Subgroups — C₁₉×#19051 #18025010

Order 4864.

950 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3545	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#3238	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1661	C₂	1	4	yes	maximal, complemented
5	C₁₉×#1660	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1659	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1533	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1532	C₂	1	2	yes	maximal, complemented
9	C₂²×Q₁₆×C₁₉	—	2	1	no	—
10	C₂²×SD₁₆×C₁₉	—	2	1	no	—
11	C₁₉×#563	C₂²	1	1	yes	characteristic
12	C₁₉×#562	C₂²	1	2	yes	—
13	C₁₉×H(3,𝔽₄)	C₂²	1	1	yes	characteristic
14	C₁₉×#555	—	2	1	no	—
15	C₁₉×#551	—	2	1	no	—
16	C₁₉×#551	—	2	2	no	—
17	C₁₉×#546	—	2	2	no	—
18	C₁₉×#542	—	2	2	no	—
19	C₁₉×#538	—	2	2	no	—
20	C₁₉×#536	—	2	1	no	—
21	C₁₉×#534	—	2	1	no	—
22	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#529	C₂²	1	2	yes	—
24	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
25	C₁₉×#501	C₂²	1	4	yes	complemented
26	C₁₉×#497	—	2	1	no	—
27	C₁₉×#497	—	2	1	no	—
28	C₁₉×#497	C₂²	1	2	yes	—
29	C₁₉×#497	C₂²	1	2	yes	complemented
30	C₁₉×#489	C₂²	1	4	yes	complemented
31	C₁₉×#483	—	2	2	no	—
32	C₁₉×#480	—	2	2	no	—
33	C₁₉×#477	—	2	2	no	—
34	C₁₉×#476	—	2	2	no	—
35	C₁₉×#432	C₂²	1	2	yes	complemented
36	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
37	C₁₉×#330	C₂²	1	4	yes	complemented
38	C₁₉×#329	C₂²	1	2	yes	—
39	C₁₉×#329	C₂²	1	4	yes	complemented
40	C₁₉×#329	C₂²	1	2	yes	complemented
41	C₂×#41×C₁₉	—	2	1	no	—
42	C₂²×Q₈×C₁₉	—	2	1	no	—
43	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	1	no	—
45	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂×Q₁₆×C₁₉	—	2	2	no	—
47	C₂×Q₁₆×C₁₉	—	2	2	no	—
48	C₂×Q₁₆×C₁₉	—	4	4	no	—
49	C₂×SD₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	4	4	no	—
52	C₂²×C₈×C₁₉	—	2	1	no	—
53	C₁₉×C₄⋊Q₈	—	2	1	no	—
54	C₁₉×C₄⋊Q₈	—	2	1	no	—
55	C₁₉×C₄⋊Q₈	—	2	2	no	—
56	C₁₉×C₄⋊Q₈	—	2	1	no	—
57	C₁₉×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₁₉×#126	—	2	2	no	—
59	C₁₉×#126	—	2	2	no	—
60	C₁₉×#126	—	2	2	no	—
61	C₁₉×#125	C₂³	1	2	yes	—
62	C₁₉×#124	—	2	1	no	—
63	C₁₉×#124	—	2	2	no	—
64	C₁₉×#124	—	2	1	no	—
65	C₁₉×#124	—	2	2	no	—
66	C₁₉×#124	—	2	2	no	—
67	C₁₉×#124	D₄	1	1	yes	characteristic
68	C₁₉×#124	D₄	1	1	yes	characteristic
69	C₁₉×#124	C₂³	1	2	yes	—
70	C₁₉×#124	C₂³	1	1	yes	characteristic
71	C₁₉×#124	C₂³	1	1	yes	characteristic
72	C₁₉×#123	—	2	1	no	—
