Finite Group Databasebeta

← #14327874

Subgroups — #14327874

Order 1920.

960 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×D5×Dic3C211yesmaximal, characteristic
2#11752449C211yesmaximal, characteristic
3C3×(C2×AGL(1,𝔽5))⋊Q8C211yesmaximal, characteristic
4#11751860C211yesmaximal, characteristic
5C4×Dic3⋊AGL(1,𝔽5)C211yesmaximal, characteristic
6#11751846C211yesmaximal, characteristic
7#11751840C212yesmaximal
8#11751839C212yesmaximal
9AGL(1,𝔽5)×C4⋊Dic3C211yesmaximal, characteristic
10#11751834C212yesmaximal
11#11751746C212yesmaximal
12#10617213—31nomaximal, Hall
13C2×C3×Q8×D5C2211yescharacteristic
14C2×C4⋊ΓL(1,𝔽16)C2211yescharacteristic
15C2×C4×ΓL(1,𝔽16)C2211yescharacteristic
16C2×C3×C4⋊AGL(1,𝔽5)C2211yescharacteristic
17C2×C3×C4×AGL(1,𝔽5)C2211yescharacteristic
18C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
19C2×Dic3⋊AGL(1,𝔽5)C2212yes—
20C2×Dic3⋊AGL(1,𝔽5)C2212yes—
21C2×Dic3⋊AGL(1,𝔽5)C2211yescharacteristic
22C2×Dic3×AGL(1,𝔽5)C2212yes—
23C2×Dic3×AGL(1,𝔽5)C2212yes—
24Q8×Dic15C411yescharacteristic, complemented
25C5×Q8×Dic3C411yescharacteristic, complemented
26D5×C4⋊Dic3C2211yescharacteristic
27D5×C4⋊Dic3C2212yes—
28C4×D5×Dic3C2212yes—
29C4×D5×Dic3C2211yescharacteristic
30#91331C411yescharacteristic, complemented
31#91331C412yescomplemented
32Dic3×Dic10C411yescharacteristic, complemented
33Dic3×Dic10C412yescomplemented
34#91235C2212yes—
35#91235C2212yes—
36C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
37C3×(C2×AGL(1,𝔽5))⋊C4C2212yes—
38(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
39(C2×AGL(1,𝔽5))⋊Dic3C2212yes—
40(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
41(C2×AGL(1,𝔽5))⋊Dic3C2211yescharacteristic
42#76489—51nomaximal, Hall
43C4×Q8×D5—31no—
44(C2×AGL(1,𝔽5))⋊Q8—31no—
45(C2×AGL(1,𝔽5))⋊Q8D311yescharacteristic
46#65711—32no—
47#65711—32no—
48C4⋊C4×AGL(1,𝔽5)—31no—
49C4⋊C4×AGL(1,𝔽5)—31no—
50#65689—32no—
51#65688—31no—
52C4×C4⋊AGL(1,𝔽5)—32no—
53C4×C4⋊AGL(1,𝔽5)—31no—
54C22×ΓL(1,𝔽16)C2312yes—
55C22×ΓL(1,𝔽16)C2311yescharacteristic
56C22×ΓL(1,𝔽16)C2311yescharacteristic
57C22×C3×AGL(1,𝔽5)C2312yes—
58C22×C3×AGL(1,𝔽5)C2311yescharacteristic
59C22×C3×AGL(1,𝔽5)C2311yescharacteristic
60C2×C3×C5×Q8C2×C411yescharacteristic
61C3×Q8×D5—22no—
62C3×Q8×D5—22no—
63C2×C3×C4×D5C2312yes—
64C2×C3×C4×D5C2311yescharacteristic
65C2×C3×Dic10C2×C411yescharacteristic
66C2×C3×Dic10C2×C412yes—
67C2×D5×Dic3C2312yes—
68C2×D5×Dic3C2311yescharacteristic
69C2×D5×Dic3C2311yescharacteristic
