Subgroups — C₁₉×#11076 #18017035

Order 4864.

1266 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₉×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₉×#102	C₂	1	2	yes	maximal
3	C₂×C₁₉×#390	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₉×#340	C₂	1	2	yes	maximal, complemented
5	C₁₉×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₄×C₁₉	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₉	C₂²	1	2	yes	—
8	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
9	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
10	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
11	C₂²×C₂²⋊C₄×C₁₉	—	2	1	no	—
12	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
13	C₂×C₁₉×C₄⋊C₈	—	2	4	no	—
14	C₂×C₁₉×C₄⋊C₈	—	2	2	no	—
15	C₂×C₁₉×#102	—	2	4	no	—
16	C₂×C₁₉×#102	—	2	4	no	—
17	C₂×C₁₉×#102	—	2	4	no	—
18	C₁₉×#390	—	2	2	no	—
19	C₁₉×#390	C₄	1	4	yes	complemented
20	C₂×C₁₉×#95	—	2	1	no	—
21	C₂×C₁₉×#95	—	2	1	no	—
22	C₁₉×#340	—	2	4	no	—
23	C₂⁵×C₁₉	—	2	1	no	—
24	C₂²×D₄×C₁₉	—	2	2	no	—
25	C₂²×D₄×C₁₉	—	2	2	no	—
26	C₂²×D₄×C₁₉	—	2	1	no	—
27	C₂²×D₄×C₁₉	—	2	2	no	—
28	C₂²×D₄×C₁₉	—	2	2	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	C₂×C₄	1	2	yes	—
32	C₂²×D₄×C₁₉	D₄	1	2	yes	—
33	C₂²×D₄×C₁₉	Q₈	1	2	yes	—
34	C₂³×C₄×C₁₉	—	2	2	no	—
35	C₂³×C₄×C₁₉	—	2	1	no	—
36	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₁₉	—	2	2	no	—
40	C₂²×C₈×C₁₉	—	2	2	no	—
41	C₂²×C₈×C₁₉	—	2	2	no	—
42	C₂²×C₈×C₁₉	—	2	2	no	—
43	C₂²×C₈×C₁₉	—	2	2	no	—
44	C₂²×C₈×C₁₉	—	2	2	no	—
45	C₂²×C₈×C₁₉	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
48	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
49	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
50	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₁₉	D₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₁₉	—	4	4	no	—
59	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
60	C₂×C₂²⋊C₄×C₁₉	—	4	2	no	—
61	C₂×C₄²×C₁₉	—	2	2	no	—
62	C₂×C₄²×C₁₉	—	2	2	no	—
63	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₁₉	D₄	1	2	yes	—
65	C₁₉×C₄⋊C₈	—	2	8	no	—
66	C₁₉×#102	—	2	16	no	—
67	C₁₉×#95	—	4	2	no	—
68	C₁₉×#95	—	4	2	no	—
69	C₂⁴×C₁₉	—	2	2	no	—
70	C₂⁴×C₁₉	—	2	2	no	—
71	C₂⁴×C₁₉	—	2	2	no	—
72	C₂⁴×C₁₉	—	4	2	no	—
73	C₂⁴×C₁₉	—	4	2	no	—
74	C₂⁴×C₁₉	—	4	1	no	—
75	C₂⁴×C₁₉	—	4	1	no	—
76	C₂⁴×C₁₉	—	4	2	no	—
77	C₂⁴×C₁₉	—	4	2	no	—
78	C₂⁴×C₁₉	—	4	1	no	—
79	C₂⁴×C₁₉	—	4	1	no	—
80	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂×D₄×C₁₉	—	2	2	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	2	no	—
86	C₂×D₄×C₁₉	—	2	4	no	—
87	C₂×D₄×C₁₉	—	2	4	no	—
88	C₂×D₄×C₁₉	—	2	2	no	—
89	C₂×D₄×C₁₉	—	2	4	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	—	4	1	no	—
94	C₂×D₄×C₁₉	—	4	2	no	—
95	C₂×D₄×C₁₉	—	4	1	no	—
