Subgroups — C₁₉×#19086 #18025045

Order 4864.

964 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3558	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3219	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#3213	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1662	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1659	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1656	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1655	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1536	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1535	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1533	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#562	C₂²	1	2	yes	—
13	C₁₉×H(3,𝔽₄)	C₂²	1	2	yes	—
14	C₁₉×#559	—	2	1	no	—
15	C₁₉×#548	—	2	1	no	—
16	C₁₉×#546	—	2	2	no	—
17	C₁₉×#546	—	2	1	no	—
18	D₄²×C₁₉	—	2	1	no	—
19	C₁₉×#542	—	2	1	no	—
20	C₁₉×#538	—	2	2	no	—
21	C₁₉×#538	—	2	1	no	—
22	C₁₉×#535	—	2	1	no	—
23	C₁₉×#534	—	2	1	no	—
24	C₁₉×#532	C₂²	1	1	yes	characteristic
25	C₁₉×#532	C₂²	1	1	yes	characteristic, complemented
26	C₁₉×#529	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#124	C₂²	1	1	yes	characteristic
28	C₁₉×#497	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#496	C₂²	1	1	yes	characteristic, complemented
30	C₁₉×#496	C₂²	1	2	yes	complemented
31	C₁₉×#496	C₂²	1	2	yes	complemented
32	C₁₉×#491	C₂²	1	1	yes	characteristic, complemented
33	C₁₉×#490	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#489	C₂²	1	2	yes	complemented
35	C₁₉×#489	C₂²	1	2	yes	complemented
36	C₁₉×#464	—	2	1	no	—
37	C₁₉×#463	—	2	2	no	—
38	C₁₉×#463	—	2	1	no	—
39	C₁₉×#461	—	2	1	no	—
40	C₁₉×#459	—	2	1	no	—
41	C₁₉×#452	—	2	1	no	—
42	C₁₉×#449	—	2	2	no	—
43	C₁₉×#449	—	2	1	no	—
44	C₁₉×#448	—	2	1	no	—
45	C₁₉×#447	—	2	1	no	—
46	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
47	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#432	C₂²	1	1	yes	characteristic, complemented
49	C₁₉×#330	C₂²	1	2	yes	complemented
50	C₁₉×#329	C₂²	1	2	yes	complemented
51	C₁₉×#329	C₂²	1	2	yes	complemented
52	C₁₉×#329	C₂²	1	2	yes	complemented
53	C₁₉×#329	C₂²	1	2	yes	complemented
54	C₁₉×#329	C₂²	1	2	yes	complemented
55	C₂×#41×C₁₉	—	2	1	no	—
56	C₂×#41×C₁₉	—	2	1	no	—
57	C₂×#41×C₁₉	D₄	1	2	yes	—
58	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
59	C₂²×D₄×C₁₉	—	2	2	no	—
60	C₂²×D₄×C₁₉	—	2	1	no	—
61	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
62	C₂×Q₁₆×C₁₉	—	2	1	no	—
63	C₂×SD₁₆×C₁₉	—	2	2	no	—
64	C₂×SD₁₆×C₁₉	—	2	2	no	—
65	C₂×SD₁₆×C₁₉	—	2	1	no	—
66	C₂×SD₁₆×C₁₉	—	2	1	no	—
67	C₂×D₈×C₁₉	—	2	2	no	—
68	C₂×D₈×C₁₉	—	2	2	no	—
69	C₂×D₈×C₁₉	—	2	1	no	—
