Subgroups — C₁₉×#34973 #18040932

Order 4864.

1716 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2524	C₂	1	4	yes	maximal, complemented
2	C₁₉×#2519	C₂	1	4	yes	maximal
3	C₁₉×#2469	C₂	1	4	yes	maximal
4	C₁₉×#2462	C₂	1	4	yes	maximal, complemented
5	C₁₉×#2402	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉×#2399	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2396	C₂	1	2	yes	maximal
8	C₄×C₁₉×#125	C₂	1	4	yes	maximal, complemented
9	C₄×C₁₉×#126	C₂	1	4	yes	maximal
10	C₁₉×#2298	C₂	1	1	yes	maximal, characteristic
11	C₄²×Q₈×C₁₉	C₂	1	2	yes	maximal, complemented
12	C₂×C₁₉×#126	C₂²	1	4	yes	—
13	C₂×C₁₉×#125	C₂²	1	4	yes	—
14	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₁₉	C₂²	1	4	yes	—
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#400	C₂²	1	4	yes	—
18	C₁₉×#400	C₂²	1	2	yes	—
19	C₁₉×#399	C₂²	1	2	yes	—
20	C₁₉×#398	C₂²	1	4	yes	—
21	C₁₉×#398	C₂²	1	4	yes	—
22	C₁₉×#398	C₂²	1	4	yes	—
23	C₁₉×#396	C₂²	1	4	yes	—
24	C₁₉×#395	C₂²	1	4	yes	—
25	C₁₉×#395	C₂²	1	2	yes	—
26	C₁₉×#393	C₂²	1	2	yes	—
27	C₁₉×#389	C₂²	1	4	yes	—
28	C₁₉×#389	C₂²	1	4	yes	—
29	C₁₉×#388	C₂²	1	4	yes	—
30	C₁₉×#388	C₂²	1	4	yes	—
31	C₁₉×#388	C₂²	1	4	yes	—
32	C₁₉×#388	C₂²	1	4	yes	—
33	C₁₉×#387	C₂²	1	4	yes	—
34	C₁₉×#387	C₂²	1	4	yes	—
35	C₁₉×#387	C₂²	1	4	yes	—
36	C₁₉×#387	C₂²	1	4	yes	—
37	C₁₉×#387	C₂²	1	4	yes	—
38	C₁₉×#387	C₂²	1	4	yes	—
39	C₁₉×#387	C₂²	1	4	yes	—
40	C₁₉×#387	C₂²	1	4	yes	—
41	C₁₉×#383	C₂²	1	4	yes	—
42	C₁₉×#382	C₂²	1	4	yes	—
43	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
44	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
45	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
46	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
47	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
48	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
50	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
51	C₄×C₄⋊C₄×C₁₉	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊C₄×C₁₉	C₂²	1	4	yes	—
54	C₁₉×#376	C₂²	1	1	yes	characteristic
55	C₄³×C₁₉	C₂²	1	1	yes	characteristic
56	C₄³×C₁₉	C₂²	1	4	yes	—
57	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
59	C₁₉×#126	—	2	16	no	—
60	C₁₉×#125	—	2	16	no	—
61	C₄×Q₈×C₁₉	—	2	16	no	—
62	C₄×Q₈×C₁₉	—	2	8	no	—
63	C₁₉×#117	—	2	4	no	—
64	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
71	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
78	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₁₉	C₂³	1	4	yes	—
80	C₂×C₂²⋊C₄×C₁₉	C₂³	1	2	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	4	yes	—
85	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
86	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
87	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
88	C₂×C₄²×C₁₉	C₂³	1	4	yes	—
89	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
90	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
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	C₁₉×#95	C₂³	1	4	yes	—
97	C₁₉×#95	C₂³	1	4	yes	—
98	C₁₉×#95	C₂³	1	2	yes	—
99	C₁₉×#95	C₂³	1	2	yes	—
100	C₁₉×#95	C₂³	1	4	yes	—
101	C₁₉×#95	C₂³	1	4	yes	—
102	C₁₉×#95	C₂³	1	4	yes	—
103	C₁₉×#95	C₂³	1	4	yes	—
104	C₁₉×#95	C₂³	1	4	yes	—
105	C₁₉×#95	C₂³	1	4	yes	—
106	C₁₉×#95	C₂³	1	4	yes	—
107	C₂⁴×C₁₉	C₂⁴	1	1	yes	characteristic
