Finite Group Databasebeta

← #14289565

Subgroups — #14289565

Order 1920.

412 conjugacy classes of subgroups; only the 104 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 104 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
1C3×Q8×Dic10C211yesmaximal, characteristic
2C5×#5021C211yesmaximal, characteristic
3#11747103C211yesmaximal, characteristic
4#11746954C211yesmaximal, characteristic
5#11746356C211yesmaximal, characteristic
6#11745861C211yesmaximal, characteristic
7#11745840C211yesmaximal, characteristic
8#10601954—31nomaximal, Hall
9C3×C4×C5×Q8C2211yescharacteristic
10C5×#869C2211yescharacteristic
11C3×Q8×Dic5—21no—
12C3×#4034—22no—
13C3×#4034—21no—
14C3×#4015—21no—
15C3×#4015C2211yescharacteristic
16C3×C4×Dic10—21no—
17C3×C4×Dic10C2211yescharacteristic
18C2×#6661—22no—
19C4⋊(C3⋊#168)C2211yescharacteristic
20C4×C3⋊#168C2211yescharacteristic
21C5×#835—21no—
22C5×#807—21no—
23C5×C4⋊(C3⋊C8)C2211yescharacteristic
24#90989—21no—
25#90970—21no—
26#71940—51nomaximal, Hall
27Q8×Dic10D311yescharacteristic
28C5×#477—31no—
29#65381—31no—
30#65380—31no—
31Q8⋊#168—31no—
32#64704—31no—
33#64701—31no—
34C2×C3×C5×Q8D411yescharacteristic
35C2×C5×Dic6—21no—
36C2×C3×Dic10—22no—
37C2×C3×Dic10D411yescharacteristic
38C2×C3×Dic10D412yes—
39C3×C5×C4⋊C4—21no—
40C3×C5×C4⋊C4D411yescharacteristic
41C3×C42×C5—21no—
42C3×C42×C5C2311yescharacteristic
43C2×C3⋊#168—21no—
44C2×C3⋊#168—21no—
45C5×C4⋊Dic3—21no—
46C5×C4⋊Dic3—21no—
47C2×C5×C3⋊C8—21no—
48C3×C4⋊Dic5—22no—
49C3×C4⋊Dic5—21no—
50C3×C4⋊Dic5—21no—
51C3×C4⋊Dic5D411yescharacteristic
52C3×#683—22no—
53C3×#683—21no—
54C3×C4×Dic5—22no—
55C3×C4×Dic5—21no—
56#6661—44no—
57C3×Q82—51no—
58#5092—51no—
59#5021—51no—
60#5021D511yescharacteristic
61#4546—51no—
62#4535—51no—
63#4535—51no—
64C5×C4⋊Q8—31no—
65C4×C5×Q8C2×D311yescharacteristic
66Q8×Dic5—21no—
67C2×#689—62no—
68#4034—22no—
69#4034—21no—
70#4015—21no—
71#4015C2×D311yescharacteristic
72C4×Dic10—21no—
73C4×Dic10C2×D311yescharacteristic
74C5×#107—61no—
75C5×C4⋊C8—31no—
76C5×#103—61no—
77#3942—61no—
78#3939—61no—
79C4⋊#168—31no—
80C4×#168—31no—
81#1633—151noSylow
82C3×C5×Q8—21no—
83C3×C5×Q8Q1612yescomplemented
84C2×C3×C4×C5—21no—
85C2×C3×C4×C5—21no—
86C2×C3×C4×C5C2×D411yescharacteristic
87C2×C3×C4×C5C2×D411yescharacteristic
88C2×C3×C4×C5C2×D411yescharacteristic
89C2×C5×Dic3—41no—
90C5×Dic6—42no—
91C2×C3×Dic5—21no—
92C2×C3×Dic5—22no—
93C2×C3×Dic5—21no—
94C3×Dic10—21no—
95C3×Dic10—42no—
96C3×Dic10—82no—
97C3×Dic10Q1612yescomplemented
98C3⋊#168—22no—
99C3⋊#168—41no—
100C5×C3⋊C8—41no—
101C3×C4⋊Q8—51no—
102C3×C4⋊Q8—101no—
103C3×C4⋊Q8—102no—
104C3×C4⋊Q8—101no—
105C3×C4×Q8—51no—
106C3×C4×Q8—101no—
107C3×C4×Q8—101no—
108C3×C4×Q8C2×D511yescharacteristic
