Subgroups — C₁₉×#62270 #18068229

Order 4864.

2032 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#3537	C₂	1	2	yes	maximal, complemented
2	C₁₉×#3339	C₂	1	4	yes	maximal, complemented
3	C₁₉×#3318	C₂	1	8	yes	maximal, complemented
4	D₄×D₈×C₁₉	C₂	1	4	yes	maximal, complemented
5	C₁₉×#3259	C₂	1	2	yes	maximal, complemented
6	C₁₉×#3199	C₂	1	2	yes	maximal, complemented
7	C₁₉×#3192	C₂	1	2	yes	maximal, complemented
8	C₁₉×#3176	C₂	1	2	yes	maximal, complemented
9	C₁₉×#3058	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₉×#466	C₂	1	2	yes	maximal, complemented
11	C₁₉×#2929	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₁₉	C₂²	1	2	yes	complemented
13	C₂²×D₈×C₁₉	C₂²	1	2	yes	complemented
14	C₂×C₁₉×#131	C₂²	1	1	yes	characteristic, complemented
15	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₁₉×#560	—	2	4	no	—
17	C₁₉×#553	C₂²	1	8	yes	complemented
18	D₄²×C₁₉	—	2	4	no	—
19	D₄²×C₁₉	C₂²	1	8	yes	complemented
20	C₁₉×#540	C₂²	1	4	yes	complemented
21	C₁₉×#538	—	2	4	no	—
22	C₁₉×#535	C₂²	1	4	yes	complemented
23	C₁₉×#534	—	2	4	no	—
24	C₁₉×#525	C₂²	1	1	yes	characteristic
25	C₂×C₁₉×#121	C₂²	1	4	yes	complemented
26	C₁₉×#499	C₂²	1	2	yes	complemented
27	C₁₉×#493	C₂²	1	2	yes	complemented
28	C₁₉×#490	C₂²	1	4	yes	complemented
29	C₁₉×#482	C₂²	1	8	yes	complemented
30	C₁₉×#481	C₂²	1	8	yes	complemented
31	C₁₉×#478	C₂²	1	8	yes	complemented
32	C₁₉×#469	C₂²	1	4	yes	complemented
33	C₁₉×#469	C₂²	1	4	yes	complemented
34	C₁₉×#469	C₂²	1	4	yes	complemented
35	C₁₉×#466	C₂²	1	4	yes	complemented
36	C₁₉×#466	C₂²	1	4	yes	complemented
37	C₁₉×#466	C₂²	1	4	yes	complemented
38	C₁₉×#466	C₂²	1	4	yes	complemented
39	C₁₉×#466	C₂²	1	4	yes	complemented
40	C₁₉×#459	C₂²	1	8	yes	complemented
41	C₁₉×#447	C₂²	1	8	yes	complemented
42	C₁₉×#447	C₂²	1	8	yes	complemented
43	C₁₉×#442	C₂²	1	4	yes	complemented
44	C₄×D₈×C₁₉	C₂²	1	4	yes	complemented
45	C₁₉×#435	C₂²	1	4	yes	complemented
46	C₈×D₄×C₁₉	C₂²	1	4	yes	complemented
47	C₁₉×#427	C₂²	1	2	yes	complemented
48	C₂×C₁₉×#107	C₂²	1	2	yes	complemented
49	C₁₉×#424	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#418	C₂²	1	4	yes	complemented
51	C₂×C₁₉×#102	C₂²	1	4	yes	complemented
52	C₁₉×#408	C₂²	1	1	yes	characteristic, complemented
53	C₁₉×#407	C₂²	1	1	yes	characteristic, complemented
54	C₁₉×#405	C₂²	1	1	yes	characteristic, complemented
55	C₂×#41×C₁₉	C₂³	1	1	yes	characteristic
56	C₂²×D₄×C₁₉	—	2	4	no	—
57	C₂²×D₄×C₁₉	—	2	8	no	—