70C4⋊ΓL(1,𝔽16)—22no—
71C4×ΓL(1,𝔽16)—22no—
72C3×C4⋊AGL(1,𝔽5)—22no—
73C3×C4×AGL(1,𝔽5)—22no—
74Dic3⋊AGL(1,𝔽5)—22no—
75Dic3⋊AGL(1,𝔽5)—24no—
76Dic3⋊AGL(1,𝔽5)—42no—
77Dic3⋊AGL(1,𝔽5)Q814yescomplemented
78Dic3×AGL(1,𝔽5)—42no—
79Dic3×AGL(1,𝔽5)—42no—
80C4⋊Dic15C2×C412yes—
81C4⋊Dic15C2×C411yescharacteristic
82C4×Dic15C2×C412yes—
83C4×Dic15C2×C411yescharacteristic
84C5×C4⋊Dic3C2×C412yes—
85C5×C4⋊Dic3C2×C411yescharacteristic
86C4×C5×Dic3C2×C412yes—
87C4×C5×Dic3C2×C411yescharacteristic
88#6668C2×C412yes—
89#6668C2×C412yes—
90#6668C2×C412yes—
91Dic3×Dic5C2×C412yes—
92Dic3×Dic5C2×C411yescharacteristic
93Dic3×Dic5C2×C412yes—
94Dic3×Dic5C2×C411yescharacteristic
95C2×Q8×Dic3—51no—
96C3×#391—51no—
97#5229—51no—
98#4975—51no—
99Dic3×C4⋊C4—51no—
100C4×C4⋊Dic3—51no—
101C4×Dic3⋊C4—51no—
102#4654—52no—
103#4653—52no—
104#4650—52no—
105#4649—52no—
106C2×Q8×D5C2×D311yescharacteristic
107C2×C4⋊AGL(1,𝔽5)—31no—
108C2×C4⋊AGL(1,𝔽5)—32no—
109C2×C4⋊AGL(1,𝔽5)—31no—
110C2×C4⋊AGL(1,𝔽5)—31no—
111C2×C4⋊AGL(1,𝔽5)—32no—
112C2×C4⋊AGL(1,𝔽5)C2×D311yescharacteristic
113C2×C4×AGL(1,𝔽5)—31no—
114C2×C4×AGL(1,𝔽5)—32no—
115C2×C4×AGL(1,𝔽5)—32no—
116C2×C4×AGL(1,𝔽5)C2×D311yescharacteristic
117C4×C5×Q8—31no—
118Q8×Dic5—31no—
119D5×C4⋊C4—31no—
120D5×C4⋊C4—32no—
121#4033—32no—
122#4033—31no—
123C42×D5—31no—
124C42×D5—32no—
125C4×Dic10—31no—
126C4×Dic10—32no—
127(C2×AGL(1,𝔽5))⋊C4—31no—
128(C2×AGL(1,𝔽5))⋊C4—31no—
129(C2×AGL(1,𝔽5))⋊C4—32no—
130(C2×AGL(1,𝔽5))⋊C4—32no—
131(C2×AGL(1,𝔽5))⋊C4—32no—
132(C2×AGL(1,𝔽5))⋊C4—32no—
133(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
134(C2×AGL(1,𝔽5))⋊C4C2×D312yes—
135#2355—151noSylow
136C22×C3×D5C2411yescharacteristic
137C2×ΓL(1,𝔽16)—21no—
138C2×ΓL(1,𝔽16)—21no—
139C2×ΓL(1,𝔽16)—21no—
140C2×ΓL(1,𝔽16)—22no—
141C2×ΓL(1,𝔽16)—21no—
142C2×ΓL(1,𝔽16)—22no—
143C2×ΓL(1,𝔽16)—22no—
144C2×ΓL(1,𝔽16)—21no—
145C2×ΓL(1,𝔽16)C2×Q812yes—
146C2×C3×AGL(1,𝔽5)—21no—
147C2×C3×AGL(1,𝔽5)—21no—
148C2×C3×AGL(1,𝔽5)—21no—
149C2×C3×AGL(1,𝔽5)—22no—
150C2×C3×AGL(1,𝔽5)—21no—
151C2×C3×AGL(1,𝔽5)—22no—
152C2×C3×AGL(1,𝔽5)—22no—
153C2×C3×AGL(1,𝔽5)—21no—
154C2×C3×AGL(1,𝔽5)C2×Q812yes—
155C3×C5×Q8—22no—
156C2×C3×C4×C5C22×C412yes—
157C2×C3×C4×C5C22×C411yescharacteristic
158C2×Dic15C22×C412yes—
159C2×Dic15C22×C411yescharacteristic
160C2×Dic15C22×C411yescharacteristic
161C2×C5×Dic3C22×C412yes—
162C2×C5×Dic3C22×C411yescharacteristic
163C2×C5×Dic3C22×C411yescharacteristic
164C2×C3×Dic5C22×C412yes—
165C2×C3×Dic5C22×C411yescharacteristic
166C3×C4×D5—22no—
167C3×C4×D5—22no—
