Subgroups — C₁₉×#19522 #18025481

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3216	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₉×#3208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#3205	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1702	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1688	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1682	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1668	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1572	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1555	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1553	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₉×#533	C₂²	1	1	yes	characteristic
13	C₁₉×#532	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
15	C₁₉×#497	—	2	1	no	—
16	C₁₉×#493	C₂²	1	1	yes	characteristic
17	C₁₉×#493	C₂²	1	1	yes	characteristic
18	C₁₉×#492	—	2	1	no	—
19	C₁₉×#489	—	2	1	no	—
20	C₁₉×#486	—	2	1	no	—
21	C₁₉×#486	C₂²	1	1	yes	characteristic
22	C₁₉×#486	C₂²	1	1	yes	characteristic
23	C₁₉×#462	C₂²	1	2	yes	complemented
24	C₁₉×#460	C₂²	1	2	yes	—
25	C₁₉×#460	C₂²	1	2	yes	—
26	C₁₉×#460	C₂²	1	2	yes	complemented
27	C₁₉×#459	—	2	2	no	—
28	C₁₉×#452	—	2	2	no	—
29	C₁₉×#450	—	2	2	no	—
30	C₁₉×#447	—	2	2	no	—
31	C₁₉×#446	—	2	2	no	—
32	C₁₉×#446	C₂²	1	2	yes	complemented
33	C₈×Q₈×C₁₉	C₂²	1	2	yes	complemented
34	C₁₉×#433	—	2	2	no	—
35	C₁₉×#432	C₂²	1	1	yes	characteristic
36	C₁₉×#432	C₂²	1	1	yes	characteristic
37	C₁₉×#431	C₂²	1	1	yes	characteristic
38	C₁₉×#431	C₂²	1	1	yes	characteristic
39	C₁₉×#335	C₂²	1	2	yes	complemented
40	C₁₉×#334	C₂²	1	2	yes	complemented
41	C₁₉×#332	C₂²	1	2	yes	complemented
42	C₁₉×#331	C₂²	1	2	yes	—
43	C₁₉×#331	C₂²	1	2	yes	—
44	C₁₉×#331	C₂²	1	2	yes	complemented
45	C₂×#41×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂×Q₁₆×C₁₉	—	2	2	no	—
50	C₂×SD₁₆×C₁₉	—	2	2	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	2	no	—
53	C₂×D₈×C₁₉	—	2	2	no	—
54	C₂×D₈×C₁₉	—	2	2	no	—
55	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
56	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
57	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₁₉×#127	—	2	1	no	—
59	C₁₉×#127	—	2	1	no	—
60	C₁₉×#127	—	2	1	no	—
61	C₁₉×#127	C₂³	1	1	yes	characteristic
62	C₁₉×#127	C₂³	1	1	yes	characteristic
63	C₁₉×#127	C₂³	1	1	yes	characteristic
64	C₁₉×#125	—	2	1	no	—
65	C₁₉×#124	—	2	1	no	—
66	C₁₉×C₂²⋊Q₈	—	2	1	no	—
67	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
68	C₁₉×#121	—	2	1	no	—
69	C₁₉×#121	—	2	1	no	—
70	C₄×Q₈×C₁₉	—	2	1	no	—
71	C₄×Q₈×C₁₉	C₂³	1	2	yes	—
72	C₄×D₄×C₁₉	—	2	1	no	—
73	C₄×D₄×C₁₉	—	2	1	no	—
74	C₁₉×#117	—	2	1	no	—
75	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
76	C₁₉×C₄⋊C₈	—	2	2	no	—
77	C₁₉×C₄⋊C₈	—	2	2	no	—
78	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
79	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
81	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
82	C₁₉×#103	—	2	2	no	—
83	C₁₉×#102	—	2	2	no	—
84	C₁₉×#102	—	2	2	no	—
85	C₁₉×#102	—	2	2	no	—
86	C₁₉×#102	—	2	2	no	—
87	C₁₉×#102	—	2	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	1	no	—
89	C₁₉×C₂²⋊C₈	—	2	1	no	—
90	C₁₉×C₂²⋊C₈	—	2	1	no	—
91	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
92	C₁₉×#97	—	2	2	no	—
93	C₁₉×#97	—	2	1	no	—
94	C₁₉×#97	—	2	1	no	—
95	C₄×C₈×C₁₉	—	2	2	no	—
96	C₄×C₈×C₁₉	—	2	1	no	—
