Finite Group Databasebeta

← #14285107

Subgroups — #14285107

Order 1920.

416 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 102 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#11756487C211yesmaximal, characteristic
2#11747000C211yesmaximal, characteristic
3#11746867C211yesmaximal, characteristic
4C5×#4547C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745859C211yesmaximal, characteristic, complemented
8#10599218—31nomaximal, Hall
9C3×C5×C4⋊Q8C2211yescharacteristic
10#91835—21no—
11Q8×Dic15—21no—
12#91786—21no—
13#91781C412yes—
14#91779C412yes—
15#91776—21no—
16C42×D15C2211yescharacteristic
17#91758C2211yescharacteristic
18C2×#6648—21no—
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C5×C4⋊(C3⋊C8)C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22C3×C4⋊#168C2211yescharacteristic
23#90983—21no—
24#90957—21no—
25#90954—21no—
26#68425—51nomaximal, Hall
27#66062—31no—
28#65124—31no—
29D5×C4⋊C8—31no—
30C5×#332—31no—
31#64767D311yescharacteristic, complemented
32#64706—31no—
33#64702—31no—
34C2×C3×C5×Q8—21no—
35C2×C4×D15C2×C411yescharacteristic
36C2×C4×D15D411yescharacteristic
37C2×C4×D15D411yescharacteristic
38C2×Dic30—21no—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4C2×C412yes—
41C3×C42×C5C2311yescharacteristic
42#6714—22no—
43C4⋊Dic15—21no—
44C4⋊Dic15—22no—
45C4⋊Dic15C2×C412yes—
46#6712—22no—
47C4×Dic15—22no—
48C4×Dic15C2×C411yescharacteristic
49C4×Dic15D411yescharacteristic
50C4×Dic15D411yescharacteristic
51C2×C5×C3⋊C8—21no—
52C2×C5×C3⋊C8—21no—
53C2×C3×#168—21no—
54C2×C3×#168—21no—
55#6648—42no—
56#5728—51no—
57#4835—51no—
58D3×C4⋊C8—51no—
59C3×#332—51no—
60#4547D511yescharacteristic, complemented
61#4486—51no—
62#4482—51no—
63C5×C4⋊Q8C2×D311yescharacteristic
64#4092—61no—
65Q8×Dic5—61no—
66C2×C8×D5—61no—
67#4043—61no—
68#4038—32no—
69#4036—32no—
70#4033—61no—
71C42×D5—31no—
72#4015—31no—
73C5×C4⋊C8—31no—
74C5×C4⋊C8—31no—
75#3952—61no—
76#3947—61no—
77#3946—61no—
78C4⋊#168C2×D311yescharacteristic
79C4⋊#168C2×D311yescharacteristic
80#1552—151noSylow
81C22×D15C22⋊C411yescharacteristic
82C3×C5×Q8—41no—
83C3×C5×Q8—41no—
84C2×C3×C4×C5—22no—
85C2×C3×C4×C5C22×C411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×Dic15—22no—
89C2×Dic15C22⋊C411yescharacteristic
90C2×Dic15C22⋊C411yescharacteristic
91C2×Dic15C22⋊C411yescharacteristic
92C4×D15—22no—
93C4×D15—21no—
94C4×D15—21no—
95C4×D15—21no—
96C4×D15—21no—
97Dic30—41no—
98Dic30—41no—
99C3×#168—41no—
100C3×#168—41no—
101C5×C3⋊C8—41no—
102C5×C3⋊C8—41no—
103C3×C4⋊Q8C2×D511yescharacteristic
104#946—101no—
105Q8×Dic3—101no—
106C2×D3×C8—101no—
107#897—101no—
108#892—52no—
109#890—52no—
110#887—101no—
111C42×D3—51no—
112#869—51no—
113C3×C4⋊C8—51no—
114C3×C4⋊C8—51no—
115(C2×D3)⋊C8—101no—