96	C₂×D₄×C₁₉	—	4	2	no	—
97	C₂×D₄×C₁₉	—	4	1	no	—
98	C₂×D₄×C₁₉	C₄⋊C₄	1	4	yes	—
99	C₂²×C₄×C₁₉	—	2	2	no	—
100	C₂²×C₄×C₁₉	—	2	2	no	—
101	C₂²×C₄×C₁₉	—	2	2	no	—
102	C₂²×C₄×C₁₉	—	2	2	no	—
103	C₂²×C₄×C₁₉	—	2	1	no	—
104	C₂²×C₄×C₁₉	—	2	1	no	—
105	C₂²×C₄×C₁₉	—	2	2	no	—
106	C₂²×C₄×C₁₉	—	2	4	no	—
107	C₂²×C₄×C₁₉	—	4	2	no	—
108	C₂²×C₄×C₁₉	—	4	2	no	—
109	C₂²×C₄×C₁₉	—	4	2	no	—
110	C₂²×C₄×C₁₉	—	4	1	no	—
111	C₂²×C₄×C₁₉	—	4	2	no	—
112	C₂²×C₄×C₁₉	—	4	1	no	—
113	C₂²×C₄×C₁₉	—	4	2	no	—
114	C₂²×C₄×C₁₉	—	4	2	no	—
115	C₂²×C₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	4	2	no	—
117	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
118	C₂²×C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
119	C₂²×C₄×C₁₉	D₈	1	2	yes	—
120	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
121	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
128	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
129	C₂²×C₄×C₁₉	#41	1	2	yes	—
130	C₂²×C₄×C₁₉	#41	1	2	yes	—
131	C₂×C₈×C₁₉	—	2	4	no	—
132	C₂×C₈×C₁₉	—	2	4	no	—
133	C₂×C₈×C₁₉	—	2	4	no	—
134	C₂×C₈×C₁₉	—	4	2	no	—
135	C₂×C₈×C₁₉	—	4	2	no	—
136	C₂×C₈×C₁₉	—	4	2	no	—
137	C₂×C₈×C₁₉	—	4	2	no	—
138	C₄⋊C₄×C₁₉	—	2	4	no	—
139	C₄⋊C₄×C₁₉	—	2	4	no	—
140	C₄⋊C₄×C₁₉	—	2	4	no	—
141	C₄⋊C₄×C₁₉	—	4	2	no	—
142	C₄⋊C₄×C₁₉	—	4	1	no	—
143	C₄⋊C₄×C₁₉	—	4	2	no	—
144	C₄⋊C₄×C₁₉	—	4	1	no	—
145	C₂²⋊C₄×C₁₉	—	4	8	no	—
146	C₂²⋊C₄×C₁₉	—	4	8	no	—
147	C₄²×C₁₉	—	2	4	no	—
148	C₄²×C₁₉	—	2	2	no	—
149	C₄²×C₁₉	—	2	2	no	—
150	#11076	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
151	C₂³×C₁₉	—	2	4	no	—
152	C₂³×C₁₉	—	4	2	no	—
153	C₂³×C₁₉	—	4	2	no	—
154	C₂³×C₁₉	—	4	4	no	—
155	C₂³×C₁₉	—	4	4	no	—
156	C₂³×C₁₉	—	4	2	no	—
157	C₂³×C₁₉	—	4	2	no	—
158	C₂³×C₁₉	—	4	2	no	—
159	C₂³×C₁₉	—	4	2	no	—
160	C₂³×C₁₉	—	4	2	no	—
161	C₂³×C₁₉	—	4	2	no	—
162	C₂³×C₁₉	—	4	4	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	4	4	no	—
166	C₂³×C₁₉	—	8	2	no	—
167	C₂³×C₁₉	—	8	2	no	—
168	C₂³×C₁₉	—	8	2	no	—
169	C₂³×C₁₉	—	8	2	no	—
170	C₂³×C₁₉	—	8	2	no	—
171	C₂³×C₁₉	—	8	2	no	—
172	C₂³×C₁₉	—	8	2	no	—
173	C₂³×C₁₉	—	8	2	no	—
174	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂³×C₁₉	#121	1	1	yes	characteristic
176	C₂³×C₁₉	#121	1	2	yes	—
177	C₂³×C₁₉	#121	1	2	yes	—
178	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂³×C₁₉	C₂×D₈	1	1	yes	characteristic
180	C₂³×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
181	C₂³×C₁₉	#135	1	2	yes	—
182	C₂³×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂³×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
184	C₂³×C₁₉	#137	1	1	yes	characteristic
185	D₄×C₁₉	—	2	8	no	—
186	D₄×C₁₉	—	4	4	no	—
187	D₄×C₁₉	—	4	2	no	—
188	D₄×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	4	2	no	—
