Subgroups — C₁₉×#14139 #18020098

Order 4864.

2526 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₉×#391	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×C₂²⋊C₄×C₁₉	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#1441	C₂	1	4	yes	maximal, complemented
6	C₁₉×C₄⋊#95	C₂	1	2	yes	maximal, complemented
7	C₁₉×C₂²⋊#95	C₂	1	4	yes	maximal
8	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₁₉	C₂²	1	2	yes	—
10	C₂⁴×C₄×C₁₉	C₂²	1	1	yes	characteristic
11	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
12	C₂×C₁₉×C₂²⋊Q₈	—	2	4	no	—
13	C₂×C₁₉×C₂²⋊Q₈	C₄	1	8	yes	complemented
14	C₂²×C₄⋊C₄×C₁₉	—	2	4	no	—
15	C₂²×C₄⋊C₄×C₁₉	—	2	8	no	—
16	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
17	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
21	C₂²×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
22	C₂²×C₄²×C₁₉	C₂²	1	2	yes	—
23	C₁₉×#391	—	2	8	no	—
24	C₄×C₂²⋊C₄×C₁₉	—	2	4	no	—
25	C₂×C₁₉×#95	C₂²	1	8	yes	—
26	C₂×C₁₉×#95	C₂²	1	2	yes	—
27	C₂×C₁₉×#95	C₂²	1	8	yes	—
28	C₂⁵×C₁₉	C₂³	1	1	yes	characteristic
29	C₂²×Q₈×C₁₉	—	2	4	no	—
30	C₂²×Q₈×C₁₉	—	2	2	no	—
31	C₂²×Q₈×C₁₉	—	2	2	no	—
32	C₂²×Q₈×C₁₉	—	2	4	no	—
33	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	complemented
34	C₂³×C₄×C₁₉	—	2	4	no	—
35	C₂³×C₄×C₁₉	—	2	4	no	—
36	C₂³×C₄×C₁₉	—	2	4	no	—
37	C₂³×C₄×C₁₉	—	2	8	no	—
38	C₂³×C₄×C₁₉	—	2	8	no	—
39	C₂³×C₄×C₁₉	—	4	4	no	—
40	C₂³×C₄×C₁₉	C₂×C₄	1	4	yes	—
41	C₂³×C₄×C₁₉	D₄	1	4	yes	—
42	C₂³×C₄×C₁₉	D₄	1	4	yes	—
43	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
47	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₁₉×C₂²⋊Q₈	—	2	32	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	32	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	8	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	4	yes	complemented
60	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	8	yes	complemented
61	C₂×C₄⋊C₄×C₁₉	D₄	1	8	yes	—
62	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
63	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	8	yes	—
67	C₂×C₂²⋊C₄×C₁₉	Q₈	1	8	yes	complemented
68	C₂×C₄²×C₁₉	—	2	4	no	—
69	C₂×C₄²×C₁₉	—	2	4	no	—
70	C₂×C₄²×C₁₉	—	2	4	no	—
71	C₁₉×#95	—	2	4	no	—
72	C₁₉×#95	—	2	16	no	—
73	C₁₉×#95	—	4	8	no	—
74	C₂⁴×C₁₉	—	2	2	no	—
75	C₂⁴×C₁₉	—	2	2	no	—
76	C₂⁴×C₁₉	—	2	2	no	—
77	C₂⁴×C₁₉	—	2	2	no	—
78	C₂⁴×C₁₉	C₂²×C₄	1	2	yes	—
79	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
80	C₂⁴×C₁₉	C₂×D₄	1	2	yes	—
81	C₂⁴×C₁₉	C₂×Q₈	1	4	yes	—
82	C₂⁴×C₁₉	#41	1	4	yes	—
83	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
84	C₂×Q₈×C₁₉	—	2	8	no	—
85	C₂×Q₈×C₁₉	—	2	16	no	—
86	C₂×Q₈×C₁₉	—	4	4	no	—
87	C₂×Q₈×C₁₉	—	4	8	no	—
88	C₂×Q₈×C₁₉	—	4	4	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	16	no	—
92	C₂²×C₄×C₁₉	—	2	8	no	—
93	C₂²×C₄×C₁₉	—	2	16	no	—
94	C₂²×C₄×C₁₉	—	2	8	no	—
95	C₂²×C₄×C₁₉	—	2	16	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	4	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	4	no	—
