Subgroups — C₁₉×#19552 #18025511

Order 4864.

666 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3254	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×#2979	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1701	C₂	1	2	yes	maximal, complemented
6	C₁₉×#1685	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1681	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1665	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1574	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1545	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1544	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×#493	—	2	1	no	—
16	C₁₉×#492	C₂²	1	2	yes	—
17	C₁₉×#486	—	2	1	no	—
18	C₁₉×#486	C₂²	1	2	yes	—
19	C₁₉×#477	—	2	1	no	—
20	C₁₉×#474	C₂²	1	2	yes	complemented
21	C₁₉×#468	—	2	2	no	—
22	C₁₉×#461	C₂²	1	2	yes	complemented
23	C₁₉×#460	—	2	1	no	—
24	C₁₉×#460	—	2	1	no	—
25	C₁₉×#460	—	2	1	no	—
26	C₁₉×#459	C₂²	1	2	yes	—
27	C₁₉×#459	C₂²	1	2	yes	—
28	C₁₉×#450	—	2	2	no	—
29	C₁₉×#447	—	2	2	no	—
30	C₁₉×#436	—	2	1	no	—
31	C₁₉×#436	C₂²	1	2	yes	complemented
32	C₈×D₄×C₁₉	—	2	1	no	—
33	C₈×D₄×C₁₉	C₂²	1	2	yes	complemented
34	C₁₉×#431	C₂²	1	1	yes	characteristic
35	C₁₉×#431	C₂²	1	1	yes	characteristic
36	C₁₉×#431	C₂²	1	1	yes	characteristic
37	C₁₉×#423	C₂²	1	1	yes	characteristic
38	C₁₉×#408	—	2	2	no	—
39	C₁₉×#335	C₂²	1	2	yes	complemented
40	C₁₉×#334	C₂²	1	2	yes	complemented
41	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
42	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
43	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
44	C₁₉×#332	C₂²	1	1	yes	characteristic, complemented
45	C₁₉×#331	C₂²	1	2	yes	—
46	C₁₉×#331	C₂²	1	2	yes	—
47	C₂×#41×C₁₉	—	2	1	no	—
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	—	2	1	no	—
51	C₂×SD₁₆×C₁₉	—	2	2	no	—
52	C₂×SD₁₆×C₁₉	—	2	2	no	—
53	C₂×SD₁₆×C₁₉	—	2	2	no	—
54	C₂×D₈×C₁₉	—	2	2	no	—
55	C₂×D₈×C₁₉	—	2	2	no	—
56	C₂×M₁₆×C₁₉	—	2	1	no	—
57	C₂×M₁₆×C₁₉	—	2	2	no	—
58	C₂²×C₈×C₁₉	—	2	2	no	—
59	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
60	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
61	C₁₉×C₄⋊Q₈	C₂³	1	1	yes	characteristic
62	C₁₉×#127	—	2	1	no	—
63	C₁₉×#127	—	2	1	no	—
64	C₁₉×#127	—	2	1	no	—
65	C₁₉×#127	D₄	1	1	yes	characteristic
66	C₁₉×#127	C₂³	1	2	yes	—
67	C₁₉×#125	—	2	1	no	—
68	C₁₉×#124	—	2	1	no	—
69	C₁₉×C₂²⋊Q₈	—	2	1	no	—
70	C₁₉×C₂²⋊Q₈	—	2	1	no	—
71	C₁₉×#121	—	2	1	no	—
72	C₁₉×#121	D₄	1	2	yes	—
73	C₄×Q₈×C₁₉	—	2	1	no	—
74	C₄×Q₈×C₁₉	—	2	1	no	—
75	C₄×D₄×C₁₉	—	2	1	no	—
76	C₄×D₄×C₁₉	C₂³	1	2	yes	—
77	C₁₉×#117	—	2	1	no	—
78	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
79	C₁₉×#107	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	2	1	no	—
81	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
82	C₁₉×C₄⋊C₈	D₄	1	1	yes	characteristic
