Subgroups — C₁₉×#34954 #18040913

Order 4864.

1948 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2593	C₂	1	4	yes	maximal, complemented
2	C₁₉×#2582	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2571	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2548	C₂	1	2	yes	maximal
5	C₁₉×#2513	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2448	C₂	1	4	yes	maximal, complemented
7	C₁₉×#2395	C₂	1	4	yes	maximal, complemented
8	C₄×C₁₉×#127	C₂	1	1	yes	maximal, characteristic
9	C₄×C₁₉×#124	C₂	1	4	yes	maximal, complemented
10	C₁₉×#2293	C₂	1	4	yes	maximal, complemented
11	C₄²×Q₈×C₁₉	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×#124	C₂²	1	4	yes	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₁₉	C₂²	1	4	yes	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
19	C₂×C₁₉×#117	C₂²	1	4	yes	—
20	C₁₉×#400	C₂²	1	4	yes	—
21	C₁₉×#399	C₂²	1	4	yes	—
22	C₁₉×#398	C₂²	1	4	yes	—
23	C₁₉×#397	C₂²	1	8	yes	—
24	C₁₉×#397	C₂²	1	4	yes	—
25	C₁₉×#394	C₂²	1	8	yes	—
26	C₁₉×#391	C₂²	1	4	yes	—
27	C₁₉×#390	C₂²	1	4	yes	—
28	C₁₉×#390	C₂²	1	4	yes	—
29	C₁₉×#390	C₂²	1	4	yes	—
30	C₁₉×#390	C₂²	1	4	yes	—
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#389	C₂²	1	4	yes	—
33	C₁₉×#389	C₂²	1	4	yes	—
34	C₁₉×#388	C₂²	1	8	yes	—
35	C₁₉×#388	C₂²	1	8	yes	—
36	C₁₉×#388	C₂²	1	8	yes	—
37	C₁₉×#388	C₂²	1	8	yes	—
38	C₁₉×#384	C₂²	1	1	yes	characteristic
39	C₁₉×#382	C₂²	1	4	yes	—
40	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
41	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
42	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
46	C₄×C₂²⋊C₄×C₁₉	C₂²	1	8	yes	—
47	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
48	C₄³×C₁₉	C₂²	1	1	yes	characteristic
49	C₄³×C₁₉	C₂²	1	4	yes	—
50	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
51	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
52	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
53	C₂³×C₄×C₁₉	C₂³	1	4	yes	—
54	C₁₉×#127	—	2	4	no	—
55	C₁₉×#124	—	2	16	no	—
56	C₄×Q₈×C₁₉	—	2	8	no	—
57	C₄×Q₈×C₁₉	—	2	8	no	—
58	C₄×Q₈×C₁₉	—	2	8	no	—
59	C₄×D₄×C₁₉	—	2	16	no	—
60	C₄×D₄×C₁₉	—	4	4	no	—
61	C₁₉×#117	—	4	8	no	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
73	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
74	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
75	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
76	C₂×C₂²⋊C₄×C₁₉	C₂³	1	8	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
78	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
80	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
81	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
87	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
89	C₁₉×#95	C₂³	1	4	yes	—
90	C₁₉×#95	C₂³	1	8	yes	—
91	C₁₉×#95	C₂³	1	8	yes	—
92	C₁₉×#95	C₂³	1	4	yes	—
93	C₁₉×#95	C₂³	1	4	yes	—
94	C₁₉×#95	C₂³	1	4	yes	—
95	C₁₉×#95	C₂³	1	4	yes	—
96	C₂⁴×C₁₉	C₂⁴	1	4	yes	—
97	C₂×Q₈×C₁₉	—	2	4	no	—
98	C₂×Q₈×C₁₉	—	2	4	no	—
99	C₂×Q₈×C₁₉	#41	1	8	yes	—
100	C₂×D₄×C₁₉	—	2	8	no	—
101	C₂×D₄×C₁₉	—	2	8	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	8	no	—
104	C₂×D₄×C₁₉	—	4	2	no	—
105	C₂×D₄×C₁₉	—	4	2	no	—
106	C₂²×C₄×C₁₉	—	2	16	no	—
107	C₂²×C₄×C₁₉	—	2	8	no	—
108	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
109	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
110	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