103	C₂²×C₄×C₁₉	—	2	4	no	—
104	C₂²×C₄×C₁₉	—	2	4	no	—
105	C₂²×C₄×C₁₉	—	2	4	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	2	8	no	—
108	C₂²×C₄×C₁₉	—	2	4	no	—
109	C₂²×C₄×C₁₉	—	2	8	no	—
110	C₂²×C₄×C₁₉	—	2	4	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	4	32	no	—
115	C₂²×C₄×C₁₉	—	4	8	no	—
116	C₂²×C₄×C₁₉	—	4	8	no	—
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	16	yes	—
118	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
120	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₁₉	C₂×D₄	1	8	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂×D₄	1	4	yes	—
128	C₂²×C₄×C₁₉	C₂×Q₈	1	8	yes	—
129	C₂²×C₄×C₁₉	#41	1	4	yes	—
130	C₄⋊C₄×C₁₉	—	2	16	no	—
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	16	no	—
133	C₄⋊C₄×C₁₉	—	2	16	no	—
134	C₂²⋊C₄×C₁₉	—	2	16	no	—
135	C₂²⋊C₄×C₁₉	—	2	16	no	—
136	C₄²×C₁₉	—	4	8	no	—
137	#14139	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
138	C₂³×C₁₉	—	2	4	no	—
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	—	2	2	no	—
141	C₂³×C₁₉	—	2	4	no	—
142	C₂³×C₁₉	—	2	2	no	—
143	C₂³×C₁₉	—	2	2	no	—
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	4	no	—
146	C₂³×C₁₉	—	2	8	no	—
147	C₂³×C₁₉	—	2	8	no	—
148	C₂³×C₁₉	—	2	8	no	—
149	C₂³×C₁₉	—	2	8	no	—
150	C₂³×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
151	C₂³×C₁₉	C₄×Q₈	1	8	yes	—
152	C₂³×C₁₉	C₂²⋊Q₈	1	8	yes	—
153	C₂³×C₁₉	#124	1	4	yes	—
154	C₂³×C₁₉	C₄⋊Q₈	1	4	yes	—
155	C₂³×C₁₉	C₂³×C₄	1	1	yes	characteristic
156	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
157	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
158	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
159	C₂³×C₁₉	C₂²×Q₈	1	2	yes	—
160	C₂³×C₁₉	C₂×#41	1	2	yes	—
161	C₂³×C₁₉	C₂×#41	1	2	yes	—
162	C₂³×C₁₉	H(5,𝔽₂)	1	2	yes	—
163	C₂³×C₁₉	2₋¹⁺⁴	1	2	yes	—
164	Q₈×C₁₉	—	4	16	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	2	no	—
169	C₂×C₄×C₁₉	—	2	32	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	8	no	—
173	C₂×C₄×C₁₉	—	2	8	no	—
174	C₂×C₄×C₁₉	—	2	8	no	—
175	C₂×C₄×C₁₉	—	2	8	no	—
176	C₂×C₄×C₁₉	—	2	16	no	—
177	C₂×C₄×C₁₉	—	2	8	no	—
178	C₂×C₄×C₁₉	—	2	8	no	—
179	C₂×C₄×C₁₉	—	4	32	no	—
180	C₂×C₄×C₁₉	—	4	2	no	—
181	C₂×C₄×C₁₉	—	4	4	no	—
182	C₂×C₄×C₁₉	—	4	4	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	4	4	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	4	no	—
189	C₂×C₄×C₁₉	—	4	4	no	—
190	C₂×C₄×C₁₉	—	4	4	no	—
191	C₂×C₄×C₁₉	—	4	8	no	—
192	C₂×C₄×C₁₉	—	4	4	no	—
193	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
194	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
195	C₂×C₄×C₁₉	C₄×D₄	1	8	yes	—
196	C₂×C₄×C₁₉	#120	1	4	yes	—
197	C₂×C₄×C₁₉	#121	1	8	yes	—
198	C₂×C₄×C₁₉	#123	1	4	yes	—
199	C₂²×C₂²⋊Q₈	C₂×C₁₉	1	1	yes	characteristic
200	C₂³×C₄⋊C₄	C₂×C₁₉	1	1	yes	characteristic
201	C₂×#391	C₂×C₁₉	1	2	yes	complemented
202	C₂×C₄×C₂²⋊C₄	C₂×C₁₉	1	1	yes	characteristic
