Subgroups — C₁₉×#24497 #18030456

Order 4864.

950 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₉×#482	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2436	C₂	1	1	yes	maximal, characteristic
4	C₁₉×#2347	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2068	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2042	C₂	1	2	yes	maximal, complemented
7	C₁₉×#1983	C₂	1	2	yes	maximal, complemented
8	C₁₉×#1927	C₂	1	2	yes	maximal, complemented
9	C₁₉×#1895	C₂	1	1	yes	maximal, characteristic
10	C₁₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₉×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₁₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#124	C₂²	1	2	yes	—
15	C₂×C₁₉×#121	C₂²	1	1	yes	characteristic
16	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
17	C₁₉×#482	—	2	4	no	—
18	C₂×C₁₉×#107	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#106	C₂²	1	1	yes	characteristic
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₁₉×#419	—	2	4	no	—
22	C₂×C₁₉×#103	C₂²	1	2	yes	—
23	C₂×C₁₉×#103	C₂²	1	2	yes	—
24	C₂×C₁₉×#103	C₂²	1	2	yes	—
25	C₂×C₁₉×#103	C₂²	1	2	yes	—
26	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
27	C₂×C₁₉×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	C₂²	1	2	yes	—
29	C₂×C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₁₉×#393	—	2	1	no	—
31	C₁₉×#393	—	2	1	no	—
32	C₁₉×#391	C₂²	1	2	yes	—
33	C₁₉×#389	C₂²	1	2	yes	—
34	C₁₉×#388	—	2	2	no	—
35	C₁₉×#386	—	2	2	no	—
36	C₁₉×#383	—	2	1	no	—
37	C₁₉×#380	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₁₉	C₂²	1	2	yes	—
40	C₄×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
41	C₁₉×#340	C₂²	1	2	yes	—
42	C₁₉×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₁₉	—	2	1	no	—
44	C₂²×Q₈×C₁₉	—	2	4	no	—
45	C₂²×Q₈×C₁₉	—	2	2	no	—
46	C₂²×Q₈×C₁₉	—	2	2	no	—
47	C₂²×Q₈×C₁₉	—	4	2	no	—
48	C₂²×Q₈×C₁₉	C₂³	1	2	yes	—
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	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₁₉	—	2	2	no	—
54	C₂×M₁₆×C₁₉	—	4	2	no	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
58	C₁₉×#124	—	2	4	no	—
59	C₁₉×#124	—	4	2	no	—
60	C₁₉×#121	—	2	2	no	—
61	C₁₉×#121	—	2	2	no	—
62	C₁₉×#117	—	2	2	no	—
63	C₁₉×#117	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₁₉	D₄	1	2	yes	—
75	C₂×C₄²×C₁₉	—	2	1	no	—
76	C₂×C₄²×C₁₉	—	2	2	no	—
77	C₂×C₄²×C₁₉	C₂³	1	2	yes	—
78	C₁₉×#107	—	2	2	no	—
79	C₁₉×#106	—	2	2	no	—
80	C₁₉×C₄⋊C₈	—	4	2	no	—
81	C₁₉×#103	—	2	4	no	—
82	C₁₉×#103	—	2	4	no	—
83	C₁₉×#103	—	2	4	no	—
84	C₁₉×#103	—	4	2	no	—
85	C₁₉×#102	—	2	2	no	—
86	C₁₉×#102	—	2	2	no	—
87	C₁₉×#102	—	4	2	no	—
88	C₁₉×C₂²⋊C₈	—	2	2	no	—
89	C₁₉×#95	—	2	1	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	C₂×Q₈×C₁₉	—	2	2	no	—
99	C₂×Q₈×C₁₉	—	2	8	no	—
100	C₂×Q₈×C₁₉	—	2	2	no	—
101	C₂×Q₈×C₁₉	—	2	2	no	—
102	C₂×Q₈×C₁₉	—	2	2	no	—
103	C₂×Q₈×C₁₉	—	2	2	no	—
104	C₂×Q₈×C₁₉	—	4	4	no	—
105	C₂×Q₈×C₁₉	—	4	8	no	—
106	C₂×Q₈×C₁₉	—	4	4	no	—
107	C₂×Q₈×C₁₉	—	4	2	no	—
108	C₂×Q₈×C₁₉	#41	1	4	yes	—
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	—	4	4	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
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	1	no	—