190	D₄×C₁₉	—	4	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	2	no	—
193	C₂×C₄×C₁₉	—	2	4	no	—
194	C₂×C₄×C₁₉	—	2	4	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	2	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	2	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	4	no	—
202	C₂×C₄×C₁₉	—	4	2	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	4	no	—
205	C₂×C₄×C₁₉	—	4	4	no	—
206	C₂×C₄×C₁₉	—	8	2	no	—
207	C₂×C₄×C₁₉	—	8	2	no	—
208	C₂×C₄×C₁₉	—	8	2	no	—
209	C₂×C₄×C₁₉	—	8	2	no	—
210	C₂×C₄×C₁₉	—	8	2	no	—
211	C₂×C₄×C₁₉	—	8	2	no	—
212	C₂×C₄×C₁₉	#102	1	4	yes	complemented
213	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
216	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
217	C₂×C₄×C₁₉	#120	1	2	yes	—
218	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
219	C₂×C₄×C₁₉	#121	1	2	yes	—
220	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
222	C₂×C₄×C₁₉	C₂²⋊Q₈	1	2	yes	—
223	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
224	C₂×C₄×C₁₉	#123	1	2	yes	—
225	C₂×C₄×C₁₉	#123	1	2	yes	—
226	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
227	C₂×C₄×C₁₉	#124	1	2	yes	—
228	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
229	C₂×C₄×C₁₉	#126	1	2	yes	—
230	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
231	C₈×C₁₉	—	4	4	no	—
232	C₂²×C₄⋊C₈	C₂×C₁₉	1	1	yes	characteristic, complemented
233	C₂²×#102	C₂×C₁₉	1	2	yes	—
234	C₂×#390	C₂×C₁₉	1	1	yes	characteristic
235	C₂×#340	C₂×C₁₉	1	2	yes	complemented
236	C₄⋊#95	C₂×C₁₉	1	1	yes	characteristic, complemented
237	C₂²×C₁₉	—	4	4	no	—
238	C₂²×C₁₉	—	4	4	no	—
239	C₂²×C₁₉	—	4	4	no	—
240	C₂²×C₁₉	—	8	4	no	—
241	C₂²×C₁₉	—	8	4	no	—
242	C₂²×C₁₉	—	8	4	no	—
243	C₂²×C₁₉	—	8	4	no	—
244	C₂²×C₁₉	—	8	2	no	—
245	C₂²×C₁₉	—	8	2	no	—
246	C₂²×C₁₉	—	8	2	no	—
247	C₂²×C₁₉	—	8	2	no	—
248	C₂²×C₁₉	#380	1	1	yes	characteristic
249	C₂²×C₁₉	#386	1	1	yes	characteristic
250	C₂²×C₁₉	#390	1	1	yes	characteristic
251	C₂²×C₁₉	#394	1	2	yes	—
252	C₂²×C₁₉	#396	1	2	yes	—
253	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
254	C₂²×C₁₉	#416	1	1	yes	characteristic
255	C₂²×C₁₉	#417	1	1	yes	characteristic
256	C₂²×C₁₉	#418	1	1	yes	characteristic
257	C₂²×C₁₉	#459	1	1	yes	characteristic
258	C₂²×C₁₉	#459	1	2	yes	—
259	C₂²×C₁₉	#460	1	2	yes	—
260	C₂²×C₁₉	#461	1	1	yes	characteristic
261	C₂²×C₁₉	#463	1	2	yes	—
262	C₂²×C₁₉	#463	1	2	yes	—
263	C₂²×C₁₉	#464	1	2	yes	—
264	C₂²×C₁₉	#465	1	2	yes	—
265	C₂²×C₁₉	#466	1	2	yes	—
266	C₂²×C₁₉	#468	1	2	yes	—
267	C₂²×C₁₉	#469	1	2	yes	—
268	C₂²×C₁₉	#474	1	1	yes	characteristic
269	C₂²×C₁₉	#476	1	1	yes	characteristic
270	C₂²×C₁₉	#478	1	2	yes	—
271	C₄×C₁₉	—	2	4	no	—
272	C₄×C₁₉	—	4	2	no	—
273	C₄×C₁₉	—	8	4	no	—
274	C₄×C₁₉	—	8	2	no	—