73	C₁₉×#123	—	2	2	no	—
74	C₁₉×#123	—	2	2	no	—
75	C₁₉×#123	—	2	1	no	—
76	C₁₉×#123	—	2	2	no	—
77	C₁₉×#123	—	2	2	no	—
78	C₁₉×#123	—	2	2	no	—
79	C₁₉×C₂²⋊Q₈	—	2	2	no	—
80	C₁₉×C₂²⋊Q₈	—	2	2	no	—
81	C₁₉×C₂²⋊Q₈	—	2	2	no	—
82	C₁₉×C₂²⋊Q₈	—	2	2	no	—
83	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
84	C₁₉×#121	—	2	2	no	—
85	C₁₉×#121	—	2	2	no	—
86	C₁₉×#121	—	2	2	no	—
87	C₁₉×#121	—	2	2	no	—
88	C₁₉×#121	D₄	1	2	yes	—
89	C₁₉×#120	—	2	1	no	—
90	C₁₉×#120	—	2	2	no	—
91	C₁₉×#120	—	2	1	no	—
92	C₁₉×#120	—	2	2	no	—
93	C₄×Q₈×C₁₉	D₄	1	2	yes	—
94	C₄×D₄×C₁₉	—	2	2	no	—
95	C₄×D₄×C₁₉	—	2	2	no	—
96	C₄×D₄×C₁₉	—	2	2	no	—
97	C₄×D₄×C₁₉	D₄	1	2	yes	—
98	C₁₉×#117	—	2	1	no	—
99	C₁₉×#117	—	2	2	no	—
100	C₁₉×#117	—	2	2	no	—
101	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
102	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
104	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
105	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
106	C₁₉×#107	—	2	4	no	—
107	C₁₉×#106	—	2	4	no	—
108	C₁₉×C₄⋊C₈	—	2	2	no	—
109	C₁₉×#103	—	2	4	no	—
110	C₁₉×#102	—	2	4	no	—
111	C₁₉×C₂²⋊C₈	—	2	2	no	—
112	C₁₉×#97	—	2	1	no	—
113	C₁₉×#97	C₂³	1	2	yes	—
114	C₁₉×#97	C₂³	1	4	yes	—
115	C₂⁴×C₁₉	—	2	1	no	—
116	C₂⁴×C₁₉	—	2	1	no	—
117	#41×C₁₉	—	8	2	no	—
118	C₂×Q₈×C₁₉	—	2	1	no	—
119	C₂×Q₈×C₁₉	—	2	1	no	—
120	C₂×Q₈×C₁₉	—	2	2	no	—
121	C₂×Q₈×C₁₉	—	4	2	no	—
122	C₂×Q₈×C₁₉	—	4	2	no	—
123	C₂×Q₈×C₁₉	—	4	2	no	—
124	C₂×Q₈×C₁₉	—	4	1	no	—
125	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
126	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₁₉	—	2	2	no	—
129	C₂×D₄×C₁₉	—	2	2	no	—
130	C₂×D₄×C₁₉	—	2	2	no	—
131	C₂×D₄×C₁₉	—	2	1	no	—
132	C₂×D₄×C₁₉	—	2	2	no	—
133	C₂×D₄×C₁₉	—	2	1	no	—
134	C₂×D₄×C₁₉	—	4	2	no	—
135	C₂×D₄×C₁₉	—	8	2	no	—
136	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
138	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₉	—	2	1	no	—
140	C₂²×C₄×C₁₉	—	2	2	no	—
141	C₂²×C₄×C₁₉	—	2	2	no	—
142	C₂²×C₄×C₁₉	—	2	1	no	—
143	C₂²×C₄×C₁₉	—	2	2	no	—
144	C₂²×C₄×C₁₉	—	4	1	no	—
145	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	Q₁₆×C₁₉	—	4	4	no	—
148	Q₁₆×C₁₉	—	4	4	no	—
149	SD₁₆×C₁₉	—	4	4	no	—
150	SD₁₆×C₁₉	—	4	4	no	—
151	C₂×C₈×C₁₉	—	2	4	no	—
152	C₂×C₈×C₁₉	—	2	2	no	—
153	C₂×C₈×C₁₉	—	2	4	no	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	2	2	no	—
161	C₄⋊C₄×C₁₉	—	2	4	no	—
162	C₄⋊C₄×C₁₉	—	4	2	no	—
163	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
