Subgroups — C₁₉×#13460 #18019419

Order 4864.

310 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3163	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2155	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#365	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#1953	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1389	C₂	1	1	yes	maximal, characteristic
6	C₁₉×#1383	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1378	C₂	1	1	yes	maximal, characteristic
8	C₁₉×#544	—	2	1	no	—
9	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×M₃₂	C₂²	1	1	yes	characteristic
11	C₁₉×#501	—	2	2	no	—
12	C₁₉×#499	—	2	1	no	—
13	C₁₉×#498	—	2	1	no	—
14	C₁₉×#430	—	2	1	no	—
15	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#108	C₂²	1	1	yes	characteristic
17	C₁₉×#428	—	2	1	no	—
18	C₁₉×#427	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
20	C₁₉×#405	C₂²	1	1	yes	characteristic
21	C₁₉×#365	—	2	2	no	—
22	C₁₉×#365	—	2	1	no	—
23	C₁₉×#365	—	2	1	no	—
24	C₁₉×#344	—	2	1	no	—
25	C₂×M₁₆×C₁₉	—	2	1	no	—
26	C₂×M₁₆×C₁₉	—	2	1	no	—
27	C₂×M₁₆×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
29	C₁₉×C₄⋊Q₈	—	2	2	no	—
30	C₁₉×C₄⋊Q₈	—	4	1	no	—
31	C₁₉×#125	—	2	2	no	—
32	C₁₉×#125	—	4	1	no	—
33	C₁₉×C₂²⋊Q₈	—	4	2	no	—
34	C₁₉×#117	—	2	1	no	—
35	C₁₉×#117	D₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₁₉×M₃₂	—	2	1	no	—
38	C₁₉×M₃₂	—	2	1	no	—
39	C₁₉×M₃₂	—	2	1	no	—
40	C₁₉×M₃₂	Q₈	1	2	yes	complemented
41	C₂×C₁₆×C₁₉	—	2	1	no	—
42	C₂×C₁₆×C₁₉	Q₈	1	2	yes	complemented
43	C₁₉×#108	—	2	1	no	—
44	C₁₉×#108	—	2	1	no	—
45	C₁₉×#108	—	2	1	no	—
46	C₁₉×#108	—	4	2	no	—
47	C₁₉×#108	Q₈	1	2	yes	complemented
48	C₁₉×#107	—	2	2	no	—
49	C₁₉×#107	—	2	1	no	—
50	C₁₉×#106	—	2	2	no	—
51	C₁₉×#106	—	2	1	no	—
52	C₁₉×#106	D₄	1	2	yes	—
53	C₁₉×#106	D₄	1	1	yes	characteristic
54	C₁₉×#106	D₄	1	1	yes	characteristic
55	C₁₉×#97	—	2	1	no	—
56	C₄×C₈×C₁₉	—	2	1	no	—
57	C₂×Q₈×C₁₉	—	4	2	no	—
58	C₂²×C₄×C₁₉	—	4	1	no	—
59	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
60	M₁₆×C₁₉	—	2	1	no	—
61	M₁₆×C₁₉	—	2	2	no	—
62	M₁₆×C₁₉	—	4	1	no	—
63	M₁₆×C₁₉	—	4	1	no	—
64	M₁₆×C₁₉	—	4	1	no	—
65	M₁₆×C₁₉	SD₁₆	1	2	yes	—
66	C₂×C₈×C₁₉	—	2	1	no	—
67	C₂×C₈×C₁₉	—	4	1	no	—
68	C₂×C₈×C₁₉	—	4	1	no	—
69	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
72	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
73	C₂×C₈×C₁₉	C₂×Q₈	1	1	yes	characteristic
74	C₂×C₈×C₁₉	#41	1	1	yes	characteristic
75	C₄⋊C₄×C₁₉	—	2	1	no	—
76	C₄⋊C₄×C₁₉	—	2	2	no	—
77	C₄⋊C₄×C₁₉	—	2	1	no	—
78	C₄⋊C₄×C₁₉	—	2	1	no	—
79	C₄⋊C₄×C₁₉	—	4	2	no	—
80	C₄⋊C₄×C₁₉	—	4	2	no	—
81	C₄⋊C₄×C₁₉	—	4	2	no	—
82	C₄⋊C₄×C₁₉	—	4	1	no	—
83	C₂²⋊C₄×C₁₉	—	4	1	no	—
84	C₂²⋊C₄×C₁₉	SD₁₆	1	2	yes	—
85	C₄²×C₁₉	—	2	1	no	—
86	C₄²×C₁₉	—	4	1	no	—
87	C₁₆×C₁₉	—	2	2	no	—
88	C₁₆×C₁₉	—	2	2	no	—
89	#13460	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
90	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
91	Q₈×C₁₉	—	16	2	no	—
92	C₂×C₄×C₁₉	—	2	2	no	—
93	C₂×C₄×C₁₉	—	4	1	no	—