275	C₄×C₁₉	#385	1	2	yes	—
276	C₄×C₁₉	#388	1	2	yes	—
277	C₄×C₁₉	#392	1	1	yes	characteristic
278	C₄×C₁₉	#393	1	1	yes	characteristic
279	C₄×C₁₉	#397	1	1	yes	characteristic
280	C₄×C₁₉	#399	1	1	yes	characteristic
281	C₂³×D₄	C₂²×C₁₉	1	1	yes	characteristic
282	C₂³×C₈	C₂²×C₁₉	1	2	yes	—
283	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
284	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
285	C₂²×C₂²⋊C₄	—	2	1	no	—
286	C₂²×C₂²⋊C₄	—	2	1	no	—
287	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
288	C₂×C₄⋊C₈	—	2	4	no	—
289	C₂×C₄⋊C₈	—	2	2	no	—
290	C₂×#102	—	2	4	no	—
291	C₂×#102	—	2	4	no	—
292	C₂×#102	—	2	4	no	—
293	#390	—	2	2	no	—
294	#390	C₄×C₁₉	1	4	yes	complemented
295	C₂×#95	—	2	1	no	—
296	C₂×#95	—	2	1	no	—
297	#340	—	2	4	no	—
298	C₂×C₁₉	—	8	4	no	—
299	C₂×C₁₉	#1439	1	1	yes	characteristic
300	C₂×C₁₉	#1802	1	1	yes	characteristic
301	C₂×C₁₉	#1804	1	1	yes	characteristic
302	C₂×C₁₉	#1893	1	1	yes	characteristic
303	C₂×C₁₉	#1895	1	1	yes	characteristic
304	C₂×C₁₉	#1982	1	1	yes	characteristic
305	C₂×C₁₉	#1983	1	1	yes	characteristic
306	C₂×C₁₉	#2054	1	2	yes	—
307	C₂×C₁₉	#2055	1	2	yes	—
308	C₂×C₁₉	#2065	1	2	yes	—
309	C₂×C₁₉	#2067	1	2	yes	—
310	C₂⁵	—	2	1	no	—
311	C₂²×D₄	—	2	2	no	—
312	C₂²×D₄	—	2	2	no	—
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	2	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	—	2	1	no	—
318	C₂²×D₄	C₂×C₄×C₁₉	1	2	yes	—
319	C₂²×D₄	D₄×C₁₉	1	2	yes	—
320	C₂²×D₄	Q₈×C₁₉	1	2	yes	—
321	C₂³×C₄	—	2	1	no	—
322	C₂³×C₄	—	2	2	no	—
323	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
324	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
326	C₂²×C₈	—	2	2	no	—
327	C₂²×C₈	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	D₄×C₁₉	1	4	yes	—
333	C₂×C₄⋊C₄	—	2	2	no	—
334	C₂×C₄⋊C₄	—	2	2	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	2	no	—
341	C₂×C₄⋊C₄	C₂×C₄×C₁₉	1	2	yes	—
342	C₂×C₄⋊C₄	D₄×C₁₉	1	4	yes	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₂²⋊C₄	—	2	4	no	—
345	C₂×C₂²⋊C₄	—	4	4	no	—
346	C₂×C₂²⋊C₄	—	4	2	no	—
347	C₂×C₂²⋊C₄	—	4	2	no	—
348	C₂×C₄²	—	2	2	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	C₂×C₄×C₁₉	1	2	yes	—
351	C₂×C₄²	D₄×C₁₉	1	2	yes	—
352	C₄⋊C₈	—	2	8	no	—
353	#102	—	2	16	no	—
354	#95	—	4	2	no	—
355	#95	—	4	2	no	—
356	C₁₉	#11076	1	1	yes	characteristic, direct product factor, Sylow
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	2	no	—
359	C₂⁴	—	2	2	no	—
360	C₂⁴	—	4	2	no	—
361	C₂⁴	—	4	2	no	—
362	C₂⁴	—	4	1	no	—
363	C₂⁴	—	4	1	no	—
364	C₂⁴	—	4	2	no	—
365	C₂⁴	—	4	2	no	—
366	C₂⁴	—	4	1	no	—
367	C₂⁴	—	4	1	no	—
368	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	4	no	—
371	C₂×D₄	—	2	4	no	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	4	no	—
