Subgroups — C₁₉×#24547 #18030506

Order 4864.

1022 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#449	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2504	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2341	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2073	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2054	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1895	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1880	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1823	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1805	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#449	—	2	4	no	—
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₁₉×#417	—	2	4	no	—
22	C₂×C₁₉×#103	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#102	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×#397	—	2	1	no	—
29	C₁₉×#397	—	2	1	no	—
30	C₁₉×#390	—	2	2	no	—
31	C₁₉×#390	C₂²	1	2	yes	—
32	C₁₉×#390	C₂²	1	2	yes	—
33	C₁₉×#386	—	2	2	no	—
34	C₁₉×#382	C₂²	1	2	yes	—
35	C₁₉×#380	—	2	1	no	—
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
38	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂×#41×C₁₉	—	2	2	no	—
44	C₂×#41×C₁₉	—	2	4	no	—
45	C₂×#41×C₁₉	—	4	2	no	—
46	C₂×#41×C₁₉	D₄	1	4	yes	—
47	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₉	—	2	1	no	—
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	—	2	1	no	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×SD₁₆×C₁₉	—	2	2	no	—
56	C₂×SD₁₆×C₁₉	—	2	4	no	—
57	C₂×D₈×C₁₉	—	2	2	no	—
58	C₂×D₈×C₁₉	—	4	2	no	—
59	C₂×M₁₆×C₁₉	—	2	2	no	—
60	C₂×M₁₆×C₁₉	—	4	2	no	—
61	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
64	C₁₉×#121	—	2	2	no	—
65	C₁₉×#121	—	2	2	no	—
66	C₄×Q₈×C₁₉	—	2	4	no	—
67	C₄×Q₈×C₁₉	—	4	2	no	—
68	C₂×C₄⋊C₄×C₁₉	—	2	2	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	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
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	D₄	1	2	yes	—
82	C₂×C₄²×C₁₉	—	2	2	no	—
83	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
84	C₁₉×C₄⋊C₈	—	4	2	no	—
85	C₁₉×#103	—	2	4	no	—
86	C₁₉×#103	—	2	2	no	—
87	C₁₉×#102	—	2	4	no	—
88	C₁₉×#102	—	2	2	no	—
89	C₁₉×#102	—	4	2	no	—
90	C₁₉×C₂²⋊C₈	—	2	2	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₁₉×#95	—	2	2	no	—
93	C₁₉×#95	—	2	2	no	—
94	C₁₉×#95	D₄	1	1	yes	characteristic
95	C₁₉×#95	D₄	1	1	yes	characteristic
96	C₂⁴×C₁₉	—	2	1	no	—
97	C₂⁴×C₁₉	—	2	1	no	—
98	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
99	#41×C₁₉	—	2	8	no	—
100	#41×C₁₉	—	4	4	no	—
101	#41×C₁₉	—	4	8	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
105	C₂×Q₈×C₁₉	#41	1	4	yes	—
106	C₂×D₄×C₁₉	—	2	4	no	—
107	C₂×D₄×C₁₉	—	2	1	no	—
108	C₂×D₄×C₁₉	—	2	2	no	—
109	C₂×D₄×C₁₉	—	2	1	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	2	2	no	—
113	C₂×D₄×C₁₉	—	2	2	no	—
114	C₂×D₄×C₁₉	—	4	4	no	—
115	C₂×D₄×C₁₉	—	4	4	no	—
116	C₂×D₄×C₁₉	—	4	2	no	—
117	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₁₉	—	2	1	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	4	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	2	2	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	4	4	no	—
126	C₂²×C₄×C₁₉	—	4	2	no	—
127	C₂²×C₄×C₁₉	—	8	1	no	—
128	C₂²×C₄×C₁₉	—	8	1	no	—
129	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₁₉	#41	1	2	yes	—
134	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
135	SD₁₆×C₁₉	—	4	4	no	—
136	D₈×C₁₉	—	4	4	no	—
137	M₁₆×C₁₉	—	4	4	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	1	no	—
