Subgroups — C₁₉×#24782 #18030741

Order 4864.

1124 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#469	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₁₉×#106	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2416	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2065	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2034	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₉×#1944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1874	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1809	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	—	2	2	no	—
16	C₂×C₁₉×#121	C₂²	1	2	yes	—
17	C₂×C₁₉×#121	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
20	C₁₉×#469	—	2	4	no	—
21	C₁₉×#466	—	2	4	no	—
22	C₁₉×#435	—	2	4	no	—
23	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#106	—	2	4	no	—
25	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#106	C₂²	1	2	yes	—
27	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₁₉×#102	C₂²	1	2	yes	—
30	C₂×C₁₉×#102	C₂²	1	2	yes	—
31	C₂×C₁₉×#102	C₂²	1	2	yes	—
32	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
35	C₁₉×#396	—	2	2	no	—
36	C₁₉×#394	—	2	2	no	—
37	C₁₉×#390	C₂²	1	2	yes	—
38	C₁₉×#389	C₂²	1	2	yes	—
39	C₁₉×#386	—	2	2	no	—
40	C₁₉×#380	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#340	C₂²	1	2	yes	—
43	C₂²×D₄×C₁₉	—	2	2	no	—
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₁₉	—	2	2	no	—
48	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×D₈×C₁₉	—	2	2	no	—
51	C₂×D₈×C₁₉	—	2	2	no	—
52	C₂×D₈×C₁₉	—	2	2	no	—
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	2	2	no	—
55	C₂×M₁₆×C₁₉	—	2	2	no	—
56	C₂²×C₈×C₁₉	—	2	2	no	—
57	C₂²×C₈×C₁₉	—	2	2	no	—
58	C₂²×C₈×C₁₉	D₄	1	4	yes	complemented
59	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₁₉×#121	—	2	4	no	—
64	C₁₉×#121	—	2	4	no	—
65	C₁₉×#121	—	2	4	no	—
66	C₁₉×#121	—	4	2	no	—
67	C₁₉×#121	—	4	8	no	—
68	C₄×D₄×C₁₉	—	2	2	no	—
69	C₄×D₄×C₁₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₁₉	—	4	2	no	—
74	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
84	C₂×C₂²⋊C₄×C₁₉	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
86	C₁₉×#107	—	2	2	no	—
87	C₁₉×#106	—	2	2	no	—
88	C₁₉×#106	—	2	4	no	—
89	C₁₉×#106	D₄	1	4	yes	complemented
90	C₁₉×C₄⋊C₈	—	2	2	no	—
91	C₁₉×#102	—	2	4	no	—
92	C₁₉×#102	—	2	4	no	—
93	C₁₉×#102	—	4	2	no	—
94	C₁₉×C₂²⋊C₈	—	2	2	no	—
95	C₁₉×C₂²⋊C₈	—	2	2	no	—
96	C₁₉×#97	—	2	2	no	—
97	C₁₉×#95	—	2	2	no	—
98	C₁₉×#95	—	2	2	no	—
99	C₂⁴×C₁₉	—	2	2	no	—
100	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
101	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	4	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	2	2	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	2	no	—
110	C₂×D₄×C₁₉	—	4	4	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂×D₄×C₁₉	—	4	4	no	—
113	C₂×D₄×C₁₉	—	4	4	no	—
114	C₂×D₄×C₁₉	—	4	4	no	—
115	C₂×D₄×C₁₉	—	8	2	no	—
116	C₂²×C₄×C₁₉	—	2	1	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	2	1	no	—
127	C₂²×C₄×C₁₉	—	2	2	no	—
128	C₂²×C₄×C₁₉	—	2	2	no	—
