Subgroups — C₁₉×#32943 #18038902

Order 4864.

1316 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×#131	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#473	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3007	C₂	1	2	yes	maximal
5	C₁₉×#1908	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1901	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1816	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1810	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₂×C₁₉×#137	C₂²	1	4	yes	—
11	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₁₉×#131	—	2	8	no	—
13	C₂×C₁₉×#131	—	2	1	no	—
14	C₂×C₁₉×#131	—	2	1	no	—
15	C₂×C₁₉×#131	C₂²	1	2	yes	—
16	C₂×C₁₉×#131	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₁₉	—	2	1	no	—
18	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₉	—	2	1	no	—
20	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
21	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	2	yes	—
22	C₁₉×#473	—	2	8	no	—
23	C₁₉×#467	—	2	1	no	—
24	C₁₉×#467	—	2	1	no	—
25	C₁₉×#467	—	2	1	no	—
26	C₁₉×#467	—	2	1	no	—
27	C₁₉×#452	—	2	4	no	—
28	C₁₉×#451	—	2	2	no	—
29	C₁₉×#450	—	2	2	no	—
30	C₂×C₁₉×#108	C₂²	1	2	yes	complemented
31	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#417	C₂²	1	4	yes	—
33	C₂×C₁₉×#103	C₂²	1	2	yes	complemented
34	C₂×C₁₉×#101	C₂²	1	4	yes	complemented
35	C₁₉×#407	C₂²	1	2	yes	—
36	C₁₉×#343	C₂²	1	4	yes	complemented
37	C₁₉×#341	C₂²	1	2	yes	complemented
38	C₂×#41×C₁₉	—	2	4	no	—
39	C₂×#41×C₁₉	—	2	4	no	—
40	C₂×#41×C₁₉	—	2	1	no	—
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂×#41×C₁₉	D₄	1	2	yes	—
43	C₂×#41×C₁₉	C₂³	1	2	yes	—
44	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
45	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₁₉	—	2	1	no	—
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₁₉×#137	—	2	8	no	—
51	C₁₉×#137	—	2	8	no	—
52	C₂×Q₁₆×C₁₉	—	2	4	no	—
53	C₂×Q₁₆×C₁₉	—	2	1	no	—
54	C₂×Q₁₆×C₁₉	—	2	1	no	—
55	C₂×Q₁₆×C₁₉	—	2	4	no	—
56	C₂×SD₁₆×C₁₉	—	2	4	no	—
57	C₁₉×#131	—	2	8	no	—
58	C₁₉×#131	—	2	8	no	—
59	C₁₉×#131	—	2	4	no	—
60	C₁₉×#131	—	2	4	no	—
61	C₁₉×#131	—	2	4	no	—
62	C₁₉×#131	D₄	1	8	yes	—
63	C₂×M₁₆×C₁₉	—	2	8	no	—
64	C₂×M₁₆×C₁₉	—	2	1	no	—
65	C₂×M₁₆×C₁₉	—	2	4	no	—
66	C₂×M₁₆×C₁₉	—	2	2	no	—
67	C₂×M₁₆×C₁₉	—	2	2	no	—
68	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
69	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
70	C₂²×C₈×C₁₉	—	2	8	no	—
71	C₂²×C₈×C₁₉	—	2	1	no	—
72	C₂²×C₈×C₁₉	—	2	2	no	—
73	C₂²×C₈×C₁₉	—	2	2	no	—
74	C₂²×C₈×C₁₉	—	2	4	no	—
75	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
77	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
78	C₂²×C₈×C₁₉	D₄	1	1	yes	characteristic
79	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	—	2	2	no	—
84	C₁₉×C₂²⋊Q₈	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₁₉×#108	—	2	4	no	—