58	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
59	C₂²×D₄×C₁₉	C₂³	1	4	yes	—
60	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
61	C₂×D₈×C₁₉	—	4	4	no	—
62	C₂×D₈×C₁₉	—	4	4	no	—
63	C₂×D₈×C₁₉	C₂³	1	4	yes	—
64	C₂×D₈×C₁₉	C₂³	1	4	yes	—
65	C₂×D₈×C₁₉	C₂³	1	4	yes	—
66	C₂×D₈×C₁₉	C₂³	1	4	yes	—
67	C₁₉×#131	—	4	2	no	—
68	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×M₁₆×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₁₉	C₂³	1	2	yes	—
71	C₂²×C₈×C₁₉	—	4	2	no	—
72	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
74	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
75	C₂²×C₈×C₁₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
77	C₁₉×#127	—	2	4	no	—
78	C₁₉×#127	C₂³	1	4	yes	—
79	C₁₉×#126	—	2	8	no	—
80	C₁₉×#125	C₂³	1	4	yes	—
81	C₁₉×#124	—	2	4	no	—
82	C₁₉×#123	—	2	8	no	—
83	C₁₉×#123	—	2	8	no	—
84	C₁₉×#123	D₄	1	2	yes	—
85	C₁₉×C₂²⋊Q₈	D₄	1	2	yes	—
86	C₁₉×#121	—	2	8	no	—
87	C₁₉×#121	—	2	4	no	—
88	C₁₉×#121	—	2	4	no	—
89	C₁₉×#121	—	2	8	no	—
90	C₁₉×#121	—	2	8	no	—
91	C₁₉×#121	D₄	1	2	yes	—
92	C₁₉×#121	C₂³	1	8	yes	—
93	C₁₉×#121	C₂³	1	8	yes	—
94	C₁₉×#121	C₂³	1	8	yes	—
95	C₁₉×#120	—	2	4	no	—
96	C₁₉×#120	—	2	4	no	—
97	C₁₉×#120	—	2	8	no	—
98	C₁₉×#120	—	2	8	no	—
99	C₁₉×#120	D₄	1	2	yes	—
100	C₄×D₄×C₁₉	—	2	8	no	—
101	C₄×D₄×C₁₉	C₂³	1	8	yes	—
102	C₄×D₄×C₁₉	C₂³	1	4	yes	—
103	C₁₉×#117	C₂³	1	4	yes	—
104	C₁₉×#117	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₁₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₁₉	—	2	4	no	—
107	C₁₉×#107	C₂³	1	4	yes	—
108	C₁₉×#107	C₂³	1	4	yes	—
109	C₁₉×#106	C₂³	1	4	yes	—
110	C₁₉×#106	C₂³	1	4	yes	—
111	C₁₉×C₄⋊C₈	C₂³	1	4	yes	—
112	C₁₉×#102	C₂³	1	8	yes	—
113	C₁₉×#102	C₂³	1	8	yes	—
114	C₁₉×#102	C₂³	1	8	yes	—
115	C₁₉×#102	C₂³	1	8	yes	—
116	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
117	C₁₉×C₂²⋊C₈	C₂³	1	4	yes	—
118	C₁₉×#97	C₂³	1	2	yes	—
119	C₄×C₈×C₁₉	C₂³	1	2	yes	—
120	C₂⁴×C₁₉	—	2	4	no	—
121	C₂⁴×C₁₉	—	2	4	no	—
122	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
123	#41×C₁₉	—	4	1	no	—
124	#41×C₁₉	—	4	1	no	—
125	C₂×Q₈×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂×D₄×C₁₉	—	2	8	no	—
127	C₂×D₄×C₁₉	—	2	8	no	—
128	C₂×D₄×C₁₉	—	2	8	no	—
129	C₂×D₄×C₁₉	—	2	4	no	—
130	C₂×D₄×C₁₉	—	2	8	no	—
131	C₂×D₄×C₁₉	—	2	4	no	—
132	C₂×D₄×C₁₉	—	4	4	no	—
133	C₂×D₄×C₁₉	—	4	4	no	—
134	C₂×D₄×C₁₉	—	4	4	no	—
135	C₂×D₄×C₁₉	—	4	4	no	—
136	C₂×D₄×C₁₉	—	8	16	no	—
137	C₂×D₄×C₁₉	—	8	8	no	—