165	C₂²⋊C₄×C₁₉	—	2	2	no	—
166	C₂²⋊C₄×C₁₉	—	2	1	no	—
167	C₂²⋊C₄×C₁₉	—	2	1	no	—
168	C₂²⋊C₄×C₁₉	—	2	2	no	—
169	C₂²⋊C₄×C₁₉	—	2	2	no	—
170	C₂²⋊C₄×C₁₉	—	2	2	no	—
171	C₂²⋊C₄×C₁₉	—	2	2	no	—
172	C₂²⋊C₄×C₁₉	—	2	2	no	—
173	C₂²⋊C₄×C₁₉	—	2	2	no	—
174	C₂²⋊C₄×C₁₉	—	2	2	no	—
175	C₂²⋊C₄×C₁₉	—	2	2	no	—
176	C₂²⋊C₄×C₁₉	—	2	2	no	—
177	C₂²⋊C₄×C₁₉	—	2	2	no	—
178	C₂²⋊C₄×C₁₉	—	2	2	no	—
179	C₂²⋊C₄×C₁₉	—	2	2	no	—
180	C₄²×C₁₉	—	2	1	no	—
181	C₄²×C₁₉	—	2	1	no	—
182	C₄²×C₁₉	—	2	2	no	—
183	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₁₉	C₂×D₄	1	2	yes	—
185	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
186	#19051	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂³×C₁₉	—	2	1	no	—
188	C₂³×C₁₉	—	2	2	no	—
189	C₂³×C₁₉	—	2	1	no	—
190	C₂³×C₁₉	—	4	2	no	—
191	C₂³×C₁₉	—	8	2	no	—
192	C₂³×C₁₉	—	8	1	no	—
193	C₂³×C₁₉	—	8	2	no	—
194	C₂³×C₁₉	#120	1	1	yes	characteristic
195	Q₈×C₁₉	—	4	1	no	—
196	Q₈×C₁₉	—	4	1	no	—
197	Q₈×C₁₉	—	4	2	no	—
198	Q₈×C₁₉	—	4	2	no	—
199	Q₈×C₁₉	—	4	2	no	—
200	Q₈×C₁₉	—	8	1	no	—
201	Q₈×C₁₉	—	8	2	no	—
202	Q₈×C₁₉	—	8	1	no	—
203	D₄×C₁₉	—	4	1	no	—
204	D₄×C₁₉	—	4	1	no	—
205	D₄×C₁₉	—	4	2	no	—
206	D₄×C₁₉	—	4	4	no	—
207	D₄×C₁₉	—	8	1	no	—
208	D₄×C₁₉	—	8	2	no	—
209	D₄×C₁₉	—	8	2	no	—
210	D₄×C₁₉	—	8	2	no	—
211	D₄×C₁₉	—	8	1	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	2	no	—
214	C₂×C₄×C₁₉	—	2	1	no	—
215	C₂×C₄×C₁₉	—	2	2	no	—
216	C₂×C₄×C₁₉	—	2	2	no	—
217	C₂×C₄×C₁₉	—	2	1	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	8	2	no	—
222	C₂×C₄×C₁₉	—	8	2	no	—
223	C₂×C₄×C₁₉	—	8	1	no	—
224	C₂×C₄×C₁₉	—	8	2	no	—
225	C₂×C₄×C₁₉	—	8	2	no	—
226	C₂×C₄×C₁₉	#120	1	2	yes	—
227	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
230	C₈×C₁₉	—	2	4	no	—
231	C₈×C₁₉	—	4	4	no	—
232	#3545	C₂×C₁₉	1	1	yes	characteristic
233	#3238	C₂×C₁₉	1	2	yes	complemented
234	C₂×#497	C₂×C₁₉	1	1	yes	characteristic, complemented
235	#1661	C₂×C₁₉	1	4	yes	complemented
236	#1660	C₂×C₁₉	1	2	yes	complemented
237	#1659	C₂×C₁₉	1	2	yes	complemented
238	#1533	C₂×C₁₉	1	1	yes	characteristic, complemented
239	#1532	C₂×C₁₉	1	2	yes	complemented
240	C₂²×C₁₉	—	2	2	no	—
241	C₂²×C₁₉	—	4	2	no	—
242	C₂²×C₁₉	—	4	1	no	—
243	C₂²×C₁₉	—	4	1	no	—
244	C₂²×C₁₉	—	4	2	no	—
245	C₂²×C₁₉	—	4	2	no	—
246	C₂²×C₁₉	—	4	2	no	—
247	C₂²×C₁₉	—	4	2	no	—
248	C₂²×C₁₉	—	16	2	no	—
249	C₂²×C₁₉	—	16	2	no	—
250	C₂²×C₁₉	#453	1	2	yes	—
251	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
252	C₄×C₁₉	—	2	1	no	—
