Subgroups — C₁₉×#13828 #18019787

Order 4864.

1630 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#381	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#380	C₂	1	2	yes	maximal
3	C₁₉×#1437	C₂	1	4	yes	maximal
4	C₁₉×#1436	C₂	1	8	yes	maximal, complemented
5	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
6	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
7	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
8	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
9	C₂²×C₄²×C₁₉	C₂²	1	4	yes	—
10	C₁₉×#381	C₄	1	8	yes	complemented
11	C₁₉×#380	C₄	1	16	yes	complemented
12	C₂×C₁₉×#95	C₂²	1	8	yes	—
13	C₂×C₁₉×#95	C₂²	1	4	yes	—
14	C₂×C₁₉×#95	C₂²	1	4	yes	—
15	C₂×C₁₉×#95	C₂²	1	4	yes	—
16	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	—	4	4	no	—
18	C₂³×C₄×C₁₉	C₂×C₄	1	8	yes	—
19	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
20	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
21	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
22	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
23	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
24	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
25	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
26	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
27	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
28	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	16	yes	—
29	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
30	C₂×C₄²×C₁₉	—	4	4	no	—
31	C₂×C₄²×C₁₉	—	4	8	no	—
32	C₁₉×#95	—	4	8	no	—
33	C₁₉×#95	—	4	4	no	—
34	C₁₉×#95	C₂×C₄	1	16	yes	—
35	C₁₉×#95	C₂×C₄	1	16	yes	—
36	C₂⁴×C₁₉	—	2	4	no	—
37	C₂⁴×C₁₉	—	2	4	no	—
38	C₂⁴×C₁₉	—	2	4	no	—
39	C₂⁴×C₁₉	C₂²×C₄	1	4	yes	—
40	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
41	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
42	C₂²×C₄×C₁₉	—	2	8	no	—
43	C₂²×C₄×C₁₉	—	2	8	no	—
44	C₂²×C₄×C₁₉	—	2	4	no	—
45	C₂²×C₄×C₁₉	—	2	8	no	—
46	C₂²×C₄×C₁₉	—	2	8	no	—
47	C₂²×C₄×C₁₉	—	2	8	no	—
48	C₂²×C₄×C₁₉	—	2	8	no	—
49	C₂²×C₄×C₁₉	—	2	4	no	—
50	C₂²×C₄×C₁₉	—	2	8	no	—
51	C₂²×C₄×C₁₉	—	2	8	no	—
52	C₂²×C₄×C₁₉	—	2	8	no	—
53	C₂²×C₄×C₁₉	—	4	16	no	—
54	C₂²×C₄×C₁₉	—	4	8	no	—
55	C₂²×C₄×C₁₉	C₄²	1	16	yes	complemented
56	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
57	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
58	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
59	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
60	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
61	C₄⋊C₄×C₁₉	—	4	16	no	—
62	C₂²⋊C₄×C₁₉	—	4	16	no	—
63	C₂²⋊C₄×C₁₉	—	4	8	no	—
64	C₄²×C₁₉	—	4	16	no	—
65	#13828	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
66	C₂³×C₁₉	—	2	4	no	—
67	C₂³×C₁₉	—	2	4	no	—
68	C₂³×C₁₉	—	2	8	no	—
69	C₂³×C₁₉	—	2	4	no	—
70	C₂³×C₁₉	—	2	8	no	—
71	C₂³×C₁₉	—	2	8	no	—
72	C₂³×C₁₉	—	4	4	no	—
73	C₂³×C₁₉	—	4	8	no	—
74	C₂³×C₁₉	—	4	4	no	—
