Subgroups — C₁₉×#11027 #18016986

Order 4864.

1498 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₁₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#418	C₂	1	2	yes	maximal, complemented
3	C₂²×C₁₉×#100	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₉×#341	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#1729	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₉	C₂²	1	2	yes	—
7	C₂²×D₈×C₁₉	—	2	4	no	—
8	C₂²×D₈×C₁₉	—	2	4	no	—
9	C₂²×D₈×C₁₉	—	2	2	no	—
10	C₂²×D₈×C₁₉	—	2	2	no	—
11	C₂²×D₈×C₁₉	C₄	1	4	yes	complemented
12	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	2	yes	—
14	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
16	C₁₉×#418	—	2	4	no	—
17	C₁₉×#418	—	2	4	no	—
18	C₂×C₁₉×#102	—	2	4	no	—
19	C₂×C₁₉×#100	—	2	4	no	—
20	C₂×C₁₉×#100	—	2	4	no	—
21	C₂×C₁₉×#100	—	2	4	no	—
22	C₁₉×#341	—	2	2	no	—
23	C₁₉×#336	—	2	2	no	—
24	C₂⁵×C₁₉	—	2	2	no	—
25	C₂²×D₄×C₁₉	—	2	2	no	—
26	C₂²×D₄×C₁₉	—	2	2	no	—
27	C₂²×D₄×C₁₉	—	2	2	no	—
28	C₂²×D₄×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	2	2	no	—
30	C₂²×D₄×C₁₉	—	2	2	no	—
31	C₂²×D₄×C₁₉	—	2	2	no	—
32	C₂²×D₄×C₁₉	—	2	2	no	—
33	C₂²×D₄×C₁₉	—	2	2	no	—
34	C₂²×D₄×C₁₉	—	2	2	no	—
35	C₂²×D₄×C₁₉	—	2	2	no	—
36	C₂²×D₄×C₁₉	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₁₉	D₄	1	4	yes	—
38	C₂²×D₄×C₁₉	D₄	1	4	yes	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×D₈×C₁₉	—	2	8	no	—
41	C₂×D₈×C₁₉	—	2	16	no	—
42	C₂×D₈×C₁₉	—	2	8	no	—
43	C₂×D₈×C₁₉	—	2	16	no	—
44	C₂×D₈×C₁₉	—	2	8	no	—
45	C₂×M₁₆×C₁₉	—	2	2	no	—
46	C₂×M₁₆×C₁₉	—	2	1	no	—
47	C₂×M₁₆×C₁₉	—	2	2	no	—
48	C₂×M₁₆×C₁₉	—	2	2	no	—
49	C₂×M₁₆×C₁₉	—	2	2	no	—
50	C₂×M₁₆×C₁₉	—	2	2	no	—
51	C₂×M₁₆×C₁₉	—	2	2	no	—
52	C₂×M₁₆×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
54	C₂×M₁₆×C₁₉	D₄	1	4	yes	—
55	C₂²×C₈×C₁₉	—	2	2	no	—
56	C₂²×C₈×C₁₉	—	2	2	no	—
57	C₂²×C₈×C₁₉	—	2	2	no	—
58	C₂²×C₈×C₁₉	—	2	1	no	—
59	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
60	C₂²×C₈×C₁₉	D₄	1	2	yes	—
61	C₂²×C₈×C₁₉	D₄	1	2	yes	—
62	C₁₉×#117	—	2	2	no	—
63	C₁₉×#117	—	2	2	no	—
64	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
65	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	—	2	1	no	—
67	C₁₉×#102	—	2	16	no	—
68	C₁₉×#100	—	2	16	no	—
69	C₂⁴×C₁₉	—	2	4	no	—
70	C₂⁴×C₁₉	—	2	4	no	—
71	C₂⁴×C₁₉	—	2	4	no	—
72	C₂⁴×C₁₉	—	4	2	no	—
73	C₂⁴×C₁₉	—	4	2	no	—
74	C₂⁴×C₁₉	—	4	2	no	—
75	C₂⁴×C₁₉	—	4	2	no	—
76	C₂⁴×C₁₉	—	8	8	no	—
77	C₂⁴×C₁₉	#41	1	1	yes	characteristic
78	C₂×D₄×C₁₉	—	2	4	no	—
79	C₂×D₄×C₁₉	—	2	4	no	—
80	C₂×D₄×C₁₉	—	2	4	no	—
81	C₂×D₄×C₁₉	—	2	4	no	—
82	C₂×D₄×C₁₉	—	2	4	no	—
