Subgroups — C₁₉×#13793 #18019752

Order 4864.

1498 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#391	C₂	1	3	yes	maximal
2	C₁₉×#1436	C₂	1	6	yes	maximal
3	C₁₉×#1434	C₂	1	3	yes	maximal
4	C₄×C₁₉×#95	C₂	1	3	yes	maximal
5	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
6	C₂²×C₄⋊C₄×C₁₉	C₂²	1	3	yes	—
7	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
8	C₂²×C₄²×C₁₉	C₂²	1	3	yes	—
9	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#391	C₄	1	24	yes	complemented
11	C₂×C₁₉×#95	C₂²	1	6	yes	—
12	C₂×C₁₉×#95	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#95	C₂²	1	3	yes	—
14	C₂×C₁₉×#95	C₂²	1	2	yes	—
15	C₂×C₁₉×#95	C₂²	1	6	yes	—
16	C₂×C₁₉×#95	C₂²	1	6	yes	—
17	C₂²×Q₈×C₁₉	—	4	1	no	—
18	C₂²×Q₈×C₁₉	—	4	3	no	—
19	C₂²×Q₈×C₁₉	C₂×C₄	1	12	yes	—
20	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
21	C₂³×C₄×C₁₉	C₂³	1	6	yes	—
22	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
23	C₂³×C₄×C₁₉	C₂³	1	3	yes	—
24	C₂×C₄⋊C₄×C₁₉	—	4	6	no	—
25	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	12	yes	—
26	C₂×C₄²×C₁₉	—	2	6	no	—
27	C₂×C₄²×C₁₉	—	4	3	no	—
28	C₂×C₄²×C₁₉	—	4	3	no	—
29	C₂×C₄²×C₁₉	—	4	1	no	—
30	C₂×C₄²×C₁₉	—	4	1	no	—
31	C₂×C₄²×C₁₉	—	4	3	no	—
32	C₂×C₄²×C₁₉	—	4	3	no	—
33	C₂×C₄²×C₁₉	C₂×C₄	1	12	yes	—
34	C₂×C₄²×C₁₉	Q₈	1	4	yes	complemented
35	C₁₉×#95	—	2	12	no	—
36	C₁₉×#95	—	4	1	no	—
37	C₁₉×#95	—	4	2	no	—
38	C₁₉×#95	—	4	3	no	—
39	C₁₉×#95	C₂×C₄	1	24	yes	—
40	C₁₉×#95	C₂×C₄	1	24	yes	—
41	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
42	C₂×Q₈×C₁₉	—	4	12	no	—
43	C₂×Q₈×C₁₉	—	4	12	no	—
44	C₂×Q₈×C₁₉	C₄²	1	16	yes	complemented
45	C₂²×C₄×C₁₉	—	2	3	no	—
46	C₂²×C₄×C₁₉	—	2	3	no	—
47	C₂²×C₄×C₁₉	—	2	3	no	—
48	C₂²×C₄×C₁₉	—	2	3	no	—
49	C₂²×C₄×C₁₉	—	2	3	no	—
50	C₂²×C₄×C₁₉	—	2	6	no	—
51	C₂²×C₄×C₁₉	—	2	3	no	—
52	C₂²×C₄×C₁₉	—	2	6	no	—
53	C₂²×C₄×C₁₉	—	2	6	no	—
54	C₂²×C₄×C₁₉	—	2	6	no	—
55	C₂²×C₄×C₁₉	—	2	6	no	—
56	C₂²×C₄×C₁₉	—	2	3	no	—
57	C₂²×C₄×C₁₉	—	2	3	no	—
58	C₂²×C₄×C₁₉	—	2	6	no	—
59	C₂²×C₄×C₁₉	—	2	6	no	—
60	C₂²×C₄×C₁₉	—	2	6	no	—
61	C₂²×C₄×C₁₉	—	2	6	no	—
62	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