89	C₁₉×#107	—	2	1	no	—
90	C₁₉×#107	—	2	1	no	—
91	C₁₉×#103	—	2	4	no	—
92	C₁₉×#103	—	2	2	no	—
93	C₁₉×#103	—	2	2	no	—
94	C₁₉×#102	—	2	4	no	—
95	C₁₉×#101	—	2	8	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×C₂²⋊C₈	—	2	2	no	—
98	C₂⁴×C₁₉	—	2	1	no	—
99	C₂⁴×C₁₉	#41	1	1	yes	characteristic
100	#41×C₁₉	—	2	4	no	—
101	#41×C₁₉	—	2	8	no	—
102	#41×C₁₉	—	2	4	no	—
103	#41×C₁₉	—	2	4	no	—
104	#41×C₁₉	—	2	4	no	—
105	#41×C₁₉	—	2	2	no	—
106	#41×C₁₉	—	2	2	no	—
107	#41×C₁₉	C₂×D₄	1	4	yes	—
108	#41×C₁₉	#41	1	4	yes	—
109	C₂×Q₈×C₁₉	—	2	4	no	—
110	C₂×Q₈×C₁₉	—	2	1	no	—
111	C₂×Q₈×C₁₉	—	2	2	no	—
112	C₂×Q₈×C₁₉	—	2	2	no	—
113	C₂×Q₈×C₁₉	—	2	4	no	—
114	C₂×Q₈×C₁₉	—	2	4	no	—
115	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
116	C₂×D₄×C₁₉	—	2	8	no	—
117	C₂×D₄×C₁₉	—	2	2	no	—
118	C₂×D₄×C₁₉	—	2	2	no	—
119	C₂×D₄×C₁₉	—	2	4	no	—
120	C₂×D₄×C₁₉	—	2	1	no	—
121	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₁₉	—	2	4	no	—
123	C₂²×C₄×C₁₉	—	2	4	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	2	no	—
126	C₂²×C₄×C₁₉	—	2	2	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	2	2	no	—
130	C₂²×C₄×C₁₉	—	2	2	no	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	Q₁₆×C₁₉	—	4	8	no	—
138	Q₁₆×C₁₉	—	4	2	no	—
139	Q₁₆×C₁₉	—	4	2	no	—
140	SD₁₆×C₁₉	—	4	8	no	—
141	M₁₆×C₁₉	—	2	4	no	—
142	M₁₆×C₁₉	—	2	8	no	—
143	M₁₆×C₁₉	—	2	2	no	—
144	M₁₆×C₁₉	—	2	8	no	—
145	M₁₆×C₁₉	—	2	4	no	—
146	M₁₆×C₁₉	—	2	4	no	—
147	M₁₆×C₁₉	C₂×D₄	1	4	yes	—
148	C₂×C₈×C₁₉	—	2	4	no	—
149	C₂×C₈×C₁₉	—	2	8	no	—
150	C₂×C₈×C₁₉	—	2	2	no	—
151	C₂×C₈×C₁₉	—	2	2	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	8	no	—
154	C₂×C₈×C₁₉	—	2	2	no	—
155	C₂×C₈×C₁₉	—	2	2	no	—
156	C₂×C₈×C₁₉	—	2	2	no	—
157	C₂×C₈×C₁₉	—	2	4	no	—
158	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×C₈×C₁₉	C₂×D₄	1	4	yes	—
162	C₂×C₈×C₁₉	C₂×D₄	1	1	yes	characteristic
163	C₄⋊C₄×C₁₉	—	2	2	no	—
164	C₄⋊C₄×C₁₉	—	2	2	no	—
165	C₄⋊C₄×C₁₉	—	4	2	no	—
166	C₄⋊C₄×C₁₉	—	4	2	no	—
167	C₂²⋊C₄×C₁₉	—	4	2	no	—
168	C₂²⋊C₄×C₁₉	—	4	2	no	—
169	#32943	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂³×C₁₉	—	2	4	no	—
171	C₂³×C₁₉	—	2	2	no	—
172	C₂³×C₁₉	—	2	2	no	—
173	C₂³×C₁₉	—	2	2	no	—
174	C₂³×C₁₉	—	4	1	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	#121	1	1	yes	characteristic
178	C₂³×C₁₉	#121	1	1	yes	characteristic
179	C₂³×C₁₉	C₂×#41	1	1	yes	characteristic
180	Q₈×C₁₉	—	2	4	no	—
181	Q₈×C₁₉	—	2	2	no	—
182	Q₈×C₁₉	—	4	2	no	—
183	Q₈×C₁₉	—	4	4	no	—
184	Q₈×C₁₉	—	4	2	no	—
185	Q₈×C₁₉	#121	1	4	yes	—
186	D₄×C₁₉	—	2	8	no	—
187	D₄×C₁₉	—	2	4	no	—
188	D₄×C₁₉	—	2	4	no	—
189	D₄×C₁₉	—	2	4	no	—
190	D₄×C₁₉	—	2	2	no	—
191	D₄×C₁₉	#121	1	4	yes	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	8	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	4	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	2	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	1	no	—