109C2×#216—102no—
110#869C2×D511yescharacteristic
111#835—21no—
112#835—101no—
113#807—21no—
114#807—101no—
115C4⋊(C3⋊C8)—51no—
116C4⋊(C3⋊C8)C2×D511yescharacteristic
117C4×C3⋊C8—51no—
118C2×C5×Q8—61no—
119C2×C5×Q8#6711yescharacteristic
120C2×Dic10—22no—
121C2×Dic10#6711yescharacteristic
122C2×Dic10#6712yes—
123C2×C5×C8—61no—
124C5×C4⋊C4—21no—
125C5×C4⋊C4—61no—
126C5×C4⋊C4—61no—
127C5×C4⋊C4#6711yescharacteristic
128C42×C5—21no—
129C42×C5C22×D311yescharacteristic
130#689—124no—
131C4⋊Dic5—22no—
132C4⋊Dic5—21no—
133C4⋊Dic5—21no—
134C4⋊Dic5#6711yescharacteristic
135#683—22no—
136#683—21no—
137C4×Dic5—22no—
138C4×Dic5—21no—
139C2×#168—61no—
140C2×#168—61no—
141Q82—51no—
142#494—151no—
143#477—31no—
144#477—151no—
145#333—151no—
146Q8⋊C8—151no—
147Q8⋊C8—151no—
148C22×C3×C5#12011yescharacteristic
149C3×C4×C5—22no—
150C3×C4×C5—21no—
151C3×C4×C5—41no—
152C3×C4×C5C2×Q1611yescharacteristic
153C3×C4×C5C2×Q1611yescharacteristic
154C3×C4×C5#13711yescharacteristic
155C3×C4×C5#13711yescharacteristic
156C3×Dic5—22no—
157C3×Dic5—42no—
158C3×Dic5—41no—
159C5×Dic3—81no—
160C2×C3×Q8—51no—
161C2×C3×Q8—52no—
162C2×C3×Q8—102no—
163C2×C3×Q8C22⋊D511yescharacteristic
164C2×Dic6—21no—
165C3×C4⋊C4—21no—
166C3×C4⋊C4—51no—
167C3×C4⋊C4—102no—
168C3×C4⋊C4—102no—
169C3×C4⋊C4—101no—
170C3×C4⋊C4—101no—
171C3×C4⋊C4—101no—
172C3×C4⋊C4C22⋊D511yescharacteristic
173C3×C42—21no—
174C3×C42—102no—
175C3×C42—101no—
176C3×C42C22×D511yescharacteristic
177#216—204no—
178C4⋊Dic3—21no—
179C4⋊Dic3—21no—
180C2×C3⋊C8—21no—
181C2×C3⋊C8—101no—
182C2×C3⋊C8—101no—
183C5×Q8—21no—
184C5×Q8—122no—
185C5×Q8#21612yescomplemented
186C2×C4×C5—21no—
187C2×C4×C5—21no—
188C2×C4×C5—121no—
189C2×C4×C5C2×#6711yescharacteristic
190C2×C4×C5C2×#6711yescharacteristic
191C2×C4×C5C2×#6711yescharacteristic
192C2×Dic5—21no—
193C2×Dic5—22no—
194C2×Dic5—21no—
195Dic10—21no—
196Dic10—42no—
197Dic10—82no—
198Dic10#21612yescomplemented
199C5×C8—121no—
200#168—62no—
201#168—121no—
202C2×Q16—302no—
203C4⋊Q8—31no—
204C4⋊Q8—51no—
205C4⋊Q8—101no—
206C4⋊Q8—102no—
207C4⋊Q8—101no—
208C4×Q8—51no—
209C4×Q8—101no—
210C4×Q8—101no—
211C4×Q8D3×D511yescharacteristic
212#107—61no—
213#107—301no—
214C4⋊C8—31no—
215C4⋊C8—151no—
216#103—61no—
217#103—301no—
218C4×C8—151no—
219C2×C3×C5#45111yescharacteristic
220C2×C3×C5#45111yescharacteristic
221C2×C3×C5#45311yescharacteristic
222C3×Q8—21no—
223C3×Q8—52no—
224C3×Q8—101no—
225C3×Q8—202no—
226C3×Q8—402no—
227C3×Q8#68912yescomplemented
228C2×C3×C4—21no—
229C2×C3×C4—21no—
230C2×C3×C4—101no—
231C2×C3×C4—101no—
232C2×C3×C4—102no—
233C2×C3×C4D4×D511yescharacteristic
234C2×C3×C4D4×D511yescharacteristic
235C2×C3×C4C2×C22⋊D511yescharacteristic
236C2×Dic3—41no—
237Dic6—42no—
238C3⋊C8—41no—
239C3⋊C8—102no—