111	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
112	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
115	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
117	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
118	C₄⋊C₄×C₁₉	—	2	8	no	—
119	C₄⋊C₄×C₁₉	—	2	8	no	—
120	C₄⋊C₄×C₁₉	—	2	8	no	—
121	C₄⋊C₄×C₁₉	—	2	8	no	—
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	4	no	—
124	C₄⋊C₄×C₁₉	—	2	4	no	—
125	C₄⋊C₄×C₁₉	—	4	4	no	—
126	C₄⋊C₄×C₁₉	—	4	4	no	—
127	C₄⋊C₄×C₁₉	—	4	2	no	—
128	C₂²⋊C₄×C₁₉	—	2	16	no	—
129	C₂²⋊C₄×C₁₉	—	2	16	no	—
130	C₂²⋊C₄×C₁₉	—	2	16	no	—
131	C₂²⋊C₄×C₁₉	—	4	8	no	—
132	C₂²⋊C₄×C₁₉	—	4	8	no	—
133	C₂²⋊C₄×C₁₉	—	4	4	no	—
134	C₄²×C₁₉	—	2	8	no	—
135	C₄²×C₁₉	—	2	4	no	—
136	C₄²×C₁₉	—	2	8	no	—
137	C₄²×C₁₉	—	2	8	no	—
138	C₄²×C₁₉	—	2	8	no	—
139	C₄²×C₁₉	—	2	8	no	—
140	C₄²×C₁₉	—	2	2	no	—
141	C₄²×C₁₉	—	4	1	no	—
142	C₄²×C₁₉	—	4	4	no	—
143	C₄²×C₁₉	#41	1	8	yes	—
144	C₄²×C₁₉	#41	1	4	yes	—
145	#34954	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
146	C₂³×C₁₉	—	2	8	no	—
147	C₂³×C₁₉	—	2	8	no	—
148	C₂³×C₁₉	—	2	4	no	—
149	C₂³×C₁₉	—	2	4	no	—
150	C₂³×C₁₉	—	2	4	no	—
151	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
152	Q₈×C₁₉	—	2	16	no	—
153	D₄×C₁₉	—	4	8	no	—
154	D₄×C₁₉	—	4	16	no	—
155	C₂×C₄×C₁₉	—	2	2	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	1	no	—
159	C₂×C₄×C₁₉	—	2	2	no	—
160	C₂×C₄×C₁₉	—	2	1	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	4	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	2	no	—
167	C₂×C₄×C₁₉	—	2	8	no	—
168	C₂×C₄×C₁₉	—	2	1	no	—
169	C₂×C₄×C₁₉	—	2	4	no	—
170	C₂×C₄×C₁₉	—	2	4	no	—
171	C₂×C₄×C₁₉	—	2	4	no	—
172	C₂×C₄×C₁₉	—	2	4	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	4	16	no	—
175	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
176	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
177	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
178	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
179	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
180	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
181	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
182	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
183	#2593	C₂×C₁₉	1	4	yes	complemented
184	#2582	C₂×C₁₉	1	1	yes	characteristic, complemented
185	#2571	C₂×C₁₉	1	1	yes	characteristic, complemented
186	#2548	C₂×C₁₉	1	2	yes	—
187	#2513	C₂×C₁₉	1	4	yes	complemented
188	#2448	C₂×C₁₉	1	4	yes	complemented
189	#2395	C₂×C₁₉	1	4	yes	complemented
190	C₄×#127	C₂×C₁₉	1	1	yes	characteristic
191	C₄×#124	C₂×C₁₉	1	4	yes	complemented
192	#2293	C₂×C₁₉	1	4	yes	complemented
193	C₄²×Q₈	C₂×C₁₉	1	2	yes	complemented
194	C₂²×C₁₉	—	4	8	no	—
195	C₂²×C₁₉	—	4	4	no	—
196	C₂²×C₁₉	—	4	4	no	—
197	C₂²×C₁₉	—	4	8	no	—
198	C₂²×C₁₉	—	4	4	no	—
199	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
200	C₂²×C₁₉	C₂²×#41	1	2	yes	—
201	C₂²×C₁₉	C₂²×#41	1	2	yes	—
202	C₂²×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
203	C₂²×C₁₉	#585	1	1	yes	characteristic
204	C₄×C₁₉	—	2	8	no	—
205	C₄×C₁₉	—	2	2	no	—
206	C₄×C₁₉	—	2	4	no	—
207	C₄×C₁₉	—	4	4	no	—
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	—	4	4	no	—
210	C₄×C₁₉	—	4	4	no	—
211	C₄×C₁₉	—	4	1	no	—
212	C₄×C₁₉	#529	1	8	yes	—
213	C₄×C₁₉	#559	1	4	yes	—
214	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
215	C₂×#124	C₂²×C₁₉	1	4	yes	—
216	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
