Finite Group Databasebeta

← #14284756

Subgroups — #14284756

Order 1920.

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

normal subgroups only

This group has 404 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#11746859C211yesmaximal, characteristic
3#11746859C211yesmaximal, characteristic
4C5×#4547C211yesmaximal, characteristic, complemented
5C3×#64767C211yesmaximal, characteristic, complemented
6#11745860C211yesmaximal, characteristic, complemented
7#11745859C211yesmaximal, characteristic, complemented
8#10599212—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
18C5×C4⋊(C3⋊C8)C2211yescharacteristic
19C5×C4⋊(C3⋊C8)C2211yescharacteristic
20C3×C4⋊#168C2211yescharacteristic
21C3×C4⋊#168C2211yescharacteristic
22#90957—21no—
23#90957—21no—
24#90951—21no—
25#90951—21no—
26#68419—51nomaximal, Hall
27#66062—31no—
28#65122—31no—
29#65122—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#5728—51no—
56#4833—51no—
57#4833—51no—
58C3×#332—51no—
59#4547D511yescharacteristic, complemented
60#4486—51no—
61#4482—51no—
62C5×C4⋊Q8C2×D311yescharacteristic
63#4092—61no—
64Q8×Dic5—61no—
65#4043—61no—
66#4038—32no—
67#4036—32no—
68#4033—61no—
69C42×D5—31no—
70#4015—31no—
71C5×C4⋊C8—31no—
72C5×C4⋊C8—31no—
73#3952—61no—
74#3952—61no—
75C8×Dic5—61no—
76C8×Dic5—61no—
77C4⋊#168C2×D311yescharacteristic
78C4⋊#168C2×D311yescharacteristic
79#1544—151noSylow
80C22×D15C22⋊C411yescharacteristic
81C3×C5×Q8—41no—
82C3×C5×Q8—41no—
83C2×C3×C4×C5—22no—
84C2×C3×C4×C5C22×C411yescharacteristic
85C2×C3×C4×C5C2×D411yescharacteristic
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×Dic15—22no—
88C2×Dic15C22⋊C411yescharacteristic
89C2×Dic15C22⋊C411yescharacteristic
90C2×Dic15C22⋊C411yescharacteristic
91C4×D15—21no—
92C4×D15—21no—
93C4×D15—21no—
94C4×D15—21no—
95C4×D15—22no—
96Dic30—41no—
97Dic30—41no—
98C3×#168—41no—
99C3×#168—41no—
100C5×C3⋊C8—41no—
101C5×C3⋊C8—41no—
102C3×C4⋊Q8C2×D511yescharacteristic
103#946—101no—
104Q8×Dic3—101no—
105#897—101no—
106#892—52no—
107#890—52no—
108#887—101no—
109C42×D3—51no—
110#869—51no—
111C3×C4⋊C8—51no—
112C3×C4⋊C8—51no—
113(C2×D3)⋊C8—101no—
114(C2×D3)⋊C8—101no—
115C8×Dic3—101no—
116C8×Dic3—101no—
117C4⋊(C3⋊C8)C2×D511yescharacteristic
118C4⋊(C3⋊C8)C2×D511yescharacteristic
119C2×C5×Q8—21no—
120C2×C4×D5—31no—
121C2×C4×D5—31no—
122C2×C4×D5—31no—
123C2×Dic10—61no—
124C2×C5×C8—61no—
125C2×C5×C8—61no—
126C5×C4⋊C4—21no—
127C5×C4⋊C4C4×D312yes—
128C42×C5C22×D311yescharacteristic
129#685—62no—
130C4⋊Dic5—32no—
131C4⋊Dic5—62no—
132C4⋊Dic5—61no—
133#683—62no—
134C4×Dic5—31no—
135C4×Dic5—31no—
136C4×Dic5—31no—
137C4×Dic5—62no—
138C2×#168—21no—
139C2×#168—21no—
140#533—151no—
141#431—151no—
142#431—151no—
143#332—31no—
144#332—51no—
145#332—151no—
146#332—151no—
147C22×C3×C5C2×C22⋊C411yescharacteristic
148C2×D15—21no—
149C2×D15—21no—
150C2×D15—21no—
151C3×C4×C5—21no—
152C3×C4×C5—42no—
153C3×C4×C5#13511yescharacteristic
154C3×C4×C5#13511yescharacteristic
155C3×C4×C5#13511yescharacteristic
156C3×C4×C5#13511yescharacteristic
157Dic15—21no—
158Dic15—21no—
159Dic15—42no—
160Dic15#10112yes—
161C2×C3×Q8—21no—
162C2×C4×D3—51no—
163C2×C4×D3—51no—
164C2×C4×D3—51no—
165C2×Dic6—101no—
166C2×C3×C8—101no—
167C2×C3×C8—101no—
168C3×C4⋊C4—21no—
169C3×C4⋊C4C4×D512yes—
170C3×C42C22×D511yescharacteristic
171(C2×D3)⋊C4—102no—
172C4⋊Dic3—52no—
173C4⋊Dic3—102no—
174C4⋊Dic3—101no—
175Dic3⋊C4—102no—
176C4×Dic3—51no—
177C4×Dic3—51no—
178C4×Dic3—51no—
179C4×Dic3—102no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—21no—
182C22×D5—31no—
183C5×Q8—41no—
184C5×Q8—41no—
185C2×C4×C5—22no—
186C2×C4×C5C2×C4×D311yescharacteristic