203	#1441	C₂×C₁₉	1	4	yes	complemented
204	C₄⋊#95	C₂×C₁₉	1	2	yes	complemented
205	C₂²⋊#95	C₂×C₁₉	1	4	yes	—
206	C₂²×C₁₉	—	2	4	no	—
207	C₂²×C₁₉	—	2	16	no	—
208	C₂²×C₁₉	—	2	16	no	—
209	C₂²×C₁₉	—	2	4	no	—
210	C₂²×C₁₉	—	2	4	no	—
211	C₂²×C₁₉	—	2	4	no	—
212	C₂²×C₁₉	—	2	4	no	—
213	C₂²×C₁₉	—	2	4	no	—
214	C₂²×C₁₉	#391	1	8	yes	complemented
215	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
216	C₂²×C₁₉	C₂×C₄×D₄	1	2	yes	—
217	C₂²×C₁₉	C₂×C₄×Q₈	1	2	yes	—
218	C₂²×C₁₉	#520	1	2	yes	—
219	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
220	C₂²×C₁₉	C₂×#121	1	2	yes	—
221	C₂²×C₁₉	C₂×C₂²⋊Q₈	1	2	yes	—
222	C₂²×C₁₉	C₂×#123	1	1	yes	characteristic
223	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
224	C₂²×C₁₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
225	C₂²×C₁₉	#535	1	1	yes	characteristic
226	C₂²×C₁₉	#536	1	1	yes	characteristic
227	C₂²×C₁₉	#537	1	2	yes	—
228	C₂²×C₁₉	#546	1	4	yes	—
229	C₂²×C₁₉	D₄×Q₈	1	4	yes	—
230	C₂²×C₁₉	#552	1	4	yes	—
231	C₂²×C₁₉	#554	1	4	yes	—
232	C₄×C₁₉	—	2	4	no	—
233	C₄×C₁₉	—	4	4	no	—
234	C₄×C₁₉	—	4	8	no	—
235	C₄×C₁₉	—	4	8	no	—
236	C₄×C₁₉	—	4	4	no	—
237	C₄×C₁₉	#386	1	8	yes	—
238	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
239	C₂⁴×C₄	C₂²×C₁₉	1	2	yes	—
240	C₂⁴×C₄	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×C₂²⋊Q₈	—	2	4	no	—
242	C₂×C₂²⋊Q₈	—	2	4	no	—
243	C₂×C₂²⋊Q₈	C₄×C₁₉	1	8	yes	complemented
244	C₂²×C₄⋊C₄	—	2	4	no	—
245	C₂²×C₄⋊C₄	—	2	8	no	—
246	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
247	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
249	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
250	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
251	C₂²×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
252	C₂²×C₄²	C₂²×C₁₉	1	2	yes	—
253	#391	—	2	8	no	—
254	C₄×C₂²⋊C₄	—	2	4	no	—
255	C₂×#95	C₂²×C₁₉	1	8	yes	—
256	C₂×#95	C₂²×C₁₉	1	2	yes	—
257	C₂×#95	C₂²×C₁₉	1	8	yes	—
258	C₂×C₁₉	—	2	8	no	—
259	C₂×C₁₉	C₂×#386	1	1	yes	characteristic
260	C₂×C₁₉	C₂×#391	1	1	yes	characteristic
261	C₂×C₁₉	#2311	1	1	yes	characteristic
262	C₂×C₁₉	#2360	1	4	yes	—
263	C₂×C₁₉	#2417	1	4	yes	—
264	C₂×C₁₉	#2434	1	1	yes	characteristic
265	C₂×C₁₉	#2435	1	1	yes	characteristic
266	C₂×C₁₉	#2502	1	1	yes	characteristic
267	C₂×C₁₉	#2503	1	1	yes	characteristic
268	C₂⁵	C₂³×C₁₉	1	1	yes	characteristic
269	C₂²×Q₈	—	2	2	no	—
270	C₂²×Q₈	—	2	2	no	—
271	C₂²×Q₈	—	2	4	no	—
272	C₂²×Q₈	—	2	4	no	—
273	C₂²×Q₈	C₂×C₄×C₁₉	1	4	yes	complemented
274	C₂³×C₄	—	2	4	no	—
275	C₂³×C₄	—	2	4	no	—
276	C₂³×C₄	—	2	4	no	—
277	C₂³×C₄	—	2	8	no	—
278	C₂³×C₄	—	2	8	no	—
279	C₂³×C₄	—	4	4	no	—
280	C₂³×C₄	C₂×C₄×C₁₉	1	4	yes	—
281	C₂³×C₄	D₄×C₁₉	1	4	yes	—
282	C₂³×C₄	D₄×C₁₉	1	4	yes	—
283	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
284	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
285	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
286	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
