Subgroups — C₁₉×#34368 #18040327

Order 4864.

2610 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#532	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2379	C₂	1	4	yes	maximal, complemented
3	C₁₉×#2369	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2366	C₂	1	2	yes	maximal, complemented
5	C₁₉×#2354	C₂	1	4	yes	maximal, complemented
6	D₄×C₄⋊C₄×C₁₉	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2324	C₂	1	8	yes	maximal, complemented
8	C₁₉×#2311	C₂	1	4	yes	maximal, complemented
9	C₁₉×#2285	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₁₉	C₂²	1	2	yes	—
11	C₁₉×#532	C₄	1	16	yes	complemented
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#124	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	C₂²	1	4	yes	—
16	C₂×C₄×D₄×C₁₉	C₂²	1	8	yes	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
18	C₂×C₁₉×#117	C₂²	1	4	yes	—
19	C₂×C₁₉×#117	C₂²	1	4	yes	—
20	C₂²×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
21	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
22	C₁₉×#391	C₂²	1	8	yes	—
23	C₁₉×#390	C₂²	1	8	yes	—
24	C₁₉×#390	C₂²	1	8	yes	—
25	C₁₉×#389	C₂²	1	8	yes	—
26	C₁₉×#388	C₂²	1	16	yes	—
27	C₁₉×#386	C₂²	1	8	yes	—
28	C₁₉×#386	C₂²	1	8	yes	—
29	C₁₉×#385	C₂²	1	16	yes	—
30	C₁₉×#384	C₂²	1	2	yes	—
31	C₁₉×#384	C₂²	1	2	yes	—
32	C₁₉×#382	C₂²	1	4	yes	—
33	C₁₉×#380	C₂²	1	4	yes	—
34	C₁₉×#380	C₂²	1	4	yes	—
35	C₁₉×#380	C₂²	1	8	yes	—
36	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
37	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
38	C₄×C₄⋊C₄×C₁₉	C₂²	1	8	yes	—
39	C₂×#41×C₁₉	—	4	4	no	—
40	C₂×#41×C₁₉	—	4	4	no	—
41	C₂×#41×C₁₉	C₂×C₄	1	16	yes	complemented
42	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
44	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
45	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
46	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
49	C₂³×C₄×C₁₉	C₂³	1	8	yes	—
50	C₁₉×C₄⋊Q₈	C₂×C₄	1	8	yes	complemented
51	C₁₉×#127	C₂×C₄	1	8	yes	—
52	C₁₉×#124	C₂×C₄	1	16	yes	complemented
53	C₁₉×#121	C₂×C₄	1	32	yes	complemented
54	C₄×D₄×C₁₉	—	4	16	no	—
55	C₄×D₄×C₁₉	C₂×C₄	1	32	yes	complemented
56	C₁₉×#117	—	4	8	no	—
57	C₁₉×#117	—	4	8	no	—
58	C₂×C₄⋊C₄×C₁₉	—	4	8	no	—
59	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	8	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
67	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
68	C₂×C₂²⋊C₄×C₁₉	C₂³	1	16	yes	—
69	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
70	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
71	C₂×C₄²×C₁₉	C₂×C₄	1	8	yes	complemented
72	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
73	C₂×C₄²×C₁₉	C₂³	1	8	yes	—
74	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
77	C₁₉×#95	C₂³	1	8	yes	—
78	C₁₉×#95	C₂³	1	8	yes	—
79	C₁₉×#95	C₂³	1	16	yes	—
80	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
81	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
82	#41×C₁₉	—	4	32	no	—
83	C₂×Q₈×C₁₉	—	4	2	no	—
84	C₂×Q₈×C₁₉	—	4	2	no	—
85	C₂×Q₈×C₁₉	C₂²×C₄	1	8	yes	—
86	C₂×D₄×C₁₉	—	2	8	no	—
87	C₂×D₄×C₁₉	—	2	8	no	—
88	C₂×D₄×C₁₉	—	4	4	no	—
89	C₂×D₄×C₁₉	—	4	4	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	C₂²×C₄	1	16	yes	—
93	C₂×D₄×C₁₉	C₂²×C₄	1	16	yes	—
94	C₂×D₄×C₁₉	C₂²×C₄	1	8	yes	—
95	C₂²×C₄×C₁₉	—	2	8	no	—
96	C₂²×C₄×C₁₉	—	2	4	no	—
97	C₂²×C₄×C₁₉	—	2	8	no	—
98	C₂²×C₄×C₁₉	—	2	2	no	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	4	8	no	—
102	C₂²×C₄×C₁₉	—	4	16	no	—
103	C₂²×C₄×C₁₉	C₂²×C₄	1	8	yes	—
104	C₂²×C₄×C₁₉	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	16	yes	—