187C2×C4×C5D3×D411yescharacteristic
188C2×C4×C5D3×D411yescharacteristic
189C2×Dic5—31no—
190C2×Dic5—31no—
191C2×Dic5—31no—
192C2×Dic5—62no—
193C4×D5—62no—
194C4×D5—61no—
195C4×D5—61no—
196C4×D5—61no—
197C4×D5—61no—
198Dic10—121no—
199Dic10—121no—
200C5×C8—121no—
201C5×C8—121no—
202#168—41no—
203#168—41no—
204C4⋊Q8—151no—
205C4⋊Q8D3×D511yescharacteristic
206#125—152no—
207C22⋊Q8—301no—
208C22⋊Q8—301no—
209C4×Q8—301no—
210C4×Q8—301no—
211#117—152no—
212C2×C42—151no—
213C4⋊C8—31no—
214C4⋊C8—31no—
215C4⋊C8—51no—
216C4⋊C8—51no—
217C22⋊C8—301no—
218C22⋊C8—301no—
219C4×C8—301no—
220C4×C8—301no—
221C2×C3×C5C2×#10111yescharacteristic
222C2×C3×C5#41611yescharacteristic
223C2×C3×C5#41611yescharacteristic
224D15—41no—
225C22×D3—51no—
226C3×Q8—41no—
227C3×Q8—41no—
228C2×C3×C4—22no—
229C2×C3×C4C2×C4×D511yescharacteristic
230C2×C3×C4D4×D511yescharacteristic
231C2×C3×C4D4×D511yescharacteristic
232C2×Dic3—51no—
233C2×Dic3—51no—
234C2×Dic3—51no—
235C2×Dic3—102no—
236C4×D3—102no—
237C4×D3—101no—
238C4×D3—101no—
239C4×D3—101no—
240C4×D3—101no—
241Dic6—201no—
242Dic6—201no—
243C3×C8—201no—
244C3×C8—201no—
245C3⋊C8—41no—
246C3⋊C8—41no—
247C22×C5D3×C22⋊C411yescharacteristic
248C2×D5—61no—
249C2×D5—61no—
250C2×D5—61no—
251C4×C5—21no—
252C4×C5—42no—
253C4×C5#91211yescharacteristic
254C4×C5#91611yescharacteristic
255C4×C5#91611yescharacteristic
256C4×C5#91911yescharacteristic
257Dic5—32no—
258Dic5—61no—
259Dic5—61no—
260Dic5—122no—
261C2×Q8—21no—
262C2×Q8—301no—
263C22×C4—151no—
264C22×C4—151no—
265C22×C4—151no—
266C2×C8—61no—
267C2×C8—61no—
268C2×C8—101no—
269C2×C8—101no—
270C4⋊C4—21no—
271C4⋊C4—152no—
272C4⋊C4—302no—
273C4⋊C4—302no—
274C4⋊C4—301no—
275C4⋊C4#120012yes—
276C22⋊C4—302no—
277C42—151no—
278C42—151no—
279C42—151no—
280C42—302no—
281C42C2×D3×D511yescharacteristic
282C3×C5#154411yescharacteristic, complemented, Hall
283C22×C3D5×C22⋊C411yescharacteristic
284C2×D3—101no—
285C2×D3—101no—
286C2×D3—101no—
287C3×C4—21no—
288C3×C4—42no—
289C3×C4#405811yescharacteristic
290C3×C4#406211yescharacteristic
291C3×C4#406211yescharacteristic
292C3×C4#406511yescharacteristic
293Dic3—52no—
294Dic3—101no—
295Dic3—101no—
296Dic3—202no—
297C2×C5D3×#10111yescharacteristic
298C2×C5#477211yescharacteristic
299C2×C5#480411yescharacteristic
300D5—121no—
301C23—151no—
302Q8—41no—
303Q8—41no—
304Q8—601no—
305Q8—601no—
306C2×C4—22no—
307C2×C4—151no—
308C2×C4—151no—
309C2×C4—151no—
310C2×C4—302no—
311C2×C4—301no—
312C2×C4—301no—
313C2×C4—301no—
314C2×C4—301no—
315C2×C4—302no—
316C2×C4C2×#120011yescharacteristic
317C2×C4#679011yescharacteristic
318C2×C4#679011yescharacteristic
319C8—121no—
320C8—121no—
321C8—201no—
322C8—201no—
323C2×C3D5×#10111yescharacteristic
324C2×C3#6506111yescharacteristic
325C2×C3#6509311yescharacteristic
326D3—201no—
327C5#6841911yescharacteristic, complemented, Sylow
328C22—301no—
329C22—301no—
330C22—301no—
331C22#9156111yescharacteristic
332C4—21no—
333C4—42no—
334C4—152no—
335C4—301no—
336C4—301no—
337C4—602no—
338C4#9149711yescharacteristic
339C4#9149911yescharacteristic
340C4#9152111yescharacteristic
341C4#9152311yescharacteristic
342C3#1059921211yescharacteristic, complemented, Sylow
343C2—601no—
344C2#1174896911yescharacteristic
345C2#1174921511yescharacteristic
346C2#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#1544
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
59. #4547D5semidirect
282. C3×C5#1544semidirect
327. C5#68419semidirect
342. C3#10599212semidirect

Maximal subgroups

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

subgroupindex
#117564872
#117468592
C5×#45472
C3×#647672
#117458602
#117458592
#105992123
#684195