240C3⋊C8—201no—
241C22×C5#95311yescharacteristic
242C4×C5—22no—
243C4×C5—21no—
244C4×C5—41no—
245C4×C5—241no—
246C4×C5#94211yescharacteristic
247C4×C5#94211yescharacteristic
248C4×C5C2×#21611yescharacteristic
249C4×C5C2×#21611yescharacteristic
250Dic5—22no—
251Dic5—42no—
252Dic5—41no—
253C2×Q8—51no—
254C2×Q8—52no—
255C2×Q8—61no—
256C2×Q8—102no—
257C2×Q8#120111yescharacteristic
258Q16—604no—
259C2×C8—61no—
260C2×C8—301no—
261C2×C8—301no—
262C4⋊C4—21no—
263C4⋊C4—51no—
264C4⋊C4—61no—
265C4⋊C4—61no—
266C4⋊C4—102no—
267C4⋊C4—102no—
268C4⋊C4—101no—
269C4⋊C4—101no—
270C4⋊C4—101no—
271C4⋊C4#120111yescharacteristic
272C42—21no—
273C42—102no—
274C42—101no—
275C42C2×D3×D511yescharacteristic
276C3×C5#163311yescharacteristic, complemented, Hall
277C22×C3#408311yescharacteristic
278C3×C4—22no—
279C3×C4—21no—
280C3×C4—41no—
281C3×C4—102no—
282C3×C4—202no—
283C3×C4—201no—
284C3×C4D5×Q1611yescharacteristic
285C3×C4#406411yescharacteristic
286C3×C4C2×#68911yescharacteristic
287C3×C4#409711yescharacteristic
288Dic3—81no—
289C2×C5#522811yescharacteristic
290C2×C5#522811yescharacteristic
291C2×C5#524111yescharacteristic
292Q8—21no—
293Q8—52no—
294Q8—101no—
295Q8—122no—
296Q8—202no—
297Q8—402no—
298Q8#666112yescomplemented
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—101no—
302C2×C4—101no—
303C2×C4—102no—
304C2×C4—121no—
305C2×C4C2×#120111yescharacteristic
306C2×C4D5×#6711yescharacteristic
307C2×C4D5×#6711yescharacteristic
308C8—121no—
309C8—302no—
310C8—601no—
311C2×C3#6533911yescharacteristic
312C2×C3#6547511yescharacteristic
313C2×C3#6548711yescharacteristic
314C5#7194011yescharacteristic, complemented, Sylow
315C22#9156311yescharacteristic
316C4—21no—
317C4—22no—
318C4—41no—
319C4—102no—
320C4—202no—
321C4—201no—
322C4—241no—
323C4#9130911yescharacteristic
324C4C2×#666111yescharacteristic
325C4D5×#21611yescharacteristic
326C4#9151511yescharacteristic
327C3#1060195411yescharacteristic, complemented, Sylow
328C2#1174855511yescharacteristic
329C2#1174929011yescharacteristic
330C2#1174941711yescharacteristic
subgroupG/H
centerC22#91563
commutator, cosocleC3×C42×C5C23
FrattiniC42C2×D3×D5
FittingC3×C4×C5×Q8C22
socle, prime radicalC22×C3×C5#120
hypercenterC4×Q8D3×D5
hypocenterC3×C5#1633
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
83. C3×C5×Q8Q16semidirect
97. C3×Dic10Q16semidirect
185. C5×Q8#216semidirect
198. Dic10#216semidirect
227. C3×Q8#689semidirect
276. C3×C5#1633semidirect
298. Q8#6661semidirect
314. C5#71940semidirect
327. C3#10601954semidirect

Maximal subgroups

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

subgroupindex
C3×Q8×Dic102
C5×#50212
#117471032
#117469542
#117463562
#117458612
#117458402
#106019543
#719405