Finite Group Databasebeta

← #14289770

Subgroups — #14289770

Order 1920.

456 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11752558C211yesmaximal, characteristic
2#11751192C211yesmaximal, characteristic, complemented
3C5×#5084C211yesmaximal, characteristic
4C3×#65370C211yesmaximal, characteristic, complemented
5#11745855C211yesmaximal, characteristic, complemented
6#11745845C211yesmaximal, characteristic, complemented
7#11745837C211yesmaximal, characteristic
8#10601935—31nomaximal, Hall
9C2×D3×Dic10—21no—
10C3×C5×C4⋊Q8C2211yescharacteristic
11C4×Dic30C2211yescharacteristic
12C4×C5×D12C2211yescharacteristic
13C3×#4015C2211yescharacteristic
14#91470—21no—
15#91436—22no—
16#91435—21no—
17#91369—21no—
18#91094—21no—
19#91091—21no—
20C4⋊(C3⋊#168)C2211yescharacteristic
21C5×#809—21no—
22C5×#808—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24C3×#3967—22no—
25C3×C4×#168C2211yescharacteristic
26#71237—51nomaximal, Hall
27D4×Dic10—31no—
28C5×#476—31no—
29#65380—31no—
30#65370D311yescharacteristic, complemented
31D4⋊#168—31no—
32#64706—31no—
33#64704—31no—
34C2×C3×C5×Q8—21no—
35C2×Dic30D411yescharacteristic
36C2×C5×D12D411yescharacteristic
37C2×C4×C5×D3—21no—
38C2×C3×Dic10—21no—
39C2×#1204—22no—
40C2×D3×Dic5—22no—
41D3×Dic10—42no—
42D3×Dic10—42no—
43C3×C5×C4⋊C4—21no—
44C3×C5×C4⋊C4—21no—
45C3×C42×C5C2311yescharacteristic
46C4⋊Dic15D411yescharacteristic
47#6712—21no—
48C4×Dic15—21no—
49C2×C3⋊#168—21no—
50C5×(C2×D3)⋊C4—21no—
51C5×C4⋊Dic3D411yescharacteristic
52C2×C5×C3⋊C8—21no—
53C3×C4⋊Dic5—21no—
54C3×C4⋊Dic5D412yes—
55C2×C3×#168—21no—
56#6669—22no—
57(C2×D3)⋊Dic5—22no—
58#5727—51no—
59C3×#487—51no—
60#5091—51no—
61#5084D511yescharacteristic
62#4547—51no—
63#4459—51no—
64#4456—51no—
65C22×Dic10—61no—
66C5×C4⋊Q8C2×D311yescharacteristic
67C4×C5×D4—31no—
68D4×Dic5—61no—
69#4070—61no—
70#4034—61no—
71#4024—62no—
72#4015C2×D311yescharacteristic
73C4×Dic10—31no—
74C5×#106—61no—
75C5×C4⋊C8—31no—
76C5×#102—61no—
77#3967—22no—
78#3942—61no—
79#3939—61no—
80C4⋊#168—31no—
81C4×#168C2×D311yescharacteristic
82#1637—151noSylow
83C22×C5×D3—21no—
84C3×C5×Q8—42no—
85C2×C3×C4×C5—41no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×Dic15—21no—
90C2×Dic15—21no—
91Dic30—21no—
92Dic30SD1612yes—
93C2×C5×Dic3—21no—
94C5×D12—21no—
95C5×D12Q1612yes—
96C4×C5×D3—41no—
97C4×C5×D3—41no—
98C2×C3×Dic5—22no—
99C3×Dic10—41no—
100C3×Dic10—41no—
101#1204—44no—
102D3×Dic5—44no—
103C3⋊#168—41no—
104C3×#168—41no—
105C5×C3⋊C8—41no—
106C2×D3×Q8—101no—
107C3×C4⋊Q8—51no—
108C3×C4⋊Q8C2×D511yescharacteristic
109#946—101no—
110#896—102no—
111#893—101no—
112#888—101no—
113C4×D12C2×D511yescharacteristic
114C4×Dic6—51no—
115C3×#103—102no—
116C3×C4×C8—51no—
117#810—101no—
118#809—21no—
119#808—21no—
120#807—101no—
121C4⋊(C3⋊C8)—51no—