168C3×C4×D5#4112yes—
169C3×C4×D5#4112yes—
170C3×Dic10—22no—
171C3×Dic10—24no—
172D5×Dic3—22no—
173D5×Dic3—21no—
174D5×Dic3—22no—
175D5×Dic3—21no—
176D5×Dic3C2×Q812yes—
177D5×Dic3#4112yes—
178C22×C3×Q8—51no—
179C2×C3×C4⋊C4—51no—
180C2×C3×C42—51no—
181Q8×Dic3—51no—
182Q8×Dic3—52no—
183Q8×Dic3—51no—
184Q8×Dic3—52no—
185Q8×Dic3—51no—
186Q8×Dic3AGL(1,𝔽5)11yescharacteristic, complemented
187C2×C4⋊Dic3—52no—
188C2×C4⋊Dic3—51no—
189C2×C4⋊Dic3—51no—
190C2×Dic3⋊C4—51no—
191C2×Dic3⋊C4—52no—
192C2×Dic3⋊C4—51no—
193C2×Dic3⋊C4—52no—
194C2×C4×Dic3—52no—
195C2×C4×Dic3—51no—
196C2×C4×Dic3—51no—
197C2×C4×Dic3—52no—
198C2×C4×Dic3—52no—
199C3×#95—52no—
200C3×#95—52no—
201C3⋊#95—52no—
202C3⋊#95—52no—
203C3⋊#95—51no—
204C3⋊#95—51no—
205C3⋊#95—52no—
206C3⋊#95—52no—
207C22×AGL(1,𝔽5)—31no—
208C22×AGL(1,𝔽5)—32no—
209C22×AGL(1,𝔽5)—31no—
210C22×AGL(1,𝔽5)C22×D312yes—
211C22×AGL(1,𝔽5)C22×D311yescharacteristic
212C22×AGL(1,𝔽5)C22×D311yescharacteristic
213C2×C5×Q8C4×D311yescharacteristic
214Q8×D5—22no—
215Q8×D5—22no—
216C2×C4×D5—31no—
217C2×C4×D5—32no—
218C2×C4×D5—31no—
219C2×C4×D5C22×D312yes—
220C2×C4×D5C22×D311yescharacteristic
221C2×Dic10C4×D311yescharacteristic
222C2×Dic10C4×D312yes—
223C4⋊AGL(1,𝔽5)—22no—
224C4⋊AGL(1,𝔽5)—34no—
225C4⋊AGL(1,𝔽5)—64no—
226C4⋊AGL(1,𝔽5)—62no—
227C4⋊AGL(1,𝔽5)—62no—
228C4⋊AGL(1,𝔽5)—122no—
229C4×AGL(1,𝔽5)—22no—
230C4×AGL(1,𝔽5)—62no—
231C4×AGL(1,𝔽5)—122no—
232C4×AGL(1,𝔽5)—122no—
233C5×C4⋊C4—32no—
234C5×C4⋊C4—31no—
235C42×C5—32no—
236C42×C5—31no—
237C4⋊Dic5—32no—
238C4⋊Dic5—31no—
239#683—32no—
240#683—32no—
241#683—32no—
242C4×Dic5—32no—
243C4×Dic5—31no—
244C4×Dic5—32no—
245C4×Dic5—31no—
246C4×Dic5—32no—
247C4×Dic5—31no—
248C2×C4×Q8—151no—
249#391—51no—
250#391—151no—
251#387—152no—
252#387—152no—
253#384—151no—
254#382—152no—
255C4×C4⋊C4—152no—
256C4×C4⋊C4—151no—
257C4×C4⋊C4—151no—
258C4×C4⋊C4—151no—
259C22×C3×C5C23×C411yescharacteristic
260C2×C3×D5C22×Q811yescharacteristic
261C2×C3×D5C2×#4111yescharacteristic
262C2×C3×D5C2×#4111yescharacteristic
263C2×C3×D5C2×#4111yescharacteristic
264C2×C3×D5H(5,𝔽2)11yescharacteristic
265C2×C3×D52−1+411yescharacteristic
266ΓL(1,𝔽16)—22no—
267ΓL(1,𝔽16)—41no—
268ΓL(1,𝔽16)—42no—
269C3×AGL(1,𝔽5)—22no—
270C3×AGL(1,𝔽5)—41no—
271C3×AGL(1,𝔽5)—42no—
272C3×C4×C5—22no—
273C3×C4×C5#11712yes—
274Dic15—22no—
275Dic15—21no—
276Dic15C4×Q812yes—
277C3×Dic5—22no—
278C3×Dic5#11712yes—
279C5×Dic3—22no—
280C5×Dic3—21no—
281C5×Dic3C4×Q812yes—
282C2×C3×Q8—52no—
283C2×C3×Q8—51no—
284C2×C3×Q8—102no—
