Subgroups — C₁₉×#23500 #18029459

Order 4864.

1422 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#421	C₂	1	2	yes	maximal, complemented
3	C₂×C₁₉×#417	C₂	1	2	yes	maximal, complemented
4	C₁₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2040	C₂	1	4	yes	maximal, complemented
6	C₁₉×#2039	C₂	1	4	yes	maximal, complemented
7	C₁₉×#1742	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₉	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
10	C₁₉×#537	C₂²	1	2	yes	—
11	C₁₉×#537	C₂²	1	2	yes	—
12	C₁₉×#536	—	2	2	no	—
13	C₁₉×#535	—	2	2	no	—
14	C₁₉×#534	—	2	2	no	—
15	C₁₉×#532	—	2	2	no	—
16	C₁₉×#525	—	2	4	no	—
17	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#421	—	2	8	no	—
21	C₂×C₁₉×#104	C₂²	1	8	yes	complemented
22	C₁₉×#417	—	2	4	no	—
23	C₁₉×#417	C₂²	1	8	yes	complemented
24	C₂×C₁₉×#103	—	2	2	no	—
25	C₂×C₁₉×#102	—	2	2	no	—
26	C₁₉×#389	—	2	2	no	—
27	C₁₉×#385	—	2	2	no	—
28	C₁₉×#384	C₂²	1	2	yes	complemented
29	C₁₉×#382	C₂²	1	2	yes	complemented
30	C₁₉×#343	C₂²	1	2	yes	complemented
31	C₁₉×#343	C₂²	1	2	yes	complemented
32	C₂×#41×C₁₉	—	2	2	no	—
33	C₂×#41×C₁₉	—	2	2	no	—
34	C₂×#41×C₁₉	—	2	4	no	—
35	C₂×#41×C₁₉	—	2	4	no	—
36	C₂×#41×C₁₉	—	2	4	no	—
37	C₂×#41×C₁₉	—	2	4	no	—
38	C₂×#41×C₁₉	D₄	1	4	yes	—
39	C₂×#41×C₁₉	C₂³	1	4	yes	—
40	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
41	C₂²×D₄×C₁₉	—	2	2	no	—
42	C₂²×D₄×C₁₉	D₄	1	2	yes	—
43	C₂³×C₄×C₁₉	—	2	2	no	—
44	C₂³×C₄×C₁₉	—	2	1	no	—
45	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₁₉	—	2	2	no	—
47	C₂×M₁₆×C₁₉	—	2	4	no	—
48	C₂×M₁₆×C₁₉	—	2	4	no	—
49	C₂×M₁₆×C₁₉	C₂³	1	4	yes	—
50	C₂²×C₈×C₁₉	—	2	2	no	—
51	C₁₉×C₄⋊Q₈	—	2	2	no	—
52	C₁₉×#127	—	2	2	no	—
53	C₁₉×#124	—	2	4	no	—
54	C₁₉×#123	—	2	8	no	—
55	C₁₉×C₂²⋊Q₈	—	2	4	no	—
56	C₁₉×C₂²⋊Q₈	—	2	4	no	—
57	C₁₉×#121	—	2	4	no	—
58	C₁₉×#121	—	2	4	no	—
59	C₁₉×#121	—	2	4	no	—
60	C₁₉×#121	—	2	4	no	—
61	C₁₉×#120	—	2	8	no	—
62	C₄×D₄×C₁₉	—	2	4	no	—
63	C₄×D₄×C₁₉	—	2	4	no	—
64	C₁₉×#117	—	2	2	no	—
65	C₁₉×#117	—	2	2	no	—
66	C₁₉×#117	—	2	2	no	—
67	C₁₉×#117	D₄	1	4	yes	complemented
68	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
69	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
78	C₂×C₄²×C₁₉	D₄	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
80	C₁₉×#104	—	2	16	no	—
81	C₁₉×#103	—	2	8	no	—
82	C₁₉×#102	—	2	8	no	—
83	C₁₉×#95	—	2	4	no	—
84	C₂⁴×C₁₉	—	2	2	no	—
85	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
86	#41×C₁₉	—	2	8	no	—
87	#41×C₁₉	—	2	8	no	—
88	#41×C₁₉	—	2	4	no	—
89	#41×C₁₉	—	2	4	no	—
90	#41×C₁₉	—	2	4	no	—
91	#41×C₁₉	—	2	4	no	—
92	#41×C₁₉	—	4	4	no	—
