Subgroups — C₁₉×#20749 #18026708

Order 4864.

1258 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3428	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2298	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#1826	C₂	1	2	yes	maximal, complemented
5	C₁₉×#1806	C₂	1	4	yes	maximal, complemented
6	C₁₉×#1789	C₂	1	2	yes	maximal
7	C₁₉×#1759	C₂	1	2	yes	maximal, complemented
8	C₄×C₁₉×#104	C₂	1	2	yes	maximal, complemented
9	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
10	C₁₉×#520	—	2	2	no	—
11	C₁₉×#520	C₄	1	4	yes	complemented
12	C₁₉×#519	C₄	1	2	yes	complemented
13	C₁₉×#518	—	2	2	no	—
14	C₁₉×#518	C₄	1	2	yes	complemented
15	C₄×#41×C₁₉	—	2	2	no	—
16	C₄×#41×C₁₉	C₂²	1	2	yes	—
17	C₄×#41×C₁₉	C₂²	1	2	yes	—
18	C₂×C₁₉×#117	—	2	2	no	—
19	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
21	C₁₉×#433	—	2	2	no	—
22	C₁₉×#433	—	2	2	no	—
23	C₁₉×#423	C₂²	1	2	yes	complemented
24	C₂×C₁₉×#104	C₂²	1	4	yes	—
25	C₂×C₁₉×#104	C₂²	1	4	yes	—
26	C₁₉×#407	C₂²	1	2	yes	—
27	C₄×M₁₆×C₁₉	C₂²	1	2	yes	complemented
28	C₁₉×#388	—	2	2	no	—
29	C₁₉×#387	—	2	2	no	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	complemented
31	C₄×C₂²⋊C₄×C₁₉	C₂²	1	2	yes	—
32	C₁₉×#376	C₂²	1	1	yes	characteristic, complemented
33	C₄³×C₁₉	C₂²	1	1	yes	characteristic, complemented
34	C₁₉×#339	C₂²	1	4	yes	complemented
35	C₁₉×#339	C₂²	1	4	yes	complemented
36	C₂×#41×C₁₉	—	2	8	no	—
37	C₂×#41×C₁₉	—	2	1	no	—
38	C₂×#41×C₁₉	—	2	1	no	—
39	C₂×#41×C₁₉	C₂×C₄	1	2	yes	—
40	C₂×#41×C₁₉	C₂³	1	2	yes	—
41	C₂²×Q₈×C₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂²×D₄×C₁₉	—	2	1	no	—
43	C₂²×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
47	C₄×Q₈×C₁₉	—	2	4	no	—
48	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
49	C₄×Q₈×C₁₉	C₂×C₄	1	4	yes	—
50	C₄×D₄×C₁₉	—	2	4	no	—
51	C₄×D₄×C₁₉	—	2	4	no	—
52	C₄×D₄×C₁₉	—	2	4	no	—
53	C₄×D₄×C₁₉	—	2	4	no	—
54	C₄×D₄×C₁₉	—	2	4	no	—
55	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
56	C₄×D₄×C₁₉	C₂×C₄	1	4	yes	—
57	C₁₉×#117	—	2	1	no	—
58	C₁₉×#117	—	2	1	no	—
59	C₁₉×#117	—	2	4	no	—
60	C₁₉×#117	—	2	4	no	—
61	C₁₉×#117	—	2	2	no	—
62	C₁₉×#117	—	2	2	no	—
63	C₁₉×#117	C₂×C₄	1	2	yes	—
64	C₁₉×#117	C₂×C₄	1	2	yes	—
65	C₁₉×#117	C₂×C₄	1	2	yes	—
66	C₁₉×#117	D₄	1	2	yes	—
67	C₁₉×#117	D₄	1	2	yes	—
68	C₁₉×#117	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
77	C₂×C₄²×C₁₉	—	2	1	no	—
78	C₂×C₄²×C₁₉	—	2	2	no	—
79	C₂×C₄²×C₁₉	—	2	2	no	—
80	C₂×C₄²×C₁₉	—	2	2	no	—
81	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
82	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
83	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
85	C₁₉×C₄⋊C₈	—	2	4	no	—
86	C₁₉×#104	—	2	8	no	—
87	C₁₉×#104	—	2	8	no	—
88	C₁₉×C₂²⋊C₈	—	2	2	no	—
89	C₁₉×C₂²⋊C₈	—	2	2	no	—
90	C₁₉×#97	—	2	2	no	—
91	C₄×C₈×C₁₉	—	2	2	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	—	2	2	no	—
95	C₂⁴×C₁₉	—	2	1	no	—
96	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
97	#41×C₁₉	—	2	8	no	—
98	#41×C₁₉	—	2	8	no	—
99	#41×C₁₉	—	2	4	no	—
100	#41×C₁₉	—	2	4	no	—
101	#41×C₁₉	—	2	4	no	—
102	#41×C₁₉	#41	1	8	yes	—
103	C₂×Q₈×C₁₉	—	2	4	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	C₂²×C₄	1	2	yes	—
106	C₂×D₄×C₁₉	—	2	8	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₁₉	—	2	8	no	—
113	C₂²×C₄×C₁₉	—	2	1	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	4	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	4	no	—
120	C₂²×C₄×C₁₉	—	2	4	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₁₉	—	2	4	no	—