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	2	2	no	—
256	C₄×C₁₉	—	4	1	no	—
257	C₄×C₁₉	—	4	1	no	—
258	C₄×C₁₉	—	4	2	no	—
259	C₄×C₁₉	—	4	2	no	—
260	C₄×C₁₉	—	4	2	no	—
261	C₄×C₁₉	—	8	2	no	—
262	C₂²×Q₁₆	—	2	1	no	—
263	C₂²×SD₁₆	—	2	1	no	—
264	#563	C₂²×C₁₉	1	1	yes	characteristic
265	#562	C₂²×C₁₉	1	2	yes	—
266	H(3,𝔽₄)	C₂²×C₁₉	1	1	yes	characteristic
267	#555	—	2	1	no	—
268	#551	—	2	1	no	—
269	#551	—	2	2	no	—
270	#546	—	2	2	no	—
271	#542	—	2	2	no	—
272	#538	—	2	2	no	—
273	#536	—	2	1	no	—
274	#534	—	2	1	no	—
275	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
276	#529	C₂²×C₁₉	1	2	yes	—
277	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
278	#501	C₂²×C₁₉	1	4	yes	complemented
279	#497	—	2	1	no	—
280	#497	—	2	1	no	—
281	#497	C₂²×C₁₉	1	2	yes	—
282	#497	C₂²×C₁₉	1	2	yes	complemented
283	#489	C₂²×C₁₉	1	4	yes	complemented
284	#483	—	2	2	no	—
285	#480	—	2	2	no	—
286	#477	—	2	2	no	—
287	#476	—	2	2	no	—
288	#432	C₂²×C₁₉	1	2	yes	complemented
289	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic, complemented
290	#330	C₂²×C₁₉	1	4	yes	complemented
291	#329	C₂²×C₁₉	1	2	yes	—
292	#329	C₂²×C₁₉	1	4	yes	complemented
293	#329	C₂²×C₁₉	1	2	yes	complemented
294	C₂×C₁₉	—	2	2	no	—
295	C₂×C₁₉	—	8	2	no	—
296	C₂×C₁₉	—	8	1	no	—
297	C₂×C₁₉	—	8	1	no	—
298	C₂×C₁₉	C₂×#453	1	1	yes	characteristic
299	C₂×C₁₉	#3022	1	2	yes	—
300	C₂×#41	—	2	1	no	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
303	C₂²×D₄	—	2	1	no	—
304	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
305	C₂×Q₁₆	—	2	2	no	—
306	C₂×Q₁₆	—	2	2	no	—
307	C₂×Q₁₆	—	4	4	no	—
308	C₂×SD₁₆	—	2	2	no	—
309	C₂×SD₁₆	—	2	2	no	—
310	C₂×SD₁₆	—	4	4	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	—	2	2	no	—
315	C₄⋊Q₈	—	2	1	no	—
316	C₄⋊Q₈	C₂³×C₁₉	1	2	yes	—
317	#126	—	2	2	no	—
318	#126	—	2	2	no	—
319	#126	—	2	2	no	—
320	#125	C₂³×C₁₉	1	2	yes	—
321	#124	—	2	1	no	—
322	#124	—	2	2	no	—
323	#124	—	2	1	no	—
324	#124	—	2	2	no	—
325	#124	—	2	2	no	—
326	#124	D₄×C₁₉	1	1	yes	characteristic
327	#124	D₄×C₁₉	1	1	yes	characteristic
328	#124	C₂³×C₁₉	1	1	yes	characteristic
329	#124	C₂³×C₁₉	1	1	yes	characteristic
330	#124	C₂³×C₁₉	1	2	yes	—
331	#123	—	2	1	no	—
332	#123	—	2	2	no	—
333	#123	—	2	2	no	—
334	#123	—	2	1	no	—
335	#123	—	2	2	no	—
336	#123	—	2	2	no	—
337	#123	—	2	2	no	—
338	C₂²⋊Q₈	—	2	2	no	—
339	C₂²⋊Q₈	—	2	2	no	—
340	C₂²⋊Q₈	—	2	2	no	—
341	C₂²⋊Q₈	—	2	2	no	—