106	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
107	C₂²×C₄×C₁₉	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
110	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
113	C₄⋊C₄×C₁₉	—	2	8	no	—
114	C₄⋊C₄×C₁₉	—	2	8	no	—
115	C₄⋊C₄×C₁₉	—	2	8	no	—
116	C₄⋊C₄×C₁₉	—	2	8	no	—
117	C₄⋊C₄×C₁₉	—	4	8	no	—
118	C₄⋊C₄×C₁₉	—	4	4	no	—
119	C₄⋊C₄×C₁₉	—	4	4	no	—
120	C₄⋊C₄×C₁₉	C₂²×C₄	1	16	yes	—
121	C₂²⋊C₄×C₁₉	—	4	8	no	—
122	C₂²⋊C₄×C₁₉	—	4	8	no	—
123	C₂²⋊C₄×C₁₉	—	4	16	no	—
124	C₂²⋊C₄×C₁₉	C₂²×C₄	1	32	yes	—
125	C₄²×C₁₉	—	2	16	no	—
126	C₄²×C₁₉	—	4	8	no	—
127	C₄²×C₁₉	C₂²×C₄	1	8	yes	—
128	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
129	C₄²×C₁₉	C₂²×C₄	1	4	yes	—
130	#34368	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	4	no	—
133	C₂³×C₁₉	—	2	8	no	—
134	C₂³×C₁₉	—	2	4	no	—
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	1	no	—
137	C₂³×C₁₉	—	2	2	no	—
138	C₂³×C₁₉	—	2	8	no	—
139	C₂³×C₁₉	C₂³×C₄	1	8	yes	—
140	C₂³×C₁₉	C₂³×C₄	1	2	yes	—
141	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
142	Q₈×C₁₉	—	4	8	no	—
143	D₄×C₁₉	—	2	32	no	—
144	D₄×C₁₉	—	4	8	no	—
145	D₄×C₁₉	—	4	16	no	—
146	C₂×C₄×C₁₉	—	2	4	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	4	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	2	no	—
152	C₂×C₄×C₁₉	—	2	32	no	—
153	C₂×C₄×C₁₉	—	2	8	no	—
154	C₂×C₄×C₁₉	—	2	16	no	—
155	C₂×C₄×C₁₉	—	2	8	no	—
156	C₂×C₄×C₁₉	—	2	8	no	—
157	C₂×C₄×C₁₉	—	2	8	no	—
158	C₂×C₄×C₁₉	—	2	8	no	—
159	C₂×C₄×C₁₉	—	2	8	no	—
160	C₂×C₄×C₁₉	—	2	8	no	—
161	C₂×C₄×C₁₉	—	8	16	no	—
162	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
163	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
164	C₂×C₄×C₁₉	C₂³×C₄	1	8	yes	—
165	C₂×C₄×C₁₉	C₂³×C₄	1	2	yes	—
166	C₂×C₄×C₁₉	C₂³×C₄	1	4	yes	—
167	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
168	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
169	C₂×C₄×C₁₉	H(5,𝔽₂)	1	4	yes	—
170	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
171	C₂×#532	C₂×C₁₉	1	1	yes	characteristic
172	#2379	C₂×C₁₉	1	4	yes	complemented
173	#2369	C₂×C₁₉	1	2	yes	complemented
174	#2366	C₂×C₁₉	1	2	yes	complemented
175	#2354	C₂×C₁₉	1	4	yes	complemented
176	D₄×C₄⋊C₄	C₂×C₁₉	1	4	yes	complemented
177	#2324	C₂×C₁₉	1	8	yes	complemented
178	#2311	C₂×C₁₉	1	4	yes	complemented
179	#2285	C₂×C₁₉	1	2	yes	complemented
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	8	no	—
182	C₂²×C₁₉	—	2	4	no	—
183	C₂²×C₁₉	—	2	16	no	—
184	C₂²×C₁₉	—	4	2	no	—
185	C₂²×C₁₉	—	4	8	no	—
186	C₂²×C₁₉	—	4	4	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	4	4	no	—
189	C₂²×C₁₉	—	4	1	no	—
190	C₂²×C₁₉	C₂⁴×C₄	1	1	yes	characteristic
191	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
192	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
193	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	2	yes	—
194	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
195	C₄×C₁₉	—	2	2	no	—
196	C₄×C₁₉	—	2	8	no	—
197	C₄×C₁₉	—	2	4	no	—
198	C₄×C₁₉	—	4	8	no	—
199	C₄×C₁₉	—	4	8	no	—
200	C₄×C₁₉	#518	1	4	yes	—
201	C₄×C₁₉	#520	1	8	yes	—
202	C₂²×#41	C₂²×C₁₉	1	2	yes	—
203	#532	C₄×C₁₉	1	16	yes	complemented
204	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
205	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
206	C₂×#124	C₂²×C₁₉	1	2	yes	—
207	C₂×#121	C₂²×C₁₉	1	4	yes	—
208	C₂×C₄×D₄	C₂²×C₁₉	1	8	yes	—
209	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
210	C₂×#117	C₂²×C₁₉	1	4	yes	—
211	C₂×#117	C₂²×C₁₉	1	4	yes	—
212	C₂²×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
213	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
214	#391	C₂²×C₁₉	1	8	yes	—
215	#390	C₂²×C₁₉	1	8	yes	—