131	M₁₆×C₁₉	—	2	4	no	—
132	C₂×C₈×C₁₉	—	2	4	no	—
133	C₄⋊C₄×C₁₉	—	2	2	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	4	4	no	—
137	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
138	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
139	C₄⋊C₄×C₁₉	C₂²×C₄	1	4	yes	—
140	C₂²⋊C₄×C₁₉	—	2	2	no	—
141	C₂²⋊C₄×C₁₉	—	2	2	no	—
142	C₂²⋊C₄×C₁₉	—	2	4	no	—
143	C₂²⋊C₄×C₁₉	—	2	4	no	—
144	C₂²⋊C₄×C₁₉	—	4	4	no	—
145	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
146	C₂²⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
147	C₄²×C₁₉	—	2	4	no	—
148	C₄²×C₁₉	—	2	4	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	C₄²×C₁₉	—	2	2	no	—
151	C₄²×C₁₉	—	2	4	no	—
152	C₄²×C₁₉	—	2	4	no	—
153	C₄²×C₁₉	—	4	4	no	—
154	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
155	C₄²×C₁₉	C₂²×C₄	1	2	yes	—
156	C₄²×C₁₉	C₂×D₄	1	2	yes	—
157	C₄²×C₁₉	C₂×D₄	1	2	yes	—
158	#20749	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂³×C₁₉	—	2	4	no	—
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	—	2	2	no	—
162	C₂³×C₁₉	—	4	2	no	—
163	C₂³×C₁₉	—	8	2	no	—
164	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₉	—	2	4	no	—
168	Q₈×C₁₉	—	2	2	no	—
169	Q₈×C₁₉	#117	1	4	yes	—
170	D₄×C₁₉	—	2	8	no	—
171	D₄×C₁₉	—	2	4	no	—
172	D₄×C₁₉	—	2	8	no	—
173	D₄×C₁₉	—	2	2	no	—
174	D₄×C₁₉	#117	1	4	yes	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	2	8	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	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	8	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	4	no	—
186	C₂×C₄×C₁₉	—	4	2	no	—
187	C₂×C₄×C₁₉	—	4	2	no	—
188	C₂×C₄×C₁₉	—	4	2	no	—
189	C₂×C₄×C₁₉	—	4	2	no	—
190	C₂×C₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	4	2	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	8	4	no	—
194	C₂×C₄×C₁₉	—	8	4	no	—
195	C₂×C₄×C₁₉	—	8	2	no	—
196	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
198	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	4	yes	—
199	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₉	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₁₉	C₂×#41	1	4	yes	—
203	C₈×C₁₉	—	4	4	no	—
204	#3428	C₂×C₁₉	1	1	yes	characteristic
205	#2921	C₂×C₁₉	1	1	yes	characteristic, complemented
206	#2298	C₂×C₁₉	1	1	yes	characteristic, complemented
207	#1826	C₂×C₁₉	1	2	yes	complemented
208	#1806	C₂×C₁₉	1	4	yes	complemented
209	#1789	C₂×C₁₉	1	2	yes	—
210	#1759	C₂×C₁₉	1	2	yes	complemented
211	C₄×#104	C₂×C₁₉	1	2	yes	complemented
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	2	1	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	4	no	—
218	C₂²×C₁₉	—	4	4	no	—
219	C₂²×C₁₉	—	8	2	no	—
220	C₂²×C₁₉	—	8	4	no	—
221	C₂²×C₁₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
222	C₂²×C₁₉	#525	1	2	yes	—
223	C₄×C₁₉	—	2	4	no	—
224	C₄×C₁₉	—	2	4	no	—
225	C₄×C₁₉	—	2	1	no	—
226	C₄×C₁₉	—	2	4	no	—
227	C₄×C₁₉	—	2	1	no	—
228	C₄×C₁₉	—	4	4	no	—
229	C₄×C₁₉	—	4	4	no	—
230	C₄×C₁₉	—	8	2	no	—
231	C₄×C₁₉	C₂×#117	1	2	yes	—
232	C₄×C₁₉	#525	1	2	yes	—
233	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
234	#520	—	2	2	no	—
235	#520	C₄×C₁₉	1	4	yes	complemented
236	#519	C₄×C₁₉	1	2	yes	complemented
237	#518	—	2	2	no	—
238	#518	C₄×C₁₉	1	2	yes	complemented
239	C₄×#41	—	2	2	no	—
240	C₄×#41	C₂²×C₁₉	1	2	yes	—
241	C₄×#41	C₂²×C₁₉	1	2	yes	—
242	C₂×#117	—	2	2	no	—
243	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
244	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