75	C₂³×C₁₉	C₂×C₄²	1	4	yes	—
76	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
77	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
78	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
79	C₂³×C₁₉	H(5,𝔽₂)	1	4	yes	—
80	C₂³×C₁₉	2₋¹⁺⁴	1	4	yes	—
81	C₂×C₄×C₁₉	—	2	8	no	—
82	C₂×C₄×C₁₉	—	2	8	no	—
83	C₂×C₄×C₁₉	—	2	8	no	—
84	C₂×C₄×C₁₉	—	2	8	no	—
85	C₂×C₄×C₁₉	—	2	16	no	—
86	C₂×C₄×C₁₉	—	2	16	no	—
87	C₂×C₄×C₁₉	—	2	16	no	—
88	C₂×C₄×C₁₉	—	2	16	no	—
89	C₂×C₄×C₁₉	—	4	16	no	—
90	C₂×C₄×C₁₉	—	4	4	no	—
91	C₂×C₄×C₁₉	—	4	8	no	—
92	C₂×C₄×C₁₉	—	4	8	no	—
93	C₂×C₄×C₁₉	—	4	8	no	—
94	C₂×C₄×C₁₉	—	4	8	no	—
95	C₂×C₄×C₁₉	—	4	8	no	—
96	C₂×C₄×C₁₉	—	4	4	no	—
97	C₂×C₄×C₁₉	C₂×C₄²	1	8	yes	—
98	C₂×#381	C₂×C₁₉	1	1	yes	characteristic
99	C₂×#380	C₂×C₁₉	1	2	yes	—
100	#1437	C₂×C₁₉	1	4	yes	—
101	#1436	C₂×C₁₉	1	8	yes	complemented
102	C₂²×C₁₉	—	2	4	no	—
103	C₂²×C₁₉	—	2	8	no	—
104	C₂²×C₁₉	—	4	8	no	—
105	C₂²×C₁₉	—	4	8	no	—
106	C₂²×C₁₉	—	4	8	no	—
107	C₂²×C₁₉	C₂²×C₄²	1	1	yes	characteristic
108	C₂²×C₁₉	#518	1	2	yes	—
109	C₂²×C₁₉	#518	1	2	yes	—
110	C₂²×C₁₉	#518	1	4	yes	—
111	C₂²×C₁₉	#519	1	2	yes	—
112	C₂²×C₁₉	#520	1	4	yes	—
113	C₂²×C₁₉	#520	1	4	yes	—
114	C₂²×C₁₉	#560	1	4	yes	—
115	C₂²×C₁₉	#562	1	8	yes	—
116	C₂²×C₁₉	#563	1	4	yes	—
117	C₄×C₁₉	—	2	8	no	—
118	C₄×C₁₉	—	4	8	no	—
119	C₄×C₁₉	—	4	16	no	—
120	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
121	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
122	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
123	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
124	C₂²×C₄²	C₂²×C₁₉	1	4	yes	—
125	#381	C₄×C₁₉	1	8	yes	complemented
126	#380	C₄×C₁₉	1	16	yes	complemented
127	C₂×#95	C₂²×C₁₉	1	8	yes	—
128	C₂×#95	C₂²×C₁₉	1	4	yes	—
129	C₂×#95	C₂²×C₁₉	1	4	yes	—
130	C₂×#95	C₂²×C₁₉	1	4	yes	—
131	C₂×C₁₉	—	4	4	no	—
132	C₂×C₁₉	#2273	1	1	yes	characteristic
133	C₂×C₁₉	#2274	1	2	yes	—
134	C₂×C₁₉	#2376	1	4	yes	—
135	C₂×C₁₉	#2377	1	4	yes	—
136	C₂×C₁₉	#2378	1	4	yes	—
137	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
138	C₂³×C₄	—	4	4	no	—
139	C₂³×C₄	C₂×C₄×C₁₉	1	8	yes	—
140	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
141	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
142	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
143	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
144	C₂×C₄⋊C₄	—	4	8	no	—
145	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
146	C₂×C₂²⋊C₄	—	4	4	no	—
147	C₂×C₂²⋊C₄	—	4	4	no	—
148	C₂×C₂²⋊C₄	—	4	4	no	—
149	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	16	yes	—
150	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
151	C₂×C₄²	—	4	8	no	—
152	C₂×C₄²	—	4	4	no	—
153	#95	—	4	8	no	—
154	#95	—	4	4	no	—
155	#95	C₂×C₄×C₁₉	1	16	yes	—
156	#95	C₂×C₄×C₁₉	1	16	yes	—
157	C₁₉	#13828	1	1	yes	characteristic, direct product factor, Sylow
158	C₂⁴	—	2	4	no	—
159	C₂⁴	—	2	4	no	—
160	C₂⁴	—	2	4	no	—
161	C₂⁴	C₂²×C₄×C₁₉	1	4	yes	—