375	C₂×D₄	—	2	4	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	1	no	—
382	C₂×D₄	—	4	2	no	—
383	C₂×D₄	—	4	1	no	—
384	C₂×D₄	—	4	2	no	—
385	C₂×D₄	—	4	1	no	—
386	C₂×D₄	C₄⋊C₄×C₁₉	1	4	yes	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	—	4	2	no	—
402	C₂²×C₄	—	4	2	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
406	C₂²×C₄	C₂²⋊C₄×C₁₉	1	2	yes	—
407	C₂²×C₄	D₈×C₁₉	1	2	yes	—
408	C₂²×C₄	SD₁₆×C₁₉	1	2	yes	—
409	C₂²×C₄	C₂²×C₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
413	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
414	C₂²×C₄	C₂×Q₈×C₁₉	1	1	yes	characteristic
415	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
416	C₂²×C₄	#41×C₁₉	1	1	yes	characteristic
417	C₂²×C₄	#41×C₁₉	1	2	yes	—
418	C₂²×C₄	#41×C₁₉	1	2	yes	—
419	C₂×C₈	—	2	4	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	2	4	no	—
422	C₂×C₈	—	4	2	no	—
423	C₂×C₈	—	4	2	no	—
424	C₂×C₈	—	4	2	no	—
425	C₂×C₈	—	4	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	4	no	—
429	C₄⋊C₄	—	4	2	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	—	4	2	no	—
432	C₄⋊C₄	—	4	1	no	—
433	C₂²⋊C₄	—	4	8	no	—
434	C₂²⋊C₄	—	4	8	no	—
435	C₄²	—	2	4	no	—
436	C₄²	—	2	2	no	—
437	C₄²	—	2	2	no	—
438	C₂³	—	2	4	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	4	no	—
442	C₂³	—	4	4	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	8	2	no	—
454	C₂³	—	8	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	—	8	2	no	—
458	C₂³	—	8	2	no	—
459	C₂³	—	8	2	no	—
460	C₂³	—	8	2	no	—
461	C₂³	C₂×C₂²⋊C₄×C₁₉	1	1	yes	characteristic
462	C₂³	C₁₉×#121	1	1	yes	characteristic
463	C₂³	C₁₉×#121	1	2	yes	—
464	C₂³	C₁₉×#121	1	2	yes	—
465	C₂³	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
466	C₂³	C₂×D₈×C₁₉	1	1	yes	characteristic
467	C₂³	C₂×SD₁₆×C₁₉	1	1	yes	characteristic
468	C₂³	C₁₉×#135	1	2	yes	—
469	C₂³	C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
470	C₂³	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
471	C₂³	C₁₉×#137	1	1	yes	characteristic
472	D₄	—	2	8	no	—
473	D₄	—	4	4	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	8	2	no	—
494	C₂×C₄	—	8	2	no	—
495	C₂×C₄	—	8	2	no	—
496	C₂×C₄	—	8	2	no	—
497	C₂×C₄	—	8	2	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	C₁₉×#102	1	4	yes	complemented
500	C₂×C₄	C₂×C₄⋊C₄×C₁₉	1	1	yes	characteristic
501	C₂×C₄	C₁₉×#117	1	1	yes	characteristic
502	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
503	C₂×C₄	C₄×D₄×C₁₉	1	2	yes	—
504	C₂×C₄	C₁₉×#120	1	2	yes	—
505	C₂×C₄	C₁₉×#120	1	1	yes	characteristic
506	C₂×C₄	C₁₉×#121	1	2	yes	—
507	C₂×C₄	C₁₉×#121	1	1	yes	characteristic
508	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
509	C₂×C₄	C₁₉×C₂²⋊Q₈	1	2	yes	—
510	C₂×C₄	C₁₉×C₂²⋊Q₈	1	1	yes	characteristic