108	C₂×Q₈×C₁₉	—	2	8	no	—
109	C₂×Q₈×C₁₉	—	2	4	no	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	4	no	—
112	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
114	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
116	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
117	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
118	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₁₉	C₂⁴	1	4	yes	—
120	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
122	C₄⋊C₄×C₁₉	—	2	4	no	—
123	C₄⋊C₄×C₁₉	—	2	8	no	—
124	C₄⋊C₄×C₁₉	—	2	8	no	—
125	C₄⋊C₄×C₁₉	—	2	8	no	—
126	C₄⋊C₄×C₁₉	—	2	4	no	—
127	C₄⋊C₄×C₁₉	—	2	8	no	—
128	C₄⋊C₄×C₁₉	—	2	8	no	—
129	C₄⋊C₄×C₁₉	—	2	8	no	—
130	C₄⋊C₄×C₁₉	—	2	8	no	—
131	C₄⋊C₄×C₁₉	—	2	8	no	—
132	C₄⋊C₄×C₁₉	—	2	8	no	—
133	C₄⋊C₄×C₁₉	—	2	8	no	—
134	C₄⋊C₄×C₁₉	#41	1	16	yes	—
135	C₂²⋊C₄×C₁₉	—	2	4	no	—
136	C₂²⋊C₄×C₁₉	—	2	8	no	—
137	C₂²⋊C₄×C₁₉	—	2	8	no	—
138	C₂²⋊C₄×C₁₉	—	2	8	no	—
139	C₄²×C₁₉	—	2	2	no	—
140	C₄²×C₁₉	—	2	8	no	—
141	C₄²×C₁₉	—	2	8	no	—
142	C₄²×C₁₉	—	2	8	no	—
143	C₄²×C₁₉	—	2	8	no	—
144	C₄²×C₁₉	—	2	8	no	—
145	C₄²×C₁₉	—	2	8	no	—
146	C₄²×C₁₉	—	2	4	no	—
147	C₄²×C₁₉	—	2	8	no	—
148	C₄²×C₁₉	—	2	4	no	—
149	C₄²×C₁₉	#41	1	4	yes	—
150	#34973	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	4	no	—
152	C₂³×C₁₉	—	2	1	no	—
153	C₂³×C₁₉	—	2	2	no	—
154	C₂³×C₁₉	C₂⁵	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	16	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	2	4	no	—
159	C₂×C₄×C₁₉	—	2	4	no	—
160	C₂×C₄×C₁₉	—	2	4	no	—
161	C₂×C₄×C₁₉	—	2	4	no	—
162	C₂×C₄×C₁₉	—	2	4	no	—
163	C₂×C₄×C₁₉	—	2	2	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	—	2	4	no	—
166	C₂×C₄×C₁₉	—	2	4	no	—
167	C₂×C₄×C₁₉	—	2	4	no	—
168	C₂×C₄×C₁₉	—	2	4	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	1	no	—
173	C₂×C₄×C₁₉	—	2	4	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	2	no	—
176	C₂×C₄×C₁₉	—	4	4	no	—
177	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
178	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
179	C₂×C₄×C₁₉	C₂×#41	1	8	yes	—
180	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
181	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
182	C₂×C₄×C₁₉	2₋¹⁺⁴	1	4	yes	—
183	#2524	C₂×C₁₉	1	4	yes	complemented
184	#2519	C₂×C₁₉	1	4	yes	—
185	#2469	C₂×C₁₉	1	4	yes	—
186	#2462	C₂×C₁₉	1	4	yes	complemented
187	#2402	C₂×C₁₉	1	1	yes	characteristic, complemented
188	#2399	C₂×C₁₉	1	1	yes	characteristic, complemented
189	#2396	C₂×C₁₉	1	2	yes	—
190	C₄×#125	C₂×C₁₉	1	4	yes	complemented
191	C₄×#126	C₂×C₁₉	1	4	yes	—
192	#2298	C₂×C₁₉	1	1	yes	characteristic
193	C₄²×Q₈	C₂×C₁₉	1	2	yes	complemented
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	1	no	—
196	C₂²×C₁₉	—	4	4	no	—
197	C₂²×C₁₉	C₂²×#41	1	1	yes	characteristic
198	C₂²×C₁₉	C₂²×#41	1	4	yes	—
199	C₂²×C₁₉	C₂×2₋¹⁺⁴	1	2	yes	—
200	C₄×C₁₉	—	2	8	no	—
201	C₄×C₁₉	—	2	4	no	—
202	C₄×C₁₉	—	2	8	no	—
203	C₄×C₁₉	—	2	8	no	—
204	C₄×C₁₉	—	4	4	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	—	4	1	no	—
207	C₄×C₁₉	—	4	4	no	—
208	C₄×C₁₉	—	4	4	no	—
209	C₄×C₁₉	#541	1	4	yes	—
210	C₂×#126	C₂²×C₁₉	1	4	yes	—
211	C₂×#125	C₂²×C₁₉	1	4	yes	—
212	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
213	C₂×C₄×Q₈	C₂²×C₁₉	1	4	yes	—
214	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
