Subgroups — C₁₉×#19033 #18024992

Order 4864.

948 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3561	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1661	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1660	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1531	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1527	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1524	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×Q₁₆×C₁₉	—	2	1	no	—
11	C₂²×SD₁₆×C₁₉	—	2	1	no	—
12	C₁₉×#563	C₂²	1	2	yes	—
13	C₁₉×#562	C₂²	1	2	yes	—
14	C₁₉×#556	—	2	1	no	—
15	C₁₉×#551	—	2	2	no	—
16	D₄×Q₈×C₁₉	—	2	1	no	—
17	C₁₉×#548	—	2	1	no	—
18	C₁₉×#546	—	2	1	no	—
19	C₁₉×#543	—	2	1	no	—
20	C₁₉×#542	—	2	1	no	—
21	C₁₉×#542	—	2	2	no	—
22	C₁₉×#538	—	2	1	no	—
23	C₁₉×#536	—	2	1	no	—
24	C₁₉×#533	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#501	C₂²	1	2	yes	complemented
29	C₁₉×#501	C₂²	1	4	yes	complemented
30	C₁₉×#500	—	2	1	no	—
31	C₁₉×#498	—	2	1	no	—
32	C₁₉×#497	—	2	2	no	—
33	C₁₉×#497	C₂²	1	4	yes	—
34	C₁₉×#489	C₂²	1	2	yes	complemented
35	C₁₉×#484	—	2	1	no	—
36	C₁₉×#481	—	2	1	no	—
37	C₁₉×#475	—	2	1	no	—
38	C₁₉×#474	—	2	1	no	—
39	C₁₉×#432	C₂²	1	1	yes	characteristic
40	C₁₉×#428	—	2	2	no	—
41	C₄×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
42	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
43	C₁₉×#330	C₂²	1	2	yes	complemented
44	C₁₉×#330	C₂²	1	4	yes	complemented
45	C₁₉×#329	C₂²	1	4	yes	—
46	C₁₉×#329	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×Q₈×C₁₉	—	2	1	no	—
49	C₂²×Q₈×C₁₉	—	2	1	no	—
50	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
52	C₂×Q₁₆×C₁₉	—	2	4	no	—
53	C₂×Q₁₆×C₁₉	—	4	4	no	—
54	C₂×SD₁₆×C₁₉	—	2	4	no	—
55	C₂×SD₁₆×C₁₉	—	4	4	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂²×C₈×C₁₉	—	2	1	no	—
58	C₁₉×C₄⋊Q₈	—	2	1	no	—
59	C₁₉×C₄⋊Q₈	—	2	2	no	—
60	C₁₉×C₄⋊Q₈	—	2	1	no	—
61	C₁₉×C₄⋊Q₈	—	2	1	no	—
62	C₁₉×C₄⋊Q₈	—	2	1	no	—
63	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
65	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₉×#126	—	2	2	no	—
67	C₁₉×#126	—	2	2	no	—
68	C₁₉×#126	—	2	2	no	—
69	C₁₉×#126	—	2	1	no	—
70	C₁₉×#125	C₂³	1	1	yes	characteristic
71	C₁₉×#125	C₂³	1	2	yes	—
72	C₁₉×#124	—	2	1	no	—
73	C₁₉×#124	—	2	2	no	—
74	C₁₉×#124	—	2	2	no	—
75	C₁₉×#124	—	2	1	no	—
76	C₁₉×#124	—	2	1	no	—
77	C₁₉×#124	D₄	1	2	yes	—
78	C₁₉×#124	C₂³	1	1	yes	characteristic
79	C₁₉×#124	C₂³	1	2	yes	—
80	C₁₉×#123	—	2	2	no	—
81	C₁₉×#123	—	2	2	no	—
82	C₁₉×#123	—	2	1	no	—
83	C₁₉×#123	—	2	2	no	—
84	C₁₉×#123	—	2	2	no	—
85	C₁₉×C₂²⋊Q₈	—	2	2	no	—
86	C₁₉×C₂²⋊Q₈	—	2	2	no	—
87	C₁₉×C₂²⋊Q₈	—	2	1	no	—
88	C₁₉×C₂²⋊Q₈	—	2	2	no	—
89	C₁₉×C₂²⋊Q₈	—	2	2	no	—
90	C₁₉×C₂²⋊Q₈	—	2	2	no	—