63	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
64	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
65	C₂²×C₄×C₁₉	C₂²×C₄	1	12	yes	—
66	C₂²×C₄×C₁₉	C₂²×C₄	1	6	yes	—
67	C₂²×C₄×C₁₉	C₂×Q₈	1	6	yes	—
68	C₂²×C₄×C₁₉	#41	1	6	yes	—
69	C₄⋊C₄×C₁₉	—	4	12	no	—
70	C₄²×C₁₉	—	4	12	no	—
71	C₄²×C₁₉	—	4	4	no	—
72	C₄²×C₁₉	—	4	12	no	—
73	#13793	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
74	C₂³×C₁₉	C₂³×C₄	1	3	yes	—
75	C₂³×C₁₉	C₂²×Q₈	1	1	yes	characteristic
76	C₂³×C₁₉	C₂×#41	1	3	yes	—
77	C₂³×C₁₉	H(5,𝔽₂)	1	3	yes	—
78	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
79	C₂³×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
80	C₂³×C₁₉	2₋¹⁺⁴	1	3	yes	—
81	Q₈×C₁₉	—	4	16	no	—
82	C₂×C₄×C₁₉	—	2	6	no	—
83	C₂×C₄×C₁₉	—	2	6	no	—
84	C₂×C₄×C₁₉	—	2	6	no	—
85	C₂×C₄×C₁₉	—	2	12	no	—
86	C₂×C₄×C₁₉	—	2	12	no	—
87	C₂×C₄×C₁₉	—	2	6	no	—
88	C₂×C₄×C₁₉	—	2	6	no	—
89	C₂×C₄×C₁₉	—	2	6	no	—
90	C₂×C₄×C₁₉	—	2	6	no	—
91	C₂×C₄×C₁₉	—	2	6	no	—
92	C₂×C₄×C₁₉	—	2	6	no	—
93	C₂×C₄×C₁₉	—	2	12	no	—
94	C₂×C₄×C₁₉	—	2	6	no	—
95	C₂×C₄×C₁₉	—	2	12	no	—
96	C₂×C₄×C₁₉	—	2	6	no	—
97	C₂×C₄×C₁₉	—	2	12	no	—
98	C₂×C₄×C₁₉	—	4	6	no	—
99	C₂×C₄×C₁₉	—	4	6	no	—
100	C₂×C₄×C₁₉	—	4	6	no	—
101	C₂×C₄×C₁₉	—	4	6	no	—
102	C₂×C₄×C₁₉	—	4	6	no	—
103	C₂×C₄×C₁₉	—	4	6	no	—
104	C₂×C₄×C₁₉	C₂×C₄²	1	12	yes	—
105	C₂×C₄×C₁₉	C₄×Q₈	1	12	yes	—
106	C₂×#391	C₂×C₁₉	1	3	yes	—
107	#1436	C₂×C₁₉	1	6	yes	—
108	#1434	C₂×C₁₉	1	3	yes	—
109	C₄×#95	C₂×C₁₉	1	3	yes	—
110	C₂²×C₁₉	C₂²×C₄²	1	1	yes	characteristic
111	C₂²×C₁₉	C₂×C₄×Q₈	1	3	yes	—
112	C₂²×C₁₉	C₄×#41	1	3	yes	—
113	C₂²×C₁₉	#518	1	3	yes	—
114	C₂²×C₁₉	#518	1	3	yes	—
115	C₂²×C₁₉	#519	1	3	yes	—
116	C₂²×C₁₉	#520	1	3	yes	—
117	C₂²×C₁₉	#538	1	3	yes	—
118	C₂²×C₁₉	#539	1	3	yes	—
119	C₂²×C₁₉	#542	1	6	yes	—
120	C₂²×C₁₉	#543	1	1	yes	characteristic
121	C₂²×C₁₉	#544	1	3	yes	—
122	C₄×C₁₉	—	2	12	no	—
123	C₄×C₁₉	—	2	12	no	—
124	C₄×C₁₉	—	4	6	no	—
125	C₄×C₁₉	—	4	12	no	—
126	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
127	C₂²×C₄⋊C₄	C₂²×C₁₉	1	3	yes	—
128	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
129	C₂²×C₄²	C₂²×C₁₉	1	3	yes	—
130	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