94	C₂×C₄×C₁₉	—	4	1	no	—
95	C₂×C₄×C₁₉	—	4	2	no	—
96	C₂×C₄×C₁₉	—	16	1	no	—
97	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
98	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
99	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
101	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
103	C₈×C₁₉	—	2	2	no	—
104	C₈×C₁₉	—	4	2	no	—
105	C₈×C₁₉	—	8	1	no	—
106	C₈×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
107	C₈×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
108	C₈×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
109	C₈×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
110	#3163	C₂×C₁₉	1	1	yes	characteristic
111	#2155	C₂×C₁₉	1	1	yes	characteristic
112	C₂×#365	C₂×C₁₉	1	1	yes	characteristic
113	#1953	C₂×C₁₉	1	1	yes	characteristic
114	#1389	C₂×C₁₉	1	1	yes	characteristic
115	#1383	C₂×C₁₉	1	1	yes	characteristic
116	#1378	C₂×C₁₉	1	1	yes	characteristic
117	C₂²×C₁₉	—	4	1	no	—
118	C₂²×C₁₉	#450	1	1	yes	characteristic
119	C₂²×C₁₉	#475	1	1	yes	characteristic
120	C₂²×C₁₉	#498	1	1	yes	characteristic
121	C₄×C₁₉	—	4	2	no	—
122	C₄×C₁₉	—	8	1	no	—
123	C₄×C₁₉	—	8	2	no	—
124	C₄×C₁₉	—	8	1	no	—
125	C₄×C₁₉	#395	1	1	yes	characteristic
126	C₄×C₁₉	#448	1	1	yes	characteristic
127	C₄×C₁₉	#476	1	1	yes	characteristic
128	C₄×C₁₉	#501	1	1	yes	characteristic
129	#544	—	2	1	no	—
130	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
131	C₂×M₃₂	C₂²×C₁₉	1	1	yes	characteristic
132	#501	—	2	2	no	—
133	#499	—	2	1	no	—
134	#498	—	2	1	no	—
135	#430	—	2	1	no	—
136	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
137	C₂×#108	C₂²×C₁₉	1	1	yes	characteristic
138	#428	—	2	1	no	—
139	#427	C₂²×C₁₉	1	1	yes	characteristic
140	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
141	#405	C₂²×C₁₉	1	1	yes	characteristic
142	#365	—	2	2	no	—
143	#365	—	2	1	no	—
144	#365	—	2	1	no	—
145	#344	—	2	1	no	—
146	C₂×C₁₉	—	2	1	no	—
147	C₂×C₁₉	—	2	1	no	—
148	C₂×C₁₉	—	2	1	no	—
149	C₂×C₁₉	#2058	1	1	yes	characteristic
150	C₂×M₁₆	—	2	1	no	—
151	C₂×M₁₆	—	2	1	no	—
152	C₂×M₁₆	D₄×C₁₉	1	1	yes	characteristic
153	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
154	C₄⋊Q₈	—	2	2	no	—
155	C₄⋊Q₈	—	4	1	no	—
156	#125	—	2	2	no	—
157	#125	—	4	1	no	—
158	C₂²⋊Q₈	—	4	2	no	—
159	#117	—	2	1	no	—
160	#117	D₄×C₁₉	1	1	yes	characteristic
161	C₂×C₄⋊C₄	—	2	1	no	—
162	M₃₂	—	2	1	no	—
163	M₃₂	—	2	1	no	—
164	M₃₂	—	2	1	no	—
165	M₃₂	Q₈×C₁₉	1	2	yes	complemented
166	C₂×C₁₆	—	2	1	no	—
167	C₂×C₁₆	Q₈×C₁₉	1	2	yes	complemented
168	#108	—	2	1	no	—
169	#108	—	2	1	no	—
170	#108	—	2	1	no	—
171	#108	—	4	2	no	—
172	#108	Q₈×C₁₉	1	2	yes	complemented
173	#107	—	2	2	no	—
174	#107	—	2	1	no	—
175	#106	—	2	2	no	—
176	#106	—	2	1	no	—
177	#106	D₄×C₁₉	1	2	yes	—
178	#106	D₄×C₁₉	1	1	yes	characteristic
179	#106	D₄×C₁₉	1	1	yes	characteristic
180	#97	—	2	1	no	—
181	C₄×C₈	—	2	1	no	—
182	C₁₉	#13460	1	1	yes	characteristic, direct product factor, Sylow
183	C₂×Q₈	—	4	2	no	—
184	C₂²×C₄	—	4	1	no	—