83	C₁₉×C₄⋊C₈	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₁₉×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₁₉×#103	—	2	2	no	—
89	C₁₉×#102	—	2	2	no	—
90	C₁₉×#102	—	2	2	no	—
91	C₁₉×#102	—	2	2	no	—
92	C₁₉×#102	—	2	2	no	—
93	C₁₉×#102	—	2	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	1	no	—
95	C₁₉×C₂²⋊C₈	—	2	1	no	—
96	C₁₉×C₂²⋊C₈	—	2	2	no	—
97	C₁₉×C₂²⋊C₈	—	2	2	no	—
98	C₁₉×C₂²⋊C₈	D₄	1	2	yes	—
99	C₄×C₈×C₁₉	—	2	1	no	—
100	C₄×C₈×C₁₉	—	2	1	no	—
101	C₄×C₈×C₁₉	C₂³	1	2	yes	—
102	C₂⁴×C₁₉	—	4	1	no	—
103	#41×C₁₉	—	8	1	no	—
104	#41×C₁₉	—	8	1	no	—
105	C₂×Q₈×C₁₉	—	2	1	no	—
106	C₂×Q₈×C₁₉	—	2	1	no	—
107	C₂×Q₈×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	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	1	no	—
118	C₂×D₄×C₁₉	—	8	1	no	—
119	C₂×D₄×C₁₉	—	8	1	no	—
120	C₂×D₄×C₁₉	—	8	1	no	—
121	C₂×D₄×C₁₉	—	8	2	no	—
122	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
127	SD₁₆×C₁₉	—	8	2	no	—
128	SD₁₆×C₁₉	—	8	2	no	—
129	SD₁₆×C₁₉	—	8	2	no	—
130	D₈×C₁₉	—	8	2	no	—
131	D₈×C₁₉	—	8	2	no	—
132	M₁₆×C₁₉	—	8	2	no	—
133	M₁₆×C₁₉	—	8	1	no	—
134	C₂×C₈×C₁₉	—	2	1	no	—
135	C₂×C₈×C₁₉	—	2	1	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	1	no	—
138	C₂×C₈×C₁₉	—	2	1	no	—
139	C₂×C₈×C₁₉	—	8	2	no	—
140	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₁₉	—	2	1	no	—
143	C₄⋊C₄×C₁₉	—	2	1	no	—
144	C₄⋊C₄×C₁₉	—	2	1	no	—
145	C₄⋊C₄×C₁₉	—	2	1	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	4	1	no	—
148	C₄⋊C₄×C₁₉	—	4	1	no	—
149	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₁₉	—	2	2	no	—
151	C₂²⋊C₄×C₁₉	—	2	2	no	—
152	C₂²⋊C₄×C₁₉	—	4	1	no	—
153	C₄²×C₁₉	—	4	1	no	—
154	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
155	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
156	C₄²×C₁₉	#41	1	1	yes	characteristic
157	C₄²×C₁₉	C₂⁴	1	1	yes	characteristic
158	#19552	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	8	2	no	—
162	C₂³×C₁₉	—	8	2	no	—
163	C₂³×C₁₉	—	8	2	no	—
164	C₂³×C₁₉	#121	1	1	yes	characteristic
165	Q₈×C₁₉	—	4	1	no	—
166	Q₈×C₁₉	—	4	1	no	—
167	Q₈×C₁₉	—	4	1	no	—
168	Q₈×C₁₉	—	4	1	no	—
169	Q₈×C₁₉	—	8	1	no	—
170	D₄×C₁₉	—	2	2	no	—
171	D₄×C₁₉	—	2	2	no	—
172	D₄×C₁₉	—	4	2	no	—
173	D₄×C₁₉	—	4	2	no	—
174	D₄×C₁₉	—	4	2	no	—
175	D₄×C₁₉	—	4	2	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	8	1	no	—
178	D₄×C₁₉	—	8	2	no	—
179	D₄×C₁₉	—	8	2	no	—
180	D₄×C₁₉	—	8	2	no	—
181	D₄×C₁₉	—	8	2	no	—
182	D₄×C₁₉	—	8	2	no	—
183	C₂×C₄×C₁₉	—	2	1	no	—
184	C₂×C₄×C₁₉	—	2	1	no	—
185	C₂×C₄×C₁₉	—	2	1	no	—
186	C₂×C₄×C₁₉	—	2	1	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	1	no	—
192	C₂×C₄×C₁₉	—	4	1	no	—
193	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
194	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
195	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