93	#41×C₁₉	—	4	4	no	—
94	#41×C₁₉	—	4	4	no	—
95	#41×C₁₉	—	4	4	no	—
96	C₂×Q₈×C₁₉	—	2	2	no	—
97	C₂×Q₈×C₁₉	—	2	4	no	—
98	C₂×Q₈×C₁₉	—	2	4	no	—
99	C₂×Q₈×C₁₉	C₂×D₄	1	4	yes	—
100	C₂×D₄×C₁₉	—	2	4	no	—
101	C₂×D₄×C₁₉	—	2	4	no	—
102	C₂×D₄×C₁₉	—	2	4	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	4	no	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	4	4	no	—
108	C₂×D₄×C₁₉	—	4	4	no	—
109	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₁₉	—	2	2	no	—
111	C₂²×C₄×C₁₉	—	2	2	no	—
112	C₂²×C₄×C₁₉	—	2	4	no	—
113	C₂²×C₄×C₁₉	—	2	4	no	—
114	C₂²×C₄×C₁₉	—	2	2	no	—
115	C₂²×C₄×C₁₉	—	4	4	no	—
116	C₂²×C₄×C₁₉	—	4	4	no	—
117	C₂²×C₄×C₁₉	—	4	2	no	—
118	C₂²×C₄×C₁₉	—	8	2	no	—
119	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	#41	1	4	yes	—
126	C₂²×C₄×C₁₉	#41	1	2	yes	—
127	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
128	M₁₆×C₁₉	—	2	4	no	—
129	M₁₆×C₁₉	—	2	4	no	—
130	M₁₆×C₁₉	—	4	4	no	—
131	C₂×C₈×C₁₉	—	2	4	no	—
132	C₂×C₈×C₁₉	—	4	4	no	—
133	C₄⋊C₄×C₁₉	—	2	4	no	—
134	C₄⋊C₄×C₁₉	—	2	4	no	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₄⋊C₄×C₁₉	—	2	2	no	—
137	C₄⋊C₄×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	4	1	no	—
140	C₄⋊C₄×C₁₉	—	4	1	no	—
141	C₄⋊C₄×C₁₉	—	8	4	no	—
142	C₂²⋊C₄×C₁₉	—	2	8	no	—
143	C₂²⋊C₄×C₁₉	—	2	8	no	—
144	C₂²⋊C₄×C₁₉	—	2	4	no	—
145	C₂²⋊C₄×C₁₉	—	2	4	no	—
146	C₄²×C₁₉	—	2	2	no	—
147	C₄²×C₁₉	—	2	2	no	—
148	C₄²×C₁₉	—	2	2	no	—
149	C₄²×C₁₉	C₂×D₄	1	4	yes	—
150	#23500	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	4	no	—
152	C₂³×C₁₉	—	4	1	no	—
153	C₂³×C₁₉	—	4	1	no	—
154	C₂³×C₁₉	—	4	4	no	—
155	C₂³×C₁₉	—	8	2	no	—
156	C₂³×C₁₉	—	8	2	no	—
157	C₂³×C₁₉	#120	1	2	yes	—
158	C₂³×C₁₉	#121	1	2	yes	—
159	C₂³×C₁₉	#124	1	2	yes	—
160	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₁₉	—	2	4	no	—
162	Q₈×C₁₉	—	2	4	no	—
163	Q₈×C₁₉	—	4	4	no	—
164	D₄×C₁₉	—	2	4	no	—
165	D₄×C₁₉	—	2	4	no	—
166	D₄×C₁₉	—	4	4	no	—
167	D₄×C₁₉	—	4	4	no	—
168	D₄×C₁₉	—	4	8	no	—
169	D₄×C₁₉	—	4	4	no	—
170	D₄×C₁₉	—	8	4	no	—
171	D₄×C₁₉	—	8	4	no	—
172	C₂×C₄×C₁₉	—	2	2	no	—
173	C₂×C₄×C₁₉	—	2	2	no	—
174	C₂×C₄×C₁₉	—	2	4	no	—
175	C₂×C₄×C₁₉	—	2	4	no	—
176	C₂×C₄×C₁₉	—	4	2	no	—
177	C₂×C₄×C₁₉	—	4	2	no	—
178	C₂×C₄×C₁₉	—	4	4	no	—
179	C₂×C₄×C₁₉	—	4	4	no	—
180	C₂×C₄×C₁₉	—	4	4	no	—
181	C₂×C₄×C₁₉	—	4	8	no	—
182	C₂×C₄×C₁₉	—	4	2	no	—
183	C₂×C₄×C₁₉	—	4	2	no	—
184	C₂×C₄×C₁₉	—	4	4	no	—
185	C₂×C₄×C₁₉	—	4	2	no	—
186	C₂×C₄×C₁₉	—	8	4	no	—
187	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#121	1	4	yes	—
190	C₂×C₄×C₁₉	#121	1	4	yes	—
191	C₂×C₄×C₁₉	#121	1	2	yes	—
192	C₂×C₄×C₁₉	#123	1	4	yes	—
193	C₂×C₄×C₁₉	#123	1	4	yes	—