70	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
71	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₁₉×#127	—	2	1	no	—
73	C₁₉×#127	D₄	1	1	yes	characteristic
74	C₁₉×#127	C₂³	1	1	yes	characteristic
75	C₁₉×#126	—	2	2	no	—
76	C₁₉×#126	—	2	1	no	—
77	C₁₉×#125	C₂³	1	1	yes	characteristic
78	C₁₉×#124	—	2	1	no	—
79	C₁₉×#124	—	2	2	no	—
80	C₁₉×#124	—	2	2	no	—
81	C₁₉×#124	—	2	2	no	—
82	C₁₉×#124	—	2	1	no	—
83	C₁₉×#124	—	2	1	no	—
84	C₁₉×#124	—	2	1	no	—
85	C₁₉×#124	D₄	1	2	yes	—
86	C₁₉×#124	C₂³	1	2	yes	—
87	C₁₉×#124	C₂³	1	2	yes	—
88	C₁₉×#124	C₂³	1	1	yes	characteristic
89	C₁₉×#123	—	2	2	no	—
90	C₁₉×#123	—	2	2	no	—
91	C₁₉×#123	—	2	1	no	—
92	C₁₉×#123	—	2	2	no	—
93	C₁₉×#123	—	2	2	no	—
94	C₁₉×C₂²⋊Q₈	—	2	1	no	—
95	C₁₉×C₂²⋊Q₈	—	2	2	no	—
96	C₁₉×C₂²⋊Q₈	—	2	2	no	—
97	C₁₉×C₂²⋊Q₈	D₄	1	1	yes	characteristic
98	C₁₉×#121	—	2	2	no	—
99	C₁₉×#121	—	2	2	no	—
100	C₁₉×#121	—	2	2	no	—
101	C₁₉×#121	—	2	1	no	—
102	C₁₉×#121	—	2	2	no	—
103	C₁₉×#121	—	2	2	no	—
104	C₁₉×#121	—	2	1	no	—
105	C₁₉×#121	—	2	1	no	—
106	C₁₉×#121	—	2	1	no	—
107	C₁₉×#121	—	2	1	no	—
108	C₁₉×#121	D₄	1	1	yes	characteristic
109	C₁₉×#120	—	2	2	no	—
110	C₁₉×#120	—	2	2	no	—
111	C₁₉×#120	—	2	2	no	—
112	C₁₉×#120	—	2	2	no	—
113	C₁₉×#120	—	2	2	no	—
114	C₄×Q₈×C₁₉	—	2	1	no	—
115	C₄×Q₈×C₁₉	D₄	1	1	yes	characteristic
116	C₄×D₄×C₁₉	—	2	2	no	—
117	C₄×D₄×C₁₉	—	2	2	no	—
118	C₄×D₄×C₁₉	—	2	1	no	—
119	C₄×D₄×C₁₉	—	2	1	no	—
120	C₄×D₄×C₁₉	—	2	1	no	—
121	C₄×D₄×C₁₉	—	2	1	no	—
122	C₄×D₄×C₁₉	—	2	1	no	—
123	C₄×D₄×C₁₉	—	2	1	no	—
124	C₄×D₄×C₁₉	D₄	1	1	yes	characteristic
125	C₁₉×#117	—	2	1	no	—
126	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
127	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
128	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
129	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
130	C₁₉×C₄⋊C₈	—	2	1	no	—
131	C₁₉×C₄⋊C₈	—	2	1	no	—
132	C₁₉×C₄⋊C₈	—	2	1	no	—
133	C₁₉×#103	—	2	2	no	—
134	C₁₉×#103	—	2	2	no	—
135	C₁₉×#103	—	2	1	no	—
136	C₁₉×#103	—	2	1	no	—
137	C₁₉×#102	—	2	2	no	—
138	C₁₉×#102	—	2	2	no	—
139	C₁₉×#102	—	2	1	no	—
140	C₁₉×#102	—	2	1	no	—
141	C₁₉×C₂²⋊C₈	—	2	1	no	—
142	C₁₉×C₂²⋊C₈	—	2	1	no	—
143	C₁₉×C₂²⋊C₈	—	2	1	no	—
144	C₁₉×#97	C₂³	1	2	yes	—
145	C₁₉×#97	C₂³	1	2	yes	—
146	C₁₉×#97	C₂³	1	1	yes	characteristic
147	C₁₉×#97	C₂³	1	1	yes	characteristic
148	C₂⁴×C₁₉	—	2	2	no	—
149	C₂⁴×C₁₉	—	2	1	no	—
150	#41×C₁₉	—	8	1	no	—
151	#41×C₁₉	—	8	1	no	—
152	#41×C₁₉	—	8	2	no	—
153	#41×C₁₉	—	8	2	no	—
154	C₂×Q₈×C₁₉	—	2	1	no	—
155	C₂×Q₈×C₁₉	—	2	1	no	—
156	C₂×Q₈×C₁₉	—	8	1	no	—
157	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
159	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
160	C₂×D₄×C₁₉	—	2	2	no	—