129	C₂²×C₄×C₁₉	—	4	4	no	—
130	C₂²×C₄×C₁₉	—	4	4	no	—
131	C₂²×C₄×C₁₉	—	8	2	no	—
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₁₉	#41	1	2	yes	—
138	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
139	D₈×C₁₉	—	4	4	no	—
140	M₁₆×C₁₉	—	4	4	no	—
141	C₂×C₈×C₁₉	—	2	1	no	—
142	C₂×C₈×C₁₉	—	2	1	no	—
143	C₂×C₈×C₁₉	—	2	8	no	—
144	C₂×C₈×C₁₉	—	2	1	no	—
145	C₂×C₈×C₁₉	—	2	1	no	—
146	C₂×C₈×C₁₉	—	2	1	no	—
147	C₂×C₈×C₁₉	—	2	1	no	—
148	C₂×C₈×C₁₉	—	2	1	no	—
149	C₂×C₈×C₁₉	—	2	1	no	—
150	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₁₉	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₁₉	#41	1	2	yes	—
154	C₄⋊C₄×C₁₉	—	2	2	no	—
155	C₄⋊C₄×C₁₉	—	2	2	no	—
156	C₄⋊C₄×C₁₉	—	2	2	no	—
157	C₄⋊C₄×C₁₉	—	2	2	no	—
158	C₄⋊C₄×C₁₉	—	2	2	no	—
159	C₄⋊C₄×C₁₉	—	2	2	no	—
160	C₄⋊C₄×C₁₉	—	4	4	no	—
161	C₄⋊C₄×C₁₉	—	4	4	no	—
162	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
163	C₂²⋊C₄×C₁₉	—	2	2	no	—
164	C₂²⋊C₄×C₁₉	—	2	2	no	—
165	C₂²⋊C₄×C₁₉	—	4	4	no	—
166	C₂²⋊C₄×C₁₉	—	4	4	no	—
167	C₂²⋊C₄×C₁₉	—	4	4	no	—
168	C₂²⋊C₄×C₁₉	—	4	4	no	—
169	C₂²⋊C₄×C₁₉	—	8	2	no	—
170	C₄²×C₁₉	—	2	1	no	—
171	C₄²×C₁₉	—	2	1	no	—
172	#24782	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂³×C₁₉	—	2	1	no	—
174	C₂³×C₁₉	—	2	1	no	—
175	C₂³×C₁₉	—	2	2	no	—
176	C₂³×C₁₉	—	2	1	no	—
177	C₂³×C₁₉	—	2	1	no	—
178	C₂³×C₁₉	—	2	1	no	—
179	C₂³×C₁₉	—	2	2	no	—
180	C₂³×C₁₉	—	2	2	no	—
181	C₂³×C₁₉	—	4	2	no	—
182	C₂³×C₁₉	—	4	2	no	—
183	C₂³×C₁₉	—	4	2	no	—
184	C₂³×C₁₉	—	4	2	no	—
185	C₂³×C₁₉	—	4	2	no	—
186	C₂³×C₁₉	—	4	2	no	—
187	C₂³×C₁₉	—	4	2	no	—
188	C₂³×C₁₉	#121	1	2	yes	—
189	C₂³×C₁₉	AGL(1,ℤ/8)	1	4	yes	—
190	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
191	D₄×C₁₉	—	4	4	no	—
192	D₄×C₁₉	—	4	2	no	—
193	D₄×C₁₉	—	4	2	no	—
194	D₄×C₁₉	—	4	2	no	—
195	D₄×C₁₉	—	4	2	no	—
196	D₄×C₁₉	—	8	8	no	—
197	D₄×C₁₉	—	8	8	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	2	no	—
201	C₂×C₄×C₁₉	—	2	2	no	—
202	C₂×C₄×C₁₉	—	2	2	no	—
203	C₂×C₄×C₁₉	—	2	2	no	—
204	C₂×C₄×C₁₉	—	2	1	no	—
205	C₂×C₄×C₁₉	—	2	1	no	—
206	C₂×C₄×C₁₉	—	2	1	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	4	no	—
209	C₂×C₄×C₁₉	—	2	1	no	—
210	C₂×C₄×C₁₉	—	2	2	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	2	no	—
219	C₂×C₄×C₁₉	—	4	2	no	—
220	C₂×C₄×C₁₉	—	4	2	no	—
221	C₂×C₄×C₁₉	—	4	2	no	—
222	C₂×C₄×C₁₉	—	4	2	no	—
223	C₂×C₄×C₁₉	—	4	2	no	—
224	C₂×C₄×C₁₉	—	8	8	no	—
225	C₂×C₄×C₁₉	#121	1	2	yes	—
226	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
232	C₈×C₁₉	—	2	2	no	—
233	C₈×C₁₉	—	4	1	no	—
234	C₈×C₁₉	—	4	1	no	—
235	C₈×C₁₉	#121	1	4	yes	complemented
236	C₂×#469	C₂×C₁₉	1	1	yes	characteristic, complemented
237	C₂×#466	C₂×C₁₉	1	1	yes	characteristic, complemented
238	C₂×#435	C₂×C₁₉	1	1	yes	characteristic, complemented
239	C₂²×#106	C₂×C₁₉	1	1	yes	characteristic, complemented
240	#2416	C₂×C₁₉	1	2	yes	complemented
241	#2065	C₂×C₁₉	1	2	yes	complemented
242	#2034	C₂×C₁₉	1	2	yes	complemented
243	#1972	C₂×C₁₉	1	1	yes	characteristic, complemented
244	#1944	C₂×C₁₉	1	1	yes	characteristic, complemented
245	#1874	C₂×C₁₉	1	2	yes	complemented