199	C₈×C₁₉	—	2	2	no	—
200	C₈×C₁₉	—	2	2	no	—
201	C₈×C₁₉	—	4	1	no	—
202	C₈×C₁₉	—	4	1	no	—
203	C₈×C₁₉	—	4	2	no	—
204	C₈×C₁₉	—	4	1	no	—
205	C₈×C₁₉	—	4	1	no	—
206	#3254	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#3208	C₂×C₁₉	1	1	yes	characteristic, complemented
208	#3205	C₂×C₁₉	1	1	yes	characteristic
209	#2979	C₂×C₁₉	1	1	yes	characteristic, complemented
210	#1701	C₂×C₁₉	1	2	yes	complemented
211	#1685	C₂×C₁₉	1	2	yes	complemented
212	#1681	C₂×C₁₉	1	2	yes	complemented
213	#1665	C₂×C₁₉	1	2	yes	complemented
214	#1574	C₂×C₁₉	1	1	yes	characteristic, complemented
215	#1545	C₂×C₁₉	1	1	yes	characteristic, complemented
216	#1544	C₂×C₁₉	1	1	yes	characteristic, complemented
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	4	2	no	—
221	C₂²×C₁₉	—	4	2	no	—
222	C₂²×C₁₉	—	4	2	no	—
223	C₂²×C₁₉	—	8	2	no	—
224	C₂²×C₁₉	—	8	2	no	—
225	C₂²×C₁₉	—	8	2	no	—
226	C₂²×C₁₉	—	16	4	no	—
227	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
228	C₄×C₁₉	—	2	1	no	—
229	C₄×C₁₉	—	2	1	no	—
230	C₄×C₁₉	—	2	1	no	—
231	C₄×C₁₉	—	4	2	no	—
232	C₄×C₁₉	—	8	1	no	—
233	C₄×C₁₉	—	8	1	no	—
234	C₄×C₁₉	#471	1	2	yes	—
235	C₄×C₁₉	#576	1	1	yes	characteristic
236	C₄×C₁₉	#576	1	1	yes	characteristic
237	C₄×C₁₉	#576	1	1	yes	characteristic
238	C₄×C₁₉	#577	1	1	yes	characteristic
239	#533	C₂²×C₁₉	1	1	yes	characteristic
240	#532	C₂²×C₁₉	1	1	yes	characteristic
241	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
242	#493	—	2	1	no	—
243	#492	C₂²×C₁₉	1	2	yes	—
244	#486	—	2	1	no	—
245	#486	C₂²×C₁₉	1	2	yes	—
246	#477	—	2	1	no	—
247	#474	C₂²×C₁₉	1	2	yes	complemented
248	#468	—	2	2	no	—
249	#461	C₂²×C₁₉	1	2	yes	complemented
250	#460	—	2	1	no	—
251	#460	—	2	1	no	—
252	#460	—	2	1	no	—
253	#459	C₂²×C₁₉	1	2	yes	—
254	#459	C₂²×C₁₉	1	2	yes	—
255	#450	—	2	2	no	—
256	#447	—	2	2	no	—
257	#436	—	2	1	no	—
258	#436	C₂²×C₁₉	1	2	yes	complemented
259	C₈×D₄	—	2	1	no	—
260	C₈×D₄	C₂²×C₁₉	1	2	yes	complemented
261	#431	C₂²×C₁₉	1	1	yes	characteristic
262	#431	C₂²×C₁₉	1	1	yes	characteristic
263	#431	C₂²×C₁₉	1	1	yes	characteristic
264	#423	C₂²×C₁₉	1	1	yes	characteristic
265	#408	—	2	2	no	—
266	#335	C₂²×C₁₉	1	2	yes	complemented
267	#334	C₂²×C₁₉	1	2	yes	complemented
268	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
269	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
270	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
271	#332	C₂²×C₁₉	1	1	yes	characteristic, complemented
272	#331	C₂²×C₁₉	1	2	yes	—
273	#331	C₂²×C₁₉	1	2	yes	—
274	C₂×C₁₉	—	4	1	no	—
275	C₂×C₁₉	—	8	2	no	—
276	C₂×C₁₉	—	16	2	no	—
277	C₂×C₁₉	#3041	1	1	yes	characteristic
278	C₂×C₁₉	#3062	1	1	yes	characteristic
279	C₂×C₁₉	C₂×#471	1	1	yes	characteristic
280	C₂×#41	—	2	1	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	1	no	—
283	C₂²×D₄	—	2	1	no	—