161	C₂×D₄×C₁₉	—	2	1	no	—
162	C₂×D₄×C₁₉	—	2	2	no	—
163	C₂×D₄×C₁₉	—	2	2	no	—
164	C₂×D₄×C₁₉	—	2	2	no	—
165	C₂×D₄×C₁₉	—	2	2	no	—
166	C₂×D₄×C₁₉	—	2	2	no	—
167	C₂×D₄×C₁₉	—	2	1	no	—
168	C₂×D₄×C₁₉	—	2	1	no	—
169	C₂×D₄×C₁₉	—	2	1	no	—
170	C₂×D₄×C₁₉	—	2	1	no	—
171	C₂×D₄×C₁₉	—	2	1	no	—
172	C₂×D₄×C₁₉	—	2	1	no	—
173	C₂×D₄×C₁₉	—	4	1	no	—
174	C₂×D₄×C₁₉	—	8	1	no	—
175	C₂×D₄×C₁₉	—	8	2	no	—
176	C₂×D₄×C₁₉	—	8	4	no	—
177	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
180	C₂²×C₄×C₁₉	—	2	2	no	—
181	C₂²×C₄×C₁₉	—	2	2	no	—
182	C₂²×C₄×C₁₉	—	2	1	no	—
183	C₂²×C₄×C₁₉	—	2	1	no	—
184	C₂²×C₄×C₁₉	—	2	2	no	—
185	C₂²×C₄×C₁₉	—	4	1	no	—
186	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
189	Q₁₆×C₁₉	—	8	1	no	—
190	SD₁₆×C₁₉	—	8	2	no	—
191	SD₁₆×C₁₉	—	8	2	no	—
192	SD₁₆×C₁₉	—	8	1	no	—
193	SD₁₆×C₁₉	—	8	1	no	—
194	D₈×C₁₉	—	8	1	no	—
195	D₈×C₁₉	—	8	2	no	—
196	D₈×C₁₉	—	8	2	no	—
197	C₂×C₈×C₁₉	—	2	2	no	—
198	C₂×C₈×C₁₉	—	2	2	no	—
199	C₂×C₈×C₁₉	—	2	1	no	—
200	C₂×C₈×C₁₉	—	2	1	no	—
201	C₄⋊C₄×C₁₉	—	2	2	no	—
202	C₄⋊C₄×C₁₉	—	2	2	no	—
203	C₄⋊C₄×C₁₉	—	2	1	no	—
204	C₄⋊C₄×C₁₉	—	2	1	no	—
205	C₄⋊C₄×C₁₉	—	2	1	no	—
206	C₄⋊C₄×C₁₉	—	2	1	no	—
207	C₄⋊C₄×C₁₉	—	2	1	no	—
208	C₄⋊C₄×C₁₉	—	2	1	no	—
209	C₄⋊C₄×C₁₉	—	2	1	no	—
210	C₄⋊C₄×C₁₉	—	2	1	no	—
211	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
212	C₄⋊C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
213	C₂²⋊C₄×C₁₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₉	—	2	2	no	—
215	C₂²⋊C₄×C₁₉	—	2	2	no	—
216	C₂²⋊C₄×C₁₉	—	2	2	no	—
217	C₂²⋊C₄×C₁₉	—	2	2	no	—
218	C₂²⋊C₄×C₁₉	—	2	1	no	—
219	C₂²⋊C₄×C₁₉	—	2	2	no	—
220	C₂²⋊C₄×C₁₉	—	2	1	no	—
221	C₂²⋊C₄×C₁₉	—	2	2	no	—
222	C₂²⋊C₄×C₁₉	—	2	1	no	—
223	C₂²⋊C₄×C₁₉	—	2	2	no	—
224	C₂²⋊C₄×C₁₉	—	2	2	no	—
225	C₂²⋊C₄×C₁₉	—	2	1	no	—
226	C₂²⋊C₄×C₁₉	—	2	1	no	—
227	C₂²⋊C₄×C₁₉	—	2	2	no	—
228	C₂²⋊C₄×C₁₉	—	2	2	no	—
229	C₂²⋊C₄×C₁₉	—	4	1	no	—
230	C₂²⋊C₄×C₁₉	—	4	1	no	—
231	C₄²×C₁₉	—	2	2	no	—
232	C₄²×C₁₉	—	2	1	no	—
233	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
236	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
237	#19086	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂³×C₁₉	—	2	1	no	—
239	C₂³×C₁₉	—	2	2	no	—
240	C₂³×C₁₉	—	2	2	no	—
241	C₂³×C₁₉	—	4	2	no	—
242	C₂³×C₁₉	—	4	1	no	—
243	C₂³×C₁₉	—	8	1	no	—
244	C₂³×C₁₉	—	8	1	no	—
245	C₂³×C₁₉	—	8	2	no	—
246	C₂³×C₁₉	—	8	2	no	—
247	C₂³×C₁₉	—	8	2	no	—
248	C₂³×C₁₉	#120	1	1	yes	characteristic
249	Q₈×C₁₉	—	4	1	no	—
250	Q₈×C₁₉	—	4	2	no	—
251	Q₈×C₁₉	—	4	2	no	—
252	Q₈×C₁₉	—	4	2	no	—
253	Q₈×C₁₉	—	4	1	no	—
254	Q₈×C₁₉	—	4	1	no	—
255	D₄×C₁₉	—	4	1	no	—
256	D₄×C₁₉	—	4	2	no	—
257	D₄×C₁₉	—	4	2	no	—
258	D₄×C₁₉	—	4	2	no	—
259	D₄×C₁₉	—	4	2	no	—
260	D₄×C₁₉	—	4	1	no	—