116#815—101no—
117Dic3⋊C8—101no—
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C4⋊(C3⋊C8)C2×D511yescharacteristic
120C2×C5×Q8—21no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×C4×D5—31no—
124C2×Dic10—61no—
125C2×C5×C8—61no—
126C2×C5×C8—61no—
127C5×C4⋊C4—21no—
128C5×C4⋊C4C4×D312yes—
129C42×C5C22×D311yescharacteristic
130#685—62no—
131C4⋊Dic5—32no—
132C4⋊Dic5—62no—
133C4⋊Dic5—61no—
134#683—62no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—31no—
138C4×Dic5—62no—
139C2×#168—21no—
140C2×#168—21no—
141C8×D5—122no—
142#533—151no—
143#432—151no—
144C2×C4⋊C8—151no—
145#332—31no—
146#332—51no—
147#332—151no—
148#332—151no—
149C22×C3×C5C2×C22⋊C411yescharacteristic
150C2×D15—21no—
151C2×D15—21no—
152C2×D15#10112yes—
153C3×C4×C5—21no—
154C3×C4×C5—42no—
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157C3×C4×C5AGL(1,ℤ/8)11yescharacteristic
158C3×C4×C5#13711yescharacteristic
159Dic15—21no—
160Dic15—21no—
161Dic15—21no—
162Dic15—42no—
163C2×C3×Q8—21no—
164C2×C4×D3—51no—
165C2×C4×D3—51no—
166C2×C4×D3—51no—
167C2×Dic6—101no—
168C2×C3×C8—101no—
169C2×C3×C8—101no—
170C3×C4⋊C4—21no—
171C3×C4⋊C4C4×D512yes—
172C3×C42C22×D511yescharacteristic
173(C2×D3)⋊C4—102no—
174C4⋊Dic3—52no—
175C4⋊Dic3—102no—
176C4⋊Dic3—101no—
177Dic3⋊C4—102no—
178C4×Dic3—51no—
179C4×Dic3—51no—
180C4×Dic3—51no—
181C4×Dic3—102no—
182C2×C3⋊C8—21no—
183C2×C3⋊C8—21no—
184D3×C8—202no—
185C22×D5—31no—
186C5×Q8—41no—
187C5×Q8—41no—
188C2×C4×C5—22no—
189C2×C4×C5C2×C4×D311yescharacteristic
190C2×C4×C5D3×D411yescharacteristic
191C2×C4×C5D3×D411yescharacteristic
192C2×Dic5—31no—
193C2×Dic5—31no—
194C2×Dic5—31no—
195C2×Dic5—62no—
196C4×D5—62no—
197C4×D5—61no—
198C4×D5—61no—
199C4×D5—61no—
200C4×D5—61no—
201Dic10—121no—
202Dic10—121no—
203C5×C8—121no—
204C5×C8—121no—
205#168—41no—
206#168—41no—
207C22×C8—301no—
208C4⋊Q8—151no—
209C4⋊Q8D3×D511yescharacteristic
210#125—152no—
211C22⋊Q8—301no—
212C22⋊Q8—301no—
213C4×Q8—301no—
214C4×Q8—301no—
215#117—152no—
216C2×C42—151no—
217C4⋊C8—31no—
218C4⋊C8—31no—
219C4⋊C8—51no—
220C4⋊C8—51no—
221C4⋊C8—301no—
222C22⋊C8—301no—
223#97—301no—
224C2×C3×C5C2×#10111yescharacteristic
225C2×C3×C5#41611yescharacteristic
226C2×C3×C5#41711yescharacteristic
227D15—22no—
228C22×D3—51no—
229C3×Q8—41no—
230C3×Q8—41no—
231C2×C3×C4—22no—
232C2×C3×C4C2×C4×D511yescharacteristic
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×Dic3—51no—
236C2×Dic3—51no—
237C2×Dic3—51no—
238C2×Dic3—102no—
239C4×D3—102no—
240C4×D3—101no—
241C4×D3—101no—
242C4×D3—101no—
243C4×D3—101no—
244Dic6—201no—
245Dic6—201no—
246C3×C8—201no—
247C3×C8—201no—
248C3⋊C8—41no—
249C3⋊C8—41no—
250C22×C5D3×C22⋊C411yescharacteristic
251C2×D5—32no—
252C2×D5—61no—
253C2×D5—61no—
254C4×C5—21no—
255C4×C5—42no—