138	C₂×D₄×C₁₉	C₂×D₄	1	4	yes	—
139	C₂×D₄×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂×D₄×C₁₉	C₂×D₄	1	2	yes	—
141	C₂×D₄×C₁₉	C₂⁴	1	8	yes	—
142	C₂²×C₄×C₁₉	—	2	4	no	—
143	C₂²×C₄×C₁₉	—	2	8	no	—
144	C₂²×C₄×C₁₉	—	4	1	no	—
145	C₂²×C₄×C₁₉	—	4	1	no	—
146	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
149	C₂²×C₄×C₁₉	C₂⁴	1	2	yes	—
150	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
151	D₈×C₁₉	—	2	8	no	—
152	D₈×C₁₉	—	4	4	no	—
153	D₈×C₁₉	—	4	4	no	—
154	D₈×C₁₉	—	4	4	no	—
155	M₁₆×C₁₉	—	4	1	no	—
156	M₁₆×C₁₉	—	4	2	no	—
157	M₁₆×C₁₉	—	4	1	no	—
158	C₂×C₈×C₁₉	—	2	2	no	—
159	C₂×C₈×C₁₉	—	2	4	no	—
160	C₂×C₈×C₁₉	—	2	4	no	—
161	C₂×C₈×C₁₉	—	4	2	no	—
162	C₂×C₈×C₁₉	—	4	1	no	—
163	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
164	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
165	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
166	C₂×C₈×C₁₉	C₂⁴	1	2	yes	—
167	C₂×C₈×C₁₉	C₂⁴	1	1	yes	characteristic
168	C₄⋊C₄×C₁₉	—	2	4	no	—
169	C₄⋊C₄×C₁₉	—	2	8	no	—
170	C₄⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
171	C₄⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
172	C₄⋊C₄×C₁₉	C₂⁴	1	8	yes	—
173	C₂²⋊C₄×C₁₉	—	2	4	no	—
174	C₂²⋊C₄×C₁₉	—	2	8	no	—
175	C₂²⋊C₄×C₁₉	—	2	8	no	—
176	C₂²⋊C₄×C₁₉	—	2	8	no	—
177	C₂²⋊C₄×C₁₉	—	2	8	no	—
178	C₂²⋊C₄×C₁₉	C₂×D₄	1	2	yes	—
179	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
180	C₂²⋊C₄×C₁₉	C₂×D₄	1	4	yes	—
181	C₄²×C₁₉	—	2	4	no	—
182	C₄²×C₁₉	C₂⁴	1	2	yes	—
183	#62270	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂³×C₁₉	—	2	4	no	—
185	C₂³×C₁₉	—	2	8	no	—
186	C₂³×C₁₉	—	4	1	no	—
187	C₂³×C₁₉	—	4	8	no	—
188	C₂³×C₁₉	—	8	4	no	—
189	C₂³×C₁₉	—	8	4	no	—
190	C₂³×C₁₉	—	8	4	no	—
191	C₂³×C₁₉	—	8	8	no	—
192	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
193	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
194	C₂³×C₁₉	C₂²×D₄	1	2	yes	—
195	Q₈×C₁₉	—	4	1	no	—
196	D₄×C₁₉	—	2	8	no	—
197	D₄×C₁₉	—	2	8	no	—
198	D₄×C₁₉	—	2	8	no	—
199	D₄×C₁₉	—	4	1	no	—
200	D₄×C₁₉	—	4	2	no	—
201	D₄×C₁₉	—	4	16	no	—
202	D₄×C₁₉	—	8	4	no	—
203	D₄×C₁₉	—	8	4	no	—
204	D₄×C₁₉	—	8	8	no	—
205	D₄×C₁₉	—	8	8	no	—
206	D₄×C₁₉	—	8	8	no	—
207	C₂×C₄×C₁₉	—	2	1	no	—
208	C₂×C₄×C₁₉	—	2	2	no	—
209	C₂×C₄×C₁₉	—	2	2	no	—
210	C₂×C₄×C₁₉	—	2	1	no	—
211	C₂×C₄×C₁₉	—	2	2	no	—
212	C₂×C₄×C₁₉	—	2	2	no	—
213	C₂×C₄×C₁₉	—	2	8	no	—
214	C₂×C₄×C₁₉	—	4	2	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	8	8	no	—
217	C₂×C₄×C₁₉	—	8	4	no	—