202	C₂×C₄×C₁₉	—	2	4	no	—
203	C₂×C₄×C₁₉	—	2	1	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	4	no	—
207	C₂×C₄×C₁₉	—	8	2	no	—
208	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
209	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
210	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
214	C₈×C₁₉	—	2	1	no	—
215	C₈×C₁₉	—	2	4	no	—
216	C₈×C₁₉	—	2	1	no	—
217	C₈×C₁₉	—	4	4	no	—
218	C₈×C₁₉	#120	1	2	yes	—
219	C₈×C₁₉	#120	1	2	yes	—
220	C₂²×#131	C₂×C₁₉	1	1	yes	characteristic
221	C₂×#473	C₂×C₁₉	1	2	yes	complemented
222	C₂×#467	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#3007	C₂×C₁₉	1	2	yes	—
224	#1908	C₂×C₁₉	1	4	yes	complemented
225	#1901	C₂×C₁₉	1	2	yes	complemented
226	#1816	C₂×C₁₉	1	2	yes	complemented
227	#1810	C₂×C₁₉	1	1	yes	characteristic, complemented
228	C₂²×C₁₉	—	2	1	no	—
229	C₂²×C₁₉	—	2	1	no	—
230	C₂²×C₁₉	—	2	1	no	—
231	C₂²×C₁₉	—	2	1	no	—
232	C₂²×C₁₉	—	2	1	no	—
233	C₂²×C₁₉	—	2	4	no	—
234	C₂²×C₁₉	—	2	1	no	—
235	C₂²×C₁₉	—	2	1	no	—
236	C₂²×C₁₉	—	4	4	no	—
237	C₂²×C₁₉	—	4	8	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	#473	1	2	yes	complemented
241	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
242	C₂²×C₁₉	#525	1	2	yes	—
243	C₄×C₁₉	—	2	1	no	—
244	C₄×C₁₉	—	2	4	no	—
245	C₄×C₁₉	—	2	1	no	—
246	C₄×C₁₉	—	8	2	no	—
247	C₄×C₁₉	—	8	2	no	—
248	C₄×C₁₉	C₂×#120	1	1	yes	characteristic
249	C₄×C₁₉	C₂×#121	1	2	yes	—
250	C₄×C₁₉	#525	1	1	yes	characteristic
251	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
252	C₂×#137	C₂²×C₁₉	1	4	yes	—
253	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic, complemented
254	C₂×#131	—	2	8	no	—
255	C₂×#131	—	2	1	no	—
256	C₂×#131	—	2	1	no	—
257	C₂×#131	C₂²×C₁₉	1	2	yes	—
258	C₂×#131	C₂²×C₁₉	1	2	yes	—
259	C₂²×M₁₆	—	2	1	no	—
260	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
261	C₂³×C₈	—	2	1	no	—
262	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	2	yes	—
264	#473	—	2	8	no	—
265	#467	—	2	1	no	—
266	#467	—	2	1	no	—
267	#467	—	2	1	no	—
268	#467	—	2	1	no	—
269	#452	—	2	4	no	—
270	#451	—	2	2	no	—
271	#450	—	2	2	no	—
272	C₂×#108	C₂²×C₁₉	1	2	yes	complemented
273	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic, complemented
274	#417	C₂²×C₁₉	1	4	yes	—
275	C₂×#103	C₂²×C₁₉	1	2	yes	complemented
276	C₂×#101	C₂²×C₁₉	1	4	yes	complemented
277	#407	C₂²×C₁₉	1	2	yes	—
278	#343	C₂²×C₁₉	1	4	yes	complemented
279	#341	C₂²×C₁₉	1	2	yes	complemented
280	C₂×C₁₉	—	2	2	no	—
281	C₂×C₁₉	—	2	2	no	—
282	C₂×C₁₉	—	4	1	no	—
283	C₂×C₁₉	—	4	4	no	—
284	C₂×C₁₉	#2847	1	1	yes	characteristic
285	C₂×C₁₉	C₂×#473	1	1	yes	characteristic
286	C₂×C₁₉	#3067	1	1	yes	characteristic
287	C₂×#41	—	2	4	no	—
288	C₂×#41	—	2	4	no	—
289	C₂×#41	—	2	1	no	—
290	C₂×#41	—	2	1	no	—
291	C₂×#41	D₄×C₁₉	1	2	yes	—
292	C₂×#41	C₂³×C₁₉	1	2	yes	—