217	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
218	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
219	C₂×C₄×D₄	C₂²×C₁₉	1	4	yes	—
220	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
221	C₂×#117	C₂²×C₁₉	1	4	yes	—
222	#400	C₂²×C₁₉	1	4	yes	—
223	#399	C₂²×C₁₉	1	4	yes	—
224	#398	C₂²×C₁₉	1	4	yes	—
225	#397	C₂²×C₁₉	1	8	yes	—
226	#397	C₂²×C₁₉	1	4	yes	—
227	#394	C₂²×C₁₉	1	8	yes	—
228	#391	C₂²×C₁₉	1	4	yes	—
229	#390	C₂²×C₁₉	1	2	yes	—
230	#390	C₂²×C₁₉	1	4	yes	—
231	#390	C₂²×C₁₉	1	4	yes	—
232	#390	C₂²×C₁₉	1	4	yes	—
233	#390	C₂²×C₁₉	1	4	yes	—
234	#389	C₂²×C₁₉	1	4	yes	—
235	#389	C₂²×C₁₉	1	4	yes	—
236	#388	C₂²×C₁₉	1	8	yes	—
237	#388	C₂²×C₁₉	1	8	yes	—
238	#388	C₂²×C₁₉	1	8	yes	—
239	#388	C₂²×C₁₉	1	8	yes	—
240	#384	C₂²×C₁₉	1	1	yes	characteristic
241	#382	C₂²×C₁₉	1	4	yes	—
242	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
243	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
244	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
245	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
246	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
247	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
248	C₄×C₂²⋊C₄	C₂²×C₁₉	1	8	yes	—
249	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
250	C₄³	C₂²×C₁₉	1	1	yes	characteristic
251	C₄³	C₂²×C₁₉	1	4	yes	—
252	C₂×C₁₉	—	8	4	no	—
253	C₂×C₁₉	C₂×#529	1	2	yes	—
254	C₂×C₁₉	#3460	1	1	yes	characteristic
255	C₂×C₁₉	C₂×#559	1	1	yes	characteristic
256	C₂×C₁₉	#3480	1	2	yes	—
257	C₂×C₁₉	#3483	1	1	yes	characteristic
258	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
259	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
260	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
261	C₂³×C₄	C₂³×C₁₉	1	4	yes	—
262	#127	—	2	4	no	—
263	#124	—	2	16	no	—
264	C₄×Q₈	—	2	8	no	—
265	C₄×Q₈	—	2	8	no	—
266	C₄×Q₈	—	2	8	no	—
267	C₄×D₄	—	2	16	no	—
268	C₄×D₄	—	4	4	no	—
269	#117	—	4	8	no	—
270	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
276	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
277	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
278	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
279	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
283	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
284	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
285	C₂×C₂²⋊C₄	C₂³×C₁₉	1	8	yes	—
286	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
287	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
288	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
289	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
290	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
291	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
292	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
293	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
294	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
295	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
296	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
297	#95	C₂³×C₁₉	1	4	yes	—
298	#95	C₂³×C₁₉	1	8	yes	—
299	#95	C₂³×C₁₉	1	8	yes	—
300	#95	C₂³×C₁₉	1	4	yes	—
301	#95	C₂³×C₁₉	1	4	yes	—
302	#95	C₂³×C₁₉	1	4	yes	—
303	#95	C₂³×C₁₉	1	4	yes	—
304	C₁₉	#34954	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁴	C₂⁴×C₁₉	1	4	yes	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	4	no	—