218	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₁₉	C₂²×D₄	1	4	yes	—
220	C₂×C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₁₉	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₁₉	C₂⁵	1	1	yes	characteristic
223	C₈×C₁₉	—	2	1	no	—
224	C₈×C₁₉	—	2	2	no	—
225	C₈×C₁₉	—	2	2	no	—
226	C₈×C₁₉	—	2	2	no	—
227	C₈×C₁₉	H(5,𝔽₂)	1	2	yes	—
228	#3537	C₂×C₁₉	1	2	yes	complemented
229	#3339	C₂×C₁₉	1	4	yes	complemented
230	#3318	C₂×C₁₉	1	8	yes	complemented
231	D₄×D₈	C₂×C₁₉	1	4	yes	complemented
232	#3259	C₂×C₁₉	1	2	yes	complemented
233	#3199	C₂×C₁₉	1	2	yes	complemented
234	#3192	C₂×C₁₉	1	2	yes	complemented
235	#3176	C₂×C₁₉	1	2	yes	complemented
236	#3058	C₂×C₁₉	1	2	yes	complemented
237	C₂×#466	C₂×C₁₉	1	2	yes	complemented
238	#2929	C₂×C₁₉	1	1	yes	characteristic, complemented
239	C₂²×C₁₉	—	2	2	no	—
240	C₂²×C₁₉	—	2	2	no	—
241	C₂²×C₁₉	—	2	1	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	2	4	no	—
244	C₂²×C₁₉	—	2	2	no	—
245	C₂²×C₁₉	—	4	4	no	—
246	C₂²×C₁₉	—	4	8	no	—
247	C₂²×C₁₉	—	4	8	no	—
248	C₂²×C₁₉	—	4	8	no	—
249	C₂²×C₁₉	—	16	8	no	—
250	C₂²×C₁₉	—	16	8	no	—
251	C₂²×C₁₉	#576	1	4	yes	—
252	C₂²×C₁₉	C₂³×D₄	1	1	yes	characteristic
253	C₄×C₁₉	—	2	1	no	—
254	C₄×C₁₉	—	2	2	no	—
255	C₄×C₁₉	—	2	2	no	—
256	C₄×C₁₉	—	2	4	no	—
257	C₄×C₁₉	—	4	8	no	—
258	C₄×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
259	C₄×C₁₉	#585	1	1	yes	characteristic
260	C₂²×D₈	C₂²×C₁₉	1	2	yes	complemented
261	C₂²×D₈	C₂²×C₁₉	1	2	yes	complemented
262	C₂×#131	C₂²×C₁₉	1	1	yes	characteristic, complemented
263	C₂³×C₈	C₂²×C₁₉	1	1	yes	characteristic, complemented
264	#560	—	2	4	no	—
265	#553	C₂²×C₁₉	1	8	yes	complemented
266	D₄²	—	2	4	no	—
267	D₄²	C₂²×C₁₉	1	8	yes	complemented
268	#540	C₂²×C₁₉	1	4	yes	complemented
269	#538	—	2	4	no	—
270	#535	C₂²×C₁₉	1	4	yes	complemented
271	#534	—	2	4	no	—
272	#525	C₂²×C₁₉	1	1	yes	characteristic
273	C₂×#121	C₂²×C₁₉	1	4	yes	complemented
274	#499	C₂²×C₁₉	1	2	yes	complemented
275	#493	C₂²×C₁₉	1	2	yes	complemented
276	#490	C₂²×C₁₉	1	4	yes	complemented
277	#482	C₂²×C₁₉	1	8	yes	complemented
278	#481	C₂²×C₁₉	1	8	yes	complemented
279	#478	C₂²×C₁₉	1	8	yes	complemented
280	#469	C₂²×C₁₉	1	4	yes	complemented
281	#469	C₂²×C₁₉	1	4	yes	complemented
282	#469	C₂²×C₁₉	1	4	yes	complemented
283	#466	C₂²×C₁₉	1	4	yes	complemented
284	#466	C₂²×C₁₉	1	4	yes	complemented
285	#466	C₂²×C₁₉	1	4	yes	complemented
286	#466	C₂²×C₁₉	1	4	yes	complemented