342	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
343	#121	—	2	2	no	—
344	#121	—	2	2	no	—
345	#121	—	2	2	no	—
346	#121	—	2	2	no	—
347	#121	D₄×C₁₉	1	2	yes	—
348	#120	—	2	1	no	—
349	#120	—	2	2	no	—
350	#120	—	2	1	no	—
351	#120	—	2	2	no	—
352	C₄×Q₈	D₄×C₁₉	1	2	yes	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	D₄×C₁₉	1	2	yes	—
357	#117	—	2	1	no	—
358	#117	—	2	2	no	—
359	#117	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	2	no	—
361	C₂×C₂²⋊C₄	—	2	1	no	—
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	C₂×C₂²⋊C₄	—	2	2	no	—
364	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
365	#107	—	2	4	no	—
366	#106	—	2	4	no	—
367	C₄⋊C₈	—	2	2	no	—
368	#103	—	2	4	no	—
369	#102	—	2	4	no	—
370	C₂²⋊C₈	—	2	2	no	—
371	#97	—	2	1	no	—
372	#97	C₂³×C₁₉	1	4	yes	—
373	#97	C₂³×C₁₉	1	2	yes	—
374	C₁₉	#19051	1	1	yes	characteristic, direct product factor, Sylow
375	C₂⁴	—	2	1	no	—
376	C₂⁴	—	2	1	no	—
377	#41	—	8	2	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	4	2	no	—
382	C₂×Q₈	—	4	2	no	—
383	C₂×Q₈	—	4	2	no	—
384	C₂×Q₈	—	4	1	no	—
385	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
386	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
387	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	—	8	2	no	—
396	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
397	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
398	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	4	1	no	—
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
407	Q₁₆	—	4	4	no	—
408	Q₁₆	—	4	4	no	—
409	SD₁₆	—	4	4	no	—
410	SD₁₆	—	4	4	no	—
411	C₂×C₈	—	2	4	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	4	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
424	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
425	C₂²⋊C₄	—	2	2	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	2	2	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	2	no	—
436	C₂²⋊C₄	—	2	2	no	—
437	C₂²⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	2	no	—
443	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
444	C₄²	C₂×D₄×C₁₉	1	2	yes	—
445	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
446	C₂³	—	2	1	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	8	2	no	—
451	C₂³	—	8	1	no	—
452	C₂³	—	8	2	no	—
453	C₂³	C₁₉×#120	1	1	yes	characteristic
454	Q₈	—	4	1	no	—
455	Q₈	—	4	1	no	—
456	Q₈	—	4	2	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	4	2	no	—
