Subgroups — C₂×C₅×#5082 #14437953

Order 1920.

768 conjugacy classes of subgroups.

The subgroup lattice has 232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#870	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#835	C₂	1	4	yes	maximal
4	C₅×#5082	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#803	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#491	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
8	C₃×C₅×C₄⋊Q₈	—	2	2	no	—
9	C₃×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
10	C₂×C₃×C₅×C₄⋊C₄	—	2	2	no	—
11	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
12	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
13	C₂×C₅×Dic₃⋊C₄	—	2	2	no	—
14	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
15	C₅×#870	—	2	2	no	—
16	C₅×#870	C₂²	1	4	yes	—
17	C₅×#835	C₂²	1	16	yes	—
18	C₅×#803	C₂²	1	4	yes	—
19	C₂×#5082	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
20	C₂×C₅×C₄⋊Q₈	D₃	1	1	yes	characteristic
21	C₂×C₅×#125	—	3	1	no	—
22	C₅×#491	—	3	8	no	—
23	C₂×C₅×#103	—	3	4	no	—
24	C₂×C₅×#97	—	3	1	no	—
25	C₂×C₃×C₅×Q₈	—	2	2	no	—
26	C₂×C₃×C₅×Q₈	—	2	8	no	—
27	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
30	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
31	C₂²×C₅×Dic₃	—	2	2	no	—
32	C₃×C₅×C₄⋊C₄	—	2	8	no	—
33	C₃×C₄²×C₅	D₄	1	2	yes	—
34	C₃×C₄²×C₅	C₂³	1	2	yes	—
35	C₅×C₄⋊Dic₃	—	2	2	no	—
36	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
37	C₅×Dic₃⋊C₄	—	2	8	no	—
38	C₂×C₅×C₃⋊C₈	—	2	4	no	—
39	C₂×C₅×C₃⋊C₈	C₂³	1	4	yes	—
40	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
41	C₂×#870	C₂×C₅	1	1	yes	characteristic
42	C₂×#835	C₂×C₅	1	4	yes	—
43	#5082	C₂×C₅	1	8	yes	direct product factor
44	C₂×#803	C₂×C₅	1	1	yes	characteristic
45	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
46	C₂²×C₅×C₈	—	3	2	no	—
47	C₅×C₄⋊Q₈	—	2	2	no	—
48	C₅×C₄⋊Q₈	C₂×D₃	1	4	yes	—
49	C₅×#125	—	3	4	no	—
50	C₅×#125	—	6	2	no	—
51	C₂×C₅×C₄⋊C₄	—	2	2	no	—
52	C₂×C₅×C₄⋊C₄	—	3	2	no	—
53	C₂×C₅×C₄⋊C₄	—	6	2	no	—
54	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
55	C₅×#103	—	3	16	no	—
56	C₅×#97	—	3	4	no	—
57	C₂×#491	—	3	1	no	Sylow
58	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
59	C₃×C₅×Q₈	—	2	8	no	—
60	C₃×C₅×Q₈	—	4	4	no	—
61	C₂×C₃×C₄×C₅	—	2	4	no	—
62	C₂×C₃×C₄×C₅	—	2	4	no	—
63	C₂×C₃×C₄×C₅	—	4	4	no	—
64	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
65	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
66	C₂×C₃×C₄×C₅	#41	1	4	yes	—
67	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
68	C₂×C₅×Dic₃	—	2	4	no	—
69	C₂×C₅×Dic₃	—	4	4	no	—
70	C₅×C₃⋊C₈	—	2	4	no	—
71	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
72	C₃×C₄⋊Q₈	—	2	2	no	—
73	C₃×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
74	C₂×C₃×C₄⋊C₄	—	2	2	no	—
75	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
76	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