287	#466	C₂²×C₁₉	1	4	yes	complemented
288	#459	C₂²×C₁₉	1	8	yes	complemented
289	#447	C₂²×C₁₉	1	8	yes	complemented
290	#447	C₂²×C₁₉	1	8	yes	complemented
291	#442	C₂²×C₁₉	1	4	yes	complemented
292	C₄×D₈	C₂²×C₁₉	1	4	yes	complemented
293	#435	C₂²×C₁₉	1	4	yes	complemented
294	C₈×D₄	C₂²×C₁₉	1	4	yes	complemented
295	#427	C₂²×C₁₉	1	2	yes	complemented
296	C₂×#107	C₂²×C₁₉	1	2	yes	complemented
297	#424	C₂²×C₁₉	1	1	yes	characteristic, complemented
298	#418	C₂²×C₁₉	1	4	yes	complemented
299	C₂×#102	C₂²×C₁₉	1	4	yes	complemented
300	#408	C₂²×C₁₉	1	1	yes	characteristic, complemented
301	#407	C₂²×C₁₉	1	1	yes	characteristic, complemented
302	#405	C₂²×C₁₉	1	1	yes	characteristic, complemented
303	C₂×C₁₉	—	2	4	no	—
304	C₂×C₁₉	—	4	1	no	—
305	C₂×C₁₉	—	4	2	no	—
306	C₂×C₁₉	—	8	8	no	—
307	C₂×C₁₉	#3496	1	1	yes	characteristic
308	C₂×C₁₉	C₂×#576	1	2	yes	—
309	C₂×#41	C₂³×C₁₉	1	1	yes	characteristic
310	C₂²×D₄	—	2	4	no	—
311	C₂²×D₄	—	2	8	no	—
312	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
313	C₂²×D₄	C₂³×C₁₉	1	4	yes	—
314	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
315	C₂×D₈	—	4	4	no	—
316	C₂×D₈	—	4	4	no	—
317	C₂×D₈	C₂³×C₁₉	1	4	yes	—
318	C₂×D₈	C₂³×C₁₉	1	4	yes	—
319	C₂×D₈	C₂³×C₁₉	1	4	yes	—
320	C₂×D₈	C₂³×C₁₉	1	4	yes	—
321	#131	—	4	2	no	—
322	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
323	C₂×M₁₆	C₂³×C₁₉	1	2	yes	—
324	C₂×M₁₆	C₂³×C₁₉	1	1	yes	characteristic
325	C₂²×C₈	—	4	2	no	—
326	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
327	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
328	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
329	C₂²×C₈	C₂³×C₁₉	1	1	yes	characteristic
330	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
331	#127	—	2	4	no	—
332	#127	C₂³×C₁₉	1	4	yes	—
333	#126	—	2	8	no	—
334	#125	C₂³×C₁₉	1	4	yes	—
335	#124	—	2	4	no	—
336	#123	—	2	8	no	—
337	#123	—	2	8	no	—
338	#123	D₄×C₁₉	1	2	yes	—
339	C₂²⋊Q₈	D₄×C₁₉	1	2	yes	—
340	#121	—	2	8	no	—
341	#121	—	2	4	no	—
342	#121	—	2	4	no	—
343	#121	—	2	8	no	—
344	#121	—	2	8	no	—
345	#121	D₄×C₁₉	1	2	yes	—
346	#121	C₂³×C₁₉	1	8	yes	—
347	#121	C₂³×C₁₉	1	8	yes	—
348	#121	C₂³×C₁₉	1	8	yes	—
349	#120	—	2	4	no	—
350	#120	—	2	4	no	—
351	#120	—	2	8	no	—
352	#120	—	2	8	no	—
353	#120	D₄×C₁₉	1	2	yes	—
354	C₄×D₄	—	2	8	no	—
355	C₄×D₄	C₂³×C₁₉	1	8	yes	—
356	C₄×D₄	C₂³×C₁₉	1	4	yes	—
357	#117	C₂³×C₁₉	1	4	yes	—
358	#117	C₂³×C₁₉	1	1	yes	characteristic
359	C₂×C₄⋊C₄	C₂³×C₁₉	1	4	yes	—
