Subgroups — C₁₉×#24545 #18030504

Order 4864.

1008 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#452	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#417	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2503	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2339	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#2074	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2056	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1894	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#1877	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#1824	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1804	C₂	1	2	yes	maximal, complemented
12	C₂²×#41×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₁₉×#452	—	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×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×#102	C₂²	1	2	yes	—
27	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
28	C₁₉×#400	—	2	1	no	—
29	C₁₉×#400	—	2	1	no	—
30	C₁₉×#391	C₂²	1	2	yes	—
31	C₁₉×#391	C₂²	1	2	yes	—
32	C₁₉×#386	—	2	2	no	—
33	C₁₉×#382	C₂²	1	2	yes	—
34	C₁₉×#381	—	2	1	no	—
35	C₁₉×#381	—	2	2	no	—
36	C₁₉×#380	C₂²	1	1	yes	characteristic
37	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
38	C₂×C₁₉×#95	—	2	1	no	—
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×Q₈×C₁₉	C₂³	1	1	yes	characteristic
49	C₂²×D₄×C₁₉	—	2	1	no	—
50	C₂²×D₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₉	—	2	1	no	—
52	C₂³×C₄×C₁₉	—	2	1	no	—
53	C₂³×C₄×C₁₉	—	2	2	no	—
54	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×Q₁₆×C₁₉	—	2	2	no	—
56	C₂×Q₁₆×C₁₉	—	4	2	no	—
57	C₂×SD₁₆×C₁₉	—	2	2	no	—
58	C₂×SD₁₆×C₁₉	—	2	4	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×C₂²⋊Q₈	—	2	2	no	—
65	C₁₉×C₂²⋊Q₈	—	2	2	no	—
66	C₄×D₄×C₁₉	—	2	4	no	—
67	C₄×D₄×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	1	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	1	no	—
76	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
79	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
80	C₁₉×C₄⋊C₈	—	4	2	no	—
81	C₁₉×#103	—	2	4	no	—
82	C₁₉×#103	—	2	2	no	—
83	C₁₉×#103	—	4	2	no	—
84	C₁₉×#102	—	2	4	no	—
85	C₁₉×#102	—	2	2	no	—
86	C₁₉×C₂²⋊C₈	—	2	2	no	—
87	C₁₉×#95	—	2	1	no	—
88	C₁₉×#95	—	2	2	no	—
89	C₁₉×#95	—	2	2	no	—
90	C₁₉×#95	—	2	2	no	—
91	C₁₉×#95	—	2	2	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	C₂×D₄	1	1	yes	characteristic
98	#41×C₁₉	—	2	8	no	—
99	#41×C₁₉	—	4	4	no	—
100	#41×C₁₉	—	4	8	no	—
101	C₂×Q₈×C₁₉	—	2	1	no	—
102	C₂×Q₈×C₁₉	—	2	1	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	2	1	no	—
105	C₂×Q₈×C₁₉	—	2	2	no	—
106	C₂×Q₈×C₁₉	—	2	2	no	—
107	C₂×Q₈×C₁₉	—	2	2	no	—
108	C₂×Q₈×C₁₉	C₂×D₄	1	2	yes	—
109	C₂×D₄×C₁₉	—	2	4	no	—
110	C₂×D₄×C₁₉	—	2	1	no	—
111	C₂×D₄×C₁₉	—	2	2	no	—
112	C₂×D₄×C₁₉	—	4	4	no	—
113	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
114	C₂×D₄×C₁₉	#41	1	4	yes	—
115	C₂²×C₄×C₁₉	—	2	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	1	no	—
118	C₂²×C₄×C₁₉	—	2	4	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	2	2	no	—
123	C₂²×C₄×C₁₉	—	4	4	no	—
124	C₂²×C₄×C₁₉	—	4	4	no	—