194	C₂×C₄×C₁₉	#124	1	2	yes	—
195	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
198	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
199	C₈×C₁₉	—	4	4	no	—
200	#3449	C₂×C₁₉	1	1	yes	characteristic
201	C₂×#421	C₂×C₁₉	1	2	yes	complemented
202	C₂×#417	C₂×C₁₉	1	2	yes	complemented
203	#2317	C₂×C₁₉	1	1	yes	characteristic, complemented
204	#2040	C₂×C₁₉	1	4	yes	complemented
205	#2039	C₂×C₁₉	1	4	yes	complemented
206	#1742	C₂×C₁₉	1	1	yes	characteristic, complemented
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	2	no	—
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	4	2	no	—
212	C₂²×C₁₉	—	4	2	no	—
213	C₂²×C₁₉	—	4	4	no	—
214	C₂²×C₁₉	—	4	4	no	—
215	C₂²×C₁₉	—	4	4	no	—
216	C₂²×C₁₉	—	8	8	no	—
217	C₂²×C₁₉	#394	1	4	yes	—
218	C₂²×C₁₉	C₂×#120	1	1	yes	characteristic
219	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
220	C₂²×C₁₉	C₂×#124	1	1	yes	characteristic
221	C₄×C₁₉	—	4	4	no	—
222	C₄×C₁₉	—	4	4	no	—
223	C₄×C₁₉	—	4	2	no	—
224	C₄×C₁₉	—	4	2	no	—
225	C₄×C₁₉	—	8	2	no	—
226	C₄×C₁₉	#394	1	2	yes	—
227	C₄×C₁₉	#394	1	2	yes	—
228	C₄×C₁₉	C₂×#121	1	2	yes	—
229	C₄×C₁₉	C₂×#123	1	2	yes	—
230	C₂²×#41	C₂²×C₁₉	1	2	yes	—
231	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
232	#537	C₂²×C₁₉	1	2	yes	—
233	#537	C₂²×C₁₉	1	2	yes	—
234	#536	—	2	2	no	—
235	#535	—	2	2	no	—
236	#534	—	2	2	no	—
237	#532	—	2	2	no	—
238	#525	—	2	4	no	—
239	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
240	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
242	#421	—	2	8	no	—
243	C₂×#104	C₂²×C₁₉	1	8	yes	complemented
244	#417	—	2	4	no	—
245	#417	C₂²×C₁₉	1	8	yes	complemented
246	C₂×#103	—	2	2	no	—
247	C₂×#102	—	2	2	no	—
248	#389	—	2	2	no	—
249	#385	—	2	2	no	—
250	#384	C₂²×C₁₉	1	2	yes	complemented
251	#382	C₂²×C₁₉	1	2	yes	complemented
252	#343	C₂²×C₁₉	1	2	yes	complemented
253	#343	C₂²×C₁₉	1	2	yes	complemented
254	C₂×C₁₉	—	2	1	no	—
255	C₂×C₁₉	—	2	4	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	—	8	4	no	—
258	C₂×C₁₉	C₂×#394	1	1	yes	characteristic
259	C₂×C₁₉	#3021	1	1	yes	characteristic
260	C₂×C₁₉	#3022	1	1	yes	characteristic
261	C₂×#41	—	2	2	no	—
262	C₂×#41	—	2	2	no	—
263	C₂×#41	—	2	4	no	—
264	C₂×#41	—	2	4	no	—
265	C₂×#41	—	2	4	no	—
266	C₂×#41	—	2	4	no	—
267	C₂×#41	D₄×C₁₉	1	4	yes	—
268	C₂×#41	C₂³×C₁₉	1	4	yes	—
269	C₂²×Q₈	D₄×C₁₉	1	2	yes	—
270	C₂²×D₄	—	2	2	no	—
271	C₂²×D₄	D₄×C₁₉	1	2	yes	—
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
275	C₂×M₁₆	—	2	2	no	—
276	C₂×M₁₆	—	2	4	no	—
277	C₂×M₁₆	—	2	4	no	—
278	C₂×M₁₆	C₂³×C₁₉	1	4	yes	—
279	C₂²×C₈	—	2	2	no	—
280	C₄⋊Q₈	—	2	2	no	—