360	C₂×C₂²⋊C₄	—	2	4	no	—
361	#107	C₂³×C₁₉	1	4	yes	—
362	#107	C₂³×C₁₉	1	4	yes	—
363	#106	C₂³×C₁₉	1	4	yes	—
364	#106	C₂³×C₁₉	1	4	yes	—
365	C₄⋊C₈	C₂³×C₁₉	1	4	yes	—
366	#102	C₂³×C₁₉	1	8	yes	—
367	#102	C₂³×C₁₉	1	8	yes	—
368	#102	C₂³×C₁₉	1	8	yes	—
369	#102	C₂³×C₁₉	1	8	yes	—
370	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
371	C₂²⋊C₈	C₂³×C₁₉	1	4	yes	—
372	#97	C₂³×C₁₉	1	2	yes	—
373	C₄×C₈	C₂³×C₁₉	1	2	yes	—
374	C₁₉	#62270	1	1	yes	characteristic, direct product factor, Sylow
375	C₂⁴	—	2	4	no	—
376	C₂⁴	—	2	4	no	—
377	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
378	#41	—	4	1	no	—
379	#41	—	4	1	no	—
380	C₂×Q₈	C₂×D₄×C₁₉	1	1	yes	characteristic
381	C₂×D₄	—	2	8	no	—
382	C₂×D₄	—	2	8	no	—
383	C₂×D₄	—	2	8	no	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	8	no	—
386	C₂×D₄	—	2	4	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	—	8	16	no	—
392	C₂×D₄	—	8	8	no	—
393	C₂×D₄	C₂×D₄×C₁₉	1	4	yes	—
394	C₂×D₄	C₂×D₄×C₁₉	1	1	yes	characteristic
395	C₂×D₄	C₂×D₄×C₁₉	1	2	yes	—
396	C₂×D₄	C₂⁴×C₁₉	1	8	yes	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	8	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	C₂×D₄×C₁₉	1	2	yes	—
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
404	C₂²×C₄	C₂⁴×C₁₉	1	2	yes	—
405	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
406	D₈	—	2	8	no	—
407	D₈	—	4	4	no	—
408	D₈	—	4	4	no	—
409	D₈	—	4	4	no	—
410	M₁₆	—	4	1	no	—
411	M₁₆	—	4	2	no	—
412	M₁₆	—	4	1	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	4	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	4	2	no	—
417	C₂×C₈	—	4	1	no	—
418	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
419	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
420	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
421	C₂×C₈	C₂⁴×C₁₉	1	2	yes	—
422	C₂×C₈	C₂⁴×C₁₉	1	1	yes	characteristic
423	C₄⋊C₄	—	2	4	no	—
424	C₄⋊C₄	—	2	8	no	—
425	C₄⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
426	C₄⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
427	C₄⋊C₄	C₂⁴×C₁₉	1	8	yes	—
428	C₂²⋊C₄	—	2	4	no	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	8	no	—
431	C₂²⋊C₄	—	2	8	no	—
432	C₂²⋊C₄	—	2	8	no	—
433	C₂²⋊C₄	C₂×D₄×C₁₉	1	2	yes	—
434	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
435	C₂²⋊C₄	C₂×D₄×C₁₉	1	4	yes	—
436	C₄²	—	2	4	no	—
437	C₄²	C₂⁴×C₁₉	1	2	yes	—
438	C₂³	—	2	4	no	—
439	C₂³	—	2	8	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	8	no	—