459	Q₈	—	8	1	no	—
460	Q₈	—	8	2	no	—
461	Q₈	—	8	1	no	—
462	D₄	—	4	1	no	—
463	D₄	—	4	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	4	4	no	—
466	D₄	—	8	1	no	—
467	D₄	—	8	2	no	—
468	D₄	—	8	1	no	—
469	D₄	—	8	2	no	—
470	D₄	—	8	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	8	2	no	—
481	C₂×C₄	—	8	1	no	—
482	C₂×C₄	—	8	2	no	—
483	C₂×C₄	—	8	2	no	—
484	C₂×C₄	—	8	2	no	—
485	C₂×C₄	C₁₉×#120	1	2	yes	—
486	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
488	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
489	C₈	—	2	4	no	—
490	C₈	—	4	4	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	4	2	no	—
497	C₂²	—	4	2	no	—
498	C₂²	—	4	2	no	—
499	C₂²	—	16	2	no	—
500	C₂²	—	16	2	no	—
501	C₂²	C₁₉×#453	1	2	yes	—
502	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	4	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	2	no	—
510	C₄	—	4	2	no	—
511	C₄	—	4	2	no	—
512	C₄	—	8	2	no	—
513	C₂	—	2	2	no	—
514	C₂	—	8	1	no	—
515	C₂	—	8	2	no	—
516	C₂	—	8	1	no	—
517	C₂	C₂×C₁₉×#453	1	1	yes	characteristic
518	C₂	C₁₉×#3022	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3545	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×#3238	C₂	semidirect
3. C₂×C₁₉×#497	C₂	semidirect
4. C₁₉×#1661	C₂	semidirect
5. C₁₉×#1660	C₂	semidirect
6. C₁₉×#1659	C₂	semidirect
7. C₁₉×#1533	C₂	semidirect
8. C₁₉×#1532	C₂	semidirect
22. C₂×C₁₉×C₄⋊Q₈	C₂²	semidirect
25. C₁₉×#501	C₂²	semidirect
29. C₁₉×#497	C₂²	semidirect
30. C₁₉×#489	C₂²	semidirect
35. C₁₉×#432	C₂²	semidirect
36. C₂×C₁₉×#97	C₂²	semidirect
37. C₁₉×#330	C₂²	semidirect
39. C₁₉×#329	C₂²	semidirect
40. C₁₉×#329	C₂²	semidirect
186. #19051	C₁₉	direct (N × H)
233. #3238	C₂×C₁₉	semidirect
234. C₂×#497	C₂×C₁₉	semidirect
235. #1661	C₂×C₁₉	semidirect
236. #1660	C₂×C₁₉	semidirect
237. #1659	C₂×C₁₉	semidirect
238. #1533	C₂×C₁₉	semidirect
239. #1532	C₂×C₁₉	semidirect
275. C₂×C₄⋊Q₈	C₂²×C₁₉	semidirect
278. #501	C₂²×C₁₉	semidirect
282. #497	C₂²×C₁₉	semidirect
283. #489	C₂²×C₁₉	semidirect
288. #432	C₂²×C₁₉	semidirect
289. C₂×#97	C₂²×C₁₉	semidirect
290. #330	C₂²×C₁₉	semidirect
292. #329	C₂²×C₁₉	semidirect
293. #329	C₂²×C₁₉	semidirect
374. C₁₉	#19051	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×#3545	2
C₁₉×#3238	2
C₂×C₁₉×#497	2
C₁₉×#1661	2
C₁₉×#1660	2
C₁₉×#1659	2
C₁₉×#1533	2
C₁₉×#1532	2
#19051	19

Subgroups — C19×#19051 #18025010

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19051 #18025010