293	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
299	#137	—	2	8	no	—
300	#137	—	2	8	no	—
301	C₂×Q₁₆	—	2	4	no	—
302	C₂×Q₁₆	—	2	1	no	—
303	C₂×Q₁₆	—	2	1	no	—
304	C₂×Q₁₆	—	2	4	no	—
305	C₂×SD₁₆	—	2	4	no	—
306	#131	—	2	8	no	—
307	#131	—	2	8	no	—
308	#131	—	2	4	no	—
309	#131	—	2	4	no	—
310	#131	—	2	4	no	—
311	#131	D₄×C₁₉	1	8	yes	—
312	C₂×M₁₆	—	2	8	no	—
313	C₂×M₁₆	—	2	1	no	—
314	C₂×M₁₆	—	2	4	no	—
315	C₂×M₁₆	—	2	2	no	—
316	C₂×M₁₆	—	2	2	no	—
317	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
318	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
319	C₂²×C₈	—	2	8	no	—
320	C₂²×C₈	—	2	1	no	—
321	C₂²×C₈	—	2	2	no	—
322	C₂²×C₈	—	2	2	no	—
323	C₂²×C₈	—	2	4	no	—
324	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
325	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
326	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
327	C₂²×C₈	D₄×C₁₉	1	1	yes	characteristic
328	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
329	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
330	C₂²⋊Q₈	—	2	2	no	—
331	C₂²⋊Q₈	—	2	2	no	—
332	C₂²⋊Q₈	—	2	2	no	—
333	C₂²⋊Q₈	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	#108	—	2	4	no	—
338	#107	—	2	1	no	—
339	#107	—	2	1	no	—
340	#103	—	2	4	no	—
341	#103	—	2	2	no	—
342	#103	—	2	2	no	—
343	#102	—	2	4	no	—
344	#101	—	2	8	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	C₂²⋊C₈	—	2	2	no	—
347	C₁₉	#32943	1	1	yes	characteristic, direct product factor, Sylow
348	C₂⁴	—	2	1	no	—
349	C₂⁴	#41×C₁₉	1	1	yes	characteristic
350	#41	—	2	4	no	—
351	#41	—	2	8	no	—
352	#41	—	2	4	no	—
353	#41	—	2	4	no	—
354	#41	—	2	4	no	—
355	#41	—	2	2	no	—
356	#41	—	2	2	no	—
357	#41	C₂×D₄×C₁₉	1	4	yes	—
358	#41	#41×C₁₉	1	4	yes	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	1	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	4	no	—
365	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
366	C₂×D₄	—	2	8	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	4	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
385	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
387	Q₁₆	—	4	8	no	—
388	Q₁₆	—	4	2	no	—
389	Q₁₆	—	4	2	no	—
390	SD₁₆	—	4	8	no	—
391	M₁₆	—	2	4	no	—
392	M₁₆	—	2	8	no	—
393	M₁₆	—	2	2	no	—
394	M₁₆	—	2	8	no	—
395	M₁₆	—	2	4	no	—
396	M₁₆	—	2	4	no	—
397	M₁₆	C₂×D₄×C₁₉	1	4	yes	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	2	8	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	8	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	4	no	—
408	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
409	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₈	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂×C₈	C₂×D₄×C₁₉	1	4	yes	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	4	2	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₂²⋊C₄	—	4	2	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	4	1	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	C₁₉×#121	1	1	yes	characteristic