261	D₄×C₁₉	—	4	2	no	—
262	D₄×C₁₉	—	4	1	no	—
263	D₄×C₁₉	—	4	1	no	—
264	D₄×C₁₉	—	4	1	no	—
265	D₄×C₁₉	—	4	2	no	—
266	D₄×C₁₉	—	4	4	no	—
267	D₄×C₁₉	—	8	1	no	—
268	D₄×C₁₉	—	8	2	no	—
269	D₄×C₁₉	—	8	2	no	—
270	D₄×C₁₉	—	8	2	no	—
271	D₄×C₁₉	—	8	2	no	—
272	D₄×C₁₉	—	8	2	no	—
273	D₄×C₁₉	—	8	2	no	—
274	C₂×C₄×C₁₉	—	2	1	no	—
275	C₂×C₄×C₁₉	—	2	2	no	—
276	C₂×C₄×C₁₉	—	2	2	no	—
277	C₂×C₄×C₁₉	—	2	1	no	—
278	C₂×C₄×C₁₉	—	2	1	no	—
279	C₂×C₄×C₁₉	—	4	1	no	—
280	C₂×C₄×C₁₉	—	4	1	no	—
281	C₂×C₄×C₁₉	—	4	1	no	—
282	C₂×C₄×C₁₉	—	4	2	no	—
283	C₂×C₄×C₁₉	—	4	1	no	—
284	C₂×C₄×C₁₉	—	8	2	no	—
285	C₂×C₄×C₁₉	—	8	2	no	—
286	C₂×C₄×C₁₉	—	8	1	no	—
287	C₂×C₄×C₁₉	—	8	2	no	—
288	C₂×C₄×C₁₉	—	8	2	no	—
289	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
290	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
291	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
292	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
295	C₈×C₁₉	—	4	2	no	—
296	C₈×C₁₉	—	4	2	no	—
297	C₈×C₁₉	—	4	1	no	—
298	C₈×C₁₉	—	4	1	no	—
299	#3558	C₂×C₁₉	1	1	yes	characteristic, complemented
300	#3219	C₂×C₁₉	1	1	yes	characteristic, complemented
301	#3214	C₂×C₁₉	1	1	yes	characteristic, complemented
302	#3213	C₂×C₁₉	1	1	yes	characteristic, complemented
303	#1662	C₂×C₁₉	1	2	yes	complemented
304	#1659	C₂×C₁₉	1	2	yes	complemented
305	#1656	C₂×C₁₉	1	2	yes	complemented
306	#1655	C₂×C₁₉	1	2	yes	complemented
307	#1536	C₂×C₁₉	1	1	yes	characteristic, complemented
308	#1535	C₂×C₁₉	1	1	yes	characteristic, complemented
309	#1533	C₂×C₁₉	1	1	yes	characteristic, complemented
310	C₂²×C₁₉	—	2	1	no	—
311	C₂²×C₁₉	—	2	1	no	—
312	C₂²×C₁₉	—	2	1	no	—
313	C₂²×C₁₉	—	4	1	no	—
314	C₂²×C₁₉	—	4	2	no	—
315	C₂²×C₁₉	—	4	2	no	—
316	C₂²×C₁₉	—	4	2	no	—
317	C₂²×C₁₉	—	4	2	no	—
318	C₂²×C₁₉	—	4	1	no	—
319	C₂²×C₁₉	—	4	1	no	—
320	C₂²×C₁₉	—	4	2	no	—
321	C₂²×C₁₉	—	4	2	no	—
322	C₂²×C₁₉	—	8	1	no	—
323	C₂²×C₁₉	—	8	1	no	—
324	C₂²×C₁₉	—	8	1	no	—
325	C₂²×C₁₉	—	16	2	no	—
326	C₂²×C₁₉	—	16	4	no	—
327	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
328	C₄×C₁₉	—	2	1	no	—
329	C₄×C₁₉	—	2	1	no	—
330	C₄×C₁₉	—	2	1	no	—
331	C₄×C₁₉	—	2	1	no	—
332	C₄×C₁₉	—	2	1	no	—
333	C₄×C₁₉	—	2	1	no	—
334	C₄×C₁₉	—	4	1	no	—
335	C₄×C₁₉	—	4	1	no	—
336	C₄×C₁₉	—	4	2	no	—
337	C₄×C₁₉	—	4	2	no	—
338	C₄×C₁₉	—	4	1	no	—
339	C₄×C₁₉	—	8	1	no	—
340	#562	C₂²×C₁₉	1	2	yes	—
341	H(3,𝔽₄)	C₂²×C₁₉	1	2	yes	—
342	#559	—	2	1	no	—
343	#548	—	2	1	no	—
344	#546	—	2	2	no	—
345	#546	—	2	1	no	—
346	D₄²	—	2	1	no	—
347	#542	—	2	1	no	—
348	#538	—	2	2	no	—
349	#538	—	2	1	no	—
350	#535	—	2	1	no	—
351	#534	—	2	1	no	—
352	#532	C₂²×C₁₉	1	1	yes	characteristic
353	#532	C₂²×C₁₉	1	1	yes	characteristic, complemented