131	#391	C₄×C₁₉	1	24	yes	complemented
132	C₂×#95	C₂²×C₁₉	1	6	yes	—
133	C₂×#95	C₂²×C₁₉	1	1	yes	characteristic
134	C₂×#95	C₂²×C₁₉	1	3	yes	—
135	C₂×#95	C₂²×C₁₉	1	2	yes	—
136	C₂×#95	C₂²×C₁₉	1	6	yes	—
137	C₂×#95	C₂²×C₁₉	1	6	yes	—
138	C₂×C₁₉	C₄²×Q₈	1	1	yes	characteristic
139	C₂×C₁₉	#2273	1	1	yes	characteristic
140	C₂×C₁₉	#2276	1	1	yes	characteristic
141	C₂×C₁₉	#2329	1	3	yes	—
142	C₂×C₁₉	#2331	1	3	yes	—
143	C₂×C₁₉	#2332	1	3	yes	—
144	C₂×C₁₉	#2337	1	3	yes	—
145	C₂²×Q₈	—	4	1	no	—
146	C₂²×Q₈	—	4	3	no	—
147	C₂²×Q₈	C₂×C₄×C₁₉	1	12	yes	—
148	C₂³×C₄	C₂³×C₁₉	1	6	yes	—
149	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
150	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
151	C₂³×C₄	C₂³×C₁₉	1	3	yes	—
152	C₂×C₄⋊C₄	—	4	6	no	—
153	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	12	yes	—
154	C₂×C₄²	—	2	6	no	—
155	C₂×C₄²	—	4	3	no	—
156	C₂×C₄²	—	4	3	no	—
157	C₂×C₄²	—	4	1	no	—
158	C₂×C₄²	—	4	1	no	—
159	C₂×C₄²	—	4	3	no	—
160	C₂×C₄²	—	4	3	no	—
161	C₂×C₄²	C₂×C₄×C₁₉	1	12	yes	—
162	C₂×C₄²	Q₈×C₁₉	1	4	yes	complemented
163	#95	—	2	12	no	—
164	#95	—	4	1	no	—
165	#95	—	4	2	no	—
166	#95	—	4	3	no	—
167	#95	C₂×C₄×C₁₉	1	24	yes	—
168	#95	C₂×C₄×C₁₉	1	24	yes	—
169	C₁₉	#13793	1	1	yes	characteristic, direct product factor, Sylow
170	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
171	C₂×Q₈	—	4	12	no	—
172	C₂×Q₈	—	4	12	no	—
173	C₂×Q₈	C₄²×C₁₉	1	16	yes	complemented
174	C₂²×C₄	—	2	3	no	—
175	C₂²×C₄	—	2	3	no	—
176	C₂²×C₄	—	2	3	no	—
177	C₂²×C₄	—	2	3	no	—
178	C₂²×C₄	—	2	3	no	—
179	C₂²×C₄	—	2	6	no	—
180	C₂²×C₄	—	2	3	no	—
181	C₂²×C₄	—	2	6	no	—
182	C₂²×C₄	—	2	6	no	—
183	C₂²×C₄	—	2	6	no	—
184	C₂²×C₄	—	2	3	no	—
185	C₂²×C₄	—	2	3	no	—
186	C₂²×C₄	—	2	6	no	—
187	C₂²×C₄	—	2	6	no	—
188	C₂²×C₄	—	2	6	no	—
189	C₂²×C₄	—	2	6	no	—
190	C₂²×C₄	—	2	6	no	—
191	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
192	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
193	C₂²×C₄	C₂²×C₄×C₁₉	1	12	yes	—
194	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
195	C₂²×C₄	C₂²×C₄×C₁₉	1	6	yes	—
196	C₂²×C₄	C₂×Q₈×C₁₉	1	6	yes	—
197	C₂²×C₄	#41×C₁₉	1	6	yes	—
198	C₄⋊C₄	—	4	12	no	—
199	C₄²	—	4	12	no	—