162	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
163	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
164	C₂²×C₄	—	2	8	no	—
165	C₂²×C₄	—	2	8	no	—
166	C₂²×C₄	—	2	8	no	—
167	C₂²×C₄	—	2	8	no	—
168	C₂²×C₄	—	2	4	no	—
169	C₂²×C₄	—	2	8	no	—
170	C₂²×C₄	—	2	8	no	—
171	C₂²×C₄	—	2	4	no	—
172	C₂²×C₄	—	2	8	no	—
173	C₂²×C₄	—	2	8	no	—
174	C₂²×C₄	—	2	8	no	—
175	C₂²×C₄	—	4	16	no	—
176	C₂²×C₄	—	4	8	no	—
177	C₂²×C₄	C₄²×C₁₉	1	16	yes	complemented
178	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
179	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
180	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
181	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
182	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
183	C₄⋊C₄	—	4	16	no	—
184	C₂²⋊C₄	—	4	16	no	—
185	C₂²⋊C₄	—	4	8	no	—
186	C₄²	—	4	16	no	—
187	C₂³	—	2	4	no	—
188	C₂³	—	2	4	no	—
189	C₂³	—	2	8	no	—
190	C₂³	—	2	4	no	—
191	C₂³	—	2	8	no	—
192	C₂³	—	2	8	no	—
193	C₂³	—	4	4	no	—
194	C₂³	—	4	8	no	—
195	C₂³	—	4	4	no	—
196	C₂³	C₂×C₄²×C₁₉	1	4	yes	—
197	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
198	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
199	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
200	C₂³	C₁₉×H(5,𝔽₂)	1	4	yes	—
201	C₂³	C₁₉×2₋¹⁺⁴	1	4	yes	—
202	C₂×C₄	—	2	8	no	—
203	C₂×C₄	—	2	8	no	—
204	C₂×C₄	—	2	8	no	—
205	C₂×C₄	—	2	8	no	—
206	C₂×C₄	—	2	16	no	—
207	C₂×C₄	—	2	16	no	—
208	C₂×C₄	—	2	16	no	—
209	C₂×C₄	—	2	16	no	—
210	C₂×C₄	—	4	16	no	—
211	C₂×C₄	—	4	4	no	—
212	C₂×C₄	—	4	8	no	—
213	C₂×C₄	—	4	8	no	—
214	C₂×C₄	—	4	8	no	—
215	C₂×C₄	—	4	8	no	—
216	C₂×C₄	—	4	8	no	—
217	C₂×C₄	—	4	4	no	—
218	C₂×C₄	C₂×C₄²×C₁₉	1	8	yes	—
219	C₂²	—	2	4	no	—
220	C₂²	—	2	8	no	—
221	C₂²	—	4	8	no	—
222	C₂²	—	4	8	no	—
223	C₂²	—	4	8	no	—
224	C₂²	C₂²×C₄²×C₁₉	1	1	yes	characteristic
225	C₂²	C₁₉×#518	1	2	yes	—
226	C₂²	C₁₉×#518	1	4	yes	—
227	C₂²	C₁₉×#518	1	2	yes	—
228	C₂²	C₁₉×#519	1	2	yes	—
229	C₂²	C₁₉×#520	1	4	yes	—
230	C₂²	C₁₉×#520	1	4	yes	—
231	C₂²	C₁₉×#560	1	4	yes	—
232	C₂²	C₁₉×#562	1	8	yes	—
233	C₂²	C₁₉×#563	1	4	yes	—
234	C₄	—	2	8	no	—
235	C₄	—	4	8	no	—
236	C₄	—	4	16	no	—
237	C₂	—	4	4	no	—
238	C₂	C₁₉×#2273	1	1	yes	characteristic
239	C₂	C₁₉×#2274	1	2	yes	—
240	C₂	C₁₉×#2376	1	4	yes	—
241	C₂	C₁₉×#2377	1	4	yes	—
242	C₂	C₁₉×#2378	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
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
4. C₁₉×#1436	C₂	semidirect
10. C₁₉×#381	C₄	semidirect
11. C₁₉×#380	C₄	semidirect
55. C₂²×C₄×C₁₉	C₄²	semidirect
65. #13828	C₁₉	direct (N × H)
101. #1436	C₂×C₁₉	semidirect
125. #381	C₄×C₁₉	semidirect
126. #380	C₄×C₁₉	semidirect
157. C₁₉	#13828	direct (N × H)
177. C₂²×C₄	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×#381	2
C₂×C₁₉×#380	2
C₁₉×#1437	2
C₁₉×#1436	2
#13828	19

Subgroups — C19×#13828 #18019787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#13828 #18019787