185	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
186	M₁₆	—	2	1	no	—
187	M₁₆	—	2	2	no	—
188	M₁₆	—	4	1	no	—
189	M₁₆	—	4	1	no	—
190	M₁₆	—	4	1	no	—
191	M₁₆	SD₁₆×C₁₉	1	2	yes	—
192	C₂×C₈	—	2	1	no	—
193	C₂×C₈	—	4	1	no	—
194	C₂×C₈	—	4	1	no	—
195	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
196	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
197	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
198	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
199	C₂×C₈	C₂×Q₈×C₁₉	1	1	yes	characteristic
200	C₂×C₈	#41×C₁₉	1	1	yes	characteristic
201	C₄⋊C₄	—	2	1	no	—
202	C₄⋊C₄	—	2	2	no	—
203	C₄⋊C₄	—	2	1	no	—
204	C₄⋊C₄	—	2	1	no	—
205	C₄⋊C₄	—	4	2	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₄⋊C₄	—	4	2	no	—
208	C₄⋊C₄	—	4	1	no	—
209	C₂²⋊C₄	—	4	1	no	—
210	C₂²⋊C₄	SD₁₆×C₁₉	1	2	yes	—
211	C₄²	—	2	1	no	—
212	C₄²	—	4	1	no	—
213	C₁₆	—	2	2	no	—
214	C₁₆	—	2	2	no	—
215	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
216	Q₈	—	16	2	no	—
217	C₂×C₄	—	2	2	no	—
218	C₂×C₄	—	4	1	no	—
219	C₂×C₄	—	4	1	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	—	16	1	no	—
222	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
223	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
224	C₂×C₄	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
225	C₂×C₄	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
226	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
227	C₂×C₄	C₁₉×#137	1	1	yes	characteristic
228	C₈	—	2	2	no	—
229	C₈	—	4	2	no	—
230	C₈	—	8	1	no	—
231	C₈	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
232	C₈	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
233	C₈	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
234	C₈	C₁₉×C₄⋊Q₈	1	1	yes	characteristic
235	C₂²	—	4	1	no	—
236	C₂²	C₁₉×#450	1	1	yes	characteristic
237	C₂²	C₁₉×#475	1	1	yes	characteristic
238	C₂²	C₁₉×#498	1	1	yes	characteristic
239	C₄	—	4	2	no	—
240	C₄	—	8	2	no	—
241	C₄	—	8	1	no	—
242	C₄	—	8	1	no	—
243	C₄	C₁₉×#395	1	1	yes	characteristic
244	C₄	C₁₉×#448	1	1	yes	characteristic
245	C₄	C₁₉×#476	1	1	yes	characteristic
246	C₄	C₁₉×#501	1	1	yes	characteristic
247	C₂	—	2	1	no	—
248	C₂	—	2	1	no	—
249	C₂	—	2	1	no	—
250	C₂	C₁₉×#2058	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₁₉	#2058
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₉
prime radical	C₂³×C₁₉	C₂×SD₁₆
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₉ ◁ C₂²×C₄×C₁₉ ◁ C₁₉×#405 ◁ G

Complements

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

N	H ≅ G/N	type
40. C₁₉×M₃₂	Q₈	semidirect
42. C₂×C₁₆×C₁₉	Q₈	semidirect
47. C₁₉×#108	Q₈	semidirect
89. #13460	C₁₉	direct (N × H)
165. M₃₂	Q₈×C₁₉	semidirect
167. C₂×C₁₆	Q₈×C₁₉	semidirect
172. #108	Q₈×C₁₉	semidirect
182. C₁₉	#13460	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3163	2
C₁₉×#2155	2
C₂×C₁₉×#365	2
C₁₉×#1953	2
C₁₉×#1389	2
C₁₉×#1383	2
C₁₉×#1378	2
#13460	19

Subgroups — C19×#13460 #18019419

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13460 #18019419