122C4⋊(C3⋊C8)C2×D511yescharacteristic
123C2×C5×Q8—21no—
124C2×C5×D4—31no—
125C22×C4×C5—61no—
126C22×Dic5—62no—
127C2×Dic10—21no—
128C2×Dic10—31no—
129C2×Dic10—62no—
130C2×Dic10—122no—
131C2×Dic10—122no—
132C2×C5×C8—61no—
133C5×C4⋊C4—21no—
134C5×C4⋊C4—21no—
135C5×C4⋊C4—31no—
136C5×C22⋊C4—61no—
137C42×C5C22×D311yescharacteristic
138C22⋊Dic5—62no—
139C4⋊Dic5—21no—
140C4⋊Dic5—31no—
141C4⋊Dic5#6712yes—
142#683—62no—
143#683—61no—
144C4×Dic5—61no—
145C2×#168—21no—
146C2×#168—61no—
147D4×Q8—151no—
148#487—51no—
149#477—151no—
150#476—31no—
151#332—151no—
152Q8⋊C8—151no—
153D4⋊C8—151no—
154C22×C3×C5#12011yescharacteristic
155C2×C5×D3—22no—
156C2×C5×D3—41no—
157C2×C5×D3—41no—
158C3×C4×C5—21no—
159C3×C4×C5—81no—
160C3×C4×C5C2×SD1611yescharacteristic
161C3×C4×C5C2×Q1611yescharacteristic
162C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
163C3×C4×C5#13711yescharacteristic
164Dic15—22no—
165Dic15—41no—
166C3×Dic5—42no—
167C5×Dic3—41no—
168C2×C3×Q8—21no—
169C2×C3×Q8—101no—
170D3×Q8—202no—
171D3×Q8—202no—
172C2×D12C22⋊D511yescharacteristic
173C2×C4×D3—21no—
174C2×C4×D3—102no—
175C2×Dic6—51no—
176C2×Dic6—102no—
177C2×C3×C8—101no—
178C3×C4⋊C4—21no—
179C3×C4⋊C4—21no—
180C3×C4⋊C4—52no—
181C3×C4⋊C4—101no—
182C3×C42C22×D511yescharacteristic
183(C2×D3)⋊C4—21no—
184(C2×D3)⋊C4—102no—
185C4⋊Dic3—51no—
186C4⋊Dic3C22⋊D511yescharacteristic
187Dic3⋊C4—102no—
188Dic3⋊C4—101no—
189C4×Dic3—101no—
190C2×C3⋊C8—21no—
191C2×C3⋊C8—101no—
192C23×C5—61no—
193C5×Q8—42no—
194C5×D4—32no—
195C5×D4—61no—
196C2×C4×C5—41no—
197C2×C4×C5—61no—
198C2×C4×C5—121no—
199C2×C4×C5—121no—
200C2×C4×C5D3×D411yescharacteristic
201C2×C4×C5D3×D411yescharacteristic
202C2×C4×C5C2×#6711yescharacteristic
203C2×Dic5—22no—
204C2×Dic5—61no—
205C2×Dic5—61no—
206C2×Dic5—124no—
207Dic10—32no—
208Dic10—41no—
209Dic10—41no—
210Dic10—61no—
211Dic10—124no—
212C5×C8—121no—
213#168—41no—
214#168—121no—
215C22×Q8—301no—
216C4⋊Q8—51no—
217C4⋊Q8—301no—
218C4⋊Q8D3×D511yescharacteristic
219C22⋊Q8—302no—
220C22⋊Q8—301no—
221C4×Q8—151no—
222C4×D4—31no—
223C4×D4—301no—
224#107—301no—
225#106—61no—
226C4⋊C8—31no—
227C4⋊C8—151no—
228#103—102no—
229#103—301no—
230#102—61no—
231C4×C8—51no—
232C2×C3×C5#45011yescharacteristic
233C2×C3×C5#45111yescharacteristic
234C2×C3×C5#45411yescharacteristic
235C5×D3—42no—
236C22×D3—21no—
237C3×Q8—42no—
238C3×Q8—201no—
239C3×Q8—201no—
240C2×C3×C4—41no—
241C2×C3×C4—102no—
242C2×C3×C4D4×D511yescharacteristic
243C2×C3×C4D4×D511yescharacteristic
244C2×C3×C4C2×C22⋊D511yescharacteristic
245C2×Dic3—21no—
246C2×Dic3—101no—
247C2×Dic3—101no—
248D12—21no—
249D12#68912yes—
250C4×D3—41no—
251C4×D3—41no—
252C4×D3—204no—
253Dic6—52no—
254Dic6—101no—
255Dic6—204no—
256C3×C8—201no—
257C3⋊C8—41no—
258C3⋊C8—201no—
259C22×C5—62no—
260C22×C5—121no—
261C22×C5—121no—