83	C₂×D₄×C₁₉	—	2	4	no	—
84	C₂×D₄×C₁₉	—	2	4	no	—
85	C₂×D₄×C₁₉	—	2	4	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	4	no	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	2	4	no	—
91	C₂×D₄×C₁₉	—	2	4	no	—
92	C₂×D₄×C₁₉	—	2	4	no	—
93	C₂×D₄×C₁₉	—	4	2	no	—
94	C₂×D₄×C₁₉	—	4	2	no	—
95	C₂×D₄×C₁₉	—	4	2	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	—	4	2	no	—
98	C₂×D₄×C₁₉	—	4	2	no	—
99	C₂×D₄×C₁₉	—	4	2	no	—
100	C₂×D₄×C₁₉	—	4	2	no	—
101	C₂×D₄×C₁₉	—	4	2	no	—
102	C₂×D₄×C₁₉	—	4	2	no	—
103	C₂×D₄×C₁₉	—	4	2	no	—
104	C₂×D₄×C₁₉	—	4	2	no	—
105	C₂×D₄×C₁₉	C₂²⋊C₄	1	8	yes	—
106	C₂²×C₄×C₁₉	—	2	2	no	—
107	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
116	C₂²×C₄×C₁₉	#41	1	2	yes	—
117	D₈×C₁₉	—	2	32	no	—
118	M₁₆×C₁₉	—	2	4	no	—
119	M₁₆×C₁₉	—	2	4	no	—
120	M₁₆×C₁₉	—	2	4	no	—
121	M₁₆×C₁₉	—	4	2	no	—
122	M₁₆×C₁₉	—	4	2	no	—
123	M₁₆×C₁₉	—	4	2	no	—
124	C₂×C₈×C₁₉	—	2	4	no	—
125	C₂×C₈×C₁₉	—	2	2	no	—
126	C₂×C₈×C₁₉	—	2	4	no	—
127	C₂×C₈×C₁₉	—	2	2	no	—
128	C₂×C₈×C₁₉	—	2	4	no	—
129	C₂×C₈×C₁₉	—	2	2	no	—
130	C₂×C₈×C₁₉	—	4	1	no	—
131	C₂×C₈×C₁₉	—	4	2	no	—
132	C₂×C₈×C₁₉	—	4	1	no	—
133	C₂×C₈×C₁₉	—	4	2	no	—
134	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
135	C₄⋊C₄×C₁₉	—	2	4	no	—
136	C₂²⋊C₄×C₁₉	—	4	2	no	—
137	C₄²×C₁₉	—	4	1	no	—
138	C₄²×C₁₉	—	4	1	no	—
139	#11027	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
140	C₂³×C₁₉	—	2	4	no	—
141	C₂³×C₁₉	—	2	8	no	—
142	C₂³×C₁₉	—	4	4	no	—
143	C₂³×C₁₉	—	4	4	no	—
144	C₂³×C₁₉	—	4	4	no	—
145	C₂³×C₁₉	—	4	4	no	—
146	C₂³×C₁₉	—	4	4	no	—
147	C₂³×C₁₉	—	4	4	no	—
148	C₂³×C₁₉	—	8	8	no	—
149	C₂³×C₁₉	—	8	8	no	—
150	C₂³×C₁₉	—	8	8	no	—
151	C₂³×C₁₉	—	8	8	no	—
152	C₂³×C₁₉	—	8	8	no	—
153	C₂³×C₁₉	—	8	8	no	—
154	C₂³×C₁₉	—	8	8	no	—
155	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
156	C₂³×C₁₉	#121	1	2	yes	—
157	C₂³×C₁₉	#121	1	1	yes	characteristic
158	C₂³×C₁₉	#123	1	2	yes	—
159	C₂³×C₁₉	#124	1	1	yes	characteristic
160	D₄×C₁₉	—	2	8	no	—
161	D₄×C₁₉	—	2	8	no	—
162	D₄×C₁₉	—	4	4	no	—
163	D₄×C₁₉	—	4	4	no	—
164	D₄×C₁₉	—	4	4	no	—
165	D₄×C₁₉	—	4	4	no	—
166	D₄×C₁₉	—	4	4	no	—
167	D₄×C₁₉	—	4	4	no	—
168	C₂×C₄×C₁₉	—	4	2	no	—
169	C₂×C₄×C₁₉	—	4	4	no	—
170	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
171	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#120	1	2	yes	—
176	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#120	1	2	yes	—
178	C₂×C₄×C₁₉	#120	1	2	yes	—
179	C₂×C₄×C₁₉	#121	1	2	yes	—
180	C₂×C₄×C₁₉	#121	1	2	yes	—
181	C₂×C₄×C₁₉	#121	1	2	yes	—
182	C₂×C₄×C₁₉	#121	1	2	yes	—
183	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#123	1	2	yes	—