140	C₂×C₈×C₁₉	—	2	1	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₂×C₈×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	1	no	—
147	C₄⋊C₄×C₁₉	—	2	2	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	2	2	no	—
151	C₄⋊C₄×C₁₉	—	4	4	no	—
152	C₄⋊C₄×C₁₉	—	4	2	no	—
153	C₂²⋊C₄×C₁₉	—	4	2	no	—
154	C₂²⋊C₄×C₁₉	—	4	4	no	—
155	C₂²⋊C₄×C₁₉	—	4	2	no	—
156	C₂²⋊C₄×C₁₉	—	8	2	no	—
157	C₂²⋊C₄×C₁₉	—	8	2	no	—
158	C₂²⋊C₄×C₁₉	—	8	2	no	—
159	C₂²⋊C₄×C₁₉	—	8	1	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	4	4	no	—
163	#24547	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₉	—	2	2	no	—
165	C₂³×C₁₉	—	2	2	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	2	no	—
169	C₂³×C₁₉	—	4	2	no	—
170	C₂³×C₁₉	—	4	2	no	—
171	C₂³×C₁₉	—	4	1	no	—
172	C₂³×C₁₉	—	4	1	no	—
173	C₂³×C₁₉	—	4	1	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	4	1	no	—
177	C₂³×C₁₉	—	4	1	no	—
178	C₂³×C₁₉	#121	1	2	yes	—
179	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₉	—	2	2	no	—
181	Q₈×C₁₉	—	2	4	no	—
182	Q₈×C₁₉	#123	1	4	yes	—
183	D₄×C₁₉	—	2	2	no	—
184	D₄×C₁₉	—	2	2	no	—
185	D₄×C₁₉	—	4	8	no	—
186	D₄×C₁₉	—	4	1	no	—
187	D₄×C₁₉	—	4	1	no	—
188	D₄×C₁₉	—	4	2	no	—
189	D₄×C₁₉	—	4	2	no	—
190	D₄×C₁₉	—	8	4	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	2	4	no	—
193	C₂×C₄×C₁₉	—	2	2	no	—
194	C₂×C₄×C₁₉	—	2	2	no	—
195	C₂×C₄×C₁₉	—	2	2	no	—
196	C₂×C₄×C₁₉	—	2	4	no	—
197	C₂×C₄×C₁₉	—	2	2	no	—
198	C₂×C₄×C₁₉	—	2	2	no	—
199	C₂×C₄×C₁₉	—	2	2	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	—	4	8	no	—
204	C₂×C₄×C₁₉	—	4	1	no	—
205	C₂×C₄×C₁₉	—	4	2	no	—
206	C₂×C₄×C₁₉	—	4	2	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	2	no	—
209	C₂×C₄×C₁₉	—	4	2	no	—
210	C₂×C₄×C₁₉	—	4	2	no	—
211	C₂×C₄×C₁₉	—	4	2	no	—
212	C₂×C₄×C₁₉	—	8	4	no	—
213	C₂×C₄×C₁₉	#121	1	2	yes	—
214	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
216	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
218	C₈×C₁₉	—	4	1	no	—
219	C₈×C₁₉	—	4	2	no	—
220	C₈×C₁₉	—	4	1	no	—
221	C₂×#449	C₂×C₁₉	1	1	yes	characteristic
222	C₂×#417	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#2504	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#2341	C₂×C₁₉	1	1	yes	characteristic, complemented
225	#2073	C₂×C₁₉	1	2	yes	complemented
226	#2054	C₂×C₁₉	1	2	yes	complemented
227	#1895	C₂×C₁₉	1	1	yes	characteristic, complemented
228	#1880	C₂×C₁₉	1	2	yes	complemented
229	#1851	C₂×C₁₉	1	1	yes	characteristic, complemented
230	#1823	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#1805	C₂×C₁₉	1	2	yes	complemented
232	C₂²×C₁₉	—	2	2	no	—
233	C₂²×C₁₉	—	2	2	no	—
234	C₂²×C₁₉	—	2	2	no	—
235	C₂²×C₁₉	—	4	2	no	—
236	C₂²×C₁₉	—	4	2	no	—
237	C₂²×C₁₉	—	4	2	no	—
238	C₂²×C₁₉	—	4	2	no	—
239	C₂²×C₁₉	—	4	2	no	—
240	C₂²×C₁₉	—	8	2	no	—
241	C₂²×C₁₉	—	8	2	no	—
242	C₂²×C₁₉	—	8	1	no	—
243	C₂²×C₁₉	—	8	1	no	—
244	C₂²×C₁₉	—	8	1	no	—
245	C₂²×C₁₉	—	8	2	no	—
246	C₂²×C₁₉	—	8	2	no	—
247	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
248	C₂²×C₁₉	#546	1	2	yes	—
249	C₂²×C₁₉	#575	1	2	yes	—
250	C₂²×C₁₉	#576	1	1	yes	characteristic
251	C₂²×C₁₉	#577	1	1	yes	characteristic
252	C₄×C₁₉	—	2	2	no	—
253	C₄×C₁₉	—	2	4	no	—
254	C₄×C₁₉	—	4	2	no	—
255	C₄×C₁₉	—	4	2	no	—
256	C₄×C₁₉	—	8	1	no	—
257	C₄×C₁₉	—	8	2	no	—
258	C₄×C₁₉	—	8	2	no	—
259	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
260	C₄×C₁₉	#534	1	1	yes	characteristic
261	C₄×C₁₉	#551	1	2	yes	—
262	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