245	#433	—	2	2	no	—
246	#433	—	2	2	no	—
247	#423	C₂²×C₁₉	1	2	yes	complemented
248	C₂×#104	C₂²×C₁₉	1	4	yes	—
249	C₂×#104	C₂²×C₁₉	1	4	yes	—
250	#407	C₂²×C₁₉	1	2	yes	—
251	C₄×M₁₆	C₂²×C₁₉	1	2	yes	complemented
252	#388	—	2	2	no	—
253	#387	—	2	2	no	—
254	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	complemented
255	C₄×C₂²⋊C₄	C₂²×C₁₉	1	2	yes	—
256	#376	C₂²×C₁₉	1	1	yes	characteristic, complemented
257	C₄³	C₂²×C₁₉	1	1	yes	characteristic, complemented
258	#339	C₂²×C₁₉	1	4	yes	complemented
259	#339	C₂²×C₁₉	1	4	yes	complemented
260	C₂×C₁₉	—	2	2	no	—
261	C₂×C₁₉	—	4	1	no	—
262	C₂×C₁₉	—	4	1	no	—
263	C₂×C₁₉	—	4	4	no	—
264	C₂×C₁₉	#2280	1	1	yes	characteristic
265	C₂×C₁₉	#2901	1	2	yes	—
266	C₂×#41	—	2	8	no	—
267	C₂×#41	—	2	1	no	—
268	C₂×#41	—	2	1	no	—
269	C₂×#41	C₂×C₄×C₁₉	1	2	yes	—
270	C₂×#41	C₂³×C₁₉	1	2	yes	—
271	C₂²×Q₈	C₂×C₄×C₁₉	1	1	yes	characteristic
272	C₂²×D₄	—	2	1	no	—
273	C₂²×D₄	C₂×C₄×C₁₉	1	1	yes	characteristic
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
276	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
277	C₄×Q₈	—	2	4	no	—
278	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
279	C₄×Q₈	C₂×C₄×C₁₉	1	4	yes	—
280	C₄×D₄	—	2	4	no	—
281	C₄×D₄	—	2	4	no	—
282	C₄×D₄	—	2	4	no	—
283	C₄×D₄	—	2	4	no	—
284	C₄×D₄	—	2	4	no	—
285	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
286	C₄×D₄	C₂×C₄×C₁₉	1	4	yes	—
287	#117	—	2	1	no	—
288	#117	—	2	1	no	—
289	#117	—	2	4	no	—
290	#117	—	2	4	no	—
291	#117	—	2	2	no	—
292	#117	—	2	2	no	—
293	#117	C₂×C₄×C₁₉	1	2	yes	—
294	#117	C₂×C₄×C₁₉	1	2	yes	—
295	#117	C₂×C₄×C₁₉	1	2	yes	—
296	#117	D₄×C₁₉	1	2	yes	—
297	#117	D₄×C₁₉	1	2	yes	—
298	#117	C₂³×C₁₉	1	2	yes	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
302	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	4	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	2	no	—
309	C₂×C₄²	—	2	2	no	—
310	C₂×C₄²	—	2	2	no	—
311	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
312	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
313	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
314	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
315	C₄⋊C₈	—	2	4	no	—
316	#104	—	2	8	no	—
317	#104	—	2	8	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	#97	—	2	2	no	—
321	C₄×C₈	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	#95	—	2	2	no	—
325	C₁₉	#20749	1	1	yes	characteristic, direct product factor, Sylow
326	C₂⁴	—	2	1	no	—
327	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
328	#41	—	2	8	no	—
329	#41	—	2	8	no	—
330	#41	—	2	4	no	—
331	#41	—	2	4	no	—
332	#41	—	2	4	no	—
333	#41	#41×C₁₉	1	8	yes	—
334	C₂×Q₈	—	2	4	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	C₂²×C₄×C₁₉	1	2	yes	—
337	C₂×D₄	—	2	8	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	4	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	C₂²×C₄×C₁₉	1	2	yes	—
343	C₂²×C₄	—	2	8	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	4	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
358	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
359	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
360	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
361	M₁₆	—	2	4	no	—
362	M₁₆	—	2	4	no	—
363	C₂×C₈	—	2	4	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	4	no	—
367	C₄⋊C₄	—	4	4	no	—
368	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
369	C₄⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