216	#390	C₂²×C₁₉	1	8	yes	—
217	#389	C₂²×C₁₉	1	8	yes	—
218	#388	C₂²×C₁₉	1	16	yes	—
219	#386	C₂²×C₁₉	1	8	yes	—
220	#386	C₂²×C₁₉	1	8	yes	—
221	#385	C₂²×C₁₉	1	16	yes	—
222	#384	C₂²×C₁₉	1	2	yes	—
223	#384	C₂²×C₁₉	1	2	yes	—
224	#382	C₂²×C₁₉	1	4	yes	—
225	#380	C₂²×C₁₉	1	4	yes	—
226	#380	C₂²×C₁₉	1	8	yes	—
227	#380	C₂²×C₁₉	1	4	yes	—
228	C₄×C₄⋊C₄	C₂²×C₁₉	1	8	yes	—
229	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
230	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
231	C₂×C₁₉	—	4	2	no	—
232	C₂×C₁₉	—	4	8	no	—
233	C₂×C₁₉	C₂×#518	1	1	yes	characteristic
234	C₂×C₁₉	C₂×#520	1	2	yes	—
235	C₂×C₁₉	#3548	1	2	yes	—
236	C₂×C₁₉	#3549	1	1	yes	characteristic
237	C₂×C₁₉	#3550	1	1	yes	characteristic
238	C₂×#41	—	4	4	no	—
239	C₂×#41	—	4	4	no	—
240	C₂×#41	C₂×C₄×C₁₉	1	16	yes	complemented
241	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
242	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
243	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
244	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
245	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
246	C₂³×C₄	C₂³×C₁₉	1	2	yes	—
247	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
248	C₂³×C₄	C₂³×C₁₉	1	8	yes	—
249	C₄⋊Q₈	C₂×C₄×C₁₉	1	8	yes	complemented
250	#127	C₂×C₄×C₁₉	1	8	yes	—
251	#124	C₂×C₄×C₁₉	1	16	yes	complemented
252	#121	C₂×C₄×C₁₉	1	32	yes	complemented
253	C₄×D₄	—	4	16	no	—
254	C₄×D₄	C₂×C₄×C₁₉	1	32	yes	complemented
255	#117	—	4	8	no	—
256	#117	—	4	8	no	—
257	C₂×C₄⋊C₄	—	4	8	no	—
258	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
259	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
260	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
261	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
262	C₂×C₄⋊C₄	C₂³×C₁₉	1	8	yes	—
263	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
264	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
265	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
266	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
267	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
268	C₂×C₂²⋊C₄	C₂³×C₁₉	1	16	yes	—
269	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
270	C₂×C₄²	C₂×C₄×C₁₉	1	8	yes	complemented
271	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
272	C₂×C₄²	C₂³×C₁₉	1	8	yes	—
273	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
274	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
276	#95	C₂³×C₁₉	1	8	yes	—
277	#95	C₂³×C₁₉	1	8	yes	—
278	#95	C₂³×C₁₉	1	16	yes	—
279	C₁₉	#34368	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
281	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
282	#41	—	4	32	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	C₂²×C₄×C₁₉	1	8	yes	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	4	4	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	C₂²×C₄×C₁₉	1	16	yes	—
293	C₂×D₄	C₂²×C₄×C₁₉	1	16	yes	—
294	C₂×D₄	C₂²×C₄×C₁₉	1	8	yes	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	4	8	no	—
302	C₂²×C₄	—	4	16	no	—
303	C₂²×C₄	C₂²×C₄×C₁₉	1	8	yes	—
304	C₂²×C₄	C₂²×C₄×C₁₉	1	4	yes	—
305	C₂²×C₄	C₂²×C₄×C₁₉	1	16	yes	—
306	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
307	C₂²×C₄	C₂⁴×C₁₉	1	8	yes	—
308	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
310	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
311	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
312	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
313	C₄⋊C₄	—	2	8	no	—
314	C₄⋊C₄	—	2	8	no	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	4	8	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	4	4	no	—