263	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
264	C₂²×D₈	C₂²×C₁₉	1	1	yes	characteristic
265	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
266	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
267	C₂×C₄×Q₈	C₂²×C₁₉	1	2	yes	—
268	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
269	#449	—	2	4	no	—
270	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
271	#417	—	2	4	no	—
272	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×#103	C₂²×C₁₉	1	2	yes	—
274	C₂×#102	C₂²×C₁₉	1	2	yes	—
275	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#102	C₂²×C₁₉	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
278	#397	—	2	1	no	—
279	#397	—	2	1	no	—
280	#390	—	2	2	no	—
281	#390	C₂²×C₁₉	1	2	yes	—
282	#390	C₂²×C₁₉	1	2	yes	—
283	#386	—	2	2	no	—
284	#382	C₂²×C₁₉	1	2	yes	—
285	#380	—	2	1	no	—
286	#380	C₂²×C₁₉	1	1	yes	characteristic
287	C₄×C₂²⋊C₄	—	2	1	no	—
288	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
289	#340	C₂²×C₁₉	1	2	yes	—
290	#340	C₂²×C₁₉	1	2	yes	—
291	#340	C₂²×C₁₉	1	2	yes	—
292	#336	C₂²×C₁₉	1	2	yes	—
293	C₂×C₁₉	—	4	2	no	—
294	C₂×C₁₉	—	8	2	no	—
295	C₂×C₁₉	—	16	1	no	—
296	C₂×C₁₉	#2412	1	1	yes	characteristic
297	C₂×C₁₉	#3040	1	1	yes	characteristic
298	C₂×C₁₉	#3045	1	1	yes	characteristic
299	C₂×C₁₉	#3309	1	2	yes	—
300	C₂×C₁₉	#3326	1	2	yes	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	4	no	—
303	C₂×#41	—	4	2	no	—
304	C₂×#41	D₄×C₁₉	1	4	yes	—
305	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	—	2	1	no	—
308	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
309	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂³×C₄	—	2	1	no	—
311	C₂³×C₄	—	2	1	no	—
312	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
313	C₂×SD₁₆	—	2	2	no	—
314	C₂×SD₁₆	—	2	4	no	—
315	C₂×D₈	—	2	2	no	—
316	C₂×D₈	—	4	2	no	—
317	C₂×M₁₆	—	2	2	no	—
318	C₂×M₁₆	—	4	2	no	—
319	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
320	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
321	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
322	#121	—	2	2	no	—
323	#121	—	2	2	no	—
324	C₄×Q₈	—	2	4	no	—
325	C₄×Q₈	—	4	2	no	—
326	C₂×C₄⋊C₄	—	2	2	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
331	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	1	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	—	2	2	no	—
339	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
340	C₂×C₄²	—	2	2	no	—
341	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
342	C₄⋊C₈	—	4	2	no	—
343	#103	—	2	4	no	—
344	#103	—	2	2	no	—
345	#102	—	2	4	no	—
346	#102	—	2	2	no	—
347	#102	—	4	2	no	—
348	C₂²⋊C₈	—	2	2	no	—
349	#95	—	2	1	no	—
350	#95	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	D₄×C₁₉	1	1	yes	characteristic
353	#95	D₄×C₁₉	1	1	yes	characteristic
354	C₁₉	#24547	1	1	yes	characteristic, direct product factor, Sylow
355	C₂⁴	—	2	1	no	—
356	C₂⁴	—	2	1	no	—
357	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
358	#41	—	2	8	no	—
359	#41	—	4	4	no	—
360	#41	—	4	8	no	—
361	C₂×Q₈	—	2	1	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
364	C₂×Q₈	#41×C₁₉	1	4	yes	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	4	4	no	—
374	C₂×D₄	—	4	4	no	—
375	C₂×D₄	—	4	2	no	—
376	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	2	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	2	no	—
386	C₂²×C₄	—	8	1	no	—
387	C₂²×C₄	—	8	1	no	—
388	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
389	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