354	#529	C₂²×C₁₉	1	1	yes	characteristic
355	C₂×#124	C₂²×C₁₉	1	1	yes	characteristic
356	#497	C₂²×C₁₉	1	1	yes	characteristic, complemented
357	#496	C₂²×C₁₉	1	1	yes	characteristic, complemented
358	#496	C₂²×C₁₉	1	2	yes	complemented
359	#496	C₂²×C₁₉	1	2	yes	complemented
360	#491	C₂²×C₁₉	1	1	yes	characteristic, complemented
361	#490	C₂²×C₁₉	1	1	yes	characteristic, complemented
362	#489	C₂²×C₁₉	1	2	yes	complemented
363	#489	C₂²×C₁₉	1	2	yes	complemented
364	#464	—	2	1	no	—
365	#463	—	2	2	no	—
366	#463	—	2	1	no	—
367	#461	—	2	1	no	—
368	#459	—	2	1	no	—
369	#452	—	2	1	no	—
370	#449	—	2	2	no	—
371	#449	—	2	1	no	—
372	#448	—	2	1	no	—
373	#447	—	2	1	no	—
374	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
375	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
376	#432	C₂²×C₁₉	1	1	yes	characteristic, complemented
377	#330	C₂²×C₁₉	1	2	yes	complemented
378	#329	C₂²×C₁₉	1	2	yes	complemented
379	#329	C₂²×C₁₉	1	2	yes	complemented
380	#329	C₂²×C₁₉	1	2	yes	complemented
381	#329	C₂²×C₁₉	1	2	yes	complemented
382	#329	C₂²×C₁₉	1	2	yes	complemented
383	C₂×C₁₉	—	4	1	no	—
384	C₂×C₁₉	—	8	2	no	—
385	C₂×C₁₉	—	8	1	no	—
386	C₂×C₁₉	—	8	2	no	—
387	C₂×C₁₉	—	16	1	no	—
388	C₂×C₁₉	#3019	1	1	yes	characteristic
389	C₂×C₁₉	#3019	1	1	yes	characteristic
390	C₂×C₁₉	#3021	1	1	yes	characteristic
391	C₂×#41	—	2	1	no	—
392	C₂×#41	—	2	1	no	—
393	C₂×#41	D₄×C₁₉	1	2	yes	—
394	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
395	C₂²×D₄	—	2	2	no	—
396	C₂²×D₄	—	2	1	no	—
397	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
398	C₂×Q₁₆	—	2	1	no	—
399	C₂×SD₁₆	—	2	2	no	—
400	C₂×SD₁₆	—	2	2	no	—
401	C₂×SD₁₆	—	2	1	no	—
402	C₂×SD₁₆	—	2	1	no	—
403	C₂×D₈	—	2	2	no	—
404	C₂×D₈	—	2	2	no	—
405	C₂×D₈	—	2	1	no	—
406	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
407	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
408	#127	—	2	1	no	—
409	#127	D₄×C₁₉	1	1	yes	characteristic
410	#127	C₂³×C₁₉	1	1	yes	characteristic
411	#126	—	2	2	no	—
412	#126	—	2	1	no	—
413	#125	C₂³×C₁₉	1	1	yes	characteristic
414	#124	—	2	1	no	—
415	#124	—	2	2	no	—
416	#124	—	2	2	no	—
417	#124	—	2	2	no	—
418	#124	—	2	1	no	—
419	#124	—	2	1	no	—
420	#124	—	2	1	no	—
421	#124	D₄×C₁₉	1	2	yes	—
422	#124	C₂³×C₁₉	1	2	yes	—
423	#124	C₂³×C₁₉	1	1	yes	characteristic
424	#124	C₂³×C₁₉	1	2	yes	—
425	#123	—	2	2	no	—
426	#123	—	2	2	no	—
427	#123	—	2	1	no	—
428	#123	—	2	2	no	—
429	#123	—	2	2	no	—
430	C₂²⋊Q₈	—	2	1	no	—
431	C₂²⋊Q₈	—	2	2	no	—
432	C₂²⋊Q₈	—	2	2	no	—
433	C₂²⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
434	#121	—	2	2	no	—
435	#121	—	2	2	no	—
436	#121	—	2	2	no	—
437	#121	—	2	1	no	—
438	#121	—	2	2	no	—
439	#121	—	2	2	no	—