427	C₂³	C₁₉×#121	1	1	yes	characteristic
428	C₂³	C₂×#41×C₁₉	1	1	yes	characteristic
429	Q₈	—	2	4	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	4	no	—
433	Q₈	—	4	2	no	—
434	Q₈	C₁₉×#121	1	4	yes	—
435	D₄	—	2	8	no	—
436	D₄	—	2	4	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	4	no	—
439	D₄	—	2	2	no	—
440	D₄	C₁₉×#121	1	4	yes	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	8	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	8	2	no	—
457	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
458	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
463	C₈	—	2	1	no	—
464	C₈	—	2	4	no	—
465	C₈	—	2	1	no	—
466	C₈	—	4	4	no	—
467	C₈	C₁₉×#120	1	2	yes	—
468	C₈	C₁₉×#120	1	2	yes	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	1	no	—
472	C₂²	—	2	1	no	—
473	C₂²	—	2	1	no	—
474	C₂²	—	2	1	no	—
475	C₂²	—	2	1	no	—
476	C₂²	—	2	4	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	8	no	—
479	C₂²	—	4	2	no	—
480	C₂²	—	4	2	no	—
481	C₂²	C₁₉×#473	1	2	yes	complemented
482	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
483	C₂²	C₁₉×#525	1	2	yes	—
484	C₄	—	2	1	no	—
485	C₄	—	2	4	no	—
486	C₄	—	2	1	no	—
487	C₄	—	8	2	no	—
488	C₄	—	8	2	no	—
489	C₄	C₂×C₁₉×#120	1	1	yes	characteristic
490	C₄	C₂×C₁₉×#121	1	2	yes	—
491	C₄	C₁₉×#525	1	1	yes	characteristic
492	C₂	—	2	2	no	—
493	C₂	—	2	2	no	—
494	C₂	—	4	1	no	—
495	C₂	—	4	4	no	—
496	C₂	C₁₉×#2847	1	1	yes	characteristic
497	C₂	C₂×C₁₉×#473	1	1	yes	characteristic
498	C₂	C₁₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#473	C₂	semidirect
3. C₂×C₁₉×#467	C₂	semidirect
5. C₁₉×#1908	C₂	semidirect
6. C₁₉×#1901	C₂	semidirect
7. C₁₉×#1816	C₂	semidirect
8. C₁₉×#1810	C₂	semidirect
11. C₂²×Q₁₆×C₁₉	C₂²	semidirect
30. C₂×C₁₉×#108	C₂²	semidirect
31. C₂×C₁₉×#107	C₂²	semidirect
33. C₂×C₁₉×#103	C₂²	semidirect
34. C₂×C₁₉×#101	C₂²	semidirect
36. C₁₉×#343	C₂²	semidirect
37. C₁₉×#341	C₂²	semidirect
169. #32943	C₁₉	direct (N × H)
221. C₂×#473	C₂×C₁₉	semidirect
222. C₂×#467	C₂×C₁₉	semidirect
224. #1908	C₂×C₁₉	semidirect
225. #1901	C₂×C₁₉	semidirect
226. #1816	C₂×C₁₉	semidirect
227. #1810	C₂×C₁₉	semidirect
240. C₂²×C₁₉	#473	semidirect
253. C₂²×Q₁₆	C₂²×C₁₉	semidirect
272. C₂×#108	C₂²×C₁₉	semidirect
273. C₂×#107	C₂²×C₁₉	semidirect
275. C₂×#103	C₂²×C₁₉	semidirect
276. C₂×#101	C₂²×C₁₉	semidirect
278. #343	C₂²×C₁₉	semidirect
279. #341	C₂²×C₁₉	semidirect
347. C₁₉	#32943	direct (N × H)
481. C₂²	C₁₉×#473	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×#131	2
C₂×C₁₉×#473	2
C₂×C₁₉×#467	2
C₁₉×#3007	2
C₁₉×#1908	2
C₁₉×#1901	2
C₁₉×#1816	2
C₁₉×#1810	2
#32943	19

Subgroups — C19×#32943 #18038902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32943 #18038902