246	#1809	C₂×C₁₉	1	1	yes	characteristic, complemented
247	C₂²×C₁₉	—	2	4	no	—
248	C₂²×C₁₉	—	2	2	no	—
249	C₂²×C₁₉	—	2	4	no	—
250	C₂²×C₁₉	—	2	2	no	—
251	C₂²×C₁₉	—	4	2	no	—
252	C₂²×C₁₉	—	4	1	no	—
253	C₂²×C₁₉	—	4	2	no	—
254	C₂²×C₁₉	—	4	1	no	—
255	C₂²×C₁₉	—	4	1	no	—
256	C₂²×C₁₉	—	8	2	no	—
257	C₂²×C₁₉	—	8	2	no	—
258	C₂²×C₁₉	—	8	2	no	—
259	C₂²×C₁₉	—	8	2	no	—
260	C₂²×C₁₉	—	8	2	no	—
261	C₂²×C₁₉	—	8	2	no	—
262	C₂²×C₁₉	—	8	2	no	—
263	C₂²×C₁₉	#469	1	4	yes	complemented
264	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
265	C₂²×C₁₉	D₄²	1	1	yes	characteristic
266	C₂²×C₁₉	#547	1	1	yes	characteristic
267	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
268	C₂²×C₁₉	#577	1	2	yes	—
269	C₄×C₁₉	—	2	2	no	—
270	C₄×C₁₉	—	4	1	no	—
271	C₄×C₁₉	—	4	4	no	—
272	C₄×C₁₉	—	4	1	no	—
273	C₄×C₁₉	—	4	1	no	—
274	C₄×C₁₉	—	8	2	no	—
275	C₄×C₁₉	—	8	2	no	—
276	C₄×C₁₉	C₂×#121	1	1	yes	characteristic
277	C₄×C₁₉	#537	1	1	yes	characteristic
278	C₄×C₁₉	#548	1	1	yes	characteristic
279	C₄×C₁₉	#553	1	1	yes	characteristic
280	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
281	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
282	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic
283	C₂×#121	—	2	2	no	—
284	C₂×#121	C₂²×C₁₉	1	2	yes	—
285	C₂×#121	C₂²×C₁₉	1	2	yes	—
286	C₂×C₄×D₄	C₂²×C₁₉	1	1	yes	characteristic
287	C₂²×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
288	#469	—	2	4	no	—
289	#466	—	2	4	no	—
290	#435	—	2	4	no	—
291	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
292	C₂×#106	—	2	4	no	—
293	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
294	C₂×#106	C₂²×C₁₉	1	2	yes	—
295	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
296	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
297	C₂×#102	C₂²×C₁₉	1	2	yes	—
298	C₂×#102	C₂²×C₁₉	1	2	yes	—
299	C₂×#102	C₂²×C₁₉	1	2	yes	—
300	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
301	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
302	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
303	#396	—	2	2	no	—
304	#394	—	2	2	no	—
305	#390	C₂²×C₁₉	1	2	yes	—
306	#389	C₂²×C₁₉	1	2	yes	—
307	#386	—	2	2	no	—
308	#380	C₂²×C₁₉	1	2	yes	—
309	#340	C₂²×C₁₉	1	2	yes	—
310	#340	C₂²×C₁₉	1	2	yes	—
311	C₂×C₁₉	—	2	4	no	—
312	C₂×C₁₉	—	8	1	no	—
313	C₂×C₁₉	—	16	2	no	—
314	C₂×C₁₉	#2416	1	1	yes	characteristic
315	C₂×C₁₉	C₂×#469	1	1	yes	characteristic
316	C₂×C₁₉	#3060	1	1	yes	characteristic
317	C₂×C₁₉	#3265	1	2	yes	—
318	C₂×C₁₉	#3345	1	2	yes	—
319	C₂²×D₄	—	2	2	no	—
320	C₂²×D₄	—	2	2	no	—
321	C₂²×D₄	D₄×C₁₉	1	1	yes	characteristic
322	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
323	C₂³×C₄	—	2	2	no	—
324	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
326	C₂×D₈	—	2	2	no	—
327	C₂×D₈	—	2	2	no	—
328	C₂×D₈	—	2	2	no	—
329	C₂×M₁₆	—	2	2	no	—
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂²×C₈	—	2	2	no	—
333	C₂²×C₈	—	2	2	no	—
334	C₂²×C₈	D₄×C₁₉	1	4	yes	complemented
335	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
336	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