440	#121	—	2	1	no	—
441	#121	—	2	1	no	—
442	#121	—	2	1	no	—
443	#121	—	2	1	no	—
444	#121	D₄×C₁₉	1	1	yes	characteristic
445	#120	—	2	2	no	—
446	#120	—	2	2	no	—
447	#120	—	2	2	no	—
448	#120	—	2	2	no	—
449	#120	—	2	2	no	—
450	C₄×Q₈	—	2	1	no	—
451	C₄×Q₈	D₄×C₁₉	1	1	yes	characteristic
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	2	no	—
454	C₄×D₄	—	2	1	no	—
455	C₄×D₄	—	2	1	no	—
456	C₄×D₄	—	2	1	no	—
457	C₄×D₄	—	2	1	no	—
458	C₄×D₄	—	2	1	no	—
459	C₄×D₄	—	2	1	no	—
460	C₄×D₄	D₄×C₁₉	1	1	yes	characteristic
461	#117	—	2	1	no	—
462	C₂×C₂²⋊C₄	—	2	2	no	—
463	C₂×C₂²⋊C₄	—	2	1	no	—
464	C₂×C₂²⋊C₄	—	2	1	no	—
465	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
466	C₄⋊C₈	—	2	1	no	—
467	C₄⋊C₈	—	2	1	no	—
468	C₄⋊C₈	—	2	1	no	—
469	#103	—	2	2	no	—
470	#103	—	2	2	no	—
471	#103	—	2	1	no	—
472	#103	—	2	1	no	—
473	#102	—	2	2	no	—
474	#102	—	2	2	no	—
475	#102	—	2	1	no	—
476	#102	—	2	1	no	—
477	C₂²⋊C₈	—	2	1	no	—
478	C₂²⋊C₈	—	2	1	no	—
479	C₂²⋊C₈	—	2	1	no	—
480	#97	C₂³×C₁₉	1	1	yes	characteristic
481	#97	C₂³×C₁₉	1	1	yes	characteristic
482	#97	C₂³×C₁₉	1	2	yes	—
483	#97	C₂³×C₁₉	1	2	yes	—
484	C₁₉	#19086	1	1	yes	characteristic, direct product factor, Sylow
485	C₂⁴	—	2	2	no	—
486	C₂⁴	—	2	1	no	—
487	#41	—	8	1	no	—
488	#41	—	8	1	no	—
489	#41	—	8	2	no	—
490	#41	—	8	2	no	—
491	C₂×Q₈	—	2	1	no	—
492	C₂×Q₈	—	2	1	no	—
493	C₂×Q₈	—	8	1	no	—
494	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
495	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
496	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
497	C₂×D₄	—	2	2	no	—
498	C₂×D₄	—	2	1	no	—
499	C₂×D₄	—	2	2	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	2	no	—
502	C₂×D₄	—	2	2	no	—
503	C₂×D₄	—	2	2	no	—
504	C₂×D₄	—	2	1	no	—
505	C₂×D₄	—	2	1	no	—
506	C₂×D₄	—	2	1	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	1	no	—
510	C₂×D₄	—	4	1	no	—
511	C₂×D₄	—	8	1	no	—
512	C₂×D₄	—	8	2	no	—
513	C₂×D₄	—	8	4	no	—
514	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
515	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
516	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	2	no	—
519	C₂²×C₄	—	2	1	no	—
520	C₂²×C₄	—	2	1	no	—
521	C₂²×C₄	—	2	2	no	—
522	C₂²×C₄	—	4	1	no	—
523	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
524	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
525	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
526	Q₁₆	—	8	1	no	—
527	SD₁₆	—	8	2	no	—
528	SD₁₆	—	8	2	no	—
529	SD₁₆	—	8	1	no	—
530	SD₁₆	—	8	1	no	—
531	D₈	—	8	1	no	—
532	D₈	—	8	2	no	—
533	D₈	—	8	2	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	2	no	—
536	C₂×C₈	—	2	2	no	—
537	C₂×C₈	—	2	1	no	—
538	C₄⋊C₄	—	2	2	no	—