262C22×C5#93711yescharacteristic
263C4×C5—21no—
264C4×C5—81no—
265C4×C5—121no—
266C4×C5D3×SD1611yescharacteristic
267C4×C5#91411yescharacteristic
268C4×C5D3×Q1611yescharacteristic
269C4×C5#91811yescharacteristic
270Dic5—42no—
271Dic5—62no—
272Dic5—121no—
273C2×Q8—21no—
274C2×Q8—101no—
275C2×Q8—151no—
276C2×Q8—302no—
277C2×Q8—602no—
278C2×Q8—602no—
279C2×D4—31no—
280C22×C4—61no—
281C22×C4—302no—
282C2×C8—61no—
283C2×C8—101no—
284C2×C8—301no—
285C4⋊C4—21no—
286C4⋊C4—21no—
287C4⋊C4—31no—
288C4⋊C4—52no—
289C4⋊C4—101no—
290C4⋊C4—151no—
291C4⋊C4—302no—
292C4⋊C4—301no—
293C22⋊C4—61no—
294C22⋊C4—302no—
295C42—301no—
296C42C2×D3×D511yescharacteristic
297C3×C5#163711yescharacteristic, complemented, Hall
298C22×C3#408311yescharacteristic
299C2×D3—22no—
300C2×D3—41no—
301C2×D3—41no—
302C3×C4—21no—
303C3×C4—81no—
304C3×C4—202no—
305C3×C4D5×SD1611yescharacteristic
306C3×C4#406011yescharacteristic
307C3×C4C2×#68911yescharacteristic
308C3×C4#409711yescharacteristic
309Dic3—41no—
310Dic3—102no—
311Dic3—201no—
312C2×C5—122no—
313C2×C5#506211yescharacteristic
314C2×C5#516911yescharacteristic
315C2×C5#518611yescharacteristic
316C23—61no—
317Q8—42no—
318Q8—152no—
319Q8—201no—
320Q8—201no—
321Q8—301no—
322Q8—604no—
323D4—32no—
324D4—61no—
325C2×C4—41no—
326C2×C4—61no—
327C2×C4—102no—
328C2×C4—121no—
329C2×C4—121no—
330C2×C4—301no—
331C2×C4—301no—
332C2×C4—604no—
333C2×C4D5×#6711yescharacteristic
334C2×C4D3×C22⋊D511yescharacteristic
335C2×C4#679011yescharacteristic
336C8—121no—
337C8—201no—
338C8—601no—
339C2×C3#6533911yescharacteristic
340C2×C3#6545811yescharacteristic
341C2×C3#6549011yescharacteristic
342D3—42no—
343C5#7123711yescharacteristic, complemented, Sylow
344C22—62no—
345C22—121no—
346C22—121no—
347C22#9157711yescharacteristic
348C4—21no—
349C4—81no—
350C4—121no—
351C4—202no—
352C4—302no—
353C4—601no—
354C4#9150511yescharacteristic
355C4#9150611yescharacteristic
356C4D3×#68911yescharacteristic
357C4#9151011yescharacteristic
358C3#1060193511yescharacteristic, complemented, Sylow
359C2—122no—
360C2#1174916811yescharacteristic
361C2#1174939911yescharacteristic
362C2#1174940111yescharacteristic
subgroupG/H
centerC22#91577
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5#120
prime radicalC2×C5×D12D4
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1637
LCSG ▷ C3×C42×C5 ▷ C22×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11751192C2semidirect
4. C3×#65370C2semidirect
5. #11745855C2semidirect
6. #11745845C2semidirect
30. #65370D3semidirect
297. C3×C5#1637semidirect
343. C5#71237semidirect
358. C3#10601935semidirect

Maximal subgroups

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

subgroupindex
#117525582
#117511922
C5×#50842
C3×#653702
#117458552
#117458452
#117458372
#106019353
#712375