97	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₂⁴×C₁₉	—	4	1	no	—
100	#41×C₁₉	—	8	2	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
104	C₂×D₄×C₁₉	—	2	1	no	—
105	C₂×D₄×C₁₉	—	2	1	no	—
106	C₂×D₄×C₁₉	—	2	1	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	1	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	1	no	—
112	C₂×D₄×C₁₉	—	2	1	no	—
113	C₂×D₄×C₁₉	—	4	1	no	—
114	C₂×D₄×C₁₉	—	4	1	no	—
115	C₂×D₄×C₁₉	—	4	1	no	—
116	C₂×D₄×C₁₉	—	4	1	no	—
117	C₂×D₄×C₁₉	—	8	2	no	—
118	C₂×D₄×C₁₉	—	8	2	no	—
119	C₂×D₄×C₁₉	—	8	2	no	—
120	C₂²×C₄×C₁₉	—	4	1	no	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
124	Q₁₆×C₁₉	—	8	2	no	—
125	SD₁₆×C₁₉	—	8	2	no	—
126	SD₁₆×C₁₉	—	8	2	no	—
127	SD₁₆×C₁₉	—	8	2	no	—
128	D₈×C₁₉	—	8	2	no	—
129	D₈×C₁₉	—	8	2	no	—
130	C₂×C₈×C₁₉	—	2	2	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	2	no	—
133	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
135	C₄⋊C₄×C₁₉	—	2	1	no	—
136	C₄⋊C₄×C₁₉	—	2	1	no	—
137	C₄⋊C₄×C₁₉	—	2	1	no	—
138	C₄⋊C₄×C₁₉	—	2	2	no	—
139	C₄⋊C₄×C₁₉	—	2	2	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂²⋊C₄×C₁₉	—	2	2	no	—
144	C₂²⋊C₄×C₁₉	—	4	1	no	—
145	C₂²⋊C₄×C₁₉	—	4	1	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₁₉	#41	1	1	yes	characteristic
150	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
151	#19522	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	1	no	—
155	C₂³×C₁₉	—	8	2	no	—
156	C₂³×C₁₉	—	8	2	no	—
157	C₂³×C₁₉	—	8	2	no	—
158	C₂³×C₁₉	#121	1	1	yes	characteristic
159	Q₈×C₁₉	—	2	2	no	—
160	Q₈×C₁₉	—	2	2	no	—
161	Q₈×C₁₉	—	4	2	no	—
162	Q₈×C₁₉	—	8	1	no	—
163	D₄×C₁₉	—	4	2	no	—
164	D₄×C₁₉	—	4	2	no	—
165	D₄×C₁₉	—	4	2	no	—
166	D₄×C₁₉	—	4	2	no	—
167	D₄×C₁₉	—	4	2	no	—
168	D₄×C₁₉	—	4	2	no	—
169	D₄×C₁₉	—	8	1	no	—
170	D₄×C₁₉	—	8	1	no	—
171	D₄×C₁₉	—	8	1	no	—
172	D₄×C₁₉	—	8	2	no	—
173	D₄×C₁₉	—	8	2	no	—
174	D₄×C₁₉	—	8	2	no	—
175	D₄×C₁₉	—	8	2	no	—
176	C₂×C₄×C₁₉	—	2	2	no	—
177	C₂×C₄×C₁₉	—	2	2	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	4	1	no	—
181	C₂×C₄×C₁₉	—	4	1	no	—
182	C₂×C₄×C₁₉	—	8	2	no	—
183	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
189	C₈×C₁₉	—	2	2	no	—
190	C₈×C₁₉	—	2	2	no	—
191	C₈×C₁₉	—	4	2	no	—
192	C₈×C₁₉	—	4	2	no	—
193	C₈×C₁₉	—	4	2	no	—
194	#3216	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
196	#3205	C₂×C₁₉	1	1	yes	characteristic
197	#2985	C₂×C₁₉	1	1	yes	characteristic, complemented
198	#1702	C₂×C₁₉	1	2	yes	complemented
199	#1688	C₂×C₁₉	1	2	yes	complemented
200	#1682	C₂×C₁₉	1	2	yes	complemented
201	#1668	C₂×C₁₉	1	2	yes	complemented
202	#1572	C₂×C₁₉	1	1	yes	characteristic, complemented
203	#1555	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#1553	C₂×C₁₉	1	1	yes	characteristic, complemented
205	C₂²×C₁₉	—	2	1	no	—
206	C₂²×C₁₉	—	2	1	no	—
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	8	1	no	—
209	C₂²×C₁₉	—	8	1	no	—
210	C₂²×C₁₉	—	8	1	no	—
211	C₂²×C₁₉	—	8	1	no	—
212	C₂²×C₁₉	—	8	1	no	—
213	C₂²×C₁₉	—	8	1	no	—
214	C₂²×C₁₉	—	8	1	no	—
215	C₂²×C₁₉	—	8	1	no	—
216	C₂²×C₁₉	—	8	1	no	—
217	C₂²×C₁₉	—	16	4	no	—
218	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
219	C₄×C₁₉	—	2	1	no	—
220	C₄×C₁₉	—	2	1	no	—
221	C₄×C₁₉	—	2	1	no	—
222	C₄×C₁₉	—	2	1	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	8	1	no	—
226	C₄×C₁₉	#576	1	2	yes	—
227	C₄×C₁₉	#577	1	2	yes	—
228	#533	C₂²×C₁₉	1	1	yes	characteristic