185	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
188	C₈×C₁₉	—	2	4	no	—
189	C₈×C₁₉	—	4	4	no	—
190	C₈×C₁₉	—	4	2	no	—
191	C₂³×D₈	C₂×C₁₉	1	1	yes	characteristic
192	C₂×#418	C₂×C₁₉	1	2	yes	complemented
193	C₂²×#100	C₂×C₁₉	1	2	yes	complemented
194	C₂×#341	C₂×C₁₉	1	1	yes	characteristic, complemented
195	#1729	C₂×C₁₉	1	1	yes	characteristic, complemented
196	C₂²×C₁₉	—	2	2	no	—
197	C₂²×C₁₉	—	2	2	no	—
198	C₂²×C₁₉	—	2	4	no	—
199	C₂²×C₁₉	—	2	4	no	—
200	C₂²×C₁₉	—	4	8	no	—
201	C₂²×C₁₉	—	8	8	no	—
202	C₂²×C₁₉	—	8	8	no	—
203	C₂²×C₁₉	—	8	8	no	—
204	C₂²×C₁₉	—	8	8	no	—
205	C₂²×C₁₉	—	8	8	no	—
206	C₂²×C₁₉	—	8	8	no	—
207	C₂²×C₁₉	—	8	8	no	—
208	C₂²×C₁₉	#386	1	2	yes	—
209	C₂²×C₁₉	#390	1	1	yes	characteristic
210	C₂²×C₁₉	#392	1	1	yes	characteristic
211	C₂²×C₁₉	#394	1	2	yes	—
212	C₂²×C₁₉	#394	1	1	yes	characteristic
213	C₂²×C₁₉	#472	1	4	yes	—
214	C₄×C₁₉	—	8	2	no	—
215	C₄×C₁₉	#379	1	1	yes	characteristic
216	C₄×C₁₉	#386	1	2	yes	—
217	C₄×C₁₉	#390	1	1	yes	characteristic
218	C₄×C₁₉	#392	1	1	yes	characteristic
219	C₄×C₁₉	#392	1	2	yes	—
220	C₄×C₁₉	#394	1	1	yes	characteristic
221	C₂³×D₄	C₂²×C₁₉	1	2	yes	—
222	C₂²×D₈	—	2	4	no	—
223	C₂²×D₈	—	2	4	no	—
224	C₂²×D₈	—	2	2	no	—
225	C₂²×D₈	—	2	2	no	—
226	C₂²×D₈	C₄×C₁₉	1	4	yes	complemented
227	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
228	C₂²×M₁₆	C₂²×C₁₉	1	2	yes	—
229	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
230	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
231	#418	—	2	4	no	—
232	#418	—	2	4	no	—
233	C₂×#102	—	2	4	no	—
234	C₂×#100	—	2	4	no	—
235	C₂×#100	—	2	4	no	—
236	C₂×#100	—	2	4	no	—
237	#341	—	2	2	no	—
238	#336	—	2	2	no	—
239	C₂×C₁₉	—	2	2	no	—
240	C₂×C₁₉	—	2	2	no	—
241	C₂×C₁₉	—	8	8	no	—
242	C₂×C₁₉	#1438	1	1	yes	characteristic
243	C₂×C₁₉	#1978	1	2	yes	—
244	C₂×C₁₉	#2018	1	2	yes	—
245	C₂×C₁₉	#2045	1	2	yes	—
246	C₂⁵	—	2	2	no	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	—	2	2	no	—
249	C₂²×D₄	—	2	2	no	—
250	C₂²×D₄	—	2	2	no	—
251	C₂²×D₄	—	2	2	no	—
252	C₂²×D₄	—	2	2	no	—
253	C₂²×D₄	—	2	2	no	—
254	C₂²×D₄	—	2	2	no	—
255	C₂²×D₄	—	2	2	no	—
256	C₂²×D₄	—	2	2	no	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	C₂×C₄×C₁₉	1	4	yes	—
259	C₂²×D₄	D₄×C₁₉	1	4	yes	—
260	C₂²×D₄	D₄×C₁₉	1	4	yes	—
261	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
262	C₂×D₈	—	2	8	no	—
263	C₂×D₈	—	2	16	no	—
264	C₂×D₈	—	2	8	no	—
265	C₂×D₈	—	2	16	no	—
266	C₂×D₈	—	2	8	no	—
267	C₂×M₁₆	—	2	2	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	2	no	—
270	C₂×M₁₆	—	2	2	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	2	no	—