215	#400	C₂²×C₁₉	1	2	yes	—
216	#400	C₂²×C₁₉	1	4	yes	—
217	#399	C₂²×C₁₉	1	2	yes	—
218	#398	C₂²×C₁₉	1	4	yes	—
219	#398	C₂²×C₁₉	1	4	yes	—
220	#398	C₂²×C₁₉	1	4	yes	—
221	#396	C₂²×C₁₉	1	4	yes	—
222	#395	C₂²×C₁₉	1	2	yes	—
223	#395	C₂²×C₁₉	1	4	yes	—
224	#393	C₂²×C₁₉	1	2	yes	—
225	#389	C₂²×C₁₉	1	4	yes	—
226	#389	C₂²×C₁₉	1	4	yes	—
227	#388	C₂²×C₁₉	1	4	yes	—
228	#388	C₂²×C₁₉	1	4	yes	—
229	#388	C₂²×C₁₉	1	4	yes	—
230	#388	C₂²×C₁₉	1	4	yes	—
231	#387	C₂²×C₁₉	1	4	yes	—
232	#387	C₂²×C₁₉	1	4	yes	—
233	#387	C₂²×C₁₉	1	4	yes	—
234	#387	C₂²×C₁₉	1	4	yes	—
235	#387	C₂²×C₁₉	1	4	yes	—
236	#387	C₂²×C₁₉	1	4	yes	—
237	#387	C₂²×C₁₉	1	4	yes	—
238	#387	C₂²×C₁₉	1	4	yes	—
239	#383	C₂²×C₁₉	1	4	yes	—
240	#382	C₂²×C₁₉	1	4	yes	—
241	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
242	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	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	2	yes	—
246	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
247	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
248	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
249	C₄×C₄⋊C₄	C₂²×C₁₉	1	4	yes	—
250	C₄×C₂²⋊C₄	C₂²×C₁₉	1	4	yes	—
251	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
252	#376	C₂²×C₁₉	1	1	yes	characteristic
253	C₄³	C₂²×C₁₉	1	4	yes	—
254	C₄³	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×C₁₉	—	8	1	no	—
256	C₂×C₁₉	#3444	1	2	yes	—
257	C₂×C₁₉	C₂×#541	1	1	yes	characteristic
258	C₂×C₁₉	#3482	1	4	yes	—
259	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
260	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
261	#126	—	2	16	no	—
262	#125	—	2	16	no	—
263	C₄×Q₈	—	2	16	no	—
264	C₄×Q₈	—	2	8	no	—
265	#117	—	2	4	no	—
266	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
267	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
268	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
269	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
270	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
272	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
273	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	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×C₂²⋊C₄	C₂³×C₁₉	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
281	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
282	C₂×C₂²⋊C₄	C₂³×C₁₉	1	4	yes	—
283	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
284	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
285	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
286	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
287	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
288	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
289	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
290	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
291	C₂×C₄²	C₂³×C₁₉	1	4	yes	—
292	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
293	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
294	#95	C₂³×C₁₉	1	4	yes	—
295	#95	C₂³×C₁₉	1	4	yes	—
296	#95	C₂³×C₁₉	1	4	yes	—
297	#95	C₂³×C₁₉	1	4	yes	—
298	#95	C₂³×C₁₉	1	4	yes	—
299	#95	C₂³×C₁₉	1	4	yes	—
300	#95	C₂³×C₁₉	1	2	yes	—
301	#95	C₂³×C₁₉	1	2	yes	—
302	#95	C₂³×C₁₉	1	4	yes	—
303	#95	C₂³×C₁₉	1	4	yes	—
304	#95	C₂³×C₁₉	1	4	yes	—