284	C₂×SD₁₆	—	2	2	no	—
285	C₂×SD₁₆	—	2	2	no	—
286	C₂×SD₁₆	—	2	2	no	—
287	C₂×D₈	—	2	2	no	—
288	C₂×D₈	—	2	2	no	—
289	C₂×M₁₆	—	2	1	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂²×C₈	—	2	2	no	—
292	C₄⋊Q₈	D₄×C₁₉	1	1	yes	characteristic
293	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
294	C₄⋊Q₈	C₂³×C₁₉	1	1	yes	characteristic
295	#127	—	2	1	no	—
296	#127	—	2	1	no	—
297	#127	—	2	1	no	—
298	#127	D₄×C₁₉	1	1	yes	characteristic
299	#127	C₂³×C₁₉	1	2	yes	—
300	#125	—	2	1	no	—
301	#124	—	2	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	#121	—	2	1	no	—
305	#121	D₄×C₁₉	1	2	yes	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	C₂³×C₁₉	1	2	yes	—
310	#117	—	2	1	no	—
311	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
312	#107	—	2	2	no	—
313	C₄⋊C₈	—	2	1	no	—
314	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
315	C₄⋊C₈	D₄×C₁₉	1	1	yes	characteristic
316	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
317	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
318	C₄⋊C₈	C₂³×C₁₉	1	2	yes	—
319	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
320	C₄⋊C₈	C₂³×C₁₉	1	1	yes	characteristic
321	#103	—	2	2	no	—
322	#102	—	2	2	no	—
323	#102	—	2	2	no	—
324	#102	—	2	2	no	—
325	#102	—	2	2	no	—
326	#102	—	2	2	no	—
327	C₂²⋊C₈	—	2	1	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	2	2	no	—
330	C₂²⋊C₈	—	2	2	no	—
331	C₂²⋊C₈	D₄×C₁₉	1	2	yes	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	—	2	1	no	—
334	C₄×C₈	C₂³×C₁₉	1	2	yes	—
335	C₁₉	#19552	1	1	yes	characteristic, direct product factor, Sylow
336	C₂⁴	—	4	1	no	—
337	#41	—	8	1	no	—
338	#41	—	8	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×D₄	—	2	2	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	8	1	no	—
352	C₂×D₄	—	8	1	no	—
353	C₂×D₄	—	8	1	no	—
354	C₂×D₄	—	8	1	no	—
355	C₂×D₄	—	8	2	no	—
356	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
360	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
361	SD₁₆	—	8	2	no	—
362	SD₁₆	—	8	2	no	—
363	SD₁₆	—	8	2	no	—
364	D₈	—	8	2	no	—
365	D₈	—	8	2	no	—
366	M₁₆	—	8	2	no	—
367	M₁₆	—	8	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	8	2	no	—
374	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
375	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	4	1	no	—
382	C₄⋊C₄	—	4	1	no	—
383	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
384	C₂²⋊C₄	—	2	2	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
389	C₄²	C₂×D₄×C₁₉	1	1	yes	characteristic
390	C₄²	#41×C₁₉	1	1	yes	characteristic
391	C₄²	C₂⁴×C₁₉	1	1	yes	characteristic
392	C₂³	—	2	2	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	8	2	no	—
395	C₂³	—	8	2	no	—
396	C₂³	—	8	2	no	—
397	C₂³	C₁₉×#121	1	1	yes	characteristic
398	Q₈	—	4	1	no	—
399	Q₈	—	4	1	no	—
400	Q₈	—	4	1	no	—