200	C₄²	—	4	4	no	—
201	C₄²	—	4	12	no	—
202	C₂³	C₂³×C₄×C₁₉	1	3	yes	—
203	C₂³	C₂²×Q₈×C₁₉	1	1	yes	characteristic
204	C₂³	C₂×#41×C₁₉	1	3	yes	—
205	C₂³	C₁₉×H(5,𝔽₂)	1	3	yes	—
206	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
207	C₂³	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
208	C₂³	C₁₉×2₋¹⁺⁴	1	3	yes	—
209	Q₈	—	4	16	no	—
210	C₂×C₄	—	2	6	no	—
211	C₂×C₄	—	2	6	no	—
212	C₂×C₄	—	2	6	no	—
213	C₂×C₄	—	2	12	no	—
214	C₂×C₄	—	2	12	no	—
215	C₂×C₄	—	2	6	no	—
216	C₂×C₄	—	2	6	no	—
217	C₂×C₄	—	2	6	no	—
218	C₂×C₄	—	2	6	no	—
219	C₂×C₄	—	2	6	no	—
220	C₂×C₄	—	2	6	no	—
221	C₂×C₄	—	2	12	no	—
222	C₂×C₄	—	2	6	no	—
223	C₂×C₄	—	2	12	no	—
224	C₂×C₄	—	2	6	no	—
225	C₂×C₄	—	2	12	no	—
226	C₂×C₄	—	4	6	no	—
227	C₂×C₄	—	4	6	no	—
228	C₂×C₄	—	4	6	no	—
229	C₂×C₄	—	4	6	no	—
230	C₂×C₄	—	4	6	no	—
231	C₂×C₄	—	4	6	no	—
232	C₂×C₄	C₂×C₄²×C₁₉	1	12	yes	—
233	C₂×C₄	C₄×Q₈×C₁₉	1	12	yes	—
234	C₂²	C₂²×C₄²×C₁₉	1	1	yes	characteristic
235	C₂²	C₂×C₄×Q₈×C₁₉	1	3	yes	—
236	C₂²	C₄×#41×C₁₉	1	3	yes	—
237	C₂²	C₁₉×#518	1	3	yes	—
238	C₂²	C₁₉×#518	1	3	yes	—
239	C₂²	C₁₉×#519	1	3	yes	—
240	C₂²	C₁₉×#520	1	3	yes	—
241	C₂²	C₁₉×#538	1	3	yes	—
242	C₂²	C₁₉×#539	1	3	yes	—
243	C₂²	C₁₉×#542	1	6	yes	—
244	C₂²	C₁₉×#543	1	1	yes	characteristic
245	C₂²	C₁₉×#544	1	3	yes	—
246	C₄	—	2	12	no	—
247	C₄	—	2	12	no	—
248	C₄	—	4	6	no	—
249	C₄	—	4	12	no	—
250	C₂	C₄²×Q₈×C₁₉	1	1	yes	characteristic
251	C₂	C₁₉×#2273	1	1	yes	characteristic
252	C₂	C₁₉×#2276	1	1	yes	characteristic
253	C₂	C₁₉×#2329	1	3	yes	—
254	C₂	C₁₉×#2331	1	3	yes	—
255	C₂	C₁₉×#2332	1	3	yes	—
256	C₂	C₁₉×#2337	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₉	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
10. C₁₉×#391	C₄	semidirect
34. C₂×C₄²×C₁₉	Q₈	semidirect
44. C₂×Q₈×C₁₉	C₄²	semidirect
73. #13793	C₁₉	direct (N × H)
131. #391	C₄×C₁₉	semidirect
162. C₂×C₄²	Q₈×C₁₉	semidirect
169. C₁₉	#13793	direct (N × H)
173. C₂×Q₈	C₄²×C₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#391	2
C₁₉×#1436	2
C₁₉×#1434	2
C₄×C₁₉×#95	2
#13793	19

Subgroups — C19×#13793 #18019752

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13793 #18019752