119	C₂²×C₄×C₁₉	—	2	2	no	—
120	C₂²×C₄×C₁₉	—	2	2	no	—
121	C₂²×C₄×C₁₉	—	2	1	no	—
122	C₂²×C₄×C₁₉	—	4	4	no	—
123	C₂²×C₄×C₁₉	—	4	2	no	—
124	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₉	#41	1	2	yes	—
129	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₁₉	—	4	4	no	—
131	C₂×C₈×C₁₉	—	2	2	no	—
132	C₂×C₈×C₁₉	—	2	1	no	—
133	C₂×C₈×C₁₉	—	2	1	no	—
134	C₂×C₈×C₁₉	—	2	2	no	—
135	C₂×C₈×C₁₉	—	2	2	no	—
136	C₂×C₈×C₁₉	—	2	2	no	—
137	C₂×C₈×C₁₉	—	2	2	no	—
138	C₄⋊C₄×C₁₉	—	2	1	no	—
139	C₄⋊C₄×C₁₉	—	2	1	no	—
140	C₄⋊C₄×C₁₉	—	2	1	no	—
141	C₄⋊C₄×C₁₉	—	2	1	no	—
142	C₄⋊C₄×C₁₉	—	2	2	no	—
143	C₄⋊C₄×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	4	4	no	—
145	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²⋊C₄×C₁₉	—	2	4	no	—
148	C₂²⋊C₄×C₁₉	—	4	2	no	—
149	C₂²⋊C₄×C₁₉	—	4	4	no	—
150	C₂²⋊C₄×C₁₉	—	4	4	no	—
151	C₂²⋊C₄×C₁₉	—	4	2	no	—
152	C₂²⋊C₄×C₁₉	—	8	1	no	—
153	C₄²×C₁₉	—	2	4	no	—
154	C₄²×C₁₉	—	2	2	no	—
155	C₄²×C₁₉	—	2	2	no	—
156	C₄²×C₁₉	—	8	2	no	—
157	#24497	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
158	C₂³×C₁₉	—	2	2	no	—
159	C₂³×C₁₉	—	2	2	no	—
160	C₂³×C₁₉	—	2	1	no	—
161	C₂³×C₁₉	—	2	1	no	—
162	C₂³×C₁₉	—	4	1	no	—
163	C₂³×C₁₉	—	4	2	no	—
164	C₂³×C₁₉	—	4	2	no	—
165	C₂³×C₁₉	—	4	1	no	—
166	C₂³×C₁₉	—	4	1	no	—
167	C₂³×C₁₉	#121	1	2	yes	—
168	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₁₉	—	2	4	no	—
170	Q₈×C₁₉	—	2	4	no	—
171	Q₈×C₁₉	—	4	8	no	—
172	Q₈×C₁₉	—	4	2	no	—
173	Q₈×C₁₉	—	4	2	no	—
174	D₄×C₁₉	—	4	1	no	—
175	D₄×C₁₉	—	4	1	no	—
176	D₄×C₁₉	—	4	2	no	—
177	D₄×C₁₉	—	8	4	no	—
178	C₂×C₄×C₁₉	—	2	2	no	—
179	C₂×C₄×C₁₉	—	2	2	no	—
180	C₂×C₄×C₁₉	—	2	2	no	—
181	C₂×C₄×C₁₉	—	2	4	no	—
182	C₂×C₄×C₁₉	—	2	2	no	—
183	C₂×C₄×C₁₉	—	2	2	no	—
184	C₂×C₄×C₁₉	—	2	2	no	—
185	C₂×C₄×C₁₉	—	2	2	no	—
186	C₂×C₄×C₁₉	—	2	4	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	—	4	8	no	—
192	C₂×C₄×C₁₉	—	4	2	no	—
193	C₂×C₄×C₁₉	—	4	2	no	—
194	C₂×C₄×C₁₉	—	4	2	no	—
195	C₂×C₄×C₁₉	—	4	1	no	—
196	C₂×C₄×C₁₉	—	4	1	no	—
197	C₂×C₄×C₁₉	—	4	1	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	2	no	—
202	C₂×C₄×C₁₉	#121	1	2	yes	—
203	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₁₉	C₂×#41	1	2	yes	—
205	C₂×C₄×C₁₉	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
207	C₈×C₁₉	—	4	1	no	—
208	C₈×C₁₉	—	4	1	no	—
209	C₈×C₁₉	—	4	2	no	—
210	C₂×#482	C₂×C₁₉	1	1	yes	characteristic
211	C₂×#419	C₂×C₁₉	1	1	yes	characteristic, complemented
212	#2436	C₂×C₁₉	1	1	yes	characteristic
213	#2347	C₂×C₁₉	1	1	yes	characteristic, complemented
214	#2068	C₂×C₁₉	1	2	yes	complemented
215	#2042	C₂×C₁₉	1	2	yes	complemented
216	#1983	C₂×C₁₉	1	2	yes	complemented
217	#1927	C₂×C₁₉	1	2	yes	complemented
218	#1895	C₂×C₁₉	1	1	yes	characteristic
219	#1851	C₂×C₁₉	1	1	yes	characteristic, complemented
220	#1787	C₂×C₁₉	1	1	yes	characteristic, complemented
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	—	2	2	no	—
223	C₂²×C₁₉	—	2	2	no	—
224	C₂²×C₁₉	—	4	2	no	—
225	C₂²×C₁₉	—	4	2	no	—
226	C₂²×C₁₉	—	8	1	no	—
227	C₂²×C₁₉	—	8	1	no	—
228	C₂²×C₁₉	—	8	1	no	—
229	C₂²×C₁₉	—	8	2	no	—
230	C₂²×C₁₉	—	8	2	no	—
231	C₂²×C₁₉	C₂×#121	1	1	yes	characteristic
232	C₂²×C₁₉	#546	1	2	yes	—
233	C₂²×C₁₉	#575	1	2	yes	—