91	C₁₉×C₂²⋊Q₈	—	2	1	no	—
92	C₁₉×C₂²⋊Q₈	—	2	1	no	—
93	C₁₉×C₂²⋊Q₈	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	2	no	—
95	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
96	C₁₉×#121	—	2	1	no	—
97	C₁₉×#121	—	2	2	no	—
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	D₄	1	1	yes	characteristic
100	C₁₉×#120	—	2	2	no	—
101	C₄×Q₈×C₁₉	—	2	1	no	—
102	C₄×Q₈×C₁₉	—	2	1	no	—
103	C₄×Q₈×C₁₉	—	2	1	no	—
104	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
105	C₄×D₄×C₁₉	—	2	2	no	—
106	C₄×D₄×C₁₉	—	2	1	no	—
107	C₄×D₄×C₁₉	—	2	2	no	—
108	C₄×D₄×C₁₉	—	2	1	no	—
109	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
110	C₁₉×#117	—	2	2	no	—
111	C₁₉×#117	—	2	1	no	—
112	C₁₉×#117	D₄	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
114	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
115	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
116	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
117	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
118	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
119	C₁₉×#107	—	2	4	no	—
120	C₁₉×#107	—	2	2	no	—
121	C₁₉×#106	—	2	4	no	—
122	C₁₉×#106	—	2	2	no	—
123	C₁₉×C₄⋊C₈	—	2	1	no	—
124	C₁₉×#103	—	2	2	no	—
125	C₁₉×#102	—	2	2	no	—
126	C₁₉×C₂²⋊C₈	—	2	1	no	—
127	C₁₉×#97	—	2	1	no	—
128	C₁₉×#97	C₂³	1	2	yes	—
129	C₁₉×#97	C₂³	1	2	yes	—
130	C₁₉×#97	C₂³	1	2	yes	—
131	C₄×C₈×C₁₉	—	2	1	no	—
132	C₂⁴×C₁₉	—	2	1	no	—
133	#41×C₁₉	—	8	2	no	—
134	C₂×Q₈×C₁₉	—	2	2	no	—
135	C₂×Q₈×C₁₉	—	2	1	no	—
136	C₂×Q₈×C₁₉	—	2	1	no	—
137	C₂×Q₈×C₁₉	—	2	1	no	—
138	C₂×Q₈×C₁₉	—	2	2	no	—
139	C₂×Q₈×C₁₉	—	4	2	no	—
140	C₂×Q₈×C₁₉	—	4	2	no	—
141	C₂×Q₈×C₁₉	—	4	2	no	—
142	C₂×Q₈×C₁₉	—	4	1	no	—
143	C₂×Q₈×C₁₉	—	8	2	no	—
144	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
146	C₂×D₄×C₁₉	—	2	1	no	—
147	C₂×D₄×C₁₉	—	2	2	no	—
148	C₂×D₄×C₁₉	—	2	2	no	—
149	C₂×D₄×C₁₉	—	2	1	no	—
150	C₂×D₄×C₁₉	—	4	2	no	—
151	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₁₉	—	2	2	no	—
154	C₂²×C₄×C₁₉	—	2	2	no	—
155	C₂²×C₄×C₁₉	—	2	2	no	—
156	C₂²×C₄×C₁₉	—	2	1	no	—
157	C₂²×C₄×C₁₉	—	2	1	no	—
158	C₂²×C₄×C₁₉	—	4	1	no	—
159	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
162	Q₁₆×C₁₉	—	4	8	no	—
163	SD₁₆×C₁₉	—	4	8	no	—
164	M₁₆×C₁₉	—	2	4	no	—
165	C₂×C₈×C₁₉	—	2	4	no	—
166	C₂×C₈×C₁₉	—	2	2	no	—
167	C₂×C₈×C₁₉	—	2	2	no	—
168	C₂×C₈×C₁₉	—	2	2	no	—
169	C₄⋊C₄×C₁₉	—	2	2	no	—
170	C₄⋊C₄×C₁₉	—	2	2	no	—
171	C₄⋊C₄×C₁₉	—	2	2	no	—
172	C₄⋊C₄×C₁₉	—	2	2	no	—
173	C₄⋊C₄×C₁₉	—	2	1	no	—
174	C₄⋊C₄×C₁₉	—	2	1	no	—
175	C₄⋊C₄×C₁₉	—	2	1	no	—
176	C₄⋊C₄×C₁₉	—	2	1	no	—
177	C₄⋊C₄×C₁₉	—	2	1	no	—
178	C₄⋊C₄×C₁₉	—	2	1	no	—
179	C₄⋊C₄×C₁₉	—	2	2	no	—
180	C₄⋊C₄×C₁₉	—	2	2	no	—
181	C₄⋊C₄×C₁₉	—	2	2	no	—
