C2×#915562
C2×Dic3×C22⋊D52
C2×#915292
C2×#914442
C2×#914042
C2×#914022
C2×#913962
#117542842
C2×#913942
C2×D5×Dic3⋊C42
C2×#913252
C2×#913232
C2×#658383
C2×#55465