370	C₄⋊C₄	C₂²×C₄×C₁₉	1	4	yes	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	2	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
377	C₂²⋊C₄	C₂²⋊C₄×C₁₉	1	4	yes	—
378	C₄²	—	2	4	no	—
379	C₄²	—	2	4	no	—
380	C₄²	—	2	2	no	—
381	C₄²	—	2	2	no	—
382	C₄²	—	2	4	no	—
383	C₄²	—	2	4	no	—
384	C₄²	—	4	4	no	—
385	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
386	C₄²	C₂²×C₄×C₁₉	1	2	yes	—
387	C₄²	C₂×D₄×C₁₉	1	2	yes	—
388	C₄²	C₂×D₄×C₁₉	1	2	yes	—
389	C₂³	—	2	4	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	—	8	2	no	—
394	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
395	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
396	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
397	Q₈	—	2	4	no	—
398	Q₈	—	2	2	no	—
399	Q₈	C₁₉×#117	1	4	yes	—
400	D₄	—	2	8	no	—
401	D₄	—	2	4	no	—
402	D₄	—	2	8	no	—
403	D₄	—	2	2	no	—
404	D₄	C₁₉×#117	1	4	yes	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	8	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	4	no	—
424	C₂×C₄	—	8	4	no	—
425	C₂×C₄	—	8	2	no	—
426	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
427	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
428	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	4	yes	—
429	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
430	C₂×C₄	C₂³×C₄×C₁₉	1	1	yes	characteristic
431	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
432	C₂×C₄	C₂×#41×C₁₉	1	4	yes	—
433	C₈	—	4	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	4	no	—
443	C₂²	C₂²×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
444	C₂²	C₁₉×#525	1	2	yes	—
445	C₄	—	2	1	no	—
446	C₄	—	2	4	no	—
447	C₄	—	2	1	no	—
448	C₄	—	2	4	no	—
449	C₄	—	2	4	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₄	—	8	2	no	—
453	C₄	C₂×C₁₉×#117	1	2	yes	—
454	C₄	C₁₉×#525	1	2	yes	—
455	C₂	—	2	2	no	—
456	C₂	—	4	1	no	—
457	C₂	—	4	1	no	—
458	C₂	—	4	4	no	—
459	C₂	C₁₉×#2280	1	1	yes	characteristic
460	C₂	C₁₉×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
socle	C₂²×C₁₉	C₂²×C₂²⋊C₄
prime radical	C₂²×#41×C₁₉	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₉ ◁ C₂×C₁₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₉×#2921	C₂	semidirect
3. C₁₉×#2298	C₂	semidirect
4. C₁₉×#1826	C₂	semidirect
5. C₁₉×#1806	C₂	semidirect
7. C₁₉×#1759	C₂	semidirect
8. C₄×C₁₉×#104	C₂	semidirect
11. C₁₉×#520	C₄	semidirect
12. C₁₉×#519	C₄	semidirect
14. C₁₉×#518	C₄	semidirect
23. C₁₉×#423	C₂²	semidirect
27. C₄×M₁₆×C₁₉	C₂²	semidirect
30. C₄×C₄⋊C₄×C₁₉	C₂²	semidirect
32. C₁₉×#376	C₂²	semidirect
33. C₄³×C₁₉	C₂²	semidirect
34. C₁₉×#339	C₂²	semidirect
35. C₁₉×#339	C₂²	semidirect
158. #20749	C₁₉	direct (N × H)
205. #2921	C₂×C₁₉	semidirect
206. #2298	C₂×C₁₉	semidirect
207. #1826	C₂×C₁₉	semidirect
208. #1806	C₂×C₁₉	semidirect
210. #1759	C₂×C₁₉	semidirect
211. C₄×#104	C₂×C₁₉	semidirect
235. #520	C₄×C₁₉	semidirect
236. #519	C₄×C₁₉	semidirect
238. #518	C₄×C₁₉	semidirect
247. #423	C₂²×C₁₉	semidirect
251. C₄×M₁₆	C₂²×C₁₉	semidirect
254. C₄×C₄⋊C₄	C₂²×C₁₉	semidirect
256. #376	C₂²×C₁₉	semidirect
257. C₄³	C₂²×C₁₉	semidirect
258. #339	C₂²×C₁₉	semidirect
259. #339	C₂²×C₁₉	semidirect
325. C₁₉	#20749	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×#3428	2
C₁₉×#2921	2
C₁₉×#2298	2
C₁₉×#1826	2
C₁₉×#1806	2
C₁₉×#1789	2
C₁₉×#1759	2
C₄×C₁₉×#104	2
#20749	19

Subgroups — C19×#20749 #18026708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#20749 #18026708