182	C₄⋊C₄×C₁₉	—	2	2	no	—
183	C₄⋊C₄×C₁₉	—	4	1	no	—
184	C₄⋊C₄×C₁₉	—	4	1	no	—
185	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
186	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
187	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₁₉	—	2	2	no	—
190	C₂²⋊C₄×C₁₉	—	2	2	no	—
191	C₂²⋊C₄×C₁₉	—	2	2	no	—
192	C₂²⋊C₄×C₁₉	—	2	2	no	—
193	C₂²⋊C₄×C₁₉	—	2	2	no	—
194	C₂²⋊C₄×C₁₉	—	2	1	no	—
195	C₂²⋊C₄×C₁₉	—	2	2	no	—
196	C₂²⋊C₄×C₁₉	—	2	2	no	—
197	C₂²⋊C₄×C₁₉	—	2	2	no	—
198	C₂²⋊C₄×C₁₉	—	2	1	no	—
199	C₂²⋊C₄×C₁₉	—	2	1	no	—
200	C₂²⋊C₄×C₁₉	—	2	2	no	—
201	C₂²⋊C₄×C₁₉	—	2	2	no	—
202	C₂²⋊C₄×C₁₉	—	2	1	no	—
203	C₂²⋊C₄×C₁₉	—	2	1	no	—
204	C₄²×C₁₉	—	2	2	no	—
205	C₄²×C₁₉	—	2	2	no	—
206	C₄²×C₁₉	—	2	1	no	—
207	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
211	#19033	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
212	C₂³×C₁₉	—	2	2	no	—
213	C₂³×C₁₉	—	2	1	no	—
214	C₂³×C₁₉	—	4	2	no	—
215	C₂³×C₁₉	—	8	1	no	—
216	C₂³×C₁₉	—	8	1	no	—
217	C₂³×C₁₉	#120	1	1	yes	characteristic
218	Q₈×C₁₉	—	4	2	no	—
219	Q₈×C₁₉	—	4	1	no	—
220	Q₈×C₁₉	—	4	2	no	—
221	Q₈×C₁₉	—	4	2	no	—
222	Q₈×C₁₉	—	4	2	no	—
223	Q₈×C₁₉	—	4	2	no	—
224	Q₈×C₁₉	—	8	1	no	—
225	Q₈×C₁₉	—	8	2	no	—
226	Q₈×C₁₉	—	8	2	no	—
227	D₄×C₁₉	—	4	2	no	—
228	D₄×C₁₉	—	4	1	no	—
229	D₄×C₁₉	—	4	2	no	—
230	D₄×C₁₉	—	4	2	no	—
231	D₄×C₁₉	—	8	2	no	—
232	D₄×C₁₉	—	8	2	no	—
233	C₂×C₄×C₁₉	—	2	2	no	—
234	C₂×C₄×C₁₉	—	2	2	no	—
235	C₂×C₄×C₁₉	—	2	1	no	—
236	C₂×C₄×C₁₉	—	2	2	no	—
237	C₂×C₄×C₁₉	—	2	1	no	—
238	C₂×C₄×C₁₉	—	2	2	no	—
239	C₂×C₄×C₁₉	—	2	2	no	—
240	C₂×C₄×C₁₉	—	2	1	no	—
241	C₂×C₄×C₁₉	—	4	1	no	—
242	C₂×C₄×C₁₉	—	4	2	no	—
243	C₂×C₄×C₁₉	—	4	2	no	—
244	C₂×C₄×C₁₉	—	8	1	no	—
245	C₂×C₄×C₁₉	—	8	2	no	—
246	C₂×C₄×C₁₉	—	8	2	no	—
247	C₂×C₄×C₁₉	—	8	2	no	—
248	C₂×C₄×C₁₉	—	8	2	no	—
249	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
250	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
251	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
253	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
255	C₈×C₁₉	—	2	4	no	—
256	C₈×C₁₉	—	2	4	no	—
257	C₈×C₁₉	—	4	2	no	—
258	#3561	C₂×C₁₉	1	1	yes	characteristic
259	#3239	C₂×C₁₉	1	1	yes	characteristic, complemented
260	#3165	C₂×C₁₉	1	1	yes	characteristic, complemented
261	C₂×#497	C₂×C₁₉	1	1	yes	characteristic, complemented
262	#1661	C₂×C₁₉	1	4	yes	complemented
263	#1660	C₂×C₁₉	1	4	yes	complemented
264	#1531	C₂×C₁₉	1	1	yes	characteristic, complemented
265	#1527	C₂×C₁₉	1	1	yes	characteristic, complemented
266	#1524	C₂×C₁₉	1	1	yes	characteristic, complemented
267	C₂²×C₁₉	—	2	1	no	—
268	C₂²×C₁₉	—	2	1	no	—
269	C₂²×C₁₉	—	4	1	no	—
270	C₂²×C₁₉	—	4	2	no	—
271	C₂²×C₁₉	—	4	1	no	—
272	C₂²×C₁₉	—	4	2	no	—
273	C₂²×C₁₉	—	4	2	no	—