320	C₄⋊C₄	C₂²×C₄×C₁₉	1	16	yes	—
321	C₂²⋊C₄	—	4	8	no	—
322	C₂²⋊C₄	—	4	8	no	—
323	C₂²⋊C₄	—	4	16	no	—
324	C₂²⋊C₄	C₂²×C₄×C₁₉	1	32	yes	—
325	C₄²	—	2	16	no	—
326	C₄²	—	4	8	no	—
327	C₄²	C₂²×C₄×C₁₉	1	8	yes	—
328	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
329	C₄²	C₂²×C₄×C₁₉	1	4	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	4	no	—
332	C₂³	—	2	8	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	8	no	—
338	C₂³	C₂³×C₄×C₁₉	1	8	yes	—
339	C₂³	C₂³×C₄×C₁₉	1	2	yes	—
340	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
341	Q₈	—	4	8	no	—
342	D₄	—	2	32	no	—
343	D₄	—	4	8	no	—
344	D₄	—	4	16	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	32	no	—
353	C₂×C₄	—	2	16	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	8	no	—
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	8	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	8	16	no	—
361	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
362	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
363	C₂×C₄	C₂³×C₄×C₁₉	1	8	yes	—
364	C₂×C₄	C₂³×C₄×C₁₉	1	2	yes	—
365	C₂×C₄	C₂³×C₄×C₁₉	1	4	yes	—
366	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
367	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
368	C₂×C₄	C₁₉×H(5,𝔽₂)	1	4	yes	—
369	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	8	no	—
372	C₂²	—	2	4	no	—
373	C₂²	—	2	16	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	8	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	1	no	—
380	C₂²	C₂⁴×C₄×C₁₉	1	1	yes	characteristic
381	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
382	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
383	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	2	yes	—
384	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
385	C₄	—	2	2	no	—
386	C₄	—	2	8	no	—
387	C₄	—	2	4	no	—
388	C₄	—	4	8	no	—
389	C₄	—	4	8	no	—
390	C₄	C₁₉×#518	1	4	yes	—
391	C₄	C₁₉×#520	1	8	yes	—
392	C₂	—	4	2	no	—
393	C₂	—	4	8	no	—
394	C₂	C₂×C₁₉×#518	1	1	yes	characteristic
395	C₂	C₂×C₁₉×#520	1	2	yes	—
396	C₂	C₁₉×#3548	1	2	yes	—
397	C₂	C₁₉×#3549	1	1	yes	characteristic
398	C₂	C₁₉×#3550	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂⁵
commutator	C₂²	C₂⁴×C₄×C₁₉
Frattini, cosocle	C₂³	C₂⁵×C₁₉
prime radical	C₂×C₁₉×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2379	C₂	semidirect
3. C₁₉×#2369	C₂	semidirect
4. C₁₉×#2366	C₂	semidirect
5. C₁₉×#2354	C₂	semidirect
6. D₄×C₄⋊C₄×C₁₉	C₂	semidirect
7. C₁₉×#2324	C₂	semidirect
8. C₁₉×#2311	C₂	semidirect
9. C₁₉×#2285	C₂	semidirect
11. C₁₉×#532	C₄	semidirect
41. C₂×#41×C₁₉	C₂×C₄	semidirect
50. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
52. C₁₉×#124	C₂×C₄	semidirect
53. C₁₉×#121	C₂×C₄	semidirect
55. C₄×D₄×C₁₉	C₂×C₄	semidirect
71. C₂×C₄²×C₁₉	C₂×C₄	semidirect
130. #34368	C₁₉	direct (N × H)
172. #2379	C₂×C₁₉	semidirect
173. #2369	C₂×C₁₉	semidirect
174. #2366	C₂×C₁₉	semidirect
175. #2354	C₂×C₁₉	semidirect
176. D₄×C₄⋊C₄	C₂×C₁₉	semidirect
177. #2324	C₂×C₁₉	semidirect
178. #2311	C₂×C₁₉	semidirect
179. #2285	C₂×C₁₉	semidirect
203. #532	C₄×C₁₉	semidirect
240. C₂×#41	C₂×C₄×C₁₉	semidirect
249. C₄⋊Q₈	C₂×C₄×C₁₉	semidirect
251. #124	C₂×C₄×C₁₉	semidirect
252. #121	C₂×C₄×C₁₉	semidirect
254. C₄×D₄	C₂×C₄×C₁₉	semidirect
270. C₂×C₄²	C₂×C₄×C₁₉	semidirect
279. C₁₉	#34368	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×C₁₉×#532	2
C₁₉×#2379	2
C₁₉×#2369	2
C₁₉×#2366	2
C₁₉×#2354	2
D₄×C₄⋊C₄×C₁₉	2
C₁₉×#2324	2
C₁₉×#2311	2
C₁₉×#2285	2
#34368	19

Subgroups — C19×#34368 #18040327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34368 #18040327