390	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
391	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
392	C₂²×C₄	#41×C₁₉	1	2	yes	—
393	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
394	SD₁₆	—	4	4	no	—
395	D₈	—	4	4	no	—
396	M₁₆	—	4	4	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	4	4	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	4	4	no	—
414	C₂²⋊C₄	—	4	2	no	—
415	C₂²⋊C₄	—	8	2	no	—
416	C₂²⋊C₄	—	8	2	no	—
417	C₂²⋊C₄	—	8	2	no	—
418	C₂²⋊C₄	—	8	1	no	—
419	C₄²	—	2	2	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	4	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	2	1	no	—
425	C₂³	—	2	1	no	—
426	C₂³	—	2	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	4	2	no	—
429	C₂³	—	4	1	no	—
430	C₂³	—	4	1	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	2	no	—
433	C₂³	—	4	2	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	C₁₉×#121	1	2	yes	—
437	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	Q₈	—	2	4	no	—
440	Q₈	C₁₉×#123	1	4	yes	—
441	D₄	—	2	2	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	8	no	—
444	D₄	—	4	1	no	—
445	D₄	—	4	1	no	—
446	D₄	—	4	2	no	—
447	D₄	—	4	2	no	—
448	D₄	—	8	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	4	no	—
471	C₂×C₄	C₁₉×#121	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
474	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
475	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
476	C₈	—	4	1	no	—
477	C₈	—	4	2	no	—
478	C₈	—	4	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	8	2	no	—
488	C₂²	—	8	2	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	—	8	1	no	—
492	C₂²	—	8	2	no	—
493	C₂²	—	8	2	no	—
494	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
495	C₂²	C₁₉×#546	1	2	yes	—
496	C₂²	C₁₉×#575	1	2	yes	—
497	C₂²	C₁₉×#576	1	1	yes	characteristic
498	C₂²	C₁₉×#577	1	1	yes	characteristic
499	C₄	—	2	2	no	—
500	C₄	—	2	4	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	8	1	no	—
504	C₄	—	8	2	no	—
505	C₄	—	8	2	no	—
506	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
507	C₄	C₁₉×#534	1	1	yes	characteristic
508	C₄	C₁₉×#551	1	2	yes	—
509	C₂	—	4	2	no	—
510	C₂	—	8	2	no	—
511	C₂	—	16	1	no	—
512	C₂	C₁₉×#2412	1	1	yes	characteristic
513	C₂	C₁₉×#3040	1	1	yes	characteristic
514	C₂	C₁₉×#3045	1	1	yes	characteristic
515	C₂	C₁₉×#3309	1	2	yes	—
516	C₂	C₁₉×#3326	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂×C₁₉×#449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₄×C₂²⋊C₄×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₉×#417	C₂	semidirect
3. C₁₉×#2504	C₂	semidirect
4. C₁₉×#2341	C₂	semidirect
5. C₁₉×#2073	C₂	semidirect
6. C₁₉×#2054	C₂	semidirect
7. C₁₉×#1895	C₂	semidirect
8. C₁₉×#1880	C₂	semidirect
9. C₁₉×#1851	C₂	semidirect
10. C₁₉×#1823	C₂	semidirect
11. C₁₉×#1805	C₂	semidirect
163. #24547	C₁₉	direct (N × H)
222. C₂×#417	C₂×C₁₉	semidirect
223. #2504	C₂×C₁₉	semidirect
224. #2341	C₂×C₁₉	semidirect
225. #2073	C₂×C₁₉	semidirect
226. #2054	C₂×C₁₉	semidirect
227. #1895	C₂×C₁₉	semidirect
228. #1880	C₂×C₁₉	semidirect
229. #1851	C₂×C₁₉	semidirect
230. #1823	C₂×C₁₉	semidirect
231. #1805	C₂×C₁₉	semidirect
354. C₁₉	#24547	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₉×#449	2
C₂×C₁₉×#417	2
C₁₉×#2504	2
C₁₉×#2341	2
C₁₉×#2073	2
C₁₉×#2054	2
C₁₉×#1895	2
C₁₉×#1880	2
C₁₉×#1851	2
C₁₉×#1823	2
C₁₉×#1805	2
#24547	19

Subgroups — C19×#24547 #18030506

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24547 #18030506