77	C₂×Dic₃⋊C₄	—	2	2	no	—
78	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
79	#870	—	2	2	no	—
80	#870	C₂²×C₅	1	4	yes	—
81	#835	C₂²×C₅	1	16	yes	—
82	#803	C₂²×C₅	1	4	yes	—
83	C₂×C₅×Q₈	—	2	2	no	—
84	C₂×C₅×Q₈	—	2	8	no	—
85	C₂×C₅×Q₈	C₂²×D₃	1	4	yes	—
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	—	6	2	no	—
88	C₂²×C₄×C₅	#67	1	2	yes	—
89	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
90	C₂×C₅×C₈	—	3	4	no	—
91	C₂×C₅×C₈	—	6	4	no	—
92	C₅×C₄⋊C₄	—	2	8	no	—
93	C₅×C₄⋊C₄	—	3	4	no	—
94	C₅×C₄⋊C₄	—	6	2	no	—
95	C₅×C₄⋊C₄	—	6	8	no	—
96	C₄²×C₅	#67	1	2	yes	—
97	C₄²×C₅	C₂²×D₃	1	2	yes	—
98	C₂×C₄⋊Q₈	C₅×D₃	1	1	yes	characteristic
99	C₂×#125	—	3	1	no	—
100	#491	—	3	8	no	—
101	C₂×#103	—	3	4	no	—
102	C₂×#97	—	3	1	no	—
103	C₂²×C₃×C₅	#124	1	2	yes	—
104	C₂²×C₃×C₅	#137	1	4	yes	—
105	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
106	C₃×C₄×C₅	—	2	4	no	—
107	C₃×C₄×C₅	—	4	4	no	—
108	C₃×C₄×C₅	#124	1	2	yes	—
109	C₃×C₄×C₅	C₂×#41	1	2	yes	—
110	C₅×Dic₃	—	4	4	no	—
111	C₂×C₃×Q₈	—	2	2	no	—
112	C₂×C₃×Q₈	—	2	8	no	—
113	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
114	C₂²×C₃×C₄	—	2	2	no	—
115	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
116	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
117	C₂²×Dic₃	—	2	2	no	—
118	C₃×C₄⋊C₄	—	2	8	no	—
119	C₃×C₄²	C₅×D₄	1	2	yes	—
120	C₃×C₄²	C₂³×C₅	1	2	yes	—
121	C₄⋊Dic₃	—	2	2	no	—
122	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
123	Dic₃⋊C₄	—	2	8	no	—
124	C₂×C₃⋊C₈	—	2	4	no	—
125	C₂×C₃⋊C₈	C₂³×C₅	1	4	yes	—
126	C₂³×C₅	C₂×#67	1	1	yes	characteristic
127	C₅×Q₈	—	2	8	no	—
128	C₅×Q₈	—	4	4	no	—
129	C₂×C₄×C₅	—	2	4	no	—
130	C₂×C₄×C₅	—	2	4	no	—
131	C₂×C₄×C₅	—	4	4	no	—
132	C₂×C₄×C₅	—	6	4	no	—
133	C₂×C₄×C₅	—	12	4	no	—
134	C₂×C₄×C₅	#237	1	4	yes	—
135	C₂×C₄×C₅	C₂×#67	1	4	yes	—
136	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
137	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
138	C₅×C₈	—	6	4	no	—
139	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
140	C₂²×C₈	—	3	2	no	—
141	C₄⋊Q₈	—	2	2	no	—
142	C₄⋊Q₈	C₂×C₅×D₃	1	4	yes	—
143	#125	—	3	4	no	—
144	#125	—	6	2	no	—
145	C₂×C₄⋊C₄	—	2	2	no	—
146	C₂×C₄⋊C₄	—	3	2	no	—
147	C₂×C₄⋊C₄	—	6	2	no	—
148	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
149	#103	—	3	16	no	—
150	#97	—	3	4	no	—
151	C₂×C₃×C₅	#491	1	4	yes	complemented
152	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
153	C₂×C₃×C₅	C₂×#137	1	2	yes	—
154	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
155	C₃×Q₈	—	2	8	no	—
156	C₃×Q₈	—	4	4	no	—
157	C₂×C₃×C₄	—	2	4	no	—
158	C₂×C₃×C₄	—	2	4	no	—
159	C₂×C₃×C₄	—	4	4	no	—
160	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
161	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄	C₅×#41	1	4	yes	—
163	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
164	C₂×Dic₃	—	2	4	no	—
165	C₂×Dic₃	—	4	4	no	—
166	C₃⋊C₈	—	2	4	no	—