229	#532	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
231	#497	—	2	1	no	—
232	#493	C₂²×C₁₉	1	1	yes	characteristic
233	#493	C₂²×C₁₉	1	1	yes	characteristic
234	#492	—	2	1	no	—
235	#489	—	2	1	no	—
236	#486	—	2	1	no	—
237	#486	C₂²×C₁₉	1	1	yes	characteristic
238	#486	C₂²×C₁₉	1	1	yes	characteristic
239	#462	C₂²×C₁₉	1	2	yes	complemented
240	#460	C₂²×C₁₉	1	2	yes	—
241	#460	C₂²×C₁₉	1	2	yes	—
242	#460	C₂²×C₁₉	1	2	yes	complemented
243	#459	—	2	2	no	—
244	#452	—	2	2	no	—
245	#450	—	2	2	no	—
246	#447	—	2	2	no	—
247	#446	—	2	2	no	—
248	#446	C₂²×C₁₉	1	2	yes	complemented
249	C₈×Q₈	C₂²×C₁₉	1	2	yes	complemented
250	#433	—	2	2	no	—
251	#432	C₂²×C₁₉	1	1	yes	characteristic
252	#432	C₂²×C₁₉	1	1	yes	characteristic
253	#431	C₂²×C₁₉	1	1	yes	characteristic
254	#431	C₂²×C₁₉	1	1	yes	characteristic
255	#335	C₂²×C₁₉	1	2	yes	complemented
256	#334	C₂²×C₁₉	1	2	yes	complemented
257	#332	C₂²×C₁₉	1	2	yes	complemented
258	#331	C₂²×C₁₉	1	2	yes	—
259	#331	C₂²×C₁₉	1	2	yes	—
260	#331	C₂²×C₁₉	1	2	yes	complemented
261	C₂×C₁₉	—	4	1	no	—
262	C₂×C₁₉	—	16	1	no	—
263	C₂×C₁₉	—	16	1	no	—
264	C₂×C₁₉	—	16	1	no	—
265	C₂×C₁₉	#3043	1	1	yes	characteristic
266	C₂×C₁₉	#3058	1	1	yes	characteristic
267	C₂×C₁₉	#3068	1	1	yes	characteristic
268	C₂×#41	—	2	1	no	—
269	C₂²×D₄	—	2	1	no	—
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂×Q₁₆	—	2	2	no	—
273	C₂×SD₁₆	—	2	2	no	—
274	C₂×SD₁₆	—	2	2	no	—
275	C₂×SD₁₆	—	2	2	no	—
276	C₂×D₈	—	2	2	no	—
277	C₂×D₈	—	2	2	no	—
278	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
279	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
280	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
281	#127	—	2	1	no	—
282	#127	—	2	1	no	—
283	#127	—	2	1	no	—
284	#127	C₂³×C₁₉	1	1	yes	characteristic
285	#127	C₂³×C₁₉	1	1	yes	characteristic
286	#127	C₂³×C₁₉	1	1	yes	characteristic
287	#125	—	2	1	no	—
288	#124	—	2	1	no	—
289	C₂²⋊Q₈	—	2	1	no	—
290	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
291	#121	—	2	1	no	—
292	#121	—	2	1	no	—
293	C₄×Q₈	—	2	1	no	—
294	C₄×Q₈	C₂³×C₁₉	1	2	yes	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	#117	—	2	1	no	—
298	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
299	C₄⋊C₈	—	2	2	no	—
300	C₄⋊C₈	—	2	2	no	—
301	C₄⋊C₈	D₄×C₁₉	1	2	yes	—
302	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
303	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
304	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
305	#103	—	2	2	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	2	no	—
309	#102	—	2	2	no	—
310	#102	—	2	2	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	1	no	—
313	C₂²⋊C₈	—	2	1	no	—
314	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
315	#97	—	2	2	no	—
316	#97	—	2	1	no	—
317	#97	—	2	1	no	—
318	C₄×C₈	—	2	2	no	—
319	C₄×C₈	—	2	1	no	—
320	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
321	C₄×C₈	C₂³×C₁₉	1	1	yes	characteristic
322	C₁₉	#19522	1	1	yes	characteristic, direct product factor, Sylow
323	C₂⁴	—	4	1	no	—
324	#41	—	8	2	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	—	2	1	no	—
332	C₂×D₄	—	2	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	4	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂×D₄	—	8	2	no	—
342	C₂×D₄	—	8	2	no	—
343	C₂×D₄	—	8	2	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
347	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