281	#127	—	2	2	no	—
282	#124	—	2	4	no	—
283	#123	—	2	8	no	—
284	C₂²⋊Q₈	—	2	4	no	—
285	C₂²⋊Q₈	—	2	4	no	—
286	#121	—	2	4	no	—
287	#121	—	2	4	no	—
288	#121	—	2	4	no	—
289	#121	—	2	4	no	—
290	#120	—	2	8	no	—
291	C₄×D₄	—	2	4	no	—
292	C₄×D₄	—	2	4	no	—
293	#117	—	2	2	no	—
294	#117	—	2	2	no	—
295	#117	—	2	2	no	—
296	#117	D₄×C₁₉	1	4	yes	complemented
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	4	no	—
302	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
304	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	2	1	no	—
306	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
307	C₂×C₄²	D₄×C₁₉	1	2	yes	—
308	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
309	#104	—	2	16	no	—
310	#103	—	2	8	no	—
311	#102	—	2	8	no	—
312	#95	—	2	4	no	—
313	C₁₉	#23500	1	1	yes	characteristic, direct product factor, Sylow
314	C₂⁴	—	2	2	no	—
315	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
316	#41	—	2	8	no	—
317	#41	—	2	8	no	—
318	#41	—	2	4	no	—
319	#41	—	2	4	no	—
320	#41	—	2	4	no	—
321	#41	—	2	4	no	—
322	#41	—	4	4	no	—
323	#41	—	4	4	no	—
324	#41	—	4	4	no	—
325	#41	—	4	4	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	4	no	—
329	C₂×Q₈	C₂×D₄×C₁₉	1	4	yes	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	4	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	4	no	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	4	4	no	—
346	C₂²×C₄	—	4	4	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	8	2	no	—
349	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
355	C₂²×C₄	#41×C₁₉	1	4	yes	—
356	C₂²×C₄	#41×C₁₉	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
358	M₁₆	—	2	4	no	—
359	M₁₆	—	2	4	no	—
360	M₁₆	—	4	4	no	—
361	C₂×C₈	—	2	4	no	—
362	C₂×C₈	—	4	4	no	—
363	C₄⋊C₄	—	2	4	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	4	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	4	1	no	—
371	C₄⋊C₄	—	8	4	no	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	4	no	—
375	C₂²⋊C₄	—	2	4	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	2	2	no	—
378	C₄²	—	2	2	no	—
379	C₄²	C₂×D₄×C₁₉	1	4	yes	—
380	C₂³	—	2	4	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	1	no	—
383	C₂³	—	4	4	no	—
384	C₂³	—	8	2	no	—
385	C₂³	—	8	2	no	—
386	C₂³	C₁₉×#120	1	2	yes	—
387	C₂³	C₁₉×#121	1	2	yes	—
388	C₂³	C₁₉×#124	1	2	yes	—
389	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
390	Q₈	—	2	4	no	—
391	Q₈	—	2	4	no	—
392	Q₈	—	4	4	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	8	no	—
396	D₄	—	4	4	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	4	no	—
399	D₄	—	8	4	no	—