274	C₂²×C₁₉	—	4	1	no	—
275	C₂²×C₁₉	—	16	2	no	—
276	C₂²×C₁₉	#456	1	2	yes	—
277	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
278	C₄×C₁₉	—	2	1	no	—
279	C₄×C₁₉	—	2	1	no	—
280	C₄×C₁₉	—	2	1	no	—
281	C₄×C₁₉	—	2	1	no	—
282	C₄×C₁₉	—	2	1	no	—
283	C₄×C₁₉	—	4	1	no	—
284	C₄×C₁₉	—	4	2	no	—
285	C₄×C₁₉	—	4	2	no	—
286	C₄×C₁₉	—	4	1	no	—
287	C₄×C₁₉	—	4	1	no	—
288	C₄×C₁₉	—	4	2	no	—
289	C₄×C₁₉	—	8	2	no	—
290	C₄×C₁₉	#453	1	2	yes	—
291	C₂²×Q₁₆	—	2	1	no	—
292	C₂²×SD₁₆	—	2	1	no	—
293	#563	C₂²×C₁₉	1	2	yes	—
294	#562	C₂²×C₁₉	1	2	yes	—
295	#556	—	2	1	no	—
296	#551	—	2	2	no	—
297	D₄×Q₈	—	2	1	no	—
298	#548	—	2	1	no	—
299	#546	—	2	1	no	—
300	#543	—	2	1	no	—
301	#542	—	2	1	no	—
302	#542	—	2	2	no	—
303	#538	—	2	1	no	—
304	#536	—	2	1	no	—
305	#533	C₂²×C₁₉	1	1	yes	characteristic
306	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
307	#529	C₂²×C₁₉	1	1	yes	characteristic
308	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
309	#501	C₂²×C₁₉	1	4	yes	complemented
310	#501	C₂²×C₁₉	1	2	yes	complemented
311	#500	—	2	1	no	—
312	#498	—	2	1	no	—
313	#497	—	2	2	no	—
314	#497	C₂²×C₁₉	1	4	yes	—
315	#489	C₂²×C₁₉	1	2	yes	complemented
316	#484	—	2	1	no	—
317	#481	—	2	1	no	—
318	#475	—	2	1	no	—
319	#474	—	2	1	no	—
320	#432	C₂²×C₁₉	1	1	yes	characteristic
321	#428	—	2	2	no	—
322	C₄×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
323	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
324	#330	C₂²×C₁₉	1	2	yes	complemented
325	#330	C₂²×C₁₉	1	4	yes	complemented
326	#329	C₂²×C₁₉	1	4	yes	—
327	#329	C₂²×C₁₉	1	2	yes	complemented
328	C₂×C₁₉	—	2	2	no	—
329	C₂×C₁₉	—	8	1	no	—
330	C₂×C₁₉	—	8	2	no	—
331	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
332	C₂×C₁₉	C₂×#456	1	1	yes	characteristic
333	C₂×C₁₉	#3022	1	1	yes	characteristic
334	C₂×#41	—	2	1	no	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×Q₈	—	2	1	no	—
337	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
338	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
339	C₂×Q₁₆	—	2	4	no	—
340	C₂×Q₁₆	—	4	4	no	—
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	4	4	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂²×C₈	—	2	1	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	2	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	—	2	1	no	—
350	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
351	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
352	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
353	#126	—	2	2	no	—
354	#126	—	2	2	no	—
355	#126	—	2	2	no	—
356	#126	—	2	1	no	—
357	#125	C₂³×C₁₉	1	1	yes	characteristic
358	#125	C₂³×C₁₉	1	2	yes	—
359	#124	—	2	1	no	—
360	#124	—	2	2	no	—
361	#124	—	2	2	no	—
362	#124	—	2	1	no	—