348	Q₁₆	—	8	2	no	—
349	SD₁₆	—	8	2	no	—
350	SD₁₆	—	8	2	no	—
351	SD₁₆	—	8	2	no	—
352	D₈	—	8	2	no	—
353	D₈	—	8	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
358	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
367	C₂²⋊C₄	—	2	2	no	—
368	C₂²⋊C₄	—	4	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₄²	—	2	2	no	—
371	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
372	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
373	C₄²	#41×C₁₉	1	1	yes	characteristic
374	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
375	C₂³	—	4	1	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	—	8	2	no	—
379	C₂³	—	8	2	no	—
380	C₂³	—	8	2	no	—
381	C₂³	C₁₉×#121	1	1	yes	characteristic
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	4	2	no	—
385	Q₈	—	8	1	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	8	1	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	1	no	—
395	D₄	—	8	2	no	—
396	D₄	—	8	2	no	—
397	D₄	—	8	2	no	—
398	D₄	—	8	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	8	2	no	—
406	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
407	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
408	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
412	C₈	—	2	2	no	—
413	C₈	—	2	2	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	2	no	—
416	C₈	—	4	2	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	1	no	—
424	C₂²	—	8	1	no	—
425	C₂²	—	8	1	no	—
426	C₂²	—	8	1	no	—
427	C₂²	—	8	1	no	—
428	C₂²	—	8	1	no	—
429	C₂²	—	16	4	no	—
430	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	1	no	—
438	C₄	C₁₉×#576	1	2	yes	—
439	C₄	C₁₉×#577	1	2	yes	—
440	C₂	—	4	1	no	—
441	C₂	—	16	1	no	—
442	C₂	—	16	1	no	—
443	C₂	—	16	1	no	—
444	C₂	C₁₉×#3043	1	1	yes	characteristic
445	C₂	C₁₉×#3058	1	1	yes	characteristic
446	C₂	C₁₉×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₉
prime radical	C₁₉×#3205	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
1. C₁₉×#3216	C₂	semidirect
2. C₁₉×#3208	C₂	semidirect
4. C₁₉×#2985	C₂	semidirect
5. C₁₉×#1702	C₂	semidirect
6. C₁₉×#1688	C₂	semidirect
7. C₁₉×#1682	C₂	semidirect
8. C₁₉×#1668	C₂	semidirect
9. C₁₉×#1572	C₂	semidirect
10. C₁₉×#1555	C₂	semidirect
11. C₁₉×#1553	C₂	semidirect
23. C₁₉×#462	C₂²	semidirect
26. C₁₉×#460	C₂²	semidirect
32. C₁₉×#446	C₂²	semidirect
33. C₈×Q₈×C₁₉	C₂²	semidirect
39. C₁₉×#335	C₂²	semidirect
40. C₁₉×#334	C₂²	semidirect
41. C₁₉×#332	C₂²	semidirect
44. C₁₉×#331	C₂²	semidirect
151. #19522	C₁₉	direct (N × H)
194. #3216	C₂×C₁₉	semidirect
195. #3208	C₂×C₁₉	semidirect
197. #2985	C₂×C₁₉	semidirect
198. #1702	C₂×C₁₉	semidirect
199. #1688	C₂×C₁₉	semidirect
200. #1682	C₂×C₁₉	semidirect
201. #1668	C₂×C₁₉	semidirect
202. #1572	C₂×C₁₉	semidirect
203. #1555	C₂×C₁₉	semidirect
204. #1553	C₂×C₁₉	semidirect
239. #462	C₂²×C₁₉	semidirect
242. #460	C₂²×C₁₉	semidirect
248. #446	C₂²×C₁₉	semidirect
249. C₈×Q₈	C₂²×C₁₉	semidirect
255. #335	C₂²×C₁₉	semidirect
256. #334	C₂²×C₁₉	semidirect
257. #332	C₂²×C₁₉	semidirect
260. #331	C₂²×C₁₉	semidirect
322. C₁₉	#19522	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×#3216	2
C₁₉×#3208	2
C₁₉×#3205	2
C₁₉×#2985	2
C₁₉×#1702	2
C₁₉×#1688	2
C₁₉×#1682	2
C₁₉×#1668	2
C₁₉×#1572	2
C₁₉×#1555	2
C₁₉×#1553	2
#19522	19

Subgroups — C19×#19522 #18025481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19522 #18025481