287	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
289	C₂²⋊Q₈	—	2	32	no	—
290	C₂×C₄⋊C₄	—	2	32	no	—
291	C₂×C₄⋊C₄	—	2	8	no	—
292	C₂×C₄⋊C₄	—	2	4	no	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	4	yes	complemented
300	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	8	yes	complemented
301	C₂×C₄⋊C₄	D₄×C₁₉	1	8	yes	—
302	C₂×C₂²⋊C₄	—	2	4	no	—
303	C₂×C₂²⋊C₄	—	2	4	no	—
304	C₂×C₂²⋊C₄	—	2	4	no	—
305	C₂×C₂²⋊C₄	—	2	4	no	—
306	C₂×C₂²⋊C₄	C₂×C₄×C₁₉	1	8	yes	—
307	C₂×C₂²⋊C₄	Q₈×C₁₉	1	8	yes	complemented
308	C₂×C₄²	—	2	4	no	—
309	C₂×C₄²	—	2	4	no	—
310	C₂×C₄²	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	2	16	no	—
313	#95	—	4	8	no	—
314	C₁₉	#14139	1	1	yes	characteristic, direct product factor, Sylow
315	C₂⁴	—	2	2	no	—
316	C₂⁴	—	2	2	no	—
317	C₂⁴	—	2	2	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	C₂²×C₄×C₁₉	1	2	yes	—
320	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
321	C₂⁴	C₂×D₄×C₁₉	1	2	yes	—
322	C₂⁴	C₂×Q₈×C₁₉	1	4	yes	—
323	C₂⁴	#41×C₁₉	1	4	yes	—
324	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	2	16	no	—
327	C₂×Q₈	—	4	4	no	—
328	C₂×Q₈	—	4	8	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	16	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	16	no	—
335	C₂²×C₄	—	2	8	no	—
336	C₂²×C₄	—	2	16	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	8	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	8	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	4	32	no	—
356	C₂²×C₄	—	4	8	no	—
357	C₂²×C₄	—	4	8	no	—
358	C₂²×C₄	C₂²⋊C₄×C₁₉	1	16	yes	—
359	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
360	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
361	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
362	C₂²×C₄	C₂²×C₄×C₁₉	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₁₉	1	8	yes	—
364	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₉	1	4	yes	—
369	C₂²×C₄	C₂×Q₈×C₁₉	1	8	yes	—
370	C₂²×C₄	#41×C₁₉	1	4	yes	—
371	C₄⋊C₄	—	2	16	no	—
372	C₄⋊C₄	—	2	8	no	—
373	C₄⋊C₄	—	2	16	no	—
374	C₄⋊C₄	—	2	16	no	—
375	C₂²⋊C₄	—	2	16	no	—
376	C₂²⋊C₄	—	2	16	no	—
377	C₄²	—	4	8	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	4	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	8	no	—
387	C₂³	—	2	8	no	—
388	C₂³	—	2	8	no	—
389	C₂³	—	2	8	no	—
390	C₂³	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
391	C₂³	C₄×Q₈×C₁₉	1	8	yes	—
392	C₂³	C₁₉×C₂²⋊Q₈	1	8	yes	—
393	C₂³	C₁₉×#124	1	4	yes	—
394	C₂³	C₁₉×C₄⋊Q₈	1	4	yes	—
395	C₂³	C₂³×C₄×C₁₉	1	1	yes	characteristic
396	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
397	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
398	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
399	C₂³	C₂²×Q₈×C₁₉	1	2	yes	—
400	C₂³	C₂×#41×C₁₉	1	2	yes	—
401	C₂³	C₂×#41×C₁₉	1	2	yes	—
402	C₂³	C₁₉×H(5,𝔽₂)	1	2	yes	—
403	C₂³	C₁₉×2₋¹⁺⁴	1	2	yes	—