125	C₂²×C₄×C₁₉	—	4	4	no	—
126	C₂²×C₄×C₁₉	—	4	4	no	—
127	C₂²×C₄×C₁₉	—	4	2	no	—
128	C₂²×C₄×C₁₉	—	8	2	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	Q₁₆×C₁₉	—	4	4	no	—
136	SD₁₆×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	2	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	1	no	—
157	C₄²×C₁₉	—	2	2	no	—
158	C₄²×C₁₉	—	2	2	no	—
159	#24545	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
160	C₂³×C₁₉	—	2	2	no	—
161	C₂³×C₁₉	—	2	4	no	—
162	C₂³×C₁₉	—	2	2	no	—
163	C₂³×C₁₉	—	2	2	no	—
164	C₂³×C₁₉	—	2	1	no	—
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	4	2	no	—
167	C₂³×C₁₉	—	4	1	no	—
168	C₂³×C₁₉	—	4	1	no	—
169	C₂³×C₁₉	#121	1	2	yes	—
170	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₁₉	—	2	2	no	—
172	Q₈×C₁₉	—	2	2	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	Q₈×C₁₉	—	4	1	no	—
175	Q₈×C₁₉	—	4	1	no	—
176	Q₈×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	2	2	no	—
178	D₄×C₁₉	—	2	4	no	—
179	D₄×C₁₉	—	4	8	no	—
180	D₄×C₁₉	#123	1	4	yes	—
181	C₂×C₄×C₁₉	—	2	2	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	4	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	2	no	—
187	C₂×C₄×C₁₉	—	2	2	no	—
188	C₂×C₄×C₁₉	—	2	2	no	—
189	C₂×C₄×C₁₉	—	2	2	no	—
190	C₂×C₄×C₁₉	—	2	2	no	—
191	C₂×C₄×C₁₉	—	2	2	no	—
192	C₂×C₄×C₁₉	—	4	8	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	1	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	2	no	—
197	C₂×C₄×C₁₉	—	4	2	no	—
198	C₂×C₄×C₁₉	—	4	2	no	—
199	C₂×C₄×C₁₉	—	4	4	no	—
200	C₂×C₄×C₁₉	—	4	2	no	—
201	C₂×C₄×C₁₉	—	4	2	no	—
202	C₂×C₄×C₁₉	—	4	1	no	—
203	C₂×C₄×C₁₉	—	4	1	no	—
204	C₂×C₄×C₁₉	—	8	8	no	—
205	C₂×C₄×C₁₉	—	8	4	no	—
206	C₂×C₄×C₁₉	#121	1	2	yes	—
207	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
209	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
211	C₈×C₁₉	—	4	1	no	—
212	C₈×C₁₉	—	4	2	no	—
213	C₈×C₁₉	—	4	1	no	—
214	C₂×#452	C₂×C₁₉	1	1	yes	characteristic
215	C₂×#417	C₂×C₁₉	1	1	yes	characteristic
216	#2503	C₂×C₁₉	1	1	yes	characteristic, complemented
217	#2339	C₂×C₁₉	1	1	yes	characteristic
218	#2074	C₂×C₁₉	1	2	yes	complemented
219	#2056	C₂×C₁₉	1	2	yes	complemented
220	#1894	C₂×C₁₉	1	1	yes	characteristic, complemented
221	#1877	C₂×C₁₉	1	2	yes	complemented
222	#1851	C₂×C₁₉	1	1	yes	characteristic, complemented
223	#1824	C₂×C₁₉	1	1	yes	characteristic, complemented
224	#1804	C₂×C₁₉	1	2	yes	complemented
225	C₂²×C₁₉	—	2	2	no	—
226	C₂²×C₁₉	—	2	4	no	—
227	C₂²×C₁₉	—	2	2	no	—
228	C₂²×C₁₉	—	2	2	no	—
229	C₂²×C₁₉	—	4	2	no	—
230	C₂²×C₁₉	—	4	2	no	—
231	C₂²×C₁₉	—	4	2	no	—
232	C₂²×C₁₉	—	4	4	no	—
233	C₂²×C₁₉	—	4	4	no	—
234	C₂²×C₁₉	—	4	2	no	—
235	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
236	C₂²×C₁₉	#546	1	2	yes	—
237	C₂²×C₁₉	#575	1	2	yes	—
238	C₂²×C₁₉	#577	1	1	yes	characteristic
239	C₂²×C₁₉	#578	1	1	yes	characteristic
240	C₄×C₁₉	—	2	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	4	2	no	—
243	C₄×C₁₉	—	4	2	no	—
244	C₄×C₁₉	—	8	1	no	—
245	C₄×C₁₉	—	8	2	no	—
246	C₄×C₁₉	—	8	1	no	—
247	C₄×C₁₉	—	8	2	no	—
248	C₄×C₁₉	C₂×#123	1	1	yes	characteristic
249	C₄×C₁₉	#534	1	1	yes	characteristic
250	C₄×C₁₉	#551	1	2	yes	—