400	D₄	—	8	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	4	no	—
408	C₂×C₄	—	4	8	no	—
409	C₂×C₄	—	4	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	4	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
417	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
418	C₂×C₄	C₁₉×#121	1	2	yes	—
419	C₂×C₄	C₁₉×#121	1	4	yes	—
420	C₂×C₄	C₁₉×#121	1	4	yes	—
421	C₂×C₄	C₁₉×#123	1	4	yes	—
422	C₂×C₄	C₁₉×#123	1	4	yes	—
423	C₂×C₄	C₁₉×#124	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
425	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
426	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
427	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
428	C₈	—	4	4	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	4	2	no	—
434	C₂²	—	4	2	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	8	8	no	—
439	C₂²	C₁₉×#394	1	4	yes	—
440	C₂²	C₂×C₁₉×#120	1	1	yes	characteristic
441	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
442	C₂²	C₂×C₁₉×#124	1	1	yes	characteristic
443	C₄	—	4	4	no	—
444	C₄	—	4	2	no	—
445	C₄	—	4	2	no	—
446	C₄	—	4	4	no	—
447	C₄	—	8	2	no	—
448	C₄	C₁₉×#394	1	2	yes	—
449	C₄	C₁₉×#394	1	2	yes	—
450	C₄	C₂×C₁₉×#121	1	2	yes	—
451	C₄	C₂×C₁₉×#123	1	2	yes	—
452	C₂	—	2	1	no	—
453	C₂	—	2	4	no	—
454	C₂	—	2	1	no	—
455	C₂	—	8	4	no	—
456	C₂	C₂×C₁₉×#394	1	1	yes	characteristic
457	C₂	C₁₉×#3021	1	1	yes	characteristic
458	C₂	C₁₉×#3022	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#3449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#421	C₂	semidirect
3. C₂×C₁₉×#417	C₂	semidirect
4. C₁₉×#2317	C₂	semidirect
5. C₁₉×#2040	C₂	semidirect
6. C₁₉×#2039	C₂	semidirect
7. C₁₉×#1742	C₂	semidirect
21. C₂×C₁₉×#104	C₂²	semidirect
23. C₁₉×#417	C₂²	semidirect
28. C₁₉×#384	C₂²	semidirect
29. C₁₉×#382	C₂²	semidirect
30. C₁₉×#343	C₂²	semidirect
31. C₁₉×#343	C₂²	semidirect
67. C₁₉×#117	D₄	semidirect
150. #23500	C₁₉	direct (N × H)
201. C₂×#421	C₂×C₁₉	semidirect
202. C₂×#417	C₂×C₁₉	semidirect
203. #2317	C₂×C₁₉	semidirect
204. #2040	C₂×C₁₉	semidirect
205. #2039	C₂×C₁₉	semidirect
206. #1742	C₂×C₁₉	semidirect
243. C₂×#104	C₂²×C₁₉	semidirect
245. #417	C₂²×C₁₉	semidirect
250. #384	C₂²×C₁₉	semidirect
251. #382	C₂²×C₁₉	semidirect
252. #343	C₂²×C₁₉	semidirect
253. #343	C₂²×C₁₉	semidirect
296. #117	D₄×C₁₉	semidirect
313. C₁₉	#23500	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×#3449	2
C₂×C₁₉×#421	2
C₂×C₁₉×#417	2
C₁₉×#2317	2
C₁₉×#2040	2
C₁₉×#2039	2
C₁₉×#1742	2
#23500	19

Subgroups — C19×#23500 #18029459

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#23500 #18029459