404	Q₈	—	4	16	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	32	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	16	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	4	32	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	4	no	—
430	C₂×C₄	—	4	8	no	—
431	C₂×C₄	—	4	4	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
434	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
435	C₂×C₄	C₄×D₄×C₁₉	1	8	yes	—
436	C₂×C₄	C₁₉×#120	1	4	yes	—
437	C₂×C₄	C₁₉×#121	1	8	yes	—
438	C₂×C₄	C₁₉×#123	1	4	yes	—
439	C₂²	—	2	16	no	—
440	C₂²	—	2	4	no	—
441	C₂²	—	2	4	no	—
442	C₂²	—	2	4	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	16	no	—
447	C₂²	C₁₉×#391	1	8	yes	complemented
448	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
449	C₂²	C₂×C₄×D₄×C₁₉	1	2	yes	—
450	C₂²	C₂×C₄×Q₈×C₁₉	1	2	yes	—
451	C₂²	C₁₉×#520	1	2	yes	—
452	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
453	C₂²	C₂×C₁₉×#121	1	2	yes	—
454	C₂²	C₂×C₁₉×C₂²⋊Q₈	1	2	yes	—
455	C₂²	C₂×C₁₉×#123	1	1	yes	characteristic
456	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
457	C₂²	C₂×C₁₉×C₄⋊Q₈	1	1	yes	characteristic
458	C₂²	C₁₉×#535	1	1	yes	characteristic
459	C₂²	C₁₉×#536	1	1	yes	characteristic
460	C₂²	C₁₉×#537	1	2	yes	—
461	C₂²	C₁₉×#546	1	4	yes	—
462	C₂²	D₄×Q₈×C₁₉	1	4	yes	—
463	C₂²	C₁₉×#552	1	4	yes	—
464	C₂²	C₁₉×#554	1	4	yes	—
465	C₄	—	2	4	no	—
466	C₄	—	4	8	no	—
467	C₄	—	4	8	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	4	no	—
470	C₄	C₁₉×#386	1	8	yes	—
471	C₂	—	2	8	no	—
472	C₂	C₂×C₁₉×#386	1	1	yes	characteristic
473	C₂	C₂×C₁₉×#391	1	1	yes	characteristic
474	C₂	C₁₉×#2311	1	1	yes	characteristic
475	C₂	C₁₉×#2360	1	4	yes	—
476	C₂	C₁₉×#2417	1	4	yes	—
477	C₂	C₁₉×#2434	1	1	yes	characteristic
478	C₂	C₁₉×#2435	1	1	yes	characteristic
479	C₂	C₁₉×#2502	1	1	yes	characteristic
480	C₂	C₁₉×#2503	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₉
Frattini, cosocle	C₂⁴	C₂⁴×C₁₉
prime radical	C₂⁵×C₁₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₉×#391	C₂	semidirect
5. C₁₉×#1441	C₂	semidirect
6. C₁₉×C₄⋊#95	C₂	semidirect
13. C₂×C₁₉×C₂²⋊Q₈	C₄	semidirect
33. C₂²×Q₈×C₁₉	C₂×C₄	semidirect
59. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
60. C₂×C₄⋊C₄×C₁₉	C₂×C₄	semidirect
67. C₂×C₂²⋊C₄×C₁₉	Q₈	semidirect
137. #14139	C₁₉	direct (N × H)
201. C₂×#391	C₂×C₁₉	semidirect
203. #1441	C₂×C₁₉	semidirect
204. C₄⋊#95	C₂×C₁₉	semidirect
214. C₂²×C₁₉	#391	semidirect
243. C₂×C₂²⋊Q₈	C₄×C₁₉	semidirect
273. C₂²×Q₈	C₂×C₄×C₁₉	semidirect
299. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
300. C₂×C₄⋊C₄	C₂×C₄×C₁₉	semidirect
307. C₂×C₂²⋊C₄	Q₈×C₁₉	semidirect
314. C₁₉	#14139	direct (N × H)
447. C₂²	C₁₉×#391	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₂²⋊Q₈	2
C₂³×C₄⋊C₄×C₁₉	2
C₂×C₁₉×#391	2
C₂×C₄×C₂²⋊C₄×C₁₉	2
C₁₉×#1441	2
C₁₉×C₄⋊#95	2
C₁₉×C₂²⋊#95	2
#14139	19

Subgroups — C19×#14139 #18020098

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#14139 #18020098