337	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
338	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
339	#121	—	2	4	no	—
340	#121	—	2	4	no	—
341	#121	—	2	4	no	—
342	#121	—	4	2	no	—
343	#121	—	4	8	no	—
344	C₄×D₄	—	2	2	no	—
345	C₄×D₄	—	2	2	no	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	2	no	—
349	C₂×C₄⋊C₄	—	4	2	no	—
350	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
352	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
353	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
354	C₂×C₂²⋊C₄	—	2	2	no	—
355	C₂×C₂²⋊C₄	—	2	2	no	—
356	C₂×C₂²⋊C₄	—	2	2	no	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	2	no	—
359	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
360	C₂×C₂²⋊C₄	D₄×C₁₉	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
362	#107	—	2	2	no	—
363	#106	—	2	2	no	—
364	#106	—	2	4	no	—
365	#106	D₄×C₁₉	1	4	yes	complemented
366	C₄⋊C₈	—	2	2	no	—
367	#102	—	2	4	no	—
368	#102	—	2	4	no	—
369	#102	—	4	2	no	—
370	C₂²⋊C₈	—	2	2	no	—
371	C₂²⋊C₈	—	2	2	no	—
372	#97	—	2	2	no	—
373	#95	—	2	2	no	—
374	#95	—	2	2	no	—
375	C₁₉	#24782	1	1	yes	characteristic, direct product factor, Sylow
376	C₂⁴	—	2	2	no	—
377	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
378	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	2	no	—
382	C₂×D₄	—	2	2	no	—
383	C₂×D₄	—	2	2	no	—
384	C₂×D₄	—	2	2	no	—
385	C₂×D₄	—	2	2	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	4	no	—
390	C₂×D₄	—	4	4	no	—
391	C₂×D₄	—	4	4	no	—
392	C₂×D₄	—	8	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	4	4	no	—
407	C₂²×C₄	—	4	4	no	—
408	C₂²×C₄	—	8	2	no	—
409	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
410	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
411	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
412	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
414	C₂²×C₄	#41×C₁₉	1	2	yes	—
415	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
416	D₈	—	4	4	no	—
417	M₁₆	—	4	4	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	8	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	2	1	no	—
423	C₂×C₈	—	2	1	no	—
424	C₂×C₈	—	2	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
428	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
429	C₂×C₈	C₂×D₄×C₁₉	1	2	yes	—
430	C₂×C₈	#41×C₁₉	1	2	yes	—
431	C₄⋊C₄	—	2	2	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	4	4	no	—
438	C₄⋊C₄	—	4	4	no	—
439	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	4	4	no	—
443	C₂²⋊C₄	—	4	4	no	—
444	C₂²⋊C₄	—	4	4	no	—
445	C₂²⋊C₄	—	4	4	no	—
446	C₂²⋊C₄	—	8	2	no	—
447	C₄²	—	2	1	no	—
448	C₄²	—	2	1	no	—
449	C₂³	—	2	1	no	—
450	C₂³	—	2	1	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	2	1	no	—
453	C₂³	—	2	1	no	—
454	C₂³	—	2	1	no	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	—	4	2	no	—
459	C₂³	—	4	2	no	—
460	C₂³	—	4	2	no	—
461	C₂³	—	4	2	no	—
462	C₂³	—	4	2	no	—
463	C₂³	—	4	2	no	—
464	C₂³	C₁₉×#121	1	2	yes	—
465	C₂³	C₁₉×AGL(1,ℤ/8)	1	4	yes	—
466	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
467	D₄	—	4	4	no	—
468	D₄	—	4	2	no	—