234	C₂²×C₁₉	#577	1	1	yes	characteristic
235	C₂²×C₁₉	#578	1	1	yes	characteristic
236	C₄×C₁₉	—	2	2	no	—
237	C₄×C₁₉	—	4	4	no	—
238	C₄×C₁₉	—	4	2	no	—
239	C₄×C₁₉	—	4	2	no	—
240	C₄×C₁₉	—	4	2	no	—
241	C₄×C₁₉	—	4	2	no	—
242	C₄×C₁₉	—	8	1	no	—
243	C₄×C₁₉	—	8	2	no	—
244	C₄×C₁₉	#525	1	1	yes	characteristic
245	C₄×C₁₉	#535	1	1	yes	characteristic
246	C₄×C₁₉	#551	1	2	yes	—
247	C₂³×Q₈	C₂²×C₁₉	1	1	yes	characteristic
248	C₂²×M₁₆	C₂²×C₁₉	1	1	yes	characteristic
249	C₂×#124	C₂²×C₁₉	1	2	yes	—
250	C₂×#121	C₂²×C₁₉	1	1	yes	characteristic
251	C₂×#117	C₂²×C₁₉	1	1	yes	characteristic
252	#482	—	2	4	no	—
253	C₂×#107	C₂²×C₁₉	1	1	yes	characteristic
254	C₂×#106	C₂²×C₁₉	1	1	yes	characteristic
255	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
256	#419	—	2	4	no	—
257	C₂×#103	C₂²×C₁₉	1	2	yes	—
258	C₂×#103	C₂²×C₁₉	1	2	yes	—
259	C₂×#103	C₂²×C₁₉	1	2	yes	—
260	C₂×#103	C₂²×C₁₉	1	2	yes	—
261	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
262	C₂×#102	C₂²×C₁₉	1	1	yes	characteristic
263	C₂×#102	C₂²×C₁₉	1	2	yes	—
264	C₂×C₂²⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
265	#393	—	2	1	no	—
266	#393	—	2	1	no	—
267	#391	C₂²×C₁₉	1	2	yes	—
268	#389	C₂²×C₁₉	1	2	yes	—
269	#388	—	2	2	no	—
270	#386	—	2	2	no	—
271	#383	—	2	1	no	—
272	#380	C₂²×C₁₉	1	1	yes	characteristic
273	C₄×C₄⋊C₄	—	2	1	no	—
274	C₄×C₄⋊C₄	C₂²×C₁₉	1	2	yes	—
275	C₄×C₂²⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
276	#340	C₂²×C₁₉	1	2	yes	—
277	#336	C₂²×C₁₉	1	2	yes	—
278	C₂×C₁₉	—	4	2	no	—
279	C₂×C₁₉	—	16	1	no	—
280	C₂×C₁₉	#2411	1	1	yes	characteristic
281	C₂×C₁₉	#3040	1	1	yes	characteristic
282	C₂×C₁₉	#3046	1	1	yes	characteristic
283	C₂×C₁₉	#3313	1	2	yes	—
284	C₂×C₁₉	#3326	1	2	yes	—
285	C₂²×Q₈	—	2	1	no	—
286	C₂²×Q₈	—	2	4	no	—
287	C₂²×Q₈	—	2	2	no	—
288	C₂²×Q₈	—	2	2	no	—
289	C₂²×Q₈	—	4	2	no	—
290	C₂²×Q₈	C₂³×C₁₉	1	2	yes	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	C₂³×C₁₉	1	1	yes	characteristic
293	C₂³×C₄	—	2	1	no	—
294	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
295	C₂×M₁₆	—	2	2	no	—
296	C₂×M₁₆	—	4	2	no	—
297	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
298	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
300	#124	—	2	4	no	—
301	#124	—	4	2	no	—
302	#121	—	2	2	no	—
303	#121	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	D₄×C₁₉	1	4	yes	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
308	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	—	2	1	no	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	D₄×C₁₉	1	2	yes	—
317	C₂×C₄²	—	2	1	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	C₂³×C₁₉	1	2	yes	—
320	#107	—	2	2	no	—
321	#106	—	2	2	no	—
322	C₄⋊C₈	—	4	2	no	—
323	#103	—	2	4	no	—
324	#103	—	2	4	no	—
325	#103	—	2	4	no	—
326	#103	—	4	2	no	—
327	#102	—	2	2	no	—
328	#102	—	2	2	no	—
329	#102	—	4	2	no	—
330	C₂²⋊C₈	—	2	2	no	—
331	#95	—	2	1	no	—
332	#95	—	2	2	no	—
333	#95	—	2	2	no	—
334	#95	—	2	2	no	—
335	#95	—	2	2	no	—
336	#95	D₄×C₁₉	1	1	yes	characteristic
337	#95	D₄×C₁₉	1	1	yes	characteristic
338	C₁₉	#24497	1	1	yes	characteristic, direct product factor, Sylow
339	C₂⁴	—	2	1	no	—
340	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	8	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	2	no	—