308	C₂×Q₈	#41×C₁₉	1	8	yes	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	8	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	8	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂²×C₄	—	2	16	no	—
316	C₂²×C₄	—	2	8	no	—
317	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
318	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
320	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
325	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
326	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	4	no	—
334	C₄⋊C₄	—	4	4	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₂²⋊C₄	—	2	16	no	—
338	C₂²⋊C₄	—	2	16	no	—
339	C₂²⋊C₄	—	2	16	no	—
340	C₂²⋊C₄	—	4	8	no	—
341	C₂²⋊C₄	—	4	8	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₄²	—	2	8	no	—
344	C₄²	—	2	4	no	—
345	C₄²	—	2	8	no	—
346	C₄²	—	2	8	no	—
347	C₄²	—	2	8	no	—
348	C₄²	—	2	8	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	4	1	no	—
351	C₄²	—	4	4	no	—
352	C₄²	#41×C₁₉	1	8	yes	—
353	C₄²	#41×C₁₉	1	4	yes	—
354	C₂³	—	2	8	no	—
355	C₂³	—	2	8	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
360	Q₈	—	2	16	no	—
361	D₄	—	4	8	no	—
362	D₄	—	4	16	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	4	16	no	—
383	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
384	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
385	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
386	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
387	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
388	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
389	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
390	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
391	C₂²	—	4	8	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	8	no	—
395	C₂²	—	4	4	no	—
396	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
397	C₂²	C₂²×#41×C₁₉	1	2	yes	—
398	C₂²	C₂²×#41×C₁₉	1	2	yes	—
399	C₂²	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
400	C₂²	C₁₉×#585	1	1	yes	characteristic
401	C₄	—	2	8	no	—
402	C₄	—	2	2	no	—
403	C₄	—	2	4	no	—
404	C₄	—	4	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	1	no	—
409	C₄	C₁₉×#529	1	8	yes	—
410	C₄	C₁₉×#559	1	4	yes	—
411	C₂	—	8	4	no	—
412	C₂	C₂×C₁₉×#529	1	2	yes	—
413	C₂	C₁₉×#3460	1	1	yes	characteristic
414	C₂	C₂×C₁₉×#559	1	1	yes	characteristic
415	C₂	C₁₉×#3480	1	2	yes	—
416	C₂	C₁₉×#3483	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂×C₁₉×#127	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#2593	C₂	semidirect
2. C₁₉×#2582	C₂	semidirect
3. C₁₉×#2571	C₂	semidirect
5. C₁₉×#2513	C₂	semidirect
6. C₁₉×#2448	C₂	semidirect
7. C₁₉×#2395	C₂	semidirect
9. C₄×C₁₉×#124	C₂	semidirect
10. C₁₉×#2293	C₂	semidirect
11. C₄²×Q₈×C₁₉	C₂	semidirect
145. #34954	C₁₉	direct (N × H)
183. #2593	C₂×C₁₉	semidirect
184. #2582	C₂×C₁₉	semidirect
185. #2571	C₂×C₁₉	semidirect
187. #2513	C₂×C₁₉	semidirect
188. #2448	C₂×C₁₉	semidirect
189. #2395	C₂×C₁₉	semidirect
191. C₄×#124	C₂×C₁₉	semidirect
192. #2293	C₂×C₁₉	semidirect
193. C₄²×Q₈	C₂×C₁₉	semidirect
304. C₁₉	#34954	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×#2593	2
C₁₉×#2582	2
C₁₉×#2571	2
C₁₉×#2548	2
C₁₉×#2513	2
C₁₉×#2448	2
C₁₉×#2395	2
C₄×C₁₉×#127	2
C₄×C₁₉×#124	2
C₁₉×#2293	2
C₄²×Q₈×C₁₉	2
#34954	19

Subgroups — C19×#34954 #18040913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34954 #18040913