539	C₄⋊C₄	—	2	2	no	—
540	C₄⋊C₄	—	2	1	no	—
541	C₄⋊C₄	—	2	1	no	—
542	C₄⋊C₄	—	2	1	no	—
543	C₄⋊C₄	—	2	1	no	—
544	C₄⋊C₄	—	2	1	no	—
545	C₄⋊C₄	—	2	1	no	—
546	C₄⋊C₄	—	2	1	no	—
547	C₄⋊C₄	—	2	1	no	—
548	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
549	C₄⋊C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
550	C₂²⋊C₄	—	2	2	no	—
551	C₂²⋊C₄	—	2	2	no	—
552	C₂²⋊C₄	—	2	2	no	—
553	C₂²⋊C₄	—	2	2	no	—
554	C₂²⋊C₄	—	2	2	no	—
555	C₂²⋊C₄	—	2	1	no	—
556	C₂²⋊C₄	—	2	2	no	—
557	C₂²⋊C₄	—	2	1	no	—
558	C₂²⋊C₄	—	2	2	no	—
559	C₂²⋊C₄	—	2	1	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	2	no	—
562	C₂²⋊C₄	—	2	1	no	—
563	C₂²⋊C₄	—	2	1	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	4	1	no	—
567	C₂²⋊C₄	—	4	1	no	—
568	C₄²	—	2	2	no	—
569	C₄²	—	2	1	no	—
570	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
571	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
572	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
573	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
574	C₂³	—	2	1	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	4	2	no	—
578	C₂³	—	4	1	no	—
579	C₂³	—	8	1	no	—
580	C₂³	—	8	1	no	—
581	C₂³	—	8	2	no	—
582	C₂³	—	8	2	no	—
583	C₂³	—	8	2	no	—
584	C₂³	C₁₉×#120	1	1	yes	characteristic
585	Q₈	—	4	1	no	—
586	Q₈	—	4	2	no	—
587	Q₈	—	4	2	no	—
588	Q₈	—	4	2	no	—
589	Q₈	—	4	1	no	—
590	Q₈	—	4	1	no	—
591	D₄	—	4	1	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	4	2	no	—
595	D₄	—	4	2	no	—
596	D₄	—	4	1	no	—
597	D₄	—	4	2	no	—
598	D₄	—	4	1	no	—
599	D₄	—	4	1	no	—
600	D₄	—	4	1	no	—
601	D₄	—	4	2	no	—
602	D₄	—	4	4	no	—
603	D₄	—	8	1	no	—
604	D₄	—	8	2	no	—
605	D₄	—	8	2	no	—
606	D₄	—	8	2	no	—
607	D₄	—	8	2	no	—
608	D₄	—	8	2	no	—
609	D₄	—	8	2	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	2	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	8	2	no	—
621	C₂×C₄	—	8	2	no	—
622	C₂×C₄	—	8	1	no	—
623	C₂×C₄	—	8	2	no	—
624	C₂×C₄	—	8	2	no	—
625	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
626	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
627	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
628	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
629	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
630	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
631	C₈	—	4	2	no	—
632	C₈	—	4	2	no	—
633	C₈	—	4	1	no	—
634	C₈	—	4	1	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	2	1	no	—
637	C₂²	—	2	1	no	—
638	C₂²	—	4	1	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	1	no	—
644	C₂²	—	4	1	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	2	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	—	8	1	no	—