274	C₂×M₁₆	—	2	2	no	—
275	C₂×M₁₆	D₄×C₁₉	1	2	yes	—
276	C₂×M₁₆	D₄×C₁₉	1	4	yes	—
277	C₂²×C₈	—	2	2	no	—
278	C₂²×C₈	—	2	2	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	C₂×C₄×C₁₉	1	2	yes	—
282	C₂²×C₈	D₄×C₁₉	1	2	yes	—
283	C₂²×C₈	D₄×C₁₉	1	2	yes	—
284	#117	—	2	2	no	—
285	#117	—	2	2	no	—
286	C₂×C₄⋊C₄	D₄×C₁₉	1	2	yes	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₄²	—	2	1	no	—
289	#102	—	2	16	no	—
290	#100	—	2	16	no	—
291	C₁₉	#11027	1	1	yes	characteristic, direct product factor, Sylow
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	4	no	—
294	C₂⁴	—	2	4	no	—
295	C₂⁴	—	4	2	no	—
296	C₂⁴	—	4	2	no	—
297	C₂⁴	—	4	2	no	—
298	C₂⁴	—	4	2	no	—
299	C₂⁴	—	8	8	no	—
300	C₂⁴	#41×C₁₉	1	1	yes	characteristic
301	C₂×D₄	—	2	4	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	4	no	—
305	C₂×D₄	—	2	4	no	—
306	C₂×D₄	—	2	4	no	—
307	C₂×D₄	—	2	4	no	—
308	C₂×D₄	—	2	4	no	—
309	C₂×D₄	—	2	4	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	4	2	no	—
317	C₂×D₄	—	4	2	no	—
318	C₂×D₄	—	4	2	no	—
319	C₂×D₄	—	4	2	no	—
320	C₂×D₄	—	4	2	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂×D₄	—	4	2	no	—
324	C₂×D₄	—	4	2	no	—
325	C₂×D₄	—	4	2	no	—
326	C₂×D₄	—	4	2	no	—
327	C₂×D₄	—	4	2	no	—
328	C₂×D₄	C₂²⋊C₄×C₁₉	1	8	yes	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
332	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
333	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
337	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
338	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
339	C₂²×C₄	#41×C₁₉	1	2	yes	—
340	D₈	—	2	32	no	—
341	M₁₆	—	2	4	no	—
342	M₁₆	—	2	4	no	—
343	M₁₆	—	2	4	no	—
344	M₁₆	—	4	2	no	—
345	M₁₆	—	4	2	no	—
346	M₁₆	—	4	2	no	—
347	C₂×C₈	—	2	4	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	4	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	4	1	no	—
354	C₂×C₈	—	4	2	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	2	no	—
357	C₂×C₈	C₂²⋊C₄×C₁₉	1	4	yes	—
358	C₄⋊C₄	—	2	4	no	—
359	C₂²⋊C₄	—	4	2	no	—
360	C₄²	—	4	1	no	—
361	C₄²	—	4	1	no	—
362	C₂³	—	2	4	no	—
363	C₂³	—	2	8	no	—
364	C₂³	—	4	4	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	4	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	8	8	no	—
371	C₂³	—	8	8	no	—
372	C₂³	—	8	8	no	—
373	C₂³	—	8	8	no	—
374	C₂³	—	8	8	no	—
375	C₂³	—	8	8	no	—
376	C₂³	—	8	8	no	—
377	C₂³	C₄×D₄×C₁₉	1	1	yes	characteristic
378	C₂³	C₁₉×#121	1	2	yes	—
379	C₂³	C₁₉×#121	1	1	yes	characteristic
380	C₂³	C₁₉×#123	1	2	yes	—
381	C₂³	C₁₉×#124	1	1	yes	characteristic
382	D₄	—	2	8	no	—
383	D₄	—	2	8	no	—