251	C₂²×#41	C₂²×C₁₉	1	1	yes	characteristic
252	C₂²×Q₁₆	C₂²×C₁₉	1	1	yes	characteristic
253	C₂²×SD₁₆	C₂²×C₁₉	1	1	yes	characteristic
254	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
256	C₂×C₄×D₄	C₂²×C₁₉	1	2	yes	—
257	C₂²×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
258	#452	—	2	4	no	—
259	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
260	#417	—	2	4	no	—
261	C₂×#103	C₂²×C₁₉	1	2	yes	—
262	C₂×#103	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#103	C₂²×C₁₉	1	2	yes	—
264	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
265	C₂×#102	C₂²×C₁₉	1	2	yes	—
266	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
267	#400	—	2	1	no	—
268	#400	—	2	1	no	—
269	#391	C₂²×C₁₉	1	2	yes	—
270	#391	C₂²×C₁₉	1	2	yes	—
271	#386	—	2	2	no	—
272	#382	C₂²×C₁₉	1	2	yes	—
273	#381	—	2	2	no	—
274	#381	—	2	1	no	—
275	#380	C₂²×C₁₉	1	1	yes	characteristic
276	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
277	C₂×#95	—	2	1	no	—
278	#340	C₂²×C₁₉	1	2	yes	—
279	#340	C₂²×C₁₉	1	2	yes	—
280	#340	C₂²×C₁₉	1	2	yes	—
281	#336	C₂²×C₁₉	1	2	yes	—
282	C₂×C₁₉	—	4	2	no	—
283	C₂×C₁₉	—	4	4	no	—
284	C₂×C₁₉	#2412	1	1	yes	characteristic
285	C₂×C₁₉	#3040	1	1	yes	characteristic
286	C₂×C₁₉	#3046	1	1	yes	characteristic
287	C₂×C₁₉	#3315	1	2	yes	—
288	C₂×C₁₉	#3323	1	2	yes	—
289	C₂×#41	—	2	2	no	—
290	C₂×#41	—	2	4	no	—
291	C₂×#41	—	4	2	no	—
292	C₂×#41	D₄×C₁₉	1	4	yes	—
293	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
294	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
295	C₂²×D₄	—	2	1	no	—
296	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
297	C₂³×C₄	—	2	1	no	—
298	C₂³×C₄	—	2	1	no	—
299	C₂³×C₄	—	2	2	no	—
300	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
301	C₂×Q₁₆	—	2	2	no	—
302	C₂×Q₁₆	—	4	2	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	4	no	—
305	C₂×M₁₆	—	2	2	no	—
306	C₂×M₁₆	—	4	2	no	—
307	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
308	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
310	C₂²⋊Q₈	—	2	2	no	—
311	C₂²⋊Q₈	—	2	2	no	—
312	C₄×D₄	—	2	4	no	—
313	C₄×D₄	—	4	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
325	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
326	C₄⋊C₈	—	4	2	no	—
327	#103	—	2	4	no	—
328	#103	—	2	2	no	—
329	#103	—	4	2	no	—
330	#102	—	2	4	no	—
331	#102	—	2	2	no	—
332	C₂²⋊C₈	—	2	2	no	—
333	#95	—	2	1	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	D₄×C₁₉	1	1	yes	characteristic
341	#95	D₄×C₁₉	1	1	yes	characteristic
342	C₁₉	#24545	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁴	—	2	1	no	—
344	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
345	#41	—	2	8	no	—
346	#41	—	4	4	no	—
347	#41	—	4	8	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	1	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	C₂×D₄×C₁₉	1	2	yes	—
356	C₂×D₄	—	2	4	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	2	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
361	C₂×D₄	#41×C₁₉	1	4	yes	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	4	4	no	—
371	C₂²×C₄	—	4	4	no	—
372	C₂²×C₄	—	4	4	no	—