511	C₂×C₄	C₁₉×#123	1	2	yes	—
512	C₂×C₄	C₁₉×#123	1	2	yes	—
513	C₂×C₄	C₁₉×#123	1	1	yes	characteristic
514	C₂×C₄	C₁₉×#124	1	2	yes	—
515	C₂×C₄	C₁₉×#124	1	1	yes	characteristic
516	C₂×C₄	C₁₉×#126	1	2	yes	—
517	C₂×C₄	C₁₉×#127	1	1	yes	characteristic
518	C₈	—	4	4	no	—
519	C₂²	—	4	4	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	4	no	—
527	C₂²	—	8	4	no	—
528	C₂²	—	8	4	no	—
529	C₂²	—	8	4	no	—
530	C₂²	C₁₉×#380	1	1	yes	characteristic
531	C₂²	C₁₉×#386	1	1	yes	characteristic
532	C₂²	C₁₉×#390	1	1	yes	characteristic
533	C₂²	C₁₉×#394	1	2	yes	—
534	C₂²	C₁₉×#396	1	2	yes	—
535	C₂²	C₂×C₁₉×#102	1	1	yes	characteristic
536	C₂²	C₁₉×#416	1	1	yes	characteristic
537	C₂²	C₁₉×#417	1	1	yes	characteristic
538	C₂²	C₁₉×#418	1	1	yes	characteristic
539	C₂²	C₁₉×#459	1	2	yes	—
540	C₂²	C₁₉×#459	1	1	yes	characteristic
541	C₂²	C₁₉×#460	1	2	yes	—
542	C₂²	C₁₉×#461	1	1	yes	characteristic
543	C₂²	C₁₉×#463	1	2	yes	—
544	C₂²	C₁₉×#463	1	2	yes	—
545	C₂²	C₁₉×#464	1	2	yes	—
546	C₂²	C₁₉×#465	1	2	yes	—
547	C₂²	C₁₉×#466	1	2	yes	—
548	C₂²	C₁₉×#468	1	2	yes	—
549	C₂²	C₁₉×#469	1	2	yes	—
550	C₂²	C₁₉×#474	1	1	yes	characteristic
551	C₂²	C₁₉×#476	1	1	yes	characteristic
552	C₂²	C₁₉×#478	1	2	yes	—
553	C₄	—	2	4	no	—
554	C₄	—	4	2	no	—
555	C₄	—	8	2	no	—
556	C₄	—	8	4	no	—
557	C₄	C₁₉×#385	1	2	yes	—
558	C₄	C₁₉×#388	1	2	yes	—
559	C₄	C₁₉×#392	1	1	yes	characteristic
560	C₄	C₁₉×#393	1	1	yes	characteristic
561	C₄	C₁₉×#397	1	1	yes	characteristic
562	C₄	C₁₉×#399	1	1	yes	characteristic
563	C₂	—	8	4	no	—
564	C₂	C₁₉×#1439	1	1	yes	characteristic
565	C₂	C₁₉×#1802	1	1	yes	characteristic
566	C₂	C₁₉×#1804	1	1	yes	characteristic
567	C₂	C₁₉×#1893	1	1	yes	characteristic
568	C₂	C₁₉×#1895	1	1	yes	characteristic
569	C₂	C₁₉×#1982	1	1	yes	characteristic
570	C₂	C₁₉×#1983	1	1	yes	characteristic
571	C₂	C₁₉×#2054	1	2	yes	—
572	C₂	C₁₉×#2055	1	2	yes	—
573	C₂	C₁₉×#2065	1	2	yes	—
574	C₂	C₁₉×#2067	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₉	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₁₉
Frattini, cosocle	C₂³×C₄	C₂³×C₁₉
prime radical	C₂³×D₄×C₁₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₉×C₄⋊C₈	C₂	semidirect
4. C₂×C₁₉×#340	C₂	semidirect
5. C₁₉×C₄⋊#95	C₂	semidirect
19. C₁₉×#390	C₄	semidirect
150. #11076	C₁₉	direct (N × H)
212. C₂×C₄×C₁₉	#102	semidirect
232. C₂²×C₄⋊C₈	C₂×C₁₉	semidirect
235. C₂×#340	C₂×C₁₉	semidirect
236. C₄⋊#95	C₂×C₁₉	semidirect
294. #390	C₄×C₁₉	semidirect
356. C₁₉	#11076	direct (N × H)
499. C₂×C₄	C₁₉×#102	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₉×C₄⋊C₈	2
C₂²×C₁₉×#102	2
C₂×C₁₉×#390	2
C₂×C₁₉×#340	2
C₁₉×C₄⋊#95	2
#11076	19

Subgroups — C19×#11076 #18017035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#11076 #18017035