285C2×C3×Q8—102no—
286C2×C3×Q8C2×AGL(1,𝔽5)11yescharacteristic
287C22×C3×C4—51no—
288C22×C3×C4—51no—
289C22×C3×C4—52no—
290C22×C3×C4—51no—
291C22×C3×C4—52no—
292C22×Dic3—51no—
293C22×Dic3—51no—
294C22×Dic3—52no—
295C22×Dic3—51no—
296C22×Dic3—51no—
297C22×Dic3—52no—
298C3×C4⋊C4—102no—
299C3×C42—102no—
300C4⋊Dic3—52no—
301C4⋊Dic3—51no—
302C4⋊Dic3—52no—
303C4⋊Dic3—52no—
304C4⋊Dic3—52no—
305C4⋊Dic3—102no—
306C4⋊Dic3C2×AGL(1,𝔽5)12yes—
307C4⋊Dic3C2×AGL(1,𝔽5)11yescharacteristic
308Dic3⋊C4—54no—
309Dic3⋊C4—104no—
310Dic3⋊C4—102no—
311Dic3⋊C4—202no—
312C4×Dic3—52no—
313C4×Dic3—51no—
314C4×Dic3—51no—
315C4×Dic3—52no—
316C4×Dic3—51no—
317C4×Dic3—52no—
318C4×Dic3—102no—
319C4×Dic3—202no—
320C4×Dic3—202no—
321C4×Dic3C2×AGL(1,𝔽5)12yes—
322C4×Dic3C2×AGL(1,𝔽5)11yescharacteristic
323C22×D5C23×D311yescharacteristic
324C2×AGL(1,𝔽5)—21no—
325C2×AGL(1,𝔽5)—21no—
326C2×AGL(1,𝔽5)—21no—
327C2×AGL(1,𝔽5)—22no—
328C2×AGL(1,𝔽5)—21no—
329C2×AGL(1,𝔽5)—21no—
330C2×AGL(1,𝔽5)—22no—
331C2×AGL(1,𝔽5)—22no—
332C2×AGL(1,𝔽5)—32no—
333C2×AGL(1,𝔽5)—61no—
334C2×AGL(1,𝔽5)—61no—
335C2×AGL(1,𝔽5)—61no—
336C2×AGL(1,𝔽5)—62no—
337C2×AGL(1,𝔽5)—61no—
338C2×AGL(1,𝔽5)—61no—
339C2×AGL(1,𝔽5)—62no—
340C2×AGL(1,𝔽5)—62no—
341C2×AGL(1,𝔽5)D3×Q812yes—
342C5×Q8—22no—
343C2×C4×C5—31no—
344C2×C4×C5—32no—
345C2×C4×C5—31no—
346C2×C4×C5C2×C4×D312yes—
347C2×C4×C5C2×C4×D311yescharacteristic
348C2×Dic5—31no—
349C2×Dic5—32no—
350C2×Dic5—31no—
351C2×Dic5C2×C4×D312yes—
352C2×Dic5C2×C4×D311yescharacteristic
353C4×D5—22no—
354C4×D5—22no—
355C4×D5—32no—
356C4×D5—32no—
357C4×D5—62no—
358C4×D5—61no—
359C4×D5—62no—
360C4×D5—61no—
361C4×D5#23712yes—
362C4×D5#23712yes—
363Dic10—22no—
364Dic10—24no—
365C22×Q8—51no—
366C4×Q8—31no—
367C4×Q8—152no—
368C4×Q8—151no—
369C4×Q8—152no—
370C4×Q8—151no—
371C4×Q8—151no—
372C2×C4⋊C4—51no—
373C2×C4⋊C4—151no—
374C2×C4⋊C4—152no—
375C2×C4⋊C4—151no—
376C2×C4⋊C4—151no—
377C2×C4⋊C4—152no—
378C2×C4⋊C4—151no—
379C2×C4⋊C4—152no—
380C2×C42—51no—
381C2×C42—152no—
382C2×C42—151no—
383C2×C42—151no—
384C2×C42—152no—
385C2×C42—152no—
386#95—52no—
387#95—52no—
388#95—152no—
389#95—152no—
390#95—151no—
391#95—151no—
392#95—152no—
393#95—152no—
394C2×C3×C5C2×#11711yescharacteristic
395C2×C3×C5C2×C4×Q811yescharacteristic
396C2×C3×C5#52011yescharacteristic
397C3×D5#55411yescharacteristic
398C3×D5#55611yescharacteristic
399C3×D5#55711yescharacteristic
400C3×D5#55911yescharacteristic
401C23×C3—51no—
402C3×Q8—22no—
403C3×Q8—104no—
404C3×Q8—102no—
405C2×C3×C4—51no—