256C4×C5#91111yescharacteristic
257C4×C5#91511yescharacteristic
258C4×C5#91611yescharacteristic
259C4×C5#91911yescharacteristic
260Dic5—61no—
261Dic5—61no—
262Dic5—61no—
263Dic5—122no—
264C2×Q8—21no—
265C2×Q8—301no—
266C22×C4—151no—
267C22×C4—151no—
268C22×C4—151no—
269C2×C8—61no—
270C2×C8—61no—
271C2×C8—101no—
272C2×C8—101no—
273C2×C8—602no—
274C4⋊C4—21no—
275C4⋊C4—152no—
276C4⋊C4—302no—
277C4⋊C4—302no—
278C4⋊C4—301no—
279C4⋊C4#120012yes—
280C22⋊C4—302no—
281C42—151no—
282C42—151no—
283C42—151no—
284C42—302no—
285C42C2×D3×D511yescharacteristic
286C3×C5#155211yescharacteristic, complemented, Hall
287C22×C3D5×C22⋊C411yescharacteristic
288C2×D3—52no—
289C2×D3—101no—
290C2×D3—101no—
291C3×C4—21no—
292C3×C4—42no—
293C3×C4#405711yescharacteristic
294C3×C4#406111yescharacteristic
295C3×C4#406211yescharacteristic
296C3×C4#406511yescharacteristic
297Dic3—101no—
298Dic3—101no—
299Dic3—101no—
300Dic3—202no—
301C2×C5D3×#10111yescharacteristic
302C2×C5#477111yescharacteristic
303C2×C5#480411yescharacteristic
304D5—62no—
305C23—151no—
306Q8—41no—
307Q8—41no—
308Q8—601no—
309Q8—601no—
310C2×C4—22no—
311C2×C4—151no—
312C2×C4—151no—
313C2×C4—151no—
314C2×C4—302no—
315C2×C4—301no—
316C2×C4—301no—
317C2×C4—301no—
318C2×C4—301no—
319C2×C4—302no—
320C2×C4C2×#120011yescharacteristic
321C2×C4#679011yescharacteristic
322C2×C4#679011yescharacteristic
323C8—121no—
324C8—121no—
325C8—201no—
326C8—201no—
327C2×C3D5×#10111yescharacteristic
328C2×C3#6506011yescharacteristic
329C2×C3#6509311yescharacteristic
330D3—102no—
331C5#6842511yescharacteristic, complemented, Sylow
332C22—152no—
333C22—301no—
334C22—301no—
335C22#9156111yescharacteristic
336C4—21no—
337C4—42no—
338C4—301no—
339C4—301no—
340C4—301no—
341C4—602no—
342C4#9148211yescharacteristic
343C4#9148811yescharacteristic
344C4#9152111yescharacteristic
345C4#9152311yescharacteristic
346C3#1059921811yescharacteristic, complemented, Sylow
347C2—302no—
348C2#1174895911yescharacteristic
349C2#1174921511yescharacteristic
350C2#1174937311yescharacteristic
subgroupG/H
centerC22#91561
commutatorC2×C3×C4×C5C22×C4
FrattiniC42C2×D3×D5
FittingC3×C5×C4⋊Q8C22
socleC22×C3×C5C2×C22⋊C4
prime radicalC22×D15C22⋊C4
cosocleC3×C42×C5C23
hypercenterC4⋊Q8D3×D5
hypocenterC3×C5#1552
LCSG ▷ C2×C3×C4×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
4. C5×#4547C2semidirect
5. C3×#64767C2semidirect
6. #11745860C2semidirect
7. #11745859C2semidirect
31. #64767D3semidirect
60. #4547D5semidirect
286. C3×C5#1552semidirect
331. C5#68425semidirect
346. C3#10599218semidirect

Maximal subgroups

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

subgroupindex
#117564872
#117470002
#117468672
C5×#45472
C3×#647672
#117458602
#117458592
#105992183
#684255