347	C₂×Q₈	—	4	4	no	—
348	C₂×Q₈	—	4	8	no	—
349	C₂×Q₈	—	4	4	no	—
350	C₂×Q₈	—	4	2	no	—
351	C₂×Q₈	#41×C₁₉	1	4	yes	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	2	2	no	—
356	C₂×D₄	—	4	4	no	—
357	C₂×D₄	—	4	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	1	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	4	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
371	C₂²×C₄	#41×C₁₉	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
373	M₁₆	—	4	4	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	1	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
389	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	4	2	no	—
392	C₂²⋊C₄	—	4	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	8	1	no	—
396	C₄²	—	2	4	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	8	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	1	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	C₁₉×#121	1	2	yes	—
410	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
411	Q₈	—	2	4	no	—
412	Q₈	—	2	4	no	—
413	Q₈	—	4	8	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	D₄	—	4	1	no	—
417	D₄	—	4	1	no	—
418	D₄	—	4	2	no	—
419	D₄	—	8	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	4	8	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	C₁₉×#121	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₁₉	1	2	yes	—
447	C₂×C₄	C₂×#41×C₁₉	1	1	yes	characteristic
448	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
449	C₈	—	4	1	no	—
450	C₈	—	4	2	no	—
451	C₈	—	4	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	C₂×C₁₉×#121	1	1	yes	characteristic
463	C₂²	C₁₉×#546	1	2	yes	—
464	C₂²	C₁₉×#575	1	2	yes	—
465	C₂²	C₁₉×#577	1	1	yes	characteristic
466	C₂²	C₁₉×#578	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	2	no	—
470	C₄	—	4	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	8	1	no	—
474	C₄	—	8	2	no	—
475	C₄	C₁₉×#525	1	1	yes	characteristic
476	C₄	C₁₉×#535	1	1	yes	characteristic
477	C₄	C₁₉×#551	1	2	yes	—
478	C₂	—	4	2	no	—
479	C₂	—	16	1	no	—
480	C₂	C₁₉×#2411	1	1	yes	characteristic
481	C₂	C₁₉×#3040	1	1	yes	characteristic
482	C₂	C₁₉×#3046	1	1	yes	characteristic
483	C₂	C₁₉×#3313	1	2	yes	—
484	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×#121	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
2. C₂×C₁₉×#419	C₂	semidirect
4. C₁₉×#2347	C₂	semidirect
5. C₁₉×#2068	C₂	semidirect
6. C₁₉×#2042	C₂	semidirect
7. C₁₉×#1983	C₂	semidirect
8. C₁₉×#1927	C₂	semidirect
10. C₁₉×#1851	C₂	semidirect
11. C₁₉×#1787	C₂	semidirect
157. #24497	C₁₉	direct (N × H)
211. C₂×#419	C₂×C₁₉	semidirect
213. #2347	C₂×C₁₉	semidirect
214. #2068	C₂×C₁₉	semidirect
215. #2042	C₂×C₁₉	semidirect
216. #1983	C₂×C₁₉	semidirect
217. #1927	C₂×C₁₉	semidirect
219. #1851	C₂×C₁₉	semidirect
220. #1787	C₂×C₁₉	semidirect
338. C₁₉	#24497	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×#482	2
C₂×C₁₉×#419	2
C₁₉×#2436	2
C₁₉×#2347	2
C₁₉×#2068	2
C₁₉×#2042	2
C₁₉×#1983	2
C₁₉×#1927	2
C₁₉×#1895	2
C₁₉×#1851	2
C₁₉×#1787	2
#24497	19

Subgroups — C19×#24497 #18030456

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#24497 #18030456