363	#124	—	2	1	no	—
364	#124	D₄×C₁₉	1	2	yes	—
365	#124	C₂³×C₁₉	1	2	yes	—
366	#124	C₂³×C₁₉	1	1	yes	characteristic
367	#123	—	2	2	no	—
368	#123	—	2	2	no	—
369	#123	—	2	1	no	—
370	#123	—	2	2	no	—
371	#123	—	2	2	no	—
372	C₂²⋊Q₈	—	2	2	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	1	no	—
375	C₂²⋊Q₈	—	2	2	no	—
376	C₂²⋊Q₈	—	2	2	no	—
377	C₂²⋊Q₈	—	2	2	no	—
378	C₂²⋊Q₈	—	2	1	no	—
379	C₂²⋊Q₈	—	2	1	no	—
380	C₂²⋊Q₈	—	2	2	no	—
381	C₂²⋊Q₈	—	2	2	no	—
382	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
383	#121	—	2	1	no	—
384	#121	—	2	2	no	—
385	#121	—	2	2	no	—
386	#121	D₄×C₁₉	1	1	yes	characteristic
387	#120	—	2	2	no	—
388	C₄×Q₈	—	2	1	no	—
389	C₄×Q₈	—	2	1	no	—
390	C₄×Q₈	—	2	1	no	—
391	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
392	C₄×D₄	—	2	2	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	2	no	—
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
397	#117	—	2	2	no	—
398	#117	—	2	1	no	—
399	#117	D₄×C₁₉	1	2	yes	—
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	2	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
406	#107	—	2	4	no	—
407	#107	—	2	2	no	—
408	#106	—	2	4	no	—
409	#106	—	2	2	no	—
410	C₄⋊C₈	—	2	1	no	—
411	#103	—	2	2	no	—
412	#102	—	2	2	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	#97	—	2	1	no	—
415	#97	C₂³×C₁₉	1	2	yes	—
416	#97	C₂³×C₁₉	1	2	yes	—
417	#97	C₂³×C₁₉	1	2	yes	—
418	C₄×C₈	—	2	1	no	—
419	C₁₉	#19033	1	1	yes	characteristic, direct product factor, Sylow
420	C₂⁴	—	2	1	no	—
421	#41	—	8	2	no	—
422	C₂×Q₈	—	2	2	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	2	no	—
427	C₂×Q₈	—	4	2	no	—
428	C₂×Q₈	—	4	2	no	—
429	C₂×Q₈	—	4	2	no	—
430	C₂×Q₈	—	4	1	no	—
431	C₂×Q₈	—	8	2	no	—
432	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
433	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	4	2	no	—
439	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
440	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	4	1	no	—
447	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
448	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
449	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
450	Q₁₆	—	4	8	no	—
451	SD₁₆	—	4	8	no	—
452	M₁₆	—	2	4	no	—
453	C₂×C₈	—	2	4	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₄⋊C₄	—	4	1	no	—
473	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
474	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
475	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
476	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	2	1	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	1	no	—
495	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
496	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