469	D₄	—	4	2	no	—
470	D₄	—	4	2	no	—
471	D₄	—	4	2	no	—
472	D₄	—	8	8	no	—
473	D₄	—	8	8	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	1	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	8	8	no	—
501	C₂×C₄	C₁₉×#121	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
504	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
505	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
506	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
507	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
508	C₈	—	2	2	no	—
509	C₈	—	4	1	no	—
510	C₈	—	4	1	no	—
511	C₈	C₁₉×#121	1	4	yes	complemented
512	C₂²	—	2	2	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	4	no	—
516	C₂²	—	4	1	no	—
517	C₂²	—	4	2	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	1	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	8	2	no	—
522	C₂²	—	8	2	no	—
523	C₂²	—	8	2	no	—
524	C₂²	—	8	2	no	—
525	C₂²	—	8	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	C₁₉×#469	1	4	yes	complemented
529	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
530	C₂²	D₄²×C₁₉	1	1	yes	characteristic
531	C₂²	C₁₉×#547	1	1	yes	characteristic
532	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	2	yes	—
533	C₂²	C₁₉×#577	1	2	yes	—
534	C₄	—	2	2	no	—
535	C₄	—	4	1	no	—
536	C₄	—	4	4	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	8	2	no	—
540	C₄	—	8	2	no	—
541	C₄	C₂×C₁₉×#121	1	1	yes	characteristic
542	C₄	C₁₉×#537	1	1	yes	characteristic
543	C₄	C₁₉×#548	1	1	yes	characteristic
544	C₄	C₁₉×#553	1	1	yes	characteristic
545	C₂	—	2	4	no	—
546	C₂	—	8	1	no	—
547	C₂	—	16	2	no	—
548	C₂	C₁₉×#2416	1	1	yes	characteristic
549	C₂	C₂×C₁₉×#469	1	1	yes	characteristic
550	C₂	C₁₉×#3060	1	1	yes	characteristic
551	C₂	C₁₉×#3265	1	2	yes	—
552	C₂	C₁₉×#3345	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₉×#469	C₂	semidirect
2. C₂×C₁₉×#466	C₂	semidirect
3. C₂×C₁₉×#435	C₂	semidirect
4. C₂²×C₁₉×#106	C₂	semidirect
5. C₁₉×#2416	C₂	semidirect
6. C₁₉×#2065	C₂	semidirect
7. C₁₉×#2034	C₂	semidirect
8. C₁₉×#1972	C₂	semidirect
9. C₁₉×#1944	C₂	semidirect
10. C₁₉×#1874	C₂	semidirect
11. C₁₉×#1809	C₂	semidirect
58. C₂²×C₈×C₁₉	D₄	semidirect
89. C₁₉×#106	D₄	semidirect
172. #24782	C₁₉	direct (N × H)
235. C₈×C₁₉	#121	semidirect
236. C₂×#469	C₂×C₁₉	semidirect
237. C₂×#466	C₂×C₁₉	semidirect
238. C₂×#435	C₂×C₁₉	semidirect
239. C₂²×#106	C₂×C₁₉	semidirect
240. #2416	C₂×C₁₉	semidirect
241. #2065	C₂×C₁₉	semidirect
242. #2034	C₂×C₁₉	semidirect
243. #1972	C₂×C₁₉	semidirect
244. #1944	C₂×C₁₉	semidirect
245. #1874	C₂×C₁₉	semidirect
246. #1809	C₂×C₁₉	semidirect
263. C₂²×C₁₉	#469	semidirect
334. C₂²×C₈	D₄×C₁₉	semidirect
365. #106	D₄×C₁₉	semidirect
375. C₁₉	#24782	direct (N × H)
511. C₈	C₁₉×#121	semidirect
528. C₂²	C₁₉×#469	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#469	2
C₂×C₁₉×#466	2
C₂×C₁₉×#435	2
C₂²×C₁₉×#106	2
C₁₉×#2416	2
C₁₉×#2065	2
C₁₉×#2034	2
C₁₉×#1972	2
C₁₉×#1944	2
C₁₉×#1874	2
C₁₉×#1809	2
#24782	19

Subgroups — C19×#24782 #18030741

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24782 #18030741