373	C₂²×C₄	—	4	4	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	8	2	no	—
376	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
378	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
379	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
380	C₂²×C₄	#41×C₁₉	1	2	yes	—
381	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
382	Q₁₆	—	4	4	no	—
383	SD₁₆	—	4	4	no	—
384	M₁₆	—	4	4	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	—	4	2	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₂²⋊C₄	—	4	4	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	8	1	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	4	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	C₁₉×#121	1	2	yes	—
416	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
417	Q₈	—	2	2	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	Q₈	—	4	2	no	—
423	D₄	—	2	2	no	—
424	D₄	—	2	4	no	—
425	D₄	—	4	8	no	—
426	D₄	C₁₉×#123	1	4	yes	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	1	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	8	8	no	—
451	C₂×C₄	—	8	4	no	—
452	C₂×C₄	C₁₉×#121	1	2	yes	—
453	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
454	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
455	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
456	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
457	C₈	—	4	1	no	—
458	C₈	—	4	2	no	—
459	C₈	—	4	1	no	—
460	C₂²	—	2	2	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	4	2	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	4	4	no	—
469	C₂²	—	4	2	no	—
470	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
471	C₂²	C₁₉×#546	1	2	yes	—
472	C₂²	C₁₉×#575	1	2	yes	—
473	C₂²	C₁₉×#577	1	1	yes	characteristic
474	C₂²	C₁₉×#578	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	4	2	no	—
479	C₄	—	8	1	no	—
480	C₄	—	8	2	no	—
481	C₄	—	8	1	no	—
482	C₄	—	8	2	no	—
483	C₄	C₂×C₁₉×#123	1	1	yes	characteristic
484	C₄	C₁₉×#534	1	1	yes	characteristic
485	C₄	C₁₉×#551	1	2	yes	—
486	C₂	—	4	2	no	—
487	C₂	—	4	4	no	—
488	C₂	C₁₉×#2412	1	1	yes	characteristic
489	C₂	C₁₉×#3040	1	1	yes	characteristic
490	C₂	C₁₉×#3046	1	1	yes	characteristic
491	C₂	C₁₉×#3315	1	2	yes	—
492	C₂	C₁₉×#3323	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₂²×#41×C₁₉	C₂²
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
3. C₁₉×#2503	C₂	semidirect
5. C₁₉×#2074	C₂	semidirect
6. C₁₉×#2056	C₂	semidirect
7. C₁₉×#1894	C₂	semidirect
8. C₁₉×#1877	C₂	semidirect
9. C₁₉×#1851	C₂	semidirect
10. C₁₉×#1824	C₂	semidirect
11. C₁₉×#1804	C₂	semidirect
159. #24545	C₁₉	direct (N × H)
216. #2503	C₂×C₁₉	semidirect
218. #2074	C₂×C₁₉	semidirect
219. #2056	C₂×C₁₉	semidirect
220. #1894	C₂×C₁₉	semidirect
221. #1877	C₂×C₁₉	semidirect
222. #1851	C₂×C₁₉	semidirect
223. #1824	C₂×C₁₉	semidirect
224. #1804	C₂×C₁₉	semidirect
342. C₁₉	#24545	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×#452	2
C₂×C₁₉×#417	2
C₁₉×#2503	2
C₁₉×#2339	2
C₁₉×#2074	2
C₁₉×#2056	2
C₁₉×#1894	2
C₁₉×#1877	2
C₁₉×#1851	2
C₁₉×#1824	2
C₁₉×#1804	2
#24545	19

Subgroups — C19×#24545 #18030504

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24545 #18030504