305	#95	C₂³×C₁₉	1	4	yes	—
306	#95	C₂³×C₁₉	1	4	yes	—
307	#95	C₂³×C₁₉	1	4	yes	—
308	#95	C₂³×C₁₉	1	4	yes	—
309	C₁₉	#34973	1	1	yes	characteristic, direct product factor, Sylow
310	C₂⁴	C₂⁴×C₁₉	1	1	yes	characteristic
311	C₂×Q₈	—	2	8	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	2	4	no	—
315	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
317	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
318	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
319	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
320	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
321	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
322	C₂²×C₄	C₂⁴×C₁₉	1	4	yes	—
323	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
324	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	8	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	2	8	no	—
333	C₄⋊C₄	—	2	8	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	2	8	no	—
336	C₄⋊C₄	—	2	8	no	—
337	C₄⋊C₄	#41×C₁₉	1	16	yes	—
338	C₂²⋊C₄	—	2	4	no	—
339	C₂²⋊C₄	—	2	8	no	—
340	C₂²⋊C₄	—	2	8	no	—
341	C₂²⋊C₄	—	2	8	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	2	8	no	—
344	C₄²	—	2	8	no	—
345	C₄²	—	2	8	no	—
346	C₄²	—	2	8	no	—
347	C₄²	—	2	8	no	—
348	C₄²	—	2	8	no	—
349	C₄²	—	2	4	no	—
350	C₄²	—	2	8	no	—
351	C₄²	—	2	4	no	—
352	C₄²	#41×C₁₉	1	4	yes	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	2	no	—
356	C₂³	C₂⁵×C₁₉	1	1	yes	characteristic
357	Q₈	—	2	16	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	4	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	1	no	—
375	C₂×C₄	—	2	4	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
380	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
381	C₂×C₄	C₂×#41×C₁₉	1	8	yes	—
382	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
383	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
384	C₂×C₄	C₁₉×2₋¹⁺⁴	1	4	yes	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	1	no	—
387	C₂²	—	4	4	no	—
388	C₂²	C₂²×#41×C₁₉	1	1	yes	characteristic
389	C₂²	C₂²×#41×C₁₉	1	4	yes	—
390	C₂²	C₂×C₁₉×2₋¹⁺⁴	1	2	yes	—
391	C₄	—	2	8	no	—
392	C₄	—	2	4	no	—
393	C₄	—	2	8	no	—
394	C₄	—	2	8	no	—
395	C₄	—	4	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	4	1	no	—
398	C₄	—	4	4	no	—
399	C₄	—	4	4	no	—
400	C₄	C₁₉×#541	1	4	yes	—
401	C₂	—	8	1	no	—
402	C₂	C₁₉×#3444	1	2	yes	—
403	C₂	C₂×C₁₉×#541	1	1	yes	characteristic
404	C₂	C₁₉×#3482	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₉
socle	C₂³×C₁₉	C₂⁵
prime radical	C₂⁴×C₁₉	C₂⁴
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×#2524	C₂	semidirect
4. C₁₉×#2462	C₂	semidirect
5. C₁₉×#2402	C₂	semidirect
6. C₁₉×#2399	C₂	semidirect
8. C₄×C₁₉×#125	C₂	semidirect
11. C₄²×Q₈×C₁₉	C₂	semidirect
150. #34973	C₁₉	direct (N × H)
183. #2524	C₂×C₁₉	semidirect
186. #2462	C₂×C₁₉	semidirect
187. #2402	C₂×C₁₉	semidirect
188. #2399	C₂×C₁₉	semidirect
190. C₄×#125	C₂×C₁₉	semidirect
193. C₄²×Q₈	C₂×C₁₉	semidirect
309. C₁₉	#34973	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×#2524	2
C₁₉×#2519	2
C₁₉×#2469	2
C₁₉×#2462	2
C₁₉×#2402	2
C₁₉×#2399	2
C₁₉×#2396	2
C₄×C₁₉×#125	2
C₄×C₁₉×#126	2
C₁₉×#2298	2
C₄²×Q₈×C₁₉	2
#34973	19

Subgroups — C19×#34973 #18040932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#34973 #18040932