650	C₂²	—	16	2	no	—
651	C₂²	—	16	4	no	—
652	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
653	C₄	—	2	1	no	—
654	C₄	—	2	1	no	—
655	C₄	—	2	1	no	—
656	C₄	—	2	1	no	—
657	C₄	—	2	1	no	—
658	C₄	—	2	1	no	—
659	C₄	—	4	1	no	—
660	C₄	—	4	1	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	1	no	—
664	C₄	—	8	1	no	—
665	C₂	—	4	1	no	—
666	C₂	—	8	1	no	—
667	C₂	—	8	2	no	—
668	C₂	—	8	2	no	—
669	C₂	—	16	1	no	—
670	C₂	C₁₉×#3019	1	1	yes	characteristic
671	C₂	C₁₉×#3019	1	1	yes	characteristic
672	C₂	C₁₉×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
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
1. C₁₉×#3558	C₂	semidirect
2. C₁₉×#3219	C₂	semidirect
3. C₁₉×#3214	C₂	semidirect
4. C₁₉×#3213	C₂	semidirect
5. C₁₉×#1662	C₂	semidirect
6. C₁₉×#1659	C₂	semidirect
7. C₁₉×#1656	C₂	semidirect
8. C₁₉×#1655	C₂	semidirect
9. C₁₉×#1536	C₂	semidirect
10. C₁₉×#1535	C₂	semidirect
11. C₁₉×#1533	C₂	semidirect
25. C₁₉×#532	C₂²	semidirect
28. C₁₉×#497	C₂²	semidirect
29. C₁₉×#496	C₂²	semidirect
30. C₁₉×#496	C₂²	semidirect
31. C₁₉×#496	C₂²	semidirect
32. C₁₉×#491	C₂²	semidirect
33. C₁₉×#490	C₂²	semidirect
34. C₁₉×#489	C₂²	semidirect
35. C₁₉×#489	C₂²	semidirect
46. C₁₉×#432	C₂²	semidirect
47. C₁₉×#432	C₂²	semidirect
48. C₁₉×#432	C₂²	semidirect
49. C₁₉×#330	C₂²	semidirect
50. C₁₉×#329	C₂²	semidirect
51. C₁₉×#329	C₂²	semidirect
52. C₁₉×#329	C₂²	semidirect
53. C₁₉×#329	C₂²	semidirect
54. C₁₉×#329	C₂²	semidirect
237. #19086	C₁₉	direct (N × H)
299. #3558	C₂×C₁₉	semidirect
300. #3219	C₂×C₁₉	semidirect
301. #3214	C₂×C₁₉	semidirect
302. #3213	C₂×C₁₉	semidirect
303. #1662	C₂×C₁₉	semidirect
304. #1659	C₂×C₁₉	semidirect
305. #1656	C₂×C₁₉	semidirect
306. #1655	C₂×C₁₉	semidirect
307. #1536	C₂×C₁₉	semidirect
308. #1535	C₂×C₁₉	semidirect
309. #1533	C₂×C₁₉	semidirect
353. #532	C₂²×C₁₉	semidirect
356. #497	C₂²×C₁₉	semidirect
357. #496	C₂²×C₁₉	semidirect
358. #496	C₂²×C₁₉	semidirect
359. #496	C₂²×C₁₉	semidirect
360. #491	C₂²×C₁₉	semidirect
361. #490	C₂²×C₁₉	semidirect
362. #489	C₂²×C₁₉	semidirect
363. #489	C₂²×C₁₉	semidirect
374. #432	C₂²×C₁₉	semidirect
375. #432	C₂²×C₁₉	semidirect
376. #432	C₂²×C₁₉	semidirect
377. #330	C₂²×C₁₉	semidirect
378. #329	C₂²×C₁₉	semidirect
379. #329	C₂²×C₁₉	semidirect
380. #329	C₂²×C₁₉	semidirect
381. #329	C₂²×C₁₉	semidirect
382. #329	C₂²×C₁₉	semidirect
484. C₁₉	#19086	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×#3558	2
C₁₉×#3219	2
C₁₉×#3214	2
C₁₉×#3213	2
C₁₉×#1662	2
C₁₉×#1659	2
C₁₉×#1656	2
C₁₉×#1655	2
C₁₉×#1536	2
C₁₉×#1535	2
C₁₉×#1533	2
#19086	19

Subgroups — C19×#19086 #18025045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19086 #18025045