167	C₂²×C₅	#936	1	2	yes	—
168	C₂²×C₅	#942	1	4	yes	—
169	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
170	C₄×C₅	—	2	4	no	—
171	C₄×C₅	—	4	4	no	—
172	C₄×C₅	—	12	4	no	—
173	C₄×C₅	#936	1	2	yes	—
174	C₄×C₅	C₂×#237	1	2	yes	—
175	C₂×Q₈	—	2	2	no	—
176	C₂×Q₈	—	2	8	no	—
177	C₂×Q₈	C₂²×C₅×D₃	1	4	yes	—
178	C₂²×C₄	—	2	2	no	—
179	C₂²×C₄	—	6	2	no	—
180	C₂²×C₄	C₅×#67	1	2	yes	—
181	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
182	C₂×C₈	—	3	4	no	—
183	C₂×C₈	—	6	4	no	—
184	C₄⋊C₄	—	2	8	no	—
185	C₄⋊C₄	—	3	4	no	—
186	C₄⋊C₄	—	6	2	no	—
187	C₄⋊C₄	—	6	8	no	—
188	C₄²	C₅×#67	1	2	yes	—
189	C₄²	C₂²×C₅×D₃	1	2	yes	—
190	C₃×C₅	C₂×#491	1	1	yes	characteristic, complemented, Hall
191	C₂²×C₃	C₅×#124	1	2	yes	—
192	C₂²×C₃	C₅×#137	1	4	yes	—
193	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
194	C₃×C₄	—	2	4	no	—
195	C₃×C₄	—	4	4	no	—
196	C₃×C₄	C₅×#124	1	2	yes	—
197	C₃×C₄	C₂×C₅×#41	1	2	yes	—
198	Dic₃	—	4	4	no	—
199	C₂×C₅	#5082	1	4	yes	direct product factor
200	C₂×C₅	C₂×#936	1	1	yes	characteristic
201	C₂×C₅	C₂×#942	1	2	yes	—
202	C₂³	C₂×C₅×#67	1	1	yes	characteristic
203	Q₈	—	2	8	no	—
204	Q₈	—	4	4	no	—
205	C₂×C₄	—	2	4	no	—
206	C₂×C₄	—	2	4	no	—
207	C₂×C₄	—	4	4	no	—
208	C₂×C₄	—	6	4	no	—
209	C₂×C₄	—	12	4	no	—
210	C₂×C₄	C₅×#237	1	4	yes	—
211	C₂×C₄	C₂×C₅×#67	1	4	yes	—
212	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
213	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
214	C₈	—	6	4	no	—
215	C₂×C₃	C₅×#491	1	4	yes	complemented
216	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
217	C₂×C₃	C₂×C₅×#137	1	2	yes	—
218	C₅	C₂×#5082	1	1	yes	characteristic, direct product factor, Sylow
219	C₂²	C₅×#936	1	2	yes	—
220	C₂²	C₅×#942	1	4	yes	—
221	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
222	C₄	—	2	4	no	—
223	C₄	—	4	4	no	—
224	C₄	—	12	4	no	—
225	C₄	C₅×#936	1	2	yes	—
226	C₄	C₂×C₅×#237	1	2	yes	—
227	C₃	C₂×C₅×#491	1	1	yes	characteristic, complemented, Sylow
228	C₂	C₅×#5082	1	4	yes	direct product factor
229	C₂	C₂×C₅×#936	1	1	yes	characteristic
230	C₂	C₂×C₅×#942	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×C₄⋊Q₈	C₂
socle, prime radical	C₂³×C₃×C₅	C₂×D₄
hypercenter	C₂×C₅×C₄⋊Q₈	D₃
hypocenter	C₃	C₂×C₅×#491
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₅×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
4. C₅×#5082	C₂	direct (N × H)
19. C₂×#5082	C₅	direct (N × H)
43. #5082	C₂×C₅	direct (N × H)
151. C₂×C₃×C₅	#491	semidirect
190. C₃×C₅	C₂×#491	semidirect
199. C₂×C₅	#5082	direct (N × H)
215. C₂×C₃	C₅×#491	semidirect
218. C₅	C₂×#5082	direct (N × H)
227. C₃	C₂×C₅×#491	semidirect
228. C₂	C₅×#5082	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×C₄⋊Q₈	2
C₂×C₅×#870	2
C₂×C₅×#835	2
C₅×#5082	2
C₂×C₅×#803	2
C₂×C₅×#491	3
C₂×#5082	5

Subgroups — C2×C5×#5082 #14437953

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5082 #14437953