498	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
499	C₂³	—	2	2	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	8	1	no	—
503	C₂³	—	8	1	no	—
504	C₂³	C₁₉×#120	1	1	yes	characteristic
505	Q₈	—	4	2	no	—
506	Q₈	—	4	1	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	2	no	—
511	Q₈	—	8	1	no	—
512	Q₈	—	8	2	no	—
513	Q₈	—	8	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	8	2	no	—
519	D₄	—	8	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	2	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	8	1	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	2	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	—	8	2	no	—
536	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
537	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
538	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
539	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
540	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
542	C₈	—	2	4	no	—
543	C₈	—	2	4	no	—
544	C₈	—	4	2	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	16	2	no	—
554	C₂²	C₁₉×#456	1	2	yes	—
555	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	2	no	—
567	C₄	—	8	2	no	—
568	C₄	C₁₉×#453	1	2	yes	—
569	C₂	—	2	2	no	—
570	C₂	—	8	2	no	—
571	C₂	—	8	1	no	—
572	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
573	C₂	C₂×C₁₉×#456	1	1	yes	characteristic
574	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3561	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#3239	C₂	semidirect
3. C₁₉×#3165	C₂	semidirect
4. C₂×C₁₉×#497	C₂	semidirect
5. C₁₉×#1661	C₂	semidirect
6. C₁₉×#1660	C₂	semidirect
7. C₁₉×#1531	C₂	semidirect
8. C₁₉×#1527	C₂	semidirect
9. C₁₉×#1524	C₂	semidirect
28. C₁₉×#501	C₂²	semidirect
29. C₁₉×#501	C₂²	semidirect
34. C₁₉×#489	C₂²	semidirect
43. C₁₉×#330	C₂²	semidirect
44. C₁₉×#330	C₂²	semidirect
46. C₁₉×#329	C₂²	semidirect
211. #19033	C₁₉	direct (N × H)
259. #3239	C₂×C₁₉	semidirect
260. #3165	C₂×C₁₉	semidirect
261. C₂×#497	C₂×C₁₉	semidirect
262. #1661	C₂×C₁₉	semidirect
263. #1660	C₂×C₁₉	semidirect
264. #1531	C₂×C₁₉	semidirect
265. #1527	C₂×C₁₉	semidirect
266. #1524	C₂×C₁₉	semidirect
309. #501	C₂²×C₁₉	semidirect
310. #501	C₂²×C₁₉	semidirect
315. #489	C₂²×C₁₉	semidirect
324. #330	C₂²×C₁₉	semidirect
325. #330	C₂²×C₁₉	semidirect
327. #329	C₂²×C₁₉	semidirect
419. C₁₉	#19033	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×#3561	2
C₁₉×#3239	2
C₁₉×#3165	2
C₂×C₁₉×#497	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1531	2
C₁₉×#1527	2
C₁₉×#1524	2
#19033	19

Subgroups — C19×#19033 #18024992

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19033 #18024992