406C2×C3×C4—52no—
407C2×C3×C4—52no—
408C2×C3×C4—52no—
409C2×C3×C4—52no—
410C2×C3×C4—102no—
411C2×C3×C4—102no—
412C2×C3×C4—101no—
413C2×C3×C4—101no—
414C2×C3×C4—102no—
415C2×C3×C4—101no—
416C2×C3×C4—102no—
417C2×C3×C4—101no—
418C2×C3×C4—102no—
419C2×C3×C4—101no—
420C2×C3×C4C22×AGL(1,𝔽5)12yes—
421C2×C3×C4C22×AGL(1,𝔽5)11yescharacteristic
422C2×Dic3—51no—
423C2×Dic3—52no—
424C2×Dic3—52no—
425C2×Dic3—52no—
426C2×Dic3—52no—
427C2×Dic3—51no—
428C2×Dic3—102no—
429C2×Dic3—101no—
430C2×Dic3—102no—
431C2×Dic3—101no—
432C2×Dic3—101no—
433C2×Dic3—101no—
434C2×Dic3—101no—
435C2×Dic3—102no—
436C2×Dic3—101no—
437C2×Dic3—102no—
438C2×Dic3—102no—
439C2×Dic3—101no—
440C2×Dic3C22×AGL(1,𝔽5)12yes—
441C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
442C2×Dic3C22×AGL(1,𝔽5)11yescharacteristic
443C22×C5C22×C4×D311yescharacteristic
444C2×D5C2×#23711yescharacteristic
445C2×D5C2×#23711yescharacteristic
446C2×D5C2×D3×Q811yescharacteristic
447C2×D5#100711yescharacteristic
448C2×D5D3×#4111yescharacteristic
449C2×D5#100911yescharacteristic
450AGL(1,𝔽5)—22no—
451AGL(1,𝔽5)—41no—
452AGL(1,𝔽5)—42no—
453AGL(1,𝔽5)—62no—
454AGL(1,𝔽5)—121no—
455AGL(1,𝔽5)—122no—
456C4×C5—22no—
457C4×C5—32no—
458C4×C5—62no—
459C4×C5—61no—
460C4×C5#87712yes—
461Dic5—22no—
462Dic5—32no—
463Dic5—62no—
464Dic5—61no—
465Dic5#87712yes—
466C2×Q8—52no—
467C2×Q8—51no—
468C2×Q8—102no—
469C2×Q8—102no—
470C2×Q8D3×AGL(1,𝔽5)11yescharacteristic
471C22×C4—51no—
472C22×C4—51no—
473C22×C4—52no—
474C22×C4—51no—
475C22×C4—52no—
476C22×C4—151no—
477C22×C4—152no—
478C22×C4—151no—
479C22×C4—151no—
480C22×C4—151no—
481C22×C4—152no—
482C4⋊C4—32no—
483C4⋊C4—31no—
484C4⋊C4—102no—
485C4⋊C4—152no—
486C4⋊C4—152no—
487C4⋊C4—152no—
488C4⋊C4—154no—
489C4⋊C4—152no—
490C4⋊C4—151no—
491C4⋊C4—302no—
492C4⋊C4—302no—
493C4⋊C4—304no—
494C4⋊C4—602no—
495C42—32no—
496C42—31no—
497C42—102no—
498C42—151no—
499C42—152no—
500C42—151no—
501C42—152no—
502C42—152no—
503C42—151no—
504C42—302no—
505C42—602no—
506C42—602no—
507C3×C5#235511yescharacteristic, complemented, Hall
508C22×C3—51no—
509C22×C3—51no—
510C22×C3—51no—
511C22×C3—51no—
512C22×C3—51no—
513C22×C3—51no—
514C22×C3C23×AGL(1,𝔽5)11yescharacteristic
515C3×C4—22no—
516C3×C4—52no—
517C3×C4—102no—
518C3×C4—102no—
519C3×C4—202no—
520C3×C4—201no—
521C3×C4#413012yes—
522Dic3—22no—
523Dic3—21no—
524Dic3—52no—
525Dic3—102no—
526Dic3—102no—
527Dic3—101no—
528Dic3—202no—
529Dic3—201no—
530Dic3Q8×AGL(1,𝔽5)12yes—
531C2×C5C2×#87711yescharacteristic