442	C₂³	—	8	4	no	—
443	C₂³	—	8	4	no	—
444	C₂³	—	8	4	no	—
445	C₂³	—	8	8	no	—
446	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
447	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
448	C₂³	C₂²×D₄×C₁₉	1	2	yes	—
449	Q₈	—	4	1	no	—
450	D₄	—	2	8	no	—
451	D₄	—	2	8	no	—
452	D₄	—	2	8	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	16	no	—
456	D₄	—	8	4	no	—
457	D₄	—	8	4	no	—
458	D₄	—	8	8	no	—
459	D₄	—	8	8	no	—
460	D₄	—	8	8	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	8	8	no	—
471	C₂×C₄	—	8	4	no	—
472	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₁₉	1	4	yes	—
474	C₂×C₄	C₂²×D₄×C₁₉	1	1	yes	characteristic
475	C₂×C₄	C₂²×D₄×C₁₉	1	2	yes	—
476	C₂×C₄	C₂⁵×C₁₉	1	1	yes	characteristic
477	C₈	—	2	1	no	—
478	C₈	—	2	2	no	—
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₈	C₁₉×H(5,𝔽₂)	1	2	yes	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	4	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	8	no	—
490	C₂²	—	4	8	no	—
491	C₂²	—	4	8	no	—
492	C₂²	—	16	8	no	—
493	C₂²	—	16	8	no	—
494	C₂²	C₁₉×#576	1	4	yes	—
495	C₂²	C₂³×D₄×C₁₉	1	1	yes	characteristic
496	C₄	—	2	1	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	4	no	—
500	C₄	—	4	8	no	—
501	C₄	C₂×C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
502	C₄	C₁₉×#585	1	1	yes	characteristic
503	C₂	—	2	4	no	—
504	C₂	—	4	1	no	—
505	C₂	—	4	2	no	—
506	C₂	—	8	8	no	—
507	C₂	C₁₉×#3496	1	1	yes	characteristic
508	C₂	C₂×C₁₉×#576	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₉ ◁ C₁₉×#525 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₉×#3537	C₂	semidirect
2. C₁₉×#3339	C₂	semidirect
3. C₁₉×#3318	C₂	semidirect
4. D₄×D₈×C₁₉	C₂	semidirect
5. C₁₉×#3259	C₂	semidirect
6. C₁₉×#3199	C₂	semidirect
7. C₁₉×#3192	C₂	semidirect
8. C₁₉×#3176	C₂	semidirect
9. C₁₉×#3058	C₂	semidirect
10. C₂×C₁₉×#466	C₂	semidirect
11. C₁₉×#2929	C₂	semidirect
12. C₂²×D₈×C₁₉	C₂²	semidirect
13. C₂²×D₈×C₁₉	C₂²	semidirect
14. C₂×C₁₉×#131	C₂²	semidirect
15. C₂³×C₈×C₁₉	C₂²	semidirect
17. C₁₉×#553	C₂²	semidirect
19. D₄²×C₁₉	C₂²	semidirect
20. C₁₉×#540	C₂²	semidirect
22. C₁₉×#535	C₂²	semidirect
25. C₂×C₁₉×#121	C₂²	semidirect
26. C₁₉×#499	C₂²	semidirect
27. C₁₉×#493	C₂²	semidirect
28. C₁₉×#490	C₂²	semidirect
29. C₁₉×#482	C₂²	semidirect
30. C₁₉×#481	C₂²	semidirect
31. C₁₉×#478	C₂²	semidirect
32. C₁₉×#469	C₂²	semidirect
33. C₁₉×#469	C₂²	semidirect
34. C₁₉×#469	C₂²	semidirect