384	D₄	—	4	4	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	4	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	2	yes	—
393	C₂×C₄	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
394	C₂×C₄	C₄×D₄×C₁₉	1	1	yes	characteristic
395	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
396	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
397	C₂×C₄	C₁₉×#120	1	2	yes	—
398	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
399	C₂×C₄	C₁₉×#120	1	2	yes	—
400	C₂×C₄	C₁₉×#120	1	2	yes	—
401	C₂×C₄	C₁₉×#121	1	2	yes	—
402	C₂×C₄	C₁₉×#121	1	2	yes	—
403	C₂×C₄	C₁₉×#121	1	2	yes	—
404	C₂×C₄	C₁₉×#121	1	2	yes	—
405	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
406	C₂×C₄	C₁₉×#123	1	2	yes	—
407	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
408	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
409	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
410	C₈	—	2	4	no	—
411	C₈	—	4	4	no	—
412	C₈	—	4	2	no	—
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	4	8	no	—
418	C₂²	—	8	8	no	—
419	C₂²	—	8	8	no	—
420	C₂²	—	8	8	no	—
421	C₂²	—	8	8	no	—
422	C₂²	—	8	8	no	—
423	C₂²	—	8	8	no	—
424	C₂²	—	8	8	no	—
425	C₂²	C₁₉×#386	1	2	yes	—
426	C₂²	C₁₉×#390	1	1	yes	characteristic
427	C₂²	C₁₉×#392	1	1	yes	characteristic
428	C₂²	C₁₉×#394	1	2	yes	—
429	C₂²	C₁₉×#394	1	1	yes	characteristic
430	C₂²	C₁₉×#472	1	4	yes	—
431	C₄	—	8	2	no	—
432	C₄	C₁₉×#379	1	1	yes	characteristic
433	C₄	C₁₉×#386	1	2	yes	—
434	C₄	C₁₉×#390	1	1	yes	characteristic
435	C₄	C₁₉×#392	1	1	yes	characteristic
436	C₄	C₁₉×#392	1	2	yes	—
437	C₄	C₁₉×#394	1	1	yes	characteristic
438	C₂	—	2	2	no	—
439	C₂	—	2	2	no	—
440	C₂	—	8	8	no	—
441	C₂	C₁₉×#1438	1	1	yes	characteristic
442	C₂	C₁₉×#1978	1	2	yes	—
443	C₂	C₁₉×#2018	1	2	yes	—
444	C₂	C₁₉×#2045	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	#121
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂³×D₈×C₁₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂³×C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#418	C₂	semidirect
3. C₂²×C₁₉×#100	C₂	semidirect
4. C₂×C₁₉×#341	C₂	semidirect
5. C₁₉×#1729	C₂	semidirect
11. C₂²×D₈×C₁₉	C₄	semidirect
139. #11027	C₁₉	direct (N × H)
192. C₂×#418	C₂×C₁₉	semidirect
193. C₂²×#100	C₂×C₁₉	semidirect
194. C₂×#341	C₂×C₁₉	semidirect
195. #1729	C₂×C₁₉	semidirect
226. C₂²×D₈	C₄×C₁₉	semidirect
291. C₁₉	#11027	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×D₈×C₁₉	2
C₂×C₁₉×#418	2
C₂²×C₁₉×#100	2
C₂×C₁₉×#341	2
C₁₉×#1729	2
#11027	19

Subgroups — C19×#11027 #18016986

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11027 #18016986