532C2×C5C4×D3×Q811yescharacteristic
533C2×C5#557411yescharacteristic
534D5#563511yescharacteristic
535D5#564111yescharacteristic
536D5#568111yescharacteristic
537D5#572111yescharacteristic
538C23—51no—
539Q8—22no—
540Q8—104no—
541Q8—102no—
542C2×C4—31no—
543C2×C4—32no—
544C2×C4—31no—
545C2×C4—51no—
546C2×C4—52no—
547C2×C4—52no—
548C2×C4—52no—
549C2×C4—52no—
550C2×C4—102no—
551C2×C4—102no—
552C2×C4—101no—
553C2×C4—101no—
554C2×C4—101no—
555C2×C4—102no—
556C2×C4—102no—
557C2×C4—101no—
558C2×C4—102no—
559C2×C4—101no—
560C2×C4—152no—
561C2×C4—152no—
562C2×C4—151no—
563C2×C4—152no—
564C2×C4—152no—
565C2×C4—151no—
566C2×C4—302no—
567C2×C4—301no—
568C2×C4—302no—
569C2×C4—301no—
570C2×C4—301no—
571C2×C4—301no—
572C2×C4—301no—
573C2×C4—302no—
574C2×C4—301no—
575C2×C4—302no—
576C2×C4—302no—
577C2×C4—301no—
578C2×C4C2×D3×AGL(1,𝔽5)12yes—
579C2×C4C2×D3×AGL(1,𝔽5)11yescharacteristic
580C2×C3—51no—
581C2×C3—51no—
582C2×C3—51no—
583C2×C3—51no—
584C2×C3C2×#413011yescharacteristic
585C2×C3C2×Q8×AGL(1,𝔽5)11yescharacteristic
586C2×C3#6626611yescharacteristic
587C5#7648911yescharacteristic, complemented, Sylow
588C22—51no—
589C22—51no—
590C22—51no—
591C22—51no—
592C22—51no—
593C22—51no—
594C22C22×D3×AGL(1,𝔽5)11yescharacteristic
595C4—22no—
596C4—32no—
597C4—52no—
598C4—62no—
599C4—61no—
600C4—102no—
601C4—102no—
602C4—152no—
603C4—202no—
604C4—201no—
605C4—302no—
606C4—302no—
607C4—301no—
608C4—602no—
609C4—601no—
610C4#9192312yes—
611C3#1061721311yescharacteristic, complemented, Sylow
612C2—51no—
613C2—51no—
614C2—51no—
615C2—51no—
616C2D3×Q8×AGL(1,𝔽5)11yescharacteristic
617C2#1175685411yescharacteristic
618C2C2×#9192311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D3×AGL(1,𝔽5)
commutator, socleC22×C3×C5C23×C4
FittingC2×C3×C5×Q8C2×C4
prime radical, cosocleC22×C3×D5C24
hypercenterC2×Q8D3×AGL(1,𝔽5)
hypocenterC3×C5#2355
LCSG ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
24. Q8×Dic15C4semidirect
25. C5×Q8×Dic3C4semidirect
30. #91331C4semidirect
31. #91331C4semidirect
32. Dic3×Dic10C4semidirect
33. Dic3×Dic10C4semidirect
77. Dic3⋊AGL(1,𝔽5)Q8semidirect
186. Q8×Dic3AGL(1,𝔽5)semidirect
507. C3×C5#2355semidirect
587. C5#76489semidirect
611. C3#10617213semidirect

Maximal subgroups

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

subgroupindex
Q8×D5×Dic32
#117524492
C3×(C2×AGL(1,𝔽5))⋊Q82
#117518602
C4×Dic3⋊AGL(1,𝔽5)2
#117518462
#117518402
#117518392
AGL(1,𝔽5)×C4⋊Dic32
#117518342
#117517462
#106172133
#764895