35. C₁₉×#466	C₂²	semidirect
36. C₁₉×#466	C₂²	semidirect
37. C₁₉×#466	C₂²	semidirect
38. C₁₉×#466	C₂²	semidirect
39. C₁₉×#466	C₂²	semidirect
40. C₁₉×#459	C₂²	semidirect
41. C₁₉×#447	C₂²	semidirect
42. C₁₉×#447	C₂²	semidirect
43. C₁₉×#442	C₂²	semidirect
44. C₄×D₈×C₁₉	C₂²	semidirect
45. C₁₉×#435	C₂²	semidirect
46. C₈×D₄×C₁₉	C₂²	semidirect
47. C₁₉×#427	C₂²	semidirect
48. C₂×C₁₉×#107	C₂²	semidirect
49. C₁₉×#424	C₂²	semidirect
50. C₁₉×#418	C₂²	semidirect
51. C₂×C₁₉×#102	C₂²	semidirect
52. C₁₉×#408	C₂²	semidirect
53. C₁₉×#407	C₂²	semidirect
54. C₁₉×#405	C₂²	semidirect
183. #62270	C₁₉	direct (N × H)
228. #3537	C₂×C₁₉	semidirect
229. #3339	C₂×C₁₉	semidirect
230. #3318	C₂×C₁₉	semidirect
231. D₄×D₈	C₂×C₁₉	semidirect
232. #3259	C₂×C₁₉	semidirect
233. #3199	C₂×C₁₉	semidirect
234. #3192	C₂×C₁₉	semidirect
235. #3176	C₂×C₁₉	semidirect
236. #3058	C₂×C₁₉	semidirect
237. C₂×#466	C₂×C₁₉	semidirect
238. #2929	C₂×C₁₉	semidirect
260. C₂²×D₈	C₂²×C₁₉	semidirect
261. C₂²×D₈	C₂²×C₁₉	semidirect
262. C₂×#131	C₂²×C₁₉	semidirect
263. C₂³×C₈	C₂²×C₁₉	semidirect
265. #553	C₂²×C₁₉	semidirect
267. D₄²	C₂²×C₁₉	semidirect
268. #540	C₂²×C₁₉	semidirect
270. #535	C₂²×C₁₉	semidirect
273. C₂×#121	C₂²×C₁₉	semidirect
274. #499	C₂²×C₁₉	semidirect
275. #493	C₂²×C₁₉	semidirect
276. #490	C₂²×C₁₉	semidirect
277. #482	C₂²×C₁₉	semidirect
278. #481	C₂²×C₁₉	semidirect
279. #478	C₂²×C₁₉	semidirect
280. #469	C₂²×C₁₉	semidirect
281. #469	C₂²×C₁₉	semidirect
282. #469	C₂²×C₁₉	semidirect
283. #466	C₂²×C₁₉	semidirect
284. #466	C₂²×C₁₉	semidirect
285. #466	C₂²×C₁₉	semidirect
286. #466	C₂²×C₁₉	semidirect
287. #466	C₂²×C₁₉	semidirect
288. #459	C₂²×C₁₉	semidirect
289. #447	C₂²×C₁₉	semidirect
290. #447	C₂²×C₁₉	semidirect
291. #442	C₂²×C₁₉	semidirect
292. C₄×D₈	C₂²×C₁₉	semidirect
293. #435	C₂²×C₁₉	semidirect
294. C₈×D₄	C₂²×C₁₉	semidirect
295. #427	C₂²×C₁₉	semidirect
296. C₂×#107	C₂²×C₁₉	semidirect
297. #424	C₂²×C₁₉	semidirect
298. #418	C₂²×C₁₉	semidirect
299. C₂×#102	C₂²×C₁₉	semidirect
300. #408	C₂²×C₁₉	semidirect
301. #407	C₂²×C₁₉	semidirect
302. #405	C₂²×C₁₉	semidirect
374. C₁₉	#62270	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#3537	2
C₁₉×#3339	2
C₁₉×#3318	2
D₄×D₈×C₁₉	2
C₁₉×#3259	2
C₁₉×#3199	2
C₁₉×#3192	2
C₁₉×#3176	2
C₁₉×#3058	2
C₂×C₁₉×#466	2
C₁₉×#2929	2
#62270	19

Subgroups — C19×#62270 #18068229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#62270 #18068229