401	Q₈	—	4	1	no	—
402	Q₈	—	8	1	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	4	2	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	2	no	—
410	D₄	—	8	1	no	—
411	D₄	—	8	2	no	—
412	D₄	—	8	2	no	—
413	D₄	—	8	2	no	—
414	D₄	—	8	2	no	—
415	D₄	—	8	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
427	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
428	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
429	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
432	C₈	—	2	2	no	—
433	C₈	—	2	2	no	—
434	C₈	—	4	1	no	—
435	C₈	—	4	1	no	—
436	C₈	—	4	2	no	—
437	C₈	—	4	1	no	—
438	C₈	—	4	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	2	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	2	no	—
448	C₂²	—	16	4	no	—
449	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	4	2	no	—
454	C₄	—	8	1	no	—
455	C₄	—	8	1	no	—
456	C₄	C₁₉×#471	1	2	yes	—
457	C₄	C₁₉×#576	1	1	yes	characteristic
458	C₄	C₁₉×#576	1	1	yes	characteristic
459	C₄	C₁₉×#576	1	1	yes	characteristic
460	C₄	C₁₉×#577	1	1	yes	characteristic
461	C₂	—	4	1	no	—
462	C₂	—	8	2	no	—
463	C₂	—	16	2	no	—
464	C₂	C₁₉×#3041	1	1	yes	characteristic
465	C₂	C₁₉×#3062	1	1	yes	characteristic
466	C₂	C₂×C₁₉×#471	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×#3254	C₂	semidirect
2. C₁₉×#3208	C₂	semidirect
4. C₁₉×#2979	C₂	semidirect
5. C₁₉×#1701	C₂	semidirect
6. C₁₉×#1685	C₂	semidirect
7. C₁₉×#1681	C₂	semidirect
8. C₁₉×#1665	C₂	semidirect
9. C₁₉×#1574	C₂	semidirect
10. C₁₉×#1545	C₂	semidirect
11. C₁₉×#1544	C₂	semidirect
20. C₁₉×#474	C₂²	semidirect
22. C₁₉×#461	C₂²	semidirect
31. C₁₉×#436	C₂²	semidirect
33. C₈×D₄×C₁₉	C₂²	semidirect
39. C₁₉×#335	C₂²	semidirect
40. C₁₉×#334	C₂²	semidirect
41. C₁₉×#332	C₂²	semidirect
42. C₁₉×#332	C₂²	semidirect
43. C₁₉×#332	C₂²	semidirect
44. C₁₉×#332	C₂²	semidirect
158. #19552	C₁₉	direct (N × H)
206. #3254	C₂×C₁₉	semidirect
207. #3208	C₂×C₁₉	semidirect
209. #2979	C₂×C₁₉	semidirect
210. #1701	C₂×C₁₉	semidirect
211. #1685	C₂×C₁₉	semidirect
212. #1681	C₂×C₁₉	semidirect
213. #1665	C₂×C₁₉	semidirect
214. #1574	C₂×C₁₉	semidirect
215. #1545	C₂×C₁₉	semidirect
216. #1544	C₂×C₁₉	semidirect
247. #474	C₂²×C₁₉	semidirect
249. #461	C₂²×C₁₉	semidirect
258. #436	C₂²×C₁₉	semidirect
260. C₈×D₄	C₂²×C₁₉	semidirect
266. #335	C₂²×C₁₉	semidirect
267. #334	C₂²×C₁₉	semidirect
268. #332	C₂²×C₁₉	semidirect
269. #332	C₂²×C₁₉	semidirect
270. #332	C₂²×C₁₉	semidirect
271. #332	C₂²×C₁₉	semidirect
335. C₁₉	#19552	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×#3254	2
C₁₉×#3208	2
C₁₉×#3205	2
C₁₉×#2979	2
C₁₉×#1701	2
C₁₉×#1685	2
C₁₉×#1681	2
C₁₉×#1665	2
C₁₉×#1574	2
C₁₉×#1545	2
C₁₉×#1544	2
#19552	19

Subgroups — C19×#19552 #18025511

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#19552 #18025511